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.

Annual variation of adult survival of a south-temperate House Wren population in Argentina

Identifying factors affecting the survival of individuals is essential for understanding the evolution of life-history traits and population dynamics.Despite numerous studies on this subject in north-temperate environments,there is a lack of equivalent studies at similar latitudes in the south.Here,we used a 14-year dataset of capture,banding,and resighting to estimate the annual variation in the apparent adult survival probability of a south-temperate population of House Wrens(Troglodytes aedon bonariae).We evaluated temporal variation in sur-vival and the effect of environmental(climatic)and demographic variables(adult abundance,total number of fledglings produced during each breeding season)on survival estimators.We found that the probability of adult survival decreased as the abundance of breeding adults increased.This density-dependent effect could be related to the resident lifestyle of southern House Wrens,which could determine an intense competition for territories and resources that ultimately would affect their survival.

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.

COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

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.

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].

Non-formation of vacuum states for Navier-Stokes equations with density-dependent viscosity

We consider the Cauchy problem, free boundary problem and piston problem for one-dimensional compressible Navier-Stokes equations with density-dependent viscosity. Using the reduction to absurdity method, we prove that the weak solutions to these systems do not exhibit vacuum states, provided that no vacuum states are present initially. The essential re- quirements on the solutions are that the mass and energy of the fluid are locally integrable at each time, and the Lloc1-norm of the velocity gradient is locally integrable in time.

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.

Ebola virus disease model with a nonlinear incidence rate and density-dependent treatment

This paper studies an Ebola epidemic model with an exponential nonlinear incidence function that considers the efficacy and the behaviour change.The current model also incorporates a new density-dependent treatment that catches the impact of the disease transmission on the treatment.Firstly,we provide a theoretical study of the nonlinear differential equations model obtained.More precisely,we derive the effective reproduction number and,under suitable conditions,prove the stability of equilibria.Afterwards,we show that the model exhibits the phenomenon of backward-bifurcation whenever the bifurcation parameter and the reproduction number are less than one.We find that the bi-stability and backward-bifurcation are not automatically connected in epidemic models.In fact,when a backward-bifurcation occurs,the disease-free equilibrium may be globally stable.Numerically,we use well-known standard tools to fit the model to the data reported for the 2018–2020 Kivu Ebola outbreak,and perform the sensitivity analysis.To control Ebola epidemics,our findings recommend a combination of a rapid behaviour change and the implementation of a proper treatment strategy with a high level of efficacy.Secondly,we propose and analyze a fractional-order Ebola epidemic model,which is an extension of the first model studied.We use the Caputo operator and construct the Grünwald-Letnikov nonstandard finite difference scheme,and show its advantages.

Effects of Distorted Wave on Proton Elastic Scattering from Light Nuclei at 200 MeV

The distorted wave is introduced into the relativistic impulse approximation to generate the Dirac optical potentials for proton elastic scattering. Those potentials, produced by folding the target ground state wavefunction with the free nucleon-nucleon interactions, are used to reevaluate scattering observables, such as differential cross section, analysing power and spin rotation function, for proton elastic scattering from ^12C and ^16O at Elab = 200 MeV, respectively. The inclusion of the distorted wave in the original relativistic impulse approximation has brought out better results of the observables, especially at small scattering angles.

Radial Excitations in the Global Colour Soliton Model

With the Munczek-Nemirovsky model of the effective gluon propagator in the global colour model, we study the radially excited solitons in which one quark is excited and the other two are at the ground state. The obtained masses of the two radial excitations are comparable with the experimental data.

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.