arXiv subjects

D. Kim

Publications and source records attributed to D. Kim.

157 records · Page 9Linked to original sources

arXiv1999

Synchronization in a System of Globally Coupled Oscillators with Time Delay

We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis of these equations reveals that the system in general exhibits discontinuous transitions in addition to the usual continuous transition, between the incoherent state and a multitude of coherent states with different synchronization frequencies. In particular, the phase diagram is obtained on the plane of the coupling strength and the delay time, and ubiquity of multistability as well as suppression of the synchronization frequency is manifested. Numerical simulations are also performed to give consistent results.

cond-mat.stat-mech↗

arXiv1999

Empirical Phase Diagram of Congested Traffic Flow

We present an empirical phase diagram of the congested traffic flow measured on a highway section with one effective on-ramp. Through the analysis of local density-flow relations and global spatial structure of the congested region, four distinct congested traffic states are identified. These states appear at different levels of the upstream flux and the on-ramp flux, thereby generating a phase digram of the congested traffic flow. Observed traffic states are discussed in connection with recent theoretical analyses.

cond-mat.stat-mech↗

arXiv1999

Dynamic States of a Continuum Traffic Equation with On-Ramp

We study the phase diagram of the continuum traffic flow model of a highway with an on-ramp. Using an open boundary condition, traffic states and metastabilities are investigated numerically for several representative values of the upstream boundary flux $f_{up}$ and for the whole range of the on-ramp flux $f_{rmp}$. An inhomogeneous but time-independent traffic state (standing localized cluster state) is found and related to a recently measured traffic state. Due to the density gradient near the on-ramp, a novel traffic jam can occur even when the downstream density is below the critical density of the usual traffic jam formation in homogeneous highways, and its structure varies qualitatively with $f_{rmp}$. The free flow, the recurring hump (RH) state, and the traffic jam can all coexist in a certain metastable region where the free flow can undergo phase transitions either to the RH state or to the traffic jam state. We also find two nontrivial analytic solutions. These solutions correspond to the standing localized cluster state and the homogeneous congested traffic state (one form of the novel traffic jam),which are observed in numerical simulations.

cond-mat.stat-mech↗

arXiv1998

Facet Formation in the Negative Quenched Kardar-Parisi-Zhang Equation

The quenched Kardar-Parisi-Zhang (QKPZ) equation with negative non-linear term shows a first order pinning-depinning (PD) transition as the driving force $F$ is varied. We study the substrate-tilt dependence of the dynamic transition properties in 1+1 dimensions. At the PD transition, the pinned surfaces form a facet with a characteristic slope $s_c$ as long as the substrate-tilt $m$ is less than $s_c$. When $m s_c$. We explain these features from a pinning mechanism involving a localized pinning center and the self-organized facet formation.

cond-mat.stat-mech↗

arXiv1998

Origin of synchronized traffic flow on highways and its dynamic phase transitions

We study the traffic flow on a highway with ramps through numerical simulations of a hydrodynamic traffic flow model. It is found that the presence of the external vehicle flux through ramps generates a new state of recurring humps (RH). This novel dynamic state is characterized by temporal oscillations of the vehicle density and velocity which are localized near ramps, and found to be the origin of the synchronized traffic flow reported recently [PRL 79, 4030 (1997)]. We also argue that the dynamic phase transitions between the free flow and the RH state can be interpreted as a subcritical Hopf bifurcation.

cond-mat.stat-mech↗

arXiv1998

Entropic Sampling and Natural Selection in Biological Evolution

With a view to connecting random mutation on the molecular level to punctuated equilibrium behavior on the phenotype level, we propose a new model for biological evolution, which incorporates random mutation and natural selection. In this scheme the system evolves continuously into new configurations, yielding non-stationary behavior of the total fitness. Further, both the waiting time distribution of species and the avalanche size distribution display power-law behaviors with exponents close to two, which are consistent with the fossil data. These features are rather robust, indicating the key role of entropy.

cond-mat↗

arXiv1998

Genetic Polymorphism in Evolving Population

We present a model for evolving population which maintains genetic polymorphism. By introducing random mutation in the model population at a constant rate, we observe that the population does not become extinct but survives, keeping diversity in the gene pool under abrupt environmental changes. The model provides reasonable estimates for the proportions of polymorphic and heterozygous loci and for the mutation rate, as observed in nature.

cond-mat.soft↗

arXiv1997

Two-way traffic flow: exactly solvable model of traffic jam

We study completely asymmetric 2-channel exclusion processes in 1 dimension. It describes a two-way traffic flow with cars moving in opposite directions. The interchannel interaction makes cars slow down in the vicinity of approaching cars in other lane. Particularly, we consider in detail the system with a finite density of cars on one lane and a single car on the other one. When the interchannel interaction reaches a critical value, traffic jam occurs, which turns out to be of first order phase transition. We derive exact expressions for the average velocities, the current, the density profile and the $k$- point density correlation functions. We also obtain the exact probability of two cars in one lane being distance $R$ apart, provided there is a finite density of cars on the other lane, and show the two cars form a weakly bound state in the jammed phase.

cond-mat.stat-mech↗

arXiv1995

Interacting dimers on the honeycomb lattice: An exact solution of the five-vertex model

The problem of close-packed dimers on the honeycomb lattice was solved by Kasteleyn in 1963. Here we extend the solution to include interactions between neighboring dimers in two spatial lattice directions. The solution is obtained by using the method of Bethe ansatz and by converting the dimer problem into a five-vertex problem. The complete phase diagram is obtained and it is found that a new frozen phase, in which the attracting dimers prevail, arises when the interaction is attractive. For repulsive dimer interactions a new first-order line separating two frozen phases occurs. The transitions are continuous and the critical behavior in the disorder regime is found to be the same as in the case of noninteracting dimers characterized by a specific heat exponent $\a=1/2$.

cond-mat↗

arXiv1995

Renormalization group analysis of the anisotropic Kardar-Parasi-Zhang equation with spatially correlated noise

We analyze the anisotropic Kardar-Parisi-Zhang equation in general substrate dimensions $d'$ with spatially correlated noise, $\langle\tilde η({\bf{k}},ω)\rangle=0$ and $\langle\tilde η({\bf{k}},ω) \tilde η({\bf{k}}',ω')\rangle$ $=2D(k)δ^{d'}({\bf{k}}+{\bf{k}}')δ(ω+ω')$ where $D(k)=D_0+D_ρk^{-2ρ}$, using the dynamic renormalization group (RG) method. When the signs of the nonlinear terms in parallel and perpendicular directions are opposite, a novel finite stable fixed point is found for $d'< d'_c \equiv 2+2ρ$ within one-loop order. The roughening exponent $α$ and the dynamic exponent $z$ associated with the stable fixed point are determined as $α={2 \over 3}\big(ρ-{{d'-2}\over 2}\big)$, and $z=2-α$. For $d' > d'_c$, the RG transformations flow to the fixed point of the weak-coupling limit, so that the dynamic exponent becomes $z=2$.

cond-mat↗

arXiv1993

Avalanche size distribution in the Toom interface

We present numerical data of the height-height correlation function and of the avalanche size distribution for the three dimensional Toom interface. The height-height correlation function behaves samely as the interfacial fluctuation width, which diverges logarithmically with space and time for both unbiased and biased cases. The avalanche size defined by the number of changing sites caused by a single noise process, exhibits an exponentially decaying distribution, which is in contrast to power-law distributions appearing in typical self-organized critical phenomena. We also generalize the Toom model into arbitrary dimensions.

cond-mat↗

arXiv1993

Dynamics of Toom interface in three dimensions

We introduce a novel three dimensional Toom model on bcc lattice, and study its physical properties. In low-noise limit, the model leads to an effective solid-on-solid-type model, which exhibits a stationary interface via depositions and evaporations with avalanche process. We find that the model is described by the Edwards-Wilkinson equation for unbiased case and the anisotropic-Kardar-Parisi-Zhang equation in the weak-coupling limit for biased case. Thus the square of the surface width diverges logarithmically with space and time for both unbiased and biased cases.

cond-mat↗

arXiv1993

Optimal storage capacity of neural networks at finite temperatures

Gardner's analysis of the optimal storage capacity of neural networks is extended to study finite-temperature effects. The typical volume of the space of interactions is calculated for strongly-diluted networks as a function of the storage ratio $α$, temperature $T$, and the tolerance parameter $m$, from which the optimal storage capacity $α_c$ is obtained as a function of $T$ and $m$. At zero temperature it is found that $α_c = 2$ regardless of $m$ while $α_c$ in general increases with the tolerance at finite temperatures. We show how the best performance for given $α$ and $T$ is obtained, which reveals a first-order transition from high-quality performance to low-quality one at low temperatures. An approximate criterion for recalling, which is valid near $m=1$, is also discussed.

cond-mat↗