Related papers: Variational methods for solving nonlinear boundary…
Soft-walled microchannels arise in many applications, ranging from organ-on-a-chip platforms to soft-robotic actuators. However, despite extensive research on their static and dynamic response, the potential failure of these devices has not…
In this paper, we consider nonlinearly perturbed Legendre differential equations subject to the usual boundary conditions. For such problems we establish sufficient conditions for the existence of solutions and in some cases we provide a…
Curvilinear, multiblock summation-by-parts finite difference operators with the simultaneous approximation term method provide a stable and accurate framework for solving the wave equation in second order form. That said, the standard…
When a colloidal particle adheres to a fluid membrane, it induces elastic deformations in the membrane which oppose its own binding. The structural and energetic aspects of this balance are theoretically studied within the framework of a…
The present article studies variational principles for the formulation of static and dynamic problems involving Kirchhoff rods in a fully nonlinear setting. These results, some of them new, others scattered in the literature, are presented…
In this paper we study a class of Riemannian metrics on the space of unparametrized curves and develop a method to compute geodesics with given boundary conditions. It extends previous works on this topic in several important ways. The…
In this thesis we deal with two different classes of variational problems: 1) the problem of closed curves with prescribed curvature, or $H$-loop problem; 2) the study of the nodal solutions of the fractional Brezis-Nirenberg problem. In…
We consider spectral discretizations of hyperbolic problems on unbounded domains using Laguerre basis functions. Taking as model problem the scalar advection equation, we perform a comprehensive stability analysis that includes strong…
Elastic confinements play an important role in many soft matter systems and affect the transport properties of suspended particles in viscous flow. On the basis of low-Reynolds-number hydrodynamics, we present an analytical theory of the…
We consider inverse problems for non-linear hyperbolic and elliptic equations and give an introduction to the method based on the multiple linearization, or on the construction of artificial sources, to solve these problems. The method is…
Soft porous materials, such as biological tissues and soils, are exposed to periodic deformations in a variety of natural and industrial contexts. The detailed flow and mechanics of these deformations have not yet been systematically…
This article proposes a novel approach for determining exact solutions to nonlinear ordinary differential equations. The recommended iterative method provides the solution via a rapidly converging series that readily approaches a closed…
A nonlinear divergence parabolic equation with dynamic boundary conditions of Wentzell type is studied. The existence and uniqueness of a strong solution is obtained as the limit of a finite difference scheme, in the time dependent case and…
We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of…
The mathematical model of a real flexible elastic system with distributed and discrete parameters is considered. It is a partial differential equation with non-classical boundary conditions. Complexity of the boundary conditions results in…
Using numerical simulations, we characterized the behavior of an elastic membrane immersed in an active fluid. Our findings reveal a nontrivial folding and re-expansion of the membrane that is controlled by the interplay of its resistance…
In this paper, we introduce a novel parallel contact algorithm designed to run efficiently in High-Performance Computing based supercomputers. Particular emphasis is put on its computational implementation in a multiphysics finite element…
The deformation and stress distribution in a stretched thin neo-Hookean circular membrane with a hole at its center are analyzed within the framework of finite deformation elasticity. Initially, we derive a simple form for the differential…
A model of unsteady filtration (seepage) in a porous medium with capillary retention is considered. It leads to a free boundary problem for a generalized porous medium equation where the location of the boundary of the water mound is…
We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…