Ultradilute low-dimensional liquids

We calculate the energy of one- and two-dimensional weakly interacting Bose-Bose mixtures analytically in the Bogoliubov approximation and by using the diffusion Monte Carlo technique. We show that in the case of attractive inter- and repulsive intraspecies interactions the energy per particle has a minimum at a finite density corresponding to a liquid state. We derive the Gross-Pitaevskii equation to describe droplets of such liquids and solve it analytically in the one-dimensional case.Comment: published version + supplemental materia

Mathematical Models of Video-Sequences of Digital Half-Tone Images

This chapter is devoted to Mathematical Models (MM) of Digital Half-Tone Images (DHTI) and their video-sequences presented as causal multi-dimensional Markov Processes (MP) on discrete meshes. The difficulties of MM development for DHTI video-sequences of Markov type are shown. These difficulties are related to the enormous volume of computational operations required for their realization. The method of MM-DHTI construction and their statistically correlated video-sequences on the basis of the causal multi-dimensional multi-value MM is described in detail. Realization of such operations is not computationally intensive; Markov models from the second to fourth order demonstrate this. The proposed method is especially effective when DHTI is represented by low-bit (4-8 bits) binary numbers

Development of Nonlinear Filtering Algorithms of Digital Half-Tone Images

This chapter is devoted to solving the problem of algorithms and structures investigations for Radio Receiver Devices (RRD) with the aim of the nonlinear filtering of Digital Half-Tone Images (DHTI) representing the discrete-time and discrete-value random Markovian process with a number of states greater than two. At that, it is assumed that each value of the DHTI element is represented by the binary g-bit number, whose bits are transmitted via digital communication links in the presence of Additive White Gaussian Noise (AWGN). The authors present the qualitative analysis of the optimal DHTI filtering algorithm. The noise immunity of the optimal radio receiver device for the DHTI filtering with varying quantization and dimension levels is investigated

Comparing the drag force on heavy quarks in N=4 super-Yang-Mills theory and QCD

Computations of the drag force on a heavy quark moving through a thermal state of strongly coupled N=4 super-Yang-Mills theory have appeared recently in hep-th/0605158, hep-ph/0605199, and hep-th/0605182. I compare the strength of this effect between N=4 gauge theory and QCD, using the static force between external quarks to normalize the 't Hooft coupling. Comparing N=4 and QCD at fixed energy density then leads to a relaxation time of roughly 2 fm/c for charm quarks moving through a quark-gluon plasma at T=250 MeV. This estimate should be regarded as preliminary because of the difficulties of comparing two such different theories.Comment: 16 pages, 1 figure. v2: corrected estimate of eta/s, refs adde

A rigorous derivation of the stationary compressible Reynolds equation via the Navier-Stokes equations

We provide a rigorous derivation of the compressible Reynolds system as a singular limit of the compressible (barotropic) Navier-Stokes system on a thin domain. In particular, the existence of solutions to the Navier-Stokes system with non-homogeneous boundary conditions is shown that may be of independent interest. Our approach is based on new a priori bounds available for the pressure law of hard sphere type. Finally, uniqueness for the limit problem is established in the 1D case

Worldsheet Matter Superfields on Half-Shell

In this paper we discuss some of the effects of using "unidexterous" worldsheet superfields, which satisfy worldsheet differential constraints and so are partly on-shell, i.e., on half-shell. Most notably, this results in a stratification of the field space that reminds of "brane-world" geometries. Linear dependence on such superfields provides a worldsheet generalization of the super-Zeeman effect. In turn, non-linear dependence yields additional left-right asymmetric dynamical constraints on the propagating fields, again in a stratified fashion.Comment: 15 pages, 2 figures; minor algebraic correction