Spatial price dynamics: From complex network perspective

The spatial price problem means that if the supply price plus the transportation cost is less than the demand price, there exists a trade. Thus, after an amount of exchange, the demand price will decrease. This process is continuous until an equilibrium state is obtained. However, how the trade network structure affects this process has received little attention. In this paper, we give a evolving model to describe the levels of spatial price on different complex network structures. The simulation results show that the network with shorter path length is sensitive to the variation of prices.     

Specific external forcing of spatiotemporal dynamics in reaction-diffusion systems

Self-organization behavior and in particular pattern forming spatiotemporal dynamics play an important role in far from equilibrium chemical and biochemical systems. Specific external forcing and control of self-organizing processes might be of great benefit in various applications ranging from technical systems to modern biomedical research. We demonstrate that in a cellular chemotaxis system modeled by one-dimensional reaction-diffusion equations particular forms of spatiotemporal dynamics can be induced and stabilized by controlling spatially distributed influx patterns of a chemical species as a function of time. In our model study we show that a propagating wave with certain shape and velocity and static symmetrical and asymmetrical patterns can be forced and manipulated by numerically computing open-loop optimal influx controls.     

Spatial resonances and superposition patterns in a reaction-diffusion model with interacting Turing modes

Spatial resonances leading to superlattice hexagonal patterns, known as "black-eyes," and superposition patterns combining stripes and/or spots are studied in a reaction-diffusion model of two interacting Turing modes with different wavelengths. A three-phase oscillatory interlacing hexagonal lattice pattern is also found, and its appearance is attributed to resonance between a Turing mode and its subharmonic.     

Karhunen-Loeve local characterization of spatiotemporal chaos in a reaction-diffusion system

By computing the Karhunen-Loeve decomposition (KLD) correlation length xi(KLD) of a reaction-diffusion system in the extensive chaos regime, we show that it is a sensitive measure of spatial dynamical inhomogeneities. It reveals substantial spatial nonuniformity of the dynamics at the boundaries and can also detect slow spatial variations in system parameters. The intensive length xi(KLD) can be easily computed from small local subsystems and is found to have a similar parametric dependence as the two-point correlation length computed over the full system size.     

Pattern formation in the thiourea-iodate-sulfite system: Spatial bistability, waves, and stationary patterns

We present a detailed study of the reaction-diffusion patterns observed in the thiourea-iodate-sulfite (TuIS) reaction, operated in open one-side-fed reactors. Besides spatial bistability and spatio-temporal oscillatory dynamics, this proton autoactivated reaction shows stationary patterns, as a result of two back-to-back Turing bifurcations, in the presence of a low-mobility proton binding agent (sodium polyacrylate). This is the third aqueous solution system to produce stationary patterns and the second to do this through a Turing bifurcation. The stationary pattern forming capacities of the reaction are explored through a systematic design method, which is applicable to other bistable and oscillatory reactions. The spatio-temporal dynamics of this reaction is compared with that of the previous ferrocyanide-iodate-sulfite mixed Landolt system.     

Control of spatiotemporal chaos: A study with an autocatalytic reaction-diffusion system

The characterization of chaotic spatiotemporal dynamics has been studied for a representative nonlinear autocatalytic reaction mechanism coupled with diffusion. This has been carried out by an analysis of the Lyapunov spectrum in spatiallylocalised regions. The linear scaling relationships observed in the invariant measures as a function of thesub-system size have been utilized to assess the controllability, stability and synchronization properties of the chaotic dynamics. The dynamical synchronization properties of this high-dimensional system has been analyzed using suitable Lyapunov functionals. The possibility of controlling spatiotemporal chaos for relevant objectives using available noisy scalar time-series data with simultaneous self-adaptation of the control parameter(s) has also been discussed.     

Polymorphic and regular localized activity structures in a two-dimensional two-component reaction-diffusion lattice with complex threshold excitation

Space-time dynamics of the system modeling collective behaviour of electrically coupled nonlinear units is investigated. The dynamics of a local cell is described by the FitzHugh-Nagumo system with complex threshold excitation. It is shown that such a system supports formation of two distinct kinds of stable two-dimensional spatially localized moving structures without any external stabilizing actions. These are regular and polymorphic structures. The regular structures preserve their shape and velocity under propagation while the shape and velocity as well as other integral characteristics of polymorphic structures show rather complex temporal behaviour. Both kinds of structures represent novel sorts of spatially temporal patterns which have not been observed before in typical two-component reaction-diffusion type systems. It is demonstrated that there exist two types of regular structures: single and bound states and three types of polymorphic structures: periodic, quasiperiodic and even chaotic ones. The partition of the parameter plane into regions corresponding to the existence of these different types of structures is carried out. High multistability of regular structures is indicated. The interaction of regular structures is investigated. The correspondence between the structures and trajectories in multidimensional phase space associated with the system is given. Bifurcation mechanisms leading to the loss of stability of regular structures as well as to a transition from one type of polymorphic structure to another are indicated. The mechanisms of formation of regular and polymorphic structures are discussed.     

Running pulses of complex shape in a reaction-diffusion model

In a one-dimensional reaction-diffusion model of an active medium, stable steady-state wave pulses of a new type are described. They are called multihumped because their waveforms contain several maxima of similar size. Presumably, the multihumped pulses arise via a bifurcation at which an unstable trigger wave disappears. The parameter governing this bifurcation is the diffusion coefficient for the model inhibitor. The model is analyzed by varying this parameter to determine the conditions for the emergence of multihumped pulses. The results of this analysis show how their waveform and dynamics of excitation depend on the inhibitor diffusion coefficient.     

From local to global spatiotemporal chaos in a cardiac tissue model

Two kinds of chaos can occur in cardiac tissue, chaotic meander of a single intact spiral wave and chaotic spiral wave breakup. We studied these behaviors in a model of two-dimensional cardiac tissue based on the Luo-Rudy I action potential model. In the chaotic meander regime, chaos is spatially localized to the core of the spiral wave. When persistent spiral wave breakup occurs, there is a transition from local to global spatiotemporal chaos.     

Nonlocal boundary dynamics of traveling spots in a reaction-diffusion system

The boundary integral method is extended to derive a closed integro-differential equation applicable to computation of the shape and propagation speed of a steadily moving spot and to the analysis of dynamic instabilities in the sharp boundary limit. Expansion of the boundary integral near the locus of traveling instability in a standard reaction-diffusion model proves that the bifurcation is supercritical whenever the spot is stable to splitting. Thus, stable propagating spots do already exist in the basic activator-inhibitor model, without additional long-range variables.     

Transition to spatiotemporal chaos in the fronts dynamics of a subcritical state

The evolution of the isolated domains of a bifurcated structure in a subcritical state is experimentally studied along the hysteresis branch, up to the critical point at which a chaotic regime is found to develop. The width of the domains is unstable and the fronts dynamics exhibit a cascade of bifurcations as the constraint increases. The chaotic regime is initiated by a splitting of the isolated domains, controlled by a width-selection mechanism. Most of these results are qualitatively reproduced in a fifth-order Ginzburg-Landau model.     

From nonlinearity to causality: statistical testing and inference of physical mechanisms underlying complex dynamics

Principles and applications of statistical testing as a tool for inference of underlying mechanisms from experimental time series are discussed. The computational realizations of the test null hypothesis known as the surrogate data are introduced within the context of discerning nonlinear dynamics from noise, and discussed in examples of testing for nonlinearity in atmospheric dynamics, solar cycle and brain signals. The concept is further generalized for detection of directional interactions, or causality in bivariate time series.     

Spatial structures and dynamics of kinetically constrained models of glasses

Kob and Andersen's simple lattice models for the dynamics of structural glasses are analyzed. Although the particles have only hard core interactions, the imposed constraint that they cannot move if surrounded by too many others causes slow dynamics. On Bethe lattices, a dynamical transition to a partially frozen phase occurs. In finite dimensions there exist rare mobile elements that destroy the transition. At low vacancy density v, the spacing Xi between mobile elements diverges exponentially or faster in 1/v. Within the mobile elements, the dynamics is intrinsically cooperative, and the characteristic time scale diverges faster than any power of 1/v (although slower than Xi). The tagged-particle diffusion coefficient vanishes roughly as Xi(-d).     

From favorable atomic configurations to supershell structures: a new interpretation of conductance histograms.

Simulated minimum cross-section histograms of breaking Al nanocontacts are produced using molecular dynamics. The results allow a new interpretation of the controverted conductance histogram peaks based on preferential geometrical arrangements of nanocontact necks. As temperature increases, lower conductance peaks decrease in favor of broader and higher conductance structures. This reveals the existence of shell and supershell structures favored by the increased mobility of Al atoms.     

Front dynamics in reaction-diffusion systems with Levy flights: a fractional diffusion approach

The use of reaction-diffusion models rests on the key assumption that the diffusive process is Gaussian. However, a growing number of studies have pointed out the presence of anomalous diffusion, and there is a need to understand reactive systems in the presence of this type of non-Gaussian diffusion. Here we study front dynamics in reaction-diffusion systems where anomalous diffusion is due to asymmetric Levy flights. Our approach consists of replacing the Laplacian diffusion operator by a fractional diffusion operator of order alpha, whose fundamental solutions are Levy alpha-stable distributions that exhibit power law decay, x(-(1+alpha)). Numerical simulations of the fractional Fisher-Kolmogorov equation and analytical arguments show that anomalous diffusion leads to the exponential acceleration of the front and a universal power law decay, x(-alpha), of the front's tail.     

Coupled fire dynamics and thermal response of complex building structures

Simulation of the effects of severe fires on the structural integrity of buildings requires a close coupling between the gas phase energy release and transport phenomena, and the stress analysis in the load-bearing materials. The connection between the two is established primarily through the interaction of the radiative heat transfer between the solid and gas phases with the conduction of heat through the structural elements. This process is made difficult in large, geometrically complex buildings by the wide disparity in length and time scales that must be accounted for in the simulations. A procedure for overcoming these difficulties used in the analysis of the collapse of the World Trade Center towers is presented. The large scale temperature and other thermophysical properties in the gas phase are predicted using the NIST Fire Dynamics Simulator. Heat transfer to subgrid scale structural elements is calculated using a simple radiative transport model that assumes the compartment is locally divided into a hot, soot laden upper layer and a cool relatively clear lower layer. The properties of the two layers are extracted from temporal averages of the results obtained from the Fire Dynamics Simulator. Explicit formulae for the heat flux are obtained as a function of temperature, hot layer depth, soot concentration, and orientation of each structural element. These formulae are used to generate realistic thermal boundary conditions for a coupled transient three-dimensional finite element code. This code is used to generate solutions for the heating of complex structural assemblies.