Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA non-equilibrium Monte Carlo approach to potential refinement in inverse problems
121
0
0.0
(
0
)
Authors
N.B. Wilding
Ask ChatGPT about the research
No Arabic abstract
The inverse problem for a disordered system involves determining the interparticle interaction parameters consistent with a given set of experimental data. Recently, Rutledge has shown (Phys. Rev. E63, 021111 (2001)) that such problems can be generally expressed in terms of a grand canonical ensemble of polydisperse particles. Within this framework, one identifies a polydisperse attribute (`pseudo-species) $sigma$ corresponding to some appropriate generalized coordinate of the system to hand. Associated with this attribute is a composition distribution $barrho(sigma)$ measuring the number of particles of each species. Its form is controlled by a conjugate chemical potential distribution $mu(sigma)$ which plays the role of the requisite interparticle interaction potential. Simulation approaches to the inverse problem involve determining the form of $mu(sigma)$ for which $barrho(sigma)$ matches the available experimental data. The difficulty in doing so is that $mu(sigma)$ is (in general) an unknown {em functional} of $barrho(sigma)$ and must therefore be found by iteration. At high particle densities and for high degrees of polydispersity, strong cross coupling between $mu(sigma)$ and $barrho(sigma)$ renders this process computationally problematic and laborious. Here we describe an efficient and robust {em non-equilibrium} simulation scheme for finding the equilibrium form of $mu[barrho(sigma)]$. The utility of the method is demonstrated by calculating the chemical potential distribution conjugate to a specific log-normal distribution of particle sizes in a polydisperse fluid.
rate research
Read More
We present a method for Monte Carlo sampling on systems with discrete variables (focusing in the Ising case), introducing a prior on the candidate moves in a Metropolis-Hastings scheme which can significantly reduce the rejection rate, called the reduced-rejection-rate (RRR) method. The method employs same probability distribution for the choice of the moves as rejection-free schemes such as the method proposed by Bortz, Kalos and Lebowitz (BKL) [Bortz et al. J.Comput.Phys. 1975]; however, it uses it as a prior in an otherwise standard Metropolis scheme: it is thus not fully rejection-free, but in a wide range of scenarios it is nearly so. This allows to extend the method to cases for which rejection-free schemes become inefficient, in particular when the graph connectivity is not sparse, but the energy can nevertheless be expressed as a sum of two components, one of which is computed on a sparse graph and dominates the measure. As examples of such instances, we demonstrate that the method yields excellent results when performing Monte Carlo simulations of quantum spin models in presence of a transverse field in the Suzuki-Trotter formalism, and when exploring the so-called robust ensemble which was recently introduced in Baldassi et al. [PNAS 2016]. Our code for the Ising case is publicly available [https://github.com/carlobaldassi/RRRMC.jl], and extensible to user-defined models: it provides efficient implementations of standard Metropolis, the RRR method, the BKL method (extended to the case of continuous energy specra), and the waiting time method [Dall and Sibani Comput.Phys.Commun. 2001].
We consider the use of a Kinetic Monte Carlo approach for the description of non-equilibrium bosonic systems, taking non-resonantly excited exciton-polariton condensates and bosonic cascade lasers as examples. In the former case, the considered approach allows the study of the cross-over between incoherent and coherent regimes, which represents the formation of a quasi-condensate that forms purely from the action of energy relaxation processes rather than interactions between the condensing particles themselves. In the latter case, we show that a bosonic cascade can theoretically develop an output coherent state.
Population annealing is a recent addition to the arsenal of the practitioner in computer simulations in statistical physics and beyond that is found to deal well with systems with complex free-energy landscapes. Above all else, it promises to deliver unrivaled parallel scaling qualities, being suitable for parallel machines of the biggest calibre. Here we study population annealing using as the main example the two-dimensional Ising model which allows for particularly clean comparisons due to the available exact results and the wealth of published simulational studies employing other approaches. We analyze in depth the accuracy and precision of the method, highlighting its relation to older techniques such as simulated annealing and thermodynamic integration. We introduce intrinsic approaches for the analysis of statistical and systematic errors, and provide a detailed picture of the dependence of such errors on the simulation parameters. The results are benchmarked against canonical and parallel tempering simulations.
Spin ice materials, such as Dy2Ti2O7 and Ho2Ti2O7, have been the subject of much interest for over the past fifteen years. Their low temperature strongly correlated state can be mapped onto the proton disordered state of common water ice and, consequently, spin ices display the same low temperature residual Pauling entropy as water ice. Interestingly, it was found in a previous study [X. Ke {it et. al.} Phys. Rev. Lett. {bf 99}, 137203 (2007)] that, upon dilution of the magnetic rare-earth ions (Dy^{3+} and Ho^{3+}) by non-magnetic Yttrium (Y^{3+}) ions, the residual entropy depends {it non-monotonically} on the concentration of Y^{3+} ions. In the present work, we report results from Monte Carlo simulations of site-diluted microscopic dipolar spin ice models (DSIM) that account quantitatively for the experimental specific heat measurements, and thus also for the residual entropy, as a function of dilution, for both Dy2Ti2O7 and Ho2Ti2O7. The main features of the dilution physics displayed by the magnetic specific heat data are quantitatively captured by the diluted DSIM up to, and including, 85% of the magnetic ions diluted (x=1.7). The previously reported departures in the residual entropy between Dy2Ti2O7 versus Ho2Ti2O7, as well as with a site-dilution variant of Paulings approximation, are thus rationalized through the site-diluted DSIM. For 90% (x=1.8) and 95% (x=1.9) of the magnetic ions diluted, we find a significant discrepancy between the experimental and Monte Carlo specific heat results. We discuss some possible reasons for this disagreement.
Efficient sampling of complex high-dimensional probability densities is a central task in computational science. Machine Learning techniques based on autoregressive neural networks have been recently shown to provide good approximations of probability distributions of interest in physics. In this work, we propose a systematic way to remove the intrinsic bias associated with these variational approximations, combining it with Markov-chain Monte Carlo in an automatic scheme to efficiently generate cluster updates, which is particularly useful for models for which no efficient cluster update scheme is known. Our approach is based on symmetry-enforced cluster updates building on the neural-network representation of conditional probabilities. We demonstrate that such finite-cluster updates are crucial to circumvent ergodicity problems associated with global neural updates. We test our method for first- and second-order phase transitions in classical spin systems, proving in particular its viability for critical systems, or in the presence of metastable states.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
