Search results for "Exponent"
showing 10 items of 896 documents
Phase transitions and phase equilibria in spherical confinement
2013
Phase transitions in finite systems are rounded and shifted and affected by boundary effects due to the surface of the system. This interplay of finite size and surface effects for fluids confined inside of a sphere of radius $R$ is studied by a phenomenological theory and Monte Carlo simulations of a model for colloid-polymer mixtures. For this system the phase separation in a colloid-rich phase and a polymer-rich phase has been previously studied extensively in the bulk. It is shown that spherical confinement can strongly enhance the miscibility of the mixture. Depending on the wall potentials at the confining surface, the wetting properties of the wall can be controlled, and this interpl…
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…
Nature of the non-exponential primary relaxation in structural glass-formers probed by dynamically selective experiments
1998
Several experimental methods feature the potential to distinguish between slow and fast contributions to the non-exponential, ensemble averaged primary response in glass-forming materials. Some of these techniques are based on the selection of subensembles using multi-dimensional nuclear magnetic resonance, optical bleaching, and non-resonant spectral hole burning. Others, such as the time-dependent solvation spectroscopy, measure microscopic responses induced by local perturbations. Using several of these methods it could be demonstrated for various glass-forming materials that the non-exponential relaxation results from a superposition of dynamically distinguishable entities. The experime…
Nonexponential 2H spin-lattice relaxation as a signature of the glassy state
1990
Abstract High-precision measurements of 2H spin-lattice relaxation on several molecular glass-forming liquids have been performed. As a general feature the following can be stated: At temperatures more than ten to twenty degrees above the calorimetric glass transition temperature Tg the 2H spin-lattice relaxation is exponential; below that temperature regime the relaxation is nonexponential. This crossover from exponential to nonexponential magnetization recovery implies that no common spin temperature caused by spin diffusion exists in a 2H glass. This contrasts 1H spin-lattice relaxation which is found to be strictly monoexponential throughout. The occurrence of nonexponential 2H relaxati…
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 phenomena in colloid-polymer mixtures: interfacial tension, order parameter, susceptibility, and coexistence diameter.
2004
The critical behavior of a model colloid-polymer mixture, the so-called AO model, is studied using computer simulations and finite size scaling techniques. Investigated are the interfacial tension, the order parameter, the susceptibility and the coexistence diameter. Our results clearly show that the interfacial tension vanishes at the critical point with exponent 2\nu ~ 1.26. This is in good agreement with the 3D Ising exponent. Also calculated are critical amplitude ratios, which are shown to be compatible with the corresponding 3D Ising values. We additionally identify a number of subtleties that are encountered when finite size scaling is applied to the AO model. In particular, we find …
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…
Conservation Laws and Asymptotic Behavior of a Model of Social Dynamics
2008
Abstract A conservative social dynamics model is developed within a discrete kinetic framework for active particles, which has been proposed in [M.L. Bertotti, L. Delitala, From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences, Math. Mod. Meth. Appl. Sci. 14 (2004) 1061–1084]. The model concerns a society in which individuals, distinguished by a scalar variable (the activity) which expresses their social state, undergo competitive and/or cooperative interactions. The evolution of the discrete probability distribution over the social state is described by a system of nonlinear ordinary differential equations. The asymptotic trend of their solutions…