Electronic properties of one-dimensional systems with long-range correlated binary potentials

We study numerically the electronic properties of one-dimensional systems with long-range correlated binary potentials. The potentials are mapped from binary sequences with a power-law power spectrum over the entire frequency range, which is characterized by correlation exponent β. We find the localization length ζ increases withβ. At system sizes N →∞, there are no extended states. However, there exists a transition at a threshold ζ. Whenβ 〉 βc, we obtain ζ 〉 0. On the other hand, at finite system sizes, ζ≥ N may happen at certain β, which makes the system ＂metallic＂, and the upper-bound system size N＊ （β） is given.

GLOBAL EXISTENCE OF STRONG SOLUTIONS OF NAVIER-STOKES EQUATIONS WITH NON-NEWTONIAN POTENTIAL FOR ONE-DIMENSIONAL ISENTROPIC COMPRESSIBLE FLUIDS

The aims of this paper are to discuss global existence and uniqueness of strong solution for a class of isentropic compressible navier-Stokes equations with non-Newtonian in one-dimensional bounded intervals. We prove two global existence results on strong solutions of isentropic compressible Navier-Stokes equations. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition.

Strong Interaction and Newtonian Potential Energy

The central part of the nuclear potential energy is shown to depend on the interacting masses of the nuclear matter. This mass dependent potential energy reduces to the usual Newtonian potential energy of the interacting masses when both the interacting masses are more than a certain limiting mass. This strong potential energy results when both the interacting masses are less than the limiting mass. The potential energy is applied to two more systems here and out of which one nucleus is in the middle of periodic table.

Analytical study of pulsatile mixed electroosmotic and shear-driven flow in a microchannel with a slip-dependent zeta potential

The escalation of zeta potential by the influence of wall slip for the electrokinetically modulated flow through a microchannel motivates to consider the impact of hydrodynamic slippage upon the zeta or surface potential.The reported study undergoes an analytical exploration of the pulsatile electroosmosis and shear-actuated flow characteristics of a fluid with a Newtonian model through a microchannel with parallel plates by invoking the reliance of a zeta or surface potential on slippage.The linearized Poisson-Boltzmann and momentum equations are solved analytically to obtain the explicit expression of the electrical potential induced in the electrical double layer(EDL),the flow velocity field,and the volumetric flow rate for an extensive span of parameters.The velocity field proximal to the microchannel wall is observed to enhance by an apparent zeta potential,and is further escalated for a thinner EDL and an oscillating electric field with a higher amplitude.However,near the core region of the microchannel,the flow velocity becomes invariant with the EDL thickness.The result shows that the lower wall velocity contributes to the flow velocity along with the electroosmotic body force and the impact of the velocity of the wall underneath diminishes proximal to the upper wall.Moreover,the volumetric flow rate increases when the thickness of the EDL decreases,owing to the influence of the wall slip.However,for thinner EDLs and medium and higher oscillating Reynolds numbers,the volumetric flow rate varies non-monotonously,correlative to the slip-free and slip cases.

Applications of Potential Theoretic Mother Bodies in Electrostatics

Any polyhedron accommodates a type of potential theoretic skeleton called a mother body. The study of such mother bodies was originally from Mathematical Physics, initiated by Zidarov [1] and developed by Björn Gustafson and Makoto Sakai [2]. In this paper, we attempt to apply the brilliant idea of mother body to Electrostatics to compute the potentials of electric fields.

Dynamics of particles around a pseudo-Newtonian Kerr black hole with halos

The regular and chaotic dynamics of test particles in a superposed field between a pseudo-Newtonian Kerr black hole and quadrupolar halos is detailed.In particular,the dependence of dynamics on the quadrupolar parameter of the halos and the spin angular momentum of the rotating black hole is studied.It is found that the small quadrupolar moment,in contrast with the spin angular momentum,does not have a great effect on the stability and radii of the innermost stable circular orbits of these test particles.In addition,chaos mainly occurs for small absolute values of the rotating parameters,and does not exist for the maximum counter-rotating case under some certain initial conditions and parameters.This means that the rotating parameters of the black hole weaken the chaotic properties.It is also found that the counter-rotating system is more unstable than the co-rotating one.Furthermore,chaos is absent for small absolute values of the quadrupoles,and the onset of chaos is easier for the prolate halos than for the oblate ones.

The Strong Solution for the Viscous Polytropic Fluids with Non-Newtonian Potential

The authors study an initial boundary value problem for the three-dimensional Navier-Stokes equations of viscous heat-conductive fluids with non-Newtonian potential in a bounded smooth domain. They prove the existence of unique local strong solutions for all initial data satisfying some compatibility conditions. The difficult of this type model is mainly that the equations are coupled with elliptic, parabolic and hyperbolic, and the vacuum of density causes also much trouble, that is, the initial density need not be positive and may vanish in an open set.

模拟Kerr度规的牛顿型引力势

本文对只局限于赤道面的模拟Ｋｅｒｒ度规的牛顿型引力势加以推广，使之能用来相当精确地描述轴对称强引力场中赤道面以外粒子和流体的运动。这种既能体现广义相对论效应而又使计算过程大为简化的牛顿势，对于许多天体物理问题（例如厚吸积盘）的研究是非常适用的。

位势井及其对具临界初始能量的非牛顿渗流方程的应用

该文研究具临界初始能量的非牛顿渗流方程的初边值问题.通过构建新的位势井及其井外集合并证明它们的不变性,得到了解的整体存在性与有限时间爆破.

非线性引力理论中整体宇宙弦的吸积

在非线性二次引力理论中，探讨了整体宇宙弦的引力场，与爱因斯坦引力理论的结果相比较，其度规获得了一个相当于长程牛顿势的修正，表明在远处有一高阶的吸引力．并在此基础上讨论了运动的整体宇宙弦的吸积问题，弦尾部的吸积效应也作了相应的修正．

二次引力理论中整体磁单极的引力效应

在二次引力理论L =-g(R+αR2 ) (α｜R｜ 1)中 ,研究整体磁单极的引力场 ,与爱因斯坦引力理论的结果相比较 ,其度规获得了一个相当于长程牛顿势的修正 ,表明在远处有一高阶的吸引力 .在此基础上探讨了整体磁单极的引力效应 ,即运动粒子在经过整体磁单极附近时的偏折 ,其偏转角表现为整体磁单极空间的亏损角、负有效质量和二次引力项 (耦合常数α)的效应 .

可压缩Navier-Stokes-Poisson方程整体解的唯一性

考虑了一维带有初始边界值的等熵可压缩的Navier-Stokes-Poisson方程整体解的唯一性问题。在满足相容性条件下,利用Gronwall's不等式和先验估计获得了解的唯一性的证明。在这里允许初始真空的存在性。

一类带非牛顿位势的广义Vlasov方程

研究了一类带非牛顿位势的广义Vlasov方程,该方程描绘了在非牛顿位势作用下粒子的运动情形。基于压缩映像原理,在没有截断速度的情况下,利用抛物方程解的正则性证明了在p≥2时mild解的整体存在唯一性,以及1<p<2时mild解的局部存在唯一性。该结论推广了文献[7]在截断速度条件下的部分结论。

一类带有非牛顿位势的可压缩Navier-Stokes方程整体强解的存在性

主要研究了一类带有非牛顿位势的可压缩Navier-Stokes方程:其中粘性系数μ依赖于密度ρ,Φ是非牛顿位势.证明了上述问题的强解的存在性.在相容性条件下,得到了强解的唯一性.

高导数引力

在Ｅｉｎｓｔｅｉｎ引力作用量中引入Ｗｅｖｌ张量的平方项，得到有度规张量高阶导数项的引力场方程，考虑其弱场线性近似解，给出了牛顿极限，并讨论了某些新结果。

A Kind of integral Representation on Riemannian Manifods

We generalized the Bochner-Martinelli integral representation to that on Riemannian manifolds. Things become quite different in such case. First we define a kind of Newtonian potential and take the interior product of its gradient to be the integral kernel. Then we prove that this kernel is harmonic in some sense. At last an integral representative theorem is proved.

A relation between long-range correlation and dielectric anomaly

A double-well potential model is established to explain the dielectric anomaly of ferroelectrics. The dielectric constant consists of two parts. One part is independent of the long-range correlation, following 1/T law. The other part originates from the long-range correlation, and can be described by the correlation length well. The deviation from Curie-Weiss law in a small size sample originates from the decrease of the long-range correlation.

On the energy conversion in electrokinetic transports

Energy conversion in micro/nano-systems is a subject of current research,among which the electrokinetic energy conversion has attracted extensive attention.However,there exist two different definitions on the electrokinetic energy conversion efficiency in literature.A few researchers defined the efficiency using the pure pressure-driven flow rate,while other groups defined the efficiency based on the flow rate with the inclusion of the effect of the streaming potential field.In this work,both definitions are investigated for different fluid types under the periodic electrokinetic flow condition.For Newtonian fluids,the two definitions give similar results.However,for viscoelastic fluids,these two definitions lead to significant difference.The efficiency defined by the pure pressure-driven flow rate even exceeds 100%in a certain range of the parameters.The result shows that in the case of viscoelastic flow,it is incorrect to define the energy conversion efficiency by pure pressure-driven flow rate.At the same time,the reason for this problem is clarified through comprehensive analysis.

Ostwald-de Waele流体解的存在唯一性

讨论了一类带有非牛顿位势的等熵可压非牛顿流方程,该方程具有很强的非线性性,在允许初值真空的条件下,证明了该方程局部强解的存在唯一性.

Bounds for the Blow-Up Time on the Pseudo-Parabolic Equation with Nonlocal Term

We investigate the initial boundary value problem of the pseudo-parabolic equation ut-/△ut-/△u=φuu+|u|p-1u,whereφu is the Newtonian potential,which was studied by Zhu et al.(Appl.Math.Comput.,329(2018)38-51),and the global existence and the finite time blow-up of the solutions were studied by the potential well method under the subcritical and critical initial energy levels.We in this note determine the upper and lower bounds for the blow-up time.While estimating the upper bound of blow-up time,we also find a sufficient condition of the solution blowingup in finite time at arbitrary initial energy level.Moreover,we also refine the upper bounds for the blow-up time under the negative initial energy.