Search results for "Exponent"
showing 10 items of 896 documents
Escape Transition of a Grafted Polymer Chain
2000
The escape transition of a flexible polymer chain of chain length N, end-grafted at a hard wall and compressed by a piston of radius R in good solvent conditions, is studied by Monte Carlo simulation and by phenomenological arguments. In contrast to previous theories which have predicted a jump in the force f at a critical value H t of the height H of the piston above the wall, we find that the transition (which is sharp only for N → ∞) is characterized by a flat region of f in the f — H isotherm, i. e. a jump in the height occurs at the transition from H esc , t to H imptt , with (H imp , t — H esc , t )/H esc , t ≈ 0.26. At the transition the constant force f t is predicted and observed t…
ac conductivity inLa2CuO4
1992
Measurements of the complex ac conductivity are reported for a single crystal of ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ for frequencies ${10}^{2}$\ensuremath{\le}\ensuremath{\nu}\ensuremath{\le}${10}^{9}$ Hz and temperatures 25\ensuremath{\le}T\ensuremath{\le}300 K. The conductivity follows a power-law behavior ${\mathrm{\ensuremath{\omega}}}^{\mathit{s}}$ with the frequency exponent s independent of temperature and independent of frequency. However, the hopping transport is strongly anisotropic, with s\ensuremath{\approxeq}0.75 within the ${\mathrm{CuO}}_{2}$ planes and s\ensuremath{\approxeq}0.25 perpendicular to the planes.
Dynamics of Dense Polymers: A Molecular Dynamics Approach
1988
The physics of polymeric materials[1, 2] is one of the most challenging problems in condensed matter physics today. It is a problem of great interest both from a fundamental viewpoint and for their various technical applications. In addition to theortical and experimental approaches, computer simulations[3–11] have played an important role in our present understanding of polymers. For static properties Monte Carlo methods have been widely used and give excellent results for static critical exponents. To investigate dynamic properties three different methods — Monte Carlo (MC)[3–7], molecular dynamics (MD)[8, 9] and Brownian dynamics methods[10] — have been used. Detailed microscopic dynamic…
Dynamic Phase Diagram of the REM
2019
International audience; By studying the two-time overlap correlation function, we give a comprehensive analysis of the phase diagram of the Random Hopping Dynamics of the Random Energy Model (REM) on time-scales that are exponential in the volume. These results are derived from the convergence properties of the clock process associated to the dynamics and fine properties of the simple random walk in the $n$-dimensional discrete cube.
H-function representations for stretched exponential relaxation and non-Debye susceptibilities in glassy systems.
2001
Analytical expressions in the time and frequency domains are derived for non-Debye relaxation processes. The complex frequency-dependent susceptibility function for the stretched exponential relaxation function is given for general values of the stretching exponent in terms of H-functions. The relaxation functions corresponding to the complex frequency-dependent Cole-Cole, Cole-Davidson, and Havriliak-Negami susceptibilities are given in the time domain in terms of H-functions. It is found that a commonly used correspondence between the stretching exponent of Kohlrausch functions and the stretching parameters of Havriliak-Negami susceptibilities are not generally valid.
Universality classes for wetting in two-dimensional random-bond systems
1991
Interface-unbinding transitions, such as those arising in wetting phenomena, are studied in two-dimensional systems with quenched random impurities and general interactions. Three distinct universality classes or scaling regimes are investigated using scaling arguments and extensive transfer-matrix calculations. Both the critical exponents and the critical amplitudes are determined for the weak- and the strong-fluctuation regime. In the borderline case of the intermediate-fluctuation regime, the asymptotic regime is not accessible to numerical simulations. We also find strong evidence for a nontrivial delocalization transition of an interface that is pinned to a line of defects.
How Universal is the Scaling Theory of Localization?
1991
The numerical implementation of the one-parameter scaling theory of localization is reviewed for the Anderson model of disordered solids. A finite-size scaling procedure is used to derive the 3D localization length and d.c.-conductivity from the raw data computed for quasi-1D systems by the strip-and-bar method. While a common scaling function can be unambiguously obtained for different distributions of the diagonal disorder in the Anderson model, discrepancies appear between the box and the Gaussian distribution with regard to the derived critical exponents. To discuss these effects, new results are presented for a triangular distribution, and a new method for the computation of the critic…
Finite-size-scaling study of the simple cubic three-state Potts glass: Possible lower critical dimension d=3.
1990
For small lattices with linear dimension L ranging from L=3 to L=8 we obtain the distribution function P(q) of the overlap q between two real replicas of the three-state Potts-glass model with symmetric nearest-neighbor interaction with a Gaussian distribution. A finite-size-scaling analysis suggests a zero-temperature transition to occur with an exponentially diverging correlation length ${\ensuremath{\xi}}_{\mathrm{SG}}$\ensuremath{\sim}exp(C/${\mathit{T}}^{\mathrm{\ensuremath{\sigma}}}$). This implies that d=3 is the lower critical dimension.
Kinetics of growth process controlled by convective fluctuations
2001
A model of the spherical (compact) growth process controlled by a fluctuating local convective velocity field of the fluid particles is introduced. It is assumed that the particle velocity fluctuations are purely noisy, Gaussian, of zero mean, and of various correlations: Dirac delta, exponential, and algebraic (power law). It is shown that for a large class of the velocity fluctuations, the long-time asymptotics of the growth kinetics is universal (i.e., it does not depend on the details of the statistics of fluctuations) and displays the power-law time dependence with the classical exponent $1/2$ resembling the diffusion limited growth. For very slow decay of algebraic correlations of flu…
Efficient full decay inversion of MRS data with a stretched-exponential approximation of the distribution
2012
SUMMARY We present a new, efficient and accurate forward modelling and inversion scheme for magnetic resonance sounding (MRS) data. MRS, also called surface-nuclear magnetic resonance (surface-NMR), is the only non-invasive geophysical technique that directly detects free water in the subsurface. Based on the physical principle of NMR, protons of the water molecules in the subsurface are excited at a specific frequency, and the superposition of signals from all protons within the excited earth volume is measured to estimate the subsurface water content and other hydrological parameters. In this paper, a new inversion scheme is presented in which the entire data set is used, and multi-expone…