Nonlinear chains inside walls

Extracting slopes from arrays of visual features is relevant to perceiving terrains and interpreting graphs. To understand slope perception in a broader context, we investigated the effects of sounds, position, and semantic priming on a visual search task in which observers searched for a specific slope pattern. We used graphs as the stimuli with the purpose of developing methods to improve graph comprehension. Four bar graphs or scatter plots were simultaneously presented in separate quadrants. The task was to press the space bar as quickly as possible if one of the graphs displayed a specific (positive or negative) slope and to refrain from response otherwise. Concurrently presented ascending (or descending) pitch slowed responses to the positive-slope (or negative-slope) targets, indicating crossmodal interference. Positive slopes were detected faster in the upper-right (than upper-left) quadrant whereas negative slopes were detected faster in the upper-left (than upper-right) quadrant, indicating position dependence. Interestingly, this position dependence is consistent with a standard mental number line with negative values extending to the left and positive values extending to the right, though the position effect occurred only in the upper visual field. Finally, positive slopes were detected faster when the search display was immediately preceded by a briefly flashed word "uphill" than "downhill" and vice versa for detecting a negative slope, indicating a semantic priming effect. This priming effect is unlikely due to reminding observers of the target because the target type was blocked (i.e., observers repeatedly searched for either a positive or negative slope), and the semantic priming only affected the perception of scatter plots (not bar graphs). In summary, perception of visual slope is systematically influenced by auditory signals, placement of graphs, and semantic priming, suggesting that slope perception can be influenced by manipulating underlying auditory-visual associations, spatial position, and semantic associations. Meeting abstract presented at VSS 2012

The relationship between overnight postabsorptive (fasting) respiratory exchange ratio (RER) and plasma FFA concentrations was addressed using data from three separate protocols, each of which involved careful control of the antecedent diet. Protocol 1 examined the relationship between fasting RER and the previous daytime RER. In Protocol 2 fasting, RER and plasma palmitate concentrations were measured in 29 women and 31 men (body mass index <30 kg.m(-2)). Protocol 3 analyzed data from Nielsen et al. (Nielsen, S., Z. K. Guo, J. B. Albu, S. Klein, P. C. O'Brien, M. D. Jensen. 2003. Energy expenditure, sex and endogenous fuel availability in humans. J. Clin. Invest. 111: 981-988.) to understand how fasting RER and palmitate concentrations relate within individuals during four consecutive measurements. The results were as follows: 1) Fasting RER was correlated (r = 0.74, P < 0.001) with the previous day's average RER, and less so with RER variability. 2) Fasting RER was correlated (r = -0.39, P = 0.007) with fasting plasma palmitate concentrations. 3) The pattern of the RER/palmitate relationship was similar within individuals and between individuals; a negative slope was observed significantly more often than a positive slope (chi(2) test; P < 0.001). Our findings suggest that, despite a fixed food quotient, the slight departures from energy equilibrium in a controlled General Clinical Research Center environment can effect plasma FFA concentrations. We suggest that including indirect calorimetry as part of FFA metabolism studies may aid in data interpretation.

The analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations composed of N stochastic excitable units each is performed by studying an approximate system, obtained by replacing each population with the corresponding mean-field model. In the exact system, one has the units within an ensemble communicating via the time-delayed linear couplings, whereas the interensemble terms involve the nonlinear time-delayed interaction mediated by the appropriate global variables. The aim is to demonstrate that the bifurcations affecting the stability of the stationary state of the original system, governed by a set of 4N stochastic delay-differential equations for the microscopic dynamics, can accurately be reproduced by a flow containing just four deterministic delay-differential equations which describe the evolution of the mean-field based variables. In particular, the considered issues include determining the parameter domains where the stationary state is stable, the scenarios for the onset, and the time-delay induced suppression of the collective mode, as well as the parameter domains admitting bistability between the equilibrium and the oscillatory state. We show how analytically tractable bifurcations occurring in the approximate model can be used to identify the characteristic mechanisms by which the stationary state is destabilized under different system configurations, like those with symmetrical or asymmetrical interpopulation couplings.

In the last few decades, the stabilization in stationary states has emerged as a new auspicious campaigner in chaos theory and found a celebrated place through various control techniques such as predictive control, delayed feedback control, constant proportional feedback control and oscillating feedback control system. Generally, it is accepted that the superiority of control systems is not only to quash the irregular distribution of stationary states, but also to illustrate its basin of attractions as large as possible depending on the numerical as well as analytical observance. In this article, the universal stabilization in unstable stationary states is studied through superior fixed point feedback control system for a family of one-dimensional maps. Further, it is interesting to know that the novel system provides freedom in the control parameter γ due to which the stabilization increases more rapidly for the lager range of parameter γ in [0,1]. The analytical as well as numerical simulations are demonstrated to examine the behavior of parameter γ for which the unstable stationary state admits universal stability.

A minimal, analytically manageable Galerkin type model for convection in binary mixtures subject to realistic boundary conditions is presented. The model elucidates and reproduces the typical bifurcation topology of extended stationary and oscillatory convective states seen for negative Soret coupling: backwards stationary and Hopf bifurcations, saddle node bifurcations to stable strongly nonlinear stationary and traveling wave (TW) states, and merging of the TW solution branch with stationary states. Also unstable standing wave solutions are obtained. A systematic analysis of the concentration balance for liquid mixture parameters has lead to a representation of the concentration field in terms of two linear and two nonlinear modes. This truncation captures the important large--scale effects in the laterally averaged concentration field resulting from advective and diffusive mixing. Also the fact that with increasing flow intensity along the TW solution branch the frequency decreases monotonically in the same way as the mixing increases --- the variance of the concentration distribution decreases --- is ensured and reproduced well. Universal scaling relations between flow intensity, frequency, and variance of the concentration distribution (degree of mixing) in a TW are predicted by the model and have been confirmed by numerical solutions of the full equations. The validity of the model is checked by comparison with numerical solutions of the full field equations.

We study heat transport in a chain of harmonic oscillators with random elastic collisions between nearest-neighbours. The equations of motion of the covariance matrix are numerically solved for free and fixed boundary conditions. In the thermodynamic limit, the shape of the temperature profile and the value of the stationary heat flux depend on the choice of boundary conditions. For free boundary conditions, they also depend on the coupling strength with the heat baths. Moreover, we find a strong violation of local equilibrium at the chain edges that determine two boundary layers of size (where N is the chain length) that are characterized by a different scaling behaviour from the bulk. Finally, we investigate the relaxation towards the stationary state, finding two long time scales: the first corresponds to the relaxation of the hydrodynamic modes; the second is a manifestation of the finiteness of the system.

Phase transitions in spin systems without detailed balance

We consider the Schrodinger–Poisson system in the repulsive (plasma physics) Coulomb case. Given a stationary state from a certain class we prove its nonlinear stability, using an appropriately defined energy-Casimir functional as Lyapunov function. To obtain such states we start with a given Casimir functional and construct a new functional which is in some sense dual to the corresponding energy-Casimir functional. This dual functional has a unique maximizer which is a stationary state of the Schrodinger–Poisson system and lies in the stability class. The stationary states are parameterized by the equation of state, giving the occupation probabilities of the quantum states as a strictly decreasing function of their energy levels.

A model based on five independent composition variables has been tested by simulating the complex bursting patterns observed experimentally for a Belousov–Zhabotinsky system in a flow reactor. If the system is in a region of constraint space where all stationary states are locally unstable, and if malonic acid concentration in the feed is decreased at constant flow of bromide ion, simple limit-cycle oscillations persist until the system reaches the Hopf bifurcation which generates a stable stationary state with low concentration of bromide ion. If bromide ion concentration in the feed is increased at constant flow of malonic acid, more and more small-amplitude oscillations are interspersed between trains of fewer and fewer large-amplitude excursions until a Hopf bifurcation leads to a stable stationary state with a high concentration of bromide ion. Patterns may be quite complex but usually repeat regularly. If a firing number is defined as ΣS/(ΣS+ΣL), where the summations represent the numbers of small- and large-amplitude oscillations in a complete pattern, then this firing number increases monotonically with increasing bromide ion in the feed. Narrow regions of chaotic mixing of patterns are also observed. The computations agree spectacularly with the careful experimental observations of Maselko and Swinney. Two separate curves are generated by the Hopf bifurcations which limit local stabilities of stationary states containing low and high concentrations of bromide ion, and the intersection of these curves provides a rationale for the ‘‘cross-shaped phase diagrams’’ which define regions of bistability and of oscillations in constraint spaces for such systems.

The link transmission model (LTM) has great potential for simulating traffic flow in large-scale networks since it is much more efficient and accurate than the Cell Transmission Model (CTM). However, there lack general continuous formulations of LTM, and there has been no systematic study on its analytical properties such as stationary states and stability of network traffic flow. In this study we attempt to fill the gaps. First we apply the Hopf–Lax formula to derive Newell’s simplified kinematic wave model with given boundary cumulative flows and the triangular fundamental diagram. We then apply the Hopf–Lax formula to define link demand and supply functions, as well as link queue and vacancy functions, and present two continuous formulations of LTM, by incorporating boundary demands and supplies as well as invariant macroscopic junction models. With continuous LTM, we define and solve the stationary states in a road network. We also apply LTM to directly derive a Poincaré map to analyze the stability of stationary states in a diverge-merge network. Finally we present an example to show that LTM is not well-defined with non-invariant junction models. We can see that Newell’s model and continuous LTM complement each other and provide an alternative formulation of the network kinematic wave theory. This study paves the way for further extensions, analyses, and applications of LTM in the future.

The unstable branch of stationary states in an illuminated thermochemical bistable system is stabilized with an external feedback loop which does not otherwise alter the autonomous system. The technique allows the measurement of the entire set of stationary states available to the system. Trajectories of transition between branches of stationary states (relaxation) are investigated theoretically and experimentally. Critical slowing down in the speed of the trajectories is predicted and measured as the points of marginal stability are approached. Trajectories are observed to spread as they depart from the unstable stationary state and then to coalesce as they approach a stable stationary state. These results are obtained due to experimental spread in initial conditions and not from noise along the relaxation trajectory.

A general formulation of boundary conditions for semiconductor-metal contacts follows from a phenomenological procedure sketched here. The resulting boundary conditions, which incorporate only physically well-defined parameters, are used to study the classical unipolar drift-diffusion model for the Gunn effect. The analysis of its stationary solutions reveals the presence of bistability and hysteresis for a certain range of contact parameters. Several types of Gunn effect are predicted to occur in the model, when no stable stationary solution exists, depending on the value of the parameters of the injecting contact appearing in the boundary condition. In this way, the critical role played by contacts in the Gunn effect is clearly established.

The statistical weights of the stationary states in various ensembles of isotopically disordered harmonic chains are compared. It is proven that the ensemble defined by boundary conditions at both ends of the chain is constructed with correct statistical weights as follows: One matches at sitei the stationary states of the ensemble defined by the boundary condition at one end and frequencyω with those of the ensemble defined by the boundary condition at the other end andω. Finally one integrates overω and sums over all sitesi. This confirms and substantiates the conjecture on the exponential localization of the eigenstates in one dimension. The matching procedure yields an equation for the density of states.

Effects of density dependent cross-diffusion on the chaotic patterns in a ratio-dependent prey-predator model

Solutions of the system of equations describing non-isothermic flow of real gases in porous media are given in the paper. Approximate solutions were obtained by the method of functional series for stationary flows, taking into account the thermal conductivity of the medium. Accurate solutions were obtained for stationary- flows without considering the thermal conductivity. Solutions are given for plane and plane-radial flows. Moreover, a method of solution is described which involves a consideration of the variation of the coefficient of gas compressibility, z, with pressure, p. Considering non-stationary non-isothermic flow, a method is given for solution with the use of the ‘minor parameter’, reducing the system of non-linear partial differential equations to the system of linear partial differential equations of the parabolic type which determine the coefficients of the solving series. The solutions may be used for the temperature testing of gas wells and production from condensate gas fields. INTRODUCTION THE FLOW OF GAS through a porous medium is determined univocally by the functions p/r, t/, T/r, t/,γ/r, t/ and v/r, t/, where p is pressure, T temperature, γ specific gravity, flow rate and r is the position vector. The distribution in time and space of the above-mentioned parameters may be obtained by solving a system of four equations: (Equation Available In Full Paper) On the whole, the flow of gas is defined in practice assuming that T = const, in a stationary state and with simple geometrical contours of the medium. There also exist several theoretical elaborations of the problems of non-stationary flow with the assumption that T = const.(2,3,4,5). The problem of non-isothermic flow has remained so far unsolved, with the exception of a few investigations. These were undertaken by Czekaluk(1,0) Czarny(4) and Gusein-Zade and Kolosovskaja(7). They referred mainly to the stationary flow of incompressible fluids, assuming that the stationary distribution of pressure in a porous medium is known, omitting the thermal conductivity of the medium. Un-dimensional flows (plane and plane-radial) were considered, with the only equation of energy being solved /3/. Thus, Gusein-Zade and Kolosovskaja(7), start from the equations of energy for linear and plane-radial flow under the form: (Equation Available In Full Paper) Equations /5/ and /6/ are directly obtained from equation /3/, assuming that A = O and ∂p / ∂t = O. Setting the original and boundary conditions in the form: (Equation Available In Full Paper) one seeks for a solution in the form of (Equation Available In Full Paper) As may be seen from the solutions obtained, the area of the temperature field is divided into area I, where x &amp;lt; u °t, and area II, where x &amp;gt; u °t; two different formulae are therefore justified. These considerations are substantial in the case of injecting a fluid into a well. Similarly in the case of plane-radial flow at the initial and boundary conditions in the form of (Equation Available In Full Paper) Solutions given in papers (1) and (4) are based on the same equations.