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At least 163 records · Page 9Linked to original sources
PubMed2004

Probing weak forces in granular media through nonlinear dynamic dilatancy: clapping contacts and polarization anisotropy.

Rectification (demodulation) of high-frequency shear acoustic bursts is applied to probe the distribution of contact forces in 3D granular media. Symmetry principles allow for rectification of the shear waves only with their conversion into longitudinal mode. The rectification is due to nonlinear dynamic dilatancy, which is found to follow a quadratic or Hertzian power law in the shear wave amplitude. Evidence is given that a significant portion of weak contact forces is localized below 10(-2) of the mean force-a range previously inaccessible by experiment. Strong anisotropy of nonlinearity for shear waves with different polarization is observed.

Journal Article↗
PubMedDate not supplied

Nonlinear dynamic perspectives on dynamic force microscopy.

Dynamic force microscopy (DFM) utilizes the dynamic response of a resonating probe tip as it approaches and retracts from a sample to measure the topography and material properties of a nanostructure. We present recent results based on nonlinear dynamical systems theory, computational continuation techniques and detailed experiments that yield new perspectives and insights into DFM.A dynamic model including van der Waals and Derjaguin-Müller-Toporov contact forces demonstrates that periodic solutions can be represented as a catastrophe surface with respect to the approach distance and excitation frequency. Turning points on the surface lead to hysteretic amplitude jumps as the tip nears/retracts from the sample. New light is cast upon sudden global changes that occur in the interaction potential at certain gap widths that cause the tip to "stick" to, or tap irregularly the sample. Experiments are performed using a tapping mode tip on a graphite sample to verify the predictions.

Journal Article↗
PubMed1996

Linear and nonlinear dynamics of heart rate variability after acute myocardial infarction with normal and reduced left ventricular ejection fraction.

We analyzed heart rate variability (HRV) in 2 groups of patients after acute myocardial infarction with normal and reduced ejection fraction (EF) by considering both the power of the 2 major harmonic components at low and high frequency and 2 indexes of nonlinear dynamics, namely the 1/f slope and the correlation dimension D2. HRV of patients with a reduced EF was characterized by a diminished RR variance as well as a different distribution of the residual power in all frequency ranges, with lower values of the low-frequency component expressed in both absolute and normalized units, and of the low- to high-frequency ratio. In these patients we also observed a steeper slope of the negative regression line between power and frequency in the very low frequency range. The presence of a smaller fractal dimension was suggested by a lower D2. Thus, in patients after acute myocardial infarction with a reduced EF, the reduction in HRV is associated with a different distribution of the residual power in the entire frequency range, which suggests a diminished responsiveness of sinus node to neural modulatory inputs.

Case-Control Studies↗
PubMed2000

The neuromuscular transform: the dynamic, nonlinear link between motor neuron firing patterns and muscle contraction in rhythmic behaviors.

The nervous system issues motor commands to muscles to generate behavior. All such commands must, however, pass through a filter that we call here the neuromuscular transform (NMT). The NMT transforms patterns of motor neuron firing to muscle contractions. This work is motivated by the fact that the NMT is far from being a straightforward, transparent link between motor neuron and muscle. The NMT is a dynamic, nonlinear, and modifiable filter. Consequently motor neuron firing translates to muscle contraction in a complex way. This complexity must be taken into account by the nervous system when issuing its motor commands, as well as by us when assessing their significance. This is the first of three papers in which we consider the properties and the functional role of the NMT. Physiologically, the motor neuron-muscle link comprises multiple steps of presynaptic and postsynaptic Ca(2+) elevation, transmitter release, and activation of the contractile machinery. The NMT formalizes all these into an overall input-output relation between patterns of motor neuron firing and shapes of muscle contractions. We develop here an analytic framework, essentially an elementary dynamical systems approach, with which we can study the global properties of the transformation. We analyze the principles that determine how different firing patterns are transformed to contractions, and different parameters of the former to parameters of the latter. The key properties of the NMT are its nonlinearity and its time dependence, relative to the time scale of the firing pattern. We then discuss issues of neuromuscular prediction, control, and coding. Does the firing pattern contain a code by means of which particular parameters of motor neuron firing control particular parameters of muscle contraction? What information must the motor neuron, and the nervous system generally, have about the periphery to be able to control it effectively? We focus here particularly on cyclical, rhythmic contractions which reveal the principles particularly clearly. Where possible, we illustrate the principles in an experimentally advantageous model system, the accessory radula closer (ARC)-opener neuromuscular system of Aplysia. In the following papers, we use the framework developed here to examine how the properties of the NMT govern functional performance in different rhythmic behaviors that the nervous system may command.

Animals↗
PubMed2005

Nonlinear dynamics of transport barrier relaxations in tokamak edge plasmas.

A new mechanism for intermittent relaxations of transport barriers is found by using three dimensional fluid turbulence simulations. This mechanism is generic since it only requires a stationary E x B shear flow. It is found here that if the flow shear increases faster than linearly with heating power, the relaxation frequency decreases with power. An analytical study reveals that this nonlinear dynamics is governed by a time delay for effective velocity shear stabilization.

Journal Article↗
PubMed2006

A closed-loop identification protocol for nonlinear dynamical systems.

A previous work introduced an optimal identification (OI) technique for reliably extracting model parameters of biochemical reaction systems from tailored laboratory experiments. The notion of optimality enters through seeking an external control in the laboratory producing data that leads to minimum uncertainties in the identified parameter distributions. A number of algorithmic and operational improvements are introduced in this paper to OI, aiming to build a more practical and efficient closed-loop identification protocol/procedure (CLIP) for nonlinear dynamical systems. The improvements in CLIP include (a) inversion cost function modification to preferably search for the upper and lower boundaries of the parameter distributions consistent with the observed data, (b) dynamic search range updating of the unknown parameters to better exploit the information from the prior iterative experiments, (c) replacing the control genetic algorithm by the simplex method to enable better balance between operational cost and inversion quality, and (d) utilizing virtual sensitivity optimization techniques to further reduce the laboratory costs. The workings of CLIP utilizing these new algorithms are illustrated in indentifying a simulated tRNA proofreading model, and the results demonstrate enhanced performance of CLIP in terms of algorithmic reliability and efficiency.

Journal Article↗
PubMed2006

Chaos without nonlinear dynamics.

A linear, second-order filter driven by randomly polarized pulses is shown to generate a waveform that is chaotic under time reversal. That is, the filter output exhibits determinism and a positive Lyapunov exponent when viewed backward in time. The filter is demonstrated experimentally using a passive electronic circuit, and the resulting waveform exhibits a Lorenz-like butterfly structure. This phenomenon suggests that chaos may be connected to physical theories whose underlying framework is not that of a traditional deterministic nonlinear dynamical system.

Journal Article↗
PubMed2025

Bistable Mutation-Selection Equilibria and Violations of Fisher's Theorem in Tetraploids: Insights from Nonlinear Dynamics.

Polyploidy and whole genome duplication (WGD) are widespread biological phenomena with substantial cellular, meiotic, and genetic effects. Despite their prevalence and significance across the tree of life, population genetics theory for polyploids is not well developed. The lack of theoretical models limits our understanding of polyploid evolution and restricts our ability to harness polyploidy for crop improvement amidst increasing environmental stress. To address this gap, we developed and analyzed deterministic models of mutation-selection balance for tetraploids under polysomic (autotetraploid) and disomic (allotetraploid) inheritance patterns and arbitrary dominance relationships. We also introduced a new mathematical framework based on ordinary differential equations and nonlinear dynamics for analyzing the models. We find that autotetraploids approach Hardy-Weinberg Equilibrium 33% faster than allotetraploids, but the different tetraploid inheritance models show little differences in mutation load and allele frequency at mutation-selection balance. Our model also reveals two bistable points of mutation-selection balance for dominant alleles with biased mutation rates over a wide range of selection coefficients in the tetraploid models compared to bistability in only a narrow range for diploids. Finally, using discrete time simulations, we explore the temporal dynamics of allele frequency and fitness change and compare these dynamics to the predictions of Fisher's Fundamental Theorem of Natural Selection. While Fisher's predictions generally hold, we show that the bistable dynamics for dominant mutations fundamentally alter the associated temporal dynamics. Overall, this work develops foundational theoretical models that will facilitate the development of population genetic models and methodologies to study evolution in empirical tetraploid populations.

Fisher’s Fundamental Theorem↗
PubMed1997

Use of serum markers to measure acute myocardial infarct size: lessons of a nonlinear dynamical model.

During acute myocardial infarction, dying cells in the myocardium release a number of chemicals that appear in the blood stream. By sampling the blood and assaying for these markers at intervals after infarction, we obtain a measure of the amount of myocardium lost, and the area under the marker concentration curve with time has been used to estimate the size of infarct. Because many of the important variables in this system are impossible to measure in patients and difficult to measure or control in experimental animals, simulations using a mathematical model provide an important way to learn about the infarct-marker relationship. This paper described a nonlinear dynamical model that allows for continuous changes in coronary flow as well as five key parameters during acute infarction. These five include amount of marker available for release from the myocardium, relative rate of release of marker from the myocardium, rate of degradation of marker in the myocardium, plasma volume, and relative rate of loss of marker from the plasma. By varying these five together with infarct size, simulations using the model demonstrate a noisy relationship between infarct size and area under the plasma marker curve. Mathematically, this noise implies that there is not a one-to-one mapping from marker curve to infarct size, and we should expect no more than a statistical mapping that fails to resolve all the uncertainty. The results do suggest that early reperfusion should reduce, rather than increase the noise in this relationship.

Biomarkers↗
PubMed1990

Nonlinear dynamic analysis of temporally heterogeneous action potential characteristics.

Rate-dependent bifurcations and aperiodic changes in action potential duration and amplitude were observed in periodically stimulated cardiac Purkinje and ventricular muscle cells isolated from dogs with quinidine-induced ventricular fibrillation and ventricular tachycardia. The slope of the action potential duration restitution curve was higher in the quinidine intoxicated fibers than in normal untreated fibers. Aperiodicity and bifurcations in action potential duration (APD) could not be observed in normal untreated cardiac fibers. The data suggest that induction of reentrant ventricular fibrillation and ventricular tachycardia could be brought about not by fixed but rather by changing alterations in cellular electrical activity. Theory based on nonlinear dynamics seems to provide a quantitative basis for such an analysis. This could have important implications in the issue of sudden cardiac death, a major problem in cardiology.

Action Potentials↗
PubMed1999

HyFIS: adaptive neuro-fuzzy inference systems and their application to nonlinear dynamical systems.

This paper proposes an adaptive neuro-fuzzy system, HyFIS (Hybrid neural Fuzzy Inference System), for building and optimising fuzzy models. The proposed model introduces the learning power of neural networks to fuzzy logic systems and provides linguistic meaning to the connectionist architectures. Heuristic fuzzy logic rules and input-output fuzzy membership functions can be optimally tuned from training examples by a hybrid learning scheme comprised of two phases: rule generation phase from data; and rule tuning phase using error backpropagation learning scheme for a neural fuzzy system. To illustrate the performance and applicability of the proposed neuro-fuzzy hybrid model, extensive simulation studies of nonlinear complex dynamic systems are carried out. The proposed method can be applied to an on-line incremental adaptive learning for the prediction and control of nonlinear dynamical systems. Two benchmark case studies are used to demonstrate that the proposed HyFIS system is a superior neuro-fuzzy modelling technique.

Journal Article↗
PubMed1996

Analysis of stimulus-response chains using nonlinear dynamics.

Stimulus chains represent those series of coupled biochemical events through which receptor occupation is transformed into physiological or pharmacological responses. These events are commonly modeled as sets of sequential hyperbolic responses that may be treated mathematically as an iterative process. Methods used in the analysis of iterated map functions such as bifurcation analysis and graphical iteration are applied to the stimulus sequence to understand the dynamics of the process. Examples are given to illustrate determination of fixed points of the map as well as techniques for determining their stability. When present, a central repelling fixed point reveals the existence and location of a stimulus threshold, while the upper attracting fixed point determines the size of the terminal stimulus (S omega) in the signaling pathway. Estimates of S omega are used to develop equations for predicting changes in agonist EC50S at each point in the stimulus chain. Similarly, Lyapunov exponents are found to provide a link between changes in cell or tissue parameters and changes in the rate of stimulus amplification and agonist maximal response. These findings demonstrate that techniques of nonlinear dynamics when combined with biochemical studies of cellular signaling, provide useful new approaches for quantitative and qualitative analysis of drug action.

Dose-Response Relationship, Drug↗
PubMed2002

Clinical applicability of heart rate variability analysis by methods based on nonlinear dynamics.

Analysis of heart rate (HR) variability has become an important widely used method for assessing cardiac autonomic regulation. Conventionally, HR variability has been analyzed with time and frequency domain methods. Analysis of HR dynamics by methods based on nonlinear systems theory has opened a novel approach for studying the abnormalities in HR behavior. Recent studies have shown that these measures, particularly scaling analysis methods of HR dynamics, are altered among various patients populations with cardiovascular diseases, and they provide prognostic information. Altered long-term scaling properties of HR dynamics and more random short-term HR fluctuation has been observed, e.g., among patients with previous myocardial infarction, and these alterations have been shown to be associated with increased mortality rate. A relatively large body of data indicate that altered scaling properties of R-R intervals are physiologically deleterious. These findings support the notion that some nonlinear methods, such as scaling and complexity measures, give clinically valuable information for risk stratification among various patient populations. This article provides a review of our current knowledge of the usefulness of dynamical measures of HR fluctuation.

Autonomic Nervous System↗
PubMed1992

Control strategies for nonlinear dynamics of muscle relaxant anaesthesia.

Using modern nonlinear identification techniques, dose-response dynamics for two muscle relaxant trials have been obtained. A so-called NARMAX model has been found for Vecuronium applied to a dog, and Atracurium given to a human. With the relaxant dynamics structure thus obtained, the work proceeded to the control phase. Simple three-term PID controllers were first designed with their parameters being optimised, off-line, using the Simplex method. The non-adaptive nature of this class of controllers makes their robustness open to question when the system parameters for which they have been optimised change. Hence, adaptive controllers in the form of linear and nonlinear generalised minimum variance self-tuners, generalised predictive control and nonlinear k-step ahead predictive controllers are also considered. All of these latter control approaches are shown to be satisfactory, in terms of transient and steady-state performance.

Algorithms↗