This paper considers the multidimensional active scalar problem of motion of a function ρ(x, t) by a velocity field obtained by v = −∇N ∗ρ, where N is the Newtonian potential. We prove well-posedness of compactly supported L∞ ∩ L1 solutions of possibly mixed sign. These solutions include an important class of solutions that are proportional to characteristic functions on a time-evolving domain....

The scalar spectral index n is an important parameter describing the nature of primordial density perturbations. Recent data, including those from the Wilkinson Microwave Anisotropy Probe satellite, show some evidence that the index runs ~changes as a function of the scale k at which it is measured! from n.1 ~blue! on long scales to n,1 ~red! on short scales. We investigate the extent to which ...

We develop a phase space distribution function approach to redshift space distortions (RSD), in which the redshift space density can be written as a sum over velocity moments of the distribution function. These moments are density weighted and have well defined physical interpretation: their lowest orders are density, momentum density, and stress energy density. The series expansion is converge...

In this work, we present results from a new formulation for determining image velocities from a time-sequence of X-ray projection images of owing uid. Starting with the conservation of mass principle, and physics of X-ray projection, we derive a motion constraint equation for projection imaging, a practical special case of which is shown to be the Horn and Schunck's optical ow constraint. We ar...

The aim of this paper is to study the L1-stability of periodic stationary solutions of scalar convection-diffusion equations. We obtain dispersion in L2 for all space dimensions using Kružkov type entropy. And when the space dimension is one, we estimate the number of sign changes of a solution to obtain L1-stability. Keyword : L-stability, periodic stationary solutions, entropy, dispersion ine...

In this paper, we have proved that locally there exist infinitely many three dimensional slant submanifolds with prescribed scalar curvature into cosymplectic space form M 5 (c) with c ∈ {−4, 4}while there does not exist flat minimal proper slant surface in M 5 (c) with c 6= 0. In section 5, we have established an inequality between mean curvature and sectional curvature of the subamnifold and ...

We present an exact formula for the β-function for the soft-breaking scalar mass in an N = 1 supersymmetric gauge theory, in the form of an operator acting on the anomalous dimension. In particular we give the exact form for the correction due to the ǫ-scalar mass, and show that it has a particularly simple form in the renormalisation scheme corresponding to the exact NSVZ gauge β-function.

We investigate the extension of the Prokof’ev-Svistunov worm algorithm to Wilson lattice fermions in an external scalar field. We effectively simulate by Monte Carlo the graphs contributing to the hopping expansion of the twopoint function on a finite lattice to arbitrary order. Tests are conducted for a constant background field i. e. free fermions at some mass. For the method introduced here ...

Let Z be a standard Gaussian random variable, X be independent of Z, and t be a strictly positive scalar. For the derivatives in t of the differential entropy of X + √ tZ, McKean noticed that Gaussian X achieves the extreme for the first and second derivatives, among distributions with a fixed variance, and he conjectured that this holds for general orders of derivatives. This conjecture implie...

A generalization of scalar electrodynamics called fluid electrodynamics is presented. In this theory a fluid replaces the Higgs scalar field. Fluid electrodynamics might have application to the theory of low temperature Helium superfluids, but here it is argued that it provides an alternative method of approaching symmetry breaking in particle physics. The method of constructing fluid electrody...