General method of synthesis by PLIC/FPGA digital devices to perform discrete orthogonal transformations

A general method is proposed to synthesize digital devices in order to perform discrete orthogonal transformations (DOT) on programmable logic integrated circuits (PLIC) of FPGA class. The basic and the most "slow" operation during DOT performance is the operation of multiplying by a constant factor (constant) - OMC. To perform DOT digital devices are implemented at the use of the same type of IP-cores, which allow to realize OMC. According to the proposed method, OMC is determined on the basis of picturing set over the elements of the Galois field. Due to the distributed computing of nonlinear polynomial function systems defined over the Galois field in PLIC/FPGA architecture, the reduction in the estimates of time complexity concerning OMC performance is achieved. Each non-linear polynomial function, like OMC, is realized on the basis of the same type of IP-cores according to one of the structural schemes in accordance with the requirements for the device to perform DOT. The use of IP cores significantly reduces the cost of designing a device that implements DOT in the PLIC/FPGA architecture.Keywords: digital signal processing, discrete orthogonal transformations, distributed computing, nonlinear polynomial functions, Galois fields, FPGAs, digital device

Representation of MarkovFunctions byMinimal Polynomials over a Finite Field

The method of representing Markov functions with minimal characteristic polynomials over a finite field is proposed. These polynomials are defined on the basis of integrated stochastic matrices. The representation accuracy of stochastic matrices is linearly dependent on the minimum degree of the polynomials. The algorithmic implementation of the method is shown to build a sequence of the Markov functions class considered, with a given linear complexity.This work was supported by RFBR Grant 18-01-00120а «Specialized devices for generating and processing data sets in the architecture of programmable logic devices class FPGA»

A constructive approach to the soliton solutions of integrable quadrilateral lattice equations

Scalar multidimensionally consistent quadrilateral lattice equations are studied. We explore a confluence between the superposition principle for solutions related by the Backlund transformation, and the method of solving a Riccati map by exploiting two kn own particular solutions. This leads to an expression for the N-soliton-type solutions of a generic equation within this class. As a particular instance we give an explicit N-soliton solution for the primary model, which is Adler's lattice equation (or Q4).Comment: 22 page

Generation of Collisionless Shocks by Laser-Plasma Piston in Magnetised Background: Experiment “BUW”

Theoretical basis and main results of the first successful large-scale, Laser-Plasma experiment “BUW”, on generation of Collisionless Shock Wave in magnetised Background Plasma, are presented. Our classic approach is based on the action of so called Magnetic Laminar Mechanism (or Larmor coupling) for collisionless interaction between interpenetrating super-Alfvenic plasma flows of Laser-Plasma and Background in transverse magnetic field

Power corrections and renormalons in Drell-Yan production

The resummed Drell-Yan cross section in the double-logarithmic approximation suffers from infrared renormalons. Their presence was interpreted as an indication for non-perturbative corrections of order \lqcd/(Q(1-z)). We find that, once soft gluon emission is accurately taken into account, the leading renormalon divergence in the resummed cross section is cancelled by higher-order perturbative contributions in the exponent of the resummed cross section. From this evidence, `higher twist' corrections to the hard cross section in Drell-Yan production should therefore intervene only at order \lqcd^2/((Q^2 (1-z)^2) in the entire perturbative domain Q (1-z) > \lqcd. We compare this result with hadronic event shape variables, comment on the potential universality of non-perturbative corrections to resummed cross sections, and on possible implications for phenomenology.Comment: 37 pages, LATEX, 3 figures as uudecoded fil

Modulational Instability in Equations of KdV Type

It is a matter of experience that nonlinear waves in dispersive media, propagating primarily in one direction, may appear periodic in small space and time scales, but their characteristics --- amplitude, phase, wave number, etc. --- slowly vary in large space and time scales. In the 1970's, Whitham developed an asymptotic (WKB) method to study the effects of small "modulations" on nonlinear periodic wave trains. Since then, there has been a great deal of work aiming at rigorously justifying the predictions from Whitham's formal theory. We discuss recent advances in the mathematical understanding of the dynamics, in particular, the instability of slowly modulated wave trains for nonlinear dispersive equations of KdV type.Comment: 40 pages. To appear in upcoming title in Lecture Notes in Physic

New experimental data for the decays ϕ→μ+μ−\phi\to\mu^+\mu^- and ϕ→π+π−\phi\to\pi^+\pi^- from SND detector

The processes $e^+e^-\to\mu^+\mu^-$ and $e^+e^-\to\pi^+\pi^-$ have been studied with SND detector at VEPP-2M $e^+e^-$ collider in the vicinity of $\phi(1020)$ resonance. The branching ratios $B(\phi\to\mu^+\mu^-)=(3.30\pm 0.45\pm 0.32)\times 10^{-4}$ and $B(\phi\to\pi^+\pi^-)=(0.71\pm 0.11\pm 0.09)\times 10^{-4}$ were obtained.Comment: 5 pages, 4 figures, talk given at 8th International Conference on Hadron Spectroscopy (HADRON 99), Beijing, China, 24-28 Aug 199

Stability of trapped Bose-Einstein condensates

In three-dimensional trapped Bose-Einstein condensate (BEC), described by the time-dependent Gross-Pitaevskii-Ginzburg equation, we study the effect of initial conditions on stability using a Gaussian variational approach and exact numerical simulations. We also discuss the validity of the criterion for stability suggested by Vakhitov and Kolokolov. The maximum initial chirp (initial focusing defocusing of cloud) that can lead a stable condensate to collapse even before the number of atoms reaches its critical limit is obtained for several specific cases. When we consider two- and three-body nonlinear terms, with negative cubic and positive quintic terms, we have the conditions for the existence of two phases in the condensate. In this case, the magnitude of the oscillations between the two phases are studied considering sufficient large initial chirps. The occurrence of collapse in a BEC with repulsive two-body interaction is also shown to be possible.Comment: 15 pages, 11 figure

Stationary solutions of the one-dimensional nonlinear Schroedinger equation: I. Case of repulsive nonlinearity

All stationary solutions to the one-dimensional nonlinear Schroedinger equation under box and periodic boundary conditions are presented in analytic form. We consider the case of repulsive nonlinearity; in a companion paper we treat the attractive case. Our solutions take the form of stationary trains of dark or grey density-notch solitons. Real stationary states are in one-to-one correspondence with those of the linear Schr\"odinger equation. Complex stationary states are uniquely nonlinear, nodeless, and symmetry-breaking. Our solutions apply to many physical contexts, including the Bose-Einstein condensate and optical pulses in fibers.Comment: 11 pages, 7 figures -- revised versio