Related papers: On the variational method for Euclidean quantum fi…
The conditioning of the linear finite volume element discretization for general diffusion equations is studied on arbitrary simplicial meshes. The condition number is defined as the ratio of the maximal singular value of the stiffness…
We introduce a new computational methodology for the identification and characterization of free volume within/around atomistic configurations. This scheme employs a three-stage workflow, by which spheres are iteratively grown inside of…
We study the length of cycles in the model of spatial random permutations in Euclidean space. In this model, for given length $L$, density $\rho$, dimension $d$ and jump density $\varphi$, one samples $\rho L^d$ particles in a…
Assuming that Bogoliubov's theory of weakly interacting dilute Bose gas defines a self-consistent model Hamiltonian, we investigate its thermodynamic limit as we take the volume to infinity. The infinite volume is taken via a sequence of…
In this work we prove an analogue, for partial differential equations on the space of probability measures, of the classical vanishing viscosity result known for equations on the Euclidean space. Our result allows in particular to show that…
The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic…
In our previous article [4] an approach to derive Papapetrou equations for constrained electromagnetic field was demonstrated by use of field variational principles. The aim of current work is to present more universal technique of…
We study a parametric class of isotropic but not necessarily stationary Poisson hyperplane tessellations in n-dimensional Euclidean space. Our focus is on the volume of the zero cell, i.e. the cell containing the origin. As a main result,…
This paper reviews the progress made over the last five years in studying boundary conditions and semiclassical properties of quantum fields about 4-real-dimensional Riemannian backgrounds. For massless spin-${1\over 2}$ fields one has a…
Examination of the Einstein energy-momentum relationship suggests that simple unbound forms of matter exist in a four-dimensional Euclidean space. Position, momentum, velocity, and other vector quantities can be expressed as Euclidean…
We propose a formalism to study dynamical properties of a quantum many-body system in the thermodynamic limit by studying a finite system with infinite boundary conditions (IBC) where both finite size effects and boundary effects have been…
We propose a toy model of quantum gravity in two dimensions with Euclidean signature. The model is given by a kind of discretization which is different from the dynamical triangulation. We show that there exists a continuum limit and we can…
A nontrivial conformally invariant model is obtained via generalization the method of obtaining conformally invariant models in $2D$ Euclidean space to the Euclidean space with dimension $D>2$. This method was previously developed by E.S.…
This article proposes a highly accurate and conservative method for hyperbolic systems using the finite volume approach. This innovative scheme constructs the intermediate states at the interfaces of the control volumes using the method of…
The deformation theory of hyperbolic and Euclidean cone-manifolds with all cone angles less then 2{\pi} plays an important role in many problems in low dimensional topology and in the geometrization of 3-manifolds. Furthermore, various old…
We give a simple proof of the Weyl asymptotic formula for eigenvalues of the Dirichlet Laplacian, the buckling problem, and the Dirichlet bi-Laplacian in Euclidean domains of finite volume, with no assumptions about the boundary.
The Turaev-Viro state sum invariant is known to give the transition amplitude for the three dimensional BF theory with cosmological term, and its deformation parameter hbar is related with the cosmological constant via hbar=sqrt{Lambda}.…
We investigate in this article the boundary layers appearing for a fluid under moderate rotation when the viscosity is small. The fluid is modeled by rotating type Stokes equations known also as the Barotropric mode equations in the…
This paper derives some discrete maximum principles for $P1$-conforming finite element approximations for quasi-linear second order elliptic equations. The results are extensions of the classical maximum principles in the theory of partial…
The various entropy bounds that exist in the literature suggest that spacetime is fundamentally discrete, and hint at an underlying relationship between geometry and "information". The foundation of this relationship is yet to be uncovered,…