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.

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.

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.

ON LOCAL CONTROLLABILITY FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY DEPENDENT VISCOSITIES

In this paper,we study the controllability of compressible Navier-Stokes equations with density dependent viscosities.For when the shear viscosityμis a positive constant and the bulk viscosityλis a function of the density,it is proven that the system is exactly locally controllable to a constant target trajectory by using boundary control functions.

Uniform Persistence, Periodicity and Extinction in a Delayed Biological System with Stage Structure and Density-Dependent Juvenile Birth Rate

A delayed biological system of predator-prey interaction with stage structure and density dependent juvenile birth rate is investigated. It is assumed that the prey population has two stages: immature and mature. The growth of the immature prey is density dependent and is a function of the density of adult prey. Such phenomenon has been reported for beetles, tribolium, copepods, scorpions, several fish species and even crows. The growth of the predator is affected by the time delay due to gestation. By some Lemmas and methods of delay differential equation, the conditions for the uniform persistence and extinction of the system are obtained. Numerical simulations illustrate the feasibility of the main results and demonstrate that the density dependent coefficient has influence on the system populations’ densities though it has no effect on uniform persistence and extinction of the system.

Hypernucleus-^(16)O in the density-dependent Hartree approach based on the chiral-σ model

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A time-dependent density functional theory investigation of plasmon resonances of linear Au atomic chains

We report theoretical studies on the plasmon resonances in linear Au atomic chains by using ab initio time- dependent density functional theory. The dipole responses are investigated each as a function of chain length. They converge into a single resonance in the longitudinal mode but split into two transverse modes. As the chain length increases, the longitudinal plasmon mode is redshifted in energy while the transverse modes shift in the opposite direction （blueshifts）. In addition, the energy gap between the two transverse modes reduces with chain length increasing. We find that there are unique characteristics, different from those of other metallic chains. These characteristics are crucial to atomic-scale engineering of single-molecule sensing, optical spectroscopy, and so on.

Time-dependent density functional theoretical studies on the photo-induced dynamics of an HCI molecule encapsulated in C60 under femtosecond laser pulses

By using first-principles simulations based on time-dependent density functional theory, the chemical reaction of an HCl molecule encapsulated in C60 induced by femtosecond laser pulses is observed. The H atom starts to leave the Cl atom and is reflected by the C60 wall. The coherent nuclear dynamic behaviors of bond breakage and recombination of the HCl molecule occurring in both polarized parallel and perpendicular to the H-Cl bond axis are investigated. The radial oscillation is also found in the two polarization directions of the laser pulse. The relaxation time of the H-Cl bond lengths in transverse polarization is slow in comparison with that in longitudinal polarization. Those results are important for studying the dynamics of the chemical bond at an atomic level.

Theoretical Study on the Optical Properties for 2,7- and 3,6-Linked Carbazole Trimers by Time-dependent Density Functional Theory

Electronic properties, such as HOMO and LUMO energies, band gaps, ionization potential （IP） and electron affinity （EA） of 2,7- and 3,6-1inked carbazole trimers, two conjugated oligomcrs with different linkages of carbazole, were studicd by the density functional theory with Becke-Lee-Young-Parr composite exchange correlation functional （B3LYP）. The absorption spectra of these compounds were also investigated by time-dependent density functional theory （TD-DFT） with 6-3 IG＊ basis set. The calculated results indicated that the HOMO and LUMO of the 2,7- and 3,6-1inked carbazole trimers are both slightly destabilized on going from methyl substitution to sec-butyl substitution. Both IP and EA exhibit their good hole-transporting but poor electronaccepting ability. The presence of alkyl groups on the nitrogen atoms does not affect the intra-chain electronic delocalization along the molecular frame. Thus no significant effect on the band gap and absorption spectra of compounds has been found.

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.

Effect of Depth-Dependent Nociceptor Density on the Heat-Induced Withdrawal Reflex

Previously we introduced a concise dose-response model for the heat-induced withdrawal reflex caused by millimeter wave radiation. The model predicts the occurrence of withdrawal reflex from the given spatial temperature profile. It was formulated on the assumption that the density of nociceptors in skin is uniform, independent of the depth. The model has only two parameters: the activation temperature of heat-sensitive nociceptors and the critical threshold on the activated volume for triggering withdrawal reflex. In this study, we consider the case of depth-dependent nociceptor density in skin. We use a general parametric form with a scaling parameter in the depth direction to represent the nociceptor density. We analyze system behaviors for four density types of this form. Based on the theoretical results, we develop a methodology for 1) identifying from test data the density form of nociceptors distribution, 2) finding from test data the scaling parameter in the density form, and 3) determining from test data the activation temperature of nociceptors.

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.

From Finite Nuclei to Neutron Stars: The Essential Role of High-Order Density Dependence in Effective Forces

A unified description of finite nuclei and equation of state of neutron stars presents both a major challenge and also opportunities for understanding nuclear interactions.Inspired by the Lee-Huang-Yang formula of hardsphere gases,we develop effective nuclear interactions with an additional high-order density dependent term.While the original Skyrme force SLy4 is widely used in studies of neutron stars,there are not satisfactory global descriptions of finite nuclei.The refitted SLy4' force can improve descriptions of finite nuclei but slightly reduces the radius of neutron star of 1.4 M_☉ with M_☉ being the solar mass.We find that the extended SLy4 force with a higher-order density dependence can properly describe properties of both finite nuclei and GW170817 binary neutron stars,including the mass-radius relation and the tidal deformability.This demonstrates the essential role of high-order density dependence at ultrahigh densities.Our work provides a unified and predictive model for neutron stars,as well as new insights for the future development of effective interactions.

Persistence in Non-Autonomous Lotka-Volterra System with Predator-Prey Ratio-Dependence and Density Dependence

The main purpose of this article is considering the persistence non-autonomous Lotka-Volterra system with predator-prey ratio-dependence and density dependence. We get the sufficient conditions of persistence of system, further have the necessary conditions, also the uniform persistence condition, which can be easily checked for the model is obtained.

Wavelet-Based Density Estimation in Presence of Additive Noise under Various Dependence Structures

We study the following model: . The aim is to estimate the distribution of X when only are observed. In the classical model, the distribution of is assumed to be known, and this is often considered as an important drawback of this simple model. Indeed, in most practical applications, the distribution of the errors cannot be perfectly known. In this paper, the author will construct wavelet estimators and analyze their asymptotic mean integrated squared error for additive noise models under certain dependent conditions, the strong mixing case, the β-mixing case and the ρ-mixing case. Under mild conditions on the family of wavelets, the estimator is shown to be -consistent and fast rates of convergence have been established.

Spin-dependent transport characteristics of nanostructures based on armchair arsenene nanoribbons

By employing non-equilibrium Green＇s function combined with the spin-polarized density-functional theory, we investigate the spin-dependent electronic transport properties of armchair arsenene nanoribbons（a As NRs）. Our results show that the spin-metal and spin-semiconductor properties can be observed in a As NRs with different widths. We also find that there is nearly 100% bipolar spin-filtering behavior in the a As NR-based device with antiparallel spin configuration. Moreover, rectifying behavior and giant magnetoresistance are found in the device. The corresponding physical analyses have been given.

Modelling and Analysis of Bacteria Dependent Infectious Diseases with Variable Contact Rates

In this research,we proposed a non-linear SIS model to study the effect of variable interaction rates and non-emigrating population of the human habitat on the spread of bacteria-infected diseases.It assumed that the growth of bacteria is logistic with an intrinsic growth rate is a linear function of infectives.In this model,we assume that contact rates between susceptibles and infectives as well as between susceptibles and bacteria depend on the density of the non-emigrating population and the total population of the habitat.The stability theory has been analyzed to analyzed to study the crucial role played by bacteria in the increased spread of an infectious disease.It is shown that as the density of non-emigrating population increases,the spread of an infectious disease increases.It is shown further that as the emigration increases,the spread of the disease decreases in both the cases of contact mentioned above rates,but this spread increases as these contact rates increase.It suggested that the control of bacteria in the human habitat is very useful to decrease the spread of an infectious disease.These results are confirmed by numerical simulation.

Interaction of Photoactive[Fe(CN)_6]^(4-) with TiO_2 Anatase(101) Surface:A Periodic Density Functional Theory Study

The plane-wave pseudopotential function method, based on density-functional theory, has been used to calculate the adsorption, electronic band structures, orbitals and optical absorption spectrum of [Fe（CN）6]^4- on TiOz anatase（101） surface. Our calculations reveal that the surface-modified anatase system has large adsorption energy and a much narrower band gap. [Fe（CN）6]^4- adsorption on the （101） surface could lead to a large red shift of the anatase optical absorption threshold, which extends into a visible region significantly. The calculated results are in agreement with the experiment and other theoretical studies reasonably. It is very important for the understanding and further development ofphotovoltaic materials that are active under visible light.

Low-Density Co-Inoculation with Bradyrhizobium japonicum SAY3-7 and Streptomyces griseoflavus P4 Promotes Plant Growth and Nitrogen Fixation in Soybean Cultivars

Inoculation density has a marked effect on nodulation and N fixation in soybean (Glycine max L.). Therefore, we conducted this study to determine the optimal inoculation density of Bradyhizobium japonicum SAY3-7 (SAY3-7) and Streptomyces griseoflavus P4 (P4) for plant growth, nodulation, and N fixation, and to investigate the effect of co-inoculation on selected soybean cultivars, using the optimal inoculation density. Nitrogen fixation, in terms of an acetylene reduction activity value, was measured using a flame ionization gas chromatograph. In this study, low-density single inoculation with P4 (105 or 106 cells mL-1) was associated with the highest plant biomass, compared with normal- and high-density single inoculation with P4 (107 or 108 cells mL-1). Moreover, low-density single or co-inoculations with SAY3-7 and/or P4 produced the highest nodule biomass and highest nitrogenase activity, compared with single or dual inoculation at other inoculation densities. Therefore, we evaluated low-density co-inoculation with P4 and SAY3-7, at the rate of 105 cells mL-1, on selected soybean cultivars. Low-density co-inoculation increased the plant biomass, compared with un-inoculated plants. The effects of single and co-inoculation on nodulation did not differ significantly for any of the cultivars, except “Yezin-9” in the first experiment and “Shan Seine” in the second experiment. Low-density inoculation with both bacteria increased N fixation by 15% - 75% for seven of the cultivars in the first experiment and by 15% - 39% for three of the cultivars in the second experiment, compared with single inoculation with SAY3-7. Based on the overall results, we concluded that low-density co-inoculation with P4 and SAY3-7 gave improved plant growth and N fixation.