arXiv subjects

Beom Jun Kim

Publications and source records attributed to Beom Jun Kim.

At least 37 records · Page 2Linked to original sources

arXiv2017

Free energy of a chemotactic model with nonlinear diffusion

The Patlak-Keller-Segel equation is a canonical model of chemotaxis to describe self-organized aggregation of organisms interacting with chemical signals. We investigate a variant of this model, assuming that the organisms exert effective pressure proportional to the number density. From the resulting set of partial differential equations, we derive a Lyapunov functional that can also be regarded as the free energy of this model, and minimize it with a Monte Carlo method to detect the condition for self-organized aggregation. Focusing on radially symmetric solutions on a two-dimensional disc, we find that the chemical interaction competes with diffusion so that aggregation occurs when the relative interaction strength exceeds a certain threshold. Based on the analysis of the free-energy landscape, we argue that the transition from a homogeneous state to aggregation is abrupt yet continuous.

cond-mat.stat-mech↗

arXiv2017

Spatial uniformity in power-grid system

Robust synchronization is indispensable for stable operation of a power grid. Recently, it has been reported that a large number of decentralized generators, rather than a small number of large power plants, provide enhanced synchronization together with greater robustness against structural failures. In this paper, we systematically control the spatial uniformity of the geographical distribution of generators, and conclude that the more uniformly generators are distributed, the more enhanced synchronization occurs. In the presence of temporal failures of power sources, we observe that spatial uniformity helps the power grid to recover stationarity in a shorter time. We also discuss practical implications of our results in designing the structure of a power-grid network.

physics.soc-ph↗

arXiv2017

Climate change alters diffusion of forest pest: A model study

Population dynamics with spatial information is applied to understand the spread of pests. We introduce a model describing how pests spread in discrete space. The number of pest descendants at each site is controlled by local information such as temperature, precipitation, and the density of pine trees. Our simulation leads to a pest spreading pattern comparable to the real data for pine needle gall midge in the past. We also simulate the model in two different climate conditions based on two different representative concentration pathways scenarios for the future. We observe that after an initial stage of a slow spread of pests, a sudden change in the spreading speed occurs, which is soon followed by a large-scale outbreak. We found that a future climate change causes the outbreak point to occur earlier and that the detailed spatio-temporal pattern of the spread depends on the source position from which the initial pest infection starts.

q-bio.PE↗

arXiv2015

Evolution of popularity in given names

An individual's identity in a human society is specified by his or her name. Differently from family names, usually inherited from fathers, a given name for a child is often chosen at the parents' disposal. However, their decision cannot be made in a vacuum but affected by social conventions and trends. Furthermore, such social pressure changes in time, as new names gain popularity while some other names are gradually forgotten. In this paper, we investigate how popularity of given names has evolved over the last century by using datasets collected in Korea, the province of Quebec in Canada, and the United States. In each of these countries, the average popularity of given names exhibits typical patterns of rise and fall with a time scale of about one generation. We also observe that notable changes of diversity in given names signal major social changes.

physics.soc-ph↗

arXiv2015

Finite-Time-Finite-Size Scaling of the Kuramoto Oscillators

Phase transition in its strict sense can only be observed in an infinite system, for which equilibration takes an infinitely long time at criticality. In numerical simulations, we are often limited both by the finiteness of the system size and by the finiteness of the observation time scale. We propose that one can overcome this barrier by measuring the nonequilibrium temporal relaxation for finite systems and by applying the finite-time-finite-size scaling (FTFSS) which systematically uses two scaling variables, one temporal and the other spatial. The FTFSS method yields a smooth scaling surface, and the conventional finite-size scaling curves can be viewed as proper cross sections of the surface. The validity of our FTFSS method is tested for the synchronization transition of Kuramoto models in the globally-coupled structure and in the small-world network structure. Our FTFSS method is also applied to the Monte-Carlo dynamics of the globally-coupled q-state clock model.

cond-mat.stat-mech↗

arXiv2015

Winding number excitation detects phase transition in one-dimensional XY model with variable interaction range

We numerically study the critical behavior of the one-dimensional XY model of the size N with variable interaction range L. As expected, the standard local order parameter of the magnetization is shown to well detect the mean-field type transition which occurs at any nonzero value of L/N. The system is particularly interesting since the underlying one-dimensional structure allows us to study the topological excitation of the winding number across the whole system even though the system shares the mean-field transition with the globally-coupled system. We propose a novel nonlocal order parameter based on the width of the winding number distribution which exhibits a clear signature of the transition nature of the system.

cond-mat.stat-mech↗

arXiv2015

Anomalous response in the vicinity of spontaneous symmetry breaking

We propose a mechanism to induce negative AC permittivity in the vicinity of a ferroelectric phase transition involved with spontaneous symmetry breaking. This mechanism makes use of responses at low frequency, yielding a high gain and a large phase delay, when the system jumps over the free-energy barrier with the aid of external fields. We illustrate the mechanism by analytically studying spin models with the Glauber-typed dynamics under periodic perturbations. Then, we show that the scenario is supported by numerical simulations of mean-field as well as two-dimensional spin systems.

cond-mat.stat-mech↗

arXiv2015

Theory of fads: Traveling-wave solution of evolutionary dynamics in a one-dimensional trait space

We consider an infinite-sized population where an infinite number of traits compete simultaneously. The replicator equation with a diffusive term describes time evolution of the probability distribution over the traits due to selection and mutation on a mean-field level. We argue that this dynamics can be expressed as a variant of the Fisher equation with high-order correction terms. The equation has a traveling-wave solution, and the phase-space method shows how the wave shape depends on the correction. We compare this solution with empirical time-series data of given names in Quebec, treating it as a descriptive model for the observed patterns. Our model explains the reason that many names exhibit a similar pattern of the rise and fall as time goes by. At the same time, we have found that their dissimilarities are also statistically significant.

cond-mat.stat-mech↗

arXiv2014

Structural Properties of Networks Grown via an Achlioptas Process

After the Achlioptas process (AP), which yields the so-called explosive percolation, was introduced, the number of papers on percolation phenomena has been literally exploding. Most of the existing studies, however, have focused only on the nature of phase transitions, not paying proper attention to the structural properties of the resulting networks, which compose the main theme of the present paper. We compare the resulting network structure of the AP with random networks and find, through observations of the distributions of the shortest-path length and the betweenness centrality in the giant cluster, that the AP makes the network less clustered and more fragile. Such structural characteristics are more directly seen by using snapshots of the network structures and are explained by the fact that the AP suppresses the formation of large clusters more strongly than the random process does. These structural differences between the two processes are shown to be less noticeable in growing networks than in static ones.

cond-mat.dis-nn↗

arXiv2014

Matchmaker, Matchmaker, Make Me a Match: Migration of Populations via Marriages in the Past

The study of human mobility is both of fundamental importance and of great potential value. For example, it can be leveraged to facilitate efficient city planning and improve prevention strategies when faced with epidemics. The newfound wealth of rich sources of data---including banknote flows, mobile phone records, and transportation data---has led to an explosion of attempts to characterize modern human mobility. Unfortunately, the dearth of comparable historical data makes it much more difficult to study human mobility patterns from the past. In this paper, we present an analysis of long-term human migration, which is important for processes such as urbanization and the spread of ideas. We demonstrate that the data record from Korean family books (called "jokbo") can be used to estimate migration patterns via marriages from the past 750 years. We apply two generative models of long-term human mobility to quantify the relevance of geographical information to human marriage records in the data, and we find that the wide variety in the geographical distributions of the clans poses interesting challenges for the direct application of these models. Using the different geographical distributions of clans, we quantify the "ergodicity" of clans in terms of how widely and uniformly they have spread across Korea, and we compare these results to those obtained using surname data from the Czech Republic. To examine population flow in more detail, we also construct and examine a population-flow network between regions. Based on the correlation between ergodicity and migration in Korea, we identify two different types of migration patterns: diffusive and convective. We expect the analysis of diffusive versus convective effects in population flows to be widely applicable to the study of mobility and migration patterns across different cultures.

physics.soc-ph↗

arXiv2014

Zero-one-only process: a correlated random walk with a stochastic ratchet

The investigation of random walks is central to a variety of stochastic processes in physics, chemistry, and biology. To describe a transport phenomenon, we study a variant of the one-dimensional persistent random walk, which we call a zero-one-only process. It makes a step in the same direction as the previous step with probability $p$, and stops to change the direction with $1-p$. By using the generating-function method, we calculate its characteristic quantities such as the statistical moments and probability of the first return.

physics.data-an↗

arXiv2014

Stochastic resonance in the two-dimensional q-state clock models

We numerically study stochastic resonance in the two-dimensional q-state clock models from q = 2 to 7 under a weak oscillating magnetic field. As in the mean-field case, we observe double resonance peaks, but the detailed response strongly depends on the direction of the field modulation for q >= 5 where the quasiliquid phase emerges. We explain this behavior in terms of free-energy landscapes on the two-dimensional magnetization plane.

cond-mat.stat-mech↗

arXiv2014

International Transmission of Shocks and Fragility of a Bank Network

The weighted and directed network of countries based on the number of overseas banks is analyzed in terms of its fragility to the banking crisis of one country. We use two different models to describe transmission of shocks, one local and the other global. Depending on the original source of the crisis, the overall size of crisis impacts is found to differ country by country. For the two-step local spreading model, it is revealed that the scale of the first impact is determined by the out-strength, the total number of overseas branches of the country at the origin of the crisis, while the second impact becomes more serious if the in-strength at the origin is increased. For the global spreading model, some countries named "triggers" are found to play important roles in shock transmission, and the importance of the feed-forward-loop mechanism is pointed out. We also discuss practical policy implications of the present work.

physics.soc-ph↗

arXiv2014

Surname statistics - Crossing the boundary between disciplines

Regarding "Surname distribution in population genetics and in statistical physics" by Rossi, we add comments on the following two points: One is a difference in his renormalization-group formulation from the traditional one in statistical physics despite apparent similarity. The other is the potential importance of the entropy maximization principle under constraints governing the evolution of surname statistics.

physics.soc-ph↗

arXiv2014

Universal statistics of the knockout tournament

We study statistics of the knockout tournament, where only the winner of a fixture progresses to the next. We assign a real number called competitiveness to each contestant and find that the resulting distribution of prize money follows a power law with an exponent close to unity if the competitiveness is a stable quantity and a decisive factor to win a match. Otherwise, the distribution is found narrow. The existing observation of power law distributions in various kinds of real sports tournaments therefore suggests that the rules of those games are constructed in such a way that it is possible to understand the games in terms of the contestants' inherent characteristics of competitiveness.

physics.soc-ph↗

arXiv2013

Fractality of profit landscapes and validation of time series models for stock prices

We apply a simple trading strategy for various time series of real and artificial stock prices to understand the origin of fractality observed in the resulting profit landscapes. The strategy contains only two parameters $p$ and $q$, and the sell (buy) decision is made when the log return is larger (smaller) than $p$ ($-q$). We discretize the unit square $(p, q) \in [0, 1] \times [0, 1]$ into the $N \times N$ square grid and the profit $Π(p, q)$ is calculated at the center of each cell. We confirm the previous finding that local maxima in profit landscapes are scattered in a fractal-like fashion: The number M of local maxima follows the power-law form $M \sim N^{a}$, but the scaling exponent $a$ is found to differ for different time series. From comparisons of real and artificial stock prices, we find that the fat-tailed return distribution is closely related to the exponent $a \approx 1.6$ observed for real stock markets. We suggest that the fractality of profit landscape characterized by $a \approx 1.6$ can be a useful measure to validate time series model for stock prices.

q-fin.ST↗

arXiv2013

Residual discrete symmetry of the five-state clock model

It is well-known that the $q$-state clock model can exhibit a Kosterlitz-Thouless (KT) transition if $q$ is equal to or greater than a certain threshold, which has been believed to be five. However, recent numerical studies indicate that helicity modulus does not vanish in the high-temperature phase of the five-state clock model as predicted by the KT scenario. By performing Monte Carlo calculations under the fluctuating twist boundary condition, we show that it is because the five-state clock model does not have the fully continuous U(1) symmetry even in the high-temperature phase while the six-state clock model does. We suggest that the upper transition of the five-state clock model is actually a weaker cousin of the KT transition so that it is $q \ge 6$ that exhibits the genuine KT behavior.

cond-mat.stat-mech↗

arXiv2013

Thermodynamic arrow of time of quantum projective measurements

We investigate a thermodynamic arrow associated with quantum projective measurements in terms of the Jensen-Shannon divergence between the probability distribution of energy change caused by the measurements and its time reversal counterpart. Two physical quantities appear to govern the asymptotic values of the time asymmetry. For an initial equilibrium ensemble prepared at a high temperature, the energy fluctuations determine the convergence of the time asymmetry approaching zero. At low temperatures, finite survival probability of the ground state limits the time asymmetry to be less than $\ln 2$. We illustrate our results for a concrete system and discuss the fixed point of the time asymmetry in the limit of infinitely repeated projections.

cond-mat.stat-mech↗