相关论文: Tube Volumes via Functional Equations
Computer simulations of inhomogeneous soft matter systems often require accurate methods for computing the local pressure. We present a simple derivation, based on the virial relation, of two equivalent expressions for the local (atomistic)…
Affine su(3) and su(4) fusion multiplicities are characterised as discretised volumes of certain convex polytopes. The volumes are measured explicitly, resulting in multiple sum formulas. These are the first polytope-volume formulas for…
A closed set of \textit{exact} equations describing statistical theory of turbulent self-diffusion by multivariate-normal turbulent velocity field is derived. In doing so, we first suggest exact formulas for correlations…
We use the theory of calibrations to write the equation of a minimal volume vector field on a given Riemann surface.
We establish an integration formula for integral foliated simplicial volume along ergodic decompositions. This is analogous to the ergodic decomposition formula for the cost of groups.
Numerical simulation of compressible fluid flows is performed using the Euler equations. They include the scalar advection equation for the density, the vector advection equation for the velocity and a given pressure dependence on the…
We obtain rigorous results concerning the evaluation of integrals on the two sphere using complex methods. It is shown that for regular as well as singular functions which admit poles, the integral can be reduced to the calculation of…
We prove a characterization of the dual mixed volume in terms of functional properties of the polynomial associated to it. To do this, we use tools from the theory of multilinear operators on spaces of continuos functions. Along the way we…
This article reviews the properties of the self-similar solutions of the Navier-Stokes equation for incompressible fluids. Since any smooth solution can be embedded into a self-similar solution at the identity scale, it follows that under…
We give a deterministic method of quasi-polynomial complexity to approximate the volume of the intersection of the unit hypercube with two specific sets. The method can actually be applied (without losing the quasi-polynomial complexity) to…
This article presents a new boundary integral approach for finding optimal shapes of peristaltic pumps that transport a viscous fluid. Formulas for computing the shape derivatives of the standard cost functionals and constraints are…
This paper deals with the solution of unified fractional reaction-diffusion systems. The results are obtained in compact and elegant forms in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for…
We consider solvability of the generalized reaction-diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction-diffusion…
We show that convexity of the effective action follows from its functional flow equation. Our analysis is based on a new, spectral representation. The results are relevant for the study of physical instabilities. We also derive constraints…
We define a Bowen-Series like map for every geometric presentation of a co-compact surface group and we prove that the volume entropy of the presentation is the topological entropy of this particular (circle) map. Finally we find the…
A numerical method is presented for first-principle simulations of charged colloidal dispersions in electrolyte solutions. Utilizing a smoothed profile for colloid-solvent boundaries, efficient mesoscopic simulations are enabled for…
We give a classification of all self-similar solutions to the curve shortening flow in the plane.
At first, pressure formulas for the electrons under the external potential produced by fixed nuclei are derived both in the surface integral and volume integral forms concerning an arbitrary volume chosen in the system; the surface integral…
We propose a two-point flux approximation finite-volume scheme for a stochastic non-linear parabolic equation with a multiplicative noise. The time discretization is implicit except for the stochastic noise term in order to be compatible…
We revisit the classical Womersley solution for pulsatile viscous flow in a circular tube and reconstruct its full time-domain geometry from first principles. By combining harmonic decomposition with exact Bessel solutions, we derive a…