arXiv subjects

Henrik Christiansen

Publications and source records attributed to Henrik Christiansen.

32 records · Page 2Linked to original sources

arXiv2024

Aging following a zero-temperature quench in the $d=3$ Ising model

Aging in phase-ordering kinetics of the $d=3$ Ising model following a quench from infinite to zero temperature is studied by means of Monte Carlo simulations. In this model the two-time spin-spin autocorrelator $C_\text{ag}$ is expected to obey dynamical scaling and to follow asymptotically a power-law decay with the autocorrelation exponent $λ$. Previous work indicated that the lower Fisher-Huse bound of $λ\geq d/2 = 1.5$ is violated in this model. Using much larger systems than previously studied, the instantaneous exponent for $λ$ we obtain at late times does \emph{not} disagree with this bound. By conducting systematic fits to the data of $C_\text{ag}$ using different ansaetze for the leading correction term, we find $λ= 1.58(14)$ with most of error attributed to the systematic uncertainty regarding the ansaetze. This result is in contrast to the recent report that below the roughening transition universality might be violated.

cond-mat.stat-mech↗

arXiv2023

Self-Tuning Hamiltonian Monte Carlo for Accelerated Sampling

The performance of Hamiltonian Monte Carlo simulations crucially depends on both the integration timestep and the number of integration steps. We present an adaptive general-purpose framework to automatically tune such parameters, based on a local loss function which promotes the fast exploration of phase-space. We show that a good correspondence between loss and autocorrelation time can be established, allowing for gradient-based optimization using a fully-differentiable set-up. The loss is constructed in such a way that it also allows for gradient-driven learning of a distribution over the number of integration steps. Our approach is demonstrated for the one-dimensional harmonic oscillator and alanine dipeptide, a small protein common as a test case for simulation methods. Through the application to the harmonic oscillator, we highlight the importance of not using a fixed timestep to avoid a rugged loss surface with many local minima, otherwise trapping the optimization. In the case of alanine dipeptide, by tuning the only free parameter of our loss definition, we find a good correspondence between it and the autocorrelation times, resulting in a $>100$ fold speed up in optimization of simulation parameters compared to a grid-search. For this system, we also extend the integrator to allow for atom-dependent timesteps, providing a further reduction of $25\%$ in autocorrelation times.

physics.comp-ph↗

arXiv2023

Superdiffusion-like behavior in zero-temperature coarsening of the $d=3$ Ising model

One key aspect of coarsening following a quench below the critical temperature is domain growth. For the non-conserved Ising model a power-law growth of domains of like spins with exponent $α= 1/2$ is predicted. Including recent work, it was not possible to clearly observe this growth law in the special case of a zero-temperature quench in the three-dimensional model. Instead a slower growth with $α<1/2$ was reported. We attempt to clarify this discrepancy by running large-scale Monte Carlo simulations of lattice sizes up to $L=2048$ employing an efficient GPU implementation. Indeed, at late times we measure domain sizes compatible with the expected growth law -- but surprisingly, at still later times domains even grow superdiffusively, i.e., with $α> 1/2$. We argue that this new problem is possibly caused by sponge-like structures emerging at early times.

cond-mat.stat-mech↗

arXiv2022

Fast, hierarchical, and adaptive algorithm for Metropolis Monte Carlo simulations of long-range interacting systems

We present a fast, hierarchical, and adaptive algorithm for Metropolis Monte Carlo simulations of systems with long-range interactions that reproduces the dynamics of a standard implementation exactly, i.e., the generated configurations and consequently all measured observables are identical, allowing in particular for nonequilibrium studies. The method is demonstrated for the power-law interacting long-range Ising model with nonconserved order parameter and a Lennard-Jones system both in two dimensions. The measured runtimes support an average complexity $O(N\log N)$, where $N$ is the number of spins or particles. Importantly, prefactors of this scaling behavior are small, which in practice manifests in speedup factors larger than $10^4$. The method is general and will allow the treatment of large systems that were out of reach before, likely enabling a more detailed understanding of physical phenomena rooted in long-range interactions.

physics.comp-ph↗

arXiv2021

Zero-Temperature Coarsening in the Two-Dimensional Long-Range Ising Model

We investigate the nonequilibrium dynamics following a quench to zero temperature of the non-conserved Ising model with power-law decaying long-range interactions $\propto 1/r^{d+σ}$ in $d=2$ spatial dimensions. The zero-temperature coarsening is always of special interest among nonequilibrium processes, because often peculiar behavior is observed. We provide estimates of the nonequilibrium exponents, viz., the growth exponent $α$, the persistence exponent $θ$, and the fractal dimension $d_f$. It is found that the growth exponent $α\approx 3/4$ is independent of $σ$ and different from $α=1/2$ as expected for nearest-neighbor models. In the large $σ$ regime of the tunable interactions only the fractal dimension $d_f$ of the nearest-neighbor Ising model is recovered, while the other exponents differ significantly. For the persistence exponent $θ$ this is a direct consequence of the different growth exponents $α$ as can be understood from the relation $d-d_f=θ/α$; they just differ by the ratio of the growth exponents $\approx 3/2$. This relation has been proposed for annihilation processes and later numerically tested for the $d=2$ nearest-neighbor Ising model. We confirm this relation for all $σ$ studied, reinforcing its general validity.

cond-mat.stat-mech↗

arXiv2020

Deep Learning-based Signal Strength Prediction Using Geographical Images and Expert Knowledge

Methods for accurate prediction of radio signal quality parameters are crucial for optimization of mobile networks, and a necessity for future autonomous driving solutions. The power-distance relation of current empirical models struggles with describing the specific local geo-statistics that influence signal quality parameters. The use of empirical models commonly results in an over- or under-estimation of the signal quality parameters and require additional calibration studies. In this paper, we present a novel model-aided deep learning approach for path loss prediction, which implicitly extracts radio propagation characteristics from top-view geographical images of the receiver location. In a comprehensive evaluation campaign, we apply the proposed method on an extensive real-world data set consisting of five different scenarios and more than 125.000 individual measurements. It is found that 1) the novel approach reduces the average prediction error by up to 53% in comparison to ray-tracing techniques, 2) A distance of 250-300 meters spanned by the images offer the necessary level of detail, 3) Predictions with a root-mean-squared error of approximately 6 dB is achieved across inherently different data sources.

cs.NI↗

arXiv2020

Aging in the long-range Ising model

The current understanding of aging phenomena is mainly confined to the study of systems with short-ranged interactions. Little is known about the aging of long-ranged systems. Here, the aging in the phase-ordering kinetics of the two-dimensional Ising model with power-law long-range interactions is studied via Monte Carlo simulations. The dynamical scaling of the two-time spin-spin autocorrelator is well described by simple aging for all interaction ranges studied. The autocorrelation exponents are consistent with $λ=1.25$ in the effectively short-range regime, while for stronger long-range interactions the data are consistent with $λ=d/2=1$. For very long-ranged interactions, strong finite-size effects are observed. We discuss whether such finite-size effects could be misinterpreted phenomenologically as sub-aging.

cond-mat.stat-mech↗

arXiv2020

Simulating Met-Enkephalin With Population Annealing Molecular Dynamics

Met-enkephalin, one of the smallest opiate peptides and an important neurotransmitter, is a widely used benchmarking problem in the field of molecular simulation. Through its range of possible low-temperature conformations separated by free-energy barriers it was previously found to be hard to thermalize using straight canonical molecular dynamics simulations. Here, we demonstrate how one can use the recently proposed population annealing molecular dynamics scheme to overcome these difficulties. We show how the use of multi-histogram reweighting allows one to accurately estimate the density of states of the system and hence derive estimates such as the potential energy as quasi continuous functions of temperature. We further investigate the free-energy surface as a function of end-to-end distance and radius-of-gyration and observe two distinct basins of attraction.

cond-mat.soft↗

arXiv2019

Understanding nonequilibrium scaling laws governing collapse of a polymer

Recent emerging interest in experiments of single-polymer dynamics urge computational physicists to revive their understandings, particularly in the nonequilibrium context. Here we briefly discuss the currently evolving approaches of investigating the evolution dynamics of homopolymer collapse in computer simulations. Primary focus of these approaches is to understand various dynamic scaling laws related to coarsening and aging during the collapse in space dimension $d=3$, using tools popular in nonequilibrium coarsening dynamics of particle or spin systems. In addition to providing an overview of those results, we also present new preliminary data for $d=2$.

cond-mat.stat-mech↗

arXiv2019

Accelerating molecular dynamics simulations with population annealing

Population annealing is a powerful tool for large-scale Monte Carlo simulations. We adapt this method to molecular dynamics simulations and demonstrate its excellent accelerating effect by simulating the folding of a short peptide commonly used to gauge the performance of algorithms. The method is compared to the well established parallel tempering approach and is found to yield similar performance for the same computational resources. In contrast to other methods, however, population annealing scales to a nearly arbitrary number of parallel processors and it is thus a unique tool that enables molecular dynamics to tap into the massively parallel computing power available in supercomputers that is so much needed for a range of difficult computational problems.

physics.comp-ph↗

arXiv2019

Phase ordering kinetics of the long-range Ising model

We use an efficient method that eases the daunting task of simulating dynamics in spin systems with long-range interaction. Our Monte Carlo simulations of the long-range Ising model for the nonequilibrium phase ordering dynamics in two spatial dimensions erform significantly faster than the standard Metropolis approach and considerably more efficiently than the kinetic Monte Carlo method. Importantly, this enables us to establish agreement with the theoretical prediction for the time dependence of domain growth, in contrast to previous numerical studies. This method can easily be generalized to applications in other systems.

cond-mat.stat-mech↗

arXiv2018

Dissipative Dynamics of a Single Polymer in Solution: A Lowe-Andersen Approach

We study the equilibrium dynamics of a single polymer chain under good solvent condition. Special emphasis is laid on varying the drag force experienced by the chain while it moves. To this end we model the solvent in a mesoscopic manner by employing the Lowe-Andersen approach of dissipative particle dynamics which is known to reproduce hydrodynamic effects. Our approach captures the correct static behavior in equilibrium. Regarding the dynamics, we investigate the scaling of the self-diffusion coefficient $D$ with respect to the length of the polymer $N$, yielding results that are compatible with the Zimm scaling $D \sim N^{-3/5}$.

cond-mat.soft↗

arXiv2017

Scaling laws during collapse of a homopolymer: Lattice versus off-lattice

We present comparative results from simulations of a lattice and an off-lattice model of a homopolymer, in the context of kinetics of the collapse transition. Scaling laws related to the collapse time, cluster coarsening and aging behavior are compared. Although in both models the cluster growth is independent of temperature, the related exponents turn out to be different. Conversely, the aging and associated scaling properties are found to be universal, with the nonequilibrium autocorrelation exponent obeying a recently derived bound.

cond-mat.stat-mech↗

arXiv2017

Coarsening and Aging of Lattice Polymers: Influence of Bond Fluctuations

We present results for the nonequilibrium dynamics of collapse for a model flexible homopolymer on simple cubic lattices with fixed and fluctuating bonds between the monomers. Results from our Monte Carlo simulations show that, phenomenologically, the sequence of events observed during the collapse are independent of the bond criterion. While the growth of the clusters (of monomers) at different temperatures exhibits a nonuniversal power-law behavior when the bonds are fixed, the introduction of fluctuations in the bonds by considering the existence of diagonal bonds produces a temperature independent growth, which can be described by a universal nonequilibrium finite-size scaling function with a non-universal metric factor. We also examine the related aging phenomenon, probed by a suitable two-time density-density autocorrelation function showing a simple power-law scaling with respect to the growing cluster size. Unlike the cluster-growth exponent $α_c $, the nonequilibrium autocorrelation exponent $λ_C$ governing the aging during the collapse, however, is independent of the bond type and strictly follows the bounds proposed by two of us in Phys. Rev. E 93, 032506 (2016) at all temperatures.

cond-mat.soft↗