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PubMed2006

Hydrodynamic lubrication in nanoscale bearings under high shear velocity.

The setting up process in a nanoscale bearing has been modeled by molecular dynamics simulation. Contrary to the prediction from the classical Reynolds' theory, simulation results show that the load capacity of the nanoscale bearing does not increase monotonically with the operation speed. This is attributed to the change of the local shear rate, which will decrease with the shear velocity of the bearing as the shear velocity exceeds a critical value, i.e., the local shear rate has an upper limit. A simple nonlinear dynamic model indicates that the momentum exchange between the liquid and the solid wall is reduced with the shear velocity when the shear velocity is above a critical value. The weak momentum exchange results in a decrease of the local shear rate, which in turn causes a sharp increase of the slip length.

Journal Article↗

PubMedDate not supplied

Laminar differences in the spatiotemporal structure of simple cell receptive fields in cat area 17.

Previous studies of cat visual cortex have shown that the spatiotemporal (S-T) structure of simple cell receptive fields correlates with direction selectivity. However, great heterogeneity exists in the relationship and this has implications for models. Here we report a laminar basis for some of the heterogeneity. S-T structure and direction selectivity were measured in 101 cells using stationary counterphasing and drifting gratings, respectively. Two procedures were used to assess S-T structure and its relation to direction selectivity. In the first, the S-T orientations of receptive fields were quantified by fitting response temporal phase versus stimulus spatial phase data. In the second procedure, conventional linear predictions of direction selectivity were computed from the amplitudes and phases of responses to stationary gratings. Extracellular recording locations were reconstructed histologically. Among direction-selective cells, S-T orientation was greatest in layer 4B and it correlated well (r = 0.76) with direction selectivity. In layer 6, S-T orientation was uniformly low, overlapping little with layer 4B, and it was not correlated with directional tuning. Layer 4A was intermediate in S-T orientation and its relation (r = 0.46) to direction selectivity. The same laminar patterns were observed using conventional linear predictions. The patterns do not reflect laminar differences in direction selectivity since the layers were equivalent in directional tuning. We also evaluated a model of linear spatiotemporal summation followed by a static nonlinear amplification (exponent model) to account for direction selectivity. The values of the exponents were estimated from differences between linearly predicted and actual amplitude modulations to counterphasing gratings. Comparing these exponents with another exponent--that required to obtain perfect matches between linearly predicted and measured directional tuning--indicates that an exponent model largely accounts for direction selectivity in most cells in layer 4, particularly layer 4B, but not in layer 6. Dynamic nonlinearities seem essential for cells in layer 6. We suggest that these laminar differences may partly reflect the differential involvement of geniculocortical and intracortical mechanisms.

Animals↗

PubMed2003

Epileptic seizure prediction and control.

Epileptic seizures are manifestations of epilepsy, a serious brain dynamical disorder second only to strokes. Of the world's approximately 50 million people with epilepsy, fully 1/3 have seizures that are not controlled by anti-convulsant medication. The field of seizure prediction, in which engineering technologies are used to decode brain signals and search for precursors of impending epileptic seizures, holds great promise to elucidate the dynamical mechanisms underlying the disorder, as well as to enable implantable devices to intervene in time to treat epilepsy. There is currently an explosion of interest in this field in academic centers and medical industry with clinical trials underway to test potential prediction and intervention methodology and devices for Food and Drug Administration (FDA) approval. This invited paper presents an overview of the application of signal processing methodologies based upon the theory of nonlinear dynamics to the problem of seizure prediction. Broader application of these developments to a variety of systems requiring monitoring, forecasting and control is a natural outgrowth of this field.

Algorithms↗

PubMed2000

Spontaneous speech recognition using a statistical coarticulatory model for the vocal-tract-resonance dynamics.

A statistical coarticulatory model is presented for spontaneous speech recognition, where knowledge of the dynamic, target-directed behavior in the vocal tract resonance is incorporated into the model design, training, and in likelihood computation. The principal advantage of the new model over the conventional HMM is the use of a compact, internal structure that parsimoniously represents long-span context dependence in the observable domain of speech acoustics without using additional, context-dependent model parameters. The new model is formulated mathematically as a constrained, nonstationary, and nonlinear dynamic system, for which a version of the generalized EM algorithm is developed and implemented for automatically learning the compact set of model parameters. A series of experiments for speech recognition and model synthesis using spontaneous speech data from the Switchboard corpus are reported. The promise of the new model is demonstrated by showing its consistently superior performance over a state-of-the-art benchmark HMM system under controlled experimental conditions. Experiments on model synthesis and analysis shed insight into the mechanism underlying such superiority in terms of the target-directed behavior and of the long-span context-dependence property, both inherent in the designed structure of the new dynamic model of speech.

Algorithms↗

PubMed2004

Spatial solitons in chiral media.

We study theoretically the nonlinear propagation of a narrow optical wave packet through a cholesteric liquid crystal. We derive the equations governing the weakly nonlinear dynamics of an optical field by taking into account the coupling with the liquid crystal. We constructed the solution as the superposition of four narrow wave packets centered around the linear eigenmodes of the helical structure whose corresponding envelopes A are slowly varying functions of their arguments. We found a system of four coupled equations to describe the resulting vector wave packet which has some integration constants and that under special conditions reduces to the nonlinear Schrödinger equation with space-dependent coefficients. We solved this equation both, using a variational approach and performing numerical calculations. We calculated analytically the soliton spatial scales, the transported power, the nonlinear refraction index, and its wavelength dependence, showing that this has its maxima at the edges of the reflection band. We also exhibit the existence of some other exact but non-self-focused solutions.

Journal Article↗

PubMed2006

Phase control of intermittency in dynamical systems.

We present a nonfeedback method to tame or enhance crisis-induced intermittency in dynamical systems. By adding a small harmonic perturbation to a parameter of the system, the intermittent behavior can be suppressed or enhanced depending on the value of the phase difference between the main driving and the perturbation. The validity of the method is shown both in the model and in an experiment with a CO2 laser. An analysis of this scheme applied to the quadratic map near crisis illustrates the role of phase control in nonlinear dynamical systems.

Journal Article↗

PubMed1993

Pattern switching in human multilimb coordination dynamics.

A relative phase model of four coupled oscillators is used to interpret experiments on the coordination between rhythmically moving human limbs. The pairwise coupling functions in the model are motivated by experiments on two-limb coordination. Stable patterns of coordination between the limbs are represented by fixed points in relative phase coordinates. Four invariant circles exist in the model, each containing two patterns of coordination seen experimentally. The direction of switches between two four-limb patterns on the same circle can be understood in terms of two-limb coordination. Transitions between patterns in the human four-limb system are theoretically interpreted as bifurcations in a nonlinear dynamical system.

Animals↗

PubMed2006

A finite element model for investigating effects of aerial architecture on tree oscillations.

A finite element model was developed to study the influence of aerial architecture on the structural dynamics of trees. The model combines a complete description of the axes of the aerial architecture of the plant with numerical techniques suitable for dynamic nonlinear analyses. Trees were modeled on the basis of morphological measurements that were previously made on three 4-year-old Pinus pinaster Ait. saplings originating from even-aged stands. Calculated and measured oscillations were compared to evaluate model behavior. The computations allowed the characteristics of the fundamental mode of vibration to be estimated with satisfactory accuracy. Inclusion of a topological description of the aerial system in a mechanical model provided insight into the effect of tree architecture on tree dynamic behavior. Simplifications of the branching pattern in the model led to overestimations of the natural swaying frequency of saplings by 10 to 20%. Inadequate values of stem and root anchorage stiffness resulted in errors of 10 to 20%. Modeling results indicated that aerodynamic drag of needles is responsible for 80% of the damping in the studied trees. Additionally, damping of stem movement is reduced by one half when branch oscillations are not considered. It appears that the efficiency of the dissipative mechanisms depends directly on crown topology.

Biomechanical Phenomena↗

PubMed1992

Dual stable point model of muscle activation and deactivation.

Two dynamic models of muscle activation and deactivation based on the concepts of ion transport, reaction rates, and muscle mechanics are proposed. Storage release and uptake of calcium by the sarcoplasmic reticulum, and a two-step chemical reaction of calcium and troponin are included in the first model. This is a concise version of the complex chemical reactions of muscle activation and deactivation in sarcoplasm. The second model is similar to the first, but calcium-troponin reactions are simplified into two nonlinear rates functions. Due to these nonlinear dynamics, the second model can explain the catch-like enhancement of isometric force response. Simulation results which match experimental data are shown. Also, two new phenomena which need further experiment to verify are predicted by the second model.

Animals↗

PubMed1997

Directional control of planar human arm movement.

We examined the patterns of joint kinematics and torques in two kinds of sagittal plane reaching movements. One consisted of movements from a fixed initial position with the arm partially outstretched, to different targets, equidistant from the initial position and located according to the hours of a clock. The other series added movements from different initial positions and directions and >40-80 cm distances. Dynamic muscle torque was calculated by inverse dynamic equations with the gravitational components removed. In making movements in almost every direction, the dynamic components of the muscle torques at both the elbow and shoulder were related almost linearly to each other. Both were similarly shaped, biphasic, almost synchronous and symmetrical pulses. These findings are consistent with our previously reported observations, which we termed a linear synergy. The relative scaling of the two joint torques changes continuously and regularly with movement direction. This was confirmed by calculating a vector defined by the dynamic components of the shoulder and elbow torques. The vector rotates smoothly about an ellipse in intrinsic, joint torque space as the direction of hand motion rotates about a circle in extrinsic Cartesian space. This confirms a second implication of linear synergy that the scaling constant between the linearly related joint torques is directionally dependent. Multiple linear regression showed that the torque at each joint scales as a simple linear function of the angular displacement at both joints, in spite of the complex nonlinear dynamics of multijoint movement. The coefficients of this function are independent of the initial arm position and movement distance and are the same for all subjects. This is an unanticipated finding. We discuss these observations in terms of the hypothesis that voluntary, multiple degrees of freedom, rapid reaching movements may use rule-based, feed-forward control of dynamic joint torque. Rule-based control of joint torque with separate dynamic and static controllers is an alternative to models such as those based on the equilibrium point hypotheses that rely on a positionally based controller to produce both dynamic and static torque components. It is also an alternative to feed-forward models that directly solve the problems of inverse dynamics. Our experimental findings are not necessarily incompatible with any of the alternative models, but they describe new, additional findings for which we need to account. The rules are chosen by the nervous system according to features of the kinematic task to couple muscle contraction at the shoulder and elbow in a linear synergy. Speed and load control preserves the relative magnitudes of the dynamic torques while directional control is accomplished by modulating them in a differential manner. This control system operates in parallel with a positional control system that solves the problems of postural stability.

Arm↗

PubMed2002

Quantitative evaluation of proteins in one- and two-dimensional polyacrylamide gels using a fluorescent stain.

The characteristics of protein detection and quantitation with SYPRO Ruby protein gel stain in one- and two-dimensional polyacrylamide gels were evaluated. Sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) analyses of three different purified recombinant proteins showed that the limits of detection were comparable to the limits of detection with ammoniacal silver staining and were protein-specific, ranging from 0.5 to 5 ng. The linearity of the relationship between protein level and SYPRO Ruby staining intensity also depended on the individual protein, with observed linear dynamic ranges of 200-, 500-, and, 1000-fold for proteins analyzed by SDS-PAGE. SYPRO Ruby protein gel stain was also evaluated in two-dimensional electrophoretic (2-DE) analysis of Escherichia coli proteins. The experiment involved analysis of replicates of the same sample as well as dilution of the sample from 0.5 to 50 nug total protein across gels. In addition to validating the 2-DE system itself, the experiment was used to evaluate three different image analysis programs: Z3 (Compugen), Progenesis (Nonlinear Dynamics), and PDQuest (Bio-Rad). In each program, we analyzed the 2-DE images with respect to sensitivity and reproducibility of overall protein spot detection, as well as linearity of response for 20 representative proteins of different molecular weights and pI. Across all three programs, coefficients of variation (CV) in total number of spots detected among replicate gels ranged from 4 to 11%. For the 20 representative proteins, spot quantitation was also comparable with CVs for gel-to-gel reproducibility ranging from 3 to 33%. Using Progenesis and PDQuest, a 1000-fold linear dynamic range of SYPRO Ruby was demonstrated with a single known protein. These two programs were more suitable than Z3 for examining individual protein spot quantity across a series of gels and gave comparable results.

Bacterial Proteins↗

PubMed2006

Dynamics and thermodynamics of axisymmetric flows: Theory.

We develop variational principles to study the structure and the stability of equilibrium states of axisymmetric flows. We show that the axisymmetric Euler equations for inviscid flows admit an infinite number of steady state solutions. We find their general form and provide analytical solutions in some special cases. The system can be trapped in one of these steady states as a result of an inviscid violent relaxation. We show that the stable steady states maximize a (nonuniversal) function while conserving energy, helicity, circulation, and angular momentum (robust constraints). This can be viewed as a form of generalized selective decay principle. We derive relaxation equations which can be used as numerical algorithm to construct nonlinearly dynamically stable stationary solutions of axisymmetric flows. We also develop a thermodynamical approach to predict the equilibrium state at some fixed coarse-grained scale. We show that the resulting distribution can be divided in two parts: one universal coming from the conservation of robust invariants and one non-universal determined by the initial conditions through the fragile invariants (for freely evolving systems) or by a prior distribution encoding nonideal effects such as viscosity, small-scale forcing, and dissipation (for forced systems). Finally, we derive a parametrization of inviscid mixing to describe the dynamics of the system at the coarse-grained scale. A conceptual interest of this axisymmetric model is to be intermediate between two-dimensional (2D) and 3D turbulence.

Journal Article↗

PubMed1985

Dynamic structures of the fructose 6-phosphate/fructose 1,6-bisphosphate cycle in a reconstituted enzyme system.

The dynamics of the fructose 6-phosphate/fructose 1,6-bisphosphate cycle was investigated in an open and homogeneous system reconstituted from purified enzymes. In addition to phosphofructokinase and fructose 1,6-bisphosphatase, pyruvate kinase, adenylate kinase and glucose 6-phosphate isomerases are involved. The time evolution of the metabolite concentrations is governed by a set of differential equations which take into account flow processes and enzymic conversions of metabolites. Depending on the experimental parameters stable attractors, multiple states and sustained oscillations occur. The main source of the nonlinear dynamics is the reciprocal effect of AMP on the activities of phosphofructokinase and fructose 1,6-bisphosphatase. States are characterized by the net flow rates of substrates and by the rate of futile substrate cycling. For efficient glycolytic states high ratios between the influx rates of fructose 6-phosphate and fructose 1,6-bisphosphate and between the maximum activities of phosphofructokinase and fructose 1,6-bisphosphatase must be maintained, while for an efficient gluconeogenic mode the reverse must hold. Fructose 2,6-bisphosphate exerts reciprocal effects on the activities of phosphofructokinase and fructose 1,6-bisphosphatase. In dependence on the experimental conditions fructose 2,6-bisphosphate was found either to generate or to extinguish oscillations.

Animals↗

PubMed2004

Dynamics of electron holes in an electron-oxygen-ion plasma.

The dynamics of electron holes (EHs) in an electron-oxygen-ion plasma is studied by means of Vlasov simulations. It is found that EHs are attracted by ion density maxima but repelled by ion density minima. Standing EHs repel ions owing to the positive EH potential, creating an ion density cavity which ejects the EH, which propagates away from the cavity with a constant speed. On the other hand, propagating EHs can be trapped at ion density maxima. The results of our simulations will help in understanding the nonlinear dynamics of EHs in space and laboratory plasmas.

Journal Article↗

PubMed2003

Collective atomic motion in an optical lattice formed inside a high finesse cavity.

We report on collective nonlinear dynamics in an optical lattice formed inside a high finesse ring cavity in a so far unexplored regime, where the light shift per photon times the number of trapped atoms exceeds the cavity resonance linewidth. We observe bistability and self-induced squeezing oscillations resulting from the retroaction of the atoms upon the optical potential wells. We can well understand most of our observations within a simplified model assuming adiabaticity of the atomic motion. Nonadiabatic aspects of the atomic motion are reproduced by solving the complete system of coupled nonlinear equations of motion.

Journal Article↗

PubMed1999

Decay of unstable equilibrium and nonequilibrium states with inverse probability current taken into account.

We study the causes of noise delayed decay of unstable states in nonlinear dynamic systems within the framework of the overdamped Brownian motion model. For the analysis, we use the exact expressions for the decay times of unstable states, which take into account the inverse probability current in contrast to the well-known mean first passage time method. These expressions are valid for any intensity of fluctuations and for arbitrary potential profiles. The effect of delay is shown to arise under the decay of unstable nonequilibrium states due to the action of two different mechanisms. These mechanisms are caused by the inverse probability current and by the nonlinearity of potential describing an unstable state.

Journal Article↗

PubMed2004

Experimental observation of delay-induced radio frequency chaos in a transmission line oscillator.

We report an experimental study of fast chaotic dynamics in a delay dynamical system. The system is an electronic device consisting of a length of coaxial cable terminated on one end with a diode and on the other with a negative resistor. When the negative resistance is large, the system evolves to a steady state. As the negative resistance is decreased, a Hopf bifurcation occurs. By varying the length of the transmission line we observe Hopf frequencies from 7-53 MHz. With the transmission line length fixed, we observe a period doubling route to chaos as the negative resistance is further reduced providing the first experimental confirmation of an existing theoretical model for nonlinear dynamics in transmission line oscillators [Corti et al., IEEE Trans. Circ. Syst., I: Fundam. Theory Appl. 41, 730 (1994)]. However, other experimental results indicate limitations to this model including an inability to predict the Hopf frequency or to produce realistic continuous wave forms. We extend the model to include finite bandwidth effects present in a real negative resistor. The resulting model is a neutral delay differential equation that provides better agreement with experimental results.

Journal Article↗

PubMed2000

Optimization of rhythmic behaviors by modulation of the neuromuscular transform.

We conclude our study of the properties and the functional role of the neuromuscular transform (NMT). The NMT is an input-output relation that formalizes the processes by which patterns of motor neuron firing are transformed to muscle contractions. Because the NMT acts as a dynamic, nonlinear, and modifiable filter, the transformation is complex. In the two preceding papers we developed a framework for analysis of the NMT and identified with it principles by which the NMT transforms different firing patterns to contractions. We then saw that, with fixed properties, the NMT significantly constrains the production of functional behavior. Many desirable behaviors are not possible with any firing pattern. Here we examine, theoretically as well as experimentally in the accessory radula closer (ARC) neuromuscular system of Aplysia, how this constraint is alleviated by making the properties of the NMT variable by neuromuscular plasticity and modulation. These processes dynamically tune the properties of the NMT to match the desired behavior, expanding the range of behaviors that can be produced. For specific illustration, we continue to focus on the relation between the speed of the NMT and the speed of cyclical, rhythmic behavior. Our analytic framework emphasizes the functional distinction between intrinsic plasticity or modulation of the NMT, dependent, like the contraction itself, on the motor neuron firing pattern, and extrinsic modulation, independent of it. The former is well suited to automatically optimizing the performance of a single behavior; the latter, to multiplying contraction shapes for multiple behaviors. In any case, to alleviate the constraint of the NMT, the plasticity and modulation must be peripheral. Such processes are likely to play a critical role wherever the nervous system must command, through the constraint of the NMT, a broad range of functional behaviors.

Animals↗