Equilibrium Spectrum Research Articles

Kinetic theory and Bose–Einstein condensation

In this article we discuss the role played by kinetic theory in describing the non-equilibrium dynamics of dilute systems of weakly interacting bosons. We illustrate how a simple kinetic equation for the time evolution of the spectral particle density can be derived from the spatially homogeneous Gross–Pitaevskii equation. This kinetic equation agrees with the usual Boltzmann–Nordheim equation of quantum kinetic theory in the long wavelength limit where the occupation numbers are expected to be large. The stationary solutions of the Gross–Pitaevskii kinetic equation are described. These include both thermodynamic equilibrium spectra and finite flux Kolmogorov–Zakharov spectra. These latter spectra are intrinsically nonequilibrium states and are expected to be relevant in the transfer of particles to low momenta in the initial stage of the condensation process. This is illustrated by some computations of a solution of the kinetic equation beginning with initial conditions far from equilibrium. The solution generates a flux of particles from large to small momenta which results in a singularity at zero momentum within finite time. We interpret this singularity as incipient condensate formation. We then present some numerical results on the post-singularity dynamics and the approach to equilibrium. Contrary to our original expectations we do not observe the Kolmogorov–Zakharov spectrum during the period of condensate growth. In the closing sections we address the issue of the connection between the Gross–Pitaevskii and Boltzmann–Nordheim kinetic equations. We argue that the two equations have differing regimes of applicability in momentum space, matching in an intermediate range. We make some suggestions of how this matching can be modeled in practice. To cite this article: C. Connaughton, Y. Pomeau, C. R. Physique 5 (2004).

Modelling of radiation transfer in low temperature nanosecond laser-induced plasma of Al vapour

Gas-dynamical expansion and radiation transfer of Al vapour breakdown plasma induced by nanosecond laser action with an intensity of 109–2 × 1010 W cm−2 at the wavelengths of 1.06, 0.512, and 0.248 µm are modelled. Plasma evolution is described in the approximation of non-stationary radiative gas dynamics in the two-dimensional axially symmetrical formulation. Radiation transfer is found to exert a considerable effect on the evolution of the laser plasma. As the intensity increases, the radiative energy losses also increase, reaching 60% at 2 × 1010 W cm−2, and cause the plasma temperature to be reduced proportionally. The energy escapes mainly through the side and, to a smaller extent, the frontal boundaries, the amount of energy escaping in the direction of the target being negligible. The dependence of plasma processes on the laser wavelength is due to specific features of the absorption mechanisms and the photo-absorption contribution under the action of visible and ultraviolet ranges of radiation. The spectral composition of the escaping radiation differs considerably from that of the equilibrium spectrum and is typical of plasma with a variable optical density. It is possible to take into account the influence of radiation on the plasma characteristics by solving the equation of radiation transfer in the multi-group approximation with several tens of spectral intervals. If the maximum available number of groups is used for selected spectrum intervals, the computational results can be compared to the experimental data of plasma emission.

Emissive properties of xenon ions from a laser-produced plasma in the 100–140 Å spectral range: Atomic-physics analysis of the experimental data

In order to design extreme ultraviolet (EUV) sources for nanolithography, xenon EUV emission has been experimentally studied in a plasma generated by the interaction of a high-power laser with a droplet jet. A theoretical model assuming that the resulting plasma is optically thick allows one to find the distribution of the relevant ions and transitions involved in the emission process. Atomic physics computations are performed using the HULLAC code to give a detailed account of the transitions involved. The importance of 4p–4d, 4d–4f, and 4d–5p transitions is stressed, as well as the need for configuration-interaction treatment of the Δn=0 transitions. Comparisons of a modeled local thermodynamical equilibrium spectrum with experiment provides qualitative agreement and permits an estimate of the plasma temperature, density, and dimensions.

Gamma-rays from the pulsar wind nebulae

We investigate the radiation processes inside supernova remnants which are powered by young pulsars. Using a recent model for particle acceleration by the pulsar wind nebulae (PWNe), in which positrons gain energy in the process of resonant scattering by the heavy nuclei, we construct a time-dependent radiation model for the PWNe. In this model, the spectra of relativistic particles, injected inside the nebula, depend on time due to the evolution of the pulsar parameters. Applying a simple model for the evolution of the PWNa, the equilibrium spectra of leptons and nuclei inside the nebula are determined as a function of time, taking into account the energy losses of particles on dierent processes and their escape from the nebula. We calculate the multiwavelength photon spectra produced by leptons and nuclei and compare them with the observations of the PWNe for which TeV-ray emission has been reported, i.e. the Crab Nebula, the Vela Supernova Remnant, and the nebula around PSR 1706-44. It is found that the emission from the Crab Nebula can be well fitted by the composition of the -ray emission produced by leptons (below10 TeV) and nuclei (10 TeV). The model is further tested by successful fitting of the high energy spectrum from the Vela SNR. In this case, the observed-ray emission is mainly due to leptons and the contribution of-rays from decay of neutral pions, produced in collision of nuclei, is significantly lower. However, the considered model does not give good fitting to the emission from PSR1706-44 for the likely parameters of this source, unless an additional target for relativistic leptons is present inside the nebula, e.g. the thermal infrared emission. Based on the knowledge obtained from these fittings, we predict the -ray fluxes in the TeV energy range from other PWNe, which are promissing TeV-ray sources due to their similarities to the -ray nebulae, i.e. MSH15-52 (PSR 1509-58), 3C58 (PSR J0205+6449), and CTB80 (PSR 1951+32). Possible detection of these sources by the new generation of Cherenkov telescopes is discussed.

Electrodynamics in the Zero-Point Field: On the Equilibrium Spectral Energy Distribution and the Origin of Inertial Mass

Attempts at an electromagnetic explanation of the inertial mass of charged particles have recently been revived within the framework of Stochastic Electrodynamics, characterized by the adoption of a classical version of the electromagnetic zero-point field (ZPF). Recent claims of progress in that area have to some extent received support from related claims that the classical equilibrium spectrum of charged matter is that of the classically conceived ZPF. The purpose of this note is to suggest that some strong qualifications should accompany these claims. It is pointed out that a classical massless charge cannot acquire mass from nothing as a result of immersion in any EM field, and therefore that the ZPF alone cannot provide a full explanation of inertial mass. Of greater concern, it is observed that the peculiar circumstances under which classical matter is in equilibrium with the ZPF do not concur with observation.

Gamma-rays and neutrinos from the pulsar wind nebulae

We construct the time dependent radiation model for the pulsar wind nebulae (PWNe), assuming that leptons are accelerated in resonant scattering with heavy nuclei, which are injected into the nebula by the pulsar. We calculate the equilibrium spectra of these particles inside the nebula taking into account their radiation and adiabatic energy losses. The spectra of γ-rays are compared with the observations of the PWNe emitting TeV γ-rays and predictions are made for the expected γ-ray fluxes from other PWNe. Expected neutrino fluxes and neutrino event rates in a 1 km 2 neutrino detector from these nebulae are also calculated. It is found that only the Crab Nebula, and possibly the Vela nebula and MSH15-52, can produce detectable neutrino event rates. 1. Introduction Young pulsars create relativistic winds which interact with the supernova envelopes creating the PWNe. These nebulae are filled with energetic particles which emit photons from radio up to TeV γ-rays (e.g. the nebulae around the Crab and Vela pulsars, PSR 1706-44, and PSR 1509-58). It is widely argued that this radiation is produced by leptons in the synchrotron and the inverse Compton (IC) processes. Here we investigate the radiation model for the PWNe in which not only leptons but also heavy nuclei can play important role. 2. The model The energetic pulsar, formated during the supernova explosion, can have strong influence on the evolution of expanding supernova envelope due to the supply of energy in the form of electromagnetic waves and relativistic particles. We construct the simple model for the evolution of such pulsar-supernova envelope system in order to consider the processes which turn to the production of high energy radiation (see for details of the model in [3]). This model allows to determine the main parameters of the expanding nebula as a function of time (the outer radius of the nebula, the radius of the pulsar wind shock, the magnetic field inside the nebula, density of matter).

Air-Sea Interaction: Laws and Mechanisms

11R58. Air-Sea Interaction: Laws and Mechanisms. - GT Csanady (Old Dominion Univ, Norfolk VA). Cambridge UP, Cambridge, UK. 2001. 239 pp. (Softcover). ISBN 0-521-79680-6. $95.00.Reviewed by JL Lumley (Dept of Mech and Aerospace Eng, Cornell Univ, 256 Upson Hall, Ithaca NY 14853-2801).This book would make a wonderful text for a graduate-level course in air-sea interaction. The style is accessible and friendly, the descriptions very clear, and the figures excellent. Unfortunately, the index is a little sketchy, but it is not a serious problem. Csanady covers the transfer laws of the air-sea interface, wind waves and the mechanisms of air-sea transfer, mixed layers in contact, hot towers, and the ocean’s warm water sphere.The transfer laws are treated by Monin-Obukhov similarity theory, and the presentation of wind waves covers the classical work on equilibrium spectra. Turbulence generation by wave breaking is much less well understood, but is clearly presented with good diagrams. The discussion of air-side and water-side gas, heat and vapor flux is excellent. The discussion of air-side and water-side mixed layers and deep convection (hot towers and chimneys) is very clear; in addition to classical material on mixed layers that is easier to deal with analytically, there are wonderful diagrams of the real world—cloud structure, upwelling, thermocline depth, thunderstorms, squall lines, hurricanes, pycnostads (well-mixed boluses of seawater). The warm water sphere discusses the relatively shallow pool of warm water that lies on the surface of the ocean that makes it possible to live in Norway, but not at the corresponding southern latitude, and that is responsible for hurricanes and monsoons. Each chapter begins with a quite general introduction, placing the phenomenon in a global context. Although, of course, this book will be of most interest to people in meteorology, oceanography and environmental engineering, it also serves as an eye-opening introduction to the complex effects of buoyancy for mechanical engineers who are accustomed to dealing with shear and nothing else. Air-Sea Interaction: Laws and Mechanisms would make a nice addition to the bookshelf of any physical scientist, and should certainly be purchased by libraries of research universities. This reviewer finds it a little distressing that, at $95, the book is worth nearly $0.40 per page, just under seven times the cost of a photocopy.

Rotamerism and electronic spectra of aza-derivatives of stilbene and diphenylbutadiene. A combined experimental and theoretical study

The experimental results on the rotameric equilibrium and electronic spectra of aza-derivatives of trans-stilbene and 1,4-diphenylbutadiene, have been rationalized by a theoretical study which combines simple ab initio calculations of molecular energies for the ground state with a theoretical analysis of the splitting of the conjugation band developed at CS INDO CI level. All results indicate that the stable conformer of each ortho aza-derivative is that corresponding to A species. As suggested by the 1H-NMR experiments, the ab initio geometry of ZE-2-pyridylphenylbutadiene is consistent with the presence of the N·H intramolecular hydrogen bond. As regards the Franck-Condon excited states of aza-derivatives, our theoretical results show that the first singlet excited state has (π H, π L*) character in all compounds except for E-4,4′-dipyridylethene, where S 1 has (n, π*) character in non-polar solvent. In this last compound, the theoretical study of solvatochromism indicates a crossing between the 1(n, π L*) and 1(π H, π L*) states which occurs in solvents of high polarity. The inclusion of the most important doubly- and triply-excited configurations in the CI calculations shows that the 1A g − excited state is above the spectral region analyzed.

Dynamic Recharging and Stationary Fluctuation Spectra in a Colloidal Plasma

An approach to the study of dynamically recharging plasmas is presented, that generalizes a number of previous treatments of complex plasmas. It is useful in various applications involving additional charged and recharging plasma components. Consideration of a dust component charge number as an independent continuous variable makes it possible to account for dynamic recharging in a comprehensive way, and to find some important plasma characteristics. As an application, the low-frequency electromagnetic excitations in a colloidal plasma with a dynamic recharging are investigated. The equilibrium and thermal fluctuation spectra are obtained. For small fluctuation amplitudes, the intensity of the potential thermal fluctuation spectrum is found to decrease due to the presence of an extra species, whereas the level of the magnetic spectrum is not changed.

Force-Free States, Relative Strain, and Soft Elasticity in Nematic Elastomers

The remarkable ability of nematic elastomers to exhibit large deformations under small applied forces is known as soft elasticity. The recently proposed neo-classical free-energy density for nematic elastomers, derived by molecular-statistical arguments, has been used to model soft elasticity. In particular, the neo-classical free-energy density allows for a continuous spectrum of equilibria, which implies that deformations may occur in the complete absence of force and energy cost. Here we study the notion of force-free states in the context of a continuum theory of nematic elastomers that allows for isotropy, uniaxiality, and biaxiality of the polymer microstructure. Within that theory, the neo-classical free-energy density is an example of a free-energy density function that depends on the deformation gradient only through a nonlinear strain measure associated with the deformation of the polymer microstructure relative to the macroscopic continuum. Among the force-free states for a nematic elastomer described by the neo-classical free energy density, there is, in particular, a continuous spectrum of states parameterized by a pair of tensors that allows for soft deformations. In these force-free states the polymer microstructure is material in the sense that it stretches and rotates with the macroscopic continuum. Limitations of and possible improvements upon the neo-classical model are also discussed.

Momentum transfer at the ocean–atmosphere interface: the wave basis for the inertial coupling approach

The inertial coupling approach for the momentum transfer at the ocean–atmosphere interface, which is based on the assumption of a similarity hypothesis in which the ratio between the water and air reference velocities is equal to the square root of the ratio between the air and water densities, is reviewed using a wave model. In this model, the air and water reference velocities are identified, respectively, with the spectrally weighted phase velocity of the gravity waves and the Stokes velocity at the water roughness length, which are evaluated in terms of the dimensionless frequency limits in Toba's equilibrium spectrum. It is shown that the similarity hypothesis is approximately satisfied by the wave model over the range of wave ages encountered in typical sea states, and that the predicted values of the dimensionless surface drift velocity, the dimensionless water reference velocity, and the Charnock constant are in reasonable agreement with observational evidence. The application of the bulk relationship for the surface shear stress, derived from the inertial coupling hypothesis in general circulation modeling, is also discussed.

Branching of 2D tori off an equilibrium of a cosymmetric system (codimension-1 bifurcation).

The standard object for vector fields with a nontrivial cosymmetry is a continuous one-parameter family of equilibria. Characteristically, the stability spectrum of equilibrium varies along such a family, though the spectrum always contains a zero point. Consequently, in the general position a family consists of stable and unstable arcs separated by boundary equilibria, which are neutrally stable in the linear approximation. In the present paper the central manifold method and the Lyapunov-Schmidt method are used to investigate the branching bifurcation of invariant two-dimensional tori in cosymmetric systems off a boundary equilibrium whose spectrum contains, besides the requisite point 0, two pairs of purely imaginary eigenvalues. A number of new effects, as compared with the classic case of an isolated equilibrium, are found: the bifurcation studied has codimension 1 (2 for an isolated equilibrium); it is accompanied by a branching bifurcation of a normal limit cycle; and, a stable arc can be created on an unstable arc. (c) 2001 American Institute of Physics.

Origin of cosmic ray electrons

Abstract Positrons (e + ) in cosmic radiation are believed to be produced by the interactions of cosmic ray nuclei with interstellar space. e + production spectrum had been calculated using a new set of invariant cross sections for the production of pions and kaons. In the case of e − , a primary component had been added to the secondary e − produced along with e + in the galaxy. The equilibrium spectra of both e + and e − were obtained and compared with the observations. An empirical relation is given for the energy loss rate due to inverse-Compton scattering, which connects smoothly the Thompson and Klein-Nishina regimes. It is found that a simple power law injection spectrum for e − can not explain the observed [e + / (e + + e − )] ratio, and one requires a spectral flattening below about 8 GeV. Flat e − spectrum similar to that in Crab supernova with a spectral break by one power around 5 GeV could explain both the observed spectrum and the [e + / (e + + e − )], suggesting that the sources of cosmic ray e − are supernovae energized by pulsars.

Parameters of Equilibrium Spectrum of Particles in Coagulating System with Aggregate Disintegration

The formation of equilibrium spectrum of particles in a disperse system with the coagulation–fragmentation of aggregates at a steady-state shear flow was analyzed in terms of two-fraction model. It was suggested that an initial dispersed phase contains only small particles coagulating by the Brownian mechanism; the growth of larger aggregates proceeds by the gradient mechanism and is accompanied by the detachment of fragments. Parameters of equilibrium spectrum characterizing average masses and the number of particles in fine and coarse fractions were determined as functions of a flow shear rate, aggregate fractal dimension, parameters of particle interaction in aggregates, and the properties of the initial dispersed phase.

Non equilibrium spectra of degenerate relic neutrinos

We calculate the exact kinetic evolution of cosmic neutrinos until complete decoupling, in the case when a large neutrino asymmetry exists. While not excluded by present observations, this large asymmetry can have relevant cosmological consequences and in particular may be helpful in reconciling Primordial Nucleosynthesis with a high baryon density as suggested by the most recent observations of the Cosmic Microwave Background Radiation. By solving numerically the Boltzmann kinetic equations for the neutrino distribution functions, we find the momentum-dependent corrections to the equilibrium spectra and briefly discuss their phenomenological implications.

The Mean-Square Slope of Ocean Surface Waves and Its Effects on Radar Backscatter

The mean-square slope (MSS) of the sea surface for upwind and crosswind is derived, based on Phillips’ equilibrium spectrum and the model herein on gravity–capillary wave spectrum. The MSS integrated from the above two spectra over high-frequency dissipation length (1 mm) fits the optical observations very well. The radar backscatter cross section (RBCS), calculated from specular reflection theory using the Ku-band filtered MSS, is in keeping with the empirically based Ku-band models by Brown for the GEOS-3 13.9-GHz altimeter, and by Witter and Chelton for the Geosat 13.5-GHz altimeter. Also, the RBCS, calculated using the C-band filtered MSS, is in keeping with the ERS-1/-2 scatterometer empirically based algorithms CMOD3 and CMOD4. The physics included in this model on gravity–capillary wave spectrum is also illustrated. The short-wave dissipation due to wave–drift interactions has the effect of suppressing the spectral density at high wind condition, which further influences the directional spreading rate. This effect can be denoted by c2/U210 or c2/c2p dependence of short-wave spectrum. It is suggested that the kp/k dependence observed in the range of gravity waves should not be extended to the region of short waves. The parasitic capillary wave dissipation due to molecular viscosity can be balanced by the energy supply from the underlying waves, hence it is removed from the model. The eddy viscosity is due to turbulence at the wind-drift layer, which suppresses the spectrum of high-frequency waves with wavelengths on the order of millimeters.

Stationary Fluctuation Spectra and Anomalous Transport in a Dynamically Recharging Colloidal Plasma: Renormalized Approach

The low-frequency excitations in a dynamically recharging colloidal plasma are investigated on the ground of the renormalized statistical approach. The equilibrium and thermal fluctuation spectra and the anomalous transport coefficients are obtained. It is shown that the dynamic recharging conditioned by electron-dope and ion-dope interaction, gives rise to additional nonlinear broadening of the electrostatic spectrum and to renormalization of the absorption frequency. The renormalized width of the long-wave potential spectrum is much larger than the conventional one and is independent on the wavenumber, so that an energy transfer towards large wavelengths is absent. An interesting result concerning the fusion problem is that the anomalous diffusion is strongly reduced by dynamic recharging.

Excess wing in the dielectric loss of glass formers: A johari-goldstein beta relaxation?

Dielectric loss spectra of glass-forming propylene carbonate and glycerol at temperatures above and below T(g) are presented. By performing aging experiments lasting up to five weeks, equilibrium spectra below T(g) have been obtained. During aging, the excess wing, showing up as a second power law at high frequencies, develops into a shoulder. The results strongly suggest that the excess wing, observed in a variety of glass formers, is the high-frequency flank of a beta relaxation.

On the Equilibrium Spectrum of Transient Waves in the Atmosphere

The spectrum of transient heat flux in the midlatitude troposphere has a maximum at a synoptic scale. The same is true of the transient energy. The wavenumber of these maxima can be explained by the theory of nonlinear baroclinic adjustment, which is also shown to predict the shape of the spectra. According to this theory, each zonal wave has a nonlinear threshold that bounds its growth, and the bounds are larger for longer waves. The most unstable wave grows and transports heat until it reaches its threshold, at which point it breaks and saturates, passing off excess energy to the next longer wave. The process repeats, with energy cascading upscale, until the total heat transport is sufficient to reduce the meridional temperature gradient down to a relatively constant equilibrium level, independent of forcing. Thus at higher forcings more heat must be transported and the cascade extends to longer scales. At equilibrium, the longest heat-transporting wave has not saturated but rather has been rendered linearly neutral by the reduction in the temperature gradient. Observations from the real atmosphere, and computations with a quasigeostrophic two-level model in a beta-plane channel, corroborate the theory presented.

Determination of Activation Energy Spectrum for Fe<sub>40</sub>Ni<sub>40</sub>B<sub>20</sub> Metallic Glasses

Very inherent metastable character of amorphous metal alloys, induces structure phase transformations which manifest themselves in thermally activated relaxation processes. The kinetics of these processes can be interpreted with the aid of two models: two equilibrium states and spectrum of activation energies. Structure relaxation of amorphous Fe 40 Ni 40 B 20 metallic glass has been observed by measuring changes in electrical resistivity at corresponding isothermal treatments. Electrical resistance changes have been measured at liquid nitrogen temperature (78 K) using the d.c. method and a fixed probe. By measuring the resistivity change during isothermal treatment, logarithmic kinetics has been observed. Also, Q(E) function has been derived having a symmetric distribution around the value of activation energy of 2.1 eV, determined by some other methods too.