A cluster expansion approach to a one-dimensional Boltzmann equation: A validity result

We consider a stochastic particle system on the line and prove that, when the number of particles diverges and the probability of a collision is suitably rescaled, the system is well described by a one-dimensional Boltzmann equation. The result holds globally in time, without any smallness assumption.     

Self-similar model of laser-induced plasma expansion affected by radiation pressure

In a stage of evolved gasdynamics a self-similar solution of laser plasma isothermal expansion including radiation pressure has been found and discussed with respect to D and D + shock profiles time evolution.     

The one-dimensional kinetic Ising model: A series expansion study

Exact power series expansions (through eight terms) in the time are derived for relaxation in the one-dimensional Ising model with nearest-neighbor interactions for a general rate parameter where the activation energy is a variable fraction of the energy required to break nearest-neighbor bonds. It is found that the qualitative nature of the relaxation is very dependent on this parameter, varying from nearly simple exponential decay (as with Glauber dynamics) for an intermediate value of this parameter, to an initial rate of change that is either much slower or faster than a simple exponential at the extremes of the range of variation of the parameter. The rate equations for the limit of rapid internal diffusion (internal equilibration) are integrated for several special values of the rate parameter. In general the internal equilibration approximation is not a good representation of the relaxation except when the relaxation is similar to Glauber dynamics.     

膨胀腔消声器声学仿真的一维修正方法

传统一维方法计算消声器声学性能随频率增加误差加大,本文应用管道末端修正系数改善一维方法的计算结果。应用二维轴对称解析方法计算管道末端修正系数,研究结构因素和频率对修正系数的影响规律,研究表明修正系数随截面半径比增加而降低,随频率增加而增加,超过截止频率后修正系数无效。根据计算结果给出修正系数拟合公式并修正传统一维方法,应用一维修正方法计算膨胀腔消声器的传递损失并和实验结果、三维有限元结果进行比较,证明一维修正方法结果精度有明显提高。     

Ion acceleration during adiabatic plasma expansion: Renormalization group approach

The renormalization group approach is applied to derive an exact solution to self-consistent Vlasov kinetic equations for plasma particles in the quasineutral approximation. The solution obtained describes the one-dimensional adiabatic expansion into vacuum of a plasma bunch with arbitrary initial velocity distributions of the electrons and ions. The ion acceleration is investigated for both a Maxwellian two-temperature initial electron distribution and a super-Gaussian initial electron distribution.     

Self-similar approach to market analysis

A novel approach to analyzing time series generated by complex systems, such as markets, is presented. The basic idea of the approach is the Law of Self-Similar Evolution, according to which any complex system develops self-similarly. There always exist some internal laws governing the evolution of a system, say of a market, so that each of such systems possesses its own character regulating its behaviour. The problem is how to discover these hidden internal laws defining the system character. This problem can be solved by employing the self-similar approximation theory, which supplies the mathematical foundation for the law of self-similar evolution. In this report, the theoretical basis of the new approach to analyzing time series is formulated, with an accurate explanation of its principal points. Received 15 August 2000     

Self-similar and charged radiating spheres: an anisotropic approach

Considering charged fluid spheres as anisotropic sources and the diffusion limit as the transport mechanism, we suppose that the inner space–time admits self-similarity. Matching the interior solution with the Reissner–Nordström–Vaidya exterior one, we find an extremely compact and oscillatory final state with a redistribution of the electric charge function and non zero pressure profiles.     

Residual conductance of correlated one-dimensional nanosystems: A numerical approach

We study a method to determine the residual conductance of a correlated system by means of the ground-state properties of a large ring composed of the system itself and a long non-interacting lead. The transmission probability through the interacting region, and thus its residual conductance, is deduced from the persistent current induced by a flux threading the ring. Density Matrix Renormalization Group techniques are employed to obtain numerical results for one-dimensional systems of interacting spinless fermions. As the flux dependence of the persistent current for such a system demonstrates, the interacting system coupled to an infinite non-interacting lead behaves as a non-interacting scatterer, but with an interaction dependent elastic transmission coefficient. The scaling to large lead sizes is discussed in detail as it constitutes a crucial step in determining the conductance. Furthermore, the method, which so far had been used at half filling, is extended to arbitrary filling and also applied to disordered interacting systems, where it is found that repulsive interaction can favor transport.Received: 19 January 2004, Published online: 18 June 2004PACS: 73.23.-b Electronic transport in mesoscopic systems - 71.10.-w Theories and models of many-electron systems - 05.60.Gg Quantum transport - 73.63.Nm Quantum wires     

Effect of ionization on laser-induced plume self-similar expansion

The dynamics of a laser ablation plume during the first stage of its expansion, just after the termination of the laser pulse is modelled. The one-dimensional expansion of the evaporated material, considered as an ideal fluid, is governed by one-fluid Euler equations. For high energetic ions, the charge separation can be neglected and the hydrodynamics equations solved using self-similar formulation. Numerical solution is obtained, first when the laser fluence range is low enough to deal with a neutral vapor, and in a second stage, when ionization effects on the expansion are taken into account, for different material targets. As a main result, we found that the presence of ions in the evaporated gas enhances the self-similar expansion.     

A mechanical approach to one-dimensional interacting gas

Derivations of the van der Waals equation typically use standard recipes involving ensemble averages of statistical mechanics. In this work, we study a box of weakly interacting gas particles in one-dimension by explicitly incorporating the mechanical point of view. This has the merit that it not only reproduces the van der Waals equation but also tells us some extra interesting physics not immediately clear from a pure statistical mechanical approach. For example, we show that the traditional handwaving argument leading to van der Waals equation requires closer scrutiny if it is to get things right.     

A cold plasma plume with a highly conductive liquid electrode

A cold dielectric barrier discharge （DBD） plasma plume with one highly conductive liquid electrode has been developed to treat thermally sensitive materials, and its preliminary discharging characteristics have been studied. The averaged electron temperature and density is estimated to be 0.6eV and 1011/cm3, respectively. The length of plasma plume can reach 5cm with helium gas （He）, and the conductivity of the outer electrode affects the plume length obviously. This plasma plume could be touched by bare hand without causing any burning or painful sensation, which may provide potential application for safe aseptic skin care. Moreover, the oxidative particles （e.g., OH, O＊, 03） in the downstream oxygen （02） gas of the plume have been applied to treat the landfill leachate. The results show that the activated 02 gas can degrade the landfill leachate effectively, and the chemical oxygen demand （COD）, conductivity, biochemical oxygen demand （BOD）, and suspended solid （SS） can be decreased by 52%, 57%, 76% and 92%, respectively.     

Temperature dependence of EPR linewidth in one-dimensional magnets: A quasi-classical approach

An analytical expression for the EPR linewidth of an exchange-coupled 1/2-spin chain originating from uniform Dzyaloshinskii-Moriya interaction is derived using a quasi-classical approach. The expression successfully reproduces the results obtained by numerical quantum mechanical calculations based on Green’s function method at T > 2J/k _B.     

Identification of discontinuities in plasma plume evolution

The ejection of material during laser ablation gives rise to the development of discontinuities in the ambient gas. Several of these discontinuities are observed and characterized, including externally and internally propagating shock waves, contact surface, and the ionization front. Qualitative experimental observations and analysis of these discontinuities are presented. Results from shadowgraphy enabled determination of an irradiance threshold between two different ablation mechanisms, and determination of several stages of plasma plume evolution. Consideration of the refractive index as a dynamic sum of the contributions from gas and electrons led to separate identification of ionization front from the contact surface. Furthermore, ionization front was observed to lead the shock wave at the earlier stage of the ablation.     

Effect of ambient gas on the expansion dynamics of plasma plume formed by laser blow off of thin film

A study has been carried out to understand the influence of ambient gases on the dynamics of laser-blow-off plumes of multi-layered LiF–C thin film. Plume images at various time intervals ranging from 100 to 3000 ns have been recorded using an intensified CCD camera. Enhancement in the plume intensity and change in size and shape occurs on introducing ambient gases and these changes are highly dependent on the nature and composition of the ambient gas used. Velocity of the plume was found to be higher in helium ambient whereas intensity enhancement is greater in argon environment. The plume shapes have maximum size at 10⁻² and 10⁻¹ Torr of Ar and He pressures, respectively. As the background pressure increases further (>10⁻² Torr: depending on the nature of gas), the plume gets compressed/focused in the lateral direction. Internal structure formation and turbulences are observed at higher pressures (>10⁻¹ Torr) in both ambient gases.