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.     

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     

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.     

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.     

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.     

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.].     

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.     

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.     

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.     

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.     

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.     

An argon ion ring laser as a gyroscope

As a prototype gyroscope for a precision measurement of the Earth's rotation _E, we set up an argon ion ring laser with an area of 1.4 m². Different cavity geometries were tested in order to achieve a cancellation of the effect of the plasma flow. In a set-up with two laser tubes of the same type facing towards opposite directions, a stability of the beat frequency of 2–3 _E was measured. In a configuration with a double transition of the laser beam through the tube, the lock-in threshold was too high for the Earth's rotation to be measured, however, no effect of the plasma flow was observed.     

Suppressed Dispersion for a Randomly Kicked Quantum Particle in a Dirac Comb

I study a model for a massive one-dimensional particle in a singular periodic potential that is receiving kicks from a gas. The model is described by a Lindblad equation in which the Hamiltonian is a Schrödinger operator with a periodic δ-potential and the noise has a frictionless form arising in a Brownian limit. I prove that an emergent Markov process in an adiabatic limit governs the momentum distribution in the extended-zone scheme. The main result is a central limit theorem for a time integral of the momentum process, which is closely related to the particle’s position. When normalized by $t^{\frac{5}{4}}$ the integral process converges to a time-changed Brownian motion whose diffusion rate depends on the momentum process. The scaling $t^{\frac{5}{4}}$ contrasts with $t^{\frac{3}{2}}$ , which would be expected for the case of a smooth periodic potential or for a comparable classical process. The difference is a wave effect driven by momentum reflections that occur when the particle’s momentum is kicked near the half-spaced reciprocal lattice of the potential.     

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.     

Self-consistent expansion of a multicomponent plasma into a vacuum

The problem of the one-dimensional collisionless expansion of a multicomponent plasma into a vacuum is considered. In the hydrodynamic approximation, an approximate analytical solution for an arbitrary set of ion species with masses M₁,..., M_n and charge numbers Z₁e, Z₂e,..., Z_ne is found by using the technique of self-similar variables employed by Gurevich, Pariiskaya, and Pitaevskii for the case of single-species ions. A numerical iterative algorithm is developed in which the analytical solution is used as a first approximation.     

Design of a Thin Film Infrared Barcode on a Flexible Substrate

We report the design, fabrication and characterization of an infrared barcode. This barcode is composed of a bilayer of titanium and amorphous silicon on a flexible Kapton substrate. Information encoded in the barcode shows high contrast when viewed with an infrared imaging system in the 8 to 12 m spectral region. The barcode information is concealed under visible viewing conditions, i.e., the barcode appears as an untreated, uniform metal sheet to a detector of visible radiation (400 to 700nm).