TIME DECAY RATE OF SOLUTIONS TO THE HYPERBOLIC MHD EQUATIONS IN R3

In this paper, we first show the global existence, uniqueness and regularity of weak solutions for the hyperbolic magnetohydrodynamics(MHD) equations in R^3. Then we establish that the solutions with initial data belonging to H^m(R^3) ∩ L^1(R^3) have the following time decay rate:║▽~mu(x, t) ║~2+║ ▽~mb(x, t)║~ 2+ ║▽^(m+1)u(x, t)║~ 2+ ║▽^(m+1)b(x, t) ║~2≤ c(1 + t)^(-3/2-m)for large t, where m = 0, 1.

Gevrey Regularity and Time Decay of Fractional Porous Medium Equation in Critical Besov Spaces

In this paper, we show the existence and regularity of mild solutions depending on the small initial data in Besov spaces to the fractional porous medium equation. When 1 < α ≤ 2, we prove global well-posedness for initial data with 1 ≤ p < ∞, 1 ≤ q ≤ ∞, and analyticity of solutions with 1 < p < ∞, 1 ≤ q ≤ ∞. In particular, we also proved that when α = 1, both u and belong to . We solve this equation through the contraction mapping method based on Littlewood-Paley theory and Fourier multiplier. Furthermore, we can get time decay estimates of global solutions in Besov spaces, which is as t → ∞.

Time Decay Rate of Solutions Toward the Viscous Shock Waves under Periodic Perturbations for the Scalar Conservation Law with Nonlinear Viscosity

In this paper,it is proved that the weak solution to the Cauchy problem for the scalar viscous conservation law,with nonlinear viscosity,different far field states and periodic perturbations,not only exists globally in time,but also converges towards the viscous shock wave of the corresponding Riemann problem as time goes to infinity.Furthermore,the decay rate is shown.The proof is given by a technical energy method.

Optimal Time Decay of Navier–Stokes Equations with Low Regularity Initial Data

In this paper, we study the optimal time decay rate of isentropic Navier-Stokes equations under the low regularity assumptions about initial data. In the previous works about optimal time decay rate, the initial data need to be small in H^[N/2]＋2（R^N）. Our work combined negative Besov space estimates and the conventional energy estimates in Besov space framework which is developed by Danchim Through our methods, we can get optimal time decay rate with initial data just small in B^N/2-1,N/2＋1∩^N/2-1,N/2 and belong to some negative Besov space （need not to be small）. Finally, combining the recent results in [25] with our methods, we only need the initial data to be small in homogeneous Besov space B^N/2-2,N/2 ∩B^N/2-1 to get the optimal time decay rate in space L2.

Data point selection for weighted least square fitting of cavity decay time constant

For the accurate extraction of cavity decay time, a selection of data points is supplemented to the weighted least square method. We derive the expected precision, accuracy and computation cost of this improved method, and examine these performances by simulation. By comparing this method with the nonlinear least square fitting （NLSF） method and the linear regression of the sum （LRS） method in derivations and simulations, we find that this method can achieve the same or even better precision, comparable accuracy, and lower computation cost. We test this method by experimental decay signals. The results are in agreement with the ones obtained from the nonlinear least square fitting method.

The effect of k-cubic Dresselhaus spin orbit coupling on the decay time of persistent spin helix states in semiconductor two-dimensional electron gases

We study the theoretical effect of k-cubic （i.e, cubic-in-momentum） Dresselhaus spin-orbit coupling on the decay time of persistent spin helix states in semiconductor two-dimensional electron gases. We show that the decay time of persistent spin helix states may be suppressed substantially by k-cubic Dresselhaus spin-orbit coupling, and after taking the effect of k-cubic Dresselhaus spin-orbit interaction into account, the theoretical results obtained accord both qualitatively and quantitatively with other recent experimental results.

TIME PERIODIC SOLUTIONS OF NON-ISENTROPIC COMPRESSIBLE MAGNETOHYDRODYNAMIC SYSTEM

In this paper, we study the non-isentropic compressible magnetohydrodynamic system with a time periodic external force in R^n. Under the condition that the optimal time decay rates are obtained by spectral analysis, we show that the existence, uniqueness and time-asymptotic stability of time periodic solutions when the space dimension n 〉 5. Our proof is based on a combination of the energy method and the contraction mapping theorem.

THE GLOBAL EXISTENCE AND A DECAY ESTIMATE OF SOLUTIONS TO THE PHAN-THEIN-TANNER MODEL

In this paper,we study the global existence and decay rates of strong solutions to the three dimensional compressible Phan-Thein-Tanner model.By a refined energy method,we prove the global existence under the assumption that the H^(3) norm of the initial data is small,but that the higher order derivatives can be large.If the initial data belong to homogeneous Sobolev spaces or homogeneous Besov spaces,we obtain the time decay rates of the solution and its higher order spatial derivatives.Moreover,we also obtain the usual L^(p)-L^(2)(1≤p≤2)type of the decay rate without requiring that the Lpnorm of initial data is small.

Global Existence and Decay of Solution to Parabolic-Parabolic Keller-Segel Model in R^(d)

We consider the global existence and decay of integral solutions to the parabolic-parabolic Keller-Segel system in d-dimension.On the one hand,by Banach fixed point theorem and some properties of heat kernel,we prove the local existence and the global existence of integral solutions for the different initial data under some conditions that involve the size of the initial data.On the other hand,in the case of global solutions,we obtain their optimal time decay by Gronwall’s lemma.

Influence of the Magnetic Field on the Transient Decay of the Density of Charge Carriers in a Silicon Photocell with Vertical Multijunctions Connected in Series Placed in Open Circuit

This study investigates the effect of the magnetic field on the transient density of excess minority charge carriers in the base of a series-connected vertical junction silicon solar cell. The solar cell is presented in open circuit transient operation. The magnetic field through the Laplace force which deflects the photogenerated carriers from their initial trajectory towards the lateral surfaces reducing their mobility, diffusion and conduction, will certainly influence the decay time of the transient regime. The transient density of excess minority carriers in the base is a sum of infinite terms whose decay time of the different harmonics is studied.

COMPRESSIBLE NAVIER-STOKES-POISSON EQUATIONS

This is a survey paper on the study of compressible Navier-Stokes-Poisson equations. The emphasis is on the long time behavior of global solutions to multi-dimensional compressible Navier-Stokes-Poisson equations, and the optimal decay rates for both unipolar and bipolar compressible Navier-Stokes-Poisson equations are discussed.

COMPRESSIBLE NON-ISENTROPIC BIPOLAR NAVIER-STOKES-POISSON SYSTEM IN R^3

The compressible non-isentropic bipolar Navier-Stokes-Poisson （BNSP） sys- tem is investigated in R3 in the present paper, and the optimal time decay rates of global strong solution are shown. For initial data being a perturbation of equilibrium state in Hl（R3） （R3） for 1 〉 4 and s E （0, 1], it is shown that the density and temperature for each charged particle （like electron or ion） decay at the same optimal rate （1 ＋ t）-3/4, but the momentum for each particle decays at the optimal rate （1 ＋ t）-1/4-3/2 which is slower than the rate （1 ＋ t）-3/4-3/2 for the compressible Navier-Stokes （NS） equations [19] for same initial data. However, the total momentum tends to the constant state at the rate （1 ＋t）-3/4 as well, due to the interplay interaction of charge particles which counteracts the influence of electric field.

THE VLASOV-MAXWELL-FOKKER-PLANCK SYSTEM WITH RELATIVISTIC TRANSPORT IN THE WHOLE SPACE

In this paper, we consider the Vlasov-Maxwell-Fokker-Planck system with relativistic transport in the whole space. The global solutions to this system near the relativistic Maxwellian are constructed and the optimal time decay rate of global solutions are also obtained by an approach by combining the compensating function and energy method.

A Note on Time-Decay Estimates for the Compressible Navier–Stokes Equations

In the recent work, we have developed a decay framework in general Lp critical spaces and established optimal time-decay estimates for barotropic compressible Navier-Stokes equations. Those decay rates of Lq-Lr type of the solution and its derivatives are available in the critical regularity framework, which were exactly firstly observed by Matsumura ＆ Nishida, and subsequently generalized by Ponce for solutions with high Sobolev regularity. We would like to mention that our approach is likely to be effective for other hyperbolic/parabolic systems that are encountered in fluid mechanics or mathematical physics. In this paper, a new observation is involved in the high frequency, which enables us to improve decay exponents for the high frequencies of solutions.

On the refracted patterns produced by liquid vortices

A theoretical analysis of the refracted shadows produced by steady and time-decaying liquid vortices under uniform illumination from above is given in this article. An expression for the induced shadow intensity is derived and found to be a function of the vortex＇s free surface profile, i.e., function of the static pressure distribution. The patterns for different focusing depth are given and compared with previous visualization results from the literature. The phenomenon is examined and illustrated as a bench mark case by using both steady and time-decaying algebraic vortex models. However, this study can be extended to check the feasibility of recovering the main flow properties by analyzing the luminous image intensity of the refracted patterns. The present analysis is valid only when the swirl velocity is order of magnitude higher than the meridional flow components and the vorticity is concentrated within the core region and of intense conditions.

Spectrum structure and decay rate estimates on the Landau equation with Coulomb potential

In this paper we first deduce the estimates on the linearized Landau operator with Coulomb potential and then analyze its spectrum structure by using semigroup theory and linear operator perturbation theory.Based on these estimates,we give the precise time decay rate estimates on the semigroup generated by the linearized Landau operator so that the optimal time decay rates of the nonlinear Landau equation follow.In addition,we present a similar result for the non-angular cutoff Boltzmann equation with soft potentials.

LiYF_(4):Yb/LiYF_(4) and LiYF_(4):Yb,Er/LiYF_(4) core/shell nanocrystals with luminescence decay times similar to YLF laser crystals and the upconversion quantum yield of the Yb,Er doped nanocrystals

We developed a procedure to prepare luminescent LiYF_(4):Yb/LiYF_(4) and LiYF_(4):Yb,Er/LiYF_(4) core/shell nanocrystals with a size of approximately 40 nm revealing luminescence decay times of the dopant ions that approach those of high-quality laser crystals of LiYF_(4):Yb(Yb:YLF)and LiYF_(4):Yb,Er(Yb,Er:YLF)with identical doping concentrations.As the luminescence decay times of Yb^(3+)and Er^(3+)are known to be very sensitive to the presence of quenchers,the long decay times of the core/shell nanocrystals indicate a very low number of defects in the core particles and at the core/shell interfaces.This improvement in the performance was achieved by introducing two important modifications in the commonly used oleic acid based synthesis.First,the shell was prepared via a newly developed method characterized by a very low nucleation rate for particles of pure LiYF_(4) shell material.Second,anhydrous acetates were used as precursors and additional drying steps were applied to reduce the incorporation of OH−in the crystal lattice,known to quench the emission of Yb^(3+)ions.Excitation power density(P)-dependent absolute measurements of the upconversion luminescence quantum yield(ΦUC)of LiYF_(4):Yb,Er/LiYF_(4) core/shell particles reveal a maximum value of 1.25%at P of 180 W·cm^(−2).Although lower than the values reported for NaYF4:18%Yb,2%Er core/shell nanocrystals with comparable sizes,theseΦUC values are the highest reported so far for LiYF_(4):18%Yb,2%Er/LiYF_(4) nanocrystals without additional dopants.Further improvements may nevertheless be possible by optimizing the dopant concentrations in the LiYF_(4) nanocrystals.

Synthesis and Analysis of Tm^(3+) Doped YF_3 Upconversion Luminescent Nano-materials

Upconversion （UC） phosphor Tm3＋ doped YF3 nano-erystals were prepared by hydrothermal method under different conditions and characterized by Field Transmission electron microscopy （TEM）, Scanning electron microscopy （SEM） and X-ray diffraction （XRD）. Their UC luminescence properties were studied by fluorescence spectrophotometer with 980 nm diode laser excitation, and impact of different grain sizes and morphology on the UC luminescence intensity was discussed. The fluorescence decay lifetime was calculated by Multi-exponential function fitting method. Results show that UC emission intensity was enhanced with the reduction of grain size, and the decay lifetime is 0.60 us.

Synthesis and luminescence properties of novel Ce^3＋-doped Yb3Al5-xGaxO12 garnets with very fast decay time

A novel series of Ce^3＋-doped Yb3 Al（5-x）GaxO（12）（x = 0, 1,2, 3,4, 5） powders of ytterbium aluminum gallium garnets were synthesized by high temperature solid-state reaction in a carbon reducing atmosphere. The ytterbium aluminum garnets were characterized by X-ray powder diffraction, UV-Vis diffuse reflectance spectra, photoluminescence spectra and decay curves. Moreover, the substitution effect for the Al^3＋ sites with Ga^3＋ in 0.5 at%Ce：Yb3 Al（5-x）GaxO（12）（x = 0,1, 2, 3, 4, 5） garnets were discussed. With the increase of Ga^3＋ ion concentration, the visible absorption peaks within 400-450 nm have blue shift phenomenon,while the absorption peaks in the range of 330-350 nm and the absorption band edge red shifts.Furthermore, the short decay times are very short with less than 10 ns due to the Yb^3＋ ＋ Ce^3＋→ Yb^2＋ ＋ Ce^4＋ electron transfer reaction.

Improvements in Inversion of Magnetic Resonance Exploration-Water Content, Decay Time, and Resistivity

In this review article, we present recent developments and improvements in magnetic resonance sounding （MRS）, a newly established geophysical exploration method that provides unique information about hydrogeophysical properties due to its direct sensitivity to hydrogen protons and proton dynamics. Starting with the most sophisticated and complete MRS formulation, we give a detailed view on how to solve the equation, i.e., inverting exactly for all model parameters： water content, decay time, and resistivity. Giving a short review of general inversion schemes used in geophysics, the special properties of MRS inversion are evaluated and the development of MRS inversion over recent years is shown. We present the extension of MRS to magnetic resonance tomography （MRT）, i.e., the extension to two-dimensional investigations and appropriate inversions. Finally, we address restrictions, limitations, and inconsistencies as well as future developments.