Degenerate nonlinear hyperbolic conservation laws: Non classical geometrical theory

Kinetic selection principles have been shown to be useful and physically reasonable in nonlinear hyperbolic problems with large amplitude phase transitions. We refer to Abeyaratne and Knowles, [A-K], for discussion on the subject. They also have been used for degenerate nonlinear problems, where the genuine nonlinearity property of Lax is violated. This is the framework of Liu, [Li], in the kinetic situation of Hayes and Le Floch, [H-L], where their so-called non classical shocks may be seen as small amplitude phase transitions. Here, we describe the local geometry generated by the generic non genuinely nonlinear assumption. A geometric kinetic criterion can be used to select indeterminate simple waves and obtain the well-posedness of the local Riemann problem. A particular case is the entropic kinetic criterion of Hayes and Le Floch.

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Sunto Principi di selezione cinetica sono stati mostrati utili e fisicamente ragionevoli in problemi iperbolici con transizioni di fase di grande ampiezza. Ci riferiamo ad Abeyaratne e Knowles, [A-K], per discussioni sull'argomento. Detti principi sono stati usati per problemi nonlineari degeneri, dove la proprietà di genuina nonlinearità di Lax è violata. Questo è la prospettiva di Liu, [Li], nella situazione cinetica di Hayes e Le Floch, [H-L], dove i loro così detti urti non classici possono essere considerati come transizioni di fase di piccola ampiezza. Qui, descriviamo la geometria locale generata dall'ipotesi generica genuinamente nonlineare. Un criterio di geometria cinetica può essere usato per selezionare onde semplici indeterminate ed ottenere la buona posizione per il problema locale di Riemann. Un caso particolare è il criterio di entropia cinetico di Hayes e Le Floc.

     

A grid‐free upwind relaxation scheme for inviscid compressible flows

A new grid‐free upwind relaxation scheme for simulating inviscid compressible flows is presented in this paper. The non‐linear conservation equations are converted to linear convection equations with non‐linear source terms by using a relaxation system and its interpretation as a discrete Boltzmann equation. A splitting method is used to separate the convection and relaxation parts. Least squares upwinding is used for discretizing the convection equations, thus developing a grid‐free scheme which can operate on any arbitrary distribution of points. The scheme is grid free in the sense that it works on any arbitrary distribution of points and it does not require any topological information like elements, faces, edges, etc. This method is tested on some standard test cases. To explore the power of the grid‐free scheme, solution‐based adaptation of points is done and the results are presented, which demonstrate the efficiency of the new grid‐free scheme. Copyright © 2005 John Wiley & Sons, Ltd.     

A Lower Bound for the Differences of Powers of Linear Operators

Let T be a bounded linear operator in a Banach space, with σ（T）={1}. In 1983, Esterle-Berkani＇ s conjecture was proposed for the decay of differences （I - T） T^n as follows： Eitheror lim inf （n→∞（n＋1）｜｜（I-T）T^n｜｜≥1/e or T = I. We prove this claim and discuss some of its consequences.     

What is novel in quantum transport for mesoscopics?

The understanding of mesoscopic transport has now attained an ultimate simplicity. Indeed, orthodox quantum kinetics would seem to say little about mesoscopics that has not been revealed — nearly effortlessly — by more popular means. Such is far from the case, however. The fact that kinetic theory remains very much in charge is best appreciated through the physics of a quantum point contact. While discretization of its conductance is viewed as the exclusive result of coherent, single-electron-wave transmission, this does not begin to address the paramount feature of all metallic conduction: dissipation. A perfect quantum point contact still has finite resistance, so its ballistic carriers must dissipate the energy gained from the applied field. How do they manage that? The key is in standard many-body quantum theory, and its conservation principles.     

Activation and Afterheat Calculation Analysis for TBM

Safety considerations of TBM are part of the design process to ensure that the TBM do not adversely affect the safety of ITER. So accurate calculations of all radioactivity and potential harmfulness are very important for designing of device, selecting of blanket and shield material, analyzing of the safety and environment, disposing of nuclear waste and operation of the reactor.     

Nonlinear Energy Transfer over the Wave Spectrum in Water Covered by Solid Ice

On the basis of the hydrodynamic equations for nonlinear elastic-gravity waves beneath a solid ice cover and their Hamiltonian representation, a three-wave kinetic equation for the time evolution of the wave spectrum is formulated. The properties of the kernel of the kinetic integral describing the nonlinear interactions between wave triplets are investigated. An algorithm for numerically calculating the kinetic integral is developed. The rate of nonlinear energy transfer over the wave spectrum is estimated quantitatively and its most important characteristics are found.     

The influence of temperature gradients on the kinetic boundary layer problem for a condensing droplet

We extend an earlier method for solving kinetic boundary layer problems to the case of particles moving in aspatially inhomogeneous background. The method is developed for a gas mixture containing a supersaturated vapor and a light carrier gas from which a small droplet condenses. The release of heat of condensation causes a temperature difference between droplet and gas in the quasistationary state; the kinetic equation describing the vapor is the stationary Klein-Kramers equation for Brownian particles diffusing in a temperature gradient. By means of an expansion in Burnett functions, this equation is transformed into a set of coupled algebrodifferential equations. By numerical integration we construct fundamental solutions of this equation that are subsequently combined linearly to fulfill appropriate mesoscopic boundary conditions for particles leaving the droplet surface. In view of the intrinsic numerical instability of the system of equations, a novel procedure is developed to remove the admixture of fast growing solutions to the solutions of interest. The procedure is tested for a few model problems and then applied to a slightly simplified condensation problem with parameters corresponding to the condensation of mercury in a background of neon. The effects of thermal gradients and thermodiffusion on the growth rate of the droplet are small (of the order of 1%), but well outside of the margin of error of the method.     

析氢反应动力学的交流阻抗法研究

利用交流阻抗法测定析氢电化学动力学参数，得到与极化曲线法一致的结果，为确定复杂析氢过程速率的决定步骤提供了判据。     

停流—荧光动力学分析法测定痕量钛的研究

利用自行组装的停流-荧光动力学分析仪,采用停流法汇合流体动力注入技术,研究了钛与3.5-二溴水杨基荧光酮的荧光增强动力学反应性质,讨论了流速、进样时间对方法灵敏度和精密度的影响,提出了一个快速、简便、精确测定钛的分析方法,并用于稀土样品及合成样品中痕量钛的测定.方法检测限为8×10~(-3)ppm,大多数元素的干扰均可用动力学方法消除.     

Distribution Functions in Quantum Mechanics and Wigner Functions

We formulate and solve the problem of finding a distribution function F(r,p,t) such that calculating statistical averages leads to the same local values of the number of particles, the momentum, and the energy as those in quantum mechanics. The method is based on the quantum mechanical definition of the probability density not limited by the number of particles in the system. The obtained distribution function coincides with the Wigner function only for spatially homogeneous systems. We obtain the chain of Bogoliubov equations, the Liouville equation for quantum distribution functions with an arbitrary number of particles in the system, the quantum kinetic equation with a self-consistent electromagnetic field, and the general expression for the dielectric permittivity tensor of the electron component of the plasma. In addition to the known physical effects that determine the dispersion of longitudinal and transverse waves in plasma, the latter tensor contains a contribution from the exchange Coulomb correlations significant for dense systems.