Classical Theory of Advance of Perihelion of Mercury with Velocity Dependent Inertial and Gravitational Masses

It is shown that Mercury's motion of the perihelion around the Sun, which is believed to be explicable quantitatively only by general relativity, can be fully understood within the frame of the dynamics of special relativity. It is only necessary to take into consideration the relativistic dependence of the planet's inertial and gravitational masses on its velocity (relative to the Sun) in the conservation equations for energy, and linear and angular momenta in the gravitational field. The physical Problem is reduced to a singular, nonlinear differential equation, which is solved numerically for the planet Mercury. The advance of the perihelion of Mercury is shown to be = 42.087' for a period of 100 years, which is in agreement with the as- tronomical observations and the result (by analytical approximations) of general relativity.

Mass Transport in a Thin Layer of Bi-Viscous Mud Under Surface Waves

The mass transport in a thin layer of non-Newtonian bed mud under surface waves is examined with a two-fluid Stokes boundary layer model. The mud is assumed to be a bi-viscous fluid, which tends to resist motion for small-applied stresses, but flows readily when the yield stress is exceeded. Asymptotic expansions suitable for shallow fluid layers are applied, and the second-order solutions for the mass transport induced by surface progressive waves are obtained numerically. It is found that the stronger the non-Newtonian behavior of the mud, the more pronounced intermittency of the flow. Consequently, the mass transport velocity is diminished in magnitude, and can even become negative (i.e., opposite to wave propagation) for a certain range of yield stress.

Mass transfer analysis for microwave hot in-place recycling of asphalt pavements

In order to realize mass transfer analysis for microwave hot in-place recycling of asphalt pavements, a volume element is established including asphalt mixtures, liquid water and vapor. A mass transfer control model is built by the theory of multiphysics, phase transformation and diffusion. The model contains continuity equation, energy conservation equation, movement equation and vapor diffusion equation. To gain the solution of the mass transfer model, the formulas are simplified to one-dimensional differential equations. And then a mathematical model of boundary conditions is established. The mass transfer velocity and dissipative energy are obtained in different moisture contents through simulation of asphalt pavements recycling. The result indicates that when initial moisture content is certain, mass transfer velocity is almost uniform in depth direction at the same heating time and enertrv absorbed by water i,~ descendino with denletion of moisture.

Hydrodynamic Analogy to Special Relativity

By studying of a slender body moving in a fluid wave-medium, e.g., in air or in shallow water, it was found that the hydrodynamic momentum mass and the total energy of the fluid field can be expressed in forms of and E=mc2, where v is the body moving speed, c is the wave speed and is the hydrodynamic mass at the zero speed. Thus a hydrodynamic analogy to the relativistic particle motion in vacuum can be traced. The velocity dependence of mass and the mass-energy equivalence are universal for any wave medium, which should not be regarded as a consequence of relative Lorentz time-space, but one of the existence of wave in the medium. Its further inference leads to an even more significant physical picture. If the mass particle moves in an unbounded space at a supercritical speed, i.e. , waves are generated and radiated from it, like the Mach waves by the supersonic plane, and the particle itself experiences a resistance as reaction from the wave radiation. By an extension of this analogy, it can be interred from a hydrodynamic superconductive phenomenon that particles or waves can move possibly at a superluminal speed without experiencing any resistance through a tunnel (a bounded space) under certain conditions. Therefore the speed of light is not the limit of our physical world and superluminal phenomena are possible.

Mass transport in a thin layer of power-law fluid in an Eulerian coordinate system

The mass transport velocity in a thin layer of muddy fluid is studied theoretically. The mud motion is driven by a periodic pressure load on the free surface, and the mud is described by a power-law model. Based on the key assumptions of the shallowness and the small deformation, a perturbation analysis is conducted up to the second order to find the mean Eulerian velocity in an Eulerian coordinate system. The numerical iteration method is adopted to solve these non-linear equations of the leading order. From the numerical results, both the first-order flow fields and the second-order mass transport velocities are examined. The verifications are made by comparing the numerical results with experimental results in the literature, and a good agreement is confirmed.

Discrete particle simulation of mixed sand transport

An Eulerian/Lagrangian numerical simulation is performed on mixed sand transport. Volume averaged Navier-Stokes equations are solved to calculate gas motion, and particle motion is calculated using Newton＇s equation, involving a hard sphere model to describe particle-to-particle and particle-to-wall collisions. The influence of wall characteristics, size distribution of sand particles and boundary layer depth on vertical distribution of sand mass flux and particle mean horizontal velocity is analyzed, suggesting that all these three factors affect sand transport at different levels. In all cases, for small size groups, sand mass flux first increases with height and then decreases while for large size groups, it decreases exponen- tially with height and for middle size groups the behavior is in-between. The mean horizontal velocity for all size groups well fits experimental data, that is, increasing logarithmically with height in the middle height region. Wall characteristics greatly affects particle to wall collision and makes the fiat bed similar to a Gobi surface and the rough bed similar to a sandy surface. Particle size distribution largely affects the sand mass flux and the highest heights they can reach especially for larger particles.

DISTRIBUTED TRACKING CONTROL OF SECONDORDER MULTI-AGENT SYSTEMS UNDER MEASU-REMENT NOISES

This paper considers a leader-following tracking control problem for second-order multiagent systems(MASs) under measurement noises and directed communication channels.It is assumed that each follower-agent can measure the relative positions and velocities of its neighbors in a noisy environment.Based on a novel velocity decomposition technique,a neighbor-based control law is designed to realize local control strategies for these continuous-time agents.It is shown that the proposed consensus protocol can guarantee that all the follower-agents track the active leader.In addition,this result is extended to a more general case with switching topologies.Finally,a numerical example is given for illustration.