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PubMed1999

Bistability and Electrokinetic Oscillations.

Nonlinear dynamic behavior and electrokinetic oscillations have been investigated for the membrane systems (a) 0.1 N NaCl/KCl parallel Millipore filter parallel 0.01 N NaCl/KCl; (b) 0.1 N NaCl/KCl parallel Whatman Inorganic filter parallel 0.01 N NaCl/KCl; and (c) 0.1 N NaCl/KCl parallel silver-coated filter parallel 0.01 N NaCl/KCl, from the viewpoint of testing the theories for the phenomena and elucidating the mechanism. To achieve these objectives, studies on hydrodynamic permeability, electroosmotic permeability, bistability, and electrokinetic oscillations were undertaken. Relaxation time for buildup and decay of electroosmotic pressures was experimentally determined. Bistability was not observed showing that it is not a prerequisite for oscillations and nonlinear relations between (J(v))(Deltarho=0) and Deltaφ involving cubic or higher-order terms are necessary for bistability. The oscillations were studied at different current strengths. The period is found to be independent of current, while amplitude A is found to be linearly related to current I which is the bifurcation parameter. The bifurcation point occurs at approximately 0.4 mA. Studies have also been made with membranes of different pore size that show that amplitude increases with increase in pore size of the membranes. The validity of the two-variable model of Teorell was examined by comparing the experimental results with computer simulation based on parameters determined experimentally. Theory does not meet expectation and the results suggest that modification of theory is needed. The weakness of the theory has been critically examined. Copyright 1999 Academic Press.

Journal Article↗

PubMed1992

Behavior dynamics: One perspective.

Behavior dynamics is a field devoted to analytic descriptions of behavior change. A principal source of both models and methods for these descriptions is found in physics. This approach is an extension of a long conceptual association between behavior analysis and physics. A theme common to both is the role of molar versus molecular events in description and prediction. Similarities and differences in how these events are treated are discussed. Two examples are presented that illustrate possible correspondence between mechanical and behavioral systems. The first demonstrates the use of a mechanical model to describe the molar properties of behavior under changing reinforcement conditions. The second, dealing with some features of concurrent schedules, focuses on the possible utility of nonlinear dynamical systems to the description of both molar and molecular behavioral events as the outcome of a deterministic, but chaotic, process.

Journal Article↗

PubMed2006

Assignment and extraction of dynamics of a small molecule with a complex vibrational spectrum: thiophosgene.

The dispersed fluorescence spectrum of the ground electronic state of thiophosgene, SCCl2, is analyzed in a very complex region of vibrational excitation, 7000-9000 cm(-1). The final result is that most of the inferred excited vibrational levels are assigned in terms of approximate constants of the motion. Furthermore, each level is associated with a rung on a ladder of quantum states on the basis of common reduced dimension fundamental motions. The resulting ladders cannot be identified by any experimental means, and it is the interspersing in energy of their rungs that makes the spectrum complex even after the process of level separation into polyads. Van Vleck perturbation theory is used to create polyad constants of the motion and a spectroscopic Hamiltonian from a potential fitted to experimental data. The eigen functions of this spectroscopic Hamiltonian are rewritten as semiclassical wave functions and transformed to a representation that allows us to analyze and assign the spectra with no other work other than to utilize concepts from nonlinear dynamics.

Fluorescence↗

PubMed1996

Scaling behaviour of heartbeat intervals obtained by wavelet-based time-series analysis.

Biological time-series analysis is used to identify hidden dynamical patterns which could yield important insights into underlying physiological mechanisms. Such analysis is complicated by the fact that biological signals are typically both highly irregular and non-stationary, that is, their statistical character changes slowly or intermittently as a result of variations in background influences. Previous statistical analyses of heartbeat dynamics have identified long-range correlations and power-law scaling in the normal heartbeat, but not the phase interactions between the different frequency components of the signal. Here we introduce a new approach, based on the wavelet transform and an analytic signal approach, which can characterize non-stationary behaviour and elucidate such phase interactions. We find that, when suitably rescaled, the distributions of the variations in the beat-to-beat intervals for all healthy subjects are described by a single function stable over a wide range of timescales. However, a similar scaling function does not exist for a group with cardiopulmonary instability caused by sleep apnoea. We attribute the functional form of the scaling observed in the healthy subjects to underlying nonlinear dynamics, which seem to be essential to normal heart function. The approach introduced here should be useful in the analysis of other nonstationary biological signals.

Adult↗

PubMed1984

Rheological approaches of arteries.

A fundamental problem of haemodynamics lies in the description of the rheological properties of arteries. The time and history dependency of stress and strain, the nonlinearity of the stress-radius relationship, and the activity of vascular smooth muscle complicate or even prevent a complete mathematical characterization of the arterial wall mechanics. Due to this nonlinearity, dynamic investigations were hitherto performed in excised arteries in vitro by means of small sinusoidal changes of stress and radius at different stress levels in a wide frequency range. To allow an analysis of the dynamic rheological properties of arteries in vivo, we have developed a procedure which permits the separate determination of the elastic, the viscous, and the inertial forces acting on the arterial wall. The stress can be subdivided into an elastic stress which is a function of radius (r), a viscous stress which is a function of dr/dt, and an inertial stress which is a function of d2r/dt2. These stresses are formulated as polynomials. Under cyclic loading and unloading, hysteresis loops appear in the stress-radius diagrams of arteries. Since the elastic stress-radius diagram must be free from any loop, the coefficients of the viscous and the inertial stress can be found by a fitting procedure, using the criterion of loop elimination. Investigations were performed on exposed canine arteries in vivo. The main result was that the elastic stress-radius curve was markedly nonlinear at greater pulse pressures. The viscous wall behaviour, too, was nonlinear and depended mainly on the square of the vessel radius.

Animals↗

PubMed2006

Dynamics analysis and analog associative memory of networks with LT neurons.

The additive recurrent network structure of linear threshold neurons represents a class of biologically-motivated models, where nonsaturating transfer functions are necessary for representing neuronal activities, such as that of cortical neurons. This paper extends the existing results of dynamics analysis of such linear threshold networks by establishing new and milder conditions for boundedness and asymptotical stability, while allowing for multistability. As a condition for asymptotical stability, it is found that boundedness does not require a deterministic matrix to be symmetric or possess positive off-diagonal entries. The conditions put forward an explicit way to design and analyze such networks. Based on the established theory, an alternate approach to study such networks is through permitted and forbidden sets. An application of the linear threshold (LT) network is analog associative memory, for which a simple design method describing the associative memory is suggested in this paper. The proposed design method is similar to a generalized Hebbian approach, but with distinctions of additional network parameters for normalization, excitation and inhibition, both on a global and local scale. The computational abilities of the network are dependent on its nonlinear dynamics, which in turn is reliant upon the sparsity of the memory vectors.

Algorithms↗

PubMed2004

An online GA-based output-feedback direct adaptive fuzzy-neural controller for uncertain nonlinear systems.

In this paper, we propose a novel design of a GA-based output-feedback direct adaptive fuzzy-neural controller (GODAF controller) for uncertain nonlinear dynamical systems. The weighting factors of the direct adaptive fuzzy-neural controller can successfully be tuned online via a GA approach. Because of the capability of genetic algorithms (GAs) in directed random search for global optimization, one is used to evolutionarily obtain the optimal weighting factors for the fuzzy-neural network. Specifically, we use a reduced-form genetic algorithm (RGA) to adjust the weightings of the fuzzy-neural network. In RGA, a sequential-search -based crossover point (SSCP) method determines a suitable crossover point before a single gene crossover actually takes place so that the speed of searching for an optimal weighting vector of the fuzzy-neural network can be improved. A new fitness function for online tuning the weighting vector of the fuzzy-neural controller is established by the Lyapunov design approach. A supervisory controller is incorporated into the GODAF controller to guarantee the stability of the closed-loop nonlinear system. Examples of nonlinear systems controlled by the GODAF controller are demonstrated to illustrate the effectiveness of the proposed method.

Journal Article↗

PubMed1999

Dynamics of Growth and Breakup of Viscous Pendant Drops into Air.

This paper presents a numerical study of the dynamics of a viscous liquid drop that is being formed directly at the tip of a vertical tube into ambient air. A model is developed to predict the evolution of the drop shape and its breakup based on RIPPLE, which is a solution algorithm for computing transient, two-dimensional, incompressible fluid flow with surface tension on free surfaces of general topology (D. B. Kothe and R. C. Mjolsness, AIAA J. 30, 2694 (1992)). The full Navier-Stokes system is solved by using finite-difference formulation on a Eulerian mesh. The mesh is fixed in space, with the flow and surface moving through it to ensure accurate calculations of complex free surface flows and topology, including surface breakup and coalescence. The novel feature of the numerical algorithm is the use of a Eulerian volume-tracking approach which allows the calculations to pass the breaking point during formation of a drop continuously without interruption or numerical modification and, therefore, to explore the features of generation of satellite droplets. The effects of physical and geometric parameters on the nonlinear dynamics of drop growth and breakup are investigated. The focus here is on drop breakup and subsequent formation of satellite droplets. The effects of finite inertial, capillary, viscous, and gravitational forces are all accounted for to classify different formation dynamics and to elucidate features of satellite droplet generation. The numerical predictions are compared with experimental measurements for water drops, and the results show good agreement. Copyright 1999 Academic Press.

Journal Article↗

PubMed1996

Extracting 1/f fluctuation from the arterial blood pressure of an artificial heart.

We have studied the fluctuations of an artificial circulation for the analysis of the physiological aspects; however, the conventionally used fast Fourier transform (FFT) method cannot separate harmonic oscillations, such as respiratory and Mayer waves, from the 1/f fluctuation, which has been though to represent underlying fractal dynamics. Fractal structure was shown in the strange attractor with chaotic dynamics, which is thought to be a flexible and intelligent system. In this study, the coarse-graining spectral analyzing (CGSA) method was utilized to quantitatively evaluate the proportion of the 1/f fluctuation in the total power in the frequency domain and to analyze artificial circulation in the whole system. We implanted two pneumatically actuated ventricular assist devices as biventricular bypasses (BVBs) in chronic animal experiments using 4 healthy adult goats. To compare the natural and prosthetic circulation of each experimental animal, the BVB-type complete prosthetic circulation model with electrically induced ventricular fibrillation was adopted. All hemodynamic parameters of natural and prosthetic circulation were recorded under awake conditions and calculated with the use of a personal computer. With the use of the CGSA method, time-series data of the hemodynamics were analyzed and fractal percentages, extracting the 1/f fluctuation from a given time series, were calculated. Fractal percentages of the arterial blood pressure were 85.8 +/- 10.7% and 82.0 +/- 7.3% with natural and artificial circulation, respectively (not significant [NS]). 1/f fluctuation showed the characteristics of being fractal in a time series. The fractal structure showed robustness and error resistance in nonlinear dynamics. Therefore, our results suggest that the circulatory regulatory system of the artificial heart may have desirable characteristics such as error resistance.

Animals↗

PubMed2004

Complexity of tissue injury-induced nociceptive discharge of dorsal horn wide dynamic range neurons in the rat, correlation with the effect of systemic morphine.

Persistent discharge of wide dynamic range (WDR) neurons was recorded from lumbar dorsal horn of anesthetized rats following subcutaneous bee venom injection into the receptive field. To quantitatively describe the complexity of this nociceptive activity, we computed the approximate entropy (ApEn) for each sampled interspike interval (ISI) series. A larger value of ApEn indicates higher complexity or less regularity and vice versa. The ApEn value varied across different WDR neurons tested, and for each neuron the ApEn remained constant through the 1-h discharge though the average ISI of the sampled data increased progressively with time (16 neurons). A low dose of intravenous morphine (0.3 mg/kg) depressed the activity of WDR neurons differentially, and the degree of this inhibition showed a significant correlation with the value of ApEn (P<0.001, 27 neurons, Spearman's correlation test). The present results suggest that the complexity feature of WDR neurons is various under tissue injury state, and for each single WDR neuron the complexity feature is relatively independent of the strength of peripheral noxious input and cannot be fully described in terms of average firing rate. Moreover, the response of the nociceptive discharge to analgesics may be related to the nonlinear dynamics feature of nociceptive neurons, which can be quantitatively characterized by the degree of complexity.

Action Potentials↗

PubMed1988

Kinetics of VO2 with impulse and step exercise in humans.

The constancy of the time course (i.e., dynamic linearity) of the O2 uptake (VO2) response to exercise was examined by testing the law of superposition on data from impulse and step work rate forcings. Two impulses (10 s at a 235-W increase above a 25-W base line, I-235; and 5 s at a 475-W increase above a 25-W base line, I-475), four steps (ST) (25-65 W, ST1; 65-105 W, ST2; 25-105 W, ST3; and 25-145 W, ST4), and the corresponding off-transient responses were performed six to eight times by each of five subjects. The integrated area (G) of the VO2 response for I-235 was similar to that of ST1 and ST2 (P greater than 0.05); the I-475 G was significantly greater (P less than 0.05). The time constant of VO2 during the step function on-transient response for the second exponential component was significantly faster for ST1 and significantly slower for I-235 and I-475 than for ST2, ST3, and ST4 (P less than 0.05). However, I-235 and I-475 time constants for VO2 were not different from the ST off-transient values. Attempts to superimpose the integral of the impulse on the ST data showed that the early rapid increase in VO2 in the ST was underpredicted by the impulse and that the impulse response lagged behind the ST at all points before steady state. It can be concluded that VO2 kinetics failed the test of superposition and are therefore described by a nonlinear dynamic system.

Adolescent↗

PubMedDate not supplied

On the physics of unstable infiltration, seepage, and gravity drainage in partially saturated tuffs.

To improve understanding of the physics of dynamic instabilities in unsaturated flow processes within the Paintbrush nonwelded unit (PTn) and the middle nonlithophysal portion of the Topopah Spring welded tuff unit (TSw) of Yucca Mountain, we analyzed data from a series of infiltration tests carried out at two sites (Alcove 4 and Alcove 6) in the Exploratory Studies Facility (ESF), using analytical and empirical functions. The analysis of infiltration rates measured at both sites showed three temporal scales of infiltration rate: (1) a macro-scale trend of overall decreasing flow, (2) a meso-scale trend of fast and slow motion exhibiting three-stage variations of the flow rate (decreasing, increasing, and [again] decreasing flow rate, as observed in soils in the presence of entrapped air), and (3) micro-scale (high frequency) fluctuations. Infiltration tests in the nonwelded unit at Alcove 4 indicate that this unit may effectively dampen episodic fast infiltration events; however, well-known Kostyakov, Horton, and Philip equations do not satisfactorily describe the observed trends of the infiltration rate. Instead, a Weibull distribution model can most accurately describe experimentally determined time trends of the infiltration rate. Infiltration tests in highly permeable, fractured, welded tuff at Alcove 6 indicate that the infiltration rate exhibits pulsation, which may have been caused by multiple threshold effects and water-air redistribution between fractures and matrix. The empirical relationships between the extrinsic seepage from fractures, matrix imbibition, and gravity drainage versus the infiltration rate, as well as scaling and self-similarity for the leading edge of the water front are the hallmark of the nonlinear dynamic processes in water flow under episodic infiltration through fractured tuff. Based on the analysis of experimental data, we propose a conceptual model of a dynamic fracture flow and fracture-matrix interaction in fractured tuff, incorporating the time-dependent processes of water redistribution in the fracture-matrix system.

Filtration↗

PubMed2003

Effects of a nonlinear perturbation on dynamical tunneling in cold atoms.

We perform a numerical analysis of the effects of a nonlinear perturbation on the quantum dynamics of two models describing noninteracting cold atoms in a standing wave of light with a periodical modulated amplitude A(t). One model is the driven pendulum, recently considered by D.A. Steck, W.H. Oskay, and M.G. Raizen [Science 293, 274 (2001)], and the other is a variant of the well-known kicked rotator model. In absence of the nonlinear perturbation, the system is invariant under some discrete symmetries and quantum dynamical tunneling between symmetric classical islands is found. The presence of nonlinearity destroys tunneling, breaking the symmetries of the system. Finally, further consequences of nonlinearity in the kicked rotator case are considered.

Journal Article↗

PubMed2001

Heterogeneous catalysis on the atomic scale.

Information about the elementary processes underlying heterogeneous catalysis may be obtained by investigating well-defined single crystal surfaces. The success of this "surface science" approach for "'real" catalysis can be demonstrated, for example, with ammonia synthesis. The progress of catalytic reactions can be observed on an atomic scale by applying scanning tunneling microscopy and other surface physical techniques, as is shown with different examples in this paper: CO oxidation on a Pt(111) surface proceeds preferentially along the boundaries between adsorbed O and CO patches. Ru is practically inactive for the same reaction under lower pressure conditions but is transformed into RuO2 under atmospheric pressure conditions, where part of the surface Ru atoms function as coordinatively unsaturated sites (cus). In contrast, in the hydrogen oxidation reaction on Pt(111), an autocatalytic reaction step comes into prominence, and is responsible for the formation of propagating concentration patterns on the surface as a characteristic of nonlinear dynamics. Additionally, the limits of the concept of thermal equilibrium in surface rate processes are explored by applying ultrafast (femtosecond) laser techniques.

Journal Article↗

PubMed1988

Determinants involved in the perception of the Necker cube: an application of catastrophe theory.

The study is concerned with evaluating interactions at the organic level within the visual perception subsystem of living systems. The reported work focuses on the identification of some of the determinants of multistable perception by experimentally testing a nonlinear dynamical systems (catastrophe) model of the Necker Cube. This technique serves as an advantage over linear threshold models which cannot effectively study multivalued functional relationships. It was proposed that manipulation of two independent control parameters (bias or changing shape by continuously varying perspective lines and selective stimulus shading) was compatible with the subjective dichotomy of bistable perception of the Necker cube. One hundred and twenty naive subjects, categorized by age, sex, and optical aids, were presented with a computer-generated sequence of 63 stimuli (7 shading levels X 9 perspective levels) to which they had to respond as to whether they saw a "hollow" or "solid" image. The work revealed that bias and shading exerted their effects in opposition and that each influenced the other. Both were decisive factors involved in the perception of the cube. These findings are supported by topological and psychological evidence.

Adolescent↗

PubMed2005

Drawing on mind's canvas: differences in cortical integration patterns between artists and non-artists.

Our primary question was to learn whether mentally composing drawings of their own choice produce different brain electric features in artists and laymen. To this purpose, we studied multichannel electroencephalograph (EEG) signals from two broad groups (all participants were females): artists (professionally trained in visual arts) and non-artists (without any training in art). To assess the underlying synchronization, which is assumed to be the platform for general cognitive integration between different cortical regions, three measures inspired by nonlinear dynamical system theory were applied as follows: (1) index based on generalized synchronization; (2) index based on mean phase coherence; and (3) index of phase synchrony based on entropy. Results consistent over all three measures were as follows: comparing the tasks to rest, the artists showed significantly stronger short- and long-range delta band synchronization, whereas the non-artists showed enhancement in short-range beta and gamma band synchronization primarily in frontal regions; comparing the two groups during the tasks, the artists showed significantly stronger delta band synchronization and alpha band desynchronization than did the non-artists. Strong right hemispheric dominance in terms of synchronization was found in the artists. In artists, the higher synchrony in the low-frequency band is possibly due to the involvement of a more advanced long-term visual art memory and to extensive top-down processing. The results demonstrate that in artists, patterns of functional cooperation between cortical regions during mental creation of drawings were significantly different from those in non-artists.

Art↗

PubMed1992

Modelling of in vivo calcium metabolism. I. Optimal cooperation between constant and rhythmic behaviours.

The relevance of nonlinear dynamics to calcium metabolism led us to reevaluate the role of Ca-regulating hormones in Ca homeostasis. We suggest that, firstly, the main Ca metabolic functions in rat-bone and gut--are organized as dynamic entities able to generate various temporal expressions, including self-oscillating patterns and, secondly, Ca homeostasis results from interaction between both metabolic and hormonal oscillators. Following this schema, a major role for the hormonal system, with its circadian pattern, could be to act directly on metabolic functions or indirectly through feeding behaviour, in order to optimize, coordinate and synchronize the Ca fluxes at ECF level.

Animals↗

PubMed1995

Analysis of an autonomous phase model for neuronal parabolic bursting.

An understanding of the nonlinear dynamics of bursting is fundamental in unraveling structure-function relations in nerve and secretory tissue. Bursting is characterized by alternations between phases of rapid spiking and slowly varying potential. A simple phase model is developed to study endogenous parabolic bursting, a class of burst activity observed experimentally in excitable membrane. The phase model is motivated by Rinzel and Lee's dissection of a model for neuronal parabolic bursting (J. Math. Biol 25, 653-675 (1987)). Rapid spiking is represented canonically by a one-variable phase equation that is coupled bi-directionally to a two-variable slow system. The model is analyzed in the slow-variable phase plane, using quasi steady-state assumptions and formal averaging. We derive a reduced system to explore where the full model exhibits bursting, steady-states, continuous and modulated spiking. The relative speed of activation and inactivation of the slow variables strongly influences the burst pattern as well as other dynamics. We find conditions of the bistability of solutions between continuous spiking and bursting. Although the phase model is simple, we demonstrate that it captures many dynamical features of more complex biophysical models.

Animals↗