Nonequilibrium measures which exhibit a temperature gradient: Study of a model

We give some rules to define measures which could describe heat flow in homogeneous crystals. We then study a particular model which is explicitly solvable: the one dimensional nearest neighborhood Ising model. We analyze two cases. In the first one the spins at the two boundaries interact with reservoirs at different temperatures; in the thermodynamical limit the measure we introduce converges locally to Gibbs measures and a temperature profile is so derived. We obtain an explicit expression for the thermal conductivity coefficient which depends on the temperature. In the second case we study the asymptotic behavior starting from an initial state in which each half of the space is at a different temperature. We find again a temperature profile which asymptotically obeys the heat equation with the thermal conductivity coefficient previously derived. From a mathematical point of view, the analysis of the invariant measure is made possible by studying a time-reversed process related to a graphical representation of an associated process. This provides us with an explicit formula for then-fold correlation function and we study the limiting behavior using both this representation (for proving an exchangeability result) and a Donsker-type, spacetime renormalization procedure.Partially supported by CNPq grant No. 402876/79Laboratoire de Recherche Associé au CNRS No. 169     

Attenuation of a light signal in a scattering medium

A quantitative assessment of effects due to the interference of waves scattered by an ensemble of particles is given. It is shown that in the propagation of a collimated beam of light in a turbid medium, interference effects give rise to an additional stretching of the scattering indicatrix for a particle system, as compared with the scattering indicatrix for a single particle. The interference tongue obtained is concentrated in a very small angle in the direction of the light beam incident on the particle system. (Over a wide range of experimental conditions this angle is of the order of a few minutes.)Formulas are obtained for the instrumental scattering coefficient in the case of light scattering by volumes in the form of a sphere, disk, or rod. The analytical form of the formulas obtained indicates the possibility of concentration effects in experiments in a turbid medium.     

Excitation of a cylinder of finite length by a Hertz azimuthal dipole

Conclusions Thus, an azimuthal dipole induces predominant currents in a narrow region near the source on the surface of a cylinder. Therefore, the presence of edges located /2 and further from the dipole has a weak effect on the directional diagrams. This fact permits using the appropriate equations for an infinite cylinder [7] for the approximate calculation of the directional diagrams in the transverse plane in the discussion of the excitation of a cylinder of length greater than by an azimuthal electric dipole further than /2 from the edges.The difference in the directional diagrams of a finite cylinder in comparison with an infinite cylinder may be significant in case of the nonobservance of one of the conditions enumerated above. In this case, it is necessary to use the method of integral equations described above to solve the problem of the excitation of a finite cylinder.Moscow Power Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 19, No. 8, pp. 1225–1230, August, 1976.     

On a new gravitational effect of a rotating mass

A new general relativistic many-body effect is described. It results in an unexpectedly large relative acceleration between neighboring test particles that follow an inclined orbit about a rotating mass. The effect vanishes if the orbit coincides with the equatorial plane of the rotating mass. The existence of this effect is due to a small divisor involving the deviation of the orbital frequency measured by a comoving clock from the frequency measured by an inertial clock. The influence of the rotation of the Sun on the Earth-Moon system is investigated, and it is shown that the new effect causes a harmonic variation in the Earth-Moon separation with an amplitude of order 1 m and dominant periods of 18.6 yr, 1/2 yr, 1 month, and 1/2 month. The confirmation of these results by the lunar laser ranging experiment would provide a significant new test of general relativity and a measurement of the angular momentum of the Sun.This essay received the fifth award from the Gravity Research Foundation for the year 1983 [Ed.].     

Stability of Equilibria with a Condensate

A quantum system composed of a spatially infinitely extended free Bose gas with a condensate, interacting with a quantum dot, which can trap finitely many Bosons, has multiple equilibria at fixed temperature. We extend the notion of return to equilibrium to systems possessing a multitude of equilibrium states and show that the above system returns to equilibrium in a weak coupling sense: any local perturbation of an equilibrium state converges in the long time limit to an asymptotic state. The latter is, modulo an error term, an equilibrium state which depends, in an explicit way, on the initial local perturbation. The error term vanishes in the small coupling limit.We deduce this stability result from properties of structure and regularity of eigenvectors of the Liouville operator, the generator of the dynamics. Among our technical results is a virial theorem for Liouville type operators which has new applications to systems with and without a condensate.Supported by a CRM-ISM postdoctoral fellowship and by McGill University     

Critical behavior of a heavy particle in a granular fluid

A second order phase transition is observed for the homogeneous cooling state of a heavy impurity particle in a granular fluid. The order parameter straight phi is the ratio of impurity mean square velocity to that of the fluid, with a conjugate field h proportional to the mass ratio. A parameter beta, measuring the fluid cooling rate relative to the impurity-fluid collision rate, is the analog of the inverse temperature. For beta<1 the fluid is "normal" with straight phi = 0 at h = 0, as in the case of elastic collisions. For beta>1 an "ordered" state with straight phi not equal0 occurs at h = 0, representing an extreme breakdown of equipartition. Critical slowing and qualitative changes in the velocity distribution function near the transition are noted.     

Validation of a medium-frequency computational method for the coupling between a plate and a water-filled cavity

The aim of this paper is the validation of a computation by a numerical method, normally adapted to the medium-frequency (MF) domain, of the strong coupling between an elastic structure (plate) and a cavity entirely filled with an internal acoustic viscous dense fluid (water). The method of computation does not lie in a modal approach (no need to extract the modal basis of the system) but it directly computes the frequency response of the system using a specific algorithm called the “Onera-MF method”.This method was developed to accurately calculate the response of complex systems in an MF broad band at a lower cost than standard modal method or direct step-by-step frequency method. The method can also be used for the low-frequency (LF) domain where modal densities of systems are low. The computation of the vibroacoustic response of the system lies in a finite element modelling of the overall system (structure and fluid) in which the coupling between the structure and the fluid (light or heavy) is directly taken into account within the formulation of the finite elements.A simple and well-known experimental case was chosen for validation: a parallelepipedic cavity entirely filled with water contained in a box defined by five rigid faces and closed at its end by an elastic clamped homogeneous plate.The validation is based on a comparison between measurement, the numerical computation and an analytical approach in the frequency band . Both the vibratory response of the plate and the acoustic pressure were compared. This study shows that the MF-method of computation used herein for this case also works in a modal domain.     

Transients in switching a diode with a thin base

An analytical expression is obtained for the duration of the shelf which is observed when a diode with a limited base is switched from the forward to the reverse direction. The problem is solved for an arbitrary value of the recombination velocity at the nonrectifying contact.     

Equations with a self-consistent field in quantum-statistical theory of a crystal

A system of equations with a self-consistent field is derived for the density of particles in the quantum case. This system has periodic solutions for a crystal. Equations for the Fourier coefficients are deduced from these solutions and are used to find equations containing only the Fourier coefficients of the density. A method is also given for solving the initial system by an expansion in powers of the Planck constant ; the terms proportional to ² and ² are calculated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 66–71, May, 1980.     

Deformation of a charge density wave in the vicinity of a point contact with a normal metal

The current-voltage characteristics of Cu-K_0.3MoO₃ point contacts between a metal and a semiconductor with a charge density wave (CDW) are studied for various diameters of the contacts in a wide range of temperatures T and voltages V. In the interval 80 K ? T ? 150 K, the current-voltage characteristics are correctly described in the framework of a semiconductor model: screening of an external electric field causes CDW deformation, shifts the chemical potential of quasiparticles, and changes the point contact resistance. It is shown that the chemical potential is above the middle of the Peierls gap in equilibrium and approaches the middle upon an increase in temperature. The current-voltage characteristics of point contacts with a diameter d ? 100 Å exhibit a sharp decrease in resistance for |V| > V _t , which is associated with the beginning of local CDW sliding within the contact region. The V _t (d, T) dependence can be explained by the size effect in the CDW phase slip.     

Excitons dressed by a sea of excitons

We here consider an exciton i embedded in a sea of N identical excitons 0. If the excitons are taken as true bosons, a bosonic enhancement factor N is found for i=0. If the exciton composite nature is kept, this enhancement not only exists for i=0, but also for any exciton having a center of mass momentum equal to the sea exciton momentum. This physically comes from the fact that an exciton with such a momentum can be transformed into a sea exciton by Pauli scattering, i.e., carrier exchange with the sea, making this exciton i not so much different from a sea exciton. This possible scattering, directly linked to the composite nature of the excitons, is irretrievably lost when the excitons are bosonized. The underlying interest of this work is in fact the calculation of the scalar products of N-exciton states, which turns out to be quite tricky, due to possible carrier exchanges between excitons. This work actually constitutes a crucial piece of our many-body theory for interacting composite bosons, because all physical effects involving composite bosons ultimately end by the calculation of such scalar products. The skeleton diagrams we here introduce to represent them, allow to visualize many-body effects linked to carrier exchanges in an easy way. They are conceptually different from Feynman diagrams, because of the special feature of the Pauli scatterings which originate from boson statistics departure.     

Dynamical properties of a gas of soliton pairs below the Neel temperature of a quasi-one-dimensional antiferromagnet

We present a theoretical analysis for dynamical properties of a classical, anisotropic quasi-one-dimensional antiferromagnet in the presence of the magnetic field below the Neel temperature of such a model. By the use of an interchain mean field approach the spin equations of motions have been reduced to the double-sine-Gordon equation in 1+1 dimensions. Special solutions are the 2-kink-solitons that have a form of pairs of coupled -kinks existing aboveT _N. Dynamical structure factores for an ideal gas of these 2-kinks have been calculated. Comparing to the corresponding structure factores for a gas of -kinks the main difference occurs in the formula for the transverse structure factor that has a Gaussian form instead of a Lorentz-like distribution. A qualitative agreement of the presented theory with experimental data of neutron scattering on TMMC has been found.     

Acceptance and transmission of a quadrupole mass filter with a prefilter

We have proposed an analytical model of a quadrupole mass filter with an additional rf quadrupole (prefilter) at its entry, which is based on the model of a transient field in the region between the edges of the mass filter electrodes and the prefilter electrodes. The characteristics of the complex mass filter have been investigated by the methods of phase space dynamics. In the presence of the entrance prefilter, instead of the entrance diaphragm, the y acceptance increases by 1.5 times relative to the x acceptance. Upon an increase in the ion residence time in the fringing field, the y acceptance contour exhibits the tendency to rotation on the phase plane, while the x acceptance contour is broadened in the x coordinate. The transmission function increases and oscillates upon an increase in the ion residence time in the fringing field. The result of numerical experiment using the SIMION 8 software differs from the result of analytical calculation by 14% for the x acceptance and by 35% for the y acceptance.     

Destabilization of a Saffman-Taylor fingerlike pattern in a granular suspension

We study the Saffman-Taylor instability in a granular suspension formed by micrometric beads immersed in a viscous liquid. When using an effective viscosity for the flow of the suspension in the Hele-Shaw cell to define the control parameter of the system, the results for the finger width of stable fingers are found to be close to the classical results of Saffman-Taylor. One observes, however, an early destabilization of the fingers that can be attributed to the discrete nature of the individual grains. Classically, the threshold of destabilization is linked to the noise in the cell and is thus difficult to quantify. We show that the grains represent a "controlled noise" and produce an initial perturbation of the interface with an amplitude proportional to the grain size. The finite amplitude instability mechanism proposed by Bensimon et al. allows us to link this perturbation to the value of the threshold observed.     

Generation of high-current electron beams by a hollow cathode with a ferroelectric plasma source

This paper presents results and analysis of an experimental investigation of the operation of a hollow cathode (HC) with an incorporated ferroelectric plasma source (FPS). It was shown that the use of FPS based on a BaTi solid solution allows one to ignite and to sustain a 10²-10³ A HC discharge with duration of 10^-3-10^-5 s at background pressure of 5 x 10^-3 Pa while keeping the HC design with small dimensions. It was found that the development of the HC discharge is accompanied by formation at the surface of the FPS of dense plasma which serves as a powerful (hundreds of kW) pulsed source of current carrying electrons. Parameters of the HC plasma (radial distribution of the plasma density and temperature and plasma potential) for different discharge current amplitudes and two types of FPS are presented. Application of the FPS as an electron source in a diode under an accelerating pulse 300 kV and pulse duration 400 ns showed that the latter operates in a plasma pre-filled mode with a current amplitude up to 1.6 kA. Parameters of the diode and electron beam for different experimental conditions are presented and discussed.Received: 10 April 2003, Published online: 12 August 2003PACS: 52.50.Dg Plasma sources - 29.25.Bx Electron sources - 52.25.Tx Emission, absorption, and scattering of particles     

Some results for a fractional diffusion equation with radial symmetry in a confined region

We investigate an N-dimensional fractional diffusion equation with radial symmetry by taking a spatial and time dependent diffusion coefficient into account, i.e.,  with . The equation is considered in a confined region and subjected to time dependent boundary conditions which may be related to inhomogeneous characteristics of the surfaces confining the system. The results show an anomalous spreading of the solutions and an unusual behavior of the survival probability.     

Stable branches of a solution for a fermion on domain wall

The case when a fermion occupies an excited nonzero frequency level in the field of domain wall is discussed. It is demonstrated that a solution exists for the coupling constant in the limited interval 1 < g < g _max ≈ 1.65. It is shown that indeed there are different branches of stable solution for g in this interval. The first one corresponds to a fermion located on the domain wall (\(1 < g < \sqrt[4]{{2\pi }}\)). The second branch, which belongs to the interval \(\sqrt[4]{{2\pi }} \leqslant g \leqslant g_{\max }\), describes a polarized fermion off the domain wall. The third branch with 1 < g < g _max describes an excited antifermion in the field of the domain wall.     

Analytical model of a Brownian motor with a fluctuating potential

We propose a model of a Brownian motor that performs a useful work against a load force F in an asymmetric periodic potential V(x) = V(x + 2L) that undergoes random shifts by a half period L with a frequency γ. An arbitrarily shaped potential profile is repeated with an energy shift ΔV in both half-periods L, while the periodicity of the function V(x) is ensured by its jumps at x = 0 and x = L. The boundary condition at x = 0 for the distribution function of a Brownian particle allows us to introduce a high and narrow potential barrier V₀ that blocks the reverse current and leads to high efficiency of the motor (the ratio of the useful work done against the load force F to the energy imparted to the particle through the potential shifts). Based on this model, we derived exact analytical expressions for the current J and the efficiency η. In the special case of piecewise-linear potentials, J and η were plotted against F and γ for various values of the parameters ΔV and V₀. We discuss the influence of the potential shape and fluctuation frequency on the main characteristics of the motor.