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Robledo L.M.,Univeridad Autonoma de Madrid | Bertsch G.F.,University of Washington
Physical Review C - Nuclear Physics | Year: 2011

A computer code is presented for solving the equations of the Hartree-Fock-Bogoliubov (HFB) theory by the gradient method, motivated by the need for efficient and robust codes to calculate the configurations required by extensions of the HFB theory, such as the generator coordinate method. The code is organized with a separation between the parts that are specific to the details of the Hamiltonian and the parts that are generic to the gradient method. This permits total flexibility in choosing the symmetries to be imposed on the HFB solutions. The code solves for both even and odd particle-number ground states, with the choice determined by the input data stream. Application is made to the nuclei in the sd shell using the universal sd-shell interaction B (USDB) shell-model Hamiltonian. © 2011 American Physical Society.

Usabiaga F.B.,Univeridad Autonoma de Madrid | Bell J.B.,Lawrence Berkeley National Laboratory | Delgado-Buscalioni R.,Univeridad Autonoma de Madrid | Donev A.,Courant Institute of Mathematical Sciences | And 3 more authors.
Multiscale Modeling and Simulation | Year: 2012

We develop numerical schemes for solving the isothermal compressible and incompressible equations of fluctuating hydrodynamics on a grid with staggered momenta. We develop a second-order accurate spatial discretization of the diffusive, advective, and stochastic fluxes that satisfies a discrete fluctuation-dissipation balance and construct temporal discretizations that are at least second-order accurate in time deterministically and in a weak sense. Specifically, the methods reproduce the correct equilibrium covariances of the fluctuating fields to the third (compressible) and second (incompressible) orders in the time step, as we verify numerically. We apply our techniques to model recent experimental measurements of giant fluctuations in diffusively mixing fluids in a microgravity environment [A. Vailati et al., Nat. Comm., 2 (2011), 290]. Numerical results for the static spectrum of nonequilibrium concentration fluctuations are in excellent agreement between the compressible and incompressible simulations and in good agreement with experimental results for all measured wavenumbers. © 2012 SIAM.

Balboa Usabiaga F.,Univeridad Autonoma de Madrid | Xie X.,New York University | Delgado-Buscalioni R.,Univeridad Autonoma de Madrid | Donev A.,Courant Institute of Mathematical Sciences
Journal of Chemical Physics | Year: 2013

The Stokes-Einstein relation for the self-diffusion coefficient of a spherical particle suspended in an incompressible fluid is an asymptotic result in the limit of large Schmidt number, that is, when momentum diffuses much faster than the particle. When the Schmidt number is moderate, which happens in most particle methods for hydrodynamics, deviations from the Stokes-Einstein prediction are expected. We study these corrections computationally using a recently developed minimally resolved method for coupling particles to an incompressible fluctuating fluid in both two and three dimensions. We find that for moderate Schmidt numbers the diffusion coefficient is reduced relative to the Stokes-Einstein prediction by an amount inversely proportional to the Schmidt number in both two and three dimensions. We find, however, that the Einstein formula is obeyed at all Schmidt numbers, consistent with linear response theory. The mismatch arises because thermal fluctuations affect the drag coefficient for a particle due to the nonlinear nature of the fluid-particle coupling. The numerical data are in good agreement with an approximate self-consistent theory, which can be used to estimate finite-Schmidt number corrections in a variety of methods. Our results indicate that the corrections to the Stokes-Einstein formula come primarily from the fact that the particle itself diffuses together with the momentum. Our study separates effects coming from corrections to no-slip hydrodynamics from those of finite separation of time scales, allowing for a better understanding of widely observed deviations from the Stokes-Einstein prediction in particle methods such as molecular dynamics. © 2013 AIP Publishing LLC.

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