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Many parts of biological organisms are comprised of deformable porous media. The biological media is both pliable enough to deform in response to an outside force and can deform by itself using the work of an embedded muscle. For example,…
We evaluate the conditions for surface stability of a layered magnetoelastic half-space subjected to large deformations and a magnetic field. After reviewing the fundamental measures of deformation and summarizing the magnetostatic…
The dynamics of supercooled liquid and glassy systems are usually studied within the Lagrangian representation, in which the positions and velocities of distinguishable interacting particles are followed. Within this representation,…
Fluid deformable surfaces are ubiquitous in cell and tissue biology, including lipid bilayers, the actomyosin cortex, or epithelial cell sheets. These interfaces exhibit a complex interplay between elasticity, low Reynolds number…
We have considered a model of a small finite system with internal particles and surface degrees of freedom. All the main statistical distributions were explicitly obtained, on a pre thermodynamic limit basis. The concept of temperature or…
A computational approach is introduced for the study of the rheological properties of complex fluids and soft materials. The approach allows for a consistent treatment of microstructure elastic mechanics, hydrodynamic coupling, thermal…
Understanding of the complex behavior of particles at surfaces requires detailed knowledge of both macroscopic and microscopic processes that take place; also certain processes depend critically on temperature and gas pressure. To link…
In continuum mechanics, stress concept plays an essential role. For complicated materials, different stress concepts are used with ambiguity or different understanding. Geometrically, a material element is expressed by a closed region with…
We consider geometric variational problems for a functional defined on a curve in three-dimensional space. The functional is assumed to be written in a form invariant under the group of Euclidean motions. We present the Euler-Lagrange…
Most approaches in Lagrangian fluid dynamics simulations proceed from the definition of particle volumes, from which discrete versions of the spatial differential operators are derived. Recently, Gallou\"et and M\'erigot [1] simultaneously…
An optimization method used in image-processing (metamorphosis) is found to imply Euler's equations for incompressible flow of an inviscid fluid, without requiring that the Lagrangian particle labels exactly follow the flow lines of the…
We develop a general incremental framework for hyperelastic solids whose surfaces exhibit both stretch-dependent and curvature-dependent elastic behavior. Building upon a variational formulation of curvature-dependent surface elasticity, we…
In this article, Euler-Lagrangian dynamics explain that the two particle interaction has non-conservative forces about the frame of the center of mass. This interpretation clarifies the underlying interaction and the system descriptions…
An arbitrary Lagrangian--Eulerian finite element method and numerical implementation for curved and deforming lipid membranes is presented here. The membrane surface is endowed with a mesh whose in-plane motion need not depend on the…
I clarify the differences between various approaches in the literature which attempt to link gravity and thermodynamics. I then describe a new perspective based on the following features: (1) As in the case of any other matter field, the…
A key aspect of fluid dynamics is the correct definition of the \textit{% phase-space} Lagrangian dynamics which characterizes arbitrary fluid elements of an incompressible fluid. Apart being an unsolved theoretical problem of fundamental…
Recent advancements have demonstrated that fully Eulerian methods can effectively model frictionless contact between deformable solids. Unlike traditional Lagrangian approaches, which require contact detection and resolution algorithms, the…
We present a fully general derivation of the Laplace--Young formula and discuss the interplay between the intrinsic surface geometry and the extrinsic one ensuing from the immersion of the surface in the ordinary euclidean three-dimensional…
A deterministic theory describing the behavior of an ultrathin lubricant film between two atomically-smooth solid surfaces is proposed. For the description of lubricant state the parameter of excess volume arising due to chaotization of…
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…