Related papers: The Diffusion Equation on a Hypersphere
In this exploratory article, we present a constructive method for scattering points on the surface of $d$ dimensional spheres which we believe is new and of interest. Indeed, the problem of uniformly distributing points on spheres is an…
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…
A possible approximate route to obtain the equation of state of the monodisperse hard-sphere system in the metastable fluid region from the knowledge of the equation of state of a hard-sphere mixture at high densities is discussed. The…
A fundamental non-classical fourth-order partial differential equation to describe small amplitude linear oscillations in a rotating compressible fluid, is obtained. The dispersion relations for such a fluid, and the different regions of…
We derive an explicit representation of the fundamental solution to the heat equation in a half-space of ${\mathbb R}^N$ with a diffusive dynamical boundary condition, and establish sharp pointwise upper and lower bounds. We also…
We investigate the fractional diffusion approximation of a kinetic equation in the upper-half plane with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…
A fourth-order dispersive flow equation for closed curves on the canonical two-dimensional unit sphere arises in some contexts in physics and fluid mechanics. In this paper, a geometric generalization of the sphere-valued model is…
We propose an alternative method for one-dimensional continuum diffusion models with spatially variable (heterogeneous) diffusivity. Our method, which extends recent work on stochastic diffusion, assumes the constant-coefficient homogenized…
The advection-diffusion equation can be approximated by a one-dimensional diffusion equation in Lagrangian coordinates along the directions of compression of fluid elements (the stable manifold). This result holds in any number of…
The fourth virial coefficient is calculated exactly for a fluid of hard spheres in even dimensions. For this purpose the complete star cluster integral is expressed as the sum of two three-folded integrals only involving spherical angular…
Motivated by the work of D. Hoff and K. Zumbrun (Indiana Univ. Math. J. 44: 603-676, 1995), we investigate the diffusion wave phenomena in three-dimensional incompressible viscoelastic flows. By employing the representation formula of the…
In this article we study the numerical approximation of a variable coefficient fractional diffusion equation. Using a change of variable, the variable coefficient fractional diffusion equation is transformed into a constant coefficient…
We consider the wave equation for sound in a moving fluid with a fourth-order anomalous dispersion relation. The velocity of the fluid is a linear function of position, giving two points in the flow where the fluid velocity matches the…
A holomorphic representation formula for special parabolic hyperspheres is given.
A theory of the propagation of acoustic waves in a porous medium filled with superfluid solution is developed. The elastic coefficients in the system of equations are expressed in terms of physically measurable quantities. The equations…
The diffusion approximation to the relaxation on the distorted Fermi surface in a Fermi liquid is considered. The dependence of the relaxation time on the multipolarity of a Fermi surface deformation is established. The time evolution of…
We consider the effective surface motion of a particle that freely diffuses in the bulk and intermittently binds to that surface. From an exact approach we derive various regimes of the effective surface motion characterized by physical…
The fourth virial coefficient is calculated exactly for a fluid of hard spheres in odd dimensions up to 11.
We exactly calculate the fourth virial coefficient for hard spheres in even dimensions for D=4,6,8,10, and 12.
The diffusion of particles in confining walls forming a tube is discussed. Such a transport phenomenon is observed in biological cells and porous media. We consider the case in which the tube is winding with curvature and torsion, and the…