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In this work a periodic crystal with point defects is described in the framework of linear response theory for broken symmetry states using correlation functions and Zwanzig-Mori equations. The main results are microscopic expressions for…
There is a compactification of the space of representations of a finitely generated group into the groups of isometries of all spaces with $\Delta$-thin triangles. The ideal points are actions on $\mathbb R$-trees. It is a geometric…
The two-phase composite approach of Estrin et al. (1998) describes an evolving dislocation cell structure. Mckenzie et al. (2007) enhanced the model to capture the effects of hydrostatic pressure and temperature during severe plastic…
We present a real-time deformation method for Escher tiles -- interlocking organic forms that seamlessly tessellate the plane following symmetry rules. We formulate the problem as determining a periodic displacement field. The goal is to…
The Gauss map of non-degenerate surfaces in the three-dimensional Minkowski space are viewed as dynamical fields of the two-dimensional O(2,1) Nonlinear Sigma Model. In this setting, the moduli space of solutions with rotational symmetry is…
The Laplace-Beltrami problem on closed surfaces embedded in three dimensions arises in many areas of physics, including molecular dynamics (surface diffusion), electromagnetics (harmonic vector fields), and fluid dynamics (vesicle…
Dislocation based modeling of plasticity is one of the central challenges at the crossover of materials science and continuum mechanics. Developing a continuum theory of dislocations requires the solution of two long standing problems: (i)…
Let M be a translation surface. We show that certain deformations of M supported on the set of all cylinders in a given direction remain in the GL(2,R)-orbit closure of M. Applications are given concerning complete periodicity, field of…
A spectral formulation of the plane-strain boundary integral equations for an interface between dissimilar elastic solids is presented. The boundary integral equations can be written in two equivalent forms: (a) The tractions can be written…
In studies on Marangoni type motion of particles the surface tension is often approximated as a linear function of temperature. For deformable particles in a linear external temperature gradient far from the reference point this…
Explicit analytical expressions for the drag and diffusion coefficients of a spherical particle attached to the interface between two immiscible fluids are constructed for the case of a small viscosity ratio between the fluid phases. The…
The local deformation of two-dimensional Lennard-Jones glasses under imposed shear strain is studied via computer simulations. Both the mean squared displacement and mean squared strain rise linearly with the length of the strain interval…
In this paper a geometric field theory of dislocation dynamics and finite plasticity in single crystals is formulated. Starting from the multiplicative decomposition of the deformation gradient into elastic and plastic parts, we use…
In this paper we introduce a mathematical model for small deformations induced by external forces of closed surfaces that are minimisers of Helfrich-type energies. Our model is suitable for the study of deformations of cell membranes…
We study the lubrication of fluid-immersed soft interfaces and show that elastic deformation couples tangential and normal forces and thus generates lift. We consider materials that deform easily, due to either geometry (e.g. a shell) or…
This paper is a continuation and elaboration of our work quant-ph/0206057 (Nucl. Phys. B, 1968, 7, 79) where some approach to the variable-mass problem were proposed. Here we have found a concret realization of irreducible representations…
In this note, we describe the possible singularities on a stable surface which is in the boundary of the moduli space of surfaces isogenous to a product. Then we use the $\mathbb Q$-Gorenstein deformation theory to get some connected…
The order parameter model based on parametric Ginzburg-Landau equation is used to describe high acceleration patterns in vibrated layer of granular material. At large amplitude of driving both hexagons and interfaces emerge. Transverse…
We comment on the macroscopic model for surface plasmons of H.-Y. Deng [New J. Phys. 21 (2019) 043055; arXiv:1712.06101] and a claim, based on energy conversion from charges to the electric field, that surface plasmons on metallic surfaces…
In this paper, a method of local perturbations, previously successfully applied to decompose the problem of elasticity in the system of connected thin rods and beams [Kolpakov and Andrianov, 2013], is used to study the asymptotic behaviour…