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.

Tracking typhoon-generated swell in the western North Pacific Ocean using satellite altimetry

This paper proposes a scheme for detecting the swell decay of a moving typhoon. We considered a typhoon that was neither far from a point source nor had a belt-like homogenous source,as previously studied. We tracked the swell close to the source during a typhoon in the western North Pacific Ocean. We used wind speed and significant wave height data derived from the Geophysical Data Record of the Jason-1 altimeter and the best-track information of the typhoon from the China Meteorological Administration tropical cyclone database. We selected three specific cases to reveal the decay characteristics of the swell generated by a moving typhoon. Based on an altimeter-based typhoon swell identification scheme and the dispersion relationship for deep water,we relocated the swell source for each altimeter measurement. The subsequent statistical decay coefficient was comparable to previous studies,and effectively depicted the swell propagation conditions induced by the typhoon. We hope that our results provide a new understanding of the characteristics and wave energy budget of the North Pacific Ocean,and significantly contribute to wave modeling in this region.

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 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 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.

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.

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.

Some Properties of Solutions for a Degenerate Diffusion System

In this paper, we prove some properties of solutions to a class of degener-ate diffusion systems which arise from modeling interacting evolution of two biological groups.

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.

THE GLOBAL EXISTENCE AND ANALYTICITY OF A MILD SOLUTION TO THE 3D REGULARIZED MHD EQUATIONS

In this paper,we study the three-dimensional regularized MHD equations with fractional Laplacians in the dissipative and diffusive terms.We establish the global existence of mild solutions to this system with small initial data.In addition,we also obtain the Gevrey class regularity and the temporal decay rate of the solution.

THE OPTIMAL LARGE TIME BEHAVIOR OF3D QUASILINEAR HYPERBOLIC EQUATIONS WITH NONLINEAR DAMPING

We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third order spatial derivatives of the solution,which are the same as those of the heat equation,and in particular,are faster than ones of previous related works.Second,for well-chosen initial data,we also show that the lower optimal L^(2) convergence rate of the k(∈[0,3])-order spatial derivatives of the solution is(1+t)^(-(2+2k)/4).Therefore,our decay rates are optimal in this sense.The proofs are based on the Fourier splitting method,low-frequency and high-frequency decomposition,and delicate energy estimates.

Effect of Stoichiometric Variables in AQUASIM ——Take the Ethanol in ADM1 for an Example

[Objective] The aim was to investigate the effect of stoichiometric variables in AQUASIM, a simulation tool for digestion process. [Method] The ADM1 was modified in AQUASIM based on the existing physical experimental data. Then the stoichiometric variables were adjusted in AQUASIM to test the effects of decay rate, maximum uptake rate and yield of ethanol in the simulation results. [Result] The biomass decay rate of ethanol was 0.02 per day; the maximum uptake rate of ethanol was 228 kgCOD_S/kg COD_X per day and the yield of ethanol was 0.029 5 kg COD_X/kg COD_S in this case. [Conclusion] The larger biomass decay rate of ethanol causes less accumulation of ethanol in the anaerobic digestion model simu- lation. Maximum uptake rate shows little effort to this modeling in a certain range. Larger yield of ethanol will get larger peak values in the simulation results.

Decomposition dynamics of coarse woody debris of three important central European tree species

Background： Coarse woody debris （CWD） is an important element of forest structure that needs to be considered when managing forests for biodiversity, carbon storage or bioenergy. To manage it effectively dynamics of CWD decomposition should be known. Methods： Using a chronosequence approach, we assessed the decomposition rates of downed CWD of Fagus sylvatica, Picea obies and Pinus sylvestfis, which was sampled from three different years of tree fall and three different initial diameter classes （〉10 - ≤20 cm, 〉20 - ≤40 cm, 〉40 cm）. Samples originating from wind throws in 1999 were collected along a temperature and precipitation gradient. Based on the decay class and associated wood densities, log volumes were converted into CWD mass and C content. Log fragmentation was assessed over one year for log segments of intermediate diameters （〉20 - 40 cm） after 8 and 18 years of decomposition. Results： Significantly higher decomposition constants （k） were found in logs of F. sylvotica （0.054 year^-1） than in P. abies （0.033 year^-1） and P. sylvestris （0.032 year^-1）. However, mass loss of P. sylvestris occurred mainly in sapwood and hence k for the whole wood may be overestimated. Decomposition rates generally decreased with increasing log diameter class except for smaller dimensions in P. obies. About 74 % of the variation in mass remaining could be explained by decomposition time （27 %）, tree species （11%）, diameter （17 %）, the interactive effects between tree species and diameter （4 %） as well as between decomposition time and tree species （3 %） and a random factor （site and tree; 9.5 %）, whereas temperature explained only 2 %. Wood fragmentation may play a more important role than previously thought. Here, between 14 % and 30 % of the decomposition rates （for the first 18 years） were attributable to this process. Carbon （C） density （mgC· cm ^-3）, which was initially highest for F. sylvatico, followed by P. sylvestris and P. obies, decreased with increasing decay stage to similar values for all species. Conclusions： The apparent lack of climate effects on decomposition of logs in the field indicates that regional decomposition models for CWD may be developed on the basis of information on decomposition time, tree species and dimension only. These can then be used to predict C dynamics in CWD as input for C accounting models and for habitat management.