Related papers: Integral representation for a relaxed optimal desi…
This work is devoted to the optimal decay problem for the Euler-Poisson two-fluid system, which is a classical hydrodynamic model arising in semiconductor sciences. By exploring the influence of the electronic field on the dissipative…
A continuum plasticity model for metals is presented from considerations of non-equilibrium thermodynamics. Of specific interest is the application of a fluctuation relation that subsumes the second law of thermodynamics en route to…
A time-dependent Ginzburg-Landau model of plastic deformation in two-dimensional solids is presented. The fundamental dynamic variables are the displacement field $\bi u$ and the lattice velocity ${\bi v}=\p {\bi u}/\p t$. Damping is…
A variational model of pressure-dependent plasticity employing a time-incremental setting is introduced. A novel formulation of the dissipation potential allows one to construct the condensed energy in a variationally consistent manner. For…
Measure structured deformations are introduced to present a unified theory of deformations of continua. The energy associated with a measure structured deformation is defined via relaxation departing either from energies associated with…
Two-particle Green's functions and the vertex functions play a critical role in theoretical frameworks for describing strongly correlated electron systems. However, numerical calculations at two-particle level often suffer from large…
We study Density Functional Theory models for systems which are translationally invariant in some directions, such as a homogeneous 2-d slab in the 3-d space. We show how the different terms of the energy are modified and we derive reduced…
At the microscopic level, plastic flow of a jammed, disordered material consists of a series of particle rearrangements that cannot be reversed by subsequent deformation. An infinitesimal deformation of the same material has no…
A shape optimization problem arising from the optimal reinforcement of a membrane by means of one-dimensional stiffeners or from the fastest cooling of a two-dimensional object by means of ``conducting wires'' is considered. The criterion…
We use a continuous mesoscopic model to address the yielding properties of plastic composites, formed by a host material and inclusions with different elastic and/or plastic properties. We investigate the flow properties of the composed…
Existing implementations of gradient-based optimisation methods typically assume that the problem is posed in Euclidean space. When solving optimality problems on function spaces, the functional derivative is then inaccurately represented…
In nonlinear elasticity, finding the deformation of a material which minimizes a given stored energy density is a challenging calculus of variations problem which may fail to have minimizers: the energy optimal material forms infinitely…
Understanding the particle-scale transition from elastic deformation to plastic flow is central to making predictions about the bulk material properties and response of disordered materials. To address this issue, we perform experiments on…
Traditionally, the deformation of continuum is divided into elastic, plastic, and flow. For a large deformation with cracking, they are combined together. So, for complicated deformation, a formulation to express the evolution of…
We analyse a numerical scheme for a system arising from a novel description of the standard elastic--perfectly plastic response. The elastic--perfectly plastic response is described via rate-type equations that do not make use of the…
We considered the thermodynamics in spaces with deformed commutation relation leading to existence of the minimal length. We developed a classical method of the partition function evaluation. We calculated the partition function and heat…
In the framework of the rate-independent large-strain Cosserat theory of plasticity we calculate analytically explicit solutions of a two-dimensional shear problem. We discuss two cases where the micro-rotations are stationary solutions of…
We consider the representation of the value of an optimal stopping problem of a linear diffusion as an expected supremum of a known function. We establish an explicit integral representation of this function by utilizing the explicitly…
In this paper, we propose an efficient numerical treatment for solving contact problems with friction between deformable bodies. The discretized normal and tangential constraints at the candidate contact interface are expressed by using…
Light reflection plays a crucial role in a number of modern technologies. In this paper, analytical expressions for maximal reflected power in any direction and for any polarization are given for generic planar structures made of a single…