On the calculation of finite-gap solutions of the KdV equation

A simple and general approach for calculating the elliptic finite-gap solutions of the Korteweg-de Vries (KdV) equation is proposed. Our approach is based on the use of the finite-gap equations and the general representation of these solutions in the form of rational functions of the elliptic Weierstrass function. The calculation of initial elliptic finite-gap solutions is reduced to the solution of the finite-band equations with respect to the parameters of the representation. The time evolution of these solutions is described via the dynamic equations of their poles, integrated with the help of the finite-gap equations. The proposed approach is applied by calculating the elliptic 1-, 2- and 3-gap solutions of the KdV equations

МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ДИНАМИКИ ДВИЖЕНИЯ ЮБКИ ПОРШНЯ В ЦИЛИНДРЕ ДВИГАТЕЛЯ ВНУТРЕННЕГО СГОРАНИЯ

There examined method theoretical research of sectional piston skirt hydrodynamic lubrication, and influence of piston and connection rod groups options on it.В статье рассмотрена методика проведения теоретического исследования гидродинамической смазки юбки составного поршня, и влияние на нее конструктивных параметров деталей поршневой и кривошипно-шатунной групп

Nonlinear parametric instability in double-well lattices

A possibility of a nonlinear resonant instability of uniform oscillations in dynamical lattices with harmonic intersite coupling and onsite nonlinearity is predicted. Numerical simulations of a lattice with a double-well onsite anharmonic potential confirm the existence of the nonlinear instability with an anomalous value of the corresponding power index, 1.57, which is intermediate between the values 1 and 2 characterizing the linear and nonlinear (quadratic) instabilities. The anomalous power index may be a result of competition between the resonant quadratic instability and nonresonant linear instabilities. The observed instability triggers transition of the lattice into a chaotic dynamical state.Comment: A latex text file and three pdf files with figures. Physical Review E, in pres

Экспериментальное исследование напряженно-деформированного состояния юбки поршня двигателя внутреннего сгорания на безмоторном стенде

The article describes the features developed by the authors of the profiling method of the piston skirt, provides the main parameters that affect the lubrication conditions of the piston skirt and the magnitude of mechanical losses. In computational studies, the basic formulas are given for determining the thickness of the oil layer in a piston skirt - cylinder sleeve conjunction to assess the nature of friction. To determine the deformations, the finite element method is used on the spatial model of the piston. To verify the finite element model, a stand for experimental studies was developed. The article describes the developed stand, the methodology and results of experimental studies of the stress-strain state of the two-piece piston skirt obtained at this stand and a comparative analysis of the results of the calculated and experimental studies of the stress-strain state of the two-piece piston skirt of a diesel engine. The research results showed that the developed stand can be used to verify mathematical models for calculating the stress-strain state of the piston skirt in the pilot production of internal combustion engine pistons to accelerate and reduce the cost of the piston design development process, as well as the results of experimental studies obtained at the stand, can be used as initial data for the developed mathematical model of the dynamics of the movement of the piston and the profiling of the piston skirt.В статье представлены особенности разработанной авторами методики профилирования юбки поршня, приведены основные параметры, влияющие на условия смазывания юбки поршня и величину механических потерь. В расчетных исследованиях даны основные формулы для определения толщины масляного слоя в сопряжении «юбка поршня - цилиндр» для оценки характера трения. Для определения деформаций используется метод конечных элементов на пространственной модели поршня. Для верификации конечно-элементной модели был разработан стенд для экспериментальных исследований. В статье описаны разработанный стенд, методика проведения и результаты экспериментальных исследований напряженно-деформированного состояния юбки составного поршня, полученные на данном стенде, выполнен сравнительный анализ результатов расчетных и экспериментальных исследований напряженно-деформированного состояния юбки составного поршня дизеля. Исследование показало, что разработанный стенд может применяться для верификации математических моделей расчета напряженно-деформированного состояния юбки поршня в опытном производстве поршней двигателя внутреннего сгорания для ускорения и удешевления процесса разработки их конструкции. Результаты экспериментальных исследований, полученные на стенде, также могут быть использованы в качестве исходных данных для разработанной математической модели динамики движения поршня и профилирования юбки поршня

On Darboux-Treibich-Verdier potentials

It is shown that the four-parameter family of elliptic functions $$u_D(z)=m_0(m_0+1)\wp(z)+\sum_{i=1}^3 m_i(m_i+1)\wp(z-\omega_i)$$ introduced by Darboux and rediscovered a hundred years later by Treibich and Verdier, is the most general meromorphic family containing infinitely many finite-gap potentials.Comment: 8 page

Search for light pseudoscalar sgoldstino in K- decays

A search for the light pseudoscalar sgoldstino production in the three body K- decay K-->pipi0P has been performed with the ISTRA+ detector exposed to the 25 GeV negative secondary beam of the U70 proton synchrotron. No signal is seen. An upper limit for the branching ratio Br(K->pipi0P), at 90% confidence level, is found to be around 9*10**-6 in the effective mass m(P) range from 0 till 200 MeV, excluding the region near m(pi0) where it degrades to 3.5*10**-5.Comment: 10 pages, LATEX, 8 EPS figures, revised version, to be published in Phys.Lett.

Measurement of the Dalitz plot slope parameters for K- -> pi0 pi0 pi- decay using ISTRA+ detector

The Dalitz plot slope parameters g, h and k for the K- -> pi0 pi0 pi- decay have been measured using in-flight decays detected with the ISTRA+ setup operating in the 25 GeV negative secondary beam of the U-70 PS. About 252 K events with four-momenta measured for the pi- and four involved photons were used for the analysis. The values obtained g=0.627+/-0.004(stat)+/-0.010(syst), h=0.046+/-0.004(stat)+/-0.012(syst), k=0.001+/-0.001(stat)+/-0.002(syst) are consistent with the world averages dominated by K+ data, but have significantly smaller errors.Comment: LaTeX, 10 pages, 8 eps-figures, update of IHEP 2002-1

Supernovae in isolated galaxies, in pairs and in groups of galaxies

In order to investigate the influence of the environment on the supernova (SN) production we have performed a statistical investigation of the SNe discovered in isolated galaxies, in pairs and in groups of galaxies. 22 SNe in 18 isolated galaxies, 48 SNe in 40 galaxies members of 37 pairs and 211 SNe in 170 galaxies members of 116 groups have been selected and studied. We found that the radial distributions of core-collapse SNe in galaxies located in different environments are similar, and consistent with that reported by Bartunov, Makarova & Tsvetkov (1992). SNe discovered in pairs do not privilege a particular direction with respect to the companion galaxy. Also the azimuthal distributions inside the hosts members of galaxy groups are consistent with being isotropics. The fact that SNe are more frequent in the brighter components of the pairs and groups is expected from the dependence of the SN rates on the galaxy luminosity. There is an indication that the SN rate is higher in galaxy pairs compared with that in groups. This can be related to the enhanced star formation rate in strongly interacting systems. It is concluded that, with the possible exception of strongly interacting system, the parent galaxy environment has no direct influence on the SN productionComment: 10 pages, accepted for publication to MNRA

Thomae type formulae for singular Z_N curves

We give an elementary and rigorous proof of the Thomae type formula for singular $Z_N$ curves. To derive the Thomae formula we use the traditional variational method which goes back to Riemann, Thomae and Fuchs.Comment: 22 page

High statistic study of the K- -> pi0 mu- nu decay

The decay K- -> pi0 mu- nu has been studied using in-flight decays detected with the "ISTRA+" spectrometer. About 540K events were collected for the analysis. The lambda+ and lambda0 slope parameters of the decay form-factors f+(t), f0(t) have been measured : lambda+ = 0.0277+-0.0013 (stat)+-0.0009 (syst), lambda0 = 0.0183+-0.0011(stat)+-0.0006(syst), and d(lambda0)/d(lambda+)=-0.348. The limits on the possible tensor and scalar couplings have been derived: fT/f+(0)=-0.0007 +- 0.0071, fS/f+(0)=0.0017 +- 0.0014. No visible non-linearity in the form-factors have been observed.Comment: 11 pages, 8 EPS figures, accepted by Physics Letters