Chaos Nameplat
  • Volume/Page
  • Keyword
  • DOI
  • Citation
  • Advanced
   
 
 
 

You Tube Flickr Twitter iResearch App Facebook

BROWSE VOLUMES

Year Range: 
Search Issue | RSS Feeds RSS
Next Issue

Mar 2013

Volume 23, Issue 1, Articles (01xxxx)

Issue Cover Spotlight Figure

Chaos 23, 013101 (2013); http://dx.doi.org/10.1063/1.4772970 (6 pages)

Hien Dao, John C. Rodgers, and Thomas E. Murphy
Enlarge Image | Read More
Page 2 of 2 Pages Previous Page | Jump to Page
back to top
RSS Feeds

Harnessing quantum transport by transient chaos

Rui Yang, Liang Huang, Ying-Cheng Lai, Celso Grebogi, and Louis M. Pecora

Chaos 23, 013125 (2013); http://dx.doi.org/10.1063/1.4790863 (9 pages)

Online Publication Date: 21 February 2013

Full Text: Read Online (HTML) | Download PDF

Show Abstract
Chaos has long been recognized to be generally advantageous from the perspective of control. In particular, the infinite number of unstable periodic orbits embedded in a chaotic set and the intrinsically sensitive dependence on initial conditions imply that a chaotic system can be controlled to a desirable state by using small perturbations. Investigation of chaos control, however, was largely limited to nonlinear dynamical systems in the classical realm. In this paper, we show that chaos may be used to modulate or harness quantum mechanical systems. To be concrete, we focus on quantum transport through nanostructures, a problem of considerable interest in nanoscience, where a key feature is conductance fluctuations. We articulate and demonstrate that chaos, more specifically transient chaos, can be effective in modulating the conductance-fluctuation patterns. Experimentally, this can be achieved by applying an external gate voltage in a device of suitable geometry to generate classically inaccessible potential barriers. Adjusting the gate voltage allows the characteristics of the dynamical invariant set responsible for transient chaos to be varied in a desirable manner which, in turn, can induce continuous changes in the statistical characteristics of the quantum conductance-fluctuation pattern. To understand the physical mechanism of our scheme, we develop a theory based on analyzing the spectrum of the generalized non-Hermitian Hamiltonian that includes the effect of leads, or electronic waveguides, as self-energy terms. As the escape rate of the underlying non-attracting chaotic set is increased, the imaginary part of the complex eigenenergy becomes increasingly large so that pointer states are more difficult to form, making smoother the conductance-fluctuation pattern.
Show PACS
05.45.Mt Quantum chaos; semiclassical methods
02.10.Ab Logic and set theory
02.10.Ud Linear algebra
03.67.Lx Quantum computation architectures and implementations
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
05.45.Gg Control of chaos, applications of chaos

On the integrable elliptic cylindrical Kadomtsev-Petviashvili equation

K. R. Khusnutdinova, C. Klein, V. B. Matveev, and A. O. Smirnov

Chaos 23, 013126 (2013); http://dx.doi.org/10.1063/1.4792268 (13 pages)

Online Publication Date: 21 February 2013

Full Text: Read Online (HTML) | Download PDF

Show Abstract
There exist two versions of the Kadomtsev-Petviashvili (KP) equation, related to the Cartesian and cylindrical geometries of the waves. In this paper, we derive and study a new version, related to the elliptic cylindrical geometry. The derivation is given in the context of surface waves, but the derived equation is a universal integrable model applicable to generic weakly nonlinear weakly dispersive waves. We also show that there exist nontrivial transformations between all three versions of the KP equation associated with the physical problem formulation, and use them to obtain new classes of approximate solutions for water waves.
Show PACS
02.30.Jr Partial differential equations
02.40.-k Geometry, differential geometry, and topology

Topology identification of uncertain nonlinearly coupled complex networks with delays based on anticipatory synchronization

Yanqiu Che, Ruixue Li, Chunxiao Han, Shigang Cui, Jiang Wang, Xile Wei, and Bin Deng

Chaos 23, 013127 (2013); http://dx.doi.org/10.1063/1.4793541 (7 pages)

Online Publication Date: 21 February 2013

Full Text: Read Online (HTML) | Download PDF

Show Abstract
This paper presents an adaptive anticipatory synchronization based method for simultaneous identification of topology and parameters of uncertain nonlinearly coupled complex dynamical networks with time delays. An adaptive controller is proposed, based on Lyapunov stability theorem and Barbǎlat's Lemma, to guarantee the stability of the anticipatory synchronization manifold between drive and response networks. Meanwhile, not only the identification criteria of network topology and system parameters are obtained but also the anticipatory time is identified. Numerical simulation results illustrate the effectiveness of the proposed method.
Show PACS
89.75.Hc Networks and genealogical trees
05.45.Xt Synchronization; coupled oscillators

Effects of time delay on the stochastic resonance in small-world neuronal networks

Haitao Yu, Jiang Wang, Jiwei Du, Bin Deng, Xile Wei, and Chen Liu

Chaos 23, 013128 (2013); http://dx.doi.org/10.1063/1.4790829 (7 pages)

Online Publication Date: 26 February 2013

Full Text: Read Online (HTML) | Download PDF

Show Abstract
The effects of time delay on stochastic resonance in small-world neuronal networks are investigated. Without delay, an intermediate intensity of additive noise is able to optimize the temporal response of the neural system to the subthreshold periodic signal imposed on all neurons constituting the network. The time delay in the coupling process can either enhance or destroy stochastic resonance of neuronal activity in the small-world network. In particular, appropriately tuned delays can induce multiple stochastic resonances, which appear intermittently at integer multiples of the oscillation period of weak external forcing. It is found that the delay-induced multiple stochastic resonances are most efficient when the forcing frequency is close to the global-resonance frequency of each individual neuron. Furthermore, the impact of time delay on stochastic resonance is largely independent of the small-world topology, except for resonance peaks. Considering that information transmission delays are inevitable in intra- and inter-neuronal communication, the presented results could have important implications for the weak signal detection and information propagation in neural systems.
Show PACS
02.50.Ey Stochastic processes
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
02.40.Pc General topology

Cross-correlation detection and analysis for California's electricity market based on analogous multifractal analysis

Fang Wang, Gui-ping Liao, Jian-hui Li, Rui-biao Zou, and Wen Shi

Chaos 23, 013129 (2013); http://dx.doi.org/10.1063/1.4793355 (9 pages)

Online Publication Date: 26 February 2013

Full Text: Read Online (HTML) | Download PDF

Show Abstract
A novel method, which we called the analogous multifractal cross-correlation analysis, is proposed in this paper to study the multifractal behavior in the power-law cross-correlation between price and load in California electricity market. In addition, a statistic ρAMF−XA, which we call the analogous multifractal cross-correlation coefficient, is defined to test whether the cross-correlation between two given signals is genuine or not. Our analysis finds that both the price and load time series in California electricity market express multifractal nature. While, as indicated by the ρAMF−XA statistical test, there is a huge difference in the cross-correlation behavior between the years 1999 and 2000 in California electricity markets.
Show PACS
84.70.+p High-current and high-voltage technology: power systems; power transmission lines and cables
89.65.Gh Economics; econophysics, financial markets, business and management
02.50.-r Probability theory, stochastic processes, and statistics

Conjugate feedback induced suppression and generation of oscillations in the Chua circuit: Experiments and simulations

Tirtha Mandal, Tanu Singla, M. Rivera, and P. Parmananda

Chaos 23, 013130 (2013); http://dx.doi.org/10.1063/1.4793539 (6 pages)

Online Publication Date: 26 February 2013

Full Text: Read Online (HTML) | Download PDF

Show Abstract
We study the suppression (amplitude death) and generation of oscillations (rhythmogenesis) in the Chua circuit using a feedback term consisting of conjugate variables (conjugate feedback). When the independent Chua circuit (without feedback) is placed in the oscillatory domain, this conjugate feedback induces amplitude death in the system. On the contrary, introducing the conjugate feedback in the system exhibiting fixed point behavior results in the generation of rhythms. Furthermore, it is observed that the dynamics of the Chua circuit could be tuned efficiently by varying the strength of this feedback term. Both experimental and numerical results are presented.
Show PACS
05.45.-a Nonlinear dynamics and chaos

Temporal dynamics and impact of event interactions in cyber-social populations

Yi-Qing Zhang and Xiang Li

Chaos 23, 013131 (2013); http://dx.doi.org/10.1063/1.4793540 (7 pages)

Online Publication Date: 26 February 2013

Full Text: Read Online (HTML) | Download PDF

Show Abstract
The advance of information technologies provides powerful measures to digitize social interactions and facilitate quantitative investigations. To explore large-scale indoor interactions of a social population, we analyze 18 715 users' Wi-Fi access logs recorded in a Chinese university campus during 3 months, and define event interaction (EI) to characterize the concurrent interactions of multiple users inferred by their geographic coincidences—co-locating in the same small region at the same time. We propose three rules to construct a transmission graph, which depicts the topological and temporal features of event interactions. The vertex dynamics of transmission graph tells that the active durations of EIs fall into the truncated power-law distributions, which is independent on the number of involved individuals. The edge dynamics of transmission graph reports that the transmission durations present a truncated power-law pattern independent on the daily and weekly periodicities. Besides, in the aggregated transmission graph, low-degree vertices previously neglected in the aggregated static networks may participate in the large-degree EIs, which is verified by three data sets covering different sizes of social populations with various rendezvouses. This work highlights the temporal significance of event interactions in cyber-social populations.
Show PACS
89.65.-s Social and economic systems
89.75.Hc Networks and genealogical trees
01.75.+m Science and society
84.40.Ua Telecommunications: signal transmission and processing; communication satellites
87.23.Ge Dynamics of social systems
Author Select

The dynamics of hybrid metabolic-genetic oscillators

Ed Reznik, Tasso J. Kaper, and Daniel Segrè

Chaos 23, 013132 (2013); http://dx.doi.org/10.1063/1.4793573 (14 pages)

Online Publication Date: 1 March 2013

Full Text: Read Online (HTML) | Download PDF

Show Abstract
The synthetic construction of intracellular circuits is frequently hindered by a poor knowledge of appropriate kinetics and precise rate parameters. Here, we use generalized modeling (GM) to study the dynamical behavior of topological models of a family of hybrid metabolic-genetic circuits known as “metabolators.” Under mild assumptions on the kinetics, we use GM to analytically prove that all explicit kinetic models which are topologically analogous to one such circuit, the “core metabolator,” cannot undergo Hopf bifurcations. Then, we examine more detailed models of the metabolator. Inspired by the experimental observation of a Hopf bifurcation in a synthetically constructed circuit related to the core metabolator, we apply GM to identify the critical components of the synthetically constructed metabolator which must be reintroduced in order to recover the Hopf bifurcation. Next, we study the dynamics of a re-wired version of the core metabolator, dubbed the “reverse” metabolator, and show that it exhibits a substantially richer set of dynamical behaviors, including both local and global oscillations. Prompted by the observation of relaxation oscillations in the reverse metabolator, we study the role that a separation of genetic and metabolic time scales may play in its dynamics, and find that widely separated time scales promote stability in the circuit. Our results illustrate a generic pipeline for vetting the potential success of a circuit design, simply by studying the dynamics of the corresponding generalized model.
Show PACS
87.16.Yc Regulatory genetic and chemical networks
05.45.Xt Synchronization; coupled oscillators
87.16.-b Subcellular structure and processes

Multifractal analysis of validated wind speed time series

A. P. García-Marín, J. Estévez, F. J. Jiménez-Hornero, and J. L. Ayuso-Muñoz

Chaos 23, 013133 (2013); http://dx.doi.org/10.1063/1.4793781 (9 pages)

Online Publication Date: 1 March 2013

Full Text: Read Online (HTML) | Download PDF

Show Abstract
Multifractal properties of 30 min wind data series recorded at six locations in Cadiz (Southern Spain) have been studied in this work with the aim of obtaining detailed information for a range of time scales. Wind speed records have been validated, applying various quality control tests as a pre-requisite before their use, improving the reliability of the results due to the identification of incorrect values which have been discarded in the analysis. The scaling of the wind speed moments has been analysed and empirical moments scaling exponent functions K(q) have been obtained. Although the same critical moment (qcrit) has been obtained for all the places, some differences appear in other multifractal parameters like γmax and the value of K(0). These differences have been related to the presence of extreme events and zero data values in the data series analysed, respectively.
Show PACS
05.45.Df Fractals
05.65.+b Self-organized systems
02.50.-r Probability theory, stochastic processes, and statistics

Non-specular reflections in a macroscopic system with wave-particle duality: Spiral waves in bounded media

Jacob Langham and Dwight Barkley

Chaos 23, 013134 (2013); http://dx.doi.org/10.1063/1.4793783 (9 pages)

Online Publication Date: 1 March 2013

Full Text: Read Online (HTML) | Download PDF

Show Abstract
Spiral waves in excitable media possess both wave-like and particle-like properties. When resonantly forced (forced at the spiral rotation frequency) spiral cores travel along straight trajectories, but may reflect from medium boundaries. Here, numerical simulations are used to study reflections from two types of boundaries. The first is a no-flux boundary which waves cannot cross, while the second is a step change in the medium excitability which waves do cross. Both small-core and large-core spirals are investigated. The predominant feature in all cases is that the reflected angle varies very little with incident angle for large ranges of incident angles. Comparisons are made to the theory of Biktashev and Holden. Large-core spirals exhibit other phenomena such as binding to boundaries. The dynamics of multiple reflections is briefly considered.
Show PACS
02.60.-x Numerical approximation and analysis

Hierarchical networks, power laws, and neuronal avalanches

Eric J. Friedman and Adam S. Landsberg

Chaos 23, 013135 (2013); http://dx.doi.org/10.1063/1.4793782 (7 pages)

Online Publication Date: 5 March 2013

Full Text: Read Online (HTML) | Download PDF

Show Abstract
We show that in networks with a hierarchical architecture, critical dynamical behaviors can emerge even when the underlying dynamical processes are not critical. This finding provides explicit insight into current studies of the brain's neuronal network showing power-law avalanches in neural recordings, and provides a theoretical justification of recent numerical findings. Our analysis shows how the hierarchical organization of a network can itself lead to power-law distributions of avalanche sizes and durations, scaling laws between anomalous exponents, and universal functions—even in the absence of self-organized criticality or critical points. This hierarchy-induced phenomenon is independent of, though can potentially operate in conjunction with, standard dynamical mechanisms for generating power laws.
Show PACS
87.19.lj Neuronal network dynamics
87.85.dq Neural networks
87.18.Sn Neural networks and synaptic communication

Effect of multiple time-delay on vibrational resonance

C. Jeevarathinam, S. Rajasekar, and M. A. F. Sanjuán

Chaos 23, 013136 (2013); http://dx.doi.org/10.1063/1.4793542 (11 pages)

Online Publication Date: 6 March 2013

Full Text: Read Online (HTML) | Download PDF

Show Abstract
We report our investigation on the effect of multiple time-delay on vibrational resonance in a single Duffing oscillator and in a system of n Duffing oscillators coupled unidirectionally and driven by both a low- and a high-frequency periodic force. For the single oscillator, we obtain analytical expressions for the response amplitude Q and the amplitude g of the high-frequency force at which resonance occurs. The regions in parameter space of enhanced Q at resonance, as compared to the case in absence of time-delay, show a bands-like structure. For the two-coupled oscillators, we explain all the features of variation of Q with the control parameter g. For the system of n-coupled oscillators with a single time-delay coupling, the response amplitudes of the oscillators are shown to be independent of the time-delay. In the case of a multi time-delayed coupling, undamped signal propagation takes place for coupling strength (δ) above a certain critical value (denoted as δu). Moreover, the response amplitude approaches a limiting value QL with the oscillator number i. We obtain analytical expressions for both δu and QL.
Show PACS
05.45.Xt Synchronization; coupled oscillators

Individuality of breathing patterns in patients under noninvasive mechanical ventilation evidenced by chaotic global models

Christophe Letellier, Giovani G. Rodrigues, Jean-François Muir, and Luis A. Aguirre

Chaos 23, 013137 (2013); http://dx.doi.org/10.1063/1.4794435 (13 pages)

Online Publication Date: 8 March 2013

Full Text: Read Online (HTML) | Download PDF

Show Abstract
Autonomous global models based on radial basis functions were obtained from data measured from patients under noninvasive mechanical ventilation. Some of these models, which are discussed in the paper, turn out to have chaotic or quasi-periodic solutions, thus providing a first piece of evidence that the underlying dynamics of the data used to estimate the global models are likely to be chaotic or, at least, have a chaotic component. It is explicitly shown that one of such global models produces attractors characterized by a Horseshoe map, two models produce toroidal chaos, and one model produces a quasi-periodic regime. These topologically inequivalent attractors evidence the individuality of breathing profiles observed in patient under noninvasive ventilation.
Show PACS
87.19.Wx Pneumodyamics, respiration
87.85.-d Biomedical engineering
05.45.-a Nonlinear dynamics and chaos
47.52.+j Chaos in fluid dynamics
47.63.Ec Pulmonary fluid mechanics

Short desynchronization episodes prevail in synchronous dynamics of human brain rhythms

Sungwoo Ahn and Leonid L. Rubchinsky

Chaos 23, 013138 (2013); http://dx.doi.org/10.1063/1.4794793 (8 pages)

Online Publication Date: 8 March 2013

Full Text: Read Online (HTML) | Download PDF

Show Abstract
Neural synchronization is believed to be critical for many brain functions. It frequently exhibits temporal variability, but it is not known if this variability has a specific temporal patterning. This study explores these synchronization/desynchronization patterns. We employ recently developed techniques to analyze the fine temporal structure of phase-locking to study the temporal patterning of synchrony of the human brain rhythms. We study neural oscillations recorded by electroencephalograms in α and β frequency bands in healthy human subjects at rest and during the execution of a task. While the phase-locking strength depends on many factors, dynamics of synchrony has a very specific temporal pattern: synchronous states are interrupted by frequent, but short desynchronization episodes. The probability for a desynchronization episode to occur decreased with its duration. The transition matrix between synchronized and desynchronized states has eigenvalues close to 0 and 1 where eigenvalue 1 has multiplicity 1, and therefore if the stationary distribution between these states is perturbed, the system converges back to the stationary distribution very fast. The qualitative similarity of this patterning across different subjects, brain states and electrode locations suggests that this may be a general type of dynamics for the brain. Earlier studies indicate that not all oscillatory networks have this kind of patterning of synchronization/desynchronization dynamics. Thus, the observed prevalence of short (but potentially frequent) desynchronization events (length of one cycle of oscillations) may have important functional implications for the brain. Numerous short desynchronizations (as opposed to infrequent, but long desynchronizations) may allow for a quick and efficient formation and break-up of functionally significant neuronal assemblies.
Show PACS
87.19.lm Synchronization in the nervous system
87.19.lp Pattern formation: activity and anatomic
87.19.le EEG and MEG

Network-based stochastic competitive learning approach to disambiguation in collaborative networks

Thiago Christiano Silva and Diego Raphael Amancio

Chaos 23, 013139 (2013); http://dx.doi.org/10.1063/1.4794795 (9 pages)

Online Publication Date: 8 March 2013

Full Text: Read Online (HTML) | Download PDF

Show Abstract
Many patterns have been uncovered in complex systems through the application of concepts and methodologies of complex networks. Unfortunately, the validity and accuracy of the unveiled patterns are strongly dependent on the amount of unavoidable noise pervading the data, such as the presence of homonymous individuals in social networks. In the current paper, we investigate the problem of name disambiguation in collaborative networks, a task that plays a fundamental role on a myriad of scientific contexts. In special, we use an unsupervised technique which relies on a particle competition mechanism in a networked environment to detect the clusters. It has been shown that, in this kind of environment, the learning process can be improved because the network representation of data can capture topological features of the input data set. Specifically, in the proposed disambiguating model, a set of particles is randomly spawned into the nodes constituting the network. As time progresses, the particles employ a movement strategy composed of a probabilistic convex mixture of random and preferential walking policies. In the former, the walking rule exclusively depends on the topology of the network and is responsible for the exploratory behavior of the particles. In the latter, the walking rule depends both on the topology and the domination levels that the particles impose on the neighboring nodes. This type of behavior compels the particles to perform a defensive strategy, because it will force them to revisit nodes that are already dominated by them, rather than exploring rival territories. Computer simulations conducted on the networks extracted from the arXiv repository of preprint papers and also from other databases reveal the effectiveness of the model, which turned out to be more accurate than traditional clustering methods.
Show PACS
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
05.90.+m Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems (restricted to new topics in section 05)
07.05.Mh Neural networks, fuzzy logic, artificial intelligence
89.20.Ff Computer science and technology
02.10.Ox Combinatorics; graph theory
02.40.Pc General topology
02.50.-r Probability theory, stochastic processes, and statistics
02.50.Ey Stochastic processes

Compound synchronization of four memristor chaotic oscillator systems and secure communication

Junwei Sun, Yi Shen, Quan Yin, and Chengjie Xu

Chaos 23, 013140 (2013); http://dx.doi.org/10.1063/1.4794794 (10 pages)

Online Publication Date: 11 March 2013

Full Text: Read Online (HTML) | Download PDF

Show Abstract
In this paper, a novel kind of compound synchronization among four chaotic systems is investigated, where the drive systems have been conceptually divided into two categories: scaling drive systems and base drive systems. Firstly, a sufficient condition is obtained to ensure compound synchronization among four memristor chaotic oscillator systems based on the adaptive technique. Secondly, a secure communication scheme via adaptive compound synchronization of four memristor chaotic oscillator systems is presented. The corresponding theoretical proofs and numerical simulations are given to demonstrate the validity and feasibility of the proposed control technique. The unpredictability of scaling drive systems can additionally enhance the security of communication. The transmitted signals can be split into several parts loaded in the drive systems to improve the reliability of communication.
Show PACS
05.45.Vx Communication using chaos
05.45.Xt Synchronization; coupled oscillators
02.60.-x Numerical approximation and analysis

Coupling and noise induced spiking-bursting transition in a parabolic bursting model

Lin Ji, Jia Zhang, Xiufeng Lang, and Xiuhui Zhang

Chaos 23, 013141 (2013); http://dx.doi.org/10.1063/1.4795281 (7 pages)

Online Publication Date: 13 March 2013

Full Text: Read Online (HTML) | Download PDF

Show Abstract
The transition from tonic spiking to bursting is an important dynamic process that carry physiologically relevant information. In this work, coupling and noise induced spiking-bursting transition is investigated in a parabolic bursting model with specific discussion on their cooperation effects. Fast/slow analysis shows that weak coupling may help to induce the bursting by changing the geometric property of the fast subsystem so that the original unstable periodical solution are stabilized. It turned out that noise can play the similar stabilization role and induce bursting at appropriate moderate intensity. However, their cooperation may either strengthen or weaken the overall effect depending on the choice of noise level.
Show PACS
02.30.-f Function theory, analysis

Robust detection of dynamic community structure in networks

Danielle S. Bassett, Mason A. Porter, Nicholas F. Wymbs, Scott T. Grafton, Jean M. Carlson, and Peter J. Mucha

Chaos 23, 013142 (2013); http://dx.doi.org/10.1063/1.4790830 (16 pages)

Online Publication Date: 18 March 2013

Full Text: Read Online (HTML) | Download PDF

Show Abstract
We describe techniques for the robust detection of community structure in some classes of time-dependent networks. Specifically, we consider the use of statistical null models for facilitating the principled identification of structural modules in semi-decomposable systems. Null models play an important role both in the optimization of quality functions such as modularity and in the subsequent assessment of the statistical validity of identified community structure. We examine the sensitivity of such methods to model parameters and show how comparisons to null models can help identify system scales. By considering a large number of optimizations, we quantify the variance of network diagnostics over optimizations (“optimization variance”) and over randomizations of network structure (“randomization variance”). Because the modularity quality function typically has a large number of nearly degenerate local optima for networks constructed using real data, we develop a method to construct representative partitions that uses a null model to correct for statistical noise in sets of partitions. To illustrate our results, we employ ensembles of time-dependent networks extracted from both nonlinear oscillators and empirical neuroscience data.
Show PACS
89.75.Hc Networks and genealogical trees
02.70.Rr General statistical methods
05.10.-a Computational methods in statistical physics and nonlinear dynamics
05.45.Tp Time series analysis

Soliton dynamics in media with space stimulated Raman scattering and synchronic spatial variation of dispersion and self-phase modulation

N. V. Aseeva, E. M. Gromov, and V. V. Tyutin

Chaos 23, 013143 (2013); http://dx.doi.org/10.1063/1.4794433 (6 pages)

Online Publication Date: 18 March 2013

Full Text: Read Online (HTML) | Download PDF

Show Abstract
Solitons dynamics in the frame of the extended nonlinear Schrödinger equation taking into account space stimulated Raman scattering (SSRS), synchronic spatial variation of inhomogeneous second-order dispersion (SOD), and self-phase modulation (SPM) is considered both analytically and numerically. Compensation of soliton Raman self–wave number down shift by synchronically increasing SOD and SPM is shown. Analytical soliton solution as a result of the equilibrium of SSRS and increasing both SOD and SPM is found. Regime of the dynamical equilibrium of SSRS and inhomogeneous media with periodical variation of soliton's parameters is found. Analytical and numerical results are in a good agreement.
Show PACS
05.45.Yv Solitons
02.30.Hq Ordinary differential equations

Tendency to occupy a statistically dominant spatial state of the flow as a driving force for turbulent transition

Sergei F. Chekmarev

Chaos 23, 013144 (2013); http://dx.doi.org/10.1063/1.4795279 (8 pages)

Online Publication Date: 18 March 2013

Full Text: Read Online (HTML) | Download PDF

Show Abstract
The transition from laminar to turbulent fluid motion occurring at large Reynolds numbers is generally associated with the instability of the laminar flow. On the other hand, since the turbulent flow characteristically appears in the form of spatially localized structures (e.g., eddies) filling the flow field, a tendency to occupy such a structured state of the flow cannot be ruled out as a driving force for turbulent transition. To examine this possibility, we propose a simple analytical model that treats the flow as a collection of localized spatial structures, each of which consists of elementary cells in which the behavior of the particles (atoms or molecules) is uncorrelated. This allows us to introduce the Reynolds number, associating it with the ratio between the total phase volume for the system and that for the elementary cell. Using the principle of maximum entropy to calculate the most probable size distribution of the localized structures, we show that as the Reynolds number increases, the elementary cells group into the localized structures, which successfully explains turbulent transition and some other general properties of turbulent flows. An important feature of the present model is that a bridge between the spatial-statistical description of the flow and hydrodynamic equations is established. We show that the basic assumptions underlying the model, i.e., that the particles are indistinguishable and elementary volumes of phase space exist in which the state of the particles is uncertain, are involved in the derivation of the Navier-Stokes equation. Taking into account that the model captures essential features of turbulent flows, this suggests that the driving force for the turbulent transition is basically the same as in the present model, i.e., the tendency of the system to occupy a statistically dominant state plays a key role. The instability of the flow at high Reynolds numbers can then be a mechanism to initiate structural rearrangement of the flow to find this state.
Show PACS
47.27.Cn Transition to turbulence
47.27.eb Statistical theories and models
47.27.Ak Fundamentals

Integrated computation of finite-time Lyapunov exponent fields during direct numerical simulation of unsteady flows

Justin Finn and Sourabh V. Apte

Chaos 23, 013145 (2013); http://dx.doi.org/10.1063/1.4795749 (14 pages)

Online Publication Date: 21 March 2013

Full Text: Read Online (HTML) | Download PDF

Show Abstract
The computation of Lagrangian coherent structures typically involves post-processing of experimentally or numerically obtained fluid velocity fields to obtain the largest finite-time Lyapunov exponent (FTLE) field. However, this procedure can be tedious for large-scale complex flows of general interest. In this work, an alternative approach involving computation of the FTLE on-the-fly during direct numerical simulation of the full three dimensional Navier-Stokes equations is developed. The implementation relies on Lagrangian particle tracking to compose forward time flow maps, and an Eulerian treatment of the backward time flow map [S. Leung, J. Comput. Phys. 230, 3500–3524 (2011)] coupled with a semi-Lagrangian advection scheme. The flow maps are accurately constructed from a sequence of smaller sub-steps stored on disk [S. Brunton and C. Rowley, Chaos 20, 017503 (2010)], resulting in low CPU and memory requirements to compute evolving FTLE fields. Several examples are presented to demonstrate the capability and parallel scalability of the approach for a variety of two and three dimensional flows.
Show PACS
47.15.Fe Stability of laminar flows
47.10.ad Navier-Stokes equations

Spike phase synchronization in delayed-coupled neural networks: Uniform vs. non-uniform transmission delay

Mahdi Jalili

Chaos 23, 013146 (2013); http://dx.doi.org/10.1063/1.4794436 (6 pages)

Online Publication Date: 25 March 2013

Full Text: Read Online (HTML) | Download PDF

Show Abstract
In this paper, we investigated phase synchronization in delayed dynamical networks. Non-identical spiking Hindmarsh-Rose neurons were considered as individual dynamical systems and coupled through a number of network structures such as scale-free, Erdős–Rényi, and modular. The individual neurons were coupled through excitatory chemical synapses with uniform or distributed time delays. The profile of spike phase synchrony was different when the delay was uniform across the edges as compared to the case when it was distributed, i.e., different delays for the edges. When an identical transmission delay was considered, a quasi-periodic pattern was observed in the spike phase synchrony. There were specific values of delay where the phase synchronization reached to its peaks. The behavior of the phase synchronization in the networks with non-uniform delays was different with the former case, where the phase synchrony decreased as distributed delays introduced to the networks.
Show PACS
87.18.Sn Neural networks and synaptic communication
87.19.L- Neuroscience

Dust-acoustic Gardner solitons and double layers in dusty plasmas with nonthermally distributed ions of two distinct temperatures

I. Tasnim, M. M. Masud, M. Asaduzzaman, and A. A. Mamun

Chaos 23, 013147 (2013); http://dx.doi.org/10.1063/1.4794796 (7 pages)

Online Publication Date: 28 March 2013

Full Text: Read Online (HTML) | Download PDF

Show Abstract
A rigorous theoretical investigation has been performed on dust-acoustic (DA) solitary structures in an unmagnetized dusty plasma, consisting of negatively charged mobile dust grains, Boltzmann distributed electrons, and nonthermally distributed ions of two distinct temperatures. The Korteweg-de Vries (K-dV), modified K-dV (mK-dV) and Gardner equations, and their solitary waves (SWs) and double layer (DL) (in case of Gardner equation) solutions are derived by using the reductive perturbation technique. The basic features of the DA Gardner solitons (GSs) and DLs are studied analytically as well as numerically. It has been observed that the GSs significantly differ from K-dV and mK-dV solitons, and only positive potential DLs exist in the system. It is also studied that two-temperature nonthermal ions significantly modify the nature and basic properties of the DA SWs. The present investigation can be very effective for understanding and studying the nonlinear characteristics of the DA waves in laboratory and space dusty plasmas.
Show PACS
52.27.Lw Dusty or complex plasmas; plasma crystals
52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
52.35.Sb Solitons; BGK modes
52.40.Kh Plasma sheaths
52.25.Kn Thermodynamics of plasmas
Page 2 of 2 Pages Previous Page | Jump to Page
Close

Google Calendar

ADVERTISEMENT

Go to AIP Home   © AIP Publishing LLC
close