On some peculiarities of the energy characteristics of the interference acoustic field in a shallow sea

The results of studies of the scalar and vector energy characteristics of a real acoustic interference field in a shallow sea are presented based on notions of monochromatic fields and common field vector ratios. The importance of the quantities under consideration is that they are the components of the energy-pulse tensor of the acoustic field. The horizontal components of the complex intensity vector are represented only by its real parts, i.e., the imaginary parts of the horizontal components of the intensity vector are equal to zero; the vertical component has both real and imaginary parts. The imaginary part of the vertical component of the complex intensity vector is related to the interference field of acoustic pressure (the potential energy). The energy characteristics of the acoustic field in a shallow sea obtained during a real experiment correspond to the common theoretical field ratios.     

Effect of the Electron‐Beam Self‐Fields on Gain in an Optical Wiggler Pumped Free‐Electron Laser

The effects of self fields on gain for a free‐electron lasers (FELs) with electromagnetic‐wave wiggler and an axial guide magnetic field is presented. The relativistic equation of motion for a single electron for all relevant fields, including wiggler, self‐fields and axial guide magnetic field has been solved. Two classes of possible single‐particle trajectories in this configuration are found. Result of the numerical calculation shown that the relativistic part of group I (group II) orbits decreases (increases) monotonically with the axial field. The gain equations for the FEL configuration by adding the effect of self‐fields have been derived. The numerical calculation has been employed to analysis the gain induced by the effects of the self‐fields. It is shown that, for group I orbits the gain decreases in the presence of self‐fields and the gain decrement increases with increasing axial guide magnetic field, while for group II orbits the self‐fields enhances the gain. The gain decrement and enhancement are due to diamagnetic and paramagnetic effects of the self‐magnetic field, respectively. The comparison of the gain for electromagnetic‐wave wiggler with the gain in helical wiggler has been done (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

平行电磁场中里德堡氢原子的自相似结构研究

利用半经典方法研究了平行电磁场中里德堡氢原子的分形自相似现象. 通过研究平行电磁场中里德堡氢原子的逃逸时间和初始出射角间的关系, 发现了逃逸时间图的自相似结构, 并通过研究与图中冰柱对应的逃逸轨道, 得到了自相似结构和逃逸轨道之间的关系, 发现了该类自相似逃逸轨道满足的规律. 进一步研究了标度能量和标度磁场对体系动力学的影响, 表明标度能量和标度磁场均控制体系的分形自相似结构. 当标度能量或标度磁场比较小时, 没有自相似现象, 随着标度能量或标度磁场的增大, 自相似出现, 体系变复杂.     

Vector-phase characteristics of acoustic fields: Statistical analysis and measurement algorithms

Statistical characteristics of an acoustic field that are based on the data of simultaneous measurements of pressure and acoustic velocity vector are investigated. Conditions of the formation of vector-phase characteristics of acoustic field are formulated in relation to the dispersion properties of the medium. Crosscorrelation functions of the components of the vector field are presented. Expressions for the characteristic functionals of vector-phase relationships in acoustic fields and, in particular, for the acoustic energy flux are derived with the use of functional methods. Algorithms of space-time processing of the energy flux vector and the optimum measurement algorithm for a Gaussian vector-phase field are considered. The signal-to-noise ratio is determined as the quality index of vector reception algorithms, and its relation to the corresponding parameter of scalar pressure field measurements is revealed. Indices of relative efficiency of vector algorithms are determined depending on the dispersion characteristics of the medium (the flux algorithm) and the dimension of the input vector of observations (the optimum algorithm).     

Conformal Vector Fields and Conformal–Type Collineations in Space-Times

Some restrictions on the existence of homothetic and conformal vector fields in space-times which already admit some Killing symmetry are established. In particular, the behaviour of Weyl invariants and the nature of the Petrov type of the Weyl tensor along the integral curves of conformal vector fields are studied. This results in important restrictions between conformal vector fields and Killing orbits. A brief remark is made on Weyl collineations.     

Dynamical algebras in classical mechanics

For a spectrum-generating algebra of classical observables, it is proven that the phase space dynamics simplifies to a Hamiltonian system on submanifolds of the algebra's dual. These submanifolds are coadjoint orbits if the algebra arises from a symplectic group action. If the Hamiltonian splits into the sum of a function of the algebra generators plus a commuting part, then the dynamics transfers to the dual space and an explicit formula is given for the flow vector field on the coadjoint orbits. A unique feature of the presentation is that all constructions are at the Lie algebra level.     

More about an analog to the equations of field-dynamic equilibrium

We consider the motion of a test particle in a central field of arbitrary physical nature. In constrast to the usual statement of the classical two-body problem assuming an infinite range of the field about a central point, real conditions are considered when the sphere of effective influence of the field about a given center is bounded and when the central body itself has finite dimensions. Motion in such a central field is called stable and the corresponding orbits stationary if the total energy and angular momentum remain constant and the particle itself does not leave the sphere of effective influence. Representing one of the vectors of the Laplace integral as a scalar product of a symmetric tensor with the radius vector, the equation for the stationary orbits are obtained after a transformation, which are analogous to the equations of field-dynamic equilibrium and are formally very similar to the Shröedinger wave equation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 39–42, February, 1973.The author thanks State prize laureate Professor D. D. Ivanenko for taking part in a discussion of the results presented in this article and for giving useful advice and critical comments on carrying out the work.     

Quantum orbits of theR-matrix type

Given a simple Lie algebra g, we consider the orbits in g^* which are of theR-matrix type, i.e., which possess a Poisson pencil generated by the Kirillov-Kostant-Souriau bracket and the so-calledR-matrix bracket. We call an algebra quantizing the latter bracket a quantum orbit of theR-matrix type. We describe some orbits of this type explicitly and we construct a quantization of the whole Poisson pencil on these orbits in a similar way. The notions ofq-deformed Lie brackets, braided coadjoint vector fields, and tangent vector fields are discussed as well.     

Floating and sinking: the imprint of massive scalars around rotating black holes

We study the coupling of massive scalar fields to matter in orbit around rotating black holes. It is generally expected that orbiting bodies will lose energy in gravitational waves, slowly inspiraling into the black hole. Instead, we show that the coupling of the field to matter leads to a surprising effect: because of superradiance, matter can hover into "floating orbits" for which the net gravitational energy loss at infinity is entirely provided by the black hole's rotational energy. Orbiting bodies remain floating until they extract sufficient angular momentum from the black hole, or until perturbations or nonlinear effects disrupt the orbit. For slowly rotating and nonrotating black holes floating orbits are unlikely to exist, but resonances at orbital frequencies corresponding to quasibound states of the scalar field can speed up the inspiral, so that the orbiting body sinks. These effects could be a smoking gun of deviations from general relativity.     

General relativistic razor-thin disks with magnetically polarized matter

The origin of magnetic fields in the universe still remains unknown and constitutes one of the most intriguing questions in astronomy and astrophysics. Their significance is enormous since they have a strong influence on many astrophysical phenomena. In regards of this motivation, theoretical models of galactic disks with sources of magnetic field may contribute to understand the physics behind them. Inspired by this, we present a new family of analytical models for thin disks composed by magnetized material. The solutions are axially symmetric, conformastatic and are obtained by solving the Einstein–Maxwell Field Equations for continuum media without the test field approximation, and assuming that the sources are razor-thin disk of magnetically polarized matter. We find analytical expressions for the surface energy density, the pressure, the polarization vector, the electromagnetic fields, the mass and the rotational velocity for circular orbits, for two particular solutions. In each case, the energy–momentum tensor agrees with the energy conditions and also the convergence of the mass for all the solutions is proved. Since the solutions are well-behaved, they may be used to model astrophysical thin disks, and also may contribute as initial data in numerical simulations. In addition, the process to obtain the solutions is described in detail, which may be used as a guide to find solutions with magnetized material in General Relativity.     

Interaction between acoustic fields of the ambient noise and point surface source

In measuring acoustic field vector properties either complete or partial cancellation between ambient noise energy flux and the oppositely directed one, radiated, for instance, by tone or noise-shaped point source can be found. In that case there is no matter coherent or incoherent fields interact. The phenomenon of interest is named compensation of opposing energy fluxes. The paper is focused on interaction between vertical component of the surface noise energy flux and that of bottom-reflected noise-shaped interfering signal from on-water source in the deep open ocean. Bottom-reflected weak broadband interfering signal measures the extent of resultant compensation. As the vertical projection of the signal energy flux makes the interference maximum, its power appears to be comparable to that of the surface noise and complete compensation takes place at a given frequency. Once it is the interference minimum, just partial compensation can be found. No compensation was observed for co-directional energy fluxes.     

Single-particle potential in a relativistic Hartree-Fock mean field approximation

A relativistic Hartree-Fock mean field approximation is investigated in a model in which the nucléon field interacts with scalar and vector meson fields. The Hartree-Fock potential felt by individual nucléons enters in a relativistic Dirac single-particle equation. It is shown that in the case of symmetric nuclear matter one can always find a potential which is fully equivalent to the most general mean field and which is only the sum of a Lorentz scalar, of one component of a Lorentz tensor and of the fourth component of a Lorentz vector. A non-relativistic potential is derived which yields exactly the same single-particle energies and elastic scattering phase shifts as the relativistic Hartree-Fock potential. Analytical results are presented in the case of nuclear matter. A local density approximation is constructed which enables one to consider finite nuclei. The input parameters of the model can be chosen in such a way that the empirical saturation properties of nuclear matter are well reproduced. Good agreement is obtained between the calculated non-relativistic potential and the empirical value of the real part of the optical-model potential at low and at intermediate energy. At intermediate energy, the wine-bottle bottom shape which had previously been found for the potential in the framework of the relativistic Hartree approximation is maintained when the Fock contribution is included.     

Recurrence spectra of non—hydrogen Rydberg atoms in paralled electric and magnetic fields

We present a new method for computing the recurrence spectra of n≈40, m=0 lithium Rydberg atoms in strong parallel external electric and magnetic fields. This method is based on an extended closed-orbit theory allowing the computation of the scattering of the electron by the ionic core. We pay particular attention to the scaling properties, which are extremely important for understanding the correspondence between classical and quantum mechanics. The spectra with a constant scaled electric field \tilde F=0.01 and a scaled energy ε=-0.03 are recorded and compared with those of hydrogen obtained by the standard closed-orbit theory. The result shows that the additional strong resonance structures can be interpreted in terms of the core-scattered classical closed orbits.     

A homogeneous multicomponent cosmological model with interacting spinor,scalar, and vector fields in the presence of dark energy

The evolution of a homogeneous multicomponent cosmological model with interacting spinor, vector, and scalar fields in the presence of dark energy described by the ideal liquid with the corresponding state equation is considered. The source of the vector and spinor fields is the kinetic energy of the inflation (scalar) field that is modeled by introduction of Lagrangians for the spinor and vector fields interacting with the scalar field through the squared gradient. A system of the dynamic Einstein–Proca–Klein–Fock and ideal liquid equations in the presence of interaction of the cosmological model components is solved. The role of individual components in the process of model evolution is elucidated.     

Hamiltonian Map to Conformal Modification of Spacetime Metric: Kaluza-Klein and TeVeS

It has been shown that the orbits of motion for a wide class of non-relativistic Hamiltonian systems can be described as geodesic flows on a manifold and an associated dual by means of a conformal map. This method can be applied to a four dimensional manifold of orbits in spacetime associated with a relativistic system. We show that a relativistic Hamiltonian which generates Einstein geodesics, with the addition of a world scalar field, can be put into correspondence in this way with another Hamiltonian with conformally modified metric. Such a construction could account for part of the requirements of Bekenstein for achieving the MOND theory of Milgrom in the post-Newtonian limit. The constraints on the MOND theory imposed by the galactic rotation curves, through this correspondence, would then imply constraints on the structure of the world scalar field. We then use the fact that a Hamiltonian with vector gauge fields results, through such a conformal map, in a Kaluza-Klein type theory, and indicate how the TeVeS structure of Bekenstein and Saunders can be put into this framework. We exhibit a class of infinitesimal gauge transformations on the gauge fields U_m(x){\mathcal{U}}_{\mu}(x) which preserve the Bekenstein-Sanders condition U_mU^m=-1{\mathcal{U}}_{\mu}{\mathcal{U}}^{\mu}=-1. The underlying quantum structure giving rise to these gauge fields is a Hilbert bundle, and the gauge transformations induce a non-commutative behavior to the fields, i.e. they become of Yang-Mills type. Working in the infinitesimal gauge neighborhood of the initial Abelian theory we show that in the Abelian limit the Yang-Mills field equations provide residual nonlinear terms which may avoid the caustic singularity found by Contaldi et al.     

电磁场统一性质的三维描述

论述了电场与磁场本质上的统一性质,构造了三维空间中电磁场的统一场量,给出它的方程、场量的模方与能量和动量的关系,发现三维空间中的统一场量自身的标积竟然是相对论变换下的不变量．     

The energy of unit vector fields on the 3-sphere

The stability of the three-dimensional Hopf vector field, as a harmonic section of the unit tangent bundle is viewed from a number of different angles. The spectrum of the vertical Jacobi operator is computed, and compared with that of the Jacobi operator of the identity map on the 3-sphere. The variational behaviour of the three-dimensional Hopf vector field is compared and contrasted with that of the closely related Hopf map. Finally, it is shown that the Hopf vector fields are the unique global minima of the energy functional restricted to unit vector fields on the 3-sphere.     

Hedgehog structures in general quark-meson Lagrangians

We investigate stationarity properties of hedgehog configurations in effective quarkmeson Lagrangians involving scalar and vector boson fields with arbitrary self-couplings. The Lagrangians are assumed to be in theSU(2)-sector and to be invariant under Lorentz-transformations, isorotations and time reversal. Restricting ourselves to the mean field solution based on valence quarks in sphericals-orbits and bilinear couplings the quark-hedgehog is shown to generate simply structured meson fields and to correspond to a stationary solution of the equations of motion. In most practical cases this is even of minimal energy.     

Three-parameter relativistic dynamics. II. Electromagnetic field with holonomic potential

It is shown that electrodynamics can be implemented in the formalism presented in the first part of this work. An electromagnetic field having a holonomic unimodular vector potential is examined. The properties of such electromagnetic fields are also examined. Krasnoyarsk State Technological Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6. pp. 43–47, June, 1997.     

Nonlinear rotary wave ion plasma

The nonlinearly coupled Vlasov-Maxwell ion-plasma field equations are solved exactly for a transversely uniform subgroup of rotational modes induced by a uniform axial magnetic field. The ion orbits in momentum space are bipolar doubly periodic eigenfunctions of ion proper time, obtained in closed form as the difference between two doubly quasi-periodic Weierstrass zeta functions. The ion orbits in position space are helical-spiral doubly quasi-periodic functions of ion proper time, expressible simply in terms of doubly quasi-periodic Weierstrass sigma functions. The complete ion distributions are flexible functions of six constants of the ion motion: wave-frame ion energy, transverse gyro center, an inner Hamiltonian correlating wave-frame ion momentum with wave-frame axial position, and both first and second axial integration constants. A rotary electromagnetic plane wave propagates along the axial magnetic field with complex cisoidal dependence upon wave-frame axial position. The eigenvalue determination intricately interrelates the wave propagation vector, the wave amplitude, the axial magnetic field, the double periods, and the bipole separation.