Friedman-like Robertson–Walker model in generalized metric space-time with weak anisotropy

A generalized FRW model of space-time is studied, taking into consideration the anisotropic structure of fields which are depended on the position and the direction (velocity). The Raychaudhouri and Friedman-like equations are investigated assuming the Finslerian character of space-time. A long range vector field of cosmological origin is considered in relation to a physical geometry where the Cartan connection has a fundamental role. The Friedman equations are produced including extra anisotropic terms. The variation of anisotropy z _t is expressed in terms of the Cartan torsion tensor of the Finslerian manifold. A physical generalization of the Hubble and other cosmological parameters arises as a direct consequence of the equations of motion.     

Magnetic relaxation in superconductors with varying creep behavior

The relaxation of an electromagnetic field inside low-and high-temperature superconductors in the case when the magnetic flux occupies the cross section incompletely is studied theoretically in the self-similar approximation. On the macroscopic level, creep is described by phenomenological equations for exponential and power I-V characteristics. A relation between the nonlinearity of the I-V curves and the magnetic relaxation process is found. The range of low electric fields is shown to be of considerable importance for the relaxation in high-temperature superconductors. In this range, the equations for exponential and power I-V curves may differ substantially from those at high fields. Complete analytical solutions are contrasted with a numerical solution to the problem.     

Meissner state in a 3D ordered Josephson medium

A system of difference equations describing current configurations in a 3D ordered Josephson medium is obtained. The system is based on the fluxoid quantization conditions in the cells. A method for the exact solution to the system is proposed for the Meissner configuration for any values of the parameters. The current configurations for the Meissner regime are computed, as well as the values of the critical fields above which the Meissner configuration does not exist. Approximate analytic solutions are obtained for the system of difference equations, which correctly describe the exact solution for the major part of the range of the parameters.     

Generation of Intense THz Pulsed Lasers Pumped Strongly by CO2 Pulsed Lasers

A theoretical method dealing with two intense laser fields interacting with a three-level molecular system is proposed. A discussion is presented on the properties of the solutions for time-independent and time-dependent absorption coefficients and gain coefficient on resonance for strong laser fields, based on analytic evaluation of the rate equations for a homogeneously broadened, three-level molecular system. The pump intensity range can be estimated according to the analytic expression of pump saturation intensity. The effects of pulse width, gas pressure and path length on the energy absorbed from pump light are studied theoretically. The results can be applied to the analysis of pulsed, optically pumped terahertz lasers.     

Green functions of scalar particles in stochastic fields

A variational method of evaluating functional integrals is proposed. This method is used to investigate the asymptotic behavior of the scalar-particle Green functions in stochastic fields. The equations for the Green functions in Euclidean space in stochastic fields are written. The solutions of these equations are represented in the form of a functional integral and then they are averaged over Gaussian stochastic fields. The variational method formulated above is used to evaluate the asymptotic behavior of these Green functions. The following equations are considered in this paper: a stochastic contribution to the mass of a scalar particle, a gauge stochastic field, and a weak stochastic contribution to the flat metric of Euclidean space.     

Scaling theory for homogenization of the Maxwell equations

A scaling theory for homogenization of the Maxwell equations is developed upon the representation of any field as a sum of its dipole, quadrupole, and magnetic dipole moments. This representation is exact and is connected neither with multipole expansion nor with the Helmholtz theorem. A chain of hierarchical equations is derived to calculate the moments. It is shown that the resulting macroscopic fields are governed by the homogenized Maxwell equations. Generally, these fields differ from the mean values of microscopic fields.     

Relativistic derivation of Maxwell's equations in vacuum and the axiomatic foundation of electrodynamics

A derivation of Maxwell's equations in vacuum for the curls of the electric and magnetic fields is given in which the starting point is the Lorentz transformation and the equations for the divergences of the fields. The derivation is used to construct a new axiomatic foundation of electrodynamics, in which the Lorentz force and the equations for the divergences of the fields are postulated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 66–71, December, 1983.     

Actions for non-abelian twisted self-duality

The dynamics of abelian vector and antisymmetric tensor gauge fields can be described in terms of twisted self-duality equations. These first-order equations relate the p-form fields to their dual forms by demanding that their respective field strengths are dual to each other. It is well known that such equations can be integrated to a local action that carries on equal footing the p-forms together with their duals and is manifestly duality invariant. Space-time covariance is no longer manifest but still present with a non-standard realization of space-time diffeomorphisms on the gauge fields. In this paper, we give a non-abelian generalization of this first-order action by gauging part of its global symmetries. The resulting field equations are non-abelian versions of the twisted self-duality equations. A key element in the construction is the introduction of proper couplings to higher-rank tensor fields. We discuss possible applications (to Yang-Mills and supergravity theories) and comment on the relation to previous no-go theorems.     

Propagation characteristics of a circular waveguide filled with a chiroferrite medium

A chiroferrite is made from chiral objects immersed in a magnetically biased ferrite. A waveguide including a chiroferrite is anticipated to possess some novel features due to the presence of chirality in combination with anisotropy. In this paper, the propagation characteristics of a circular metal waveguide filled with a chiroferrite medium are investigated by an analytical procedure. The equations of relations between the transverse components and the longitudinal ones of electromagnetic fields in general chiroferrite waveguides are derived in a cylindrical coordinate system. The coupled wave equations for the longitudinal electric and magnetic fields are decoupled into two Helmholtz equations which are then solved analytically. The characteristic equation is formulated for the circular chiroferrite waveguide. Propagation constants varying with the structural and material parameters have been calculated for several lower chiral modes. A number of interesting features have been revealed by the numerical results.     

Recent developments in conformal invariant quantum field theory

A review of the recent results concerning the kinematics of conformal fields, the analysis of dynamical equations and dynamical derivation of the operator product expansion is given.The classification and transformational properties of fields which are transformed according to the representations of the universal covering group of the conformal group have been considered. A derivation of the partial wave expansion of Wightman functions is given. The analytical continuation to the Euclidean domain of coordinates is discussed. As shown, in the Euclidean space the partial wave expansion can be applied either to one-particle irreducible vertices or to the Green functions, depending on the dimensions of the fields.The structure of Green functions, which contain a conserved current and the energy-momentum tensor, has been studied. Their partial wave expansion has been obtained. A solution of the Ward identity has been found. Special cases are discussed.The program of the construction of exact solution of dynamical equations is discussed. It is shown, that integral dynamical equations for vertices (or Green's functions) can be diagonalized by means of the partial wave expansion. The general solution of these equations is obtained. The equations of motion for renormalized fields are considered. The way to define the product of renormalized fields at coinciding points (arising on the right-hand side) is discussed. A recipe for calculating this product is presented. It is shown, that this recipe necessarily follows from the renormalized equations.The role of bare term and of canonical commutation relations (for unrenormalized fields) is discussed in connection with the problem of the field product determination at coinciding points. As a result an exact relation between fundamental field dimensions is found for various three-linear interactions (section 16 and Appendix 6). The problem of closing the infinite system of dynamical equations is discussed.Al above said results are demonstrated using Thirring model as an example. A new approach to its solving is developed.The program od closing the infinite system of dynamical equations is discussed. The Thirring model is considered as an example. A new approach to the solution of this model is discussed.Methods are developed for the approximate calculation of dimensions and coupling constants in the 3-vertex and 5-vertex approximations. The dimensions are calculated in the γ_?³ theory in 6-dimensional space.The problem of calculating the critical indices in statistics (3-dimensional Euclidean space) is considered. The calculation of the dimension is carried out in the framework of the γ_?⁴ model. The value of the dimension and the critical indices thus obtained coincide with the experimental ones.     

利用等效电路模型计算耦合腔行波管注-波互作用

通过研究Curnow等效电路模型,得到进行单腔计算的矩阵方程,进而获得线路场方程, 结合运动方程和空间电荷场方程,从而推导出耦合腔行波管一维注波互作用非线性理论模型. 该理论能计算任意的切断、跳变、渐变等结构以及多信号模拟.利用该理论编制的软件计算了 59 GHz-64 GHz耦合腔行波管AM-PM相位失真,三阶互调以及五阶互调分量. 同时模拟得到了59 GHz-64 GHz带内饱和输出功率分布,理论结果与热测结果误差在5%以内.     

Light and thermal fields in multilayer skin tissue exposed to laser irradiation

A simple model for calculating the light fields created by a laser beam in a multilayer biological tissue is proposed. On the basis of this model, the coefficient of diffuse reflection of skin and the penetration depth of light are found for the wavelength range 400–850 nm and for a wide range of variation in the structural and optical characteristics of the medium. The effect of localized light absorption by blood vessels is taken into account. The results obtained are shown to agree reasonably with published theoretical and experimental data. Using the found depth distributions of the absorbed energy as source functions for the thermal problem, the analytical solution for the spatiotemporal structure of the temperature field in the cutaneous covering irradiated by a laser beam was obtained. The thermal fields determined in terms of single-and two-layer models are compared, and the corresponding differences are discussed. Examples of the temperature depth profiles obtained at different instants after the beginning of irradiation are presented. The results obtained in terms of the analytical method proposed are demonstrated to agree satisfactorily with those yielded by the numerical finite difference scheme of the solution of the system of heat conduction equations.     

Frame-like actions for massless mixed-symmetry fields in Minkowski space

A frame-like action for arbitrary mixed-symmetry bosonic massless fields in Minkowski space is constructed. The action is given in a simple form and consists of two terms for a field of any spin. The fields and gauge parameters are certain tensor-valued differential forms. The formulation is based on the unfolded form of equations for mixed-symmetry fields.     

A three-dimensional time-dependent theory for helix traveling wave tubes in beam-wave interaction

This paper presents a three-dimensional time-dependent nonlinear theory of helix traveling wave tubes for beamwave interaction.The radio frequency electromagnetic fields are represented as the superposition of azimuthally symmetric waves in a vacuum sheath helix.Coupling impedance is introduced to the electromagnetic field equations’ stimulating sources,which makes the theory easier and more flexible to realize.The space charge fields are calculated by electron beam space-charge waves expressed as the superposition solutions of Helmholtz equations.The focusing forces due to either a solenoidal field or a periodic permanent magnetic field is also included.The dynamical equations of electrons are Lorentz equations associating with electromagnetic fields,focusing fields and space-charge fields.The numerically simulated results of a tube are presented.     

SiO2波导布拉格器件中声表面波及声光相互作用分析

针对SiO2光波导声光布拉格器件,计算了SiO2非对称平板波导TE模式的横向场分布;给出了SiO2/ZnO/Air层状介质结构的性能方程、运动方程和麦克斯韦方程,推导出这种层状结构的特征方程,并结合所满足的边界条件,得到了各层介质的位移及电磁场分布;计算了声表面波所引起的光学相对介质隔离率张量的变化,最后讨论了声光衍射效率和光场与声场的重叠积分、声功率、声频率、声孔径和光波导参数之间的关系。结果表明,在低频范围内光场与声表面波场重叠良好;低阶模的重叠积分始终大于高阶模重叠积分,最低阶模与声表面波相互作用最强,所需声功率最小;当声功率一定时,增加声孔径可以提高衍射效率。     

Spherical symmetry of generalized EYMH fields

The possible actions of symmetry groups on generalized Higgs fields coupled to an Einstein–Yang–Mills field are studied with differential geometrical techniques involving principal and associated bundles. A classification of conjugacy classes of these actions and the form of the corresponding invariant Einstein–Yang–Mills–Higgs (EYMH) fields is obtained and then applied to the case of static spherically symmetric fields over four-dimensional space-time. We identify the representations of the gauge group for which spherically symmetric Higgs fields exist. Then the set of all field equations for the independent functions that describe these fields is analyzed and the corresponding ordinary system of differential equations is derived and shown to be consistent.     

Effective dynamics of an electrically charged string with a current

Equations of motion for an electrically charged string with a current in an external electromagnetic field with regard to the first correction due to the self-action are derived. It is shown that the reparameterization invariance of the free action of the string imposes constraints on the possible form of the current. The effective equations of motion are obtained for an absolutely elastic charged string in the form of a ring (circle). Equations for the external electromagnetic fields that admit stationary states of such a ring are derived. Solutions to the effective equations of motion of an absolutely elastic charged ring in the absence of external fields as well as in an external uniform magnetic field are obtained. In the latter case, the frequency at which one can observe radiation emitted by the ring is evaluated. A model of an absolutely nonstretchable charged string with a current is proposed. The effective equations of motion are derived within this model, and a class of solutions to these equations is found.