36,180 research outputs found
Fast uncertainty quantification of tracer distribution in the brain interstitial fluid with multilevel and quasi Monte Carlo
Efficient uncertainty quantification algorithms are key to understand the
propagation of uncertainty -- from uncertain input parameters to uncertain
output quantities -- in high resolution mathematical models of brain
physiology. Advanced Monte Carlo methods such as quasi Monte Carlo (QMC) and
multilevel Monte Carlo (MLMC) have the potential to dramatically improve upon
standard Monte Carlo (MC) methods, but their applicability and performance in
biomedical applications is underexplored. In this paper, we design and apply
QMC and MLMC methods to quantify uncertainty in a convection-diffusion model of
tracer transport within the brain. We show that QMC outperforms standard MC
simulations when the number of random inputs is small. MLMC considerably
outperforms both QMC and standard MC methods and should therefore be preferred
for brain transport models.Comment: Multilevel Monte Carlo, quasi Monte Carlo, brain simulation, brain
fluids, finite element method, biomedical computing, random fields,
diffusion-convectio
A Generalisation of Malliavin Weighted Scheme for Fast Computation of the Greeks
This paper presented a new technique for the simulation of the Greeks (i.e. price sensitivities to parameters), efficient for strongly discontinuous payo¤ options. The use of Malliavin calculus, by means of an integration by parts, enables to shift the differentiation operator from the payo¤ function to the diffusion kernel, introducing a weighting function.(Fournie et al. (1999)). Expressing the weighting function as a Skorohod integral, we show how to characterize the integrand with necessary and sufficient conditions, giving a complete description of weighting function solutions. Interestingly, for adapted process, the Skorohod integral turns to be the classical Ito integral.Monte-Carlo, Quasi-Monte Carlo, Greeks,Malliavin Calculus, Wiener Chaos.
A Multilevel Monte Carlo Asymptotic-Preserving Particle Method for Kinetic Equations in the Diffusion Limit
We propose a multilevel Monte Carlo method for a particle-based
asymptotic-preserving scheme for kinetic equations. Kinetic equations model
transport and collision of particles in a position-velocity phase-space. With a
diffusive scaling, the kinetic equation converges to an advection-diffusion
equation in the limit of zero mean free path. Classical particle-based
techniques suffer from a strict time-step restriction to maintain stability in
this limit. Asymptotic-preserving schemes provide a solution to this time step
restriction, but introduce a first-order error in the time step size. We
demonstrate how the multilevel Monte Carlo method can be used as a bias
reduction technique to perform accurate simulations in the diffusive regime,
while leveraging the reduced simulation cost given by the asymptotic-preserving
scheme. We describe how to achieve the necessary correlation between simulation
paths at different levels and demonstrate the potential of the approach via
numerical experiments.Comment: 20 pages, 7 figures, published in Monte Carlo and Quasi-Monte Carlo
Methods 2018, correction of minor typographical error
Diffusion in 2D quasi-crystals
Self-diffusion induced by phasonic flips is studied in an octagonal model quasi-crystal. To determine the temperature dependence of the diffusion coefficient, we apply a Monte Carlo simulation with specific energy values of local configurations. We compare the results of the ideal quasi-periodic tiling and a related periodic approximant and comment on possible implications to real quasi-crystals
Computer simulation of the velocity diffusion of cosmic rays
Monte Carlo simulation experiments were performed in order to study the velocity diffusion of charged particles in a static turbulent magnetic field. By following orbits of particles moving in a large ensemble of random magnetic field realizations with suitable chosen statistical properties, a pitch-angle diffusion coefficient is derived. Results are presented for a variety of particle rigidities and rms random field strengths and compared with the predictions of standard quasi-linear theory and the nonlinear partially averaged field theory
Reducing quasi-ergodicity in a double well potential by Tsallis Monte Carlo simulation
A new Monte Carlo scheme based on the system of Tsallis's generalized
statistical mechanics is applied to a simple double well potential to calculate
the canonical thermal average of potential energy. Although we observed serious
quasi-ergodicity when using the standard Metropolis Monte Carlo algorithm, this
problem is largely reduced by the use of the new Monte Carlo algorithm.
Therefore the ergodicity is guaranteed even for short Monte Carlo steps if we
use this new canonical Monte Carlo scheme.Comment: 12 pages including 12 eps figures, to appear in Physica
Acceleration of Solar Wind Ions by Nearby Interplanetary Shocks: Comparison of Monte Carlo Simulations with Ulysses Observations
The most stringent test of theoretical models of the first-order Fermi
mechanism at collisionless astrophysical shocks is a comparison of the
theoretical predictions with observational data on particle populations. Such
comparisons have yielded good agreement between observations at the
quasi-parallel portion of the Earth's bow shock and three theoretical
approaches, including Monte Carlo kinetic simulations. This paper extends such
model testing to the realm of oblique interplanetary shocks: here observations
of proton and alpha particle distributions made by the SWICS ion mass
spectrometer on Ulysses at nearby interplanetary shocks are compared with test
particle Monte Carlo simulation predictions of accelerated populations. The
plasma parameters used in the simulation are obtained from measurements of
solar wind particles and the magnetic field upstream of individual shocks. Good
agreement between downstream spectral measurements and the simulation
predictions are obtained for two shocks by allowing the the ratio of the
mean-free scattering length to the ionic gyroradius, to vary in an optimization
of the fit to the data. Generally small values of this ratio are obtained,
corresponding to the case of strong scattering. The acceleration process
appears to be roughly independent of the mass or charge of the species.Comment: 26 pages, 6 figures, AASTeX format, to appear in the Astrophysical
Journal, February 20, 199
Theoretical properties of quasi-stationary Monte Carlo methods
This paper gives foundational results for the application of
quasi-stationarity to Monte Carlo inference problems. We prove natural
sufficient conditions for the quasi-limiting distribution of a killed diffusion
to coincide with a target density of interest. We also quantify the rate of
convergence to quasi-stationarity by relating the killed diffusion to an
appropriate Langevin diffusion. As an example, we consider in detail a killed
Ornstein--Uhlenbeck process with Gaussian quasi-stationary distribution.Comment: 27 pages, 1 figure. Final version of accepted paper. Minor typos
correcte
Monte Carlo Methods for Equilibrium and Nonequilibrium Problems in Interfacial Electrochemistry
We present a tutorial discussion of Monte Carlo methods for equilibrium and
nonequilibrium problems in interfacial electrochemistry. The discussion is
illustrated with results from simulations of three specific systems: bromine
adsorption on silver (100), underpotential deposition of copper on gold (111),
and electrodeposition of urea on platinum (100).Comment: RevTex, 14 pages, 8 figures. To appear in book _Interfacial
Electrochemisty
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