Related papers: Mechanistic Modeling of Longitudinal Shape Changes…
This paper studies a longitudinal shape transformation model in which shapes are deformed in response to an internal growth potential that evolves according to an advection reaction diffusion process. This model extends prior works that…
We study a shape evolution framework in which the deformation of shapes from time t to t + dt is governed by a regularized anisotropic elasticity model. More precisely, we assume that at each time shapes are infinitesimally deformed from a…
Living biological tissue is a complex system, constantly growing and changing in response to external and internal stimuli. These processes lead to remarkable and intricate changes in shape. Modeling and understanding both natural and…
This work studies a variational formulation and numerical solution of a regularized morphoelasticity problem of shape evolution. The foundation of our analysis is based on the governing equations of linear elasticity, extended to account…
This work builds on an existing model of discrete canonical evolution and applies it to the general case of a linear dynamical system, i.e., a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q} $ and linear…
In this paper we study the locomotion of a shape-changing body swimming in a two-dimensional perfect fluid of infinite extent. The shape-changes are prescribed as functions of time satisfying constraints ensuring that they result from the…
Models for fluid deformable surfaces provide valid theories to describe the dynamics of thin fluidic sheets of soft materials. To use such models in morphogenesis and development requires to incorporate active forces. We consider active…
We study how the encasement of a growing elastic bulk within a possibly differently growing elastic coat may induce mechanical instabilities in the equilibrium shape of the combined body. The inhomogeneities induced in an incompressible…
Extending our previous work on 2D growth for the Laplace equation we study here {\it multidimensional} growth for {\it arbitrary elliptic} equations, describing inhomogeneous and anisotropic pattern formations processes. We find that these…
Equations for dislocation evolution bridge the gap between dislocation properties and continuum descriptions of plastic behavior of crystalline materials. Computer simulations can help us verify these evolution equations and find their…
Alternative approach for description of the non-equilibrium phenomena arising in solids at a severe external loading is analyzed. The approach is based on the new form of kinetic equations in terms of the internal and modified free energy.…
A complete representation of 3D objects requires characterizing the space of deformations in an interpretable manner, from articulations of a single instance to changes in shape across categories. In this work, we improve on a prior…
This paper reviews several Riemannian metrics and evolution equations in the context of diffeomorphic shape analysis. After a short review of of various approaches at building Riemannian spaces of shapes, with a special focus on the…
We consider an electrodiffusion model describing the evolution of $N$ ionic species in a three-dimensional fluid flowing through a porous medium and forced by added body charges. We address the global well-posedness and long-time dynamics…
This paper is concerned with the uniqueness, existence, comparison principle and long-time behavior of solutions to the initial-boundary value problem for a unidirectional diffusion equation. The unidirectional evolution often appears in…
This thesis consists of two parts, connected by one central theme: the dynamics of the "shape of space". The first part of the thesis concerns the construction of a theory of gravity dynamically equivalent to general relativity (GR) in 3+1…
In theoretical ecology, models describing the spatial dispersal and the temporal evolution of species having non-overlapping generations are often based on integrodifference equations. For various such applications the environment has an…
C. N. Yang's ideas about local gauge symmetry and non-integrable phases have been enormously fertile sources of inspiration in fundamental physics and in the quantum theory of matter. They also arise naturally in describing the dynamics of…
Evolution and development operate at different timescales; generations for the one, a lifetime for the other. These two processes, the basis of much of life on earth, interact in many non-trivial ways, but their temporal hierarchy --…
Data-driven and deep learning approaches have demonstrated to have the potential of replacing classical constitutive models for complex materials. Yet, the necessity of structuring constitutive models with an incremental formulation has…