Multistable switching series in chaotic nets

Examples of conscious and interpretable responses that have two or more forms alternating to the same stimuli have been known for centuries, and methods of describing how such situations arise have evolved in biological science. When switches between transient, perceptual or cognitive responses can occur and are mixed serially within time series exhibiting local terminal stability, then patterns arise where psychological data series are too brief to analyse empirically, and neurophysiological data and mathematical simulation are necessary. Modelling such conditions can be approached by using one modified Markov matrix, which we illustrate if we allow some singularities to exist in the dynamics. As soon as networks cease to be homogeneous and have a number of attractors present and operate with different local structures, then one or more response patterns may potentially exist at the same time. The patterns may be addressed within the behavioural dynamics by incorporating in turn very short transients that can be voluntary or involuntary, in sensory and cognitive data. Related software work for modelling, employing hierarchical Dirichlet structures projected into hidden Markov matrices is noted.     

Similarity of apparently random structures in the outer region of wall turbulence

Structural similarities between samples of individual, apparently random structures in various wall-bounded turbulent flows are examined using a template-matching technique. Two-dimensional structural patterns obtained by particle image velocimetry in a turbulent boundary layer are sampled along streamwise lines to extract one-dimensional spatial series that are used as templates. These templates are correlated with time series data obtained in turbulent pipe flow, turbulent channel flow, and atmospheric boundary layer flow in order to determine the frequency and coherency with which similar structures occur. The results indicate that a small ensemble of templates from one flow can be concatenated to represent a large fraction of the entire velocity-time history of each of the other flows by using episodes during which the various templates correlate well. Thus, within the pipe flow, channel flow, and atmospheric boundary layer, one frequently finds detailed time series segments that coincide closely, i.e., in fine detail, with a handful of templates found in a laboratory boundary layer. This type of similarity, which includes seemingly random, fine details at large and small scales, is much stronger than similarity based on statistical comparisons. The individual templates that work best, i.e., those that most frequently yield episodes of high correlation, are segments of hairpin-vortex packets. The high frequency with which these particular structures occur suggests that they are common features of all wall-bounded turbulent flows, including turbulent flows at very high Reynolds number such as the atmospheric boundary layer.     

A measure of complexity based on the order patterns

Cumulative Tsallis entropy (CE) is a recently introduced entropy metric to quantify the uncertainty of time series, and its expressions of continuous random variable and discrete random variable are consistents. So far, it has proved to have a good performance in the characteristics of time series. This paper presents a new method to measure the complexity and similarity of systems—cumulative Tsallis entropy based on the dispersion entropy (DCE). It is different from the traditional PE method to simply symbolize the sequence. Instead, the complexity of the system is characterized by focusing on the amplitude information of the time series and considering the influence of past events. We applied DCE to two kinds of simulation data and six global financial time series. The results show that DCE can be used as a diagnostic model to classify global financial data according to regional characteristics, financial background and government policies. In addition, as a classical method of non-stationary time series, we combine the MSE method with DCE to observe the financial market from different time scales and obtain rich intrinsic properties.

     

Free convection in a saturated porous medium beyond the similarity solution

The non-similar problems associated with a non-isothermal vertical flat plate embedded in a fluid-saturated porous medium were considered to assess the performances of the two distinctive boundary layer solution methods, namely, the local similarity solution and the integral method. The results generated from these two approximate solution methods are compared against the results from a two-point finite difference and those based on a Merk-type series expansion. Comparison of the results reveals that both integral and local similarity methods perform excellently. Especially, the accuracy acquired by the local similarity solution is so high that the difference between the results from the local similarity solution and those from the two-point finite difference and local non-similarity solution methods is hardly discernible for the case of monotonic increasing wall temperature.     

Series solutions of unsteady MHD flows above a rotating disk

The series solutions of unsteady flows of a viscous incompressible electrically conducting fluid caused by an impulsively rotating infinite disk are given by means of an analytic technique, namely the homotopy analysis method. Using a set of new similarity transformations, we transfer the Navier–Stokes equations into a pair of nonlinear partial differential equations. The convergent series solutions are obtained, which are uniformly valid for all dimensionless time 0 ≤ τ < ∞ in the whole spatial region 0 ≤ η < ∞. To the best of our knowledge, such kind of series solutions have never been reported. The effect of magnetic number on the velocity is investigated.     

Double-Diffusive Natural Convection Flows with Thermosolutal Symmetry in Porous Media in the Presence of the Soret–Dufour Effects

The double-diffusive natural convection past a vertical plate embedded in a fluid-saturated porous medium is considered in the boundary-layer and Boussinesq approximations. It is assumed that the Soret–Dufour cross-diffusion effects are significant. The heat and mass fluxes on the plate are prescribed as functions of the surface coordinate x. The general similarity reduction of the problem for power-law and exponential variation of the wall fluxes is given. In the case of thermosolutal symmetry, when the similar temperature and concentration fields become coincident, exact analytical as well as numerical solutions are reported and discussed in some detail. For the flows without thermosolutal symmetry, the final similarity equations have been solved numerically, by paying attention to the influence of the Soret and Dufour numbers on the departure from thermosolutal symmetry. The reported results focus on the wall temperatures and concentrations, whose reciprocals are Nusselt and Sherwood numbers, respectively.     

MHD rotating flow of a viscous fluid over a shrinking surface

This study is concerned with the magnetohydrodynamic (MHD) rotating boundary layer flow of a viscous fluid caused by the shrinking surface. Homotopy analysis method (HAM) is employed for the analytic solution. The similarity transformations have been used for reducing the partial differential equations into a system of two coupled ordinary differential equations. The series solution of the obtained system is developed and convergence of the results are explicitly given. The effects of the parameters M, s and λ on the velocity fields are presented graphically and discussed. It is worth mentioning here that for the shrinking surface the stable and convergent solutions are possible only for MHD flows.     

The characterization of telephone cord buckling of compressed thin films on substrates

The topology of the telephone cord buckling of compressed diamond-like carbon films (DLC) on glass substrates has been characterized with atomic force microscopy (AFM) and with the focused ion beam (FIB) imaging system. The profiles of the several buckles have been measured by AFM to establish the symmetry of each repeat unit, revealing similarity with a circular buckle pinned at its center. By making parallel cuts through the buckle in small, defined locations, straight-sided buckles have been created on the identical films, enabling the residual stress in the film to be determined from the profile.It has been shown that the telephone cord topology can be effectively modeled as a series of pinned circular buckles along its length, with an unpinned circular buckle at its front. The unit segment comprises a section of a full circular buckle, pinned to the substrate at its center. The model is validated by comparing radial profiles measured for the telephone cord with those calculated for the pinned buckle, upon using the residual stress in the film, determined as above. Once validated, the model has been used to determine the energy release rate and mode mixity, G(ψ).The results for G(ψ) indicate that the telephone cord configuration is preferred when the residual stress in the DLC is large, consistent with observations that straight-sided buckles are rarely observed, and, when they occur, are generally narrower than telephone cords. Telephone cords are observed in many systems, and can be regarded as the generic morphology. Nevertheless, they exist subject to a limited set of conditions, residing within the margin between complete adherence and complete delamination, provided that the interface has a mode II toughness low enough to ensure that the buckle crack does not kink into the substrate.     

Magnitude Estimations for Line Bisection Under Lateral Visuo-Spatial Neglect

Human subjects can bisect a line, with error, even when they have neglect on one side. How this skill, even though inefficient, can be represented in nonlinear psychophysical theory is explored here. A problem for previous theoretical explanations of lateral neglect bisection, where the errors of bisection are reversed in sign for brain-damaged subjects, when very short lines are used as stimuli, is shown not in fact to be a problem for N(onlinear) P(sychophysical) D(ynamics) theory at all, but is exactly what is expected to arise when sensitivities are biassed on one side. It is suggested that an imbalance in channel inputs in a nonlinear system representation has results which do not follow from a more conventional connectionist approach.     

The swirling radial free jet

Summary A general similarity solution suggested by Watson for the problem of the laminar, radial, free-jet with swirl has been previously discussed by Riley who also calculated the order to which the solution was valid. That problem is considered in more detail here and higher order terms are given. It is shown that a perturbation scheme for the stream function consisting of a series of inverse powers of and which uses the asymptotic similarity solution as the basic solution is inadequate, and a modification to the series so as to include terms like ⁿ (ln ) ^m must be adopted in order to satisfy the boundary conditions. It is also shown that the general similarity solution may be obtained from the asymptotic series representing the general case with swirl for certain special values of the free constants and also for the no-swirl or free-jet problem. The asymptotic series is given to order ^–13 for the case of swirl and to order ^–29 when there is no swirl.     

基于范例推理的黄土路堑高边坡稳定性预测研究

充分利用大量公路黄土路堑高边坡实例,构建了基于范例推理的边坡稳定性预测模型。该模型是将已建黄土路堑高边坡实例作为源范例,而将待分析边坡作为目标范例,通过源范例和边坡范例之间的相似度计算,得到目标范例与源范例之间的相似性序列,找出与目标边坡范例最相似的源范例,从而实现了黄土路堑高边坡的稳定性预测。实例分析表明,该法不仅原理简单、使用方便,而且效果良好。     

基于转换模板的三维实体全六面体网格生成方法

以四面体一六面体基本转换模板为基础,提出一系列具有伸缩性的扩展转换模板．可根据需要选择不同模板及其组合,将四面体分解为不同数量、不同密度过渡形式的六面体单元。这样,初始四面体网格不需要划分得很细,生成的六面体单元数量也可以通过采用不同规格的扩展转换模板而得到控制。提出了基于CAD几何造型的边界节点坐标修正方法．从而使边界网格更好地拟合几何模型边界。     

Exponential numerical methods for one-dimensional one-phase Stefan problems

Summary Three exponential iterative methods for one-dimensional one-phase Stefan problems based on the transformation of the moving boundary problem into a mixed one, the discretization of the time variable, and the piecewise linearization of the resulting two-point boundary-value problem at each time step are proposed. Two of the methods are based on the strong conservation-law form of the governing equation and analytically solve a piecewise advection–diffusion equation, whereas the third exponential technique accounts for transient, advective, and diffusive effects when determining the solution. These exponential methods provide piecewise-analytical (exponential) solutions, which, by imposing continuity conditions, are globally continuous throughout the domain, and one of them provides globally smooth solutions. The methods have been applied to the classical one-phase Stefan problem and solutions in excellent agreement with the exact ones have been obtained for several Stefan numbers. In addition, it is shown that the method that accounts for transient, advective, and diffusive effects preserves the similarity of the analytical solution to Stefan problems, yields a tridiagonal matrix, and exhibits a spatial accuracy of, at least, fourth order. Application of this method to a forced one-phase Stefan problem indicates that it provides solutions in excellent agreement with those obtained by means of explicit finite difference and nodal integral techniques, and that the melting-front location exhibits some oscillations in the initial stages whose amplitude decreases as the Stefan number is decreased and as time increases, but which increases as the amplitude of the forcing temperature is increased. It is also shown that the temperature profiles in the liquid are affected by the amplitude and frequency of the forcing and the Stefan number.This research was partially financed by Project BFM2001–1902 from the Ministerio de Educación y Ciencia of Spain and Fondos FEDER.The author gratefully acknowledges the comments made by the referees,which have resulted in a clearer presentation.     

On stability analysis via Lyapunov exponents calculated from a time series using nonlinear mapping—a case study

The concept of Lyapunov exponents has been mainly used for analyzing chaotic systems, where at least one exponent is positive. The methods for calculating Lyapunov exponents based on a time series have been considered not reliable for computing negative and zero exponents, which prohibits their applications to potentially stable systems. It is believed that the local linear mapping leads to inaccurate matrices which prevent them from calculating negative exponents. In this work, the nonlinear approximation of the local neighborhood-to-neighborhood mapping is derived for constructing more accurate matrices. To illustrate the approach, the Lyapunov exponents for a stable balancing control system of a bipedal robot during standing are calculated. The time series is generated by computer simulations. Nonlinear mapping is constructed for calculating the whole spectrum of Lyapunov exponents. It is shown that, as compared with those from the linear mapping, (1) the accuracy of the negative exponents calculated using the nonlinear mapping is significantly improved; (2) their sensitivity to the time lag and the evolution time is significantly reduced; and (3) no spurious Lyapunov exponent is generated if the dimension of the state space is known. Thus, the work can contribute significantly to stability analysis of robotic control systems. Issues on extending the concept of Lyapunov exponents to analyzing stable systems are also addressed.     

Numerical simulations of shock wave reflection phenomena in non-stationary flows using regularized smoothed particle hydrodynamics (RSPH)

In this paper we wish to demonstrate to what extent the numerical method regularized smoothed particle hydrodynamics (RSPH) is capable of modelling shocks and shock reflection patterns in a satisfactory manner. The use of SPH based methods to model shock wave problems has been relatively sparse, both due to historical reasons, as the method was originally developed for studies of astrophysical gas dynamics, but also due to the fact that boundary treatment in Lagrangian methods may be a difficult task. The boundary conditions have therefore been given special attention in this paper. Results presented for one quasi-stationary and three non-stationary flow tests reveal a high degree of similarity, when compared to published numerical and experimental data. The difference is found to be below 5, in the case where experimental data was found tabulated. The transition from regular reflection (RR) to Mach reflection (MR) and the opposite transition from MR to RR are studied. The results are found to be in close agreement with the results obtained from various empirical and semi-empirical formulas published in the literature. A convergence test shows a convergence rate slightly steeper than linear, comparable to what is found for other numerical methods when shocks are involved.     

Designing of Partial Similarity Models and Evaluation Method in Polymer Flooding Experiment

Based on the scaling criteria of polymer flooding reservoir obtained in our previous work in which the gravity and capillary forces, compressibility, non-Newtonian behavior, absorption, dispersion, and diffusion are considered, eight partial similarity models are designed. A new numerical approach of sensitivity analysis is suggested to quantify the dominance degree of relaxed dimensionless parameters for partial similarity model. The sensitivity factor quantifying the dominance degree of relaxed dimensionless parameter is defined. By solving the dimensionless governing equations including all dimensionless parameters, the sensitivity factor of each relaxed dimensionless parameter is calculated for each partial similarity model; thus, the dominance degree of the relaxed one is quantitatively determined. Based on the sensitivity analysis, the effect coefficient of partial similarity model is defined as the summation of product of sensitivity factor of relaxed dimensionless parameter and its relative relaxation quantity. The effect coefficient is used as a criterion to evaluate each partial similarity model. Then the partial similarity model with the smallest effect coefficient can be singled out to approximate to the prototype. Results show that the precision of partial similarity model is not only determined by the number of satisfied dimensionless parameters but also the relative relaxation quantity of the relaxed ones.     

Sample entropy of ECG time series of fearful flyers: preliminary results

Research within the framework of the nonlinear dynamical systems (NDS) in the field of anxiety disorders has shown that greater irregularity/complexity appears in the output from healthy systems. In this study we measured the Heart rate variability (HRV) and the sample sntropy (SampEn) of the ECG mV time series of fearful flyers (N = 15) and a matched control group (N = 15) when confronted with three combinations of feared stimuli (pictures, sounds, and pictures with sounds) as well as relaxing stimuli (pictures and sounds). Fearful flyers had lower SampEn than controls in all conditions, including baseline. Non-phobics showed significant entropy decreases from baseline in two out of three exposure conditions. No differences on HRV were found between groups, and HRV was not sensitive to condition changes. The main finding of the study is that the SampEn calculated on very short ECG mV recordings (10 to 60 seconds, easy to obtain in clinical settings) may be a useful diagnostic measure since it can distinguish fearful from non-fearful flyers.     

On 3-dimensional non-axisymmetrical deformation analyses for finite hollow circular cylinders

In this paper, 3-dimensional non-axisymmetrical deformation analyses for finite hollow circular cylinders have been carried out by Pickett's double series expansion method^[1]. Through expanding the displacement potentials as the sum of fourier series and Fourier-Bessel series, we could express the coefficients of one series by those of another under certain boundary conditions. Thus, a set of linear algebraic equations were derived. Solving these equations, we could obtain the solutions of the problems. Numerical examples have been given to show that the method presented here is workable for practical applications.     

The race to the nociceptor: mechanical versus temperature effects in thermal pain of dental neurons

The sensing of hot and cold stimuli by dental neurons differs in several fundamental ways. These sensations have been characterized quantitatively through the measured time course of neural discharge signals that result from hot or cold stimuli applied to the teeth of animal models. Although various hypotheses have been proposed to explain the underlying mechanism, the ability to test competing hypotheses against experimental recorded data using biophysical models has been hindered by limitations in our understanding of the specific ion channels involved in nociception of dental neurons. Here we apply recent advances in established biophysical models to test the competing hypotheses. We show that a sharp shooting pain sensa-tion experienced shortly following cold stimulation cannot be attributed to the activation of thermosensitive ion channels, thereby falsifying the so-called neuronal hypothesis,which states that rapidly transduced sensations of coldness are related to thermosensitive ion channels. Our results support a central role of mechanosensitive ion channels and the associated hydrodynamic hypothesis. In addition to the hydrodynamic hypothesis, we also demonstrate that the long time delay of dental neuron responses after hot stimulation could be attributed to the neuronal hypothesis—that a relatively long time is required for the temperature around nociceptors to reach some threshold. The results are useful as a model of how multiphysical phenomena can be combined to provide mechanistic insight into different mechanisms underlying pain sensations.     

Particle-driven gravity currents: asymptotic and box model solutions

We employ shallow water analysis to model the flow of particle-driven gravity currents above a horizontal boundary. While there exist similarity solutions for the propagation of a homogeneous gravity current, in which the density difference between the current and ambient is constant, there are no such similarity solutions for particle-driven currents. However, because the settling velocity of the particles is often much less than the initial velocity of propagation of these currents, we can develop an asymptotic series to obtain the deviations from the similarity solutions for homogeneous currents which describe particle-driven currents. The asymptotic results render significant insight into the dynamics of these flows and their domain of validity is determined by comparison with numerical integration of the governing equations and also with experimental measurements. An often used simplification of the governing equations leads to `box' models wherein horizontal variations within the flow are neglected. We show how to derive these models rigorously by taking horizontal averages of the governing equations. The asymptotic series are then used to explain the origin of the scaling of these `box' models and to assess their accuracy.