Related papers: Spatial heterogeneity in 3D-2D dimensional reducti…
Three-dimensional turbulence is usually studied experimentally by using a spatially localized forcing at large scales (e.g. via rotating blades or oscillating grids), often in a deterministic way. Here, we report an original technique where…
We consider a class of models motivated by previous numerical studies of wrinkling in highly stretched, thin rectangular elastomer sheets. The model used is characterized by a finite-strain hyperelastic membrane energy perturbed by small…
We use variational convergence to derive a hierarchy of one-dimensional rod theories, starting out from three-dimensional models in nonlinear elasticity subject to local volume-preservation. The densities of the resulting $\Gamma$-limits…
In this paper we study the derivation of nonlinear bending models for prestrained elastic plates from three-dimensional non-linear elasticity via homogenization and dimension reduction. We compare effective models obtained by either…
We consider the Cauchy problem for wave equations with localized damping in ${\bf R}^{2}$. The damping is effective only near spatial infinity. We obtain fast energy decay estimate such that $O(t^{-2}\log t)$ as $t \to \infty$. Unlike the…
The aim of this article is to prove strong convergence results on the difference between the solution to highly oscillatory problems posed in thin domains and its two-scale expansion. We first consider the case of the linear diffusion…
It is well known that the toroidal dimensional reduction of supergravities gives rise in three dimensions to theories whose bosonic sectors are described purely in terms of scalar degrees of freedom, which parameterise sigma-model coset…
We prove that that for nonlinear elastic energies with strong enough energetic control of the outer distortion of admissible deformations, almost everywhere global invertibility as constraint can be obtained in the $\Gamma$-limit of the…
We present Monte Carlo simulations of an ultra coarse-grained lipid bilayer with different number of lipids on both leaflets. In the simulations, we employ a new method for measuring the elastic parameters of the membrane, including the…
Three-body systems that are continuously squeezed from a three-dimensional (3D) space into a two-dimensional (2D) space are investigated. Such a squeezing can be obtained by means of an external confining potential acting along a single…
The quantum mechanical definition of probability, the uncertainty principle and Poincare invariance provide strong basic restrictions on the ability to define spatial densities associated with form factors describing the properties of…
A reason has been given for the inverse energy cascade in the two-dimensionalised rapidly rotating 3D incompressible turbulence. For such system, literature shows a possibility of the exponent of wavenumber in the energy spectrum's relation…
Unlike conventional two-dimensional (2D) semiconductor superlattices, moir\'{e} patterns in 2D materials are flexible and their electronic, magnetic, optical, and mechanical properties depend on their topography. Within a…
The problem of the sudden growth and coalescence of voids in elastic media is considered. The Dirichlet energy is minimized among incompressible and invertible Sobolev deformations of a two-dimensional domain having $n$ microvoids of radius…
Exact solutions are derived for the problem of a two-dimensional, infinitely anisotropic, linear-elastic medium containing a periodic lattice of voids. The matrix material possesses either one infinitely soft, or one infinitely hard loading…
In this paper, we investigate the global existence of strong solutions for the inhomogeneous incompressible viscoelastic system with only velocity dissipation on $\mathbb{R}^{2}$. Due to the criticality of the time-weight, the methods for…
An exact description is provided of an almost spherical fluid vesicle with a fixed area and a fixed enclosed volume locally deformed by external normal forces bringing two nearby points on the surface together symmetrically. The conformal…
The virtual element method (VEM) allows discretization of the problem domain with polygons in 2D. The polygons can have an arbitrary number of sides and can be concave or convex. These features, among others, are attractive for meshing…
The present paper is concerned with a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of a homogenization theorem (i.e., convergence of…
In this thesis we study field theoretic viewpoints on certain fluid mechanical phenomena. In the Higgs mechanism, the weak gauge bosons acquire masses by interacting with a scalar field, leading to a vector boson mass matrix. On the other…