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Laser action on a single spatially chaotic wave function is obtained as a final stable state in a nonlinear dynamical model of a stadium shaped resonant cavity with an active medium. The stable single-mode lasing state corresponds to a particular metastable resonance of the cavity which wins a competition among multiple modes with positive net linear gain and has a distinct lasing threshold.
Locking of two resonance modes of different symmetry classes and different frequencies in 2D resonant microcavity lasers is investigated by using a nonlinear dynamical model. The patterns of stationary lasing states and far fields are asymmetric in spite of the symmetric shape of the resonant microcavity. The corresponding phenomenon is actually observed in the experiment of a 2D semiconductor microcavity laser diode.
We present the first study of parametric resonance in quantum field theory from a complete next-to-leading order calculation in a 1/N expansion of the two-particle irreducible effective action, which includes scattering and memory effects. We present a complete numerical solution for an O(N)-symmetric scalar theory and provide an approximate analytic description of the nonlinear dynamics in the entire amplification range. We find that the classical resonant amplification at early times is followed by a collective amplification regime with explosive particle production in a broad momentum range, which is not accessible in a leading-order calculation.
We analyze the effects of a random magnetic potential in a microfabricated waveguide for ultracold atoms. We find that the shape and position fluctuations of a current carrying wire induce a strong Gaussian correlated random potential with a length scale set by the atom-wire separation. The theory is used to explain quantitatively the observed fragmentation of the Bose-Einstein condensates in atomic waveguides. Furthermore, we show that nonlinear dynamics can be used to provide important insights into the nature of the strongly fragmented condensates. We argue that a quantum phase transition from the superfluid to the insulating Bose glass phase may be reached and detected under the realistic experimental conditions.
Local bifurcation control is a topic of fundamental importance in the field of nonlinear dynamical systems. We discuss an original example within the context of storage-ring free-electron laser physics by presenting a new model that enables analytical insight into the system dynamics. The transition between the stable and the unstable regimes, depending on the temporal overlapping between the light stored in the optical cavity and the electrons circulating into the ring, is found to be a Hopf bifurcation. A feedback procedure is implemented and shown to provide an effective stabilization of the unstable steady state.
Colored conical emission was observed experimentally in a thick beta-barium borate crystal as a result of spatiotemporal modulational instability. In the presence of both dispersion and diffraction, colored conical emission showed specific features that were characteristic of the nonlinear dynamics of the strongly coupled fundamental and harmonic fields. Experimental observation directly demonstrated that beam angular spectra were substantially modified as a result of exponential growth of perturbations by means of parametric wave mixing. Seeded amplification of colored conical emission was demonstrated to support ultrabroadband up-conversion.
We apply nonlinear dynamical system techniques to recurrent neural networks. In particular, we numerically analyze the dynamical system characteristics of the online learning process. By introducing the notion of inaccessibility, we show that the learning process is well characterized by strong nonhyperbolicity and inaccessibility, which is a greater uncertainty than chaotic unpredictability. These results are clearly contrasted with a gradient descent dynamics, or ordinary chaos.
We consider the charge shuttle proposed by Gorelik et al. driven by a time-dependent voltage bias. In the case of asymmetric setup, the system behaves as a rectifier. For pure ac drive, the rectified current shows a rather rich frequency dependent response characterized by frequency locking at fractional values of the external frequency. Because of the nonlinear dynamics of the shuttle, rectification is present also for very low frequencies. These effects could be useful to unveil the internal dynamics of nanomechanical devices.
Collective field theory for the Calogero model represents particles with fractional statistics in terms of hydrodynamic modes--density and velocity fields. We show that the quantum hydrodynamics of this model can be written as a single evolution equation on a real holomorphic Bose field--the quantum integrable Benjamin-Ono equation. It renders tools of integrable systems to studies of nonlinear dynamics of 1D quantum liquids.
Turbulent flows are notoriously difficult to describe and understand based on first principles. One reason is that turbulence contains highly intermittent bursts of vorticity and strain rate with highly non-Gaussian statistics. Quantitatively, intermittency is manifested in highly elongated tails in the probability density functions of the velocity increments between pairs of points. A long-standing open issue has been to predict the origins of intermittency and non-Gaussian statistics from the Navier-Stokes equations. Here we derive, from the Navier-Stokes equations, a simple nonlinear dynamical system for the Lagrangian evolution of longitudinal and transverse velocity increments. From this system we are able to show that the ubiquitous non-Gaussian tails in turbulence have their origin in the inherent self-amplification of longitudinal velocity increments, and cross amplification of the transverse velocity increments.
The generation and nonlinear dynamics of multidimensional optical dissipative solitonic pulses are examined. The variational method is extended to complex dissipative systems, in order to obtain steady state solutions of the (D + 1)-dimensional complex cubic-quintic Ginzburg-Landau equation (D = 1, 2, 3). A stability criterion is established fixing a domain of dissipative parameters for stable steady state solutions. Following numerical simulations, evolution of any input pulse from this domain leads to stable dissipative solitons.
Electrosprays have diverse applications including protein analysis, electrospinning, and nanoencapsulation for drug delivery. We show that a variety of electrospray regimes exhibit fundamental analogy with the nonlinear dynamics of a dripping faucet. The applied voltage in electrosprays results in additional period doublings and temporal order-chaos-order transitions. Attractors in the return maps show logarithmic self-similarity in time, suggesting self-similar capillary waves on the meniscus. The bifurcations in ejection time can be explained by phase variations between capillary waves and pinch-off conditions and by ejection mode changes due to contact angle variations.
The open morphogenesis of plants requires coordination of patterning by intercellular signals. The tobacco (Nicotiana tabacum cv Virginia Bright Italia) cell line VBI-0 provides a simple model system to study the role of intercellular communication in patterning. In this cell line, singular cells divide axially to produce linear cell files of distinct polarity. The trigger for this axial division is exogenous auxin. When frequency distributions of files are constructed over the number of cells per file during the exponential phase of the culture, even numbers are found to be frequent, whereas files consisting of uneven numbers of cells are rare. We can simulate these distributions with a mathematical model derived from nonlinear dynamics, which describes a chain of cell-division oscillators where elementary oscillators are coupled unidirectionally and where the number of oscillators is not conserved. The model predicts several nonintuitive properties of our experimental system. For instance, files consisting of six cells are more frequent than expected from a strictly binary division system. More centrally, the model predicts a polar transport of the coordinating signal. We therefore tested the patterns obtained after treatment with 1-N-naphthylphthalamic acid, an inhibitor of auxin efflux carriers. Using low concentrations of 1-N-naphthylphthalamic acid that leave cell division and axiality of division unaltered, we observe that the frequencies of files with even and uneven cell numbers are equalized. Our findings are discussed in the context of auxin transport as synchronizing signal in cell patterning.
The projected crystal potential is reconstructed from a nonperiodic high-resolution transmission electron microscopy exit wave function using a maximum-likelihood refinement algorithm. The convergence and the accuracy of the algorithm are investigated using simulated exit wave functions of SiGe, a Shockley partial dislocation in Ge and an area containing randomly distributed Ge columns at different specimen thicknesses. The performance of two different start models for the projected crystal potential is investigated: the weak-phase-object model and a model based on the electron-channelling approximation. The reconstruction is successful even under the strongly nonlinear dynamical diffraction conditions at larger specimen thicknesses, relevant for high-resolution work, and on specimen areas large enough to cover defects in crystalline materials.
This paper presents a phasic excitation-activation (PEXA) model of the process of motoneuron excitation and the resultant activation and force development of a motor unit. The model input is an amount of depolarizing current (as when injected with an intracellular electrode) and the model output is muscle force. The model includes dynamics and nonlinearities similar to phenomena discovered experimentally by others: the firing rate response of motoneurons to steps of depolarizing current and the "catch-like enhancement" of force produced by overlapping motor neuron action potentials. The parameter values used in this model are derived from experimentally measured data and expressed in physical units, and model predictions extend to published data beyond those used in generating the model parameter values.
The ability of the cat's ankle joint to track various input signals when controlled by electrically elicited motor unit recruitment, firing rate and antagonist muscle coactivation was examined. Pseudo-random, sinusoidal and staircase signals were used to control the soleus and tibialis anterior muscles isometrically and with a 250-g pendulum. Tracking was evaluated through cross correlation for pseudo-random and sinusoidal signals, and by rise time and steady-state error in step signals. Better tracking was obtained in isometric conditions than in load-moving conditions. Pseudo-random signals resulted in 250-ms delay between input and isometric torque output. For load-moving conditions, 340-ms and 400-ms delay in torque and angle were obtained. For sinusoids, delays decreased from 240 ms at 0.5 Hz, to 140 ms at 2 Hz in isometric conditions. Time delays for angle were between 300 and 400 ms, decreasing as frequency increased. Poor cross correlation was found for torque in load-moving conditions, because of pendulum nonlinear dynamics. Step size was not uniform in staircase trials, with steady-state errors between 9% and 39%, and rise times between 200 and 1000 ms. It is concluded that open-loop joint control results in poor tracking, presumably because it is devoid of feedback mechanisms.
Since its inception 30 years ago, AEEG has continued to evolve--from four-channel tape recorders to 32-channel digital recorders with sophisticated automatic spike and seizure detection algorithms. AEEG remains an important tool in epilepsy evaluation. In the near future, smaller, faster, and more sophisticated AEEGs will be developed. Seizure detection/anticipation systems will allow the wearer to be forewarned of a seizure so that appropriate safety measures can be taken. With further refinement in our understanding of nonlinear dynamic analysis to define the pre-ictal state, AEEG will be coupled with an accurate seizure anticipation device in a closed-loop system, providing a time window during which therapeutic intervention can occur, to prevent a seizure. The therapeutic intervention will most likely involve vagus nerve or deep brain stimulation. An alternative is that the patient may learn to recognize early symptoms of the pre-ictal state and use behavioral biofeedback interventions to avoid a clinical seizure. In order to achieve convenient ambulatory recording and seizure detection that could realistically improve the lives of patients with refractory epilepsy, the process of miniaturization of such a device to a convenient size must be accomplished. One of the aspects of epilepsy that patients find most frustrating, and that most limits activities, is the vulnerability to sudden unexpected incapacitation due to the occurrence of a seizure. With miniaturization of AEEG and seizure anticipation technology, and advancements in our ability to identify the transition from pre-ictal to ictal state, there is realistic hope that patients with refractory epilepsy may gain control over their seizures and enjoy significantly improved quality of life.
Nonlinear dynamical analysis was performed on the phrenic neurogram before and after vagotomy in order to study the influence of the vagus nerve on the complexity of the phrenic neurogram in piglets in three age groups: 3-7 days (n = 7); 11-19 days (n = 6); and 29-34 days (n = 8). The phrenic neurogram, generated by the respiratory neural networks in the medulla, projects on the diaphragm muscles and initiate the respiratory movement. On the other hand, the vagus nerves carry the information from mechanoreceptors, located at the lower airway and lungs, to the medulla. The data was recorded during normal breathing (eupnea) before and after vagotomy while piglets were ventilated with 40% O2 in N2 and analyzed using the approximate entropy (ApEn) method. The mean values of the approximate entropy before and after vagotomy during the first 7 days of the postnatal age were 1.32 +/- 0.1 (standard deviation) and 1.34 +/- 0.07, respectively. These values before and after vagotomy during the 11-19 days age group were 1.15 +/- 0.09 and 1.12 +/- 0.05, respectively. For the 29-34 days age group, they were 1.14 +/- 0.05 before vagotomy and 1.19 +/- 0.08 after vagotomy. These differences in the ApEn (complexity) values of the phrenic neurogram before and after vagotomy are not statistically different at each age group. However, the mean mean approximate entropy (complexity) values between the 3-7 days age group and the other two groups were significantly different both before and after vagotomy (p < 0.05) using an analysis off variance test. These results suggest that the vagus nerve may not be mature during early maturation in piglets.