Search results for "Boundary Condition"
showing 10 items of 235 documents
Theory overview of Heavy Ion collisions
2016
This presentation discusses some recently active topics in the theoretical interpretation of high energy heavy ion collisions at the LHC and at RHIC. We argue that the standard paradigm for understanding the spacetime evolution of the bulk of the matter produced in the collision is provided by viscous relativistic hydrodynamics, which can be used to systematically extract properties of the QCD medium from experimental results. The initial conditions of this hydrodynamical evolution are increasingly well understood in terms of gluon saturation, and can be quantified using Classical Yang-Mills fields and QCD effective kinetic theory. Hard and electromagnetic probes of the plasma provide addit…
Simulation of the glass transition in polymeric systems: Evidence for an underlying phase transition?
1998
Abstract The bond fluctuation model of polymer chains on sc lattices with an energy that favours long bonds can describe the slowing down of supercooled melts that approach the glass transition in qualitative similarity with various experiments. In this paper we focus on the question of whether there exists a correlation length that increases to large values when the temperature is lowered towards the glass transition. Two types of analysis are presented: firstly density oscillations near hard walls become long range, and the resulting correlation length becomes larger than the gyration radius, secondly oscillations in the pair correlation function in real space also become long range, and …
Isolated photon production in proton-nucleus collisions at forward rapidity
2018
We calculate isolated photon production at forward rapidities in proton-nucleus collisions in the Color Glass Condensate framework. Our calculation uses dipole cross sections solved from the running coupling Balitsky-Kovchegov equation with an initial condition fit to deep inelastic scattering data. For comparison, we also update the results for the nuclear modification factor for pion production in the same kinematics. We present predictions for future forward RHIC and LHC measurements at $\sqrt{s_{NN}}=200$ GeV and $\sqrt{s_{NN}}=8$ TeV.
A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional
2012
Abstract We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the radiation condition. The index of refraction does not need to be constant at infinity and may have some angular dependency as well as perturbations. We prove analytical results on the convergence of the approximate solution. Numerical examples for different shapes of the artificial boundary and for non-constant indexes of refraction will be presented.
Bifurcation of traveling waves in a Keller–Segel type free boundary model of cell motility
2018
We study a two-dimensional free boundary problem that models motility of eukaryotic cells on substrates. This problem consists of an elliptic equation describing the flow of cytoskeleton gel coupled with a convection-diffusion PDE for the density of myosin motors. The two key properties of this problem are (i) presence of the cross diffusion as in the classical Keller-Segel problem in chemotaxis and (ii) nonlinear nonlocal free boundary condition that involves curvature of the boundary. We establish the bifurcation of the traveling waves from a family of radially symmetric steady states. The traveling waves describe persistent motion without external cues or stimuli which is a signature of …
Curvature dependence of surface free energy of liquid drops and bubbles: A simulation study.
2010
We study the excess free energy due to phase coexistence of fluids by Monte Carlo simulations using successive umbrella sampling in finite LxLxL boxes with periodic boundary conditions. Both the vapor-liquid phase coexistence of a simple Lennard-Jones fluid and the coexistence between A-rich and B-rich phases of a symmetric binary (AB) Lennard-Jones mixture are studied, varying the density rho in the simple fluid or the relative concentration x_A of A in the binary mixture, respectively. The character of phase coexistence changes from a spherical droplet (or bubble) of the minority phase (near the coexistence curve) to a cylindrical droplet (or bubble) and finally (in the center of the misc…
Computing bulk and shear viscosities from simulations of fluids with dissipative and stochastic interactions
2016
Exact values for bulk and shear viscosity are important to characterize a fluid and they are a necessary input for a continuum description. Here we present two novel methods to compute bulk viscosities by non-equilibrium molecular dynamics (NEMD) simulations of steady-state systems with periodic boundary conditions -- one based on frequent particle displacements and one based on the application of external bulk forces with an inhomogeneous force profile. In equilibrium simulations, viscosities can be determined from the stress tensor fluctuations via Green-Kubo relations; however, the correct incorporation of random and dissipative forces is not obvious. We discuss different expressions pro…
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…
Approximate Modeling of Spherical Membrane
2010
Spherical symmetry is ubiquitous in nature. It's therefore unfortunate that spherical system simulations are so hard, and require complete spheres with millions of interacting particles. Here we introduce an approach to model spherical systems, using revised periodic boundary conditions adapted to spherical symmetry. Method reduces computational costs by orders of magnitude, and is applicable for both solid and liquid membranes, provided the curvature is sufficiently small. We demonstrate the method by calculating the bending and Gaussian curvature moduli of single- and multi-layer graphene. Method works with any interaction (ab initio, classical interactions), with any approach (molecular …
Revised periodic boundary conditions: Fundamentals, electrostatics, and the tight-binding approximation
2011
Many nanostructures today are low-dimensional and flimsy, and therefore get easily distorted. Distortion-induced symmetry-breaking makes conventional, translation-periodic simulations invalid, which has triggered developments for new methods. Revised periodic boundary conditions (RPBC) is a simple method that enables simulations of complex material distortions, either classically or quantum-mechanically. The mathematical details of this easy-to-implement approach, however, have not been discussed before. Therefore, in this paper we summarize the underlying theory, present the practical details of RPBC, especially related to a non-orthogonal tight-binding formulation, discuss selected featur…