Hydrodynamic interaction between two rotating tori

The hydrodynamic interactions between two rotating tori is studied. Two kinds of problems are addressed. The interaction between two force free tori is examined, for co and counter rotating cases, which should be relevant in the case of swimming of two toroidal animals and form the basis for interaction of a swarm of such swimmers, apart from the dynamics of a collection of stiff polymer rings. The second problem is the case of two non-translating rotating tori, a possible configuration in toroidal mixers for microfluidic devices. In the former case, analytical expression for translational velocity shows good agreement with the theory in the far field case and show a strong reduction in the velocities in the lubrication limit for the co-rotating case. The velocities are found to monotonically reduce to zero in the case of counter-rotating tori. For the latter case, the expression for velocity field is derived the net force acting on the torus is analytically calculated. The comparison with numerical results is encouraging both in the case of co as well as counter-rotation. The expressions derived for velocities should be useful in estimating pseudo-potentials between such pairs.     

Nonsteady waves in distributed dynamical systems

The paper is devoted to the study of one-dimensional and two-dimensional transient wave regimes in nonlinear systems of the reaction-diffusion type. In a one-dimensional case the process of collision of two travelling waves is considered. It is demonstrated that in the case of a nondispersive nonlinear system, where a steady regime of the collision is not possible, the process can be described by means of an approximation which is nonuniform in a spatial coordinate. The collision results, in a general case, in formation of an oscillatory shock wave moving with varying velocity. In a two-dimensional situation the transition of a rotating vortex into a rotating spiral wave in the case of dispersive systems and the inverse transition in the case of nondispersive systems are considered.     

The width of a chaotic layer

A model of nonlinear resonance as a periodically perturbed pendulum is considered, and a new method of analytical estimating the width of a chaotic layer near the separatrices of the resonance is derived for the case of slow perturbation (the case of adiabatic chaos). The method turns out to be successful not only in the case of adiabatic chaos, but in the case of intermediate perturbation frequencies as well.     

Quantum Light Excitation of Atoms in Ideal Bose-Einstein condensate

The spectrum shape of atomic radiation in the case of ideal Bose-Einstein condensate (BEC)excited by quantized light is derived through the Wigner-Weisskopf approximation. Besides the split and gap in the excitation spectrum, a doublet structure appears in the emission spectrum with different widths for the non-resonant case and the same widths for the resonant case. The survival probability is found to decrease exponentially for the non-resonan t case and with oscillation for the resonant case. A suppressed radiation also appears in the nonresonant case. All these results can be used to detect the existence of BE condensation.     

Separation of Variables in the Elliptic Gaudin Model

For the elliptic Gaudin model (a degenerate case of the XYZ integrable spin chain) a separation of variables is constructed in the classical case. The corresponding separated coordinates are obtained as the poles of a suitably normalized Baker-Akhiezer function. The classical results are generalized to the quantum case where the kernel of the separating integral operator is constructed. The simplest one-degree-of-freedom case is studied in detail. Received: 21 August 1998 / Accepted: 12 January 1999     

Scalar-tensor theory of gravitation: Generalizations and experimental limitations

Several theories with scalar field can be derived from different variational principles. Here we consider a very general variational principle and we prove that, in the exterior case without electromagnetic field, the solution for a particular case generates the set of solutions for the general case. This is applied to the exterior solution in the static case with spherical symmetry without electromagnetic field. We investigate the predictions for the classic effects and the event horizons. Then we get some limitations for the variational principles which generalize the usual limitations. In all these cases the Schwarzschild solution with his horizon appears as a very particular case.     

Les pseudopotentiels à norme conservée relativistes étendus

The extended norm-conserving pseudopotentials developed by Shirley et al., in the nonrelativistic case, has been extended to the relativistic case. We have discussed the importance of the relativistic terms added in the case of the hard pseudopotentials. This correction allows us to revise the precision linked to the nonlinearity of the electronic structure methods on a solid in the particular case of heavy atoms.     

Study of reflection of light by a moving mirror

The law of reflection of light by a moving mirror in the case of special Lorentz transformation is well known. We have derived the law of reflection of light by a moving mirror in the case of the most general Lorentz transformation. It has been observed that in the case of special Lorentz transformation, the law of reflection of light by a moving mirror is very simple but in the case of the most general Lorentz transformation, the law of reflection of light by a moving mirror is very complex.      

Intermittency of velocity time increments in turbulence

We analyze the statistics of turbulent velocity fluctuations in the time domain. Three cases are computed numerically and compared: (i) the time traces of Lagrangian fluid particles in a (3D) turbulent flow (referred to as the dynamic case); (ii) the time evolution of tracers advected by a frozen turbulent field (the static case); (iii) the evolution in time of the velocity recorded at a fixed location in an evolving Eulerian velocity field, as it would be measured by a local probe (referred to as the virtual probe case). We observe that the static case and the virtual probe cases share many properties with Eulerian velocity statistics. The dynamic (Lagrangian) case is clearly different; it bears the signature of the global dynamics of the flow.     

Effective Impedance of a Slightly Rough Surface of an Arbitrarily Anisotropic Medium

We consider a boundary-value problem for the electromagnetic field in an arbitrarily anisotropic half-space with a rough surface. In the case of a small roughness height, we derive the impedance boundary condition with a nonlocal impedance in the fourth order of the perturbation theory. In addition to the general case, we analyze the case of a perfectly conductive surface with a Gaussian roughness.     

Electrothermal Oscillatory Instability in Spherical Ferroelectric Resonators. Three-Mode Case

We consider the equations of interaction between electromagnetic oscillations and the temperature in a nonlinear dielectric resonator and study the dynamics of the oscillatory instability in the system. The threshold conditions (power and self-modulation frequency) of electrothermal excitation are calculated for microwave potassium-tantalate resonators for the case of three-mode interaction. The conditions for observing electrothermal excitation in the three-mode case are found to be quite favorable. In this case, the threshold power of excitation of temperature oscillations is smaller than that in the two-mode case and can amount to a few microwatts.     

热带对流活动日变化的模拟研究

利用一个云分辨与海洋的耦合模式,模拟研究了热带对流活动的日变化.通过对模拟结果的分析,揭示了热带地区不同海温日变化条件下,对流活动的云物理特征.利用热带海洋与全球大气响应观测实验（TOGA COARE）的观测资料作为模式的初始与边界场,来驱动耦合模式.对热带海表温度按照其日变化幅度的大小进行了分类,分为强、弱海表温度日变化两种类型,并在此基础上进行了合成分析.结果表明：1）在弱的海表温度日变化下,云中的云冰含量大于云水含量,说明云中以层状云为主;而在强的海温日变化下,云中的云水含量大于云冰含量,说明云中以 关键词： 热带对流日变化 地面降水率 云冰含量 云水含量     

On the reality of supraluminal group velocity and negative delay time for a wave packet in a dispersion medium

It is shown that, in the case of the supraluminal group velocity of a wave packet in a dispersion medium, a wave packet with a smooth (analytical) envelope does propagate with a supraluminal velocity. In the case of a negative group velocity, the signal maximum does arrive at the detector earlier than at the transmitter. These facts are consistent with both the finiteness of the velocity of light in free space for information transfer (in the case of supraluminal propagation velocity) and the principle of causality (in the case of negative delay time). Basically, the effect of negative delay time may be employed for predicting an observable effect.     

Topological invariants for fractional quantum hall states

We calculate a topological invariant, whose value would coincide with the Chern number in the case of integer quantum Hall effect, for fractional quantum Hall states. In the case of Abelian fractional quantum Hall states, this invariant is shown to be equal to the trace of the K-matrix. In the case of non-Abelian fractional quantum Hall states, this invariant can be calculated on a case by case basis from the conformal field theory describing these states. This invariant can be used, for example, to distinguish between different fractional Hall states numerically even though, as a single number, it cannot uniquely label distinct states.     

Heat-to-Work Conversion by Exploiting Full or Partial Correlations of Quantum Particles

It is shown how information contained in the pairwise correlations (in general, partial) between atoms of a gas can be used to completely convert heat taken from a thermostat into mechanical work in a process of relaxation of the system to its thermal equilibrium state. Both classical correlations and quantum correlations (entanglement) are considered. The amount of heat converted into work is proportional to the entropy defect of the initial state of the system. For fully correlated particles, in the case of entanglement the amount of work obtained per particle is twice as large as in the case of classical correlations. However, in the case of entanglement, the amount of work does not depend on the degree of correlation, in contrast to the case of classical correlations. The results explicitly demonstrate the equivalence relation between information and work for the case of two-particle correlations.     

Quantum statistics of multimode parametric amplification

The effect of a multimode interaction on the squeezing attainable in parametric amplification is investigated. In the non degenerate case the maximum squeezing attainable is reduced from the single mode case, whereas in the degenerate case the squeezing is essentially unaffected by the multimode nature of the interaction.     

Monomer Migration and Annihilation Processes

We propose a two-species monomer migration-annihilation model, in which monomer migration reactions occur between any two aggregates of the same species and monomer annihilation reactions occur between two different species. Based on the mean-field rate equations, we investigate the evolution behaviors of the processes. For the case with an annihilation rate kernel proportional to the sizes of the reactants, the aggregation size distribution of either species approaches the modified scaling form in the symmetrical initial case, while for the asymmetrical initial case the heavy species with a large initial data scales according to the conventional form and the light one does not scale. Moreover, at most one species can survive finally. For the case with a constant annihilation rate kernel, both species may scale according to the conventional scaling law in the symmetrical case and survive together at the end.     

Jahn-Teller effect at exciton self-trapping

In the adiabatic approximation two limiting cases of exciton self-trapping have been considered for a degenerate atomic term creating the bands of Frenkel excitons, which interact with all crystal deformations admitted by symmetry: a case of a large radius excitation on the self-trapping barrier and a small-radius case. In the first case wave functions and deformations have been found which correspond to the barrier, in the second case the adiabatic surface of self-trapping excitons have been obtained. It is shown that the interaction with non-totally symmetric deformations leads to a lowering of the crystal point symmetry in a state corresponding to the lowest self-trapping barrier, that is the manifestation of the Jahn-Teller effect applied to a self-trapping exciton.     

Analytic solution for magnetohydrodynamic boundary layer flow of Casson fluid over a stretching/shrinking sheet with wall mass transfer

In this analysis,the magnetohydrodynamic boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet in the presence of wall mass transfer is studied.Using similarity transformations,the governing equations are converted to an ordinary differential equation and then solved analytically.The introduction of a magnetic field changes the behavior of the entire flow dynamics in the shrinking sheet case and also has a major impact in the stretching sheet case.The similarity solution is always unique in the stretching case,and in the shrinking case the solution shows dual nature for certain values of the parameters.For stronger magnetic field,the similarity solution for the shrinking sheet case becomes unique.