随机扰动下三维流体界面不稳定性的并行计算

对三维流体界面不稳定性的数值模拟引进了新的数值计算方法,并在MPI并行计算环境下进行了数值模拟.利用LevelSet方法确定界面位置,零水平集对应界面位置.对应离散LevelSet方程和界面两侧的两套Euler方程,借助于Ghost网格方法来完成离散.对最后网格点上的两套状态量的辨认依赖于该点的LevelSet值的符号.并进行了数值计算.     

Neutron skin thickness of 90Zr and symmetry energy constrained by charge exchange spin-dipole excitations

The charge exchange spin-dipole (SD) excitations of \begin{document}$ ^{90} $\end{document}Zr are studied using the Skyrme Hartee-Fock plus proton-neutron random phase approximation with SAMi-J interactions. The experimental value of the model-independent sum rule obtained from the SD strength distributions of \begin{document}$ ^{90} $\end{document}Zr(p, n)\begin{document}$ ^{90} $\end{document}Nb and \begin{document}$ ^{90} $\end{document}Zr(n, p)\begin{document}$ ^{90} $\end{document}Y is used to deduce the neutron skin thickness. The neutron skin thickness \begin{document}$ \Delta r_{np} $\end{document} of \begin{document}$ ^{90} $\end{document}Zr is extracted as \begin{document}$ 0.083\pm0.032 $\end{document} fm, which is similar to the results of other studies. Based on the correlation analysis of the neutron skin thickness \begin{document}$ \Delta r_{np} $\end{document} and the nuclear symmetry energy J as well as its slope parameter L, a constraint from the extracted \begin{document}$ \Delta r_{np} $\end{document} leads to the limitation of J to \begin{document}$ 29.2 \pm 2.6 $\end{document} MeV and L to \begin{document}$ 53.3 \pm 28.2 $\end{document} MeV.     

A branching process model for sand avalanches

An analytically solvable model for sand avalanches of noninteracting grains of sand, based on the Chapman-Kolmogorov equations, is presented. For a single avalanche, distributions of lifetimes, sizes of overflows and avalanches, and correlation functions are calculated. Some of these are exponentials, some are power laws. Spatially homogeneous distributions of avalanches are also studied. Computer simulations of avalanches of interacting grains of sand are compared to the solutions to the Chapman-Kolmogorov equations. We find that within the range of parameters explored in the simulation, the approximation of noninteracting grains of sand is a good one.     

On the invariant measures for the two-dimensional euler flow

It is proven that the canonical Gibbs measure associated with a gas of vortices of intensity ± converges, in the limitN, 0,Nconst, to a Gaussian measure, which is invariant for the two-dimensional Euler equation.On leave from Dipartimento di Matematica Università di Roma Tor Vergata Roma, Italy.On leave from Dipartimento di Matematica Università di Roma La Sapienza, Roma, Italy.     

Universality of a dynamical percolative approach to 1/f γ noise

A dynamical percolative model explaining the universality of 1/ f ^γ noise is reported. Exponents γ ranging from 0 to 2 are obtained under the hypothesis that noise originates from random switching events between two ON-OFF states in elemental parts (switchers) of a physical system. The usual noise behaviour with γ very close to 1 in an arbitrarily wide frequency range is obtained assuming a statistical distribution of switcher relaxation time τ proportional to τ ^-1 , as in McWhorter's model. The impact of these results with respect to recent self-organised criticality models is discussed. Received 6 November 2000 and Received in final form 22 May 2001     

Discrete Green's Function for Lattice Random Walk

A lattice random walk model based on particles scattering on discrete lattice of homogenous space is introduced. The discrete Green's function (DFG) for two-dimensional and three-dimensional lattice random walk of photon is found and proved by mathematical induction. The convolution theorem of photon lattice random walk is presented. They can be used with the method of images to calculate the photon density distribution in semi-infinite and finite slab homogenous turbid media such as tissue.     

Collision problems of random walks in two-dimensional time

The collision problems of two-parameter random walks are studied. That is, some criteria have been established in terms of the characteristic functions of two or more mutually independent random walks in order to determine if they meet infinitly often in certain restricted time sets.     

Random magnetic interactions and spin glass order competing with superconductivity: Interference of the quantum Parisi phase

We analyse the competition between spin glass (SG) order and local pairing superconductivity (SC) in the fermionic Ising spin glass with frustrated fermionic spin interaction and nonrandom attractive interaction. The phase diagram is presented for all temperatures T and chemical potentials μ. SC-SG transitions are derived for the relevant ratios between attractive and frustrated-magnetic interaction. Characteristic features of pairbreaking caused by random magnetic interaction and/or by spin glass proximity are found. The existence of low-energy excitations, arising from replica permutation symmetry breaking (RPSB) in the Quantum Parisi Phase, is shown to be relevant for the SC-SG phase boundary. Complete 1-step RPSB-calculations for the SG-phase are presented together with a few results for -step breaking. Suppression of reentrant SG-SC-SG transitions due to RPSB is found and discussed in context of ferromagnet-SG boundaries. The relative positioning of the SC and SG phases presents a theoretical landmark for comparison with experiments in heavy fermion systems and high superconductors. We find a crossover line traversing the SG-phase with as its quantum critical (end)point in complete RPSB, and scaling is proposed for its vicinity. We argue that this line indicates a random field instability and suggest Dotsenko-Mézard vector replica symmetry breaking to occur at low temperatures beyond. Received 26 November 1998 and Received in final form 25 January 1999     

Random walk on distant mesh points Monte Carlo methods

A new technique for obtaining Monte Carlo algorithms based on the Markov chains with a finite number of states is suggested. Instead of the classical random walk on neighboring mesh points, a general way of constructing Monte Carlo algorithms that could be called random walk on distant mesh points is considered. It is applied to solve boundary value problems. The numerical examples indicate that the new methods are less laborious and therefore more efficient.In conclusion, we mention that all Monte Carlo algorithms are parallel and could be easily realized on parallel computers.     

Dissipation, decoherence and preparation effects in the spin-boson system

The dynamics of the reduced density matrix of the driven dissipative two-state system is studied for a general diagonal/off-diagonal initial state. We derive exact formal series expressions for the populations and coherences and show that they can be cast into the form of coupled nonconvolutive exact master equations and integral relations. We show that neither the asymptotic distributions, nor the transition temperature between coherent and incoherent motion, nor the dephasing rate and relaxation rate towards the equilibrium state depend on the particular initial state chosen. However, in the underdamped regime, effects of the particular initial preparation, e.g. in an off-diagonal state of the density matrix, strongly affect the transient dynamics. We find that an appropriately tuned external ac-field can slow down decoherence and thus allow preparation effects to persist for longer times than in the absence of driving. Received 23 October 1998 and Received in final form 26 February 1999