Search results for " exponent"
showing 10 items of 315 documents
Simulation of Models for Isotropic and Anisotropic Orientational Glasses
1992
“Orientational glass” behavior is found when molecular crystals are randomly diluted, and quadrupole moments get frozen by random alignment of the molecules, similar to “spin glass” behavior of randomly diluted magnets. Monte Carlo simulation of lattice models where quadrupole moments interact with nearest neighbor Gaussian coupling is a unique tool to study this behavior. The time-dependent glass order parameter exhibits anomalously slow relaxation, compatible with the Kohlrausch-Williams-Watts (KWW) stretched exponential function. Both isotropic and anisotropic models exhibit in d=2 and d=3 spatial dimensions glass transitions at zero temperature only. While the glass correlation length a…
Dynamic Anomalies and their Relation to the Glass Transition: A Neutron Scattering Study of the Glass Forming Van der Waals Liquid Ortho-terphenyl
1991
Neutron scattering experiments on the molecular glass former ortho-terphenyl reveal a dynamic anomaly at a temperature Tc ≈ 290 K well above the calorimetric glass temperature Tg = 243 K. Close above Tc the density autocorrelation function ΦQ(t) shows a two step decay over 4–5 decades in time. The slower component obeys the time-temperature superposition principle. Its line shape can be well parametrized by a Kohlrausch law and is strongly temperature dependent as its relaxation time scales with the shear viscosity. Thus this component is identified with the structural relaxation (α-process). The faster component (β-process) is much less temperature dependent. Its line shape factorizes in a…
Testing Mode-Coupling Theory for a Supercooled Binary Lennard-Jones Mixture I: The van Hove Correlation Function
1995
We report the results of a large scale computer simulation of a binary supercooled Lennard-Jones liquid. We find that at low temperatures the curves for the mean squared displacement of a tagged particle for different temperatures fall onto a master curve when they are plotted versus rescaled time $tD(T)$, where $D(T)$ is the diffusion constant. The time range for which these curves follow the master curve is identified with the $\alpha$-relaxation regime of mode-coupling theory (MCT). This master curve is fitted well by a functional form suggested by MCT. In accordance with idealized MCT, $D(T)$ shows a power-law behavior at low temperatures. The critical temperature of this power-law is t…
Critical Exponents and Randomness in SrTiO3 : Ca
1994
Since its discovery, the SrTiO3: Ca system is known to exhibit a number of features which were thought to arise from an impurity induced disorder. Non-linear dielectric measurements are used to obtain a more quantitative insight into this disorder. For 0.001 < xCa < 0.05, it is found that the non-linear susceptibility diverges at low temperatures. This is similar to what was previously reported in the dielectric random system KTaO3: Na. A method is proposed to quantify the contribution of the disorder to the non-linearities. It is found that the deviation from a true ferroelectric behaviour is not enough to call the low-temperature phase of SrTiO3: Ca a glass one. The maximum non-linearity …
Glass transition of hard spheres in high dimensions
2009
We have investigated analytically and numerically the liquid-glass transition of hard spheres for dimensions $d\to \infty $ in the framework of mode-coupling theory. The numerical results for the critical collective and self nonergodicity parameters $f_{c}(k;d) $ and $f_{c}^{(s)}(k;d) $ exhibit non-Gaussian $k$ -dependence even up to $d=800$. $f_{c}^{(s)}(k;d) $ and $f_{c}(k;d) $ differ for $k\sim d^{1/2}$, but become identical on a scale $k\sim d$, which is proven analytically. The critical packing fraction $\phi_{c}(d) \sim d^{2}2^{-d}$ is above the corresponding Kauzmann packing fraction $\phi_{K}(d)$ derived by a small cage expansion. Its quadratic pre-exponential factor is different fr…
Non-linear dynamics of alpha and theta rhythm: correlation dimensions and Lyapunov exponents from healthy subject's spontaneous EEG.
1997
The aim of the present paper was to analyze some non-linear dynamic properties of the resting EEG from healthy subjects under eyes closed conditions. For this purpose we digitally filtered the spontaneous EEG in the theta (3-8 Hz) and alpha frequency range (8-13 Hz) and considered these independent rhythms as signals from a deterministic system. Under certain conditions non-linear dynamic systems are able to generate deterministic chaos, which means that similar causes do not produce similar effects. This phenomenon is called sensitive dependence on initial conditions. From different lead positions (F3, F4, Cz, P3, P4, O1 and O2) we calculated the so-called correlation dimension D2, which i…
Nonlinear dynamical aspects of the human sleep EEG.
1994
This article deals with the application of methods from the theory of nonlinear dynamical systems to EEG signals. Theoretical background, mathematical concepts and algorithms for the calculation of "non-linear parameters" are reviewed and influences of the structure of reconstructed data sets on the calculations are pointed out. We present results for the estimation of the correlation dimension D2 and the principal Lyapunov-exponent lambda 1 for sleep EEG data respectively from 10 and 15 healthy subjects corresponding to different sleep stages. Essentially, we found a statistically significant decrease of both D2 and lambda 1 as sleep moves towards slow wave stages. The values for REM sleep…
Monte Carlo study of surface critical behavior in the XY model.
1989
We have used Monte Carlo simulations to study the behavior of $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}D$ slabs containing classical spins which interact via nearest-neighbor $\mathrm{XY}$ coupling. The coupling constant ${J}_{S}$ for spins in the surface layer is fixed at $0.5J$. Finite-size scaling is used to analyze data for $D=59$ and to extract estimates for the surface critical exponents. We find that ${\ensuremath{\beta}}_{1}$ is in good agreement with theoretical predictions.
Etude numérique d'équations aux dérivées partielles non linéaires et dispersives
2011
Numerical analysis becomes a powerful resource in the study of partial differential equations (PDEs), allowing to illustrate existing theorems and find conjectures. By using sophisticated methods, questions which seem inaccessible before, like rapid oscillations or blow-up of solutions can be addressed in an approached way. Rapid oscillations in solutions are observed in dispersive PDEs without dissipation where solutions of the corresponding PDEs without dispersion present shocks. To solve numerically these oscillations, the use of efficient methods without using artificial numerical dissipation is necessary, in particular in the study of PDEs in some dimensions, done in this work. As stud…
Aerosol optical properties and instantaneous radiative forcing based on high temporospatial resolution CARSNET ground-based measurements over eastern…
2017
Abstract. Variations in the optical properties of aerosols and their radiative forcing were investigated based on long-term synchronous observations made at three-minute intervals from 2011 to 2015 over seven adjacent CARSNET (China Aerosol Remote Sensing NETwork) urban (Hangzhou), suburban (Xiaoshan, Fuyang, LinAn, Tonglu, Jiande) and rural (ChunAn) stations in the Yangtze River Delta region, eastern China. The aerosol optical depth (AOD) varied from 0.68 to 0.76, with two peaks in June and September, and decreased from the eastern coast to western inland areas. The ratio of the AOD of fine-mode particles to the total AOD was > 0.90 and the extinction Angström exponent was > 1.20 thr…