Related papers: New examples of three-dimensional dilational mater…
We introduce an (equi-)affine invariant diffusion geometry by which surfaces that go through squeeze and shear transformations can still be properly analyzed. The definition of an affine invariant metric enables us to construct an invariant…
Dissipative phenomena manifest in multiple mechanical systems. In this dissertation, different geometric frameworks for modelling non-conservative dynamics are considered. The objective is to generalize several results from conservative…
A wide range of materials can exist in microscopically disordered solid forms, referred to as amorphous solids or glasses. Such materials -- oxide glasses and metallic glasses, to polymer glasses, and soft solids such as colloidal glasses,…
This text is an introduction to dilation surfaces. We attempt to expose some geometric and dynamical aspects of the subject: moduli spaces, directional foliations and the Teichm\"uller flow.
In the recent development in a various disciplines of physics, it is noted the need for including the deformed versions of the exponential functions. In this paper, we consider the deformations which have two purposes: to have them like…
Recently, we pointed out that on a class on non exactly decimable fractals two different parameters are required to describe diffusive and vibrational dynamics. This phenomenon we call dynamical dimension splitting is related to the lack of…
In contrast to three-dimensional (3D) crystals that melt via a first-order transition, two-dimensional (2D) crystals can exhibit various melting scenarios under different temperatures, pressures, and particle interactions, particularly when…
The bi-continuum model composed of two interpenetrating and dynamically coupled material continua is analysed as a simplified but relatively accurate way to describe some physical phenomena in crystalline solids. The essential novelty of…
The Comments are devoted to the recently published paper 'Modelling and nonclassical symmetry analysis of a complex porous media flow in a dilating channel' (Physica D. 481 (2025) 134834), in which a model describing an unsteady…
The Discrete Dislocation (DD) analysis and its computional modeling have been advanced significantly over the past decade. This progress has been further magnified by the idea to couple DD with continuum mechanics analysis in association…
We predict a phenomenon of catastrophic material failure arising suddenly within an amorphous material, with an extremely long delay time since the material was last deformed. By simulating a mesoscopic soft glassy rheology model in one…
Amorphous materials driven away from equilibrium display a diverse repertoire of complex, history-dependent behaviors. One striking feature is a failure to return to equilibrium after an abrupt change in otherwise static external…
Here we explore the geometry of the osculating spaces to projective varieties of arbitrary dimension. In particular, we classify varieties having very degenerate higher order osculating spaces and we determine mild conditions for the…
We present a new definition of defects which is based on a Riemannian formulation of incompatible elasticity. Defects are viewed as local deviations of the material's reference metric field, $\bar{\mathfrak{g}}$, from a Euclidian metric.…
We suggest a scalar model for deformation and flow of an amorphous material such as a foam or an emulsion. To describe elastic, plastic and viscous behaviours, we use three scalar variables: elastic deformation, plastic deformation rate and…
This work presents a survey of mechanical models describing van der Waals interactions between 2D materials, encompassing both continuous elastomer-like materials and discrete (crystalline) 2D materials such as graphene. These interactions…
The classical low-dimensional models of thin structures are based on certain a priori assumptions on the three-dimensional deformation and/or stress fields, diverse in nature but all motivated by the smallness of certain dimensions with…
A method to define the complex structure and separate the conformal mode is proposed for a surface constructed by two-dimensional dynamical triangulation. Applications are made for surfaces coupled to matter fields such as $n$ scalar fields…
We briefly present two-dimensional dilaton gravity from the point of view of integrable systems.
We study large deformations of hyperelastic membranes using a purely two-dimensional formulation derived from basic balance principles within a modern geometric setting, ensuring a framework that is independent of an underlying…