Related papers: On the material time derivative of volume, surface…
We discuss general 2-fluid hydrodynamic equations for complex fluids, where one kind is a simple Newtonian fluid, while the other is either liquid-crystalline or polymeric/elastomeric, thus being applicable to lyotropic liquid crystals,…
We provide a detailed derivation of a recently developed first-principles approach to calculating averages in systems of interacting, spherical Brownian particles under time-dependent flow. Although we restrict ourselves to flows which are…
Many complex structures and stochastic patterns emerge from simple kinetic rules and local interactions, and are governed by scale invariance properties in combination with effects of the global geometry. We consider systems that can be…
Two questions are investigated by looking successively at classical mechanics, special relativity, and relativistic gravity: first, how is space related with spacetime? The proposed answer is that each given reference fluid, that is a…
This paper is concerned with the inverse problem of determining the time and space dependent source term of diffusion equations with constant-order time-fractional derivative in $(0,2)$. We examine two different cases. In the first one, the…
We present a systematic derivation of the constraints that the relativity principle imposes between coefficients of a deformed (but rotational invariant) momentum composition law, dispersion relation, and momentum transformation laws, at…
In studies of interfaces with dynamic chemical composition, bulk and interfacial quantities coupled via surface conservation laws of excess surface quantities. While this approach is for microscopically sharp interfaces, its applicability…
Inspired by the works of \cite{baz2} and \cite{kian}, this study develops an abstract framework for analyzing differential equations with space-dependent fractional time derivatives and bounded operators. Within this framework, we establish…
The invariant is one of central topics in science, technology and engineering. The differential invariant is essential in understanding or describing some important phenomena or procedures in mathematics, physics, chemistry, biology or…
Electromagnetic waves in a system with a space and time dependent boundary experience both diffraction and Doppler-like frequency conversion. In order to analyse such situations, conventional methods call for either the eigenmodes or the…
Recently a new theory for the transport of energetic particles across a mean magnetic field was presented. Compared to other non-linear theories the new approach has the advantage that it provides a full time-dependent description of the…
We investigate diffusion equations with time-fractional derivatives of space-dependent variable order. We examine the well-posedness issue and prove that the space-dependent variable order coefficient is uniquely determined among other…
Differential transfer relations of flux density, general physics quantities' and its corresponding energy's, between time domains of source and observer are derived from conservative rule of various physical quantities and time function…
Let $N$ be a Riemannian, neutral or Lorentzian $4$-dimensional space form. In this paper, the expressions of the equations of Gauss, Codazzi and Ricci of a space-like or time-like surface in $N$ given in [7] are naturally understood in…
Analytic relations are derived for finite volume integrals over the radial distribution function of a fluid, so-called Kirkwood-Buff integrals. Closed form expressions are obtained for cubes and cuboids, the system shapes commonly employed…
We derive formulae for the time variation of the gravitational ``constant'' and of the fine structure ``constant'' in various models with extra dimensions and analyze their consistency with the observational data.
We study the shape differentiability of a cost function for the flow of an incompressible viscous fluid of power-law type. The fluid is confined to a bounded planar domain surrounding an obstacle. For smooth perturbations of the shape of…
The relationship between the foundations of mathematics and physics is a topic of of much interest. This paper continues this exploration by examination of the effect of space and time dependent number scaling on theoretical descriptions of…
In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form…
There are theories which implement the idea that the constants of nature may be "time dependent." These introduce new fields representing "evolving constants," in addition to physical fields. We argue that dynamical matter coupling…