Related papers: Rare Event Sampling Improves Mercury Instability S…
In a previous paper (J. Comp. Phys. 230 (2011), 3668--3694), the authors proposed a new practical method for computing expected values of functionals of solutions for certain classes of elliptic partial differential equations with random…
A large number of statistical models are "doubly-intractable": the likelihood normalising term, which is a function of the model parameters, is intractable, as well as the marginal likelihood (model evidence). This means that standard…
An accurate algorithm is proposed to improve the prediction of a particle in collision with a moving wall within the direct simulation Monte Carlo (DSMC) framework for the simulation of unsteady rarefied flows. This algorithm is able to…
Earth-based radar observations of the rotational dynamics of Mercury (Margot et al. 2012) combined with the determination of its gravity field by MESSENGER (Smith et al. 2012) give clues on the internal structure of Mercury, in particular…
While it is accepted that the eccentricity of Mercury (0.206) favours entrapment into the 3:2 spin-orbit resonance, open is the question how and when the capture took place. A recent work by Makarov (2012) has demonstrated that trapping…
Langevin Monte Carlo (LMC) and its stochastic gradient versions are powerful algorithms for sampling from complex high-dimensional distributions. To sample from a distribution with density $\pi(\theta)\propto \exp(-U(\theta)) $, LMC…
Precise radial velocity measurements have led to the discovery of ~100 extrasolar planetary systems. We investigate the uncertainty in the orbital solutions that have been fit to these observations. Understanding these uncertainties will…
This paper proposes an eigenvalue-based small-sample approximation of the celebrated Markov Chain Monte Carlo that delivers an invariant steady-state distribution that is consistent with traditional Monte Carlo methods. The proposed…
We propose a quantum Monte Carlo (QMC) algorithm for non-equilibrium dynamics in a system with a parameter varying as a function of time. The method is based on successive applications of an evolving Hamiltonian to an initial state and…
By their very nature, rare event probabilities are expensive to compute; they are also delicate to estimate as their value strongly depends on distributional assumptions on the model parameters. Hence, understanding the sensitivity of the…
We study rare events in systems of diffusive fields driven out of equilibrium by the boundaries. We present a numerical technique and use it to calculate the probabilities of rare events in one and two dimensions. Using this technique, we…
Rare events in molecular dynamics are often related to noise-induced transitions between different macroscopic states (e.g., in protein folding). A common feature of these rare transitions is that they happen on timescales that are on…
We examine the effects that dynamical instability has on shaping the orbital properties of exoplanetary systems. Using N-body simulations of non-EMS (Equal Mutual Separation), multi-planet systems we find that the lower limit of the…
Magnetorotational instability (MRI) is one of the most important and most common instabilities in astrophysics, it is widely accepted that it serves as a source of turbulent viscosity in accretion disks -- the most energy efficient objects…
Computer simulation plays a central role in modern day materials science. The utility of a given computational approach depends largely on the balance it provides between accuracy and computational cost. Molecular crystals are a class of…
Having reliable estimates of the occurrence rates of extreme events is highly important for insurance companies, government agencies and the general public. The rarity of an extreme event is typically expressed through its return period,…
This paper addresses the problem of Monte Carlo approximation of posterior probability distributions. In particular, we have considered a recently proposed technique known as population Monte Carlo (PMC), which is based on an iterative…
Atomistic simulations provide valuable insights into the physical processes governing material behavior. However, their applicability is fundamentally constrained by the limited time scales accessible to brute-force simulations. This…
Understanding the stability of exoplanet systems is crucial for constraining planetary formation and evolution theories. We use the machine-learning stability indicator, SPOCK, to characterize the stability of 126 high-multiplicity systems…
The origin of Mercury still remains poorly understood compared to the other rocky planets of the Solar System. One of the most relevant constraints that any formation model has to fulfill refers to its internal structure, with a predominant…