Algebraic time-decay for the bipolar quantum hydrodynamic model

The initial value problem is considered in the present paper for bipolar quantum hydrodynamic model for semiconductors (QHD) in $\mathbb{R}^3$. We prove that the unique strong solution exists globally in time and tends to the asymptotical state with an algebraic rate as $t\to+\infty$. And, we show that the global solution of linearized bipolar QHD system decays in time at an algebraic decay rate from both above and below. This means in general, we can not get exponential time-decay rate for bipolar QHD system, which is different from the case of unipolar QHD model (where global solutions tend to the equilibrium state at an exponential time-decay rate) and is mainly caused by the nonlinear coupling and cancelation between two carriers. Moreover, it is also shown that the nonlinear dispersion does not affect the long time asymptotic behavior, which by product gives rise to the algebraic time-decay rate of the solution of the bipolar hydrodynamical model in the semiclassical limit.Comment: 23 page

Convergence of an entropic semi-discretization for nonlinear Fokker-Planck equations in Rd

A nonlinear degenerate Fokker-Planck equation in the whole space is analyzed. The existence of solutions to the corresponding implicit Euler scheme is proved, and it is shown that the semi-discrete solution converges to a solution of the continuous problem. Furthermore, the discrete entropy decays monotonically in time and the solution to the continuous problem is unique. The nonlinearity is assumed to be of porous-medium type. For the (given) potential, either a less than quadratic growth condition at infinity is supposed or the initial datum is assumed to be compactly supported. The existence proof is based on regularization and maximum principle arguments. Upper bounds for the tail behavior in space at infinity are also derived in the at-most-quadratic growth case

Entropy diminishing finite volume approximation of a cross-diffusion system

International audienceWe propose a two-point flux approximation finite volume scheme for the approximation of the solutions of a entropy dissipative cross-diffusion system. The scheme is shown to preserve several key properties of the continuous system, among which positivity and decay of the entropy. Numerical experiments illustrate the behaviour of our scheme

Fluid moment hierarchy equations derived from quantum kinetic theory

A set of quantum hydrodynamic equations are derived from the moments of the electrostatic mean-field Wigner kinetic equation. No assumptions are made on the particular local equilibrium or on the statistical ensemble wave functions. Quantum diffraction effects appear explicitly only in the transport equation for the heat flux triad, which is the third-order moment of the Wigner pseudo-distribution. The general linear dispersion relation is derived, from which a quantum modified Bohm-Gross relation is recovered in the long wave-length limit. Nonlinear, traveling wave solutions are numerically found in the one-dimensional case. The results shed light on the relation between quantum kinetic theory, the Bohm-de Broglie-Madelung eikonal approach, and quantum fluid transport around given equilibrium distribution functions.Comment: 5 pages, three figures, uses elsarticle.cl

On the Finite Energy Weak Solutions to a System in Quantum Fluid Dynamics

In this paper we consider the global existence of weak solutions to a class of Quantum Hydrodynamics (QHD) systems with initial data, arbitrarily large in the energy norm. These type of models, initially proposed by Madelung, have been extensively used in Physics to investigate Supefluidity and Superconductivity phenomena and more recently in the modeling of semiconductor devices . Our approach is based on various tools, namely the wave functions polar decomposition, the construction of approximate solution via a fractional steps method, which iterates a Schr\"odinger Madelung picture with a suitable wave function updating mechanism. Therefore several \emph{a priori} bounds of energy, dispersive and local smoothing type allow us to prove the compactness of the approximating sequences. No uniqueness result is provided

Analysis of a diffusive effective mass model for nanowires

We propose in this paper to derive and analyze a self-consistent model describing the diffusive transport in a nanowire. From a physical point of view, it describes the electron transport in an ultra-scaled confined structure, taking in account the interactions of charged particles with phonons. The transport direction is assumed to be large compared to the wire section and is described by a drift-diffusion equation including effective quantities computed from a Bloch problem in the crystal lattice. The electrostatic potential solves a Poisson equation where the particle density couples on each energy band a two dimensional confinement density with the monodimensional transport density given by the Boltzmann statistics. On the one hand, we study the derivation of this Nanowire Drift-Diffusion Poisson model from a kinetic level description. On the other hand, we present an existence result for this model in a bounded domain

Histone deacetylase 7, a potential target for the antifibrotic treatment of systemic sclerosis

OBJECTIVE: We have recently shown a significant reduction in cytokine-induced transcription of type I collagen and fibronectin in systemic sclerosis (SSc) skin fibroblasts upon treatment with trichostatin A (TSA). Moreover, in a mouse model of fibrosis, TSA prevented the dermal accumulation of extracellular matrix. The purpose of this study was to analyze the silencing of histone deacetylase 7 (HDAC-7) as a possible mechanism by which TSA exerts its antifibrotic function. METHODS: Skin fibroblasts from patients with SSc were treated with TSA and/or transforming growth factor beta. Expression of HDACs 1-11, extracellular matrix proteins, connective tissue growth factor (CTGF), and intercellular adhesion molecule 1 (ICAM-1) was analyzed by real-time polymerase chain reaction, Western blotting, and the Sircol collagen assay. HDAC-7 was silenced using small interfering RNA. RESULTS: SSc fibroblasts did not show a specific pattern of expression of HDACs. TSA significantly inhibited the expression of HDAC-7, whereas HDAC-3 was up-regulated. Silencing of HDAC-7 decreased the constitutive and cytokine-induced production of type I and type III collagen, but not fibronectin, as TSA had done. Most interestingly, TSA induced the expression of CTGF and ICAM-1, while silencing of HDAC-7 had no effect on their expression. CONCLUSION: Silencing of HDAC-7 appears to be not only as effective as TSA, but also a more specific target for the treatment of SSc, because it does not up-regulate the expression of profibrotic molecules such as ICAM-1 and CTGF. This observation may lead to the development of more specific and less toxic targeted therapies for SSc

PU.1 controls fibroblast polarization and tissue fibrosis

Fibroblasts are polymorphic cells with pleiotropic roles in organ morphogenesis, tissue homeostasis and immune responses. In fibrotic diseases, fibroblasts synthesize abundant amounts of extracellular matrix, which induces scarring and organ failure. By contrast, a hallmark feature of fibroblasts in arthritis is degradation of the extracellular matrix because of the release of metalloproteinases and degrading enzymes, and subsequent tissue destruction. The mechanisms that drive these functionally opposing pro-fibrotic and pro-inflammatory phenotypes of fibroblasts remain unknown. Here we identify the transcription factor PU.1 as an essential regulator of the pro-fibrotic gene expression program. The interplay between transcriptional and post-transcriptional mechanisms that normally control the expression of PU.1 expression is perturbed in various fibrotic diseases, resulting in the upregulation of PU.1, induction of fibrosis-associated gene sets and a phenotypic switch in extracellular matrix-producing pro-fibrotic fibroblasts. By contrast, pharmacological and genetic inactivation of PU.1 disrupts the fibrotic network and enables reprogramming of fibrotic fibroblasts into resting fibroblasts, leading to regression of fibrosis in several organs