141 research outputs found
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 and from SND detector
The processes and have been
studied with SND detector at VEPP-2M collider in the vicinity of
resonance. The branching ratios and 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
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