arXiv subjects

B. Kahng

Publications and source records attributed to B. Kahng.

At least 91 records · Page 5Linked to original sources

arXiv2009

Large 1/f noise of unipolar resistance switching and its percolating nature

We investigated the 1/f noise of Pt/NiO/Pt capacitors that show unipolar resistance switching. When they were switched from the low to high resistance states, the power spectral density of the voltage fluctuation was increased by approximately five orders of magnitude. At 100 K, the relative resistance fluctuation, SR/R2, in the low resistance state displayed a power law dependence on the resistance R with exponent w = 1.6. This behavior can be explained by percolation theory; however, at higher temperatures or near the switching voltage, SR/R2 becomes enhanced further. This large 1/f noise can be therefore an important problem in the development of resistance random access memory devices.

cond-mat.mtrl-sci↗

arXiv2009

Disassortativity of random critical branching trees

Random critical branching trees (CBTs) are generated by the multiplicative branching process, where the branching number is determined stochastically, independent of the degree of their ancestor. Here we show analytically that despite this stochastic independence, there exists the degree-degree correlation (DDC) in the CBT and it is disassortative. Moreover, the skeletons of fractal networks, the maximum spanning trees formed by the edge betweenness centrality, behave similarly to the CBT in the DDC. This analytic solution and observation support the argument that the fractal scaling in complex networks originates from the disassortativity in the DDC.

cond-mat.stat-mech↗

arXiv2009

Priority queues with bursty arrivals of incoming tasks

Recently increased accessibility of large-scale digital records enables one to monitor human activities such as the interevent time distributions between two consecutive visits to a web portal by a single user, two consecutive emails sent out by a user, two consecutive library loans made by a single individual, etc. Interestingly, those distributions exhibit a universal behavior, $D(τ)\sim τ^{-δ}$, where $τ$ is the interevent time, and $δ\simeq 1$ or 3/2. The universal behaviors have been modeled via the waiting-time distribution of a task in the queue operating based on priority; the waiting time follows a power law distribution $P_{\rm w}(τ)\sim τ^{-α}$ with either $α=1$ or 3/2 depending on the detail of queuing dynamics. In these models, the number of incoming tasks in a unit time interval has been assumed to follow a Poisson-type distribution. For an email system, however, the number of emails delivered to a mail box in a unit time we measured follows a powerlaw distribution with general exponent $γ$. For this case, we obtain analytically the exponent $α$, which is not necessarily 1 or 3/2 and takes nonuniversal values depending on $γ$. We develop the generating function formalism to obtain the exponent $α$, which is distinct from the continuous time approximation used in the previous studies.

physics.soc-ph↗

arXiv2008

Segregation in the annihilation of two-species reaction-diffusion processes on fractal scale-free networks

In the reaction-diffusion process $A+B \to \varnothing$ on random scale-free (SF) networks with the degree exponent $γ$, the particle density decays with time in a power law with an exponent $α$ when initial densities of each species are the same. The exponent $α$ is $α> 1$ for $2 < γ< 3$ and $α=1$ for $γ\ge 3$. Here, we examine the reaction process on fractal SF networks, finding that $α< 1$ even for $2 < γ< 3$. This slowly decaying behavior originates from the segregation effect: Fractal SF networks contain local hubs, which are repulsive to each other. Those hubs attract particles and accelerate the reaction, and then create domains containing the same species of particles. It follows that the reaction takes place at the non-hub boundaries between those domains and thus the particle density decays slowly. Since many real SF networks are fractal, the segregation effect has to be taken into account in the reaction kinetics among heterogeneous particles.

cond-mat.dis-nn↗

arXiv2008

Jamming transition in traffic flow under the priority queuing protocol

Packet traffic in complex networks undergoes the jamming transition from free-flow to congested state as the number of packets in the system increases. Here we study such jamming transition when queues are operated by the priority queuing protocol and packets are guided by the dynamic routing protocol. We introduce a minimal model in which there are two types of packets distinguished by whether priority is assigned. Based on numerical simulations, we show that traffic is improved in the congested region under the priority queuing protocol, and it is worsened in the free-flow region. Also, we find that at the transition point, the waiting-time distribution follows a power law, and the power spectrum of traffic exhibits a crossover between two 1/f^a behaviors with exponent a ~ 1 and 1 < a < 2 in low and high frequency regime, respectively. This crossover is originated from a characteristic waiting time of packets in the queue.

cond-mat.other↗

arXiv2008

Scaling behaviors of RESET voltages and currents in unipolar resistance switching

Unipolar switching phenomena have attracted a great deal of recent attention, but the wide distributions of switching voltages still pose major obstacles for scientific advancement and practical applications. Using NiO capacitors, we investigated the distributions of the RESET voltage and current. We found that they scaled with the resistance value Ro in the low resistance state, and that the scaling exponents varied at Ro = 30 Ohm. We explain these intriguing scaling behaviors and their crossovers by analogy with percolation theory. We show that the connectivity of conducting filaments plays a crucial role in the RESET process.

cond-mat.mtrl-sci↗

arXiv2008

Strong resistance nonlinearity and third harmonic generation in the unipolar resistance switching of NiO thin films

We investigated third harmonic generation in NiO thin films, which exhibit unipolar resistance switching behavior. We found that the low resistance states of the films were strongly nonlinear, with variations in the resistance R as large as 60%. This strong nonlinear behavior was most likely caused by Joule heating of conducting filaments inside the films. By carefully controlling the applied dc bias, we obtained several low resistance states, whose values of the third harmonic coefficient B3f were proportional to R2+w (with w = 2.07). This suggested that the resistance changes of the NiO films were accompanied by connectivity changes of the conducting filaments, as observed in classical percolating systems.

cond-mat.mtrl-sci↗

arXiv2008

Modular synchronization in complex networks with a gauge Kuramoto model

We modify the Kuramoto model for synchronization on complex networks by introducing a gauge term that depends on the edge betweenness centrality (BC). The gauge term introduces additional phase difference between two vertices from 0 to $π$ as the BC on the edge between them increases from the minimum to the maximum in the network. When the network has a modular structure, the model generates the phase synchronization within each module, however, not over the entire system. Based on this feature, we can distinguish modules in complex networks, with relatively little computational time of $\mathcal{O}(NL)$, where $N$ and $L$ are the number of vertices and edges in the system, respectively. We also examine the synchronization of the modified Kuramoto model and compare it with that of the original Kuramoto model in several complex networks.

cond-mat.dis-nn↗

arXiv2008

Self-similarity in Fractal and Non-fractal Networks

We study the origin of scale invariance (SI) of the degree distribution in scale-free (SF) networks with a degree exponent $γ$ under coarse graining. A varying number of vertices belonging to a community or a box in a fractal analysis is grouped into a supernode, where the box mass $M$ follows a power-law distribution, $P_m(M)\sim M^{-η}$. The renormalized degree $k^{\prime}$ of a supernode scales with its box mass $M$ as $k^{\prime} \sim M^θ$. The two exponents $η$ and $θ$ can be nontrivial as $η\ne γ$ and $θ<1$. They act as relevant parameters in determining the self-similarity, i.e., the SI of the degree distribution, as follows: The self-similarity appears either when $γ\le η$ or under the condition $θ=(η-1)/(γ-1)$ when $γ> η$, irrespective of whether the original SF network is fractal or non-fractal. Thus, fractality and self-similarity are disparate notions in SF networks.

cond-mat.stat-mech↗

arXiv2008

Percolation Model Explaining Both Unipolar Memory and Threshold Resistance Switchings in NiO Film

We observed two types of unipolar resistance switching (RS) in NiO film: memory RS at low temperature and threshold RS at high temperature. We explain these phenomena using a bond percolation model that describes the forming and rupturing of conducting filaments. Assuming Joule heating and thermal dissipation processes in the bonds, we explain how both RS types could occur and be controlled by temperature. We show that these unipolar RS are closely related and can be explained by a simple unified percolation picture.

cond-mat.mtrl-sci↗

arXiv2008

Effects of heat dissipation on unipolar resistance switching in Pt/NiO/Pt capacitors

We fabricated Pt/NiO/Pt capacitor structures with various bottom electrode thicknesses, $t_{BE}$, and investigated their resistance switching behaviors. The capacitors with $t_{BE} \geq 50$ nm exhibited typical unipolar resistance memory switching, while those with $t_{BE} \leq 30$ nm showed threshold switching. This interesting phenomenon can be explained in terms of the temperature-dependent stability of conducting filaments. In particular, the thinner $t_{BE}$ makes dissipation of Joule heat less efficient, so the filaments will be at a higher temperature and become less stable. This study demonstrates the importance of heat dissipation in resistance random access memory.

cond-mat.mtrl-sci↗

arXiv2008

Abnormal Resistance Switching Behaviors of NiO Thin Films: Possible Occurrence of Simultaneous Formation and Rupture of Conducting Channels

We report the detailed current-voltage (I-V) characteristics of resistance switching in NiO thin films. In unipolar resistance switching, it is commonly believed that conducting filaments will rupture when NiO changes from a low resistance to a high resistance state. However, we found that this resistance switching can sometimes show abnormal behavior during voltage- and current-driven I-V measurements. We used the random circuit breaker network model to explain how abnormal switching behaviors could occur. We found that this resistance change can occur via a series of avalanche processes, where conducting filaments could be formed as well as ruptured.

cond-mat.mtrl-sci↗

arXiv2007

Surface versus bulk characterization of the electronic inhomogeneity in a VO_{2} film

We investigated the inhomogeneous electronic properties at the surface and interior of VO_{2} thin films that exhibit a strong first-order metal-insulator transition (MIT). Using the crystal structural change that accompanies a VO_{2} MIT, we used bulk-sensitive X-ray diffraction (XRD) measurements to estimate the fraction of metallic volume p^{XRD} in our VO_{2} film. The temperature dependence of the p$^{XRD}$ was very closely correlated with the dc conductivity near the MIT temperature, and fit the percolation theory predictions quite well: $σ$ $\sim$ (p - p_{c})^{t} with t = 2.0$\pm$0.1 and p_{c} = 0.16$\pm$0.01. This agreement demonstrates that in our VO$_{2}$ thin film, the MIT should occur during the percolation process. We also used surface-sensitive scanning tunneling spectroscopy (STS) to investigate the microscopic evolution of the MIT near the surface. Similar to the XRD results, STS maps revealed a systematic decrease in the metallic phase as temperature decreased. However, this rate of change was much slower than the rate observed with XRD, indicating that the electronic inhomogeneity near the surface differs greatly from that inside the film. We investigated several possible origins of this discrepancy, and postulated that the variety in the strain states near the surface plays an important role in the broad MIT observed using STS. We also explored the possible involvement of such strain effects in other correlated electron oxide systems with strong electron-lattice interactions.

cond-mat.str-el↗

arXiv2007

Spectral densities of scale-free networks

The spectral densities of the weighted Laplacian, random walk and weighted adjacency matrices associated with a random complex network are studied using the replica method. The link weights are parametrized by a weight exponent $β$. Explicit results are obtained for scale-free networks in the limit of large mean degree after the thermodynamic limit, for arbitrary degree exponent and $β$.

cond-mat.stat-mech↗

arXiv2007

Scale-free random branching tree in supercritical phase

We study the size and the lifetime distributions of scale-free random branching tree in which $k$ branches are generated from a node at each time step with probability $q_k\sim k^{-γ}$. In particular, we focus on finite-size trees in a supercritical phase, where the mean branching number $C=\sum_k k q_k$ is larger than 1. The tree-size distribution $p(s)$ exhibits a crossover behavior when $2 < γ< 3$; A characteristic tree size $s_c$ exists such that for $s \ll s_c$, $p(s)\sim s^{-γ/(γ-1)}$ and for $s \gg s_c$, $p(s)\sim s^{-3/2}\exp(-s/s_c)$, where $s_c$ scales as $\sim (C-1)^{-(γ-1)/(γ-2)}$. For $γ> 3$, it follows the conventional mean-field solution, $p(s)\sim s^{-3/2}\exp(-s/s_c)$ with $s_c\sim (C-1)^{-2}$. The lifetime distribution is also derived. It behaves as $\ell(t)\sim t^{-(γ-1)/(γ-2)}$ for $2 < γ< 3$, and $\sim t^{-2}$ for $γ> 3$ when branching step $t \ll t_c \sim (C-1)^{-1}$, and $\ell(t)\sim \exp(-t/t_c)$ for all $γ> 2$ when $t \gg t_c$. The analytic solutions are corroborated by numerical results.

cond-mat.stat-mech↗

arXiv2007

A box-covering algorithm for fractal scaling in scale-free networks

A random sequential box-covering algorithm recently introduced to measure the fractal dimension in scale-free networks is investigated. The algorithm contains Monte Carlo sequential steps of choosing the position of the center of each box, and thereby, vertices in preassigned boxes can divide subsequent boxes into more than one pieces, but divided boxes are counted once. We find that such box-split allowance in the algorithm is a crucial ingredient necessary to obtain the fractal scaling for fractal networks; however, it is inessential for regular lattice and conventional fractal objects embedded in the Euclidean space. Next the algorithm is viewed from the cluster-growing perspective that boxes are allowed to overlap and thereby, vertices can belong to more than one box. Then, the number of distinct boxes a vertex belongs to is distributed in a heterogeneous manner for SF fractal networks, while it is of Poisson-type for the conventional fractal objects.

cond-mat.stat-mech↗

arXiv2006

Internet data packet transport: from global topology to local queueing dynamics

We study structural feature and evolution of the Internet at the autonomous systems level. Extracting relevant parameters for the growth dynamics of the Internet topology, we construct a toy model for the Internet evolution, which includes the ingredients of multiplicative stochastic evolution of nodes and edges and adaptive rewiring of edges. The model reproduces successfully structural features of the Internet at a fundamental level. We also introduce a quantity called the load as the capacity of node needed for handling the communication traffic and study its time-dependent behavior at the hubs across years. The load at hub increases with network size $N$ as $\sim N^{1.8}$. Finally, we study data packet traffic in the microscopic scale. The average delay time of data packets in a queueing system is calculated, in particular, when the number of arrival channels is scale-free. We show that when the number of arriving data packets follows a power law distribution, $\sim n^{-λ}$, the queue length distribution decays as $n^{1-λ}$ and the average delay time at the hub diverges as $\sim N^{(3-λ)/(γ-1)}$ in the $N \to \infty$ limit when $2 < λ< 3$, $γ$ being the network degree exponent.

physics.soc-ph↗

arXiv2006

Synchronization transition of heterogeneously coupled oscillators on scale-free networks

We investigate the synchronization transition of the modified Kuramoto model where the oscillators form a scale-free network with degree exponent $λ$. An oscillator of degree $k_i$ is coupled to its neighboring oscillators with asymmetric and degree-dependent coupling in the form of $\couplingcoeff k_i^{η-1}$. By invoking the mean-field approach, we determine the synchronization transition point $J_c$, which is zero (finite) when $η> λ-2$ ($η< λ-2$). We find eight different synchronization transition behaviors depending on the values of $η$ and $λ$, and derive the critical exponents associated with the order parameter and the finite-size scaling in each case. The synchronization transition is also studied from the perspective of cluster formation of synchronized vertices. The cluster-size distribution and the largest cluster size as a function of the system size are derived for each case using the generating function technique. Our analytic results are confirmed by numerical simulations.

cond-mat.stat-mech↗