O(3) symmetric merons in an SU(3) Yang-Mills theory

We investigate irreducible, O(3) symmetric multiple-meron solutions to the classical SU(3) Yang-Mills equations in four-dimensional Euclidean space. The solutions have topological charge density equal to a sum of delta-functions with integer coefficients, and correspond to solutions of a system of two coupled singular elliptic equations. We prove the existence of twomeron solutions of the coupled system.Supported in part by the National Science Foundation under Grant No. PHY77-18762.     

An existence theorem for multimeron solutions to classical Yang-Mills field equations

In this paper we prove the existence of solutions to a class of boundary value problems for a singular nonlinear elliptic partial differential equation in a half plane. By a recent paper of J. Glimm and A. Jaffe, this proves the existence of multimeron solutions to the classical SU(2) Yang-Mills field equations in Euclidean space.Supported in part by the National Science Foundation under Grant PHY 77-18762Supported in part by the Icelandic Science FoundationSupported in part by Grant MCS 76-06524     

A generalized Reissner-Nordström solution

A new class of solutions to the Einstein-Maxwell equations is presented; it stands in the same relation to the Robinson & Robinson (1969) metrics as the Reissner-Nordström solution to Schwarzschild's.This work was supported in part by the Aerospace Research Laboratories, Office of Aerospace Research, United States Air Force, under Contract F33615-68-C-1675; Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force, under AFOSR Grant No. 903-67; National Aeronautics and Space Administration under NASA Grant No. NGL 44-004-001; and National Science Foundation under Travel Grant GP-14505.     

Turbulent gas-dispersed flow in a pipe with sudden expansion: numerical simulation

A mathematical model was developed to simulate two-phase gas-dispersed flow moving through a pipe with axisymmetric sudden expansion. In the model, the two-fluid Euler approach was used. The model is based on solving Reynolds-averaged Navier — Stokes equations for a two-phase stream. In calculating the fluctuating characteristics of the dispersed phase, equations borrowed from the models by Simonin (1991), Zaichik et al. (1994), and Derevich (2002) were used. Results of a comparative analysis with previously reported experimental and numerical data on two-phase flows with separation past sudden expansion in a plane channel and in a pipe are given. This work was supported by the President of the Russian Federation through the Foundation for Young Candidates of Sciences under Grant MK-186.2007.8 and by the Russian Foundation for Basic Research (Grants Nos. 05-08-33586 and 06-08-00967).     

Peculiarities of the ignition of propane-air premixed flows by CO2 laser radiation

Results of an experimental study of the ignition dynamics of propane-air premixed flows under pulsed-periodic laser irradiation are reported. Ignition of homogeneous flows emanating into free atmosphere is considered. A comparative analysis of experimental and predicted delay times for the ignition for a medium at rest is given. This work was supported by the President of the Russian Federation (Grant No. NSh-8597. 2006.1), by the Russian Foundation for Basic Research (Grant No. 05-01-00560) and by the Presidium of the Russian Academy of Sciences (under the Program “Fundamental Problems in Magnetoplasma Aerodynamics”).     

Note on loss of regularity for solutions of the 3—D incompressible euler and related equations

One of the central problems in the mathematical theory of turbulence is that of breakdown of smooth (indefinitely differentiable) solutions to the equations of motion. In 1934 J. Leray advanced the idea that turbulence may be related to the spontaneous appearance of singularities in solutions of the 3—D incompressible Navier-Stokes equations. The problem is still open. We show in this report that breakdown of smooth solutions to the 3—D incompressible slightly viscous (i.e. corresponding to high Reynolds numbers, or highly turbulent) Navier-Stokes equations cannot occur without breakdown in the corresponding solution of the incompressible Euler (ideal fluid) equation. We prove then that solutions of distorted Euler equations, which are equations closely related to the Euler equations for short term intervals, do breakdown.Sponsored by the United States Army under Contract No. DAAG29-80-C-0041, and partially supported by the National Science Foundation under Grant No. MCS-82-01599     

Vanishing Shear Viscosity Limit in the Magnetohydrodynamic Equations

We study an initial boundary value problem for the equations of plane magnetohydrodynamic compressible flows, and prove that as the shear viscosity goes to zero, global weak solutions converge to a solution of the original equations with zero shear viscosity. As a by-product, this paper improves the related results obtained by Frid and Shelukhin for the case when the magnetic effect is neglected. Supported by NSFC (Grant No. 10301014, 10225105) and the National Basic Research Program (Grant No. 2005CB321700) of China.     

The Hamiltonian in relativistic systems of interacting particles

The dynamics of a system of relativistically interacting particles is determined by a set of constraints, some combination of which has been frequently identified with the Hamiltonian. These constraints differ from the generators of the Poincaré transformations, among whichp ₀ generates translations along the time axis and hence is to be considered as the energy of the system. There are thus grounds for consideringP ₀ as the appropriate Hamiltonian. In this paper we establish a close relationship between transformations generated by the constraints and those generated by the Poincaré generators. In particular we find that the true Hamiltonian is a rather complicated but well-defined function ofp ₀ and all the constraints. We show that the generators of the entire algebra of the Poincaré group can be realized in such a fashion that the Hamiltonian is correctly included among them, and such that particle world lines in Minkowski space-time generated by this Hamiltonian transform correctly under the Poincaré group.This work was partially supported by the National Science Foundation Grant No. PHY 79-0887 to Syracuse University and by Grant No. PHY 79-09405 to Yeshiva University.     

Structure of the electromagnetic fields of loop radiators in magnetized plasmas over the whistler frequency range

The role of different sections of the spatial spectrum of whistler waves excited by a loop antenna in the formation of an electromagnetic field structure is investigated experimentally and theoretically. Primary attention is given to the intermediate range of distances between the source and the observation point.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 2, pp. 192–202, February, 1996.T. M. Zaboronkova, A. V. Kostrov, A. I. Smirnov, and A. A. Shaikin are grateful to The Russian Foundation for Fundamental Research (Grant No.94-02-05447a) and the George Soros International Foundation (Grant No. NOP 300) for financial support. A. V. Kudrin is grateful to the Russian Fund for Fundamental Research (Grant No. 96-02-18666) for financial support.     

Turbulent vortex wake: Classification principles,gauge equivalence,examples, and applications

The paper proposes a system of second-order ordinary differential equations with solutions interpreted as trajectories of a turbulent vortex wake. The trajectories are modeled by complexes of geodesic lines in non-Euclidean geometries and are analyzed to select a proper geometry by choosing a particular gauge for modeling the whole class of turbulent vortex wake trajectories. Examples are given of geodesic and partially geodesic gauges to model a particular complex of linear vortex wake trajectories, and possible ways are suggested to apply the theory to turbulence mesodynamics in cosmic plasma.     

The hyperspherical-harmonics expansion method and the integral-equation approach to solving the few-body problem in momentum space

The Faddeev and Faddeev-Yakubovsky equations for three- and four-body systems are solved by applying the hyperspherical-harmonics expansion to them in momentum space. This coupling of two popular approaches to the few-body problem together with the use of the so-called Raynal-Revai transformation, which relates hyperspherical functions, allows the few-body equations to be written as one-dimensional coupled integral equations. Numerical solutions for these are achieved through standard matrix methods; these are made straightforward, because a second transformation renders potential multipoles easily calculable. For sample potentials and a restricted size of matrix in each case, the binding energies extracted match those previously obtained in solving the Schrödinger equation through the hyperspherical-harmonics expansion in coordinate space.Work supported in part by the National Science Foundation through grant No. PHY83-06584 and grant No. PHY87-12229     

O(2) symmetric connections in an SU(2) Yang-Mills theory

The general O(2) symmetric Yang-Mills equations are derived. An ansatz for O(2) symmetric merons is presented and it is shown that any connection in this ansatz will have SU(2) topological charge density which is a sum of delta functions at points in a plane with weights ± 1/2. It is shown that any connection in this ansatz will beC away from these points.National Science Foundation Pre-doctoral FellowSupported in part by the National Science Foundation under Grant PHY 77-18762     

Uniform expansion of the transition rate in Kramers' problem

Kramers' model of diffusion over potential barriers, e.g., chemical reactions, based on the noise activated escape of a particle from a potential well, is considered. Kramers derived escape rates valid for intermediate and large damping, and in a separate analysis, for small damping. In the small damping limit, Kramers' intermediate result reduces to the transition state rate which does not agree with the small damping result. A new escape rate is derived that is uniformly valid for all values of the damping coefficient. The new rate reduces to Kramers' results in the appropriate limits and, in particular, connects Kramers' intermediate and small damping results.This work was partially supported by the Air Force Office of Scientific Research under Grant No. AFOSR-83-0086, U.S. Department of Energy under Grant No. DE-AC02-78ERO-4650, and the National Science Foundation under Grant No. MCS-83-00562. One of us (BJM) gratefully acknowledges the support of a John Simon Guggenheim Memorial Foundation Fellowship.     

Solutions of the Einstein-Maxwell equations with many black holes

In Newtonian gravitational theory a system of point charged particles can be arranged in static equilibrium under their mutual gravitational and electrostatic forces provided that for each particle the charge,e, is related to the mass,m, bye=G ^1/2 m. Corresponding static solutions of the coupled source free Einstein-Maxwell equations have been given by Majumdar and Papapetrou. We show that these solutions can be analytically extended and interpreted as a system of charged black holes in equilibrium under their gravitational and electrical forces.We also analyse some of stationary solutions of the Einstein-Maxwell equations discovered by Israel and Wilson. If space is asymptotically Euclidean we find that all of these solutions have naked singularities.Alfred P. Sloan Research Fellow, supported in part by the National Science Foundation.     

Approximate homotopy symmetry method: Homotopy series solutions to the sixth-order Boussinesq equation

An approximate homotopy symmetry method for nonlinear problems is proposed and applied to the sixth-order Boussinesq equation,which arises from fluid dynamics.We summarize the general formulas for similarity reduction solutions and similarity reduction equations of different orders,educing the related homotopy series solutions.Zero-order similarity reduction equations are equivalent to the Painlevé IV type equation or Weierstrass elliptic equation.Higher order similarity solutions can be obtained by solving...     

The refined theory of deep rectangular beams for symmetrical deformation

Based on elasticity theory, various one-dimensional equations for symmetrical deformation have been deduced systematically and directly from the two-dimensional theory of deep rectangular beams by using the Papkovich-Neuber solution and the Lur’e method without ad hoc assumptions, and they construct the refined theory of beams for symmetrical deformation. It is shown that the displacements and stresses of the beam can be represented by the transverse normal strain and displacement of the mid-plane. In the case of homogeneous boundary conditions, the exact solutions for the beam are derived, and the exact equations consist of two governing differential equations: the second-order equation and the transcendental equation. In the case of non-homogeneous boundary conditions, the approximate governing differential equations and solutions for the beam under normal loadings only and shear loadings only are derived directly from the refined beam theory, respectively, and the correctness of the stress assumptions in classic extension or compression problems is revised. Meanwhile, as an example, explicit expressions of analytical solutions are obtained for beams subjected to an exponentially distributed load along the length of beams. Supported by the National Natural Science Foundation of China (Grant Nos. 10702077, 10672001, and 10602001), the Beijing Natural Science Foundation (Grant No. 1083012), and the Alexander von Humboldt Foundation in Germany     

Bäcklund transformations and new solutions of nonlinear wave equations in four-dimensional space-time

Bäcklund transformations for several nonlinear field equations in four-dimensional space-time relating two solutions of the same equation (symmetry), or two different equations (dynamical), are given. These transformations can be used to generate new families of solutions and infinitely many conservation laws for nonlinear equations.Bäcklund transformations and solutions of nonlinear equations have been studied extensively in one-space and one-time dimension. We give here a fairly general method for a class of equations in four-dimensional space-time which paves the way for many further generalizations.Supported in part by the U.S. National Academy of Sciences Foundation Grant No. INT 73-20002 A01 (formerly GF-41958).     

On the generation of new metrics containing arbitrary functions

We present simple methods by which certain solutions of the Einstein vacuum equation (and some other equations) can be used to generate further solutions of these equations. In some cases the new solutions admit a smaller number of metric automorphisms than the original ones and are, in this sense, more general.Supported by N.R.C. Grant No. A-5205.Supported by N.R.C. Grant No. A-3993.     

High-latitude and polar heliosphere

A short review of the recent studies of the three-dimensional structure of the heliosphere is presented. The main progress is due to direct plasma and magnetic field measurements from the Ulysses spacecraft outside the ecliptic plane in heliolatitudes of up to ±80°.The new data are used for the development of theoretical models.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 10, pp. 1257–1267, October, 1996.This work was supported in part by the Russian Foundation for Fundamental Research under Grant No. 95-02-06074 a.     

Yang-Lee zeros of the Potts model

The Yang-Lee zeros of the three-component ferromagnetic Potts model in one dimension in the complex plane of an applied field are determined. The phase diagram consists of a triple point where three phases coexist. Emerging from the triple point are three lines on which two phases coexist and which terminate at critical points (Yang-Lee edge singularity). The zeros do not all lie on the imaginary axis but along the three two-phase lines. The model can be generalized to give rise to a tricritical point which is a new type of Yang-Lee edge singularity. Gibbs phase rule is generalized to apply to coexisting phases in the complex plane.Supported in part by the National Science Foundation under Grant No. DMR-81-06151.