1,720,966 research outputs found
Derivation of Isothermal Quantum Fluid Equations with Fermi-Dirac and Bose-Einstein Statistics
No full textBy using the quantum maximum entropy principle we formally derive, from a underlying kinetic description, isothermal (hydrodynamic and diffusive) quantum fluid equations for particles with Fermi-Dirac and Bose-Einstein statistics. A semiclassical expansion of the quantum fluid equations, up to Ohstroke 2 -terms, leads to classical fluid equations with statistics-dependent quantum corrections, including a modified Bohm potential. The Maxwell-Boltzmann limit and the zero temperature limit are eventually discussed
Radiative transfer modelling in protoplanetary disks with the P-N approximation and Monte Carlo techniques
No full textA protoplanetary disk is a quasi-toroidal gas-dust mixture rotating around a protostar that creates a complex intensity field in the internal disk medium in which planets are believed to form. In this work we start to model an idealized disk describing the radiation intensity propagating along a vertical disk section using the P-N Approximation. This unidimensional approach can be extended to a flared surface case but the problem rapidly raises complexity in solving a simple cylindrical mid-plane region. The full 3D case is then handled with a Monte Carlo (MC) code reusing the idealized model to test the software reliability. The Monte Carlo lack in precision is fully repaid by the flexibility in describing the light-to-dust interaction moving the model towards a more realistic micro-physics based approach. Copyright © 2010 John Wiley & Sons, Ltd
Recent advances in the numerical solution of the Nonlinear Schrödinger Equation
No full textIn this review we collect some recent achievements in the accurate and efficient solution of the Nonlinear Schrödinger Equation (NLSE), with the preservation of its Hamiltonian structure. This is achieved by using the energy-conserving Runge–Kutta methods named Hamiltonian Boundary Value Methods (HBVMs) after a proper space semi-discretization. The main facts about HBVMs, along with their application for solving the given problem, are here recalled and explained in detail. In particular, their use as spectral methods in time, which allows efficiently solving the problems with spectral space–time accuracy
Analytical study of non Gaussian fluctuations in a stochastic scheme of autocatalytic reactions
No full textA complex network of autocatalytic chemical reactions is studied both numerically and analytically. The van Kampen perturbative scheme is implemented, beyond the second order approximation, so to capture the non Gaussianity traits as displayed by the simulations. The method is targeted to the characterization of the third moments of the distribution of fluctuations, originating from a system of four populations in mutual interaction. The theory predictions agree well with the simulations, pointing to the validity of the van Kampen expansion beyond the conventional Gaussian solution. © 2012 EDP Sciences and Springer
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