arXiv subjects

Beom Jun Kim

Publications and source records attributed to Beom Jun Kim.

At least 55 records · Page 3Linked to original sources

arXiv2013

Percolation properties of growing networks under an Achlioptas process

We study the percolation transition in growing networks under an Achlioptas process (AP). At each time step, a node is added in the network and, with the probability $δ$, a link is formed between two nodes chosen by an AP. We find that there occurs the percolation transition with varying $δ$ and the critical point $δ_c=0.5149(1)$ is determined from the power-law behavior of order parameter and the crossing of the fourth-order cumulant at the critical point, also confirmed by the movement of the peak positions of the second largest cluster size to the $δ_c$. Using the finite-size scaling analysis, we get $β/\barν=0.20(1)$ and $1/\barν=0.40(1)$, which implies $β\approx 1/2$ and $\barν \approx 5/2$. The Fisher exponent $τ= 2.24(1)$ for the cluster size distribution is obtained and shown to satisfy the hyperscaling relation.

cond-mat.stat-mech↗

arXiv2013

Analysis of one-dimensional Yut-Nori game: winning strategy and avalanche-size distribution

In the Korean traditional board game Yut-Nori, teams compete by moving their pieces on the two-dimensional game board, and the team whose all pieces complete a round trip on the board wins. In every round, teams throw four wooden sticks of the shape of half-cut cylinder and the number of sticks that show belly sides, i.e., the flat sides, determines the number of steps the team's piece can advance on the board. It is possible to pile up one team's pieces if their sites are identical so that pieces as a group can move together afterwards (piling). If a piece of the opponent team is at the new site of one team's piece, the piece is caught and removed from the board, and the team is given one more chance to throw sticks and proceed (catching). For a simplicity, we simulate this game on one-dimensional board with the same number of sites as the original game, and show that catching is more advantageous strategy than piling to win. We also study the avalanche-size distribution in thermodynamic limit to find that it follows an exponential form.

physics.soc-ph↗

arXiv2013

Allometric Exponent and Randomness

An allometric height-mass exponent $γ$ gives an approximative power-law relation $< M> \propto H^γ$ between the average mass $< M>$ and the height $H$, for a sample of individuals. The individuals in the present study are humans but could be any biological organism. The sampling can be for a specific age of the individuals or for an age-interval. The body-mass index (BMI) is often used for practical purposes when characterizing humans and it is based on the allometric exponent $γ=2$. It is here shown that the actual value of $γ$ is to large extent determined by the degree of correlation between mass and height within the sample studied: no correlation between mass and height means $γ=0$, whereas if there was a precise relation between mass and height such that all individuals had the same shape and density then $γ=3$. The connection is demonstrated by showing that the value of $γ$ can be obtained directly from three numbers characterizing the spreads of the relevant random Gaussian statistical distributions: the spread of the height and mass distributions together with the spread of the mass distribution for the average height. Possible implications for allometric relations in general are discussed.

physics.soc-ph↗

arXiv2013

Nonequilbrium work by charge control in a Josephson junction

We consider a single Josephson junction in the presence of time varying gate charge, and examine the nonequilibrium work done by the charge control in the framework of fluctuation theorems. We obtain the probability distribution functions of the works performed by forward protocol and by its time reversed protocol, which from the Crooks relation gives the estimation of the free energy changes ΔF =0. The reliability of ΔF estimated from the Jarzynksi equality is crucially dependent on protocol parameters, while Bennett's acceptance ratio method confirms consistently ΔF=0. The error of the Jarzynski estimator either grows or becomes saturated as the duration of the work protocol increases, which depends on the protocol rapidity determining the existence of the oscillatory motion of the phase difference across the junction. The average of the work also shows similar behaviors and its saturation value is given by the relative weight of the oscillatory trajectory with respect to running trajectories with constant acceleration. We discuss non-negativity of the work average and its relation to heat and entropy production associated with the circuit control.

cond-mat.stat-mech↗

arXiv2013

Phase transition in a coevolving network of conformist and contrarian voters

In the coevolving voter model, each voter has one of two diametrically opposite opinions, and a voter encountering a neighbor with the opposite opinion may either adopt it or rewire the connection to another randomly chosen voter sharing the same opinion. As we smoothly change the relative frequency of rewiring compared to that of adoption, there occurs a phase transition between an active phase and a frozen phase. By performing extensive Monte Carlo calculations, we show that the phase transition is characterized by critical exponents β=0.54(1) and ν =1.5(1), which differ from the existing mean-field-type prediction. We furthermore extend the model by introducing a contrarian type that tries to have neighbors with the opposite opinion, and show that the critical behavior still belongs to the same universality class irrespective of such contrarians' fraction.

physics.soc-ph↗

arXiv2012

Cluster-size heterogeneity in the two-dimensional Ising model

We numerically investigate the heterogeneity in cluster sizes in the two-dimensional Ising model and verify its scaling form recently proposed in the context of percolation problems [Phys. Rev. E 84, 010101(R) (2011)]. The scaling exponents obtained via the finite-size scaling analysis are shown to be consistent with theoretical values of the fractal dimension $d_f$ and the Fisher exponent $τ$ for the cluster distribution. We also point out that strong finite-size effects exist due to the geometric nature of the cluster-size heterogeneity.

cond-mat.stat-mech↗

arXiv2012

Double resonance in the infinite-range quantum Ising model

We study quantum resonance behavior of the infinite-range kinetic Ising model at zero temperature. Numerical integration of the time-dependent Schrödinger equation in the presence of an external magnetic field in the $z$ direction is performed at various transverse field strengths $g$. It is revealed that two resonance peaks occur when the energy gap matches the external driving frequency at two distinct values of $g$, one below and the other above the quantum phase transition. From the similar observations already made in classical systems with phase transitions, we propose that the double resonance peaks should be a generic feature of continuous transitions, for both quantum and classical many-body systems.

cond-mat.stat-mech↗

arXiv2012

Double stochastic resonance in the mean-field $q$-state clock models

A magnetic system with a phase transition at temperature $T_c$ may exhibit double resonance peaks under a periodic external magnetic field because the time scale matches the external frequency at two different temperatures, one above $T_c$ and the other below $T_c$. We study the double resonance phenomena for the mean-field $q$-state clock model based on the heat-bath-typed master equation. We find double peaks as observed in the kinetic Ising case ($q=2$) for all $q\ge 4$, but for the three-state clock model ($q=3$), the existence of double peaks is possible only above a certain external frequency since it undergoes a discontinuous phase transition.

cond-mat.stat-mech↗

arXiv2012

Dworkin's Paradox

How to distribute welfare in a society is a key issue in the subject of distributional justice, which is deeply involved with notions of fairness. Following a thought experiment by Dworkin, this work considers a society of individuals with different preferences on the welfare distribution and an official to mediate the coordination among them. Based on a simple assumption that an individual's welfare is proportional to how her preference is fulfilled by the actual distribution, we show that an egalitarian preference is a strict Nash equilibrium and can be favorable even in certain inhomogeneous situations. These suggest how communication can encourage and secure a notion of fairness.

physics.soc-ph↗

arXiv2012

Traveling Baseball Players' Problem in Korea

We study the so-called the traveling tournament problem (TTP), to find an optimal tournament schedule. Differently from the original TTP, in which the total travel distance of all the participants is the objective function to minimize, we instead seek to maximize the fairness of the round robin tournament schedule of the Korean Baseball League. The standard deviation of the travel distances of teams is defined as the energy function, and the Metropolis Monte-Carlo method combined with the simulated annealing technique is applied to find the ground state configuration. The resulting tournament schedule is found to satisfy all the constraint rules set by the Korean Baseball Organization, but with drastically increased fairness in traveling distances.

physics.soc-ph↗

arXiv2012

Fractal Profit Landscape of the Stock Market

We investigate the structure of the profit landscape obtained from the most basic, fluctuation based, trading strategy applied for the daily stock price data. The strategy is parameterized by only two variables, p and q. Stocks are sold and bought if the log return is bigger than p and less than -q, respectively. Repetition of this simple strategy for a long time gives the profit defined in the underlying two-dimensional parameter space of p and q. It is revealed that the local maxima in the profit landscape are spread in the form of a fractal structure. The fractal structure implies that successful strategies are not localized to any region of the profit landscape and are neither spaced evenly throughout the profit landscape, which makes the optimization notoriously hard and hypersensitive for partial or limited information. The concrete implication of this property is demonstrated by showing that optimization of one stock for future values or other stocks renders worse profit than a strategy that ignores fluctuations, i.e., a long-term buy-and-hold strategy.

q-fin.ST↗

arXiv2012

Critical condition of the water-retention model

We study how much water can be retained without leaking through boundaries when each unit square of a two-dimensional lattice is randomly assigned a block of unit bottom area but with different heights from zero to $n-1$. As more blocks are put into the system, there exists a phase transition beyond which the system retains a macroscopic volume of water. We locate the critical points and verify that the criticality belongs to the two-dimensional percolation universality class. If the height distribution can be approximated as continuous for large $n$, the system is always close to a critical point and the fraction of the area below the resulting water level is given by the percolation threshold. This provides a universal upper bound of areas that can be covered by water in a random landscape.

cond-mat.stat-mech↗

arXiv2012

Critical Points of Correlated Percolation in a Gravitational Link-adding Network Model

Motivated by the importance of geometric information in real systems, a new model for long-range correlated percolation in link-adding networks is proposed with the connecting probability decaying with a power-law of the distance on the two-dimensional(2D) plane. By overlapping it with Achlioptas process, it serves as a gravity model which can be tuned to facilitate or inhibit the network percolation in a generic view, cover a broad range of thresholds. Moreover, it yields a set of new scaling relations. In the present work, we develop an approach to determine critical points for them by simulating the temporal evolutions of type-I, type-II and type-III links(chosen from both inter-cluster links, an intra-cluster link compared with an inter-cluster one, and both intra-cluster ones, respectively) and corresponding average lengths. Numerical results have revealed objective competition between fractions, average lengths of three types of links, verified the balance happened at critical points. The variation of decay exponents $a$ or transmission radius $R$ always shifts the temporal pace of the evolution, while the steady average lengths and the fractions of links always keep unchanged just as the values in Achlioptas process. Strategy with maximum gravity can keep steady average length, while that with minimum one can surpass it. Without the confinement of transmission range, $\bar{l} \to \infty$ in thermodynamic limit, while $\bar{l}$ does not when with it. However, both mechanisms support critical points. In two-dimensional free space, the relevance of correlated percolation in link-adding process is verified by validation of new scaling relations with various exponent $a$, which violates the scaling law of Weinrib's.

cond-mat.dis-nn↗

arXiv2012

Neutral theory of chemical reaction networks

To what extent do the characteristic features of a chemical reaction network reflect its purpose and function? In general, one argues that correlations between specific features and specific functions are key to understanding a complex structure. However, specific features may sometimes be neutral and uncorrelated with any system-specific purpose, function or causal chain. Such neutral features are caused by chance and randomness. Here we compare two classes of chemical networks: one that has been subjected to biological evolution (the chemical reaction network of metabolism in living cells) and one that has not (the atmospheric planetary chemical reaction networks). Their degree distributions are shown to share the very same neutral system-independent features. The shape of the broad distributions is to a large extent controlled by a single parameter, the network size. From this perspective, there is little difference between atmospheric and metabolic networks; they are just different sizes of the same random assembling network. In other words, the shape of the degree distribution is a neutral characteristic feature and has no functional or evolutionary implications in itself; it is not a matter of life and death.

cond-mat.stat-mech↗

arXiv2012

Force correlations in molecular and stochastic dynamics

A molecular gas system in three dimensions is numerically studied by the energy conserving molecular dynamics (MD). The autocorrelation functions for the velocity and the force are computed and the friction coefficient is estimated. From the comparison with the stochastic dynamics (SD) of a Brownian particle, it is shown that the force correlation function in MD is different from the delta-function force correlation in SD in short time scale. However, as the measurement time scale is increased further, the ensemble equivalence between the microcanonical MD and the canonical SD is restored. We also discuss the practical implication of the result.

cond-mat.stat-mech↗

arXiv2012

Time Reversibility of Quantum Diffusion in Small-world Networks

We study the time-reversal dynamics of a tight-binding electron in the Watts-Strogatz (WS) small-world networks. The localized initial wave packet at time $t=0$ diffuses as time proceeds until the time-reversal operation, together with the momentum perturbation of the strength $η$, is made at the reversal time $T$. The time irreversibility is measured by $I \equiv |Π(t = 2T) - Π(t = 0)|$, where $Π$ is the participation ratio gauging the extendedness of the wavefunction and for convenience, $t$ is measured forward even after the time reversal . When $η= 0$, the time evolution after $T$ makes the wavefunction at $t=2T$ identical to the one at $t=0$, and we find I=0, implying a null irreversibility or a complete reversibility. On the other hand, as $η$ is increased from zero, the reversibility becomes weaker, and we observe enhancement of the irreversibility. We find that $I$ linearly increases with increasing $η$ in the weakly-perturbed region, and that the irreversibility is much stronger in the WS network than in the local regular network.

cond-mat.stat-mech↗

arXiv2011

Quantum Monte Carlo study of the transverse-field quantum Ising model on infinite-dimensional structures

In a number of classical statistical-physical models, there exists a characteristic dimensionality called the upper critical dimension above which one observes the mean-field critical behavior. Instead of constructing high-dimensional lattices, however, one can also consider infinite-dimensional structures, and the question is whether this mean-field character extends to quantum-mechanical cases as well. We therefore investigate the transverse-field quantum Ising model on the globally coupled network and the Watts-Strogatz small-world network by means of quantum Monte Carlo simulations and the finite-size scaling analysis. We confirm that both the structures exhibit critical behavior consistent with the mean-field description. In particular, we show that the existing cumulant method has a difficulty in estimating the correct dynamic critical exponent and suggest that an order parameter based on the quantum-mechanical expectation value can be a practically useful numerical observable to determine critical behavior when there is no well-defined dimensionality.

cond-mat.stat-mech↗

arXiv2011

The Ten Thousand Kims

In the Korean culture the family members are recorded in special family books. This makes it possible to follow the distribution of Korean family names far back in history. It is here shown that these name distributions are well described by a simple null model, the random group formation (RGF) model. This model makes it possible to predict how the name distributions change and these predictions are shown to be borne out. In particular, the RGF model predicts that, for married women entering a collection of family books in a certain year, the occurrence of the most common family name "Kim" should be directly proportional the total number of married women with the same proportionality constant for all the years. This prediction is also borne out to high degree. We speculate that it reflects some inherent social stability in the Korean culture. In addition, we obtain an estimate of the total population of the Korean culture down to year 500 AD, based on the RGF model and find about ten thousand Kims.

physics.soc-ph↗