arXiv subjects

Per Arne Rikvold

Publications and source records attributed to Per Arne Rikvold.

At least 19 recordsLinked to original sources

arXiv2026

Effective length scales, dispersion relations, and discrete densities of states for Laplacian eigenvectors on complex networks

To construct dispersion relations for diffusion or oscillation processes on random networks, it is necessary to obtain effective length scales for the eigenvectors of a graph Laplacian matrix, whose eigenvalues represent inverse time scales. For this purpose, we adapt a method originally introduced in condensed-matter physics to estimate correlation lengths for disordered materials as the ratio of volume to interface area [P. Debye, H.R. Anderson and H. Brumberger, J. Appl. Phys. 28, 679 (1957)]. In a graph setting of vertices connected by edges, we interpret this as the ratio of twice the total number of edges to the number of edges connecting vertices bearing values of different sign on the particular eigenvector. After describing the method and the necessary concepts in pedagogical detail, we apply it to nine different graphs representing natural and artificial networks, including two tree graphs without and with random shortcuts, the nervous system of a roundworm, a food web, a social network of dolphins, an electrical power grid, and a model porous material. The results identify both distributed and localized eigenvectors. They are given in graphical format showing example eigenvectors, dispersion relations, and discrete densities of states, as well as tables summarizing the main numerical results.

cond-mat.dis-nn↗

arXiv2025

A comparative review of recent results on supercritical anomalies in two-dimensional kinetic Ising and Blume-Capel ferromagnets

Following the unexpected experimental discovery of ``sideband'' peaks in the fluctuation spectrum of thin Co films driven by a slowly oscillating magnetic field with a constant bias [P.~Riego et al., Phys. Rev. Lett. 118, 117202 (2017)] numerical studies of two-state Ising and three-state Blume-Capel (BC) ferromagnets in this dynamically supercritical regime have flourished and been successful in explaining this phenomenon. Here, we give a comparative review of this new literature and its connections to earlier work. Following an introduction and a presentation of the two models and the computational method used in many of these studies, we present numerical results for both models. Particular attention is paid to the fact that zero spins in the BC model tend to collect at he interfaces between regions of the two nonzero spin values, +/-1. We present strong arguments that this phenomenon leads to a reduction of the effective interface tension in the BC model, compared to the Ising model.

cond-mat.stat-mech↗

arXiv2025

Interface instability of two-phase flow in a three-dimensional porous medium

We present an experimental study of immiscible, two-phase fluid flow through a three-dimensional porous medium consisting of randomly-packed, monodisperse glass spheres. Our experiments combine refractive-index matching and laser-induced fluorescence imaging to resolve the morphology and stability of the moving interface resulting from the injection of one fluid into another. The imposed injection rate sets a balance between gravitational and viscous forces, producing interface morphologies which range from unstable collections of tangled fingers at low rates to stable sheets at high rates. The image data are complemented by time-resolved pressure measurements. We develop a stability criterion for the fluid interface based on the analysis of the 3D images and the pressure data. This criterion involves the Darcy permeability in each of the two phases and the time derivative of the pressure drop across the medium. We observe that the relative permeability encountered by the invading fluid is modified by the imposed flow rate in our experiment, which impacts the two-phase flow dynamics. We show that, in addition to the balance between the relevant forces driving the dynamics, local regions of crystalline order in the beadpack (crystallites) affect the stability of the invading front. This work provides insights into how disorder on multiple length scales in porous media can interact with viscous, capillary, and gravitational forces to determine the stability and dynamics of immiscible fluid interfaces.

physics.flu-dyn↗

arXiv2024

Numerical Simulation of a Two-Dimensional Blume-Capel Ferromagnet in an Oscillating Magnetic Field with a Constant Bias

We perform a numerical study of the kinetic Blume-Capel (BC) model to find if it exhibits the metamagnetic anomalies previously observed in the kinetic Ising model for supercritical periods. We employ a heat-bath Monte Carlo (MC) algorithm on a square lattice in which spins can take values of $\pm 1, 0$, with a non-zero crystal field, subjected to a sinusoidal oscillating field in conjunction with a constant bias. In the ordered region, we find an equivalent hysteretic response of the order parameters with its respective conjugate fields between the kinetic and the equilibrium model. In the disordered region (supercritical periods), we observed two peaks, symmetrical with respect to zero bias, in the susceptibility and scaled variance curves, consistent with the numerical and experimental findings on the kinetic Ising model. This behavior does not have a counterpart in the equilibrium model. Furthermore, we find that the peaks occur at higher values of the bias field and become progressively smaller as the density of zeros, or the amplitude of the oscillating field, increases. Using nucleation theory, we demonstrate that these fluctuations, as in the Ising model, are not a critical phenomenon, but that they are associated with a crossover between a single-droplet (SD) and a multi-droplet (MD) magnetization switching mechanism. For strong (weak) bias, the SD (MD) mechanism dominates. We also found that the zeros concentrate on the droplets' surfaces, which may cause a reduced interface tension in comparison with the Ising model . Our results suggest that metamagnetic anomalies are not particular to the kinetic Ising model, but rather are a general characteristic of spin kinetic models, and provide further evidence that the equivalence between dynamical phase transitions and equilibrium ones is only valid near the critical point.

cond-mat.stat-mech↗

arXiv2024

Interaction between corner and bulk flows during drainage in granular porous media

Drainage in porous media can be broken down into two main mechanisms: a primary piston-like displacement of the interfaces through the bulk of pore bodies and throats, and a secondary slow flow through corners and films in the wake of the invasion front. In granular porous media, this secondary drainage mechanism unfolds in connected pathways of pendular structures, such as capillary bridges and liquid rings, formed between liquid clusters. To represent both mechanisms, we proposed a dynamic dual-network model for drainage, considering that a gas displaces a wetting liquid from quasi-2D granular porous media. For this model, dedicated analyses of the capillary bridge shapes and hydraulic conductivity were conducted so that the secondary drainage mechanism could be properly quantified at finite speeds. With the model, an investigation of the wetting-phase connectivity and flow during drainage was carried out, covering a broad range of flow conditions. Results indicate that the span of liquid-connected structures in the unsaturated region, as well as their ability to contribute to flow, varies significantly with Capillary and Bond numbers.

cond-mat.soft↗

arXiv2023

Multicritical Bifurcation and First-order Phase Transitions in a Three-dimensional Blume-Capel Antiferromagnet

We present a detailed study by Monte Carlo simulations and finite-size scaling analysis of the phase diagram and ordered bulk phases for the three-dimensional Blume-Capel antiferromagnet in the space of temperature and magnetic and crystal fields (or two chemical potentials in an equivalent lattice-gas model with two particle species and vacancies). The phase diagram consists of surfaces of second- and first-order transitions that enclose a ``volume'' of ordered phases in the phase space. At relatively high temperatures, these surfaces join smoothly along a line of tricritical points, and at zero magnetic field we obtain good agreement with known values for tricritical exponent ratios [Y. Deng and H.W.J. Bl{ö}te, Phys. Rev. E {70}, 0456111 (2004)]. In limited field regions at lower temperatures (symmetric under reversal of the magnetic field), the tricritical line for this three-dimensional model bifurcates into lines of critical endpoints and critical points, connected by a surface of weak first-order transitions {inside} the region of ordered phases. This phenomenon is not seen in the two-dimensional version of the same model. We confirm the location of the bifurcation as previously reported [Y.L. Wang and J.D. Kimel, J. Appl. Phys. {69}, 6176 (1991)], and we identify the phases separated by this first-order surface as antiferromagnetically (three-dimensional checker-board) ordered with different vacancy densities. We visualize the phases by real-space snapshots and by structure factors in the three-dimensional space of wave vectors.

cond-mat.stat-mech↗

arXiv2023

A simplified pore-scale model for slow drainage including film-flow effects

Film flow through networks of corners and capillary bridges can establish connections between seemingly isolated clusters during drainage in porous media. Coupled with drainage through the bulk of pores and throats, the flow through these networks constitutes a secondary drainage mechanism that can significantly affect fluid configurations and residual saturations. In order to investigate the prevalence of this drainage mechanism, we propose a quasi-static pore-network model based on modifying the trapped-cluster-identification algorithm in an invasion-percolation model. With the modification, wetting-phase connectivity could be provided by direct successions of pores and throats, represented by sites and bonds, as well as by chains of interconnected capillary bridges. The advancement of the fluid interface in the porous matrix was determined by the bonds' invasion thresholds, calculated based on local capillary pressure values that could be perturbed to accommodate gravitational effects. With the proposed model, experimentally verified phenomena related to slow drainage in granular porous media were reproduced, showing good qualitative agreement.

physics.flu-dyn↗

arXiv2022

Competing gravitational and viscous efects in 3D two-phase flow investigated with a table-top optical scanner

We present experiments and theory describing the transition from viscosity-stabilized flow to gravitationally unstable fingering for two-phase flow in a 3D synthetic porous medium. Observation is made possible by the use of our newly developed table-top 3D-scanner based on optical index matching and laser-induced fluorescence, which is described in detail. In the experiment, a more dense, more viscous fluid injected at a fixed flow-rate from a point source at the top of the flow cell displaces a less viscous, less dense fluid. We observe a stable invasion zone near the inlet, which increases in size with increasing flow rates, and presents initially a close to hemispherical shape. At later times, the invasion front transits to an unstable mode and a fingering flow regime. The transition occurs at a predicted critical radius, Rc, corresponding to the zero of the combined viscous and gravitational pressure gradient.

physics.flu-dyn↗

arXiv2021

Adjustable reach in a network centrality based on current flows

Centrality, which quantifies the "importance" of individual nodes, is among the most essential concepts in modern network theory. Most prominent centrality measures can be expressed as an aggregation of influence flows between pairs of nodes. As there are many ways in which influence can be defined, many different centrality measures are in use. Parametrized centralities allow further flexibility and utility by tuning the centrality calculation to the regime most appropriate for a given network. Here, we identify two categories of centrality parameters. Reach parameters control the attenuation of influence flows between distant nodes. Grasp parameters control the centrality's potential to send influence flows along multiple, often nongeodesic paths. Combining these categories with Borgatti's centrality types [S. P. Borgatti, Social Networks 27, 55-71 (2005)], we arrive at a novel classification system for parametrized centralities. Using this classification, we identify the notable absence of any centrality measures that are radial, reach parametrized, and based on acyclic, conservative flows of influence. We therefore introduce the ground-current centrality, which is a measure of precisely this type. Because of its unique position in the taxonomy, the ground-current centrality has significant advantages over similar centralities. We demonstrate that, compared to other conserved-flow centralities, it has a simpler mathematical description. Compared to other reach centralities, it robustly preserves an intuitive rank ordering across a wide range of network architectures. We also show that it produces a consistent distribution of centrality values among the nodes, neither trivially equally spread (delocalization), nor overly focused on a few nodes (localization). Other reach centralities exhibit both of these behaviors on regular networks and hub networks, respectively.

physics.soc-ph↗

arXiv2020

Visualization by optical fluorescence of two-phase flow in a three-dimensional porous medium

Slow flow of a single fluid through a porous medium is well understood on a macroscopic level through Darcy's law, a linear relation between flow rate and a combination of pressure differences, viscosity, and gravitational forces. Two-phase flow is complicated by the interface separating the fluids, but understanding of two-dimensional, two-phase flow has been obtained from experiments using transparent cells. In most three-dimensional media, however, visual observation is difficult. Here, we present preliminary results of experiments on a model medium consisting of randomly packed glass spheres, in which one fluorescent liquid invades another. By refractive index matching and scanning with a sheet-shaped laser beam, we obtain slices of the flow patterns, which we combine into three-dimensional pictures. We observe a compact region of invading fluid, surrounded by finger-like protrusions. The compact region becomes more dominant with increasing invader flow rate. The patterns are theoretically analyzed in terms of the interplay between gravitational, viscous, and capillary forces.

cond-mat.soft↗

arXiv2020

Absorbing Random Walks Interpolating Between Centrality Measures on Complex Networks

Centrality, which quantifies the "importance" of individual nodes, is among the most essential concepts in modern network theory. As there are many ways in which a node can be important, many different centrality measures are in use. Here, we concentrate on versions of the common betweenness and it closeness centralities. The former measures the fraction of paths between pairs of nodes that go through a given node, while the latter measures an average inverse distance between a particular node and all other nodes. Both centralities only consider shortest paths (i.e., geodesics) between pairs of nodes. Here we develop a method, based on absorbing Markov chains, that enables us to continuously interpolate both of these centrality measures away from the geodesic limit and toward a limit where no restriction is placed on the length of the paths the walkers can explore. At this second limit, the interpolated betweenness and closeness centralities reduce, respectively, to the well-known it current betweenness and resistance closeness (information) centralities. The method is tested numerically on four real networks, revealing complex changes in node centrality rankings with respect to the value of the interpolation parameter. Non-monotonic betweenness behaviors are found to characterize nodes that lie close to inter-community boundaries in the studied networks.

physics.soc-ph↗

arXiv2019

Complete catalog of ground-state diagrams for the general three-state lattice-gas model with nearest-neighbor interactions on a square lattice

The ground states of the general three-state lattice-gas (equivalently, $S=1$ Ising) model with nearest-neighbor interactions on a square lattice are explored in the full, five-dimensional parameter space of three interaction constants and two generalized chemical potentials or fields. The resulting, complete catalog of fifteen topologically different ground-state diagrams (zero-temperature phase diagrams) is discussed in both lattice-gas and Ising-spin language. The results extend those of a recent study in a reduced parameter space [V. F. Fefelov, et al., Phys. Chem. Chem. Phys., 2018, 20, 10359--10368], which identified six different ground-state diagrams.

cond-mat.stat-mech↗

arXiv2018

Multistability in an unusual phase diagram induced by the competition between antiferromagnetic-like short-range and ferromagnetic-like long-range interactions

The interplay between competing short-range (SR) and long-range (LR) interactions can cause nontrivial structures in phase diagrams. Recently, horn-shaped unusual structures were found by Monte Carlo simulations in the phase diagram of the Ising antiferromagnet (IA) with infinite-range ferromagnetic-like (F) interactions [Phys. Rev. B {\bf 93}, 064109 (2016); {\bf 96}, 174428 (2017)], and also in an IA with LR interactions of elastic origin modeling spin-crossover materials [Phys. Rev. B {\bf 96}, 144425 (2017)]. To clarify the nature of the phases associated with the horn structures, we study the phase diagram of the IA model with infinite-range F interactions by applying a variational free energy in a cluster mean-field (CMF) approximation. While the simple Bragg-Williams mean-field theory for each sublattice does not produce a horn structure, we find such structures with the CMF method. This confirms that the local thermal fluctuations enabled by the multisite clusters are essential for this phenomenon. We investigate in detail the structure of metastable phases in the phase diagram. In contrast to the phase diagram obtained by the Monte Carlo studies, we find a triple point, at which ferromagnetic-like, antiferromagnetic-like, and disordered phases coexist, and also six tristable regions accompanying the horn structure. We also point out that several characteristic endpoints of first-order transitions appear in the phase diagram. We propose three possible scenarios for the transitions related to the tristable regions. Finally, we discuss the relation between the triple point in this phase diagram and that of a possible lattice-gas model, in which solid, liquid, and gas phases can coexist.

cond-mat.stat-mech↗

arXiv2018

Conservation of population size is required for self-organized criticality in evolution models

We study models of biological evolution and investigate a key factor to yield self-organized criticality (SOC). The Bak-Sneppen (BS) model is the most basic model that shows an SOC state, which is developed based on minimal and plausible assumptions of Darwinian competition. Another class of models, which have population dynamics and simple rules for species migrations, has also been studied. It turns out that they do not show an SOC state although the assumptions made in these models are similar to those in the BS model. To clarify the origin of these differences and to identify a key ingredient of SOC, we study models that bridge the BS model and the Dynamical Graph model, which is a representative of the population dynamics models. From a comparative study of the models, we find that SOC is found when the fluctuations of the number of species $N$ are suppressed, while it shows off-critical states when $N$ changes according to its evolutionary dynamics. This indicates that the assumption of the fixed system size in the BS model plays a pivotal role to drive the system into an SOC state, and casts doubt on its applicability to actual evolutionary dynamics.

q-bio.PE↗

arXiv2017

Density of states for systems with multiple order parameters: a constrained Wang-Landau method

A macroscopically constrained Wang-Landau Monte Carlo method was recently proposed to calculate the joint density of states (DOS) for systems with multiple order parameters. Here we demonstrate results for a nearest-neighbor Ising antiferromagnet with ferromagnetic long-range interactions (a model spin-crossover material). Its two relevant order parameters are the magnetization $M$ and the staggered magnetization $M_{\rm s}$. The joint DOS, $g(E,M,M_{\rm s})$ where $E$ is the total system energy, is calculated for zero external field and long-range interaction strength, and then obtained for arbitrary values of these two field-like model parameters by a simple transformation of $E$. Illustrations are shown for several parameter sets.

cond-mat.stat-mech↗

arXiv2017

Phase diagrams and free-energy landscapes for model spin-crossover materials with antiferromagnetic-like nearest-neighbor and ferromagnetic-like long-range interactions

We present phase diagrams, free-energy landscapes, and order-parameter distributions for a model spin-crossover material with a two-step transition between the high-spin and low-spin states (a square-lattice Ising model with antiferromagnetic-like nearest-neighbor and ferromagnetic-like long-range interactions) [P. A. Rikvold et al., Phys. Rev. B 93, 064109 (2016)]. The results are obtained by a recently introduced, macroscopically constrained Wang-Landau Monte Carlo simulation method [C. H. Chan, G. Brown, and P. A. Rikvold, Phys. Rev. E 95, 053302 (2017)]. The method's computational efficiency enables calculation of thermodynamic quantities for a wide range of temperatures, applied fields, and long-range interaction strengths. For long-range interactions of intermediate strength, tricritical points in the phase diagrams are replaced by pairs of critical end points and mean-field critical points that give rise to horn-shaped regions of metastability. The corresponding free-energy landscapes offer insights into the nature of asymmetric, multiple hysteresis loops that have been experimentally observed in spin-crossover materials characterized by competing short-range interactions and long-range elastic interactions.

cond-mat.mtrl-sci↗

arXiv2017

Nontrivial phase diagram for an elastic interaction model of spin crossover materials with antiferromagnetic-like short-range interactions

We study the phase diagram of an elastic interaction model for spin crossover (SC) materials with antiferromagnetic-like short-range interactions. In this model, the interplay between the short-range interaction and the long-range interaction of elastic origin causes complex phase transitions. For relatively weak elastic interactions, the phase diagram is characterized by tricritical points, at which antiferromagnetic (AF) -like and ferromagnetic (F) -like spinodal lines and a critical line merge. On the other hand, for relatively strong elastic interactions, unusual "horn structures," which are surrounded by the F-like spinodal lines, disorder (D) spinodal lines, and the critical line, are realized at higher temperatures. These structures are similar to those obtained in our previous study [Phys. Rev. B {\bf 93}, 064109 (2016)] of an Ising antiferromagnet with infinite-range ferromagnetic interactions, and we find universal features caused by the interplay between the competing short-range and long-range interactions. The long-range interaction of elastic origin is irrelevant (inessential) for the critical line. In contrast, the AF-like, F-like, and D spinodal lines result from the long-range interaction of elastic origin. This difference causes qualitatively different features of domain formation or nucleation of the new phase: clustering occurs in the former case, while clustering is absent in the latter. Based on the phase diagrams, we discuss the patterns and clustering features of two-step SC transitions, in which the AF-like phase is realized in the intermediate temperature region.

cond-mat.stat-mech↗

arXiv2017

Fluctuations in a model ferromagnetic film driven by a slowly oscillating field with a constant bias

We present a numerical and theoretical study that supports and explains recent experimental results on anomalous magnetization fluctuations of a uniaxial ferromagnetic film in its low-temperature phase, which is forced by an oscillating field above the critical period of the associated dynamic phase transition (DPT) [P. Riego, P. Vavassori, A. Berger, Phys. Rev. Lett. 118, 117202 (2017)]. For this purpose, we perform kinetic Monte Carlo simulations of a two-dimensional Ising model with nearest-neighbor ferromagnetic interactions in the presence of a sinusoidally oscillating field, to which is added a constant bias field. We study a large range of system sizes and supercritical periods and analyze the data using a droplet-theoretical description of magnetization switching. We find that the period-averaged magnetization, which plays the role of the order parameter for the DPT, presents large fluctuations that give rise to well-defined peaks in its scaled variance and its susceptibility with respect to the bias field. The peaks are symmetric with respect to zero bias and located at values of the bias field that increase toward the field amplitude as an inverse logarithm of the field oscillation period. Our results indicate that this effect is independent of the system size for large systems, ruling out critical behavior associated with a phase transition. Rather, it is a stochastic-resonance phenomenon that has no counterpart in the corresponding thermodynamic phase transition, providing a reminder that the equivalence of the DPT to an equilibrium phase transition is limited to the critical region near the critical period and zero bias.

cond-mat.mtrl-sci↗