Search results for "statistical [methods]"
showing 10 items of 1664 documents
Kac-potential treatment of nonintegrable interactions.
2000
We consider d-dimensional systems with nonintegrable, algebraically decaying pairwise interactions. It is shown that, upon introduction of periodic boundary conditions and a long-distance cutoff in the interaction range, the bulk thermodynamics can be obtained rigorously by means of a Kac-potential treatment, leading to an exact, mean-field-like theory. This explains various numerical results recently obtained for finite systems in the context of ``nonextensive thermodynamics,'' and in passing exposes a strong regulator dependence not discussed in these studies. Our findings imply that, contrary to some claims, Boltzmann-Gibbs statistics are sufficient for a standard description of this cla…
Monte Carlo Test of the Classical Theory for Heterogeneous Nucleation Barriers
2010
Flat walls facilitate the condensation of a supersaturated vapor: Classical theory of heterogeneous nucleation predicts that the free energy barrier $\Delta F_{\rm het}^*$ which needs to be overcome for the formation of sphere-cap shaped nucleation seeds is smaller than the barrier $\Delta F^*_{\rm hom}$ for spherical droplets in the bulk by a factor $0<f(\theta)<1$, which only depends on the contact angle $\theta$. In this letter we compute both $\Delta F^*_{\rm hom}$ and $\Delta F^*_{\rm het}$ from Monte Carlo simulations and test the theory for the lattice gas model (for which $\theta$ can be readily controlled). Even though the theory is only based on macroscopic arguments, it is shown …
Collective forces in scalar active matter.
2020
Large-scale collective behavior in suspensions of many particles can be understood from the balance of statistical forces emerging beyond the direct microscopic particle interactions. Here we review some aspects of the collective forces that can arise in suspensions of self-propelled active Brownian particles: wall forces under confinement, interfacial forces, and forces on immersed bodies mediated by the suspension. Even for non-aligning active particles, these forces are intimately related to a non-uniform polarization of particle orientations induced by walls and bodies, or inhomogeneous density profiles. We conclude by pointing out future directions and promising areas for the applicati…
Quorum-sensing active particles with discontinuous motility
2019
We develop a dynamic mean-field theory for polar active particles that interact through a self-generated field, in particular one generated through emitting a chemical signal. While being a form of chemotactic response, it is different from conventional chemotaxis in that particles discontinuously change their motility when the local concentration surpasses a threshold. The resulting coupled equations for density and polarization are linear and can be solved analytically for simple geometries, yielding inhomogeneous density profiles. Specifically, here we consider a planar and circular interface. Our theory thus explains the observed coexistence of dense aggregates with an active gas. There…
Exercises, Hints and Selected Solutions
2016
1.1. Prove the formula (1.8a) in Sect. 1.3, $$\displaystyle{ \int \mathrm{d}^{n}x\; =\int _{ 0}^{+\infty }\!\!\!\mathrm{d}r\;r^{n-1}\int _{ 0}^{2\pi }\!\!\!\mathrm{d}\phi \prod _{ k=1}^{n-2}\int _{ 0}^{\pi }\!\!\!\mathrm{d}\theta _{ k}\sin ^{k}(\theta _{ k}) }$$ (1.1) by means of induction.
Indefinitely growing self-avoiding walk.
1985
We introduce a new random walk with the property that it is strictly self-avoiding and grows forever. It belongs to a different universality class from the usual self-avoiding walk. By definition the critical exponent $\ensuremath{\gamma}$ is equal to 1. To calculate the exponent $\ensuremath{\nu}$ of the mean square end-to-end distance we have performed exact enumerations on the square lattice up to 22 steps. This gives the value $\ensuremath{\nu}=0.57\ifmmode\pm\else\textpm\fi{}0.01$.
Geometry-Based Statistical Modeling of Non-WSSUS Mobile-to-Mobile Rayleigh Fading Channels
2017
In this paper, we present a novel geometry-based statistical model for small-scale non-wide-sense stationary uncorrelated scattering (non-WSSUS) mobile-to-mobile (M2M) Rayleigh fading channels. The proposed model builds on the principles of plane wave propagation to capture the temporal evolution of the propagation delay and Doppler shift of the received multipath signal. This is different from existing non-WSSUS geometry-based statistical channel models, which are based on a spherical wave propagation approach, that in spite of being more realistic is more mathematically intricate. By considering an arbitrary geometrical configuration of the propagation area, we derive general expressions …
Field Dependence of the Electron Spin Relaxation in Quantum Dots
2005
Interaction of the electron spin with local elastic twists due to transverse phonons has been studied. Universal dependence of the spin relaxation rate on the strength and direction of the magnetic field has been obtained in terms of the electron gyromagnetic tensor and macroscopic elastic constants of the solid. The theory contains no unknown parameters and it can be easily tested in experiment. At high magnetic field it provides parameter-free lower bound on the electron spin relaxation in quantum dots.
Surface contribution to the anisotropy of magnetic nanoparticles.
2002
We calculate the contribution of the Neel surface anisotropy to the effective anisotropy of magnetic nanoparticles of spherical shape cut out of a simple cubic lattice. The effective anisotropy arises because deviations of atomic magnetizations from collinearity and thus the energy depends on the orientation of the global magnetization. The result is second order in the Neel surface anisotropy, scales with the particle volume and has cubic symmetry with preferred directions [+-1,+-1,+-1].
Universal mechanism of spin relaxation in solids
2005
We consider relaxation of a rigid spin cluster in an elastic medium in the presence of the magnetic field. Universal simple expression for spin-phonon matrix elements due to local rotations of the lattice is derived. The equivalence of the lattice frame and the laboratory frame approaches is established. For spin Hamiltonians with strong uniaxial anisotropy the field dependence of the transition rates due to rotations is analytically calculated and its universality is demonstrated. The role of time reversal symmetry in spin-phonon transitions has been elucidated. The theory provides lower bound on the decoherence of any spin-based solid-state qubit.