arXiv subjects

Raoul D. Schram

Publications and source records attributed to Raoul D. Schram.

7 recordsLinked to original sources

arXiv2025

Python-JAX-based Fast Stokesian Dynamics

Stokesian Dynamics (SD) is a powerful computational framework for simulating the motion of particles in a viscous Newtonian fluid under Stokes-flow conditions. Traditional SD implementations can be computationally expensive as they rely on the inversion of large mobility matrices to determine hydrodynamic interactions. Recently, however, the simulation of thermalized systems with large numbers of particles has become feasible [Fiore and Swan, J. Fluid. Mech. $\textbf{878}$, 544 (2019)]. Their ``fast Stokesian dynamics'' (FSD) method leverages a saddle-point formulation to ensure overall scaling of the algorithm that is linear in the number of particles $\mathcal{O}(N)$; performance relies on dedicated graphics-processing-unit computing. Here, we present a different route toward implementing FSD, which instead leverages the Just-in-Time (JIT) compilation capabilities of Google JAX. We refer to this implementation as JFSD and perform benchmarks on it to verify that it has the right scaling and is sufficiently fast by the standards of modern computational physics. In addition, we provide a series of physical test cases that help ensure accuracy and robustness, as the code undergoes further development. Thus, JFSD is ready to facilitate the study of hydrodynamic effects in particle suspensions across the domains of soft, active, and granular matter.

physics.flu-dyn↗

arXiv2022

Hidden dependence of spreading vulnerability on topological complexity

Many dynamical phenomena in complex systems concern spreading that plays out on top of networks with changing architecture over time -- commonly known as temporal networks. A complex system's proneness to facilitate spreading phenomena, which we abbreviate as its `spreading vulnerability', is often surmised to be related to the topology of the temporal network featured by the system. Yet, cleanly extracting spreading vulnerability of a complex system directly from the topological information of the temporal network remains a challenge. Here, using data from a diverse set of real-world complex systems, we develop the `entropy of temporal entanglement' as a novel and insightful quantity to measure topological complexities of temporal networks. We show that this parameter-free quantity naturally allows for topological comparisons across vastly different complex systems. Importantly, by simulating three different types of stochastic dynamical processes playing out on top of temporal networks, we demonstrate that the entropy of temporal entanglement serves as a quantitative embodiment of the systems' spreading vulnerability, irrespective of the details of the processes. In being able to do so, i.e., in being able to quantitatively extract a complex system's proneness to facilitate spreading phenomena from topology, this entropic measure opens itself for applications in a wide variety of natural, social, biological and engineered systems.

physics.soc-ph↗

arXiv2019

Local loop opening in untangled ring polymer melts: A detailed "Feynman test" of models for the large scale structure

The conformational statistics of ring polymers in melts or dense solutions is strongly affected by their quenched microscopic topological state. The effect is particularly strong for untangled (i.e. non-concatenated and unknotted) rings, which are known to crumple and segregate. Here we study these systems using a computationally efficient multi-scale approach, where we combine massive simulations on the fiber level with the explicit construction of untangled ring melt configurations based on theoretical ideas for their large scale structure. We find (i) that topological constraints may be neglected on scales below the standard entanglement length, $L_e$, (ii) that rings with a size $1 \le L_r/L_e \le 30$ exhibit nearly ideal lattice tree behavior characterized by primitive paths which are randomly branched on the entanglement scale, and (iii) that larger rings are compact with gyration radii $\langle R_g^2(L_r) \rangle \propto L_r^{2/3}$. The detailed comparison between equilibrated and constructed ensembles allows us to perform a `Feynman test' of our understanding of untangled rings: can we convert ideas for the large-scale ring structure into algorithms for constructing (nearly) equilibrated ring melt samples? We show that most structural observables are quantitatively reproduced by two different construction schemes: hierarchical crumpling and ring melts derived from the analogy to interacting branched polymers. However, the latter fail the `Feynman test' with respect to the magnetic radius, $R_m$, which we have defined based on an analogy to magnetostatics. While $R_m$ is expected to vanish for double-folded structures, the observed values of $\langle R_m^2(L_r) \rangle \propto \langle R_g^2(L_r) \rangle$ provide a simple and computationally convenient measure of the presence of a non-negligible amount of local loop opening in crumpled rings.

cond-mat.soft↗

arXiv2017

Exact enumeration of self-avoiding walks on BCC and FCC lattices

Self-avoiding walks on the body-centered-cubic (BCC) and face-centered-cubic (FCC) lattices are enumerated up to lengths 28 and 24, respectively, using the length-doubling method. Analysis of the enumeration results yields values for the exponents $γ$ and $ν$ which are in agreement with, but less accurate than those obtained earlier from enumeration results on the simple cubic lattice. The non-universal growth constant and amplitudes are accurately determined, yielding for the BCC lattice $μ=6.530520(20)$, $A=1.1785(40)$, and $D=1.0864(50)$, and for the FCC lattice $μ=10.037075(20)$, $A=1.1736(24)$, and $D=1.0460(50)$.

cond-mat.stat-mech↗

arXiv2013

Universality of the triplet contact process with diffusion

The one-dimensional triplet contact process with diffusion (TCPD) model has been studied using fast multispin GPU Monte Carlo simulations. In particular, the particle density ρand the density of pairs of neighboring particles ρ_p have been monitored as a function of time. Mean field predictions for the time evolution of these observables in the critical point are ρ\sim t^{-δ} and ρ_p\sim t^{-δ_p} with δ=1/3 and δ_p=2/3. We observe that in the vicinity of the critical point of the model, the ratio ρ_p/ρtends to a constant, which shows that the one-dimensional TCPD model is not described by mean field behavior. Furthermore, our long simulations allow us to conclude that the mean field prediction of the exponent $δ$ is almost certainly not correct either. Since the crossover to the critical regime is extremely slow for the TCPD model, we are unable to pinpoint a precise value for δ, though we find as an upper bound δ< 0.32.

cond-mat.stat-mech↗

arXiv2012

SAWdoubler: a program for counting self-avoiding walks

This article presents SAWdoubler, a package for counting the total number Z(N) of self-avoiding walks (SAWs) on a regular lattice by the length-doubling method, of which the basic concept has been published previously by us. We discuss an algorithm for the creation of all SAWs of length N, efficient storage of these SAWs in a tree data structure, and an algorithm for the computation of correction terms to the count Z(2N) for SAWs of double length, removing all combinations of two intersecting single-length SAWs. We present an efficient numbering of the lattice sites that enables exploitation of symmetry and leads to a smaller tree data structure; this numbering is by increasing Euclidean distance from the origin of the lattice. Furthermore, we show how the computation can be parallelised by distributing the iterations of the main loop of the algorithm over the cores of a multicore architecture. Experimental results on the 3D cubic lattice demonstrate that Z(28) can be computed on a dual-core PC in only 1 hour and 40 minutes, with a speedup of 1.56 compared to the single-core computation and with a gain by using symmetry of a factor of 26. We present results for memory use and show how the computation is made to fit in 4 Gbyte RAM. It is easy to extend the SAWdoubler software to other lattices; it is publicly available under the GNU LGPL license.

cond-mat.stat-mech↗

arXiv2011

Exact enumeration of self-avoiding walks

A prototypical problem on which techniques for exact enumeration are tested and compared is the enumeration of self-avoiding walks. Here, we show an advance in the methodology of enumeration, making the process thousands or millions of times faster. This allowed us to enumerate self-avoiding walks on the simple cubic lattice up to a length of 36 steps.

math-ph↗