Related papers: The variational modeling of hierarchical structure…
Structured deformations provide a multiscale geometry that captures the contributions at the macrolevel of both smooth geometrical changes and non-smooth geometrical changes (disarrangements) at submacroscopic levels. For each (first-order)…
Hierarchical microstructures are often invoked to explain the high resilience and fracture toughness of biological materials such as bone and nacre. Biomimetic material models inspired by those structural arrangements face the obvious…
We introduce a new variational inference (VI) framework, called energetic variational inference (EVI). It minimizes the VI objective function based on a prescribed energy-dissipation law. Using the EVI framework, we can derive many existing…
Dense suspensions of deformable particles can exhibit rich nonequilibrium dynamics arising from complex flow-structure coupling. Using a multi-phase field model, we show that steady shear drives an initially disordered, dense, soft…
In this article, we discuss new models for static nonlinear deformations via scale-invariant conformal energy functionals based on the linear distortion. In particular, we give examples to show that, despite equicontinuity estimates giving…
We employ a canonical variational framework for the predictive characterization of structural instabilities that develop during the diffusion-driven transient swelling of hydrogels under geometrical constraints. The variational formulation…
A variational method is studied based on the minimum of energy variance. The method is tested on exactly soluble problems in quantum mechanics, and is shown to be a useful tool whenever the properties of states are more relevant than the…
The existence and the regularity results obtained in [37] for the variational model introduced in [36] to study the optimal shape of crystalline materials in the setting of stress-driven rearrangement instabilities (SDRI) are extended from…
Atomistic simulations are employed to study structural evolution of pore ensembles in binary glasses under periodic shear deformation with varied amplitude. The consideration is given to porous systems in the limit of low porosity. The…
Spectral methods of moments provide a powerful tool for learning the parameters of latent variable models. Despite their theoretical appeal, the applicability of these methods to real data is still limited due to a lack of robustness to…
This chapter covers methodological issues related to estimation, testing and computation for models involving structural changes. Our aim is to review developments as they relate to econometric applications based on linear models.…
In this work, a higher-order irrotational strain gradient plasticity theory is studied in the small strain regime. A detailed numerical study is based on the problem of simple shear of a non-homogeneous block comprising an elastic-plastic…
Using a well defined soft model glass in the framework of Molecular Dynamics simulations, the inherent structures are probed by means of a recently developed deformation protocol that aims to capture the Dynamical Heterogeneities (DH), as…
We introduce and study a variational framework for the analysis of empirical risk based inference for dynamical systems and ergodic processes. The analysis applies to a two-stage estimation procedure in which (i) the trajectory of an…
We obtain variational formulas for holomorphic objects on Riemann surfaces with respect to arbitrary local coordinates on the moduli space of complex structures. These formulas are written in terms of a canonical object on the moduli space…
In this paper we propose a new refined shear deformation plate theory which possesses a series of desirable features, the most salient of which are as follows: (i) The loads, which are generally considered to be applied on the middle…
We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance…
The central question that we address is: How can structured information be stored in a hierarchical Hopfield model involving hidden layers? To this end, we develop a formalism of strokes and concepts that allows us to appropriately…
The study is devoted to geometrically non-linear modelling of viscoplastic structures with residual stresses. We advocate and develop a special approach to residual stresses based on the transition between reference configurations. The…
Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied…