Boltzmann distribution

A new two-temperature chemical kinetics model for nitrogen plasmas is presented. The model is used together with the ûibrationally-specific collisional-radiatiûe model to study the effects of ûibrational nonequilibrium distributions on the chemical composition of two-temperature atmospheric pressure nitrogen plasmas. It is found that oûer a wide range of conditions the ûibrational leûels follow Boltzmann distributions and that the ûibrational temperature T v is well approximated by gas temperature T g at low electron number densities and by electron temperature T e at high electron number densities. This result suggests that simple kinetic models with two-temperature rate coefficients can be used to reliably model nonthermal plasmas. The calculation also yields a surprising result that, for a giûen constant gas temperature, the steady-state electron number density exhibits an S-shaped dependence on the electron temperature. This S-shaped behaûior is caused by competing ionization, charge transfer reactions, two-body dissociatiûe recombination, and three-body electron recombination reactions, and therefore is characteristic of molecular plasmas.

In this work the evolution of the surface concentration, surface potential, and surface tension for adsorption of a charged amphiphile at an interface is studied numerically. While the results are of interest for any amphiphile, the simulations are performed for typical surfactant material parameters. The surface potential is related at each time step to the instantaneous surface charge density determined by the surfactant surface concentration using the Gouy-Chapman model. The sublayer concentration at each time step is a Boltzmann distribution in instantaneous equilibrium with the surface potential. At equilibrium, the surfactant is assumed to obey the Davies adsorption isotherm.

Markov chain methods for Boltzmann sampling work in phases with decreasing temperatures. The number of transitions in each phase crucially affects terminal state distribution. We employ dynamic programming to allocate iterations to phases to improve guarantees on sample quality. Numerical experiments on the Ising model are presented.

The weakly bound HOONO product of the OHϩNO 2 ϩM reaction is studied using the vibrational predissociation that follows excitation of the first OH overtone (2 1 ). We observe formation of both cis-cis and trans-perp conformers of HOONO. The trans-perp HOONO 2 1 band is observed under thermal ͑223-238 K͒ conditions at 6971 cm Ϫ1 . We assign the previously published ͑warmer temperature͒ HOONO spectrum to the 2 1 band at 6365 cm Ϫ1 and 2 1 -containing combination bands of the cis-cis conformer of HOONO. The band shape of the trans-perp HOONO spectrum is in excellent agreement with the predicted rotational contour based on previous experimental and theoretical results, but the apparent origin of the cis-cis HOONO spectrum at 6365 cm Ϫ1 is featureless and significantly broader, suggesting more rapid intramolecular vibrational redistribution or predissociation in the latter isomer. The thermally less stable trans-perp HOONO isomerizes rapidly to cis-cis HOONO with an experimentally determined lifetime of 39 ms at 233 K at 13 hPa ͑in a buffer gas of predominantly Ar͒. The temperature dependence of the trans-perp HOONO lifetime in the range 223-238 K yields an isomerization barrier of 33Ϯ12 kJ/mol. New ab initio calculations of the structure and vibrational mode frequencies of the transition state perp-perp HOONO are performed using the coupled cluster singles and doubles with perturbative triples ͓CCSD͑T͔͒ model, using a correlation consistent polarized triple basis set ͑cc-pVTZ͒. The energetics of cis-cis, trans-perp, and perp-perp HOONO are also calculated at this level ͓CCSD͑T͒/ cc-pVTZ͔ and with a quadruple basis set using the structure determined at the triple basis set ͓CCSD͑T͒/cc-pVQZ//CCSD͑T͒/cc-pVTZ͔. These calculations predict that the anti form of perp-perp HOONO has an energy of ⌬E 0 ϭ42.4 kJ/mol above trans-perp HOONO, corresponding to an activation enthalpy of ⌬H 298 ‡0 ϭ41.1 kJ/mol. These results are in good agreement with statistical simulations based on a model developed by Golden, Barker, and Lohr. The simulated isomerization rates match the observed decay rates when modeled with a trans-perp to cis-cis HOONO isomerization barrier of 40.8 kJ/mol and a strong collision model. The quantum yield of cis-cis HOONO dissociation to OH and NO 2 is also calculated as a function of photon excitation energy in the range 3500-7500 cm Ϫ1 , assuming D 0 ϭ83 kJ/mol. The quantum yield is predicted to vary from 0.15 to 1 over the observed spectrum at 298 K, leading to band intensities in the action spectrum that are highly temperature dependent; however, the observed relative band strengths in the cis-cis HOONO spectrum do not change substantially with temperature over the range 193-273 K. Semiempirical calculations of the oscillator strengths for 2 1 (cis-cis HOONO) and 2 1 (trans-perp HOONO) are performed using ͑1͒ a one-dimensional anharmonic model and ͑2͒ a͒

The paper investigates the idle operating condition of a current production turbocharged Gasoline Direct Injected (GDI) high performance engine both from an experimental and a numerical perspective. Due to the low engine speed, to the low injection pressure and to the null contribution of the turbocharger, the engine condition is far from the standard points of investigation. According to the low heat flux due to combustion, temperature levels are low and reduced fuel evaporation is expected. Consequently, fuel spray evolution within the combustion chamber and spray/wall interaction are key points for the understanding of the combustion process.
In order to properly investigate and understand the many complex phenomena, a wide set of engine speeds was experimentally investigated and, as far as the understanding of the physics of spray/wall interaction is concerned, many different injection strategies are tested. Among the wide set of experiments, the present paper focuses on a restricted portion which is then numerically reproduced and further investigated.
UV-visible imaging and spectral measurements are carried out in the engine to investigate the spray characteristics and flame propagation. Measurements are performed in the optically accessible combustion chamber realized by modifying the actual engine. The cylinder head is modified in order to allow the visualization of the fuel injection and the combustion process in the fourth cylinder using a high spatial and temporal resolution ICCD detector.
The complete engine cycle is reproduced by means of 3D-CFD simulations using a commercial code; due to the many physical sub-models an ad hoc numerical methodology is validated and implemented. The CFD models are validated against experiments and particular care is devoted to the spray and wall film simulations. A lagrangian approach is implemented in order to simulate the GDI multihole spray. The experimental and numerical comparisons, in terms fuel mixing and flame front propagation, give a good understanding of the idle condition.
CFD analyses prove to be a very useful tool to investigate and understand the effects generated by the direct injection into the combustion chamber and they integrate the information provided by the optical investigations.

In generalized statistical mechanics the second link is customarily relaxed. Of course, the generalized exponential function defining the probability distribution function after inversion, produces a generalized logarithm Λ(pi). But, in general, the mean value of −Λ(pi) is not the entropy of the system. Here we reconsider the question first posed in [Phys. Rev. E 66, 056125 (2002) and 72, 036108 ], if and how is it possible to select generalized statistical theories in which the above mentioned twofold link between entropy and the distribution function continues to hold, such as in the case of ordinary statistical mechanics.

Ion acoustic shock waves in dissipative plasmas are studied. The target medium contains Relativistic ions, nonthermal electrons and positrons with Maxwell–Boltzmann distribution. Kinematic viscosity among the plasma constituents has been considered. The effects of kinematic viscosity on the general behavior of plasma and specifically on nonthermal distribution of electrons are studied. Results would be helpful for understanding the localized structures that may occur in space plasmas.

The phenomenon of Debye shielding is investigated in a dusty plasma consisting of Boltzmann electrons and ions, and negatively charged, massive dust grains. Both small and large amplitude electrostatic potentials are considered and a parameter study conducted.

We review the historical and modern understanding of the most basic equation of friction, Amontons' law, which describes phenomena that were already understood and studied by Leonardo da Vinci 500 years ago. This law states that for any two materials the (lateral) friction force is directly proportional to the (normal) applied load, with a constant of proportionality, the friction coefficient, that is constant and independent of the contact area, the surface roughness, and the sliding velocity. No theory has yet satisfactorily explained this surprisingly general law; all attempts have been model or system dependent. We review the experimental evidence and find, for example, that the same friction coefficient is often measured for the same system of materials with junctions whose areas differ by more than 6 orders of magnitude. The trends obtained through molecular dynamics (MD) simulations agree with recent and past experiments and with Amontons' law, and they suggest that the local energy-dissipating mechanisms are not merely "mechanical", as assumed in most models, but "thermodynamic" in nature, like miniature irreversible compression-decompression cycles of the trapped molecules between the surface asperities as they pass over each other. The MD analysis reveals that, for such dynamic, nonequilibrium, energy-dissipating processes, a proper statistical description can be formulated through the use of the Weibull distribution of the local friction forces, which may be regarded to serve in this context a similar purpose as the Boltzmann distribution for classical systems at equilibrium. Another important conclusion is that the concept of the "real" area of contact is a nonfundamental quantity, whether at the nano-, micro-, or macroscale. However, it may serve as a convenient scaling parameter for describing the really fundamental parameters, which are the number density of atoms, molecules, or bonds involved in an adhesive or frictional interaction.

We propose the multipoint Metropolis algorithm as an extension of the orientationalbias Monte Carlo of Frenkel and Smit. A ratio statistics similar to that in the Metropolis algorithm is introduced to maintain the detailed balance. The multipoint idea can be applied to improve the efficiency of a general Markov chain-based Monte Carlo algorithm. To illustrate, we describe two variations of the idea-the random-grid Metropolis and the multipoint Hybrid Monte Carlo-and apply them to a number of examples.

Traditionally, it is understood that fluctuations in the equilibrium distribution are not evident in thermodynamic systems of large $N$ (the number of particles in the system) \cite{Huang}. In this paper we examine the validity of this perception by investigating whether such fluctuations can in reality depend on temperature. Firstly, we describe fluctuations in the occupation numbers of the energy levels in the microcanonical ensemble, using previously unknown identities that we have derived for the purpose, which allow us to calculate the moments of the occupation numbers. Then we compute analytically the probability distribution of these fluctuations. We show that, for every system of fixed and finite $N$, fluctuations about the equilibrium distribution do in fact depend on the temperature. Indeed, at higher temperatures the fluctuations can be so large that the system does not fully converge on the Maxwell-Boltzmann distribution but actually fluctuates around it. We term this st...

Optimized geometries, HOMO-LUMO gaps, vertical ionization potentials and electron affinities are obtained using HF, and B3LYP methods with 6-311G, B3LYP calculations are performed with LANL2DZ effective core potential. Electron correlation is included by doing MP2 calculation. The harmonic frequencies of all the compounds are obtained using B3LYP with 6-311G** and/or LANL2DZ basis sets. The force field and vibrational spectra are analyzed and 74 symmetry unique non-redundant local force constants are evaluated. Probable assignments are proposed for all the fundamentals based on the potential energy distribution. q

This paper proposes the Protein Ensemble Method (PEM) to model equilibrium fluctuations in proteins where fragments of the protein polypeptide chain can move independently of one another. PEM models global equilibrium fluctuations of a polypeptide chain by combining local fluctuations of consecutive overlapping fragments of the chain. Local fluctuations are computed by a probabilistic exploration that exploits analogies between proteins and robots. All generated conformations are subjected to energy minimization and then are weighted according to a Boltzmann distribution. Using the theory of statistical mechanics the Boltzmann-weighted fluctuations corresponding to each fragment are combined to obtain fluctuations for the entire protein. The agreement obtained between PEM-modeled fluctuations, wet-lab experiment and guided simulation measurements, indicates that PEM is able to reproduce with high accuracy protein equilibrium fluctuations that occur over a broad range of timescales.

This work introduces a link-based covariance measure between the nodes of a weighted directed graph where a cost is associated to each arc. To this end, a probability distribution on the (usually infinite) countable set of paths through the graph is defined by minimizing the total expected cost between all pairs of nodes while fixing the total relative entropy spread in the graph. This results in a Boltzmann distribution on the set of paths such that long (high-cost) paths occur with a low probability while short (low-cost) paths occur with a high probability. The sum-over-paths (SoP) covariance measure between nodes is then defined according to this probability distribution: two nodes are considered as highly correlated if they often co-occur together on the same -preferably shortpaths. The resulting covariance matrix between nodes (say n nodes in total) is a Gram matrix and therefore defines a valid kernel on the graph. It is obtained by inverting a n × n matrix depending on the costs assigned to the arcs. In the same spirit, a betweenness score is also defined, measuring the expected number of times a node occurs on a path. The proposed measures could be used for various graph mining tasks such as computing betweenness centrality, semi-supervised classification of nodes, visualization, etc, as shown in the experimental section.

The Korteweg-de Vries-Burgers (KdV-Burgers) equation and modified Korteweg-de Vries-Burgers equation are derived in strongly coupled dusty plasmas containing nonthermal ions and Boltzmann distributed electrons. It is found that solitary waves and shock waves can be produced in this medium. The effects of important parameters such as ion nonthermal parameter, temperature, density and velocity on the properties of shock waves and solitary waves are discussed.

General fluid dispersion relations for the Jeans instability in a complex plasma have been derived in two cases: (i) electrons, positive ions and negative ions are all Boltzmann distributed and dust grains are cold and inertial, (ii) electrons are Boltzmann distributed, positive ions and negative ions are inertial and dust grains are streaming. In both the cases grain charge fluctuation has been considered. Results of earlier studies are special cases of these general disperssion relations. Both the disperssion relations show the presence of negative ions reduces the threshold of the Jeans instability in the complex plasma system. Streaming motion of dust grains is responsible for the devlopment of an unstable mode which is not purely growing.

New insights into interdisciplinary engineering endeavors, from classical modeling to nano-macroscale extrapolation and critical evaluation, weigh heavily on the pervasive nature of thermodynamics in the physical world. Just as statistical thermodynamic approaches provide a beneficial complement to a process-based macroscale thermodynamic approaches with physical systems, a Lagrangian approach to energetics in biological systems can, we believe, provide a beneficial complement to popular Eulerian approaches.

A study of laser-generated plasma by visible laser ablation of aluminium, in high vacuum (3 · 10 À7 mbar), by using 3 ns Nd:YAG laser radiation, is reported. Nanosecond pulsed ablation, at intensity of the order of 10 10 W/cm 2 , gives an emission of neutral and charged particles. A special mass quadrupole spectrometer, operating in the 1-300 amu mass range, was used to analyse the energetic atomic emission produced by the laser ablation. Neutrals show typical Boltzmann distributions, directly correlated to the plasma temperature, while ions show Coulomb-Boltzmann-shifted distributions depending on their charge state. Surface profiles of the craters and microscopy investigations permitted to study the ablation threshold and the ablation yields. The multi-component structure of the plasma plume emission is investigated in terms of charge state, neutrals and ions temperature. A special regard is given to the study of the ion acceleration process occurring inside the plasma due to a high electrical field generated in the non-equilibrium plasma. The angular distributions of the neutral and ion particles are also presented and discussed.

Dystrophin-deficient muscle fibers from mdx mice are believed to suffer from increased calcium entry and elevated submembranous calcium level, the actual source and functional consequences of which remain obscure. Here we compare the properties of the dihydropyridine receptor as voltage sensor and calcium channel in control and mdx muscle fibers, using the silicone-voltage clamp technique. In control fibers charge movement followed a two-state Boltzmann distribution with values for maximal charge, midpoint voltage, and steepness of 23 6 2 nC/mF, ÿ37 6 3 mV, and 13 6 1 mV (n ¼ 7). Essentially identical values were obtained in mdx fibers and the time course of charge recovery from inactivation was also similar in the two populations (t ' 6 s). In control fibers the voltage dependence of the slow calcium current elicited by 100-ms-long pulses gave values for maximal conductance, apparent reversal potential, half-activation potential, and steepness factor of 156 6 15 S/F, 65.5 6 2.9 mV, ÿ0.76 6 1.2 mV, and 6.2 6 0.5 mV (n ¼ 17). In mdx fibers, the half-activation potential of the calcium current was slightly more negative (ÿ6.2 6 1.2 mV, n ¼ 16). Also, when using longer pulses, the time constant of calcium current decay was found to be significantly larger (by a factor of 1.5-2) in mdx than in control fibers. These changes in calcium current properties are unlikely to be primarily responsible for a dramatic alteration of intracellular calcium homeostasis. They may be speculated to result, at least in part, from remodeling of the submembranous cytoskeleton network due to the absence of dystrophin.

The chaotic profile of dust grain dynamics associated with dust-acoustic oscillations in a dusty plasma is considered. The collective behaviour of the dust plasma component is described via a multi-fluid model, comprising Boltzmann distributed electrons and ions, as well as an equation of continuity possessing a source term for the dust grains, the dust momentum and Poisson's equations. A Van der Pol-Mathieu-type nonlinear ordinary differential equation for the dust grain density dynamics is derived. The dynamical system is cast into an autonomous form by employing an averaging method. Critical stability boundaries for a particular trivial solution of the governing equation with varying parameters are specified. The equation is analysed to determine the resonance region, and finally numerically solved by using a fourth-order Runge-Kutta method. The presence of chaotic limit cycles is pointed out.

A Boolean structure of the genetic code where Boolean deductions have biological and physicochemical meanings was discussed in a previous paper. Now, from these Boolean deductions we propose to define the value of amino acid information in order to consider the genetic information system as a communication system and to introduce the semantic content of information ignored by the conventional information theory. In this proposal, the value of amino acid information is proportional to the molecular weight of amino acids with a proportional constant of about 1.96×10 25 bits per kg. In addition to this, for the experimental estimations of the minimum energy dissipation in genetic logic operations, we present two postulates: (1) the energy E i (i = 1, 2, . . . , 20) of amino acids in the messages conveyed by proteins is proportional to the value of information, and (2) amino acids are distributed according to their energy E i so the amino acid population in proteins follows a Boltzmann distribution. Specifically, in the genetic message carried by the DNA from the genomes of living organisms, we found that the minimum energy dissipation in genetic logic operations was close to kT Ln(2) joules per bit.

A rigorous theoretical investigation has been made of obliquely propagating electrostatic solitary structures in a hot magnetized dusty plasma which consists of a negatively charged, extremely massive, hot, dust Ñuid and Maxwellian distributed ions and electrons. The reductive perturbation method has been employed to derive the KortewegÈde Vries (KÈdV) equation which admits a solitary wave solution for small but Ðnite amplitude limit. It has been shown that the e †ects of dust-temperature, obliqueness, magnetic Ðeld and free electrons have changed the nature of the electrostatic solitary structures. The result of the present investigation for unmagnetized case, parallel propagation, no free electron and cold dust Ñuid completely agrees with the existing published results (Mamun et al. [4]).

Thin current sheets represent important and puz- zling sites of magnetic energy storage and subsequent fast release. Such structures are observed in planetary magneto- spheres, solar atmosphere and are expected to be widespread in nature. The thin current sheet structure resembles a col- lapsing MHD solution with a plane singularity. Being po- tential sites of effective energy accumulation, these struc-

We introduce a fractional Kramers equation for a particle interacting with a thermal heat bath and external non-linear force field. For the force free case the velocity damping follows the Mittag-Leffler relaxation and the diffusion is enhanced. The equation obeys the generalized Einstein relation, and its stationary solution is the Boltzmann distribution. Our results are compared to previous results on enhanced Lévy type of diffusion derived from stochastic collision models.

Variable-rate data transmission schemes in which constellation points are selected according to a nonuniform probability distribution are studied. When the criterion is one of minimizing the average transmitted energy for a given average bit rate, the best possible distribution with which to select constellation points is a Maxwell-Bdtzmann distribution. In principle, when constellation points are selected according to a Maxwell-Boltzmann distribution, the ultimate shaping gain (7re/6 or 1.53 dB) can be achieved in any dimension. Nonuniform signaling schemes can be designed by mapping simple variable-length prefix codes onto the constellation. Using the Huffman procedure, prefix codes can be designed that approach the optimal performance. These schemes provide a fixed-rate primary channel and a variable-rate secondary channel, and are easily incorporated into standard lattice-type coded modulation schemes.

We present measurements of neutron scattering from solid 4 He at high momentum transfer. The solid is held close to the melting line at molar volume 20:87 cm 3 =mol and temperature T 1:6 K. From the data, we determine the shape of the momentum distribution, nk, of atoms in the solid and the leading final state contribution to the scattering. We show that nk in this highly anharmonic, quantum solid differs significantly from a Gaussian. The nk is more sharply peaked with larger occupation of low momentum states than in a Maxwell-Boltzmann distribution, as found in liquid 4 He and predicted qualitatively by path integral Monte Carlo calculations. The atomic kinetic energy is hKi 24:25 0:30 K. If nk is assumed to be Gaussian, as is usually the practice, a hKi 10% smaller is obtained.

By using the reductive perturbation theory, the Kadomstev-Petviashvili (KP) equation in unmagnetized dusty plasmas with variable dust charge, electrons with Boltzmann distribution and nonthermal ions, is derived and the propagation of nonlinear waves is analyzed. It is found that compressive and rarefactive solitons can be appeared. Amplitude of solitonic solutions of KP equation becomes diverges at the critical densities.

We investigate a family of single-particle anomalous velocity distribution by solving a particular class of stochastic Liouville equations. The stationary state is obtained analytically and the Maxwell-Boltzmann distribution is reobtained in a particular limit. We discuss the comparison with other different methods to obtain the stationary state. Extensions when the models cannot be solved in an exact way are also pointed out in connection with the one-ficton approximation.

We incorporate ion polarizabilities into the Poisson-Boltzmann equation by modifying the effective dielectric constant and the Boltzmann distribution of ions. The extent of the polarizability effects is controlled by two parameters, γ(1) and γ(2); γ(1) determines the polarization effects in a dilute system and γ(2) regulates the dependence of the polarizability effects on the concentration of ions. For a polarizable ion in an aqueous solution γ(1) ≈ 0.01 and the polarizability effects are negligible. The conditions where γ(1) and/or γ(2) are large and the polarizability is relevant involve the low dielectric constant media, high surface charge, and/or large ionic concentrations.

Dust acoustic solitary waves are studied in a four-component dusty plasma. Positively and negatively charged mobile dust and Boltzmann-distributed electrons are considered. The ion distribution is taken as nonthermal. The Korteweg-de Vries equation is derived using reductive perturbation technique. We are able to reproduce the results obtained by Sayed and Mamun ͓Phys. Plasmas 14, 014501 ͑2007͔͒ provided the Boltzmann distribution is considered for the ions. Higher order inhomogeneous differential equation is obtained for the dressed soliton. By using the renormalization method of Kodama and Taniuti ͓J. Phys. Soc. Jpn. 45, 298 ͑1978͔͒, we derived the expression for the dressed soliton.

A low-cost Raman system was constructed and used to perform Raman scattering measurements on liquid carbon disulfide at different sample temperatures. The 1 and 3 bands are identified based on the frequencies calculated by the normal mode analysis. The ratio of the intensities of the anti-Stokes and Stokes bands can be used to illustrate the Boltzmann distribution of the molecules among the vibrational energy levels.

Mesoscale experiment and simulation permit harvesting information about both geometric features and texture in polycrystals. The grain boundary character distribution (GBCD) is an empirical distribution of the relative length [in two dimensions (2D)] or area (in 3D) of an interface with a given lattice misorientation and normal. During the growth process, an initially random distribution of boundary types reaches a steady state that is strongly correlated to the interfacial energy density. In simulation, it is found that if the given energy density depends only on lattice misorientation, then the steady-state GBCD and the energy are related by a Boltzmann distribution. This is among the simplest nonrandom distributions, corresponding to independent trials with respect to the energy. In this paper, we derive an entropy-based theory that suggests that the evolution of the GBCD satisfies a Fokker-Planck equation, an equation whose stationary state is a Boltzmann distribution. Cellular structures coarsen according to a local evolution law, curvature-driven growth, and are limited by space-filling constraints. The interaction between the evolution law and the constraints is governed primarily by the force balance at triple junctions, the natural boundary condition associated with curvature-driven growth, and determines a dissipation relation. A simplified coarsening model is introduced that is driven by the boundary conditions and reflects the network level dissipation relation of the grain growth system. It resembles an ensemble of inertia-free spring-mass dashpots. Application is made of the recent characterization of Fokker-Planck kinetics as a gradient flow for a free energy in deriving the theory. The theory predicts the results of large-scale two-dimensional simulations and is consistent with experiment.

Dust acoustic double layers are studied in a four component dusty plasma. Positively and negatively charged mobile dust and Boltzmann distributed electrons are considered. The ion distribution is taken as nonthermal. The existence of compressive and rarefractive double layers is studied by pseudopotential approach. The effect of non-thermal ions on small amplitude and arbitrary amplitude double layers are also studied.

Thin current sheets (TCSs) are sites of energy storage and release in the Earth's magnetosphere. A self-consistent analytical model of 1D TCS is presented in which the tension of the magnetic field lines is balanced by ion inertia rather than plasma pressure. The influence of the electron population and the corresponding electrostatic electric fields required to maintain quasineutrality are taken into account under the realistic assumption that electron motion is fast enough to support quasi-equilibrium Boltzmann distribution along field lines. Electrostatic effects can lead to specific features of local current density profiles inside TCS, for example, to their partial splitting. The dependence of electrostatic effects on the electron temperature, the form of electron distribution function, and the curvature of magnetic field lines are analyzed. Possible implications of these effects on the fine structure of current sheets and some dynamic phenomena in the Earth's magnetotail are discussed.

The absolute value of the quantum yield of the fluorescence of the 1B3u 0-0 state of pyrazine as a function of the rotational quantum numbers de Lange, Pieter J.; van der Meer, Barend J.; Drabe, Karel E.; Kommandeur , Jan; Meerts, W. Leo; Majewski, W. A. . The absolute value of the quantum yield of the fluorescence of the 1B3u 0-0 state of pyrazine as a function of the rotational quantum numbers. Journal of Chemical Physics, 86 , 4004-4010.

Arbitrary amplitude dust acoustic waves in a dusty plasma with a high-energy-tail electron distribution are investigated. The effects of charge variation and electron deviation from the Boltzmann distribution on the dust acoustic soliton are then considered. The dust charge variation makes the dust acoustic soliton more spiky. The dust grain surface collects less electrons as the latter evolves far away from their thermodynamic equilibrium. The dust accumulation caused by a balance of the electrostatic forces acting on the dust grains is more effective for lower values of the electron spectral index. Under certain conditions, the dust charge fluctuation may provide an alternate physical mechanism causing anomalous dissipation, the strength of which becomes important and may prevail over that of dispersion as the suprathermal character of the plasma becomes important. Our results may explain the strong spiky waveforms observed in auroral plasmas.

Dynamic aspects of the electroosmotic flow (EOF) in a cylindrical capillary are analysed. An analytical solution for electrostatic potential of the double layer has been derived by solving the complete Poisson-Boltzmann equation for arbitrary zeta-potentials under an analytical scheme. Transient EOF field in response to the application of time dependent electric field is obtained analytically by using GreenÕs function method. Specifically, sinusoidally alternating (AC) electric fields are used to study the effect of frequency-dependent oscillation on the EOF. Limiting cases of zero frequency and pulsed electric field are also discussed.

The chaotic profile of dust grain dynamics associated with dust-acoustic oscillations in a dusty plasma is considered. The collective behaviour of the dust plasma component is described via a multi-fluid model, comprising Boltzmann distributed electrons and ions, as well as an equation of continuity possessing a source term for the dust grains, the dust momentum and Poisson's equations. A Van der Pol-Mathieu-type nonlinear ordinary differential equation for the dust grain density dynamics is derived. The dynamical system is cast into an autonomous form by employing an averaging method. Critical stability boundaries for a particular trivial solution of the governing equation with varying parameters are specified. The equation is analysed to determine the resonance region, and finally numerically solved by using a fourth-order Runge-Kutta method. The presence of chaotic limit cycles is pointed out.

A new method to calculate two-and three-body collisions in a non-dilute gas is introduced and applied to a Maxwell-Boltzmann distribution at a given density and temperature. The number of two-and three-body scatterings is computed and compared to an analytical result. The agreement of the numerical to the analytical calculation is excellent for all temperatures, densities and elementary cross sections. The method is extended to quantum gases for future heavy-ion collision applications. We discuss the differences between the classical and the Fermi-Dirac distribution and in particular demonstrate the important role of Pauli blocking even at temperatures as high as 100 MeV.

Two sets of high quality income data are analysed in detail, one set from the UK, one from the USA. It is firstly demonstrated that both a log-normal distribution and a Boltzmann distribution can give very accurate fits to both these data sets. The absence of a power tail in the US data set is then discussed. Taken in conjunction with detailed evidence from the UK and Japanese income data, a strong case is made for the mathematically separate treatment of waged and unwaged income. The authors present a case for preferring the use of the Boltzmann distribution over the log-normal function, this leads to a brief review of the work of a number of researchers, which shows that a coherent theory for the distribution of all income can be postulated.

The Khinchin theorem provides the condition that a stationary process is ergodic, in terms of the behavior of the corresponding correlation function. Many physical systems are governed by non-stationary processes in which correlation functions exhibit aging. We classify the ergodic behavior of such systems and provide a generalization of Khinchin's theorem. Our work quantifies deviations from ergodicity in terms of aging correlation functions. Using the framework of the fractional Fokker-Planck equation we obtain a simple analytical expression for the two-time correlation function of the particle displacement in a general binding potential, revealing universality in the sense that the binding potential only enters into the prefactor through the first two moments of the corresponding Boltzmann distribution. We discuss applications to experimental data from systems exhibiting anomalous dynamics.

Statistical models of economic distributions lead to Boltzmann distributions rather than a Pareto power law. This result is supported by two facts: 1. the distributions of income, car sales, marriages or jobs are a matter of chances and luck and not of reason! 2. Data for property, automobile sales, marriages and job markets were analyzed by two models: the Pareto law and the Boltzmann distribution of stochastic systems. In all cases the best fits to data were obtained by the Boltzmann function. This may indicate that the principles of stochastic systems like in physics, chemistry, thermodynamics may also be applied to economic systems.

The theory for the calculation of excited state dipole moments from electrooptical emission measurements, developed by Baumann and Deckers (Ber. Bunsenges. Phys. Chem. 81 (1977) 786) presupposes a Boltzmann distribution for the emitting molecules. Using the anisotropic rotational diffusion model and taking into account all important electric field induced effects, we derive equations that describe quantitatively the electric field effect on the fluorescence of an ensemble of solute rigid molecules which are not yet equilibrated with respect to their orientation when emitting. Numerical simulations are performed to compare the general case and the limiting case of a prevailing Boltzmann distribution and to examine the influence of "slip" and "stick" boundary conditions, as well as the assumption of isotropic diffusion.

A new, low power capacitively coupled plasma microtorch (30 W, 13.56 MHz, 0.5 L min −1 Ar) was investigated in conjunction with commercially available microspectrometers for the simultaneous multielemental analysis by atomic emission spectrometry of liquid samples without desolvation. Emission spectrum is simpler than in ICP-AES, the resonance lines are the most intense, so that a microspectrometer with FWHM of at least 1.5 nm is satisfactory for the record. The deviation from the Boltzmann distribution for Fe I has demonstrated the departure from the LTE in plasma. The non-spectral matrix effects of Li, Na, K, Ca and Mg on analytes emission are depressive and depend on matrix volatility, ionization potential of the interferent and analyte excitation energy. The detection limits (μg mL −1 ) are in the range 0.003 (Li) and 1.5 (Mn). The use of the standard additions method allowed the simultaneous determination of elements in environmental certified reference materials with overall recovery of 95 ± 10% and relative standard deviation of 1.7-8.2%. Compared to the traditional ICP, the microtorch has a simple construction, runs at low argon flow and can be integrated in a portable system suitable for in-situ simultaneous determination of elements.

The Kramers' theory of activated processes is generalized for nonequilibrium open one-dimensional systems. We consider both the internal noise due to thermal bath and the external noise which are stationary, Gaussian and are characterized by arbitrary decaying correlation functions. We stress the role of a nonequilibrium stationary state distribution for this open system which is reminiscent of an equilibrium Boltzmann distribution in calculation of rate. The generalized rate expression we derive here reduces to the specific limiting cases pertaining to the closed and open systems for thermal and non-thermal steady state activation processes. PACS number(s) : 05.40.-a, 02.50.Ey, 05.70.Ln, 82.20.-w Typeset using REVT E X

We analyze the structure of stochastic dynamics near either a stable or unstable fixed point, where force can be approximated by linearization. We find that a cost function that determines a Boltzmann-like stationary distribution can always be defined near it. Such a stationary distribution does not need to satisfy the usual detailed balance condition, but might have instead a divergence-free probability current. In the linear case the force can be split into two parts, one of which gives detailed balance with the diffusive motion, while the other induces cyclic motion on surfaces of constant cost function. Using the Jordan transformation for the force matrix, we find an explicit construction of the cost function. We discuss singularities of the transformation and their consequences for the stationary distribution. This Boltzmann-like distribution may be not unique, and nonlinear effects and boundary conditions may change the distribution and induce additional currents even in the neighborhood of a fixed point.