Structural evolution of the Tropical Pacific climate network

An attempt is made to develop an equilibrium kinetic equation for a weakly non ideal inhomogeneous gravitational system utilizing the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations. It is shown that the pair correlational function explicitly depends upon the nature of binary interaction between particles. The corresponding kinetic equation containing pair correlation corrections is devoid of the degeneracy present in the collisionless Boltzmann equation with respect to the nature of the two particle interactions, unlike the Vlasov equation that cannot recognize the nature of two particle interaction. A net effect of the particle correlations can be realized only if the spatial symmetry of the correlation interaction is broken due to a spatial inhomogeneity. Such an inhomogeneity is inherently present in a bulk gravitational system in view of the unshielded long range nature of the two-particle interactions. In a finite gravitational system, the effects of pair correlations in the first order kinetic equation can be expressed in terms of the macroscopic gravitational potential to obtain a modified Boltzmann distribution that includes the effects of correlations.     

Effect of polarization force on the Jeans instability of self-gravitating dusty plasma

The effect of polarization force acting on massive charged dust grains is investigated analytically on the Jeans instability of self-gravitating dusty plasma. The gravitational force acting on the massive negatively charged interstellar dust grains are considered in presence of both electrical and polarization forces. The basic equations of the problem are formulated and a general dispersion relation is obtained using plane wave approximation in low frequency wave mode. The effect of polarization force in the dispersion relation of the problem, condition of the Jeans instability and expression of the critical Jeans wave number is examined. The unstable growing modes due to self-gravitational force are studied in the situation when polarization force on the dust grain exceeds over the electrical force in magnitude. It is observed that the polarization force increases the growth rate of the system.     

Quantum Cherenkov radiation at the motion of a small neutral particle parallel to the surface of a transparent dielectric

Quantum Cherenkov radiation and quantum friction at the motion of a small neutral particle parallel to the surface of a transparent dielectric with the refractive index n have been studied in a fully relativistic theory. Radiation appears at velocities above the threshold value, v > v _c = c/n. The friction force in the particle–plate configuration has been derived from the friction force in the plate–plate configuration under the assumption that one of the plates is significantly decharged. A decrease in the kinetic energy of the particle near the threshold velocity is due to its radiation and near the speed of light is determined by the heat power absorbed by the particle in the rest frame. The powers of quantum and classical Cherenkov radiation can be comparable in the relativistic case.     

Collapse of a null fluid

An exact cylindrically symmetric solution of Einstein's gravitational field equations is given for a null fluid imploding radially along an infinite axis. This solution plays an important rôle in the late stages of collapse of a long cylinder of matter. One might expect that self-gravitational effects due to the increasingly relativistic mass of the collapsing matter would create arbitrarily large gravitational fields. It is shown, however, that in the null-fluid approximation the metric is everywhere regular.     

One-body nuclear friction

We have calculated the velocity dependent forces acting between two nuclei that arise due to one-body mechanism of nuclear excitation when they are dragged against one another with constant velocity. The nuclear friction coefficients are then extracted from the velocity dependence of these forces which is found to be strongly linear. The one-body force is calculated by solving the time-dependent Schrödinger equation for all the occupied single-particle states of a nuclear system in a central collision. Each nucleus in this model is assumed to be described by a single-particle Woods-Saxon potential filled with 40 nucleons each. The magnitude of the resulting one-body friction is found to be in between the proximity and surface frictions. The proximity-friction is too small by about an order of magnitude. To check this result, we calculated the one-sided flux from one nucleus to the other. The friction force connected to this flux (i.e. the one-body exchange friction) turns out to be about half or less than the one body friction. We conclude that theproximity-friction grossly underestimates the one-body exchange friction. Furthermore,inelastic excitations are at least as important for one-body dissipation at distances beyond the touching point as is particle exchange.     

Cosmic origin of quantization

The origin of quantization is attributed - via the mechanism of “stochastic quantization” - to the universal interaction of every particle with the background gravitational force due to all other particles of the Universe. A formula for Planck's action constant h, obtained on the basis of this idea, yields the correct order of magnitude for h when implemented with current cosmological data.     

Scattering of Hawking photons as a barrier to particle absorption by black holes

Electromagnetic scattering interactions between photons emanating from a Schwarzschild black hole and an incident charged particle should generate a repulsive force between the particle and black hole. The net scattering cross-section is calculated here as a function of the mass M of the black hole and the mass m of the particle for scenarios in which the particle is point-like and initially stationary, with proper energy ε=m, at some location far from the black hole. It follows from comparing the repulsive scattering force to the corresponding gravitational force that, in order for the particle to be drawn to the black hole, ε/Tbh must be greater than a certain lower bound that is of the order ¹⁰−3 for spin-1/2 or spin-0 particles with unit-charge. Although the scattering restriction is weaker than the requirement ε/Tbh?1 obtained independently from field-theoretic and thermodynamic treatments, the recurrence of a lower bound on the Boltzmann factor ε/Tbh in limitations on particle absorption suggests a physical unity whose nature is fundamentally thermodynamic.     

Liquid-Droplet as a model for the rotation curve problem

The dynamics of large scale gravitational structures like galaxies, local groups and clusters is studied based on the so-called Liquid-Droplet model describing the saturation property of the nuclear force. Using the assumption that the gravitational force is also saturated over large scale structures, it is argued that the Newtonian gravitational potential may be replaced by an effective Machian gravitational potential. Application of this new potential at these large scale structures may give the rotation curves in good agreement with observations. Then, the virial theorem for this kind of gravitational interaction is developed and also the Tully-Fisher relation is obtained. A physical explanation is given for the so-called constant acceleration in the MOND as the effective gravitational strength of these structures. Finally, a brief argument is given for comparison with dark matter models.     

Proposed null experiment to test the inverse square nature of gravitation

A null Cavendish experiment is proposed for testing the validity of the inverse square gravitational force law: one searches for spherically·symmetric excitations in a hollow spherical fluid-filled resonator in the presence of a mass quadrupole rotating at half the lowest resonant frequency of the fluid sphere. By Gauss' law, there is no nonstatic Newtonian coupling to the resonator. The experiment can be made sensitive enough to detect a Yukawa-type force with a strength less than 10^–3 G and a range on the order of 10 cm.     

Determination of the friction coefficient via the force autocorrelation function. A molecular dynamics investigation for a dense Lennard-Jones fluid

For a large region of dense fluid states of a Lennard-Jones system, we have calculated the friction coefficient by the force autocorrelation function of a Brownian-type particle by molecular dynamics (MD). The time integral over the force autocorrelation function showed an interesting behavior and the expected plateau value when the mass of the Brownian particle was chosen to be about a factor of 100 larger than the mass of the fluid particle. Sufficient agreement was found for the friction coefficient calculated by this way and that obtained by MD calculations of the self-diffusion coefficient using the common relation between these coefficients. Furthermore, a modified friction coefficient was determined by integration of the force autocorrelation function up to the first maximum. This coefficient can successfully be used to derive a reasonable soft part of the friction coefficient necessary for the Rice-Allnatt approximation for the shear viscosity of simple liquids.     

The friction coefficient of a Lennard-Jones fluid from the random force autocorrelation function determined as a memory function by molecular dynamics calculations

A recent molecular dynamics (MD) study showed that the friction coefficient of a simple fluid is obtainable by the integral over the autocorrelation function (ACF) of the total force of a Brownian-type particle. The results indicated that mass ratios 50M/m200 of the massive and the light particle suffice to yield accurate friction coefficients. Complementarily, we calculate the random force ACF of the light particle, which is the memory function force of the ACF of the velocity apart from a constant factor, for all the states of the Lennard-Jones system investigated previously. A detailed comparison is presented of the memory function, the total force ACF of the fluid particle, and the total force ACF of the massive particle. The MD results confirm quantitatively our theoretical predictions: (i) on a time scale corresponding to the dynamics of the massive particle the total force ACF of that particle approximates well the memory function, while there are slight differences between them on a short time scale, (ii) the total force ACF of the liquid particle deviates significantly from the memory function already after extremely short time and is thus completely useless for the determination of the friction coefficient, (iii) using the total force ACF of a heavy particle for the determination of the friction constant with mass ratios ofM/m=50 up to 200, the pseudo plateau value of the time integral is often not very noticeable, as the memory function is only approximated and the total force ACF of the massive particle has a negative part at medium times. In those cases the integration has to be extended to include the negative part.     

On Relativistic Generalization of Gravitational Force

In relativistic theories, the assumption of proper mass constancy generally holds. We study gravitational relativistic mechanics of point particle in the novel approach of proper mass varying under Minkowski force action. The motivation and objective of this work are twofold: first, to show how the gravitational force can be included in the Special Relativity Mechanics framework, and, second, to investigate possible consequences of the revision of conventional proper mass concept (in particular, to clarify a proper mass role in the divergence problem). It is shown that photon motion in the gravitational field can be treated in terms of massless refracting medium, what makes the gravity phenomenon compatible with SR Mechanics framework in the variable proper mass approach. Specifically, the problem of point particle in the spherical symmetric stationary gravitational field is studied in SR-based Mechanics, and equations of motion in the Lorentz covariant form are obtained in the relativistic Lagrangean problem formulation. The dependence of proper mass on potential field strength is derived from the Euler-Lagrange equations as well. One of new results is the elimination of conventional 1/r divergence, which is known to be not removable in Schwarzschild gravitomechanics. Predictions of particle and photon gravitational properties are in agreement with GR classical tests under weak-field conditions; however, deviations rise with potential field strength. The conclusion is made that the approach of field-dependent proper mass is perspective for development of SR gravitational mechanics and further studies of gravitational problems.     

Fokker–Planck Equation,Molecular Friction,and Molecular Dynamics for Brownian Particle Transport near External Solid Surfaces

The Fokker–Planck (FP) equation describing the dynamics of a single Brownian particle near a fixed external surface is derived using the multiple-time-scales perturbation method, previously used by Cukier and Deutch and Nienhuis in the absence of any external surfaces, and Piasecki et al. for two Brownian spheres in a hard fluid. The FP equation includes an explicit expression for the (time-independent) particle friction tensor in terms of the force autocorrelation function and equilibrium average force on the particle by the surrounding fluid and in the presence of a fixed external surface, such as an adsorbate. The scaling and perturbation analysis given here also shows that the force autocorrelation function must decay rapidly on the zeroth-order time scale ₀, which physically requires N _Kn1, where N _Kn is the Knudsen number (ratio of the length scale for fluid intermolecular interactions to the Brownian particle length scale). This restricts the theory given here to liquid systems where N _Kn1. For a specified particle configuration with respect to the external surface, equilibrium canonical molecular dynamics (MD) calculations are conducted, as shown here, in order to obtain numerical values of the friction tensor from the force autocorrelation expression. Molecular dynamics computations of the friction tensor for a single spherical particle in the absence of a fixed external surface are shown to recover Stokes' law for various types of fluid molecule–particle interaction potentials. Analytical studies of the static force correlation function also demonstrate the remarkable principle of force-time parity whereby the particle friction coefficient is nearly independent of the fluid molecule–particle interaction potential. Molecular dynamics computations of the friction tensor for a single spherical particle near a fixed external spherical surface (adsorbate) demonstrate a breakdown in continuum hydrodynamic results at close particle–surface separation distances on the order of several molecular diameters.     

Machian Inertia and the Isotropic Universe

This paper addresses the origin of the forces of inertia. It proposes a Newton-Mach particle interaction force between all pairs of particles that depends on their relative acceleration and is proportional to the gravitational force between them. The motion of all objects therefore becomes directly influenced by all of the matter in the universe, as prescribed by Mach's principle. The effect of the observed hierarchical structure of the universe is considered and is used to ensure that the inertial force on an object is finite and isotropic. The instantaneous matter interaction force is justified and both Einstein's and Mach's objections to a Newtonian framework are discussed and shown to be absorbed by the proposed universal law of inertia.     

Impossibility of collapse under the law of gravitationR 44=0

Radial motion of a small point mass in the gravitational field of a large point mass is investigated for the law of gravitationR ₄₄ =0. When geodesic equations are expressed in terms of components of acceleration, it is found that the normally “attractive force” of gravitation gradually weakens as the large mass is approached, and becomes “repulsive” inside a critical nonsingular radius close to the origin of coordinates. A particle requires an infinite time to reach the origin, regardless of its initial distance. Gravitational collapse, or at least violent collapse, is thus precluded.     

Hamiltonian and Brownian systems with long-range interactions: IV. General kinetic equations from the quasilinear theory

We develop the kinetic theory of Hamiltonian systems with weak long-range interactions. Starting from the Klimontovich equation and using a quasilinear theory, we obtain a general kinetic equation that can be applied to spatially inhomogeneous systems and that takes into account memory effects. This equation is valid at order 1/N in a proper thermodynamic limit and it coincides with the kinetic equation obtained from the BBGKY hierarchy. For N→+∞, it reduces to the Vlasov equation governing collisionless systems. We describe the process of phase mixing and violent relaxation leading to the formation of a quasistationary state (QSS) on the coarse-grained scale. We interpret the physical nature of the QSS in relation to Lynden-Bell’s statistical theory and discuss the problem of incomplete relaxation. In the second part of the paper, we consider the relaxation of a test particle in a thermal bath. We derive a Fokker-Planck equation by directly calculating the diffusion tensor and the friction force from the Klimontovich equation. We give general expressions of these quantities that are valid for possibly spatially inhomogeneous systems with long correlation time. We show that the diffusion and friction terms have a very similar structure given by a sort of generalized Kubo formula. We also obtain non-Markovian kinetic equations that can be relevant when the auto-correlation function of the force decreases slowly with time. An interesting factor in our approach is the development of a formalism that remains in physical space (instead of Fourier space) and that can deal with spatially inhomogeneous systems.     

论地震发生机制

地震发生的物理机理和过程是还没有认识清楚的问题. 此前人们将浅源地震归因于弹性回跳,根据这一观点和岩石实验结果计算得到的地震能量与实际观测结果有很大矛盾,被称之为“热流佯谬”. 中源和深源地震发生在地幔区域,其成因也没有合理的解释. 考虑到地壳和地幔是离散集合态物质体系及其慢动力学运动行为的基本特点,本文根据物理学原理,特别是近年凝聚态物理发展出来的相关新观念,并依据已有观测事实,从新的视角探究地震发生的物理机制. 1) 关于地壳岩石层中的应力分布:在不考虑构造力时,依据万物皆流的流变学原理,原始地壳岩石在自重压强长时间作用下,纵向和横向应力相同,没有差应力. 大地构造力推动岩块滞滑移动挤压断层泥,施加于其他岩块,逐渐传递和积累. 这种附加的横向构造力与原始岩石中应力叠加,形成地壳岩石层中的实时应力. 由于断层泥属于颗粒物质体系,具有与岩石不同的力学特征,其弹性模量比岩石小得多,且随压强而增大,导致构造作用力随深度非线性增大. 给出了地壳中构造应力分布及其变化规律. 2) 关于地壳岩石层强度:地壳岩石的自重会使岩石发生弹性–塑性转变. 通过对弹性–塑性转变深度的计算,并根据实际情况分析,给出了地壳岩石弹性、部分塑性和完全塑性三个区域的典型深度范围. 在部分塑性区,塑性体比例达到约10%以上时,发生塑性连通,这时岩石剪切强度由塑性特征决定. 塑性滑移的等效摩擦系数比脆性破裂小一个数量级以上,致使塑性滑移时岩石剪切强度比脆性破裂小得多. 同时,随深度增大,有多种因素使得岩石剪切屈服强度减小. 另一方面,地震是大范围岩石破坏,破坏必然沿薄弱路径发生. 因此,浅源地震岩石的实际破坏强度必定比通常观测到的岩石剪切强度值低. 给出了地壳岩石平均强度和实际破坏强度典型值随深度的分布规律. 3) 关于地震发生的条件和机制:地震发生必定产生体积膨胀,只有突破阻挡才可膨胀. 地震发生的条件是:大地构造力超过岩石破坏强度、断层边界摩擦力以及所受阻挡力之和. 因此,浅源地震是岩石突破阻挡发生的塑性滑移. 在此基础上提出了浅源地震发生的四种可能模式. 深源地震是冲破阻挡发生的大范围岩块流. 浅源地震和深源地震都是堵塞–解堵塞转变,是解堵塞后岩石层块滑移或流动造成的能量释放. 4) 关于地震能量和临震前兆信息:地震能量即为堵塞–解堵塞转变过程释放的动能. 以实例估算表明,地震岩石滑移动能与使岩块剪切破坏和克服周围摩擦阻力所需做的功相一致,不会出现热流佯谬. 同时指出,通过观测地震发生前构造力的积累过程、局域地区地质变迁以及岩石状态变化等所产生的效应,均可能获得有价值的地震前兆信息. 关键词： 地震发生机制 热流佯谬 地壳岩石应力和强度 堵塞–解堵塞转变     

Statistics of the gravitational force in various dimensions of space: from Gaussian to Lévy laws

We discuss the distribution of the gravitational force created by a Poissonian distribution of field sources (stars, galaxies,...) in different dimensions of space d. In d = 3, when the particle number N →+∞, it is given by a Lévy law called the Holtsmark distribution. It presents an algebraic tail for large fluctuations due to the contribution of the nearest neighbor. In d = 2, for large but finite values of N, it is given by a marginal Gaussian distribution intermediate between Gaussian and Lévy laws. It presents a Gaussian core and an algebraic tail. In d = 1, it is exactly given by the Bernouilli distribution (for any particle number N) which becomes Gaussian for N ≫ 1. Therefore, the dimension d = 2 is critical regarding the statistics of the gravitational force. We generalize these results for inhomogeneous systems with arbitrary power-law density profile and arbitrary power-law force in a d-dimensional universe.     

Gravitational Deflection of Light in Rindler-Type Potential as a Possible Resolution to the Observations of Bullet Cluster 1E0657-558

The surface density Σ-map and the convergence κ-map of Bullet Cluster 1E0657-558 show that the center of baryonic matters separates from the center of gravitational force,and the distribution of gravitational force do not possess spherical symmetry.This hints that a modified gravity with difference to Newtonian inverse-square law at large scale,and less symmetry is worth investigating.In this paper,we study the dynamics in Randers-Finsler spacetime.The Newtonian limit and gravitational deflection of light in a Rindler-type potential is focused in particular.It is shown that the convergence in Finsler spacetime could account for the observations of Bullet Cluster.