The boundary of a boundary principle: A unified approach

The boundary of a boundary principle in field theories is described. The difference in treatment of the principle in electrodynamics and general relativity is pointed out and reformulated in terms of underlying mathematical structure of the theories. The problem of unifying the treatment is formulated and solved. The role of E. Cartan's concept of the moment of rotation associated with the curvature of a Levi-Civita connection on a frame bundle is shown to be crucial for the unification. The analysis of the boundary of a boundary principle in Kaluza-Klein theory is performed and the recipe for a unified treatment of the principle in electrodynamics and general relativity is shown to follow from the analysis. It is pointed out that the unification cand be extended to Yang-Mills fields easily.     

Bose-Einstein condensation and the glassy state

The distinction between a classical glass and a classical liquid is difficult, since both are disordered. The difference is in the fact that a glass is frozen while the liquid is not. In this Letter an equilibrium measure is suggested that distinguishes between a glass and a liquid. The choice of this measure is based on the idea that in a system which is not frozen symmetry under permutation of particles is physically relevant, because particles can be permuted by actual physical motion. This is not the case in a frozen system. In this Letter it is shown how to generalize naturally the quantum mechanical concept of Bose condensed fraction to classical systems in order to distinguish between the glass and the liquid. It is finite in the liquid and zero in the frozen state. The actual value of the condensed fraction in the liquid may serve also as a measure of the glassiness in the liquid.     

On reflection from a suddenly created plasma half-space: transientsolution

The reflection by a suddenly created plasma half-space of a time-harmonic plane electromagnetic wave propagating in free space is considered. The problem involves a temporal discontinuity, a spatial discontinuity, and a dispersive medium. The steady-state solution is obtained by considering the basic features of the scattering processes due to each of the discontinuities in terms of analogous transmission-line models. The electric field of the reflected wave consists of two components. One component (called component A) is of the same frequency as the incident wave frequency and is due to the spatial discontinuity. The other component (called component B) is of a different frequency and arises because of the temporal discontinuity. The B component is damped out even if the plasma is only slightly lossy. The damping rate of the B component is calculated. The transient solution is obtained through the use of Laplace transforms. The solution is given in terms of Bessel-like functions. The limiting value of this solution is shown to agree with the steady-state solution. Numerical results illustrating the transient effects are for two typical cases     

Sound scattering by a potential vortex

The scattering of a monopole wavefield by the flow of a potential vortex is considered by using a scheme due to Lighthill. The problem is two-dimensional, the monopole being a line source adjacent to a parallel line vortex. The cases of large and small separation of vortex and source are examined in detail. The far field density is asymptotically estimated in both limits. A quadrupole type radiation field is calculated in each case.     

Clausius-Mossotti-Type relation for planar monolayers

The dielectric properties of a quasi-two-dimensional molecular monolayer are analyzed. The dielectric function of the monolayer is expressed in terms of molecular polarizability and monolayer characteristics. The expression is analogous to the well-known Clausius-Mossotti equation for three-dimensional systems. The response of the monolayer to an external field is calculated. The case of a planar array of nanoparticles is also considered. The solution is obtained in the framework of a local-field theory.     

Critical dynamics and fluctuations for a mean-field model of cooperative behavior

The main objective of this paper is to examine in some detail the dynamics and fluctuations in the critical situation for a simple model exhibiting bistable macroscopic behavior. The model under consideration is a dynamic model of a collection of anharmonic oscillators in a two-well potential together with an attractive mean-field interaction. The system is studied in the limit as the number of oscillators goes to infinity. The limit is described by a nonlinear partial differential equation and the existence of a phase transition for this limiting system is established. The main result deals with the fluctuations at the critical point in the limit as the number of oscillators goes to infinity. It is established that these fluctuations are non-Gaussian and occur at a time scale slower than the noncritical fluctuations. The method used is based on the perturbation theory for Markov processes developed by Papanicolaou, Stroock, and Varadhan adapted to the context of probability-measure-valued processes.     

Vibrations of double-string complex system under moving forces. Closed solutions

In this paper the dynamic response of a double-string system traversed by a constant or a harmonically oscillating moving force is considered. The force is moving with a constant velocity on the top string. The strings are identical, parallel, one upon the other and continuously coupled by a linear Winkler elastic element. The classical solution of the response of a double-string system subjected to a force moving with a constant velocity has a form of an infinite series. The main goal of this paper is to show that in the considered case a part of the solution can be presented in a closed, analytical form instead of an infinite series. The presented method of finding the solution in a closed, analytical form is based on the observation that the solution of the system of partial differential equations in the form of an infinite series is also a solution of an appropriate system of ordinary differential equations.     

The shape gradient of the least-squares objective functional in optimal shape design problems of radiative heat transfer

Optimal shape design problems of steady-state radiative heat transfer are considered. The optimal shape design problem (in the three-dimensional space) is formulated as an inverse one, i.e., in the form of an operator equation of the first kind with respect to a surface to be optimized. The operator equation is reduced to a minimization problem via a least-squares objective functional. The minimization problem has to be solved numerically. Gradient minimization methods need the gradient of a functional to be minimized. In this paper the shape gradient of the least-squares objective functional is derived with the help of the shape sensitivity analysis and adjoint problem method. In practice a surface to be optimized may be (or, most likely, is to be) given in a parametric form by a finite number of parameters. In this case the objective functional is, in fact, a function in a finite-dimensional space and the shape gradient becomes an ordinary gradient. The gradient of the objective functional, in the case that the surface to be optimized is given in a finite-parametric form, is derived from the shape gradient. A particular case, that a surface to be optimized is a “two-dimensional” polyhedral one, is considered. The technique, developed in the paper, is applied to a synthetic problem of designing a “two-dimensional” radiant enclosure.     

A new way of gas cooling by light

The gas behaviour in the presence of monochromator laser radiation is considered. The change of the collision cross-section as a result of the excitation of the colliding particles is taken into account. The total velocity distribution is found as a steady-state Boltzmann equation solution. The appearance of a light-induced heat flux in the gas is predicted and the application of this effect for gas cooling is discussed.     

Acoustic Transducer of Turbulent Pressure Fluctuations in a Temperature-Stratified Medium

The operation of an acoustic transducer in a temperature-stratified medium is investigated. The formation of a response of piezoceramic transducers of pressure fluctuations under the action of temperature fluctuations in a working medium on the sensor element is considered. The attenuation of the temperature signal of a pressure transducer in a turbulent boundary layer is calculated numerically. The effect of distortions of the spectral levels of pressure fluctuations detected by a sound transducer in the field of temperature inhomogeneities is investigated for the example of measurements of turbulent pressure fluctuations in a boundary layer during vertical ascent of the device to the surface from a specified depth in a deep sea.     

Nonlinearity of solids with micro- and nanodefects and characteristic features of its macroscopic manifestations

The meaning of the experimentally measured nonlinear parameters of a medium is discussed. The difference in meaning between the local nonlinearity, which is measured in the vicinity of a single defect and depends on the size of the region of averaging, and the effective volume nonlinearity of the medium containing numerous defects is emphasized. The local nonlinearity arising at the tip of a crack is calculated; this non-linearity decreases with an increase in the region of second harmonic generation. The volume nonlinearity is calculated for a solid containing spherical cavities. The volume nonlinearity is also calculated for a medium containing infinitely thin cracks in the form of circular disks, which assume the shape of ellipsoids in the course of the crack opening. The nonlinear acoustic parameter is calculated with the use of the exact classical results of the theory of cracks.     

Rotational dynamics of a molecular ensemble in the presence of a strong laser field

The rotational dynamics of a molecular ensemble in the presence of a strong laser field is investigated in the framework of the density-matrix approach. The results obtained are compared with the rotation of molecules in a classical ensemble. The thermal molecular motion in the ensemble is taken into account in a model of random collisions, and various values of the relaxation time are considered. The effect of the relaxation process on molecular alignment is analyzed for the laser-pulse action and in the afterpulse regime. The similarity between quantum and classical rotational dynamics of a molecular ensemble is examined.     

光纤激光器反馈耦合损耗分析

将双包层光纤基模LP01模近似表示为拉盖尔-高斯光束的线性叠加,前六阶的拉盖尔-高斯光束包含了LP01模能量的99.99％.利用拉盖尔-高斯光束的传输特性计算了腔镜分别为球面镜和透镜加平面反射镜时的反馈耦合损耗.结果表明,腔镜为球面镜时,只有当球面镜和到达球面镜光束的曲率半径匹配时才能获得最小的耦合损耗,特别是当平面镜紧贴光纤端面时,耦合损耗为0;当腔镜为透镜加平面反射镜时,将平面镜放置在透镜焦平面时获得最小反馈耦合损耗为0.25％.     

Quenching Properties of an Arc in a Double Flow with a Vortex

The effect of a vortex in a gas flow on an air-blast arc is investigated. The radial density of a vortex in the compressible flow is evaluated with a simple model. The experiments show that the width of a low pressure channel on the axis of the nozzle is comparable to the theoretical values. The measured electric field strength profile is strongly influenced by the presence of such a vortex. In addition, the thermal interrupting capability is drastically lowered by vortex superimposed on the axial gas flow.     

A General Theory of Non-Abelian Electrodynamics

The general theory of gauge fields is used to develop a theory of electrodynamics in which the fundamental structure is non-Abelian and in which the internal gauge field symmetry is O(3), based on the existence of circular polarization and the third Stokes parameter. The theory is used to provide an explanation for the Sagnac effect with platform at rest and in motion. The Sagnac formula is obtained by considering the platform in motion to be a gauge transformation. The topological phases can be described straightforwardly with non Abelian electrodynamics, which produces a novel magnetic field component for all types of radiation, a component which is proportional to the third Stokes parameter. The theory provides a natural explanation for the inverse Faraday effect without phenomenology.     

Focusing of an X-ray spherical wave by a uniaxially bent crystal: Johann scheme and logarithmic spiral

Focusing of a spherical wave in the well-known Johann scheme is considered theoretically. An analytical formula for the size of the crystal bent surface reflecting radiation in the Johann scheme is derived. The intensity distribution near the focus is found. The spherical aberration of the diffracted beam is analyzed. Back scattering is shown to minimize the aberration. Spectral characteristics of an Johann spectrometer are discussed. The focusing of a spherical wave by a crystal bent into a logarithmic spiral is considered. It is shown that the Johann scheme is a specific case of a logarithmic spiral.     

Relaxation properties of weakly coupled classical systems

The relaxation properties of a small classical system weakly coupled to a large classical system which acts as a heat bath are described using a generalized Fokker-Planck equation. The Fokker-Planck equation is derived in general using a modification of the elimination of fast variables techniques previously described. The specific example in which the small system is a harmonic oscillator linearly coupled to the heat bath is treated in detail and it is demonstrated that there is a dynamic frequency shift as well as a statistical shift of the oscillator frequency.     

Quantum Nernst effect

It is theoretically predicted that the Nernst coefficient is strongly suppressed and the thermal conductance is quantized in the quantum Hall regime of the two-dimensional electron gas. The Nernst effect is the induction of a thermomagnetic electromotive force in the y-direction under a temperature bias in the x-direction and a magnetic field in the z-direction. The quantum nature of the Nernst effect is analyzed with the use of a circulating edge current and is demonstrated numerically. The present system is a physical realization of the non-equilibrium steady state.     

Measurement of the parameters of the natural waveguide mode

The possibilities of using the decomposition of natural waveguide modes in a shallow-water sea in case there is a sound velocity gradient into sinusoidal modes of an ideal waveguide is grounded. The applicability range of such decomposition is shown. Dispersion in signals of the modes presented in such a way is determined by mathematical reversal without a test source. The structure of discrete modes in a natural waveguide is determined without utilizing the bottom parameters and sound velocity’s distribution over the waveguide depth. The coefficient of the mode signal’s correlation with the measured parameters of the mode signal and a real signal, introduced into it, is shown to be 0.973. The signals from a point emitter positioned at the depth of 50 m in the frequency range of 90–280 Hz in a shallow-water sea (the Barents Sea, a 120 m depth, a 7 km distance), received by a vertical antenna array comprising 32 receivers spaced equidistantly with a 3-m step are used in the experiment. A real signal has been successfully reversed using a mathematical model.