In this section we will consider the general properties of the solution p(r, t) of the Smoluchowski equation in the case that the force field is derived from a potential, i.e., F (r) = −∇U(r) and that the potential is finite everywhere in the diffusion doamain Ω. We will demonstrate first that the solutions, in case of reaction-free boundary conditions, obey an extremum principle, namely, that ...

We write a non-relativistic Lagrangian for a hierarchical universe. The equations of motion are solved numerically and the evolution of the fractal dimension is obtained for different initial conditions. We show that our model is homogeneous at the time of the last scattering, but evolves into a self-similar universe with a remarkably constant fractal dimension. We also show that the Hubble law...

The problem of determining a current density confined to a volume from measurements of the magnetic and electric fields it produces exterior to that volume is known to have nonunique solutions. Despite the nonuniqueness of the inversion we show that one may nevertheless uniquely determine certain moments of the vector spherical harmonic expansion of the current. It is demonstrated that the dete...

We present a semiclassical perturbation method for the description of atomic diffraction by a weakly modulated potential. It proceeds in a way similar to the treatment of light diffraction by a thin phase grating, and consists in calculating the atomic wavefunction by mean~ of action integrals along the classical trajectories of the atoms in the absence of the modulated part of the potential. T...

In the approach of the effective field theory of modified gravity, we derive the equations of motion for linear perturbations in the presence of a barotropic perfect fluid on the flat isotropic cosmological background. In a simple version of Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories, which is the minimum extension of Horndeski theories, we show that a slight deviation of the tensor propa...

We consider the anisotropic XY chain in a magnetic field with special boundary conditions described by a two-parameter Hamiltonian. It is shown that the exchange of the parameters corresponds to a similarity transformation, which reduces in a special limit to the Ising duality transformation. BONN HE-93-40 cond-mat/9310055 October 1993 In this paper we consider the anisotropic XY chain in a mag...

Seery and Lidsey have calculated the three-point correlator of the light scalar fields, a few Hubble times after horizon exit during inflation. Lyth and Rodriguez have calculated the contribution of this correlator to the three-point correlator of the primordial curvature perturbation. We calculate an upper bound on that contribution, showing that it is too small ever to be observable. Introduc...

Improving the spatial resolution of an image sequence critically depends upon the accuracy of the motion estimator. The problem is complicated by the fact that the motion field is prone to significant errors since original high resolution images are not available. In earlier work, bilinearly interpolated images were used as initial conditions for the proposed algorithm. In this paper, the use o...

In this paper we examine the performance of a number of linear techniques for reconstructing the 3-D distribution of absorption coefficient within a highly scattering medium using the diffuse photon density wave (DPDW) approximation. The simulation consists of a coplanar array of sources and detectors at the boundary of an infinite slab medium. The primary difficulty in the linear reconstructio...

According to the Water Framework Directive (WFD), "good ecological status" of all aquatic environments should be achieved by 2015. To validate this objective, we set up management tools to assess the physical condition of rivers. To avoid field work, which is a long and tedious work, and in order to achieve homogeneous data throughout the network, we created geomatic tools based on an object-or...