Related papers: Curvature-dimension conditions for diffusions unde…
This work contributes to an understanding of the domain size's effect on the existence and uniqueness of the linear convection--diffusion equation with integral-type boundary conditions, where boundary conditions depend non-locally on…
The nonlocal models of peridynamics have successfully predicted fractures and deformations for a variety of materials. In contrast to local mechanics, peridynamic boundary conditions must be defined on a finite volume region outside the…
We relate the (non)existence of lower scalar curvature bounds to the existence of certain distance-decreasing maps. We also give a sufficient condition for the existence of a limiting scalar curvature measure in the backward limit of a…
We review how reparametrization of space and time, namely the procedure where both are made to depend on yet another parameter, can be used to formulate quantum physics in a way that is naturally conducive to relativity. This leads us to a…
In this paper, we derive a general regularity estimate for any 4-d spacetime, in terms of a priori bounds of the Ricci curvature and Lie derivative of the Lorentzian metric with respect to an arbitrary timelike vector field.
A distributed order fractional diffusion equation is considered. Distributed order derivatives are fractional derivatives that have been integrated over the order of the derivative within a given range. In this paper sub-diffusive cases are…
In this paper, it is shown why Lorentz Transformation implies the general case where observed events are not necessarily in the inertia frame of any observer but assumes a special scenario when determining the length contraction and time…
Crystals form regular and robust structures that under extreme conditions can melt and recrystallize into different arrangements in a process that is called crystal metamorphism. While crystals exist due to the breaking of a continuous…
Riemannian metric on real 2n-dimensional space associated with the equation governing complex diffusion of pure states of an open quantum system is introduced and studied. Examples of a qubit under the influence of dephasing and thermal…
Time-space noncommutativity leads to quantisation of time and energy nonconservation when time is conjugate to a compact spatial direction like a circle. In this context energy is conserved only modulo some fixed unit. Such a possibility…
We introduce a curvature-dimension condition for autonomous Lagrangians on weighted manifolds, which depends on the Euler-Lagrange dynamics on a single energy level. By generalizing Klartag's needle decomposition technique to the Lagrangian…
The problem of boundary behaviour at the origin of coordinates is discussed for D-dimensional Schrodinger equation in the framework of hyper spherical formalism, which have been often considered last time. We show that the Dirichlet…
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…
We prove comparison theorems for the sub-Riemannian distortion coefficients appearing in interpolation inequalities. These results, which are equivalent to a sub-Laplacian comparison theorem for the sub-Riemannian distance, are obtained by…
We study curvature dimension inequalities for the sub-Laplacian on contact Riemannian manifolds. This new curvature dimension condition is then used to obtain: 1) Geometric conditions ensuring the compactness of the underlying manifold…
Assuming the existence of a preferred aether frame and the anisotropy of the one-way speed of light in platforms different from the aether frame, we derive the space and time transformations relative to bodies moving in any direction of…
In this article we study inverse source problems for time-fractional diffusion equations from \textit{a posteriori} boundary measurement. Using the memory effect of these class of equations, we solve these inverse problems for several class…
Unifying quantum theory and gravity remains a fundamental challenge in physics. While most existing literature focuses on the ultraviolet (UV) modifications of quantum theory due to gravity, this work shows that generic infrared (IR)…
Given a Fourier transformable measure in two dimensions, we find a formula for the intensity of its Fourier transform along circles. In particular, we obtain a formula for the diffraction measure along a circle in terms of the…
The apparent times and positions of moving clocks as predicted by both `non-local' and `local' Lorentz Transformations are considered. Only local transformations respect translational invariance. Such transformations change temporal but not…