Jiang, Jin-Wu; Park, Harold S; Rabczuk, Timon
2012-11-30
We perform classical molecular dynamics simulations to investigate the enhancement of the mass sensitivity and resonant frequency of graphene nanomechanical resonators that is achieved by driving them into the nonlinear oscillation regime. The mass sensitivity as measured by the resonant frequency shift is found to triple if the actuation energy is about 2.5 times the initial kinetic energy of the nanoresonator. The mechanism underlying the enhanced mass sensitivity is found to be the effective strain that is induced in the nanoresonator due to the nonlinear oscillations, where we obtain an analytic relationship between the induced effective strain and the actuation energy that is applied to the graphene nanoresonator. An important implication of this work is that there is no need for experimentalists to apply tensile strain to the resonators before actuation in order to enhance the mass sensitivity. Instead, enhanced mass sensitivity can be obtained by the far simpler technique of actuating nonlinear oscillations of an existing graphene nanoresonator.
Burioni, Raffaella; di Santo, Serena; di Volo, Matteo; Vezzani, Alessandro
2014-10-01
Self-organized quasiperiodicity is one of the most puzzling dynamical phases observed in systems of nonlinear coupled oscillators. The single dynamical units are not locked to the periodic mean field they produce, but they still feature a coherent behavior, through an unexplained complex form of correlation. We consider a class of leaky integrate-and-fire oscillators on random sparse and massive networks with dynamical synapses, featuring self-organized quasiperiodicity, and we show how complex collective oscillations arise from constructive interference of microscopic dynamics. In particular, we find a simple quantitative relationship between two relevant microscopic dynamical time scales and the macroscopic time scale of the global signal. We show that the proposed relation is a general property of collective oscillations, common to all the partially synchronous dynamical phases analyzed. We argue that an analogous mechanism could be at the origin of similar network dynamics.
NASA Astrophysics Data System (ADS)
Hagedorn, P.
The mathematical pendulum is used to provide a survey of free and forced oscillations in damped and undamped systems. This simple model is employed to present illustrations for and comparisons between the various approximation schemes. A summary of the Liapunov stability theory is provided. The first and the second method of Liapunov are explained for autonomous as well as for nonautonomous systems. Here, a basic familiarity with the theory of linear oscillations is assumed. La Salle's theorem about the stability of invariant domains is explained in terms of illustrative examples. Self-excited oscillations are examined, taking into account such oscillations in mechanical and electrical systems, analytical approximation methods for the computation of self-excited oscillations, analytical criteria for the existence of limit cycles, forced oscillations in self-excited systems, and self-excited oscillations in systems with several degrees of freedom. Attention is given to Hamiltonian systems and an introduction to the theory of optimal control is provided.
Nonlinear Neural Network Oscillator.
A nonlinear oscillator (10) includes a neural network (12) having at least one output (12a) for outputting a one dimensional vector. The neural ... neural network and the input of the input layer for modifying a magnitude and/or a polarity of the one dimensional output vector prior to the sample of...first or a second direction. Connection weights of the neural network are trained on a deterministic sequence of data from a chaotic source or may be a
Nonlinear Oscillators in Space Physics
NASA Technical Reports Server (NTRS)
Lester,Daniel; Thronson, Harley
2011-01-01
We discuss dynamical systems that produce an oscillation without an external time dependent source. Numerical results are presented for nonlinear oscillators in the Em1h's atmosphere, foremost the quasi-biennial oscillation (QBOl. These fluid dynamical oscillators, like the solar dynamo, have in common that one of the variables in a governing equation is strongly nonlinear and that the nonlinearity, to first order, has particular form. of 3rd or odd power. It is shown that this form of nonlinearity can produce the fundamental li'equency of the internal oscillation. which has a period that is favored by the dynamical condition of the fluid. The fundamental frequency maintains the oscillation, with no energy input to the system at that particular frequency. Nonlinearities of 2nd or even power could not maintain the oscillation.
NASA Astrophysics Data System (ADS)
Chowdhury, A.; Yeo, I.; Tsvirkun, V.; Raineri, F.; Beaudoin, G.; Sagnes, I.; Raj, R.; Robert-Philip, I.; Braive, R.
2016-04-01
We investigate the non-linear mechanical dynamics of a nano-optomechanical mirror formed by a suspended membrane pierced by a photonic crystal. By applying to the mirror a periodic electrostatic force induced by interdigitated electrodes integrated below the membrane, we evidence superharmonic resonances of our nano-electro-mechanical system; the constant phase shift of the oscillator across the resonance tongues is observed on the onset of principal harmonic and subharmonic excitation regimes.
Nonlinear nanomechanical oscillators for ultrasensitive inertial detection
Datskos, Panagiotis George; Lavrik, Nickolay V
2013-08-13
A system for ultrasensitive mass and/or force detection of this invention includes a mechanical oscillator driven to oscillate in a nonlinear regime. The mechanical oscillator includes a piezoelectric base with at least one cantilever resonator etched into the piezoelectric base. The cantilever resonator is preferably a nonlinear resonator which is driven to oscillate with a frequency and an amplitude. The system of this invention detects an amplitude collapse of the cantilever resonator at a bifurcation frequency as the cantilever resonator stimulated over a frequency range. As mass and/or force is introduced to the cantilever resonator, the bifurcation frequency shifts along a frequency axis in proportion to the added mass.
Zweig, George
2016-05-01
An earlier paper characterizing the linear mechanical response of the organ of Corti [J. Acoust. Soc. Am. 138, 1102-1121 (2015)] is extended to the nonlinear domain. Assuming the existence of nonlinear oscillators nonlocally coupled through the pressure they help create, the oscillator equations are derived and examined when the stimuli are modulated tones and clicks. The nonlinearities are constrained by the requirements of oscillator stability and the invariance of zero crossings in the click response to changes in click amplitude. The nonlinear oscillator equations for tones are solved in terms of the fluid pressure that drives them, and its time derivative, presumably a proxy for forces created by outer hair cells. The pressure equation is reduced to quadrature, the integrand depending on the oscillators' responses. The resulting nonlocally coupled nonlinear equations for the pressure, and oscillator amplitudes and phases, are solved numerically in terms of the fluid pressure at the stapes. Methods for determining the nonlinear damping directly from measurements are described. Once the oscillators have been characterized from their tone and click responses, the mechanical response of the cochlea to natural sounds may be computed numerically. Signal processing inspired by cochlear mechanics opens up a new area of nonlocal nonlinear time-frequency analysis.
Frequency stabilization in nonlinear micromechanical oscillators
NASA Astrophysics Data System (ADS)
Antonio, Dario; Zanette, Damián H.; López, Daniel
2012-05-01
Mechanical oscillators are present in almost every electronic device. They mainly consist of a resonating element providing an oscillating output with a specific frequency. Their ability to maintain a determined frequency in a specified period of time is the most important parameter limiting their implementation. Historically, quartz crystals have almost exclusively been used as the resonating element, but micromechanical resonators are increasingly being considered to replace them. These resonators are easier to miniaturize and allow for monolithic integration with electronics. However, as their dimensions shrink to the microscale, most mechanical resonators exhibit nonlinearities that considerably degrade the frequency stability of the oscillator. Here we demonstrate that, by coupling two different vibrational modes through an internal resonance, it is possible to stabilize the oscillation frequency of nonlinear self-sustaining micromechanical resonators. Our findings provide a new strategy for engineering low-frequency noise oscillators capitalizing on the intrinsic nonlinear phenomena of micromechanical resonators.
Cubication of Conservative Nonlinear Oscillators
ERIC Educational Resources Information Center
Belendez, Augusto; Alvarez, Mariela L.; Fernandez, Elena; Pascual, Immaculada
2009-01-01
A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear…
Linearization of Conservative Nonlinear Oscillators
ERIC Educational Resources Information Center
Belendez, A.; Alvarez, M. L.; Fernandez, E.; Pascual, I.
2009-01-01
A linearization method of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force which allows us to obtain a frequency-amplitude relation which is valid not only for small but also for large amplitudes and, sometimes, for…
Competing Synchronization of Nonlinear Oscillators
NASA Astrophysics Data System (ADS)
Rosa, Epaminondas
2006-03-01
Coupled nonlinear oscillators abound in nature and in man-made devices. Think for example of two neurons in the brain competing to get the attention of a third neuron, and eventually developing some sort of synchronization process. This is a common feature involving oscillators in general, and can be studied using numerical simulations and/or experimental setups. In this talk, results involving electronic circuits and plasma discharges will be presented showing interesting features related to the types of oscillators and to the types of couplings. In particular, for the case of two oscillators competing for synchronization with a third one, the target oscillator synchronizes alternately to one or the other of the competing oscillators. The time intervals of synchronous states vary in a random-like manner. Numerical and experimental results will be presented and the consistency between them will be discussed.
Nonlinear oscillations of coalescing magnetic flux ropes
NASA Astrophysics Data System (ADS)
Kolotkov, Dmitrii Y.; Nakariakov, Valery M.; Rowlands, George
2016-05-01
An analytical model of highly nonlinear oscillations occurring during a coalescence of two magnetic flux ropes, based upon two-fluid hydrodynamics, is developed. The model accounts for the effect of electric charge separation, and describes perpendicular oscillations of the current sheet formed by the coalescence. The oscillation period is determined by the current sheet thickness, the plasma parameter β , and the oscillation amplitude. The oscillation periods are typically greater or about the ion plasma oscillation period. In the nonlinear regime, the oscillations of the ion and electron concentrations have a shape of a narrow symmetric spikes.
Palevicius, Paulius; Ragulskis, Minvydas; Palevicius, Arvydas; Ostasevicius, Vytautas
2014-01-01
Optical investigation of movable microsystem components using time-averaged holography is investigated in this paper. It is shown that even a harmonic excitation of a non-linear microsystem may result in an unpredictable chaotic motion. Analytical results between parameters of the chaotic oscillations and the formation of time-averaged fringes provide a deeper insight into computational and experimental interpretation of time-averaged MEMS holograms. PMID:24451467
Study of Nonlinear Oscillations of Elastic Membrane
2006-09-26
Nonlinear Elastic Membrane Oscillations by Eigenfunction Expansion, WSEAS Transactions of Systems, 3 (4) (2004), 1430-1435. 2.V. Varlamov, Convolution...proceedings 1. A. Balogh and V. Varlamov, Analysis of Nonlinear Elastic Membrane Oscillations by Eigenfunction Expansion, 6th WSEAS International...Eigenfunction Expansion, 6th WSEAS International Conference on Algorithms, Scientific Computing, Modelling and Simulation, Cancun, Mexico, May 12--15
Nonlinear dynamics of plasma oscillations modeled by an anharmonic oscillator
Enjieu Kadji, H. G.; Nana Nbendjo, B. R.; Chabi Orou, J. B.; Talla, P. K.
2008-03-15
This paper considers nonlinear dynamics of plasma oscillations modeled by an anharmonic oscillator. These plasma oscillations are described by a nonlinear differential equation of the form xe+{epsilon}(1+x{sup 2})x+x+{kappa}x{sup 2}+{delta}x{sup 3}=F cos {omega}t. The amplitudes of the forced harmonic, superharmonic, and subharmonic oscillatory states are obtained using the harmonic balance technique and the multiple time scales method. Admissible values of the amplitude of the external strength are derived. Bifurcation sequences displayed by the model for each type of oscillatory states are performed numerically through the fourth-order Runge-Kutta scheme.
Energy harvesting from the nonlinear oscillations of magnetic levitation
NASA Astrophysics Data System (ADS)
Mann, B. P.; Sims, N. D.
2009-01-01
This paper investigates the design and analysis of a novel energy harvesting device that uses magnetic levitation to produce an oscillator with a tunable resonance. The governing equations for the mechanical and electrical domains are derived to show the designed system reduces to the form of a Duffing oscillator under both static and dynamic loads. Thus, nonlinear analyses are required to investigate the energy harvesting potential of this prototypical nonlinear system. Theoretical investigations are followed by a series of experimental tests that validate the response predictions. The motivating hypothesis for the current work was that nonlinear phenomenon could be exploited to improve the effectiveness of energy harvesting devices.
Fläschner, G.; Ruschmeier, K.; Schwarz, A. Wiesendanger, R.; Bakhtiari, M. R.; Thorwart, M.
2015-03-23
The sensitivity of atomic force microscopes is fundamentally limited by the cantilever temperature, which can be, in principle, determined by measuring its thermal spectrum and applying the equipartition theorem. However, the mechanical response can be affected by the light field inside the cavity of a Fabry-Perot interferometer due to light absorption, radiation pressure, photothermal forces, and laser noise. By evaluating the optomechanical Hamiltonian, we are able to explain the peculiar distance dependence of the mechanical quality factor as well as the appearance of thermal spectra with symmetrical Lorentzian as well as asymmetrical Fano line shapes. Our results can be applied to any type of mechanical oscillator in an interferometer-based detection system.
NASA Astrophysics Data System (ADS)
Ghalambaz, Mohammad; Ghalambaz, Mehdi; Edalatifar, Mohammad
2016-03-01
The energy balance method is utilized to analyze the oscillation of a nonlinear nanoelectro-mechanical system resonator. The resonator comprises an electrode, which is embedded between two substrates. Two types of clamped-clamped and cantilever nano-resonators are studied. The effects of the van der Waals attractions, Casimir force, the small size, the fringing field, the mid-plane stretching, and the axial load are taken into account. The governing partial differential equation of the resonator is reduced using the Galerkin method. The energy method is applied to obtain an analytical solution without considering any linearization or small parameter. The results of the present study are compared with the results available in the literature. In addition, the results of the present analytical solution are compared with the Runge-Kutta numerical results. An excellent agreement between the present analytical solution, numerical solution, and the results available in the literature was found. The influences of the van der Waals force, Casimir force, size effect, and fringing field effect on the oscillation frequency of resonators are studied. The results indicate that the presence of the intermolecular forces (van der Waals), Casimir force, and fringing field effect decreases the oscillation frequency of the resonator. In contrast, the presence of the size effect increases the oscillation frequency of the resonator.
Transmitting information by controlling nonlinear oscillators
NASA Astrophysics Data System (ADS)
Tôrres, Leonardo A. B.; Aguirre, Luis A.
2004-09-01
The transmission of information relying on the perturbation of nonlinear oscillators vector fields can be approached in a unified manner. This can be accomplished by making use of the Information Transmission Via Control principle, which is stated and proved in the present work. In short, this principle establishes that any controller used to identically synchronize pairs of nonlinear oscillators, including chaotic ones as a special case, can be actually employed as demodulator/decoder in the process of information recovery. Other theoretical results related to the practical realization of the ITVC principle are presented and experimental data is provided showing a good agreement with the proposed theory.
Fourier series expansion for nonlinear Hamiltonian oscillators.
Méndez, Vicenç; Sans, Cristina; Campos, Daniel; Llopis, Isaac
2010-06-01
The problem of nonlinear Hamiltonian oscillators is one of the classical questions in physics. When an analytic solution is not possible, one can resort to obtaining a numerical solution or using perturbation theory around the linear problem. We apply the Fourier series expansion to find approximate solutions to the oscillator position as a function of time as well as the period-amplitude relationship. We compare our results with other recent approaches such as variational methods or heuristic approximations, in particular the Ren-He's method. Based on its application to the Duffing oscillator, the nonlinear pendulum and the eardrum equation, it is shown that the Fourier series expansion method is the most accurate.
Phase reduction approach to synchronisation of nonlinear oscillators
NASA Astrophysics Data System (ADS)
Nakao, Hiroya
2016-04-01
Systems of dynamical elements exhibiting spontaneous rhythms are found in various fields of science and engineering, including physics, chemistry, biology, physiology, and mechanical and electrical engineering. Such dynamical elements are often modelled as nonlinear limit-cycle oscillators. In this article, we briefly review phase reduction theory, which is a simple and powerful method for analysing the synchronisation properties of limit-cycle oscillators exhibiting rhythmic dynamics. Through phase reduction theory, we can systematically simplify the nonlinear multi-dimensional differential equations describing a limit-cycle oscillator to a one-dimensional phase equation, which is much easier to analyse. Classical applications of this theory, i.e. the phase locking of an oscillator to a periodic external forcing and the mutual synchronisation of interacting oscillators, are explained. Further, more recent applications of this theory to the synchronisation of non-interacting oscillators induced by common noise and the dynamics of coupled oscillators on complex networks are discussed. We also comment on some recent advances in phase reduction theory for noise-driven oscillators and rhythmic spatiotemporal patterns.
Spontaneous Oscillations in Nonlinear Active Solids
NASA Astrophysics Data System (ADS)
Banerjee, Shiladitya; Liverpool, Tanniemola B.; Marchetti, M. Cristina
2011-03-01
We present a generic continuum model of a nonlinear active gel with both passive and active crosslinks. The model is relevant for actin gels with passive elasticity provided by ABPs such as filamin-A or α -actinin and dynamic active crosslinkers such as myosin-II. We consider an one dimensional continuum active solid where compressional deformations are coupled to molecular motor dynamics. Three kinds of nonlinearities are incorporated : (a) nonlinear load dependence of unbinding rate of molecular motors, (b) pressure nonlinearities stemming from excluded volume interactions, and (c) nonlinearity due to convection of bound motors along the gel. Unbinding rate nonlinearity stabilizes the oscillatory instabilities predicted by the linear theory and lead to sustained oscillations at intermediate concentrations of ATP. Pressure nonlinearity due to excluded volume interactions stabilizes the contractile instability and leads to a contracted ground state. Our work provides a generic framework for the description of the large scale properties of nonlinear isotropic active solids. This work is supported by the NSF on grants DMR-MWN-0806511 and DMR-100478.
Phase reduction theory for hybrid nonlinear oscillators
NASA Astrophysics Data System (ADS)
Shirasaka, Sho; Kurebayashi, Wataru; Nakao, Hiroya
2017-01-01
Hybrid dynamical systems characterized by discrete switching of smooth dynamics have been used to model various rhythmic phenomena. However, the phase reduction theory, a fundamental framework for analyzing the synchronization of limit-cycle oscillations in rhythmic systems, has mostly been restricted to smooth dynamical systems. Here we develop a general phase reduction theory for weakly perturbed limit cycles in hybrid dynamical systems that facilitates analysis, control, and optimization of nonlinear oscillators whose smooth models are unavailable or intractable. On the basis of the generalized theory, we analyze injection locking of hybrid limit-cycle oscillators by periodic forcing and reveal their characteristic synchronization properties, such as ultrafast and robust entrainment to the periodic forcing and logarithmic scaling at the synchronization transition. We also illustrate the theory by analyzing the synchronization dynamics of a simple physical model of biped locomotion.
NASA Astrophysics Data System (ADS)
De, Saumyendu; Sahai, Atul Kumar; Nath Goswami, Bhupendra
2013-04-01
energy and the scale interactions in terms of the wave-wave exchanges among nonlinear triads are formulated and the above hypothesis is tested through a diagnostic analysis of the error energetics in two different model predictions at the lower troposphere (850hPa). It has been revealed that nonlinear triad interactions lead to advection of errors from short and synoptic waves (wave number >10) to long waves (wave numbers 5 - 10) and from long waves to ultra-long waves (wave numbers 1 - 4) and is responsible for the rapid growth of errors in the planetary waves. The continuous generation and then, non-linear propagation of error upto the planetary scales in the course of prediction increase the uncertainty in ultra-long scales which actually inhibit to predict accurately the planetary scale waves in tropics during medium range forecasts. Unraveling this exact mechanism through which upscale transfer of errors take place may help us devising a method to limit the mixing of small scale error with the error in forecast of tropical Intra-seasonal Oscillations and improve the prediction of lower tropospheric ISOs. Keywords: Predictability, Systematic error energetics, Scale interactions, Triads, Intra-seasonal Oscillations. Reference: The YOTC Science Plan (2008) prepared by Duane Waliser and Mitch Moncrieff. A joint WCRP-WWRP/THORPEX International Initiative, WMO/TD-No. 1452, pp. 20. Baumhefner D P and Downey P 1978 Forecast intercomparisons from three numerical weather prediction models; Mon. Weather Rev. 106 1245 - 1279. Krishnamurti T N, Subramanium M, Oosteroff D K, Daughenbaugh G. 1990 Predictability of low frequency modes. Meteorol. Atmos. phys. 44 63 - 83.
Limit cycles in nonlinear excitation of clusters of classical oscillators
NASA Astrophysics Data System (ADS)
De Lauro, E.; De Martino, S.; Falanga, M.; Ixaru, L. Gr.
2009-10-01
In this paper we develop a numerical procedure for detecting the existence of limit cycles in nonlinear excitation of clusters of classical harmonic oscillators. Our technique is able to compute also the main parameters of a limit cycle, that is the amplitudes and the period. The numerical method, based on the propagation matrix formalism, is transparent and easy to apply. It may find application in various areas where nonlinear excitations are involved, e.g., sound and mechanic vibrations in musical instruments, ground vibrations in volcanic areas, and sea tides.
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network
Goto, Hayato
2016-01-01
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence. PMID:26899997
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network
NASA Astrophysics Data System (ADS)
Goto, Hayato
2016-02-01
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network.
Goto, Hayato
2016-02-22
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.
Phase-selective entrainment of nonlinear oscillator ensembles
Zlotnik, Anatoly; Nagao, Raphael; Kiss, István Z.; Li, Jr-Shin
2016-01-01
The ability to organize and finely manipulate the hierarchy and timing of dynamic processes is important for understanding and influencing brain functions, sleep and metabolic cycles, and many other natural phenomena. However, establishing spatiotemporal structures in biological oscillator ensembles is a challenging task that requires controlling large collections of complex nonlinear dynamical units. In this report, we present a method to design entrainment signals that create stable phase patterns in ensembles of heterogeneous nonlinear oscillators without using state feedback information. We demonstrate the approach using experiments with electrochemical reactions on multielectrode arrays, in which we selectively assign ensemble subgroups into spatiotemporal patterns with multiple phase clusters. The experimentally confirmed mechanism elucidates the connection between the phases and natural frequencies of a collection of dynamical elements, the spatial and temporal information that is encoded within this ensemble, and how external signals can be used to retrieve this information. PMID:26988313
Phase-selective entrainment of nonlinear oscillator ensembles
Zlotnik, Anatoly V.; Nagao, Raphael; Kiss, Istvan Z.; Li, Jr -Shin
2016-03-18
The ability to organize and finely manipulate the hierarchy and timing of dynamic processes is important for understanding and influencing brain functions, sleep and metabolic cycles, and many other natural phenomena. However, establishing spatiotemporal structures in biological oscillator ensembles is a challenging task that requires controlling large collections of complex nonlinear dynamical units. In this report, we present a method to design entrainment signals that create stable phase patterns in ensembles of heterogeneous nonlinear oscillators without using state feedback information. We demonstrate the approach using experiments with electrochemical reactions on multielectrode arrays, in which we selectively assign ensemble subgroups into spatiotemporal patterns with multiple phase clusters. As a result, the experimentally confirmed mechanism elucidates the connection between the phases and natural frequencies of a collection of dynamical elements, the spatial and temporal information that is encoded within this ensemble, and how external signals can be used to retrieve this information.
Phase-selective entrainment of nonlinear oscillator ensembles
NASA Astrophysics Data System (ADS)
Zlotnik, Anatoly; Nagao, Raphael; Kiss, István Z.; Li-Shin, Jr.
2016-03-01
The ability to organize and finely manipulate the hierarchy and timing of dynamic processes is important for understanding and influencing brain functions, sleep and metabolic cycles, and many other natural phenomena. However, establishing spatiotemporal structures in biological oscillator ensembles is a challenging task that requires controlling large collections of complex nonlinear dynamical units. In this report, we present a method to design entrainment signals that create stable phase patterns in ensembles of heterogeneous nonlinear oscillators without using state feedback information. We demonstrate the approach using experiments with electrochemical reactions on multielectrode arrays, in which we selectively assign ensemble subgroups into spatiotemporal patterns with multiple phase clusters. The experimentally confirmed mechanism elucidates the connection between the phases and natural frequencies of a collection of dynamical elements, the spatial and temporal information that is encoded within this ensemble, and how external signals can be used to retrieve this information.
Phase-selective entrainment of nonlinear oscillator ensembles
Zlotnik, Anatoly V.; Nagao, Raphael; Kiss, Istvan Z.; ...
2016-03-18
The ability to organize and finely manipulate the hierarchy and timing of dynamic processes is important for understanding and influencing brain functions, sleep and metabolic cycles, and many other natural phenomena. However, establishing spatiotemporal structures in biological oscillator ensembles is a challenging task that requires controlling large collections of complex nonlinear dynamical units. In this report, we present a method to design entrainment signals that create stable phase patterns in ensembles of heterogeneous nonlinear oscillators without using state feedback information. We demonstrate the approach using experiments with electrochemical reactions on multielectrode arrays, in which we selectively assign ensemble subgroups intomore » spatiotemporal patterns with multiple phase clusters. As a result, the experimentally confirmed mechanism elucidates the connection between the phases and natural frequencies of a collection of dynamical elements, the spatial and temporal information that is encoded within this ensemble, and how external signals can be used to retrieve this information.« less
Self-sustained micro mechanical oscillator with linear feedback
Chen, Changyao; Zanette, Damian H.; Guest, Jeffrey R.; ...
2016-07-01
Autonomous oscillators, such as clocks and lasers, produce periodic signals without any external frequency reference. In order to sustain stable periodic motions, there needs to be external energy supply as well as nonlinearity built into the oscillator to regulate the amplitude. Usually, nonlinearity is provided by the sustaining feedback mechanism, which also supplies energy, whereas the constituent resonator that determines the output frequency stays linear. Here we propose a new self-sustaining scheme that relies on the nonlinearity originating from the resonator itself to limit the oscillation amplitude, while the feedback remains linear. We introduce a model to describe the workingmore » principle of the self-sustained oscillations and validate it with experiments performed on a nonlinear microelectromechanical (MEMS) based oscillator.« less
Self-sustained micro mechanical oscillator with linear feedback
Chen, Changyao; Zanette, Damian H.; Guest, Jeffrey R.; Czaplewski, David A.; Lopez, Daniel
2016-07-01
Autonomous oscillators, such as clocks and lasers, produce periodic signals without any external frequency reference. In order to sustain stable periodic motions, there needs to be external energy supply as well as nonlinearity built into the oscillator to regulate the amplitude. Usually, nonlinearity is provided by the sustaining feedback mechanism, which also supplies energy, whereas the constituent resonator that determines the output frequency stays linear. Here we propose a new self-sustaining scheme that relies on the nonlinearity originating from the resonator itself to limit the oscillation amplitude, while the feedback remains linear. We introduce a model to describe the working principle of the self-sustained oscillations and validate it with experiments performed on a nonlinear microelectromechanical (MEMS) based oscillator.
A survey on non-linear oscillations
NASA Astrophysics Data System (ADS)
Atherton, D. P.; Dorrah, H. T.
1980-06-01
This survey paper presents a comprehensive review of work in the field of non-linear oscillations. A brief discussion of second-order systems is followed by a presentation of exact criteria, approximate analytical methods and computational techniques for limit cycles in single variable systems. Multivariable systems are then covered from an analogous viewpoint which allows the reader to clearly identify both how single variable methods have been extended and the possibilities for further research. Particular emphasis is placed on describing function methods since it is believed that, where exact solutions are not possible, the approach may not only give approximate solutions but provides good insight for further computational or simulation studies. The coverage is essentially restricted to continuous lumped parameter systems and includes both free and forced oscillations. Several applications of the theories in various fields of engineering and science are discussed and indicate the broad interest in non-linear oscillatory phenomena. Finally, a detailed bibliography on the subject is provided.
Inference of Stochastic Nonlinear Oscillators with Applications to Physiological Problems
NASA Technical Reports Server (NTRS)
Smelyanskiy, Vadim N.; Luchinsky, Dmitry G.
2004-01-01
A new method of inferencing of coupled stochastic nonlinear oscillators is described. The technique does not require extensive global optimization, provides optimal compensation for noise-induced errors and is robust in a broad range of dynamical models. We illustrate the main ideas of the technique by inferencing a model of five globally and locally coupled noisy oscillators. Specific modifications of the technique for inferencing hidden degrees of freedom of coupled nonlinear oscillators is discussed in the context of physiological applications.
Seasonality and mechanisms of tropical intraseasonal oscillations
NASA Astrophysics Data System (ADS)
Hazra, Abheera; Krishnamurthy, V.
2017-03-01
This study has compared the monsoon intraseasonal oscillation (MISO) during the boreal summer and Madden Julian Oscillation (MJO) during the boreal winter. Based on MISO and MJO in high-resolution three-dimensional diabatic heating, the possible mechanisms are discussed through observational analyses of dynamical and thermodynamical variables. The MISO and MJO are extracted as nonlinear oscillations during boreal summer and winter, respectively, by applying multi-channel singular spectrum analysis on daily anomalies of diabatic heating over the Indo-Pacific region. Lead and lag relations among moisture, temperature and surface fields relative to diabatic heating are analyzed to compare the mechanisms of MISO and MJO. While both the oscillations show eastward propagation, MISO has a strong northward propagation and MJO has a weak southward propagation as well. The analysis shows that MJO and MISO are essentially driven by the same mechanisms but with some difference in the meridional propagation. The westerly shear leads the diabatic heating, while the vorticity has weak correlation. Large-scale circulation creates positive moisture preconditioning before convection and negative moisture preconditioning before suppressed conditions. A positive lower level horizontal advection of temperature and upper level temperature tendencies lead the convective state while a negative lower level horizontal advection of temperature and upper level temperature tendencies lead the suppressed state. There is positive feedback from the SST to atmosphere. The difference in the meridional propagation of MISO and MJO is hypothesized to be because of the different differential heating meridionally during the two seasons.
Pathological tremors: Deterministic chaos or nonlinear stochastic oscillators?
NASA Astrophysics Data System (ADS)
Timmer, Jens; Häußler, Siegfried; Lauk, Michael; Lücking, Carl
2000-02-01
Pathological tremors exhibit a nonlinear oscillation that is not strictly periodic. We investigate whether the deviation from periodicity is due to nonlinear deterministic chaotic dynamics or due to nonlinear stochastic dynamics. To do so, we apply methods from linear and nonlinear time series analysis to tremor time series. The results of the different methods suggest that the considered types of pathological tremors represent nonlinear stochastic second order processes.
Influence of nonlinearities on the power output of the Self-Oscillating Fluidic Heat Engine (SOFHE)
NASA Astrophysics Data System (ADS)
Tessier-Poirier, A.; Monin, T.; Léveillé, E.; Formosa, F.; Monfray, S.; Fréchette, L. G.
2016-11-01
In this paper, it is shown that two non-linearities drive the oscillations amplitude and the potential power density of the Self-Oscillating Fluidic Heat Engine (SOFHE). This new type of engine converts thermal energy into mechanical energy by producing self-sustained oscillations of a liquid column from a continuous heat source to power wireless sensors from waste heat. The underlying theoretical modeling shows that the pressure and the temperature nonlinearities limit the final oscillations amplitude, hence its achievable power density.
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network
NASA Astrophysics Data System (ADS)
Goto, Hayato
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via its bifurcation with a slowly varying parameter. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing. To distinguish them, we refer to the present approach as bifurcation-based adiabatic quantum computation. Our numerical simulation results suggest that quantum superposition and quantum fluctuation work effectively to find optimal solutions.
Universal quantum computation with a nonlinear oscillator network
NASA Astrophysics Data System (ADS)
Goto, Hayato
2016-05-01
We theoretically show that a nonlinear oscillator network with controllable parameters can be used for universal quantum computation. The initialization is achieved by a quantum-mechanical bifurcation based on quantum adiabatic evolution, which yields a Schrödinger cat state. All the elementary quantum gates are also achieved by quantum adiabatic evolution, in which dynamical phases accompanying the adiabatic evolutions are controlled by the system parameters. Numerical simulation results indicate that high gate fidelities can be achieved, where no dissipation is assumed.
Stochastic regimes in the driven oscillator with a step-like nonlinearity
Bulanov, S. V.; Esirkepov, T. Zh.; Koga, J. K.; Kondo, K.; Kando, M.; Yogo, A.; Bulanov, S. S.
2015-06-15
A nonlinear oscillator with an abruptly inhomogeneous restoring force driven by an uniform oscillating force exhibits stochastic properties under specific resonance conditions. This behaviour elucidates the elementary mechanism of the electron energization in the strong electromagnetic wave interaction with thin targets.
Bounds on the Fourier coefficients for the periodic solutions of non-linear oscillator equations
NASA Technical Reports Server (NTRS)
Mickens, R. E.
1988-01-01
The differential equations describing nonlinear oscillations (as seen in mechanical vibrations, electronic oscillators, chemical and biochemical reactions, acoustic systems, stellar pulsations, etc.) are investigated analytically. The boundedness of the Fourier coefficients for periodic solutions is demonstrated for two special cases, and the extrapolation of the results to higher-dimensionsal systems is briefly considered.
Microwave Oscillators Based on Nonlinear WGM Resonators
NASA Technical Reports Server (NTRS)
Maleki, Lute; Matsko, Andrey; Savchenkov, Anatoliy; Strekalov, Dmitry
2006-01-01
Optical oscillators that exploit resonantly enhanced four-wave mixing in nonlinear whispering-gallery-mode (WGM) resonators are under investigation for potential utility as low-power, ultra-miniature sources of stable, spectrally pure microwave signals. There are numerous potential uses for such oscillators in radar systems, communication systems, and scientific instrumentation. The resonator in an oscillator of this type is made of a crystalline material that exhibits cubic Kerr nonlinearity, which supports the four-photon parametric process also known as four-wave mixing. The oscillator can be characterized as all-optical in the sense that the entire process of generation of the microwave signal takes place within the WGM resonator. The resonantly enhanced four-wave mixing yields coherent, phase-modulated optical signals at frequencies governed by the resonator structure. The frequency of the phase-modulation signal, which is in the microwave range, equals the difference between the frequencies of the optical signals; hence, this frequency is also governed by the resonator structure. Hence, further, the microwave signal is stable and can be used as a reference signal. The figure schematically depicts the apparatus used in a proof-of-principle experiment. Linearly polarized pump light was generated by an yttrium aluminum garnet laser at a wavelength of 1.32 microns. By use of a 90:10 fiber-optic splitter and optical fibers, some of the laser light was sent into a delay line and some was transmitted to one face of glass coupling prism, that, in turn, coupled the laser light into a crystalline CaF2 WGM disk resonator that had a resonance quality factor (Q) of 6x10(exp 9). The output light of the resonator was collected via another face of the coupling prism and a single-mode optical fiber, which transmitted the light to a 50:50 fiber-optic splitter. One output of this splitter was sent to a slow photodiode to obtain a DC signal for locking the laser to a particular
Wave Driven Non-linear Flow Oscillator for the 22-Year Solar Cycle
NASA Technical Reports Server (NTRS)
Mayr, Hans G.; Wolff, Charles L.; Hartle, Richard E.; Einaudi, Franco (Technical Monitor)
2000-01-01
In the Earth's atmosphere, a zonal flow oscillation is observed with periods between 20 and 32 months, the Quasi Biennial Oscillation. This oscillation does not require external time dependent forcing but is maintained by non-linear wave momentum deposition. It is proposed that such a mechanism also drives long-period oscillations in planetary and stellar interiors. We apply this mechanism to generate a flow oscillation for the 22-year solar cycle. The oscillation would occur just below the convective envelope where waves can propagate. Using scale analysis, we present results from a simplified model that incorporates Hines' gravity wave parameterization. Wave amplitudes less than 10 m/s can produce reversing zonal flows of 25 m/s that should be sufficient to generate a corresponding oscillation in the poloidal magnetic field. Low buoyancy frequency and the associated increase in turbulence help to produce the desired oscillation period of the flow.
Scleronomic Holonomic Constraints and Conservative Nonlinear Oscillators
ERIC Educational Resources Information Center
Munoz, R.; Gonzalez-Garcia, G.; Izquierdo-De La Cruz, E.; Fernandez-Anaya, G.
2011-01-01
A bead sliding, under the sole influence of its own weight, on a rigid wire shaped in the fashion of a plane curve, will describe (generally anharmonic) oscillations around a local minimum. For given shapes, the bead will behave as a harmonic oscillator in the whole range, such as an unforced, undamped, Duffing oscillator, etc. We also present…
Spectra of delay-coupled heterogeneous noisy nonlinear oscillators
NASA Astrophysics Data System (ADS)
Vüllings, Andrea; Schöll, Eckehard; Lindner, Benjamin
2014-02-01
Nonlinear oscillators that are subject to noise and delayed interaction have been used to describe a number of dynamical phenomena in Physics and beyond. Here we study the spectral statistics (power and cross-spectral densities) of a small number of noisy nonlinear oscillators and derive analytical approximations for these spectra. In our paper, individual oscillators are described by the normal form of a supercritical or subcritical Hopf bifurcation supplemented by Gaussian white noise. Oscillators can be distinguished from each other by their frequency, bifurcation parameter, and noise intensity. Extending previous results from the literature, we first calculate in linear response theory the power spectral density and response function of the single oscillator in both super- and subcritical parameter regime and test them against numerical simulations. For small heterogeneous groups of oscillators (N = 2 or 3), which are coupled by a delayed linear term, we use a linear response ansatz to derive approximations for the power and cross-spectral densities of the oscillators within this small network. These approximations are confirmed by comparison with extensive numerical simulations. Using the theory we relate the peaks in the spectra of the homogeneous system (identical oscillators) to periodic solutions of the deterministic (noiseless) system. For two delay-coupled subcritical Hopf oscillators, we show that the coupling can enhance the coherence resonance effect, which is known to occur for the single subcritical oscillator. In the case of heterogeneous oscillators, we find that the delay-induced characteristic profile of the spectra is conserved for moderate frequency detuning.
Nonlinear normal modes and localization in two bubble oscillators.
Sugita, Naohiro; Sugiura, Toshihiko
2017-02-01
We investigated a bifurcation structure of coupled nonlinear oscillation of two spherical gas bubbles subject to a stationary sound field by means of nonlinear modal analysis. The goal of this paper is to describe an energy localization phenomenon of coupled two-bubble oscillators, resulting from symmetry-breaking bifurcation of the steady-state oscillation. Approximate asymptotic solutions of nonlinear normal modes (NNMs) and steady state oscillation are obtained based on the method of multiple scales. It is found that localized oscillation arises in a neighborhood of the localized normal modes. The analytical solutions of the amplitude and the phase shift of the steady-state oscillation are compared to numerical results and found to be in good agreement within the limit of small-amplitude oscillation. For larger amplitude oscillation, a bifurcation diagram of the localized solution as a function of the driving frequency and the separation distance between the bubbles is provided in the presence of the thermal damping. The numerical results show that the localized oscillation can occur for a fairly typical parameter range used in practical experiments and simulations in the early literatures.
Zang, Xiao-Fei; Jiang, Chun; Zhu, Hai-Bin
2009-09-01
We study nonlinear dynamics of classical electromagnetic wave propagation in a one-dimensional nonlinear periodic photonic structure. It is found that the period of Rabi oscillations can be modulated by the relatively weak nonlinearity (2V0/gamma>1). When nonlinearity is relatively strong compared to the strength of resonant coupling (2V0/gamma<1), Rabi oscillations is suppressed and the system shows a dynamical behavior, i.e., energy localizes in one mode rather than full oscillation between two degenerated modes. Phase plane analysis is applied to explain these dynamical phenomena.
Nonlinear modulation of Rabi oscillations in a one-dimensional nonlinear periodic photonic structure
NASA Astrophysics Data System (ADS)
Zang, Xiao-Fei; Jiang, Chun; Zhu, Hai-Bin
2009-09-01
We study nonlinear dynamics of classical electromagnetic wave propagation in a one-dimensional nonlinear periodic photonic structure. It is found that the period of Rabi oscillations can be modulated by the relatively weak nonlinearity (2V0/γ>1) . When nonlinearity is relatively strong compared to the strength of resonant coupling (2V0/γ<1) , Rabi oscillations is suppressed and the system shows a dynamical behavior, i.e., energy localizes in one mode rather than full oscillation between two degenerated modes. Phase plane analysis is applied to explain these dynamical phenomena.
Nonlinear self-excited oscillations of a ducted flame
NASA Astrophysics Data System (ADS)
Dowling, A. P.
1997-09-01
Self-excited oscillations of a confined flame, burning in the wake of a bluff-body flame-holder, are considered. These oscillations occur due to interaction between unsteady combustion and acoustic waves. According to linear theory, flow disturbances grow exponentially with time. A theory for nonlinear oscillations is developed, exploiting the fact that the main nonlinearity is in the heat release rate, which essentially ‘saturates’. The amplitudes of the pressure fluctuations are sufficiently small that the acoustic waves remain linear. The time evolution of the oscillations is determined by numerical integration and inclusion of nonlinear effects is found to lead to limit cycles of finite amplitude. The predicted limit cycles are compared with results from experiments and from linear theory. The amplitudes and spectra of the limit-cycle oscillations are in reasonable agreement with experiment. Linear theory is found to predict the frequency and mode shape of the nonlinear oscillations remarkably well. Moreover, we find that, for this type of nonlinearity, describing function analysis enables a good estimate of the limit-cycle amplitude to be obtained from linear theory.
Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity
NASA Astrophysics Data System (ADS)
Jeevarekha, A.; Paul Asir, M.; Philominathan, P.
2016-06-01
This paper addresses the problem of sharing common nonlinearity among nonautonomous and autonomous oscillators. By choosing a suitable common nonlinear element with the driving point characteristics capable of bringing out chaotic motion in a combined system, we obtain identical chaotic states. The dynamics of the coupled system is explored through numerical and experimental studies. Employing the concept of common nonlinearity, a simple chaotic communication system is modeled and its performance is verified through Multisim simulation.
Nonlinear tearing modes stabilization by oscillating the resonant surface
NASA Astrophysics Data System (ADS)
Yang, Xiaoqing; Wang, Shaojie
2016-09-01
The stabilization of the nonlinear tearing mode by rapidly oscillating the resonant surface has been investigated numerically in a large aspect ratio tokamak with a circular cross-section. By means of the radio frequency current drive, the plasma current can be modulated to make the resonant surface (rs) oscillate in time near its mean position. Previous results show that the linear tearing mode can be suppressed by oscillating the resonant surface with a suitable frequency and amplitude. At the nonlinear stage, the tearing mode stabilization shows different properties. The suppression effects not only depend on the modulation frequency and the oscillation width of the resonant surface but also depend on the relative size of χ0 to δ (here, χ0 is the oscillation width of the resonant surface and δ is the width of tearing layer) and the relative width of χ0 to the magnetic island width W.
Electromagnetic radiation due to nonlinear oscillations of a charged drop
NASA Astrophysics Data System (ADS)
Shiryaeva, S. O.; Grigor'ev, A. N.; Kolbneva, N. Yu.
2016-03-01
The nonlinear oscillations of a spherical charged drop are asymptotically analyzed under the conditions of a multimode initial deformation of its equilibrium shape. It is found that if the spectrum of initially excited modes contains two adjacent modes, the translation mode of oscillations is excited among others. In this case, the center of the drop's charge oscillates about the equilibrium position, generating a dipole electromagnetic radiation. It is shown that the intensity of this radiation is many orders of magnitude higher than the intensity of the drop's radiation, which arises in calculations of the first order of smallness and is related to the drop's charged surface oscillations.
Hopf bifurcation with dihedral group symmetry - Coupled nonlinear oscillators
NASA Technical Reports Server (NTRS)
Golubitsky, Martin; Stewart, Ian
1986-01-01
The theory of Hopf bifurcation with symmetry developed by Golubitsky and Stewart (1985) is applied to systems of ODEs having the symmetries of a regular polygon, that is, whose symmetry group is dihedral. The existence and stability of symmetry-breaking branches of periodic solutions are considered. In particular, these results are applied to a general system of n nonlinear oscillators coupled symmetrically in a ring, and the generic oscillation patterns are described. It is found that the symmetry can force some oscillators to have twice the frequency of others. The case of four oscillators has exceptional features.
Non-linear Oscillations of Compact Stars and Gravitational Waves
NASA Astrophysics Data System (ADS)
Passamonti, Andrea
2006-07-01
This thesis investigates in the time domain a particular class of second order perturbations of a perfect fluid non-rotating compact star: those arising from the coupling between first order radial and non-radial perturbations. This problem has been treated by developing a gauge invariant formalism based on the 2-parameter perturbation theory (Sopuerta, Bruni and Gualtieri, 2004) where the radial and non-radial perturbations have been separately parameterized. The non-linear perturbations obey inhomogeneous partial differential equations, where the structure of the differential operator is given by the previous perturbative orders and the source terms are quadratic in the first order perturbations. In the exterior spacetime the sources vanish, thus the gravitational wave properties are completely described by the second order Zerilli and Regge-Wheeler functions. As main initial configuration we have considered a first order differentially rotating and radially pulsating star. Although at first perturbative order this configuration does not exhibit any gravitational radiation, we have found a new interesting gravitational signal at non-linear order, in which the radial normal modes are precisely mirrored. In addition, a resonance effect is present when the frequencies of the radial pulsations are close to the first axial w-mode. Finally, we have roughly estimated the damping times of the radial pulsations due to the non-linear gravitational emission. The coupling near the resonance results to be a very effective mechanism for extracting energy from the radial oscillations.
Manimala, James M; Sun, C T
2016-06-01
The amplitude-dependent dynamic response in acoustic metamaterials having nonlinear local oscillator microstructures is studied using numerical simulations on representative discrete mass-spring models. Both cubically nonlinear hardening and softening local oscillator cases are considered. Single frequency, bi-frequency, and wave packet excitations at low and high amplitude levels were used to interrogate the models. The propagation and attenuation characteristics of harmonic waves in a tunable frequency range is found to correspond to the amplitude and nonlinearity-dependent shifts in the local resonance bandgap for such nonlinear acoustic metamaterials. A predominant shift in the propagated wave spectrum towards lower frequencies is observed. Moreover, the feasibility of amplitude and frequency-dependent selective filtering of composite signals consisting of individual frequency components which fall within propagating or attenuating regimes is demonstrated. Further enrichment of these wave manipulation mechanisms in acoustic metamaterials using different combinations of nonlinear microstructures presents device implications for acoustic filters and waveguides.
On the nonlinear dissipative dynamics of weakly overdamped oscillators
Brezhnev, Yu. V.; Sazonov, S. V.
2014-11-15
We consider the motion of weakly overdamped linear oscillators. Weak overdamping of an oscillator is defined as a slight excess of the damping decrement over its natural frequency. Exact solutions are obtained for a certain relation between the decrement and the natural frequency and qualitatively different regimes of motion are analyzed. The threshold conditions corresponding to changes of regimes are established; one-component models with an arbitrary degree of nonlinearity are analyzed, and quadratic and cubic nonlinearities are considered in detail. If the nonlinearity in a multicomponent model is determined by a homogeneous function, transformations of the Kummer-Liouville type can be reduced to an autonomous system of second-order differential equations in the case when the relation between the decrement and the natural frequency has been established. Some integrable multicomponent models with quadratic and cubic nonlinearities are analyzed.
Multisynchronization of Chaotic Oscillators via Nonlinear Observer Approach
Aguilar-López, Ricardo; Martínez-Guerra, Rafael; Mata-Machuca, Juan L.
2014-01-01
The goal of this work is to synchronize a class of chaotic oscillators in a master-slave scheme, under different initial conditions, considering several slaves systems. The Chen oscillator is employed as a benchmark model and a nonlinear observer is proposed to reach synchronicity between the master and the slaves' oscillators. The proposed observer contains a proportional and integral form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Numerical experiments were carried out to show the operation of the considered methodology. PMID:24578671
Multisynchronization of chaotic oscillators via nonlinear observer approach.
Aguilar-López, Ricardo; Martínez-Guerra, Rafael; Mata-Machuca, Juan L
2014-01-01
The goal of this work is to synchronize a class of chaotic oscillators in a master-slave scheme, under different initial conditions, considering several slaves systems. The Chen oscillator is employed as a benchmark model and a nonlinear observer is proposed to reach synchronicity between the master and the slaves' oscillators. The proposed observer contains a proportional and integral form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Numerical experiments were carried out to show the operation of the considered methodology.
Optimal operating points of oscillators using nonlinear resonators.
Kenig, Eyal; Cross, M C; Villanueva, L G; Karabalin, R B; Matheny, M H; Lifshitz, Ron; Roukes, M L
2012-11-01
We demonstrate an analytical method for calculating the phase sensitivity of a class of oscillators whose phase does not affect the time evolution of the other dynamic variables. We show that such oscillators possess the possibility for complete phase noise elimination. We apply the method to a feedback oscillator which employs a high Q weakly nonlinear resonator and provide explicit parameter values for which the feedback phase noise is completely eliminated and others for which there is no amplitude-phase noise conversion. We then establish an operational mode of the oscillator which optimizes its performance by diminishing the feedback noise in both quadratures, thermal noise, and quality factor fluctuations. We also study the spectrum of the oscillator and provide specific results for the case of 1/f noise sources.
Mechanical Parametric Oscillations and Waves
ERIC Educational Resources Information Center
Dittrich, William; Minkin, Leonid; Shapovalov, Alexander S.
2013-01-01
Usually parametric oscillations are not the topic of general physics courses. Probably it is because the mathematical theory of this phenomenon is relatively complicated, and until quite recently laboratory experiments for students were difficult to implement. However parametric oscillations are good illustrations of the laws of physics and can be…
Tunneling control using classical non-linear oscillator
Kar, Susmita; Bhattacharyya, S. P.
2014-04-24
A quantum particle is placed in symmetric double well potential which is coupled to a classical non-linear oscillator via a coupling function. With different spatial symmetry of the coupling and under various controlling fashions, the tunneling of the quantum particle can be enhanced or suppressed, or totally destroyed.
An exactly solvable three-dimensional nonlinear quantum oscillator
Schulze-Halberg, A.; Morris, J. R.
2013-11-15
Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dependent mass. This system is the generalization of the corresponding one-dimensional system, which has been the focus of recent attention. In contrast to other approaches, we are able to obtain solutions in terms of special functions, without a reliance upon a Rodrigues-type of formula. The wave functions of the quantum oscillator have the familiar spherical harmonic solutions for the angular part. For the s-states of the system, the radial equation accepts solutions that have been recently found for the one-dimensional nonlinear quantum oscillator, given in terms of associated Legendre functions, along with a constant shift in the energy eigenvalues. Radial solutions are obtained for all angular momentum states, along with the complete energy spectrum of the bound states.
Graphene mechanical oscillators with tunable frequency.
Chen, Changyao; Lee, Sunwoo; Deshpande, Vikram V; Lee, Gwan-Hyoung; Lekas, Michael; Shepard, Kenneth; Hone, James
2013-12-01
Oscillators, which produce continuous periodic signals from direct current power, are central to modern communications systems, with versatile applications including timing references and frequency modulators. However, conventional oscillators typically consist of macroscopic mechanical resonators such as quartz crystals, which require excessive off-chip space. Here, we report oscillators built on micrometre-size, atomically thin graphene nanomechanical resonators, whose frequencies can be electrostatically tuned by as much as 14%. Self-sustaining mechanical motion is generated and transduced at room temperature in these oscillators using simple electrical circuitry. The prototype graphene voltage-controlled oscillators exhibit frequency stability and a modulation bandwidth sufficient for the modulation of radiofrequency carrier signals. As a demonstration, we use a graphene oscillator as the active element for frequency-modulated signal generation and achieve efficient audio signal transmission.
Nonlinear saturation of thermoacoustic oscillations in annular combustion chambers
NASA Astrophysics Data System (ADS)
Ghirardo, Giulio; Juniper, Matthew
2014-11-01
Continuous combustion systems such as aeroplane engines can experience self-sustained pressure oscillations, called thermoacoustic oscillations. Quite often the combustion chamber is rotationally symmetric and confined between inner and outer walls, with a fixed number of burners equispaced along the annulus, at the chamber inlet. We focus on thermoacoustic oscillations in the azimuthal direction, and discuss the nonlinear saturation of the system towards 2 types of solutions: standing waves (with velocity and pressure nodes fixed in time and in space) and spinning waves (rotating waves, in clockwise or anti-clockwise direction). We neglect the effect of the transverse velocity oscillating in the azimuthal direction in the combustion chamber, and focus the model on the nonlinear effect that the longitudinal velocity, just upstream of each burner, has on the fluctuating heat-release response in the chamber. We present a low-order analytical framework to discuss the stability of the 2 types of solutions. We discuss how the stability and amplitudes of the 2 solutions depend on: 1) the acoustic damping in the system; 2) the number of injectors equispaced in the annulus; 3) the nonlinear response of the flames.
Nonlinear magnetotransport theory and Hall induced resistance oscillations in graphene.
Gutiérrez-Jáuregui, R; Torres, M
2014-06-11
The quantum oscillations of nonlinear magnetoresistance in graphene that occur in response to a dc current bias are investigated. We present a theoretical model for the nonlinear magnetotransport of graphene carriers. The model is based on the exact solution of the effective Dirac equation in crossed electric and magnetic fields, while the effects of randomly distributed impurities are perturbatively added. To compute the nonlinear current effects, we develop a covariant formulation of the migration center theory. The current is calculated for short- and large-range scatterers. The analysis of the differential resistivity in the large magnetic field region, shows that the extrema of the Shubnikov de Hass oscillations invert when the dc currents exceed a threshold value. These results are in good agreement with experimental observations. In the small magnetic field regime, corresponding to large filling factors, the existence of Hall induced resistance oscillations are predicted for ultra clean graphene samples. These oscillations originate from Landau-Zener tunneling between Landau levels, that are tilted by the strong electric Hall field.
Suppression of limit cycle oscillations using the nonlinear tuned vibration absorber
Habib, G.; Kerschen, G.
2015-01-01
The objective of this study is to mitigate, or even completely eliminate, the limit cycle oscillations in mechanical systems using a passive nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA). An unconventional aspect of the NLTVA is that the mathematical form of its restoring force is not imposed a priori, as it is the case for most existing nonlinear absorbers. The NLTVA parameters are determined analytically using stability and bifurcation analyses, and the resulting design is validated using numerical continuation. The proposed developments are illustrated using a Van der Pol–Duffing primary system. PMID:27547085
Nonlinear Rabi oscillations in a Bose-Einstein condensate
NASA Astrophysics Data System (ADS)
Rosanov, Nikolay N.
2013-12-01
For a Bose-Einstein condensate in a trap with oscillating barriers, in the resonance approximation, evolution equations are derived. Their analytical solution reveals the existence of two fundamentally different types of nonlinear conservative Rabi oscillations: (i) with periodic temporal variation of moduli and phase difference of levels’ amplitudes of probability, and (ii) with monotonic temporal variation of the phase difference. It is shown that the two types can be realized for the same parameters of the scheme, but for different initial conditions. Analytical predictions are confirmed by numerical solution to the Gross-Pitaevskii equation.
Supersonic flow past oscillating airfoils including nonlinear thickness effects
NASA Technical Reports Server (NTRS)
Van Dyke, Milton D
1954-01-01
A solution to second order in thickness is derived for harmonically oscillating two-dimensional airfoils in supersonic flow. For slow oscillations of an arbitrary profile, the result is found as a series including the third power of frequency. For arbitrary frequencies, the method of solution for any specific profile is indicated, and the explicit solution derived for a single wedge. Nonlinear thickness effects are found generally to reduce the torsional damping, and so enlarge the range of Mach numbers within which torsional instability is possible.
Front spreading with nonlinear sorption for oscillating flow
NASA Astrophysics Data System (ADS)
Cirkel, D. G.; van der Zee, S. E. A. T. M.; Meeussen, J. C. L.
2015-04-01
In this paper, we consider dispersive and chromatographic mixing at an interface, under alternating flow conditions. In case of a nonreactive or linearly sorbing solute, mixing is in complete analogy with classical dispersion theory. For nonlinear exchange, however, oscillating convective flow leads to an alternation of sharpening (Traveling Wave TW) and spreading (Rarefaction Wave RW). As the limiting TW form is not necessarily accomplished at the end of the TW half cycle, the oscillating fronts show gradual continuous spreading that converges to a zero-convection nonlinear pure diffusion spreading, which is mathematically of quite different nature. This behavior is maintained in case the total (background) concentration differs at both sides of the initial exchange front.
Entanglement dynamics of quantum oscillators nonlinearly coupled to thermal environments
NASA Astrophysics Data System (ADS)
Voje, Aurora; Croy, Alexander; Isacsson, Andreas
2015-07-01
We study the asymptotic entanglement of two quantum harmonic oscillators nonlinearly coupled to an environment. Coupling to independent baths and a common bath are investigated. Numerical results obtained using the Wangsness-Bloch-Redfield method are supplemented by analytical results in the rotating wave approximation. The asymptotic negativity as function of temperature, initial squeezing, and coupling strength, is compared to results for systems with linear system-reservoir coupling. We find that, due to the parity-conserving nature of the coupling, the asymptotic entanglement is considerably more robust than for the linearly damped cases. In contrast to linearly damped systems, the asymptotic behavior of entanglement is similar for the two bath configurations in the nonlinearly damped case. This is due to the two-phonon system-bath exchange causing a suppression of information exchange between the oscillators via the bath in the common-bath configuration at low temperatures.
Quadratic and Cubic Nonlinear Oscillators with Damping and Their Applications
NASA Astrophysics Data System (ADS)
Li, Jibin; Feng, Zhaosheng
We apply the qualitative theory of dynamical systems to study exact solutions and the dynamics of quadratic and cubic nonlinear oscillators with damping. Under certain parametric conditions, we also consider the van der Waals normal form, Chaffee-Infante equation, compound Burgers-KdV equation and Burgers-KdV equation for explicit representations of kink-profile wave solutions and unbounded traveling wave solutions.
Closed-loop suppression of chaos in nonlinear driven oscillators
NASA Astrophysics Data System (ADS)
Aguirre, L. A.; Billings, S. A.
1995-05-01
This paper discusses the suppression of chaos in nonlinear driven oscillators via the addition of a periodic perturbation. Given a system originally undergoing chaotic motions, it is desired that such a system be driven to some periodic orbit. This can be achieved by the addition of a weak periodic signal to the oscillator input. This is usually accomplished in open loop, but this procedure presents some difficulties which are discussed in the paper. To ensure that this is attained despite uncertainties and possible disturbances on the system, a procedure is suggested to perform control in closed loop. In addition, it is illustrated how a model, estimated from input/output data, can be used in the design. Numerical examples which use the Duffing-Ueda and modified van der Pol oscillators are included to illustrate some of the properties of the new approach.
Experimental Observation of Bohr's Nonlinear Fluidic Surface Oscillation.
Moon, Songky; Shin, Younghoon; Kwak, Hojeong; Yang, Juhee; Lee, Sang-Bum; Kim, Soyun; An, Kyungwon
2016-01-25
Niels Bohr in the early stage of his career developed a nonlinear theory of fluidic surface oscillation in order to study surface tension of liquids. His theory includes the nonlinear interaction between multipolar surface oscillation modes, surpassing the linear theory of Rayleigh and Lamb. It predicts a specific normalized magnitude of 0.416η(2) for an octapolar component, nonlinearly induced by a quadrupolar one with a magnitude of η much less than unity. No experimental confirmation on this prediction has been reported. Nonetheless, accurate determination of multipolar components is important as in optical fiber spinning, film blowing and recently in optofluidic microcavities for ray and wave chaos studies and photonics applications. Here, we report experimental verification of his theory. By using optical forward diffraction, we measured the cross-sectional boundary profiles at extreme positions of a surface-oscillating liquid column ejected from a deformed microscopic orifice. We obtained a coefficient of 0.42 ± 0.08 consistently under various experimental conditions. We also measured the resonance mode spectrum of a two-dimensional cavity formed by the cross-sectional segment of the liquid jet. The observed spectra agree well with wave calculations assuming a coefficient of 0.414 ± 0.011. Our measurements establish the first experimental observation of Bohr's hydrodynamic theory.
Experimental Observation of Bohr’s Nonlinear Fluidic Surface Oscillation
Moon, Songky; Shin, Younghoon; Kwak, Hojeong; Yang, Juhee; Lee, Sang-Bum; Kim, Soyun; An, Kyungwon
2016-01-01
Niels Bohr in the early stage of his career developed a nonlinear theory of fluidic surface oscillation in order to study surface tension of liquids. His theory includes the nonlinear interaction between multipolar surface oscillation modes, surpassing the linear theory of Rayleigh and Lamb. It predicts a specific normalized magnitude of 0.416η2 for an octapolar component, nonlinearly induced by a quadrupolar one with a magnitude of η much less than unity. No experimental confirmation on this prediction has been reported. Nonetheless, accurate determination of multipolar components is important as in optical fiber spinning, film blowing and recently in optofluidic microcavities for ray and wave chaos studies and photonics applications. Here, we report experimental verification of his theory. By using optical forward diffraction, we measured the cross-sectional boundary profiles at extreme positions of a surface-oscillating liquid column ejected from a deformed microscopic orifice. We obtained a coefficient of 0.42 ± 0.08 consistently under various experimental conditions. We also measured the resonance mode spectrum of a two-dimensional cavity formed by the cross-sectional segment of the liquid jet. The observed spectra agree well with wave calculations assuming a coefficient of 0.414 ± 0.011. Our measurements establish the first experimental observation of Bohr’s hydrodynamic theory. PMID:26803911
Experimental Observation of Bohr’s Nonlinear Fluidic Surface Oscillation
NASA Astrophysics Data System (ADS)
Moon, Songky; Shin, Younghoon; Kwak, Hojeong; Yang, Juhee; Lee, Sang-Bum; Kim, Soyun; An, Kyungwon
2016-01-01
Niels Bohr in the early stage of his career developed a nonlinear theory of fluidic surface oscillation in order to study surface tension of liquids. His theory includes the nonlinear interaction between multipolar surface oscillation modes, surpassing the linear theory of Rayleigh and Lamb. It predicts a specific normalized magnitude of 0.416η2 for an octapolar component, nonlinearly induced by a quadrupolar one with a magnitude of η much less than unity. No experimental confirmation on this prediction has been reported. Nonetheless, accurate determination of multipolar components is important as in optical fiber spinning, film blowing and recently in optofluidic microcavities for ray and wave chaos studies and photonics applications. Here, we report experimental verification of his theory. By using optical forward diffraction, we measured the cross-sectional boundary profiles at extreme positions of a surface-oscillating liquid column ejected from a deformed microscopic orifice. We obtained a coefficient of 0.42 ± 0.08 consistently under various experimental conditions. We also measured the resonance mode spectrum of a two-dimensional cavity formed by the cross-sectional segment of the liquid jet. The observed spectra agree well with wave calculations assuming a coefficient of 0.414 ± 0.011. Our measurements establish the first experimental observation of Bohr’s hydrodynamic theory.
Freezing of nonlinear Bloch oscillations in the generalized discrete nonlinear Schrödinger equation.
Cao, F J
2004-09-01
The dynamics in a nonlinear Schrödinger chain in a homogeneous electric field is studied. We show that discrete translational invariant integrability-breaking terms can freeze the Bloch nonlinear oscillations and introduce new faster frequencies in their dynamics. These phenomena are studied by direct numerical integration and through an adiabatic approximation. The adiabatic approximation allows a description in terms of an effective potential that greatly clarifies the phenomena.
Cooling Mechanical Oscillators by Coherent Control
NASA Astrophysics Data System (ADS)
Frimmer, Martin; Gieseler, Jan; Novotny, Lukas
2016-10-01
In optomechanics, electromagnetic fields are harnessed to control a single mode of a mechanically compliant system, while other mechanical degrees of freedom remain unaffected due to the modes' mutual orthogonality and high quality factor. Extension of the optical control beyond the directly addressed mode would require a controlled coupling between mechanical modes. Here, we introduce an optically controlled coupling between two oscillation modes of an optically levitated nanoparticle. We sympathetically cool one oscillation mode by coupling it coherently to the second mode, which is feedback cooled. Furthermore, we demonstrate coherent energy transfer between mechanical modes and discuss its application for ground-state cooling.
Hazledine, Saul; Sun, Jongho; Wysham, Derin; Downie, J. Allan; Oldroyd, Giles E. D.; Morris, Richard J.
2009-01-01
Legume plants form beneficial symbiotic interactions with nitrogen fixing bacteria (called rhizobia), with the rhizobia being accommodated in unique structures on the roots of the host plant. The legume/rhizobial symbiosis is responsible for a significant proportion of the global biologically available nitrogen. The initiation of this symbiosis is governed by a characteristic calcium oscillation within the plant root hair cells and this signal is activated by the rhizobia. Recent analyses on calcium time series data have suggested that stochastic effects have a large role to play in defining the nature of the oscillations. The use of multiple nonlinear time series techniques, however, suggests an alternative interpretation, namely deterministic chaos. We provide an extensive, nonlinear time series analysis on the nature of this calcium oscillation response. We build up evidence through a series of techniques that test for determinism, quantify linear and nonlinear components, and measure the local divergence of the system. Chaos is common in nature and it seems plausible that properties of chaotic dynamics might be exploited by biological systems to control processes within the cell. Systems possessing chaotic control mechanisms are more robust in the sense that the enhanced flexibility allows more rapid response to environmental changes with less energetic costs. The desired behaviour could be most efficiently targeted in this manner, supporting some intriguing speculations about nonlinear mechanisms in biological signaling. PMID:19675679
Mathematical Modeling and Control of Nonlinear Oscillators with Shape Memory Alloys
NASA Astrophysics Data System (ADS)
Bendame, Mohamed
for the system's thermo-mechanical dynamics are constructed using conservation laws of mass, momentum, and energy. Due to the complexity of the derived thermo-mechanical model, and the need to control the nonlinear oscillator, a model reduction based on the Galerkin method is applied to the new system in order to derive a low-dimensional model which is then solved numerically. A linear feedback control strategy for nonlinear systems is then implemented to design a tracking controller that makes the system follow a given reference input signal. The work presented in this thesis demonstrates how SMAs can be modeled by using efficient methodologies in order to capture their behavior, and how SMAs can be made stable and their chaotic behavior can be controlled by using linear and nonlinear control methods.
Nonreciprocal wave scattering on nonlinear string-coupled oscillators
Lepri, Stefano; Pikovsky, Arkady
2014-12-01
We study scattering of a periodic wave in a string on two lumped oscillators attached to it. The equations can be represented as a driven (by the incident wave) dissipative (due to radiation losses) system of delay differential equations of neutral type. Nonlinearity of oscillators makes the scattering non-reciprocal: The same wave is transmitted differently in two directions. Periodic regimes of scattering are analyzed approximately, using amplitude equation approach. We show that this setup can act as a nonreciprocal modulator via Hopf bifurcations of the steady solutions. Numerical simulations of the full system reveal nontrivial regimes of quasiperiodic and chaotic scattering. Moreover, a regime of a “chaotic diode,” where transmission is periodic in one direction and chaotic in the opposite one, is reported.
Nonlinear oscillations in a muscle pacemaker cell model
NASA Astrophysics Data System (ADS)
González-Miranda, J. M.
2017-02-01
This article presents a numerical simulation study of the nonlinear oscillations displayed by the Morris-Lecar model [Biophys. J. 35 (1981) 193] for the oscillations experimentally observed in the transmembrane potential of a muscle fiber subject to an external electrical stimulus. We consider the model in the case when there is no external stimulation, aiming to establish the ability of the model to display biophysically reasonable pacemaker dynamics. We obtain 2D bifurcation diagrams showing that indeed the model presents oscillatory dynamics, displaying the two main types of action potentials that are observed in muscle fibers. The results obtained are shown to be structurally stable; that is, robust against changes in the values of system parameters. Moreover, it is demonstrated how the model is appropriate to analyze the action potentials observed in terms of the transmembrane currents creating them.
Nonlinear inertial oscillations of a multilayer eddy: An analytical solution
NASA Astrophysics Data System (ADS)
Dotsenko, S. F.; Rubino, A.
2008-06-01
Nonlinear axisymmetric oscillations of a warm baroclinic eddy are considered within the framework of an reduced-gravity model of the dynamics of a multilayer ocean. A class of exact analytical solutions describing pure inertial oscillations of an eddy formation is found. The thicknesses of layers in the eddy vary according to a quadratic law, and the horizontal projections of the velocity in the layers depend linearly on the radial coordinate. Owing to a complicated structure of the eddy, weak limitations on the vertical distribution of density, and an explicit form of the solution, the latter can be treated as a generalization of the exact analytical solutions of this form that were previously obtained for homogeneous and baroclinic eddies in the ocean.
A New Chaotic Electro-Mechanical Oscillator
NASA Astrophysics Data System (ADS)
Buscarino, Arturo; Famoso, Carlo; Fortuna, Luigi; Frasca, Mattia
In this paper, a new electro-mechanical chaotic oscillator is presented. The system is based on the motion of the metal tip of a beam in a double-well potential generated by two magnets, and works thanks to the vibrations generated in the flexible mechanical structure by two rotating coils that produce noise-like signals. As the source of vibration is internal, the system may be considered an autonomous oscillator. Chaotic motion is experimentally observed and verified with a mathematical model of the phenomenon.
Nonlinear dynamics of the wake of an oscillating cylinder
NASA Astrophysics Data System (ADS)
Olinger, D. J.; Sreenivasan, K. R.
1988-02-01
The wake of an oscillating cylinder at low Reynolds numbers is a nonlinear system in which a limit cycle due to natural vortex shedding is modulated, generating in phase space a flow on a torus. It is experimentally shown that the system displays Arnol'd tongues for rational frequency ratios, and approximates the devil's staircase along the critical line. The 'singularity spectrum' as well as spectral peaks at various Fibonacci sequences accompanying quasi-periodic transition to chaos shows that the system belongs to the same universality class as the sine circle map.
Existence of Forced Oscillations for Some Nonlinear Differential Equations.
1982-11-01
groups of level sets of the functional associated with the system are ", -t4 . I not trivial. Some more general results concerning systems of the type, f... general non autonomous systems of the type (1.3) 9 + v;(t,x) - 0 There is a vast literature devoted to the subject of nonlinear oscillations in systems...g(t,x) - 0 (x(t) .3) quite general results on the existence of periodic solutions have been obtained by Hartman 114] and Jacobovitz (151 (by using
Diagnosis of nonlinear BWR oscillations using TRAC/BF1
Borkowski, J.A.; Robinson, G.E.; Baratta, A.J. )
1990-01-01
The nonlinear nature of boiling water reactor (BWR) stability has been demonstrated in both experimental tests and lumped parameter calculational models. Point kinetic reactivity feedback is nonlinear because of its functional dependence on fuel temperature and moderator density. The TRAC/BF1 model used in this analysis differs from a lumped parameter model in its spatial extent. The model, intended to be consistent with a BWR/4, was developed with four active fuel channel components representing one hot, two average, and one peripheral bundles. The vessel internals were modeled explicitly. These internals include lower and upper plena, separator/dryers, core shroud, and dryer skirt. The jet pump/recirculation system is modeled in an azimuthally symmetric fashion. The feedwater and steam line boundary conditions are based on time-dependent data representative of that observed during the LaSalle oscillation event.
Geometric phases in neutrino oscillations with nonlinear refraction
NASA Astrophysics Data System (ADS)
Johns, Lucas; Fuller, George M.
2017-02-01
Neutrinos propagating in dense astrophysical environments sustain nonlinear refractive effects due to neutrino-neutrino forward scattering. We study geometric phases in neutrino oscillations that arise out of cyclic evolution of the potential generated by these forward-scattering processes. We perform several calculations, exact and perturbative, that illustrate the robustness of such phases, and of geometric effects more broadly, in the flavor evolution of neutrinos. The scenarios we consider are highly idealized in order to make them analytically tractable, but they suggest the possible presence of complicated geometric effects in realistic astrophysical settings. We also point out that in the limit of extremely high neutrino densities, the nonlinear potential in three flavors naturally gives rise to non-Abelian geometric phases. This paper is intended to be accessible to neutrino experts and nonspecialists alike.
Frequency Response and Gap Tuning for Nonlinear Electrical Oscillator Networks
Bhat, Harish S.; Vaz, Garnet J.
2013-01-01
We study nonlinear electrical oscillator networks, the smallest example of which consists of a voltage-dependent capacitor, an inductor, and a resistor driven by a pure tone source. By allowing the network topology to be that of any connected graph, such circuits generalize spatially discrete nonlinear transmission lines/lattices that have proven useful in high-frequency analog devices. For such networks, we develop two algorithms to compute the steady-state response when a subset of nodes are driven at the same fixed frequency. The algorithms we devise are orders of magnitude more accurate and efficient than stepping towards the steady-state using a standard numerical integrator. We seek to enhance a given network's nonlinear behavior by altering the eigenvalues of the graph Laplacian, i.e., the resonances of the linearized system. We develop a Newton-type method that solves for the network inductances such that the graph Laplacian achieves a desired set of eigenvalues; this method enables one to move the eigenvalues while keeping the network topology fixed. Running numerical experiments using three different random graph models, we show that shrinking the gap between the graph Laplacian's first two eigenvalues dramatically improves a network's ability to (i) transfer energy to higher harmonics, and (ii) generate large-amplitude signals. Our results shed light on the relationship between a network's structure, encoded by the graph Laplacian, and its function, defined in this case by the presence of strongly nonlinear effects in the frequency response. PMID:24223751
Chimera states in mechanical oscillator networks
Martens, Erik Andreas; Thutupalli, Shashi; Fourrière, Antoine; Hallatschek, Oskar
2013-01-01
The synchronization of coupled oscillators is a fascinating manifestation of self-organization that nature uses to orchestrate essential processes of life, such as the beating of the heart. Although it was long thought that synchrony and disorder were mutually exclusive steady states for a network of identical oscillators, numerous theoretical studies in recent years have revealed the intriguing possibility of “chimera states,” in which the symmetry of the oscillator population is broken into a synchronous part and an asynchronous part. However, a striking lack of empirical evidence raises the question of whether chimeras are indeed characteristic of natural systems. This calls for a palpable realization of chimera states without any fine-tuning, from which physical mechanisms underlying their emergence can be uncovered. Here, we devise a simple experiment with mechanical oscillators coupled in a hierarchical network to show that chimeras emerge naturally from a competition between two antagonistic synchronization patterns. We identify a wide spectrum of complex states, encompassing and extending the set of previously described chimeras. Our mathematical model shows that the self-organization observed in our experiments is controlled by elementary dynamical equations from mechanics that are ubiquitous in many natural and technological systems. The symmetry-breaking mechanism revealed by our experiments may thus be prevalent in systems exhibiting collective behavior, such as power grids, optomechanical crystals, or cells communicating via quorum sensing in microbial populations. PMID:23759743
Chimera states in mechanical oscillator networks.
Martens, Erik Andreas; Thutupalli, Shashi; Fourrière, Antoine; Hallatschek, Oskar
2013-06-25
The synchronization of coupled oscillators is a fascinating manifestation of self-organization that nature uses to orchestrate essential processes of life, such as the beating of the heart. Although it was long thought that synchrony and disorder were mutually exclusive steady states for a network of identical oscillators, numerous theoretical studies in recent years have revealed the intriguing possibility of "chimera states," in which the symmetry of the oscillator population is broken into a synchronous part and an asynchronous part. However, a striking lack of empirical evidence raises the question of whether chimeras are indeed characteristic of natural systems. This calls for a palpable realization of chimera states without any fine-tuning, from which physical mechanisms underlying their emergence can be uncovered. Here, we devise a simple experiment with mechanical oscillators coupled in a hierarchical network to show that chimeras emerge naturally from a competition between two antagonistic synchronization patterns. We identify a wide spectrum of complex states, encompassing and extending the set of previously described chimeras. Our mathematical model shows that the self-organization observed in our experiments is controlled by elementary dynamical equations from mechanics that are ubiquitous in many natural and technological systems. The symmetry-breaking mechanism revealed by our experiments may thus be prevalent in systems exhibiting collective behavior, such as power grids, optomechanical crystals, or cells communicating via quorum sensing in microbial populations.
Nonlinear mechanical resonators for ultra-sensitive mass detection
NASA Astrophysics Data System (ADS)
Datskos, P. G.; Lavrik, N. V.
2014-10-01
The fundamental sensitivity limit of an appropriately scaled down mechanical resonator can approach one atomic mass unit when only thermal noise is present in the system. However, operation of such nanoscale mechanical resonators is very challenging due to minuteness of their oscillation amplitudes and presence of multiple noise sources in real experimental environments. In order to surmount these challenges, we use microscale cantilever resonators driven to large amplitudes, far beyond their nonlinear instability onset. Our experiments show that such a nonlinear cantilever resonator, described analytically as a Duffing oscillator, has mass sensing performance comparable to that of much smaller resonators operating in a linear regime. We demonstrate femtogram level mass sensing that relies on a bifurcation point tracking that does not require any complex readout means. Our approaches enable straightforward detection of mass changes that are near the fundamental limit imposed by thermo-mechanical fluctuations.
NASA Astrophysics Data System (ADS)
Lee, Chin Yik; Li, Larry Kin Bong; Juniper, Matthew P.; Cant, Robert Stewart
2016-01-01
Turbulent premixed flames often experience thermoacoustic instabilities when the combustion heat release rate is in phase with acoustic pressure fluctuations. Linear methods often assume a priori that oscillations are periodic and occur at a dominant frequency with a fixed amplitude. Such assumptions are not made when using nonlinear analysis. When an oscillation is fully saturated, nonlinear analysis can serve as a useful avenue to reveal flame behaviour far more elaborate than period-one limit cycles, including quasi-periodicity and chaos in hydrodynamically or thermoacoustically self-excited system. In this paper, the behaviour of a bluff-body stabilised turbulent premixed propane/air flame in a model jet-engine afterburner configuration is investigated using computational fluid dynamics. For the frequencies of interest in this investigation, an unsteady Reynolds-averaged Navier-Stokes approach is found to be appropriate. Combustion is represented using a modified laminar flamelet approach with an algebraic closure for the flame surface density. The results are validated by comparison with existing experimental data and with large eddy simulation, and the observed self-excited oscillations in pressure and heat release are studied using methods derived from dynamical systems theory. A systematic analysis is carried out by increasing the equivalence ratio of the reactant stream supplied to the premixed flame. A strong variation in the global flame structure is observed. The flame exhibits a self-excited hydrodynamic oscillation at low equivalence ratios, becomes steady as the equivalence ratio is increased to intermediate values, and again exhibits a self-excited thermoacoustic oscillation at higher equivalence ratios. Rich nonlinear behaviour is observed and the investigation demonstrates that turbulent premixed flames can exhibit complex dynamical behaviour including quasiperiodicity, limit cycles and period-two limit cycles due to the interactions of various
Petrov, E Yu; Kudrin, A V
2012-05-01
Many intriguing properties of driven nonlinear resonators, including the appearance of chaos, are very important for understanding the universal features of nonlinear dynamical systems and can have great practical significance. We consider a cylindrical cavity resonator driven by an alternating voltage and filled with a nonlinear nondispersive medium. It is assumed that the medium lacks a center of inversion and the dependence of the electric displacement on the electric field can be approximated by an exponential function. We show that the Maxwell equations are integrated exactly in this case and the field components in the cavity are represented in terms of implicit functions of special form. The driven electromagnetic oscillations in the cavity are found to display very interesting temporal behavior and their Fourier spectra contain singular continuous components. This is a demonstration of the existence of a singular continuous (fractal) spectrum in an exactly integrable system.
Modeling Wave Driven Non-linear Flow Oscillations: The Terrestrial QBO and a Solar Analog
NASA Technical Reports Server (NTRS)
Mayr, Hans G.; Bhartia, P. K. (Technical Monitor)
2001-01-01
The Quasi Biennial Oscillation (QBO) of the zonal circulation observed in the terrestrial atmosphere at low latitudes is driven by wave mean flow interaction as was demonstrated first by Lindzen and Holton (1968), shown in a laboratory experiment by Plumb and McEwan (1978), and modeled by others (e.g., Plumb, Dunkerton). Although influenced by the seasonal cycle of solar forcing, the QBO, in principle, represents a nonlinear flow oscillation that can be maintained by a steady source of upward propagating waves. The wave driven non-linearity is of third or odd order in the flow velocity, which regenerates the fundamental harmonic itself to keep the oscillation going - the fluid dynamical analog of the displacement mechanism in the mechanical clock. Applying Hines' Doppler Spread Parameterization (DSP) for gravity waves (GW), we discuss with a global-scale spectral model numerical experiments that elucidate some properties of the QBO and its possible effects on the climatology of the atmosphere. Depending on the period of the QBO, wave filtering can cause interaction with the seasonal variations to produce pronounced oscillations with beat periods around 10 years. Since the seasonal cycle and its variability influence the period of the QBO, it may also be a potent conduit of solar activity variations to lower altitudes. Analogous to the terrestrial QBO, we propose that a flow oscillation may account for the 22-year periodicity of the solar magnetic cycle, potentially answering Dicke (1978) who asked, "Is there a chronometer hidden deep inside the Sun?" The oscillation would occur below the convection region, where gravity waves can propagate. Employing a simplified, analytic model, Hines' DSP is applied to estimate the flow oscillation. Depending on the adopted horizontal wavelengths of GW's, wave amplitudes less than 10 m/s can be made to produce oscillating zonal flows of about 20 m/s that should be large enough to generate a significant oscillation in the magnetic
Chaotic motion of a weakly nonlinear, modulated oscillator
Miles, John
1984-01-01
A weakly nonlinear oscillator of natural frequency ω0 and damping ratio δ is driven by an amplitude-modulated force of dimensionless amplitude ε, carrier frequency ω, and modulation frequency ω1. Each of (ω - ω0)/ω0, ω1/ω0, and δ is O(ε2/3) as ε → 0. The response in this resonant neighborhood is a slowly modulated sine wave, the envelope of which is described by three first-order, autonomous, ordinary differential equations. This envelope, which is periodic for δ >> ε2/3, is chaotic in certain ranges of (ω - ω0)/ω0 and ω1/ω0 if δ/ε2/3 is sufficiently small. PMID:16593480
Barut—Girardello Coherent States for Nonlinear Oscillator with Position-Dependent Mass
NASA Astrophysics Data System (ADS)
Amir, Naila; Iqbal, Shahid
2016-07-01
Using ladder operators for the non-linear oscillator with position-dependent effective mass, realization of the dynamic group SU(1,1) is presented. Keeping in view the algebraic structure of the non-linear oscillator, coherent states are constructed using Barut—Girardello formalism and their basic properties are discussed. Furthermore, the statistical properties of these states are investigated by means of Mandel parameter and second order correlation function. Moreover, it is shown that in the harmonic limit, all the results obtained for the non-linear oscillator with spatially varying mass reduce to corresponding results of the linear oscillator with constant mass.
NASA Astrophysics Data System (ADS)
Bryuhanov, Yu. A.
2010-08-01
We consider a method for calculating forced oscillations in nonlinear discrete-time systems under periodic external actions. The method is based on representing the stationary oscillations in the form of an invariant set of nonlinear discrete point mappings and allows one to calculate the nonlinear-system response in the steady-state regime. The examples of using this method for calculating forced oscillations in the first- and second-order nonlinear recursive systems under the harmonic-signal action on such systems are presented.
Flagellar oscillation: a commentary on proposed mechanisms.
Woolley, David M
2010-08-01
Eukaryotic flagella and cilia have a remarkably uniform internal 'engine' known as the '9+2' axoneme. With few exceptions, the function of cilia and flagella is to beat rhythmically and set up relative motion between themselves and the liquid that surrounds them. The molecular basis of axonemal movement is understood in considerable detail, with the exception of the mechanism that provides its rhythmical or oscillatory quality. Some kind of repetitive 'switching' event is assumed to occur; there are several proposals regarding the nature of the 'switch' and how it might operate. Herein I first summarise all the factors known to influence the rate of the oscillation (the beating frequency). Many of these factors exert their effect through modulating the mean sliding velocity between the nine doublet microtubules of the axoneme, this velocity being the determinant of bend growth rate and bend propagation rate. Then I explain six proposed mechanisms for flagellar oscillation and review the evidence on which they are based. Finally, I attempt to derive an economical synthesis, drawing for preference on experimental research that has been minimally disruptive of the intricate structure of the axoneme. The 'provisional synthesis' is that flagellar oscillation emerges from an effect of passive sliding direction on the dynein arms. Sliding in one direction facilitates force-generating cycles and dynein-to-dynein synchronisation along a doublet; sliding in the other direction is inhibitory. The direction of the initial passive sliding normally oscillates because it is controlled hydrodynamically through the alternating direction of the propulsive thrust. However, in the absence of such regulation, there can be a perpetual, mechanical self-triggering through a reversal of sliding direction due to the recoil of elastic structures that deform as a response to the prior active sliding. This provisional synthesis may be a useful basis for further examination of the problem.
An analytical study of nonlinear oscillations during uncontrolled descent in the atmosphere
NASA Astrophysics Data System (ADS)
Privarnikov, O. A.
Reference is made to an earlier study (Privarnikov, 1980) in which expressions have been obtained for the analysis of plane nonlinear oscillations during uncontrolled ballistic descent in the atmosphere. Here, a more accurate solution to the ballistic descent problem is obtained which allows for the nonlinearity of the aerodynamic coefficients and for the effect of oscillations on the motion of the center of mass. The accuracy of the solution is estimated for different degrees of nonlinearity of the aerodynamic coefficients.
NASA Astrophysics Data System (ADS)
Korman, M. S.; Duong, D. V.; Kalsbeck, A. E.
2015-10-01
An apparatus (SPO), designed to study flexural vibrations of a soil loaded plate, consists of a thin circular elastic clamped plate (and cylindrical wall) supporting a vertical soil column. A small magnet attached to the center of the plate is driven by a rigid AC coil (located coaxially below the plate) to complete the electrodynamic soil plate oscillator SPO design. The frequency dependent mechanical impedance Zmech (force / particle velocity, at the plate's center) is inversely proportional to the electrical motional impedance Zmot. Measurements of Zmot are made using the complex output to input response of a Wheatstone bridge that has an identical coil element in one of its legs. Near resonance, measurements of Zmot (with no soil) before and after a slight point mass loading at the center help determine effective mass, spring, damping and coupling constant parameters of the system. "Tuning curve" behavior of real{ Zmot } and imaginary{ Zmot } at successively higher vibration amplitudes of dry sifted masonry sand are measured. They exhibit a decrease "softening" in resonance frequency along with a decrease in the quality Q factor. In soil surface vibration measurements a bilinear hysteresis model predicts the tuning curve shape for this nonlinear mesoscopic elastic SPO behavior - which also models the soil vibration over an actual plastic "inert" VS 1.6 buried landmine. Experiments are performed where a buried 1m cube concrete block supports a 12 inch deep by 30 inch by 30 inch concrete soil box for burying a VS 1.6 in dry sifted masonry sand for on-the-mine and off-the-mine soil vibration experiments. The backbone curve (a plot of the peak amplitude vs. corresponding resonant frequency from a family of tuning curves) exhibits mostly linear behavior for "on target" soil surface vibration measurements of the buried VS 1.6 or drum-like mine simulants for relatively low particle velocities of the soil. Backbone curves for "on target" measurements exhibit
Analytical solutions to nonlinear conservative oscillator with fifth-order nonlinearity
NASA Astrophysics Data System (ADS)
Sfahani, M. G.; Ganji, S. S.; Barari, Amin; Mirgolbabaei, H.; Domairry, G.
2010-09-01
This paper describes analytical and numerical methods to analyze the steady state periodic response of an oscillator with symmetric elastic and inertia nonlinearity. A new implementation of the homotopy perturbation method (HPM) and an ancient Chinese method called the max-min approach are presented to obtain an approximate solution. The major concern is to assess the accuracy of these approximate methods in predicting the system response within a certain range of system parameters by examining their ability to establish an actual (numerical) solution. Therefore, the analytical results are compared with the numerical results to illustrate the effectiveness and convenience of the proposed methods.
The numerical modelling of a driven nonlinear oscillator
Shew, C.
1995-11-01
The torsional oscillator in the Earth Sciences Division was developed at Lawrence Livermore National Laboratory and is the only one of its kind. It was developed to study the way rocks damp vibrations. Small rock samples are tested to determine the seismic properties of rocks, but unlike other traditional methods that propagate high frequency waves through small samples, this machine forces the sample to vibrate at low frequencies, which better models real-life properties of large masses. In this particular case, the rock sample is tested with a small crack in its middle. This forces the rock to twist against itself, causing a {open_quotes}stick-slip{close_quotes} friction, known as stiction. A numerical model that simulates the forced torsional osillations of the machine is currently being developed. The computer simulation implements the graphical language LabVIEW, and is looking at the nonlinear spring effects, the frictional forces, and the changes in amplitude and frequency of the forced vibration. Using LabVIEW allows for quick prototyping and greatly reduces the {open_quotes}time to product{close_quotes} factor. LabVIEW`s graphical environment allows scientists and engineers to use familiar terminology and icons (e.g. knobs, switches, graphs, etc.). Unlike other programming systems that use text-based languages, such as C and Basic, LabVIEW uses a graphical programming language to create programs in block diagram form.
Nonequilibrium / nonlinear chemical oscillation in the virtual absence of gravity
NASA Astrophysics Data System (ADS)
Fujieda, S.; Mogami, Y.; Moriyasu, K.; Mori, Y.
1999-01-01
The Belousov-Zhabotinsky (BZ) reactions were used as typical examples of a nonlinear system far from equilibrium in connection with biological evolution. The virtual absence of gravity in the present work was given from the free-fall facility of Japan Microgravity Center (JAMIC) in Hokkaido. The reaction solution of BZ reaction was composed of bromate in sulfuric acid, 1,4-cyclohexanedione and ferroin to visualize the time development of patterns of chemical oscillations in the reaction-diffusion system. It is a bubble-free constitution in the aging of the reaction. Therefore, the setup constructed to collect image data via CCD cameras was simplified. The operation sequences of necessary devices were comprised of simple solid state relays which were started by a command from the operation room of JAMIC. The propagation profile of chemical patterns under microgravity of 10-5 g was collected as image data for 9.8 s, and processed by a software of STM-STS2. In the aqueous solutions, propagation velocity of chemical patterns under microgravity was decreased to 80.9 % of that under normal gravity, owing to suppression of convection. On the other hand, in gel matrix, gravity did not influence the propagation velocity.
Nonlinear harmonic generation in finite amplitude black hole oscillations
NASA Astrophysics Data System (ADS)
Papadopoulos, Philippos
2002-04-01
The nonlinear generation of harmonics in gravitational perturbations of black holes is explored using numerical relativity based on an ingoing light-cone framework. Localized, finite, perturbations of an isolated black hole are parametrized by amplitude and angular harmonic form. The response of the black hole spacetime is monitored and its harmonic content analyzed to identify the strength of the nonlinear generation of harmonics as a function of the initial data amplitude. It is found that overwhelmingly the black hole responds at the harmonic mode perturbed, even for spacetimes with 10% of the black hole mass radiated. The coefficients for down and up scattering in harmonic space are computed for a range of couplings. Down scattering, leading to smoothing out of angular structure, is found to be equally as or more efficient than the up scatterings that would lead to increased rippling. The details of this nonlinear balance may form the quantitative mechanism by which black holes avoid fission even for arbitrary strong distortions.
Frequency stabilization in nonlinear MEMS and NEMS oscillators
Lopez, Omar Daniel; Antonio, Dario
2014-09-16
An illustrative system includes an amplifier operably connected to a phase shifter. The amplifier is configured to amplify a voltage from an oscillator. The phase shifter is operably connected to a driving amplitude control, wherein the phase shifter is configured to phase shift the amplified voltage and is configured to set an amplitude of the phase shifted voltage. The oscillator is operably connected to the driving amplitude control. The phase shifted voltage drives the oscillator. The oscillator is at an internal resonance condition, based at least on the amplitude of the phase shifted voltage, that stabilizes frequency oscillations in the oscillator.
Stimulus statistics shape oscillations in nonlinear recurrent neural networks.
Lefebvre, Jérémie; Hutt, Axel; Knebel, Jean-François; Whittingstall, Kevin; Murray, Micah M
2015-02-18
Rhythmic activity plays a central role in neural computations and brain functions ranging from homeostasis to attention, as well as in neurological and neuropsychiatric disorders. Despite this pervasiveness, little is known about the mechanisms whereby the frequency and power of oscillatory activity are modulated, and how they reflect the inputs received by neurons. Numerous studies have reported input-dependent fluctuations in peak frequency and power (as well as couplings across these features). However, it remains unresolved what mediates these spectral shifts among neural populations. Extending previous findings regarding stochastic nonlinear systems and experimental observations, we provide analytical insights regarding oscillatory responses of neural populations to stimulation from either endogenous or exogenous origins. Using a deceptively simple yet sparse and randomly connected network of neurons, we show how spiking inputs can reliably modulate the peak frequency and power expressed by synchronous neural populations without any changes in circuitry. Our results reveal that a generic, non-nonlinear and input-induced mechanism can robustly mediate these spectral fluctuations, and thus provide a framework in which inputs to the neurons bidirectionally regulate both the frequency and power expressed by synchronous populations. Theoretical and computational analysis of the ensuing spectral fluctuations was found to reflect the underlying dynamics of the input stimuli driving the neurons. Our results provide insights regarding a generic mechanism supporting spectral transitions observed across cortical networks and spanning multiple frequency bands.
Probabilistic characteristics of noisy Van der Pol type oscillator with nonlinear damping
NASA Astrophysics Data System (ADS)
Dubkov, A. A.; Litovsky, I. A.
2016-05-01
The exact Fokker-Planck equation for the joint probability distribution of amplitude and phase of a Van der Pol oscillator perturbed by both additive and multiplicative noise sources with arbitrary nonlinear damping is first derived by the method of functional splitting of averages. We truncate this equation in the usual manner using the smallness of the damping parameter and obtain a general expression for the stationary probability density function of oscillation amplitude, which is valid for any nonlinearity in the feedback loop of the oscillator. We analyze the dependence of this stationary solution on system parameters and intensities of noise sources for two different situations: (i) Van der Pol generator with soft and hard excitation regimes; (ii) Van der Pol oscillator with negative nonlinear damping. As shown, in the first case the probability distribution of amplitude demonstrates one characteristic maximum, which indicates the presence of a stable limit cycle in the system. The non-monotonic dependence of stationary probability density function on oscillation frequency is also detected. In the second case we examine separately three situations: linear oscillator with two noise sources, nonlinear oscillator with additive noise and nonlinear oscillator with frequency fluctuations. For the last two situations, noise-induced transitions in the system under consideration are found.
Quantum versus classical phase-locking transition in a frequency-chirped nonlinear oscillator
Barth, I.; Friedland, L.; Gat, O.; Shagalov, A. G.
2011-07-15
Classical and quantum-mechanical phase-locking transition in a nonlinear oscillator driven by a chirped-frequency perturbation is discussed. Different limits are analyzed in terms of the dimensionless parameters P{sub 1}={epsilon}/{radical}(2m({Dirac_h}/2{pi}){omega}{sub 0}{alpha}) and P{sub 2}=(3({Dirac_h}/2{pi}){beta})/(4m{radical}({alpha})) ({epsilon}, {alpha}, {beta}, and {omega}{sub 0} being the driving amplitude, the frequency chirp rate, the nonlinearity parameter, and the linear frequency of the oscillator). It is shown that, for P{sub 2}<
>P{sub 1}+1, the transition involves quantum-mechanical energy ladder climbing (LC). The threshold for the phase-locking transition and its width in P{sub 1} in both AR and LC limits are calculated. The theoretical results are tested by solving the Schroedinger equation in the energy basis and illustrated via the Wigner function in phase space.
Mechanical Properties of a Primary Cilium Measured by Resonant Oscillation
NASA Astrophysics Data System (ADS)
Resnick, Andrew
Primary cilia are ubiquitous mammalian cellular substructures implicated in an ever-increasing number of regulatory pathways. The well-established `ciliary hypothesis' states that physical bending of the cilium (for example, due to fluid flow) initiates signaling cascades, yet the mechanical properties of the cilium remain incompletely measured, resulting in confusion regarding the biological significance of flow-induced ciliary mechanotransduction. In this work we measure the mechanical properties of a primary cilium by using an optical trap to induce resonant oscillation of the structure. Our data indicate 1), the primary cilium is not a simple cantilevered beam, 2), the base of the cilium may be modeled as a nonlinear rotatory spring, the linear spring constant `k' of the cilium base calculated to be (4.6 +/- 0.62)*10-12 N/rad and nonlinear spring constant ` α' to be (-1 +/- 0.34) *10-10 N/rad2 , and 3) the ciliary base may be an essential regulator of mechanotransduction signalling. Our method is also particularly suited to measure mechanical properties of nodal cilia, stereocilia, and motile cilia, anatomically similar structures with very different physiological functions.
Mechanical mixing in nonlinear nanomechanical resonators
NASA Astrophysics Data System (ADS)
Erbe, A.; Krömmer, H.; Kraus, A.; Blick, R. H.; Corso, G.; Richter, K.
2000-11-01
The physics of nonlinear dynamics has been studied in detail in macroscopic mechanical systems like the driven classical pendulum. By now, it is possible to build mechanical devices on the nanometer scale with eigenfrequencies on the order of several 100 MHz. In this work, we want to present how to machine such nanomechanical resonators out of silicon-on-insulator wafers and how to operate them in the nonlinear regime in order to investigate higher-order mechanical mixing at radio frequencies. The nonlinear response then is compared in detail to nth-order perturbation theory and nonperturbative numerical calculations.
Tunability versus deviation sensitivity in a nonlinear vortex oscillator
NASA Astrophysics Data System (ADS)
Martin, S. Y.; Thirion, C.; Hoarau, C.; Baraduc, C.; Diény, B.
2013-07-01
Frequency modulation experiments were performed on a spin torque vortex oscillator for a wide range of modulation frequencies, up to 10% of the oscillator frequency. A thorough analysis of the intermodulation products shows that the key parameter that describes these experiments is the deviation sensitivity, which is the dynamical frequency-current dependence. It differs significantly from the oscillator tunability discussed so far in the context of spin-transfer oscillators. The essential difference between these two concepts is related to the response time of the vortex oscillator, driven either in quasisteady state or in a transient regime.
Random perturbations of a periodically driven nonlinear oscillator: escape from a resonance zone
NASA Astrophysics Data System (ADS)
Lingala, Nishanth; Sri Namachchivaya, N.; Pavlyukevich, Ilya
2017-04-01
For nonlinear oscillators, frequency of oscillations depends on the oscillation amplitude. When a nonlinear oscillator is periodically driven, the phase space consists of many resonance zones where the oscillator frequency and the driving frequency are commensurable. It is well known that, a small subset of initial conditions can lead to capture in one of the resonance zones. In this paper we study the effect of weak noise on the escape from a resonance zone. Using averaging techniques we obtain the mean exit time from a resonance zone and study the dependence of the exit rate on the parameters of the oscillator. Paper dedicated to Professor Peter W Sauer of University of Illinois on the occasion of his 70th birthday.
Nonlinear dynamics of cable galloping via a two-degree-of-freedom nonlinear oscillator
NASA Astrophysics Data System (ADS)
Yu, Bo
The galloping vibrations of a single transmission cable that may vibrate transversely and torsionally has been investigated via a two-degree-of-freedom oscillator. The analytical solutions of periodic motions for this two-degree-of-freedom system are represented by the finite Fourier series. The analytical bifurcation trees of periodic motions to chaos of a transmission line under both steady and unsteady flows are discussed from the generalized harmonic balance method. The analytical solutions for stable and unstable periodic motions in such a two degree-of-freedom system are achieved, and the corresponding stability and bifurcation was discussed. The limit cycle for the linear cable structure are obtained by gradually decreasing the sinusoidal excitation amplitude. In addition, the numerical simulations of stable and unstable periodic motions are illustrated. The rich dynamical behavior in such a nonlinear cable structure are discovered, and this investigation may help one better understand the galloping phenomena for any elastic structures.
Research in nonlinear structural and solid mechanics
NASA Technical Reports Server (NTRS)
Mccomb, H. G., Jr. (Compiler); Noor, A. K. (Compiler)
1981-01-01
Recent and projected advances in applied mechanics, numerical analysis, computer hardware and engineering software, and their impact on modeling and solution techniques in nonlinear structural and solid mechanics are discussed. The fields covered are rapidly changing and are strongly impacted by current and projected advances in computer hardware. To foster effective development of the technology perceptions on computing systems and nonlinear analysis software systems are presented.
NASA Astrophysics Data System (ADS)
Zhang, Xian-tao; Yang, Jian-min; Xiao, Long-fei
2016-07-01
Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off (PTO) system is a directly linear electric generator or a hydraulic motor that drives an electric generator. The PTO system is simplified as a linear spring and a linear damper. However the conversion is less powerful with wave periods off resonance. Thus, a nonlinear snap-through mechanism with two symmetrically oblique springs and a linear damper is applied in the PTO system. The nonlinear snap-through mechanism is characteristics of negative stiffness and double-well potential. An important nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two springs to the original length of both springs. Time domain method is applied to the dynamics of wave energy converter in regular waves. And the state space model is used to replace the convolution terms in the time domain equation. The results show that the energy harvested by the nonlinear PTO system is larger than that by linear system for low frequency input. While the power captured by nonlinear converters is slightly smaller than that by linear converters for high frequency input. The wave amplitude, damping coefficient of PTO systems and the nonlinear parameter γ affect power capture performance of nonlinear converters. The oscillation of nonlinear wave energy converters may be local or periodically inter well for certain values of the incident wave frequency and the nonlinear parameter γ, which is different from linear converters characteristics of sinusoidal response in regular waves.
NASA Astrophysics Data System (ADS)
Fukuyama, T.; Okugawa, M.
2017-03-01
We have experimentally investigated the dynamic behavior of coupled nonlinear oscillators, including chaos caused by the instability of ionization waves in a glow discharge plasma. We studied the phase synchronization process of coupled asymmetric oscillators with increasing coupling strength. Coherence resonance and phase synchronization were observed in the coupled systems. The phase synchronization process revealed scaling laws with a tendency of Type-I intermittency in the relationships between the coupling strength and the average duration of successive laminar states interrupted by a phase slip. Coupled periodic oscillators changed from a periodic state to chaos caused by the interaction of nonlinear periodic waves at increasing coupling strength.
NASA Astrophysics Data System (ADS)
Chen, Y. Y.; Chen, S. H.; Zhao, W.
2017-07-01
An improved procedure for perturbation method is presented for constructing homoclinic solutions of strongly nonlinear self-excited oscillators. Compared with current perturbation methods based on nonlinear time transformations, the preference of the present method is that the explicit solutions, in respect to the original time variable, can be derived. In the paper, the equivalence and unified perturbation procedure with nonlinear time transformations, by which implicit solutions can be derived at nonlinear time scales, are firstly presented. Then an explicit generating homoclinic solution for power-law strongly nonlinear oscillator is derived with proposed hyperbolic function balance procedure. An approximation scheme is presented to improve the perturbation procedure and the explicit expression for nonlinear time transformation can be achieved. Applications and comparisons with other methods are performed to assess the advantage of the present method.
An atomistic approach to viral mechanical oscillations
NASA Astrophysics Data System (ADS)
Sankey, Otto F.
2009-03-01
Viruses are the simplest ``life'' form. These parasites reproduce by borrowing the machinery of their host cell. Many are pathogenic to plants, animals, and humans. Viruses possess an outer protein coat (capsid) that protects its genomic material that resides inside. We have developed a theoretical technique to model the very low frequency mechanical modes of the viral capsid with atomic resolution. The method uses empirical force fields and a mathematical framework borrowed from electronic structure theory for finding low energy states. The low frequency modes can be ``pinged'' with an ultra-short laser pulse and the aim of the light/vibrational coupling is to interfere with the viral life cycle. The theoretical work here is motivated by the recent work of Tsen et al. [2] who have used ultra-short pulsed laser scattering to inactivate viruses. The methodology can be applied to many systems, and the coupled mechanical oscillations of other floppy biomolecules such as a complete ATP binding cassette (ABC transporter) will also be discussed. Co-authors of this work are Dr. Eric Dykeman, Prof. K.-T. Tsen and Daryn Benson. [4pt] [1] E.C. Dykeman et al., Phys. Rev. Lett., 100, 028101 (2008). [0pt] [2] K-T. Tsen et al., J. of Physics -- Cond. Mat. 19, 472201 (2007).
Nonlinear optomechanical measurement of mechanical motion
Brawley, G. A.; Vanner, M. R.; Larsen, P. E.; Schmid, S.; Boisen, A.; Bowen, W. P.
2016-01-01
Precision measurement of nonlinear observables is an important goal in all facets of quantum optics. This allows measurement-based non-classical state preparation, which has been applied to great success in various physical systems, and provides a route for quantum information processing with otherwise linear interactions. In cavity optomechanics much progress has been made using linear interactions and measurement, but observation of nonlinear mechanical degrees-of-freedom remains outstanding. Here we report the observation of displacement-squared thermal motion of a micro-mechanical resonator by exploiting the intrinsic nonlinearity of the radiation-pressure interaction. Using this measurement we generate bimodal mechanical states of motion with separations and feature sizes well below 100 pm. Future improvements to this approach will allow the preparation of quantum superposition states, which can be used to experimentally explore collapse models of the wavefunction and the potential for mechanical-resonator-based quantum information and metrology applications. PMID:26996234
Nonlinear mechanics of graphene membranes and related systems
NASA Astrophysics Data System (ADS)
De Alba, Roberto
Micro- and nano-mechanical resonators with low mass and high vibrational frequency are often studied for applications in mass and force detection where they can offer unparalleled precision. They are also excellent systems with which to study nonlinear phenomena and fundamental physics due to the numerous routes through which they can couple to each other or to external systems. In this work we study the structural, thermal, and nonlinear properties of various micro-mechanical systems. First, we present a study of graphene-coated silicon nitride membranes; the resulting devices demonstrate the high quality factors of silicon nitride as well as the useful electrical and optical properties of graphene. We then study nonlinear mechanics in pure graphene membranes, where all vibrational eigenmodes are coupled to one another through the membrane tension. This effect enables coherent energy transfer from one mechanical mode to another, in effect creating a graphene mechanics-based frequency mixer. In another experiment, we measure the resonant frequency of a graphene membrane over a wide temperature range, 80K - 550K, to determine whether or not it demonstrates the negative thermal expansion coefficient predicted by prevailing theories; our results indicate that this coefficient is positive at low temperatures - possibly due to polymer contaminants on the graphene surface - and negative above room temperature. Lastly, we study optically-induced self-oscillation in metal-coated silicon nitride nanowires. These structures exhibit self-oscillation at extremely low laser powers ( 1muW incident on the nanowire), and we use this photo-thermal effect to counteract the viscous air-damping that normally inhibits micro-mechanical motion.
NASA Technical Reports Server (NTRS)
Lyell, M. J.; Zhang, L.
1994-01-01
The aspects of nonlinear behavior of a finite length liquid column is investigated with an emphasis on bridge dynamics. The primary objectives are to determine the nonlinear corrections to the interface shape of a naturally oscillating finite length liquid column and to determine the nonlinear corrections to the oscillation frequencies for various modes of oscillation. Application of the Lindstedt-Poincare expansion in conjunction with the domain perturbation techniques results in an hierarchical system of equations.
NASA Astrophysics Data System (ADS)
Chen, Zhen; Li, Yang; Liu, Xianbin
2016-06-01
Noise induced escape from the domain of attraction of a nonhyperbolic chaotic attractor in a periodically excited nonlinear oscillator is investigated. The general mechanism of the escape in the weak noise limit is studied in the continuous case, and the fluctuational path is obtained by statistical analysis. Selecting the primary homoclinic tangency as the initial condition, the action plot is presented by parametrizing the set of escape trajectories and the global minimum gives rise to the optimal path. Results of both methods show good agreements. The entire process of escape is discussed in detail step by step using the fluctuational force. A structure of hierarchical heteroclinic crossings of stable and unstable manifolds of saddle cycles is found, and the escape is observed to take place through successive jumps through this deterministic hierarchical structure.
Linear and nonlinear aspects of the tropical 30-60 day oscillation: A modeling study
NASA Technical Reports Server (NTRS)
Stevens, Duane E.; Stephens, Graeme L.
1991-01-01
The scientific problem focused on study of the tropical 30-60 day oscillation and explanation for this phenomenon is discussed. The following subject areas are covered: the scientific problem (the importance of low frequency oscillations; suggested mechanisms for developing the tropical 30-60 day oscillation); proposed research and its objective; basic approach to research; and results (satellite data analysis and retrieval development; thermodynamic model of the oscillation; the 5-level GCM).
Mechanical Motion Induced by Spatially Distributed Limit-Cycle Oscillators
NASA Astrophysics Data System (ADS)
Sakaguchi, Hidetsugu; Mukae, Yuuki
2017-03-01
Spatially distributed limited-cycle oscillators are seen in various physical and biological systems. In internal organs, mechanical motions are induced by the stimuli of spatially distributed limit-cycle oscillators. We study several mechanical motions by limit-cycle oscillators using simple model equations. One problem is deformation waves of radius oscillation induced by desynchronized limit-cycle oscillators, which is motivated by peristaltic motion of the small intestine. A resonance-like phenomenon is found in the deformation waves, and particles can be transported by the deformation waves. Another is the beating motion of the heart. The expansion and contraction motion is realized by a spatially synchronized limit-cycle oscillation; however, the strong beating disappears by spiral chaos, which is closely related to serious arrhythmia in the heart.
Classical mechanics approach applied to analysis of genetic oscillators.
Vasylchenkova, Anastasiia; Mraz, Miha; Zimic, Nikolaj; Moskon, Miha
2016-04-05
Biological oscillators present a fundamental part of several regulatory mechanisms that control the response of various biological systems. Several analytical approaches for their analysis have been reported recently. They are, however, limited to only specific oscillator topologies and/or to giving only qualitative answers, i.e., is the dynamics of an oscillator given the parameter space oscillatory or not. Here we present a general analytical approach that can be applied to the analysis of biological oscillators. It relies on the projection of biological systems to classical mechanics systems. The approach is able to provide us with relatively accurate results in the meaning of type of behaviour system reflects (i.e. oscillatory or not) and periods of potential oscillations without the necessity to conduct expensive numerical simulations. We demonstrate and verify the proposed approach on three different implementations of amplified negative feedback oscillator.
How does non-linear dynamics affect the baryon acoustic oscillation?
Sugiyama, Naonori S.; Spergel, David N. E-mail: dns@astro.princeton.edu
2014-02-01
We study the non-linear behavior of the baryon acoustic oscillation in the power spectrum and the correlation function by decomposing the dark matter perturbations into the short- and long-wavelength modes. The evolution of the dark matter fluctuations can be described as a global coordinate transformation caused by the long-wavelength displacement vector acting on short-wavelength matter perturbation undergoing non-linear growth. Using this feature, we investigate the well known cancellation of the high-k solutions in the standard perturbation theory. While the standard perturbation theory naturally satisfies the cancellation of the high-k solutions, some of the recently proposed improved perturbation theories do not guarantee the cancellation. We show that this cancellation clarifies the success of the standard perturbation theory at the 2-loop order in describing the amplitude of the non-linear power spectrum even at high-k regions. We propose an extension of the standard 2-loop level perturbation theory model of the non-linear power spectrum that more accurately models the non-linear evolution of the baryon acoustic oscillation than the standard perturbation theory. The model consists of simple and intuitive parts: the non-linear evolution of the smoothed power spectrum without the baryon acoustic oscillations and the non-linear evolution of the baryon acoustic oscillations due to the large-scale velocity of dark matter and due to the gravitational attraction between dark matter particles. Our extended model predicts the smoothing parameter of the baryon acoustic oscillation peak at z = 0.35 as ∼ 7.7Mpc/h and describes the small non-linear shift in the peak position due to the galaxy random motions.
Statistical mechanics of a discrete nonlinear system
Rasmussen; Cretegny; Kevrekidis; Gronbech-Jensen
2000-04-24
Statistical mechanics of the discrete nonlinear Schrodinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for positive temperatures. Beyond the line of T = infinity, we identify a phase transition through a discontinuity in the partition function. The phase transition is demonstrated to manifest itself in the creation of breatherlike localized excitations. Interrelation between the statistical mechanics and the nonlinear dynamics of the system is explored numerically in both regimes.
Vibration energy harvesting using the nonlinear oscillations of a magnetostrictive material
NASA Astrophysics Data System (ADS)
Tsutsumi, Erika; del Rosario, Zachary; Lee, Christopher
2012-04-01
A novel magnetostrictive-material-based device concept to convert ambient mechanical vibration into electricity has been designed, fabricated, and tested. In order to harvest energy over a greater frequency range as compared to state-of- the-art devices, an L-shaped beam which is tuned so that the first two (bending) natural frequencies have a (near) two-to-one ratio is used as a mechanical transducer to generate nonlinear oscillations. Under harmonic excitation, an internal resonance or autoparametric, dynamic response can occur in which one vibration mode parametrically excites a second vibration mode resulting in significant displacement of both modes over an extended frequency range. A magnetostrictive material, Metglas 2605SA1, is used to convert vibration into electricity. Vibration-induced strain in the Metglas changes its magnetization which in turn generates current in a coil of wire. Metglas is highly flexible so it can undergo large displacement and does not fatigue under extended excitation. Demonstration devices are used to study how this nonlinear response can be exploited to generate electricity under single-frequency, harmonic and random base excitation.
Kudo, Kiwamu Suto, Hirofumi; Nagasawa, Tazumi; Mizushima, Koichi; Sato, Rie
2014-10-28
The fundamental function of any oscillator is to produce a waveform with a stable frequency. Here, we show a method of frequency stabilization for spin-torque nano-oscillators (STNOs) that relies on coupling with an adjacent nanomagnet through the magnetic dipole–dipole interaction. It is numerically demonstrated that highly stable oscillations occur as a result of mutual feedback between an STNO and a nanomagnet. The nanomagnet acts as a nonlinear resonator for the STNO. This method is based on the nonlinear behavior of the resonator and can be considered as a magnetic analogue of an optimization scheme in nanoelectromechanical systems. The oscillation frequency is most stabilized when the nanomagnet is driven at a special feedback point at which the feedback noise between the STNO and resonator is completely eliminated.
Factorization solution of a family of quantum nonlinear oscillators
NASA Astrophysics Data System (ADS)
Fellows, Jonathan M.; Smith, Robert A.
2009-08-01
In a recent paper, Cariñena J F, Perelomov A M, Rañada M F and Santander M (2008 J. Phys. A: Math. Gen. 41 085301) analyzed a non-polynomial one-dimensional quantum potential representing an oscillator which they argued was intermediate between the harmonic and isotonic oscillators. In particular they proved that it is Schrödinger soluble, and explicitly obtained the wavefunctions and energies of the bound states. In this paper we show that these results can be obtained much more simply by noting that this potential is a supersymmetric partner potential of the harmonic oscillator. We then use this observation to generate an infinite set of potentials which can exactly be solved in a similar manner.
Quantum mechanics of the inverted oscillator potential
NASA Astrophysics Data System (ADS)
Barton, G.
1986-02-01
The Hamiltonian ( 1/2m)p 2 - 1/2mω 2x 2 yields equations solvable in closed form; one is led to them by questions about the longest mean sojourn time T allowed by quantum mechanics to a system near unstable equilibrium. These equations are then studied further in their own right. After criticism of earlier arguments, one finds, by aid of the Green's function, that T ˜ ω -1log{ l/( {h̷}/{mω) 1/2}} for sojourn in the region | x| < l, where l is the resolving power of the detector. Without appeal to some parameter like l one would get nonsense estimates T ˜ ω-1 (e.g., from the nondecay probability familiar in the decay of metastable states). in this potential wavepackets Gaussian in position do not split on impact: their peaks are either transmitted or reflected, depending on the sign of the energy E ≷ 0; however, they spread so fast that not all the probability ends up on the same side of the origin as the peak. The energy eigenfunctions (parabolic cylinder functions) identify the transmission and reflection amplitudes as T = (1 + e -2πE) -1/2eiφ, R = -i(1 + e -2πE) -1/2 e -πE e iφ, where φ = arg Γ( 1/2 - iE) (in units where 2m = 1 = ω = h̷). The density of states for the interval | x| ≤ L is 2π -1 log L + π -1ϕ'( E). Wavepackets that are peaked sharply enough in energy travel without dispersion in the asymptotic region | x| > | E|, and do split on impact in the usual way. The travel times and time delays of these packets are determined. For both reflection and transmission, and for both E ≷ 0, the time delays are given by φ'( E), which is a symmetric function of E, with a positive maximum at E = 0. In particular, packets tunneling under the barrier reemerge sooner if their energy is more negative. This paradox (which occurs also in other tunneling problems) is elucidated as far as possible. Coherent states are constructed by analogy to those of the ordinary oscillator. Though not integrable, their probability distributions do have a
Properties of finite difference models of non-linear conservative oscillators
NASA Technical Reports Server (NTRS)
Mickens, R. E.
1988-01-01
Finite-difference (FD) approaches to the numerical solution of the differential equations describing the motion of a nonlinear conservative oscillator are investigated analytically. A generalized formulation of the Duffing and modified Duffing equations is derived and analyzed using several FD techniques, and it is concluded that, although it is always possible to contstruct FD models of conservative oscillators which are themselves conservative, caution is required to avoid numerical solutions which do not accurately reflect the properties of the original equation.
Double Fourier Harmonic Balance Method for Nonlinear Oscillators by Means of Bessel Series
2014-10-16
Double Fourier harmonic balance method for nonlinear oscillators by means of Bessel series T.C. Lipscombe∗1 and C.E. Mungan†2 1Catholic University of... harmonic balance method consists in expanding the displacement of an oscillator as a Fourier cosine series in time. A key modification is proposed here, in...than the exact value. Even better, the predicted frequency for the V-ramp case turns out to be exact. Keywords: Fourier expansion, harmonic balance
Nonlinear Dynamics of a Smooth and Discontinuous Oscillator with Multiple Stability
NASA Astrophysics Data System (ADS)
Han, Yanwei; Cao, Qingjie; Ji, Jinchen
2015-12-01
A novel nonlinear oscillator with multiple stabilities is proposed in this paper based on the original SD oscillator [Cao et al., 2006] and the generalized SD oscillator [Han et al., 2012; Cao et al., 2014]. The mathematical model of this system is formulated by using Lagrange equation. Even when all the springs are linear, the system admits strongly irrational nonlinearities due to the geometry configuration. The investigation shows that the nonlinear oscillator exhibits complex equilibrium bifurcations of single-, double-, triple- and quadruple-well properties, and the singular closed orbits of homoclinic, heteroclinic and homo-heteroclinic types as well for both smooth and discontinuous cases. The chaotic behaviors are also presented numerically for the perturbed system under the perturbation of both viscous-damping and external excitation. This oscillator can be extended to a high-order-quasi-zero-stiffness isolator and a nonlinear supporting system for ground vibration test for large-scale structures to achieve the high-static-low-dynamic-stiffness.
Remote synchronization of amplitudes across an experimental ring of non-linear oscillators
Minati, Ludovico E-mail: ludovico.minati@unitn.it
2015-12-15
In this paper, the emergence of remote synchronization in a ring of 32 unidirectionally coupled non-linear oscillators is reported. Each oscillator consists of 3 negative voltage gain stages connected in a loop to which two integrators are superimposed and receives input from its preceding neighbour via a “mixing” stage whose gains form the main system control parameters. Collective behaviour of the network is investigated numerically and experimentally, based on a custom-designed circuit board featuring 32 field-programmable analog arrays. A diverse set of synchronization patterns is observed depending on the control parameters. While phase synchronization ensues globally, albeit imperfectly, for certain control parameter values, amplitudes delineate subsets of non-adjacent but preferentially synchronized nodes; this cannot be trivially explained by synchronization paths along sequences of structurally connected nodes and is therefore interpreted as representing a form of remote synchronization. Complex topology of functional synchronization thus emerges from underlying elementary structural connectivity. In addition to the Kuramoto order parameter and cross-correlation coefficient, other synchronization measures are considered, and preliminary findings suggest that generalized synchronization may identify functional relationships across nodes otherwise not visible. Further work elucidating the mechanism underlying this observation of remote synchronization is necessary, to support which experimental data and board design materials have been made freely downloadable.
Coherent states for nonlinear harmonic oscillator and some of its properties
Amir, Naila E-mail: naila.amir@sns.nust.edu.pk; Iqbal, Shahid E-mail: siqbal@sns.nust.edu.pk
2015-06-15
A one-dimensional nonlinear harmonic oscillator is studied in the context of generalized coherent states. We develop a perturbative framework to compute the eigenvalues and eigenstates for the quantum nonlinear oscillator and construct the generalized coherent states based on Gazeau-Klauder formalism. We analyze their statistical properties by means of Mandel parameter and second order correlation function. Our analysis reveals that the constructed coherent states exhibit super-Poissonian statistics. Moreover, it is shown that the coherent states mimic the phenomena of quantum revivals and fractional revivals during their time evolution. The validity of our results has been discussed in terms of various parametric bounds imposed by our computational scheme.
Nerve Pulse Propagation in a Chain of Fhn Nonlinear Oscillators
NASA Astrophysics Data System (ADS)
Bountis, T.; Christodoulidi, H.; Anastassiou, S.
2008-11-01
A particularly useful and instructive model for the study of nerve pulse propagation is described by the well—known FitzHugh Nagumo (FHN) partial differential equations. In the absence of diffusion, the FHN system represents a single point—like neuron and is expressed in terms of two Ordinary Differential Equations (ODEs) for the membrane electric potential and the recovery (ion) current. In this work, we connect N such FHN oscillators in a unidirectional way, using the same coupling constant K. We then apply to the first ODE a periodic square wave of period T, amplitude h and duration ΔT, sufficient to excite the first neuronal oscillator. First, we investigate ranges of parameter values for which the excited action potential wave train is transmitted successfully to the subsequent FHN oscillators of the chain with the same period T. We also discover conditions on the coupling constant K and/or the amplitude of the applied periodic wave h under which the transmitted pulses have a period approximately equal to 2T, 4T,̤, or fail to be transmitted, along the chain of FHN oscillators.
Nerve pulse propagation in a chain of FHN nonlinear oscillators
Bountis, T.; Christodoulidi, H.; Anastassiou, S.
2008-11-13
A particularly useful and instructive model for the study of nerve pulse propagation is described by the well--known FitzHugh Nagumo (FHN) partial differential equations. In the absence of diffusion, the FHN system represents a single point--like neuron and is expressed in terms of two Ordinary Differential Equations (ODEs) for the membrane electric potential and the recovery (ion) current. In this work, we connect N such FHN oscillators in a unidirectional way, using the same coupling constant K. We then apply to the first ODE a periodic square wave of period T, amplitude h and duration {delta}T, sufficient to excite the first neuronal oscillator. First, we investigate ranges of parameter values for which the excited action potential wave train is transmitted successfully to the subsequent FHN oscillators of the chain with the same period T. We also discover conditions on the coupling constant K and/or the amplitude of the applied periodic wave h under which the transmitted pulses have a period approximately equal to 2T, 4T,..., or fail to be transmitted, along the chain of FHN oscillators.
Generation of mechanical oscillation applicable to vibratory rate gyroscopes
NASA Technical Reports Server (NTRS)
Lemkin, Mark A. (Inventor); Juneau, Thor N. (Inventor); Clark, William A. (Inventor); Roessig, Allen W. (Inventor)
2001-01-01
To achieve a drive-axis oscillation with improved frequency and amplitude stability, additional feedback loops are used to adjust force-feedback loop parameters. An amplitude-control loop measures oscillation amplitude, compares this value to the desired level, and adjusts damping of the mechanical sense-element to grow or shrink oscillation amplitude as appropriate. A frequency-tuning loop measures the oscillation frequency, compares this value with a highly stable reference, and adjusts the gain in the force-feedback loop to keep the drive-axis oscillation frequency at the reference value. The combined topology simultaneously controls both amplitude and frequency. Advantages of the combined topology include improved stability, fast oscillation start-up, low power consumption, and excellent shock rejection.
Finite-size-induced transitions to synchrony in oscillator ensembles with nonlinear global coupling.
Komarov, Maxim; Pikovsky, Arkady
2015-08-01
We report on finite-sized-induced transitions to synchrony in a population of phase oscillators coupled via a nonlinear mean field, which microscopically is equivalent to a hypernetwork organization of interactions. Using a self-consistent approach and direct numerical simulations, we argue that a transition to synchrony occurs only for finite-size ensembles and disappears in the thermodynamic limit. For all considered setups, which include purely deterministic oscillators with or without heterogeneity in natural oscillatory frequencies, and an ensemble of noise-driven identical oscillators, we establish scaling relations describing the order parameter as a function of the coupling constant and the system size.
A quantum exactly solvable nonlinear oscillator related to the isotonic oscillator
NASA Astrophysics Data System (ADS)
Cariñena, J. F.; Perelomov, A. M.; Rañada, M. F.; Santander, M.
2008-02-01
A nonpolynomial one-dimensional quantum potential representing an oscillator, which can be considered as placed in the middle between the harmonic oscillator and the isotonic oscillator (harmonic oscillator with a centripetal barrier), is studied. First the general case, that depends on a parameter a, is considered and then a particular case is studied with great detail. It is proven that it is Schrödinger solvable and then the wavefunctions Ψn and the energies En of the bound states are explicitly obtained. Finally, it is proven that the solutions determine a family of orthogonal polynomials {\\cal P}_n(x) related to the Hermite polynomials and such that: (i) every {\\cal P}_n is a linear combination of three Hermite polynomials and (ii) they are orthogonal with respect to a new measure obtained by modifying the classic Hermite measure.
Electromagnetic radiation from linearly and nonlinearly oscillating charge drops
NASA Astrophysics Data System (ADS)
Grigor'ev, A. I.; Shiryaeva, S. O.
2016-12-01
It has been shown that analytic calculations of the intensity of electromagnetic radiation from an oscillating charged drop in the approximation linear in the oscillation amplitude (small parameter is on the order of 0.1) give only the quadrupole component of the total radiation. The dipole component can only be obtained in calculations using higher-order approximations. Nevertheless, the intensity of the dipole radiation turns out to be substantially higher (by 14-15 orders of magnitude). This is because the decomposition of radiation from a system of charges into multipole components (differing even in the rates of decrease in the potential with the distance) is carried out using the expansion in a substantially smaller parameter, viz., the ratio of the size of the emitting system (in our case, a drop of radius 10 μm) to the distance to the point of observation in the wave zone of the emission of radiation (emitted wavelength) of 100-1000 m. As a result, this second small parameter is on the order of 10-7 to 10-8. On the other hand, in accordance with the field theory, the ratio of intensities of quadrupole and dipole radiations is proportional to the squared ratio of the hydrodynamic velocity of the oscillating surface of a charged drop to the velocity of propagation of an electromagnetic signal in vacuum (velocity of light), which yields a ratio of 10-14 to 10-15.
Nonlinear Oscillations of Microscale Piezoelectric Resonators and Resonator Arrays
2006-06-30
static buckling deflection of the resonator d3E, kI(x) d 3 , k(x) can be expressed as Elt -t = Elk ----- T- at X = Xk-_ Here, it is important to note that...a number of the parameters can resonators clearly reveal nonlinear characteristics. Although b icted by usng the ro rg met ersal the dimensions of
Coriolis effects on nonlinear oscillations of rotating cylinders and rings
NASA Technical Reports Server (NTRS)
Padovan, J.
1976-01-01
The effects which moderately large deflections have on the frequency spectrum of rotating rings and cylinders are considered. To develop the requisite solution, a variationally constrained version of the Lindstedt-Poincare procedure is employed. Based on the solution developed, in addition to considering the effects of displacement induced nonlinearity, the role of Coriolis forces is also given special consideration.
NASA Astrophysics Data System (ADS)
Yu, Da-ren; Wei, Li-qiu; Ding, Yong-jie; Han, Ke; Yan, Guo-jun; Qi, Feng-yan
2007-11-01
In order to study the physical mechanism of an oscillation newly discovered by the Harbin Institute of Technology Plasma Propulsion Lab (HPPL) in the range of hundreds of kHz to several MHz, Hall thrusters with different magnetic coils are studied by changing one of the following three parameters: discharge voltage, anode flow and coil current, directly measuring the coil current and measuring plasma oscillations related to coil current oscillation with the Langmuir probe. Experimental results indicated that in the discharge process of a Hall thruster the broadband turbulence of the Hall current causes an unstable spatial magnetic field and this field causes the magnetic circuit to resonate as an equivalent high level resistance-inductance-capacitance (RLC) network. As the response of the network, the oscillation of the coil current has a large oscillating component at the natural frequencies of the network. Also, the oscillation of coil current has an effect on the discharge process at the same time, so that they reach a self-consistent equilibrium state. As a result of such a coupling, both coil current and the discharge current exhibit their oscillating component at the natural frequencies of the magnetic circuit. It is therefore concluded that the newly discovered oscillation is caused by the coupling between the magnetic circuit and the discharge circuit.
Saturation in coupled oscillators
NASA Astrophysics Data System (ADS)
Roman, Ahmed; Hanna, James
2015-03-01
We consider a weakly nonlinear system consisting of a resonantly forced oscillator coupled to an unforced oscillator. It has long been known that, for quadratic nonlinearities and a 2:1 resonance between the oscillators, a perturbative solution of the dynamics exhibits a phenomenon known as saturation. At low forcing, the forced oscillator responds, while the unforced oscillator is quiescent. Above a critical value of the forcing, the forced oscillator's steady-state amplitude reaches a plateau, while that of the unforced oscillator increases without bound. We show that, contrary to established folklore, saturation is not unique to quadratically nonlinear systems. We present conditions on the form of the nonlinear couplings and resonance that lead to saturation. Our results elucidate a mechanism for localization or diversion of energy in systems of coupled oscillators, and suggest new approaches for the control or suppression of vibrations in engineered systems.
Rational extension and Jacobi-type X{sub m} solutions of a quantum nonlinear oscillator
Schulze-Halberg, Axel; Roy, Barnana
2013-12-15
We construct a rational extension of a recently studied nonlinear quantum oscillator model. Our extended model is shown to retain exact solvability, admitting a discrete spectrum and corresponding closed-form solutions that are expressed through Jacobi-type X{sub m} exceptional orthogonal polynomials.
An Apparatus to Demonstrate Linear and Nonlinear Oscillations of a Pendulum
ERIC Educational Resources Information Center
Mayer, V. V.; Varaksina, E. I.
2016-01-01
A physical pendulum with a magnetic load is proposed for comparison of linear and nonlinear oscillations. The magnetic load is repelled by permanent magnets which are disposed symmetrically relative to the load. It is established that positions of the pendulum and the magnets determine the dependence of restoring force on displacement of the load.…
Non-linear shape oscillations of rising drops and bubbles: Experiments and simulations
NASA Astrophysics Data System (ADS)
Lalanne, Benjamin; Abi Chebel, Nicolas; Vejražka, Jiří; Tanguy, Sébastien; Masbernat, Olivier; Risso, Frédéric
2015-12-01
This paper focuses on shape-oscillations of a gas bubble or a liquid drop rising in another liquid. The bubble/drop is initially attached to a capillary and is released by a sudden motion of that capillary, resulting in the rise of the bubble/drop along with the oscillations of its shape. Such experimental conditions make difficult the interpretation of the oscillation dynamics with regard to the standard linear theory of oscillation because (i) amplitude of deformation is large enough to induce nonlinearities, (ii) the rising motion may be coupled with the oscillation dynamics, and (iii) clean conditions without residual surfactants may not be achieved. These differences with the theory are addressed by comparing experimental observation with numerical simulation. Simulations are carried out using Level-Set and Ghost-Fluid methods with clean interfaces. The effect of the rising motion is investigated by performing simulations under different gravity conditions. Using a decomposition of the bubble/drop shape into a series of spherical harmonics, experimental and numerical time evolutions of their amplitudes are compared. Due to large oscillation amplitude, non-linear couplings between the modes are evidenced from both experimental and numerical signals; modes of lower frequency influence modes of higher frequency, whereas the reverse is not observed. Nevertheless, the dominant frequency and overall damping rate of the first five modes are in good agreement with the linear theory. Effect of the rising motion on the oscillations is globally negligible, provided the mean shape of the oscillation remains close to a sphere. In the drop case, despite the residual interface contamination evidenced by a reduction in the terminal velocity, the oscillation dynamics is shown to be unaltered compared to that of a clean drop.
Assessing Aircraft Susceptibility to Nonlinear Aircraft-Pilot Coupling/Pilot-Induced Oscillations
NASA Technical Reports Server (NTRS)
Hess, R.A.; Stout, P. W.
1997-01-01
A unified approach for assessing aircraft susceptibility to aircraft-pilot coupling (or pilot-induced oscillations) which was previously reported in the literature and applied to linear systems is extended to nonlinear systems, with emphasis upon vehicles with actuator rate saturation. The linear methodology provided a tool for predicting: (1) handling qualities levels, (2) pilot-induced oscillation rating levels and (3) a frequency range in which pilot-induced oscillations are likely to occur. The extension to nonlinear systems provides a methodology for predicting the latter two quantities. Eight examples are presented to illustrate the use of the technique. The dearth of experimental flight-test data involving systematic variation and assessment of the effects of actuator rate limits presently prevents a more thorough evaluation of the methodology.
Exploitation of a tristable nonlinear oscillator for improving broadband vibration energy harvesting
NASA Astrophysics Data System (ADS)
Zhou, Shengxi; Cao, Junyi; Lin, Jing; Wang, Zezhou
2014-09-01
Numerical and experimental investigations of a broadband vibration energy harvester with triple-well are presented. The nonlinear restoring force of the tristable oscillator is experimentally identified as a high order polynomial that depends on the relative spacing and locations of the magnets in the magnetically coupled piezoelectric cantilever. Simulations and experiments are performed at different harmonic excitation levels ranging from 10 to 35 Hz. The tristable energy harvester possesses the unique jump characteristics of oscillation center stemming from excitation level and initial displacements. Its broad frequency range of 15.1-32.5 Hz is obtained from the transition among three wells. It is also demonstrated that the tristable nonlinear oscillator will be more helpful to improve the broadband performance for harvesting vibration energy under low frequency excitations.
The quadratically damped oscillator: A case study of a non-linear equation of motion
NASA Astrophysics Data System (ADS)
Smith, B. R.
2012-09-01
The equation of motion for a quadratically damped oscillator, where the damping is proportional to the square of the velocity, is a non-linear second-order differential equation. Non-linear equations of motion such as this are seldom addressed in intermediate instruction in classical dynamics; this one is problematic because it cannot be solved in terms of elementary functions. Like all second-order ordinary differential equations, it has a corresponding first-order partial differential equation, whose independent solutions constitute the constants of the motion. These constants readily provide an approximate solution correct to first order in the damping constant. They also reveal that the quadratically damped oscillator is never critically damped or overdamped, and that to first order in the damping constant the oscillation frequency is identical to the natural frequency. The technique described has close ties to standard tools such as integral curves in phase space and phase portraits.
Nonlinear longitudinal space charge oscillations in relativistic electron beams.
Musumeci, P; Li, R K; Marinelli, A
2011-05-06
In this Letter we study the evolution of an initial periodic modulation in the temporal profile of a relativistic electron beam under the effect of longitudinal space-charge forces. Linear theory predicts a periodic exchange of the modulation between the density and the energy profiles at the beam plasma frequency. For large enough initial modulations, wave breaking occurs after 1/2 period of plasma oscillation leading to the formation of short current spikes. We confirm this effect by direct measurements on a ps-modulated electron beam from an rf photoinjector. These results are useful for the generation of intense electron pulse trains for advanced accelerator applications.
Nonlinear Longitudinal Space Charge Oscillations in Relativistic Electron Beams
Musumeci, P.; Li, R. K.; Marinelli, A.
2011-05-06
In this Letter we study the evolution of an initial periodic modulation in the temporal profile of a relativistic electron beam under the effect of longitudinal space-charge forces. Linear theory predicts a periodic exchange of the modulation between the density and the energy profiles at the beam plasma frequency. For large enough initial modulations, wave breaking occurs after 1/2 period of plasma oscillation leading to the formation of short current spikes. We confirm this effect by direct measurements on a ps-modulated electron beam from an rf photoinjector. These results are useful for the generation of intense electron pulse trains for advanced accelerator applications.
Lavrov, Roman; Peil, Michael; Jacquot, Maxime; Larger, Laurent; Udaltsov, Vladimir; Dudley, John
2009-08-01
We demonstrate experimentally how nonlinear optical phase dynamics can be generated with an electro-optic delay oscillator. The presented architecture consists of a linear phase modulator, followed by a delay line, and a differential phase-shift keying demodulator (DPSK-d). The latter represents the nonlinear element of the oscillator effecting a nonlinear transformation. This nonlinearity is considered as nonlocal in time since it is ruled by an intrinsic differential delay, which is significantly greater than the typical phase variations. To study the effect of this specific nonlinearity, we characterize the dynamics in terms of the dependence of the relevant feedback gain parameter. Our results reveal the occurrence of regular GHz oscillations (approximately half of the DPSK-d free spectral range), as well as a pronounced broadband phase-chaotic dynamics. Beyond this, the observed dynamical phenomena offer potential for applications in the field of microwave photonics and, in particular, for the realization of novel chaos communication systems. High quality and broadband phase-chaos synchronization is also reported with an emitter-receiver pair of the setup.
Model Order and Identifiability of Non-Linear Biological Systems in Stable Oscillation.
Wigren, Torbjörn
2015-01-01
The paper presents a theoretical result that clarifies when it is at all possible to determine the nonlinear dynamic equations of a biological system in stable oscillation, from measured data. As it turns out the minimal order needed for this is dependent on the minimal dimension in which the stable orbit of the system does not intersect itself. This is illustrated with a simulated fourth order Hodgkin-Huxley spiking neuron model, which is identified using a non-linear second order differential equation model. The simulated result illustrates that the underlying higher order model of the spiking neuron cannot be uniquely determined given only the periodic measured data. The result of the paper is of general validity when the dynamics of biological systems in stable oscillation is identified, and illustrates the need to carefully address non-linear identifiability aspects when validating models based on periodic data.
Nonlinear mode interactions and frequency-jump effects in a doubly tuned oscillator configuration
NASA Astrophysics Data System (ADS)
Grun, J.; Lashinsky, H.
1980-05-01
Frequency-jump effects associated with nonlinear mode competition are investigated in an oscillator configuration consisting of a passive linear resonance system coupled to an active nonlinear resonance system. These effects give rise to a hysteresis pattern whose height and width can be related to system parameters such as the resonance frequencies, dissipation, coupling coefficient, etc. It is noted that these effects offer a novel means of determining these parameters in cases in which conventional techniques may not be desirable or as advantageous. The analysis provides an qualitative explanation of empirical observations in a recent nuclear magnetic resonance experiment (Timsit and Daniels, 1976). The results also apply to other nonlinear resonance systems such as lasers, microwave generators, and electronic oscillators.
Liao, Fuyuan; Garrison, David W; Jan, Yih-Kuen
2010-07-01
The purposes of this study were to quantify the nonlinear properties of sacral skin blood flow oscillations (BFO) and to explore their relationships with impaired vasodilatory function in people at risk for pressure ulcers. A total of 25 people with various levels of vasodilatory functions were studied, 10 people with normal vasodilatory function (Biphasic thermal index, BTI (5.5, 4.5, 10.1)), 10 people with slight impaired vasodilatory function (BTI (3.7, 3.2, 6.7)), and 5 people with severe impaired vasodilation (BTI (2.4, 1.7, 4.5)). A non-painful fast heating protocol was applied to the sacral region to induce biphasic vasodilation, axon reflex mediated and nitric oxide mediated. Biphasic thermal index is defined as ratios of first peak, nadir, and second peak to baseline blood flow. Laser Doppler flowmetry was used to record the BFO signals. Nonlinear properties of BFO were quantified based on self-similarity using Hurst exponent (HE) and detrended fluctuation analysis (DFA), regularity using sample entropy (SampEn), complexity using correlation dimension (CD), and chaotic behavior using largest Lyapunov exponent (LLE). The Wilcoxon signed rank tests were used to examine the differences between groups. Our results showed that local heating reduces the self-similarity and increases complexity of skin blood flow oscillations. Vasodilatory function has an inverse relationship with nonlinear properties in sacral skin baseline BFO. Nonlinear indexes, including HE, DFA, CD, and LLE, are appropriate tools to quantify nonlinear properties of BFO to study the microvascular dysfunction (p<0.05), and that SampEn may not be appropriate for this purpose (p>0.05). Our study supports the use of nonlinear indexes to predict the vasodilatory function, which can complement current analysis of blood flow control mechanisms using spectral (wavelet) analysis.
Research in nonlinear structural and solid mechanics
NASA Technical Reports Server (NTRS)
Mccomb, H. G., Jr. (Compiler); Noor, A. K. (Compiler)
1980-01-01
Nonlinear analysis of building structures and numerical solution of nonlinear algebraic equations and Newton's method are discussed. Other topics include: nonlinear interaction problems; solution procedures for nonlinear problems; crash dynamics and advanced nonlinear applications; material characterization, contact problems, and inelastic response; and formulation aspects and special software for nonlinear analysis.
Seismic metamaterials based on isochronous mechanical oscillators
Finocchio, G. Garescì, F.; Azzerboni, B.; Casablanca, O.; Chiappini, M.; Ricciardi, G.; Alibrandi, U.
2014-05-12
This Letter introduces a seismic metamaterial (SM) composed by a chain of mass-in-mass system able to filter the S-waves of an earthquake. We included the effect of the SM into the mono dimensional model for the soil response analysis. The SM modifies the soil behavior and in presence of an internal damping the amplitude of the soil amplification function is reduced also in a region near the resonance frequency. This SM can be realized by a continuous structure with inside a 3d-matrix of isochronous oscillators based on a sphere rolling over a cycloidal trajectory.
Geometric approach to nonlinear coherent states using the Higgs model for harmonic oscillator
NASA Astrophysics Data System (ADS)
Mahdifar, A.; Roknizadeh, R.; Naderi, M. H.
2006-06-01
In this paper, we investigate the relation between the curvature of the physical space and the deformation function of the deformed oscillator algebra using the nonlinear coherent states approach. For this purpose, we study two-dimensional harmonic oscillators on the flat surface and on a sphere by applying the Higgs model. With the use of their algebras, we show that the two-dimensional oscillator algebra on a surface can be considered as a deformed one-dimensional oscillator algebra where the effect of the curvature of the surface appears as a deformation function. We also show that the curvature of the physical space plays the role of deformation parameter. Then we construct the associated coherent states on the flat surface and on a sphere and compare their quantum statistical properties, including quadrature squeezing and antibunching effect.
Friction self-oscillation decrease in nonlinear system of locomotive traction drive
NASA Astrophysics Data System (ADS)
Antipin, D. Ya; Vorobiyov, V. I.; Izmerov, O. V.; Shorokhov, S. G.; Bondarenko, D. A.
2017-02-01
The problems of the friction self-oscillation decrease in a nonlinear system of a locomotive traction drive are considered. It is determined that the self-oscillation amplitude decrease in a locomotive wheel pair during boxing in traction drives with an elastic linkage between an armature of a traction electric motor and gearing can be achieved due to drive damping capacity during impact vibro-damping in an axle reduction gear with a hard driven gear. The self-oscillation amplitude reduction in a wheel pair in the designs of locomotive traction drives with the location of elastic elements between a wheel pair and gearing can be obtained owing to the application of drive inertial masses as an anti-vibrator. On the basis of the carried out investigations, a design variant of a self-oscillation shock absorber of a traction electric motor framework on a reduction gear suspension with an absorber located beyond a wheel-motor unit was offered.
NASA Astrophysics Data System (ADS)
Pope, D. T.; Drummond, P. D.; Munro, W. J.
2000-10-01
Intracavity and external third order correlations in the damped nondegenerate parametric oscillator are calculated for quantum mechanics and stochastic electrodynamics (SED), a semiclassical theory. The two theories yield greatly different results, with the correlations of quantum mechanics being cubic in the system's nonlinear coupling constant and those of SED being linear in the same constant. In particular, differences between the two theories are present in at least a mesoscopic regime. They also exist when realistic damping is included. Such differences illustrate distinctions between quantum mechanics and a hidden variable theory for continuous variables.
Mechanisms and nonlinear waves from topological modes
NASA Astrophysics Data System (ADS)
Chen, Bryan
Topological protection can arise in mechanical structures such as linkages, frames, or rigid origami. The key ingredients are a balance of degrees of freedom and constraints away from the boundaries. In this setting certain zero energy modes of the system can be made robust against a broad class of perturbations and noise. However, since there are no restoring forces to these modes to linear order, they result in flexes and mechanisms which must be treated as nonlinear waves. I will discuss several simple and concrete examples which illustrate these ideas.
NASA Astrophysics Data System (ADS)
Premraj, D.; Suresh, K.; Banerjee, Tanmoy; Thamilmaran, K.
2016-08-01
Understanding the effect of slowly varying control parameters in dynamical systems is important in many fields such as mechanics, biology, ecology and social sciences, where normally changes in parameters take place very slowly. When a control parameter becomes time varying, the system dynamics exhibits a delay in bifurcation, i.e., the system responds to the bifurcation scenario with a lag in real time. In this paper, we experimentally explore the delay associated with Hopf and pitchfork bifurcations in a parametrically driven nonlinear oscillator. For this study we choose a generic nonlinear oscillator, namely the parametrically driven Murali-Lakshmanan-Chua (PDMLC) oscillator. We identify and characterize the occurrence of delay in bifurcations in both the rising and falling edges of the external force and measure the delay associated with these bifurcations in both the edges. We show that the delay in Hopf and pitchfork bifurcations increase when the rate of change of control parameter decreases. We further show that the delay obeys a power law as a function of the external frequency. All the numerical simulation results are corroborated with the real-time electronic circuit experiment and we find a good qualitative agreement between the numerical and experimental results.
Observation of Nonclassical Radiation Pressure Forces on a Mechanical Oscillator
NASA Astrophysics Data System (ADS)
Clark, Jeremy; Lecocq, Florent; Simmonds, Raymond; Aumentado, Jose; Teufel, John
Squeezed states of light are known to be useful for enhancing mechanical displacement sensing since they can be tailored to reduce the ``photon counting noise'' that limits the measurement's noise floor. On the other hand, recent experiments in cavity optomechanics have reached measurement regimes where an interrogating light field exerts radiation pressure noise on a mechanical oscillator. One outstanding challenge has been to explore the intersection between such experiments. I will present data obtained using a superconducting cavity optomechanical system wherein a mechanical oscillator is driven by nonclassical radiation pressure imparted by squeezed microwave fields. JBC acknowledges the NRC for financial support.
Magneto-elastic oscillator: Modeling and analysis with nonlinear magnetic interaction
NASA Astrophysics Data System (ADS)
Kumar, K. Aravind; Ali, Shaikh Faruque; Arockiarajan, A.
2017-04-01
The magneto-elastically buckled beam is a classic example of a nonlinear oscillator that exhibits chaotic motions. This system serves as a model to analyze the motion of elastic structures in magnetic fields. The system follows a sixth order magneto-elastic potential and may have up to five static equilibrium positions. However, often the non-dimensional Duffing equation is used to approximate the system, with the coefficients being derived from experiments. In few other instances, numerical methods are used to evaluate the magnetic field values. These field values are then used to approximate the nonlinear magnetic restoring force. In this manuscript, we derive analytical closed form expressions for the magneto-elastic potential and the nonlinear restoring forces in the system. Such an analytical formulation would facilitate tracing the effect of change in a parameter, such as the magnet dimension, on the dynamics of the system. The model is derived assuming a single mode approximation, taking into account the effect of linear elastic and nonlinear magnetic forces. The developed model is then numerically simulated to show that it is accurate in capturing the system dynamics and bifurcation of equilibrium positions. The model is validated through experiments based on forced vibrations of the magneto-elastic oscillator. To gather further insights about the magneto-elastic oscillator, a parametric study has been conducted based on the field strength of the magnets and the distance between the magnets and the results are reported.
Nonlinear Dynamics of Neuronal Excitability, Oscillations, and Coincidence Detection
RINZEL, JOHN; HUGUET, GEMMA
2014-01-01
We review some widely studied models and firing dynamics for neuronal systems, both at the single cell and network level, and dynamical systems techniques to study them. In particular, we focus on two topics in mathematical neuroscience that have attracted the attention of mathematicians for decades: single-cell excitability and bursting. We review the mathematical framework for three types of excitability and onset of repetitive firing behavior in single-neuron models and their relation with Hodgkin’s classification in 1948 of repetitive firing properties. We discuss the mathematical dissection of bursting oscillations using fast/slow analysis and demonstrate the approach using single-cell and mean-field network models. Finally, we illustrate the properties of Type III excitability in which case repetitive firing for constant or slow inputs is absent. Rather, firing is in response only to rapid enough changes in the stimulus. Our case study involves neuronal computations for sound localization for which neurons in the auditory brain stem perform extraordinarily precise coincidence detection with submillisecond temporal resolution. PMID:25392560
Coherent energy transport in classical nonlinear oscillators: An analogy with the Josephson effect.
Borlenghi, Simone; Iubini, Stefano; Lepri, Stefano; Bergqvist, Lars; Delin, Anna; Fransson, Jonas
2015-04-01
By means of a simple theoretical model and numerical simulations, we demonstrate the presence of persistent energy currents in a lattice of classical nonlinear oscillators with uniform temperature and chemical potential. In analogy with the well-known Josephson effect, the currents are proportional to the sine of the phase differences between the oscillators. Our results elucidate general aspects of nonequilibrium thermodynamics and point towards a way to practically control transport phenomena in a large class of systems. We apply the model to describe the phase-controlled spin-wave current in a bilayer nanopillar.
Multi-resonant optical parametric oscillator based on 2D-PPLT nonlinear photonic crystal.
Lazoul, Mohamed; Boudrioua, Azzedine; Simohamed, Lotfy-Mokhtar; Peng, Lung-Han
2015-04-15
The aim of this work is to achieve an optical parametric oscillator based on two-dimensional periodically poled lithium tantalate (2D-PPLT) crystals that are designed to allow multiple reciprocal lattice-vector contribution to the quasi-phase matching scheme. We are particularly interested in the effect of the multi-wavelength parametric generation performed by the 2D nonlinear photonic crystal to achieve a multi-resonant optical parametric oscillator. The performances are studied in terms of generation efficiency and multi-wavelength generation.
A Possible Mechanism for Driving Oscillations in Hot Giant Planets
NASA Astrophysics Data System (ADS)
Dederick, Ethan; Jackiewicz, Jason
2017-03-01
The κ-mechanism has been successful in explaining the origin of observed oscillations of many types of “classical” pulsating variable stars. Here we examine quantitatively if that same process is prominent enough to excite the potential global oscillations within Jupiter, whose energy flux is powered by gravitational collapse rather than nuclear fusion. Additionally, we examine whether external radiative forcing, i.e., starlight, could be a driver for global oscillations in hot Jupiters orbiting various main-sequence stars at defined orbital semimajor axes. Using planetary models generated by the Modules for Experiments in Stellar Astrophysics and nonadiabatic oscillation calculations, we confirm that Jovian oscillations cannot be driven via the κ-mechanism. However, we do show that, in hot Jupiters, oscillations can likely be excited via the suppression of radiative cooling due to external radiation given a large enough stellar flux and the absence of a significant oscillatory damping zone within the planet. This trend does not seem to be dependent on the planetary mass. In future observations, we can thus expect that such planets may be pulsating, thereby giving greater insight into the internal structure of these bodies.
NASA Astrophysics Data System (ADS)
de, S.
2010-11-01
Dominant scale of tropical boreal summer intraseasonal oscillations (BSISOs) being in the range of wave numbers 1-4, dynamical extended range prediction of BSISO is limited by rapid buildup of errors in ultra-long/planetary waves in almost all prediction models. While the initial errors are largely on the small scales, within 3-5 days of forecasts maximum errors appear in the ultra-long waves such as the tropical convergence zone. Spectral decomposition of errors with forecast lead time indicate that the initial error in the small scales is already close to its saturation value at these scales, whereas that in ultra-long waves is about two orders of magnitude smaller than their saturation values. Such an increase of errors in ultra-long waves cannot be explained as growth of initial errors. It is proposed that the fast growth of errors in the planetary waves is due to continuous generation of errors in the small scales (due to inadequacy of the physical parameterizations such as formulation of cumulus clouds) and upscale propagation of these errors through the process of scale interactions. Basic systematic error kinetic energy and the scale interactions in terms of the wave-wave exchanges among nonlinear triads are formulated and the above hypothesis is tested through a diagnostic analysis of the error energetics in two different model predictions at the lower troposphere. It has been revealed that nonlinear triad interactions lead to advection of errors from short and synoptic waves (wave number > 10) to long waves (wave numbers 5-10) and from long waves to ultra-long waves (wave numbers 1-4) and are responsible for the rapid growth of errors in the planetary waves. Unraveling the exact mechanism through which upscale transfer of errors take place may help us in devising a method to inhibit the mingling of small-scale error with the error in prediction of tropical intraseasonal oscillations and improve extended range prediction of the lower tropospheric BSISOs.
Galilean conformal mechanics from nonlinear realizations
Fedoruk, Sergey; Ivanov, Evgeny; Lukierski, Jerzy
2011-04-15
We apply the nonlinear realizations method for constructing new Galilean conformal mechanics models. Our starting point is the Galilean conformal algebra which is a nonrelativistic contraction of its relativistic counterpart. We calculate Maurer-Cartan one-forms, examine various choices of the relevant coset spaces, and consider the geometric inverse Higgs-type constraints which reduce the number of the independent coset parameters and, in some cases, provide dynamical equations. New Galilean conformally invariant actions are derived in arbitrary space-time dimension D=d+1 (no central charges), as well as in the special dimension D=2+1 with one exotic central charge. We obtain new classical mechanics models which extend the standard (D=0+1) conformal mechanics in the presence of d nonvanishing space dimensions.
A study of synchronization of nonlinear oscillators: Application to epileptic seizures
NASA Astrophysics Data System (ADS)
Takeshita, Daisuke
This dissertation focuses on several problems in neuroscience from the perspective of nonlinear dynamics and stochastic processes. The first part concerns a method to visualize the idea of the power spectrum of spike trains, which has an educational value to introductory students in biophysics. The next part consists of experimental and computational work on drug-induced epileptic seizures in the rat neocortex. In the experimental part, spatiotemporal patterns of electrical activities in the rat neocortex are measured using voltage-sensitive dye imaging. Epileptic regions show well-synchronized, in-phase activity during epileptic seizures. In the computational part, a network of a Hodgkin-Huxley type neocortical neural model is constructed. Phase reduction, which is a dimension reduction technique for a stable limit cycle, is applied to the system. The results propose a possible mechanism for the initiation of the drug-induced seizure as a result of a bifurcation. In the last part, a theoretical framework is developed to obtain the statistics for the period of oscillations of a stable limit cycle under stochastic perturbation. A stochastic version of phase reduction and first passage time analysis are utilized for this purpose. The method presented here shows a good agreement with numerical results for the weak noise regime.
On Measurement Uncertainty of ADC Nonlinearities in Oscillation-Based Test
NASA Astrophysics Data System (ADS)
Mrak, Peter; Biasizzo, Anton; Novak, Franc
2011-11-01
Oscillation-based test (OBT) is one of the approaches for measuring static ADC parameters such as differential nonlinearity (DNL) and integral nonlinearity (INL) that can be implemented in a built-in self-test arrangement. When applying the OBT approach in practice we noticed an inherent measurement uncertainty related to the slope of the ADC input signal in OBT test mode. Experimental environment in Matlab has been set up to study the phenomenon. Experiments with varying values of slope were performed to demonstrate the margins of DNL measurement uncertainty.
NASA Astrophysics Data System (ADS)
Emenheiser, Jeffrey; Chapman, Airlie; Pósfai, Márton; Crutchfield, James P.; Mesbahi, Mehran; D'Souza, Raissa M.
2016-09-01
Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between distinct trajectories in a network of synchronized oscillators. Our system, consisting of nonlinear amplitude-phase oscillators arranged in a ring topology with reactive nearest-neighbor coupling, is simple and connects directly to experimental realizations. We seek to understand how the multiple stable synchronized states connect to each other in state space by applying Gaussian white noise to each of the oscillators' phases. To do this, we first analytically identify a set of locally stable limit cycles at any given coupling strength. For each of these attracting states, we analyze the effect of weak noise via the covariance matrix of deviations around those attractors. We then explore the noise-induced attractor switching behavior via numerical investigations. For a ring of three oscillators, we find that an attractor-switching event is always accompanied by the crossing of two adjacent oscillators' phases. For larger numbers of oscillators, we find that the distribution of times required to stochastically leave a given state falls off exponentially, and we build an attractor switching network out of the destination states as a coarse-grained description of the high-dimensional attractor-basin architecture.
Nonlinear Schrödinger solitons oscillate under a constant external force
NASA Astrophysics Data System (ADS)
Mertens, Franz G.; Quintero, Niurka R.; Bishop, A. R.
2013-03-01
We investigate the dynamics of solitons of the cubic nonlinear Schrödinger equation with an external time-independent force of the form f(x)=rexp(-iKx). Here the solitons travel with an oscillating velocity and all other characteristics of the solitons (amplitude, width, momentum, and phase) also oscillate. This behavior was predicted by a collective variable theory and confirmed by simulations. However, the reason for these oscillations remains unclear. Moreover, the spectrum of the oscillations exhibits a second strong peak, in addition to the intrinsic soliton peak. We show that the additional frequency belongs to a certain extended linear mode (which we refer to as a phonon for short) close to the lower band edge of the phonon continuum. Initially the soliton is at rest. When it starts to move it is deformed, begins to oscillate, and excites the above phonon mode such that the total momentum in a certain moving frame is conserved. In this frame the phonon does not move. However, not only does the soliton move in the homogeneous, time-periodic field of the phonon, but it also oscillates.
Charge sensitivity enhancement via mechanical oscillation in suspended carbon nanotube devices.
Häkkinen, Pasi; Isacsson, Andreas; Savin, Alexander; Sulkko, Jaakko; Hakonen, Pertti
2015-03-11
Single electron transistors (SETs) fabricated from single-walled carbon nanotubes (SWNTs) can be operated as highly sensitive charge detectors reaching sensitivity levels comparable to metallic radio frequency SETs (rf-SETs). Here, we demonstrate how the charge sensitivity of the device can be improved by using the mechanical oscillations of a single-walled carbon nanotube quantum dot. To optimize the charge sensitivity δQ, we drive the mechanical resonator far into the nonlinear regime and bias it to an operating point where the mechanical third order nonlinearity is canceled out. This way we enhance δQ, from 6 μe/(Hz)(1/2) for the static case to 0.97 μe/(Hz)(1/2) at a probe frequency of ∼1.3 kHz.
NASA Astrophysics Data System (ADS)
Guédra, Matthieu; Inserra, Claude; Mauger, Cyril; Gilles, Bruno
2016-11-01
We report observations of strong nonlinear interactions between the spherical, translational, and shape oscillations of micrometer-size bubbles. This is achieved through high-speed recordings of single bubble dynamics driven by amplitude-modulated ultrasound. The features of mode coupling are highlighted through (i) the exponential growth of the parametrically excited mode (n =3 ) triggered by the spherical oscillations followed by a saturation due to energy transfer towards the translation and even modes, (ii) the excitation of modes well below their parametric pressure threshold, and (iii) clear modification of the breathing mode R (t ) . These results are compared to recent theories accounting for nonlinear mode coupling, providing predictions in agreement with the observed bubble dynamics.
Mechanical cooling in single-photon optomechanics with quadratic nonlinearity
NASA Astrophysics Data System (ADS)
Gu, Wen-ju; Yi, Zhen; Sun, Li-hui; Xu, Da-hai
2015-08-01
In the paper we study the nonlinear mechanical cooling processes in an intrinsic quadratically optomechanical coupling system without linearizing the optomechanical interaction. We apply scattering theory to calculate the transition rates between different mechanical Fock states using the resolvent of the Hamiltonian, which allows for a direct identification of the underlying physical processes, where only even-phonon transitions are permitted and odd-phonon transitions are forbidden. We verify the feasibility of the approach by comparing the steady-state mean phonon number obtained from transition rates with the simulation of the full quantum master equation, and also discuss the analytical results in the weak coupling limit that coincide with two-phonon mechanical cooling processes. Furthermore, to evaluate the statistical properties of steady mechanical state, we respectively apply the Mandel Q parameter to show that the oscillator can be in nonclassical mechanical states, and the phonon number fluctuations F to display that the even-phonon transitions favor suppressing the phonon number fluctuations compared to the linear coupling optomechanical system.
An Acoustic Levitation Technique for the Study of Nonlinear Oscillations of Gas Bubbles in Liquids.
1983-08-15
alcohol and a mixture of glycerine and water (33-1/3% glycerine by volume) were the two liquids used in this research. Bubbles were levitated near the...bubble can be trapped over a - -range of positions near a pressure antinode as a result of the balancing of these two forces. * The acoustic...then used to investigate the nonlinear oscillations of the bubble over a range of sizes. The bubbles were studied in two liq- uids: isopropyl alcohol
Cold atoms coupled with mechanical oscillators
NASA Astrophysics Data System (ADS)
Valencia, Jose; Montoya, Cris; Ranjit, Gambhir; Geraci, Andrew; Eardley, Matt; Kitching, John
2015-05-01
Mechanical resonators can be used to probe and manipulate atomic spins with nanometer spatial resolution and single-spin sensitivity, ultimately enabling new approaches in neutral-atom quantum computation, quantum simulation, or precision sensing. We describe our experiment that manipulates the spin of trapped, cold Rb atoms using magnetic material on a cantilever. Cold atoms can also be used as a coolant for mechanical resonators: we estimate that ground state cooling of an optically trapped nano-sphere is achievable when starting at room temperature, by sympathetic cooling of a cold atomic gas optically coupled to the nanoparticle.
NASA Astrophysics Data System (ADS)
Muhammad, Riaz; Muhammad, Rehan; Keum-Shik, Hong; Muhammad, Ashraf; Haroon, Ur Rasheed
2014-11-01
This paper addresses the control law design for synchronization of two different chaotic oscillators with mutually Lipschitz nonlinearities. For analysis of the properties of two different nonlinearities, an advanced mutually Lipschitz condition is proposed. This mutually Lipschitz condition is more general than the traditional Lipschitz condition. Unlike the latter, it can be used for the design of a feedback controller for synchronization of chaotic oscillators of different dynamics. It is shown that any two different Lipschitz nonlinearities always satisfy the mutually Lipschitz condition. Applying the mutually Lipschitz condition, a quadratic Lyapunov function and uniformly ultimately bounded stability, easily designable and implementable robust control strategies utilizing algebraic Riccati equation and linear matrix inequalities, are derived for synchronization of two distinct chaotic oscillators. Furthermore, a novel adaptive control scheme for mutually Lipschitz chaotic systems is established by addressing the issue of adaptive cancellation of unknown mismatch between the dynamics of different chaotic systems. The proposed control technique is numerically tested for synchronization of two different chaotic Chua's circuits and for obtaining identical behavior between the modified Chua's circuit and the Rössler system.
Noid, W G; Loring, Roger F
2004-10-15
Observables in coherent, multiple-pulse infrared spectroscopy may be computed from a vibrational nonlinear response function. This response function is conventionally calculated quantum-mechanically, but the challenges in applying quantum mechanics to large, anharmonic systems motivate the examination of classical mechanical vibrational nonlinear response functions. We present an approximate formulation of the classical mechanical third-order vibrational response function for an anharmonic solute oscillator interacting with a harmonic solvent, which establishes a clear connection between classical and quantum mechanical treatments. This formalism permits the identification of the classical mechanical analog of the pure dephasing of a quantum mechanical degree of freedom, and suggests the construction of classical mechanical analogs of the double-sided Feynman diagrams of quantum mechanics, which are widely applied to nonlinear spectroscopy. Application of a rotating wave approximation permits the analytic extraction of signals obeying particular spatial phase matching conditions from a classical-mechanical response function. Calculations of the third-order response function for an anharmonic oscillator coupled to a harmonic solvent are compared to numerically correct classical mechanical results.
Resonance frequencies of lipid-shelled microbubbles in the regime of nonlinear oscillations.
Doinikov, Alexander A; Haac, Jillian F; Dayton, Paul A
2009-02-01
Knowledge of resonant frequencies of contrast microbubbles is important for the optimization of ultrasound contrast imaging and therapeutic techniques. To date, however, there are estimates of resonance frequencies of contrast microbubbles only for the regime of linear oscillation. The present paper proposes an approach for evaluating resonance frequencies of contrast agent microbubbles in the regime of nonlinear oscillation. The approach is based on the calculation of the time-averaged oscillation power of the radial bubble oscillation. The proposed procedure was verified for free bubbles in the frequency range 1-4 MHz and then applied to lipid-shelled microbubbles insonified with a single 20-cycle acoustic pulse at two values of the acoustic pressure amplitude, 100 kPa and 200 kPa, and at four frequencies: 1.5, 2.0, 2.5, and 3.0 MHz. It is shown that, as the acoustic pressure amplitude is increased, the resonance frequency of a lipid-shelled microbubble tends to decrease in comparison with its linear resonance frequency. Analysis of existing shell models reveals that models that treat the lipid shell as a linear viscoelastic solid appear may be challenged to provide the observed tendency in the behavior of the resonance frequency at increasing acoustic pressure. The conclusion is drawn that the further development of shell models could be improved by the consideration of nonlinear rheological laws.
Application of the green function formalism to nonlinear evolution of the low gain FEL oscillator
Shvets, G.; Wurtele, J.S.; Gardent, D.
1995-12-31
A matrix formalism for the optical pulse evolution in the frequency domain, is applied to the nonlinear regime of operation. The formalism was previously developed for studies of the linear evolution of the low-gain FEL oscillator with an arbitrary shape of the electron beam. By varying experimentally controllable parameters, such as cavity detunning and cavity losses, different regimes of operation of the FEL oscillator, such as a steady state saturation and limit cycle saturation, are studied numerically. It is demonstrated that the linear supermodes, numerically obtained from the matrix formalism, provide an appropriate framework for analyzing the periodic change in the output power in the limit cycle regime. The frequency of this oscillation is related to the frequencies of the lowest-order linear supermodes. The response of the output radiation to periodic variation of the electron energy is studied. It is found that the response is enhanced when the frequency of the energy variation corresponds to the difference of per-pass phase advances of the lowest linear supermodes. Finally, various nonlinear models are tested to capture the steady state saturation and limit cycle variation of the EM field in the oscillator cavity.
Experimental Observation of Multifrequency Patterns in Arrays of Coupled Nonlinear Oscillators
NASA Astrophysics Data System (ADS)
in, Visarath; Kho, Andy; Neff, Joseph D.; Palacios, Antonio; Longhini, Patrick; Meadows, Brian K.
2003-12-01
Frequency-related oscillations in coupled oscillator systems, in which one or more oscillators oscillate at different frequencies than the other oscillators, have been studied using group theoretical methods by Armbruster and Chossat [
NASA Astrophysics Data System (ADS)
Blade, Ileana
This dissertation examines two possible mechanisms proposed to be responsible for the selection of the preferred period of the Madden and Julian (40-50 day) oscillation and discusses the dynamical interactions between the intraseasonal convection and the extratropical circulation. A global two-level nonlinear model with a positive -only CISK-type cumulus heating parameterization is used to simulate the oscillation, which appears when the SST exceeds a critical value for instability of CISK type. Longitudinal variations of tropical SST are imposed, so that a stable and an unstable region coexist. When the cold SST sector is sufficiently stable, the CISK wave propagates efficiently through the stable region in the form of a damped moisture -modified Kelvin wave, and reemerges in the unstable region where its amplitude grows. When the SST in the stable sector is set closer to the instability threshold, the moist Kelvin wave slows down and decays before reentering the unstable region, but the CISK perturbation periodically regenerates over the warm waters in response to a local build-up of instability. This last experiment implies a new mechanism for setting the time-scale of the oscillation, alternative to that of simple zonal propagation around the globe. A "discharge-recharge" theory is proposed whereby the 40-day recurrence period in the model is set by the growth and duration times of the convective episode together with the recharge time for the instability. It is shown that the midlatitude baroclinic eddies provide the quasi -stochastic forcing required to excite each new intraseasonal episode by organizing a region of subtropical convection which then grows and expands equatorwards due to the effect of the latent heating. The dynamical picture that emerges from the above results is consistent with observations that suggest a local thermodynamically-based time scale for the oscillation, and with case studies indicating that extratropical processes might be
Nonlinear Coupling between Cortical Oscillations and Muscle Activity during Isotonic Wrist Flexion
Yang, Yuan; Solis-Escalante, Teodoro; van de Ruit, Mark; van der Helm, Frans C. T.; Schouten, Alfred C.
2016-01-01
Coupling between cortical oscillations and muscle activity facilitates neuronal communication during motor control. The linear part of this coupling, known as corticomuscular coherence, has received substantial attention, even though neuronal communication underlying motor control has been demonstrated to be highly nonlinear. A full assessment of corticomuscular coupling, including the nonlinear part, is essential to understand the neuronal communication within the sensorimotor system. In this study, we applied the recently developed n:m coherence method to assess nonlinear corticomuscular coupling during isotonic wrist flexion. The n:m coherence is a generalized metric for quantifying nonlinear cross-frequency coupling as well as linear iso-frequency coupling. By using independent component analysis (ICA) and equivalent current dipole source localization, we identify four sensorimotor related brain areas based on the locations of the dipoles, i.e., the contralateral primary sensorimotor areas, supplementary motor area (SMA), prefrontal area (PFA) and posterior parietal cortex (PPC). For all these areas, linear coupling between electroencephalogram (EEG) and electromyogram (EMG) is present with peaks in the beta band (15–35 Hz), while nonlinear coupling is detected with both integer (1:2, 1:3, 1:4) and non-integer (2:3) harmonics. Significant differences between brain areas is shown in linear coupling with stronger coherence for the primary sensorimotor areas and motor association cortices (SMA, PFA) compared to the sensory association area (PPC); but not for the nonlinear coupling. Moreover, the detected nonlinear coupling is similar to previously reported nonlinear coupling of cortical activity to somatosensory stimuli. We suggest that the descending motor pathways mainly contribute to linear corticomuscular coupling, while nonlinear coupling likely originates from sensory feedback. PMID:27999537
Nonlinear Coupling between Cortical Oscillations and Muscle Activity during Isotonic Wrist Flexion.
Yang, Yuan; Solis-Escalante, Teodoro; van de Ruit, Mark; van der Helm, Frans C T; Schouten, Alfred C
2016-01-01
Coupling between cortical oscillations and muscle activity facilitates neuronal communication during motor control. The linear part of this coupling, known as corticomuscular coherence, has received substantial attention, even though neuronal communication underlying motor control has been demonstrated to be highly nonlinear. A full assessment of corticomuscular coupling, including the nonlinear part, is essential to understand the neuronal communication within the sensorimotor system. In this study, we applied the recently developed n:m coherence method to assess nonlinear corticomuscular coupling during isotonic wrist flexion. The n:m coherence is a generalized metric for quantifying nonlinear cross-frequency coupling as well as linear iso-frequency coupling. By using independent component analysis (ICA) and equivalent current dipole source localization, we identify four sensorimotor related brain areas based on the locations of the dipoles, i.e., the contralateral primary sensorimotor areas, supplementary motor area (SMA), prefrontal area (PFA) and posterior parietal cortex (PPC). For all these areas, linear coupling between electroencephalogram (EEG) and electromyogram (EMG) is present with peaks in the beta band (15-35 Hz), while nonlinear coupling is detected with both integer (1:2, 1:3, 1:4) and non-integer (2:3) harmonics. Significant differences between brain areas is shown in linear coupling with stronger coherence for the primary sensorimotor areas and motor association cortices (SMA, PFA) compared to the sensory association area (PPC); but not for the nonlinear coupling. Moreover, the detected nonlinear coupling is similar to previously reported nonlinear coupling of cortical activity to somatosensory stimuli. We suggest that the descending motor pathways mainly contribute to linear corticomuscular coupling, while nonlinear coupling likely originates from sensory feedback.
A Gravitational-Tidal Mechanism for the Earth's Polar Oscillations
NASA Astrophysics Data System (ADS)
Akulenko, L. D.; Kumakshev, S. A.; Markov, Yu. G.; Rykhlova, L. V.
2005-10-01
Perturbed, rotational-oscillational motions of the Earth induced by the gravitational torques exerted by the Sun and Moon are studied using a linear mechanical model for a viscoelastic rigid body. A tidal mechanism is identified for the excitation of polar oscillations, i.e., for oscillations of the angular-velocity vector specified in a fixed coordinate frame, attributed to the rotational-progressive motion of the barycenter of the Earth-Moon “binary planet” about the Sun. The main features of the oscillations remain stable and do not change considerably over time intervals significantly exceeding the precessional period of the Earth’s axis. A simple mathematical model containing two frequencies, namely, the Chandler and annual frequencies, is constructed using the methods of celestial mechanics. This model is adequate to the astrometric measurements performed by the International Earth Rotation Service (IERS). The parameters of the model are identified via least-squares fitting and a spectral analysis of the IERS data. Statistically valid interpolations of the data for time intervals covering from several months to 15 20 yr are obtained. High-accuracy forecasting of the polar motions for 0.5 1 yr and reasonably trustworthy forecasting for 1 3 yr demonstrated by observations over the last few years are presented for the first time. The results obtained are of theoretical interest for dynamical astronomy, geodynamics, and celestial mechanics, and are also important for astrometrical, navigational, and geophysical applications.
A Simple Mechanical Model for the Isotropic Harmonic Oscillator
ERIC Educational Resources Information Center
Nita, Gelu M.
2010-01-01
A constrained elastic pendulum is proposed as a simple mechanical model for the isotropic harmonic oscillator. The conceptual and mathematical simplicity of this model recommends it as an effective pedagogical tool in teaching basic physics concepts at advanced high school and introductory undergraduate course levels. (Contains 2 figures.)
NASA Astrophysics Data System (ADS)
Zhang, Zhen; Koroleva, I.; Manevitch, L. I.; Bergman, L. A.; Vakakis, A. F.
2016-09-01
We study the dynamics and acoustics of a nonlinear lattice with fixed boundary conditions composed of a finite number of particles coupled by linear springs, undergoing in-plane oscillations. The source of the strongly nonlinearity of this lattice is geometric effects generated by the in-plane stretching of the coupling linear springs. It has been shown that in the limit of low energy the lattice gives rise to a strongly nonlinear acoustic vacuum, which is a medium with zero speed of sound as defined in classical acoustics. The acoustic vacuum possesses strongly nonlocal coupling effects and an orthogonal set of nonlinear standing waves [or nonlinear normal modes (NNMs)] with mode shapes identical to those of the corresponding linear lattice; in contrast to the linear case, however, all NNMs except the one with the highest wavelength are unstable. In addition, the lattice supports two types of waves, namely, nearly linear sound waves (termed "L waves") corresponding to predominantly axial oscillations of the particles and strongly nonlinear localized propagating pulses (termed "N L pulses") corresponding to predominantly transverse oscillating wave packets of the particles with localized envelopes. We show the existence of nonlinear nonreciprocity phenomena in the dynamics and acoustics of the lattice. Two opposite cases are examined in the limit of low energy. The first gives rise to nonreciprocal dynamics and corresponds to collective, spatially extended transverse loading of the lattice leading to the excitation of individual, predominantly transverse NNMs, whereas the second case gives rise to nonreciprocal acoutics by considering the response of the lattice to spatially localized, transverse impulse or displacement excitations. We demonstrate intense and recurring energy exchanges between a directly excited NNM and other NNMs with higher wave numbers, so that nonreciprocal energy exchanges from small-to-large wave numbers are established. Moreover, we show the
Zhang, Zhen; Koroleva, I; Manevitch, L I; Bergman, L A; Vakakis, A F
2016-09-01
We study the dynamics and acoustics of a nonlinear lattice with fixed boundary conditions composed of a finite number of particles coupled by linear springs, undergoing in-plane oscillations. The source of the strongly nonlinearity of this lattice is geometric effects generated by the in-plane stretching of the coupling linear springs. It has been shown that in the limit of low energy the lattice gives rise to a strongly nonlinear acoustic vacuum, which is a medium with zero speed of sound as defined in classical acoustics. The acoustic vacuum possesses strongly nonlocal coupling effects and an orthogonal set of nonlinear standing waves [or nonlinear normal modes (NNMs)] with mode shapes identical to those of the corresponding linear lattice; in contrast to the linear case, however, all NNMs except the one with the highest wavelength are unstable. In addition, the lattice supports two types of waves, namely, nearly linear sound waves (termed "L waves") corresponding to predominantly axial oscillations of the particles and strongly nonlinear localized propagating pulses (termed "NL pulses") corresponding to predominantly transverse oscillating wave packets of the particles with localized envelopes. We show the existence of nonlinear nonreciprocity phenomena in the dynamics and acoustics of the lattice. Two opposite cases are examined in the limit of low energy. The first gives rise to nonreciprocal dynamics and corresponds to collective, spatially extended transverse loading of the lattice leading to the excitation of individual, predominantly transverse NNMs, whereas the second case gives rise to nonreciprocal acoutics by considering the response of the lattice to spatially localized, transverse impulse or displacement excitations. We demonstrate intense and recurring energy exchanges between a directly excited NNM and other NNMs with higher wave numbers, so that nonreciprocal energy exchanges from small-to-large wave numbers are established. Moreover, we show the
Modal self-excitation by nonlinear acceleration feedback in a class of mechanical systems
NASA Astrophysics Data System (ADS)
Malas, Anindya; Chatterjee, S.
2016-08-01
The article proposes an acceleration feedback based technique for exciting modal self-oscillation in a class of multi degrees-of-freedom mechanical systems. The controller comprises a bank of second-order filters and the control law is formulated as the nonlinear function of the filter output. A design methodology is developed to excite self-oscillation in any desired mode or combination of modes (mixed-mode oscillation). The choice of control parameters takes into account the control cost and robustness of the controller. The effects of structural damping on the system performance are also studied. Analytical results are confirmed by numerical simulations. An adaptive control is proposed to maintain the oscillation amplitude at the desired level.
McCullagh, Nuala; Szalay, Alexander S.
2015-01-10
Baryon acoustic oscillations (BAO) are a powerful probe of the expansion history of the universe, which can tell us about the nature of dark energy. In order to accurately characterize the dark energy equation of state using BAO, we must understand the effects of both nonlinearities and redshift space distortions on the location and shape of the acoustic peak. In a previous paper, we introduced a novel approach to second order perturbation theory in configuration space using the Zel'dovich approximation, and presented a simple result for the first nonlinear term of the correlation function. In this paper, we extend this approach to redshift space. We show how to perform the computation and present the analytic result for the first nonlinear term in the correlation function. Finally, we validate our result through comparison with numerical simulations.
Predator-prey dynamics stabilised by nonlinearity explain oscillations in dust-forming plasmas
NASA Astrophysics Data System (ADS)
Ross, A. E.; McKenzie, D. R.
2016-04-01
Dust-forming plasmas are ionised gases that generate particles from a precursor. In nature, dust-forming plasmas are found in flames, the interstellar medium and comet tails. In the laboratory, they are valuable in generating nanoparticles for medicine and electronics. Dust-forming plasmas exhibit a bizarre, even puzzling behaviour in which they oscillate with timescales of seconds to minutes. Here we show how the problem of understanding these oscillations may be cast as a predator-prey problem, with electrons as prey and particles as predators. The addition of a nonlinear loss term to the classic Lotka-Volterra equations used for describing the predator-prey problem in ecology not only stabilises the oscillations in the solutions for the populations of electrons and particles in the plasma but also explains the behaviour in more detail. The model explains the relative phase difference of the two populations, the way in which the frequency of the oscillations varies with the concentration of the precursor gas, and the oscillations of the light emission, determined by the populations of both species. Our results demonstrate the value of adopting an approach to a complex physical science problem that has been found successful in ecology, where complexity is always present.
Predator-prey dynamics stabilised by nonlinearity explain oscillations in dust-forming plasmas
Ross, A. E.; McKenzie, D. R.
2016-01-01
Dust-forming plasmas are ionised gases that generate particles from a precursor. In nature, dust-forming plasmas are found in flames, the interstellar medium and comet tails. In the laboratory, they are valuable in generating nanoparticles for medicine and electronics. Dust-forming plasmas exhibit a bizarre, even puzzling behaviour in which they oscillate with timescales of seconds to minutes. Here we show how the problem of understanding these oscillations may be cast as a predator-prey problem, with electrons as prey and particles as predators. The addition of a nonlinear loss term to the classic Lotka-Volterra equations used for describing the predator-prey problem in ecology not only stabilises the oscillations in the solutions for the populations of electrons and particles in the plasma but also explains the behaviour in more detail. The model explains the relative phase difference of the two populations, the way in which the frequency of the oscillations varies with the concentration of the precursor gas, and the oscillations of the light emission, determined by the populations of both species. Our results demonstrate the value of adopting an approach to a complex physical science problem that has been found successful in ecology, where complexity is always present. PMID:27046237
Parametric amplification and self-oscillation in a nanotube mechanical resonator.
Eichler, Alexander; Chaste, Julien; Moser, Joel; Bachtold, Adrian
2011-07-13
A hallmark of mechanical resonators made from a single nanotube is that the resonance frequency can be widely tuned. Here, we take advantage of this property to realize parametric amplification and self-oscillation. The gain of the parametric amplification can be as high as 18.2 dB and tends to saturate at high parametric pumping due to nonlinear damping. These measurements allow us to determine the coefficient of the linear damping force. The corresponding damping rate is lower than the one obtained from the line shape of the resonance (without pumping), supporting the recently reported scenario that describes damping in nanotube resonators by a nonlinear force. The possibility to combine nanotube resonant mechanics and parametric amplification holds promise for future ultralow force sensing experiments.
The Natural Frequency of Nonlinear Oscillation of Ultrasound Contrast Agents in Microvessels
Qin, Shengping; Ferrara, Katherine W.
2009-01-01
Ultrasound Contrast Agent (UCAs) are under intensive investigation for their applications in physiological and molecular imaging and drug delivery. Prediction of the natural frequency of the oscillation of UCAs in microvessels has drawn increasing attention. To our knowledge, the existing models to predict the natural frequency of oscillation of UCAs in microvessels all apply the linear approximation and treat the blood vessel wall as a rigid boundary. In the potential applications of ultrasound imaging drug and gene delivery, the compliance of small vessels may play an important role in the bubble’s oscillation. The goal of this work is to provide a lumped-parameter model to study the natural frequency of nonlinear oscillation of UCAs in microvessels. Three types of the blood vessel conditions have been considered. i.e. rigid vessels, normal compliable vessels and vessels with increasing stiffness that could correspond to tumor vasculature. The corresponding bubble oscillation frequencies in the vessels with radius less than 100 μm are examined in detail. When a bubble with a radius of 4 μm is confined in a compliable vessel (inner radius 5 μm and length 100μm), the natural frequency of bubble oscillation increases by a factor of 1.7 as compared with a bubble in an unbounded field. The natural frequency of oscillation of a bubble in a compliable vessel increases with decreasing vessel size while decreasing with increasing values of vessel rigidity. This model suggests that contrast agent size, blood vessel size distribution and the type of vasculature should be comprehensively considered for choosing the transmitted frequency in ultrasound contrast imaging and drug delivery. PMID:17478030
Introduction: Collective dynamics of mechanical oscillators and beyond
NASA Astrophysics Data System (ADS)
Belykh, Igor V.; Porfiri, Maurizio
2016-11-01
This focus issue presents a collection of research papers from a broad spectrum of topics related to the modeling, analysis, and control of mechanical oscillators and beyond. Examples covered in this focus issue range from bridges and mechanical pendula to self-organizing networks of dynamic agents, with application to robotics and animal grouping. This focus issue brings together applied mathematicians, physicists, and engineers to address open questions on various theoretical and experimental aspects of collective dynamics phenomena and their control.
Introduction: Collective dynamics of mechanical oscillators and beyond.
Belykh, Igor V; Porfiri, Maurizio
2016-11-01
This focus issue presents a collection of research papers from a broad spectrum of topics related to the modeling, analysis, and control of mechanical oscillators and beyond. Examples covered in this focus issue range from bridges and mechanical pendula to self-organizing networks of dynamic agents, with application to robotics and animal grouping. This focus issue brings together applied mathematicians, physicists, and engineers to address open questions on various theoretical and experimental aspects of collective dynamics phenomena and their control.
Neutrino oscillations: Quantum mechanics vs. quantum field theory
Akhmedov, Evgeny Kh.; Kopp, Joachim
2010-01-01
A consistent description of neutrino oscillations requires either the quantum-mechanical (QM) wave packet approach or a quantum field theoretic (QFT) treatment. We compare these two approaches to neutrino oscillations and discuss the correspondence between them. In particular, we derive expressions for the QM neutrino wave packets from QFT and relate the free parameters of the QM framework, in particular the effective momentum uncertainty of the neutrino state, to the more fundamental parameters of the QFT approach. We include in our discussion the possibilities that some of the neutrino's interaction partners are not detected, that the neutrino is produced in the decay of an unstable parent particle, and that the overlap of the wave packets of the particles involved in the neutrino production (or detection) process is not maximal. Finally, we demonstrate how the properly normalized oscillation probabilities can be obtained in the QFT framework without an ad hoc normalization procedure employed in the QM approach.
Romera, M.; Monteblanco, E.; Garcia-Sanchez, F.; Buda-Prejbeanu, L. D.; Ebels, U.; Delaët, B.
2015-05-11
The influence of dynamic coupling in between magnetic layers of a standard spin torque nano-oscillator composed of a synthetic antiferromagnet (SyF) as a polarizer and an in-plane magnetized free layer has been investigated. Experiments on spin valve nanopillars reveal non-continuous features such as kinks in the frequency field dependence that cannot be explained without such interactions. Comparison of experiments to numerical macrospin simulations shows that this is due to non-linear interaction between the spin torque (STT) driven mode and a damped mode that is mediated via the third harmonics of the STT mode. It only occurs at large applied currents and thus at large excitation amplitudes of the STT mode. Under these conditions, a hybridized mode characterized by a strong reduction of the linewidth appears. The reduced linewidth can be explained by a reduction of the non-linear contribution to the linewidth via an enhanced effective damping. Interestingly, the effect depends also on the exchange interaction within the SyF. An enhancement of the current range of reduced linewidth by a factor of two and a reduction of the minimum linewidth by a factor of two are predicted from simulation when the exchange interaction strength is reduced by 30%. These results open directions to optimize the design and microwave performances of spin torque nano-oscillators taking advantage of the coupling mechanisms.
NASA Astrophysics Data System (ADS)
Plata, J.
2016-01-01
We study the dynamics of a classical nonlinear oscillator subject to noise and driven by a sinusoidal force. In particular, we give an analytical identification of the mechanisms responsible for the supernarrow peaks observed recently in the spectrum of a mechanical realization of the system. Our approach, based on the application of averaging techniques, simulates standard detection schemes used in practice. The spectral peaks, detected in a range of parameters corresponding to the existence of two attractors in the deterministic system, are traced to characteristics already present in the linearized stochastic equations. It is found that, for specific variations of the parameters, the characteristic frequencies near the attractors converge on the driving frequency and, as a consequence, the widths of the peaks in the spectrum are significantly reduced. The implications of the study to the control of the observed coherent response of the system are discussed.
Phase-noise reduction in surface wave oscillators by using nonlinear sustaining amplifiers.
Avramov, Ivan D
2006-04-01
Nonlinear sustaining amplifier operation has been investigated and applied to high-power negative resistance oscillators (NRO), using single-port surface transverse wave (STW) resonators, and single-transistor sustaining amplifiers for feedback-loop STW oscillators (FLSO) stabilized with two-port STW devices. In all cases, self-limiting, silicon (Si)-bipolar sustaining amplifiers that operate in the highly nonlinear AB-, B-, or C-class modes are implemented. Phase-noise reduction is based on the assumption that a sustaining amplifier, operating in one of these modes, uses current limiting and remains cut off over a significant portion of the wave period. Therefore, it does not generate 1/f noise over the cut-off portion of the radio frequency (RF) cycle, and this reduces the close-in oscillator phase noise significantly. The proposed method has been found to provide phase-noise levels in the -111 to -119 dBc/Hz range at 1 KHz carrier offset in 915 MHz C-class power NRO and FLSO generating up to 23 dBm of RF-power at RF versus dc (RF/dc) efficiencies exceeding 40%. C-class amplifier design techniques are used for adequate matching and high RF/dc efficiency.
Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations
Sandhu, Rimple; Poirel, Dominique; Pettit, Chris; Khalil, Mohammad; Sarkar, Abhijit
2016-07-01
A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid–structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic system leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib–Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.
Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations
NASA Astrophysics Data System (ADS)
Sandhu, Rimple; Poirel, Dominique; Pettit, Chris; Khalil, Mohammad; Sarkar, Abhijit
2016-07-01
A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid-structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic system leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib-Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.
Effects on the bifurcation and chaos in forced Duffing oscillator due to nonlinear damping
NASA Astrophysics Data System (ADS)
Sharma, Anjali; Patidar, Vinod; Purohit, G.; Sud, K. K.
2012-06-01
In this communication, the two-well Duffing oscillator with non-linear damping term proportional to the power of velocity is considered. We mainly focus our attention on how the damping exponent affects the global dynamical behaviour of the oscillator. In particular, we obtain analytically the threshold condition for the occurrence of homoclinic bifurcation using Melnikov technique and compare the results with the computational results. We also identify the major route to chaos and the regions of the 2D parameter space (consists of external forcing amplitude and damping coefficient) corresponding to the various types of asymptotic dynamics under linear (viscous or friction like) and nonlinear (drag like) damping. We also attempt to analyze how the basins of attraction patterns change with the introduction of nonlinear damping. We also present our analysis for the physically less-interesting cases where damping is proportional to the 3rd and 4th power of velocity for the sake of generalizing our findings and establishing firm conclusion.
The Mechanical Environment Modulates Intracellular Calcium Oscillation Activities of Myofibroblasts
Godbout, Charles; Follonier Castella, Lysianne; Smith, Eric A.; Talele, Nilesh; Chow, Melissa L.; Garonna, Adriano; Hinz, Boris
2013-01-01
Myofibroblast contraction is fundamental in the excessive tissue remodeling that is characteristic of fibrotic tissue contractures. Tissue remodeling during development of fibrosis leads to gradually increasing stiffness of the extracellular matrix. We propose that this increased stiffness positively feeds back on the contractile activities of myofibroblasts. We have previously shown that cycles of contraction directly correlate with periodic intracellular calcium oscillations in cultured myofibroblasts. We analyze cytosolic calcium dynamics using fluorescent calcium indicators to evaluate the possible impact of mechanical stress on myofibroblast contractile activity. To modulate extracellular mechanics, we seeded primary rat subcutaneous myofibroblasts on silicone substrates and into collagen gels of different elastic modulus. We modulated cell stress by cell growth on differently adhesive culture substrates, by restricting cell spreading area on micro-printed adhesive islands, and depolymerizing actin with Cytochalasin D. In general, calcium oscillation frequencies in myofibroblasts increased with increasing mechanical challenge. These results provide new insight on how changing mechanical conditions for myofibroblasts are encoded in calcium oscillations and possibly explain how reparative cells adapt their contractile behavior to the stresses occurring in normal and pathological tissue repair. PMID:23691248
Zeng, An-Ping; Modak, Jayant; Deckwer, Wolf-Dieter
2002-01-01
Pyruvate conversion to acetyl-CoA by the pyruvate dehydrogenase (PDH) multienzyme complex is known as a key node in affecting the metabolic fluxes of animal cell culture. However, its possible role in causing possible nonlinear dynamic behavior such as oscillations and multiplicity of animal cells has received little attention. In this work, the kinetic and dynamic behavior of PDH of eucaryotic cells has been analyzed by using both in vitro and simplified in vivo models. With the in vitro model the overall reaction rate (nu(1)) of PDH is shown to be a nonlinear function of pyruvate concentration, leading to oscillations under certain conditions. All enzyme components affect nu(1) and the nonlinearity of PDH significantly, the protein X and the core enzyme dihydrolipoamide acyltransferase (E2) being mostly predominant. By considering the synthesis rates of pyruvate and PDH components the in vitro model is expanded to emulate in vivo conditions. Analysis using the in vivo model reveals another interesting kinetic feature of the PDH system, namely, multiple steady states. Depending on the pyruvate and enzyme levels or the operation mode, either a steady state with high pyruvate decarboxylation rate or a steady state with significantly lower decarboxylation rate can be achieved under otherwise identical conditions. In general, the more efficient steady state is associated with a lower pyruvate concentration. A possible time delay in the substrate supply and enzyme synthesis can also affect the steady state to be achieved and leads to oscillations under certain conditions. Overall, the predictions of multiplicity for the PDH system agree qualitatively well with recent experimental observations in animal cell cultures. The model analysis gives some hints for improving pyruvate metabolism in animal cell culture.
Botari, Tiago; Leonel, Edson D
2013-01-01
A modification of the one-dimensional Fermi accelerator model is considered in this work. The dynamics of a classical particle of mass m, confined to bounce elastically between two rigid walls where one is described by a nonlinear van der Pol type oscillator while the other one is fixed, working as a reinjection mechanism of the particle for a next collision, is carefully made by the use of a two-dimensional nonlinear mapping. Two cases are considered: (i) the situation where the particle has mass negligible as compared to the mass of the moving wall and does not affect the motion of it; and (ii) the case where collisions of the particle do affect the movement of the moving wall. For case (i) the phase space is of mixed type leading us to observe a scaling of the average velocity as a function of the parameter (χ) controlling the nonlinearity of the moving wall. For large χ, a diffusion on the velocity is observed leading to the conclusion that Fermi acceleration is taking place. On the other hand, for case (ii), the motion of the moving wall is affected by collisions with the particle. However, due to the properties of the van der Pol oscillator, the moving wall relaxes again to a limit cycle. Such kind of motion absorbs part of the energy of the particle leading to a suppression of the unlimited energy gain as observed in case (i). The phase space shows a set of attractors of different periods whose basin of attraction has a complicated organization.
Graphene NanoElectroMechanical Resonators and Oscillators
NASA Astrophysics Data System (ADS)
Chen, Changyao
Made of only one sheet of carbon atoms, graphene is the thinnest yet strongest material ever exist. Since its discovery in 2004, graphene has attracted tremendous research effort worldwide. Guaranteed by the superior electrical and excellent mechanical properties, graphene is the ideal building block for NanoElectroMechanical Systems (NEMS). In the first parts of the thesis, I will discuss the fabrications and measurements of typical graphene NEMS resonators, including doubly clamped and fully clamped graphene mechanical resonators. I have developed a electrical readout technique by using graphene as frequency mixer, demonstrated resonant frequencies in range from 30 to 200 MHz. Furthermore, I developed the advanced fabrications to achieve local gate structure, which led to the real-time resonant frequency detection under resonant channel transistor (RCT) scheme. Such real-time detection improve the measurement speed by 2 orders of magnitude compared to frequency mixing technique, and is critical for practical applications. Finally, I employed active balanced bridge technique in order to reduce overall electrical parasitics, and demonstrated pure capacitive transduction of graphene NEMS resonators. Characterizations of graphene NEMS resonators properties are followed, including resonant frequency and quality factor (Q) tuning with tension, mass and temperatures. A simple continuum mechanics model was constructed to understand the frequency tuning behavior, and it agrees with experimental data extremely well. In the following parts of the thesis, I will discuss the behavior of graphene mechanical resonators in applied magnetic field, i.e. in Quantum Hall (QH) regime. The couplings between mechanical motion and electronic band structure turned out to be a direct probe for thermodynamic quantities, i.e., chemical potential and compressibility. For a clean graphene resonators, with quality factors of 1 x 104, it underwent resonant frequency oscillations as applied
Preparing a mechanical oscillator in non-gaussian quantum states.
Khalili, Farid; Danilishin, Stefan; Miao, Haixing; Müller-Ebhardt, Helge; Yang, Huan; Chen, Yanbei
2010-08-13
We propose a protocol for coherently transferring non-Gaussian quantum states from an optical field to a mechanical oscillator. We demonstrate its experimental feasibility in future gravitational-wave detectors and tabletop optomechanical devices. This work not only outlines a feasible way to investigate nonclassicality in macroscopic optomechanical systems, but also presents a new and elegant approach for solving non-Markovian open quantum dynamics in general linear systems.
NASA Astrophysics Data System (ADS)
Cuevas-Maraver, J.; Chacón, R.; Palmero, F.
2016-12-01
We study discrete breathers in prototypical nonlinear oscillator networks subjected to nonharmonic zero-mean periodic excitations. We show how the generation of stationary and moving discrete breathers are optimally controlled by solely varying the impulse transmitted by the periodic excitations, while keeping constant the excitation's amplitude and period. Our theoretical and numerical results show that the enhancer effect of increasing values of the excitation's impulse, in the sense of facilitating the generation of stationary and moving breathers, is due to a correlative increase of the breather's action and energy.
NASA Astrophysics Data System (ADS)
Ivanov, I. N.; Melnikov, V. A.
1997-02-01
The correlation between the requirements for the quality of a beam and parameters of systems of damping of transverse coherent oscillations for modern hadron accelerators and colliders is considered. Special attention is directed to systems in which the signal in the kicker is not proportional to the signal of the pickup. It is shown that a nonlinear mode of suppression can provide a greater damping rate. Limiting beam blow-up at injection and accumulation is made possible by an appropriate choice of the discrimination level of the pickup signal.
Balskus, Karolis; Fleming, Melissa; McCracken, Richard A; Zhang, Zhaowei; Reid, Derryck T
2016-03-01
By exploiting the correlation between changes in the wavelength and the carrier-envelope offset frequency (f(CEO)) of the signal pulses in a synchronously pumped optical parametric oscillator, we show that f(CEO) can be stabilized indefinitely to a few megahertz in a 333 MHz repetition-rate system. Based on a position-sensitive photodiode, the technique is easily implemented, requires no nonlinear interferometry, has a wide capture range, and is compatible with feed-forward techniques that can enable f(CEO) stabilization at loop bandwidths far exceeding those currently available to OPO combs.
Exact Nonlinear Fourth-order Equation for Two Coupled Oscillators: Metamorphoses of Resonance Curves
NASA Astrophysics Data System (ADS)
Kyzioł, J.; Okniński, A.
We study dynamics of two coupled periodically driven oscillators. The internal motion is separated off exactly to yield a nonlinear fourth-order equation describing inner dynamics. Periodic steady-state solutions of the fourth-order equation are determined within the Krylov-Bogoliubov-Mitropolsky approach - we compute the amplitude profiles, which from mathematical point of view are algebraic curves. In the present paper we investigate metamorphoses of amplitude profiles induced by changes of control parameters near singular points of these curves. It follows that dynamics changes qualitatively in the neighbourhood of a singular point.
Cuevas-Maraver, J; Chacón, R; Palmero, F
2016-12-01
We study discrete breathers in prototypical nonlinear oscillator networks subjected to nonharmonic zero-mean periodic excitations. We show how the generation of stationary and moving discrete breathers are optimally controlled by solely varying the impulse transmitted by the periodic excitations, while keeping constant the excitation's amplitude and period. Our theoretical and numerical results show that the enhancer effect of increasing values of the excitation's impulse, in the sense of facilitating the generation of stationary and moving breathers, is due to a correlative increase of the breather's action and energy.
Dynamic mechanical oscillations during metamorphosis of the monarch butterfly.
Pelling, Andrew E; Wilkinson, Paul R; Stringer, Richard; Gimzewski, James K
2009-01-06
The mechanical oscillation of the heart is fundamental during insect metamorphosis, but it is unclear how morphological changes affect its mechanical dynamics. Here, the micromechanical heartbeat with the monarch chrysalis (Danaus plexippus) during metamorphosis is compared with the structural changes observed through in vivo magnetic resonance imaging (MRI). We employ a novel ultra-sensitive detection approach, optical beam deflection, in order to measure the microscale motions of the pupae during the course of metamorphosis. We observed very distinct mechanical contractions occurring at regular intervals, which we ascribe to the mechanical function of the heart organ. Motion was observed to occur in approximately 15 min bursts of activity with frequencies in the 0.4-1.0 Hz range separated by periods of quiescence during the first 83 per cent of development. In the final stages, the beating was found to be uninterrupted until the adult monarch butterfly emerged. Distinct stages of development were characterized by changes in frequency, amplitude, mechanical quality factor and de/repolarization times of the mechanical pulsing. The MRI revealed that the heart organ remains functionally intact throughout metamorphosis but undergoes morphological changes that are reflected in the mechanical oscillation.
NASA Astrophysics Data System (ADS)
Pelinovsky, Dmitry; Penati, Tiziano; Paleari, Simone
2016-08-01
Small-amplitude weakly coupled oscillators of the Klein-Gordon lattices are approximated by equations of the discrete nonlinear Schrödinger type. We show how to justify this approximation by two methods, which have been very popular in the recent literature. The first method relies on a priori energy estimates and multi-scale decompositions. The second method is based on a resonant normal form theorem. We show that although the two methods are different in the implementation, they produce equivalent results as the end product. We also discuss the applications of the discrete nonlinear Schrödinger equation in the context of existence and stability of breathers of the Klein-Gordon lattice.
Khorashadizadeh, S. M. Taheri Boroujeni, S.; Niknam, A. R.
2015-11-15
In this paper, we have investigated the nonlinear interaction between high-frequency surface plasmons and low-frequency ion oscillations in a semi-bounded collisional quantum plasma. By coupling the nonlinear Schrodinger equation and quantum hydrodynamic model, and taking into account the ponderomotive force, the dispersion equation is obtained. By solving this equation, it is shown that there is a modulational instability in the system, and collisions and quantum forces play significant roles on this instability. The quantum tunneling increases the phase and group velocities of the modulated waves and collisions increase the growth rate of the modulational instability. It is also shown that the effect of quantum forces and collisions is more significant in high modulated wavenumber regions.
Existence of periodic orbits in nonlinear oscillators of Emden-Fowler form
NASA Astrophysics Data System (ADS)
Mancas, Stefan C.; Rosu, Haret C.
2016-01-01
The nonlinear pseudo-oscillator recently tackled by Gadella and Lara is mapped to an Emden-Fowler (EF) equation that is written as an autonomous two-dimensional ODE system for which we provide the phase-space analysis and the parametric solution. Through an invariant transformation we find periodic solutions to a certain class of EF equations that pass an integrability condition. We show that this condition is necessary to have periodic solutions and via the ODE analysis we also find the sufficient condition for periodic orbits. EF equations that do not pass integrability conditions can be made integrable via an invariant transformation which also allows us to construct periodic solutions to them. Two other nonlinear equations, a zero-frequency Ermakov equation and a positive power Emden-Fowler equation, are discussed in the same context.
Phase Structure of the Non-Linear σ-MODEL with Oscillator Representation Method
NASA Astrophysics Data System (ADS)
Mishchenko, Yuriy; Ji, Chueng-R.
2004-03-01
Non-Linear σ-model plays an important role in many areas of theoretical physics. Been initially uintended as a simple model for chiral symmetry breaking, this model exhibits such nontrivial effects as spontaneous symmetry breaking, asymptotic freedom and sometimes is considered as an effective field theory for QCD. Besides, non-linear σ-model can be related to the strong-coupling limit of O(N) ϕ4-theory, continuous limit of N-dim. system of quantum spins, fermion gas and many others and takes important place in undertanding of how symmetries are realized in quantum field theories. Because of this variety of connections, theoretical study of the critical properties of σ-model is interesting and important. Oscillator representation method is a theoretical tool for studying the phase structure of simple QFT models. It is formulated in the framework of the canonical quantization and is based on the view of the unitary non-equivalent representations as possible phases of a QFT model. Successfull application of the ORM to ϕ4 and ϕ6 theories in 1+1 and 2+1 dimensions motivates its study in more complicated models such as non-linear σ-model. In our talk we introduce ORM, establish its connections with variational approach in QFT. We then present results of ORM in non-linear σ-model and try to interprete them from the variational point of view. Finally, we point out possible directions for further research in this area.
Berman, G.P.; Bulgakov, E.N.; Campbell, D.K.; Krive, I.V.
1997-10-01
We consider Aharonov-Bohm oscillations in a mesoscopic semiconductor ring threaded by both a constant magnetic flux and a time-dependent, resonant magnetic field with one or two frequencies. Working in the ballistic regime, we establish that the theory of {open_quotes}quantum nonlinear resonance{close_quotes} applies, and thus that this system represents a possible solid-state realization of {open_quotes}quantum nonlinear resonance{close_quotes} and {open_quotes}quantum chaos.{close_quotes} In particular, we investigate the behavior of the time-averaged electron energy at zero temperature in the regimes of (i) an isolated quantum nonlinear resonance and (ii) the transition to quantum chaos, when two quantum nonlinear resonances overlap. The time-averaged energy exhibits sharp resonant behavior as a function of the applied constant magnetic flux, and has a staircase dependence on the amplitude of the external time-dependent field. In the chaotic regime, the resonant behavior exhibits complex structure as a function of flux and frequency. We compare and contrast the quantum chaos expected in these mesoscopic {open_quotes}solid-state atoms{close_quotes} with that observed in Rydberg atoms in microwave fields, and discuss the prospects for experimental observation of the effects we predict. {copyright} {ital 1997} {ital The American Physical Society}
Nature's Autonomous Oscillators
NASA Technical Reports Server (NTRS)
Mayr, H. G.; Yee, J.-H.; Mayr, M.; Schnetzler, R.
2012-01-01
Nonlinearity is required to produce autonomous oscillations without external time dependent source, and an example is the pendulum clock. The escapement mechanism of the clock imparts an impulse for each swing direction, which keeps the pendulum oscillating at the resonance frequency. Among nature's observed autonomous oscillators, examples are the quasi-biennial oscillation and bimonthly oscillation of the Earth atmosphere, and the 22-year solar oscillation. The oscillations have been simulated in numerical models without external time dependent source, and in Section 2 we summarize the results. Specifically, we shall discuss the nonlinearities that are involved in generating the oscillations, and the processes that produce the periodicities. In biology, insects have flight muscles, which function autonomously with wing frequencies that far exceed the animals' neural capacity; Stretch-activation of muscle contraction is the mechanism that produces the high frequency oscillation of insect flight, discussed in Section 3. The same mechanism is also invoked to explain the functioning of the cardiac muscle. In Section 4, we present a tutorial review of the cardio-vascular system, heart anatomy, and muscle cell physiology, leading up to Starling's Law of the Heart, which supports our notion that the human heart is also a nonlinear oscillator. In Section 5, we offer a broad perspective of the tenuous links between the fluid dynamical oscillators and the human heart physiology.
Selective use of a reserved mechanism for inducing calcium oscillations.
Ma, Chun Yan; Chen, Chun Ying; Cui, Zong Jie
2004-12-01
Concentration-dependent transformation of hormone- and neurotransmitter-induced calcium oscillation is a common phenomenon in diverse types of cells especially of the secretory type. The rodent submandibular acinar cells are an exception to this rule, which show elevated plateau increase in intracellular calcium under all stimulatory concentrations of both norepinephrine and acetylcholine. However, under depolarized state this cell type could also show a variation of periodic calcium changes. This reserved mechanism of calcium oscillation is jump-started by depolarization only with muscarinic cholinergic stimulation, but not with adrenergic stimulation. This latter effect is attributable to alpha receptor activation, not due to simultaneous activation of alpha and beta receptors, with beta receptor activation only serving to enhance the magnitude. These data suggest that this reserved mechanism for inducing calcium oscillation can be selectively used only by specific receptor-signaling pathways, and may therefore partly explain the long-known differences between secretion induced by sympathetic and parasympathetic stimulation in the submandibular gland.
Ruan, Haowen; Mather, Melissa L.
2015-01-01
Background Ultrasound modulated optical tomography (USMOT) is an imaging technique used to provide optical functional information inside highly scattering biological tissue. One of the challenges facing this technique is the low image contrast. Methods A contrast enhancement imaging technique based on the non-linear oscillation of microbubbles is demonstrated to improve image contrast. The ultrasound modulated signal was detected using a laser pulse based speckle contrast detection system. Better understanding of the effects of microbubbles on the optical signals was achieved through simultaneous measurement of the ultrasound scattered by the microbubbles. Results The length of the laser pulse was found to affect the system response of the speckle contrast method with shorter pulses suppressing the fundamental ultrasound modulated optical signal. Using this property, image contrast can be enhanced by detection of the higher harmonic ultrasound modulated optical signals due to nonlinear oscillation and destruction of the microbubbles. Experimental investigations were carried out to demonstrate a doubling in contrast by imaging a scattering phantom containing an embedded silicone tube with microbubbles flowing through it. Conclusions The contrast enhancement in USMOT resulting from the use of ultrasound microbubbles has been demonstrated. Destruction of the microbubbles was shown to be the dominant effect leading to contrast improvement as shown by simultaneously detecting the ultrasound and speckle contrast signals. Line scans of a microbubble filled silicone tube embedded in a scattering phantom demonstrated experimentally the significant image contrast improvement that can be achieved using microbubbles and demonstrates the potential as a future clinical imaging tool. PMID:25694948
Partial synchronization in networks of non-linearly coupled oscillators: The Deserter Hubs Model
Freitas, Celso Macau, Elbert; Pikovsky, Arkady
2015-04-15
We study the Deserter Hubs Model: a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity of interactions. Under weak force, an oscillator tends to follow the phase of its neighbors, but if an oscillator is compelled to follow its peers by a sufficient large number of cohesive neighbors, then it actually starts to act in the opposite manner, i.e., in anti-phase with the majority. Analytic results yield that if the repulsion parameter is small enough in comparison with the degree of the maximum hub, then the full synchronization state is locally stable. Numerical experiments are performed to explore the model beyond this threshold, where the overall cohesion is lost. We report in detail partially synchronous dynamical regimes, like stationary phase-locking, multistability, periodic and chaotic states. Via statistical analysis of different network organizations like tree, scale-free, and random ones, we found a measure allowing one to predict relative abundance of partially synchronous stationary states in comparison to time-dependent ones.
NASA Astrophysics Data System (ADS)
Peng, Cui; Han, Jinglong
2011-05-01
This article presents numerical simulations of the limit-cycle oscillation (LCO) of a cropped delta wing in order to investigate the effects of structural geometric and material nonlinearities on aeroelastic behavior. In the computational model, the structural part included both the geometric nonlinearity that arises from large deflections, and the material nonlinearity that originates from plasticity. The Euler equations were employed in the fluid part to describe the transonic aerodynamics. Moreover, the load transfer was conducted using a 3-D interpolating procedure, and the interfaces between the structural and aerodynamic domains were constructed in the form of an exact match. The flutter and LCO behaviors of the cropped delta wing were simulated using the coupling model, and the results were compared with existing experimental measurements. For lower dynamic pressures, the geometric nonlinearity provided the proper mechanism for the development of the LCO, and the numerical results correlated with the experimental values. For higher dynamic pressures, the material nonlinearity led to a rapid rise in the LCO amplitude, and the simulated varying trend was consistent with the experimental observation. This study demonstrated that the LCO of the cropped delta wing was not only closely related to geometric nonlinearity, but was also remarkably affected by material nonlinearity.
Synaptic Mechanisms of Memory Consolidation during Sleep Slow Oscillations
Wei, Yina; Krishnan, Giri P.
2016-01-01
Sleep is critical for regulation of synaptic efficacy, memories, and learning. However, the underlying mechanisms of how sleep rhythms contribute to consolidating memories acquired during wakefulness remain unclear. Here we studied the role of slow oscillations, 0.2–1 Hz rhythmic transitions between Up and Down states during stage 3/4 sleep, on dynamics of synaptic connectivity in the thalamocortical network model implementing spike-timing-dependent synaptic plasticity. We found that the spatiotemporal pattern of Up-state propagation determines the changes of synaptic strengths between neurons. Furthermore, an external input, mimicking hippocampal ripples, delivered to the cortical network results in input-specific changes of synaptic weights, which persisted after stimulation was removed. These synaptic changes promoted replay of specific firing sequences of the cortical neurons. Our study proposes a neuronal mechanism on how an interaction between hippocampal input, such as mediated by sharp wave-ripple events, cortical slow oscillations, and synaptic plasticity, may lead to consolidation of memories through preferential replay of cortical cell spike sequences during slow-wave sleep. SIGNIFICANCE STATEMENT Sleep is critical for memory and learning. Replay during sleep of temporally ordered spike sequences related to a recent experience was proposed to be a neuronal substrate of memory consolidation. However, specific mechanisms of replay or how spike sequence replay leads to synaptic changes that underlie memory consolidation are still poorly understood. Here we used a detailed computational model of the thalamocortical system to report that interaction between slow cortical oscillations and synaptic plasticity during deep sleep can underlie mapping hippocampal memory traces to persistent cortical representation. This study provided, for the first time, a mechanistic explanation of how slow-wave sleep may promote consolidation of recent memory events. PMID
Kengne, Jacques; Kenmogne, Fabien
2014-12-15
The nonlinear dynamics of fourth-order Silva-Young type chaotic oscillators with flat power spectrum recently introduced by Tamaseviciute and collaborators is considered. In this type of oscillators, a pair of semiconductor diodes in an anti-parallel connection acts as the nonlinear component necessary for generating chaotic oscillations. Based on the Shockley diode equation and an appropriate selection of the state variables, a smooth mathematical model (involving hyperbolic sine and cosine functions) is derived for a better description of both the regular and chaotic dynamics of the system. The complex behavior of the oscillator is characterized in terms of its parameters by using time series, bifurcation diagrams, Lyapunov exponents' plots, Poincaré sections, and frequency spectra. It is shown that the onset of chaos is achieved via the classical period-doubling and symmetry restoring crisis scenarios. Some PSPICE simulations of the nonlinear dynamics of the oscillator are presented in order to confirm the ability of the proposed mathematical model to accurately describe/predict both the regular and chaotic behaviors of the oscillator.
NASA Astrophysics Data System (ADS)
Kengne, Jacques; Kenmogne, Fabien
2014-12-01
The nonlinear dynamics of fourth-order Silva-Young type chaotic oscillators with flat power spectrum recently introduced by Tamaseviciute and collaborators is considered. In this type of oscillators, a pair of semiconductor diodes in an anti-parallel connection acts as the nonlinear component necessary for generating chaotic oscillations. Based on the Shockley diode equation and an appropriate selection of the state variables, a smooth mathematical model (involving hyperbolic sine and cosine functions) is derived for a better description of both the regular and chaotic dynamics of the system. The complex behavior of the oscillator is characterized in terms of its parameters by using time series, bifurcation diagrams, Lyapunov exponents' plots, Poincaré sections, and frequency spectra. It is shown that the onset of chaos is achieved via the classical period-doubling and symmetry restoring crisis scenarios. Some PSPICE simulations of the nonlinear dynamics of the oscillator are presented in order to confirm the ability of the proposed mathematical model to accurately describe/predict both the regular and chaotic behaviors of the oscillator.
A model for the nonlinear mechanism responsible for cochlear amplification.
Fessel, Kimberly; Holmes, Mark H
2014-12-01
A nonlinear model for the mechanism responsible for the amplification of the sound wave in the ear is derived using the geometric and material properties of the system. The result is a nonlinear beam equation, with the nonlinearity appearing in a coefficient of the equation. Once derived, the beam problem is analyzed for various loading conditions. Based on this analysis it is seen that the mechanism is capable of producing a spatially localized gain, as required by any amplification mechanism, but it is also capable of increasing the spatial contrast in the signal.
Sage, Cindy
2015-01-01
The 'informational content' of Earth's electromagnetic signaling is like a set of operating instructions for human life. These environmental cues are dynamic and involve exquisitely low inputs (intensities) of critical frequencies with which all life on Earth evolved. Circadian and other temporal biological rhythms depend on these fluctuating electromagnetic inputs to direct gene expression, cell communication and metabolism, neural development, brainwave activity, neural synchrony, a diversity of immune functions, sleep and wake cycles, behavior and cognition. Oscillation is also a universal phenomenon, and biological systems of the heart, brain and gut are dependent on the cooperative actions of cells that function according to principles of non-linear, coupled biological oscillations for their synchrony. They are dependent on exquisitely timed cues from the environment at vanishingly small levels. Altered 'informational content' of environmental cues can swamp natural electromagnetic cues and result in dysregulation of normal biological rhythms that direct growth, development, metabolism and repair mechanisms. Pulsed electromagnetic fields (PEMF) and radiofrequency radiation (RFR) can have the devastating biological effects of disrupting homeostasis and desynchronizing normal biological rhythms that maintain health. Non-linear, weak field biological oscillations govern body electrophysiology, organize cell and tissue functions and maintain organ systems. Artificial bioelectrical interference can give false information (disruptive signaling) sufficient to affect critical pacemaker cells (of the heart, gut and brain) and desynchronize functions of these important cells that orchestrate function and maintain health. Chronic physiological stress undermines homeostasis whether it is chemically induced or electromagnetically induced (or both exposures are simultaneous contributors). This can eventually break down adaptive biological responses critical to health
Design of triply-resonant microphotonic parametric oscillators based on Kerr nonlinearity.
Zeng, Xiaoge; Popović, Miloš A
2014-06-30
We propose optimal designs for triply-resonant optical parametric oscillators (OPOs) based on degenerate four-wave mixing (FWM) in microcavities. We show that optimal designs in general call for different external coupling to pump and signal/idler resonances. We provide a number of normalized performance metrics including threshold pump power and maximum achievable conversion efficiency for OPOs with and without two-photon (TPA) and free-carrier absorption (FCA). We find that the maximum achievable conversion efficiency is bound to an upper limit by nonlinear and free-carrier losses independent of pump power, while linear losses only increase the pump power required to achieve a certain conversion efficiency. The results of this work suggest unique advantages in on-chip implementations that allow explicit engineering of resonances, mode field overlaps, dispersion, and wavelength-and mode-selective coupling. We provide universal design curves that yield optimum designs, and give example designs of microring-resonator-based OPOs in silicon at the wavelengths 1.55 μm (with TPA) and 2.3 μm (no TPA) as well as in silicon nitride (Si(3)N(4)) at 1.55 μm. For typical microcavity quality factor of 10(6), we show that the oscillation threshold in excitation bus can be well into the sub-mW regime for silicon microrings and a few mW for silicon nitride microrings. The conversion efficiency can be a few percent when pumped at 10 times of the threshold. Next, based on our results, we suggest a family of synthetic "photonic molecule"-like, coupled-cavity systems to implement optimum FWM, where structure design for control of resonant wavelengths can be separated from that of optimizing nonlinear conversion efficiency, and where furthermore pump, signal, and idler coupling to bus waveguides can be controlled independently, using interferometric cavity supermode coupling as an example. Finally, consideration of these complex geometries calls for a generalization of the nonlinear
NASA Astrophysics Data System (ADS)
Hoefer, Mark A.
This thesis examines nonlinear wave phenomena, in two physical systems: a Bose-Einstein condensate (BEC) and thin film ferromagnets where the magnetization dynamics are excited by the spin momentum transfer (SMT) effect. In the first system, shock waves generated by steep gradients in the BEC wavefunction are shown to be of the disperse type. Asymptotic and averaging methods are used to determine shock speeds and structure in one spatial dimension. These results are compared with multidimensional numerical simulations and experiment showing good, qualitative agreement. In the second system, a model of magnetization dynamics due to SMT is presented. Using this model, nonlinear oscillating modes---nano-oscillators---are found numerically and analytically using perturbative methods. These results compare well with experiment. A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, e.g. traveling fronts with steep gradients. However, the governing Gross-Pitaevskii (GP) equation that describes the mean field of a BEC admits no dissipation hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave (DSW). Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical 1D dissipative and dispersive shock problem shows significant differences in shock structure and shock front speed. Numerical results associated with laboratory experiments show that three and two-dimensional approximations are in excellent agreement and one dimensional approximations are in qualitative agreement. The interaction of two DSWs is investigated analytically and numerically. Using one dimensional DSW theory it is argued
Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators
NASA Astrophysics Data System (ADS)
Duanmu, M.; Whitaker, N.; Kevrekidis, P. G.; Vainchtein, A.; Rubin, J. E.
2016-06-01
Motivated by earlier studies of artificial perceptions of light called phosphenes, we analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model problem in its co-traveling frame and systematically obtain the corresponding traveling waves in one spatial dimension. Direct numerical simulations as well as linear stability analysis are employed to reveal the parameter regions where the traveling waves are stable, and these waves are, in turn, connected to the standing waves analyzed in earlier work. We also consider a two-dimensional extension of the model and demonstrate the robust evolution and stability of planar fronts. Our simulations also suggest the radial fronts tend to either annihilate or expand and flatten out, depending on the phase value inside and the parameter regime. Finally, we observe that solutions that initially feature two symmetric fronts with bulged centers evolve in qualitative agreement with experimental observations of phosphenes.
NASA Technical Reports Server (NTRS)
Smith, J. W.; Edwards, J. W.
1980-01-01
Analysis of a longitudinal pilot-induced oscillation (PIO) experienced just prior to touchdown on the final flight of the space shuttle's approach landing tests indicated that the source of the problem was a combination of poor basic handling qualities aggravated by time delays through the digital flight control computer and rate limiting of the elevator actuators due to high pilot gain. A nonlinear PIO suppression (PIOS) filter was designed and developed to alleviate the vehicle's PIO tendencies by reducing the gain in the command path. From analytical and simulator studies it was shown that the PIOS filter, in an adaptive fashion, can attenuate the command path gain without adding phase lag to the system. With the pitch attitude loop of a simulated shuttle model closed, the PIOS filter increased the gain margin by a factor of about two.
Chimera regimes in a ring of oscillators with local nonlinear interaction
NASA Astrophysics Data System (ADS)
Shepelev, Igor A.; Zakharova, Anna; Vadivasova, Tatiana E.
2017-03-01
One of important problems concerning chimera states is the conditions of their existence and stability. Until now, it was assumed that chimeras could arise only in ensembles with nonlocal character of interactions. However, this assumption is not exactly right. In some special cases chimeras can be realized for local type of coupling [1-3]. We propose a simple model of ensemble with local coupling when chimeras are realized. This model is a ring of linear oscillators with the local nonlinear unidirectional interaction. Chimera structures in the ring are found using computer simulations for wide area of values of parameters. Diagram of the regimes on plane of control parameters is plotted and scenario of chimera destruction are studied when the parameters are changed.
Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators
Duanmu, M.; Whitaker, N.; Kevrekidis, P. G.; Vainchtein, A.; Rubin, J. E.
2016-02-27
Artificial perceptions of light called phosphenes were motivated by earlier studies. We analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model problem in its co-traveling frame and systematically obtain the corresponding traveling waves in one spatial dimension. Direct numerical simulations as well as linear stability analysis are employed to reveal the parameter regions where the traveling waves are stable, and these waves are, in turn, connected to the standing waves analyzed in earlier work. We also consider a two-dimensional extension of the model and demonstrate the robust evolution and stability of planar fronts. Moreover, our simulations also suggest the radial fronts tend to either annihilate or expand and flatten out, depending on the phase value inside and the parameter regime. Finally, we observe that solutions that initially feature two symmetric fronts with bulged centers evolve in qualitative agreement with experimental observations of phosphenes.
Verified solutions of two-point boundary value problems for nonlinear oscillators
NASA Astrophysics Data System (ADS)
Bünger, Florian
Using techniques introduced by Nakao [4], Oishi [5, 6] and applied by Takayasu, Oishi, Kubo [11, 12] to certain nonlinear two-point boundary value problems (see also Rump [7], Chapter 15), we provide a numerical method for verifying the existence of weak solutions of two-point boundary value problems of the form -u″ = a(x, u) + b(x, u)u‧, 0 < x < 1, u(0) = 0 = u(1), in the vicinity of a given approximate numerical solution, where a and b are functions that fulfill some regularity properties. The numerical approximation is done by cubic spline interpolation. Finally, the method is applied to the Duffing, the van der Pol and the Toda oscillator. The rigorous numerical computations were done with INTLAB [8].
NASA Astrophysics Data System (ADS)
Donoso, Guillermo; Ladera, Celso L.
2016-09-01
An accurate linear optical displacement transducer of about 0.2 mm resolution over a range of ∼40 mm is presented. This device consists of a stack of thin cellulose acetate strips, each strip longitudinally slid ∼0.5 mm over the precedent one so that one end of the stack becomes a stepped wedge of constant step. A narrowed light beam from a white LED orthogonally incident crosses the wedge at a known point, the transmitted intensity being detected with a phototransistor whose emitter is connected to a diode. We present the interesting analytical proof that the voltage across the diode is linearly dependent upon the ordinate of the point where the light beam falls on the wedge, as well as the experimental validation of such a theoretical proof. Applications to nonlinear oscillations are then presented—including the interesting case of a body moving under dry friction, and the more advanced case of an oscillator in a quartic energy potential—whose time-varying positions were accurately measured with our transducer. Our sensing device can resolve the dynamics of an object attached to it with great accuracy and precision at a cost considerably less than that of a linear neutral density wedge. The technique used to assemble the wedge of acetate strips is described.
Nonlinear Resonance of Mechanically Excited Sessile Drops
NASA Astrophysics Data System (ADS)
Chang, Chun-Ti; Daniel, Susan; Steen, Paul
2013-11-01
The spectrum of frequencies and mode shapes for an inviscid drop on a planar substrate have recently been documented. For vertical excitation, zonal modes respond to the driving frequency harmonically and non-zonal modes subharmonically, consistent with the prior literature. In this study, we report observations from the regime of nonlinear response. Here, zonals can respond non-harmonically, both sub- and super-harmonic responses are reported. The principal challenge to generating and observing superharmonic resonances of higher zonal modes is a mode-mixing behavior. However, using a simple visual simulation based on the ray-tracing technique, the individual contributions to the mixed resonance behavior can be extracted. In summary, results from experiment and theory show that the zonal modes, which respond harmonically and can mix with non-zonal modes without interfering with one another in the linear regime, tend to respond sub- or superharmonically and compete with non-zonal modes in the nonlinear regime.
Kesarkar, Ameya Anil; Selvaganesan, N; Priyadarshan, H
2015-07-01
This paper proposes a novel constrained optimization problem to design a controller for plants containing relay nonlinearity to reduce the amplitude of sustained oscillations. The controller is additionally constrained to satisfy desirable loop specifications. The proposed formulation is validated by designing a fractional PI controller for a plant with relay.
Mechanical properties of a primary cilium as measured by resonant oscillation.
Resnick, Andrew
2015-07-07
Primary cilia are ubiquitous mammalian cellular substructures implicated in an ever-increasing number of regulatory pathways. The well-established ciliary hypothesis states that physical bending of the cilium (for example, due to fluid flow) initiates signaling cascades, yet the mechanical properties of the cilium remain incompletely measured, resulting in confusion regarding the biological significance of flow-induced ciliary mechanotransduction. In this work we measure the mechanical properties of a primary cilium by using an optical trap to induce resonant oscillation of the structure. Our data indicate 1) the primary cilium is not a simple cantilevered beam; 2) the base of the cilium may be modeled as a nonlinear rotatory spring, with the linear spring constant k of the cilium base calculated to be (4.6 ± 0.62) × 10(-12) N/rad and nonlinear spring constant α to be (-1 ± 0.34) × 10(-10) N/rad(2); and 3) the ciliary base may be an essential regulator of mechanotransduction signaling. Our method is also particularly suited to measure mechanical properties of nodal cilia, stereocilia, and motile cilia-anatomically similar structures with very different physiological functions.
Optimal state discrimination and unstructured search in nonlinear quantum mechanics
NASA Astrophysics Data System (ADS)
Childs, Andrew M.; Young, Joshua
2016-02-01
Nonlinear variants of quantum mechanics can solve tasks that are impossible in standard quantum theory, such as perfectly distinguishing nonorthogonal states. Here we derive the optimal protocol for distinguishing two states of a qubit using the Gross-Pitaevskii equation, a model of nonlinear quantum mechanics that arises as an effective description of Bose-Einstein condensates. Using this protocol, we present an algorithm for unstructured search in the Gross-Pitaevskii model, obtaining an exponential improvement over a previous algorithm of Meyer and Wong. This result establishes a limitation on the effectiveness of the Gross-Pitaevskii approximation. More generally, we demonstrate similar behavior under a family of related nonlinearities, giving evidence that the ability to quickly discriminate nonorthogonal states and thereby solve unstructured search is a generic feature of nonlinear quantum mechanics.
Fidler, Andrew F; Engel, Gregory S
2013-10-03
We present a theory for a bath model in which we approximate the adiabatic nuclear potential surfaces on the ground and excited electronic states by displaced harmonic oscillators that differ in curvature. Calculations of the linear and third-order optical response functions employ an effective short-time approximation coupled with the cumulant expansion. In general, all orders of correlation contribute to the optical response, indicating that the solvation process cannot be described as Gaussian within the model. Calculations of the linear absorption and fluorescence spectra resulting from the theory reveal a stronger temperature dependence of the Stokes shift along with a general asymmetry between absorption and fluorescence line shapes, resulting purely from the difference in the phonon side band. We discuss strategies for controlling spectral tuning and energy-transfer dynamics through the manipulation of the excited-state and ground-state curvature. Calculations of the nonlinear response also provide insights into the dynamics of the system-bath interactions and reveal that multidimensional spectroscopies are sensitive to a difference in curvature between the ground- and excited-state adiabatic surfaces. This extension allows for the elucidation of short-time dynamics of dephasing that are accessible in nonlinear spectroscopic methods.
SEACAS Theory Manuals: Part II. Nonlinear Continuum Mechanics
Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.
1998-09-01
This report summarizes the key continuum mechanics concepts required for the systematic prescription and numerical solution of finite deformation solid mechanics problems. Topics surveyed include measures of deformation appropriate for media undergoing large deformations, stress measures appropriate for such problems, balance laws and their role in nonlinear continuum mechanics, the role of frame indifference in description of large deformation response, and the extension of these theories to encompass two dimensional idealizations, structural idealizations, and rigid body behavior. There are three companion reports that describe the problem formulation, constitutive modeling, and finite element technology for nonlinear continuum mechanics systems.
NASA Astrophysics Data System (ADS)
Younespour, Amir; Ghaffarzadeh, Hosein
2016-06-01
This paper applied the idea of block pulse (BP) transform in the equivalent linearization of a nonlinear system. The BP transform gives effective tools to approximate complex problems. The main goal of this work is on using BP transform properties in process of linearization. The accuracy of the proposed method compared with the other equivalent linearization including the stochastic equivalent linearization and the regulation linearization methods. Numerical simulations are applied to the nonlinear Van der Pol oscillator system under Gaussian white noise excitation to demonstrate the feasibility of the present method. Different values of nonlinearity are considered to show the effectiveness of the present method. Besides, by comparing the mean-square responses for divers values of nonlinearity and excitation intensity depicted the present method is able to approximate the behavior of nonlinear system and is in agreement with other methods.
Optical mechanical analogy and nonlinear nonholonomic constraints.
Bloch, Anthony M; Rojo, Alberto G
2016-02-01
In this paper we establish a connection between particle trajectories subject to a nonholonomic constraint and light ray trajectories in a variable index of refraction. In particular, we extend the analysis of systems with linear nonholonomic constraints to the dynamics of particles in a potential subject to nonlinear velocity constraints. We contrast the long time behavior of particles subject to a constant kinetic energy constraint (a thermostat) to particles with the constraint of parallel velocities. We show that, while in the former case the velocities of each particle equalize in the limit, in the latter case all the kinetic energies of each particle remain the same.
Johansson, Magnus; Gorbach, Andrey V
2004-11-01
We present an example of an exact quasiperiodic localized stable solution with spatially symmetric large-amplitude oscillations in a nonintegrable Hamiltonian lattice model. The model is a one-dimensional discrete nonlinear Schrödinger equation with alternating on-site energies, modeling, e.g., an array of optical waveguides with alternating widths. The solution bifurcates from a stationary discrete gap soliton, and in a regime of large oscillations its intensity oscillates periodically between having one peak at the central site and two symmetric peaks at the neighboring sites with a dip in the middle. Such solutions, termed "pulsons," are found to exist in continuous families ranging arbitrarily close to both the anticontinuous and continuous limits. Furthermore, it is shown that they may be linearly stable also in a regime of large oscillations.
Nonlinear geometric effects in mechanical bistable morphing structures.
Chen, Zi; Guo, Qiaohang; Majidi, Carmel; Chen, Wenzhe; Srolovitz, David J; Haataja, Mikko P
2012-09-14
Bistable structures associated with nonlinear deformation behavior, exemplified by the Venus flytrap and slap bracelet, can switch between different functional shapes upon actuation. Despite numerous efforts in modeling such large deformation behavior of shells, the roles of mechanical and nonlinear geometric effects on bistability remain elusive. We demonstrate, through both theoretical analysis and tabletop experiments, that two dimensionless parameters control bistability. Our work classifies the conditions for bistability, and extends the large deformation theory of plates and shells.
OSCILLATION MECHANICS OF THE RESPIRATORY SYSTEM: APPLICATIONS TO LUNG DISEASE
Kaczka, David W.; Dellacá, Raffaele L.
2011-01-01
Since its introduction in the 1950s, the forced oscillation technique (FOT) and the measurement of respiratory impedance have evolved into powerful tools for the assessment of various mechanical phenomena in the mammalian lung during health and disease. In this review, we highlight the most recent developments in instrumentation, signal processing, and modeling relevant to FOT measurements. We demonstrate how FOT provides unparalleled information on the mechanical status of the respiratory system compared to more widely-used pulmonary function tests. The concept of mechanical impedance is reviewed, as well as the various measurement techniques used to acquire such data. Emphasis is placed on the analysis of lower, physiologic frequency ranges (typically less than 10 Hz) that are most sensitive to normal physical processes as well as pathologic structural alterations. Various inverse modeling approaches used to interpret alterations in impedance are also discussed, specifically in the context of three common respiratory diseases: asthma, chronic obstructive pulmonary disease, and acute lung injury. Finally, we speculate on the potential role for FOT in the clinical arena. PMID:22011237
NASA Astrophysics Data System (ADS)
Petrov, Valentin; Marchev, Georgi; Tyazhev, Aleksey; Starikova, Marina; Esteban-Martin, Adolfo; Panyutin, Vladimir; Badikov, Valeriy; Shevyrdyaeva, Galina; Badikov, Dmitrii; Reza, Manuel; Sheina, Svetlana; Fintisova, Anna
2013-07-01
We investigated optical damage (surface and bulk) in wide band-gap (absorption edge below 532 nm) sulphide and selenide nonlinear crystals that can be used in 1064-nm pumped optical parametric oscillators (OPOs) for generation of idler pulses above 4 μm without two-photon absorption losses at the pump wavelength. The optical damage has been characterized at the pump wavelength for different repetition rates. Surface damage has been studied for uncoated and antireflection-coated (mainly with a single layer for pump and signal wavelengths) samples. Optical damage inside the OPO has a lower threshold and represents at present the principal limitation for the achievable output. It is related to peak and not to average intensities and in many of the studied crystals bulk damage in the form of scattering centers occurs before surface damage. Such bulk damage formation is faster at higher repetition rate. Lower repetition rates increase the lifetime of the crystal but do not solve the problem. In the most successful nonlinear crystal (both in terms of output energy and average power), orange-phase HgGa2S4, the safe pump intensity in extracavity measurements is below 100 MW/cm2 which corresponds to less than 1 J/cm2 for the 8 ns pulse duration (both values peak on-axis). In the OPO, however, peak on-axis fluence should not exceed 0.3 J/cm2 limited by the formation of bulk scattering centers. The damage resistivity of yellow-phase HgGa2S4 or Cd-doped HgGa2S4 is higher and of the almost colorless CdGa2S4 it is roughly two times higher but the latter has no sufficient birefringence for phase-matching.
Passive dynamic controllers for nonlinear mechanical systems
NASA Technical Reports Server (NTRS)
Juang, Jer-Nan; Wu, Shih-Chin; Phan, Minh; Longman, Richard W.
1991-01-01
A methodology for model-independant controller design for controlling large angular motion of multi-body dynamic systems is outlined. The controlled system may consist of rigid and flexible components that undergo large rigid body motion and small elastic deformations. Control forces/torques are applied to drive the system and at the same time suppress the vibration due to flexibility of the components. The proposed controller consists of passive second-order systems which may be designed with little knowledge of the system parameter, even if the controlled system is nonlinear. Under rather general assumptions, the passive design assures that the closed loop system has guaranteed stability properties. Unlike positive real controller design, stabilization can be accomplished without direct velocity feedback. In addition, the second-order passive design allows dynamic feedback controllers with considerable freedom to tune for desired system response, and to avoid actuator saturation. After developing the basic mathematical formulation of the design methodology, simulation results are presented to illustrate the proposed approach to a flexible six-degree-of-freedom manipulator.
Signatures of nonlinear optomechanics and engineering of nonclassical mechanical steady states
NASA Astrophysics Data System (ADS)
Borkje, Kjetil
2013-03-01
Motivated by recent improvements in coupling strength between light and mechanical motion, we study the strong coupling regime of cavity optomechanics theoretically. We focus on the regime where the optomechanical coupling rate is still small compared to the mechanical resonance frequency, but where the mechanically induced Kerr nonlinearity is significant. The response of the system to an optical drive is characterized. The average photon number in the cavity as a function of drive detuning can feature several peaks due to multi-photon transitions. Furthermore, we show that by optically driving the system at multiple frequencies, multi-photon transitions can facilitate the engineering of nonclassical steady states of the mechanical oscillator. The author acknowledges financial support from The Danish Council for Independent Research under the Sapere Aude program.
On-chip Electrical Soliton Oscillators for Picosecond Pulse Self-Generation and THz Electronics
2012-01-17
nonlinear line substantially sharpens the pulse . This work is in contrast to our earlier circular soliton oscillator... sharpening mechanism provided at the open end of the nonlinear line further compresses the pulse . In an experimental prototype (discrete prototype for proof... nonlinear properties, to ensure oscillation stability. The nonlinear line substantially sharpens the pulse . This work is in contrast to our
Nonlinear mechanics of thermoreversibly associating dendrimer glasses
NASA Astrophysics Data System (ADS)
Srikanth, Arvind; Hoy, Robert S.; Rinderspacher, Berend C.; Andzelm, Jan W.
2013-10-01
We model the mechanics of associating trivalent dendrimer network glasses with a focus on their energy dissipation properties. Various combinations of sticky bond (SB) strength and kinetics are employed. The toughness (work to fracture) of these systems displays a surprising deformation-protocol dependence; different association parameters optimize different properties. In particular, “strong, slow” SBs optimize strength, while “weak, fast” SBs optimize ductility via self-healing during deformation. We relate these observations to breaking, reformation, and partner switching of SBs during deformation. These studies point the way to creating associating-polymer network glasses with tailorable mechanical properties.
NASA Astrophysics Data System (ADS)
Liu, Yunqiao; Calvisi, Michael L.; Wang, Qianxi
2017-04-01
Encapsulated microbubbles (EMBs) are widely used in medical ultrasound imaging as contrast-enhanced agents. However, the potential damaging effects of violent collapsing EMBs to cells and tissues in clinical settings have remained a concern. Dual-frequency ultrasound is a promising technique for improving the efficacy and safety of sonography. The system modeled consists of the external liquid, membrane and internal gases of an EMB. The microbubble dynamics are simulated using a simple nonlinear interactive theory, considering the compressibility of the internal gas, viscosity of the liquid flow and viscoelasticity of the membrane. The radial oscillation and interfacial stability of an EMB under single- and dual-frequency excitations are compared. The simulation results show that the dual-frequency technique produces larger backscatter pressure at higher harmonics of the primary driving frequency—this enriched acoustic spectrum can enhance blood-tissue contrast and improve the quality of sonographic images. The results further show that the acoustic pressure threshold associated with the onset of shape instability is greater for dual-frequency driving. This suggests that the dual-frequency technique stabilizes the encapsulated bubble, thereby improving the efficacy and safety of contrast-enhanced agents.
NASA Astrophysics Data System (ADS)
Calvisi, Michael; Liu, Yunqiao; Wang, Qianxi
2016-11-01
Encapsulated microbubbles (EMBs) are widely used in medical ultrasound imaging as contrast-enhanced agents. However, the potential damaging effects of violent, collapsing EMBs to cells and tissues in clinical practice have remained a concern. Dual-frequency ultrasound is a promising technique for improving the efficacy and safety of sonography. The EMB system modeled consists of the external liquid, membrane, and internal gases. The microbubble dynamics are simulated using a simple nonlinear interactive theory, considering the compressibility of the internal gas, viscosity of the liquid flow, and elasticity of the membrane. The radial oscillation and interfacial stability of an EMB under single and dual-frequency excitations are compared. The simulation results show that the dual-frequency technique produces larger backscatter pressure at higher harmonics of the primary driving frequency. This enriched acoustic spectrum can enhance blood-tissue contrast and improve sonographic image quality. The results further show that the acoustic pressure threshold associated with the onset of shape instability is greater for dual-frequency driving. This suggests that the dual-frequency technique stabilizes the EMB, thereby improving the efficacy and safety of contrast-enhanced agents.
NASA Technical Reports Server (NTRS)
Bogdan, V. M.; Bond, V. B.
1980-01-01
The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.
New Facts on the Nature of Gravitational Force And Nonlinear Oscillations of Space
NASA Astrophysics Data System (ADS)
Kursunoglu, Behram N.
2002-07-01
This paper discusses the letters received by this author from Albert Einstein, Erwin Schrodinger, and Paul Adrian Maurice Dirac, about fifty years ago which comment on my nonsymmetrical generalization of Einstein's general relativistic theory of gravitation. The writing of this paper, because of the dates of the letters, seems to have been delayed by half a century. Of the three versions of the nonsymmetrical theory (Einstein, Schrodinger and Kursunoglu Theories) my own paper contains results obtained as solutions of Generalized Theory of Gravitation field equations. In this paper it is shown that the field equations yield space nonlinear oscillations; a quartet of gravitational forces, quintessence, and replace Einstein's Cosmological Constant by two invariant parameters r0 and q related according to r02 q2 = c4/2G, where r0 is a length varying between zero and infinity and where q2 has the dimensions of energy density. These parameters govern the expansion of the universe with increasing acceleration and their existence yield four different solutions at each space-time point.
Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators
Duanmu, M.; Whitaker, N.; Kevrekidis, P. G.; ...
2016-02-27
Artificial perceptions of light called phosphenes were motivated by earlier studies. We analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model problem in its co-traveling frame and systematically obtain the corresponding traveling waves in one spatial dimension. Direct numerical simulations as well as linear stability analysis are employed to reveal the parameter regions where the traveling waves are stable, and these waves are, in turn, connected to the standing waves analyzed in earlier work. We also consider a two-dimensional extension of the model and demonstrate the robust evolutionmore » and stability of planar fronts. Moreover, our simulations also suggest the radial fronts tend to either annihilate or expand and flatten out, depending on the phase value inside and the parameter regime. Finally, we observe that solutions that initially feature two symmetric fronts with bulged centers evolve in qualitative agreement with experimental observations of phosphenes.« less
Yoshimura
2000-11-01
We study analytically the induction phenomenon in the Fermi-Pasta-Ulam beta oscillator chain under initial conditions consisting of single mode excitation. Our study is based on the analytical computation of the largest characteristic exponent of an approximate version of the variational equation. The main results can be summarized as follows: (1) the energy density epsilon scaling of the induction time T is given by T approximately epsilon(-1), and T becomes smaller for higher-frequency mode excitation; (2) there is a threshold energy density epsilon(c) such that the induction time diverges when epsilon
He, Qingbo Xu, Yanyan; Lu, Siliang; Dai, Daoyi
2014-04-28
This Letter reports an out-of-resonance vibro-acoustic modulation (VAM) effect in nonlinear ultrasonic evaluation of a microcracked cantilever beam. We design a model to involve the microcracked cantilever beam in a nonlinear oscillator system whose dynamics is introduced to extend the operating vibration excitation band of the VAM out of resonance. The prototype model exhibits an effective bandwidth four times that of the traditional linear model. The reported VAM effect allows efficiently enhancing the detection, localization, and imaging of various types of microcracks in solid materials at out-of-resonance vibration excitation frequencies.
The Two-Capacitor Problem Revisited: A Mechanical Harmonic Oscillator Model Approach
ERIC Educational Resources Information Center
Lee, Keeyung
2009-01-01
The well-known two-capacitor problem, in which exactly half the stored energy disappears when a charged capacitor is connected to an identical capacitor, is discussed based on the mechanical harmonic oscillator model approach. In the mechanical harmonic oscillator model, it is shown first that "exactly half" the work done by a constant applied…
NASA Astrophysics Data System (ADS)
Marquez, Bicky A.; Larger, Laurent; Brunner, Daniel; Chembo, Yanne K.; Jacquot, Maxime
2016-12-01
We report on experimental and theoretical analysis of the complex dynamics generated by a nonlinear time-delayed electro-optic bandpass oscillator. We investigate the interaction between the slow- and fast-scale dynamics of autonomous oscillations in the breather regime. We analyze in detail the coupling between the fast-scale behavior associated to a characteristic low-pass Ikeda behavior and the slow-scale dynamics associated to a Liénard limit-cycle. Finally, we show that when projected onto a two-dimensional phase space, the attractors corresponding to periodic and chaotic breathers display a spiral-like pattern, which strongly depends on the shape of the nonlinear function.
Marquez, Bicky A; Larger, Laurent; Brunner, Daniel; Chembo, Yanne K; Jacquot, Maxime
2016-12-01
We report on experimental and theoretical analysis of the complex dynamics generated by a nonlinear time-delayed electro-optic bandpass oscillator. We investigate the interaction between the slow- and fast-scale dynamics of autonomous oscillations in the breather regime. We analyze in detail the coupling between the fast-scale behavior associated to a characteristic low-pass Ikeda behavior and the slow-scale dynamics associated to a Liénard limit-cycle. Finally, we show that when projected onto a two-dimensional phase space, the attractors corresponding to periodic and chaotic breathers display a spiral-like pattern, which strongly depends on the shape of the nonlinear function.
Schüngel, Edmund; Brandt, Steven; Schulze, Julian; Korolov, Ihor; Derzsi, Aranka; Donkó, Zoltán
2015-04-15
The self-excitation of plasma series resonance (PSR) oscillations is a prominent feature in the current of low pressure capacitive radio frequency discharges. This resonance leads to high frequency oscillations of the charge in the sheaths and enhances electron heating. Up to now, the phenomenon has only been observed in asymmetric discharges. There, the nonlinearity in the voltage balance, which is necessary for the self-excitation of resonance oscillations with frequencies above the applied frequencies, is caused predominantly by the quadratic contribution to the charge-voltage relation of the plasma sheaths. Using Particle In Cell/Monte Carlo collision simulations of single- and multi-frequency capacitive discharges and an equivalent circuit model, we demonstrate that other mechanisms, such as a cubic contribution to the charge-voltage relation of the plasma sheaths and the time dependent bulk electron plasma frequency, can cause the self-excitation of PSR oscillations, as well. These mechanisms have been neglected in previous models, but are important for the theoretical description of the current in symmetric or weakly asymmetric discharges.
Kovachev, L. M.
2009-10-29
We present an analytical approach to the theory of optical pulses with superbroad spectrum propagated in air. The corresponding modified amplitude envelope equation admits oscillated with terahertz frequency nonlinear term The fluctuation is due to the group and phase velocity difference. In the partial case of femtosecond pulses with power, little above the critical for self-focusing, exact (3+1)D particle-like solution is found.
Sheetz, Kraig E; Hoover, Erich E; Carriles, Ramón; Kleinfeld, David; Squier, Jeff A
2008-10-27
We present a novel Yb:KGd(WO(4))(2) oscillator design that generates six beams of temporally delayed, 253 fs, 11 nJ pulses. This allows multifocal nonlinear microscopy to be performed without the need for complicated optical multiplexers. We demonstrate our design with twelve simultaneously acquired two-photon, second-harmonic and/or third-harmonic images generated from six laterally separated foci.
High-efficiency quantum state transfer and quantum memory using a mechanical oscillator
NASA Astrophysics Data System (ADS)
Sete, Eyob A.; Eleuch, H.
2015-03-01
We analyze an optomechanical system that can be used to efficiently transfer a quantum state between an optical cavity and a distant mechanical oscillator coupled to a second optical cavity. We show that for a moderate mechanical Q factor it is possible to achieve a transfer efficiency of 99.4 % by using adjustable cavity damping rates and destructive interference. We also show that the quantum mechanical oscillator can be used as a quantum memory device with an efficiency of 96 % employing a pulsed optomechanical coupling. Although the mechanical dissipation slightly decreases the efficiency, its effect can be significantly reduced by designing a high-Q mechanical oscillator.
Minati, Ludovico E-mail: ludovico.minati@unitn.it
2015-03-15
In this paper, the topographical relationship between functional connectivity (intended as inter-regional synchronization), spectral and non-linear dynamical properties across cortical areas of the healthy human brain is considered. Based upon functional MRI acquisitions of spontaneous activity during wakeful idleness, node degree maps are determined by thresholding the temporal correlation coefficient among all voxel pairs. In addition, for individual voxel time-series, the relative amplitude of low-frequency fluctuations and the correlation dimension (D{sub 2}), determined with respect to Fourier amplitude and value distribution matched surrogate data, are measured. Across cortical areas, high node degree is associated with a shift towards lower frequency activity and, compared to surrogate data, clearer saturation to a lower correlation dimension, suggesting presence of non-linear structure. An attempt to recapitulate this relationship in a network of single-transistor oscillators is made, based on a diffusive ring (n = 90) with added long-distance links defining four extended hub regions. Similarly to the brain data, it is found that oscillators in the hub regions generate signals with larger low-frequency cycle amplitude fluctuations and clearer saturation to a lower correlation dimension compared to surrogates. The effect emerges more markedly close to criticality. The homology observed between the two systems despite profound differences in scale, coupling mechanism and dynamics appears noteworthy. These experimental results motivate further investigation into the heterogeneity of cortical non-linear dynamics in relation to connectivity and underline the ability for small networks of single-transistor oscillators to recreate collective phenomena arising in much more complex biological systems, potentially representing a future platform for modelling disease-related changes.
Minati, Ludovico; Chiesa, Pietro; Tabarelli, Davide; D'Incerti, Ludovico; Jovicich, Jorge
2015-03-01
In this paper, the topographical relationship between functional connectivity (intended as inter-regional synchronization), spectral and non-linear dynamical properties across cortical areas of the healthy human brain is considered. Based upon functional MRI acquisitions of spontaneous activity during wakeful idleness, node degree maps are determined by thresholding the temporal correlation coefficient among all voxel pairs. In addition, for individual voxel time-series, the relative amplitude of low-frequency fluctuations and the correlation dimension (D2), determined with respect to Fourier amplitude and value distribution matched surrogate data, are measured. Across cortical areas, high node degree is associated with a shift towards lower frequency activity and, compared to surrogate data, clearer saturation to a lower correlation dimension, suggesting presence of non-linear structure. An attempt to recapitulate this relationship in a network of single-transistor oscillators is made, based on a diffusive ring (n = 90) with added long-distance links defining four extended hub regions. Similarly to the brain data, it is found that oscillators in the hub regions generate signals with larger low-frequency cycle amplitude fluctuations and clearer saturation to a lower correlation dimension compared to surrogates. The effect emerges more markedly close to criticality. The homology observed between the two systems despite profound differences in scale, coupling mechanism and dynamics appears noteworthy. These experimental results motivate further investigation into the heterogeneity of cortical non-linear dynamics in relation to connectivity and underline the ability for small networks of single-transistor oscillators to recreate collective phenomena arising in much more complex biological systems, potentially representing a future platform for modelling disease-related changes.
NASA Astrophysics Data System (ADS)
Minati, Ludovico; Chiesa, Pietro; Tabarelli, Davide; D'Incerti, Ludovico; Jovicich, Jorge
2015-03-01
In this paper, the topographical relationship between functional connectivity (intended as inter-regional synchronization), spectral and non-linear dynamical properties across cortical areas of the healthy human brain is considered. Based upon functional MRI acquisitions of spontaneous activity during wakeful idleness, node degree maps are determined by thresholding the temporal correlation coefficient among all voxel pairs. In addition, for individual voxel time-series, the relative amplitude of low-frequency fluctuations and the correlation dimension (D2), determined with respect to Fourier amplitude and value distribution matched surrogate data, are measured. Across cortical areas, high node degree is associated with a shift towards lower frequency activity and, compared to surrogate data, clearer saturation to a lower correlation dimension, suggesting presence of non-linear structure. An attempt to recapitulate this relationship in a network of single-transistor oscillators is made, based on a diffusive ring (n = 90) with added long-distance links defining four extended hub regions. Similarly to the brain data, it is found that oscillators in the hub regions generate signals with larger low-frequency cycle amplitude fluctuations and clearer saturation to a lower correlation dimension compared to surrogates. The effect emerges more markedly close to criticality. The homology observed between the two systems despite profound differences in scale, coupling mechanism and dynamics appears noteworthy. These experimental results motivate further investigation into the heterogeneity of cortical non-linear dynamics in relation to connectivity and underline the ability for small networks of single-transistor oscillators to recreate collective phenomena arising in much more complex biological systems, potentially representing a future platform for modelling disease-related changes.
Statistical Mechanics of Node-Perturbation Learning for Nonlinear Perceptron
NASA Astrophysics Data System (ADS)
Hara, Kazuyuki; Katahira, Kentaro; Okanoya, Kazuo; Okada, Masato
2013-05-01
Node-perturbation learning is a type of statistical gradient descent algorithm that can be applied to problems where the objective function is not explicitly formulated, including reinforcement learning. Node-perturbation learning with M linear perceptrons has previously been analyzed using the methods of statistical mechanics. It was shown that cross-talk noise, which originates from the error of the other outputs, increases the generalization error as the number of outputs increases. On the other hand, a nonlinear perceptron has several advantages over a linear perceptron, such as the ability to use nonlinear outputs, learnability, storage capacity, and so forth. However, node-perturbation for a nonlinear perceptron has yet to be analyzed theoretically. In this paper, we derive a learning rule of node-perturbation learning for a nonlinear perceptron within the framework of REINFORCE learning and analyze the learning behavior by using statistical mechanical methods. From the results, we found that the signal and cross-talk terms of the order parameter Q have different forms for a nonlinear perceptron. Moreover, the increase in the generalization error with increasing number of outputs is less than for a linear perceptron.
A nonlinear high temperature fracture mechanics basis for strainrange partitioning
NASA Technical Reports Server (NTRS)
Kitamura, Takayuki; Halford, Gary R.
1989-01-01
A direct link was established between Strainrange Partitioning (SRP) and high temperature fracture mechanics by deriving the general SRP inelastic strain range versus cyclic life relationships from high temperature, nonlinear, fracture mechanics considerations. The derived SRP life relationships are in reasonable agreement based on the experience of the SRP behavior of many high temperature alloys. In addition, fracture mechanics has served as a basis for derivation of the Ductility-Normalized SRP life equations, as well as for examination of SRP relations that are applicable to thermal fatigue life prediction. Areas of additional links between nonlinear fracture mechanics and SRP were identified for future exploration. These include effects of multiaxiality as well as low strain, nominally elastic, long life creep fatigue interaction.
NASA Astrophysics Data System (ADS)
Georgiou, K.; Tang, J.; Riley, W. J.; Torn, M. S.
2014-12-01
Soil organic matter (SOM) decomposition is regulated by biotic and abiotic processes. Feedback interactions between such processes may act to dampen oscillatory responses to perturbations from equilibrium. Indeed, although biological oscillations have been observed in small-scale laboratory incubations, the overlying behavior at the plot-scale exhibits a relatively stable response to disturbances in input rates and temperature. Recent studies have demonstrated the ability of microbial models to capture nonlinear feedbacks in SOM decomposition that linear Century-type models are unable to reproduce, such as soil priming in response to increased carbon input. However, these microbial models often exhibit strong oscillatory behavior that is deemed unrealistic. The inherently nonlinear dynamics of SOM decomposition have important implications for global climate-carbon and carbon-concentration feedbacks. It is therefore imperative to represent these dynamics in Earth System Models (ESMs) by introducing sub-models that accurately represent microbial and abiotic processes. In the present study we explore, both analytically and numerically, four microbe-enabled model structures of varying levels of complexity. The most complex model combines microbial physiology, a non-linear mineral sorption isotherm, and enzyme dynamics. Based on detailed stability analysis of the nonlinear dynamics, we calculate the system modes as functions of model parameters. This dependence provides insight into the source of state oscillations. We find that feedback mechanisms that emerge from careful representation of enzyme and mineral interactions, with parameter values in a prescribed range, are critical for both maintaining system stability and capturing realistic responses to disturbances. Corroborating and expanding upon the results of recent studies, we explain the emergence of oscillatory responses and discuss the appropriate microbe-enabled model structure for inclusion in ESMs.
Nonlinear mechanical behavior of thermoplastic matrix materials for advanced composites
NASA Technical Reports Server (NTRS)
Arenz, R. J.; Landel, R. F.
1989-01-01
Two recent theories of nonlinear mechanical response are quantitatively compared and related to experimental data. Computer techniques are formulated to handle the numerical integration and iterative procedures needed to solve the associated sets of coupled nonlinear differential equations. Problems encountered during these formulations are discussed and some open questions described. Bearing in mind these cautions, the consequences of changing parameters that appear in the formulations on the resulting engineering properties are discussed. Hence, engineering approaches to the analysis of thermoplastic matrix material can be suggested.
A mechanical-thermal noise analysis of a nonlinear microgyroscope
NASA Astrophysics Data System (ADS)
Lajimi, S. A. M.; Heppler, G. R.; Abdel-Rahman, E. M.
2017-01-01
The mechanical-thermal noise (MTN) equivalent rotation rate (Ωn) is computed by using the linear approximation of the system response and the nonlinear "slow" system. The slow system, which is obtained using the method of multiple scales, is used to identify the linear single-valued response of the system. The linear estimate of the noise equivalent rate fails as the drive direction stroke increases. It becomes imperative in these conditions to use a more complex nonlinear estimate of the noise equivalent rate developed here for the first time in literature. The proposed design achieves a high performance regarding noise equivalent rotation rate.
Ionic mechanisms for intrinsic slow oscillations in thalamic relay neurons.
Destexhe, A; Babloyantz, A; Sejnowski, T J
1993-01-01
The oscillatory properties of single thalamocortical neurons were investigated by using a Hodgkin-Huxley-like model that included Ca2+ diffusion, the low-threshold Ca2+ current (lT) and the hyperpolarization-activated inward current (lh). lh was modeled by double activation kinetics regulated by intracellular Ca2+. The model exhibited waxing and waning oscillations consisting of 1-25-s bursts of slow oscillations (3.5-4 Hz) separated by long silent periods (4-20 s). During the oscillatory phase, the entry of Ca2+ progressively shifted the activation function of lh, terminating the oscillations. A similar type of waxing and waning oscillation was also observed, in the absence of Ca2+ regulation of lh, from the combination of lT, lh, and a slow K+ current. Singular approximation showed that for both models, the activation variables of lh controlled the dynamics of thalamocortical cells. Dynamical analysis of the system in a phase plane diagram showed that waxing and waning oscillations arose when lh entrained the system alternately between stationary and oscillating branches. Images FIGURE 1 PMID:8274647
A generalized harmonic balance method for forced non-linear oscillations: the subharmonic cases
NASA Astrophysics Data System (ADS)
Wu, J. J.
1992-12-01
This paper summarizes and extends results in two previous papers, published in conference proceedings, on a variant of the generalized harmonic balance method (GHB) and its application to obtain subharmonic solutions of forced non-linear oscillation problems. This method was introduced as an alternative to the method of multiple scales, and it essentially consists of two parts. First, the part of the multiple scales method used to reduce the problem to a set of differential equations is used to express the solution as a sum of terms of various harmonics with unknown, time dependent coefficients. Second, the form of solution so obtained is substituted into the original equation and the coefficients of each harmonic are set to zero. Key equations of approximations for a subharmonic case are derived for the cases of both "small" damping and excitations, and "Large" damping and excitations, which are shown to be identical, in the intended order of approximation, to those obtained by Nayfeh using the method of multiple scales. Detailed numerical formulations, including the derivation of the initial conditions, are presented, as well as some numerical results for the frequency-response relations and the time evolution of various harmonic components. Excellent agreement is demonstrated between results by GHB and by integrating the original differential equation directly. The improved efficiency in obtaining numerical solutions using GHB as compared with integrating the original differential equation is demonstrated also. For the case of large damping and excitations and for non-trivial solutions, it is noted that there exists a threshold value of the force beyond which no subharmonic excitations are possible.
NASA Astrophysics Data System (ADS)
ElNady, Khaled; Goda, Ibrahim; Ganghoffer, Jean-François
2016-12-01
The asymptotic homogenization technique is presently developed in the framework of geometrical nonlinearities to derive the large strains effective elastic response of network materials viewed as repetitive beam networks. This works extends the small strains homogenization method developed with special emphasis on textile structures in Goda et al. (J Mech Phys Solids 61(12):2537-2565, 2013). A systematic methodology is established, allowing the prediction of the overall mechanical properties of these structures in the nonlinear regime, reflecting the influence of the geometrical and mechanical micro-parameters of the network structure on the overall response of the chosen equivalent continuum. Internal scale effects of the initially discrete structure are captured by the consideration of a micropolar effective continuum model. Applications to the large strain response of 3D hexagonal lattices and dry textiles exemplify the powerfulness of the proposed method. The effective mechanical responses obtained for different loadings are validated by FE simulations performed over a representative unit cell.
The use of normal forms for analysing nonlinear mechanical vibrations
Neild, Simon A.; Champneys, Alan R.; Wagg, David J.; Hill, Thomas L.; Cammarano, Andrea
2015-01-01
A historical introduction is given of the theory of normal forms for simplifying nonlinear dynamical systems close to resonances or bifurcation points. The specific focus is on mechanical vibration problems, described by finite degree-of-freedom second-order-in-time differential equations. A recent variant of the normal form method, that respects the specific structure of such models, is recalled. It is shown how this method can be placed within the context of the general theory of normal forms provided the damping and forcing terms are treated as unfolding parameters. The approach is contrasted to the alternative theory of nonlinear normal modes (NNMs) which is argued to be problematic in the presence of damping. The efficacy of the normal form method is illustrated on a model of the vibration of a taut cable, which is geometrically nonlinear. It is shown how the method is able to accurately predict NNM shapes and their bifurcations. PMID:26303917
Are nonlinear discrete cellular automata compatible with quantum mechanics?
NASA Astrophysics Data System (ADS)
Elze, Hans-Thomas
2015-07-01
We consider discrete and integer-valued cellular automata (CA). A particular class of which comprises “Hamiltonian CA” with equations of motion that bear similarities to Hamilton's equations, while they present discrete updating rules. The dynamics is linear, quite similar to unitary evolution described by the Schrödinger equation. This has been essential in our construction of an invertible map between such CA and continuous quantum mechanical models, which incorporate a fundamental discreteness scale. Based on Shannon's sampling theory, it leads, for example, to a one-to-one relation between quantum mechanical and CA conservation laws. The important issue of linearity of the theory is examined here by incorporating higher-order nonlinearities into the underlying action. These produce inconsistent nonlocal (in time) effects when trying to describe continuously such nonlinear CA. Therefore, in the present framework, only linear CA and local quantum mechanical dynamics are compatible.
Ohshima, Daisuke; Ichikawa, Kazuhisa
2015-01-01
The activated transcription factor NF-κB shuttles between the cytoplasm and the nucleus resulting in the oscillation of nuclear NF-κB (NF-κBn). The oscillation pattern of NF-κBn is implicated in the regulation of gene expression profiles. Using computational models, we previously reported that spatial parameters, such as the diffusion coefficient, nuclear to cytoplasmic volume ratio, transport through the nuclear envelope, and the loci of translation of IκB protein, modified the oscillation pattern of NF-κBn. In a subsequent report, we elucidated the importance of the "reset" of NF-κBn (returning of NF-κB to the original level) and of a "reservoir" of IκB in the cytoplasm. When the diffusion coefficient of IκB was large, IκB stored at a distant location from the nucleus diffused back to the nucleus and "reset" NF-κBn. Herein, we report mechanisms that regulate the persistency and frequency of NF-κBn oscillation by nuclear transport. Among the four parameters of nuclear transport tested in our spatio-temporal computational model, the export of IκB mRNA from the nucleus regulated the persistency of oscillation. The import of IκB to the nucleus regulated the frequency of oscillation. The remaining two parameters, import and export of NF-κB to and from the nucleus, had virtually no effect on the persistency or frequency. Our analyses revealed that lesser export of IκB mRNA allowed NF-κBn to transcript greater amounts of IκB mRNA, which was retained in the nucleus, and was subsequently exported to the cytoplasm, where large amounts of IκB were synthesized to "reset" NF-κBn and drove the persistent oscillation. On the other hand, import of greater amounts of IκB led to an increase in the influx and the efflux of NF-κB to and from the nucleus, resulting in an increase in the oscillation frequency. Our study revealed the importance of nuclear transport in regulating the oscillation pattern of NF-κBn.
Experimental evidence of directivity-enhancing mechanisms in nonlinear lattices
NASA Astrophysics Data System (ADS)
Ganesh, R.; Gonella, Stefano
2017-02-01
In this letter, we experimentally investigate the directional characteristics of propagating, finite-amplitude wave packets in lattice materials, with an emphasis on the functionality enhancement due to the nonlinearly generated higher harmonics. To this end, we subject a thin, periodically perforated sheet to out-of-plane harmonic excitations, and we design a systematic measurement and data processing routine that leverages the full-wavefield reconstruction capabilities of a laser vibrometer to precisely delineate the effects of nonlinearity. We demonstrate experimentally that the interplay of dispersion, nonlinearity, and modal complexity which is involved in the generation and propagation of higher harmonics gives rise to secondary wave packets with characteristics that conform to the dispersion relation of the corresponding linear structure. Furthermore, these nonlinearly generated wave features display modal and directional characteristics that are complementary to those exhibited by the fundamental harmonic, thus resulting in an augmentation of the functionality landscape of the lattice. These results provide a proof of concept for the possibility to engineer the nonlinear wave response of mechanical metamaterials through a geometric and topological design of the unit cell.
NASA Astrophysics Data System (ADS)
Wan, Yu; Jin, Kai; Ahmad, Talha J.; Black, Michael J.; Xu, Zhiping
2017-03-01
Fluidic environment is encountered for mechanical components in many circumstances, which not only damps the oscillation but also modulates their dynamical behaviors through hydrodynamic interactions. In this study, we examine energy transfer and motion synchronization between two mechanical micro-oscillators by performing thermal lattice-Boltzmann simulations. The coefficient of inter-oscillator energy transfer is measured to quantify the strength of microhydrodynamic coupling, which depends on their distance and fluid properties such as density and viscosity. Synchronized motion of the oscillators is observed in the simulations for typical parameter sets in relevant applications, with the formation and loss of stable anti-phase synchronization controlled by the oscillating frequency, amplitude, and hydrodynamic coupling strength. The critical ranges of key parameters to assure efficient energy transfer or highly synchronized motion are predicted. These findings could be used to advise mechanical design of passive and active devices that operate in fluid.
Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode.
Verhagen, E; Deléglise, S; Weis, S; Schliesser, A; Kippenberg, T J
2012-02-01
Optical laser fields have been widely used to achieve quantum control over the motional and internal degrees of freedom of atoms and ions, molecules and atomic gases. A route to controlling the quantum states of macroscopic mechanical oscillators in a similar fashion is to exploit the parametric coupling between optical and mechanical degrees of freedom through radiation pressure in suitably engineered optical cavities. If the optomechanical coupling is 'quantum coherent'--that is, if the coherent coupling rate exceeds both the optical and the mechanical decoherence rate--quantum states are transferred from the optical field to the mechanical oscillator and vice versa. This transfer allows control of the mechanical oscillator state using the wide range of available quantum optical techniques. So far, however, quantum-coherent coupling of micromechanical oscillators has only been achieved using microwave fields at millikelvin temperatures. Optical experiments have not attained this regime owing to the large mechanical decoherence rates and the difficulty of overcoming optical dissipation. Here we achieve quantum-coherent coupling between optical photons and a micromechanical oscillator. Simultaneously, coupling to the cold photon bath cools the mechanical oscillator to an average occupancy of 1.7 ± 0.1 motional quanta. Excitation with weak classical light pulses reveals the exchange of energy between the optical light field and the micromechanical oscillator in the time domain at the level of less than one quantum on average. This optomechanical system establishes an efficient quantum interface between mechanical oscillators and optical photons, which can provide decoherence-free transport of quantum states through optical fibres. Our results offer a route towards the use of mechanical oscillators as quantum transducers or in microwave-to-optical quantum links.
Probing wave function collapse models with a classically driven mechanical oscillator
NASA Astrophysics Data System (ADS)
Ho, Melvyn; Lafont, Ambroise; Sangouard, Nicolas; Sekatski, Pavel
2016-03-01
We show that the interaction of a pulsed laser light with a mechanical oscillator through the radiation pressure results in an opto-mechanical entangled state in which the photon number is correlated with the oscillator position. Interestingly, the mechanical oscillator can be delocalized over a large range of positions when driven by an intense laser light. This provides a simple yet sensitive method to probe hypothetical post-quantum theories including an explicit wave function collapse model, like the Diosi & Penrose model. We propose an entanglement witness to reveal the quantum nature of this opto-mechanical state as well as an optical technique to record the decoherence of the mechanical oscillator. We also report on a detailed feasibility study giving the experimental challenges that need to be overcome in order to confirm or rule out predictions from explicit wave function collapse models.
Sugimoto, N; Masuda, M; Hashiguchi, T
2003-10-01
Nonlinear cubic theory is developed to obtain a frequency response of shock-free, forced oscillations of an air column in a closed tube with an array of Helmholtz resonators connected axially. The column is assumed to be driven by a plane piston sinusoidally at a frequency close or equal to the lowest resonance frequency with its maximum displacement fixed. By applying the method of multiple scales, the equation for temporal modulation of a complex pressure amplitude of the lowest mode is derived in a case that a typical acoustic Mach number is comparable with the one-third power of the piston Mach number, while the relative detuning of a frequency is comparable with the quadratic order of the acoustic Mach number. The steady-state solution gives the asymmetric frequency response curve with bending (skew) due to nonlinear frequency upshift in addition to the linear downshift. Validity of the theory is checked against the frequency response obtained experimentally. For high amplitude of oscillations, an effect of jet loss at the throat of the resonator is taken into account, which introduces the quadratic loss to suppress the peak amplitude. It is revealed that as far as the present check is concerned, the weakly nonlinear theory can give quantitatively adequate description up to the pressure amplitude of about 3% to the equilibrium pressure.
Damped Mechanical Oscillator: Experiment and Detailed Energy Analysis
ERIC Educational Resources Information Center
Corridoni, Tommaso; D'Anna, Michele; Fuchs, Hans
2014-01-01
The damped oscillator is discussed in every high school textbook or introductory physics course, and a large number of papers are devoted to it in physics didactics journals. Papers typically focus on kinematic and dynamic aspects and less often on energy. Among the latter, some are devoted to the peculiar decreasing behavior of energy…
Development of drive mechanism for an oscillating airfoil
NASA Technical Reports Server (NTRS)
Sticht, Clifford D.
1988-01-01
The design and development of an in-draft wind tunnel test section which will be used to study the dynamic stall of airfoils oscillating in pitch is described. The hardware developed comprises a spanned airfoil between schleiren windows, a four bar linkage, flywheels, a drive system and a test section structure.
Enhanced nonlinear interactions in quantum optomechanics via mechanical amplification
Lemonde, Marc-Antoine; Didier, Nicolas; Clerk, Aashish A.
2016-01-01
The quantum nonlinear regime of optomechanics is reached when nonlinear effects of the radiation pressure interaction are observed at the single-photon level. This requires couplings larger than the mechanical frequency and cavity-damping rate, and is difficult to achieve experimentally. Here we show how to exponentially enhance the single-photon optomechanical coupling strength using only additional linear resources. Our method is based on using a large-amplitude, strongly detuned mechanical parametric drive to amplify mechanical zero-point fluctuations and hence enhance the radiation pressure interaction. It has the further benefit of allowing time-dependent control, enabling pulsed schemes. For a two-cavity optomechanical set-up, we show that our scheme generates photon blockade for experimentally accessible parameters, and even makes the production of photonic states with negative Wigner functions possible. We discuss how our method is an example of a more general strategy for enhancing boson-mediated two-particle interactions and nonlinearities. PMID:27108814
Nonlinear effects in transonic flutter with emphasis on manifestations of limit cycle oscillations
NASA Astrophysics Data System (ADS)
Schewe, G.; Mai, H.; Dietz, G.
2003-08-01
This paper presents flutter and forced oscillation experiments in a transonic wind tunnel. For an aeroelastic supercritical 2-D airfoil configuration we studied typical transonic phenomena in as pure a form as possible. Various manifestations of small-amplitude limit cycle oscillations were observed for different flow conditions as well as coexisting limit cycles. We demonstrated how very small control forces were sufficient to excite or suppress flutter oscillations. Limit cycle oscillations occurred under free and forced turbulent boundary layer transition in a perforated wall test-section. Flutter calculations based on experimental aerodynamic forces yield stability limits which show good agreement with directly measured experimental flutter values. The results indicate that flow separation at the trailing edge, and the interactions between the shock and the marginal region of separated flow beneath it, may be responsible for limiting the amplitude of the observed limit cycle oscillations.
Quantum interface between Rydberg ensembles and mechanical oscillators in free space
NASA Astrophysics Data System (ADS)
Bariani, Francesco; Otterbach, Johannes; Tan, Huatang; Buchmann, L. F.; Meystre, Pierre
2013-05-01
We analyze theoretically an electro-mechanical interface between a charged mechanical oscillator and an ensemble of Rydberg atoms. The charged mechanical oscillator acting as an oscillating electric dipole is coupled to the large electric dipole of the Rydberg transition. The Rydberg blockade effect guarantees that only a single collective spin wave is excited in the atomic ensemble. This hybrid system allows for quantum control of the state of one or more mechanical oscillators. The rich atomic Rydberg spectrum and high level of control of atomic transitions allow to build feedback protocols that maximize its fidelity. We also comment on the use of this interface for phononic state tomography. We ackowledge financial support from NSF, ARO and the DARPA QuaSAR and ORCHID programs.
Mechanism behind self-sustained oscillations in direct current glow discharges and dusty plasmas
Cho, Sung Nae
2013-04-15
An alternative explanation to the mechanism behind self-sustained oscillations of ions in direct current (DC) glow discharges is provided. Such description is distinguished from the one provided by the fluid models, where oscillations are attributed to the positive feedback mechanism associated with photoionization of particles and photoemission of electrons from the cathode. Here, oscillations arise as consequence of interaction between an ion and the surface charges induced by it at the bounding electrodes. Such mechanism provides an elegant explanation to why self-sustained oscillations occur only in the negative resistance region of the voltage-current characteristic curve in the DC glow discharges. Furthermore, this alternative description provides an elegant explanation to the formation of plasma fireballs in the laboratory plasma. It has been found that oscillation frequencies increase with ion's surface charge density, but at the rate which is significantly slower than it does with the electric field. The presented mechanism also describes self-sustained oscillations of ions in dusty plasmas, which demonstrates that self-sustained oscillations in dusty plasmas and DC glow discharges involve common physical processes.
Theory of ground state cooling of a mechanical oscillator using dynamical backaction.
Wilson-Rae, I; Nooshi, N; Zwerger, W; Kippenberg, T J
2007-08-31
A quantum theory of cooling of a mechanical oscillator by radiation pressure-induced dynamical backaction is developed, which is analogous to sideband cooling of trapped ions. We find that final occupancies well below unity can be attained when the mechanical oscillation frequency is larger than the optical cavity linewidth. It is shown that the final average occupancy can be retrieved directly from the optical output spectrum.
Influence of fluid and volume state on PaO2 oscillations in mechanically ventilated pigs.
Bodenstein, Marc; Bierschock, Stephan; Boehme, Stefan; Wang, Hemei; Vogt, Andreas; Kwiecien, Robert; David, Matthias; Markstaller, Klaus
2013-03-01
Varying pulmonary shunt fractions during the respiratory cycle cause oxygen oscillations during mechanical ventilation. In artificially damaged lungs, cyclical recruitment of atelectasis is responsible for varying shunt according to published evidence. We introduce a complimentary hypothesis that cyclically varying shunt in healthy lungs is caused by cyclical redistribution of pulmonary perfusion. Administration of crystalloid or colloid infusions would decrease oxygen oscillations if our hypothesis was right. Therefore, n=14 mechanically ventilated healthy pigs were investigated in 2 groups: crystalloid (fluid) versus no-fluid administration. Additional volume interventions (colloid infusion, blood withdrawal) were carried out in each pig. Intra-aortal PaO2 oscillations were recorded using fluorescence quenching technique. Phase shift of oxygen oscillations during altered inspiratory to expiratory (I:E) ventilation ratio and electrical impedance tomography (EIT) served as control methods to exclude that recruitment of atelectasis is responsible for oxygen oscillations. In hypovolemia relevant oxygen oscillations could be recorded. Fluid and volume state changed PaO2 oscillations according to our hypothesis. Fluid administration led to a mean decline of 105.3 mmHg of the PaO2 oscillations amplitude (P<0.001). The difference of the amplitudes between colloid administration and blood withdrawal was 62.4 mmHg in pigs not having received fluids (P=0.0059). Fluid and volume state also changed the oscillation phase during altered I:E ratio. EIT excluded changes of regional ventilation (i.e., recruitment of atelectasis) to be responsible for these oscillations. In healthy pigs, cyclical redistribution of pulmonary perfusion can explain the size of respiratory-dependent PaO2 oscillations.
Floating Oscillator-Embedded Triboelectric Generator for Versatile Mechanical Energy Harvesting
Seol, Myeong-Lok; Han, Jin-Woo; Jeon, Seung-Bae; Meyyappan, M.; Choi, Yang-Kyu
2015-01-01
A versatile vibration energy harvesting platform based on a triboelectricity is proposed and analyzed. External mechanical vibration repeats an oscillating motion of a polymer-coated metal oscillator floating inside a surrounding tube. Continuous sidewall friction at the contact interface of the oscillator induces current between the inner oscillator electrode and the outer tube electrode to convert mechanical vibrations into electrical energy. The floating oscillator-embedded triboelectric generator (FO-TEG) is applicable for both impulse excitation and sinusoidal vibration which universally exist in usual environment. For the impulse excitation, the generated current sustains and slowly decays by the residual oscillation of the floating oscillator. For the sinusoidal vibration, the output energy can be maximized by resonance oscillation. The operating frequency range can be simply optimized with high degree of freedom to satisfy various application requirements. In addition, the excellent immunity against ambient humidity is experimentally demonstrated, which stems from the inherently packaged structure of FO-TEG. The prototype device provides a peak-to-peak open-circuit voltage of 157 V and instantaneous short-circuit current of 4.6 μA, within sub-10 Hz of operating frequency. To visually demonstrate the energy harvesting behavior of FO-TEG, lighting of an array of LEDs is demonstrated using artificial vibration and human running. PMID:26553524
Tests of Mach's Principle With a Mechanical Oscillator
NASA Technical Reports Server (NTRS)
Millis, Marc G. (Technical Monitor); Cramer, John G.; Fey, Curran W.; Casissi, Damon V.
2004-01-01
James F. Woodward has made a prediction, based on Sciama's formulation of Mach's Principle in the framework of general relativity, that in the presence of an energy flow the inertial mass of an object may undergo sizable variations, changing as the second time derivative of the energy. We describe an attempt to test for the predicted effect with a charging capacitor, using a technique that does not require an unbalanced force or any local violation of Newton s 3rd law of motion. We attempt to observe: (1) the gravitational effect of the varying mass and (2) the effect of the mass variation on a driven harmonic oscillator with the charging capacitor as the oscillating mass. We report on the predicted effect, the design and implementation of the measurement apparatus, and initial experience with the apparatus. At this time, however, we will not report on observations of the presence or absence of the Woodward effect.
Carbon-nanotube based nano-electro-mechanical oscillators
NASA Astrophysics Data System (ADS)
Papadakis, S. J.; Hall, A. R.; Spivak, D. M.; Falvo, M. R.; Superfine, R.; Washburn, S.
2004-03-01
We report on the fabrication and performance of nanometer-scale electromechanical oscillators which use multi-walled carbon nanotubes as torsional springs. Carbon nanotube devices may offer high quality factors due to the inert surface of the torsional member, and high sensitivity due to their nanoscale dimensions. They also provide a means to study the effects of torsion on nanotube transport. The devices have a paddle-oscillator geometry and are driven electrostatically. In previous work we manipulated these devices directly with a scanning probe to measure the torsional properties of the nanotube, its shear modulus, and its subsequent stiffening under repeated strain [1]. Here we use both optical and electron-beam techniques to measure the response of the devices to applied voltages. We demonstrate both quasi-static and on-resonance performance characteristics. 1. P. A. Williams, S. J. Papadakis, A. M. Patel, M. R. Falvo, S. Washburn, and R. Superfine, Phys. Rev. Lett. 89, 255502 (2002).
Apical oscillations in amnioserosa cells: basolateral coupling and mechanical autonomy.
Jayasinghe, Aroshan K; Crews, Sarah M; Mashburn, David N; Hutson, M Shane
2013-07-02
Holographic laser microsurgery is used to isolate single amnioserosa cells in vivo during early dorsal closure. During this stage of Drosophila embryogenesis, amnioserosa cells undergo oscillations in apical surface area. The postisolation behavior of individual cells depends on their preisolation phase in these contraction/expansion cycles: cells that were contracting tend to collapse quickly after isolation; cells that were expanding do not immediately collapse, but instead pause or even continue to expand for ∼40 s. In either case, the postisolation apical collapse can be prevented by prior anesthetization of the embryos with CO2. These results suggest that although the amnioserosa is under tension, its cells are subjected to only small elastic strains. Furthermore, their postisolation apical collapse is not a passive elastic relaxation, and both the contraction and expansion phases of their oscillations are driven by intracellular forces. All of the above require significant changes to existing computational models.
Apical Oscillations in Amnioserosa Cells: Basolateral Coupling and Mechanical Autonomy
Jayasinghe, Aroshan K.; Crews, Sarah M.; Mashburn, David N.; Hutson, M. Shane
2013-01-01
Holographic laser microsurgery is used to isolate single amnioserosa cells in vivo during early dorsal closure. During this stage of Drosophila embryogenesis, amnioserosa cells undergo oscillations in apical surface area. The postisolation behavior of individual cells depends on their preisolation phase in these contraction/expansion cycles: cells that were contracting tend to collapse quickly after isolation; cells that were expanding do not immediately collapse, but instead pause or even continue to expand for ∼40 s. In either case, the postisolation apical collapse can be prevented by prior anesthetization of the embryos with CO2. These results suggest that although the amnioserosa is under tension, its cells are subjected to only small elastic strains. Furthermore, their postisolation apical collapse is not a passive elastic relaxation, and both the contraction and expansion phases of their oscillations are driven by intracellular forces. All of the above require significant changes to existing computational models. PMID:23823245
DEVELOPMENT OF NONLINEAR HARMONIC SENSORS FOR DETECTION OF MECHANICAL DAMAGE
Alfred E. Crouch; Alan Dean; Carl Torres; Jeff Aron
2004-03-01
In a joint effort with Tuboscope Pipeline Services of Houston, Texas, Southwest Research Institute (SwRI) adapted its nonlinear harmonic (NLH) sensing technology for use on a new in-line inspection system (smart pig). Nonlinear harmonics, an AC magnetic method for detecting local anomalies of stress and plastic deformation, shows promise of improved characterization of mechanical damage defects such as gouged dents, even though the dents may have re-rounded. The SwRI-Tuboscope project produced a sensor design, electronic design, and sensor suspension design that are directly adaptable to a multitechnology ILI system. This report describes the NLH method, the sensor, circuit, and suspension designs, and shows results from the supporting laboratory work.
Nonlinear Viscoelastic Stress Transfer As a Possible Aftershock Triggering Mechanism
NASA Astrophysics Data System (ADS)
Zhang, X.; Shcherbakov, R.
2014-12-01
The earthquake dynamics can be modelled by employing the spring-block system [Burridge and Knopoff, 1967]. In this approach the earthquake fault is modelled by an array of blocks coupling the loading plate and the lower plate. The dynamics of the system is governed by the system of equations of motion for each block. It is possible to map this system into a cellular automata model, where the stress acting on each block is increased in each time step, and the failing process (frictional slip) is described by stress transfer rules [Olami et al, 1992]. The OFC model produces a power-law distribution for avalanche statistics but it is not capable of producing robust aftershock sequences which follow Omori's law.We propose a nonlinear viscoelastic stress transfer mechanism in the aftershock triggering. In a basic spring-block model setting, we introduce the nonlinear viscoelastic stress transfer between neighbouring blocks, as well as between blocks and the top loading plate. The shear stress of the viscous component is a power-law function of the velocity gradient with an exponent smaller or greater than 1 for the nonlinear viscoelasticity, or 1 for the linear case. The stress transfer function of this nonlinear viscoelastic model has a power-law time-dependent form. It features an instantaneous stress transmission triggering an instantaneous avalanche, which is the same as the original spring-block model; and a power-law relaxation term, which could trigger further aftershocks. We incorporate this nonlinear viscoelasticity mechanism in a lattice cellular automata model. The model could exhibit both the Gutenberg-Richter scaling for the frequency-magnitude distribution and a power-law time decay of aftershocks, which is in accordance with Omori's law. Our study suggests that the stress transfer function may play an important role in the aftershock triggering. We have found that the time decay curve of aftershocks is affected by the shape of the stress transfer function
Parametric oscillator based on nonlinear vortex dynamics in low-resistance magnetic tunnel junctions
NASA Astrophysics Data System (ADS)
Martin, S. Y.; de Mestier, N.; Thirion, C.; Hoarau, C.; Conraux, Y.; Baraduc, C.; Diény, B.
2011-10-01
Radiofrequency vortex spin-transfer oscillators based on magnetic tunnel junctions with very low-resistance area product were investigated. A high power of excitations has been obtained characterized by a power spectral density containing a very sharp peak at the fundamental frequency and a series of harmonics. The observed behavior is ascribed to the combined effect of spin-transfer torque and Oersted-Ampère field generated by the large applied dc current. We furthermore show that the synchronization of a vortex oscillation by applying an ac bias current is mostly efficient when the external frequency is twice the oscillator fundamental frequency. This result is interpreted in terms of a parametric oscillator.
NASA Astrophysics Data System (ADS)
Zemma, E.; Luzuriaga, J.
2013-08-01
By examining the resonance curves of an oscillator submerged in superfluid liquid helium, it is found that their shape is affected by two distinct dissipation regimes when the amplitude is large enough to generate turbulence in the liquid. In a resonance curve, the central part close to resonance, may be in a turbulent regime, but the response is of much lower amplitude away from the resonance frequency, so that the oscillation can still be in the linear regime for frequencies not exactly at resonance. This introduces an ambiguity in estimating the inverse quality factor Q -1 of the oscillator. By analyzing experimental data we consider a way of matching the two ways of estimating Q -1 and use the information to evaluate the frictional force as a function of velocity in a silicon paddle oscillator generating turbulence in the superfluid.
Nonlinear Insolation Forcing: A Physical Mechanism for Climate Change
NASA Technical Reports Server (NTRS)
Liu, H. S.
1998-01-01
This paper focuses on recent advances in the understanding of nonlinear insolation forcing for climate change. The amplitude-frequency resonances in the insolation variations induced by the Earth's changing obliquity are emergent and may provide a physical mechanism to drive the glaciation cycles. To establish the criterion that nonlinear insolation forcing is responsible for major climate changes, the cooperative phenomena between the frequency and amplitude of the insolation are defined as insolation pulsation. Coupling of the insolation frequency and amplitude variations has established an especially new and interesting series of insolation pulses. These pulses would modulate the insolation in such a way that the mode of insolation variations could be locked to generate the 100-kyr ice age cycle which is a long-time geophysical puzzle. The nonlinear behavior of insolation forcing is tested by energy balance and ice sheet climate models and the physical mechanism behind this forcing is explained in terms of pulse duration in the incoming solar radiation. Calculations of the solar energy flux at the top of the atmosphere show that the duration of the negative and positive insolation pulses is about 2 thousand years which is long enough to prolong glaciation into deep ice ages and cause rapid melting of large ice sheets in the high latitudes of the northern hemisphere. We have performed numerical simulations of climate response to nonlinear insolation forcing for the past 2 million years. Our calculated results of temperature fluctuations are in good agreement with the climate cycles as seen in the terrestrial biogenic silica (BDP-96-2) data as well as in the marine oxygen isotope (delta(sup 18)O) records.
Effects of insoluble surfactants on the nonlinear dynamics of oscillating liquid bridges
NASA Astrophysics Data System (ADS)
Whitaker, John; Ambravaneswaran, Balasubramanian; Basaran, Osman A.
1998-11-01
The dynamics of oscillating liquid bridges is of importance in applications including drop and jet breakup, measurement of physical properties of high temperature materials, and agglomeration of powders. Although the stability of static bridges and the dynamics of oscillating and stretching bridges of pure liquids have been extensively studied, even a rudimentary understanding of the dynamics of oscillating bridges of surfactant-laden liquids is lacking. In this work, the dynamics of a bridge of a Newtonian liquid containing an insoluble surfactant are analyzed by solving numerically the complete free boundary problem comprised of the transient Navier-Stokes system that governs fluid flow and the convection-diffusion equation that governs surfactant transport. The dynamical response of oscillating bridges are determined here by performing both a frequency response analysis (FRA) and a sweep procedure in which either the forcing frequency or forcing amplitude is first increased and then decreased over a range. Results of FRA reveal how unintended contaminants present on the fluid interface can alter property measurements made with the oscillating bridge technique. Furthermore, it is shown that the relative importance of surfactant convection to surfactant diffusion plays a complex role in setting the dynamic response of oscillating liquid bridges and their resonance frequencies.
A mechanism for generation of long-range synchronous fast oscillations in the cortex
NASA Astrophysics Data System (ADS)
Traub, Roger D.; Whittington, Miles A.; Stanford, Ian M.; Jefferys, John G. R.
1996-10-01
SYNCHRONOUS neuronal oscillations in the 30-70 Hz range, known as gamma oscillations, occur in the cortex of many species1-6. This synchronization can occur over large distances, and in some cases over multiple cortical areas7,8 and in both hemispheres2; it has been proposed to underlie the binding of several features into a single perceptual entity4. The mechanism by which coherent oscillations are generated remains unclear, because they often show zero or near-zero phase lags over long distances, whereas much greater phase lags would be expected from the slow speed of axonal conduction. We have previously shown that interneuron networks alone can generate gamma oscillations9,10; here we propose a simple model to explain how an interconnected chain of such networks can generate coherent oscillations. The model incorporates known properties of excitatory pyramidal cells and inhibitory interneurons; it predicts that when excitation of inter-neurons reaches a level sufficient to induce pairs of spikes in rapid succession (spike doublets), the network will generate gamma oscillations that are synchronized on a millisecond time-scale from one end of the chain to the other. We show that in rat hippocampal slices interneurons do indeed fire spike doublets under conditions in which gamma oscillations are synchronized over several millimetres, whereas they fire single spikes under other conditions. Thus, known properties of neurons and local synaptic circuits can account for tightly synchronized oscillations in large neuronal ensembles.
Grain Refinement in Al-Mg-Si Alloy TIG Welds Using Transverse Mechanical Arc Oscillation
NASA Astrophysics Data System (ADS)
Biradar, N. S.; Raman, R.
2012-11-01
Reduction in grain size in weld fusion zones (FZs) presents the advantages of increased resistance to solidification cracking and improvement in mechanical properties. Transverse mechanical arc oscillation was employed to obtain grain refinement in the weldment during tungsten inert gas welding of Al-Mg-Si alloy. Electron backscattered diffraction analysis was carried out on AA6061-AA4043 filler metal tungsten inert gas welds. Grain size, texture evolution, misorientation distribution, and aspect ratio of weld metal, PMZ, and BM have been observed at fixed arc oscillation amplitude and at three different frequencies levels. Arc oscillation showed grain size reduction and texture formation. Fine-grained arc oscillated welds exhibited better yield and ultimate tensile strengths and significant improvement in percent elongation. The obtained results were attributed to reduction in equivalent circular diameter of grains and increase in number of subgrain network structure of low angle grain boundaries.
Gutierrez, Gabrielle J; O'Leary, Timothy; Marder, Eve
2013-03-06
Rhythmic oscillations are common features of nervous systems. One of the fundamental questions posed by these rhythms is how individual neurons or groups of neurons are recruited into different network oscillations. We modeled competing fast and slow oscillators connected to a hub neuron with electrical and inhibitory synapses. We explore the patterns of coordination shown in the network as a function of the electrical coupling and inhibitory synapse strengths with the help of a novel visualization method that we call the "parameterscape." The hub neuron can be switched between the fast and slow oscillators by multiple network mechanisms, indicating that a given change in network state can be achieved by degenerate cellular mechanisms. These results have importance for interpreting experiments employing optogenetic, genetic, and pharmacological manipulations to understand circuit dynamics.
Nonlinear Oscillations and Flow of Gas Within Closed and Open Conical Resonators
NASA Technical Reports Server (NTRS)
Daniels, Christopher; Finkbeiner, Joshua; Steinetz, Bruce; Li, Xiaofan; Raman, Ganesh
2004-01-01
A dissonant acoustic resonator with a conical shaped cavity was tested in four configurations: (A) baseline resonator with closed ends and no blockage; (B) closed resonator with internal blockage; (C) ventilated resonator with no blockage; and (D) ventilated resonator with an applied pressure differential. These tests were conducted to investigate the effects of blockage and ventilation holes on dynamic pressurization. Additionally, the investigation was to determine the ability of acoustic pressurization to impede flow through the resonator. In each of the configurations studied, the entire resonator was oscillated at the gas resonant frequency while dynamic pressure, static pressure, and temperature of the fluid were measured. In the final configuration, flow through the resonator was recorded for three oscillation conditions. Ambient condition air was used as the working fluid. The baseline results showed a marked reduction in the amplitude of the dynamic pressure waveforms over previously published studies due to the use of air instead of refrigerant as the working fluid. A change in the resonant frequency was recorded when blockages of differing geometries were used in the closed resonator, while acoustic pressure amplitudes were reduced from baseline measurements. A sharp reduction in the amplitude of the acoustic pressure waves was expected and recorded when ventilation ports were added. With elevated pressure applied to one end of the resonator, flow was reduced by oscillating the cavity at the fluid fundamental resonant frequency compared to cases without oscillation and oscillation off-resonance.
Photonic cavity synchronization of nanomechanical oscillators.
Bagheri, Mahmood; Poot, Menno; Fan, Linran; Marquardt, Florian; Tang, Hong X
2013-11-22
Synchronization in oscillatory systems is a frequent natural phenomenon and is becoming an important concept in modern physics. Nanomechanical resonators are ideal systems for studying synchronization due to their controllable oscillation properties and engineerable nonlinearities. Here we demonstrate synchronization of two nanomechanical oscillators via a photonic resonator, enabling optomechanical synchronization between mechanically isolated nanomechanical resonators. Optical backaction gives rise to both reactive and dissipative coupling of the mechanical resonators, leading to coherent oscillation and mutual locking of resonators with dynamics beyond the widely accepted phase oscillator (Kuramoto) model. In addition to the phase difference between the oscillators, also their amplitudes are coupled, resulting in the emergence of sidebands around the synchronized carrier signal.
Nonlinear conduction via solitons in a topological mechanical insulator
Chen, Bryan Gin-ge; Upadhyaya, Nitin; Vitelli, Vincenzo
2014-01-01
Networks of rigid bars connected by joints, termed linkages, provide a minimal framework to design robotic arms and mechanical metamaterials built of folding components. Here, we investigate a chain-like linkage that, according to linear elasticity, behaves like a topological mechanical insulator whose zero-energy modes are localized at the edge. Simple experiments we performed using prototypes of the chain vividly illustrate how the soft motion, initially localized at the edge, can in fact propagate unobstructed all of the way to the opposite end. Using real prototypes, simulations, and analytical models, we demonstrate that the chain is a mechanical conductor, whose carriers are nonlinear solitary waves, not captured within linear elasticity. Indeed, the linkage prototype can be regarded as the simplest example of a topological metamaterial whose protected mechanical excitations are solitons, moving domain walls between distinct topological mechanical phases. More practically, we have built a topologically protected mechanism that can perform basic tasks such as transporting a mechanical state from one location to another. Our work paves the way toward adopting the principle of topological robustness in the design of robots assembled from activated linkages as well as in the fabrication of complex molecular nanostructures. PMID:25157161
NASA Astrophysics Data System (ADS)
Bhardwaj, R.; Bhatnagar, K. B.
1995-12-01
The rotational motion of a satellite in a circular orbit under the influence of magnetic torque is being studied. The present paper deals with the non-resonance and resonance cases. By using Melnikov's method, the authors have shown that the equation of motion is non-integrable. Taking the magnetic torque perturbation to be small (ɛ ≪ 1) and using BKM method, it is observed that the amplitude of the oscillation remains constant up to the second order of approximation. The main resonance has been shown to exist. The analysis regarding the stability near the resonance frequency shows that discontinuity occurs in the amplitude of the oscillation at a frequency of the external periodic force which is less than the frequency of the natural oscillation.
Cellular Mechanisms of a Synchronized Oscillation in the Thalamus
NASA Astrophysics Data System (ADS)
von Krosigk, Marcus; Bal, Thierry; McCormick, David A.
1993-07-01
Spindle waves are a prototypical example of synchronized oscillations, a common feature of neuronal activity in thalamic and cortical systems in sleeping and waking animals. Spontaneous spindle waves recorded from slices of the ferret lateral geniculate nucleus were generated by rebound burst firing in relay cells. This rebound burst firing resulted from inhibitory postsynaptic potentials arriving from the perigeniculate nucleus, the cells of which were activated by burst firing in relay neurons. Reduction of γ-aminobutyric acid_A (GABA_A) receptor-mediated inhibition markedly enhanced GABA_B inhibitory postsynaptic potentials in relay cells and subsequently generated a slowed and rhythmic population activity resembling that which occurs during an absence seizure. Pharmacological block of GABA_B receptors abolished this seizure-like activity but not normal spindle waves, suggesting that GABA_B antagonists may be useful in the treatment of absence seizures.
Compressive nonlinearity in the hair bundle's active response to mechanical stimulation.
Martin, P; Hudspeth, A J
2001-12-04
The auditory system's ability to interpret sounds over a wide range of amplitudes rests on the nonlinear responsiveness of the ear. Whether measured by basilar-membrane vibration, nerve-fiber activity, or perceived loudness, the ear is most sensitive to small signals and grows progressively less responsive as stimulation becomes stronger. Seeking a correlate of this behavior at the level of mechanoelectrical transduction, we examined the responses of hair bundles to direct mechanical stimulation. As reported by the motion of an attached glass fiber, an active hair bundle from the bullfrog's sacculus oscillates spontaneously. Sinusoidal movement of the fiber's base by as little as +/-1 nm, corresponding to the application at the bundle's top of a force of +/-0.3 pN, causes detectable phase-locking of the bundle's oscillations to the stimulus. Although entrainment increases as the stimulus grows, the amplitude of the hair-bundle movement does not rise until phase-locking is nearly complete. A bundle is most sensitive to stimulation at its frequency of spontaneous oscillation. Far from that frequency, the sensitivity of an active hair bundle resembles that of a passive bundle. Over most of its range, an active hair bundle's response grows as the one-third power of the stimulus amplitude; the bundle's sensitivity declines accordingly in proportion to the negative two-thirds power of the excitation. This scaling behavior, also found in the response of the mammalian basilar membrane to sound, signals the operation of an amplificatory process at the brink of an oscillatory instability, a Hopf bifurcation.
The Slow Oscillation in Cortical and Thalamic Networks: Mechanisms and Functions
Neske, Garrett T.
2016-01-01
During even the most quiescent behavioral periods, the cortex and thalamus express rich spontaneous activity in the form of slow (<1 Hz), synchronous network state transitions. Throughout this so-called slow oscillation, cortical and thalamic neurons fluctuate between periods of intense synaptic activity (Up states) and almost complete silence (Down states). The two decades since the original characterization of the slow oscillation in the cortex and thalamus have seen considerable advances in deciphering the cellular and network mechanisms associated with this pervasive phenomenon. There are, nevertheless, many questions regarding the slow oscillation that await more thorough illumination, particularly the mechanisms by which Up states initiate and terminate, the functional role of the rhythmic activity cycles in unconscious or minimally conscious states, and the precise relation between Up states and the activated states associated with waking behavior. Given the substantial advances in multineuronal recording and imaging methods in both in vivo and in vitro preparations, the time is ripe to take stock of our current understanding of the slow oscillation and pave the way for future investigations of its mechanisms and functions. My aim in this Review is to provide a comprehensive account of the mechanisms and functions of the slow oscillation, and to suggest avenues for further exploration. PMID:26834569
Suppression of nonlinear oscillations in combustors with partial length acoustic liners
NASA Technical Reports Server (NTRS)
Espander, W. R.; Mitchell, C. E.; Baer, M. R.
1975-01-01
An analytical model is formulated for a three-dimensional nonlinear stability problem in a rocket motor combustion chamber. The chamber is modeled as a right circular cylinder with a short (multi-orifice) nozzle, and an acoustic linear covering an arbitrary portion of the cylindrical periphery. The combustion is concentrated at the injector and the gas flow field is characterized by a mean Mach number. The unsteady combustion processes are formulated using the Crocco time lag model. The resulting equations are solved using a Green's function method combined with numerical evaluation techniques. The influence of acoustic liners on the nonlinear waveforms is predicted. Nonlinear stability limits and regions where triggering is possible are also predicted for both lined and unlined combustors in terms of the combustion parameters.
Nonlinear dilational mechanics of Langmuir lipid monolayers: a lateral diffusion mechanism.
Arriaga, Laura R; López-Montero, Iván; Rodríguez-García, Ruddi; Monroy, Francisco
2008-06-01
We propose a theoretical model for the nonlinear mechanical response of Langmuir lipid monolayers subjected to a dilational in-plane deformation. Lateral diffusion in conjunction with free convection has been considered to drive nonlinear mass transport in Langmuir lipid monolayers. The present model combines the conservative dynamical equations for lipid transport along the monolayer plane together with a material relationship accounting for nonlinear hypoelasticity, as experimentally observed from high-strain rheological measurements [Hilles, Adv. Colloid Interface Sci. 122, 67 (2007)]. The dynamical equations have been resolved for oscillatory nonlinear motion, the theoretical spectral amplitudes being found in quantitative agreement with the experimental values obtained from surface rheology experiments performed in Langmuir monolayers of two different lipid systems, namely DPPC and native E. Coli lipids. The presence of micrometer-sized phase coexistence domains in these lipid systems has been claimed to pump diffusive transport along the monolayer plane. This dynamical scenario defines a relaxation regime compatible with the observed nonlinear mechanical behavior.
Scholz, Alexander-Wigbert; Weiler, Norbert; David, Matthias; Markstaller, Klaus
2011-05-01
The forced oscillation technique (FOT) allows the measurement of respiratory mechanics in the intensive care setting. The aim of this study was to compare the FOT with a reference method during mechanical ventilation through a tracheal tube. The respiratory impedance spectra were measured by FOT in nine anaesthetized pigs, and resistance and compliance were estimated on the basis of a linear resistance-compliance inertance model. In comparison, resistance and compliance were quantified by the multiple linear regression analysis (LSF) of conventional ventilator waveforms to the equation of motion. The resistance of the sample was found to range from 6 to 21 cmH(2)O s l(-1) and the compliance from 12 to 32 ml cmH(2)O(-1). A Bland-Altman analysis of the resistance resulted in a sufficient agreement (bias -0.4 cmH(2)O s l(-1); standard deviation of differences 1.4 cmH(2)O s l(-1); correlation coefficient 0.93) and test-retest reliability (coefficient of variation of repeated measurements: FOT 2.1%; LSF 1.9%). The compliance, however, was poor in agreement (bias -8 ml cmH(2)O(-1), standard deviation of differences 7 ml cmH(2)O(-1), correlation coefficient 0.74) and repeatability (coefficient of variation: FOT 23%; LSF 1.7%). In conclusion, FOT provides an alternative for monitoring resistance, but not compliance, in tracheally intubated and ventilated subjects.
Geometric control of quantum mechanical and nonlinear classical systems
NASA Astrophysics Data System (ADS)
Nelson, Richard Joseph
1999-10-01
Geometric control refers to the judicious use of the non- commuting nature of inputs and natural dynamics as the basis for control. The last few decades in control system theory have seen the application of differential geometry in proving several important properties of systems, including controllability and observability. Until recently, however, the results of this mathematical geometry have rarely been used as the basis for designing and implementing an actual controller. This thesis demonstrates the application of a judicious selection of inputs, so that if the system is proven to be controllable using geometric methods, one can design input sequences using the same geometry. A demonstration of this method is shown in simulating the attitude control of a satellite: a highly non-linear, non- holonomic control problem. Although not a practical method for large re-orientations of a typical satellite, the approach can be applied to other nonlinear systems. The method is also applied to the closed-loop performance of a quantum mechanical system to demonstrate the feasibility of coherent quantum feedback-something impossible using a conventional controller. Finally, the method is applied in the open-loop control of a quantum mechanical system: in this case, the creation of Greenberger-Horne-Zeilinger correlations among the nuclei of an ensemble of alanine molecules in a nuclear magnetic resonance spectrometer. In each case, the data demonstrate the usefulness of a geometric approach to control. In addition to demonstrations of geometric control in practice, the quantum mechanical experiments also demonstrate for the first time peculiar quantum correlations, including GHZ correlations, that have no classical analog. The quantum experiments further establish nuclear magnetic resonance as a viable and accessible testbed of quantum predictions and processes. (Copies available exclusively from MIT Libraries, Rm. 14- 0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax
Atomimetic Mechanical Structures with Nonlinear Topological Domain Evolution Kinetics.
Frazier, Michael J; Kochmann, Dennis M
2017-03-21
A mechanical metamaterial, a simple, periodic mechanical structure, is reported, which reproduces the nonlinear dynamic behavior of materials undergoing phase transitions and domain switching at the structural level. Tunable multistability is exploited to produce switching and transition phenomena whose kinetics are governed by the same Allen-Cahn law commonly used to describe material-level, structural-transition processes. The reported purely elastic mechanical system displays several key features commonly found in atomic- or mesoscale physics of solids. The rotating-mass network shows qualitatively analogous features as, e.g., ferroic ceramics or phase-transforming solids, and the discrete governing equation is shown to approach the phase field equation commonly used to simulate the above processes. This offers untapped opportunities for reproducing material-level, dissipative and diffusive kinetic phenomena at the structural level, which, in turn, invites experimental realization and paves the road for new active, intelligent, or phase-transforming mechanical metamaterials bringing small-scale processes to the macroscopically observable scale.
NASA Astrophysics Data System (ADS)
King, J. R. C.; Ziolkowski, A. M.; Ruffert, M.
2015-03-01
We have developed a new boundary condition for finite volume simulations of oscillating bubbles. Our method uses an approximation to the motion outside the domain, based on the solution at the domain boundary. We then use this approximation to apply boundary conditions by defining incoming characteristic waves at the domain boundary. Our boundary condition is applicable in regions where the motion is close to spherically symmetric. We have tested our method on a range of one- and two-dimensional test cases. Results show good agreement with previous studies. The method allows simulations of oscillating bubbles for long run times (5 ×105 time steps with a CFL number of 0.8) on highly truncated domains, in which the boundary condition may be applied within 0.1% of the maximum bubble radius. Conservation errors due to the boundary conditions are found to be of the order of 0.1% after 105 time steps. The method significantly reduces the computational cost of fixed grid finite volume simulations of oscillating bubbles. Two-dimensional results demonstrate that highly asymmetric bubble features, such as surface instabilities and the formation of jets, may be captured on a small domain using this boundary condition.
Nonlinear oscillations of a sessile drop on a hydrophobic surface induced by ac electrowetting
NASA Astrophysics Data System (ADS)
Lee, Joohee; Park, Jun Kwon; Hong, Jiwoo; Lee, Sang Joon; Kang, Kwan Hyoung; Hwang, Hyung Ju
2014-09-01
We examine the nature of ac electrowetting (EW)-driven axisymmetric oscillations of a sessile water drop on a dielectric substrate. In ac EW, small-amplitude oscillations of a drop differ from the Rayleigh linear modes of freely oscillating drops. In this paper, we demonstrate that changes in the time-averaged contact angle of the sessile drop attributed to the presence of an electric field and a solid substrate mainly caused this discrepancy. We combine the domain perturbation method with the Lindsted-Poincaré method to derive an asymptotic formula for resonant frequency. Theoretical analysis shows that the resonant frequency is a function of the time-averaged contact angle. Each mode of the resonance frequency is a linear function of ɛ1, which is the magnitude of the cosine of the time-averaged contact angle. The most dominant mode in this study, that is, the fundamental mode n =2, decreases linearly with ɛ1. The results of the theoretical model are compared with those of both the experiments and numerical simulations. The average resonant frequency deviation between the perturbation solutions and numerical simulations is 4.3%, whereas that between the perturbation solutions and the experiments is 1.8%.
Nonlinear oscillations of a sessile drop on a hydrophobic surface induced by ac electrowetting.
Lee, Joohee; Park, Jun Kwon; Hong, Jiwoo; Lee, Sang Joon; Kang, Kwan Hyoung; Hwang, Hyung Ju
2014-09-01
We examine the nature of ac electrowetting (EW)-driven axisymmetric oscillations of a sessile water drop on a dielectric substrate. In ac EW, small-amplitude oscillations of a drop differ from the Rayleigh linear modes of freely oscillating drops. In this paper, we demonstrate that changes in the time-averaged contact angle of the sessile drop attributed to the presence of an electric field and a solid substrate mainly caused this discrepancy. We combine the domain perturbation method with the Lindsted-Poincaré method to derive an asymptotic formula for resonant frequency. Theoretical analysis shows that the resonant frequency is a function of the time-averaged contact angle. Each mode of the resonance frequency is a linear function of ɛ(1), which is the magnitude of the cosine of the time-averaged contact angle. The most dominant mode in this study, that is, the fundamental mode n=2, decreases linearly with ɛ(1). The results of the theoretical model are compared with those of both the experiments and numerical simulations. The average resonant frequency deviation between the perturbation solutions and numerical simulations is 4.3%, whereas that between the perturbation solutions and the experiments is 1.8%.
Gottschall, Thomas; Meyer, Tobias; Schmitt, Michael; Popp, Jürgen; Limpert, Jens; Tünnermann, Andreas
2015-09-07
A novel concept for an optical parametric oscillator based on four-wave mixing (FOPO) in an optical fiber is presented. This setup has the ability of generating highly chirped signal and idler pulses with compressed pulse durations below 600 fs and pulse energies of up to 250 nJ. At a fixed pump wavelength of 1040 nm, the emerging signal and idler wavelengths can be easily tuned between 867 to 918 nm and 1200 to 1300 nm, respectively, only by altering the cavity length. With compressed peak powers >100 kW and a repetition rate of only 785 kHz, this source provides tunable intense ultra-short pulses at moderate average powers. This setup constitutes a stable, simple and in many ways superior alternative to bulk state-of-the-art OPO light converters for demanding biomedical applications and non-linear microspectroscopy.
NASA Astrophysics Data System (ADS)
He, Chong; Chiam, Keng-Hwee; Chew, Lock Yue
2016-10-01
Ultradian cycles are frequently observed in biological systems. They serve important roles in regulating, for example, cell fate and the development of the organism. Many mathematical models have been developed to analyze their behavior. Generally, these models can be classified into two classes: Deterministic models that generate oscillatory behavior by incorporating time delays or Hopf bifurcations, and stochastic models that generate oscillatory behavior by noise driven resonance. However, it is still unclear which of these two mechanisms applies to cellular oscillations. In this paper, we show through theoretical analysis and numerical simulation that we can distinguish which of these two mechanisms govern cellular oscillations, by measuring statistics of oscillation amplitudes for cells of different sizes. We found that, for oscillations driven deterministically, the normalized average amplitude is constant with respect to cell size, while the coefficient of variation of the amplitude scales with cell size with an exponent of -0.5 . On the other hand, for oscillations driven stochastically, the coefficient of variation of the amplitude is constant with respect to cell size, while the normalized average amplitude scales with cell size with an exponent of -0.5 . Our results provide a theoretical basis to discern whether a particular oscillatory behavior is governed by a deterministic or stochastic mechanism.
Mechanical energy oscillations of two brachiation gaits: measurement and simulation.
Bertram, J E; Chang, Y H
2001-08-01
How do arm-swinging apes locomote effectively over a variety of speeds? One way to reduce the metabolic energy cost of locomotion is to transfer energy between reversible mechanical modes. In terrestrial animals, at least two transfer mechanisms have been identified: 1) a pendulum-like mechanism for walking, with exchange between gravitational potential energy and translational kinetic energy, and 2) a spring-like mechanism for running, where the elastic strain energy of stretched muscle and tendon is largely returned to reaccelerate the animal. At slower speeds, a brachiator will always have at least one limb in contact with the support, similar to the overlap of foot contact in bipedal walking. At faster speeds, brachiators exhibit an aerial phase, similar to that seen in bipedal running. Are there two distinct brachiation gaits even though the animal appears to simply swing beneath its overhead support? If so, are different exchange mechanisms employed? Our kinetic analysis of brachiation in a white-handed gibbon (Hylobates lar) indicates that brachiation is indeed comprised of two mechanically distinct gaits. At slower speeds in "continuous contact" brachiation, the gibbon utilizes a simple pendulum-like transfer of mechanical energy within each stride. At faster speeds in "ricochetal" brachiation, translational and rotational kinetic energy are exchanged in a novel "whip-like" transfer. We propose that brachiators utilize the transfer between translational and rotational kinetic energy to control the dynamics of their swing. This maneuver may allow muscle action at the shoulder to control the transfer and adjust the ballistic portion of the step to meet the requirements for the next hand contact.
Ultrahigh-Q mechanical oscillators through optical trapping
NASA Astrophysics Data System (ADS)
Kimble, H. Jeff
2011-05-01
Rapid advances are being made toward optically cooling a single mode of a micro-mechanical system to its quantum ground state and observing quantum behavior at macroscopic scales. Reaching this regime in room-temperature environments requires a stringent condition on the mechanical quality factor Qm and frequency fm, QmfmkBTbath / h , which so far has been marginally satisfied only in a small number of systems. Here we propose and analyze a new class of systems that should enable unprecedented Qmfm values. The technique is based upon using optical forces to ``trap'' and stiffen the motion of a tethered mechanical structure, thereby freeing the resultant mechanical frequencies and decoherence rates from underlying material properties. We have lithographically fabricated a diverse set of planar structures in Silicon Nitride, made measurements of their optical and mechanical properties, and compared these results to numerical models by finite element analysis. This work has been carried out in collaboration with D. E. Chang, K.-K. Ni, R. Norte, O. J. Painter, and D. J. Wilson. Work supported by DARPA ORCHID program, NSF, and NSSEFF.
Nonlinear mechanics of composite materials with periodic microstructure
NASA Technical Reports Server (NTRS)
Jordan, E. H.; Walker, K. P.
1991-01-01
This report summarizes the result of research done under NASA NAG3-882 Nonlinear Mechanics of Composites with Periodic Microstructure. The effort involved the development of non-finite element methods to calculate local stresses around fibers in composite materials. The theory was developed and some promising numerical results were obtained. It is expected that when this approach is fully developed, it will provide an important tool for calculating local stresses and averaged constitutive behavior in composites. NASA currently has a major contractual effort (NAS3-24691) to bring the approach developed under this grant to application readiness. The report has three sections. One, the general theory that appeared as a NASA TM, a second section that gives greater details about the theory connecting Greens functions and Fourier series approaches, and a final section shows numerical results.
Anomalous nonlinear attenuation of ultrasound in solid 4He in a torsional oscillator below 200 mK
NASA Astrophysics Data System (ADS)
Iwasa, I.; Goodkind, J. M.; Kojima, H.
2014-12-01
In order to elucidate the ultra-low temperature behavior of solid 4He, simultaneous measurements of longitudinal ultrasound (US) and torsional oscillation have been made. Changes in attenuation and velocity of US at 10 MHz have been measured in polycrystalline hcp 4He samples (0.3 or 20 ppm of 3He impurity) grown in a 1 kHz torsional oscillator (TO). In a 0.3 ppm 3He sample, the US attenuation and velocity were found to depend on the US drive voltage at temperatures below 70 mK where the anomalies in the TO frequency and dissipation were also observed. The US attenuation at low T (10 mK) decreased monotonically as the drive voltage was decreased but then remained small and constant as the drive voltage was increased again. The US velocity change at low T was negative with respect to the high-T (400 mK) value, contrary to the positive sign expected from the known variation in the shear modulus. In a 20 ppm 3He sample, both the US and TO anomalies shifted to 150 mK. The amplitude dependence and hysteresis of US attenuation were related to pinning of dislocations by 3He impurities, and nonlinear spatial variations of the amplitude of US pulses were derived.
Fluctuating Nonlinear Spring Model of Mechanical Deformation of Biological Particles
Kononova, Olga; Snijder, Joost; Kholodov, Yaroslav; Marx, Kenneth A.; Wuite, Gijs J. L.; Roos, Wouter H.; Barsegov, Valeri
2016-01-01
The mechanical properties of virus capsids correlate with local conformational dynamics in the capsid structure. They also reflect the required stability needed to withstand high internal pressures generated upon genome loading and contribute to the success of important events in viral infectivity, such as capsid maturation, genome uncoating and receptor binding. The mechanical properties of biological nanoparticles are often determined from monitoring their dynamic deformations in Atomic Force Microscopy nanoindentation experiments; but a comprehensive theory describing the full range of observed deformation behaviors has not previously been described. We present a new theory for modeling dynamic deformations of biological nanoparticles, which considers the non-linear Hertzian deformation, resulting from an indenter-particle physical contact, and the bending of curved elements (beams) modeling the particle structure. The beams’ deformation beyond the critical point triggers a dynamic transition of the particle to the collapsed state. This extreme event is accompanied by a catastrophic force drop as observed in the experimental or simulated force (F)-deformation (X) spectra. The theory interprets fine features of the spectra, including the nonlinear components of the FX-curves, in terms of the Young’s moduli for Hertzian and bending deformations, and the structural damage dependent beams’ survival probability, in terms of the maximum strength and the cooperativity parameter. The theory is exemplified by successfully describing the deformation dynamics of natural nanoparticles through comparing theoretical curves with experimental force-deformation spectra for several virus particles. This approach provides a comprehensive description of the dynamic structural transitions in biological and artificial nanoparticles, which is essential for their optimal use in nanotechnology and nanomedicine applications. PMID:26821264
NASA Astrophysics Data System (ADS)
Kar, Jyotirmaya; Roy, Sanat Kumar; Roy, Gour Gopal
2017-04-01
The properties of electron beam-welded AISI 316L stainless steel butt joints prepared with and without beam oscillation were evaluated by microstructural analysis, mechanical testing like microhardness measurements, tensile tests at room and elevated temperature 973 K (700 °C), three-point bend, and Charpy impact tests. All joints, irrespective of being prepared with or without beam oscillation, were found to be defect free. Welds produced by beam oscillation exhibited narrower fusion zone (FZ) with lathy ferrite morphology, while the weld without beam oscillation was characterized by wider FZ and skeletal ferrite morphology. During tensile tests at room and elevated temperature 973 K (700 °C), all samples fractured in the base metal (BM) and showed almost the same tensile properties as that of the BM. However, the notch tensile tests at room temperature demonstrated higher strength for joints prepared with the oscillating beam. Besides, face and root bend tests, as well as Charpy impact tests, showed higher bending strength and notch toughness, respectively, for joints prepared with beam oscillation.
NASA Astrophysics Data System (ADS)
Kar, Jyotirmaya; Roy, Sanat Kumar; Roy, Gour Gopal
2017-02-01
The properties of electron beam-welded AISI 316L stainless steel butt joints prepared with and without beam oscillation were evaluated by microstructural analysis, mechanical testing like microhardness measurements, tensile tests at room and elevated temperature 973 K (700 °C), three-point bend, and Charpy impact tests. All joints, irrespective of being prepared with or without beam oscillation, were found to be defect free. Welds produced by beam oscillation exhibited narrower fusion zone (FZ) with lathy ferrite morphology, while the weld without beam oscillation was characterized by wider FZ and skeletal ferrite morphology. During tensile tests at room and elevated temperature 973 K (700 °C), all samples fractured in the base metal (BM) and showed almost the same tensile properties as that of the BM. However, the notch tensile tests at room temperature demonstrated higher strength for joints prepared with the oscillating beam. Besides, face and root bend tests, as well as Charpy impact tests, showed higher bending strength and notch toughness, respectively, for joints prepared with beam oscillation.
Numerical computation of nonlinear normal modes in mechanical engineering
NASA Astrophysics Data System (ADS)
Renson, L.; Kerschen, G.; Cochelin, B.
2016-03-01
This paper reviews the recent advances in computational methods for nonlinear normal modes (NNMs). Different algorithms for the computation of undamped and damped NNMs are presented, and their respective advantages and limitations are discussed. The methods are illustrated using various applications ranging from low-dimensional weakly nonlinear systems to strongly nonlinear industrial structures.
ERIC Educational Resources Information Center
Donoso, Guillermo; Ladera, Celso L.
2012-01-01
We study the nonlinear oscillations of a forced and weakly dissipative spring-magnet system moving in the magnetic fields of two fixed coaxial, hollow induction coils. As the first coil is excited with a dc current, both a linear and a cubic magnet-position dependent force appear on the magnet-spring system. The second coil, located below the…
Symmetry effects on naturally arising chimera states in mechanical oscillator networks
NASA Astrophysics Data System (ADS)
Blaha, Karen; Burrus, Ryan J.; Orozco-Mora, Jorge L.; Ruiz-Beltrán, Elvia; Siddique, Abu B.; Hatamipour, V. D.; Sorrentino, Francesco
2016-11-01
Coupled oscillators were believed to exclusively exist in a state of synchrony or disorder until Kuramoto theoretically proved that the two states could coexist, called a chimera state, when portions of the population had a spatial dependent coupling. Recent work has demonstrated the spontaneous emergence of chimera states in an experiment involving mechanical oscillators coupled through a two platform swing. We constructed an experimental apparatus with three platforms that each contains a population of mechanical oscillators in order investigate the effects of a network symmetry on naturally arising chimera states. We considered in more detail the case of 15 metronomes per platform and observed that chimera states emerged as a broad range of parameters, namely, the metronomes' nominal frequency and the coupling strength between the platforms. A scalability study shows that chimera states no longer arise when the population size is reduced to three metronomes per platform. Furthermore, many chimera states are seen in the system when the coupling between platforms is asymmetric.
Ground-State Cooling of a Mechanical Oscillator by Interference in Andreev Reflection
NASA Astrophysics Data System (ADS)
Stadler, P.; Belzig, W.; Rastelli, G.
2016-11-01
We study the ground-state cooling of a mechanical oscillator linearly coupled to the charge of a quantum dot inserted between a normal metal and a superconducting contact. Such a system can be realized, e.g., by a suspended carbon nanotube quantum dot with a capacitive coupling to a gate contact. Focusing on the subgap transport regime, we analyze the inelastic Andreev reflections which drive the resonator to a nonequilibrium state. For small coupling, we obtain that vibration-assisted reflections can occur through two distinct interference paths. The interference determines the ratio between the rates of absorption and emission of vibrational energy quanta. We show that ground-state cooling of the mechanical oscillator can be achieved for many of the oscillator's modes simultaneously or for single modes selectively, depending on the experimentally tunable coupling to the superconductor.
Ground-State Cooling of a Mechanical Oscillator by Interference in Andreev Reflection.
Stadler, P; Belzig, W; Rastelli, G
2016-11-04
We study the ground-state cooling of a mechanical oscillator linearly coupled to the charge of a quantum dot inserted between a normal metal and a superconducting contact. Such a system can be realized, e.g., by a suspended carbon nanotube quantum dot with a capacitive coupling to a gate contact. Focusing on the subgap transport regime, we analyze the inelastic Andreev reflections which drive the resonator to a nonequilibrium state. For small coupling, we obtain that vibration-assisted reflections can occur through two distinct interference paths. The interference determines the ratio between the rates of absorption and emission of vibrational energy quanta. We show that ground-state cooling of the mechanical oscillator can be achieved for many of the oscillator's modes simultaneously or for single modes selectively, depending on the experimentally tunable coupling to the superconductor.
Coupling mechanism in the gate and oscillator model of the SCN
NASA Astrophysics Data System (ADS)
Li, Ying; Liu, Zengrong
2016-09-01
In mammals, the suprachiasmatic nucleus (SCN) of the hypothalamus is considered as the master circadian pacemaker. The SCN is divided into two subgroups of gate and oscillator cells: the ventrolateral (VL) neurons, which receive the periodic light-dark (LD) signal, and the dorsomedial (DM) neurons, which are coupled to the VL cells. The fundamental question is how the individual cellular oscillators, expressing a wide range of periods, interact and assemble to create an integrated pacemaker that can govern behavioral and physiological rhythmicity and be reset by environmental light. The key is that the heterogeneous network formed by the cellular clocks within the SCN must synchronize to maintain timekeeping activity. Based on the structural and functional heterogeneity of the SCN, the authors bring forward a mathematical model including gate cells and oscillator cells with a wide range of periods. The gate neurons offer daily injection to oscillator neurons and the activation of gate is determined by the output of the oscillator neurons. In this model, the authors consider two kinds of coupling: interior coupling among the oscillator cells and exterior coupling from the gate cells to the oscillator cells. The authors mainly analyze the combined effects of these two kinds of coupling on the entrainment of the oscillator cells in the DM part. It is found that the interior coupling is conducive to entrainment, but a stronger coupling is not beneficial to entrainment. The gate mechanism in exterior coupling is more propitious to entrainment than continuous coupling. This study helps to understand collective circadian rhythm in the mammals.
Pavlides, Alex; Hogan, S. John; Bogacz, Rafal
2015-01-01
In Parkinson’s disease, an increase in beta oscillations within the basal ganglia nuclei has been shown to be associated with difficulty in movement initiation. An important role in the generation of these oscillations is thought to be played by the motor cortex and by a network composed of the subthalamic nucleus (STN) and the external segment of globus pallidus (GPe). Several alternative models have been proposed to describe the mechanisms for generation of the Parkinsonian beta oscillations. However, a recent experimental study of Tachibana and colleagues yielded results which are challenging for all published computational models of beta generation. That study investigated how the presence of beta oscillations in a primate model of Parkinson’s disease is affected by blocking different connections of the STN-GPe circuit. Due to a large number of experimental conditions, the study provides strong constraints that any mechanistic model of beta generation should satisfy. In this paper we present two models consistent with the data of Tachibana et al. The first model assumes that Parkinsonian beta oscillation are generated in the cortex and the STN-GPe circuits resonates at this frequency. The second model additionally assumes that the feedback from STN-GPe circuit to cortex is important for maintaining the oscillations in the network. Predictions are made about experimental evidence that is required to differentiate between the two models, both of which are able to reproduce firing rates, oscillation frequency and effects of lesions carried out by Tachibana and colleagues. Furthermore, an analysis of the models reveals how the amplitude and frequency of the generated oscillations depend on parameters. PMID:26683341
Strain-driven criticality underlies nonlinear mechanics of fibrous networks
NASA Astrophysics Data System (ADS)
Sharma, A.; Licup, A. J.; Rens, R.; Vahabi, M.; Jansen, K. A.; Koenderink, G. H.; MacKintosh, F. C.
2016-10-01
Networks with only central force interactions are floppy when their average connectivity is below an isostatic threshold. Although such networks are mechanically unstable, they can become rigid when strained. It was recently shown that the transition from floppy to rigid states as a function of simple shear strain is continuous, with hallmark signatures of criticality [Sharma et al., Nature Phys. 12, 584 (2016), 10.1038/nphys3628]. The nonlinear mechanical response of collagen networks was shown to be quantitatively described within the framework of such mechanical critical phenomenon. Here, we provide a more quantitative characterization of critical behavior in subisostatic networks. Using finite-size scaling we demonstrate the divergence of strain fluctuations in the network at well-defined critical strain. We show that the characteristic strain corresponding to the onset of strain stiffening is distinct from but related to this critical strain in a way that depends on critical exponents. We confirm this prediction experimentally for collagen networks. Moreover, we find that the apparent critical exponents are largely independent of the spatial dimensionality. With subisostaticity as the only required condition, strain-driven criticality is expected to be a general feature of biologically relevant fibrous networks.
Olson, C C; Nichols, J M; Michalowicz, J V; Bucholtz, F
2011-06-01
This work describes an approach for efficiently shaping the response characteristics of a fixed dynamical system by forcing with a designed input. We obtain improved inputs by using an evolutionary algorithm to search a space of possible waveforms generated by a set of nonlinear, ordinary differential equations (ODEs). Good solutions are those that result in a desired system response subject to some input efficiency constraint, such as signal power. In particular, we seek to find inputs that best disrupt a phase-locked loop (PLL). Three sets of nonlinear ODEs are investigated and found to have different disruption capabilities against a model PLL. These differences are explored and implications for their use as input signal models are discussed. The PLL was chosen here as an archetypal example but the approach has broad applicability to any input∕output system for which a desired input cannot be obtained analytically.
NASA Astrophysics Data System (ADS)
Abed, I.; Kacem, N.; Bouhaddi, N.; Bouazizi, M. L.
2016-02-01
We propose a multi-modal vibration energy harvesting approach based on arrays of coupled levitated magnets. The equations of motion which include the magnetic nonlinearity and the electromagnetic damping are solved using the harmonic balance method coupled with the asymptotic numerical method. A multi-objective optimization procedure is introduced and performed using a non-dominated sorting genetic algorithm for the cases of small magnet arrays in order to select the optimal solutions in term of performances by bringing the eigenmodes close to each other in terms of frequencies and amplitudes. Thanks to the nonlinear coupling and the modal interactions even for only three coupled magnets, the proposed method enable harvesting the vibration energy in the operating frequency range of 4.6-14.5 Hz, with a bandwidth of 190% and a normalized power of 20.2 {mW} {{cm}}-3 {{{g}}}-2.
NASA Technical Reports Server (NTRS)
Li, Xiaofan; Finkbeiner, Joshua; Raman, Ganesh; Daniels, Christopher; Steinetz, Bruce M.
2003-01-01
Optimizing resonator shapes for maximizing the ratio of maximum to minimum gas pressure at an end of the resonator is investigated numerically. It is well known that the resonant frequencies and the nonlinear standing waveform in an acoustical resonator strongly depend on the resonator geometry. A quasi-Newton type scheme was used to find optimized axisymmetric resonator shapes achieving the maximum pressure compression ratio with an acceleration of constant amplitude. The acoustical field was solved using a one-dimensional model, and the resonance frequency shift and hysteresis effects were obtained through an automation scheme based on continuation method. Results are presented for optimizing three types of geometry: a cone, a horn-cone and a half cosine-shape. For each type, different optimized shapes were found when starting with different initial guesses. Further, the one-dimensional model was modified to study the effect of an axisymmetric central blockage on the nonlinear standing wave.
Moon, Francis C.
2002-04-01
Large numbers of fluid elastic structures are part of many power plant systems and vibration of these systems sometimes are responsible for plant shut downs. Earlier research at Cornell in this area had centered on nonlinear dynamics of fluid-elastic systems with low degrees of freedom. The focus of current research is the study of the dynamics of thousands of closely arrayed structures in a cross flow under both fluid and impact forces. This research is relevant to two areas: (1) First, fluid-structural problems continue to be important in the power industry, especially in heat exchange systems where up to thousands of pipe-like structures interact with a fluid medium. [Three years ago in Japan for example, there was a shut down of the Monju nuclear power plant due to a failure attributed to flow induced vibrations.] (2) The second area of relevance is to nonlinear systems and complexity phenomena; issues such as spatial temporal dynamics, localization and coherent patterns entropy measures as well as other complexity issues. Early research on flow induced vibrations in tube row and array structures in cross flow goes back to Roberts in 1966 and Connors in 1970. These studies used linear models as have many of the later work in the 1980's. Nonlinear studies of cross flow induced vibrations have been undertaken in the last decade. The research at Cornell sponsored by DOE has explored nonlinear phenomena in fluid-structure problems. In the work at Cornell we have documented a subcritical Hopf bifurcation for flow around a single row of flexible tubes and have developed an analytical model based on nonlinear system identification techniques. (Thothadri, 1998, Thothadri and Moon, 1998, 1999). These techniques have been applied to a wind tunnel experiment with a row of seven cylinders in a cross flow. These system identification methods have been used to calculate fluid force models that have replicated certain quantitative vibration limit cycle behavior of the
Linear and nonlinear theory of the proton beam transit-time oscillator (TTO)
NASA Astrophysics Data System (ADS)
Walsh, John E.; Mostrom, Michael A.; Clark, Randy M.; Arman, M. Joseph; Campbell, Mark M.
1989-07-01
A theoretical characterization is presented for both the small- and large-amplitude behaviors of the intense beam-driven transit-time oscillator device which encompasses the effects of the beam self-fields and space-charge effects. The theory has been employed in the development of expressions for comparison with particle simulation results. Attention is given to the effect of beam-plasma frequency on gain, saturation growth in the monotron, the effects of space-charge depression on the transit angle, and the dependence of monotron performance on beam energy.
Modulation of mechanical resonance by chemical potential oscillation in graphene
NASA Astrophysics Data System (ADS)
Chen, Changyao; Deshpande, Vikram V.; Koshino, Mikito; Lee, Sunwoo; Gondarenko, Alexander; MacDonald, Allan H.; Kim, Philip; Hone, James
2016-03-01
The classical picture of the force on a capacitor assumes a large density of electronic states, such that the electrochemical potential of charges added to the capacitor is given by the external electrostatic potential and the capacitance is determined purely by geometry. Here we consider capacitively driven motion of a nano-mechanical resonator with a low density of states, in which these assumptions can break down. We find three leading-order corrections to the classical picture: the first of which is a modulation in the static force due to variation in the internal chemical potential; the second and third are changes in the static force and dynamic spring constant due to the rate of change of chemical potential, expressed as the quantum (density of states) capacitance. As a demonstration, we study capacitively driven graphene mechanical resonators, where the chemical potential is modulated independently of the gate voltage using an applied magnetic field to manipulate the energy of electrons residing in discrete Landau levels. In these devices, we observe large periodic frequency shifts consistent with the three corrections to the classical picture. In devices with extremely low strain and disorder, the first correction term dominates and the resonant frequency closely follows the chemical potential. The theoretical model fits the data with only one adjustable parameter representing disorder-broadening of the Landau levels. The underlying electromechanical coupling mechanism is not limited by the particular choice of material, geometry, or mechanism for variation in the chemical potential, and can thus be extended to other low-dimensional systems.
Mechanism of Spontaneous Oscillation Emerging from Collective Molecular Motors
NASA Astrophysics Data System (ADS)
Shimamoto, Yuta; Ishiwata, Shin'ichi
2008-04-01
Biological systems include a large number and various kinds of molecular machines. Individual molecular machines work stochastically, while the systems constructed of the ensembles of these machines exhibit dynamically-ordered phenomena, rather than a simple sum of individual parts. Here we focus on the spontaneous oscillatory contraction (SPOC) observed in the contractile system of muscle. From the mechanical measurements in the precursor state of SPOC, we discuss how the functions of individual molecular motors are autonomously regulated in the contractile system.
NASA Astrophysics Data System (ADS)
Xiaofang, Zhang; Lei, Wu; Qinsheng, Bi
2016-07-01
We explore the complicated bursting oscillations as well as the mechanism in a high-dimensional dynamical system. By introducing a periodically changed electrical power source in a coupled BVP oscillator, a fifth-order vector field with two scales in frequency domain is established when an order gap exists between the natural frequency and the exciting frequency. Upon the analysis of the generalized autonomous system, bifurcation sets are derived, which divide the parameter space into several regions associated with different types of dynamical behaviors. Two typical cases are focused on as examples, in which different types of bursting oscillations such as subHopf/subHopf burster, subHopf/fold-cycle burster, and double-fold/fold burster can be observed. By employing the transformed phase portraits, the bifurcation mechanism of the bursting oscillations is presented, which reveals that different bifurcations occurring at the transition between the quiescent states (QSs) and the repetitive spiking states (SPs) may result in different forms of bursting oscillations. Furthermore, because of the inertia of the movement, delay may exist between the locations of the bifurcation points on the trajectory and the bifurcation points obtained theoretically. Project supported by the National Natural Science Foundation of China (Grant No. 21276115).
Rigatos, Gerasimos
2014-12-01
A synchronizing control scheme for coupled neural oscillators of the FitzHugh-Nagumo type is proposed. Using differential flatness theory the dynamical model of two coupled neural oscillators is transformed into an equivalent model in the linear canonical (Brunovsky) form. A similar linearized description is succeeded using differential geometry methods and the computation of Lie derivatives. For such a model it becomes possible to design a state feedback controller that assures the synchronization of the membrane's voltage variations for the two neurons. To compensate for disturbances that affect the neurons' model as well as for parametric uncertainties and variations a disturbance observer is designed based on Kalman Filtering. This consists of implementation of the standard Kalman Filter recursion on the linearized equivalent model of the coupled neurons and computation of state and disturbance estimates using the diffeomorphism (relations about state variables transformation) provided by differential flatness theory. After estimating the disturbance terms in the neurons' model their compensation becomes possible. The performance of the synchronization control loop is tested through simulation experiments.
ERIC Educational Resources Information Center
And Others; Gilmartin, Harvey
1979-01-01
Presented is a form of Hamilton's principle for classical mechanics appropriate to the study of arbitrary self-sustained vibrations in one dimension. It is applied as an approximate computational tool to the study of several examples of anharmonic oscillation. (Author/GA)
An Ekman Transport Mechanism for the Atlantic Multidecadal Oscillation
NASA Astrophysics Data System (ADS)
Pratt, V. R.
2014-12-01
Multidecadal global climate since 1850 consists of the expected greenhouse warming and two cycles of a fluctuation commonly associated with the AMO that so far has not been satisfactorily explained. In GC53C-06 at AGUFM13 we compared land and sea temperatures during the global warmings of 1860-1880 and 1910-1940 and inferred that heat flowed sea to land, ruling out aerosol-based external forcings and indicating an internal source such as an instability in the AMOC. Length of day during the past century has varied by ~4 ms inversely with the AMO. Noting that the ocean floor is some five times thinner than the continental crust, we propose here that Earth's rotation regulates heat flux through the ocean floor. One mechanism for this is centrifugal force pulling plates apart, particularly along the Mid-Atlantic Ridge and around the Ring of Fire, increasing flux by an amount that would easily pass unnoticed in the 1930s. Another mechanism, perhaps less strong, is stress from rotational acceleration increasing the thermal conductivity of the young rocks comprising the ocean floor. A difficulty is that the ocean would absorb the fluctuations before reaching the surface. We overcome this difficulty via Ekman transport. This mechanism acts on a 50 m deep layer at the surface to drive it polewards from the ITCZ at 3 cm/sec or 1000 km/yr, orders of magnitude faster than the MOC which therefore cannot interfere. This creates a suction at the ITCZ and a downwards pumping action at 30°. In order to close this cycle there must be a flow equal in volume rate towards the ITCZ at depth. We propose that the heat entering the ocean bottom between 30° S and 30° N enters these two "Ekman cells", which carry it to the surface via the ITCZ. To evaluate feasibility, take the area of the participating 50m surface layer to be 1014 m2, making the volume of the top and bottom layers 1016 m3. Only 1022 J of heat is needed to warm or cool this by 1/3.85 = 0.26 °C. Over the 30 years 1910
Lyapunov based nonlinear control of electrical and mechanical systems
NASA Astrophysics Data System (ADS)
Behal, Aman
fusing a filtered tracking error transformation with the dynamic oscillator design presented in [20]. The proposed tracking controller yields a GUUB result for the regulation problem also. In the final chapter, a nonlinear controller is designed for the kinematic model of an underactuated rigid spacecraft that ensures uniform, ultimately bounded (UUB) tracking provided the initial errors are selected sufficiently small. The result is achieved via a judicious formulation of the spacecraft kinematics and the novel design of a Lyapunov-based controller. It is also demonstrated how standard backstepping control techniques can be fused with the kinematic controller to solve the full-order regulation problem for an axisymmetric spacecraft. Simulation results are included to demonstrate the efficacy of the proposed algorithm. 1It is to be noted that the controller presented in [16] was originally designed to obtain exponential rotor position /rotor flux tracking for the full-order induction motor model (i.e., stator current dynamics are included).
Armitage, C.A.; Mastorakos, E.; Cant, R.S.; Balachandran, R.
2006-08-15
Acoustically forced lean premixed turbulent bluff-body stabilized flames are investigated using turbulent combustion CFD. The calculations simulate aspects of the experimental investigation by Balachandran et al. [R. Balachandran, B. Ayoola, C. Kaminski, A. Dowling, E. Mastorakos, Combust. Flame 143 (2005) 37-55] and focus on the amplitude dependence of the flame response. For the frequencies of interest in this investigation an unsteady Reynolds-averaged Navier-Stokes (URANS) approach is appropriate. The combustion is represented using a modified laminar flamelet approach with an algebraic representation of the flame surface density. The predictions are compared with flame surface density (FSD) and OH* chemiluminescence measurements. In the experiments the response of the flame has been quantified by means of a number of single-frequency, amplitude-dependent transfer functions. The predicted flame shape and position are in good agreement with the experiment. The dynamic response of the flame to inlet velocity forcing is also well captured by the calculations. At moderate frequencies nonlinear behavior of the transfer functions is observed as the forcing amplitude is increased. In the experiments this nonlinearity was attributed in part to the rollup of the reacting shear layer into vortices and in part to the collision of the inner and outer flame sheets. This transition to nonlinearity is also observed in the transfer functions obtained from the predictions. Furthermore, the vortex shedding and flame-sheet collapse may be seen in snapshots of the predicted flow field taken throughout the forcing cycle. The URANS methodology successfully predicts the behavior of the forced premixed turbulent flames and captures the effects of saturation in the transfer function of the response of the heat release to velocity fluctuations. (author)
Generic mechanisms of decoherence of quantum oscillations in magnetic double-well systems
NASA Astrophysics Data System (ADS)
M. Chudnovsky, Eugene
2004-05-01
Fundamental conservation laws mandate parameter-free generic mechanisms of decoherence of quantum oscillations in double-well systems. We consider two examples: tunneling of the magnetic moment in nanomagnets and tunneling between macroscopic current states in SQUIDs. In both cases the decoherence occurs via emission of phonons and photons at the oscillation frequency. We also show that in a system of identical qubits the decoherence greatly increases due to the superradiance of electromagnetic and sound waves. Our findings have important implications for building elements of quantum computers based upon nanomagnets and SQUIDs.
Brinkmann, Maximilian; Janfrüchte, Sarah; Hellwig, Tim; Dobner, Sven; Fallnich, Carsten
2016-05-15
We present a fiber-based optical parametric oscillator (FOPO) pumped by a fiber-coupled laser diode. The FOPO consisted of a photonic crystal fiber to convert the pump pulses via four-wave mixing and a dispersive resonator formed by a single-mode fiber. Via dispersion filtering, output pulses with a bandwidth of about 3 nm, a temporal duration of about 8 ps and a pulse energy of up to 22 nJ could be generated. By changing the repetition frequency of the pump laser diode by about ±1 kHz, the wavelength of the output pulses could be tuned between 1130 and 1310 nm within 8 μs, without the need to change the length of the resonator. Therewith, the FOPO should especially be suited for hyperspectral imaging, while its all-electronic control constitutes a promising approach to a turnkey and alignment-free light source.
NASA Astrophysics Data System (ADS)
Xiong, Huai; Kong, Xianren; Li, Haiqin; Yang, Zhenguo
2017-01-01
This paper considers dynamics of bilinear hysteretic systems, which are widely used for vibration control and vibration absorption such as magneto-rheological damper, metal-rubber. The method of incremental harmonic balance (IHB) technique that hysteresis is considered in the corrective term is improved in order to determine periodic solutions of bilinear hysteretic systems. The improved continuation method called two points tracing algorithm which is stable to the turning point makes the calculation more efficient for tracing amplitude-frequency response. Precise Hsu's method for analysing the stability of periodic solutions is introduced. The effects of different parameters of bilinear hysteretic oscillator on the response are discussed numerically. Some numerical simulations of considered bilinear hysteretic systems, including a single DOF and a 2DOF system, are effectively obtained by the modified IHB method and the results compare very well with the 4-oder Runge-Kutta method.
Squeezing a thermal mechanical oscillator by stabilized parametric effect on the optical spring.
Pontin, A; Bonaldi, M; Borrielli, A; Cataliotti, F S; Marino, F; Prodi, G A; Serra, E; Marin, F
2014-01-17
We report the confinement of an optomechanical micro-oscillator in a squeezed thermal state, obtained by parametric modulation of the optical spring. We propose and implement an experimental scheme based on parametric feedback control of the oscillator, which stabilizes the amplified quadrature while leaving the orthogonal one unaffected. This technique allows us to surpass the -3 dB limit in the noise reduction, associated with parametric resonance, with a best experimental result of -7.4 dB. While the present experiment is in the classical regime, in a moderately cooled system our technique may allow squeezing of a macroscopic mechanical oscillator below the zero-point motion.
NASA Astrophysics Data System (ADS)
Palevicius, P.; Aleksa, A.; Maskeliunas, R.; Ragulskis, M.
2017-03-01
An experimental technique based on time-averaged circular geometric moiré for optical measurement of angular oscillations is presented in this paper. The pitch of the circular moiré is preselected in such a way that angular oscillations of different amplitudes yield time-averaged moiré fringes at different locations of the cover image. This optical effect enables to construct an optical scale for direct measurement of angular oscillations. The proposed technique is similar to visual cryptography, which is a cryptographic technique that allows encryption of visual information in such a way, that decryption can be done without use of any computational device. The efficiency and the applicability of the proposed technique for performance degradation prediction of rotating mechanical components is illustrated and validated by computational simulations and experimental tests.
Network mechanisms of gamma oscillations in the CA3 region of the hippocampus.
Hájos, Norbert; Paulsen, Ole
2009-10-01
Neural networks of the brain display multiple patterns of oscillatory activity. Some of these rhythms are generated intrinsically within the local network, and can therefore be studied in isolated preparations. Here we discuss local-circuit mechanisms involved in hippocampal CA3 gamma oscillations, one of the best understood locally generated network patterns in the mammalian brain. Perisomatic inhibitory cells are crucial players in gamma oscillogenesis. They provide prominent rhythmic inhibition to CA3 pyramidal cells and are themselves synchronized primarily by excitatory synaptic inputs derived from the local collaterals of CA3 pyramidal cells. The recruitment of this recurrent excitatory-inhibitory feedback loop during hippocampal gamma oscillations suggests that local gamma oscillations not only control when, but also how many and which pyramidal cells will fire during each gamma cycle.
Quantum noise of a Michelson-Sagnac interferometer with a translucent mechanical oscillator
Yamamoto, Kazuhiro; Friedrich, Daniel; Westphal, Tobias; Gossler, Stefan; Danzmann, Karsten; Schnabel, Roman; Somiya, Kentaro; Danilishin, Stefan L.
2010-03-15
Quantum fluctuations in the radiation pressure of light can excite stochastic motions of mechanical oscillators thereby realizing a linear quantum opto-mechanical coupling. When performing a precise measurement of the position of an oscillator, this coupling results in quantum radiation pressure noise. Up to now this effect has not been observed yet. Generally speaking, the strength of radiation pressure noise increases when the effective mass of the oscillator is decreased or when the power of the reflected light is increased. Recently, extremely light SiN membranes ({approx_equal}100 ng) with high mechanical Q values at room temperature ({>=}10{sup 6}) have attracted attention as low thermal noise mechanical oscillators. However, the power reflectance of these membranes is much lower than unity (<0.4 at a wavelength of 1064 nm) which makes the use of advanced interferometer recycling techniques to amplify the radiation pressure noise in a standard Michelson interferometer inefficient. Here, we propose and theoretically analyze a Michelson-Sagnac interferometer that includes the membrane as a common end mirror for the Michelson interferometer part. In this topology, both power and signal recycling can be used even if the reflectance of the membrane is much lower than unity. In particular, signal recycling is a useful tool because it does not involve a power increase at the membrane. We derive the formulas for the quantum radiation pressure noise and the shot noise of an oscillator position measurement and compare them with theoretical models of the thermal noise of a SiN membrane with a fundamental resonant frequency of 75 kHz and an effective mass of125 ng. We find that quantum radiation pressure noise should be observable with a power of 1 W at the central beam splitter of the interferometer and a membrane temperature of 1 K.
NASA Astrophysics Data System (ADS)
Gao, Guangzhong; Zhu, Ledong
2015-10-01
The wind tunnel test of spring-suspended sectional models (SSSM) is an important means in the research of wind engineering, which is very frequently employed to check the performances of flutter and vortex-induced resonance of bridges as well as to identify the various aerodynamic and aeroelastic parameters of bridge components, such as aerodynamic derivatives of self-excited forces. However, in practice, the mechanical damping ratios and natural frequencies of SSSM system are prevailingly supposed to be constant in the whole procedure of a test. This assumption often leads to notable errors of the test results or dispersion of the identified aerodynamic parameters because the mechanical damping ratios and natural frequencies of SSSM system are proved to vary in fact to some extent with the change of oscillating amplitude. On that account, the mechanical nonlinearity of SSSM system is investigated and discussed in this paper by taking a flat-closed box section as a research background. The conventional linear model is firstly proved to fail to predict precisely the long-duration free decay responses of the SSSM system. The formulae of equivalent linearization approximation (ELA) are then derived by using a multiple-scale method to model the mechanical nonlinearities in the first-order approximate sense, and a time-domain system identification method is proposed on this basis to identify equivalent amplitude-dependent (EAD) damping ratio and frequency. The proposed ELA and nonlinear system identification methods are then found to be precise enough to model the mechanical nonlinearities of SSSM system. The characteristics of EAD damping ratio and frequency of both the bending and torsional modes are then discussed in detail. It is then found that the major energy dissipation of SSSM vibrations at both the bending and torsional modes generally comes from the combined effect of viscous damping and quadratic damping. However, for the vibration at the bending mode with
NASA Astrophysics Data System (ADS)
Kevorkian, J.; Li, Y. P.
1987-08-01
The first part of this paper summarizes the mathematical modeling of free electron lasers (FEL), and the remainder concerns general perturbation methods for solving free electron laser (FEL) and other strictly nonlinear oscillatory problems with slowly varying parameters and small perturbations. We review and compare the methods of Kuzmak-Luke and of near-identity averaging transformations. In order to implement the calculation of explicit solutions we develop two approximation schemes. The first involves use of finite Fourier series to present either the leading approximation of the solution or the transformation of the governing equations to a standard form appropriate for the method of averaging. In the second scheme we fit a cubic polynomial to the potential such that the leading approximation is expressible in terms of elliptic functions. The ideas are illustrated with a number of examples which are also solved numerically to assess the accuracy of the various approximations.
Goodfellow, Marc; Glendinning, Paul
2013-08-14
We investigate the dynamic mechanisms underlying intermittent state transitions in a recently proposed neural mass model of epilepsy. A low dimensional model is constructed, which preserves two key features of the neural mass model, namely (i) coupling between oscillators and (ii) heterogeneous proximity of these oscillators to a bifurcation between distinct limit cycles. We demonstrate that state transitions due to intermittency occur in the abstract model. This suggests that there is a general bifurcation mechanism responsible for this behaviour and that this is independent of the precise form of the evolution equations. Such abstractions of neural mass models allow a deeper insight into underlying dynamic and physiological mechanisms, and also allow the more efficient exploration of large scale brain dynamics in disease.
Zhang, Zhengbo; Ni, Lu; Liu, Xiaoli; Li, Deyu; Wang, Weidong
2015-11-01
The forced oscillation technique (FOT) is a noninvasive method for respiratory mechanics measurement. For the FOT, external signals (e.g. forced oscillations around 4-40 Hz) are used to drive the respiratory system, and the mechanical characteristic of the respiratory system can be determined with the linear system identification theory. Thus, respiratory mechanical properties and components at different frequency and location of the airway can be explored by specifically developed forcing waveforms. In this paper, the theory, methodology and clinical application of the FOT is reviewed, including measure ment theory, driving signals, models of respiratory system, algorithm for impedance identification, and requirement on apparatus. Finally, the future development of this technique is also discussed.
Observation of strong radiation pressure forces from squeezed light on a mechanical oscillator
NASA Astrophysics Data System (ADS)
Clark, Jeremy B.; Lecocq, Florent; Simmonds, Raymond W.; Aumentado, José; Teufel, John D.
2016-07-01
In quantum-enhanced sensing, non-classical states are used to improve the sensitivity of a measurement. Squeezed light, in particular, has proved a useful resource in enhanced mechanical displacement sensing, although the fundamental limit to this enhancement due to the Heisenberg uncertainty principle has not been encountered experimentally. Here we use a microwave cavity optomechanical system to observe the squeezing-dependent radiation pressure noise that necessarily accompanies any quantum enhancement of the measurement precision and ultimately limits the measurement noise performance. By increasing the measurement strength so that radiation pressure forces dominate the thermal motion of the mechanical oscillator, we exploit the optomechanical interaction to implement an efficient quantum nondemolition measurement of the squeezed light. Thus, our results show how the mechanical oscillator improves the measurement of non-classical light, just as non-classical light enhances the measurement of the motion.
A nonlinear piezoelectric energy harvester for various mechanical motions
Fan, Kangqi; Chang, Jianwei; Liu, Zhaohui; Zhu, Yingmin; Pedrycz, Witold
2015-06-01
This study presents a nonlinear piezoelectric energy harvester with intent to scavenge energy from diverse mechanical motions. The harvester consists of four piezoelectric cantilever beams, a cylindrical track, and a ferromagnetic ball, with magnets integrated to introduce the magnetic coupling between the ball and the beams. The experimental results demonstrate that the harvester is able to collect energy from various directions of vibrations. For the vibrations perpendicular to the ground, the maximum peak voltage is increased by 3.2 V and the bandwidth of the voltage above 4 V is increased by more than 4 Hz compared to the results obtained when using a conventional design. For the vibrations along the horizontal direction, the frequency up-conversion is realized through the magnetic coupling. Moreover, the proposed design can harvest energy from the sway motion around different directions on the horizontal plane. Harvesting energy from the rotation motion is also achieved with an operating bandwidth of approximately 6 Hz.
Hybrid plasmonic nanodevices: Switching mechanism for the nonlinear emission
Bragas, Andrea V.; Singh, Mahi R.
2014-03-31
Control of the light emission at the nanoscale is of central interest in nanophotonics due to the many applications in very different fields, ranging from quantum information to biophysics. Resonant excitation of surface plasmon polaritons in metal nanoparticles create nanostructured and enhanced light fields around those structures, which produce their strong interaction in a hybrid nanodevice with other plasmonic or non-plasmonic objects. This interaction may in turn also modulate the far field with important consequences in the applications. We show in this paper that the nonlinear emission from semiconductor quantum dots is strongly affected by the close presence of metal nanoparticles, which are resonantly excited. Using a pulsed laser, optical second harmonic is generated in the quantum dot, and it is highly enhanced when the laser is tuned around the nanoparticle plasmon resonance. Even more interesting is the demonstration of a switching mechanism, controlled by an external continuous-wave field, which can enhance or extinguish the SH signal, even when the pulsed laser is always on. Experimental observations are in excellent agreement with the theoretical calculations, based on the dipole-dipole near-field coupling of the objects forming the hybrid system.
On the nonlinear electromagnetic coupling between a coil and an oscillating magnet
NASA Astrophysics Data System (ADS)
Sneller, Adam J.; Mann, Brian P.
2010-07-01
The electromagnetic induction of voltage across a coil due to the motion of a magnet is among the fundamental problems of physics, and it has a broad range of practical applications. While Maxwell's equations exactly describe this phenomenon, the physical complexity inherent in most realistic situations often prevents the generation of closed-form expressions for the electromagnetic coupling. This paper uses basic principles to develop an approximate analytical expression for the induced voltage in terms of a set of physical parameters, and experimental results demonstrate a high level of validity in the model over the parameter values tested. For oscillatory magnet motion about a point on a coil's axis, it is shown that the induced voltage is an infinite sum of harmonics at integer multiples of the oscillation frequency; the relative amplitudes of these harmonics vary as the magnet's equilibrium position migrates along the coil's axis, causing the odd and even harmonics to vanish, reappear and reach peak values at predictable locations. Several simplifications to the model are considered, and their validity is investigated analytically over a range of parameters.
Barbini, Paolo; Cevenini, Gabriele; Avanzolni, Guido
2003-09-01
A nonlinear model of breathing mechanics, in which the tracheobronchial airways are considered in three serial segments, is presented to obtain insights into the mechanisms underlying expiratory flow limitation (EFL) in mechanically ventilated patients. Chronic obstructive pulmonary disease (COPD) and normal conditions were simulated and EFL was detected by application of negative expiratory pressure at the mouth or resistance reduction of the expiratory circuit. Simulation results confirm that both techniques reveal remarkable differences in the flow-volume curves between normal subjects and COPD patients, the former showing absence of EFL and the latter exhibiting EFL over most of the expiration. To interpret the role of different nonlinear mechanisms in producing EFL, different flow-volume curves obtained by changing model parameter values were analyzed. An increase in lower-airway resistance did not give rise to EFL, whereas a change in the pressure-volume characteristic of the intermediate-airway segment, towards increased resistance and easier collapse, significantly modified system behavior. In particular, EFL was observed when this intermediate-segment change was combined with an increase in lower-airway resistance. This evidence suggests that modifications, producing loss of radial traction and consequent narrowing of the airways in the peribronchial region, may play a leading role in EFL in COPD patients.
Coherent spin oscillations and non-linear dynamics in two quantum magnets
NASA Astrophysics Data System (ADS)
Schmidt, Michael Andrew
I present experimental studies of the low-temperature linear and nonlinear AC magnetic behavior of two insulating magnetic materials: the dilute Ising magnet Lithium Yttrium Holmium Tetraflouride (LiHo0.045Y0.955 F4); and the frustrated Heisenberg magnet Neodymium Gadolinium Gallium Garnet (NdxGd3-xGa5O12 for x={0.01, 0.05, 0.1}). We find that under certain thermodynamic limits, LiHo 0.045Y0.955F4 can be continuously tuned between competing low-temperature states by cooling the sample in an external, DC magnetic field. Furthermore, we demonstrate the magnetic pump/probe technique as a powerful tool to quantify the stability of the magnetic state in the presence of disorder, and to probe the coupling between the spin states and the incoherent nuclear spin bath. In addition, I present susceptibility data for the three different concentrations of NdxGd3-x Ga5O12, which show that the doped samples possess the same coherent spin degrees of freedom as is seen in the pure sample. We find that even in the lightest-doped sample (0.1%), the presence of disorder suppresses the onset of Antiferromagnetic order by a factor of two, and that any transition in the other samples (0.5% and 1%) must be below 50 mK.
Step potential problem and harmonic oscillator problem in the minimum length quantum mechanics
NASA Astrophysics Data System (ADS)
Park, Soyeon; Woo, Byeong Hyo; Jung, Min; Jang, Eun Ji; Chung, Won Sang
2015-05-01
In this paper, we use the quasi-position representation of the minimum length quantum mechanics (MLQM) to study the effects of minimum length uncertainty principle (MLUP) on the quantum mechanical system up to a first-order in β. We introduce the probability density and the probability flux to discuss two problems such as particle in a box and step potential problem. For the step potential, we compute the transmission coefficient and the reflection coefficient and compare them with those of the ordinary quantum mechanics. We also discuss the harmonic oscillator problem in MLQM.
NASA Astrophysics Data System (ADS)
Popov, Pavel; Sideris, Athanasios; Sirignano, William
2014-11-01
We examine the non-linear dynamics of the transverse modes of combustion-driven acoustic instability in a liquid-propellant rocket engine. Triggering can occur, whereby small perturbations from mean conditions decay, while larger disturbances grow to a limit-cycle of amplitude that may compare to the mean pressure. For a deterministic perturbation, the system is also deterministic, computed by coupled finite-volume solvers at low computational cost for a single realization. The randomness of the triggering disturbance is captured by treating the injector flow rates, local pressure disturbances, and sudden acceleration of the entire combustion chamber as random variables. The combustor chamber with its many sub-fields resulting from many injector ports may be viewed as a multi-scale complex system wherein the developing acoustic oscillation is the emergent structure. Numerical simulation of the resulting stochastic PDE system is performed using the polynomial chaos expansion method. The overall probability of unstable growth is assessed in different regions of the parameter space. We address, in particular, the seven-injector, rectangular Purdue University experimental combustion chamber. In addition to the novel geometry, new features include disturbances caused by engine acceleration and unsteady thruster nozzle flow.
NASA Astrophysics Data System (ADS)
Sabeerali, C. T.; Ajayamohan, R. S.; Giannakis, Dimitrios; Majda, Andrew J.
2017-01-01
An improved index for real-time monitoring and forecast verification of monsoon intraseasonal oscillations (MISOs) is introduced using the recently developed nonlinear Laplacian spectral analysis (NLSA) technique. Using NLSA, a hierarchy of Laplace-Beltrami (LB) eigenfunctions are extracted from unfiltered daily rainfall data from the Global Precipitation Climatology Project over the south Asian monsoon region. Two modes representing the full life cycle of the northeastward-propagating boreal summer MISO are identified from the hierarchy of LB eigenfunctions. These modes have a number of advantages over MISO modes extracted via extended empirical orthogonal function analysis including higher memory and predictability, stronger amplitude and higher fractional explained variance over the western Pacific, Western Ghats, and adjoining Arabian Sea regions, and more realistic representation of the regional heat sources over the Indian and Pacific Oceans. Real-time prediction of NLSA-derived MISO indices is demonstrated via extended-range hindcasts based on NCEP Coupled Forecast System version 2 operational output. It is shown that in these hindcasts the NLSA MISO indices remain predictable out to ˜ 3 weeks.
Quantum enhanced feedback cooling of a mechanical oscillator using nonclassical light
NASA Astrophysics Data System (ADS)
Schäfermeier, Clemens; Kerdoncuff, Hugo; Hoff, Ulrich B.; Fu, Hao; Huck, Alexander; Bilek, Jan; Harris, Glen I.; Bowen, Warwick P.; Gehring, Tobias; Andersen, Ulrik L.
2016-11-01
Laser cooling is a fundamental technique used in primary atomic frequency standards, quantum computers, quantum condensed matter physics and tests of fundamental physics, among other areas. It has been known since the early 1990s that laser cooling can, in principle, be improved by using squeezed light as an electromagnetic reservoir; while quantum feedback control using a squeezed light probe is also predicted to allow improved cooling. Here we show the implementation of quantum feedback control of a micro-mechanical oscillator using squeezed probe light. This allows quantum-enhanced feedback cooling with a measurement rate greater than it is possible with classical light, and a consequent reduction in the final oscillator temperature. Our results have significance for future applications in areas ranging from quantum information networks, to quantum-enhanced force and displacement measurements and fundamental tests of macroscopic quantum mechanics.
Quantum enhanced feedback cooling of a mechanical oscillator using nonclassical light
Schäfermeier, Clemens; Kerdoncuff, Hugo; Hoff, Ulrich B.; Fu, Hao; Huck, Alexander; Bilek, Jan; Harris, Glen I.; Bowen, Warwick P.; Gehring, Tobias; Andersen, Ulrik L.
2016-01-01
Laser cooling is a fundamental technique used in primary atomic frequency standards, quantum computers, quantum condensed matter physics and tests of fundamental physics, among other areas. It has been known since the early 1990s that laser cooling can, in principle, be improved by using squeezed light as an electromagnetic reservoir; while quantum feedback control using a squeezed light probe is also predicted to allow improved cooling. Here we show the implementation of quantum feedback control of a micro-mechanical oscillator using squeezed probe light. This allows quantum-enhanced feedback cooling with a measurement rate greater than it is possible with classical light, and a consequent reduction in the final oscillator temperature. Our results have significance for future applications in areas ranging from quantum information networks, to quantum-enhanced force and displacement measurements and fundamental tests of macroscopic quantum mechanics. PMID:27897181
Quantum enhanced feedback cooling of a mechanical oscillator using nonclassical light.
Schäfermeier, Clemens; Kerdoncuff, Hugo; Hoff, Ulrich B; Fu, Hao; Huck, Alexander; Bilek, Jan; Harris, Glen I; Bowen, Warwick P; Gehring, Tobias; Andersen, Ulrik L
2016-11-29
Laser cooling is a fundamental technique used in primary atomic frequency standards, quantum computers, quantum condensed matter physics and tests of fundamental physics, among other areas. It has been known since the early 1990s that laser cooling can, in principle, be improved by using squeezed light as an electromagnetic reservoir; while quantum feedback control using a squeezed light probe is also predicted to allow improved cooling. Here we show the implementation of quantum feedback control of a micro-mechanical oscillator using squeezed probe light. This allows quantum-enhanced feedback cooling with a measurement rate greater than it is possible with classical light, and a consequent reduction in the final oscillator temperature. Our results have significance for future applications in areas ranging from quantum information networks, to quantum-enhanced force and displacement measurements and fundamental tests of macroscopic quantum mechanics.
Measurement-based control of a mechanical oscillator at its thermal decoherence rate
NASA Astrophysics Data System (ADS)
Wilson, D. J.; Sudhir, V.; Piro, N.; Schilling, R.; Ghadimi, A.; Kippenberg, T. J.
2015-08-01
In real-time quantum feedback protocols, the record of a continuous measurement is used to stabilize a desired quantum state. Recent years have seen successful applications of these protocols in a variety of well-isolated micro-systems, including microwave photons and superconducting qubits. However, stabilizing the quantum state of a tangibly massive object, such as a mechanical oscillator, remains very challenging: the main obstacle is environmental decoherence, which places stringent requirements on the timescale in which the state must be measured. Here we describe a position sensor that is capable of resolving the zero-point motion of a solid-state, 4.3-megahertz nanomechanical oscillator in the timescale of its thermal decoherence, a basic requirement for real-time (Markovian) quantum feedback control tasks, such as ground-state preparation. The sensor is based on evanescent optomechanical coupling to a high-Q microcavity, and achieves an imprecision four orders of magnitude below that at the standard quantum limit for a weak continuous position measurement--a 100-fold improvement over previous reports--while maintaining an imprecision-back-action product that is within a factor of five of the Heisenberg uncertainty limit. As a demonstration of its utility, we use the measurement as an error signal with which to feedback cool the oscillator. Using radiation pressure as an actuator, the oscillator is cold damped with high efficiency: from a cryogenic-bath temperature of 4.4 kelvin to an effective value of 1.1 +/- 0.1 millikelvin, corresponding to a mean phonon number of 5.3 +/- 0.6 (that is, a ground-state probability of 16 per cent). Our results set a new benchmark for the performance of a linear position sensor, and signal the emergence of mechanical oscillators as practical subjects for measurement-based quantum control.
Breuer; Huber; Petruccione
2000-05-01
The dynamics of periodically driven quantum systems coupled to a thermal environment is investigated. The interaction of the system with the external coherent driving field is taken into account exactly by making use of the Floquet picture. Treating the coupling to the environment within the Born-Markov approximation one finds a Pauli-type master equation for the diagonal elements of the reduced density matrix in the Floquet representation. The stationary solution of the latter yields a quasistationary, time-periodic density matrix which describes the long-time behavior of the system. Taking the example of a periodically driven particle in a box, the stationary solution is determined numerically for a wide range of driving amplitudes and temperatures. It is found that the quasistationary distribution differs substantially from a Boltzmann-type distribution at the temperature of the environment. For large driving fields it exhibits a plateau region describing a nearly constant population of a certain number of Floquet states. This number of Floquet states turns out to be nearly independent of the temperature. The plateau region is sharply separated from an exponential tail of the stationary distribution which expresses a canonical Boltzmann-type distribution over the mean energies of the Floquet states. These results are explained in terms of the structure of the matrix of transition rates for the dissipative quantum system. Investigating the corresponding classical, nonlinear Hamiltonian system, one finds that in the semiclassical range essential features of the quasistationary distribution can be understood from the structure of the underlying classical phase space.
A defence-like reaction: an emergent property of a system of coupled non-linear oscillators.
Gebber, G L
2001-01-01
1. The present paper deals with the central mechanisms responsible for the defence-like differential pattern of spinal sympathetic outflow elicited by electrical activation of the midbrain periaqueductal grey (PAG) in urethane-anaesthetized, baroreceptor-denervated cats. The pattern is characterized by increases in the 10 Hz discharges of the inferior cardiac (CN) and renal (RN) sympathetic nerves and a decrease in 10 Hz activity of the vertebral sympathetic nerve (VN) that supplies vasoconstrictor outflow to the forelimb. 2. The model used to explain this pattern is based on the self-organizing properties of a system of coupled brainstem oscillators rather than the activation of point-to-point hard-wired connections leading to increases in sympathetic outflow to some targets and decreases to others. 3. The fact that VN 10 Hz activity was inhibited by PAG stimulus frequencies equal to or just above, but not just below, that of the free-running (control) rhythm argues against a 'hard-wired' model. 4. The evidence supporting the hypothesis that the defence-like pattern is an emergent property of a system of coupled oscillators includes changes in the phase lag of VN 10 Hz activity relative to that in the CN, temporal correlation of the changes in phase angle and 10 Hz powers and the direct relationship between the magnitude of the change in phase angle and the degree to which PAG stimulation reciprocally affected the 10 Hz discharges of the CN and VN. 5. It is proposed that changes in phase angle reflect the reorganization of the coupling of 10 Hz oscillators and that such changes in state lead to differential patterns of spinal sympathetic outflow.
NASA Astrophysics Data System (ADS)
Szczepanek, Jan; Kardaś, Tomasz; Nejbauer, Michał; Radzewicz, Czesław; Stepanenko, Yuriy
2016-03-01
In this paper we report an all-PM-fiber laser amplifier system seeded by an all-normal-dispersion oscillator mode-locked with a Nonlinear Optical Loop Mirror (NOLM). The presented all-normal-dispersion cavity works in a dissipative soliton regime and delivers highly-chirped, high energy pulses above 2.5 nJ with full width at half maximum below 200 fs. The ultrafast oscillator followed by the all-PM-fiber amplifying stage delivered pulses with the energy of 42.5 nJ and time duration below 190 fs. The electrical field of optical pulses from the system was reconstructed using the SPIDER technique. The influence of nonlinear processes on the pulse temporal envelope was investigated.
From mechanical to biological oscillator networks: The role of long range interactions
NASA Astrophysics Data System (ADS)
Bountis, T.
2016-09-01
The study of one-dimensional particle networks of Classical Mechanics, through Hamiltonian models, has taught us a lot about oscillations of particles coupled to each other by nearest neighbor (short range) interactions. Recently, however, a careful analysis of the role of long range interactions (LRI) has shown that several widely accepted notions concerning chaos and the approach to thermal equilibrium need to be modified, since LRI strongly affects the statistics of certain very interesting, long lasting metastable states. On the other hand, when LRI (in the form of non-local or all-to-all coupling) was introduced in systems of biological oscillators, Kuramoto's theory of synchronization was developed and soon thereafter researchers studied amplitude and phase oscillations in networks of FitzHugh Nagumo and Hindmarsh Rose (HR) neuron models. In these models certain fascinating phenomena called chimera states were discovered where populations of synchronous and asynchronous oscillators are seen to coexist in the same system. Currently, their synchronization properties are being widely investigated in HR mathematical models as well as realistic neural networks, similar to what one finds in simple living organisms like the C.elegans worm.
Continuous lateral oscillations as a core mechanism for taxis in Drosophila larvae
Wystrach, Antoine; Lagogiannis, Konstantinos; Webb, Barbara
2016-01-01
Taxis behaviour in Drosophila larva is thought to consist of distinct control mechanisms triggering specific actions. Here, we support a simpler hypothesis: that taxis results from direct sensory modulation of continuous lateral oscillations of the anterior body, sparing the need for ‘action selection’. Our analysis of larvae motion reveals a rhythmic, continuous lateral oscillation of the anterior body, encompassing all head-sweeps, small or large, without breaking the oscillatory rhythm. Further, we show that an agent-model that embeds this hypothesis reproduces a surprising number of taxis signatures observed in larvae. Also, by coupling the sensory input to a neural oscillator in continuous time, we show that the mechanism is robust and biologically plausible. The mechanism provides a simple architecture for combining information across modalities, and explaining how learnt associations modulate taxis. We discuss the results in the light of larval neural circuitry and make testable predictions. DOI: http://dx.doi.org/10.7554/eLife.15504.001 PMID:27751233
Mechanical Properties of Laminate Materials: From Surface Waves to Bloch Oscillations
NASA Astrophysics Data System (ADS)
Liang, Z.; Willatzen, M.; Christensen, J.
2015-10-01
We propose hitherto unexplored and fully analytical insights into laminate elastic materials in a true condensed-matter-physics spirit. Pure mechanical surface waves that decay as evanescent waves from the interface are discussed, and we demonstrate how these designer Scholte waves are controlled by the geometry as opposed to the material alone. The linear surface wave dispersion is modulated by the crystal filling fraction such that the degree of confinement can be engineered without relying on narrow-band resonances but on effective stiffness moduli. In the same context, we provide a theoretical recipe for designing Bloch oscillations in classical plate structures and show how mechanical Bloch oscillations can be generated in arrays of solid plates when the modal wavelength is gradually reduced. The design recipe describes how Bloch oscillations in classical structures of arbitrary dimensions can be generated, and we demonstrate this numerically for structures with millimeter and centimeter dimensions in the kilohertz to megahertz range. Analytical predictions agree entirely with full wave simulations showing how elastodynamics can mimic quantum-mechanical condensed-matter phenomena.
ERIC Educational Resources Information Center
Parnis, J. Mark; Thompson, Matthew G. K.
2004-01-01
An introductory undergraduate physical organic chemistry exercise that introduces the harmonic oscillator's use in vibrational spectroscopy is developed. The analysis and modeling exercise begins with the students calculating the stretching modes of common organic molecules with the help of the quantum mechanical harmonic oscillator (QMHO) model.
Parametric oscillations of a singularly perturbed telegraph equation with a pendulum non-linearity
Kolesov, Yu S
1998-04-30
The solution of the problem in the title is reduced to an analysis of the question of the number of and stability of equilibrium states of the quasi-normal form of the boundary-value problem under consideration. A mechanism is revealed for the origin of its so-called simple equilibrium states. It is shown that as the coefficient of elasticity decreases, the number of such states increases, and that those of them with the most complex spatial structure are stable.
Jing, Da; Baik, Andrew D.; Lu, X. Lucas; Zhou, Bin; Lai, Xiaohan; Wang, Liyun; Luo, Erping; Guo, X. Edward
2014-01-01
Osteocytes have been hypothesized to be the major mechanosensors in bone. How in situ osteocytes respond to mechanical stimuli is still unclear because of technical difficulties. In vitro studies have shown that osteocytes exhibited unique calcium (Ca2+) oscillations to fluid shear. However, whether this mechanotransduction phenomenon holds for in situ osteocytes embedded within a mineralized bone matrix under dynamic loading remains unknown. Using a novel synchronized loading/imaging technique, we successfully visualized in real time and quantified Ca2+ responses in osteocytes and bone surface cells in situ under controlled dynamic loading on intact mouse tibia. The resultant fluid-induced shear stress on the osteocyte in the lacunocanalicular system (LCS) was also quantified. Osteocytes, but not surface cells, displayed repetitive Ca2+ spikes in response to dynamic loading, with spike frequency and magnitude dependent on load magnitude, tissue strain, and shear stress in the LCS. The Ca2+ oscillations were significantly reduced by endoplasmic reticulum (ER) depletion and P2 purinergic receptor (P2R)/phospholipase C (PLC) inhibition. This study provides direct evidence that osteocytes respond to in situ mechanical loading by Ca2+ oscillations, which are dependent on the P2R/PLC/inositol trisphosphate/ER pathway. This study develops a novel approach in skeletal mechanobiology and also advances our fundamental knowledge of bone mechanotransduction.—Jing, D., Baik, A. D., Lu, X. L., Zhou, B., Lai, X., Wang, L., Luo, E., Guo, X. E. In situ intracellular calcium oscillations in osteocytes in intact mouse long bones under dynamic mechanical loading. PMID:24347610
Estimation of Nonlinear Mechanical Properties of Vascular Tissues via Elastography
Karimi, Reza; Zhu, Ting; Bouma, Brett E.
2009-01-01
A new method is proposed for estimation of nonlinear elastic properties of soft tissues. The proposed approach involves a combination of nonlinear finite element methods with a genetic algorithm for estimating tissue stiffness profile. A multipoint scheme is introduced that satisfies the uniqueness condition, improves the estimation performance, and reduces the sensitivity to image noise. The utility of the proposed techniques is demonstrated using optical coherence tomography (OCT) images. The approach is, however, applicable to other imaging systems and modalities, as well, provided a reliable image registration scheme. The proposed algorithm is applied to realistic (2D) and idealized (3D) arterial plaque models, and proves promising for the estimation of intra-plaque distribution of nonlinear material properties. PMID:19048372
NASA Astrophysics Data System (ADS)
Habibi, Hojat; Zeuthen, Emil; Ghanaatshoar, Majid; Hammerer, Klemens
2016-08-01
We revisit the problem of preparing a mechanical oscillator in the vicinity of its quantum-mechanical ground state by means of feedback cooling based on continuous optical detection of the oscillator position. In the parameter regime relevant to ground-state cooling, the optical back-action and imprecision noise set the bottleneck of achievable cooling and must be carefully balanced. This can be achieved by adapting the phase of the local oscillator in the homodyne detection realizing a so-called variational measurement. The trade-off between accurate position measurement and minimal disturbance can be understood in terms of Heisenberg’s microscope and becomes particularly relevant when the measurement and feedback processes happen to be fast within the quantum coherence time of the system to be cooled. This corresponds to the regime of large quantum cooperativity {C}{{q}}≳ 1, which was achieved in recent experiments on feedback cooling. Our method provides a simple path to further pushing the limits of current state-of-the-art experiments in quantum optomechanics.
A unified control framework of the non-regular dynamics of mechanical oscillators
NASA Astrophysics Data System (ADS)
Lenci, S.; Rega, G.
2004-12-01
A method for controlling non-linear dynamics and chaos based on avoiding homo/heteroclinic bifurcations is considered in a unified framework. Various non-linear oscillators, both hardening and softening, symmetric and asymmetric, considered as archetypes of a more general class of single-d.o.f. systems, are analyzed. The Melnikov's method is applied to analytically detect the homo/heteroclinic bifurcations, and the results are used to select the optimal shape of the excitation permitting the maximum shift of the undesired bifurcations in parameter space. The generic character of the optimization problem is highlighted, and the problem itself is discussed in detail. Various control strategies are proposed, based on the elimination either of a single bifurcation (one-side controls) or of all bifurcations (global control). The optimization problems are solved, analytically and numerically, under various forms, by taking into account the physical admissibility of the related optimal excitation and the easiness of implementation in practical applications. It is shown that the solutions of one-side control problems are always system independent. In turn, the solutions of global control problems are system independent for the large class of (symmetric) systems considered in this work, although there are other systems whose solutions are system dependent. These considerations support the very generic nature of the optimal control.
Thermal Noise Reduction of Mechanical Oscillators by Actively Controlled External Dissipative Forces
NASA Technical Reports Server (NTRS)
Liang, Shoudan; Medich, David; Czajkowsky, Daniel M.; Sheng, Sitong; Yuan, Jian-Yang; Shao, Zhifeng
1999-01-01
We show that the thermal fluctuations of very soft mechanical oscillators, such as the cantilever in an atomic force microscope (AFM), can be reduced without changing the stiffness of the spring or having to lower the environment temperature. We derive a theoretical relationship between the thermal fluctuations of an oscillator and an actively external-dissipative force. This relationship is verified by experiments with an AFM cantilever where the external active force is coupled through a magnetic field. With simple instrumentation, we have reduced the thermal noise amplitude of the cantilever by a factor of 3.4, achieving an apparent temperature of 25 K with the environment at 295K. This active noise reduction approach can significantly improve the accuracy of static position or static force measurements in a number of practical applications.
Network mechanisms of spindle-burst oscillations in the neonatal rat barrel cortex in vivo.
Minlebaev, Marat; Ben-Ari, Yehezkel; Khazipov, Rustem
2007-01-01
Early in development, cortical networks generate particular patterns of activity that participate in cortical development. The dominant pattern of electrical activity in the neonatal rat neocortex in vivo is a spatially confined spindle-burst. Here, we studied network mechanisms of generation of spindle-bursts in the barrel cortex of neonatal rats using a superfused cortex preparation in vivo. Both spontaneous and sensory-evoked spindle-bursts were present in the superfused barrel cortex. Pharmacological analysis revealed that spindle-bursts are driven by glutamatergic synapses with a major contribution of AMPA/kainate receptors, but slight participation of NMDA receptors and gap junctions. Although GABAergic synapses contributed minimally to the pacing the rhythm of spindle-burst oscillations, surround GABAergic inhibition appeared to be crucial for their compartmentalization. We propose that local spindle-burst oscillations, driven by glutamatergic synapses and spatially confined by GABAergic synapses, contribute to the development of barrel cortex during the critical period of developmental plasticity.
NASA Astrophysics Data System (ADS)
Sudhir, Vivishek; Wilson, Dalziel; Schilling, Ryan; Schuetz, Hendrik; Nunnenkamp, Andreas; Kippenberg, Tobias
Measurement-based feedback provides an avenue to study the delicate interplay between the quantum correlations established during the process of measurement, and their progressive obfuscation when exposed to uncorrelated noise in the form of fundamental quantum fluctuations in the feedback path. Here we demonstrate this tradeoff using a feedback strategy whose objective is to cool a nano-mechanical oscillator close to its ground state. The correlations established due to the measurement are revealed in the appearance of motional sideband asymmetry. The latter, faithfully measured using an optical heterodyne interferometer with an imprecision ~17 dB below that at the standard quantum limit, increases to 6% as the oscillator is feedback cooled to an occupation of 15 phonons. Further increase in the gain of the feedback loop leads to a decrease in the asymmetry. This is due to the addition of unavoidable quantum fluctuations in a feedback amplifier - photon shot-noise amplified by a homodyne detector in our case.
Atom-assisted quadrature squeezing of a mechanical oscillator inside a dispersive cavity
NASA Astrophysics Data System (ADS)
Chauhan, Anil Kumar; Biswas, Asoka
2016-08-01
We present a hybrid optomechanical scheme to achieve dynamical squeezing of position quadrature of a mesoscopic mechanical oscillator, that can be externally controlled by classical fields. A membrane-in-the-middle setup is employed, in which an atom in Λ configuration is considered to be trapped on either side of the membrane inside the cavity. We show that a considerable amount of squeezing (beyond the 3-dB limit) can be achieved and maintained at a transient time scale that is not affected by the spontaneous emission of the atom. Squeezing depends upon the initial preparation of atomic states. Further, a strong effective coupling (larger than the relevant decay rates) between the atom and the oscillator can be attained by using large control fields that pump the atom and the cavity. The effects of cavity decay and the phononic bath on squeezing are studied. The results are supported by the detailed analytical calculations.
NASA Astrophysics Data System (ADS)
Petrov, Valentin; Marchev, Georgi; Tyazhev, Aleksey; Beutler, Marcus; Panyutin, Vladimir; Starikova, Marina; Esteban-Martin, Adolfo; Badikov, Valeriy; Shevyrdyaeva, Galina; Badikov, Dmitrii; Reza, Manuel; Sheina, Svetlana; Fintisova, Anna
2013-11-01
We investigated optical damage (surface and bulk) in one of the most promising wide bandgap nonoxide nonlinear crystals, HgGaS, that can be used in ˜1-μm pumped optical parametric oscillators (OPOs) and synchronously pumped OPOs (SPOPOs) for generation of idler pulses above 4 μm without two-photon absorption losses at the pump wavelength. The optical damage has been characterized at the pump wavelength for different repetition rates using uncoated and antireflection-coated (mainly with a single layer for pump and signal wavelengths) samples. HgGaS is the most successful nonlinear crystal (both in terms of output energy and average power) for such OPOs, but optical damage inside the OPO has a lower threshold and represents at present the principal limitation for the achievable output. It is related to peak pulse and not to average intensity, and bulk damage in the form of scattering centers occurs before surface damage. Such bulk damage formation is faster at higher repetition rates. Lower repetition rates increase the lifetime of the crystal but do not solve the problem. The safe pump fluence in extracavity measurements is <1 J/cm2, which corresponds to ˜100 MW/cm2 for the 8-ns pulse duration (both values peak on-axis). In the OPO, however, peak on-axis fluence should not exceed 0.3 J/cm2 limited by the formation of bulk scattering centers in orange-phase HgGaS. In the nanosecond OPO regime, the damage resistivity of Cd-doped HgGaS is higher and that of the almost colorless CdGa2S4 is roughly two times higher, but the latter has no sufficient birefringence for phase-matching. In SPOPOs operating in the ˜100 MHz regime, the damage limitations are related both to the peak pulse and the average intensities, but here HgGaS seems the best nonoxide candidate to obtain first steady-state operation with Yb-based mode-locked laser pump sources.
NASA Astrophysics Data System (ADS)
Luo, Dehai; Cha, Jing; Zhong, Linhao; Dai, Aiguo
2014-05-01
In this paper, a nonlinear multi-scale interaction (NMI) model is used to propose an eddy-blocking matching (EBM) mechanism to account for how synoptic eddies reinforce or suppress a blocking flow. It is shown that the spatial structure of the eddy vorticity forcing (EVF) arising from upstream synoptic eddies determines whether an incipient block can grow into a meandering blocking flow through its interaction with the transient synoptic eddies from the west. Under certain conditions, the EVF exhibits a low-frequency oscillation on timescales of 2-3 weeks. During the EVF phase with a negative-over- positive dipole structure, a blocking event can be resonantly excited through the transport of eddy energy into the incipient block by the EVF. As the EVF changes into an opposite phase, the blocking decays. The NMI model produces life cycles of blocking events that resemble observations. Moreover, it is shown that the eddy north-south straining is a response of the eddies to a dipole- or Ω-type block. In our model, as in observations, two synoptic anticyclones (cyclones) can attract and merge with one another as the blocking intensifies, but only when the feedback of the blocking on the eddies is included. Thus, we attribute the eddy straining and associated vortex interaction to the feedback of the intensified blocking on synoptic eddies. The results illustrate the concomitant nature of the eddy deformation, whose role as a PV source for the blocking flow becomes important only during the mature stage of a block. Our EBM mechanism suggests that an incipient block flow is amplified (or suppressed) under certain conditions by the EVF coming from the upstream of the blocking region.
Contreras, D; Timofeev, I; Steriade, M
1996-01-01
1. To explore the nature of the long-lasting hyperpolarizations that characterize slow oscillations in corticothalamic circuits in vivo, intracellular recordings were obtained under ketamine-xylazine anaesthesia from cortical (Cx) cells of the cat precruciate motor cortex, thalamic reticular (RE) cells from the rostrolateral sector, and thalamocortical (TC) cells from the ventrolateral (VL) nucleus. 2. Measurements in the three cell types showed input resistance (Rin) to be highest during the long-lasting hyperpolarizations that correspond to depth-positive waves of the cortical EEG. Rin was lowest during the early phase of high-amplitude depth-negative EEG waves and increased thereafter until the next cycle of the slow oscillation. 3. Spontaneous long-lasting hyperpolarizations were compared with those evoked by dorsal thalamic stimulation. Voltage versus current (V-I) plots showed similar membrane potential (Vm) ranges and slopes for spontaneous and evoked hyperpolarizations in both Cx and RE cells. V-I plots from TC cells had similar slopes, but Vm during evoked hyperpolarizations was displaced towards more negative values. 4. Intracellular injection of constant hyperpolarizing current in Cx cells increased the amplitude of the initial part of the depolarizing plateau of the slow oscillation, but decreased the amplitude of the last part. 5. These results suggest disfacilitation to be the dominant mechanism in the membrane of cortical and thalamic cells during the spontaneous long-lasting hyperpolarizations, which shape and synchronize slow oscillations in corticothalamic networks. In Cx and RE cells, the same mechanism underlies thalamically evoked long-lasting hyperpolarizations. By contrast, evoked responses in TC cells show a strong additional hyperpolarizing factor. We propose that GABAB processes are stronger in TC than in Cx neurones, thus rendering the thalamus an easier target for absence-type epileptic phenomena through potentiation of thalamic rebound
NASA Astrophysics Data System (ADS)
Sasaki, Minoru; Kumagai, Shinya
2014-03-01
The suspended MEMS structure is suitable for reducing the energy loss due to the thermal conduction. There is the possibility that IR photon energy can be well-controlled to generate some physical effects. A new method bases on the nonlinear oscillation for the detector. The thin film torsional spring exhibits a large hard spring effect when the deflection occurs in the out-of-plane direction of the film. When IR is absorbed, the resonator bends due to the thermal expansion. The torsional spring becomes harder increasing the resonant frequency. The frequency measurement is suited for the precise sensing. The device response is measured using the laser (wavelength of 650nm). The resonant frequency is 88-94kHz. Q factor is about 1600 in vacuum (1Pa). The sensitivity is -0.144[kHz/(kW/m2)]. As for the emitter, nondispersive IR gas sensor is considered. The molecules have their intrinsic absorptions. CO2 absorbs the wavelength 4.2- 4.3μm. The major incandescent light bulbs have the broad spectrum emitting IR which is not used for gas sensing. The wavelength selectivity at the gas bandwidth will improve the efficiency. A new principle uses the microheater placed facing to the grating. SPP is excited carrying IR energy on the grating surface. IR emission is the reverse process of excitation occurring at the output end. The emission spectra show SPP related peak having the width of 190nm. When the input power increases from 0.3 to 1.9W, the peak at wavelength of 3.5μm becomes clearer.
Passive dynamic controllers for non-linear mechanical systems
NASA Technical Reports Server (NTRS)
Juang, Jer-Nan; Wu, Shih-Chin; Phan, Minh; Longman, Richard W.
1992-01-01
The objective is to develop active model-independent controllers for slewing and vibration control of nonlinear multibody flexible systems, including flexible robots. The topics are presented in viewgraph form and include: passive stabilization; work-energy rate principle; Liapunov theory; displacement feedback; dynamic controller; displacement and acceleration feedback; velocity feedback; displacement feedback; physical interaction; a 6-DOF robot; and simulation results.
Methodology for model updating of mechanical components with local nonlinearities
NASA Astrophysics Data System (ADS)
Kurt, Mehmet; Eriten, Melih; McFarland, D. Michael; Bergman, Lawrence A.; Vakakis, Alexander F.
2015-11-01
In this work, we propose a new nonlinear model updating strategy based on global/local nonlinear system identification of the dynamics. The main objective of this study is to construct and update reduced-order models (ROM) of a dynamical system based solely on measured data. The approach relies on analyzing transient system responses (local dynamics) in the frequency-energy domain, and based on these, constructing damped frequency-energy plots - FEPs (global dynamics) under the assumption of weak damping. The system parameters are characterized and updated by matching the backbone branches of the FEPs with reduced-order model FEPs using experimental or computational data. The main advantage of this method is that the system model is updated solely based on simulation and/or experimental results. It follows that the approach is purely data-driven. By matching the frequency-energy dependences of the dynamics of the physical dynamical system and its reduced order model, we are able to identify, update and reconstruct not only the global features of the dynamics in the frequency and energy ranges of interest, but also the local dynamics, i.e., individual time series for specific initial or excitation conditions. Hence, this work paves the way toward a nonlinear model updating methodology with broad applicability. The main features of the proposed methodology are demonstrated with a system of nonlinearly coupled beams excited by a concentrated transient force.
Nicu, Valentin Paul
2016-08-03
Motivated by the renewed interest in the coupled oscillator (CO) model for VCD, in this work a generalised coupled oscillator (GCO) expression is derived by introducing the concept of a coupled oscillator origin. Unlike the standard CO expression, the GCO expression is exact within the harmonic approximation. Using two illustrative example molecules, the theoretical concepts introduced here are demonstrated by performing a GCO decomposition of the rotational strengths computed using DFT. This analysis shows that: (1) the contributions to the rotational strengths that are normally neglected in the standard CO model can be comparable to or larger than the CO contribution, and (2) the GCO mechanism introduced here can affect the VCD intensities of all types of modes in symmetric and asymmetric molecules.
Neuronal mechanisms of the anoxia-induced network oscillations in the rat hippocampus in vitro.
Dzhala, V; Khalilov, I; Ben-Ari, Y; Khazipov, R
2001-10-15
1. A spindle of fast network oscillations precedes the ischaemia-induced rapid depolarisation in the rat hippocampus in vivo. However, this oscillatory pattern could not be reproduced in slices and the underlying mechanisms remain poorly understood. We have found that anoxia-induced network oscillations (ANOs, 20-40 Hz, lasting for 1-2 min) can be reproduced in the intact hippocampi of postnatal day P7-10 rats in vitro, and we have examined the underlying mechanisms using whole-cell and extracellular field potential recordings in a CA3 pyramidal layer. 2. ANOs were generated at the beginning of the anoxic depolarisation, when pyramidal cells depolarised to subthreshold values. Maximal power of the ANOs was attained when pyramidal cells depolarised to -56 mV; depolarisation above -47 mV resulted in a depolarisation block of pyramidal cells and a waning of ANOs. 3. A multiple unit activity in extracellular field recordings was phase locked to the negative and ascending phases of ANOs. Pyramidal cells recorded in current-clamp mode generated action potentials with an average probability of about 0.05 per cycle. The AMPA receptor-mediated EPSCs and the GABA receptor-mediated IPSCs in CA3 pyramidal cells were also phase locked with ANOs. 4. ANOs were prevented by tetrodotoxin and glutamate receptor antagonists CNQX and APV, and were slowed down by the allosteric GABA(A) receptor modulator diazepam. In the presence of the GABA(A) receptor antagonist bicuculline, ANOs were transformed to epileptiform discharges. 5. In the presence of the A1 adenosine receptor antagonist 8-cyclopentyl-1,3-dipropylxanthine (DPCPX), the anoxia induced an epileptiform activity and no ANOs were observed. 6. In normoxic conditions, a rise of extracellular potassium to 10 mM induced an epileptiform activity. Increasing extracellular potassium in conjunction with a bath application of the adenosine A1 receptor agonist cyclopentyladenosine induced oscillations similar to ANOs. 7. Multisite
Neuronal mechanisms of the anoxia-induced network oscillations in the rat hippocampus in vitro
Dzhala, Volodymyr; Khalilov, Ilgam; Ben-Ari, Yehezkiel; Khazipov, Roustem
2001-01-01
A spindle of fast network oscillations precedes the ischaemia-induced rapid depolarisation in the rat hippocampus in vivo. However, this oscillatory pattern could not be reproduced in slices and the underlying mechanisms remain poorly understood. We have found that anoxia-induced network oscillations (ANOs, 20–40 Hz, lasting for 1–2 min) can be reproduced in the intact hippocampi of postnatal day P7–10 rats in vitro, and we have examined the underlying mechanisms using whole-cell and extracellular field potential recordings in a CA3 pyramidal layer.ANOs were generated at the beginning of the anoxic depolarisation, when pyramidal cells depolarised to subthreshold values. Maximal power of the ANOs was attained when pyramidal cells depolarised to −56 mV; depolarisation above −47 mV resulted in a depolarisation block of pyramidal cells and a waning of ANOs.A multiple unit activity in extracellular field recordings was phase locked to the negative and ascending phases of ANOs. Pyramidal cells recorded in current-clamp mode generated action potentials with an average probability of about 0.05 per cycle. The AMPA receptor-mediated EPSCs and the GABA receptor-mediated IPSCs in CA3 pyramidal cells were also phase locked with ANOs.ANOs were prevented by tetrodotoxin and glutamate receptor antagonists CNQX and APV, and were slowed down by the allosteric GABAA receptor modulator diazepam. In the presence of the GABAA receptor antagonist bicuculline, ANOs were transformed to epileptiform discharges.In the presence of the A1 adenosine receptor antagonist 8-cyclopentyl-1,3-dipropylxanthine (DPCPX), the anoxia induced an epileptiform activity and no ANOs were observed.In normoxic conditions, a rise of extracellular potassium to 10 mm induced an epileptiform activity. Increasing extracellular potassium in conjunction with a bath application of the adenosine A1 receptor agonist cyclopentyladenosine induced oscillations similar to ANOs.Multisite recordings along the septo
Statistical mechanics of a discrete Schrödinger equation with saturable nonlinearity.
Samuelsen, Mogens R; Khare, Avinash; Saxena, Avadh; Rasmussen, Kim Ø
2013-04-01
We study the statistical mechanics of the one-dimensional discrete nonlinear Schrödinger (DNLS) equation with saturable nonlinearity. Our study represents an extension of earlier work [Phys. Rev. Lett. 84, 3740 (2000)] regarding the statistical mechanics of the one-dimensional DNLS equation with a cubic nonlinearity. As in this earlier study, we identify the spontaneous creation of localized excitations with a discontinuity in the partition function. The fact that this phenomenon is retained in the saturable DNLS is nontrivial, since in contrast to the cubic DNLS whose nonlinear character is enhanced as the excitation amplitude increases, the saturable DNLS, in fact, becomes increasingly linear as the excitation amplitude increases. We explore the nonlinear dynamics of this phenomenon by direct numerical simulations.
Mayeri, Earl
1973-01-01
Properties of the neural mechanism responsible for generating the periodic burst of spike potentials in the nine ganglion neurons were investigated by applying brief, single shocks to the four small cells with extracellular electrodes placed near the trigger zones of the small cells. The shock elicited a burst if presented during the latter portion of the silent period, terminated a burst during the latter portion of the burst period, and was followed by a newly initiated burst during the early portion of the burst period. The resultant changes in burst and silent period durations were quantitatively described by a second-order non-linear differential equation similar to the van der Pol equation for a relaxation oscillator. The equation also qualitatively described changes in firing threshold of the small cells during the burst cycle. The first derivative of the solution to the equation is similar to slow transmembrane potentials in neurons that are involved in generation of burst activity in other crustacean cardiac ganglia. PMID:19873681
Cazau, Dorian; Adam, Olivier; Aubin, Thierry; Laitman, Jeffrey T.; Reidenberg, Joy S.
2016-01-01
Although mammalian vocalizations are predominantly harmonically structured, they can exhibit an acoustic complexity with nonlinear vocal sounds, including deterministic chaos and frequency jumps. Such sounds are normative events in mammalian vocalizations, and can be directly traceable to the nonlinear nature of vocal-fold dynamics underlying typical mammalian sound production. In this study, we give qualitative descriptions and quantitative analyses of nonlinearities in the song repertoire of humpback whales from the Ste Marie channel (Madagascar) to provide more insight into the potential communication functions and underlying production mechanisms of these features. A low-dimensional biomechanical modeling of the whale’s U-fold (vocal folds homolog) is used to relate specific vocal mechanisms to nonlinear vocal features. Recordings of living humpback whales were searched for occurrences of vocal nonlinearities (instabilities). Temporal distributions of nonlinearities were assessed within sound units, and between different songs. The anatomical production sources of vocal nonlinearities and the communication context of their occurrences in recordings are discussed. Our results show that vocal nonlinearities may be a communication strategy that conveys information about the whale’s body size and physical fitness, and thus may be an important component of humpback whale songs. PMID:27721476
The nonlinear chemo-mechanic coupled dynamics of the F 1 -ATPase molecular motor.
Xu, Lizhong; Liu, Fang
2012-03-01
The ATP synthase consists of two opposing rotary motors, F0 and F1, coupled to each other. When the F1 motor is not coupled to the F0 motor, it can work in the direction hydrolyzing ATP, as a nanomotor called F1-ATPase. It has been reported that the stiffness of the protein varies nonlinearly with increasing load. The nonlinearity has an important effect on the rotating rate of the F1-ATPase. Here, considering the nonlinearity of the γ shaft stiffness for the F1-ATPase, a nonlinear chemo-mechanical coupled dynamic model of F1 motor is proposed. Nonlinear vibration frequencies of the γ shaft and their changes along with the system parameters are investigated. The nonlinear stochastic response of the elastic γ shaft to thermal excitation is analyzed. The results show that the stiffness nonlinearity of the γ shaft causes an increase of the vibration frequency for the F1 motor, which increases the motor's rotation rate. When the concentration of ATP is relatively high and the load torque is small, the effects of the stiffness nonlinearity on the rotating rates of the F1 motor are obvious and should be considered. These results are useful for improving calculation of the rotating rate for the F1 motor and provide insight about the stochastic wave mechanics of F1-ATPase.
NASA Astrophysics Data System (ADS)
Cazau, Dorian; Adam, Olivier; Aubin, Thierry; Laitman, Jeffrey T.; Reidenberg, Joy S.
2016-10-01
Although mammalian vocalizations are predominantly harmonically structured, they can exhibit an acoustic complexity with nonlinear vocal sounds, including deterministic chaos and frequency jumps. Such sounds are normative events in mammalian vocalizations, and can be directly traceable to the nonlinear nature of vocal-fold dynamics underlying typical mammalian sound production. In this study, we give qualitative descriptions and quantitative analyses of nonlinearities in the song repertoire of humpback whales from the Ste Marie channel (Madagascar) to provide more insight into the potential communication functions and underlying production mechanisms of these features. A low-dimensional biomechanical modeling of the whale’s U-fold (vocal folds homolog) is used to relate specific vocal mechanisms to nonlinear vocal features. Recordings of living humpback whales were searched for occurrences of vocal nonlinearities (instabilities). Temporal distributions of nonlinearities were assessed within sound units, and between different songs. The anatomical production sources of vocal nonlinearities and the communication context of their occurrences in recordings are discussed. Our results show that vocal nonlinearities may be a communication strategy that conveys information about the whale’s body size and physical fitness, and thus may be an important component of humpback whale songs.
NASA Astrophysics Data System (ADS)
Mu, Mu; Duan, Wansuo; Wang, Bin
2007-05-01
Most state-of-the-art climate models have difficulty in the prediction of El Niño-Southern Oscillation (ENSO) starting from preboreal spring seasons. The causes of this spring predictability barrier (SPB) remain elusive. With a theoretical ENSO system model, we investigate this controversial issue by tracing the evolution of conditional nonlinear optimal perturbation (CNOP) and by analyzing the behavior of initial error growth. The CNOPs are the errors in the initial states of ENSO events, which have the biggest impact on the uncertainties at the prediction time under proper physical constraints. We show that the evolution of CNOP-type errors associated with El Niño episodes depends remarkably on season with the fastest growth occurring during boreal spring in the onset phase. There also exist other kinds of initial errors, which have either somewhat smaller growth rates or neutral ones during spring. However, for La Niña events, even if initial errors are of CNOP-type, the errors grow without significant seasonal dependence. These findings suggest that the SPB in this model results from combined effects of three factors: the annual cycle of the mean state, the structure of El Niño, and the pattern of the initial errors. On the basis of the error tendency equations derived from the model, we addressed how the combination of the three factors causes the SPB and proposed a mechanism responsible for the error growth in the model ENSO events. Our results help in clarifying the role of the initial error pattern in SPB, which may provide a clue for explaining why SPB can be eliminated by improving initial conditions. The results also illustrate a theoretical basis for improving data assimilation in ENSO prediction.
NASA Astrophysics Data System (ADS)
Molz, F. J.; Faybishenko, B.; Jenkins, E. W.
2012-12-01
Mass and energy fluxes within the soil-plant-atmosphere continuum are highly coupled and inherently nonlinear. The main focus of this presentation is to demonstrate the results of numerical modeling of a system of 4 coupled, nonlinear ordinary differential equations (ODEs), which are used to describe the long-term, rhizosphere processes of soil microbial dynamics, including the competition between nitrogen-fixing bacteria and those unable to fix nitrogen, along with substrate concentration (nutrient supply) and oxygen concentration. Modeling results demonstrate the synchronized patterns of temporal oscillations of competing microbial populations, which are affected by carbon and oxygen concentrations. The temporal dynamics and amplitude of the root exudation process serve as a driving force for microbial and geochemical phenomena, and lead to the development of the Gompetzian dynamics, synchronized oscillations, and phase-space attractors of microbial populations and carbon and oxygen concentrations. The nonlinear dynamic analysis of time series concentrations from the solution of the ODEs was used to identify several types of phase-space attractors, which appear to be dependent on the parameters of the exudation function and Monod kinetic parameters. This phase space analysis was conducted by means of assessing the global and local embedding dimensions, correlation time, capacity and correlation dimensions, and Lyapunov exponents of the calculated model variables defining the phase space. Such results can be used for planning experimental and theoretical studies of biogeochemical processes in the fields of plant nutrition, phyto- and bio-remediation, and other ecological areas.
Physical Mechanism of Photon Pairing in a Kerr Nonlinear Medium
NASA Astrophysics Data System (ADS)
Cheng, Ze
2017-01-01
We establish that Cooper instability of the ground state of a normal blackbody triggers the attractive photons to form the pairs. We next find that however small the effective interphoton attraction V 0 is, Cooper pairs of photon always exist in the ground state of a Kerr nonlinear blackbody. It has been pointed out that there are the three fundamental properties of the Cooper pair of photon: the extremely large binding energy, the extremely small radius, and the extremely high critical temperature. These properties are reflected in the many-photon bound state described by the optical superfluid theory.
NASA Astrophysics Data System (ADS)
Al Hamidi, Yasser; Rakotondrabe, Micky
2016-05-01
This paper deals with the control of a two degrees of freedom (2-DOF) piezoelectric cantilever actuator which is characterized by badly damped oscillations, hysteresis nonlinearity and cross-couplings. First, a feedforward control scheme based on the zero placement technique is introduced to annihilate the oscillations. Then a disturbance observer and a disturbance compensator are introduced to reduce the effects of low frequencies phenomena (hysteresis and creep) which were approximated by a fictive disturbance. Finally an output feedback scheme based on the linear quadratic regulator is added in order to reduce the cross-couplings effects to improve the tracking performances, and eventually to add robustness. Experiments were carried out and confirm the predicted performances.
Beda, Alessandro; Carvalho, Nadja C; Güldner, Andreas; Koch, Thea; de Abreu, Marcelo Gama
2011-08-01
The vast majority of the available literature regarding cardiovascular oscillations refers to spontaneously breathing subjects. Only a few studies investigated cardiovascular oscillations, and especially respiration-related ones (RCVO), during intermittent positive pressure mechanical ventilation (IPPV) under anaesthesia. Only a handful considered assisted IPPV, in which spontaneous breathing activity is supported, rather than replaced as in controlled IPPV. In this paper, we review the current understanding of RCVO physiology during IPPV, from literature retrieved through PubMed website. In particular, we describe how during controlled IPPV under anaesthesia respiratory sinus arrhythmia appears to be generated by non-neural mechano-electric feedback in the heart (indirectly influenced by tonic sympathetic regulation of vascular tone and heart contractility) and not by phasic vagal modulation of central origin and/or baroreflex mechanisms. Furthermore, assisted IPPV differs from controlled IPPV in terms of RCVO, reintroducing significant central respiratory vagal modulation of respiratory sinus arrhythmia. This evidence indicates against applying to IPPV interpretative paradigms of RCVO derived from spontaneously breathing subjects, and against considering together IPPV and spontaneously breathing subjects for RCVO-based risk assessment. Finally, we highlight the opportunities that IPPV offers for future investigations of RCVO genesis and interactions, and we indicate several possibilities for clinical applications of RCVO during IPPV.
A Shock-Driven Mechanism for Standing-Wave Patterns in Vertically Oscillated Grains
NASA Astrophysics Data System (ADS)
Gilman, Alex; Bougie, Jon
2014-11-01
We develop a simplified model for standing-wave pattern formation in vertically oscillated granular layers based on an instability in shocks found in these layers. When layers of particles are oscillated at accelerational amplitudes greater than that of gravity, the layers leave the plate, and shocks are created upon re-established contact with the plate. Additionally, standing-wave patterns form when the accelerational amplitude exceeds a critical value. For a given layer depth and accelerational amplitude, varying driving frequency alters the shock strength as well as pattern wavelength; increasing layer depth produces stronger shocks and longer pattern wavelengths for a given frequency. We demonstrate relationships between properties associated with shocks and properties associated with standing wave patterns, and present a simple mechanism by which a non-uniform shock front drives standing-wave configurations. We justify this mechanism using mathematical relationships derived from a continuum granular model. We then compare these mathematical relationships to full numerical solutions of continuum equations to Navier-Stokes order for uniform, frictionless, inelastic spheres. This research is supported by the Loyola Undergraduate Research Opportunities Program.
Oscillating Permanent Magnets.
ERIC Educational Resources Information Center
Michaelis, M. M.; Haines, C. M.
1989-01-01
Describes several ways to partially levitate permanent magnets. Computes field line geometries and oscillation frequencies. Provides several diagrams illustrating the mechanism of the oscillation. (YP)
NASA Astrophysics Data System (ADS)
Borrielli, A.; Bonaldi, M.; Serra, E.; Bagolini, A.; Boscardin, M.; Cataliotti, F. S.; Marin, F.; Marino, F.; Pontin, A.; Prodi, G. A.
2013-05-01
The interaction of the radiation pressure with micro-mechanical oscillators is earning a growing interest for its wide-range applications (including high sensitivity measurements of force and position) and for fundamental research (entanglement, ponderomotive squeezing, quantum non-demolition measurements). In this contribution we describe the fabrication of a family of opto-mechanical devices specifically designed to ease the detection of ponderomotive squeezing and of entanglement between macroscopic objects and light. These phenomena are not easily observed, due to the overwhelming effects of classical noise sources of thermal origin with respect to the weak quantum fluctuations of the radiation pressure. Therefore, a low thermal noise background is required, together with a weak interaction between the micro-mirror and this background (i.e. high mechanical quality factors). The device should also be capable to manage a relatively large amount of dissipated power at cryogenic temperatures, as the use of a laser with power up to a ten of mW can be useful to enhance radiation pressure effects. In the development of our opto-mechanical devices, we are exploring an approach focused on relatively thick silicon oscillators with high reflectivity coating. The relatively high mass is compensated by the capability to manage high power at low temperatures, owing to a favourable geometric factor (thicker connectors) and the excellent thermal conductivity of silicon crystals at cryogenic temperature. We have measured at cryogenic temperatures mechanical quality factors up to 105 in a micro-oscillator designed to reduce as much as possible the strain in the coating layer and the consequent energy dissipation. This design improves an approach applied in micro-mirror and micro-cantilevers, where the coated surface is reduced as much as possible to improve the quality factor. The deposition of the highly reflective coating layer has been carefully integrated in the
Parametric and nonparametric nonlinear system identification of lung tissue strip mechanics.
Yuan, H; Westwick, D T; Ingenito, E P; Lutchen, K R; Suki, B
1999-01-01
Lung parenchyma is a soft biological material composed of many interacting elements such as the interstitial cells, extracellular collagen-elastin fiber network, and proteoglycan ground substance. The mechanical behavior of this delicate structure is complex showing several mild but distinct types of nonlinearities and a fractal-like long memory stress relaxation characterized by a power-law function. To characterize tissue nonlinearity in the presence of such long memory, we investigated the robustness and predictive ability of several nonlinear system identification techniques on stress-strain data obtained from lung tissue strips with various input wave forms. We found that in general, for a mildly nonlinear system with long memory, a nonparametric nonlinear system identification in the frequency domain is preferred over time-domain techniques. More importantly, if a suitable parametric nonlinear model is available that captures the long memory of the system with only a few parameters, high predictive ability with substantially increased robustness can be achieved. The results provide evidence that the first-order kernel of the stress-strain relationship is consistent with a fractal-type long memory stress relaxation and the nonlinearity can be described as a Wiener-type nonlinear structure for displacements mimicking tidal breathing.
NASA Astrophysics Data System (ADS)
Theocharis, A.; Krokos, G.; Korres, G.
2012-04-01
This work focuses on the interdependence among the Dense Water Formation (DWF) activity in the Adriatic and Aegean Seas (Dense Water source areas), the changes in the characteristic water mass circulation patterns and the salinity oscillations occurring in all basins of the Eastern Mediterranean. We use both numerical model results (1960-2000 hindcast experiment using a 1/10o x 1/10o POM model implemented within the Mediterranean basin) and field observations. Model results reveal that water mass exchanges through the straits of Dense Water (DW) source areas (the Otranto and Cretan Arc Straits respectively), give evidence of DW outflow anticorrelated decadal oscillations, during the simulated 40-year period. This leads to the finding that the Eastern Mediterranean Transient (EMT) event was not a unique phenomenon, although being the strongest, in the study period. The alteration of DWF sites activity is found strongly correlated with periods of increased salinity and temperature over each basin, which present the same decadal variability. Atmospheric forcing analysis has shown that it cannot account for such decadal oscillations although unambiguously plays a key role on DWF processes. On the other hand, the model results show that the change of the Atlantic Water pathway in the Ionian basin and the subsequent modification of the Levantine and/or Cretan Intermediate Water (LIW/CIW) pathways is the main factor for the salinity redistribution in the Eastern Mediterranean, as the observations also revealed for the EMT period. According to the mechanism proposed here, the dense water formation process taking place in an active source area (either the Adriatic or the Aegean) modifies the AW pathway due to lateral advection changes. The increased AW volume received by the active area progressively leads to a long term freshening and subsequent reduction of the DWF intensity. At the same time this process preconditions the inactive area through the corresponding changes
A Quasi-ARX Neural Network with Switching Mechanism to Adaptive Control of Nonlinear Systems
NASA Astrophysics Data System (ADS)
Wang, Lan; Cheng, Yu; Hu, Jinglu
This paper introduces an improved quasi-ARX neural network and discusses its application to adaptive control of nonlinear systems. A switching mechanism is employed to improve the performance of the quasi-ARX neural network prediction model which has linear and nonlinear parts. An adaptive controller for a nonlinear system is established based on the proposed prediction model and some stability analysis of the control system is shown. Simulations are given to show the effectiveness of the proposed method both on stability and accuracy.
A novel class of highly efficient and accurate time-integrators in nonlinear computational mechanics
NASA Astrophysics Data System (ADS)
Wang, Xuechuan; Atluri, Satya N.
2017-01-01
A new class of time-integrators is presented for strongly nonlinear dynamical systems. These algorithms are far superior to the currently common time integrators in computational efficiency and accuracy. These three algorithms are based on a local variational iteration method applied over a finite interval of time. By using Chebyshev polynomials as trial functions and Dirac-Delta functions as the test functions over the finite time interval, the three algorithms are developed into three different discrete time-integrators through the collocation method. These time integrators are labeled as Chebyshev local iterative collocation methods. Through examples of the forced Duffing oscillator, the Lorenz system, and the multiple coupled Duffing equations (which arise as semi-discrete equations for beams, plates and shells undergoing large deformations), it is shown that the new algorithms are far superior to the 4th order Runge-Kutta and ODE45 of MATLAB, in predicting the chaotic responses of strongly nonlinear dynamical systems.
Nonlinear Viscoelastic Mechanics of Cross-linked Rubbers
NASA Technical Reports Server (NTRS)
Freed, Alan D.; Leonov, Arkady I.; Gray, Hugh R. (Technical Monitor)
2002-01-01
The paper develops a general theory for finite rubber viscoelasticity, and specifies it in the form, convenient for solving problems important for rubber, tire and space industries. Based on the quasi-linear approach of non-equilibrium thermodynamics, a general nonlinear theory has been developed for arbitrary nonisothermal deformations of viscoelastic solids. In this theory, the constitutive equations are presented as the sum of known equilibrium (rubber elastic) and non-equilibrium (liquid polymer viscoelastic) terms. These equations are then simplified using several modeling arguments. Stability constraints for the proposed constitutive equations are also discussed. It is shown that only strong ellipticity criteria are applicable for assessing stability of the equations governing viscoelastic solids.
The 1/r1/r singularity in weakly nonlinear fracture mechanics
NASA Astrophysics Data System (ADS)
Bouchbinder, Eran; Livne, Ariel; Fineberg, Jay
2009-09-01
Material failure by crack propagation essentially involves a concentration of large displacement-gradients near a crack's tip, even at scales where no irreversible deformation and energy dissipation occurs. This physical situation provides the motivation for a systematic gradient expansion of general nonlinear elastic constitutive laws that goes beyond the first order displacement-gradient expansion that is the basis for linear elastic fracture mechanics (LEFM). A weakly nonlinear fracture mechanics theory was recently developed by considering displacement-gradients up to second order. The theory predicts that, at scales within a dynamic lengthscale ℓ from a crack's tip, significant logr displacements and 1/r displacement-gradient contributions arise. Whereas in LEFM the 1/r singularity generates an unbalanced force and must be discarded, we show that this singularity not only exists but is also necessary in the weakly nonlinear theory. The theory generates no spurious forces and is consistent with the notion of the autonomy of the near-tip nonlinear region. The J-integral in the weakly nonlinear theory is also shown to be path-independent, taking the same value as the linear elastic J-integral. Thus, the weakly nonlinear theory retains the key tenets of fracture mechanics, while providing excellent quantitative agreement with measurements near the tip of single propagating cracks. As ℓ is consistent with lengthscales that appear in crack tip instabilities, we suggest that this theory may serve as a promising starting point for resolving open questions in fracture dynamics.
Tunable Coupling to a Mechanical Oscillator Circuit Using a Coherent Feedback Network
NASA Astrophysics Data System (ADS)
Kerckhoff, Joseph; Andrews, Reed W.; Ku, H. S.; Kindel, William F.; Cicak, Katarina; Simmonds, Raymond W.; Lehnert, K. W.
2013-04-01
We demonstrate a fully cryogenic microwave feedback network composed of modular superconducting devices connected by transmission lines and designed to control a mechanical oscillator that is coupled to one of the devices. The network features an electromechanical device and a tunable controller that coherently receives, processes, and feeds back continuous microwave signals that modify the dynamics and readout of the mechanical state. While previous electromechanical systems represent some compromise between efficient control and efficient readout of the mechanical state, as set by the electromagnetic decay rate, the tunable controller produces a closed-loop network that can be dynamically and continuously tuned between both extremes much faster than the mechanical response time. We demonstrate that the microwave decay rate may be modulated by at least a factor of 10 at a rate greater than 104 times the mechanical response rate. The system is easy to build and suggests that some useful functions may arise most naturally at the network level of modular, quantum electromagnetic devices.
Norris, G; McConnell, G
2010-03-01
A novel bi-directional pump geometry that nonlinearly increases the nonlinear optical conversion efficiency of a synchronously pumped optical parametric oscillator (OPO) is reported. This bi-directional pumping method synchronizes the circulating signal pulse with two counter-propagating pump pulses within a linear OPO resonator. Through this pump scheme, an increase in nonlinear optical conversion efficiency of 22% was achieved at the signal wavelength, corresponding to a 95% overall increase in average power. Given an almost unchanged measured pulse duration of 260 fs under optimal performance conditions, this related to a signal wavelength peak power output of 18.8 kW, compared with 10 kW using the traditional single-pass geometry. In this study, a total effective peak intensity pump-field of 7.11 GW/cm(2) (corresponding to 3.55 GW/cm(2) from each pump beam) was applied to a 3 mm long periodically poled lithium niobate crystal, which had a damage threshold intensity of 4 GW/cm(2), without impairing crystal integrity. We therefore prove the application of this novel pump geometry provides opportunities for power-scaling of synchronously pumped OPO systems together with enhanced nonlinear conversion efficiency through relaxed damage threshold intensity conditions.
NASA Technical Reports Server (NTRS)
1975-01-01
An engineering model opto-mechanical subsystem for a 10.6-micrometer laser heterodyne receiver is developed, and a CO2 waveguide local oscillator and servo electronics are provided for the receiver. Design goals are presented for the subsystems and overall package design is described. Thermal and mechanical distortion loading tests were performed and the results are included.
Soavi, Giancarlo; Tempra, Iacopo; Pantano, Maria F; Cattoni, Andrea; Collin, Stéphane; Biagioni, Paolo; Pugno, Nicola M; Cerullo, Giulio
2016-02-23
Mechanical vibrational resonances in metal nanoparticles are intensively studied because they provide insight into nanoscale elasticity and for their potential application to ultrasensitive mass detection. In this paper, we use broadband femtosecond pump-probe spectroscopy to study the longitudinal acoustic phonons of arrays of gold nanorods with different aspect ratios, fabricated by electron beam lithography with very high size uniformity. We follow in real time the impulsively excited extensional oscillations of the nanorods by measuring the transient shift of the localized surface plasmon band. Broadband and high-sensitivity detection of the time-dependent extinction spectra enables one to develop a model that quantitatively describes the periodic variation of the plasmon extinction coefficient starting from the steady-state spectrum with only one additional free parameter. This model allows us to retrieve the time-dependent elongation of the nanorods with an ultrahigh sensitivity and to measure oscillation amplitudes of just a few picometers and plasmon energy shifts on the order of 10(-2) meV.
Passive dynamic controllers for non-linear mechanical systems
NASA Technical Reports Server (NTRS)
Juang, Jer-Nan; Wu, Shih-Chin; Phan, Minh; Longman, Richard W.
1991-01-01
A methodology for model-independent controller design for controlling large angular motion of multi-body dynamic systems is outlined.The controlled system may consist of rigid and flexible components that undergo large rigid body motion and small elastic deformations. Control forces/torques are applied to drive the system, and at the same time suppress the vibrations due to flexibility of the components. The proposed controller consists of passive second-order systems which may be designed with little knowledge of the system parameters, even if the controlled system is non-linear. Under rather general assumptions, the passive design assures that the closed loop system has guaranteed stability properties. Unlike positive real controller design, stabilization can be accomplished without direct velocity feedback. In addition, the second-order passive design allows dynamic feedback controllers with considerable freedom to tune for desired system response, and to avoid actuator saturation. After developing the basic mathematical formulation of the design methodology, simulation results are presented to illustrate the proposed approach applied to a flexible six-degree-of-freedom manipulator.
Ultra-fast nonlinear optical properties and photophysical mechanism of a novel pyrene derivative
NASA Astrophysics Data System (ADS)
Zhang, Youwei; Yang, Junyi; Xiao, Zhengguo; Song, Yinglin
2016-10-01
The third-order nonlinear optical properties of 1-(pyrene-1-y1)-3-(3-methylthiophene) acrylic keton named PMTAK was investigated by using Z-scan technique. The light sources for picoseconds(ps) and femtosecond(fs) Z-scan were a mode-locked Nd: YAG laser (21 ps, 532 nm,10 Hz) and an Yb: KGW based fiber laser (190 fs, 515 nm,532 nm, 20 Hz), respectively. In the two cases, reverse saturation absorption(RSA) are observed. The dynamics of the sample's optical nonlinearity is discussed via the femtosecond time-resolved pump probe with phase object at 515nm. We believe that the molecules in excited state of particle population count is caused by two-photon absorption(TPA). The five-level theoretical model is used to analysis the optical nonlinear mechanism. Combining with the result of picosecond Z-scan experiment, a set of optical nonlinear parameters are calculated out. The femtosecond Z-scan experiment is taken to confirm these parameters. The obvious excited-state nonlinearity is found by the set of parameters. The result shows that the sample has good optical nonlinearity which indicates it has potential applications in nonlinear optics field.
2011-07-21
motions. Nayfeh and Mook [4] discuss such techniques, but their applications are mostly limited to single-degree-of-freedom systems. Multiple-degree...second edn., 1986. [4] A. H. Nayfeh and D. T. Mook . Nonlinear Oscillations. John Wiley & Sons, New York, NY, 1979. [5] R. M. Rosenberg. The normal
Nonlinear dynamic mechanism of vocal tremor from voice analysis and model simulations
Zhang, Yu; Jiang, Jack J.
2009-01-01
Nonlinear dynamic analysis and model simulations are used to study the nonlinear dynamic characteristics of vocal folds with vocal tremor, which can typically be characterized by low frequency modulation and aperiodicity. Tremor voices from patients with disorders such as paresis, Parkinson's disease, hyperfunction, and adductor spasmodic dysphonia show low-dimensional characteristics, differing from random noise. Correlation dimension analysis statistically distinguishes tremor voices from normal voices. Furthermore, a nonlinear tremor model is proposed to study the vibrations of the vocal folds with vocal tremor. Fractal dimensions and positive Lyapunov exponents demonstrate the evidence of chaos in the tremor model, where amplitude and frequency play important roles in governing vocal fold dynamics. Nonlinear dynamic voice analysis and vocal fold modeling may provide a useful set of tools for understanding the dynamic mechanism of vocal tremor in patients with laryngeal diseases. PMID:22505778
Nonlinear dynamic mechanism of vocal tremor from voice analysis and model simulations
NASA Astrophysics Data System (ADS)
Zhang, Yu; Jiang, Jack J.
2008-09-01
Nonlinear dynamic analysis and model simulations are used to study the nonlinear dynamic characteristics of vocal folds with vocal tremor, which can typically be characterized by low-frequency modulation and aperiodicity. Tremor voices from patients with disorders such as paresis, Parkinson's disease, hyperfunction, and adductor spasmodic dysphonia show low-dimensional characteristics, differing from random noise. Correlation dimension analysis statistically distinguishes tremor voices from normal voices. Furthermore, a nonlinear tremor model is proposed to study the vibrations of the vocal folds with vocal tremor. Fractal dimensions and positive Lyapunov exponents demonstrate the evidence of chaos in the tremor model, where amplitude and frequency play important roles in governing vocal fold dynamics. Nonlinear dynamic voice analysis and vocal fold modeling may provide a useful set of tools for understanding the dynamic mechanism of vocal tremor in patients with laryngeal diseases.
Thermodynamics and nonlinear mechanics of materials with photoresponsive microstructure
NASA Astrophysics Data System (ADS)
Oates, William S.; Bin, Jonghoon
2014-03-01
The ability to directly convert visible light radiation into useful mechanical work provides many opportunities in the field of smart materials and adaptive structures ranging from biomedical applications to control of heliostat mirrors for solar harvesting. The complexities associated with coupling time-dependent Maxwell's equations with linear momentum and mechanics is discussed by introducing a set of electronic order parameters that govern the coupling between electromagnetic radiation and mechanics of a deformable solid. Numerical examples are given illustrating how this methodology is applied to a special class of liquid crystal polymer networks containing azobenzene. The dynamics associated with light absorption and its effect on deformation of the polymer are solved in three dimensions using finite difference methods and compared to experimental results. Particular emphasis is placed on the effect of polarized light on microstructure evolution and stresses that occur during photoisomerization of the optically active microstructure.
NASA Technical Reports Server (NTRS)
Espinosa, Ismael; Gonzalez, Hortensia; Quiza, Jorge; Gonazalez, J. Jesus; Arroyo, Ruben; Lara, Ritaluz
1995-01-01
Oscillation of electrical activity has been found in many nervous systems, from invertebrates to vertebrates including man. There exists experimental evidence of very simple circuits with the capability of oscillation. Neurons with intrinsic oscillation have been found and also neural circuits where oscillation is a property of the network. These two types of oscillations coexist in many instances. It is nowadays hypothesized that behind synchronization and oscillation there is a system of coupled oscillators responsible for activities that range from locomotion and feature binding in vision to control of sleep and circadian rhythms. The huge knowledge that has been acquired on oscillators from the times of Lord Rayleigh has made the simulation of neural oscillators a very active endeavor. This has been enhanced with more recent physiological findings about small neural circuits by means of intracellular and extracellular recordings as well as imaging methods. The future of this interdisciplinary field looks very promising; some researchers are going into quantum mechanics with the idea of trying to provide a quantum description of the brain. In this work we describe some simulations using neuron models by means of which we form simple neural networks that have the capability of oscillation. We analyze the oscillatory activity with root locus method, cross-correlation histograms, and phase planes. In the more complicated neural network models there is the possibility of chaotic oscillatory activity and we study that by means of Lyapunov exponents. The companion paper shows an example of that kind.
Hervás, C; Toledo, R; Silva, M
2001-01-01
The suitability of pruned computational neural networks (CNNs) for resolving nonlinear multicomponent systems involving synergistic effects by use of oscillating chemical reaction-based methods implemented using the analyte pulse perturbation technique is demonstrated. The CNN input data used for this purpose are estimates provided by the Levenberg-Marquardt method in the form of a three-parameter Gaussian curve associated with the singular profile obtained when the oscillating system is perturbed by an analyte mixture. The performance of the proposed method was assessed by applying it to the resolution of mixtures of pyrogallol and gallic acid based on their perturbating effect on a classical oscillating chemical system, viz. the Belousov-Zhabotinskyi reaction. A straightforward network topology (3:3:2, with 18 connections after pruning) allowed the resolution of mixtures of the two analytes in concentration ratios from 1:7 to 6:2 with a standard error of prediction for the testing set of 4.01 and 8.98% for pyrogallol and gallic acid, respectively. The reduced dimensions of the selected CNN architecture allowed a mathematical transformation of the input vector into the output one that can be easily implemented via software. Finally, the suitability of response surface analysis as an alternative to CNNs was also tested. The results were poor (relative errors were high), which confirms that properly selected pruned CNNs are effective tools for solving the analytical problem addressed in this work.
Wharton, A. M.; Sekar Iyengar, A. N.; Janaki, M. S.
2013-02-15
Hilbert Huang transform (HHT) based time series analysis was carried out on nonlinear floating potential fluctuations obtained from hollow cathode glow discharge plasma in the presence of anode glow. HHT was used to obtain contour plots and the presence of nonlinearity was studied. Frequency shift with time, which is a typical nonlinear behaviour, was detected from the contour plots. Various plasma parameters were measured and the concepts of correlation coefficients and the physical contribution of each intrinsic mode function have been discussed. Physically important quantities such as instantaneous energy and their uses in studying physical phenomena such as intermittency and non-stationary data have also been discussed.
Nicu, Valentin Paul
2016-08-03
Using two illustrative examples it is shown that the generalised coupled oscillator (GCO) mechanism implies that the stability of the VCD sign computed for a given normal mode is not reflected by the magnitude of the ratio ζ between the rotational strength and dipole strength of the respective mode, i.e., the VCD robustness criterium proposed by Góbi and Magyarfalvi. The performed VCD GCO analysis brings further insight into the GCO mechanism and also into the VCD robustness concept. First, it shows that the GCO mechanism can be interpreted as a VCD resonance enhancement mechanism, i.e. very large VCD signals can be observed when the interacting molecular fragments are in favourable orientation. Second, it shows that the uncertainties observed in the computed VCD signs are associated to uncertainties in the relative orientation of the coupled oscillator fragments and/or to uncertainties in the predicted nuclear displacement vectors, i.e. not uncertainties in the computed magnetic dipole transition moments as was originally assumed. Since it is able to identify such situations easily, the VCD GCO analysis can be used as a VCD robustness analysis.
Guerin, Heather Lynch; Elliott, Dawn M
2007-04-01
The annulus fibrosus of the intervertebral disc is comprised of concentric lamella of oriented collagen fibers embedded in a hydrated proteoglycan matrix with smaller amounts of minor collagens, elastin, and small proteoglycans. Its structure and composition enable the disc to withstand complex loads and result in inhomogeneous, anisotropic, and nonlinear mechanical behaviors. The specific contributions of the annulus fibrosus constituent structures to mechanical function remain unclear. Therefore, the objective of this study was to use a structurally motivated, anisotropic, nonlinear strain energy model of annulus fibrosus to determine the relative contributions of its structural components to tissue mechanical behavior. A nonlinear, orthotropic hyperelastic model was developed for the annulus fibrosus. Terms to describe fibers, matrix, and interactions between annulus fibrosus structures (shear and normal to the fiber directions) were explicitly included. The contributions of these structures were analyzed by including or removing terms and determining the effect on the fit to multidimensional experimental data. Correlation between experimental and model-predicted stress, a Bland-Altman analysis of bias and standard deviation of residuals, and the contribution of structural terms to overall tissue stress were calculated. Both shear and normal interaction terms were necessary to accurately model multidimensional behavior. Inclusion of shear interactions more accurately described annulus fibrosus nonlinearity. Fiber stretch and shear interactions dominated contributions to circumferential direction stress, while normal and shear interactions dominated axial stress. The results suggest that interactions between fibers and matrix, perhaps facilitated by crosslinks, elastin, or minor collagens, augment traditional (i.e., fiber-uncrimping) models of nonlinearity.
Alvarado-Rojas, C; Huberfeld, G; Baulac, M; Clemenceau, S; Charpier, S; Miles, R; Menendez de la Prida, L; Le Van Quyen, M
2015-01-01
Transient high-frequency oscillations (150-600 Hz) in local field potential generated by human hippocampal and parahippocampal areas have been related to both physiological and pathological processes. The cellular basis and effects of normal and abnormal forms of high-frequency oscillations (HFO) has been controversial. Here, we searched for HFOs in slices of the subiculum prepared from human hippocampal tissue resected for treatment of pharmacoresistant epilepsy. HFOs occurred spontaneously in extracellular field potentials during interictal discharges (IID) and also during pharmacologically induced preictal discharges (PID) preceding ictal-like events. While most of these events might be considered pathological since they invaded the fast ripple band (>250 Hz), others were spectrally similar to physiological ripples (150-250 Hz). Do similar cellular mechanisms underly IID-ripples and PID-ripples? Are ripple-like oscillations a valid proxy of epileptogenesis in human TLE? With combined intra- or juxta-cellular and extracellular recordings, we showed that, despite overlapping spectral components, ripple-like IID and PID oscillations were associated with different cellular and synaptic mechanisms. IID-ripples were associated with rhythmic GABAergic and glutamatergic synaptic potentials with moderate neuronal firing. In contrast, PID-ripples were associated with depolarizing synaptic inputs frequently reaching the threshold for bursting in most cells. Thus ripple-like oscillations (100-250 Hz) in the human epileptic hippocampus are associated with different mechanisms for synchrony reflecting distinct dynamic changes in inhibition and excitation during interictal and pre-ictal states. PMID:25448920
Hydrodynamic synchronization of flagellar oscillators
NASA Astrophysics Data System (ADS)
Friedrich, Benjamin
2016-11-01
In this review, we highlight the physics of synchronization in collections of beating cilia and flagella. We survey the nonlinear dynamics of synchronization in collections of noisy oscillators. This framework is applied to flagellar synchronization by hydrodynamic interactions. The time-reversibility of hydrodynamics at low Reynolds numbers requires swimming strokes that break time-reversal symmetry to facilitate hydrodynamic synchronization. We discuss different physical mechanisms for flagellar synchronization, which break this symmetry in different ways.
The mechanism and realization of a band-agile coaxial relativistic backward-wave oscillator
Ge, Xingjun; Zhang, Jun; Zhong, Huihuang; Qian, Baoliang; Wang, Haitao
2014-11-03
The mechanism and realization of a band-agile coaxial relativistic backward-wave oscillator (RBWO) are presented. The operation frequency tuning can be easily achieved by merely altering the inner-conductor length. The key effects of the inner-conductor length contributing to the mechanical frequency tunability are investigated theoretically and experimentally. There is a specific inner-conductor length where the operation frequency can jump from one mode to another mode, which belongs to a different operation band. In addition, the operation frequency is tunable within each operation band. During simulation, the L-band microwave with a frequency of 1.61 GHz is radiated when the inner-conductor length is 39 cm. Meanwhile, the S-band microwave with a frequency of 2.32 GHz is radiated when the inner-conductor length is 5 cm. The frequency adjustment bandwidths of L-band and S-band are about 8.5% and 2%, respectively. Moreover, the online mechanical tunability process is described in detail. In the initial experiment, the generated microwave frequencies remain approximately 1.59 GHz and 2.35 GHz when the inner-conductor lengths are 39 cm and 5 cm. In brief, this technical route of the band-agile coaxial RBWO is feasible and provides a guide to design other types of band-agile high power microwaves sources.
The mechanism and realization of a band-agile coaxial relativistic backward-wave oscillator
NASA Astrophysics Data System (ADS)
Ge, Xingjun; Zhang, Jun; Zhong, Huihuang; Qian, Baoliang; Wang, Haitao
2014-11-01
The mechanism and realization of a band-agile coaxial relativistic backward-wave oscillator (RBWO) are presented. The operation frequency tuning can be easily achieved by merely altering the inner-conductor length. The key effects of the inner-conductor length contributing to the mechanical frequency tunability are investigated theoretically and experimentally. There is a specific inner-conductor length where the operation frequency can jump from one mode to another mode, which belongs to a different operation band. In addition, the operation frequency is tunable within each operation band. During simulation, the L-band microwave with a frequency of 1.61 GHz is radiated when the inner-conductor length is 39 cm. Meanwhile, the S-band microwave with a frequency of 2.32 GHz is radiated when the inner-conductor length is 5 cm. The frequency adjustment bandwidths of L-band and S-band are about 8.5% and 2%, respectively. Moreover, the online mechanical tunability process is described in detail. In the initial experiment, the generated microwave frequencies remain approximately 1.59 GHz and 2.35 GHz when the inner-conductor lengths are 39 cm and 5 cm. In brief, this technical route of the band-agile coaxial RBWO is feasible and provides a guide to design other types of band-agile high power microwaves sources.
NASA Astrophysics Data System (ADS)
London, Yosef; Diamandi, Hilel Hagai; Zadok, Avi
2017-04-01
An opto-electronic radio-frequency oscillator that is based on forward scattering by the guided acoustic modes of a standard single-mode optical fiber is proposed and demonstrated. An optical pump wave is used to stimulate narrowband, resonant guided acoustic modes, which introduce phase modulation to a co-propagating optical probe wave. The phase modulation is converted to an intensity signal at the output of a Sagnac interferometer loop. The intensity waveform is detected, amplified, and driven back to modulate the optical pump. Oscillations are achieved at a frequency of 319 MHz, which matches the resonance of the acoustic mode that provides the largest phase modulation of the probe wave. Oscillations at the frequencies of competing acoustic modes are suppressed by at least 40 dB. The linewidth of the acoustic resonance is sufficiently narrow to provide oscillations at a single longitudinal mode of the hybrid cavity. Competing longitudinal modes are suppressed by at least 38 dB as well. Unlike other opto-electronic oscillators, no radio-frequency filtering is required within the hybrid cavity. The frequency of oscillations is entirely determined by the fiber opto-mechanics.
Nonlinear fracture mechanics-based analysis of thin wall cylinders
NASA Technical Reports Server (NTRS)
Brust, Frederick W.; Leis, Brian N.; Forte, Thomas P.
1994-01-01
This paper presents a simple analysis technique to predict the crack initiation, growth, and rupture of large-radius, R, to thickness, t, ratio (thin wall) cylinders. The method is formulated to deal both with stable tearing as well as fatigue mechanisms in applications to both surface and through-wall axial cracks, including interacting surface cracks. The method can also account for time-dependent effects. Validation of the model is provided by comparisons of predictions to more than forty full scale experiments of thin wall cylinders pressurized to failure.
Merton, S. R.; Smedley-Stevenson, R. P.; Pain, C. C.
2012-07-01
This paper describes a Non-Linear Discontinuous Petrov-Galerkin method and its application to the one-speed Boltzmann Transport Equation (BTE) for space-time problems. The purpose of the method is to remove unwanted oscillations in the transport solution which occur in the vicinity of sharp flux gradients, while improving computational efficiency and numerical accuracy. This is achieved by applying artificial dissipation in the solution gradient direction, internal to an element using a novel finite element (FE) Riemann approach. The added dissipation is calculated at each node of the finite element mesh based on local behaviour of the transport solution on both the spatial and temporal axes of the problem. Thus a different dissipation is used in different elements. The magnitude of dissipation that is used is obtained from a gradient-informed scaling of the advection velocities in the stabilisation term. This makes the method in its most general form non-linear. The method is implemented within a very general finite element Riemann framework. This makes it completely independent of choice of angular basis function allowing one to use different descriptions of the angular variation. Results show the non-linear scheme performs consistently well in demanding time-dependent multi-dimensional neutron transport problems. (authors)
NASA Astrophysics Data System (ADS)
Aerts, J. R. M.; Dirckx, J. J. J.; Pintelon, R.
2008-06-01
Recently, a measurement set-up was presented to detect small nonlinear distortions in the vibration of acoustically driven mechanical systems. A speaker generates a specially designed multisine excitation signal that drives the vibration of a test object. The generated sound pressure is measured with a probe microphone in front of the test object, and an heterodyne vibrometer measures the corresponding vibration. Due to the high degree of linearity of the heterodyne technique, very small nonlinear distortions can be detected. In this paper the set-up is used to verify whether small nonlinear distortions are present in the vibration of the middle ear system, which is classically considered to be a completely linear system. In vitro measurements on the right ear of an adult male gerbil proved that nonlinear distortions are present in the vibration of the tympanic membrane. Similar results were seen in measurements on the left ear. The influence of post-mortem changes on the nonlinear behaviour of the middle ear was verified in a number of successive measurements. These indicated that the nonlinear behaviour of the middle ear decreases in time.
Quantum dynamics of a macroscopic magnet operating as an environment of a mechanical oscillator
NASA Astrophysics Data System (ADS)
Foti, C.; Cuccoli, A.; Verrucchi, P.
2016-12-01
We study the dynamics of a bipartite quantum system in a way such that its formal description keeps holding even if one of its parts becomes macroscopic; the problem is related to the analysis of the quantum-to-classical crossover, but our approach implies that the whole system stays genuinely quantum. The aim of the work is to understand (1) if, (2) to what extent, and possibly (3) how the evolution of a macroscopic environment testifies to the coupling with its microscopic quantum companion. To this purpose we consider a magnetic environment made of a large number of spin-1/2 particles, coupled with a quantum mechanical oscillator, possibly in the presence of an external magnetic field. We take the value of the total environmental spin S constant and large, which allows us to consider the environment as one single macroscopic system, and further deal with the hurdles of the spin-algebra via approximations that are valid in the large-S limit. We find an insightful expression for the propagator of the whole system, where we identify an effective "back-action" term, i.e., an operator acting on the magnetic environment only, and yet missing in the absence of the quantum principal system. This operator emerges as a time-dependent magnetic anisotropy whose character, whether uniaxial or planar, also depends on the detuning between the frequency of the oscillator and the level splitting in the spectrum of the free magnetic system, induced by the possible presence of the external field. The time dependence of the anisotropy is analyzed, and its effects on the dynamics of the magnet, as well as its relation to the entangling evolution of the overall system, are discussed.
Weinberg's nonlinear quantum mechanics and the Einstein-Podolsky-Rosen paradox
NASA Technical Reports Server (NTRS)
Polchinski, Joseph
1991-01-01
The constraints imposed on observables by the requirement that transmission not occur in the Einstein-Podolsky-Rosen (EPR) experiment are determined, leading to a different treatment of separated systems from that originally proposed by Weinberg (1989). It is found that forbidding EPR communication in nonlinear quantum mechanics necessarily leads to another sort of unusual communication: that between different branches of the wave function.
Nonlinear vibrational excitations in molecular crystals molecular mechanics calculations
NASA Astrophysics Data System (ADS)
Pumilia, P.; Abbate, S.; Baldini, G.; Ferro, D. R.; Tubino, R.
1992-03-01
The coupling constant for vibrational solitons χ has been examined in a molecular mechanics model for acetanilide (ACN) molecular crystal. According to A.C. Scott, solitons can form and propagate in solid acetanilide over a threshold energy value. This can be regarded as a structural model for the spines of hydrogen bond chains stabilizing the α helical structure of proteins. A one dimensional hydrogen bond chain of ACN has been built, for which we have found that, even though experimental parameters are correctly predicted, the excessive rigidity of the isolated chain prevents the formation of a localized distortion around the excitation. Yet, C=O coupling value with softer lattice modes could be rather high, allowing self-trapping to take place.
Nonlinear viscoelastic characterization of polymer materials using a dynamic-mechanical methodology
NASA Technical Reports Server (NTRS)
Strganac, Thomas W.; Payne, Debbie Flowers; Biskup, Bruce A.; Letton, Alan
1995-01-01
Polymer materials retrieved from LDEF exhibit nonlinear constitutive behavior; thus the authors present a method to characterize nonlinear viscoelastic behavior using measurements from dynamic (oscillatory) mechanical tests. Frequency-derived measurements are transformed into time-domain properties providing the capability to predict long term material performance without a lengthy experimentation program. Results are presented for thin-film high-performance polymer materials used in the fabrication of high-altitude scientific balloons. Predictions based upon a linear test and analysis approach are shown to deteriorate for moderate to high stress levels expected for extended applications. Tests verify that nonlinear viscoelastic response is induced by large stresses. Hence, an approach is developed in which the stress-dependent behavior is examined in a manner analogous to modeling temperature-dependent behavior with time-temperature correspondence and superposition principles. The development leads to time-stress correspondence and superposition of measurements obtained through dynamic mechanical tests. Predictions of material behavior using measurements based upon linear and nonlinear approaches are compared with experimental results obtained from traditional creep tests. Excellent agreement is shown for the nonlinear model.
Mechanism and function of mixed-mode oscillations in vibrissa motoneurons.
Golomb, David
2014-01-01
Vibrissa motoneurons in the facial nucleus innervate the intrinsic and extrinsic muscles that move the whiskers. Their intrinsic properties affect the way they process fast synaptic input from the vIRT and Bötzinger nuclei together with serotonergic neuromodulation. In response to constant current (I(app)) injection, vibrissa motoneurons may respond with mixed mode oscillations (MMOs), in which sub-threshold oscillations (STOs) are intermittently mixed with spikes. This study investigates the mechanisms involved in generating MMOs in vibrissa motoneurons and their function in motor control. It presents a conductance-based model that includes the M-type K+ conductance, g(M), the persistent Na+ conductance, g(NaP), and the cationic h conductance, g(h). For g(h) = 0 and moderate values of g(M) and g(NaP), the model neuron generates STOs, but not MMOs, in response to I(app) injection. STOs transform abruptly to tonic spiking as the current increases. In addition to STOs, MMOs are generated for g(h)>0 for larger values of I(app); the I(app) range in which MMOs appear increases linearly with g(h). In the MMOs regime, the firing rate increases with I(app) like a Devil's staircase. Stochastic noise disrupts the temporal structure of the MMOs, but for a moderate noise level, the coefficient of variation (CV) is much less than one and varies non-monotonically with I(app). Furthermore, the estimated time period between voltage peaks, based on Bernoulli process statistics, is much higher in the MMOs regime than in the tonic regime. These two phenomena do not appear when moderate noise generates MMOs without an intrinsic MMO mechanism. Therefore, and since STOs do not appear in spinal motoneurons, the analysis can be used to differentiate different MMOs mechanisms. MMO firing activity in vibrissa motoneurons suggests a scenario in which moderate periodic inputs from the vIRT and Bötzinger nuclei control whisking frequency, whereas serotonergic neuromodulation controls
Digiuni, Simona; Berne-Dedieu, Annik; Martinez-Torres, Cristina; Szecsi, Judit; Bendahmane, Mohammed; Arneodo, Alain; Argoul, Françoise
2015-05-05
Individual plant cells are rather complex mechanical objects. Despite the fact that their wall mechanical strength may be weakened by comparison with their original tissue template, they nevertheless retain some generic properties of the mother tissue, namely the viscoelasticity and the shape of their walls, which are driven by their internal hydrostatic turgor pressure. This viscoelastic behavior, which affects the power-law response of these cells when indented by an atomic force cantilever with a pyramidal tip, is also very sensitive to the culture media. To our knowledge, we develop here an original analyzing method, based on a multiscale decomposition of force-indentation curves, that reveals and quantifies for the first time the nonlinearity of the mechanical response of living single plant cells upon mechanical deformation. Further comparing the nonlinear strain responses of these isolated cells in three different media, we reveal an alteration of their linear bending elastic regime in both hyper- and hypotonic conditions.
An L-band transit-time oscillator with mechanical frequency tunability
NASA Astrophysics Data System (ADS)
Song, Lili; He, Juntao; Ling, Junpu; Cao, Yibing
2017-02-01
An L-band coaxial Transit-time Oscillator (TTO) with mechanical frequency tunability is introduced in this paper. Particle-in-cell simulations have been done. The output power efficiency has been improved at least 20% under a 10.2 GW input power and with a tunable range from 1.57 GHz to 1.90 GHz by modulating the outer conductor. It is worth to note that the efficiency can reach as high as 41% at 1.75 GHz. The mechanical engineering method is also detailed in this work. The frequency tuning range of the coaxial TTO is 22.6% of the central frequency. On the other hand, the frequency can be tuned from 1.6 GHz to 1.85 GHz by modulating the inner conductor. The author highlights a hollow structure of the L-band coaxial TTO which can work from 1.03 GHz to 1.31 GHz via modulating the outer conductor in the rest of the article. The frequency tuning range of the hollow TTO is 21.4% of the central frequency. More importantly, the hollow TTO can be easily achieved after the inner conductor is removed from the coaxial TTO. The electric field distributions of the coaxial and hollow TTOs are analyzed, resulting in that the longitudinal and transverse working modes are TM01 and π mode, respectively. The same working mode from these two structures implies the stability of the TTOs mentioned above.
NASA Astrophysics Data System (ADS)
Conti, Livia; De Gregorio, Paolo; Bonaldi, Michele; Borrielli, Antonio; Crivellari, Michele; Karapetyan, Gagik; Poli, Charles; Serra, Enrico; Thakur, Ram-Krishna; Rondoni, Lamberto
2012-06-01
We study experimentally, numerically, and theoretically the elastic response of mechanical resonators along which the temperature is not uniform, as a consequence of the onset of steady-state thermal gradients. Two experimental setups and designs are employed, both using low-loss materials. In both cases, we monitor the resonance frequencies of specific modes of vibration, as they vary along with variations of temperatures and of temperature differences. In one case, we consider the first longitudinal mode of vibration of an aluminum alloy resonator; in the other case, we consider the antisymmetric torsion modes of a silicon resonator. By defining the average temperature as the volume-weighted mean of the temperatures of the respective elastic sections, we find out that the elastic response of an object depends solely on it, regardless of whether a thermal gradient exists and, up to 10% imbalance, regardless of its magnitude. The numerical model employs a chain of anharmonic oscillators, with first- and second-neighbor interactions and temperature profiles satisfying Fourier's Law to a good degree. Its analysis confirms, for the most part, the experimental findings and it is explained theoretically from a statistical mechanics perspective with a loose notion of local equilibrium.
NASA Astrophysics Data System (ADS)
Phillipson-Nichols, Rebecca A.; Boyd, Patricia T.; Smale, Alan P.
2015-01-01
4U 1705-44 is a bright low mass x-ray binary (LMXB) containing a neutron star and a close, low mass companion. The Rossi X-ray Timing Explorer (RXTE) All-Sky Monitor obtained approximately 14 years of daily monitoring on 4U 1705-44 in the 2-20 keV energy range. Understanding the x-ray variability of 4U1705-44 is critical to the study of all low mass x-ray binaries because they share many of the same global characteristics in their high-amplitude transitions and non-periodic variability. After comparing the longterm light curve and phase space trajectories of 4U1705-44 to various nonlinear oscillators, the Duffing Oscillator was revealed to be a strong candidate to describe these systems. The parameters of the Duffing equation were optimized and six solutions sharing the same characteristics as 4U1705-44 were found. Striking commonalities were revealed via a phase-space analysis of both 4U1705-44 and the six Duffing solutions: the low-order driving period is no less than 87 days and spans up to 180 days, which is seenand highlighted in the power spectra, zero-crossings and close returns analysis of4U1705-44. Furthermore, the driving frequency of all six Duffing solutions tend toconverge to a range of 3.6 - 4.5, corresponding to driving periods in the range from 130 to 175 days, in agreement with that found in 4U1705-44. Nonlinear analysis methods such as close returns and zero-crossings of the Duffing solutions also show the same trends. This strongly suggests that 4U1705-44 shares the same topological characteristics as the Duffing equation. With further analysis, we hope to develop a model to explain why 4U1705-44 shares the unique topology of the Duffing Oscillator specifically, rather than those of other families of nonlinear differential equations.
A brief review on nonlinear modeling methods and applications of compliant mechanisms
NASA Astrophysics Data System (ADS)
Hao, Guangbo; Yu, Jingjun; Li, Haiyang
2016-06-01
Compliant mechanisms (CMs) have become one of the most popular research themes in mechanisms and robotics because of their merits. This paper aims to provide a brief systematic review on the advances of nonlinear static modeling approaches and the applications of CMs to promote interdisciplinary/multidisciplinary development for associated theories and other new applications. It also predicts likely future directions of applications and theory development.
NASA Astrophysics Data System (ADS)
Senthil, S.; Pari, S.; Joseph, Ginson P.; Sagayaraj, P.; Madhavan, J.
2009-08-01
Optically transparent semiorganic nonlinear optical bulk single crystal of L-ornithine monohydrochloride (LOMHCL) of dimension 11×3×2 mm 3 has been grown from its aqueous solution by slow solvent evaporation technique. The grown crystal was characterized by powder X-ray diffraction to confirm the crystal structure. Investigation has been carried out to assign the vibrational frequencies of the grown crystals by Fourier transform infrared spectroscopy technique. Thermal behavior of the grown crystals was studied by thermogravimetric analysis. The second harmonic generation (SHG) efficiency of LOMHCL was determined by Kurtz and Perry powder technique. The optical absorption study confirms the suitability of the crystal for device applications. The mechanical properties of the grown crystals have been studied using Vickers microhardness tester. Dielectric and photoconductivity studies are also carried out for the grown samples.
Solving Nonlinear Solid Mechanics Problems with the Jacobian-Free Newton Krylov Method
J. D. Hales; S. R. Novascone; R. L. Williamson; D. R. Gaston; M. R. Tonks
2012-06-01
The solution of the equations governing solid mechanics is often obtained via Newton's method. This approach can be problematic if the determination, storage, or solution cost associated with the Jacobian is high. These challenges are magnified for multiphysics applications with many coupled variables. Jacobian-free Newton-Krylov (JFNK) methods avoid many of the difficulties associated with the Jacobian by using a finite difference approximation. BISON is a parallel, object-oriented, nonlinear solid mechanics and multiphysics application that leverages JFNK methods. We overview JFNK, outline the capabilities of BISON, and demonstrate the effectiveness of JFNK for solid mechanics and solid mechanics coupled to other PDEs using a series of demonstration problems.
Nonlinear Analysis and Optimal Design of Dynamic Mechanical Systems for Spacecraft Application.
1987-09-01
links were considered flexible, and thus a S-.quasi- static (linear) finite element analysis was used to obtain deformations and stresses. The GRG...Alga ൴ NONLINEAR ANALYSIS AMD OPTINALfDSIGN OFDYNAMIC l’ MECHANICAL SYSTEMS FOR SPACECRAFT APPLICATION(U) CLARKSON_ NIV POTSDAM NY K D MILINERT ET...TEST CHART .’.. Nŕ. :4. St 0 0 0 0 0 0 0 0 0 0 0 5 0. 6 0." UJEILL cony Io RIALFinal Report AFOSR 84-0076 * DE7H Nonlinear Analysis and Optimal
Li, Hancao; Haddad, Wassim M.
2012-01-01
We develop optimal respiratory airflow patterns using a nonlinear multicompartment model for a lung mechanics system. Specifically, we use classical calculus of variations minimization techniques to derive an optimal airflow pattern for inspiratory and expiratory breathing cycles. The physiological interpretation of the optimality criteria used involves the minimization of work of breathing and lung volume acceleration for the inspiratory phase, and the minimization of the elastic potential energy and rapid airflow rate changes for the expiratory phase. Finally, we numerically integrate the resulting nonlinear two-point boundary value problems to determine the optimal airflow patterns over the inspiratory and expiratory breathing cycles. PMID:22719793
Li, Hancao; Haddad, Wassim M
2012-01-01
We develop optimal respiratory airflow patterns using a nonlinear multicompartment model for a lung mechanics system. Specifically, we use classical calculus of variations minimization techniques to derive an optimal airflow pattern for inspiratory and expiratory breathing cycles. The physiological interpretation of the optimality criteria used involves the minimization of work of breathing and lung volume acceleration for the inspiratory phase, and the minimization of the elastic potential energy and rapid airflow rate changes for the expiratory phase. Finally, we numerically integrate the resulting nonlinear two-point boundary value problems to determine the optimal airflow patterns over the inspiratory and expiratory breathing cycles.
Fano resonances in the nonlinear optical response of coupled plasmonic nanostructures.
Butet, Jérémy; Martin, Olivier J F
2014-12-01
The coupling between metallic nanostructures is a common and easy way to control the optical properties of plasmonic systems. Even though the coupling between plasmonic oscillators has been widely studied in the linear regime, its influence on the nonlinear optical response of metallic nanostructures has been sparsely considered. Using a surface integral equation method, we investigate the second order nonlinear optical response of plasmonic metamolecules supporting Fano resonances revealing that the typical lineshape of Fano resonances is also clearly observable in the nonlinear regime. The physical mechanisms leading to nonlinear Fano resonances are revealed by the coupled oscillator model and the symmetry subgroup decomposition. It is found that the origin of the nonlinear scattered wave, i. e. the active plasmonic oscillator, can be selectively chosen. Furthermore, interferences between nonlinear emissions are clearly observed in specific configurations. The results presented in this article pave the way for the design of efficient nonlinear plasmonic metamolecules with controlled nonlinear radiation.
A novel auto-tuning PID control mechanism for nonlinear systems.
Cetin, Meric; Iplikci, Serdar
2015-09-01
In this paper, a novel Runge-Kutta (RK) discretization-based model-predictive auto-tuning proportional-integral-derivative controller (RK-PID) is introduced for the control of continuous-time nonlinear systems. The parameters of the PID controller are tuned using RK model of the system through prediction error-square minimization where the predicted information of tracking error provides an enhanced tuning of the parameters. Based on the model-predictive control (MPC) approach, the proposed mechanism provides necessary PID parameter adaptations while generating additive correction terms to assist the initially inadequate PID controller. Efficiency of the proposed mechanism has been tested on two experimental real-time systems: an unstable single-input single-output (SISO) nonlinear magnetic-levitation system and a nonlinear multi-input multi-output (MIMO) liquid-level system. RK-PID has been compared to standard PID, standard nonlinear MPC (NMPC), RK-MPC and conventional sliding-mode control (SMC) methods in terms of control performance, robustness, computational complexity and design issue. The proposed mechanism exhibits acceptable tuning and control performance with very small steady-state tracking errors, and provides very short settling time for parameter convergence.
Mechanisms underlying very-low-frequency RR-interval oscillations in humans
NASA Technical Reports Server (NTRS)
Taylor, J. A.; Carr, D. L.; Myers, C. W.; Eckberg, D. L.
1998-01-01
BACKGROUND: Survival of post-myocardial infarction patients is related inversely to their levels of very-low-frequency (0.003 to 0.03 Hz) RR-interval variability. The physiological basis for such oscillations is unclear. In our study, we used blocking drugs to evaluate potential contributions of sympathetic and vagal mechanisms and the renin-angiotensin-aldosterone system to very-low-frequency RR-interval variability in 10 young healthy subjects. METHODS AND RESULTS: We recorded RR intervals and arterial pressures during three separate sessions, with the patient in supine and 40 degree upright tilt positions, during 20-minute frequency (0.25 Hz) and tidal volume-controlled breathing after intravenous injections: saline (control), atenolol (0.2 mg/kg, beta-adrenergic blockade), atropine sulfate (0.04 mg/kg, parasympathetic blockade), atenolol and atropine (complete autonomic blockade), and enalaprilat (0.02 mg/kg, ACE blockade). We integrated fast Fourier transform RR-interval spectral power at very low (0.003 to 0.03 Hz), low (0.05 to 0. 15 Hz), and respiratory (0.2 to 0.3 Hz) frequencies. Beta-adrenergic blockade had no significant effect on very-low- or low-frequency RR-interval power but increased respiratory frequency power 2-fold. ACE blockade had no significant effect on low or respiratory frequency RR-interval power but modestly (approximately 21%) increased very-low-frequency power in the supine (but not upright tilt) position (P<0.05). The most profound effects were exerted by parasympathetic blockade: Atropine, given alone or with atenolol, abolished nearly all RR-interval variability and decreased very-low-frequency variability by 92%. CONCLUSIONS: Although very-low-frequency heart period rhythms are influenced by the renin-angiotensin-aldosterone system, as low and respiratory frequency RR-interval rhythms, they depend primarily on the presence of parasympathetic outflow. Therefore the prognostic value of very-low-frequency heart period oscillations may
NASA Astrophysics Data System (ADS)
Aul'chenko, S. M.; Zamuraev, V. P.; Kalinina, A. P.
2014-05-01
The present work is devoted to a criterial analysis and mathematical modeling of the influence of forced oscillations of surface elements of a wing airfoil on the shock-wave structure of transonic flow past it. Parameters that govern the regimes of interaction of the oscillatory motion of airfoil sections with the breakdown compression shock have been established. The qualitative and quantitative influence of these parameters on the wave resistance of the airfoil has been investigated.
Mechanisms of gamma oscillations in the hippocampus of the behaving rat.
Csicsvari, Jozsef; Jamieson, Brian; Wise, Kensall D; Buzsáki, György
2003-01-23
Gamma frequency oscillations (30-100 Hz) have been suggested to underlie various cognitive and motor functions. Here, we examine the generation of gamma oscillation currents in the hippocampus, using two-dimensional, 96-site silicon probes. Two gamma generators were identified, one in the dentate gyrus and another in the CA3-CA1 regions. The coupling strength between the two oscillators varied during both theta and nontheta states. Both pyramidal cells and interneurons were phase-locked to gamma waves. Anatomical connectivity, rather than physical distance, determined the coupling strength of the oscillating neurons. CA3 pyramidal neurons discharged CA3 and CA1 interneurons at latencies indicative of monosynaptic connections. Intrahippocampal gamma oscillation emerges in the CA3 recurrent system, which entrains the CA1 region via its interneurons.
Introduction of a co-resonant detection concept for mechanical oscillation-based sensors.
Reiche, Christopher F; Körner, Julia; Büchner, Bernd; Mühl, Thomas
2015-08-21
Micro- and nanoelectromechanical oscillators driven at or close to their resonance frequency are used as sensors in many fields of science and technology. A decrease in the oscillator's effective spring constant and/or mass holds great potential for an increase in the sensor's sensitivity. This is usually accompanied by a reduction in spatial dimensions, which in most cases requires more complex detection methods. By analyzing the complex behavior of a simple asymmetric coupled harmonic oscillator model we propose a novel sensor concept which combines the advantages of bigger and smaller oscillators, i.e. ease of detection and high sensitivity. The concept is based on matching the resonance frequencies of two otherwise very different oscillators. To support our theoretical considerations, we present an experimental implementation of such a sensor and respective experimental data, verifying a substantial signal enhancement by several orders of magnitude.
Bezaire, Marianne J; Raikov, Ivan; Burk, Kelly; Vyas, Dhrumil; Soltesz, Ivan
2016-12-23
The hippocampal theta rhythm plays important roles in information processing; however, the mechanisms of its generation are not well understood. We developed a data-driven, supercomputer-based, full-scale (1:1) model of the rodent CA1 area and studied its interneurons during theta oscillations. Theta rhythm with phase-locked gamma oscillations and phase-preferential discharges of distinct interneuronal types spontaneously emerged from the isolated CA1 circuit without rhythmic inputs. Perturbation experiments identified parvalbumin-expressing interneurons and neurogliaform cells, as well as interneuronal diversity itself, as important factors in theta generation. These simulations reveal new insights into the spatiotemporal organization of the CA1 circuit during theta oscillations.
Bezaire, Marianne J; Raikov, Ivan; Burk, Kelly; Vyas, Dhrumil; Soltesz, Ivan
2016-01-01
The hippocampal theta rhythm plays important roles in information processing; however, the mechanisms of its generation are not well understood. We developed a data-driven, supercomputer-based, full-scale (1:1) model of the rodent CA1 area and studied its interneurons during theta oscillations. Theta rhythm with phase-locked gamma oscillations and phase-preferential discharges of distinct interneuronal types spontaneously emerged from the isolated CA1 circuit without rhythmic inputs. Perturbation experiments identified parvalbumin-expressing interneurons and neurogliaform cells, as well as interneuronal diversity itself, as important factors in theta generation. These simulations reveal new insights into the spatiotemporal organization of the CA1 circuit during theta oscillations. DOI: http://dx.doi.org/10.7554/eLife.18566.001 PMID:28009257
SEACAS Theory Manuals: Part III. Finite Element Analysis in Nonlinear Solid Mechanics
Laursen, T.A.; Attaway, S.W.; Zadoks, R.I.
1999-03-01
This report outlines the application of finite element methodology to large deformation solid mechanics problems, detailing also some of the key technological issues that effective finite element formulations must address. The presentation is organized into three major portions: first, a discussion of finite element discretization from the global point of view, emphasizing the relationship between a virtual work principle and the associated fully discrete system, second, a discussion of finite element technology, emphasizing the important theoretical and practical features associated with an individual finite element; and third, detailed description of specific elements that enjoy widespread use, providing some examples of the theoretical ideas already described. Descriptions of problem formulation in nonlinear solid mechanics, nonlinear continuum mechanics, and constitutive modeling are given in three companion reports.
Nonlinear mechanical response of the extracellular matrix: learning from articular cartilage
NASA Astrophysics Data System (ADS)
Kearns, Sarah; Das, Moumita
2015-03-01
We study the mechanical structure-function relations in the extracellular matrix (ECM) with focus on nonlinear shear and compression response. As a model system, our study focuses on the ECM in articular cartilage tissue which has two major mechanobiological components: a network of the biopolymer collagen that acts as a stiff, reinforcing matrix, and a flexible aggrecan network that facilitates deformability. We model this system as a double network hydrogel made of interpenetrating networks of stiff and flexible biopolymers respectively. We study the linear and nonlinear mechanical response of the model ECM to shear and compression forces using a combination of rigidity percolation theory and energy minimization approaches. Our results may provide useful insights into the design principles of the ECM as well as biomimetic hydrogels that are mechanically robust and can, at the same time, easily adapt to cues in their surroundings.
Cheng, Yu; Muroski, Megan E; Petit, Dorothée C M C; Mansell, Rhodri; Vemulkar, Tarun; Morshed, Ramin A; Han, Yu; Balyasnikova, Irina V; Horbinski, Craig M; Huang, Xinlei; Zhang, Lingjiao; Cowburn, Russell P; Lesniak, Maciej S
2016-02-10
Magnetic particles that can be precisely controlled under a magnetic field and transduce energy from the applied field open the way for innovative cancer treatment. Although these particles represent an area of active development for drug delivery and magnetic hyperthermia, the in vivo anti-tumor effect under a low-frequency magnetic field using magnetic particles has not yet been demonstrated. To-date, induced cancer cell death via the oscillation of nanoparticles under a low-frequency magnetic field has only been observed in vitro. In this report, we demonstrate the successful use of spin-vortex, disk-shaped permalloy magnetic particles in a low-frequency, rotating magnetic field for the in vitro and in vivo destruction of glioma cells. The internalized nanomagnets align themselves to the plane of the rotating magnetic field, creating a strong mechanical force which damages the cancer cell structure inducing programmed cell death. In vivo, the magnetic field treatment successfully reduces brain tumor size and increases the survival rate of mice bearing intracranial glioma xenografts, without adverse side effects. This study demonstrates a novel approach of controlling magnetic particles for treating malignant glioma that should be applicable to treat a wide range of cancers.
Proposed Mechanism for Shock-Driven Stripe Patterns in Vertically Oscillated Granular Systems
NASA Astrophysics Data System (ADS)
Gilman, Alex; Moertl, Stefanie; Bougie, Jon
2013-11-01
We investigate vertically shaken granular systems using numerical solutions of continuum equations to Navier-Stokes order for uniform, frictionless, inelastic spheres. When layers of particles are oscillated at accelerational amplitudes greater than that of gravity, the layers leave the plate, and shocks are created upon re-established contact with the plate. Additionally, standing-wave patterns form when the accelerational amplitude exceeds a critical value. We demonstrate relationships between properties associated with shocks and properties associated with standing wave patterns, and propose a mechanism by which a non-uniform shock front drives standing-wave configurations. For a given layer depth and accelerational amplitude, varying driving frequency alters the shock strength as well as pattern wavelength; increasing layer depth produces stronger shocks and longer wavelengths for a given frequency. We use non-dimensional versions of the Navier-Stokes equations to mathematically derive relationships between these variables. We compare these mathematical relationships to those found empirically through simulations conducted at various layer depths and frequencies. This research is supported by the Loyola Undergraduate Research Opportunities Program.
NASA Astrophysics Data System (ADS)
Pérez-Molina, Manuel; Pérez-Polo, Manuel F.
2014-10-01
This paper analyzes a controlled servomechanism with feedback and a cubic nonlinearity by means of the Bogdanov-Takens and Andronov-Poincaré-Hopf bifurcations, from which steady-state, self-oscillating and chaotic behaviors will be investigated using the center manifold theorem. The system controller is formed by a Proportional plus Integral plus Derivative action (PID) that allows to stabilize and drive to a prescribed set point a body connected to the shaft of a DC motor. The Bogdanov-Takens bifurcation is analyzed through the second Lyapunov stability method and the harmonic-balance method, whereas the first Lyapunov value is used for the Andronov-Poincaré-Hopf bifurcation. On the basis of the results deduced from the bifurcation analysis, we show a procedure to select the parameters of the PID controller so that an arbitrary steady-state position of the servomechanism can be reached even in presence of noise. We also show how chaotic behavior can be obtained by applying a harmonical external torque to the device in self-oscillating regime. The advantage of achieving chaotic behavior is that it can be used so that the system reaches a set point inside a strange attractor with a small control effort. The analytical calculations have been verified through detailed numerical simulations.
Bossé, Dominick; Beaulieu, Alexandre; Avoine, Olivier; Micheau, Philippe; Praud, Jean-Paul; Walti, Hervé
2010-08-01
This study aimed to implement low-frequency forced oscillation technique (LFFOT) in neonatal total liquid ventilation (TLV) and to provide the first insight into respiratory impedance under this new modality of ventilation. Thirteen newborn lambs, weighing 2.5 + or - 0.4 kg (mean + or - SD), were premedicated, intubated, anesthetized, and then placed under TLV using a specially design liquid ventilator and a perfluorocarbon. The respiratory mechanics measurements protocol was started immediately after TLV initiation. Three blocks of measurements were first performed: one during initial respiratory system adaptation to TLV, followed by two other series during steady-state conditions. Lambs were then divided into two groups before undergoing another three blocks of measurements: the first group received a 10-min intravenous infusion of salbutamol (1.5 microg x kg(-1) x min(-1)) after continuous infusion of methacholine (9 microg x kg(-1) x min(-1)), while the second group of lambs was chest strapped. Respiratory impedance was measured using serial single-frequency tests at frequencies ranging between 0.05 and 2 Hz and then fitted with a constant-phase model. Harmonic test signals of 0.2 Hz were also launched every 10 min throughout the measurement protocol. Airway resistance and inertance were starkly increased in TLV compared with gas ventilation, with a resonant frequency < or = 1.2 Hz. Resistance of 0.2 Hz and reactance were sensitive to bronchoconstriction and dilation, as well as during compliance reduction. We report successful implementation of LFFOT to neonatal TLV and present the first insight into respiratory impedance under this new modality of ventilation. We show that LFFOT is an effective tool to track respiratory mechanics under TLV.
Structural basis for the nonlinear mechanics of fibrin networks under compression
Kim, Oleg V.; Litvinov, Rustem I.; Weisel, John W.; Alber, Mark S.
2014-01-01
Fibrin is a protein polymer that forms a 3D filamentous network, a major structural component of protective physiological blood clots as well as life threatening pathological thrombi. It plays an important role in wound healing, tissue regeneration and is widely employed in surgery as a sealant and in tissue engineering as a scaffold. The goal of this study was to establish correlations between structural changes and mechanical responses of fibrin networks exposed to compressive loads. Rheological measurements revealed nonlinear changes of fibrin network viscoelastic properties under dynamic compression, resulting in network softening followed by its dramatic hardening. Repeated compression/decompression enhanced fibrin clot stiffening. Combining fibrin network rheology with simultaneous confocal microscopy provided direct evidence of structural modulations underlying nonlinear viscoelasticity of compressed fibrin networks. Fibrin clot softening in response to compression strongly correlated with fiber buckling and bending, while hardening was associated with fibrin network densification. Our results suggest a complex interplay of entropic and enthalpic mechanisms accompanying structural changes and accounting for the nonlinear mechanical response in fibrin networks undergoing compressive deformations. These findings provide new insight into the fibrin clot structural mechanics and can be useful for designing fibrin-based biomaterials with modulated viscoelastic properties. PMID:24840618
Structural basis for the nonlinear mechanics of fibrin networks under compression.
Kim, Oleg V; Litvinov, Rustem I; Weisel, John W; Alber, Mark S
2014-08-01
Fibrin is a protein polymer that forms a 3D filamentous network, a major structural component of protective physiological blood clots as well as life threatening pathological thrombi. It plays an important role in wound healing, tissue regeneration and is widely employed in surgery as a sealant and in tissue engineering as a scaffold. The goal of this study was to establish correlations between structural changes and mechanical responses of fibrin networks exposed to compressive loads. Rheological measurements revealed nonlinear changes of fibrin network viscoelastic properties under dynamic compression, resulting in network softening followed by its dramatic hardening. Repeated compression/decompression enhanced fibrin clot stiffening. Combining fibrin network rheology with simultaneous confocal microscopy provided direct evidence of structural modulations underlying nonlinear viscoelasticity of compressed fibrin networks. Fibrin clot softening in response to compression strongly correlated with fiber buckling and bending, while hardening was associated with fibrin network densification. Our results suggest a complex interplay of entropic and enthalpic mechanisms accompanying structural changes and accounting for the nonlinear mechanical response in fibrin networks undergoing compressive deformations. These findings provide new insight into the fibrin clot structural mechanics and can be useful for designing fibrin-based biomaterials with modulated viscoelastic properties.
NASA Astrophysics Data System (ADS)
Yasumura, Kevin Youl
In 1986 the atomic force microscope (AFM) was invented by Binnig, Quate, and Gerber. Cantilever based force microscopy has been used in a wide range of fields including the study of biological samples, data storage media, and microelectronics. These AFM-based imaging techniques typically measure forces in the piconewton (10-12 N) range. Recent developments in microcantilever fabrication and optical fiber displacement sensors have allowed for the construction of force microscope systems that are capable of measuring forces in the attonewton (10-18 N) range. Applications such as magnetic resonance force microscopy (MRFM) require the cantilevers used to have subattonewton force resolution in order to eventually detect single nuclear spins. It is believed that improvements in cantilever and experimental design will allow for improved force resolution. A fundamental limit to the detection of small forces is thermomechanical noise. The thermal noise force limit, via the fluctuation dissipation theorem, is directly related to the amount of mechanical energy dissipation in the cantilever-based force sensor. Work has therefore been focused on developing an understanding of which mechanisms are limiting the force resolution of these microcantilever oscillators. Arrays of silicon nitride, single-crystal silicon, and polysilicon cantilevers have been fabricated and studied. By measuring the dependence of Q on cantilever material, geometry, and surface treatments, significant insight into the dissipation mechanisms has been obtained. For submicron thick cantilevers, Q is found to decrease with decreasing cantilever thickness, indicative of surface loss mechanisms. For single-crystal silicon cantilevers, significant increase in room temperature Q is obtained after 700 C heat treatment in either N 2 or forming gas. Thermoelastic dissipation is not a factor for submicron thick cantilevers, but is shown to be significant for silicon nitride cantilevers as thin as 2.3 um. At low
Resolving the mystery of milliwatt-threshold opto-mechanical self-oscillation in dual-nanoweb fiber
NASA Astrophysics Data System (ADS)
Koehler, J. R.; Noskov, R. E.; Sukhorukov, A. A.; Butsch, A.; Novoa, D.; Russell, P. St. J.
2016-08-01
It is interesting to pose the question: How best to design an optomechanical device, with no electronics, optical cavity, or laser gain, that will self-oscillate when pumped in a single pass with only a few mW of single-frequency laser power? One might begin with a mechanically resonant and highly compliant system offering very high optomechanical gain. Such a system, when pumped by single-frequency light, might self-oscillate at its resonant frequency. It is well-known, however, that this will occur only if the group velocity dispersion of the light is high enough so that phonons causing pump-to-Stokes conversion are sufficiently dissimilar to those causing pump-to-anti-Stokes conversion. Recently it was reported that two light-guiding membranes 20 μm wide, ˜500 nm thick and spaced by ˜500 nm, suspended inside a glass fiber capillary, oscillated spontaneously at its mechanical resonant frequency (˜6 MHz) when pumped with only a few mW of single-frequency light. This was surprising, since perfect Raman gain suppression would be expected. In detailed measurements, using an interferometric side-probing technique capable of resolving nanoweb movements as small as 10 pm, we map out the vibrations along the fiber and show that stimulated intermodal scattering to a higher-order optical mode frustrates gain suppression, permitting the structure to self-oscillate. A detailed theoretical analysis confirms this picture. This novel mechanism makes possible the design of single-pass optomechanical oscillators that require only a few mW of optical power, no electronics nor any optical resonator. The design could also be implemented in silicon or any other suitable material.
Nonlinear damping in mechanical resonators made from carbon nanotubes and graphene
NASA Astrophysics Data System (ADS)
Eichler, A.; Moser, J.; Chaste, J.; Zdrojek, M.; Wilson-Rae, I.; Bachtold, A.
2011-06-01
The theory of damping is discussed in Newton's Principia and has been tested in objects as diverse as the Foucault pendulum, the mirrors in gravitational-wave detectors and submicrometre mechanical resonators. In general, the damping observed in these systems can be described by a linear damping force. Advances in nanofabrication mean that it is now possible to explore damping in systems with one or more atomic-scale dimensions. Here we study the damping of mechanical resonators based on carbon nanotubes and graphene sheets. The damping is found to strongly depend on the amplitude of motion, and can be described by a nonlinear rather than a linear damping force. We exploit the nonlinear nature of damping in these systems to improve the figures of merit for both nanotube and graphene resonators. For instance, we achieve a quality factor of 100,000 for a graphene resonator.
Nonlinear damping in mechanical resonators made from carbon nanotubes and graphene.
Eichler, A; Moser, J; Chaste, J; Zdrojek, M; Wilson-Rae, I; Bachtold, A
2011-05-15
The theory of damping is discussed in Newton's Principia and has been tested in objects as diverse as the Foucault pendulum, the mirrors in gravitational-wave detectors and submicrometre mechanical resonators. In general, the damping observed in these systems can be described by a linear damping force. Advances in nanofabrication mean that it is now possible to explore damping in systems with one or more atomic-scale dimensions. Here we study the damping of mechanical resonators based on carbon nanotubes and graphene sheets. The damping is found to strongly depend on the amplitude of motion, and can be described by a nonlinear rather than a linear damping force. We exploit the nonlinear nature of damping in these systems to improve the figures of merit for both nanotube and graphene resonators. For instance, we achieve a quality factor of 100,000 for a graphene resonator.
Identification of Nonlinear Micron-Level Mechanics for a Precision Deployable Joint
NASA Technical Reports Server (NTRS)
Bullock, S. J.; Peterson, L. D.
1994-01-01
The experimental identification of micron-level nonlinear joint mechanics and dynamics for a pin-clevis joint used in a precision, adaptive, deployable space structure are investigated. The force-state mapping method is used to identify the behavior of the joint under a preload. The results of applying a single tension-compression cycle to the joint under a tensile preload are presented. The observed micron-level behavior is highly nonlinear and involves all six rigid body motion degrees-of-freedom of the joint. it is also suggests that at micron levels of motion modelling of the joint mechanics and dynamics must include the interactions between all internal components, such as the pin, bushings, and the joint node.
Sciascia, Luciana; Lombardo, Renato; Turco Liveri, Maria Liria
2007-02-15
The response of the Belousov-Zhabotinsy (BZ) system to the addition of increasing amounts of the anionic surfactant sodium dodecyl sulfate (SDS) was monitored at 25.0 degrees C in stirred batch conditions. The presence of SDS in the reaction mixture influences the oscillatory parameters, i.e., induction period and oscillation period, to an extent that depends on the surfactant concentration. The experimental results have shown that the induction period increases slightly on increasing surfactant concentration and, then, a further increase in the [SDS] leads to an enhancement while the oscillation period increases monotonously on increasing SDS concentration. It has been proposed that the response of the oscillatory BZ system to the addition of SDS is due to the peculiar capability of the organized surfactant assemblies to affect the reactivity by selectively sequestering some key reacting species. Indeed, explanations of the experimental results have been given on the basis of the role played by the micellar shape, which in turn dictates the hydrophobic nature. The suggested perturbation effects have been supported by performing viscosity measurements on the aqueous SDS solutions and by the spectrophotometric estimation of the binding constant of the bromine species to the micellar aggregates. This study has indirectly corroborated the existence of two kind of micelles and unambiguously revealed that the bromine species show a different affinity toward the spherical and rod-like micelles.
NASA Astrophysics Data System (ADS)
Devi, T. Uma; Prabha, A. Josephine; Meenakshi, R.; Kalpana, G.; Dilip, C. Surendra
2017-02-01
The FTIR and UV spectroscopic analysis have been carried out on guanidinium phthalate (GUP) crystal, an organic nonlinear optical material. The spectra are interpreted with the aid of normal coordinate analysis following structure optimizations and force field calculations based on density functional theory (DFT). The thermogravimetric (TG) and differential thermal analysis (DTA) ensures the thermal stability of the compound. Vickers microhardness values reveals the mechanical strength of the crystal.
NASA Astrophysics Data System (ADS)
Chen, Chun-Wei; Khoo, Iam Choon; Zhao, Shuo; Lin, Tsung-Hsien; Ho, Tsung-Jui
2015-10-01
We have investigated the mechanisms responsible for nonlinear optical processes occurring in azobenzene-doped blue phase liquid crystals (BPLC), which exhibit two thermodynamically stable BPs: BPI and BPII. In coherent two wave-mixing experiments, a slow (minutes) and a fast (few milliseconds) side diffractions are observed. The underlying mechanisms were disclosed by monitoring the dynamics of grating formation and relaxation as well as by some supplementary experiments. We found the photothermal indexing and dye/LC intermolecular torque leading to lattice distortion to be the dominant mechanisms for the observed nonlinear response in BPLC. Moreover, the response time of the nonlinear optical process varied with operating phase. The rise time of the thermal indexing process was in good agreement with our findings on the temperature dependence of BP refractive index: τ(ISO) > τ(BPI) > τ(BPII). The relaxation time of the torque-induced lattice distortion was analogue to its electrostriction counterpart: τ'(BPI) > τ'(BPII). In a separate experiment, lattice swelling with selective reflection of <110> direction changed from green to red was also observed. This was attributable to the isomerization-induced change in cholesteric pitch, which directly affects the lattice spacing. The phenomenon was confirmed by measuring the optical rotatory power of the BPLC.
In, Visarath; Longhini, Patrick; Kho, Andy; Neff, Joseph D; Leung, Daniel; Liu, Norman; Meadows, Brian K; Gordon, Frank; Bulsara, Adi R; Palacios, Antonio
2012-12-01
The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz.
Huang, X.R.; Peng, Ru-Wen
2010-03-15
Interactions between light and conducting microstructures or nanostructures can result in a variety of novel phenomena, but their underlying mechanisms have not been completely understood. From calculations of surface charge density waves on conducting gratings and by comparing them with classical surface plasmons, we revealed a general yet concrete picture regarding the coupling of light to free electron oscillation on structured conducting surfaces that can lead to oscillating subwavelength charge patterns (i.e., structured surface plasmons). New wavelets emitted from these light sources then destructively interfere to form evanescent waves. This principle, usually combined with other mechanisms, is mainly a geometrical effect that can be universally involved in light scattering from all periodic and non-periodic structures containing free electrons. This picture may provide clear guidelines for developing conductor-based nano-optical devices.
Tankanag, A V; Tikhonova, I V; Chemeris, N K
2008-03-01
Study of peripheral microhaemodynamics was carried out with laser Doppler flowmetry in healthy volunteers of different age groups. The ageing changes in the state of the skin peripheral blood flow, in the functioning of separate links and regulatory systems ofmicrovascular bed have been estimated in terms of relative entropy and fractal dimension values. The revealed significant age-dependent decrease of relative entropy values in the respiratory rhythm ranges, the neurogenic and myogenic activities yielded some evidence concerning the reduction of the microcirculation system chaotic changes within these frequency ranges during the ageing. The significant increase of fractal dimension values in the ranges of cardio-rhythm and the endothelial activity in the oldest group with the mean age of 77 years indicated that the structural complexity of the oscillations in these frequency ranges increased during ageing.
NASA Astrophysics Data System (ADS)
Astakhov, Sergey; Astakhov, Oleg; Astakhov, Vladimir; Kurths, Jürgen
2016-06-01
In this paper, the bifurcational mechanism of frequency entrainment in a van der Pol oscillator coupled with an additional oscillatory circuit is studied. It is shown that bistability observed in the system is based on two bifurcations: a supercritical Andronov-Hopf bifurcation and a sub-critical Neimark-Sacker bifurcation. The attracting basin boundaries are determined by stable and unstable invariant manifolds of a saddle two-dimensional torus.
Nonlinearity of a Voltage-Gated Potassium Channel Revealed by the Mechanical Susceptibility
NASA Astrophysics Data System (ADS)
Ariyaratne, Amila; Zocchi, Giovanni
2013-01-01
The voltage-gated potassium channel from Aeropyrum pernix operates by coupling the voltage-driven motion of a charged group of amino acids to the opening and closing of the pore. In this experiment, we drive this charged group with an ac field and observe the effect on the gating. The measurements for different frequencies and amplitudes of the forcing reveal an essential nonlinearity in the mechanical behavior of the molecule. Within a continuum-mechanics description, we extract the effective dissipation parameter γ for this conformational motion and find γ≈0.2g/s, similar to recent nanorheology measurements on the conformational motion of an enzyme.
Quantum mechanical treatment of parametric amplification in an absorptive nonlinear medium
NASA Astrophysics Data System (ADS)
Inoue, K.
2017-01-01
Generally, loss phenomena are known to affect the quantum properties of a light wave. This paper describes a quantum mechanical treatment of parametric amplification in an absorptive nonlinear medium. An expression of the quantum mechanical field operator in such a physical system is presented based on the Heisenberg equation, using which the quantum properties of traveling light suffering from medium absorption are quantitatively evaluated. Calculations using the obtained operator indicate that some degradation of noise performance is caused by the absorption. The influence of the absorption on the squeezing performance in phase-sensitive parametric amplification is also evaluated.
Gupta, Rahul Kumar; Shi, Qiongfeng; Dhakar, Lokesh; Wang, Tao; Heng, Chun Huat; Lee, Chengkuo
2017-01-25
Over the years, several approaches have been devised to widen the operating bandwidth, but most of them can only be triggered at high accelerations. In this work, we investigate a broadband energy harvester based on combination of non-linear stiffening effect and multimodal energy harvesting to obtain high bandwidth over wide range of accelerations (0.1 g-2.0 g). In order to achieve broadband behavior, a polymer based spring exhibiting multimodal energy harvesting is used. Besides, non-linear stiffening effect is introduced by using mechanical stoppers. At low accelerations (<0.5 g), the nearby mode frequencies of polymer spring contribute to broadening characteristics, while proof mass engages with mechanical stoppers to introduce broadening by non-linear stiffening at higher accelerations. The electromagnetic mechanism is employed in this design to enhance its output at low accelerations when triboelectric output is negligible. Our device displays bandwidth of 40 Hz even at low acceleration of 0.1 g and it is increased up to 68 Hz at 2 g. When non-linear stiffening is used along with multimodal energy-harvesting, the obtained bandwidth increases from 23 Hz to 68 Hz with percentage increment of 295% at 1.8 g. Further, we have demonstrated the triboelectric output measured as acceleration sensing signals in terms of voltage and current sensitivity of 4.7 Vg(-1) and 19.7 nAg(-1), respectively.
NASA Astrophysics Data System (ADS)
Gupta, Rahul Kumar; Shi, Qiongfeng; Dhakar, Lokesh; Wang, Tao; Heng, Chun Huat; Lee, Chengkuo
2017-01-01
Over the years, several approaches have been devised to widen the operating bandwidth, but most of them can only be triggered at high accelerations. In this work, we investigate a broadband energy harvester based on combination of non-linear stiffening effect and multimodal energy harvesting to obtain high bandwidth over wide range of accelerations (0.1 g–2.0 g). In order to achieve broadband behavior, a polymer based spring exhibiting multimodal energy harvesting is used. Besides, non-linear stiffening effect is introduced by using mechanical stoppers. At low accelerations (<0.5 g), the nearby mode frequencies of polymer spring contribute to broadening characteristics, while proof mass engages with mechanical stoppers to introduce broadening by non-linear stiffening at higher accelerations. The electromagnetic mechanism is employed in this design to enhance its output at low accelerations when triboelectric output is negligible. Our device displays bandwidth of 40 Hz even at low acceleration of 0.1 g and it is increased up to 68 Hz at 2 g. When non-linear stiffening is used along with multimodal energy-harvesting, the obtained bandwidth increases from 23 Hz to 68 Hz with percentage increment of 295% at 1.8 g. Further, we have demonstrated the triboelectric output measured as acceleration sensing signals in terms of voltage and current sensitivity of 4.7 Vg‑1 and 19.7 nAg‑1, respectively.