Transparent Boundary Conditions for Split-Step Padé Approximations of the One-Way Helmholtz Equation

In this paper, we generalize the nonlocal discrete transparent boundary condition introduced by F. Schmidt and P. Deuflhard (1995, Comput. Math. Appl.29, 53–76) and by F. Schmidt and D. Yevick (1997, J. Comput. Phys.134, 96–107) to propagation methods based on arbitrary Padé approximations of the two-dimensional one-way Helmholtz equation. Our approach leads to a recursive formula for the coefficients appearing in the nonlocal condition, which then yields an unconditionally stable propagation method.     

The Padé Approximation and its Physical Applications

The Padé approximation, its mathematical features, and its practical and physical applications are reviewed. We describe the present status of the convergence problem. Among the physical applications, we give particular emphasis to elementary particle theory. We discuss various proofs of convergence, and show why the approximation is particularly well suited for studying strong interaction dynamics. We finally review the various achievements of the approximation in the determination of ππ, πN and NN scattering amplitudes.     

Variational Matrix Padé Approximants in Two Body Scattering

The convergence and bounding properties of the variational matrix Padé approximants are investigated for non relativistic two body interactions. Selecting L – 1 discrete values qi, i = 1, …, L – 1 and the physical momentum q₀ the off shell scattering amplitudes are L X L matrices. The [N/N] Padé approximants to the Born series of these matrices are the variational solution of the Schwinger principle and the corresponding physical amplitude has variational properties in the off shell momenta. For positive interactions the best approximants to the phase shift is an absolute minimum on the q_i and monotonic convergence to the exact result for N → ∞ or L → ∞ ca be proved. Similar properties are shown for the bound states using the Ritz variational principle. The required mathematical background is extensively worked out, the extensions to non positive, singular and long range potentials are considered and some numerical examples are presented.     

Padé–Legendre approximants for uncertainty analysis with discontinuous response surfaces

A novel uncertainty propagation method for problems characterized by highly non-linear or discontinuous system responses is presented. The approach is based on a Padé–Legendre (PL) formalism which does not require modifications to existing computational tools (non-intrusive approach) and it is a global method. The paper presents a novel PL method for problems in multiple dimensions, which is non-trivial in the Padé literature. In addition, a filtering procedure is developed in order to minimize the errors introduced in the approximation close to the discontinuities. The numerical examples include fluid dynamic problems characterized by shock waves: a simple dual throat nozzle problem with uncertain initial state, and the turbulent transonic flow over a transonic airfoil where the flight conditions are assumed to be uncertain. Results are presented in terms of statistics of both shock position and strength and are compared to Monte Carlo simulations.     

Caratheodory and the Foundations of Thermodynamics and Statistical Physics

Constantin Caratheodory offered the first systematic and contradiction free formulation of thermodynamics on the basis of his mathematical work on Pfaff forms. Moreover, his work on measure theory provided the basis for later improved formulations of thermodynamics and physics of continua where extensive variables are measures and intensive variables are densities. Caratheodory was the first to see that measure theory and not topology is the natural tool to understand the difficulties (ergodicity, approach to equilibrium, irreversibility) in the Foundations of Statistical Physics. He gave a measure-theoretic proof of Poincaré's recurrence theorem in 1919. This work paved the way for Birkhoff to identify later ergodicity as metric transitivity and for Koopman and von Neumann to introduce spectral analysis of dynamical systems in Hilbert spaces. Mixing provided an explanation of the approach to equilibrium but not of irreversibility. The recent extension of spectral theory of dynamical systems to locally convex spaces, achieved by the Brussels–Austin groups, gives new nontrivial time asymmetric spectral decompositions for unstable and/or non-integrable systems. In this way irreversibility is resolved in a natural way.     

Modeling of the Dynamic Plasma Pinch in Plasma Focus Discharges Based in Von Karman Approximations

Dynamic plasma pinches occur in a variety of devices, as $Z$ -pinches and plasma focus. In this paper, a lumped parameter model of a dynamic plasma pinch produced in a plasma focus discharge is presented. The model is based in Von Karman approximations of the radial density and velocity profiles, which leads to the reduction to a system of ordinary differential equations describing the dynamic evolution of the pinch compression and expansion. The model was coupled with a fusion kernel to produce an estimate of the neutron yield per pulse. The calculations were tested against available data of the pressure–yield curve of seven experimental devices ranging from 1 to 250 kJ, showing excellent agreement, particularly regarding the curvature of the pressure–yield curve.      

Extending the Fast Multipole Method for Charges inside a Dielectric Sphere in an Ionic Solvent: High Order Image Approximations for Reaction Fields

As a sequel to our previous paper on extending the Fast Multipole Method (FMM) for charges inside a dielectric sphere [J. Comput. Phys. 223 (2007) 846–864], this paper further extends the FMM to the electrostatic calculation for charges inside a dielectric sphere immersed in an ionic solvent, a scenery with more relevance in biological applications. The key findings include two fourth-order multiple discrete image approximations in terms of u = λa to the reaction field induced by the ionic solvent, provided that u = λa < 1 where λ is the inverse Debye screening length of the ionic solvent and a is the radius of the dielectric sphere. A 10⁻⁴ relative accuracy in the reaction field of a source charge within the sphere can be achieved with only 3–4 point image charges. Together with the image charges, the FMM can be used to speed up the calculation of electrostatic interactions of charges in a dielectric sphere immersed in an ionic solvent.     

Nonideal Plasma Thermodynamics: Separate Account of Short‐ and Long‐Range Interaction

The method is developed to calculate the thermodynamic functions of strongly non‐ideal plasma by separate treating of short‐ and long‐range interaction contributions, the border of the separation depending on the charge number density as ∼n^1/3. The result for one‐component plasma (OCP) reproduce the Monte Carlo results in the overall interval of non‐ideality parameter values. The method is generalized to treat two‐component plasma (TCP) in the most essential range of non‐ideality parameter. The existence of a double‐phase domain in the pressure‐volume plane is discussed.     

Rényi Entropy in Statistical Mechanics

Rényi entropy was originally introduced in the field of information theory as a parametric relaxation of Shannon (in physics, Boltzmann–Gibbs) entropy. This has also fuelled different attempts to generalise statistical mechanics, although mostly skipping the physical arguments behind this entropy and instead tending to introduce it artificially. However, as we will show, modifications to the theory of statistical mechanics are needless to see how Rényi entropy automatically arises as the average rate of change of free energy over an ensemble at different temperatures. Moreover, this notion is extended by considering distributions for isospectral, non-isothermal processes, resulting in relative versions of free energy, in which the Kullback–Leibler divergence or the relative version of Rényi entropy appear within the structure of the corrections to free energy. These generalisations of free energy recover the ordinary thermodynamic potential whenever isothermal processes are considered.     

Statistical Mechanics and Thermodynamics: Boltzmann’s versus Planck’s State Definitions and Counting

During the physical foundation of his radiation formula in his December 1900 talk and subsequent 1901 article, Planck refers to Boltzmann’s 1877 combinatorial-probabilistic treatment and obtains his quantum distribution function, while Boltzmann did not. For this, Boltzmann’s memoirs are usually ascribed to classical statistical mechanics. Agreeing with Bach, it is shown that Boltzmann’s 1868 and 1877 calculations can lead to a Planckian distribution function, where those of 1868 are even closer to Planck than that of 1877. Boltzmann’s and Planck’s calculations are compared based on Bach’s three-level scheme ‘configuration–occupation–occupancy’. Special attention is paid to the concepts of interchangeability and the indistinguishability of particles and states. In contrast to Bach, the level of exposition is most elementary. I hope to make Boltzmann’s work better known in English and to remove misunderstandings in the literature.     

Rényi Entropy and Free Energy

The Rényi entropy is a generalization of the usual concept of entropy which depends on a parameter q. In fact, Rényi entropy is closely related to free energy. Suppose we start with a system in thermal equilibrium and then suddenly divide the temperature by q. Then the maximum amount of work the system can perform as it moves to equilibrium at the new temperature divided by the change in temperature equals the system’s Rényi entropy in its original state. This result applies to both classical and quantum systems. Mathematically, we can express this result as follows: the Rényi entropy of a system in thermal equilibrium is without the ‘q−1-derivative’ of its free energy with respect to the temperature. This shows that Rényi entropy is a q-deformation of the usual concept of entropy.     

An Alternative Study about the Geometry and the First Law of Thermodynamics for AdS Lovelock Gravity,Using the Definition of Conserved Charges

In this work, we introduce an extension of the study of the first law of thermodynamics of black holes based on the geometry of the extended phase space for AdS Lovelock gravities, which includes changes in scales. As expected, the result obtained coincides with the previously known four-dimensional case. For higher dimensions, the result is the rise of two new contributions to the first law of thermodynamics. The first term corresponds to corrections of the usual definition of thermodynamic volumes at the horizon due to the presence of the higher curvature terms. The second term arises in odd dimensions, comes from the asymptotic region, and corresponds to a scale transformation of the form ∝δ^ln(l/ℓ), with l the AdS radius and ℓ a parameter. A particularly interesting case corresponds to the Chern Simons gravity where the change scale does not generate a contribution at the asymptotic region, likely due to the Chern Simons AdS local symmetry.     

Free Surface and Interface Thermodynamics of Liquid Nickel in Contact with Alumina

Sessile drop experiments of Ni and Ni(2at.%Al) were conducted under controlled working conditions, at 1500°C, P(O₂) 10^–9 Torr. It is shown that Al and oxygen atoms engaged in the capillary driven mass transport at the interface have a significant impact on the surface/interface thermodynamics. The surface energy of liquid Ni determined from experiments in which Ni comes into contact with Al₂O₃ is significantly lower than that of high purity Ni, due to the segregation of Al. The free energy of segregation of Al to the free surface of Ni ( G _S) was found to range from –164 to –152 kJ/mol, indicating a relatively strong tendency for segregation of Al to the free surface of Ni(Al). It is proposed that an Al(O)-rich liquid layer forms adjacent to the Ni-Al₂O₃ interface, which improves interfacial adhesion. In the Ni(Al)-Al₂O₃ system, an increase in the Al content of the alloy leads to the improvement of both wetting and adhesion of the alloy on the ceramic, correlating with the improvement in the interface strength after solidification.     

Exact Results for Thermodynamics of the Hydrogen Plasma: Low-Temperature Expansions Beyond Saha Theory

We study hydrogen in the Saha regime, within the physical picture in terms of a quantum proton-electron plasma. Long ago, Saha showed that, at sufficiently low densities and low temperatures, the system behaves almost as an ideal mixture made with hydrogen atoms in their groundstate, ionized protons and ionized electrons. More recently, that result has been rigorously proved in some scaling limit where both temperature and density vanish. In that Saha regime, we derive exact low-temperature expansions for the pressure and internal energy, where density ρ is rescaled in units of a temperature-dependent density ρ ^* which controls the cross-over between full ionization (ρ ≪ ρ ^* ) and full atomic recombination (ρ≫ρ ^* ). Each term reduces to a function of ρ/ρ ^* times temperature-dependent functions which decay exponentially fast when temperature T vanishes. Scaled expansions are ordered with respect to the corresponding decay rates. Leading terms do reduce to ideal contributions obtained within Saha theory. We consistently compute all corrections which are exponentially smaller by a factor exp (β E _H ) at most, where E _H is the negative groundstate energy of a hydrogen atom and β=1/(k _B T). They include all effects arising from both the Coulomb potential and the quantum nature of the particles: excitations of atoms H, formation of molecules H ₂, ions H ₂⁺ and H ⁻, thermal and pressure ionization, plasma polarization, screening, interactions between atoms and ionized charges, etc. Scaled low-temperature expansions can be viewed as partial resummations of usual virial expansions up to arbitrary high orders in the density.     

The Representations of the Poincaré Group in the Framework of Free Quantum Fields

This review article arose while the author tried to get acquainted with the recent developments in the domain of the representations of the Poincaré group in the quantum field theory. Special emphasis was put in this article on the case of massless free fields. Some ideas concerning general restrictions imposed upon the spinorial fields in order to get irreducible representations seem to be new and original.     

A New Scheme for High‐Intensity Laser‐Driven Electron Acceleration in a Plasma

We propose a new approach to high‐intensity relativistic laser‐driven electron acceleration in a plasma. Here, we demonstrate that a plasma wave generated by a stimulated forward‐scattering of an incident laser pulse can be in the longest acceleration phase with injected relativistic beam electrons. This is why the plasma wave has the maximum amplification coefficient which is determined by the acceleration time and the breakdown (overturn) electric field in which the acceleration of the injected beam electrons occurs. We must note that for the longest acceleration phase the relativity of the injected beam electrons plays a crucial role in our scheme. We estimate qualitatively the acceleration parameters of relativistic electrons in the field of a plasma wave generated at the stimulated forward‐scattering of a high‐intensity laser pulse in a plasma. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

血浆中游离还原型及氧化型谷胱甘肽的荧光测定法

文章建立了快速、可同时检测血浆中游离的还原型和氧化型谷胱甘肽(即GSH和GSSG)的方法, 并评价了血浆中GSH/GSSG的氧化还原状态。利用二硫苏糖醇将GSSG还原成两分子的GSH,使GSH在pH 8.0时与邻苯二甲醛(OPA)结合生成荧光产物GSH-OPA,用荧光分光光度仪测定其荧光值,从而对GSH和GSSG进行定量分析。并运用此方法测量青年健康志愿者静脉血中的游离GSH和GSSG。该法最低可检测出测定管中11.4 pmol·L-1GSH以及5.7 pmol·L-1GSSG。测量GSH批内和批间变异系数分别4.6%和3.9%,GSSG批内和批间变异系数分别为3.5%和4.1%,GSH,GSSG加标准品后的回收率分别为(99.77±5.70)%和(99.28±4.73)%。测定健康青年志愿者血浆中游离GSH,GSSG的含量分别为(16.5±2.4) nmol·mL-1和(1.7±0.35) nmol·mL-1。