Search results for "statistical [methods]"
showing 10 items of 1664 documents
Regular packings on periodic lattices.
2011
We investigate the problem of packing identical hard objects on regular lattices in d dimensions. Restricting configuration space to parallel alignment of the objects, we study the densest packing at a given aspect ratio X. For rectangles and ellipses on the square lattice as well as for biaxial ellipsoids on a simple cubic lattice, we calculate the maximum packing fraction \phi_d(X). It is proved to be continuous with an infinite number of singular points X^{\rm min}_\nu, X^{\rm max}_\nu, \nu=0, \pm 1, \pm 2,... In two dimensions, all maxima have the same height, whereas there is a unique global maximum for the case of ellipsoids. The form of \phi_d(X) is discussed in the context of geomet…
From scalar to polar active matter: Connecting simulations with mean-field theory
2019
We study numerically the phase behavior of self-propelled elliptical particles interacting through the ``hard'' repulsive Gay-Berne potential at infinite P\'eclet number. Changing a single parameter, the aspect ratio, allows us to continuously go from discoid active Brownian particles to elongated polar rods. Discoids show phase separation, which changes to a cluster state of polar domains, which then form polar bands as the aspect ratio is increased. From the simulations, we identify and extract the two effective parameters entering the mean-field description: the force imbalance coefficient and the effective coupling to the local polarization. These two coefficients are sufficient to obta…
Observation of a tricritical wedge filling transition in the 3D Ising model
2014
In this Letter we present evidences of the occurrence of a tricritical filling transition for an Ising model in a linear wedge. We perform Monte Carlo simulations in a double wedge where antisymmetric fields act at the top and bottom wedges, decorated with specific field acting only along the wegde axes. A finite-size scaling analysis of these simulations shows a novel critical phenomenon, which is distinct from the critical filling. We adapt to tricritical filling the phenomenological theory which successfully was applied to the finite-size analysis of the critical filling in this geometry, observing good agreement between the simulations and the theoretical predictions for tricritical fil…
How Does the Relaxation of a Supercooled Liquid Depend on Its Microscopic Dynamics?
1998
Using molecular dynamics computer simulations we investigate how the relaxation dynamics of a simple supercooled liquid with Newtonian dynamics differs from the one with a stochastic dynamics. We find that, apart from the early beta-relaxation regime, the two dynamics give rise to the same relaxation behavior. The increase of the relaxation times of the system upon cooling, the details of the alpha-relaxation, as well as the wave vector dependence of the Edwards-Anderson-parameters are independent of the microscopic dynamics.
The structural relaxation of molten sodium disilicate
2002
We use molecular dynamics computer simulations to study the relaxation dynamics of Na2O-2(SiO2) in its molten, highly viscous state. We find that at low temperatures the incoherent intermediate scattering function for Na relaxes about 100 times faster than the one of the Si and O atoms. In contrast to this all coherent functions relax on the same time scale if the wave-vector is around 1AA^-1. This anomalous relaxation dynamics is traced back to the channel-like structure for the Na atoms that have been found for this system. We find that the relaxation dynamics for Si and O as well as the time dependence of the coherent functions for Na can be rationalized well by means of mode-coupling th…
Microscopic theory of glassy dynamics and glass transition for molecular crystals.
2004
We derive a microscopic equation of motion for the dynamical orientational correlators of molecular crystals. Our approach is based upon mode coupling theory. Compared to liquids we find four main differences: (i) the memory kernel contains Umklapp processes, (ii) besides the static two-molecule orientational correlators one also needs the static one-molecule orientational density as an input, where the latter is nontrivial, (iii) the static orientational current density correlator does contribute an anisotropic, inertia-independent part to the memory kernel, (iv) if the molecules are assumed to be fixed on a rigid lattice, the tensorial orientational correlators and the memory kernel have …
Low-energy fixed points of random Heisenberg models
2002
The effect of quenched disorder on the low-energy and low-temperature properties of various two- and three-dimensional Heisenberg models is studied by a numerical strong disorder renormalization group method. For strong enough disorder we have identified two relevant fixed points, in which the gap exponent, omega, describing the low-energy tail of the gap distribution, P(Delta) ~ Delta^omega is independent of disorder, the strength of couplings and the value of the spin. The dynamical behavior of non-frustrated random antiferromagnetic models is controlled by a singlet-like fixed point, whereas for frustrated models the fixed point corresponds to a large spin formation and the gap exponent …
Numerical tests of conjectures of conformal field theory for three-dimensional systems
1999
The concept of conformal field theory provides a general classification of statistical systems on two-dimensional geometries at the point of a continuous phase transition. Considering the finite-size scaling of certain special observables, one thus obtains not only the critical exponents but even the corresponding amplitudes of the divergences analytically. A first numerical analysis brought up the question whether analogous results can be obtained for those systems on three-dimensional manifolds. Using Monte Carlo simulations based on the Wolff single-cluster update algorithm we investigate the scaling properties of O(n) symmetric classical spin models on a three-dimensional, hyper-cylindr…
Universality in disordered systems: The case of the three-dimensional random-bond Ising model
2010
We study the critical behavior of the $d=3$ Ising model with bond randomness through extensive Monte Carlo simulations and finite-size scaling techniques. Our results indicate that the critical behavior of the random-bond model is governed by the same universality class as the site- and bond-diluted models, clearly distinct from that of the pure model, thus providing a complete set of universality in disordered systems.
Test of mode coupling theory for a supercooled liquid of diatomic molecules. II.q-dependent orientational correlators
1997
Using molecular dynamics computer simulations we study the dynamics of a molecular liquid by means of a general class of time-dependent correlators S_{ll'}^m(q,t) which explicitly involve translational (TDOF) and orientational degrees of freedom (ODOF). The system is composed of rigid, linear molecules with Lennard- Jones interactions. The q-dependence of the static correlators S_{ll'}^m(q) strongly depend on l, l' and m. The time dependent correlators are calculated for l=l'. A thorough test of the predictions of mode coupling theory (MCT) is performed for S_{ll}^m(q,t) and its self part S_{ll}^{(s)m}(q,t), for l=1,..,6. We find a clear signature for the existence of a single temperature T…