Improved spatial decay bounds in the plane Stokes flow

This paper investigates spatial decay bounds and a decay rate for the time- dependent Stokes flow of a viscous fluid in a semi-infinite channel. We show how to obtain a near optimal decay rate that is independent of the Reynolds number. We also show that a modification to an analysis given in the literature and a better choice of arbitrary constants yield a decay rate 1.328, which is clearly an improvement compared to 0.91 obtained in the referenced work.

Boltzmann Equations with Quantum Effects (2): Entropy Identity, Existence and Uniqueness of Spatial Decay Solutions

A previous study is continued by investigating the Boltzmann equation for particles with quantum effects (BQE). First, the corresponding entropy identity is proved, then if the initial data f(x,v,0) satisfies 0≤f(x,v,0)≤CΦ(x,v,0) for a constant 0<C<∞ and function Φ(x,v,t), we prove the existence and uniqueness of spatial decay solutions of the BQE within a given function space B(Φ) using fixed point theory. Moreover, if there is a continuous function F(x,v) which belongs to a function set, then there exists a mild solution f(x,v,t) of the BQE such that f ∞(x,v)= limt→∞f(x+vt,v,t)=F(x,v).

Boltzmann Equations with Quantum Effects (1):Long Time Behavior of Spatial Decay Solutions

The Boltzmann equations for Fermi-Dirac particles and Bose-Einstein particles, both in the absence of external force fields, are combined into a more general form called the Boltzmann equation with quantum effects (BQE). It is assumed that the initial data f(x,v,0) satisfies 0≤f(x,v,0)≤cΦ(x,v,0) for a positive constant c and certain types of control functions Φ(x,v,t). Then within a given function space B(Φ), we prove that f(x+tv,v,t) uniformly converges to f ∞(x,v) in a certain norm where f ∞(x,v)= limt→∞f(x+tv,v,t) and different initial data determines different long time limits.

Stokes方程组的解在四种半无穷柱体上空间衰减性

This paper investigates the spatial behavior of the solutions of the Stokes equations in a semi-infinite cylinder.We consider four kinds of semi-infinite cylinders with boundary conditions of Dirichlet type.For each type of cylinder we obtain the spatial decay estimates for the solutions.To make the attenuation meaningful,we derive the explicit bound for the total energy in terms of the initial boundary data.

Asymptotic and other estimates for semilinear parabolic problem in semi-infinite cylinder

The spatial decay of solutions to initial-boundary value problems for a semilinear parabolic equation in a semi-infinite cylinder of variable cross-section subject to zero condition on the lateral boundaries is investigated. A second-order differential inequality that shows the spatial decay O（exp（-z2/（4（t ＋ t0）））） for an L2p cross-sectional measure of the solution is obtained. A first-order differential inequality leading to growth or decay is also derived. In the case of growth, an upper bound for blow-up in space is obtained, while in the case of decay an upper bound for the total energy in terms of data is obtained.

A position-sensitive detector with lithium glass and MaPMT

A position-sensitive detector is designed for neutron detection. It uses a single continuous screen of a self-made lithium glass scintillator, rather than discrete crystal implementations, coupling with a multi-anode PMT （MaPMT）. The scintillator is fast and efficient; with a decay time of 34 ns and thermal neutron detection efficiency of around 95.8% for the 3 mm thick screen, and its light yield is around 5670 photons per neutron and 3768 photons per MeV γ rays deposition. The spatial resolution is around 1.6 mm （FWHM） with the energy resolution around 34.7% by using α （5.2 MeV） rays test.