arXiv subjects

Hyun Keun Lee

Publications and source records attributed to Hyun Keun Lee.

At least 19 recordsLinked to original sources

arXiv2025

Circular current induced by angular dynamics in swarmalator populations

We propose a modified swarmalator model that generates collective rotational currents in phase synchronization. Our approach builds on the original swarmalator model [4], introducing a key modification: the phase-dependent terms in the spatial dynamics are replaced with a simpler driving term that depends on both the phase and a specified origin. We investigate the dynamics of this model through extensive numerical simulations. When the origin is fixed, spiral motions of synchronized and clustered swarmalators emerge from a finite fraction of random initial conditions, resulting in collective currents. To prevent the unrealistic divergence of these spirals, we introduce a dynamic origin, defined as the center of the swarmalators' positions. With this dynamic origin, the system evolves into rotating collective currents, where synchronized swarmalators form stable circular patterns. In both the fixed and dynamic origin cases, we also observe no-current states, in which synchronized swarmalators aggregate near the origin. Finally, we find that the formation of collective currents can be facilitated by tuning the phase variables either at initialization or during the system's evolution.

nlin.AO↗

arXiv2023

Improved Numerical Scheme for the Generalized Kuramoto Model

We present an improved and more accurate numerical scheme for a generalization of the Kuramoto model of coupled phase oscillators to the three-dimensional space. The present numerical scheme relies crucially on our observation that the generalized Kuramoto model corresponds to particles on the unit sphere undergoing rigid body rotations with position-dependent angular velocities. We demonstrate that our improved scheme is able to reproduce known analytic results and capture the expected behavior of the three-dimensional oscillators in various cases. On the other hand, we find that the conventional numerical method, which amounts to a direct numerical integration with the constraint that forces the particles to be on the unit sphere at each time step, may result in inaccurate and misleading behavior especially in the long time limit. We analyze in detail the origin of the discrepancy between the two methods and present the effectiveness of our method in studying the limit cycle of the Kuramoto oscillators.

cond-mat.soft↗

arXiv2022

Statistical inference as Green's functions

Statistical inference from data is a foundational task in science. Recently, it has received growing attention for its central role in inference systems of primary interest in data sciences and machine learning. However, the understanding of statistical inference is not that solid while remains as a matter of subjective belief or as the routine procedures once claimed objective. We here show that there is an objective description of statistical inference for long sequence of exchangeable binary random variables, the prototypal stochasticity in theories and applications. A linear differential equation is derived from the identity known as de Finetti's representation theorem, and it turns out that statistical inference is given by the Green's functions. Our finding is an answer to the normative issue of science that pursues the objectivity based on data, and its significance will be far-reaching in most pure and applied fields.

cond-mat.stat-mech↗

arXiv2021

Coupling disorder in a population of swarmalators

We consider a population of two-dimensional oscillators with random couplings, and explore the collective states. The coupling strength between oscillators is randomly quenched with two values one of which is positive while the other is negative, and the oscillators can spatially {\it{move}} depending on the state variables for phase and position. We find that the system shows the phase transition from the incoherent state to the fully synchronized one at a proper ratio of the number of positive couplings to the total. The threshold is numerically measured, and analytically predicted by the linear stability analysis of the fully synchronized state. It is found that the random couplings induces the long-term state patterns appearing for constant strength. The oscillators move to the places where the randomly quenched couplings work as if annealed. We further observe that the system with mixed randomnesses for quenched couplings shows the combination of the deformed patterns understandable with each annealed averages.

cond-mat.soft↗

arXiv2021

Thermodynamic uncertainty relation for underdamped dynamics driven by time-dependent protocols

The thermodynamic uncertainty relation (TUR) for underdamped dynamics has intriguing problems while its counterpart for overdamped dynamics has recently been derived. Even for the case of steady states, a proper way to match underdamped and overdamped TURs has not been found. We derive the TUR for underdamped systems subject to general time-dependent protocols, that covers steady states, by using the Cramér-Rao inequality. We show the resultant TUR to give rise to the inequality of the product of the variance and entropy production. We prove it to approach to the known overdamped result for large viscosity limit. We present three examples to confirm our rigorous result.

cond-mat.stat-mech↗

arXiv2021

Collective steady-state patterns of swarmalators with finite-cutoff interaction distance

We study the steady-state patterns of population of the coupled oscillators that sync and swarm, where the interaction distances among oscillators have finite-cutoff in interaction distance. We examine how the static patterns known in the infinite-cutoff are reproduced or deformed, and explore a new static pattern that does not appear until a finite-cutoff is considered. All steady-state patterns of the infinite-cutoff, static sync, static async, and static phase wave are respectively repeated in space for proper finite-cutoff ranges. Their deformation in shape and density takes place for the other finite-cutoff ranges. Bar-like phase wave states are observed, which has not been the case for the infinite-cutoff. All the patterns are investigated via numerical and theoretical analysis.

cond-mat.soft↗

arXiv2018

Public opinion by a poll process: model study and Bayesian view

We study the formation of public opinion in a poll process where the current score is open to public. The voters are assumed to vote probabilistically for or against their own preference considering the group opinion collected up to then in the score. The poll-score probability is found to follow the beta distribution in the large polls limit. We demonstrate that various poll results even contradictory to the population preference are possible with non-zero probability density and that such deviations are readily triggered by initial bias. It is mentioned that our poll model can be understood in the Bayesian viewpoint.

physics.soc-ph↗

arXiv2017

Nonequilibrium steady states in Langevin thermal systems

Equilibrium is characterized by its fundamental properties such as the detailed balance, the fluctuation-dissipation relation, and no heat dissipation. Based on the stochastic thermodynamics, we show that these three properties are equivalent to each other in conventional Langevin thermal systems with microscopic reversibility. Thus, a conventional steady state has either all three properties (equilibrium) or none of them (nonequilibrium). In contrast, with velocity-dependent forces breaking the microscopic reversibility, we prove that the detailed balance and the fluctuation-dissipation relation mutually exclude each other and no equivalence relation is possible between any two of the three properties. This implies that a steady state of Langevin systems with velocity-dependent forces may maintain some equilibrium properties but not all of them. Our results are illustrated with a few example systems.

cond-mat.stat-mech↗

arXiv2016

Housekeeping Entropy in Continuous Stochastic Dynamics with Odd-Parity Variables

We investigate the decomposition of the total entropy production in continuous stochastic dynamics when there are odd-parity variables that change their signs under time reversal. The first component of the entropy production, which satisfies the fluctuation theorem, is associated with the usual excess heat that appears during transitions between stationary states. The remaining housekeeping part of the entropy production can be further split into two parts. We show that this decomposition can be achieved in infinitely many ways characterized by a single parameter σ. For an arbitrary value of σ, one of the two parts contributing to the housekeeping entropy production satisfies the fluctuation theorem. We show that for a range of σ values this part can be associated with the breakage of the detailed balance in the steady state, and can be regarded as a continuous version of the corresponding entropy production that has been obtained previously for discrete state variables. The other part of the housekeeping entropy does not satisfy the fluctuation theorem and is related to the parity asymmetry of the stationary state distribution. We discuss our results in connection with the difference between continuous and discrete variable cases especially in the conditions for the detailed balance and the parity symmetry of the stationary state distribution.

cond-mat.stat-mech↗

arXiv2015

Unconventional entropy production in the presence of momentum-dependent forces

We investigate an unconventional nature of the entropy production (EP) in nonequilibrium systems with odd-parity variables that change signs under time reversal. We consider the Brownian motion of a particle in contact with a heat reservoir, where particle momentum is an odd-parity variable. In the presence of an {\it external} momentum-dependent force, the EP transferred to environment is found {\em not} equivalent to usual reservoir entropy change due to heat transfer. There appears an additional unconventional contribution to the EP, which is crucial for maintaining the non-negativity of the (average) total EP enforced by the thermodynamic second law. A few examples are considered to elucidate the novel nature of the EP. We also discuss detailed balance conditions with a momentum-dependent force.

cond-mat.stat-mech↗

arXiv2015

Traffic model by braking capability and response time

We propose a microscopic traffic model where the update velocity is determined by the deceleration capacity and response time. It is found that there is a class of collisions that cannot be distinguished by simply comparing the stop positions. The model generates the safe, comfortable, and efficient traffic flow in numerical simulations with the reasonable values of the parameters, and this is analytically supported. Our approach provides a new perspective in modeling the traffic-flow safety and the perturbing situations like lane change.

cond-mat.stat-mech↗

arXiv2014

Degree-ordered percolation on hierarchical scale-free network

We investigate the critical phenomena of the degree-ordered percolation (DOP) model on the hierarchical $(u,v)$ flower network. Using the renormalization-group like procedure, we derive the recursion relations for the percolating probability and the percolation order parameter, from which the percolation threshold and the critical exponents are obtained. When $u\neq 1$, the DOP critical behavior turns out to be identical to that of the bond percolation with a shifted nonzero percolation threshold. When $u=1$, the DOP and the bond percolation have the same vanishing percolation threshold but the critical behaviors are different. Implication to an epidemic spreading phenomenon is discussed.

cond-mat.stat-mech↗

arXiv2013

Comment on "Nature of the Epidemic Threshold for the Susceptible-Infected-Susceptible Dynamics in Networks" [arXiv:1305.4819]

Recently, Boguñá {\it et. al.} [Phys. Rev. Lett. {\bf 111}, 068701 (2013), arXiv:1305.4819] claimed that the epidemic threshold of the susceptible-infected-susceptible (SIS) model is zero on random scale-free (SF) networks with the small-world (SW) property. They drew the conclusion by taking into account a long-range reinfection mechanism. In this Comment, we will show that such an effect is too weak to guarantee an endemic phase with a {\em finite} fraction of infected nodes. Consequently, the epidemic threshold can be finite in random SF networks.

physics.soc-ph↗

arXiv2012

Epidemic Threshold of Susceptible-Infected-Susceptible Model on Complex Networks

We demonstrate that the susceptible-infected-susceptible (SIS) model on complex networks can have an inactive Griffiths phase characterized by a slow relaxation dynamics. It contrasts with the mean field theoretical prediction that the SIS model on complex networks is active at any nonzero infection rate. The dynamic fluctuation of infected nodes, ignored in the mean field approach, is responsible for the inactive phase. It is proposed that the question whether the epidemic threshold of the SIS model on complex networks is zero or not can be resolved by the percolation threshold in a model where nodes are occupied in the degree-descending order. Our arguments are supported by the numerical studies on scale-free network models.

physics.soc-ph↗

arXiv2012

Fluctuation theorems in general stochastic processes with odd-parity variables

We show that the total entropy production in stochastic processes with odd-parity variables (under time reversal) is separated into three parts, only two of which satisfy the integral fluctuation theorems in general. One is the usual excess entropy production, which can appear only transiently and is called nonadiabatic. Another one is attributed solely to the breakage of detailed balance. The last part not satisfying the fluctuation theorem comes from the steady-state distribution asymmetry for odd-parity variables, which is activated in a non-transient manner. The latter two contributions combine together as the house-keeping (adiabatic) entropy production, whose positivity is not guaranteed except when the excess entropy production completely vanishes.

cond-mat.stat-mech↗

arXiv2012

Percolation transitions with nonlocal constraint

We investigate percolation transitions in a nonlocal network model numerically. In this model, each node has an exclusive partner and a link is forbidden between two nodes whose $r$-neighbors share any exclusive pair. The $r$-neighbor of a node $x$ is defined as a set of at most $N^r$ neighbors of $x$, where $N$ is the total number of nodes. The parameter $r$ controls the strength of a nonlocal effect. The system is found to undergo a percolation transition belonging to the mean field universality class for $r< 1/2$. On the other hand, for $r>1/2$, the system undergoes a peculiar phase transition from a non-percolating phase to a quasi-critical phase where the largest cluster size $G$ scales as $G \sim N^α$ with $α= 0.74 (1)$. In the marginal case with $r=1/2$, the model displays a percolation transition that does not belong to the mean field universality class.

cond-mat.stat-mech↗

arXiv2011

Dissolution of traffic jam via additional local interactions

We use a cellular automata approach to numerically investigate traffic flow patterns on a single lane. The free-flow phase (F), the synchronized phase (S), and the jam phase (J) are observed and the transitions among them are studied as the vehicular density $ρ$ is slowly varied. If $ρ$ is decreased from well inside the J phase, the flux $Φ$ follows the lower branch of the hysteresis loop, implying that the adiabatic decrease of $ρ$ is not an efficient way to put the system back into S or F phases. We propose a simple way to help the system to escape out of J phase, which is based on the local information of the velocities of downstream vehicles.

nlin.CG↗

arXiv2011

Antiphase synchronization of two nonidentical pendulums

We numerically study the synchronization of two nonidentical pendulum motions, pivoting on a common movable frame in the point of view of the dynamic phase transition. When the difference in the pendulum lengths is not too large, it is shown that the system settles down into the dynamic state of the antiphase synchronization with the phase difference $π$. We observe that there is a bistable region where either the antiphase synchronized state or the desynchronized state can be stabilized. We also find that there exists a hysteresis effect around the dynamic phase transition as the length difference is adiabatically changed.

cond-mat.stat-mech↗