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At least 1,189 records · Page 66Linked to original sources
PubMed2002

Single-file transport of water molecules through a carbon nanotube.

Recent molecular dynamics simulations of water transport through the interior channel of a carbon nanotube in contact with an aqueous reservoir showed that conduction occurred in bursts with collective water motion. A continuous-time random-walk model is used to describe concerted transport through channels densely filled with molecules in a single-file arrangement, as also found in zeolites, as well as ion channels and aquaporins in biological membranes. Theoretical predictions for different collective properties of the single-file transport agree with the simulation results.

Biological Transport↗
PubMed2002

Universality class of nonequilibrium phase transitions with infinitely many absorbing states.

We consider systems whose steady states exhibit a nonequilibrium phase transition from an active state to one-among an infinite number-absorbing state, as some control parameter is varied across a threshold value. The pair contact process, stochastic fixed-energy sandpiles, activated random walks, and many other cellular automata or reaction-diffusion processes are covered by our analysis. We argue that the upper-critical dimension below which anomalous fluctuation driven scaling appears is d(c)=6, in contrast to a widespread belief. We provide the exponents governing the critical behavior close to or at the transition point to first order in an epsilon =6-d expansion.

Journal Article↗
PubMed2003

Dislocation lines as the precursor of the melting of crystalline solids observed in Monte Carlo simulations.

The microscopic mechanism of the melting of a crystal is analyzed by the constant-pressure Monte Carlo simulation of a Lennard-Jones fcc system. Beyond a temperature of the order of 0.8 of the melting temperature, we found that the relevant excitations are lines of defects. Each of these lines has the structure of a random walk of various lengths on an fcc defect lattice. We identify these lines with the dislocation ones proposed in recent phenomenological theories of melting. Near melting we find the appearance of long lines that cross the whole system. We suggest that these long lines are the precursor of the melting process.

Journal Article↗
PubMed2003

Aging in subdiffusion generated by a deterministic dynamical system.

We investigate aging behavior in a simple dynamical system: a nonlinear map which generates subdiffusion deterministically. Asymptotic behaviors of the diffusion process are described using aging continuous time random walks. We show how these processes are described by an aging diffusion equation which is of fractional order. Our work demonstrates that aging behavior can be found in deterministic low dimensional dynamical systems.

Journal Article↗
PubMed2003

Confinement-induced relaxation process in thin films of cis-polyisoprene.

Broadband dielectric spectroscopy is employed to investigate the molecular dynamics of cis-1,4-polyisoprene (PI) in thin layers down to thicknesses comparable with the chain extension. The segmental and the normal mode dynamics of the PI chains is found not to depend on the layer thickness. Additionally, a novel confinement-induced relaxation process is detected. It is assigned to fluctuations of terminal subchains which are formed due to the immobilization of chain segments at an interface. Most of the experimental findings can be well described by simulations of the chains as ideal random walks.

Journal Article↗
PubMed2003

Behavior of complex knots in single DNA molecules.

We used optical tweezers to tie individual DNA molecules in knots. Although these knots become highly localized under tension, they remain surprisingly mobile and undergo thermal diffusion with classical random walk statistics. The diffusion constants of knots with different complexities correlate with theoretical calculations of knot sizes. We show that this correlation can be explained by a simple hydrodynamical model of "self-reptation" of the knot along a polymer.

Bacteriophage lambda↗
PubMed2004

Performance limitations of flat-histogram methods.

We determine the optimal scaling of local-update flat-histogram methods with system size by using a perfect flat-histogram scheme based upon the exact density of states of 2D Ising models. The typical tunneling time needed to sample the entire bandwidth does not scale with the number of spins N as the minimal N2 of an unbiased random walk in energy space. While the scaling is power law for the ferromagnetic and fully frustrated Ising model, for the +/-J nearest-neighbor spin glass the distribution of tunneling times is governed by a fat-tailed Fréchet extremal value distribution that obeys exponential scaling. Furthermore, the shape parameters of these distributions indicate that statistical sample means become ill defined already for moderate system sizes within these complex energy landscapes.

Journal Article↗
PubMed2004

Nonperturbative renormalization-group study of reaction-diffusion processes.

We generalize nonperturbative renormalization group methods to nonequilibrium critical phenomena. Within this formalism, reaction-diffusion processes are described by a scale-dependent effective action, the flow of which is derived. We investigate branching and annihilating random walks with an odd number of offspring. Along with recovering their universal physics (described by the directed percolation universality class), we determine their phase diagrams and predict that a transition occurs even in three dimensions, contrarily to what perturbation theory suggests.

Diffusion↗
PubMed2004

Beyond the diffusing-wave spectroscopy model for the temporal fluctuations of scattered light.

We extend the theory of diffusing-wave spectroscopy using a random-walk approach and a numerical solution of the radiative transfer equation. The theory is not restricted to the diffusive regime and allows one to describe the crossover between the single-scattering and the diffusive regimes, which has been observed experimentally. It also predicts a lower bound of the scattered-field correlation time at long paths. This extended theory should have broad experimental applications in the field of imaging through biological tissues.

Journal Article↗
PubMed2004

Phase diagram of optimal paths.

We show that by choosing appropriate distributions of the randomness the search for optimal paths links diverse problems of disordered media, such as directed percolation, invasion percolation, and directed and nondirected spanning polymers. We also introduce a simple and efficient algorithm, which solves the d-dimensional model numerically in O(N(1+df/d)) steps, where df is the fractal dimension of the path. Using extensive simulations in two dimensions, we identify the phase boundaries of the directed polymer universality class. A new strong-disorder phase occurs where the optimum paths are self-affine with parameter-dependent scaling exponents. Furthermore, the phase diagram contains directed and nondirected percolation as well as the directed random walk models at specific points and lines.

Journal Article↗
PubMed2004

Nonstochastic behavior of atomic surface diffusion on Cu(111) down to low temperatures.

Atomic diffusion is usually understood as a succession of random, independent displacements of an adatom over the surface's potential energy landscape. Nevertheless, an analysis of molecular dynamics simulations of self-diffusion on Cu(111) demonstrates the existence of different types of correlations in the atomic jumps at all temperatures. Thus, the atomic displacements cannot be correctly described in terms of a random walk model. This fact has a profound impact on the determination and interpretation of diffusion coefficients and activation barriers.

Journal Article↗
PubMed2004

Magnetic filaments in resistive manganites.

The magnetic phase separation in single crystals of the Pr0.67Ca0.33MnO3 manganites is studied using polarized small angle neutron scattering. The measured spectra give a fractal dimension consistent with a configuration in ferromagnetic filaments of nanometric diameter. We argue here that localized charge carriers hop in a random walk fashion mediating a ferromagnetic "hopping exchange" which coexists with superexchange to create the filamentary phase separation. The arguments for this physical picture are validated by Monte Carlo simulations, where magnetism and transport are treated in a self-consistent manner.

Journal Article↗
PubMed2004

Quasi-two-dimensional diffusive random laser action.

We report on random lasing in a disordered system in which the multiple scattering feedback mechanism can be switched from a three-dimensional random walk to a quasi-two-dimensional type of transport. The emission from this system is anisotropic, extraordinary polarized, and is controlled via an external electric field. The phenomenon is observed in dye-doped polymer dispersed liquid crystals and makes use of the strong scattering anisotropies in these materials.

Journal Article↗
PubMed2005

Diffusion and pair interactions of CO molecules on Pd(111).

The diffusion and interactions of CO molecules on Pd(111) were studied by scanning tunneling microscopy. By following the random walk motion of individual molecules as a function of temperature, an activation energy barrier for diffusion of 118 +/- 5 meV was determined. The interaction between CO molecules was found to be repulsive for pairs separated by one or two Pd(111) lattice distances, and weakly attractive at a separation of sqrt[3].

Journal Article↗
PubMed2005

First principles calculation of the interdiffusion coefficient in binary alloys.

The atomic mechanisms of diffusion in alloys are complex due to the variations of migration energies with environment and the correlations induced by short-range order between the different components. We present a first-principles approach for calculating vacancy-mediated diffusion coefficients in crystalline binary alloys and apply it to obtain the interdiffusion coefficient of Al(1-x)Lix. The rigorous treatment of atomic migration indicates that short- and long-range order induces strongly correlated migration mechanisms that deviate from random walk behavior.

Journal Article↗
PubMed2005

Diffusion-reaction in branched structures: theory and application to the lung acinus.

An exact "branch by branch" calculation of the diffusional flux is proposed for partially absorbed random walks on arbitrary tree structures. In the particular case of symmetric trees, an explicit analytical expression is found which is valid whatever the size of the tree. Its application to the respiratory phenomena in pulmonary acini gives an analytical description of the crossover regime governing the human lung efficiency.

Animals↗
PubMed2005

Non-markovian transport of DNA in microfluidic post arrays.

We present an analytically solvable model for the transport of long DNA through microfluidic arrays of posts. The motion is a repetitive three-part cycle: (i) collision with the post and extension of the arms; (ii) rope-over-pulley post disengagement; and (iii) a random period of uniform translation before the next collision. This cycle, inspired by geometration, is a nonseparable (Scher-Lax) continuous-time random walk on a lattice defined by the posts. Upon adopting a simple model for the transition probability density on the lattice, we analytically compute the mean DNA velocity and dispersivity in the long-time limit without any adjustable parameters. The results compare favorably with the limited amount of experimental data on separations in self-assembled arrays of magnetic beads. The Scher-Lax formalism provides a template for incorporating more sophisticated microscale models.

Bacteriophage T4↗
PubMed2005

Weak measurements are universal.

It is well known that any projective measurement can be decomposed into a sequence of weak measurements, which cause only small changes to the state. Similar constructions for generalized measurements, however, have relied on the use of an ancilla system. We show that any generalized measurement can be decomposed into a sequence of weak measurements without the use of an ancilla, and give an explicit construction for these weak measurements. The measurement procedure has the structure of a random walk along a curve in state space, with the measurement ending when one of the end points is reached. This shows that any measurement can be generated by weak measurements, and hence that weak measurements are universal. This may have important applications to the theory of entanglement.

Journal Article↗