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13:00  Foundation of first order kinetics: the quasi stationary distribution approach. ABSTRACT. We are interested in the connection between a metastable continuous state space Markov process (satisfying e.g. the Langevin or overdamped Langevin equation) and a jump Markov process in a discrete state space. We use the notion of quasistationary distribution within a metastable state for the continuous state space Markov process to parametrize the exit event from the state. This approach is useful to analyze and justify methods which use the jump Markov process underlying a metastable dynamics as a support to efficiently sample the statetostate dynamics (accelerated dynamics techniques à la Arthur Voter). Moreover, it is possible by this approach to quantify the error on the exit event when the parametrization of the jump Markov model is based on the EyringKramers formula. This therefore provides a mathematical framework to justify the use of transition state theory and the EyringKramers formula to build kinetic Monte Carlo or Markov state models. References:  G. Di Gesu, T. Lelièvre, D. Le Peutrec and B. Nectoux, Jump Markov models and transition state theory: the QuasiStationary Distribution approach, Faraday Discussion, 2016.  G. Di Gesu, T. Lelièvre, D. Le Peutrec and B. Nectoux, Sharp asymptotics of the first exit point density, Annals of PDE, 2019. 
13:30  Shape Fluctuation of Metallic Nanoclusters: Observations from Long Timescale Simulations PRESENTER: Rao Huang ABSTRACT. Metallic nanoclusters are functional materials with many applications owing to their unique physical and chemical properties, which are sensitively controlled by their shapes and structures. An indepth understanding of their morphology stability is therefore of crucial importance. It has been well documented by transmission electron microscopy (TEM) studies that metallic nanoclusters can interconvert between different isomers. However, the relevant mechanisms remain elusive because the timescales of such shape fluctuations are too short to be resolved experimentally and yet too long for conventional atomistic simulations. By employing a recently introduced Accelerated Molecular Dynamics method, Parallel Trajectory Splicing, we present simulations that reached timescales of milliseconds and thus provide a clear description of the dynamic process of the experimentally observed shape fluctuation in metallic nanoclusters. We observe transformations back and forth between facecenteredcubic (fcc) and structures with fivefold symmetry (decahedron or icosahedron). These transitions occur following either by a partialdislocationmediated twinning mechanism or by a surfacereconstruction driven process. The identified pathway is in remarkable agreement with the existing microscopy results and serves as further evidence that shape fluctuation can occur directly through thermal activation, without involving melting or other external factors. 
14:00  Automated discovery and analytic calculation of defect diffusion with quantified uncertainty PRESENTER: Thomas Swinburne ABSTRACT. Defect transport is a key process in materials science, but atomistic mechanisms are often too complex to enumerate a priori, complicating uncertainty analysis and observable convergence. I will describe an asynchronous, massively parallel accelerated sampling scheme[1], autonomously controlled by rigorous Bayesian estimators of statewise sampling completeness, which builds atomistic kinetic Monte Carlo models on a state space irreducible under exchange and space group symmetries. A combined Monte Carlo and analytic procedure is outlined which provides a novel convergence metric for defect transport coefficients, via a KullbackLeiber divergence across the ensemble of diffusion processes consistent with the sampling uncertainty. The autonomy and efficacy of the method is demonstrated on a range of challenging materials science problems. [1] "Automated calculation and convergence of defect transport tensors" TD Swinburne and D Perez, NPJ Computational Materials, December 2020 
14:30  Langevin processes in boundedinposition domains: application to quasistationary distributions PRESENTER: Mouad Ramil ABSTRACT. Quasistationary distributions can be seen as the first eigenvector associated with the generator of the stochastic differential equation at hand, on a domain with Dirichlet boundary conditions (which corresponds to absorbing boundary conditions at the level of the underlying stochastic processes). Many results on the quasistationary distribution hold for non degenerate stochastic dynamics, whose associated generator is elliptic. The case of degenerate dynamics is less clear. In this work, together with T. Lelièvre and J. Reygner (Ecole des Ponts, France) we generalize wellknown results on the probabilistic representation of solutions to parabolic equations on bounded domains to the socalled kinetic Fokker Planck equation on bounded domains in positions, with absorbing boundary conditions. Furthermore, a Harnack inequality, as well as a maximum principle, is provided for solutions to this kinetic FokkerPlanck equation, as well as the existence of a smooth transition density for the associ ated absorbed Langevin dynamics. The continuity of this transition density at the boundary is studied as well as the compactness, in various functional spaces, of the associated semigroup. This work is a cornerstone to prove the consistency of some algorithms used to simulate metastable trajectories of the Langevin dynamics, for example the Parallel Replica algorithm. 
13:00  Flexible quadsurfaces: beyond Miuraori ABSTRACT. A quadsurface is made of rigid quadrilateral plates connected by rotational joints in the square grid pattern. Generic quadsurfaces are rigid, so that flexible instances are exceptional. A widely known flexible example is Miuraori. In this talk I will present an approach which has led to a classification of all flexible quadsurfaces and some ongoing research into the design methods. 
13:30  The designs of rigidly deployable quadrilateral origami and kirigami PRESENTER: Fan Feng ABSTRACT. Quadrilateral origami and kirigami with rigid panels connected by flexible hinges are generically nondeployable due to the geometrical constraints. Special patterns with twodimensional symmetry are found to satisfy these constraints to achieve rigid deployability. Examples include the famed Miura origami and the twistingsquare kirigami. Here we formulate the geometrical compatibility conditions for the deployability of quadrilateral origami and kirigami by composing the folding angle functions and the opening angle functions respectively. Solving these conditions leads to the designs of general deployable patterns capable of achieving the desired functionality such as approximating curved surfaces and boundaries.

14:00  Origami with Conformal and Helical Symmetry ABSTRACT. Many symmetric origami structures can be obtained as the orbit of a partially folded unit cell under a certain discrete group of isometries; for instance, the classical Miuraori can be obtained by applying a translation group to a unit cell, and recent work of Feng, Plucinsky, and James investigates a miuraori structure obtained by applying a helical group to a unit cell. Firstly, we consider a generalisation of the above: origami obtained by applying conformal affine linear transformations of R^n to a unit cell. For our purposes, we develop a classification of all groups of such transformations that are "semidiscrete": where in the orbit of any point, there is a fixed positive distance between accumulation points. We will use these groups to create conformal Miuraori and waterbomb origami. Secondly, we will consider the problem of creating generalised waterbomb origami tubes with helical symmetry, with a view towards applications in medical stents. We will use an inverse approach which makes use of several necessary symmetries in these objects. 
14:30  Foldable Structures and Materials ABSTRACT. Folding is a systematic method that transforms planar material into threedimensional rigid structures. Depending on the organization of folds, structures can be flatpacked for ease of transport. By beginning with a flat plane, there is the potential to reduce production costs associated with manufacturing parts with curvature. Additionally, there are numerous variations possible with one systematic method. This research seeks to move beyond origami — the art of folding paper — by embracing material and structural constraints. Computationbased simulation and analysis is used to design stronger lightweight structures. Additionally, more efficient methods to manufacture parts are being developed in direct dialogue with industry sponsors and collaborators. Lastly, new methods and materials are being invented to expand the possibilities of translating paper folding into materials which have the potential to scaleup. Folding is embraced as a means to tackle industry related problems. Applications include: lightweight deployable structures, ultrathin formwork for concrete casting, and stayinplace formwork for shell structures and concrete slabs. 
13:00  Stochastic Homogenisation of FreeDiscontinuity Problems ABSTRACT. We will discuss the stochastic homogenisation of freediscontinuity functionals. Assuming stationarity for the random volume and surface integrands, we prove the existence of a homogenised functional, whose volume and surface integrands are characterised by asymptotic formulas involving minimisation problems on larger and larger cubes with special boundary conditions. In the proof we combine a recent deterministic Gammaconvergence result for freediscontinuity functionals with the Subadditive Ergodic Theorem by Akcoglu and Krengel. This is a joint work in collaboration with Gianni Dal Maso (SISSA), Lucia Scardia (HeriotWatt University), and Caterina Zeppieri (University of Münster). 
13:30  Korn inequalities in GSBD and applications ABSTRACT. In this talk I will present a regularity result and a Korn inequality in the space $GSBD^p$ of generalised functions with bounded deformation, for any $p> 1$ and any dimension $n \geq 2$. Then I will present some consequences and applications, including an extension result. This is work in collaboration with F. Cagnetti, A. Chambolle and M. Perugini. 
14:00  LOWER SEMICONTINUITY FOR FUNCTIONALS DEFINED ON PIECEWISE RIGID FUNCTIONS AND ON GSBD PRESENTER: Matteo Perugini ABSTRACT. In this work, we provide a characterization result for lower semicontinuity of surface energies defined on piecewise rigid functions, i.e., functions which are piecewise affine on a Caccioppoli partition where the derivative in each component is a skew symmetric matrix. This characterization is achieved by means of an integral condition, called BDellipticity, which is in the spirit of BV ellipticity defined by Ambrosio and Braides. By specific examples we show that this novel concept is in fact stronger compared to its BV analog. We further provide a sufficient condition implying BDellipticity which we call symmetric joint convexity. This notion can be checked explicitly for certain classes of surface energies which are relevant for applications, e.g., for variational fracture models. Finally, we give a direct proof that surface energies with symmetric jointly convex integrands are lower semicontinuous also on the larger space of GSBD^p functions. 
14:30  Asymptotic analysis of singularly perturbed elliptic functionals PRESENTER: Roberta Marziani ABSTRACT. The talk is based on a joint work with Annika Bach and Caterina Ida Zeppieri. There we study the $\Gamma$convergence of singularly perturbed elliptic functionals that generalizes the functionals of AmbrosioTortorelli type. It is well known that the latter approximate, in the sense of $\Gamma$convergence, the free discontinuity functional of MumfordShah which models for example image segmentation. Accordingly to this, the asymptotic analysis of these functionals gives rise to a decoupling volumesurface effect also in the more general setting that we consider. In particular, if $u$ is a function describing the image segmentation effect, we derive that the surface term of the limit functional does not depend on the jump opening $[u]$. Our general result applies, for example, to the case of stochastic homogenization. 
13:00  Online Materials Studies by the Bilbao Crystallographic Server PRESENTER: Mois Ilia Aroyo ABSTRACT. The Bilbao Crystallographic Server (www.cryst.ehu.es) is a free web site with an access to crystallographic data of space and point groups, magnetic and subperiodic groups, their representations and groupsubgroup relations. A database on incommensurate structures incorporating modulated structures and composites, a magneticstructure database and a kvector database with Brillouinzone figures are also available. Wide range of complex solidstate physics and structurechemistry aspects of materials studies are facilitated by the specialized software provided by the server. The server offers a set of structureutility programs including tools for crystalstructure transformations, for a quantitative analysis of structuremodel similarities and for studies of crystalstructure relationships. There are tools for a systematic research of phasetransition mechanisms including the evaluation of the structure pseudosymmetry which proves to be a powerful method for the prediction of new ferroic materials. Recently implemented computational tools and databases allow the systematic application of symmetry arguments in the study of magnetic structures. The presentation of the databases and programs offered by the Bilbao Crystallographic Server will be accompanied by case studies illustrating the capacity and efficiency of the online tools in material studies. 
13:30  The study of layer and multilayer materials using the Bilbao Crystallographic Server PRESENTER: Gemma de la Flor ABSTRACT. Operating since 1997, the Bilbao Crystallographic Server (www.cryst.ehu.es) is a free web server that grants access to specialized databases and tools for the resolution of different types of crystallographic, structural chemistry and solidstate physics problems. Recently, new tools dedicated to the study of materials with layer and multilayer symmetry have been developed due to the arising interest in these type of materials. The aim of this contribution is to report the current state of the programs in the server related to the study of materials with layer group symmetry. The section dedicate to Subperiodic groups gives access to the layer groups databases which contains the basic crystallographic information (generators, general positions, Wyckoff positions and maximal subgroups) and the Brillouin zone and kvectors tables that form the background and classification of the irreducible representations of layer groups. Moreover, programs to identify the layer symmetry of periodic sections and to describe the electronic structure and surface states of crystals are also available. The last tool to join this section is able to calculate the irreducible representations of layer groups. The utility of the available applications will be demonstrated by illustrative examples. 
14:00  Exploiting superspace symmetry for characterizing modulation functions with firstprinciples calculations PRESENTER: Paul Benjamin Klar ABSTRACT. Incommensurately modulated structures (IMS) are aperiodic, but longrange ordered, in physical space. IMS can be described as periodic structures in higherdimensional superspace by defining a 3dimensional basic structure and a set of modulation parameters accounting for displacive and/or occupation modulations. Experimentally determined IMS cannot be validated by means of density functional theory (DFT) or similar computational methods, which require an atomic model described in 3D space. Likewise, structures that show static disorder, e.g. atomic sites that are partially occupied in the average structure, are another class of materials for which a clear approach for structure model validation from first principles is missing. The industrially important ceramic material mullite, an aluminium silicate, is both incommensurately modulated and disordered with respect to Al/Si ordering and vacancy ordering. The underlying ordering patterns were identified based on DFT calculations on fully ordered, commensurate approximations that were generated taking the full superspace symmetry into account. A consistent model for a broad range of compositions was derived, capable of explaining the vacancy and Al/Si ordering in the IMS of mullite. 
14:30  Polytypic and symmetry relations between Na2Mn3(SO4)4 polymorphs PRESENTER: Sergey Aksenov ABSTRACT. Alkaline sulfates of transition elements attract interest because of their electrochemical properties and application as electrode materials. The crystal structures of Na2Mn3(SO4)4 polymorphs are based upon heteropolyhedral frameworks formed by Mnφn polyhedra (n = 5,6) and SO4 tetrahedra and display orderdisorder (OD) character and can be described using the same OD groupoid family, more precisely a family of OD structures built up by two kinds of nonpolar layers, with layer symmetry Pmc21 (L2n+1 type) and Pbcm (L2n type) (category IV). All ordered polytypes as well as disordered structures can be obtained by means of the following symmetry operators that may be active active in the L2n type layers with symmetry Pbcm: the 21 screw axis parallel to c [  21] or inversion centres and the 21 screw axis parallel to b [ 21 ]. The relationships between different polytypes is represented by the presence in their structures of common tilings, in particular, 3T2M[43], 4T3M[4.62], and 2T3M[32.42]. The geometry optimization of the hypothetical structure of the MDO2polytype predicted using the OD approach demonstrates its reasonability as another possible stable polymorph of Na2Mn3(SO4)4. The calculated enthalpy factors of the polytypes decreases in the following order: non MDO4O > MDO1 > MDO2. 
13:00  Lower bound for the coalescence load in 2D neoHookean materials PRESENTER: Duvan Henao ABSTRACT. This work (IFB 2020) forms part of the variational analysis of cavitation (Gent & Lindley '59, Ball '82, Muller & Spector '95, Sivaloganathan & Spector '00). It is known (Sivaloganathan & Spector '10; H. & Serfaty '13) that the energetically most favourable cavities are spherical; nonetheless, for large external loads incompressiblity makes it impossible to create only spherical cavities. For a simplified 2D setting, we give a geometric sufficient condition for a given load to be compatible with the existence of deformations opening only round cavities: that the radius of each cavity, after the deformation, is smaller than a certain value comparable to the distance, in the reference configuration, between cavitation points. When this condition is satisfied, we prove that the minimizers of the Dirichlet energy among incompressible deformations of the domain with epsiloninitial holes tend to produce circular cavities as epsilon tends to zero. This gives a lower bound for the coalescence load: for coalescence the displacement load on the boundary must be large enough for our geometric sufficient condition to fail. 
13:30  Separately Global Solutions to RateIndependent Systems  Applications to LargeStrain Deformations of Damageable Solids PRESENTER: Petr Pelech ABSTRACT. Rateindependent systems (RIS) are characterized by the lack of any internal time length scale: rescaling the input of the system in time leads to the very same rescaling of its solution. In continuum mechanics, rateindependent models represent a reasonable approximation whenever the external conditions change slowly enough so that the system can always reach its equilibrium. This applies if inertial, viscous, and thermal effects are neglected. RIS have proven to be useful in modeling of hysteresis, phase transitions in solids, elastoplasticity, damage, or fracture in small and large strain regimes. The talk introduces the notion of separately global solutions for RIS with nonconvex functionals and describes an existence result for a model of bulk damage at large strains. The analysis covers nonconvex energies blowing up for extreme compression, yields solutions excluding interpenetration of matter, and allows for handling nonlinear couplings of the deformation and the internal variable, which emerges e.g. from the interplay between Eulerian and Lagrangian description. It extends the theory developed so far in the small strain setting. 
14:00  Nonlocal models in Elasticity PRESENTER: Carlos MoraCorral ABSTRACT. We present a nonlocal variational model in nonlinear elasticity, based on the concept of Riesz fractional gradient. We explain how the theory of polyconvexity applies in this context. We also prove the Gammaconvergence to the local (classical) model as the nonlocality vanishes. 
14:30  Relaxation of static problems PRESENTER: Michael Ortiz ABSTRACT. It has been long known in geophysics that materials such as silica glass exhibit anomalous pressuredependent strength characterized by a strongly nonconvex elastic domain. This lack of convexity violates the standard Drucker principles of classical plasticity, including the principle of maximum dissipation, and may result in finescale patterning of the stress field. In order to understand these phenomena, we consider problems of static equilibrium in which the primary unknown is the stress field and the solution maximizes a complementary energy subject to equilibrium constraints. A necessary and sufficient condition for the sequential lowersemicontinuity of such functionals is symmetric divquasiconvexity in the sense of Fonseca and Muller's Aquasiconvexity. We specifically consider the example of the static problem of plastic limit analysis and seek to characterize its relaxation in the nonstandard case of a nonconvex elastic domain. We show that the symmetric divquasiconvex envelope of the elastic domain, which describes the effective or macroscopic plastic behavior of the material, can be characterized explicitly by means of a rank2 hull construction for isotropic materials whose elastic domain depends on pressure and Mises effective shear stress. The resulting relaxed elastic domain closely matches that obtained by means of molecular dynamics calculations for silica glass. 
13:00  On the BourgainSpencer conjecture in stochastic homogenization ABSTRACT. In the context of stochastic homogenization, the BourgainSpencer conjecture states that the ensembleaveraged solution of a divergenceform linear elliptic equation with random coefficients allows for an intrinsic description in terms of higherorder homogenized equations with an accuracy four times better than the almost sure solution itself. While previous rigorous results are restricted to a perturbative regime with small ellipticity ratio, we shall explain how half of the conjecture can be established in a nonperturbative regime. Our approach involves the construction of a new corrector theory in stochastic homogenization: while only a bounded number of correctors can be constructed as L^2 stationary random fields, we show that twice as many can be usefully defined in a Schwartzlike distributional sense on the probability space. We shall also discuss corresponding results for linear waves in random media. 
13:30  Regularity for nonuniformly elliptic equations and applications to the random conductance model PRESENTER: Mathias Schäffner ABSTRACT. I will discuss regularity properties for solutions of linear second order nonuniformly elliptic and parabolic equations in divergence form. Assuming certain integrability conditions on the coefficient field, we obtain local boundedness and validity of Harnack inequality. The assumed integrability assumptions are essentially sharp and improve upon classical results in the literature. These determistic regularity results are key ingredients in homogenization results, namely quenched invariance principle and local limit theorem, for random walks in a random degenerate environment. 
14:00  Quantitative homogenization of HelfferSjöstrand equations ABSTRACT. In 1997, A. Naddaf and T. Spencer established that the scaling limit of the GinzburgLandau random surface model is a Gaussian free field. Their proof relies on the observation that the behavior of the random surface is characterized by the largescale properties of the solutions of an infinite dimensional elliptic PDE, called the HelfferSjöstrand equation, which can be understood through techniques of stochastic homogenization. In this talk, we will describe the arguments developed by Naddaf and Spencer, explain how they can be reworked using the tools of the quantitative theory of stochastic homogenization, and present some of the (quantitative) results on the model which can be obtained by these techniques. We will then explain how these arguments can be used to understand the largescale behavior of another model of statistical physics: the Villain rotator model. This is based joint work with W. Wu. 
14:30  A PDE hierarchy for directed polymers in random environments ABSTRACT. We are interested in the endpoint distribution a directed polymer in a Gaussian random environment. A PDE hierarchy governing the evolution of the npoint density functions is derived, and we will discuss its applications. 
13:00  Microfluidic flow of colloidliquid crystal composite materials PRESENTER: Oliver Henrich ABSTRACT. Colloidal particles in liquid crystals exhibit a flow behaviour that is strikingly different from that in isotropic media. On one hand, the emerging topological defects give rise to highly complex, anisotropic elastic forces that the liquid crystal exerts on the colloidal particles. On the other hand, nonlinear, flowdependent forces are also involved, which are impossible to predict analytically. Studies of particles in nematics were therefore generally limited to how the molecules reorder around the solute particles. We present new results of latticeBoltzmann simulations of colloidliquid crystal composite materials in Poiseuille flow. At the singleparticle level we observe a new, hydrodynamic and very fast separation effect that is distinct from the wellknown SegreSilberberg effect in isotropic media at low volume fractions. Contrary to the latter, there is no single attractors: where and how particles accumulate depends sensitively on the imposed flow rate and particle size. At higher volume fractions we observe a range of other intriguing features, like the reorientation of the local defect network around the colloidal particles, states where a significant fraction of the particles has temporarily negative mobilities, as well as percolating networks of topological defects that appear to act as lowviscosity conduits for the flow. 
13:30  Flowinduced states and transitions in pressuredriven nematic fluids PRESENTER: Uroš Tkalec ABSTRACT. Flow of liquid crystals is inherently complex due to the coupling between their orientational order and the imposed shear velocity. Experiments carried out with channelconfined nematic fluids reveal strong influence of boundary conditions, elasticity, viscosity, and external fields on observed nonequilibrium states. I will present how different orientational states in pressuredriven nematics can coexist and get stabilized by precisely engineered microflows. The mechanisms that connect the behavior of the nematic liquid crystal with its material parameters will be discussed in the framework of EricksenLeslieParodi formulation of nematodynamics, and supported with the results of numerical modelling. The symmetrybreaking transition to chiral states will be explained through geometric and topological assumptions of a phenomenological Landau model. I will also demonstrate how geometric variations of the confinement can contribute to dynamic reshaping of the steadystate flow structures. Our findings could find use in outofequilibrium lyotropic liquid crystals and active nematics where additional dynamic response is expected due to density and activitydependence of their elastic properties. The research was conducted with support from the Slovenian Research Agency (ARRS), and with support from the National Science Foundation (NSF) of the United States of America. 
14:00  Hydrodynamic cavitation in Stokes flow of anisotropic fluids ABSTRACT. Cavitation, the nucleation of vapor in liquids, is ubiquitous in fluid dynamics, and is often implicated in a myriad of industrial and biomedical applications. Although extensively studied in isotropic liquids, corresponding investigations in anisotropic liquids are largely lacking. We reveal flowinduced cavitation in liquid crystals at low Reynolds numbers [1]. We combine liquid crystal microfluidic experiments, nonequilibrium molecular dynamics simulations and theoretical arguments to identify the mechanism underpinning LC cavitation. The cavitation domain nucleates due to sudden pressure drop upon flow past a cylindrical obstacle within a microchannel. The inception and growth of the cavitation domain ensued in the Stokes regime, while no cavitation was observed in isotropic liquids flowing under similar hydrodynamic parameters. Using simulations we identify a critical value of the Reynolds number for cavitation inception that scales inversely with the order parameter of the fluid. Strikingly, the critical Reynolds number for anisotropic fluids can be 50% lower than that of isotropic fluids. [1] T. Stieger, Hakam Agha, Martin Schoen, Marco G. Mazza, Anupam Sengupta, Nature Communications 8, 15550 (2017). 
14:30  The role of elasticity in a thin flowing nematic layer under electric field PRESENTER: Carl Brown ABSTRACT. We report results and simulations for Poiseuille flow, parallel to the zeropretilt surface alignment direction, of a thin (d = 25 micrometer) layer of nematic liquid crystal with positive dielectric anisotropy and an electric field orthogonal to the layer and to the flow direction. We demonstrate how flow significantly extends the low director distortion state to higher voltages and removes the tilt reorientation direction degeneracy of the classical Freedericksz switching. We show switching between the flow stabilized, low director distortion state and the flow modified high director distortion state via abrupt removal and reapplication of externally driven flow. Our numerical simulations using the EricksenLeslie dynamic equations reveal how the asymmetry of the director distortion (about z = d/2) in the flow modified state becomes more pronounced as the flow rate is increased. At very high flow rates there is predicted to be a narrow reorientation region in which there is transition between director alignment close to the positive Leslie angle for z < d/2 to director alignment close to the pi radians minus the Leslie angle for z > d/2. 
13:00  NMRTS: de novo molecule identification from NMR spectra PRESENTER: Jinzhe Zhang ABSTRACT. Nuclear magnetic resonance (NMR) spectroscopy is an effective tool for identifying molecules in a sample. Although many previously observed NMR spectra are accumulated in public databases, they cover only a tiny fraction of the chemical space, and molecule identification is typically accomplished manually based on expert knowledge. Herein, we propose NMRTS, a machinelearningbased python library, to automatically identify a molecule from its NMR spectrum. NMRTS discovers candidate molecules whose NMR spectra match the target spectrum by using deep learning and density functional theory (DFT)computed spectra. As a proofofconcept, we identify prototypical metabolites from their computed spectra. After an average 5451 DFT runs for each spectrum, six of the nine molecules are identified correctly, and proximal molecules are obtained in the other cases. This encouraging result implies that de novo molecule generation can contribute to the fully automated identification of chemical structures. 
13:30  Inverse materials design using machine learning PRESENTER: Yousung Jung ABSTRACT. With an incredible volume of chemical and crystal database accumulated so far well as the hardware to process such large information, datadriven chemical science is expected play an important role, particularly in discovering novel functional molecules and crystals. In this talk, I will present several machine learning models that can allow efficient exploration of chemical space towards a new discovery. Examples could include crystal structure prediction, synthesizability prediction, and chemical pathway planning. 
14:00  How can Machine Learning Aid Computational Chemistry in Data Generation PRESENTER: Chenru Duan ABSTRACT. Machine learning (ML) has proven invaluable in accelerating materials discovery, both in forward design, where we use ML models to rapidly screen large chemical spaces, and in inverse design where we build generative models to design molecules with targetted properties. Large datasets are indispensable for training reasonably accurate ML models that drive highthroughput virtual screening. Highthroughput computation with density functional theory (DFT) enables the costefficient generation of relatively accurate datasets. A naive workflow for DFTbased highthroughput computation, however, may suffer from both wasting computational resources on failed calculations and domain of application errors from DFT, especially for transition metal containing molecules. We apply ML to aid this highthroughput computation in two ways: i) we build classification models to both prescreen a large chemical space and monitor a calculation onthefly to avoid unproductive calculations that would waste computational resources, and ii) we build a semisupervised classification model to predict when molecules contain strong static correlation and thus require more accurate but more expensive wavefunction theory calculations. We anticipate these ML models to be useful in making the data generation process more efficient and accurate with currently available electronic structure methods. 
13:00  Oscillatory behavior of bubbleator dynamics PRESENTER: André Schlichting ABSTRACT. It is well known that kinetic models satisfying the socalled detailed balance condition have an entropy functional which can be used to derive convergence to equilibrium results. On the other hand, there are many physical situations (typically open systems) where it is natural to use kinetic equations for which a detailed balance condition does not hold. In these cases, more complicated dynamical behavior can arise, for instance, oscillatory behaviors. A class of kinetic equations where it is not a priori evident if temporal oscillations can occur are the coagulationfragmentation equations. In the talk, we concentrate on BeckerDöring type dynamics, in which only a single monomer can attach or detach from a cluster. These equations have been extensively used to model chemicalphysical systems and especially bubbleator dynamics. In this talk, I will describe such models for which the onset of periodic oscillations can be proven by formal asymptotics. One of the models represents the formation of large clusters in a BeckerDöring equation having a source of monomers and removal of large clusters. 
13:30  The initialboundary value problem for the LifshitzSlyozov equation with nonsmooth rates at the boundary PRESENTER: Juan Calvo ABSTRACT. The LifshitzSlyozov system describes the temporal evolution of a mixture of monomers and aggregates, where individual monomers can attach to or detach from already existing clusters. The aggregate distribution follows a transport equation with respect to a size variable, whose transport rates are coupled to the monomer dynamics through a mass conservation relation. Being a model traditionally designed to describe phase transitions, the attachment and detachment rates proposed by Lifshitz and Slyozov do not require a boundary condition at zero size. However, this model is now used in a number of different contexts (e.g. protein polymerization or tentative applications to Oceanography). These situations impose attachment and detachment rates that requiere a boundary condition at zero size, which is intepreted as the synthesis of new clusters from monomers by a nucleation process. Up to date, the mathematical results on this new setting are scarce. In this contribution we study existence and uniquenes of localintime solutions for nonlinear boundary conditions, together with continuation criteria and results on longtime behavior. We are able to deal with attachment and detachment rates that may lack Lipschitz regularity, like power law rates. This requires a careful analysis of the characteristic curves associated to the transport process. 
14:00  Growthfragmentationcoagulation equations with unbounded coagulation kernels PRESENTER: Jacek Banasiak ABSTRACT. In this lecture, we discuss the global in time solvability of the continuous growthfragmentationcoagulation equation with unbounded coagulation kernels, in spaces of functions having finite moments of a sufficiently high order. The main tool is the recently established result on moment regularization of the linear growthfragmentation semigroup that allows us to consider coagulation kernels whose growth for large clusters is controlled by how good the regularization is, in a similar manner to the case when the semigroup is analytic. 
13:00  A field theory for plant tropisms and axonal durotaxis ABSTRACT. In many growing filamentary structures such as neurons, roots, and stems, the intrinsic shapes and material response are produced by differential growth of the tissue. Therefore, a key problem is to link the growth field at the microscopic level to the macroscopic shape and properties of the filaments. In this talk, starting with a morphoelastic tubular structure and assuming an arbitrary local growth law on the growth tensor, I will give a multiscale method to obtain the overall curvature, torsion, and material parameters of a growing filament. Various examples of curvature and torsion generation are given and the impact of residual stress on the generation of curvature is demonstrated. Applications to plants and axons will be given 
13:30  Approaches to the 2D Nematic Elastomers Inverse Design Problem ABSTRACT. Thin nematic elastomer sheets can be programmed, via the nematic director field embedded into them, to take different shapes in different environments. Recent experiments from various groups demonstrate excellent control over the director field, thus opening a door for achieving accurate and versatile designs of shapeshifting surfaces. At the crux of any effort to implement this design mechanism lies the inverse design problem  given an arbitrary surface geometry, constructing the director field that would induce it upon actuation. In this talk I describe several aspects of this inverse problem. I present a numerical algorithm for finding approximate global solutions to the inverse problem for any 2D geometry. I show analytically the existence of many local solutions for any smooth geometry, provide an algorithm for their integration, and show a convenient classification useful for finding optimized director fields per given surface geometry. I further discuss nonsmooth surface geometries, and how these can be realized via topological defects and domain walls in the nematic director field. 
14:00  Asymptotic rigidity for shells in nonEuclidean elasticity PRESENTER: Itai Alpern ABSTRACT. Consider a prototypical “stretching plus bending” functional of an elastic shell, E(f), where the shell is modeled as a ddimensional Riemannian manifold endowed with a reference second fundamental form, which is being immersed by f into a (d + 1)dimensional ambient space. It is well known that when the ambient space is Euclidean, there exists a zeroenergy configuration, f, if and only if the reference metric and second fundamental form satisfy the GaussCodazziMainardi compatibility conditions. It is therefore natural to ask whether inf E = 0 implies that the reference metric and second fundamental form are compatible, and in this case, whether any minimizing sequence converges to a zeroenergy reference configuration. In this lecture I will show that this is indeed true. In particular, under the assumption that the ambient space is of constant sectional curvature, any sequence of immersions of asymptotically vanishing energy converges to an isometric immersion of the shell into ambient space, having the reference second fundamental form. I will present a sketch of the proof of this theorem, emphasizing its main ideas. 
14:30  Contact geometry and the structure and elasticity of chiral materials PRESENTER: Thomas Machon ABSTRACT. Chirality in materials, such as liquid crystals, often entails a high degree of geometric frustration, leading to a rich array of morphological phenomena. The mathematics of such systems is similarly complex, with chirality often manifesting nonlinearly. Here I will discuss how methods from contact geometry and topology can be used to give a qualitative understanding of the behaviour of chiral materials. Using experiments on cylindrically confined lyotropic chromonic liquid crystals as a model system, I will show how contact topologytheoretic methods lead to a topological description of the various metastable minima in the energy landscape, as well as explaining the existence of novel chirallyprotected solitons. I will further show how the same perspective can be used to understand the structural stability of highlytwisted Skyrmions in chiral ferromagnets, with applications to racetrack memory devices. Finally, I will present the results of transition path sampling calculations describing generic features of chiral morphological transitions in liquid crystalline systems. 
16:30  On the physical origin of the MeyerNeldel rule or compensation effects : the link between prefactors and energy barriers PRESENTER: Normand Mousseau ABSTRACT. For more than 120 years, experiments on a range of systems have shown an unexpected correlation between diffusion preexponential factors and energy barriers. This compensation effect, or the MeyerNeldel rule, implies a universal linear relation between the activation energy and the entropy. While a number of phenomenological explanations have been proposed, these could not be directly tested against experimental data. Building on extensive catalogs of activated events generated with the activationrelaxation technique (ART nouveau) in a number of disordered systems, we lift this restriction and demonstrate how the deformation of the energy landscape affects the vibrational density of state that dominates the entropic contributions. Showing that the harmonic approximation captures the essential part of the compensation effect, we find that the deformation associated with diffusion both softens low and stiffens high frequency phonons. Softening generally dominates as barrier increase, creating a compensation effect. This correlation, however, is held only on average and huge fluctuations in prefactors are observed on an event by event basis. These can affect the evolution of materials and cannot be neglected without being assessed. Part of the work is done in collaboration with Alecsandre SauvéLacoursière (U. Montréal), Gilles Adjanor and Christophe Domain (EDF, France) 
17:00  Atomistic understanding of interface migration  Combining machine learning, path collective variables, and enhanced sampling ABSTRACT. Atomistic simulations of solidsolid phase transformations provide insight into the microscopic processes that govern the kinetics and mechanisms of the transition. Understanding these processes is of considerable technological importance in a wide range of materials such as metals and alloys, minerals, or molecular crystals. To achieve an efficient sampling of the underlying high dimensional phase space with often complex features typically requires the application of enhanced simulation approaches. Here, we combine machine learning with enhanced sampling algorithms to explore structural phase transformations induced by interface migration. Specifically, we employ a neural network based identification of local structural environments that are then used to construct global structural classifiers. Within the space of global classifiers a onedimensional path collective variable is defined that is subsequently used in the enhanced sampling. We illustrate our approach by exploring the complex migration of a phase boundary during the solidsolid transformation between the bcc and A15 phase in molybdenum. We were able to observe the growth of both phases, and estimate the free energy profile along the transformation. The approach presented here is generally applicable, and the efficient sampling of the phase space can facilitate the study of structural transformations in various complex condensed matter systems. 
17:30  SubLattice Parallel Trajectory Splicing: Application to Adatom Migration in Tungsten PRESENTER: Enrique Martinez ABSTRACT. Exascale computing presents a challenge for the scientific community as new algorithms must be developed to take full advantage of the new computing paradigm. Atomistic simulation methods that offer full fidelity to the underlying potential, i.e., molecular dynamics (MD) approaches, fail to use the whole machine speedup, leaving a region in time and sample size space that is unattainable with current algorithms. We present here an extension of the Parallel Trajectory Splicing algorithm that relies on a synchronous sublattice decomposition to further parallelize the process in space. This algorithm is based on a domain decomposition in which events happen independently in different regions in the sample as Parallel Trajectory Splicing is run in each subdomain. Extra care must be taken to ensure that the dynamics remain accurate including in the local subdomain ghost atoms from neighboring subdomains. We validate the algorithm comparing the rates for adatom hopping on a {110} surface in W obtained from direct MD, traditional Parallel Replica Dynamics, Parallel Trajectory Splicing and the SubLattice Parallel Trajectory Splicing. Once validated we applied the algorithm to study clustering formation of adatoms in large samples relevant for fusion applications. 
18:00  EyringKramers law for overdamped Langevin process ABSTRACT. In molecular dynamics, several algorithms have been designed over the past few years to accelerate the sampling of the exit event from a metastable domain, i.e. the time spent and the exit point from the domain. Some of them are based on the fact that the exit event from a metastable region is well approximated by a Markov jump process. In this talk, I will present recent results on the exit event from a metastable region for the overdamped Langevin dynamics. These results aim in particular at justifying the use of a Markov jump process parametrized by the EyringKramers law to model the exit event from a metastable region. This is a joint work with G. Di Gesù, T. Lelièvre, and D. Le Peutrec. 
16:30  Piecewise isometric origami PRESENTER: Huan Liu ABSTRACT. Most origami structures and much of recreational origami is designed as piecewise rigid origami. In some cases it would be desirable to allow smooth, nonaffine isometric deformations of the tiles, for example, when one wishes to buildin some elastic energy that would bias the structure toward some particular configuration so that the structure would tend to return to that configuration upon release. Additional possibilities would arise for functional isometrically deforming tiles, such as shape memory tiles. Using a Lagrangian description of isometric deformations and formalizing the compatibility conditions at the folds, we present a theory for piecewise isometric origami. For related ideas, particularly in the case of functional materials, see #442 of this session by Feng, Duffy, Biggins and Warner. 
17:00  Shape programming using lines of concentrated Gaussian curvature PRESENTER: Daniel Duffy ABSTRACT. Liquid crystal elastomers (LCEs) can undergo large reversible contractions along their nematic director upon heating or illumination. A spatially patterned director within a flat LCE sheet thus encodes a pattern of contraction on heating, which can morph the sheet into a curved shell, akin to a pattern of growth sculpting a developing organism. Here we consider, theoretically, numerically and experimentally, patterns constructed from regions of radial and circular director, which, in isolation, would form cones and anticones. The resultant surfaces contain curved ridges with sharp Vshaped crosssections, associated with the interfaces between regions in the patterns. Such ridges may be created in positively and negatively curved variants and, since they bear Gauss curvature, they cannot be flattened without energetically prohibitive stretch. Our experiments and numerics highlight that, although such ridges cannot be flattened isometrically, they can deform isometrically by trading the (singular) curvature of the “V” angle against the (finite) curvature of the ridge line. In finite thickness sheets, the sharp ridges are nonisometrically blunted to relieve bend, resulting in a “smearing out” of the encoded singular Gauss curvature. We discuss possible applications as actuators, as well as similarities to shape changes found during the morphogenesis of several biological systems. 
17:30  Joining metriccompatible actuated shapes at creases with Gaussian curvature PRESENTER: John Simeon Biggins ABSTRACT. Curved fold, nonisometric origami, actuated by light or heat, can be realised in flat sheets of nematic glasses and elastomers with a programmed inplane director field. Large ($\sim 30$\%), reversible contractions arise along the director in elastomers. An inplane logspiral/circular director pattern actuates to a cone with Gaussian curvature (GC) localised at its tip and Gaussianflat flanks. Joining such cones requires an interface between two such spiral/circular director patterns in the reference domain that gives a target space crease where lengths from actuation under each pattern are identical. Such interfaces obey a metric compatibility condition in the reference space and are characterized as hyperbolictype or elliptictype. Fitting the two cones together forms curved creases and requires isometries that we compute analytically for the circular cases and numerically for the spiral cases. Unlike isometric curvedfold origami, the creases carry nontrivial concentrated GC that can be calculated analytically. The computational results illustrate that creases are slightly diffuse and so is the GC, whereby the divergent bend is relieved at the cost of some stretch. A rich variety of shapes with points and lines of GC will be presented. 
16:30  Flexoelectric fluid membranes in confinement PRESENTER: Martin Michael Müller ABSTRACT. The morphology of spherically confined flexoelectric fluid membrane vesicles in an external uniform electric field is studied numerically. Due to the deformations induced by the confinement, the membrane gets polarized resulting in an interaction with the external field. The equilibrium shapes of the vesicle without electric field can be classified in a geometrical phase diagram as a function of scaled area and reduced volume. When the area of the membrane is only slightly larger than the area of the confining sphere, a single axisymmetric invagination appears. A nonvanishing electric field induces an additional elongation of the confined vesicle which is either perpendicular or parallel depending on the sign of the electric field parameter. Higher values of the surface area or the electric field parameter can reduce the symmetry of the system leading to more complex folding. We present the resulting shapes and show that transition lines are shifted in the presence of an electric field. The obtained folding patterns could be of interest for biophysical and technological applications alike. 
17:00  Hyperbolic MongeAmpere equations, Lorentz surfaces and thin sheet elasticity. ABSTRACT. I will talk about some geometric questions that arise in the study of soft/thin objects with negative curvature. I will motivate the need for new "geometric" methods, for studying the mechanics of leaves, flowers, and seaslugs. I will also discuss how this view naturally leads to a formulation of thinsheet mechanics in terms of additional "natural" frames, in contrast with the usual formulation in terms of the Lagrangian (material) and Eulerian (Lab) frames. 
17:30  Exact minimal parking garages: Optimal packing of biological membranes with helical motifs requires pitch balance PRESENTER: Luiz C B da Silva ABSTRACT. From soap films and liquid crystals to biological membranes, minimal surfaces arise as the ground state of a variety of manmade and naturally occurring membranes and lamellar structures. Recently, helical motifs were discovered in the lamellar structure of the endoplasmic reticulum and thylakoids [1]. In both systems right and lefthanded motifs were observed in stoichiometry that suggested global pitch balance [2]. Theoretical treatment of such helical motifs in minimal surfaces has been so far limited to the smallslope approximation, which breaks in the biological settings. We provide a recipe for constructing exact and analytically tractable minimal surfaces in which the appropriate distribution of helical motifs are embedded [3]. We analyze the fundamental structure and interaction between two helical motifs of opposite and similar handedness. Finally, we exploit the newly devised method to construct a minimal surface with an arbitrary array of $N$ helical motifs and show that area minimization leads to global pitch balance. [1] Mustárdy, et al. Plant Cell, 20 (2008) 2552; Liberton, et al. Plant Physiol., 155 (2011) 1656; Terasaki, et al. Cell, 154 (2013) 285. [2] Bussi, et al. PNAS, 116 (2019) 22366. [3] da Silva and Efrati, Proc. R. Soc. A, 477 (2021) 20200891. 
18:00  Flower Pigment Patterns PRESENTER: Patrick Shipman ABSTRACT. Anthocyanins are cell vacuolar pigments responsible for the orange, pink, red, purple, and blue colors of flowers, fruits, vegetables, and leaves. Chromatic patterns form in vitro and in vivo. 
16:30  Motion of droplets in the stochastic CahnHilliard model PRESENTER: Dirk Blömker ABSTRACT. We study the stochastic motion of a droplet in a stochastic Cahn–Hilliard equation in the sharp interface limit for sufficiently small noise. The key ingredient in the proof is a deterministic slow manifold parametrized by the position of the droplet. We show its stability for long times under small stochastic perturbations, and also reduce the dynamics to a stochastic differential equation for the stochastic motion of the center of the droplet. 
17:00  Minimizers for the CahnHilliard Energy Functional under Strong Anchoring Conditions PRESENTER: Shibin Dai ABSTRACT. We study the minimizers for the CahnHilliard energy functional with a symmetric quartic doublewell potential and under a strong anchoring condition on the domain boundary. We show a bifurcation phenomenon determined by the boundary value and a parameter $\kappa$ that describes the thickness of a transition layer separating the two phases. When the boundary value is exactly the average of the two pure phases, if $\kappa$ is larger than or equal to a critical value, the minimizer is unique and is exactly the homogeneous state. Otherwise, there are exactly two symmetric minimizers. The critical bifurcation value is inversely proportional to the first eigenvalue of the negative Laplace operator with the zero Dirichlet boundary condition. When the boundary value is larger (or smaller) than the average of the two pure phases, the symmetry is broken and there is only one minimizer. We also obtain the bounds and morphological properties of the minimizers under additional assumptions on the domain. Our analysis utilizes the notion of the Nehari manifold and connects it to the eigenvalue problem for the negative Laplacian with the homogeneous boundary condition. We will also present our numerical simulations and discuss them in the context of our analytical results. 
17:30  Sharpinterface limits in the dynamics of phase transitions: from the AllenCahn equation to liquid crystals PRESENTER: Tim Laux ABSTRACT. The largescale behavior of phase transitions has a long history. In this talk, I want to present two recent projects which establish convergence results based on a new relative entropy for phasefield models. With Julian Fischer and Theresa M. Simon, we prove optimal convergence rates for the AllenCahn equation to mean curvature flow before the onset of singularities. The proof does not rely on the maximum principle and does not require to understand the spectral properties of the linearized AllenCahn operator. With Yuning Liu, we consider the dynamics in the Landaude Gennes theory of liquid crystals. We show that at the critical temperature, a scaling limit can be derived: The interface between the isotropic and nematic phases moves by mean curvature flow. Furthermore, in the nematic phase, the director field is a harmonic map heat flow with homogeneous Neumann boundary conditions. To derive the equations, we combine the relative entropy method with weak convergence methods. 
18:00  Physicsbased datadriven discovery of continuum equations ABSTRACT. Can atomistic simulations tell us their corresponding evolution equations in the continuum limit? Can a nonequilibrium process be interpreted as an equilibrium one? In this talk, various coarsegraining strategies will be discussed to elucidate these questions and provide important connections between atomistic and continuum models. 
16:30  Computational topology meets material science ABSTRACT. There are multiple tools in computational topology that can be used in material science. Starting from persistent homology (joint with vectorization methods and learning procedures), Euler characteristic curves, Mapper algorithm and beyond. In this talk I will give a general overview of those techniques and show how they can be applied to solve concrete problems. 
17:00  Data Analysis in Soft Matter and Molecular Simulations using Topology and Random Field Theory PRESENTER: Alexander Smith ABSTRACT. Statistics, machine learning, and signal processing are dominant paradigms used to analyze data; unfortunately, such techniques provide limited capabilities to capture topological features of data. This limitation often requires models that are overparameterized and difficult to interpret. Random field theory is an area of mathematics that integrates topology, geometry, and statistics and introduces descriptors to characterize data topology, such as the Euler characteristic (EC). The EC does not require strict statistical assumptions for data (e.g., stationarity, isotropy), generalizes to high dimensions, and provides dimensionality reduction capabilities. In this talk, I discuss concepts of the EC, and demonstrate its application to data from liquid crystal experiments and molecular dynamics (MD) simulations. I demonstrate how the EC provides concise summaries of topological defect textures in liquid crystal films. I also show how the EC can be used to quantify 2dimensional MD simulations for the analysis of selfassembled monolayers (SAMs). The EC can be used as a preprocessing step for these datasets, which simplifies the models needed to perform classification and regression tasks (i.e., complex CNNs simplified to linear regression models). I will also explore some future research areas, such as applications to model fitting and parameterization. 
17:30  From topology of force networks to avalanche prediction in sheared particulate systems PRESENTER: Lou Kondic ABSTRACT. Many natural process, including various types of avalanches and earthquakes involve stickslip type of dynamics. While there has been many attempts to understand in precise terms the mechanisms that lead to granular failure, important aspects of stickslip dynamics are still not understood. One important question is whether there are clear precursor events to slip, or in other words, is there some information in the system that could be used to predict slip events. In this presentation, we will discuss the insights that can be reached by analyzing the force networks obtained in discrete element simulations of sheared granular systems using the tools of computational topology. The topological tools have been already successfully used to discuss evolution of force networks through jamming, as well as influence of particle geometry on force networks properties. One significant advantage of this approach is significant data reduction, allowing to describe crucial properties of complicated force networks by considering only a few relatively simple measures. We will use this approach to discuss whether the static and dynamic measures describing the force networks before slip events can be used to provide more information about the conditions that lead to stickslip type of dynamics. 
18:00  Comparing Local Atomic Environments by the GromovWasserstein Distance PRESENTER: Jeremy Mason ABSTRACT. Largescale molecular dynamic simulations routinely involve millions of atoms, and identifying a process of interest can usually be reduced to a comparison of local atomic environments. These consist of the intersection of a point cloud with a ball of fixed radius, though any local atomic environments related by the action of various symmetry groups are physically indistinguishable. Specifically, the space of local atomic environments is equivalent to that of a set of points in the unit ball quotiented by the orthogonal group acting on the point coordinates and the symmetric group acting on the index set of the points. This work proposes to metrize this space by viewing a local atomic environment as a finite metric measure space, and constructing a distance function on the space of local atomic environments using a variant of the GromovWasserstein distance. This approach differs from those already in the literature in that the distance is continuous rather than discrete, and that local atomic environments of arbitrary spatial extent and composition can be compared. Numerical examples illustrate the efficiency and versatility of the algorithm which is expected to be useful in analyzing the points clouds that arise in other contexts. 
16:30  Pinning of interfaces in a random medium with zero mean PRESENTER: Patrick Dondl ABSTRACT. We consider a fully discrete model for interface propagation in a random environment. The interface, given as the graph of a discrete function, may jump to the next site with a rate depending on the random force at the current site as well as the states of its neighbors and is zero if the sum of the local force and the discrete Laplacian at a site is nonpositive. Pinning then occurs when the jump rate is zero for all points on the interface. We first consider the case where the pinning force's expectation vanishes (or is even positive). Our proof for pinning consists of the construction a supersolution employing a local path optimization procedure. A similar construction also leads to the phenomenon of infinite pinning if the pinning force has infinite second moment. This stands in contrast to the results for related continuum models, which require much fatter tails to obtain infinite pinning. This is joint work with Martin Jesenko (Ljubljana) and Michael Scheutzow (Berlin). 
17:00  Homogenization in randomly perforated domains PRESENTER: Arianna Giunti ABSTRACT. In this talk we discuss some results concerning the homogenization of solutions to a Stokes system in a domain having many small random holes. The main application for these models arises from the study of the flow of a viscous incompressible fluid through a porous medium or in the quasistatic regime of sedimenting particles. Our main focus is the rigorous derivation of the homogenization limit and the quantification of the convergence to the effective problem. In particular, we are interested in the case in which the holes in the domain under consideration are randomly distributed and may give rise to complicated geometries by overlapping and concentrating in certain regions of the domain. 
17:30  Homogenization of freediscontinuity functionals in randomly perforated domains PRESENTER: Caterina Ida Zeppieri ABSTRACT. We study the asymptotic behavior of freediscontinuity functionals defined on randomly perforated domains, as the size of the perforations goes to zero. To gain compactness for minimizing sequences we need to overcome the lack of equicoercivity of the functionals by means of an extension result, under the assumption that the random perforations cannot come too close to one another. The effective limiting energy is then obtained by first applying a general stochastic homogenization result for freediscontinuity functionals to a perturbed coercive version of the energies and eventually by identifying the homogenized volume and surface integrands by means of a careful limit procedure. 
18:00  Stochastic homogenization on randomly perforated domains ABSTRACT. We prove existence of uniformly bounded extension and trace operators on stationary randomly perforated domains. The extension operators are uniformly preserving the norm of the gradient and the symmetric gradient of vector valued functions. This leads to suitable Poincare and Korn inequalities on the perforated domains. In contrast to earlier work, we can deal with nonuniformly Lipschitz domains with infinitely connected holes. 
16:30  Multiscale modelling of dislocation patterning PRESENTER: Peter Dusan Ispanovity ABSTRACT. The plasticity transition at the yield strength of a crystal typically signifies the tendency of dislocation defects towards relatively unrestricted motion. For an isolated dislocation the motion is in the slip plane with velocity proportional to the shear stress, while due to the long range interaction dislocation ensembles move towards satisfying emergent collective elastoplastic modes. Such collective motions have been discussed in terms of the elusively defined backstress. In this talk, a twodimensional stochastic continuum dislocation dynamics theory will be presented that clarifies the role of backstress and demonstrates a precise agreement with the collective behavior of its discrete counterpart, as a function of applied load and with only three essential free parameters. The main ingredients of the continuum theory are the evolution equations of statistically stored and geometrically necessary dislocation densities, which are driven by the longrange internal stress, a stochastic flow stress term and, finally, two local diffusionlike terms. The agreement is shown primarily in terms of the patterning characteristics that include the formation of dipolar dislocation walls. 
17:00  Predicting complex dislocation dynamics using machine learning ABSTRACT. I will present an overview of our recent efforts to apply machine learning to study the problem of predicting the fluctuating plastic deformation process of small crystals containing dislocations. First, I will discuss the problem of predicting the stressstrain curves of individual samples from 2D discrete dislocation dynamics (DDD) simulations [1]. There, the key findings include nonmonotonic strain dependence of predictability, as well as a size effect "larger is more predictable". Then, I will proceed to consider dislocation pileups interacting with frozen disorder, exhibiting a depinning phase transition [2]. Also in that case we find a nonmonotonic dependence of predictability on strain. I will also discuss our attempts to predict the individual strain bursts in that case. Finally, I will describe our very recent results using data from strainratecontrolled 2D DDD simulations. Specifically, we find that predictability of the deformation process exhibits rate dependence. [1] H. Salmenjoki, M. J. Alava, and L. Laurson, Machine learning plastic deformation of crystals, Nat. Commun. 9, 5307 (2018). [2] M. Sarvilahti, A. Skaugen, and L. Laurson, Machine learning depinning of dislocation pileups, APL Mater. 8, 101109 (2020). 
17:30  Multiscale modeling of plasticity in multicomponent alloys: A statistical and data science perspective ABSTRACT. Predicting features of mechanical deformation represents a fantastic challenge as it depends on a myriad of factors related to material microstructure, specimen geometry and loading conditions. Micromechanical approaches try to bridge microstructural features of solids with their mechanical response, but they are confronted to the high level of complexity of microstructures and microscopic damage processes involved in materials, especially in multicomponent crystalline materials, such as high entropy alloys. Recently, new approaches inspired from data science have emerged: the key microscale parameters that control mechanical deformation at large scale can be identified, and even learned, from the statistical analysis of a large amount of data. Statistical predictions range in a wide gamut of applications, from indentation of composites, to neural networks for understanding of elastic and plastic features of deformation in crystals. I will present a set of tools that utilize the dynamical stability of elasticity as an asset towards microstructural characterization and parameterfree multiscale modeling. Through this approach, I will demonstrate applications for synthetic data and will discuss possible experimental validation routes. 
16:30  Asymptotic localization in multicomponent coagulation equations PRESENTER: Marina A. Ferreira ABSTRACT. Atmospheric aerosol particles undergo complex phenonena that influence their movement, size and chemical composition. These particles grow due to coalescence, however, how they grow and how their composition changes is not well understood. We consider a simplified setting where particles are homogeneously distributed in space. The distribution of particle composition over time may be described by the multicomponent Smoluchowski's coagulation equation. We study existence and properties of massconserving solutions for a large class of kernels. Curiously, the mass tends to localize along a direction in the size space, forming a pattern for large times. This property is specific to the multicomponent setting and it occurs on all solutions for all kernels in the class considered. 
17:00  Stationary nonequilibrium solutions for coagulation equations ABSTRACT. Smoluchowski’s coagulation equation is a classical model for mass aggregation phenomena extensively used in the analysis of problems of polymerization, particle aggregation in aerosols, drop formation in rain and several other situations. In this talk I will present some recent results on the problem of existence or nonexistence of stationary solutions to coagulation equations, for single and multicomponent systems, under nonequilibrium conditions which are induced by the addition of a source term for small cluster sizes. The most striking feature of these stationary solutions is that, whenever they exist, the solutions to multicomponent systems exhibit an unusual “spontaneous localization” phenomena. More precisely, the stationary solutions to the multicomponent coagulation equation asymptotically localize into a direction determined by the source term. (Joint work with M.A. Ferreira, J. Lukkarinen and J.J.L. Velázquez) 
17:30  The scaling hypothesis for Smoluchowski's coagulation equation: perturbations of the constant kernel PRESENTER: Sebastian Throm ABSTRACT. We will show that solutions of Smoluchowski's classical coagulation model exhibit a universal selfsimilar longtime behaviour if the rate kernel is sufficiently close to the constant one. In particular, we will also provide explicit rates of convergence towards the scaling profile. 
18:00  Large Deviations for Coagulation including the Gel ABSTRACT. Exploiting connections between coagulation and random graphs I will present a large deviations result that explicitly includes microscopic and macroscopic (gel) particles as well as giving some information about intermediate scales. One sees that multiple gel particles are possible for finite large deviations cost, but that having only one gel particle is optimal. The initial results assume an initial particle population of identical monomers. However, I will also discuss the extension of the work to include heterogeneous initial particle distribution. This is joint work with Luisa Andreis, Wolfgang Koenig and Heida Langhammer. 
16:30  A onedimensional model for elastic ribbons covering a broad range of thicknesstowidth ratios PRESENTER: Basile Audoly ABSTRACT. Starting from the theory of elastic plates, we derive a nonlinear onedimensional model for elastic ribbons with thickness t, width a and length L, assuming t<<a<<L. It takes the form of a rod model with a special nonlinear constitutive law accounting for both the stretching and the bending of the ribbon midsurface. The model is asymptotically correct and can handle finite rotations. Both Kirchhoff's linear beam theory and Sadowsky's inextensible ribbon model can be recovered as limit cases, for small (respectively, large) values of the bending and twisting strain. The lateraltorsional buckling of an elastic ribbon is solved as an illustration: an excellent agreement with both tabletop experiments and finiteelement shell simulations is obtained. 
17:00  Simulation of free boundaries and interfaces in nonlinear plate bending ABSTRACT. The bending behavior of plates is often described using dimensionally reduced models. We propose a practical method for the numerical simulation of bilayer plate bending that is based on a nonlinear twodimensional plate model. Our method employs a discretization of the resulting energy using DKT (discrete Kirchhoff triangle) elements in space and a discrete gradient flow restricted to appropriate tangent spaces for the minimization of the energy functional. Particularly, we discuss the simulation of (self)contact and the applicability of the method for simulating plates of nematic liquid crystal elastomers. 
17:30  Twisted topological tangles or: the knot theory of knitting ABSTRACT. Imagine a 1D curve. Use it to fill a 2D manifold that covers an arbitrary 3D object. This computationally intensive materials challenge has been realized in the ancient technology known as knitting. This process for making functional materials 2D materials from 1D filaments dates back to prehistory. Knitted textiles are ubiquitous as they are easy and cheap to create, lightweight, portable, flexible and stretchy. As with many functional materials, the key to knitting’s extraordinary properties lies in its microstructure. Knits are composed of an interlocking series of slip knots. There is only one manipulation that creates a knitted stitch – pulling a loop of yarn through another loop. However, there exist hundreds of books with thousands of patterns of stitches with seemingly unbounded complexity. The topology of knitted stitches has a profound impact on the geometry and elasticity of the resulting fabric. This puts a new spin on additive manufacturing – not only can stitch pattern control the local and global geometry of a textile, but the creation process encodes mechanical properties within the material itself. Unlike additive manufacturing techniques, the innate properties of the stitch microstructure has a direct effect on the global geometry and mechanics of knitted fabrics. 
18:00  Mechanics of Masks ABSTRACT. The current pandemic has sparked a great deal of debate over the efficacy of cloth masks as an alternative to medical masks for the general public. In this talk we will discuss the mechanics of masks. Despite an abundance of experimental studies on the filtration of aerosols by cloth masks, we currently lack the capability to predict mask performance a priori. In this talk I will establish quantitative models for pressure drops across cloth masks and filtration efficiencies which include the mesoscale heterogeneities that naturally arise in woven textiles. This trade space between filtration efficacy and breathability is presented in a decision map to offer practical guidance for designing and/or purchasing cloth masks. Finally, the impact of the predicted mask efficiencies on the spread of the pandemic is quantified as a correction factor to the basic reproduction number, R0. 
16:30  Datadriven learning of nonlocal physics from highfidelity synthetic data PRESENTER: Yue Yu ABSTRACT. A key challenge to nonlocal models is the analytical complexity of deriving them from first principles, and frequently their use is justified a posteriori. In this work we extract nonlocal models from data, circumventing these challenges and providing datadriven justification for the resulting model form. Extracting datadriven surrogates is a major challenge for machine learning (ML) approaches, due to nonlinearities and lack of convexity  it is particularly challenging to extract surrogates which are provably wellposed and numerically stable. Our scheme not only yields a convex optimization problem, but also allows extraction of nonlocal models whose kernels may be partially negative while maintaining wellposedness even in smalldata regimes. To achieve this, based on established nonlocal theory, we embed in our algorithm sufficient conditions on the nonpositive part of the kernel that guarantee wellposedness of the learnt operator. These conditions are imposed as inequality constraints to meet the requisite conditions of the nonlocal theory. We demonstrate this workflow for a range of applications, including reproduction of manufactured nonlocal kernels; numerical homogenization of Darcy flow associated with a heterogeneous periodic microstructure; nonlocal approximation to highorder local transport phenomena; and approximation of globally supported fractional diffusion operators by truncated kernels. 
17:00  Datadriven learning of nonlocal models:from highfidelity simulations to constitutive laws PRESENTER: Huaiqian You ABSTRACT. We show that machine learning can improve the accuracy of simulations of stress waves in onedimensional composite materials. We propose a datadriven technique to learn nonlocal constitutive laws for stress wave propagation models. The method is an optimizationbased technique in which the nonlocal kernel function is approximated via Bernstein polynomials. The kernel, including both its functional form and parameters, is derived so that when used in a nonlocal solver, it generates solutions that closely match highfidelity data. The optimal kernel, therefore, acts as a homogenized nonlocal continuum model that accurately reproduces wave motion ina smallerscale, more detailed model that can include multiple materials. We apply this technique to wave propagation within a heterogeneous bar with a periodic microstructure. Several onedimensional numerical tests illustrate the accuracy of our algorithm. The optimal kernel is demonstrated to reproduce highfidelity data for composite material in applications that are substantially different from the problems used as training data. 
17:30  A machinelearning framework for peridynamic material models with physical constraints PRESENTER: Xiao Xu ABSTRACT. As a nonlocal extension of continuum mechanics, peridynamics has been widely and effectively applied in different fields where discontinuities in the field variables arise from an initially continuous body. An important component of the constitutive model in peridynamics is the influence function which weights the contribution of all the interactions over a nonlocal region surrounding a point of interest. Recent work has shown that in solid mechanics the influence function has a strong relationship with the heterogeneity of a material's microstructure. However, determining an accurate influence function analytically from a given microstructure typically requires lengthy derivations and complex mathematical models. To avoid these complexities, the goal of this paper is to develop a datadriven regression algorithm to find the optimal bondbased peridynamic model to describe the macroscale deformation of linear elastic medium with periodic heterogeneity. We generate macroscale deformation training data by averaging over periodic microstructure unit cells and add a physical energy constraint representing the homogenized elastic modulus of the microstructure to the regression algorithm. We demonstrate this scheme for examples of one and twodimensional linear elastodynamics and show that the energy constraint improves the accuracy of the resulting peridynamic model. 
18:00  fVPINNs: Variational PhysicsInformed Neural Networks for Fractional Differential Equations PRESENTER: Ehsan Kharazmi ABSTRACT. We develop a physicsinformed machine learning algorithm to infer the fractional order of derivatives in fractional differential equations. In particular, we use the variational physicsinformed neural networks (VPINNs). The VPINN formulation constructs a general framework based on the nonlinear approximation of deep neural networks and projection onto the space of highorder polynomials. It provides the flexibility of reducing the order of differential operators via integrationbyparts. Here, we extend this formulation to fractional differential equations with distributed/variable order derivatives. Given the sparse spacetime observations of dynamics, we discover the corresponding kernel of fractional derivatives in an inverse problem setting. 
16:30  A GinzburgLandau model for the lightmatter interaction in nematic liquid crystals PRESENTER: Panayotis Smyrnelis ABSTRACT. We study global minimizers of an energy functional arising as a thin sample limit in the theory of lightmatter interaction in nematic liquid crystals. We show that depending on the parameters various defects are predicted by the model. In particular we show existence of a new type of topological defect which we call the shadow vortex. Finally, we discovered that at the boundary of the illuminated region, the profile of the minimizers is given by the universal equation of Painlevé. 
17:00  Axisymmetry of critical points of the Onsager functional for liquid crystals ABSTRACT. The talk will discuss critical points of the Onsager functional for liquid crystals, giving in particular a simple proof of their axisymmetry in the case of the MaierSaupe molecular interaction, a classical result of Fatkullin & Slastikov (2005) and Liu, Zhang & Zhang (2005). The proof avoids spherical polar coordinates, instead using an integral identity on the sphere. The connection with the singular potential of Majumdar and the author for the MaierSaupe interaction is addressed. For general molecular interactions the smoothness of critical points is proved, and for a wide class of interactions the existence of nonaxisymmetric critical points established. 
17:30  A unified divergent approach to HardyPoincaré Inequalities PRESENTER: Giovanni Di Fratta ABSTRACT. Hardy and Poincarétype inequalities are among the most frequently used inequalities in the analysis of PDE. The aim of this talk is to present a unified strategy to derive HardyPoincaré inequalities on bounded and unbounded domains. The approach allows proving a general HaryPoincaré inequality from which the classical Poincaré and Hardy inequalities immediately follow. The argument also applies to the more general context of variable exponent Sobolev spaces. The argument, concise and constructive, does not require a priori knowledge of compactness results and returns geometric information on the optimal constants. 
18:00  Energy minimizing twisting twin patterns in nonlinear elasticity ABSTRACT. In my talk I will describe a geometrically nonlinear model for microstructure formation under bending in shapememory alloys, restricted to a twodimensional situation with a single rankone connection. We show that the optimal scaling on the energy with Dirichlet boundary conditions is attained by a complex pattern with microstructure around both boundaries. Furthermore, if one prohibits the microstructure around the boundaries, then the optimal scaling law changes significantly. Both scaling laws are different from the one, previously obtained in the literature for multiple variants of the classic KohnMuller energy, which mimics the situation with two rankone connections. This is a joint project with S.Conti and R.Kohn. 