Signal formation in NMR is due to incoherent dephasing of nuclear spins. Of particular practical importance is the situation of nuclear spins undergoing independent stochastic motion in inhomogeneous local magnetic fields, e.g., created by magnetized objects. Since it was demonstrated recently that the frequency correlation function of nuclear spins can be measured directly, a theoretical analysis of such functions is of interest. Here, we provide a numerically exact analysis of that correlation function for the inhomogeneous fields around two particular geometries: cylinders and spheres. The functional form exhibits three regimes: after an initial transient, there is an algebraic regime with a t−d/2 time dependence (d being the space dimension), followed by an exponential cutoff due to microscopic system size effects. The main parameter controlling the range of the individual regimes is the volume fraction of the magnetized objects. In addition to our numerical analysis, which is based on eigenfunction expansions, we provide analytical results and approximations based on the generalized moment expansion.

1. Allolio, B., Is endoscopic adrenalectomy the treatment of choice for large primaryDifferential diagnosis of dyspnea-usefulness of clinic aspects, imaging and biomarkers for the identification of heart failure.].A., et al., Medroxyprogesterone acetate but not drospirenone ablates the protective function of 17 beta-estradiol in aldosterone salt-treated rats. Molecular transport through channels and pores: effects of in-channel interactions and blocking. Simvastatin improves left ventricular function after myocardial infarction in hypercholesterolemic rabbits by anti-inflammatory effects. Energetic differences between viable and non-viable myocardium in patients with recent myocardial infarction are not an effect of differences in wall thinning-a multivoxel (31)P-MR-spectroscopy and MRI study. Eur Radiol, 2006. 14. Beer, M., et al., Impact of enzyme replacement therapy on cardiac morphology and function and late enhancement in Fabry's cardiomyopathy. High-dose 17beta-estradiol treatment prevents development of heart failure post-myocardial infarction in the rat.A., et al., Time-varying elastance concept applied to the relation of carotid arterial flow velocity and ventricular area.

The scaling behaviour of randomly branched polymers in a good solvent is studied in two to nine dimensions, using as microscopic models lattice animals and lattice trees on simple hypercubic lattices. As a stochastic sampling method we use a biased sequential sampling algorithm with re-sampling, similar to the pruned-enriched Rosenbluth method (PERM) used extensively for linear polymers. Essentially we start simulating percolation clusters (either site or bond), re-weigh them according to the animal (tree) ensemble, and prune or branch the further growth according to a heuristic fitness function. In contrast to previous applications of PERM, this fitness function is not the weight with which the actual configuration would contribute to the partition sum, but is closely related to it. We obtain high statistics of animals with up to several thousand sites in all dimension 2 less than or equal to d less than or equal to 9. In addition to the partition sum (number of different animals.) we estimate gyration radii and numbers of perimeter sites. In all dimensions we verify the Parisi-Sourlas prediction, and we verify all exactly known critical exponents in dimensions 2, 3, 4 and greater than or equal to 8. In addition, we present the hitherto most precise estimates for growth constants in d greater than or equal to, 3. For clusters with one site attached to an attractive surface, we verify for d greater than or equal to 3 the superuniversality of the cross-over exponent phi at the adsorption transition predicted by Janssen and Lyssy, but not for d = 2. There, we find phi = 0.480(4) instead of the conjectured phi = 1/2. Finally, we discuss the collapse of animals and trees, arguing that our present version of the algorithm is also efficient for some of the models studied in this context, but showing that it is not very efficient for the 'classical' model for collapsing animals.

A generalized macroscopic Fick’s first diffusion law is derived which describes steady-state particle flow between two baths explicitly as a function of the concentration gradient, acting as the thermodynamic driving force, times a functional of the first passage time. The latter is shown to be the ratio of the number of particles trapped between the baths and the first passage time. Particle trapping is shown to be a powerful mechanism by which flow can be enhanced. This is analyzed for two examples: a potential and an entropy trap.

The scaling behavior of randomly branched polymers in a good solvent is studied in two to nine dimensions, modeled by lattice animals on simple hypercubic lattices. For the simulations, we use a biased sequential sampling algorithm with re-sampling, similar to the pruned-enriched Rosenbluth method (PERM) used extensively for linear polymers. We obtain high statistics of animals with up to several thousand sites in all dimension 2⩽d⩽9. The partition sum (number of different animals) and gyration radii are estimated. In all dimensions we verify the Parisi–Sourlas prediction, and we verify all exactly known critical exponents in dimensions 2, 3, 4, and ⩾8. In addition, we present the hitherto most precise estimates for growth constants in d⩾3. For clusters with one site attached to an attractive surface, we verify the superuniversality of the cross-over exponent at the adsorption transition predicted by Janssen and Lyssy.

Lattice animals are one of the few critical models in statistical mechanics violating conformal invariance. We present here simulations of two-dimensional site animals on square and triangular lattices in nontrivial geometries. The simulations are done with the pruned-enriched Rosenbluth method (PERM) algorithm, which gives very precise estimates of the partition sum, yielding precise values for the entropic exponent theta (Z(N) approximately micro(N)N(-theta)). In particular, we studied animals grafted to the tips of wedges with a wide range of angles alpha, to the tips of cones (wedges with the sides glued together), and to branching points of Riemann surfaces. The latter can either have k sheets and no boundary, generalizing in this way cones to angles alpha>360 degrees, or can have boundaries, generalizing wedges. We find conformal invariance behavior, theta approximately 1/alpha , only for small angles (alpha << 2pi) , while theta approximately = const-alpha/2pi for alpha << 2pi. These scalings hold both for wedges and cones. A heuristic (nonconformal) argument for the behavior at large alpha is given, and comparison is made with critical percolation.

We present large statistics simulations of 3-dimensional star polymers with up to $f=80$ arms, and with up to 4000 monomers per arm for small values of $f$. They were done for the Domb-Joyce model on the simple cubic lattice. This is a model with soft core exclusion which allows multiple occupancy of sites but punishes each same-site pair of monomers with a Boltzmann factor $v<1$. We use this to allow all arms to be attached at the central site, and we use the `magic' value $v=0.6$ to minimize corrections to scaling. The simulations are made with a very efficient chain growth algorithm with resampling, PERM, modified to allow simultaneous growth of all arms. This allows us to measure not only the swelling (as observed from the center-to-end distances), but also the partition sum. The latter gives very precise estimates of the critical exponents $\gamma_f$. For completeness we made also extensive simulations of linear (unbranched) polymers which give the best estimates for the exponent $\gamma$.

An improved version of the pruned-enriched-Rosenbluth method (PERM) is proposed and tested on finding lowest energy states in simple models of lattice heteropolymers. It is found to outperform not only the previous version of PERM, but also all other fully blind general purpose stochastic algorithms which have been employed on this problem. In many cases, it found new lowest energy states missed in previous papers. Limitations are discussed.

Two improved versions of the pruned-enriched-Rosenbluth method (PERM) are proposed and tested on simple models of lattice heteropolymers. Both are found to outperform not only the previous version of PERM, but also all other stochastic algorithms which have been employed on this problem, except for the core directed chain growth method (CG) of Beutler & Dill. In nearly all test cases they are faster in finding low-energy states, and in many cases they found new lowest energy states missed in previous papers. The CG method is superior to our method in some cases, but less efficient in others. On the other hand, the CG method uses heavily heuristics based on presumptions about the hydrophobic core and does not give thermodynamic properties, while the present method is a fully blind general purpose algorithm giving correct Boltzmann-Gibbs weights, and can be applied in principle to any stochastic sampling problem.

We present large scale simulations for a one-dimensional chain of hard-point particles with alternating masses and correct several claims in recent literature based on much smaller simulations. We find heat conductivities kappa to diverge with the number N of particles. These depended strongly on the mass ratio, and extrapolations to N--> infinity, and t--> infinity, are difficult due to very large finite-size and finite-time corrections. Nevertheless, our data seem compatible with a universal power law kappa approximately N(alpha) with alpha approximately 0.33 suggesting a relation to the Kardar-Parisi-Zhang model. We finally discuss why the system leads nevertheless to energy dissipation and entropy production, in spite of not being chaotic in the usual sense.

We describe a general strategy for sampling configurations from a given (Gibbs-Boltzmann or other) distribution. It is not based on the Metropolis concept of establishing a Markov process whose stationary state is the wanted distribution. Instead, it builds weighted instances according to a biased distribution. If the bias is optimal, all weights are equal and importance sampling is perfect. If not, "population control" is applied by cloning/killing configurations with too high/low weight. It uses the fact that nontrivial problems in statistical physics are high dimensional. Therefore, instances are built up in many steps, and the final weight can be guessed at an early stage. In contrast to evolutionary algorithms, the cloning/killing is done such that the wanted distribution is strictly observed without simultaneously keeping a large population in computer memory. We apply this method (which is also closely related to diffusion type quantum Monte Carlo) to several problems of polymer statistics, population dynamics, and percolation.

This article presents an analytical approach for the quantification of the blood oxygen level dependent (BOLD) effect in the capillary region. The capillary geometry of myocardium is considered. The relaxation rate R(2)* is determined as a function of the capillary radius R(c), the intracapillary volume fraction REV, and the diffusion coefficient D, When the intracapillary volume fraction is small, the approximation R(2)* - RBV . tau(-1) . (root 1 + (tau delta omega)(2) - 1) is valid, with the correlation time tau = (R(c)(2)/4D) . (\In RBV\/(1 - RBV)). The predictions of this model agree well with numerical simulations and experimental data of others and with data recently measured by our group. Magn Reson Med 41:51-62, 1999. (C) 1999 Wiley-Liss, Inc.

: We apply a Monte Carlo simulation method to lattice systems to study the effect of an intrinsic curvature on the mechanical property of a semiflexible biopolymer. We find that when the intrinsic curvature is sufficiently large, the extension of a semiflexible biopolymer can undergo a first-order transition at finite temperature. The critical force increases with increasing intrinsic curvature. However, the relationship and which exploited the exciting ways in which MCMC spreads across different disciplines. Monte Carlo Simulations and Their Statistical Analysis (B A Berg)An Introduction to Monte Carlo Methods in Statistical Physics (D P Landau)Notes on Perfect Simulation (W S Kendall)Sequential Monte Carlo Methods and Their Applications (R Chen)MCMC in the Analysis of Genetic Data on Pedigrees (E A Thompson) Readership: Academic researchers in physics, statistics and bioinformatics.

We present an analytical theory of susceptibility induced nuclear spin dephasing in the capillary network of myocardium. Using a strong collision approach, equations are obtained for the relaxation rate of the free induction and the spin echo decay. Simulation and experimental data are well predicted by the theory. Since paramagnetic deoxyhemoglobin as the origin of nuclear spin dephasing has a higher tissue concentration in myocardium supplied by a stenotic, i.e., significantly narrowed, coronary artery, spin dephasing might serve as a diagnostic tool. Our approach can be modified for capillary networks in other tissues than myocardium and may be applied in material science.

Recently the blood oxygenation level-dependent (BOLD)related T*(2) of myocardium was derived as an analytical function of intracapillary blood volume, blood oxygenation, and nuclear spin diffusion. The basis of this approach was to approximate the diffusion-induced field fluctuations a nuclear spin is subjected to by strong collision dynamics, i.e., the field fluctuations are uncorrelated. The same analysis is now performed for spin echo experiments that gives myocardiaI T-2 as a function of the parameters above and the echotime. An analytical relationship between T-2 and T*(2) relaxation is derived. The dependence of T-2 on diffusion, echo time, and blood oxygenation is congruent with simulation and experimental data. (C) 1999 Wiley-Liss, Inc.

Recently the blood oxygenation level–dependent (BOLD)‐related T2* of myocardium was derived as an analytical function of intracapillary blood volume, blood oxygenation, and nuclear spin diffusion. The basis of this approach was to approximate the diffusion‐induced field fluctuations a nuclear spin is subjected to by strong collision dynamics, i.e., the field fluctuations are uncorrelated. The same analysis is now performed for spin echo experiments that gives myocardial T2 as a function of the parameters above and the echotime. An analytical relationship between T2 and T2* relaxation is derived. The dependence of T2 on diffusion, echo time, and blood oxygenation is congruent with simulation and experimental data. Magn Reson Med 42:1004–1010, 1999. © 1999 Wiley‐Liss, Inc.

We describe a general strategy, PERM (Pruned-Enriched Rosenbluth Method), for sampling configurations from a given Gibbs-Boltzmann distribution. The method is not based on the Metropolis concept of establishing a Markov process whose stationary state is the wanted distribution. Instead, it starts off building instances according to a biased distribution, but corrects for this by cloning "good" and killing "bad" configurations. In doing so, it uses the fact that nontrivial problems in statistical physics are high dimensional. Therefore, instances are built step by step, and the final "success" of an instance can be guessed at an early stage. Using weighted samples, this is done so that the final distribution is strictly unbiased. In contrast to evolutionary algorithms, the cloning/killing is done without simultaneously keeping a large population in computer memory. We apply this in large scale simulations of homopolymers near the theta and unmixing critical points. In addition we sketch other applications, notably to polymers in confined geometries and to randomly branched polymers. For theta polymers we confirm the very strong logarithmic corrections found in previous work. For critical unmixing we essentially confirm the Flory-Huggins mean field theory and the logarithmic corrections to it computed by Duplantier. We suggest that the latter are responsible for some apparent violations of mean field behavior. This concerns in particular the exponent for the chain length dependence of the critical density which is 1/2 in Flory-Huggins theory, but is claimed to be $\approx 0.38$ in several experiments.

We demonstrate that the recently proposed pruned-enriched Rosenbluth method PERM (P. Grassberger, Phys. Rev. E 56 (1997) 3682) leads to very efficient algorithms for the folding of simple model proteins. We test it on several models for lattice heteropolymers, and compare to published Monte Carlo studies of the properties of particular sequences. In all cases our method is faster than the previous ones, and in several cases we find new minimal energy states. In addition to producing more reliable candidates for ground states, our method gives detailed information about the thermal spectrum and, thus, allows to analyze static aspects of the folding behavior of arbitrary sequences.

In the two-dimensional HAP Model we analyze the thermodynamic folding behavior of sequences that have n-helix and n-member beta-sheet ground state structures.