New Green-Kubo formulas for transport coefficients in hard sphere-, Langevin fluids and the likes

We present generalized Green-Kubo expressions for thermal transport coefficients $\mu$ in non-conservative fluid-type systems, of the generic form, $\mu$ $= \mu_\infty$ +\int^\infty_0 dt V^{-1} \av{I_\epsilon \exp(t {\cal L}) I}_0 where $\exp(t{\cal L})$ is a pseudo-streaming operator. It consists of a sum of an instantaneous transport coefficient $\mu_\infty$, and a time integral over a time correlation function in a state of thermal equilibrium between a current $I$ and its conjugate current $I_\epsilon$. This formula with $\mu_\infty \neq 0$ and $I_\epsilon \neq I$ covers vastly different systems, such as strongly repulsive elastic interactions in hard sphere fluids, weakly interacting Langevin fluids with dissipative and stochastic interactions satisfying detailed balance conditions, and "the likes", defined in the text. For conservative systems the results reduce to the standard formulas.Comment: 7 pages, no figures. Version 2: changes in the text and references adde

Thermodynamically admissible form for discrete hydrodynamics

We construct a discrete model of fluid particles according to the GENERIC formalism. The model has the form of Smoothed Particle Hydrodynamics including correct thermal fluctuations. A slight variation of the model reproduces the Dissipative Particle Dynamics model with any desired thermodynamic behavior. The resulting algorithm has the following properties: mass, momentum and energy are conserved, entropy is a non-decreasing function of time and the thermal fluctuations produce the correct Einstein distribution function at equilibrium.Comment: 4 page

Treatment of predominantly antibody primary immunodeficiency diseases

As imunodeficiências primárias (IDP) por défice predominante de anticorpos são as IDP mais frequentes. Apresentam fenótipos muito diversos, com espectro de manifestações clinicas muito variável que pode atrasar o diagnóstico. O seguimento destes doentes implica na maioria dos casos, a instituição a longo prazo de terapêutica substitutiva com gamaglobulina intravenosa ou subcutânea. A dose terapêutica com gamablobulina deve ser ajustada a cada doente com o objectivo de manter os níveis de IgG superiores a 500mg/dl. Apresenta-se um protocolo, elaborado a partir da experiência partilhada no estágio efectuado no Hospital de Vall d´Hebron. Inclui-se as doses, forma de administração de GGIV, reacções adversas e medidas de avaliação clínica e laboratorial da sua eficácia e eventual iatrogenia. São referidas as principais complicações associadas a este tipo de IDP: infecciosa, envolvendo diversos sistemas e outras menos frequentes como doenças autoimunes, neoplásicas e linfoproliferativas. O diagnóstico precoce e instituição terapêutica adequada são factores determinantes na evolução clínica, qualidade de vida e prognóstico destes doentes

On the basic set of solutions of a high-order linear difference equation

16 pages, no figures.-- MSC2000 codes: 42C05.MR#: MR2205410 (2007m:39002)Zbl#: Zbl 1100.42022In this paper, we analyze the set of solutions of a linear difference equation of high-order. More precisely, we obtain a basis of such a linear subspace. We deduce integral representations for elements of this basis.The research of the first author has been supported by Dirección General de Investigación (Ministerio de Educación y Ciencia) of Spain under grant BFM 2003-06335-C03-02, and INTAS Research Network NeCCA INTAS 03-51-6637.Publicad

On Alpert multiwavelets

The multiresolution analysis of Alpert is considered. Explicit formulas for the entries in the matrix coefficients of the refinement equation are given in terms of hypergeometric functions. These entries are shown to solve generalized eigenvalue equations as well as partial difference equations. The matrix coefficients in the wavelet equation are also considered and conditions are given to obtain a unique solution.The first author was supported in part by a Simons Foundation Grant. The second author was supported by grant MTM2012-36732-C03-01 from the Dirección General de Investigación Científica y Técnica, Ministerio de Economía y Competitividad of Spain

Second structure relation for q-semiclassical polynomials of the Hahn Tableau

23 pages, no figures.MR#: MR2306798 (2009c:33042)Zbl#: Zbl 1113.33022The q-classical orthogonal polynomials of the q-Hahn Tableau are characterized from their orthogonality condition and by a first and a second structure relation. Unfortunately, for the q-semiclassical orthogonal polynomials (a generalization of the classical ones) we find only in the literature the first structure relation. In this paper, a second structure relation is deduced. In particular, by means of a general finite-type relation between a q-semiclassical polynomial sequence and the sequence of its q-differences such a structure relation is obtained.This work has been supported by Dirección General de Investigación (Ministerio de Educación y Ciencia) of Spain, grant BFM03-06335-C03-02 and INTAS research network NeCCA 03-51-6637.Publicad

Asymptotics for Sobolev orthogonal polynomials for exponential weights

38 pages, no figures.-- MSC2000 codes: 42C05, 33C25.MR#: MR2164139 (2006c:41040)Zbl#: Zbl 1105.42016^aLet $\lambda >0,\alpha >1$, and let $W( x) =\exp ( -\vert x\vert ^{\alpha })$, x\in \mbox{\smallbf R}. Let \psi \in L_{\infty }(\mbox{\smallbf R}) be positive on a set of positive measure. For $n\geq 1$, one may form Sobolev orthonormal polynomials $( q_{n})$, associated with the Sobolev inner product ( f,g) =\int_{\mbox{\scriptsize\bf R}}fg( \psi W) ^{2}+\lambda \int_{\mbox{\scriptsize\bf R}}f^{\prime }g^{\prime }W^{2}. We establish strong asymptotics for the $( q_{n})$ in terms of the ordinary orthonormal polynomials $( p_{n})$ for the weight $W^{2}$, on and off the real line. More generally, we establish a close asymptotic relationship between $( p_{n})$ and $( q_{n})$ for exponential weights $W=\exp ( -Q)$ on a real interval $I$, under mild conditions on $Q$. The method is new and will apply to many situations beyond that treated in this paper.The work by F. Marcellan has been supported by Dirección General de Investigación (Ministerio de Ciencia y Technología) of Spain under grant BFM 2003-06335-C03-07, as well as NATO Collaborative grant PST.CLG 979738. J. Geronimo and D. Lubinsky, respectively, acknowledge support by NSF grants DMS-0200219 and DMS-0400446.Publicad

Generalized Green-Kubo formulas for fluids with impulsive, dissipative, stochastic and conservative interactions

We present a generalization of the Green-Kubo expressions for thermal transport coefficients $\mu$ in complex fluids of the generic form, $\mu= \mu_\infty +\int^\infty_0 dt V^{-1} _0$, i.e. a sum of an instantaneous transport coefficient $\mu_\infty$, and a time integral over a time correlation function in a state of thermal equilibrium between a current $J$ and a transformed current $J_\epsilon$. The streaming operator $\exp(t{\cal L})$ generates the trajectory of a dynamical variable $J(t) =\exp(t{\cal L}) J$ when used inside the thermal average $_0$. These formulas are valid for conservative, impulsive (hard spheres), stochastic and dissipative forces (Langevin fluids), provided the system approaches a thermal equilibrium state. In general $\mu_\infty \neq 0$ and $J_\epsilon \neq J$, except for the case of conservative forces, where the equality signs apply. The most important application in the present paper is the hard sphere fluid.Comment: 14 pages, no figures. Version 2: expanded Introduction and section II specifying the classes of fluids covered by this theory. Some references added and typos correcte

Vapour-liquid coexistence in many-body dissipative particle dynamics

Many-body dissipative particle dynamics is constructed to exhibit vapour-liquid coexistence, with a sharp interface, and a vapour phase of vanishingly small density. In this form, the model is an unusual example of a soft-sphere liquid with a potential energy built out of local-density dependent one-particle self energies. The application to fluid mechanics problems involving free surfaces is illustrated by simulation of a pendant drop.Comment: 8 pages, 6 figures, revtex

Static and Dynamic Properties of Dissipative Particle Dynamics

The algorithm for the DPD fluid, the dynamics of which is conceptually a combination of molecular dynamics, Brownian dynamics and lattice gas automata, is designed for simulating rheological properties of complex fluids on hydrodynamic time scales. This paper calculates the equilibrium and transport properties (viscosity, self-diffusion) of the thermostated DPD fluid explicitly in terms of the system parameters. It is demonstrated that temperature gradients cannot exist, and that there is therefore no heat conductivity. Starting from the N-particle Fokker-Planck, or Kramers' equation, we prove an H-theorem for the free energy, obtain hydrodynamic equations, and derive a non-linear kinetic equation (the Fokker-Planck-Boltzmann equation) for the single particle distribution function. This kinetic equation is solved by the Chapman-Enskog method. The analytic results are compared with numerical simulations.Comment: 22 pages, LaTeX, 3 Postscript figure