GLOBAL SOLUTIONS TO 1D COMPRESSIBLE NAVIER-STOKES/ALLEN-CAHN SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND FREE-BOUNDARY

This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth.

THE ZERO LIMIT OF THERMAL DIFFUSIVITY FOR THE 2D DENSITY-DEPENDENT BOUSSINESQ EQUATIONS

This paper is concerned with the asymptotic behavior of solutions to the initial boundary problem of the two-dimensional density-dependent Boussinesq equations.It is shown that the solutions of the Boussinesq equations converge to those of zero thermal diffusivity Boussinesq equations as the thermal diffusivity tends to zero,and the convergence rate is established.In addition,we prove that the boundary-layer thickness is of the valueδ(k)=k^(α)with anyα∈(0,1/4)for a small diffusivity coefficient k>0,and we also find a function to describe the properties of the boundary layer.

Incompressible Limit of the Oldroyd-B Model with Density-Dependent Viscosity

This paper studies the existence and uniqueness of local strong solutions to an Oldroyd-B model with density-dependent viscosity in a bounded domain Ω ⊂ Rd, d = 2 or 3 via incompressible limit, in which the initial data is “well-prepared” and the velocity field enjoys the slip boundary conditions. The main idea is to derive the uniform energy estimates for nonlinear systems and corresponding incompressible limit.

GLOBAL CLASSICAL SOLUTION TO THE CAUCHY PROBLEM OF THE 3-D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

In this paper, we consider the global existence of classical solution to the 3-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient λ(ρ)provided that the initial energy is small in some sense. In our result, we give a relation between the initial energy and the viscosity coefficient μ, and it shows that the initial energy can be large if the coefficient of the viscosity μ is taken to be large, which implies that large viscosity μ means large solution.

STABILITY OF VISCOUS SHOCK WAVES FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

We study the large-time behavior toward viscous shock waves to the Cauchy problem of the one-dimensional compressible isentropic Navier-Stokes equations with density- dependent viscosity. The nonlinear stability of the viscous shock waves is shown for certain class of large initial perturbation with integral zero which can allow the initial density to have large oscillation. Our analysis relies upon the technique developed by Kanel~ and the continuation argument.

FREE BOUNDARY VALUE PROBLEM FOR THE CYLINDRICALLY SYMMETRIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

In this paper, we investigate the free boundary value problem （FBVP） for the cylindrically symmetric isentropic compressible Navier-Stokes equations （CNS） with density- dependent viscosity coefficients in the case that across the free surface stress tensor is balanced by a constant exterior pressure. Under certain assumptions imposed on the initial data, we prove that there exists a unique global strong solution which tends pointwise to a non-vacuum equilibrium state at an exponential time-rate as the time tends to infinity.

GLOBAL SOLUTIONS TO A 3D AXISYMMETRIC COMPRESSIBLE NAVIER-STOKES SYSTEM WITH DENSITY-DEPENDENT VISCOSITY

In this paper,we consider the 3D compressible isentropic Navier-Stokes equations when the shear viscosityμis a positive constant and the bulk viscosity is λ(ρ)=ρ^(β) with β>2,which is a situation that was first introduced by Vaigant and Kazhikhov in[1].The global axisymmetric classical solution with arbitrarily large initial data in a periodic domain Ω={(r,z)|r=√x^(2)+y^(2),(x,y,z)∈R^(3),r∈I⊂(0,+∞),-∞<z<+∞} is obtained.Here the initial density keeps a non-vacuum state ρ>0 when z→±∞.Our results also show that the solution will not develop the vacuum state in any finite time,provided that the initial density is uniformly away from the vacuum.

ZERO DISSIPATION LIMIT TO RAREFACTION WAVES FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH SELECTED DENSITY-DEPENDENT VISCOSITY

This paper is devoted to studying the zero dissipation limit problem for the one-dimensional compressible Navier-Stokes equations with selected density-dependent viscosity.In particular,we focus our attention on the viscosity taking the formμ(ρ)=ρ^(ϵ)(ϵ>0).For the selected density-dependent viscosity,it is proved that the solutions of the one-dimensional compressible Navier-Stokes equations with centered rarefaction wave initial data exist for all time,and converge to the centered rarefaction waves as the viscosity vanishes,uniformly away from the initial discontinuities.New and subtle analysis is developed to overcome difficulties due to the selected density-dependent viscosity to derive energy estimates,in addition to the scaling argument and elementary energy analysis.Moreover,our results extend the studies in[Xin Z P.Comm Pure Appl Math,1993,46(5):621-665].

Illusion of a Density-Dependent Effect in Biology

Population changes are believed to be controlled by multiple factors, including an important density-dependent effect. This paper reviews the literature on this topic and shows that this density-dependent effect does not exist. This paper also gives a typical example in which no density-dependent effect was detected in the stock-recruitment relationship in Japanese sardines. The recruitment was found to be determined in proportion to the spawning stock biomass and to be affected by environmental factors. This simple mechanism is applicable not only in fish species but also in insects such as Thrips imaginis in Australia. The reason that many biologists have not become aware that the density-dependent effect does not exist is discussed using a metaphor. This paper proposes a new concept in the study of population change. The new concept proposed here will replace the currently used basic concept that has been assumed to be correct for more than 50 years.

STABILITY OF STATIONARY STATE SOLUTION FOR A REACTION DENSITY-DEPENDENT DIFFUSION EQUATION

In this paper we are interested in the large time behavior of the nonlinear diffusion equationWe consider functions which allow the equation to possess traveling wave solutions. We first present an existence and uniqueness as well as some comparison principle result of generalized solutions to the Cauchy problem. Then we give for some threshold results, from which we can see that u=a is stable, while u= 0 or u=1 is unstable under some assumptions, etc.

1-10 Density-dependent Symmetry Energy at Subsaturation Densities

The symmetry energy which characterizes the isospin dependence of the equation of state of asymmetric nuclearmatter, plays a crucial role in understanding a variety of issues in nuclear physics and astrophysics, such as heavyion collisions, exotic nuclei, stability of superheavy nuclei, fusion cross sections, the structures, composition andcooling of neutron stars[1??5]. Much theoretical and experimental effort has been made to constrain the densitydependence of symmetry energy. Up to now, we have got some basic knowledge about the symmetry energy at lowdensities, while at high densities we even do not know its variation tendency as a function of density. The problemremains unsolved due to the difficulty of nucleon-nucleon interactions and many-body problems.

Habitat heterogeneity and biotic interactions mediate climate influences on seedling survival in a temperate forest

Seedling stage has long been recognized as the bottleneck of forest regeneration,and the biotic and abiotic processes that dominate at seedling stage largely affect the dynamics of forest.Seedlings might be particularly vulnerable to climate stress,so elucidating the role of interannual climate variation in fostering community dynamics is crucial to understanding the response of forest to climate change.Using seedling survival data of 69 woody species collected for five consecutive years from a 25-ha permanent plot in a temperate deciduous forest,we identified the effects of biotic interactions and habitat factors on seedling survival,and examined how those effects changed over time.We found that interannual climate variations,followed by biotic interactions and habitat conditions,were the most significant predictors of seedling survival.Understory light showed a positive impact on seedling mortality,and seedling survival responded differently to soil and air temperature.Effects of conspecific neighbor density were significantly strengthened with the increase of maximum air temperature and vapor pressure deficits in the growing season,but were weakened by increased maximum soil temperature and precipitation in the non-growing season.Surprisingly,seedling survival was strongly correlated with interannual climate variability at all life stages,and the strength of the correlation increased with seedling age.In addition,the importance of biotic and abiotic factors on seedling survival differed significantly among species-trait groups.Thus,the neighborhood-mediated effects on mortality might be significantly contributing or even inverting the direct effects of varying abiotic conditions on seedling survival,and density-dependent effects could not be the only important factor influencing seedling survival at an early stage.

GLOBAL WEAK SOLUTIONS TO A THREE-DIMENSIONAL QUANTUM KINETIC-FLUID MODEL

In this paper,we study a quantum kinetic-fluid model in a three-dimensional torus.This model is a coupling of the Vlasov-Fokker-Planck equation and the compressible quantum Navier-Stokes equations with degenerate viscosity.We establish a global weak solution to this model for arbitrarily large initial data when the pressure takes the form p(ρ)=ργ+pc(ρ),whereγ>1 is the adiabatic coefficient and pc(ρ)satisfies■for k≥4 and some constant c>0.

Exploring the sensitivity of α-decay half-life to neutron skin thickness for nuclei around ^(208)Pb

Based on the newest experimentally extracted nuclear density distributions for double-magic nucleus208Pb(Tarbert et al. in Phys Rev Lett 112:242502, 2014),the sensitivity of α-decay half-life to nuclear skin thickness is explored in the vicinity of the shell closure region around208 Pb, i.e., isotopes of Z ? 82 and isotones of N ? 126.With the two-parameter Fermi(2PF) density distributions and an analytically derived formula, the α-decay half-life is found to be closely related to the magnitude of nuclear skin thickness. For a decays to the Z ? 82 isotopes, the α-decay half-life is found to decrease with the increasing neutron skin thickness, while the opposite behavior is found for a decays to the N ? 126 isotones. Therefore, it could be a possible way to extract the nuclear skin thickness from measured α-decay half-lives.

Model for stock-recruitment dynamics of the Peruvian anchoveta (<i>Eugraulis ringens</i>) off Peru

This paper was aimed at re-examining the validity of the results from Cahuin et al. (Estuar. Coast. Shelf Sci. 84, 2009) and identifying a model to describe the stock-recruitment relationship of the Peruvian anchoveta (Eugraulis ringens). Regression analysis was used to determine if density-dependent effects were present. The analysis did not show the existence of any densitydependent effects. It is important to use environmental factors and take observational and process errors into account when attempting to identify density-dependent effects in fish populations. Sea surface temperature (SST) and Southern Oscillation Index (SOI) were used as independent variables to fit the recruitment dynamics of the anchoveta. Both SST and SOI were found to be significantly important parameters in structuring anchoveta dynamics according to Akaike Information Criterion (AIC) and R2 values. The results of this study do not correlate with the findings of Cahuin et al., (2009), where density-dependent effects and the presence of regimes were detected. In conclusion, the recruitment Rt is essentially determined in proportion to spawning stock biomass St, and then environmental factors in year t further change the recruitments. This mechanism is completely same with that for Japanese sardine proposed by Sakuramoto (The Open Fish. Sci. 5, 2012).

粘性依赖于密度的可压缩Navier-Stokes方程(英文)

The global existence of solutions to the equations of one-dimensional compressible flow with density-dependent viscosity is proved. Specifically,the assumptions on initial data are that the modulo constant is stated at x=∞ ＋and x=-∞ ,which may be different ,the density and velocity are in L^z ,and the density is bounded above and below away from zero. The results also show that even under these conditions, neither vacuum states nor concentration states can be formed in finite time.

Density effect and intraspecific competition in a leaf-mining moth on bamboo leaves

When confined to a single leaf, the larvae of most leafminers should suffer intense intraspecific competition. The survival and performance of individuals are expected to decline with increasing larval density within a leaf, showing a negative density-dependent effect. The maximum density of an Elachista Treitschke(Lepidoptera:Elachistidae) miner on Indocalamus tessellatus(Munro)Keng f.(Poaceae: Bambusoideae) under natural conditions can be greater than 40 per leaf, making this a good system for studying intraspecific competition and density effects.We counted the number of leaves with different mine densities in the field and found a clumped distribution of leafminer larvae among host leaves. The emergence rates of pupae(and last-instar larvae), adults and parasitoids were inversely correlated with larval density. Pupal weight and adult weight also showed negative relationships with larval density. However, pairwise tests showed that there might be no differences in pupal or adult weight at larval densities of 1–10 mines per leaf, indicating that densitydependent effects are more obvious at densities greater than 10 mines per leaf. Intraspecific competition could lead to stable density and consistent body size in surviving individual insects, which would help maintain a sustainable population size. The density threshold could be an indicator of the balance between intraspecific competitive detriments and conspecific aggregation benefits; however, the validity of the threshold density hypothesis requires further testing and confirmation.

Optimal Extraction of Groundwater in Gaza Coastal Aquifer

Two multi-objective management models are applied on a local area selected from the regional Gaza coastal aquifer. The objectives and constraints of these management scenarios include maximizing the total volume of water pumped, minimizing the salt concentration of the pumped water, and controlling the drawdown limits. The physical model is based on the CODESA-3D density-dependent advective-dispersive solute transport model. Genetic algorithm is used as the optimization tool. The models are tested on a part of the aquifer ( ) with 9 existing pumping wells located at various depths. The results of the optimization show that the optimization/simulation approach can give better decision if there is enough information to feed to the model. It confirms that the use of the concept of safe yield alone is not enough for sustainable develop-ment of the coastal aquifer. It shows that the optimum pumping rate is in the range of 26%–34% of the total natural replenishment. The application shows that the proposed technique is a powerful tool for solving this type of management problems.

A delayed stage-structure brucellosis model with interaction among seasonality, time-varying incubation and density-dependent growth

In this paper,a class of brucellosis transmission model with seasonal alternation,density-dependent growth,stage-structure,maturation delay,time-varying incubation is established.The basic reproduction number Ro is derived,by which we find that the brucellosis is uniformly persistent if R_(0)>1,while the disease-free periodic solution is globally attractive if R_(0)<1.The theoretical results are illustrated by numerical simulation,from which we find that the brucellosis transmission would be overestimated(or underestimated)if we ignore the influence of time-varying incubation or maturation delay.If density-dependent growth of animals is ignored,the risk of brucellosis may be far underestimated,the extinction of brucellosis can be obtained by numerical simulation under the same conditions.Seasonality significantly affects the long-term dynamic behavior of brucellosis,and the inconsistency of parameter periods results in complex dynamic behavior.

Theoretical predictions on cluster radioactivity of superheavy nuclei with Z=119,120

In this study,we investigate the cluster radioactivity(CR)of new superheavy elements with Z=119 and 120 based on two successful theoretical methods with modified parameters:the density-dependent cluster model(DDCM)and unified decay formula(UDF).First,we employ the DDCM and UDF to accurately reproduce the experimental half-lives of cluster emissions,which demonstrates the high reliability of our theoretical methods.Then,we systematically predict the probable cluster modes of ^(293-311)119 and ^(293-302)120 as well as their corresponding decay energies and half-lives.The half-lives of cluster decay derived from the DDCM are consistent with those from the UDF.Therefore,our results reveal that the cluster emission of ^(8)Be,emitted from the Z=119 and 120 isotopic chains,exhibits the minimum half-life for cluster emission,and hence,^(8)Be emission is considered the most probable cluster decay mode.Moreover,we explore the competition betweenαdecay and CR and find thatαdecay may be the dominant decay mode against CR.Furthermore,the good linear relationship between the decay energy and the number ofαparticles within the emitted cluster is extended to the range of superheavy nuclei(SHN).We anticipate that our theoretical predictions for CR will provide valuable references for the experimental synthesis of new SHN.