246 research outputs found
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 . We prove
that the unique strong solution exists globally in time and tends to the
asymptotical state with an algebraic rate as . 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
An inverse problem in quantum statistical physics
International audienceWe address the following inverse problem in quantum statistical physics: does the quantum free energy (von Neumann entropy + kinetic energy) admit a unique minimizer among the density operators having a given local density ? We give a positive answer to that question, in dimension one. This enables to define rigourously the notion of local quantum equilibrium, or quantum Maxwellian, which is at the basis of recently derived quantum hydrodynamic models and quantum drift-diffusion models. We also characterize this unique minimizer, which takes the form of a global thermodynamic equilibrium (canonical ensemble) with a quantum chemical potential
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
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