Lorentz Transformations from Reflections: Some Applications

We point out, by exhibiting two examples and mentioning a third one, that it is sometimes useful to consider Lorentz transformations as generated from hyperplane or line reflections. One example concerns the construction of boosts linking two given 4-vectors, the other one concerns the Minkowski geometric understanding of V. Moretti's polar decomposition of orthochronous Lorentz matrices.     

Exact solutions to the time-dependent Lorentz gas Boltzmann Equation: The approach to hydrodynamics

New exact solutions to the time-dependent Lorentz gas Boltzmann equation are presented for two classes of nonequilibrium initial value problems: thedecay of localized disturbances and theresponse to applied electric fields. These exact results are used to gain some insight into the crossover of the nonequilibrium state from the early-timekinetic regime to the late-timehydrodynamic regime.     

Time-dependent correlation functions for random walks on bond disordered cubic lattices

For hopping models on cubic lattices with a fractionc of impurity bonds, time-dependent transport properties and correlation functions (long-time tails) are calculated through a systematicc-expansion (in the percolation literature referred to as high-density expansion), using a method developed in an earlier paper. The time-dependent diffusion coefficient, velocity autocorrelation function (VACF), and Burnett functions are calculated exact toO(c) for allt, and exact toO(c ₂ ) for long times only. A comparison is made with the results of the effective medium approximation, and numerical results are given for the square lattice.     

Bond percolation in two and three dimensions: Numerical evaluation of time-dependent transport properties

For random walks on two- and three-dimensional cubic lattices, numerical results are obtained for the static,D(), and time-dependent diffusion coefficientD(t), as well as for the velocity autocorrelation function (VACF). The results cover all times and include linear and quadratic terms in the density expansions. Within the context of kinetic theory this is the only model in two and three dimensions for which the time-dependent transport properties have been calculated explicitly, including the long-time tails.     

Thermodynamic formalism and localization in Lorentz gases and hopping models

The thermodynamic formalism expresses chaotic properties of dynamical systems in terms of the Ruelle pressure (). The inverse-temperature-like variable allows one to scan the structure of the probability distributin in the dynamic phase space. This formalism is applied here to a lorentz lattice gas. where a particle moving on a lattice of sizeL ^d collides with fixed scatterers placed at random locations. Here we give rigorous arguments that the Ruelle pressure in the limit of infinite systems has two branches joining with a slope discontinuity at =1. The low- and high- branches correspond to localization of trajectories on respectively the most chaotic (highest density) region and the most deterministic (lowest density) region, i.e. () is completely controlled by rare fluctuations in the distribution of scatterers on the lattice. and it dose not carry and information on the global structure of the static disorder. As approaches unity from either side, a localization-delocalization transition leads to a state where trajectories are extended and carry information on transprot properties. At finiteL the narrow region around =1 where the trajectories are extended scales as (InL)^–2. where depends on the sign of 1–, ifd>1, and as (L InL)^–1 ifd=1. This result appears to be general for diffusive systems with static disorder, such as random walks in random environments or for the continuous Lorentz gas. Other models of random walks on disordered lattices, showing the same phenomenon, are discussed.     

Long-time tails of the velocity autocorrelation functions for the triangular periodic Lorentz gas

We present numrical results on the velocity autocorrelation function (VACF)C(t)=<ν(t)·ν(0)> for the periodic Lorentz gas on a two-dimensional triangular lattice as a function of the radiusR of the hard disk scatterers on the lattice. Our results for the unbounded horizon case confirm 1/t decay of the VACF for long times (out to 100 times the mean free time between collisions) and provide strong support for the conjecture by Friedman and Martin that the 1/t decay is due to long free paths along which a moving particle does not scatter up to timet. Even after new sets of long free paths become available forR<1/4, we continue to find good agreement between numerical results and an analytically estimated 1/t decay. For the bounded horizon case , our numerical VACFs decay exponentially, although it is difficult to discriminate among pure exponential decay, exponential decay with prefactor, and stretched exponential decay.     

狭义相对论中的与门佯谬

提出了一个所谓“与门佯谬”问题,并利用狭义相对论进行了详细的分析和计算,消除和此佯谬。     

磁场对蔗糖转化影响的研究

一．引言化学反应的发生是各种能量的综合体现，福井谦一曾指出：“由于离域化能而产生的稳定化究竟能抵消由于交换能而产生的不稳定化到何种程度，就是实际能否发生反应的关键。”［１］“一个化学反应在开始阶段有最强离域相互作用的路径，即为经过过渡态而达产物具有最...     

Sublattices of the banach envelope of weak

We prove that every separable Banach lattice is lattice isometric to a closed sublattice of the Banach envelope of Weak

     

局部Hardy与Lorentz空间的关系

本文研究局部Hardy空间Hloc1(Ω)与局部Lorentz空间Lloc1,γ(Ω)(0<γ≤1)之间的关系.当0<γ≤1/2时,两者无不包含;当1/2<γ≤1时,Hloc1(Ω)中的非负函数必然属于Lloc1,γ(Ω).