Energy spectra for decaying 2D turbulence in a bounded domain

We use results derived in the framework of the replica approach to study the liquid-glass thermodynamic transition. The main results are derived without using replicas and applied to the study of the Lennard-Jones binary mixture introduced by Kob and Andersen. We find that there is a phase transition due to the entropy crisis. We compute both analytically and numerically the value of the phase transition point T(K) and the specific heat in the low temperature phase.     

Hit-and-run algorithms for the identification of nonredundant linear inequalities

Two probabilistic hit-and-run algorithms are presented to detect nonredundant constraints in a full dimensional system of linear inequalities. The algorithms proceed by generating a random sequence of interior points whose limiting distribution is uniform, and by searching for a nonredundant constraint in the direction of a random vector from each point in the sequence. In the hypersphere directions algorithm the direction vector is drawn from a uniform distribution on a hypersphere. In the computationally superior coordinate directions algorithm a search is carried out along one of the coordinate vectors. The algorithms are terminated through the use of a Bayesian stopping rule. Computational experience with the algorithms and the stopping rule will be reported.     

A stochastic method for global optimization

A stochastic method for global optimization is described and evaluated. The method involves a combination of sampling, clustering and local search, and terminates with a range of confidence intervals on the value of the global optimum. Computational results on standard test functions are included as well.     

Study of DyFe12−xMx compounds by57Fe and161Dy Mössbauer spectroscopy

DyFe_12?xM_x (M=Si,Ti,Cr) were studied with⁵⁷Fe and¹⁶¹Dy Mössbauer spectroscopy. The deduced coupling constants J_RFe of these compounds are about equal. It is found that Si is substituting one particular Fe-site, while Cr is substituting Fe randomly. In DyFe₁₀Si₂ two Fe-sites favour a c-axis anisotropy, while the third one favours the basal plane.     

Phase Sensitive Detection of 2D Homonuclear Correlation Spectra in MAS NMR

A pulse scheme for phase sensitive detection of two-dimensional (2D) homonuclear correlation magic angle spinning (MAS) NMR spectra is proposed. This scheme combines the time proportional phase increment phase cycling scheme and the time reversal 2D MAS experiment. This approach enables the direct detection of purely absorptive 2D MAS spectra, containing cross peaks that connect only diagonal peaks of dipolar correlated spins.     

On when to stop sampling for the maximum

Suppose a sequential sample is taken from an unknown discrete probability distribution on an unknown range of integers, in an effort to sample its maximum. A crucial issue is an appropriate stopping rude determining when to terminate the sampling process. We approach this problem from a Bayesian perspective, and derive stopping rules that minimize loss functions which assign a loss to the sample size and to the deviation between the maximum in the sample and the true (unknown) maximum. We will show that our rules offer an extremely simple approximate solution to the well-known problem to terminate the Multistart method for continuous global optimization.     

Bayesian stopping rules for multistart global optimization methods

By far the most efficient methods for global optimization are based on starting a local optimization routine from an appropriate subset of uniformly distributed starting points. As the number of local optima is frequently unknown in advance, it is a crucial problem when to stop the sequence of sampling and searching. By viewing a set of observed minima as a sample from a generalized multinomial distribution whose cells correspond to the local optima of the objective function, we obtain the posterior distribution of the number of local optima and of the relative size of their regions of attraction. This information is used to construct sequential Bayesian stopping rules which find the optimal trade off between reliability and computational effort.