10,928 research outputs found
A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments
The computational study of chemical reactions in complex, wet environments is
critical for applications in many fields. It is often essential to study
chemical reactions in the presence of applied electrochemical potentials,
taking into account the non-trivial electrostatic screening coming from the
solvent and the electrolytes. As a consequence the electrostatic potential has
to be found by solving the generalized Poisson and the Poisson-Boltzmann
equation for neutral and ionic solutions, respectively. In the present work
solvers for both problems have been developed. A preconditioned conjugate
gradient method has been implemented to the generalized Poisson equation and
the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the
minimization problem with some ten iterations of a ordinary Poisson equation
solver. In addition, a self-consistent procedure enables us to solve the
non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy
and parallel efficiency, and allow for the treatment of different boundary
conditions, as for example surface systems. The solver has been integrated into
the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be
released as an independent program, suitable for integration in other codes
Portable implementation of a quantum thermal bath for molecular dynamics simulations
Recently, Dammak and coworkers (H. Dammak, Y. Chalopin, M. Laroche, M.
Hayoun, and J.J. Greffet. Quantumthermal bath for molecular dynamics
simulation. Phys. Rev. Lett., 103:190601, 2009.) proposed that the quantum
statistics of vibrations in condensed systems at low temperature could be
simulated by running molecular dynamics simulations in the presence of a
colored noise with an appropriate power spectral density. In the present
contribution, we show how this method can be implemented in a flexible manner
and at a low computational cost by synthesizing the corresponding noise 'on the
fly'. The proposed algorithm is tested for a simple harmonic chain as well as
for a more realistic model of aluminium crystal. The energy and Debye-Waller
factor are shown to be in good agreement with those obtained from harmonic
approximations based on the phonon spectrum of the systems. The limitations of
the method associated with anharmonic effects are also briefly discussed. Some
perspectives for disordered materials and heat transfer are considered.Comment: Accepted for publication in Journal of Statistical Physic
Generalized thick strip modelling for vortex-induced vibration of long flexible cylinders
We propose a generalized strip modelling method that is computationally efficient for the VIV prediction of long flexible cylinders in three-dimensional incompressible flow. In order to overcome the shortcomings of conventional strip-theory-based 2D models, the fluid domain is divided into “thick” strips, which are sufficiently thick to locally resolve the small scale turbulence effects and three dimensionality of the flow around the cylinder. An attractive feature of the model is that we independently construct a three-dimensional scale resolving model for individual strips, which have local spanwise scale along the cylinder's axial direction and are only coupled through the structural model of the cylinder. Therefore, this approach is able to cover the full spectrum for fully resolved 3D modelling to 2D strip theory. The connection between these strips is achieved through the calculation of a tensioned beam equation, which is used to represent the dynamics of the flexible body. In the limit, however, a single “thick” strip would fill the full 3D domain. A parallel Fourier spectral/hp element method is employed to solve the 3D flow dynamics in the strip-domain, and then the VIV response prediction is achieved through the strip-structure interactions. Numerical tests on both laminar and turbulent flows as well as the comparison against the fully resolved DNS are presented to demonstrate the applicability of this approach
Dynamical fermions as a global correction
In the simplified setting of the Schwinger model we present a systematic
study on the simulation of dynamical fermions by global accept/reject steps
that take into account the fermion determinant. A family of exact algorithms is
developed, which combine stochastic estimates of the determinant ratio with the
exploitation of some exact extremal eigenvalues of the generalized problem
defined by the `old' and the `new' Dirac operator. In this way an acceptable
acceptance rate is achieved with large proposed steps and over a wide range of
couplings and masses.Comment: 39 pages, 9 figures, small changes in the text, Fig.5 and Tab.2
(incl. 1 corrected typo
Energy preserving model order reduction of the nonlinear Schr\"odinger equation
An energy preserving reduced order model is developed for two dimensional
nonlinear Schr\"odinger equation (NLSE) with plane wave solutions and with an
external potential. The NLSE is discretized in space by the symmetric interior
penalty discontinuous Galerkin (SIPG) method. The resulting system of
Hamiltonian ordinary differential equations are integrated in time by the
energy preserving average vector field (AVF) method. The mass and energy
preserving reduced order model (ROM) is constructed by proper orthogonal
decomposition (POD) Galerkin projection. The nonlinearities are computed for
the ROM efficiently by discrete empirical interpolation method (DEIM) and
dynamic mode decomposition (DMD). Preservation of the semi-discrete energy and
mass are shown for the full order model (FOM) and for the ROM which ensures the
long term stability of the solutions. Numerical simulations illustrate the
preservation of the energy and mass in the reduced order model for the two
dimensional NLSE with and without the external potential. The POD-DMD makes a
remarkable improvement in computational speed-up over the POD-DEIM. Both
methods approximate accurately the FOM, whereas POD-DEIM is more accurate than
the POD-DMD
Generalized Langevin equation with colored noise description of the stochastic oscillations of accretion disks
We consider a description of the stochastic oscillations of the general
relativistic accretion disks around compact astrophysical objects interacting
with their external medium based on a generalized Langevin equation with
colored noise, which accounts for the general memory and retarded effects of
the frictional force, and on the fluctuation-dissipation theorem. The presence
of the memory effects influences the response of the disk to external random
interactions, and modifies the dynamical behavior of the disk, as well as the
energy dissipation processes. The generalized Langevin equation of the motion
of the disk in the vertical direction is studied numerically, and the vertical
displacements, velocities and luminosities of the stochastically perturbed
disks are explicitly obtained for both the Schwarzschild and the Kerr cases.
The Power Spectral Distribution (PSD) of the disk luminosity is also obtained.
As a possible astrophysical application of the formalism we investigate the
possibility that the Intra Day Variability (IDV) of the Active Galactic Nuclei
(AGN) may be due to the stochastic disk instabilities. The perturbations due to
colored/nontrivially correlated noise induce a complicated disk dynamics, which
could explain some astrophysical observational features related to disk
variability.Comment: 17 pages, 10 figures, accepted for publication in EPJ
Dealing with missing data: An inpainting application to the MICROSCOPE space mission
Missing data are a common problem in experimental and observational physics.
They can be caused by various sources, either an instrument's saturation, or a
contamination from an external event, or a data loss. In particular, they can
have a disastrous effect when one is seeking to characterize a
colored-noise-dominated signal in Fourier space, since they create a spectral
leakage that can artificially increase the noise. It is therefore important to
either take them into account or to correct for them prior to e.g. a
Least-Square fit of the signal to be characterized. In this paper, we present
an application of the {\it inpainting} algorithm to mock MICROSCOPE data; {\it
inpainting} is based on a sparsity assumption, and has already been used in
various astrophysical contexts; MICROSCOPE is a French Space Agency mission,
whose launch is expected in 2016, that aims to test the Weak Equivalence
Principle down to the level. We then explore the {\it inpainting}
dependence on the number of gaps and the total fraction of missing values. We
show that, in a worst-case scenario, after reconstructing missing values with
{\it inpainting}, a Least-Square fit may allow us to significantly measure a
Equivalence Principle violation signal, which is
sufficiently close to the MICROSCOPE requirements to implement {\it inpainting}
in the official MICROSCOPE data processing and analysis pipeline. Together with
the previously published KARMA method, {\it inpainting} will then allow us to
independently characterize and cross-check an Equivalence Principle violation
signal detection down to the level.Comment: Accepted for publication in Physical Review D. 12 pages, 6 figure
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