INTERFACE BEHAVIOR AND DECAY RATES OF COMPRESSIBLE NAVIER-STOKES SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND A VACUUM

In this paper,we study the one-dimensional motion of viscous gas near a vacuum,with the gas connecting to a vacuum state with a jump in density.The interface behavior,the pointwise decay rates of the density function and the expanding rates of the interface are obtained with the viscosity coefficientμ(ρ)=ρ^(α)for any 0<α<1;this includes the timeweighted boundedness from below and above.The smoothness of the solution is discussed.Moreover,we construct a class of self-similar classical solutions which exhibit some interesting properties,such as optimal estimates.The present paper extends the results in[Luo T,Xin Z P,Yang T.SIAM J Math Anal,2000,31(6):1175-1191]to the jump boundary conditions case with density-dependent viscosity.

Decay rates and time lags of heat conduction in building construction under field conditions

The field measurements of decay rates and time lags of heat conduction in a building construction taken in Nanjing during the summer of 2001 are presented.The decay rates and time lags are calculated according to the frequency responses of the heat absorbed by the room＇s internal surfaces,inside surface temperature,indoor air temperature and outdoor synthetic temperature.The measured results match very well with the theoretical results of the zeroth and the first order values of the decay rates and time lags of heat conduction in the building construction,but the difference between the measured values and the theoretical values for the second order is too great to be accepted.It is therefore difficult to accurately test the second order value.However,it is still advisable to complete the analysis using the zeroth-and the first-orders values of the decay rates and time lags of heat conduction in building construction under field conditions,because in these cases the decay rates of heat conduction reach twenty which meets the requirements of engineering plans.

DECAY RATE FOR DEGENERATE CONVECTION DIFFUSION EQUATIONS IN BOTH ONE AND SEVERAL SPACE DIMENSIONS

We consider degenerate convection-diffusion equations in both one space dimension and several space dimensions. In the first part of this article, we are concerned with the decay rate of solutions of one dimension convection diffusion equation. On the other hand, in the second part of this article, we are concerned with a decay rate of derivatives of solution of convection diffusion equation in several space dimensions.

Decay rates of higher-order norms of solutions to the Navier-Stokes-Landau-Lifshitz system

In this paper, we investigate a system of the incompressible Navier-Stokes equations coupled with Landau-Lifshitz equations in three spatial dimensions. Under the assumption of small initial data, we establish the global solutions with the help of an energy method. Furthermore, we obtain the time decay rates of the higher-order spatial derivatives of the solutions by applying a Fourier splitting method introduced by Schonbek(SCHONBEK, M. E. L2decay for weak solutions of the Navier-Stokes equations. Archive for Rational Mechanics and Analysis, 88, 209–222(1985)) under an additional assumption that the initial perturbation is bounded in L1(R3).

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.

Decay rate of Larix gmelinii coarse woody debris on burned patches in the Greater Khingan Mountains

The decomposition of coarse woody debris(CWD)affects the energy flow and nutrient cycling in forest ecosystems.Previous studies on CWD have focused on the input,decomposition,reserve dynamics,and CWD functions,but coarse woody debris decomposition is complex and the results from different regions vary considerably.It is not clear which factors affect decay rate(k),especially at different decomposition stages.In this study,a single-exponential decay model was used to analyze the characteristics of CWD decomposition in Larix gmelinii forests over the 33 years following a fire in the Greater Khingan Mountains.The results show that the decay rate of coarse woody debris was positively correlated to decay class.The average decomposition rate was 0.019,and 41 years and 176 years are needed for a 50%and 95%mass loss,respectively.CWD nutrient content,density,and water content could explain the variance in the decay rate(~42%)of the decay factors such as amount of leaching,degree of fragmentation,respiration of the debris,and biotransformation,and varied significantly between different decay classes.Using the space-time substitution method,this study arranged the coarse woody debris of different mortality times to form a 33 year chronosequence which revealed the decomposition process.It was concluded that the decay rate was mainly explained by structural component of the debris and its nitrogen and water contents.This paper quantifies the indicators affecting CWD decay to explain the decomposition process.

DECAY RATES OF PLANAR VISCOUS RAREFACTION WAVE FOR MULTI-DIMENSIONAL SCALAR CONSERVATION LAW WITH DEGENERATE VISCOSITY ON HALF SPACE

We investigate the decay rates of the planar viscous rarefaction wave of the initial-boundary value problem to scalar conservation law with degenerate viscosity in several dimensions on the half-line space, where the corresponding one-dimensional problem admits the rarefaction wave as an asymptotic state. The analysis is based on the standard L2-energy method and L1-estimate.

DECAY RATE OF FOURIER TRANSFORMS OF SOME SELF-SIMILAR MEASURES

This paper is concerned with the Diophantine properties of the sequence {ξθn}, where 1 ≤ξ 〈 θ and θ is a rational or an algebraic integer. We establish a combinatorial proposition which can be used to study such two cases in the same manner. It is shown that the decay rate of the Fourier transforms of self-similar measures μλ with λ = θ-1 as the uniform contractive ratio is logarithmic. This generalizes some results of Kershner and Bufetov-Solomyak, who consider the case of Bernoulli convolutions. As an application, we prove that μλ ahaost every x is normal to any base b ≥ 2, which implies that there exist infinitely many absolute normal numbers on the corresponding self-similar set. This can be seen as a complementary result of the well-known Cassels-Schmidt theorem.

Influence of Thermal Radiation on Hot Cluster Decay Rates and Abundances

The influence of radiative cooling on the unimolecular decay rates of free, hot clusters and molecules with unspecified excitation energies is quantified. Two different regimes, dedined by the magnitude of the energy of the photons emitted, are identified and the boundary between them is given. The boundary is determined in terms of the photon emission rate constants and thermal properties of the particles. Also the abundance spectra are calculated for the continuous cooling case, corresponding to small photon energies. The two regimes correspond to continuous cooling and single photon quenching of the unimolecular decay. The radiative effect can be parametrized by a redefinition of the time each individual cluster has available to undergo evaporation, expressed by an effective radiative time constant.

THE TIME DECAY RATES OF THE CLASSICAL SOLUTION TO THE POISSON-NERNST-PLANCK-FOURIER EQUATIONS IN R^(3)

In this work,the Poisson-Nernst-Planck-Fourier system in three dimensions is considered.For when the initial data regards a small perturbation around the constant equilibrium state in a H^(3)∩■^(-s)(0≤s≤1/2)norm,we obtain the time convergence rate of the global solution by a regularity interpolation trick and an energy method.

GLOBAL WELL-POSEDNESS AND OPTIMAL TIME DECAY RATES FOR THE GENERALIZED PHAN-THIEN-TANNER MODEL IN R^(3)

In this paper, we consider the initial value problem for the incompressible generalized Phan-Thien-Tanner(GPTT) model. This model pertains to the dynamic properties of polymeric fluids. Under appropriate assumptions on smooth function f, we find a particular solution to the GPTT model. In dimension three, we establish the global existence and the optimal time decay rates of strong solutions provided that the initial data is close to the particular solution. The results which are presented here are generalizations of the network viscoelastic models.

Time-Dependent Density Matrix Renormalization Group Coupled with n-Mode Representation Potentials for the Excited State Radiationless Decay Rate:Formalism and Application to Azulene

We propose a method for calculating the nonradiative decay rates for polyatomic molecules including anharmonic effects of the potential energy surface(PES)in the Franck-Condon region.The method combines the n-mode repre-sentation method to construct the ab initio PES and the nearly exact time-dependent density matrix renormalization group method(TD-DMRG)to simulate quantum dynamics.In addition,in the framework of TD-DMRG,we further develop an algorithm to calculate the final-state-resolved rate coefficient which is very useful to analyze the contribution from each vibrational mode to the transition process.We use this method to study the internal conversion(IC)process of azulene after taking into account the anharmonicity of the ground state PES.The results show that even for this semi-rigid molecule,the intramode anharmonicity enhances the IC rate significantly,and after considering the two-mode coupling effect,the rate increases even further.The reason is that the anharmonicity enables the C-H vibrations to receive electronic energy while C-H vibrations do not contribute on the harmonic PES as the Huang-Rhys factor is close to 0.

A solution of the complex Ginzburg-Landau equation with a continuum of decay rates

We prove the existence of a uniform initial datum whose solution decays, in var- ious Lp spaces, at different rates along different time sequences going to infinity, for complex Ginzburg-Landau equation on RN, of various parameters θ and γ.

Rational Energy Decay Rate of a Wave Equation: the Case of Dimension ≥ 2

We apply the multiplier method to obtain the rational energy decay rate of the energy of wave equation in case n ≥ 2, under an assumption on the potential energy.

Re-analysis of temperature dependent neutron capture rates and stellarβ-decay rates of^(95-98)Mo

The neutron capture rates and temperature dependent stellar beta decay rates of Mo isotopes are investigated within the framework of the statistical code TALYS v1.96 and the proton neutron quasi particle random phase approximation(pn-QRPA)model.The Maxwellian average cross-section(MACS)and neutron capture rates for the^(95-98)Mo(n,γ)^(96-99)Mo radiative capture process are analyzed within the framework of the statistical code TALYS v1.96 based on the phenomenological nuclear level density model and gamma strength functions.The present model-based computations for the MACS are comparable to the existing measured data.The sensitivity of stellar weak interaction rates to various densities and temperatures is investigated within the framework of the pn-QRPA model.Particular attention is paid to the impact of thermally filled excited states in the decaying nuclei(^(95-98)Mo)on electron emission and positron capture rates.Furthermore,we compare the neutron capture rates and stellar beta decay rates.It is found that neutron capture rates are higher than stellar beta decay rates at both lower and higher temperatures.

DECAY RATE OF SAINT-VENANT END EFFECTS FOR PLANE DEFORMATIONS OF PIEZOELECTRIC-PIEZOMAGNETIC SANDWICH STRUCTURES

This paper is concerned with the decay of Saint-Venant end effects for plane deformations of piezoelectric （PE）-piezomagnetic （PM） sandwich structures, where a PM layer is located between two PE layers with the same material properties or reversely. The end of the sandwich structure is subjected to a set of self-equilibrated magneto-electro-elastic loads. The upper and lower surfaces of the sandwich structure axe mechanically free, electrically open or shorted as well as magnetically open or shorted. Firstly the constitutive equations of PE mate- rials and PM materials for plane strain are given and normalized. Secondly, the simplified state space approach is employed to arrange the constitutive equations into differential equations in a matrix form. Finally, by using the transfer matrix method, the characteristic equations for eigen- values or decay rates axe derived. Based on the obtained characteristic equations, the decay rates for the PE-PM-PE and PM-PE-PM sandwich structures are calculated. The influences of the electromagnetic boundary conditions, material properties of PE layers and volume fraction on the decay rates are discussed in detail.

Global existence and time decay rates for the 3D bipolar compressible Navier-Stokes-Poisson system with unequal viscosities

We consider the Cauchy problem for the three-dimensional bipolar compressible Navier-Stokes-Poisson system with unequal viscosities.Under the assumption that the H_(3) norm of the initial data is small but its higher order derivatives can be arbitrarily large,the global existence and uniqueness of smooth solutions are obtained by an ingenious energy method.Moreover,if additionally,the H^(−s)(1/2≤s<3/2)or B^(−s)_(2,∞)(1/2<s≤3/2)norm of the initial data is small,the optimal decay rates of solutions are also established by a regularity interpolation trick and delicate energy methods.

Environmental effects on nuclear decay rates

The possible change of nuclear decay rates in different environments has long been an interesting topic due to its importance not only in nuclear physics but also in astrophysics, geological dating, condensed matter physics, etc. The progress in the investigation of variations in nuclear decay rates are reviewed.

OPTIMAL DECAY RATE OF THE COMPRESSIBLE QUANTUM NAVIER-STOKES EQUATIONS

For quantum fluids governed by the compressible quantum Navier-Stokes equations in R;with viscosity and heat conduction, we prove the optimal L;- L;decay rates for the classical solutions near constant states. The proof is based on the detailed linearized decay estimates by Fourier analysis of the operators, which is drastically different from the case when quantum effects are absent.

Global Existence and Optimal Decay Rate of the Compressible Magnetohydrodynamic Equation with Potential Force

In this paper, we consider the three dimensional compressible viscous magnetohydrodynamic equations（MHD） with the external potential force. We first derive the corresponding non-constant stationary solutions. Next, we show global wellposedness of the initial value problem for the three dimensional compressible viscous magnetohydrodynamic equations, provided that the initial data is close to the stationary solution. Finally, based on the elaborate energy estimates for the nonlinear system and L^p-L^q decay estimates of the linearized equation, we show the optimal convergence rates of the solution in L^q-norm with 2≤q≤6 and its first derivative in L^2-norm when the initial perturbation is bounded in L^p-norm with 1≤p〈6/5.