Related papers: A 4D geometrical modeling of a material aging
The known possibility to consider the (vacuum) Maxwell equations in a curved space-time as Maxwell equations in flat space-time(Mandel'stam L.I., Tamm I.E.) taken in an effective media the properties of which are determined by metrical…
A model in statistical mechanics, characterised by the corresponding Gibbs measure, is a subset of the totality of probability distributions on the phase space. The shape of this subset, i.e., the geometry, then plays an important role in…
We propose a coordinate-invariant geometric formulation of the GENERIC stochastic differential equation, unifying reversible Hamiltonian and irreversible dissipative dynamics within a differential-geometric framework. Our construction…
Novel view synthesis of dynamic scenes is fundamental to achieving photorealistic 4D reconstruction and immersive visual experiences. Recent progress in Gaussian-based representations has significantly improved real-time rendering quality,…
Human motion generation is often learned in Euclidean spaces, although valid motions follow structured non-Euclidean geometry. We present Riemannian Motion Generation (RMG), a unified framework that represents motion on a product manifold…
Process-structure-property relationships are fundamental in materials science and engineering and are key to the development of new and improved materials. Symbolic regression serves as a powerful tool for uncovering mathematical models…
It has been shown previously, that the spatial thermal variation of a thermal medium can be recast as a variation in the Euclidean metric. It is now extended to temporal variations in temperature, for a non-relativistic thermal bath, which…
We develop computational methods that incorporate shear into fluctuating hydrodynamics methods. We are motivated by the rheological responses of complex fluids and soft materials. Our approach is based on continuum stochastic hydrodynamic…
It is well established that glassy materials can undergo aging, i.e., their properties gradually change over time. There is rapidly growing evidence that dense active and living systems also exhibit many features of glassy behavior, but it…
Purpose: This essay is a retelling of general relativity in a language in which space-time geometry is expressed as a fluid. This trivial and useful reformulation gives 1) a non-perturbative covariant description of cosmological…
Random fields are ubiquitous mathematical structures in physics, with applications ranging from thermodynamics and statistical physics to quantum field theory and cosmology. Recent works on information geometry of Gaussian random fields…
The simulation of viscoelastic time-evolution problems described by a large number of internal variables and with a large spectrum of relaxation times requires high computational resources for their resolution. Furthermore, the internal…
Surface growth, i.e., the addition or removal of mass from the boundary of a solid body, occurs in a wide range of processes, including the growth of biological tissues, solidification and melting, and additive manufacturing. To understand…
Futher development is made of a consept of space-time as multidimensional elastic plate, proposed earlier in [20,21]. General equilibrium equations, including 4-dimensional tangent stress tensor - energy-momentum tensor of matter - are…
We show that thermodynamics can be formulated naturally from the intrinsic geometry of phase space alone-without postulating an ensemble, which instead emerges from the geometric structure itself. Within this formulation, phase transitions…
In this manuscript, we show how conformal invariance can be incorporated in a classical theory of gravitation, in the context of metric measure space. Metric measure space involves a geometrical scalar $f$, dubbed as density function, which…
The vertex model with homogeneous cell properties is known to exhibit a parameter degeneracy in which the system's dynamics is independent of the target area. Here, we show, for the heterogeneous vertex model where cells differ in size and…
A comprehensive 3-D finite element formulation for the coupled thermoelastic system is proposed based on the Total Lagrangian framework to study the thermoelastic damping (TED) in small scale structures. The proposed formulation takes into…
It is the author's belief that a perfect theory will eventually be formulated, where geometry and physics become indistinguishable, so that the complete understanding of space properties, together with proper assignments between geometric…
During the wear process of surfaces in sliding friction, there is a running-in period during which the topography of surfaces changes with time before reaching the steady wear regime. In the steady wear regime, the statistical parameters…