Single-ion nonlinear mechanical oscillator
Akerman, N.; Kotler, S.; Glickman, Y.; Dallal, Y.; Keselman, A.; Ozeri, R.
2010-12-15
We study the steady-state motion of a single trapped ion oscillator driven to the nonlinear regime. Damping is achieved via Doppler laser cooling. The ion motion is found to be well described by the Duffing oscillator model with an additional nonlinear damping term. We demonstrate here the unique ability of tuning both the linear as well as the nonlinear damping coefficients by controlling the laser-cooling parameters. Our observations pave the way for the investigation of nonlinear dynamics on the quantum-to-classical interface as well as mechanical noise squeezing in laser-cooling dynamics.
Single-ion nonlinear mechanical oscillator
NASA Astrophysics Data System (ADS)
Akerman, N.; Kotler, S.; Glickman, Y.; Dallal, Y.; Keselman, A.; Ozeri, R.
2010-12-01
We study the steady-state motion of a single trapped ion oscillator driven to the nonlinear regime. Damping is achieved via Doppler laser cooling. The ion motion is found to be well described by the Duffing oscillator model with an additional nonlinear damping term. We demonstrate here the unique ability of tuning both the linear as well as the nonlinear damping coefficients by controlling the laser-cooling parameters. Our observations pave the way for the investigation of nonlinear dynamics on the quantum-to-classical interface as well as mechanical noise squeezing in laser-cooling dynamics.
Linear and nonlinear oscilations in Classical Mechanics
NASA Astrophysics Data System (ADS)
Cruz, Enrique; Martinez, Juan L.; Camacho, Edgar
1997-04-01
The theory of small oscilations is very important in many areas of physics and others sciences due to the simple form of the equations and the easy interpretetion of the results. In this work we show three examples of mechanical systems and using the Lagrangian formulation, we study the linear regime making approaches to the Lagrange's equations, and for the analysis of the nonlinear behavior of the systems we use the Hamiltonian formulation, we use the program MATHEMATICA for the whole analysis. MATHEMATICA is useful because many students can approach to the analysis and simulations using modern tools like the simbolic and numerical computacional packages.
A single ion anharmonic mechanical oscillator with nonlinear dissipation
NASA Astrophysics Data System (ADS)
Akerman, Nitzan; Kotler, Shlomi; Glickman, Yinnon; Keselman, Anna; Dallal, Yehonatan; Ozeri, Roee
2010-03-01
A driven, damped, nearly harmonic oscillator with a small cubic term in the force, is known as the Duffing oscillator. The Duffing oscillator shows various interesting features of non-linear response such as bistability and hysteresis. Several features of the Duffing instability have been recently measured using superconducting qubits and nano-mechanical resonators. Linear Paul traps can be well approximated as harmonic but have a small an-harmonicity due to their deviation from an ideal quadruple geometry. We study the steady state motion of a single trapped Sr^+ ion, subject to a near-resonance drive and dissipation in a linear Paul trap with a small anharmonicity. The driving force is applied by an oscillating voltage on the trap end-caps. Dissipation is the result of laser Doppler cooling. We measure both the amplitude and phase of the driven oscillations and find a good agreement with the Duffing oscillator model. When the cooling laser is close to resonance the standard Duffing model has to be extended to account for non-linearity in the dissipative force. Both the linear and the nonlinear terms of the dissipative force for various cooling laser detunings are determined by the line-shape of the - cooling transition and the cooling laser intensity and can therefore be conveniently controlled.
Tomlin, R.
1990-01-27
A nonlinear oscillator design was imported from Cornell modified, and built for the purpose of simulating the chaotic states of a forced pendulum. Similar circuits have been investigated in the recent nonlinear explosion.
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)
Johnson, Sarah; Edmonds, Terrence
Micro-electro-mechanical systems or MEMS are used in a variety of today's technology and can be modeled using equations for nonlinear damped harmonic oscillators. Mathematical expressions have been formulated to determine resonance frequency shifts as a result of hardening and softening effects in MEMS devices. In this work we experimentally test the previous theoretical analysis of MEMS resonance frequency shifts in the nonlinear regime. Devices were put under low pressure at room temperature and swept through a range of frequencies with varying AC and DC excitation voltages to detect shifts in the resonant frequency. The MEMS device studied in this work exhibits a dominating spring softening effect due to the device's physical make-up. The softening effect becomes very dominant as the AC excitation is increased and the frequency shift of the resonance peak becomes quite significant at these larger excitations. Hardening effects are heavily dependent on mechanical factors that make up the MEMS devices. But they are not present in these MEMS devices. I will present our results along with the theoretical analysis of the Duffing oscillator model. This work was supported by NSF grant DMR-1461019 (REU) and DMR-1205891 (YL).
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.
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.
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. PMID:27250151
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.
Accurate Energy Spectrum for the Quantum Yang-Mills Mechanics with Nonlinear Color Oscillations
NASA Astrophysics Data System (ADS)
Pedram, Pouria
2015-01-01
Yang-Mills theory as the foundation for quantum chromodynamics is a non-Abelian gauge theory with self-interactions between vector particles. Here, we study the Yang-Mills Hamiltonian with nonlinear color oscillations in the absence of external sources corresponding to the group SU(2). In the quantum domain, we diagonalize the Hamiltonian using the optimized trigonometric basis expansion method and find accurate energy eigenvalues and eigenfunctions for one and two degrees of freedom. We also compare our results with the semiclassical solutions.
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…
Mobius Strip underlying Nonlinear Oscillators
NASA Astrophysics Data System (ADS)
Lopaz, Edaurdo; Satija, Indubala
2004-03-01
Geometrical and topolgocial aspects of phase space orbits of driven nonlinear oscillators are shown to share many features with the circuits on the mobius strips. Most important characteristic shared by nonlinear oscillators and the mobius strip is the first order geometrical phase transition characterized in terms of local variable torsion and the global variable the geometrical phase . These geometrical transitions are geometrical resonances and lead to geometrical localization that underlie not only limit cycles but also the strange attractors.
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…
Nonlinear oscillations in marine hydroids
NASA Astrophysics Data System (ADS)
Venslauskas, Mindaugas S.; Asmantas, Sarunas
2003-06-01
Irregular oscillations in a colony of marine hydroids Podocoryne carnea were investigated. Quantitative characteristics were obtained as a result of long term (10-12 h) monitoring of oscillations at arbitrary sites. The sliding window spectra as well as the pulse-to-pulse dynamics argue the transient chaotic behavior of hydroid colony. The significant change of amplitudes and frequencies in intact colony oscillations after feeding and long sustained oscillations of stolons separated from colony suggest that the irregular activity could be determined by the network of pacemakers residing in stolon wall cells. These are influenced mechanically by the amount of digesting food and/or by chemical action of nutrients inside the stolon lumen. The possible correlation of these oscillations which can evoke Ca2+ waves in stolon wall cells is discussed.
Nonlinear oscillations of coalescing magnetic flux ropes.
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. PMID:27300993
Palevicius, Paulius; Ragulskis, Minvydas; Palevicius, Arvydas; Ostasevicius, Vytautas
2014-01-21
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.
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
A simple approach to nonlinear oscillators
NASA Astrophysics Data System (ADS)
Ren, Zhong-Fu; He, Ji-Huan
2009-10-01
A very simple and effective approach to nonlinear oscillators is suggested. Anyone with basic knowledge of advanced calculus can apply the method to finding approximately the amplitude-frequency relationship of a nonlinear oscillator. Some examples are given to illustrate its extremely simple solution procedure and an acceptable accuracy of the obtained solutions.
Nonlinear electron oscillations in a warm plasma
Sarkar, Anwesa; Maity, Chandan; Chakrabarti, Nikhil
2013-12-15
A class of nonstationary solutions for the nonlinear electron oscillations of a warm plasma are presented using a Lagrangian fluid description. The solution illustrates the nonlinear steepening of an initial Gaussian electron density disturbance and also shows collapse behavior in time. The obtained solution may indicate a class of nonlinear transient structures in an unmagnetized warm plasma.
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.
Entangled mechanical oscillators.
Jost, J D; Home, J P; Amini, J M; Hanneke, D; Ozeri, R; Langer, C; Bollinger, J J; Leibfried, D; Wineland, D J
2009-06-01
Hallmarks of quantum mechanics include superposition and entanglement. In the context of large complex systems, these features should lead to situations as envisaged in the 'Schrödinger's cat' thought experiment (where the cat exists in a superposition of alive and dead states entangled with a radioactive nucleus). Such situations are not observed in nature. This may be simply due to our inability to sufficiently isolate the system of interest from the surrounding environment-a technical limitation. Another possibility is some as-yet-undiscovered mechanism that prevents the formation of macroscopic entangled states. Such a limitation might depend on the number of elementary constituents in the system or on the types of degrees of freedom that are entangled. Tests of the latter possibility have been made with photons, atoms and condensed matter devices. One system ubiquitous to nature where entanglement has not been previously demonstrated consists of distinct mechanical oscillators. Here we demonstrate deterministic entanglement of separated mechanical oscillators, consisting of the vibrational states of two pairs of atomic ions held in different locations. We also demonstrate entanglement of the internal states of an atomic ion with a distant mechanical oscillator. These results show quantum entanglement in a degree of freedom that pervades the classical world. Such experiments may lead to the generation of entangled states of larger-scale mechanical oscillators, and offer possibilities for testing non-locality with mesoscopic systems. In addition, the control developed here is an important ingredient for scaling-up quantum information processing with trapped atomic ions.
Nonlinear radial oscillations of neutron stars
Gabler, Michael; Sperhake, Ulrich; Andersson, Nils
2009-09-15
The effects of nonlinear oscillations in compact stars are attracting considerable current interest. In order to study such phenomena in the framework of fully nonlinear general relativity, highly accurate numerical studies are required. A numerical scheme specifically tailored for such a study is based on formulating the time evolution in terms of deviations from a stationary equilibrium configuration. Using this technique, we investigate over a wide range of amplitudes nonlinear effects in the evolution of radial oscillations of neutron stars. In particular, we discuss mode coupling due to nonlinear interaction, the occurrence of resonance phenomena, shock formation near the stellar surface as well as the capacity of nonlinearities to stabilize perturbatively unstable neutron star models.
Harvesting vibration energy using nonlinear oscillations of an electromagnetic inductor
NASA Astrophysics Data System (ADS)
Lee, Christopher; Stamp, David; Kapania, Nitin R.; Mur-Miranda, José Oscar
2010-04-01
Harvesting energy from ambient vibration is a promising method for providing a continuous source of power for wireless sensor nodes. However, traditional energy harvesters are often derived from resonant linear oscillators which are capable of providing sufficient output power only if the dominant frequency of input vibrations closely matches the device resonant frequency. The limited scope of such devices has sparked an interest in the use of nonlinear oscillators as mechanisms for broadband energy harvesting. In this study, we investigate the harvesting performance of an electromagnetic harvester sustaining oscillations through the phenomena of magnetic levitation. The nonlinear behavior of the device is effectively modeled by Duffing's equation, and direct numerical integration confirms the broadband frequency response of the nonlinear harvester. The nonlinear harvester's power generation capabilities are directly compared to a linear electromagnetic harvester with similar dynamic parameters. Experimental testing shows that the presence of both high and low amplitude solutions for the nonlinear energy harvester results in a tendency for the oscillator to remain in a low energy state for non-harmonic vibration inputs, unless continuous energy impulses are provided. We conclude by considering future applications and improvements for such nonlinear devices.
He's Frequency Formulation for Nonlinear Oscillators
ERIC Educational Resources Information Center
Geng, Lei; Cai, Xu-Chu
2007-01-01
Based on an ancient Chinese algorithm, J H He suggested a simple but effective method to find the frequency of a nonlinear oscillator. In this paper, a modified version is suggested to improve the accuracy of the frequency; two examples are given, revealing that the obtained solutions are of remarkable accuracy and are valid for the whole solution…
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. PMID:20866495
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.
Nonlinear oscillations of automotive turbocharger turbines
NASA Astrophysics Data System (ADS)
Schweizer, Bernhard; Sievert, Mario
2009-04-01
Turbines, especially turbines supported in hydrodynamic bearings, often exhibit interesting oscillation effects, which result from the bearing nonlinearities. In the present work, an automotive turbocharger rotor is investigated. The rotor of the turbocharger examined here is supported in full-floating ring bearings, which give rise to complex system vibrations. Frequency spectra of run-up measurements, carried out on a hot-gas turbocharger test rig, are presented. The occurring nonlinear effects—self-excited vibrations, oil whirl/whip phenomena, subharmonics, superharmonics, combination frequencies and jump phenomena—are explained in detail with the help of a gyroscopic eigenvalue analysis and by run-up simulations with a multibody model of the rotor/bearing system. The influence of different operating conditions—oil supply pressure, oil supply temperature and rotor imbalance—on the rotor oscillations and the system bifurcations is studied.
Perturbation technique to analyze nonlinear oscillations
Tu, S.T.
1986-01-01
Using perturbation and asymptotic methods, the author analyzes the nonlinear oscillations of two dynamical systems: the Bonhoeffer-van der Pol equations and the forced Duffing equation. In the two-dimensional model of the former system, he studies the transition from stable steady-state to relaxation oscillation as a parameter is varied. The analysis also helps to clarify a phenomenon commonly known as the duck trajectory. In the three-dimensional model, bursting oscillation is explained. In the forced Duffing equation, the main interest is the trajectory near the homoclinic orbit and the saddle point. A map of that trajectory is analytically constructed. From that map, limit cycles and their linear stability are investigated.
A self-saturating mechanical oscillator with linear feedback
NASA Astrophysics Data System (ADS)
Chen, Changyao; Zanette, Damian; Czaplewski, David; Guest, Jeffrey; Lopez, Daniel
Oscillators, opposed to resonators, produce a prescribed periodic signal without any external frequency reference. In order to maintain stable oscillations, there needs to be an amplitude limiting mechanism, which is usually realized by saturating at least one of the sustaining amplifiers. Here we demonstrate a simple oscillator structure that solely relies on the nonlinearity inherent to the constituent mechanical resonator to limit the oscillating amplitude, while the performance of the feedback loop remains in the linear regime. To validate the model, we experimentally demonstrate the principle using a non-linear silicon microelectromechanical (MEMS) resonator, and perform comprehensive characterizations that agree well with the theoretical predictions.
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
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.
Thermal nonlinearities in a nanomechanical oscillator
NASA Astrophysics Data System (ADS)
Gieseler, Jan; Novotny, Lukas; Quidant, Romain
2013-12-01
Nano- and micromechanical oscillators with high quality (Q)-factors have gained much attention for their potential application as ultrasensitive detectors. In contrast to micro-fabricated devices, optically trapped nanoparticles in vacuum do not suffer from clamping losses, hence leading to much larger Q-factors. We find that for a levitated nanoparticle the thermal energy suffices to drive the motion of the nanoparticle into the nonlinear regime. First, we experimentally measure and fully characterize the frequency fluctuations originating from thermal motion and nonlinearities. Second, we demonstrate that feedback cooling can be used to mitigate these fluctuations. The high level of control allows us to fully exploit the force-sensing capabilities of the nanoresonator. Our approach offers a force sensitivity of 20zNHz-1/2, which is the highest value reported so far at room temperature, sufficient to sense ultraweak interactions, such as non-Newtonian gravity-like forces.
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; 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; 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 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
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.
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.
Nonlinear Oscillations of Two-Dimensional, Rotating Inviscid Drops
NASA Astrophysics Data System (ADS)
Patzek, T. W.; Basaran, O. A.; Benner, R. E.; Scriven, L. E.
1995-01-01
We examine the nonlinear response of a drop, rotating as a rigid body at fixed angular velocity, to two-dimensional finite-amplitude disturbances. With these restrictions, the liquid velocity becomes a superposition of the solid-body rotation and the gradient of a velocity potential. To find the drop motion, we solve an integro-differential Bernoulli's equation for the drop shape and Laplace's equation for the velocity potential field within the drop. The integral part of Bernoulli's equation couples all parts of the drop's surface and sets this problem apart from that of the oscillations of nonrotating drops. We use Galerkin's weighted residual method with finite element basis functions which are deployed on a mesh that deforms in proportion to the deformation of the free surface. To alleviate the roundoff error in the initial conditions of the drop motion, we use a Fourier filter which turns off as soon as the highest resolved oscillation mode grows above the machine noise level. The results include sequences of drop shapes, Fourier analysis of oscillation frequencies, and evolution in time of the components of total mechanical energy of the drop. The Fourier power spectral analysis of large-amplitude oscillations of the drop reveals frequency shifts similar to those of the nonrotating free drops. Constant drop volume, total energy, and angular momentum as well as vanishing mass flow across the drop surface are the standards of accuracy against which we test the nonlinear motion of the drop over tens or hundreds of oscillation periods. Finally, we demonstrate that our finite element method has superior stability, accuracy, and computational efficiency over several boundary element algorithms that have previously appeared in the literature.
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
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.
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.
Nonlinear oscillation behavior of a driven gyrotron backward-wave oscillator
NASA Astrophysics Data System (ADS)
Yeh, Y. S.; Chang, T. H.; Fan, C. T.; Hung, C. L.; Jhou, J. N.; Huang, J. M.; Shiao, J. L.; Wu, Z. Q.; Chiu, C. C.
2010-11-01
Controlling the phase and frequency of a gyrotron backward-wave oscillator (gyro-BWO) by means of injection-locking techniques is of practical importance. This study employed a nonlinear self-consistent time-independent code to analyze the nonlinear oscillation behavior of a driven gyro-BWO. There are three regimes in the driven gyro-BWO, including amplification, injection-locked oscillation, and mode competition regimes. Based on the theory of nonlinear oscillation, the amplification and injection-locked oscillation modes are the stable modes and compete with each other in the mode competition regime. An oscillator plane of the driven gyro-BWO is elucidated in the paper. This work demonstrates for the first time that the amplification mode transits to the injection-locked oscillation mode in the driven gyro-BWO. Moreover, the signification efficiency enhancement of the driven gyro-BWO over the free-running efficiency is found.
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…
Self-Consistent Nonlinear Dynamics of Fishbone Oscillations
NASA Astrophysics Data System (ADS)
Candy, J.; Berk, H.; Breizman, B.; Porcelli, F.
1997-11-01
The excitation of the internal kink mode by fast-ions (produced by neutral beam injection or ion-cyclotron resonance heating) has been identified as the mechanism for plasma oscillations known as fishbones. To describe the nonlinear evolution of the fishbone instability, we present a numerical model which includes the detailed linear physics of the bulk plasma (multiple poloidal harmonics of the n=1 mode, q=1 layer physics including plasma resistivity, ion FLR, and ion viscosity) together with the energetic particle current. This current is computed numerically in realistic tokamak geometry, including orbit nonlinearities (i.e., particle trapping), by the δf particle-code FAC. The resulting model is valid over a wide frequency range, and thus unifies the treatment of low-frequency diamagnetic (ω ~ wdia) and high-frequency precessional drift (ω ~ wdhot) fishbones. We compute saturation levels for diamagnetic modes, and also reproduce the nonlinear frequency downshift characteristic of the precessional drift branch during the nonlinear pulse. Orbit loss characteristics for fishbone activity in both JET and PDX discharges are discussed.
From linear mechanics to nonlinear mechanics
NASA Technical Reports Server (NTRS)
Loeb, Julian
1955-01-01
Consideration is given to the techniques used in telecommunication where a nonlinear system (the modulator) results in a linear transposition of a signal. It is then shown that a similar method permits linearization of electromechanical devices or nonlinear mechanical devices. A sweep function plays the same role as the carrier wave in radio-electricity. The linearizations of certain nonlinear functionals are presented.
Hydrodynamic synchronization of nonlinear oscillators at low Reynolds number.
Leoni, M; Liverpool, T B
2012-04-01
We introduce a generic model of a weakly nonlinear self-sustained oscillator as a simplified tool to study synchronization in a fluid at low Reynolds number. By averaging over the fast degrees of freedom, we examine the effect of hydrodynamic interactions on the slow dynamics of two oscillators and show that they can lead to synchronization. Furthermore, we find that synchronization is strongly enhanced when the oscillators are nonisochronous, which on the limit cycle means the oscillations have an amplitude-dependent frequency. Nonisochronity is determined by a nonlinear coupling α being nonzero. We find that its (α) sign determines if they synchronize in phase or antiphase. We then study an infinite array of oscillators in the long-wavelength limit, in the presence of noise. For α>0, hydrodynamic interactions can lead to a homogeneous synchronized state. Numerical simulations for a finite number of oscillators confirm this and, when α<0, show the propagation of waves, reminiscent of metachronal coordination.
Transitory behaviors in diffusively coupled nonlinear oscillators.
Tadokoro, Satoru; Yamaguti, Yutaka; Fujii, Hiroshi; Tsuda, Ichiro
2011-03-01
We study collective behaviors of diffusively coupled oscillators which exhibit out-of-phase synchrony for the case of weakly interacting two oscillators. In large populations of such oscillators interacting via one-dimensionally nearest neighbor couplings, there appear various collective behaviors depending on the coupling strength, regardless of the number of oscillators. Among others, we focus on an intermittent behavior consisting of the all-synchronized state, a weakly chaotic state and some sorts of metachronal waves. Here, a metachronal wave means a wave with orderly phase shifts of oscillations. Such phase shifts are produced by the dephasing interaction which produces the out-of-phase synchronized states in two coupled oscillators. We also show that the abovementioned intermittent behavior can be interpreted as in-out intermittency where two saddles on an invariant subspace, the all-synchronized state and one of the metachronal waves play an important role.
Coupled electron and ion nonlinear oscillations in a collisionless plasma
Karimov, A. R.
2013-05-15
Dynamics of coupled electrostatic electron and ion nonlinear oscillations in a collisionless plasma is studied with reference to a kinetic description. Proceeding from the exact solution of Vlasov-Maxwell equations written as a function of linear functions in the electron and ion velocities, we arrive at the two coupled nonlinear equations which describe the evolution of the system.
Microcomputer Simulation of Nonlinear Systems: From Oscillations to Chaos.
ERIC Educational Resources Information Center
Raw, Cecil J. G.; Stacey, Larry M.
1989-01-01
Presents two short microcomputer programs which illustrate features of nonlinear dynamics, including steady states, periodic oscillations, period doubling, and chaos. Logistic maps are explained, inclusion in undergraduate chemistry and physics courses to teach nonlinear equations is discussed, and applications in social and biological sciences…
A study of nonlinear dynamics of single- and two-phase flow oscillations
NASA Astrophysics Data System (ADS)
Mawasha, Phetolo Ruby
The dynamics of single- and two-phase flows in channels can be contingent on nonlinearities which are not clearly understood. These nonlinearities could be interfacial forces between the flowing fluid and its walls, variations in fluid properties, growth of voids, etc. The understanding of nonlinear dynamics of fluid flow is critical in physical systems which can undergo undesirable system operating scenarios such an oscillatory behavior which may lead to component failure. A nonlinear lumped mathematical model of a surge tank with a constant inlet flow into the tank and an outlet flow through a channel is derived from first principles. The model is used to demonstrate that surge tanks with inlet and outlet flows contribute to oscillatory behavior in laminar, turbulent, single-phase, and two-phase flow systems. Some oscillations are underdamped while others are self-sustaining. The mechanisms that are active in single-phase oscillations with no heating are presented using specific cases of simplified models. Also, it is demonstrated how an external mechanism such as boiling contributes to the oscillations observed in two-phase flow and gives rise to sustained oscillations (or pressure drop oscillations). A description of the pressure drop oscillation mechanism is presented using the steady state pressure drop versus mass flow rate characteristic curve of the heated channel, available steady state pressure drop versus mass flow rate from the surge tank, and the transient pressure drop versus mass flow rate limit cycle. Parametric studies are used to verify the theoretical pressure drop oscillations model using experimental data by Yuncu's (1990). The following contributions are unique: (1) comparisons of nonlinear pressure drop oscillation models with and without the effect of the wall thermal heat capacity and (2) comparisons of linearized pressure drop oscillation models with and without the effect of the wall thermal heat capacity to identify stability boundaries.
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.
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.
Detecting nonlinear oscillations in broadband signals
NASA Astrophysics Data System (ADS)
Vejmelka, Martin; Paluš, Milan
2009-03-01
A framework for detecting nonlinear oscillatory activity in broadband time series is presented. First, a narrow-band oscillatory mode is extracted from a broadband background. Second, it is tested whether the extracted mode is significantly different from linearly filtered noise, modeled as a linear stochastic process possibly passed through a static nonlinear transformation. If a nonlinear oscillatory mode is positively detected, it can be further analyzed using nonlinear approaches such as phase synchronization analysis. For linear processes standard approaches, such as the coherence analysis, are more appropriate. The method is illustrated in a numerical example and applied to analyze experimentally obtained human electroencephalogram time series from a sleeping subject.
Classical Mechanics as Nonlinear Quantum Mechanics
Nikolic, Hrvoje
2007-12-03
All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schroedinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a linear equation is real and positive, rather than complex. This has profound implications on the role of the Bohmian classical-like interpretation of linear quantum mechanics, as well as on the possibilities to find a consistent interpretation of arbitrary nonlinear generalizations of quantum mechanics.
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.
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. PMID:27369163
Class of solvable nonlinear oscillators with isochronous orbits.
Iacono, R; Russo, F
2011-02-01
The nonlinear oscillator x¨+(2m+3)x(2m+1)x˙+x+x(4m+3)=0, with m a non-negative integer, is known to have a center in the origin, in a neighborhood of which are isochronous orbits, i.e., orbits with fixed period, not dependent on the amplitude. Here, we show that this oscillator can be explicitly integrated, and that its phase space can be completely characterized.
Mechanical and current oscillations in corroding electrodes
Teschke, O.; Galembeck, F.; Tenan, M.A.
1985-06-01
Mechanical oscillations of the solution meniscus risen around a corroding wire electrode were observed in synchronism with electrical current oscillations. Scanning electron microscopy coupled to microprobe analysis was used to investigate the topochemistry of the system under study. Solution capillarity effects on iron and on iron compounds are related to the oscillations detected in this system.
First-harmonic approximation in nonlinear chirped-driven oscillators.
Uzdin, Raam; Friedland, Lazar; Gat, Omri
2014-01-01
Nonlinear classical oscillators can be excited to high energies by a weak driving field provided the drive frequency is properly chirped. This process is known as autoresonance (AR). We find that for a large class of oscillators, it is sufficient to consider only the first harmonic of the motion when studying AR, even when the dynamics is highly nonlinear. The first harmonic approximation is also used to relate AR in an asymmetric potential to AR in a "frequency equivalent" symmetric potential and to study the autoresonance breakdown phenomenon.
The rapidly convergent solutions of strongly nonlinear oscillators.
Alam, M S; Abdur Razzak, Md; Alal Hosen, Md; Riaz Parvez, Md
2016-01-01
Based on the harmonic balance method (HBM), an approximate solution is determined from the integral expression (i.e., first order differential equation) of some strongly nonlinear oscillators. Usually such an approximate solution is obtained from second order differential equation. The advantage of the new approach is that the solution converges significantly faster than that obtained by the usual HBM as well as other analytical methods. By choosing some well known nonlinear oscillators, it has been verified that an n-th (n ≥ 2) approximate solution (concern of this article) is very close to (2n - 1)-th approximations obtained by usual HBM. PMID:27536541
Some heuristic procedures for analyzing random vibration of nonlinear oscillators.
NASA Technical Reports Server (NTRS)
Crandall, S. H.
1971-01-01
The stationary response of a lightly damped nonlinear oscillator subjected to wideband random excitation can be examined as an example of thermal equilibrium. It may be assumed that the response consists of a series of free-vibration cycles with small random fluctuations in phase and amplitude. Certain statistical properties of the response can be estimated by averaging corresponding properties of the free vibration with respect to cycle amplitude distributions. Such heuristic procedures for determining the expected frequency and the autocorrelation function of the stationary response are outlined. Some additional results concerning first-passage problems for nonlinear oscillators are included.
On the nonlinear dissipative dynamics of weakly overdamped oscillators
NASA Astrophysics Data System (ADS)
Brezhnev, Yu. V.; Sazonov, S. V.
2014-11-01
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.
Nonlinear transient waves in coupled phase oscillators with inertia
NASA Astrophysics Data System (ADS)
Jörg, David J.
2015-05-01
Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here, we show that finite inertia of individual oscillators enables nonlinear phase waves in spatially extended coupled systems. Using a discrete model of coupled phase oscillators with inertia, we investigate these wave phenomena numerically, complemented by a continuum approximation that permits the analytical description of the key features of wave propagation in the long-wavelength limit. The ability to exhibit traveling waves is a generic feature of systems with finite inertia and is independent of the details of the coupling function.
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
Nonlinear transient waves in coupled phase oscillators with inertia.
Jörg, David J
2015-05-01
Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here, we show that finite inertia of individual oscillators enables nonlinear phase waves in spatially extended coupled systems. Using a discrete model of coupled phase oscillators with inertia, we investigate these wave phenomena numerically, complemented by a continuum approximation that permits the analytical description of the key features of wave propagation in the long-wavelength limit. The ability to exhibit traveling waves is a generic feature of systems with finite inertia and is independent of the details of the coupling function.
A nonlinear piezoelectric energy harvester with magnetic oscillator
NASA Astrophysics Data System (ADS)
Tang, Lihua; Yang, Yaowen
2012-08-01
This letter proposes a magnetic coupled piezoelectric energy harvester (PEH), in which the magnetic interaction is introduced by a magnetic oscillator. For comparison purpose, lumped parameter models are established for the conventional linear PEH, the nonlinear PEH with a fixed magnet, and the proposed PEH with a magnetic oscillator. Both experiment and simulation show the benefits from the dynamics of the magnetic oscillator. In the experiment, nearly 100% increase in the operating bandwidth and 41% increase in the magnitude of the power output are achieved at an excitation level of 2 m/s2.
Optimal Parametric Feedback Excitation of Nonlinear Oscillators
NASA Astrophysics Data System (ADS)
Braun, David J.
2016-01-01
An optimal parametric feedback excitation principle is sought, found, and investigated. The principle is shown to provide an adaptive resonance condition that enables unprecedentedly robust movement generation in a large class of oscillatory dynamical systems. Experimental demonstration of the theory is provided by a nonlinear electronic circuit that realizes self-adaptive parametric excitation without model information, signal processing, and control computation. The observed behavior dramatically differs from the one achievable using classical parametric modulation, which is fundamentally limited by uncertainties in model information and nonlinear effects inevitably present in real world applications.
Optimal Parametric Feedback Excitation of Nonlinear Oscillators.
Braun, David J
2016-01-29
An optimal parametric feedback excitation principle is sought, found, and investigated. The principle is shown to provide an adaptive resonance condition that enables unprecedentedly robust movement generation in a large class of oscillatory dynamical systems. Experimental demonstration of the theory is provided by a nonlinear electronic circuit that realizes self-adaptive parametric excitation without model information, signal processing, and control computation. The observed behavior dramatically differs from the one achievable using classical parametric modulation, which is fundamentally limited by uncertainties in model information and nonlinear effects inevitably present in real world applications. PMID:26871336
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.
2013-01-01
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. PMID:23214857
Optomechanical response of a nonlinear mechanical resonator
NASA Astrophysics Data System (ADS)
Shevchuk, Olga; Singh, Vibhor; Steele, Gary A.; Blanter, Ya. M.
2015-11-01
We investigate theoretically in detail the nonlinear effects in the response of an optical/microwave cavity coupled to a Duffing mechanical resonator. The cavity is driven by a laser at a red or blue mechanical subband, and a probe laser measures the reflection close to the cavity resonance. Under these conditions, we find that the cavity exhibits optomechanically induced reflection (OMIR) or absorption (OMIA) and investigate the optomechanical response in the limit of nonlinear driving of the mechanics. Similar to linear mechanical drive, in an overcoupled cavity the red sideband drive may lead to both OMIA and OMIR depending on the strength of the drive, whereas the blue sideband drive only leads to OMIR. The dynamics of the phase of the mechanical resonator leads to the difference between the shapes of the response of the cavity and the amplitude response of the driven Duffing oscillator, for example, at weak red sideband drive the OMIA dip has no inflection point. We also verify that mechanical nonlinearities beyond Duffing model have little effect on the size of the OMIA dip though they affect the width of the dip.
Phase and amplitude dynamics of nonlinearly coupled oscillators.
Cudmore, P; Holmes, C A
2015-02-01
This paper addresses the amplitude and phase dynamics of a large system of nonlinearly coupled, non-identical damped harmonic oscillators, which is based on recent research in coupled oscillation in optomechanics. Our goal is to investigate the existence and stability of collective behaviour which occurs due to a play-off between the distribution of individual oscillator frequency and the type of nonlinear coupling. We show that this system exhibits synchronisation, where all oscillators are rotating at the same rate, and that in the synchronised state the system has a regular structure related to the distribution of the frequencies of the individual oscillators. Using a geometric description, we show how changes in the non-linear coupling function can cause pitchfork and saddle-node bifurcations which create or destroy stable and unstable synchronised solutions. We apply these results to show how in-phase and anti-phase solutions are created in a system with a bi-modal distribution of frequencies.
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.
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…
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. PMID:24240431
Graphene mechanical oscillators with tunable frequency
NASA Astrophysics Data System (ADS)
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.
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
NASA Astrophysics Data System (ADS)
Kang, Dong-Keun; Yang, Hyun-Ik; Kim, Chang-Wan
2015-11-01
A mass sensor using a nano-resonator has high detection sensitivity, and mass sensitivity is higher with smaller resonators. Therefore, carbon nanotubes (CNTs) are the ultimate materials for these applications and have been actively studied. In particular, CNT-based nanomechanical devices may experience high temperatures that lead to thermal expansion and residual stress in devices, which affects the device reliability. In this letter, to demonstrate the influence of the temperature change (i.e., thermal effect) on the mass detection sensitivity of CNT-based mass sensor, dynamic analysis is carried out for a CNT resonator with thermal effects in both linear and nonlinear oscillation regimes. Based on the continuum mechanics model, the analytical solution method with an assumed deflection eigenmode is applied to solve the nonlinear differential equation which involves the von Karman nonlinear strain-displacement relation and the additional axial force associated with thermal effects. A thermal effect on the fundamental resonance behavior and resonance frequency shift due to adsorbed mas, i.e., mass detection sensitivity, is examined in high-temperature environment. Results indicate a valid improvement of fundamental resonance frequency by using nonlinear oscillation in a thermal environment. In both linear and nonlinear oscillation regimes, the mass detection sensitivity becomes worse due to the increasing of temperature in a high-temperature environment. The thermal effect on the detection sensitivity is less effective in the nonlinear oscillation regime. It is concluded that a temperature change of a mass sensor with a CNT-based resonator can be utilized to enhance the detection sensitivity depending on the CNT length, linear/nonlinear oscillation behaviors, and the thermal environment.
Frequency analysis of nonlinear oscillations via the global error minimization
NASA Astrophysics Data System (ADS)
Kalami Yazdi, M.; Hosseini Tehrani, P.
2016-06-01
The capacity and effectiveness of a modified variational approach, namely global error minimization (GEM) is illustrated in this study. For this purpose, the free oscillations of a rod rocking on a cylindrical surface and the Duffing-harmonic oscillator are treated. In order to validate and exhibit the merit of the method, the obtained result is compared with both of the exact frequency and the outcome of other well-known analytical methods. The corollary reveals that the first order approximation leads to an acceptable relative error, specially for large initial conditions. The procedure can be promisingly exerted to the conservative nonlinear problems.
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.
Surpassing Fundamental Limits of Oscillators Using Nonlinear Resonators
Villanueva, L. G.; Kenig, E.; Karabalin, R. B.; Matheny, M. H.; Lifshitz, Ron; Cross, M. C.; Roukes, M. L.
2013-01-01
In its most basic form an oscillator consists of a resonator driven on resonance, through feedback, to create a periodic signal sustained by a static energy source. The generation of a stable frequency, the basic function of oscillators, is typically achieved by increasing the amplitude of motion of the resonator while remaining within its linear, harmonic regime. Contrary to this conventional paradigm, in this Letter we show that by operating the oscillator at special points in the resonator’s anharmonic regime we can overcome fundamental limitations of oscillator performance due to thermodynamic noise as well as practical limitations due to noise from the sustaining circuit. We develop a comprehensive model that accounts for the major contributions to the phase noise of the nonlinear oscillator. Using a nano-electromechanical system based oscillator, we experimentally verify the existence of a special region in the operational parameter space that enables suppressing the most significant contributions to the oscillator’s phase noise, as predicted by our model. PMID:23679770
Self-synchronization in an ensemble of nonlinear oscillators.
Ostrovsky, L A; Galperin, Y V; Skirta, E A
2016-06-01
The paper describes the results of study of a system of coupled nonlinear, Duffing-type oscillators, from the viewpoint of their self-synchronization, i.e., generation of a coherent field (order parameter) via instability of an incoherent (random-phase) initial state. We consider both the cases of dissipative coupling (e.g., via the joint radiation) and reactive coupling in a Hamiltonian system. PMID:27368772
Self-synchronization in an ensemble of nonlinear oscillators
NASA Astrophysics Data System (ADS)
Ostrovsky, L. A.; Galperin, Y. V.; Skirta, E. A.
2016-06-01
The paper describes the results of study of a system of coupled nonlinear, Duffing-type oscillators, from the viewpoint of their self-synchronization, i.e., generation of a coherent field (order parameter) via instability of an incoherent (random-phase) initial state. We consider both the cases of dissipative coupling (e.g., via the joint radiation) and reactive coupling in a Hamiltonian system.
Synchronization of weakly nonlinear oscillators with Huygens' coupling.
Ramirez, J Pena; Fey, Rob H B; Nijmeijer, H
2013-09-01
In this paper, the occurrence of synchronization in pairs of weakly nonlinear self-sustained oscillators that interact via Huygens' coupling, i.e., a suspended rigid bar, is treated. In the analysis, a generalized version of the classical Huygens' experiment of synchronization of two coupled pendulum clocks is considered, in which the clocks are replaced by arbitrary self-sustained oscillators. Sufficient conditions for the existence and stability of synchronous solutions in the coupled system are derived by using the Poincaré method. The obtained results are supported by computer simulations and experiments conducted on a dedicated experimental platform. It is demonstrated that the mass of the coupling bar is an important parameter with respect to the limit synchronous behaviour in the oscillators.
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.
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.
Out-of-unison resonance in weakly nonlinear coupled oscillators
Hill, T. L.; Cammarano, A.; Neild, S. A.; Wagg, D. J.
2015-01-01
Resonance is an important phenomenon in vibrating systems and, in systems of nonlinear coupled oscillators, resonant interactions can occur between constituent parts of the system. In this paper, out-of-unison resonance is defined as a solution in which components of the response are 90° out-of-phase, in contrast to the in-unison responses that are normally considered. A well-known physical example of this is whirling, which can occur in a taut cable. Here, we use a normal form technique to obtain time-independent functions known as backbone curves. Considering a model of a cable, this approach is used to identify out-of-unison resonance and it is demonstrated that this corresponds to whirling. We then show how out-of-unison resonance can occur in other two degree-of-freedom nonlinear oscillators. Specifically, an in-line oscillator consisting of two masses connected by nonlinear springs—a type of system where out-of-unison resonance has not previously been identified—is shown to have specific parameter regions where out-of-unison resonance can occur. Finally, we demonstrate how the backbone curve analysis can be used to predict the responses of forced systems. PMID:25568619
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.
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.
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 0.416η(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. PMID:26803911
Experimental demonstration of revival of oscillations from death in coupled nonlinear oscillators.
Senthilkumar, D V; Suresh, K; Chandrasekar, V K; Zou, Wei; Dana, Syamal K; Kathamuthu, Thamilmaran; Kurths, Jürgen
2016-04-01
We experimentally demonstrate that a processing delay, a finite response time, in the coupling can revoke the stability of the stable steady states, thereby facilitating the revival of oscillations in the same parameter space where the coupled oscillators suffered the quenching of oscillation. This phenomenon of reviving of oscillations is demonstrated using two different prototype electronic circuits. Further, the analytical critical curves corroborate that the spread of the parameter space with stable steady state is diminished continuously by increasing the processing delay. Finally, the death state is completely wiped off above a threshold value by switching the stability of the stable steady state to retrieve sustained oscillations in the same parameter space. The underlying dynamical mechanism responsible for the decrease in the spread of the stable steady states and the eventual reviving of oscillation as a function of the processing delay is explained using analytical results. PMID:27131491
Experimental demonstration of revival of oscillations from death in coupled nonlinear oscillators
NASA Astrophysics Data System (ADS)
Senthilkumar, D. V.; Suresh, K.; Chandrasekar, V. K.; Zou, Wei; Dana, Syamal K.; Kathamuthu, Thamilmaran; Kurths, Jürgen
2016-04-01
We experimentally demonstrate that a processing delay, a finite response time, in the coupling can revoke the stability of the stable steady states, thereby facilitating the revival of oscillations in the same parameter space where the coupled oscillators suffered the quenching of oscillation. This phenomenon of reviving of oscillations is demonstrated using two different prototype electronic circuits. Further, the analytical critical curves corroborate that the spread of the parameter space with stable steady state is diminished continuously by increasing the processing delay. Finally, the death state is completely wiped off above a threshold value by switching the stability of the stable steady state to retrieve sustained oscillations in the same parameter space. The underlying dynamical mechanism responsible for the decrease in the spread of the stable steady states and the eventual reviving of oscillation as a function of the processing delay is explained using analytical results.
Forced oscillations of nonlinear damped equation of suspended string
NASA Astrophysics Data System (ADS)
Yamaguchi, Masaru; Nagai, Tohru; Matsukane, Katsuya
2008-06-01
We shall study the existence of time-periodic solutions of nonlinear damped equation of suspended string to which a periodic nonlinear force works. We shall be conterned with weak, strong and classical time-periodic solutions and also the regularity of the solutions. To formulate our results, we shall take suitable weighted Sobolev-type spaces introduced by [M. Yamaguchi, Almost periodic oscillations of suspended string under quasiperiodic linear force, J. Math. Anal. Appl. 303 (2) (2005) 643-660; M. Yamaguchi, Infinitely many time-periodic solutions of nonlinear equation of suspended string, Funkcial. Ekvac., in press]. We shall study properties of the function spaces and show inequalities on the function spaces. To show our results we shall apply the Schauder fixed point theorem and the fixed point continuation theorem in the function spaces.
Assessing instantaneous synchrony of nonlinear nonstationary oscillators in the brain.
Fine, Ananda S; Nicholls, David P; Mogul, David J
2010-01-30
Neuronal populations throughout the brain achieve levels of synchronous electrophysiological activity as a consequence of both normal brain function as well as during pathological states such as in epileptic seizures. Understanding this synchrony and being able to quantitatively assess the dynamics with which neuronal oscillators across the brain couple their activity is a critical component toward decoding such complex behavior. Commonly applied techniques to resolve relationships between oscillators typically make assumptions of linearity and stationarity that are likely not to be valid for complex neural signals. In this study, intracranial electroencephalographic activity was recorded bilaterally in both hippocampi and in anteromedial thalamus of rat under normal conditions and during hypersynchronous seizure activity induced by focal injection of the epileptogenic agent kainic acid. Nonlinear oscillators were first extracted using empirical mode decomposition. The technique of eigenvalue decomposition was used to assess global phase synchrony of the highest energy oscillators. The Hilbert analytical technique was then used to measure instantaneous phase synchrony of these oscillators as they evolved in time. To test the reliability of this method, we first applied it to a system of two coupled Rössler attractors under varying levels of coupling with small frequency mismatch. The application of these analytical techniques to intracranially recorded brain signals provides a means for assessing how complex oscillatory behavior in the brain evolves and changes during both normal activity and as a consequence of diseased states without making restrictive and possibly erroneous assumptions of the linearity and stationarity of the underlying oscillatory activity.
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.
Experiments on oscillator ensembles with global nonlinear coupling.
Temirbayev, Amirkhan A; Zhanabaev, Zeinulla Zh; Tarasov, Stanislav B; Ponomarenko, Vladimir I; Rosenblum, Michael
2012-01-01
We experimentally analyze collective dynamics of a population of 20 electronic Wien-bridge limit-cycle oscillators with a nonlinear phase-shifting unit in the global feedback loop. With an increase in the coupling strength we first observe formation and then destruction of a synchronous cluster, so that the dependence of the order parameter on the coupling strength is not monotonic. After destruction of the cluster the ensemble remains nevertheless coherent, i.e., it exhibits an oscillatory collective mode (mean field). We show that the system is now in a self-organized quasiperiodic state, predicted in Rosenblum and Pikovsky [Phys. Rev. Lett. 98, 064101 (2007)]. In this state, frequencies of all oscillators are smaller than the frequency of the mean field, so that the oscillators are not locked to the mean field they create and their dynamics is quasiperiodic. Without a nonlinear phase-shifting unit, the system exhibits a standard Kuramoto-like transition to a fully synchronous state. We demonstrate a good correspondence between the experiment and previously developed theory. We also propose a simple measure which characterizes the macroscopic incoherence-coherence transition in a finite-size ensemble.
Experiments on oscillator ensemble with global nonlinear coupling
NASA Astrophysics Data System (ADS)
Rosenblum, Michael; Temirbayev, Amirkhan; Zhanabaev, Zeinulla; Tarasov, Stanislav; Ponomarenko, Vladimir
2012-02-01
We experimentally analyze collective dynamics of a population of 20 electronic Wien-bridge limit-cycle oscillators with a linear or nonlinear phase-shifting unit in the global feedback loop. With linear unit we observe, with increase of the coupling strength, a standard Kuramoto-like transition to a fully synchronous state; the threshold of the transition depends on the phase shift. In case of nonlinear global coupling we first observe a transition to a state when approximately half of the population forms a synchronous cluster. With further increase of the coupling strength we observe destruction of this cluster and formation of a self-organized quasiperiodic state, predicted in [M. Rosenblum and A. Pikovsky, PRL, 98, 064101 (2007)]. In this state, frequencies of all oscillators are smaller than the frequency of the mean field, so that the oscillators are not locked to the mean field they create and their dynamics is quasiperiodic. The transition is characterized by a non-monotonic dependence of the order parameter on the coupling strength. We demonstrate a good correspondence between theory and experiment.
Experiments on oscillator ensembles with global nonlinear coupling
NASA Astrophysics Data System (ADS)
Temirbayev, Amirkhan A.; Zhanabaev, Zeinulla Zh.; Tarasov, Stanislav B.; Ponomarenko, Vladimir I.; Rosenblum, Michael
2012-01-01
We experimentally analyze collective dynamics of a population of 20 electronic Wien-bridge limit-cycle oscillators with a nonlinear phase-shifting unit in the global feedback loop. With an increase in the coupling strength we first observe formation and then destruction of a synchronous cluster, so that the dependence of the order parameter on the coupling strength is not monotonic. After destruction of the cluster the ensemble remains nevertheless coherent, i.e., it exhibits an oscillatory collective mode (mean field). We show that the system is now in a self-organized quasiperiodic state, predicted in Rosenblum and Pikovsky [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.98.064101 98, 064101 (2007)]. In this state, frequencies of all oscillators are smaller than the frequency of the mean field, so that the oscillators are not locked to the mean field they create and their dynamics is quasiperiodic. Without a nonlinear phase-shifting unit, the system exhibits a standard Kuramoto-like transition to a fully synchronous state. We demonstrate a good correspondence between the experiment and previously developed theory. We also propose a simple measure which characterizes the macroscopic incoherence-coherence transition in a finite-size ensemble.
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.
Wave Driven Non-Linear Flow Oscillator for the 22-Year Solar Cycle
NASA Technical Reports Server (NTRS)
Mayr, H. G.; Wolff, C. L.; Hartle, R. E.; Einaudi, Franco (Technical Monitor)
2000-01-01
We propose that waves generate an oscillation in the Sun to account for the 22-year magnetic cycle. The mechanism we envision is analogous to that driving the Quasi Biennial Oscillation (QBO) observed in the terrestrial atmosphere, which is well understood in principal. Planetary waves and gravity waves deposit momentum in the background atmosphere and accelerate the flow under viscous dissipation. Analysis shows that such a momentum source represents a non-linearity of third or generally odd order, which generates also the fundamental frequency/period so that an oscillation is maintained without external time dependent forcing. For the Sun, we propose that the wave driven oscillation would occur just below the convection region, where the buoyancy frequency or convective stability becomes small to favor wave breaking and wave mean flow interaction. Using scale analysis to extrapolate from terrestrial to solar conditions, we present results from a simplified analytical model, applied to the equator, that incorporates Hines'Doppler Spread Parameterization for gravity waves (GW). Based on a parametric study, we conclude: (1) Depending on the adopted horizontal wavelengths of GW's, wave amplitudes < 10 m/s can be made to produce oscillating zonal winds of about 25 m/s that should be large enough to generate a corresponding oscillation in the main poloidal magnetic field; (2) The oscillation period can be made to be 22 years provided the buoyancy frequency (stability) is sufficiently small, which would place the oscillating wind field near the base of the convection region; (3) In this region, the turbulence associated with wave processes would be enhanced by low stability, and this also helps to produce the desired oscillation period and generate the dynamo currents that would produce the reversing magnetic field. We suggest that the above mechanism may also drive other long-period metronomes in planetary and stellar interiors.
Nonlinear oscillations of semigeostrophic Eady waves in the presence of diffusivity
NASA Astrophysics Data System (ADS)
Xu, Qin; Gu, Wei; Shouting, Gao
2005-01-01
Analyses are performed to examine the physical processes involved in nonlinear oscillations of Eady baroclinic waves obtained from viscous semigeostrophic models with two types of boundary conditions (freeslip and non-slip). By comparing with previous studies for the case of the free-slip boundary condition, it is shown that the nonlinear oscillations are produced mainly by the interaction between the baroclinic wave and zonal-mean state (total zonal-mean flow velocity and buoyancy stratification) but the timescale of the nonlinear oscillations is largely controlled by the diffusivity. When the boundary condition is non-slip, the nonlinear oscillations are further damped and slowed by the diffusive process. Since the free-slip (non-slip) boundary condition is the zero drag (infinite drag) limit of the more realistic drag boundary condition, the nonlinear oscillations obtained with the two types of boundary conditions are two extremes for more realistic nonlinear oscillations.
Nonlinear longitudinal oscillations of fuel in rockets feed lines with gas-liquid damper
NASA Astrophysics Data System (ADS)
Avramov, K. V.; Filipkovsky, S.; Tonkonogenko, A. M.; Klimenko, D. V.
2016-03-01
The mathematical model of the fuel oscillations in the rockets feed lines with gas-liquid dampers is derived. The nonlinear model of the gas-liquid damper is suggested. The vibrations of fuel in the feed lines with the gas-liquid dampers are considered nonlinear. The weighted residual method is applied to obtain the finite degrees of freedom nonlinear model of the fuel oscillations. Shaw-Pierre nonlinear normal modes are applied to analyze free vibrations. The forced oscillations of the fuel at the principle resonances are analyzed. The stability of the forced oscillations is investigated. The results of the forced vibrations analysis are shown on the frequency responses.
Nonlinear mechanical resonators for ultra-sensitive mass detection
Datskos, Panos G; Lavrik, Nickolay V
2014-01-01
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.
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 novel oscillation of polaritons in the optical microcavity
NASA Astrophysics Data System (ADS)
Zhang, Yongchang; Zhou, Xiangfa; Guo, Guangcan; Zhou, Xingxiang; Pu, Han; Zhou, Zhengwei
2014-03-01
As a kind of new state of matter, Bose-Einstein condensation (BEC) in a dilute gas of trapped atoms is able to exhibit quantum phenomena on macroscopic scales. Recently, BEC of microcavity polaritons had been experimentally demonstrated. As a kind of bosonic quasi-particle which generates from the strong light-matter coupling, the polariton can be manipulated by the external laser field, and it provides a platform to simulate strongly correlated many-body models in the photon-coupled microcavity array. In this talk we present a scheme for simulating the nonlinear tunneling between two bosonic condensations in the microcavity system. Due to the controllability of the polariton, the effective nonlinear tunneling between two condensates of polaritons can be easily induced by the external controlling fields. In our work, a kind of two modes polariton model is derived, in which nonlinear tunneling strength depends on the difference of the particles in such two kinds of modes. We investigate the mean-field behaviors for such kind of double-mode polariton model, and we find that it is analogous to the model of the pendulum with variable pendulum length. Furthermore, some novel oscillation modes are revealed.
Non-Linear Oscillation in Ionic Current Due to Size Effect in Glass Nanopipette
NASA Astrophysics Data System (ADS)
Takami, Tomohide; Deng, Xiao Long; Son, Jong Wan; Kang, Eun Ji; Kawai, Tomoji; Park, Bae Ho
2012-11-01
We studied the size effect of the ionic current in glass pipette, and found an interesting 2.7 mHz oscillation at 50 nm. In this study, we would like to discuss the mechanism of the non-linear oscillation. Cation-rich layer with its Debye length λ exists in nanopipette, and its conductivity σd is lower than that in the central bulk layer σb in this study. The pressure difference ΔP = ΔcRT where Δc is the difference in concentrations between in and out of the pipette. Then, the ionic current I can be estimated by using Hagen-Poiseuille equation; I =π/8 η ΔcRT/l {σdr4 + (σb -σd) (λ - r) 2 (r2 + 2 rλ -λ2) } . (r : inner radius, l: pipette length, η: viscosity) The last term indicates the non-linear oscillation. Moreover, we roughly estimated λ = 2.08 ×(2r) 1 / 2. Then, the bulk layer appears appropriately when 2 r 50 nm, which causes the effective ionic current oscillation. This work was supported by KOSEF NRL Program grant funded by the Korea Government MEST (Grant No. 2010-0024525 and R0A-2008-000-20052-0), and WCU Program through the KOSEF funded by the MEST (Grant No. R31-2008-000-10057-0).
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
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
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.
Transient dynamics of pulse-coupled oscillators with nonlinear charging curves.
O'Keeffe, Kevin P
2016-03-01
We consider the transient behavior of globally coupled systems of identical pulse-coupled oscillators. Synchrony develops through an aggregation phenomenon, with clusters of synchronized oscillators forming and growing larger in time. Previous work derived expressions for these time dependent clusters, when each oscillator obeyed a linear charging curve. We generalize these results to cases where the charging curves have nonlinearities.
Nonlinear oscillations in an electrolyte solution under ac voltage.
Schnitzer, Ory; Yariv, Ehud
2014-03-01
The response of an electrolyte solution bounded between two blocking electrodes subjected to an ac voltage is considered. We focus on the pertinent thin-double-layer limit, where this response is governed by a reduced dynamic model [L. Højgaard Olesen, M. Z. Bazant, and H. Bruus, Phys. Rev. E 82, 011501 (2010)]. During a transient stage, the system is nonlinearly entrained towards periodic oscillations of the same frequency as that of the applied voltage. Employing a strained-coordinate perturbation scheme, valid for moderately large values of the applied voltage amplitude V, we obtain a closed-form asymptotic approximation for the periodic orbit which is in remarkable agreement with numerical computations. The analysis elucidates the nonlinear characteristics of the system, including a slow (logarithmic) growth of the zeta-potential amplitude with V and a phase straining scaling as V-1lnV. In addition, an asymptotic current-voltage relation is provided, capturing the numerically observed rapid temporal variations in the electric current. PMID:24730837
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
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. PMID
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.
Chemical oscillations arise solely from kinetic nonlinearity and hence can occur near equilibrium.
Walz, D; Caplan, S R
1995-01-01
A minimal kinetic scheme for a system displaying sustained chemical oscillations is presented. The system is isothermal, and all steps in the scheme are kinetically reversible. The oscillations are analyzed and the crucial points elucidated. Both positive and negative feedback, if properly introduced, support oscillations, provided the state responsible for feedback is optimally buffered. It is shown that the requisite nonlinearity is introduced at the kinetic level because of feedback regulation and not, as is usually assumed, by large affinities that introduce nonlinearity at the thermodynamic level. Hence, sustained oscillations may occur near equilibrium. PMID:8580313
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.
Fundamental threshold of chaos in some nonlinear oscillators
Ryabov, V.B.
1996-06-01
A technique for predicting chaos arising in a broad class of nonlinear oscillatory systems is proposed. It is based on the notion of running Lyapunov exponents and uses the local stability properties of trajectories for determining the {open_quote}{open_quote}safe{close_quote}{close_quote} areas in the phase space where any trajectory is regular and stable in the sense of Lyapunov. The combination of this approach with harmonic balance method permits to obtain the corresponding {open_quote}{open_quote}safe{close_quote}{close_quote} regions in the control parameter space. The borders of these regions may be considered as threshold lines delimiting the areas of possible chaotic instability. An example of the two-well Duffing oscillator demonstrates good agreement between theoretically predicted values of control parameters where chaos arises with those obtained numerically. The technique is especially effective for rather high dissipation levels when other known methods such as Melnikov{close_quote}s criterion or combination of harmonic balance with analysis of variational equations fail to provide correct results. {copyright} {ital 1996 American Institute of Physics.}
Observation of chaotic dynamics of coupled nonlinear oscillators
Van Buskirk, R.; Jeffries, C.
1985-05-01
The nonlinear charge storage property of driven Si p-n junction passive resonators gives rise to chaotic dynamics: period doubling, chaos, periodic windows, and an extended period-adding sequence corresponding to entrainment of the resonator by successive subharmonics of the driving frequency. The physical system is described; equations of motion and iterative maps are reviewed. Computed behavior is compared to data, with reasonable agreement for Poincare sections, bifurcation diagrams, and phase diagrams in parameter space (drive voltage, drive frequency). N = 2 symmetrically coupled resonators are found to display period doubling, Hopf bifurcations, entrainment horns (''Arnol'd tongues''), breakup of the torus, and chaos. This behavior is in reasonable agreement with theoretical models based on the characteristics of single-junction resonators. The breakup of the torus is studied in detail, by Poincare sections and by power spectra. Also studied are oscillations of the torus and cyclic crises. A phase diagram of the coupled resonators can be understood from the model. Poincare sections show self-similarity and fractal structure, with measured values of fractal dimension d = 2.03 and d = 2.23 for N = 1 and N = 2 resonators, respectively. Two line-coupled resonators display first a Hopf bifurcation as the drive parameter is increased, in agreement with the model. For N = 4 and N = 12 line-coupled resonators complex quasiperiodic behavior is observed with up to 3 and 4 incommensurate frequencies, respectively.
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.
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.
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.
Deck the Halls. Animated Displays: Coupled Mechanical Oscillators.
ERIC Educational Resources Information Center
Pizzo, Joe, Ed.
1992-01-01
Describes a set of displays on the theme of coupled mechanical oscillators. Displays encompass three common demonstrations: (1) a coupled pair of identical pendulums; (2) a multiple-pendulum resonance demonstration; and (3) a Wilberforce coupled oscillator. (MDH)
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.
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.
Wave breaking of nonlinear electron oscillations in a warm magnetized plasma
Pramanik, Sourav; Maity, Chandan; Chakrabarti, Nikhil
2014-02-15
Wave breaking phenomena of nonlinear electron oscillations around a homogeneous background of massive ions have been studied in a warm magnetized plasma by using Lagrangian variables. An inhomogeneity in the background magnetic field is shown to induce phase mixing and thus breaking of the oscillations. A nonlinear analysis in Lagrangian variables predicts that wave breaking may disappear above a critical value of the electron temperature. An estimate for the critical temperature has been provided.
Sufficient conditions for oscillation of a nonlinear fractional nabla difference system.
Li, Wei Nian; Sheng, Weihong
2016-01-01
In this paper, we study the oscillation of nonlinear fractional nabla difference equations of the form [Formula: see text]where c and α are constants, [Formula: see text] is the Riemann-Liouville fractional nabla difference operator of order [Formula: see text] is a real number, and [Formula: see text]. Some sufficient conditions for oscillation are established. PMID:27512637
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
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)
Leadenham, S.; Erturk, A.
2014-11-01
Over the past few years, nonlinear oscillators have been given growing attention due to their ability to enhance the performance of energy harvesting devices by increasing the frequency bandwidth. Duffing oscillators are a type of nonlinear oscillator characterized by a symmetric hardening or softening cubic restoring force. In order to realize the cubic nonlinearity in a cantilever at reasonable excitation levels, often an external magnetic field or mechanical load is imposed, since the inherent geometric nonlinearity would otherwise require impractically high excitation levels to be pronounced. As an alternative to magnetoelastic structures and other complex forms of symmetric Duffing oscillators, an M-shaped nonlinear bent beam with clamped end conditions is presented and investigated for bandwidth enhancement under base excitation. The proposed M-shaped oscillator made of spring steel is very easy to fabricate as it does not require extra discrete components to assemble, and furthermore, its asymmetric nonlinear behavior can be pronounced yielding broadband behavior under low excitation levels. For a prototype configuration, linear and nonlinear system parameters extracted from experiments are used to develop a lumped-parameter mathematical model. Quadratic damping is included in the model to account for nonlinear dissipative effects. A multi-term harmonic balance solution is obtained to study the effects of higher harmonics and a constant term. A single-term closed-form frequency response equation is also extracted and compared with the multi-term harmonic balance solution. It is observed that the single-term solution overestimates the frequency of upper saddle-node bifurcation point and underestimates the response magnitude in the large response branch. Multi-term solutions can be as accurate as time-domain solutions, with the advantage of significantly reduced computation time. Overall, substantial bandwidth enhancement with increasing base excitation is
Surface acoustic wave opto-mechanical oscillator and frequency comb generator
NASA Astrophysics Data System (ADS)
Savchenkov, A. A.; Matsko, A. B.; Ilchenko, V. S.; Seidel, D.; Maleki, L.
2011-09-01
We report on realization of an efficient triply resonant coupling between two long lived optical modes and a high frequency surface acoustic wave (SAW) mode of the same monolithic crystalline whispering gallery mode resonator. The coupling results in an opto-mechanical oscillation and generation of a monochromatic SAW. A strong nonlinear interaction of this mechanical mode with other equidistant SAW modes leads to mechanical hyperparametric oscillation and generation of a SAW pulse train and associated frequency comb in the resonator. We visualized the comb by observing the modulation of the light escaping the resonator.
Nonlinear analysis of ubitron, orbitron, and gyroharmonitron mechanisms. Final report
Not Available
1987-11-01
The research program during the contract period consisted of the analysis of the Ubitron/FEL amplifier in three-dimensions. The principal configuration of interest consisted of the propagation of an energetic electron beam through a loss-free rectangular waveguide in the presence of a linearly polarized wiggler field with parabolically tapered pole pieces. The purpose of the tapered pole faces is to provide a mechanism for focussing the electron beam in the plane of the bulk wiggler induced oscillation. A nonlinear theory and simulation code has been developed to study this configuration which can treat a multiple mode interaction, harmonic growth, efficiency enhancement by means of a tapered wiggler, the effect of beam thermal spread on the interaction, the injection of the beam into the wiggler, and detailed facets of the particle dynamics such as Betatron oscillations and velocity shear. Comparisons of the experiment at the Lawrence Livermore National Laboratory are excellent.
Nonlinear dynamics of the heartbeat I. The AV junction: Passive conduit or active oscillator?
NASA Astrophysics Data System (ADS)
West, Bruce J.; Goldberger, Ary L.; Rovner, Galina; Bhargava, Valmik
1985-10-01
Under physiologic conditions, the AV junction is traditionally regarded as a passive conduit for the conduction of impulses from the atria to the ventricles. An alternative view, namely that subsidiary pacemakers play an active role in normal electrophysiologic dynamics during sinus rhythm, has been suggested based on nonlinear models of cardiac oscillators. A central problem has been the development of a simple but explicit mathematical model for coupled nonlinear oscillators relevant both to stable and perturbed cardiac dynamics. We use equations describing an analog electrical circuit with an external d.c. voltage source ( V0) and two nonlinear oscillators with intrinsic frequencies in the ratio of 3:2, comparable to the SA node and AV junction rates. The oscillators are coupled by means of a resistor. 1:1 (SA:AV) phase-locking of the oscillators occurs over a critical range of V0. Externally driving the SA oscillator at increasing rates results in 3:2 AV Wenckebach periodicity and a 2:1 AV block. These findings appear with no assumptions about conduction time or refractoriness. This dynamical model is consistent with the new interpretation that normal sinus rhythm may represent 1:1 coupling of two or more active nonlinear oscillators and also accounts for the appearance of an AV block with critical changes in a single parameter such as the pacing rate.
An apparatus to demonstrate linear and nonlinear oscillations of a pendulum
NASA Astrophysics Data System (ADS)
Mayer, V. V.; Varaksina, E. I.
2016-07-01
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. The dependence can be both linear and nonlinear. The apparatus is equipped with a photoelectric transducer. The signal goes to a computer and is displayed on the monitor as the dependence of the oscillation period on its number. If the position of the pendulum is normal then the oscillations are approximately linear. If the pendulum is turned over then its oscillations become substantially nonlinear.
Phase-flip transition in nonlinear oscillators coupled by dynamic environment.
Sharma, Amit; Shrimali, Manish Dev; Dana, Syamal Kumar
2012-06-01
We study the dynamics of nonlinear oscillators indirectly coupled through a dynamical environment or a common medium. We observed that this form of indirect coupling leads to synchronization and phase-flip transition in periodic as well as chaotic regime of oscillators. The phase-flip transition from in- to anti-phase synchronization or vise-versa is analyzed in the parameter plane with examples of Landau-Stuart and Rössler oscillators. The dynamical transitions are characterized using various indices such as average phase difference, frequency, and Lyapunov exponents. Experimental evidence of the phase-flip transition is shown using an electronic version of the van der Pol oscillators.
Non-Newtonian mechanics of oscillation centers
Dodin, I. Y.; Fisch, N. J.
2008-10-15
Classical particles oscillating in high-frequency or static fields effectively exhibit a modified rest mass m{sub eff} which determines the oscillation center motion. Unlike the true mass, m{sub eff} depends on the field parameters and can be a nonanalytic function of the particle average velocity and the oscillation energy; hence non-Newtonian ''metaplasmas'' that permit a new type of plasma maser, signal rectification, frequency doubling, and one-way walls.
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).
Approximate analytic solutions for singular non-linear oscillators
NASA Technical Reports Server (NTRS)
Bota, K. B.; Mickens, R. E.
1984-01-01
Mickens (1981, 1984) has considered analytic techniques for obtaining approximate solutions to one-dimensional nonlinear oscillatory systems x(double-dot) + x = lambda f(x, x/dot/, lambda) where lambda is a small positive parameter and f is a nonlinear polynomial function of its arguments. However, in certain cases there is interest in the analysis of physical systems for which the nonlinear function f(x, x/dot/, lambda) is singular for finite values of x or x(dot). The present investigation is concerned with the use of existing approximate analytic schemes to obtain solutions to singular nonlinear oscillatory differential equations.
Study of nonlinear oscillations due to exciter control
Abed, E.; Tsolas, N.; Varaiya, P.
1983-01-01
The effect of excitation system parameters on power system stability is studied here. The classical swing equation for a power generator augmented with an exciter is shown to undergo a Hopf bifurcation to periodic solutions. Only unstable oscillations occur for realistic parameter values and characterize the attractor of the stable equilibrium point. Attention is focussed on the global behavior of the oscillations as the critical parameter is varied. The analysis is carried out for a single machine connected to an infinite bus case.
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.
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. PMID:27368777
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.
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).
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.
Nonlinear Mechanics of Athermal Branched Biopolymer Networks.
Rens, R; Vahabi, M; Licup, A J; MacKintosh, F C; Sharma, A
2016-07-01
Naturally occurring biopolymers such as collagen and actin form branched fibrous networks. The average connectivity in branched networks is generally below the isostatic threshold at which central force interactions marginally stabilize the network. In the submarginal regime, for connectivity below this threshold, such networks are unstable toward small deformations unless stabilized by additional interactions such as bending. Here we perform a numerical study on the elastic behavior of such networks. We show that the nonlinear mechanics of branched networks is qualitatively similar to that of filamentous networks with freely hinged cross-links. In agreement with a recent theoretical study,1 we find that branched networks also exhibit nonlinear mechanics consistent with athermal critical phenomena controlled by strain. We obtain the critical exponents capturing the nonlinear elastic behavior near the critical point by performing scaling analysis of the stiffening curves. We find that the exponents evolve with the connectivity in the network. We show that the nonlinear mechanics of disordered networks, independent of the detailed microstructure, can be characterized by a strain-driven second-order phase transition, and that the primary quantitative differences among different architectures are in the critical exponents describing the transition.
New approximate solutions for the strongly nonlinear cubic-quintic duffing oscillators
NASA Astrophysics Data System (ADS)
Karahan, M. M. Fatih; Pakdemirli, Mehmet
2016-06-01
Strongly nonlinear cubic-quintic Duffing oscillator is considered. Approximate solutions are derived using the multiple scales Lindstedt Poincare method (MSLP), a relatively new method developed for strongly nonlinear oscillators. The free undamped oscillator is considered first. Approximate analytical solutions of the MSLP are contrasted with the classical multiple scales (MS) method and numerical simulations. It is found that contrary to the classical MS method, the MSLP can provide acceptable solutions for the case of strong nonlinearities. Next, the forced and damped case is treated. Frequency response curves of both the MS and MSLP methods are obtained and contrasted with the numerical solutions. The MSLP method and numerical simulations are in good agreement while there are discrepancies between the MS and numerical solutions.
Nonlinear Actuation Dynamics of Driven Casimir Oscillators with Rough Surfaces
NASA Astrophysics Data System (ADS)
Broer, Wijnand; Waalkens, Holger; Svetovoy, Vitaly B.; Knoester, Jasper; Palasantzas, George
2015-11-01
At separations below 100 nm, Casimir-Lifshitz forces strongly influence the actuation dynamics of microelectromechanical systems (MEMS) in dry vacuum conditions. For a micron-size plate oscillating near a surface, which mimics a frequently used setup in experiments with MEMS, we show that the roughness of the surfaces significantly influences the qualitative dynamics of the oscillator. Via a combination of analytical and numerical methods, it is shown that surface roughness leads to a clear increase of initial conditions associated with chaotic motion, that eventually lead to stiction between the surfaces. Since stiction leads to a malfunction of MEMS oscillators, our results are of central interest for the design of microdevices. Moreover, stiction is of significance for fundamentally motivated experiments performed with MEMS.
Pradeep, R. Gladwin; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2009-05-15
In this paper we point out the existence of a remarkable nonlocal transformation between the damped harmonic oscillator and a modified Emden-type nonlinear oscillator equation with linear forcing, xe+{alpha}xx+{beta}x{sup 3}+{gamma}x=0, which preserves the form of the time independent integral, conservative Hamiltonian, and the equation of motion. Generalizing this transformation we prove the existence of nonstandard conservative Hamiltonian structure for a general class of damped nonlinear oscillators including Lienard-type systems. Further, using the above Hamiltonian structure for a specific example, namely, the generalized modified Emden equation xe+{alpha}x{sup q}x+{beta}x{sup 2q+1}=0, where {alpha}, {beta}, and q are arbitrary parameters, the general solution is obtained through appropriate canonical transformations. We also present the conservative Hamiltonian structure of the damped Mathews-Lakshmanan oscillator equation. The associated Lagrangian description for all the above systems is also briefly discussed.
Periodically forced ensemble of nonlinearly coupled oscillators: from partial to full synchrony.
Baibolatov, Yernur; Rosenblum, Michael; Zhanabaev, Zeinulla Zh; Kyzgarina, Meyramgul; Pikovsky, Arkady
2009-10-01
We analyze the dynamics of a periodically forced oscillator ensemble with global nonlinear coupling. Without forcing, the system exhibits complicated collective dynamics, even for the simplest case of identical phase oscillators: due to nonlinearity, the synchronous state becomes unstable for certain values of the coupling parameter, and the system settles at the border between synchrony and asynchrony, what can be denoted as partial synchrony. We find that an external common forcing can result in two synchronous states: (i) a weak forcing entrains only the mean field, whereas the individual oscillators remain unlocked to the force and, correspondingly, to the mean field; (ii) a strong forcing fully synchronizes the system, making the phases of all oscillators identical. Analytical results are confirmed by numerics.
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.
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.
Rabi oscillations of two-photon states in nonlinear optical resonators
NASA Astrophysics Data System (ADS)
Sherkunov, Y.; Whittaker, David M.; Fal'ko, Vladimir
2016-02-01
We demonstrate that four-wave mixing processes in high-quality nonlinear resonators can lead to Rabi-like oscillations in photon occupation numbers and second-order correlation functions, being a characteristic feature of the presence of entangled photon pairs in the optical signal. In the case of a system driven by a continuous coherent pump, the oscillations occur in the transient regime. We show that driving the system with pulsed coherent pumping would generate strongly antibunched photon states.
Parametric excitation of high-mode oscillations for a non-linear telegraph equation
Kolesov, Andrei Yu; Rozov, Nikolai Kh
2000-08-31
The problem of parametric excitation of high-mode oscillations is solved for a non-linear telegraph equation with a parametric external excitation and small diffusion. The equation is considered on a finite (spatial) interval with Neumann boundary conditions. It is shown that under a proper choice of parameters of the external excitation this boundary-value problem can have arbitrarily many exponentially stable solutions that are periodic in time and rapidly oscillate with respect to the spatial variable.
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.
Sisto, Renata; Moleti, Arturo
2004-09-01
In this work, growth-rate curves of the 2 f1-f2 distortion product otoacoustic emission (DPOAE) are analyzed in a population of 30 noise exposed subjects, including both normal-hearing and hearing impaired subjects. A particular embedded limit-cycle oscillator equation is used to model the cochlear resonant response at the cochlear places of the primary and secondary tone frequencies (f2 and 2 f1-f2). The parameters of the oscillator equation can be directly interpreted in terms of effectiveness of the cochlear feedback mechanisms associated with the active filter amplification. A two-sources paradigm is included in the model, in agreement with experimental evidence and with the assumptions of more detailed full cochlear models based on the transmission line formalism. According to this paradigm, DPOAEs are nonlinearly generated at the cochlear place that is resonant at frequency f2, and coherently reflected at the 2 f1-f2 place. The analysis shows that the model, which had been previously used to describe the relaxation dynamics of transient evoked otoacoustic emissions (TEOAEs), also correctly predicts the observed growth rate of the DPOAE response as a function of the primary tones amplitude. A significant difference is observed between normal and impaired ears. The comparison between the growth rate curves at different frequencies provides information about the dependence of cochlear tuning on frequency.
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
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.
Ultrasensitive hysteretic force sensing with parametric nonlinear oscillators.
Papariello, Luca; Zilberberg, Oded; Eichler, Alexander; Chitra, R
2016-08-01
We propose a method for linear detection of weak forces using parametrically driven nonlinear resonators. The method is based on a peculiar feature in the response of the resonator to a near resonant periodic external force. This feature stems from a complex interplay among the parametric drive, external force, and nonlinearities. For weak parametric drive, the response exhibits the standard Duffing-like single jump hysteresis. For stronger drive amplitudes, we find a qualitatively new double jump hysteresis which arises from stable solutions generated by the cubic Duffing nonlinearity. The additional jump exists only if the external force is present and the frequency at which it occurs depends linearly on the amplitude of the external force, permitting a straightforward ultrasensitive detection of weak forces. With state-of-the-art nanomechanical resonators, our scheme should permit force detection in the attonewton range. PMID:27627292
Ultrasensitive hysteretic force sensing with parametric nonlinear oscillators
NASA Astrophysics Data System (ADS)
Papariello, Luca; Zilberberg, Oded; Eichler, Alexander; Chitra, R.
2016-08-01
We propose a method for linear detection of weak forces using parametrically driven nonlinear resonators. The method is based on a peculiar feature in the response of the resonator to a near resonant periodic external force. This feature stems from a complex interplay among the parametric drive, external force, and nonlinearities. For weak parametric drive, the response exhibits the standard Duffing-like single jump hysteresis. For stronger drive amplitudes, we find a qualitatively new double jump hysteresis which arises from stable solutions generated by the cubic Duffing nonlinearity. The additional jump exists only if the external force is present and the frequency at which it occurs depends linearly on the amplitude of the external force, permitting a straightforward ultrasensitive detection of weak forces. With state-of-the-art nanomechanical resonators, our scheme should permit force detection in the attonewton range.
Failure of the method of slowly varying amplitude and phase for non-linear, singular oscillators
NASA Technical Reports Server (NTRS)
Mickens, R. E.; Ramadhani, I.
1992-01-01
It is shown that the method of slowly varying amplitude and phase yields erroneous results in the study of the mathematical properties of nonlinear singular oscillator systems. The analytical solution is described in which the phase function is constant and for which a special limiting behavior exists when the wavelength is zero. The previous method based on the condition of boundedness cannot be satisfied for nonlinear singular characteristics, and the erroneous designation of the expansion parameter is identified.
Finite-size-induced transitions to synchrony in oscillator ensembles with nonlinear global coupling
NASA Astrophysics Data System (ADS)
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 nonlinear characteristic of El Niño-Southern Oscillation events
NASA Astrophysics Data System (ADS)
Duan, Wansuo; Xue, Feng; Mu, Mu
2010-05-01
We use the approach of conditional nonlinear optimal perturbation (CNOP) to investigate the optimal precursory disturbances in a theoretical El Niño-Southern Oscillation (ENSO) model and then an intermediate model. By exploring the dynamical behaviors of the El Niño events caused by these CNOP-type precursors, a characteristic for this kind of theoretical El Niño events is shown, i.e., the stronger El Niño events tend to decay faster and have shorter durations of the decaying phase. By examining the observed El Niño events, it is found that the Niño-3.4 SSTA are more potential than the Niño-3 SSTA in illustrating the decaying characteristic of the theoretical El Niño events. In particular, it is the Niño-3.4 indices for the strong El Niño events during 1981-2007 that roughly show the decaying characteristic. Based on the physics of the theoretical model, the mechanism responsible for the above decaying characteristic of strong El Niño events is explored. The analysis demonstrates that the property of the stronger El Niño event decaying faster can be realized only through the linear dynamics with the combined effects of the rising of thermocline and the mean upwelling, but that of the stronger El Niño event having a shorter duration of the decaying phase results from a nonlinear mechanism. It is shown that the nonlinearity related to the anomalous temperature advection in the tropical Pacific shortens the duration of the decaying phase for El Niño event. The stronger the El Niño event, the stronger the nonlinearity, then the more considerable the suppressing of the nonlinearity on the duration of the decaying phase for El Niño event. This explains why the stronger El Niño events have shorter durations of the decaying phase. Also, this sheds light on why the observed strong El Niño events are more likely to show this characteristic.
NASA Astrophysics Data System (ADS)
Janagal, Lavneet; Parmananda, P.
2012-11-01
We study synchronization in an ensemble of oscillators residing in a finite two-dimensional space. The interaction between the oscillators is governed by their spatial movement. The coupling is unidirectional and is of the intermediate kind, with the spatial vision of each oscillator deciding the number of oscillators to which it is coupled. We also analyze how the extent of synchronization, characterized by the order parameter, depends upon the system parameters, such as spatial vision, spatial motion, and strength of the coupling. The model systems employed here are the Van der Pol oscillator and the Brusselator. Furthermore, for the same spatial configuration, both linear and nonlinear coupling schemes are studied and their results compared.
Janagal, Lavneet; Parmananda, P
2012-11-01
We study synchronization in an ensemble of oscillators residing in a finite two-dimensional space. The interaction between the oscillators is governed by their spatial movement. The coupling is unidirectional and is of the intermediate kind, with the spatial vision of each oscillator deciding the number of oscillators to which it is coupled. We also analyze how the extent of synchronization, characterized by the order parameter, depends upon the system parameters, such as spatial vision, spatial motion, and strength of the coupling. The model systems employed here are the Van der Pol oscillator and the Brusselator. Furthermore, for the same spatial configuration, both linear and nonlinear coupling schemes are studied and their results compared. PMID:23214863
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.
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.
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.
Synchronization properties of self-sustained mechanical oscillators.
Arroyo, Sebastián I; Zanette, Damián H
2013-05-01
We study, both analytically and numerically, the dynamics of mechanical oscillators kept in motion by a feedback force, which is generated electronically from a signal produced by the oscillators themselves. This kind of self-sustained systems may become standard in the design of frequency-control devices at microscopic scales. Our analysis is thus focused on their synchronization properties under the action of external forces and on the joint dynamics of two to many coupled oscillators. Existence and stability of synchronized motion are assessed in terms of the mechanical properties of individual oscillators, namely, their natural frequencies and damping coefficients, and synchronization frequencies are determined. Similarities and differences with synchronization phenomena in other coupled oscillating systems are emphasized.
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.…
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.
RF Spectrum Sensing Based on an Overdamped Nonlinear Oscillator Ring for Cognitive Radios.
Tang, Zhi-Ling; Li, Si-Min; Yu, Li-Juan
2016-01-01
Existing spectrum-sensing techniques for cognitive radios require an analog-to-digital converter (ADC) to work at high dynamic range and a high sampling rate, resulting in high cost. Therefore, in this paper, a spectrum-sensing method based on a unidirectionally coupled, overdamped nonlinear oscillator ring is proposed. First, the numerical model of such a system is established based on the circuit of the nonlinear oscillator. Through numerical analysis of the model, the critical condition of the system's starting oscillation is determined, and the simulation results of the system's response to Gaussian white noise and periodic signal are presented. The results show that once the radio signal is input into the system, it starts oscillating when in the critical region, and the oscillating frequency of each element is fo/N, where fo is the frequency of the radio signal and N is the number of elements in the ring. The oscillation indicates that the spectrum resources at fo are occupied. At the same time, the sampling rate required for an ADC is reduced to the original value, 1/N. A prototypical circuit to verify the functionality of the system is designed, and the sensing bandwidth of the system is measured. PMID:27294928
RF Spectrum Sensing Based on an Overdamped Nonlinear Oscillator Ring for Cognitive Radios.
Tang, Zhi-Ling; Li, Si-Min; Yu, Li-Juan
2016-01-01
Existing spectrum-sensing techniques for cognitive radios require an analog-to-digital converter (ADC) to work at high dynamic range and a high sampling rate, resulting in high cost. Therefore, in this paper, a spectrum-sensing method based on a unidirectionally coupled, overdamped nonlinear oscillator ring is proposed. First, the numerical model of such a system is established based on the circuit of the nonlinear oscillator. Through numerical analysis of the model, the critical condition of the system's starting oscillation is determined, and the simulation results of the system's response to Gaussian white noise and periodic signal are presented. The results show that once the radio signal is input into the system, it starts oscillating when in the critical region, and the oscillating frequency of each element is fo/N, where fo is the frequency of the radio signal and N is the number of elements in the ring. The oscillation indicates that the spectrum resources at fo are occupied. At the same time, the sampling rate required for an ADC is reduced to the original value, 1/N. A prototypical circuit to verify the functionality of the system is designed, and the sensing bandwidth of the system is measured.
RF Spectrum Sensing Based on an Overdamped Nonlinear Oscillator Ring for Cognitive Radios
Tang, Zhi-Ling; Li, Si-Min; Yu, Li-Juan
2016-01-01
Existing spectrum-sensing techniques for cognitive radios require an analog-to-digital converter (ADC) to work at high dynamic range and a high sampling rate, resulting in high cost. Therefore, in this paper, a spectrum-sensing method based on a unidirectionally coupled, overdamped nonlinear oscillator ring is proposed. First, the numerical model of such a system is established based on the circuit of the nonlinear oscillator. Through numerical analysis of the model, the critical condition of the system’s starting oscillation is determined, and the simulation results of the system’s response to Gaussian white noise and periodic signal are presented. The results show that once the radio signal is input into the system, it starts oscillating when in the critical region, and the oscillating frequency of each element is fo/N, where fo is the frequency of the radio signal and N is the number of elements in the ring. The oscillation indicates that the spectrum resources at fo are occupied. At the same time, the sampling rate required for an ADC is reduced to the original value, 1/N. A prototypical circuit to verify the functionality of the system is designed, and the sensing bandwidth of the system is measured. PMID:27294928
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.
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. PMID:26671817
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.
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.
Sustained small oscillations in nonlinear control systems. [launch vehicle dynamics
NASA Technical Reports Server (NTRS)
George, J. H.; Gunderson, R. W.; Hahn, H.
1975-01-01
Some results of bifurcation theory were used to study the existence of small-amplitude periodic behavior in launch vehicle dynamics, assuming that nonlinearity exists as a cubic term in the rudder response. The analysis follows closely Sattinger's (1973) approach to the theory of periodic bifurcations. The conditions under which a bifurcating branch of orbitally stable periodic solutions will exist are determined. It is shown that in more complicated cases, the conditions under which the system matrix has a pair of simple purely imaginary eigenvalues can be determined with the aid of linear stability techniques.
Integrable nonlinear parity-time-symmetric optical oscillator.
Hassan, Absar U; Hodaei, Hossein; Miri, Mohammad-Ali; Khajavikhan, Mercedeh; Christodoulides, Demetrios N
2016-04-01
The nonlinear dynamics of a balanced parity-time-symmetric optical microring arrangement are analytically investigated. By considering gain and loss saturation effects, the pertinent conservation laws are explicitly obtained in the Stokes domain, thus establishing integrability. Our analysis indicates the existence of two regimes of oscillatory dynamics and frequency locking, both of which are analogous to those expected in linear parity-time-symmetric systems. Unlike other saturable parity-time-symmetric systems considered before, the model studied in this work first operates in the symmetric regime and then enters the broken parity-time phase.
Integrable nonlinear parity-time-symmetric optical oscillator.
Hassan, Absar U; Hodaei, Hossein; Miri, Mohammad-Ali; Khajavikhan, Mercedeh; Christodoulides, Demetrios N
2016-04-01
The nonlinear dynamics of a balanced parity-time-symmetric optical microring arrangement are analytically investigated. By considering gain and loss saturation effects, the pertinent conservation laws are explicitly obtained in the Stokes domain, thus establishing integrability. Our analysis indicates the existence of two regimes of oscillatory dynamics and frequency locking, both of which are analogous to those expected in linear parity-time-symmetric systems. Unlike other saturable parity-time-symmetric systems considered before, the model studied in this work first operates in the symmetric regime and then enters the broken parity-time phase. PMID:27176305
Interfacing ultracold atoms and mechanical oscillators on an atom chip
NASA Astrophysics Data System (ADS)
Treutlein, Philipp
2010-03-01
Ultracold atoms can be trapped and coherently manipulated close to a chip surface using atom chip technology. This opens the exciting possibility of studying interactions between atoms and on-chip solid-state systems such as micro- and nanostructured mechanical oscillators. One goal is to form hybrid quantum systems, in which atoms are used to read out, cool, and coherently manipulate the oscillators' state. In our work, we investigate different coupling mechanisms between ultracold atoms and mechanical oscillators. In a first experiment, we use atom-surface forces to couple the vibrations of a mechanical cantilever to the motion of a Bose-Einstein condensate in a magnetic microtrap on an atom chip. The atoms are trapped at about one micrometer distance from the cantilever surface. We make use of the coupling to read out the cantilever vibrations with the atoms and observe resonant coupling to several well-resolved mechanical modes of the condensate. In a second experiment, we investigate coupling via a 1D optical lattice that is formed by a laser beam retroreflected from a SiN membrane oscillator. The optical lattice serves as a `transfer rod' that couples vibrations of the membrane to the atoms and vice versa. We point out that the strong coupling regime can be reached in coupled atom-oscillator systems by placing both the atoms and the oscillator in a high-finesse optical cavity.
Role of fluctuations and nonlinearities on field emission nanomechanical self-oscillators
NASA Astrophysics Data System (ADS)
Barois, T.; Perisanu, S.; Vincent, P.; Purcell, S. T.; Ayari, A.
2013-11-01
A theoretical and experimental description of the threshold, amplitude, and stability of a self-oscillating nanowire in a field emission configuration is presented. Two thresholds for the onset of self-oscillation are identified, one induced by fluctuations of the electromagnetic environment and a second revealed by these fluctuations by measuring the probability density function of the current. The ac and dc components of the current and the phase stability are quantified. An ac to dc ratio above 100% and an Allan deviation of 1.3×10-5 at room temperature can be attained. Finally, it is shown that a simple nonlinear model cannot describe the equilibrium effective potential in the self-oscillating regime due to the high amplitude of oscillations.
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.
NASA Astrophysics Data System (ADS)
Hosen, Md. Alal; Chowdhury, M. S. H.; Ali, Mohammad Yeakub; Ismail, Ahmad Faris
In the present paper, a novel analytical approximation technique has been proposed based on the energy balance method (EBM) to obtain approximate periodic solutions for the focus generalized highly nonlinear oscillators. The expressions of the natural frequency-amplitude relationship are obtained using a novel analytical way. The accuracy of the proposed method is investigated on three benchmark oscillatory problems, namely, the simple relativistic oscillator, the stretched elastic wire oscillator (with a mass attached to its midpoint) and the Duffing-relativistic oscillator. For an initial oscillation amplitude A0 = 100, the maximal relative errors of natural frequency found in three oscillators are 2.1637%, 0.0001% and 1.201%, respectively, which are much lower than the errors found using the existing methods. It is highly remarkable that an excellent accuracy of the approximate natural frequency has been found which is valid for the whole range of large values of oscillation amplitude as compared with the exact ones. Very simple solution procedure and high accuracy that is found in three benchmark problems reveal the novelty, reliability and wider applicability of the proposed analytical approximation technique.
Scaling and synchronization in a ring of diffusively coupled nonlinear oscillators.
Senthilkumar, D V; Muruganandam, P; Lakshmanan, M; Kurths, J
2010-06-01
Chaos synchronization in a ring of diffusively coupled nonlinear oscillators driven by an external identical oscillator is studied. Based on numerical simulations we show that by introducing additional couplings at (mN(c)+1)-th oscillators in the ring, where m is an integer and N(c) is the maximum number of synchronized oscillators in the ring with a single coupling, the maximum number of oscillators that can be synchronized can be increased considerably beyond the limit restricted by size instability. We also demonstrate that there exists an exponential relation between the number of oscillators that can support stable synchronization in the ring with the external drive and the critical coupling strength ε(c) with a scaling exponent γ. The critical coupling strength is calculated by numerically estimating the synchronization error and is also confirmed from the conditional Lyapunov exponents of the coupled systems. We find that the same scaling relation exists for m couplings between the drive and the ring. Further, we have examined the robustness of the synchronous states against Gaussian white noise and found that the synchronization error exhibits a power-law decay as a function of the noise intensity indicating the existence of both noise-enhanced and noise-induced synchronizations depending on the value of the coupling strength ε. In addition, we have found that ε(c) shows an exponential decay as a function of the number of additional couplings. These results are demonstrated using the paradigmatic models of Rössler and Lorenz oscillators.
Yousif, Nada A B; Denham, Michael
2005-12-01
The thalamocortical network is modelled using the Wilson-Cowan equations for neuronal population activity. We show that this population model with biologically derived parameters possesses intrinsic nonlinear oscillatory dynamics, and that the frequency of oscillation lies within the spindle range. Spindle oscillations are an early sleep oscillation characterized by high-frequency bursts of action potentials followed by a period of quiescence, at a frequency of 7-14 Hz. Spindles are generally regarded as being generated by intrathalamic circuitry, as decorticated thalamic slices and the isolated thalamic reticular nucleus exhibit spindles. However, the role of cortical feedback has been shown to regulate and synchronize the oscillation. Previous modelling studies have mainly used conductance-based models and hence the mechanism relied upon the inclusion of ionic currents, particularly the T-type calcium current. Here we demonstrate that spindle-frequency oscillatory activity can also arise from the nonlinear dynamics of the thalamocortical circuit, and we use bifurcation analysis to examine the robustness of this oscillation in terms of the functional range of the parameters used in the model. The results suggest that the thalamocortical circuit has intrinsic nonlinear population dynamics which are capable of providing robust support for oscillatory activity within the frequency range of spindle oscillations.
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.
Global oscillation mechanism in the stochastic Lotka model.
Kashcheyevs, V; Kuzovkov, V N
2001-06-01
The microscopic one-parameter kinetic model of the oscillatory A+B-->2 B reaction (Lotka model) is studied using direct Monte Carlo simulations and analytical methods. Percolation is proposed as the mechanism of global oscillations that are not limited to any finite size of a system. An analytical estimate of the oscillation frequency is derived and compared to computer simulations. We also observe the transition from synchronized oscillations to specific f(-2) noise in two dimensions which was previously reported for self-organized critical models.
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
NASA Astrophysics Data System (ADS)
Di Egidio, Angelo; Contento, Alessandro; Vestroni, Fabrizio
2015-12-01
An open-cross section thin-walled beam model, already developed by the authors, has been conveniently simplified while maintaining the capacity of accounting for the significant nonlinear warping effects. For a technical range of geometrical and mechanical characteristics of the beam, the response is characterized by the torsional curvature prevailing over the flexural ones. A Galerkin discretization is performed by using a suitable expansion of displacements based on shape functions. The attention is focused on the dynamic response of the beam to a harmonic force, applied at the free end of the cantilever beam. The excitation is directed along the symmetry axis of the beam section. The stability of the one-component oscillations has been investigated using the analytical model, showing the importance of the internal resonances due to the nonlinear warping coupling terms. Comparison with the results provided by a computational finite element model has been performed. The good agreement among the results of the analytical and the computational models confirms the effectiveness of the simplified model of a nonlinear open-cross section thin-walled beam and overall the important role of the warping and of the torsional elongation in the study of the one-component dynamic oscillations and their stability.
Noise-induced transitions in a double-well oscillator with nonlinear dissipation
NASA Astrophysics Data System (ADS)
Semenov, Vladimir V.; Neiman, Alexander B.; Vadivasova, Tatyana E.; Anishchenko, Vadim S.
2016-05-01
We develop a model of bistable oscillator with nonlinear dissipation. Using a numerical simulation and an electronic circuit realization of this system we study its response to additive noise excitations. We show that depending on noise intensity the system undergoes multiple qualitative changes in the structure of its steady-state probability density function (PDF). In particular, the PDF exhibits two pitchfork bifurcations versus noise intensity, which we describe using an effective potential and corresponding normal form of the bifurcation. These stochastic effects are explained by the partition of the phase space by the nullclines of the deterministic oscillator.
Noise-induced transitions in a double-well oscillator with nonlinear dissipation.
Semenov, Vladimir V; Neiman, Alexander B; Vadivasova, Tatyana E; Anishchenko, Vadim S
2016-05-01
We develop a model of bistable oscillator with nonlinear dissipation. Using a numerical simulation and an electronic circuit realization of this system we study its response to additive noise excitations. We show that depending on noise intensity the system undergoes multiple qualitative changes in the structure of its steady-state probability density function (PDF). In particular, the PDF exhibits two pitchfork bifurcations versus noise intensity, which we describe using an effective potential and corresponding normal form of the bifurcation. These stochastic effects are explained by the partition of the phase space by the nullclines of the deterministic oscillator.
Noise-induced transitions in a double-well oscillator with nonlinear dissipation.
Semenov, Vladimir V; Neiman, Alexander B; Vadivasova, Tatyana E; Anishchenko, Vadim S
2016-05-01
We develop a model of bistable oscillator with nonlinear dissipation. Using a numerical simulation and an electronic circuit realization of this system we study its response to additive noise excitations. We show that depending on noise intensity the system undergoes multiple qualitative changes in the structure of its steady-state probability density function (PDF). In particular, the PDF exhibits two pitchfork bifurcations versus noise intensity, which we describe using an effective potential and corresponding normal form of the bifurcation. These stochastic effects are explained by the partition of the phase space by the nullclines of the deterministic oscillator. PMID:27300883
Javanainen, Juha
2010-05-15
We study theoretically an atomic Bose-Einstein condensate in a double-well trap, both quantum-mechanically and classically, under conditions such that in the classical model an unstable equilibrium dissolves into large-scale oscillations of the atoms between the potential wells. Quantum mechanics alone does not exhibit such nonlinear dynamics, but measurements of the atom numbers in the potential wells may nevertheless cause the condensate to behave essentially classically.
Nazarov, V E; Kolpakov, A B; Radostin, A V
2012-07-01
The results of experimental and theoretical studies of low-frequency nonlinear acoustics phenomena (amplitude-dependent loss, resonance frequency shifts, and a generation of second and third harmonics) in a magnesite rod resonator are presented. Acceleration and velocity oscillograms of vibrations of the free boundary of the resonator caused by harmonic excitations were measured and analyzed. A theoretical description of the observed amplitude dependences was carried out within the framework of the phenomenological state equations that contain either of the two types of hysteretic nonlinearity (elastic and inelastic). The type of hysteresis and parameters of acoustic nonlinearity of magnesite were established from comparing the experimental measurements with the theoretical dependences. The values of the parameters were anomalously high even when compared to those of other strongly nonlinear polycrystalline materials such as granite, marble, limestone, sandstone, etc.
Single-atom quantum control of macroscopic mechanical oscillators
NASA Astrophysics Data System (ADS)
Bariani, F.; Otterbach, J.; Tan, Huatang; Meystre, P.
2014-01-01
We investigate a hybrid electromechanical system consisting of a pair of charged macroscopic mechanical oscillators coupled to a small ensemble of Rydberg atoms. The resonant dipole-dipole coupling between an internal atomic Rydberg transition and the mechanics allows cooling to its motional ground state with a single atom despite the considerable mass imbalance between the two subsystems. We show that the rich electronic spectrum of Rydberg atoms, combined with their high degree of optical control, paves the way towards implementing various quantum-control protocols for the mechanical oscillators.
Negative nonlinear damping of a multilayer graphene mechanical resonator
NASA Astrophysics Data System (ADS)
Singh, Vibhor; Shevchuk, Olga; Blanter, Ya. M.; Steele, Gary A.
2016-06-01
We experimentally investigate the nonlinear response of a multilayer graphene resonator using a superconducting microwave cavity to detect its motion. The radiation pressure force is used to drive the mechanical resonator in an optomechanically induced transparency configuration. By varying the amplitudes of drive and probe tones, the mechanical resonator can be brought into a nonlinear limit. Using the calibration of the optomechanical coupling, we quantify the mechanical Duffing nonlinearity. By increasing the drive force, we observe a decrease in the mechanical dissipation rate at large amplitudes, suggesting a negative nonlinear damping mechanism in the graphene resonator. Increasing the optomechanical backaction further, we observe instabilities in the mechanical response.
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.
Quantum correlations and entanglement in a model comprised of a short chain of nonlinear oscillators
NASA Astrophysics Data System (ADS)
Kalaga, J. K.; Kowalewska-Kudłaszyk, A.; Leoński, W.; Barasiński, A.
2016-09-01
We discuss a model comprised of a chain of three Kerr-like nonlinear oscillators pumped by two modes of external coherent field. We show that the system can be treated as nonlinear quantum scissors and behave as a three-qubit model. For such situation, different types of tripartite entangled states can be generated, even when damping effects are present in the system. Some amount of such entanglement can survive even in a long-time limit. The flow of bipartite entanglement between subsystems of the model and relations among first-order correlations, second-order correlations, and the entanglement are discussed.
Heat transfer during nonlinear gas oscillations in a pipe open at one end
NASA Astrophysics Data System (ADS)
Khalimov, G. G.; Galiullin, R. G.; Podymov, V. N.
1983-02-01
The results of an experimental study of heat transfer in a pipe open at one end in which gas oscillations are generated by a flat piston moving harmonically are presented. The oscillograms of pressure and velocity pulsations in those sections of the pipe that are near the linear and second nonlinear resonance provide evidence of pressure and velocity discontinuities. The frequency distributions of the velocity half-amplitudes and Nusselt numbers have a resonant character, and the resonant frequencies are coincident. Heat transfer in pipes open at one end under nonlinear pulsations with the generation of periodic shock waves is adequately described by a quasi-stationary theory with allowance for thermoacoustic effects.
Nonlinear auditory mechanism enhances female sounds for male mosquitoes.
Jackson, Joseph C; Robert, Daniel
2006-11-01
Sound plays an important role in the life history of mosquitoes. Male mosquitoes detect females by the sound generated by their wingbeat. Because female wings are weak acoustic radiators, males have been driven by sexual selection to evolve sensitive acoustic sensors. Mosquito antennae are very sensitive acoustic receivers, featuring up to 16,000 sensory cells, a number comparable with that contained in the human cochlea. The antennal sound receiver exhibits frequency selectivity, input amplification, and self-generated oscillations, features that parallel the functional sophistication of the cochlear amplifier. Although arguably the male antenna is well suited to receiving weak female sounds, the role of active mechanisms in mosquito hearing is far from understood. Previous mechanical studies on mosquito hearing largely focused on the steady-state antennal response to harmonic sounds, mostly evaluating the data through conventional Fourier transforms. Here, we report on the time-resolved mechanical behavior of the male antenna in response to female sounds. Crucially, stimuli were designed to reflect the temporal acoustic profile of a female flying by. With these stimuli, several previously unreported nonlinear features were unveiled, involving amplification, compression, and hysteresis. The time-resolved analysis reveals that, through the active participation of the sensory neurons, the antenna mechanically responds to enlarge its own range of detection. This behavior augments the capacity of the antennal receiver to detect female sounds, enhancing the male's chance to successfully pursue a passing female.
NASA Astrophysics Data System (ADS)
Sun, Yuan Gong; Wong, James S. W.
2007-10-01
We present new oscillation criteria for the second order forced ordinary differential equation with mixed nonlinearities: where , p(t) is positive and differentiable, [alpha]1>...>[alpha]m>1>[alpha]m+1>...>[alpha]n. No restriction is imposed on the forcing term e(t) to be the second derivative of an oscillatory function. When n=1, our results reduce to those of El-Sayed [M.A. El-Sayed, An oscillation criterion for a forced second order linear differential equation, Proc. Amer. Math. Soc. 118 (1993) 813-817], Wong [J.S.W. Wong, Oscillation criteria for a forced second linear differential equations, J. Math. Anal. Appl. 231 (1999) 235-240], Sun, Ou and Wong [Y.G. Sun, C.H. Ou, J.S.W. Wong, Interval oscillation theorems for a linear second order differential equation, Comput. Math. Appl. 48 (2004) 1693-1699] for the linear equation, Nazr [A.H. Nazr, Sufficient conditions for the oscillation of forced super-linear second order differential equations with oscillatory potential, Proc. Amer. Math. Soc. 126 (1998) 123-125] for the superlinear equation, and Sun and Wong [Y.G. Sun, J.S.W. Wong, Note on forced oscillation of nth-order sublinear differential equations, JE Math. Anal. Appl. 298 (2004) 114-119] for the sublinear equation.
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.
The effect of process delay on dynamical behaviors in a self-feedback nonlinear oscillator
NASA Astrophysics Data System (ADS)
Yao, Chenggui; Ma, Jun; Li, Chuan; He, Zhiwei
2016-10-01
The delayed feedback loops play a crucial role in the stability of dynamical systems. The effect of process delay in feedback is studied numerically and theoretically in the delayed feedback nonlinear systems including the neural model, periodic system and chaotic oscillator. The process delay is of key importance in determining the evolution of systems, and the rich dynamical phenomena are observed. By introducing a process delay, we find that it can induce bursting electric activities in the neural model. We demonstrate that this novel regime of amplitude death also exists in the parameter space of feedback strength and process delay for the periodic system and chaotic oscillator. Our results extend the effect of process delay in the paper of Zou et al.(2013) where the process delay can eliminate the amplitude death of the coupled nonlinear systems.
Mechanical oscillations enhance gene delivery into suspended cells
Zhou, Z. L.; Sun, X. X.; Ma, J.; Man, C. H.; Wong, A. S. T.; Leung, A. Y.; Ngan, A. H. W.
2016-01-01
Suspended cells are difficult to be transfected by common biochemical methods which require cell attachment to a substrate. Mechanical oscillations of suspended cells at certain frequencies are found to result in significant increase in membrane permeability and potency for delivery of nano-particles and genetic materials into the cells. Nanomaterials including siRNAs are found to penetrate into suspended cells after subjecting to short-time mechanical oscillations, which would otherwise not affect the viability of the cells. Theoretical analysis indicates significant deformation of the actin-filament network in the cytoskeleton cortex during mechanical oscillations at the experimental frequency, which is likely to rupture the soft phospholipid bilayer leading to increased membrane permeability. The results here indicate a new method for enhancing cell transfection. PMID:26956215
Stochastic non-linear oscillator models of EEG: the Alzheimer's disease case.
Ghorbanian, Parham; Ramakrishnan, Subramanian; Ashrafiuon, Hashem
2015-01-01
In this article, the Electroencephalography (EEG) signal of the human brain is modeled as the output of stochastic non-linear coupled oscillator networks. It is shown that EEG signals recorded under different brain states in healthy as well as Alzheimer's disease (AD) patients may be understood as distinct, statistically significant realizations of the model. EEG signals recorded during resting eyes-open (EO) and eyes-closed (EC) resting conditions in a pilot study with AD patients and age-matched healthy control subjects (CTL) are employed. An optimization scheme is then utilized to match the output of the stochastic Duffing-van der Pol double oscillator network with EEG signals recorded during each condition for AD and CTL subjects by selecting the model physical parameters and noise intensity. The selected signal characteristics are power spectral densities in major brain frequency bands Shannon and sample entropies. These measures allow matching of linear time varying frequency content as well as non-linear signal information content and complexity. The main finding of the work is that statistically significant unique models represent the EC and EO conditions for both CTL and AD subjects. However, it is also shown that the inclusion of sample entropy in the optimization process, to match the complexity of the EEG signal, enhances the stochastic non-linear oscillator model performance. PMID:25964756
Stochastic non-linear oscillator models of EEG: the Alzheimer's disease case
Ghorbanian, Parham; Ramakrishnan, Subramanian; Ashrafiuon, Hashem
2015-01-01
In this article, the Electroencephalography (EEG) signal of the human brain is modeled as the output of stochastic non-linear coupled oscillator networks. It is shown that EEG signals recorded under different brain states in healthy as well as Alzheimer's disease (AD) patients may be understood as distinct, statistically significant realizations of the model. EEG signals recorded during resting eyes-open (EO) and eyes-closed (EC) resting conditions in a pilot study with AD patients and age-matched healthy control subjects (CTL) are employed. An optimization scheme is then utilized to match the output of the stochastic Duffing—van der Pol double oscillator network with EEG signals recorded during each condition for AD and CTL subjects by selecting the model physical parameters and noise intensity. The selected signal characteristics are power spectral densities in major brain frequency bands Shannon and sample entropies. These measures allow matching of linear time varying frequency content as well as non-linear signal information content and complexity. The main finding of the work is that statistically significant unique models represent the EC and EO conditions for both CTL and AD subjects. However, it is also shown that the inclusion of sample entropy in the optimization process, to match the complexity of the EEG signal, enhances the stochastic non-linear oscillator model performance. PMID:25964756
Non-linear Collective Oscillations of Electrons in a Diamagnetic Kepler Trap
NASA Astrophysics Data System (ADS)
Godino, Joseph; Kunhardt, Erich; Carr, Wayne
2001-10-01
The Diamagnetic Kepler Trap is a potential energy well that arises from a static Coulomb potential in a superimposed uniform magnetic field. In an experimental arrangement with this configuration, we generate a system of electrons and ions by ionization of the neutral background gas that has a typical density of 10^12 particles per cubic centimeter. The lifetime of the trapped electrons is sufficiently long that we can observe collective oscillations. Here, we examine these oscillations by coupling a probe to the plasma and measuring the induced current. We find that as we deepen the potential energy well these oscillations progress through a sequence of linear, non-linear and chaotic behavior. Using the photographs of the light emission from the excited neutrals, we observe that the non-linearity of the collective oscillations results from an increase in the trapped electron density that moves in a direction parallel to the magnetic field lines. From the FFT of the induced current, we find that the transition from linearity to chaos occurs through intermittent fluctuations in the measured signal that are manifest in the broadening of the spectrum. Since the applied sphere voltage never collapses, the electrons remain trapped in the potential energy well and we conclude that the chaos results from a breakdown of the collective behavior into that of many individual singly trapped electrons.
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.
Resonance frequencies of lipid-shelled microbubbles in the regime of nonlinear oscillations
Doinikov, Alexander A.; Haac, Jillian F.; Dayton, Paul A.
2009-01-01
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. PMID:18977009
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.
Coupling cold atoms with mechanical oscillators
NASA Astrophysics Data System (ADS)
Montoya, Cris; Valencia, Jose; Geraci, Andrew; Eardley, Matthew; Kitching, John
2014-05-01
Macroscopic systems, coupled to quantum systems with well understood coherence properties, can enable the study of the boundary between quantum microscopic phenomena and macroscopic systems. Ultra-cold atoms can be probed and manipulated with micro-mechanical resonators that provide single-spin sensitivity and sub-micron spatial resolution, facilitating studies of decoherence and quantum control. In the future, hybrid quantum systems consisting of cold atoms interfaced with mechanical devices may have applications in quantum information science. We describe our experiment to couple laser-cooled Rb atoms to a magnetic cantilever tip. This cantilever is precisely defined on the surface of a chip with lithography and the atoms are trapped at micron-scale distances from this chip. To match cantilever mechanical resonances, atomic magnetic resonances are tuned with a magnetic field.
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.
Shukla, P K; Eliasson, B
2007-08-31
We consider nonlinear interactions between intense circularly polarized electromagnetic (CPEM) waves and electron plasma oscillations (EPOs) in a dense quantum plasma, taking into account the electron density response in the presence of the relativistic ponderomotive force and mass increase in the CPEM wave fields. The dynamics of the CPEM waves and EPOs is governed by the two coupled nonlinear Schrödinger equations and Poisson's equation. The nonlinear equations admit the modulational instability of an intense CPEM pump wave against EPOs, leading to the formation and trapping of localized CPEM wave pipes in the electron density hole that is associated with a positive potential distribution in our dense plasma. The relevance of our investigation to the next generation intense laser-solid density plasma interaction experiments is discussed.
Isochronal synchrony and bidirectional communication with delay-coupled nonlinear oscillators.
Zhou, Brian B; Roy, Rajarshi
2007-02-01
We propose a basic mechanism for isochronal synchrony and communication with mutually delay-coupled chaotic systems. We show that two Ikeda ring oscillators, mutually coupled with a propagation delay, synchronize isochronally when both are symmetrically driven by a third Ikeda oscillator. This synchronous operation, unstable in the two delay-coupled oscillators alone, facilitates simultaneous, bidirectional communication of messages with chaotic carrier wave forms. This approach to combine both bidirectional and unidirectional coupling represents an application of generalized synchronization using a mediating drive signal for a spatially distributed and internally synchronized multicomponent system.
Nonlinear in-plane vibrations of inclined cables carrying moving oscillators
NASA Astrophysics Data System (ADS)
Sofi, Alba
2013-04-01
In-plane dynamics of small-sag inclined cables carrying a stream of oscillators moving with arbitrarily varying velocity is addressed. A condensed model of the coupled cable-moving oscillators system is derived by referring cable vibrations to a local Cartesian coordinate system. Specifically, relying on the negligible influence of the inertia forces along the cable chord and assuming a quasi-static stretching during the motion, an appropriate static condensation procedure is applied which enables to account for the chordwise components of the interaction forces between the cable and the moving sub-systems . Thus, the governing equations are reduced to a unique nonlinear integro-differential equation in the transverse displacement of the cable coupled to the ordinary differential equations ruling the response of the moving oscillators in terms of absolute displacements. The condensed model is discretized by the Galerkin method assuming an improved series expansion of cable response able to accurately reproduce the abrupt changes of cable profile at the contact points with the moving oscillators. A numerical application is presented to validate the proposed condensed model of the inclined cable under moving oscillators as well as the improved series representation of cable response.
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.
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
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
Phonon mechanisms of nonlinear decay and dephasing of mesoscopic vibrational systems
NASA Astrophysics Data System (ADS)
Atalaya, Juan; Kenny, Thomas W.; Dykman, Mark I.
2015-03-01
The frequencies and the decay rates of mesoscopic oscillators depend on vibration amplitudes. Nonlinear decay has been seen recently in various nano- and micro-mechanical systems. Here we consider a microscopic mechanism of nonlinear decay, the nonlinear coupling of the vibrational mode of interest, for example, a flexural mode, to other vibrations. Typically, the modes of interest have low eigenfrequencies ω0. Their decay comes from the coupling to acoustic-phonon type vibrations with much higher frequency and density of states. Thus, nonlinear decay requires quartic anharmonic coupling or cubic anharmonicity in the higher order. We find the decay rate for the inverse lifetime of the involved phonons, which is determined by the internal nonlinearity and the boundary scattering, being either much larger or smaller than ω0. The results extend the thermo-elastic, Akhiezer, and Landau-Rumer decay theory to nonlinear decay of mesoscopic modes and make specific predictions on the temperature and frequency dependence of the decay rate for different types of systems. We show that nonlinear decay is invariably accompanied by dephasing. We also show that in nano-electro-mechanical systems the decay rate can be electrostatically controlled.
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.)
Analysis of the Non-Linearity of El Niño Southern Oscillation Teleconnections
NASA Astrophysics Data System (ADS)
Frauen, Claudia; Dommenget, Dietmar; Rezny, Michael; Wales, Scott
2014-05-01
The El Niño Southern Oscillation (ENSO) has significant variations and non-linearities in its pattern and strength. ENSO events are shifted along the equator, with some located in the central Pacific (CP) and others in the east Pacific (EP). To study how these variations are reflected in global ENSO teleconnections we analyze observations and idealized atmospheric general circulation model (AGCM) simulations. Clear non-linearities exist in observed teleconnections of sea level pressure (SLP) and precipitation. However, it is difficult to distinguish if these are caused by the different signs, strengths or spatial patterns of events (strong El Niño events mostly being EP events and strong La Niña events mostly being CP events) or by combinations of these. Therefore, sensitivity experiments are performed with an AGCM forced with idealized EP and CP ENSO sea surface temperature (SST) patterns with varying signs and strengths. It can be shown that in general the response is stronger for warm events than for cold events and the teleconnections shift following the SST anomaly patterns. EP events show stronger non-linearities than CP events. The non-linear responses to ENSO events can be explained as a combination of non-linear responses to a linear ENSO (fixed pattern but varying signs and strengths) and a linear response to a non-linear ENSO (varying patterns). Any observed event is a combination of these aspects. While in most tropical regions these add up leading to stronger non-linear responses than expected from the single components, in some regions they cancel each other resulting in little overall non-linearity. This leads to strong regional differences in ENSO teleconnections.
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.
Interplay between electrical and mechanical domains in a high performance nonlinear energy harvester
NASA Astrophysics Data System (ADS)
Mallick, Dhiman; Amann, Andreas; Roy, Saibal
2015-12-01
This paper reports a comprehensive experimental characterization and modeling of a compact nonlinear energy harvester for low frequency applications. By exploiting the interaction between the electrical circuitry and the mechanical motion of the device, we are able to improve the power output over a large frequency range. This improvement is quantified using a new figure of merit based on a suitably defined ‘power integral (P f)’ for nonlinear vibrational energy harvesters. The developed device consists of beams with fixed-guided configuration which produce cubic monostable nonlinearity due to stretching strain. Using a high efficiency magnetic circuit a maximum output power of 488.47 μW across a resistive load of 4000 Ω under 0.5g input acceleration at 77 Hz frequency with 9.55 Hz of bandwidth is obtained. The dynamical characteristics of the device are theoretically reproduced and explained by a modified nonlinear Duffing oscillator model.
Mechanisms underlying angiotensin II-induced calcium oscillations
Edwards, Aurélie; Pallone, Thomas L.
2008-01-01
To gain insight into the mechanisms that underlie angiotensin II (ANG II)-induced cytoplasmic Ca2+ concentration ([Ca]cyt) oscillations in medullary pericytes, we expanded a prior model of ion fluxes. ANG II stimulation was simulated by doubling maximal inositol trisphosphate (IP3) production and imposing a 90% blockade of K+ channels. We investigated two configurations, one in which ryanodine receptors (RyR) and IP3 receptors (IP3R) occupy a common store and a second in which they reside on separate stores. Our results suggest that Ca2+ release from stores and import from the extracellular space are key determinants of oscillations because both raise [Ca] in subplasmalemmal spaces near RyR. When the Ca2+-induced Ca2+ release (CICR) threshold of RyR is exceeded, the ensuing Ca2+ release is limited by Ca2+ reuptake into stores and export across the plasmalemma. If sarco(endo)plasmic reticulum Ca2+-ATPase (SERCA) pumps do not remain saturated and sarcoplasmic reticulum Ca2+ stores are replenished, that phase is followed by a resumption of leak from internal stores that leads either to [Ca]cyt elevation below the CICR threshold (no oscillations) or to elevation above it (oscillations). Our model predicts that oscillations are more prone to occur when IP3R and RyR stores are separate because, in that case, Ca2+ released by RyR during CICR can enhance filling of adjacent IP3 stores to favor a high subsequent leak that generates further CICR events. Moreover, the existence or absence of oscillations depends on the set points of several parameters, so that biological variation might well explain the presence or absence of oscillations in individual pericytes. PMID:18562632
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.
Limit cycle oscillations in a nonlinear state space model of the human cochlea.
Ku, Emery M; Elliott, Stephen J; Lineton, Ben
2009-08-01
It is somewhat surprising that linear analysis can account for so many features of the cochlea when it is inherently nonlinear. For example, the commonly detected spacing between adjacent spontaneous otoacoustic emissions (SOAEs) is often explained by a linear theory of "coherent reflection" [Zweig and Shera (1995). J. Acoust. Soc. Am. 98, 2018-2047]. The nonlinear saturation of the cochlear amplifier is, however, believed to be responsible for stabilizing the amplitude of a SOAE. In this investigation, a state space model is used to first predict the linear instabilities that arise, given distributions of cochlear inhomogeneities, and then subsequently to simulate the time-varying spectra of the nonlinear models. By comparing nonlinear simulation results to linear predictions, it is demonstrated that nonlinear effects can have a strong impact on the steady-state response of an unstable cochlear model. Sharply tuned components that decay away exponentially within 100 ms are shown to be due to linearly resonant modes of the model generated by the cochlear inhomogeneities. Some oscillations at linearly unstable frequencies are suppressed over a longer time scale, whereas those that persist are due to linear instabilities and their distortion products. PMID:19640040
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.
Ramos, Daniel Frank, Ian W.; Deotare, Parag B.; Bulu, Irfan; Lončar, Marko
2014-11-03
We investigate the coupling between mechanical and optical modes supported by coupled, freestanding, photonic crystal nanobeam cavities. We show that localized cavity modes for a given gap between the nanobeams provide weak optomechanical coupling with out-of-plane mechanical modes. However, we show that the coupling can be significantly increased, more than an order of magnitude for the symmetric mechanical mode, due to optical resonances that arise from the interaction of the localized cavity modes with standing waves formed by the reflection from thesubstrate. Finally, amplification of motion for the symmetric mode has been observed and attributed to the strong optomechanical interaction of our hybrid system. The amplitude of these self-sustained oscillations is large enough to put the system into a non-linear oscillation regime where a mixing between the mechanical modes is experimentally observed and theoretically explained.
The concentration mechanisms of cubic nonlinearity in dispersive media
NASA Astrophysics Data System (ADS)
Ivanov, V. I.; Ivanova, G. D.; Kirjushina, S. I.; Mjagotin, A. V.
2016-08-01
The comparative analysis of the dynamic holograms recording efficiency in media with non-resonance mechanisms of optical nonlinearity is carried out. It is showed that the greatest values of this parameter are provided by thermodiffusion and electrostrictive mechanisms of concentration nonlinearity of liquid dispersed media.
Cavity Optomechanics: Coherent Coupling of Light and Mechanical Oscillators
NASA Astrophysics Data System (ADS)
Kippenberg, Tobias J.
2012-06-01
The mutual coupling of optical and mechanical degrees of freedom via radiation pressure has been a subject of interest in the context of quantum limited displacements measurements for Gravity Wave Detection for many decades, however light forces have remained experimentally unexplored in such systems. Recent advances in nano- and micro-mechanical oscillators have for the first time allowed the observation of radiation pressure phenomena in an experimental setting and constitute the expanding research field of cavity optomechanics [1]. These advances have allowed achieving to enter the quantum regime of mechanical systems, which are now becoming a third quantum technology after atoms, ions and molecules in a first and electronic circuits in a second wave. In this talk I will review these advances. Using on-chip micro-cavities that combine both optical and mechanical degrees of freedom in one and the same device [2], radiation pressure back-action of photons is shown to lead to effective cooling [3-6]) of the mechanical oscillator mode using dynamical backaction, which has been predicted by Braginsky as early as 1969 [4]. This back-action cooling exhibits many close analogies to atomic laser cooling. With this novel technique the quantum mechanical ground state of a micromechanical oscillator has been prepared with high probability using both microwave and optical fields. In our research this is reached using cryogenic precooling to ca. 800 mK in conjunction with laser cooling, allowing cooling of micromechanical oscillator to only motional 1.7 quanta, implying that the mechanical oscillator spends about 40% of its time in the quantum ground state. Moreover it is possible in this regime to observe quantum coherent coupling in which the mechanical and optical mode hybridize and the coupling rate exceeds the mechanical and optical decoherence rate [7]. This accomplishment enables a range of quantum optical experiments, including state transfer from light to mechanics
NASA Astrophysics Data System (ADS)
Han, Qun; Xu, Wei; Sun, Jian-Qiao
2016-09-01
The stochastic response of nonlinear oscillators under periodic and Gaussian white noise excitations is studied with the generalized cell mapping based on short-time Gaussian approximation (GCM/STGA) method. The solutions of the transition probability density functions over a small fraction of the period are constructed by the STGA scheme in order to construct the GCM over one complete period. Both the transient and steady-state probability density functions (PDFs) of a smooth and discontinuous (SD) oscillator are computed to illustrate the application of the method. The accuracy of the results is verified by direct Monte Carlo simulations. The transient responses show the evolution of the PDFs from being Gaussian to non-Gaussian. The effect of a chaotic saddle on the stochastic response is also studied. The stochastic P-bifurcation in terms of the steady-state PDFs occurs with the decrease of the smoothness parameter, which corresponds to the deterministic pitchfork bifurcation.
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.
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. PMID:26974092
Construction of approximate analytical solutions to a new class of non-linear oscillator equation
NASA Technical Reports Server (NTRS)
Mickens, R. E.; Oyedeji, K.
1985-01-01
The principle of harmonic balance is invoked in the development of an approximate analytic model for a class of nonlinear oscillators typified by a mass attached to a stretched wire. By assuming that harmonic balance will hold, solutions are devised for a steady state limit cycle and/or limit point motion. A method of slowly varying amplitudes then allows derivation of approximate solutions by determining the form of the exact solutions and substituting into them the lowest order terms of their respective Fourier expansions. The latter technique is actually a generalization of the method proposed by Kryloff and Bogoliuboff (1943).
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.
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.
Nonlinear oscillations and waves in an arbitrary mass ratio cold plasma
Verma, Prabal Singh
2011-12-15
It is well known that nonlinear standing oscillations in an arbitrary mass ratio cold plasma always phase mix away. However, there exist nonlinear electron-ion traveling wave solutions, which do not exhibit phase mixing because they have zero ponderomotive force. The existence of these waves has been demonstrated using a perturbation method. Moreover, it is shown that cold plasma BGK waves [Albritton et al., Nucl. Fusion 15, 1199 (1975)] phase mix away if ions are allowed to move and the scaling of phase mixing is found to be different from earlier work [Sengupta et al., Phys. Rev. Lett. 82, 1867 (1999)]. Phase mixing of these waves has been further verified in 1-D particle in cell simulation.
Non-Linear High Amplitude Oscillations in Wave-shaped Resonators
NASA Astrophysics Data System (ADS)
Antao, Dion; Farouk, Bakhtier
2011-11-01
A numerical and experimental study of non-linear, high amplitude standing waves in ``wave-shaped'' resonators is reported here. These waves are shock-less and can generate peak acoustic overpressures that can exceed the ambient pressure by three/four times its nominal value. A high fidelity compressible axisymmetric computational fluid dynamic model is used to simulate the phenomena in cylindrical and arbitrarily shaped axisymmetric resonators. Working fluids (Helium, Nitrogen and R-134a) at various operating pressures are studied. The experiments are performed in a constant cross-section cylindrical resonator in atmospheric pressure nitrogen and helium to provide model validation. The high amplitude non-linear oscillations demonstrated can be used as a prime mover in a variety of applications including thermoacoustic cryocooling. The work reported is supported by the US National Science Foundation under grant CBET-0853959.
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
NASA Astrophysics Data System (ADS)
Li, Hao; Dai, Fuhong; Du, Shanyi
2015-04-01
Recently bistable composite laminates have been investigated for broadband energy harvesting, by taking advantage of their nonlinear oscillations around the first vibration mode. However, it has been reported that the excitation acceleration needed for the desired large amplitude limit cycle oscillation is too high, if the first vibration mode is elevated to relative higher frequencies (60 Hz e.g.). This study investigates the feasibility of exploiting the nonlinear oscillations around the second vibration mode of a rectangular piezoelectric bistable laminate (RPBL), for broadband vibration energy harvesting at relative higher frequencies, but with relative low excitation acceleration. The proposed RPBL has three oscillation patterns around the second vibration mode, including single-well oscillation, chaotic intermittency oscillation and limit cycle oscillation. The broadband characteristics and the considerable energy conversion efficiency of the RPBL are demonstrated in experiments. The static nonlinearity and the dynamic responses of the RPBL are investigated by finite element method. Finite element analysis (FEA) reveals that the enhanced dynamic responses of the RPBL are due to its softening bending stiffness and the local snap through phenomenon. The FEA results coincide reasonably well with experimental results.
Dynamics of dipoles and vortices in nonlinearly coupled three-dimensional field oscillators.
Driben, R; Konotop, V V; Malomed, B A; Meier, T
2016-07-01
The dynamics of a pair of harmonic oscillators represented by three-dimensional fields coupled with a repulsive cubic nonlinearity is investigated through direct simulations of the respective field equations and with the help of the finite-mode Galerkin approximation (GA), which represents the two interacting fields by a superposition of 3+3 harmonic-oscillator p-wave eigenfunctions with orbital and magnetic quantum numbers l=1 and m=1, 0, -1. The system can be implemented in binary Bose-Einstein condensates, demonstrating the potential of the atomic condensates to emulate various complex modes predicted by classical field theories. First, the GA very accurately predicts a broadly degenerate set of the system's ground states in the p-wave manifold, in the form of complexes built of a dipole coaxial with another dipole or vortex, as well as complexes built of mutually orthogonal dipoles. Next, pairs of noncoaxial vortices and/or dipoles, including pairs of mutually perpendicular vortices, develop remarkably stable dynamical regimes, which feature periodic exchange of the angular momentum and periodic switching between dipoles and vortices. For a moderately strong nonlinearity, simulations of the coupled-field equations agree very well with results produced by the GA, demonstrating that the dynamics is accurately spanned by the set of six modes limited to l=1. PMID:27575123
Dynamics of dipoles and vortices in nonlinearly coupled three-dimensional field oscillators
NASA Astrophysics Data System (ADS)
Driben, R.; Konotop, V. V.; Malomed, B. A.; Meier, T.
2016-07-01
The dynamics of a pair of harmonic oscillators represented by three-dimensional fields coupled with a repulsive cubic nonlinearity is investigated through direct simulations of the respective field equations and with the help of the finite-mode Galerkin approximation (GA), which represents the two interacting fields by a superposition of 3 +3 harmonic-oscillator p -wave eigenfunctions with orbital and magnetic quantum numbers l =1 and m =1 , 0, -1 . The system can be implemented in binary Bose-Einstein condensates, demonstrating the potential of the atomic condensates to emulate various complex modes predicted by classical field theories. First, the GA very accurately predicts a broadly degenerate set of the system's ground states in the p -wave manifold, in the form of complexes built of a dipole coaxial with another dipole or vortex, as well as complexes built of mutually orthogonal dipoles. Next, pairs of noncoaxial vortices and/or dipoles, including pairs of mutually perpendicular vortices, develop remarkably stable dynamical regimes, which feature periodic exchange of the angular momentum and periodic switching between dipoles and vortices. For a moderately strong nonlinearity, simulations of the coupled-field equations agree very well with results produced by the GA, demonstrating that the dynamics is accurately spanned by the set of six modes limited to l =1 .
Dynamics of dipoles and vortices in nonlinearly coupled three-dimensional field oscillators.
Driben, R; Konotop, V V; Malomed, B A; Meier, T
2016-07-01
The dynamics of a pair of harmonic oscillators represented by three-dimensional fields coupled with a repulsive cubic nonlinearity is investigated through direct simulations of the respective field equations and with the help of the finite-mode Galerkin approximation (GA), which represents the two interacting fields by a superposition of 3+3 harmonic-oscillator p-wave eigenfunctions with orbital and magnetic quantum numbers l=1 and m=1, 0, -1. The system can be implemented in binary Bose-Einstein condensates, demonstrating the potential of the atomic condensates to emulate various complex modes predicted by classical field theories. First, the GA very accurately predicts a broadly degenerate set of the system's ground states in the p-wave manifold, in the form of complexes built of a dipole coaxial with another dipole or vortex, as well as complexes built of mutually orthogonal dipoles. Next, pairs of noncoaxial vortices and/or dipoles, including pairs of mutually perpendicular vortices, develop remarkably stable dynamical regimes, which feature periodic exchange of the angular momentum and periodic switching between dipoles and vortices. For a moderately strong nonlinearity, simulations of the coupled-field equations agree very well with results produced by the GA, demonstrating that the dynamics is accurately spanned by the set of six modes limited to l=1.
Partial synchronization in networks of non-linearly coupled oscillators: The Deserter Hubs Model.
Freitas, Celso; Macau, Elbert; Pikovsky, Arkady
2015-04-01
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.
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.
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.
Fujimoto, Kazuya; Tsubota, Makoto
2011-05-15
We consider a trapped atomic Bose-Einstein condensate penetrated by a repulsive Gaussian potential and theoretically investigate the dynamics induced by oscillating the Gaussian potential. Our study is based on the numerical calculation of the two-dimensional Gross-Pitaevskii equation. Our calculation reveals the dependence of the characteristic behavior of the condensate on the amplitude and frequency of the oscillating potential. These dynamics are deeply related to the nucleation and dynamics of quantized vortices and solitons. When the potential oscillates with a large amplitude, it nucleates many vortex pairs that move away from the potential. When the amplitude of the oscillation is small, it nucleates solitons through an annihilation of vortex pairs. We discuss three issues concerning the nucleation of vortices. The first is the phase diagram for the nucleation of vortices and solitons near the oscillating potential. The second is the mechanism and critical velocity of the nucleation. The critical velocity of the nucleation is an important issue in quantum fluids, and we propose an expression for the velocity containing both the coherence length and the size of the potential. The third is the divergence of the nucleation time, which is the time it takes for the potential to nucleate vortices, near the critical parameters for vortex nucleation.
NASA Astrophysics Data System (ADS)
Charlemagne, S.; Lamarque, C.-H.; Ture Savadkoohi, A.
2016-08-01
The dynamical behavior of a two degree-of-freedom system made up of a linear oscillator and a coupled nonlinear energy sink with nonlinear global and local potentials is studied. The nonlinear global potential of the energy sink performs direct interactions with the linear oscillator, while its local potential depends only on its own behavior during vibratory energy exchanges between two oscillators. A time multiple scale method around 1:1:1 resonance is used to detect slow invariant manifold of the system, its equilibrium and singular points. Detected equilibrium points permit us to predict periodic regime(s) while singular points can lead the system to strongly modulated responses characterized by persistent bifurcations. Several possible scenarios occurring during these strongly modulated regimes are highlighted. All analytical predictions are compared with those which are obtained by direct numerical integration of system equations.
Doroudi, Alireza
2009-11-01
In this paper the homotopy perturbation method is used for calculation of the frequencies of the coupled secular oscillations and axial secular frequencies of a nonlinear ion trap. The motion of the ion in a rapidly oscillating field is transformed to the motion in an effective potential. The equations of ion motion in the effective potential are in the form of a Duffing-like equation. The homotopy perturbation method is used for solving the resulted system of coupled nonlinear differential equations and the resulted axial equation for obtaining the expressions for ion secular frequencies as a function of nonlinear field parameters and amplitudes of oscillations. The calculated axial secular frequencies are compared with the results of Lindstedt-Poincare method and the exact results. PMID:20365087
NASA Astrophysics Data System (ADS)
Lakshmanan, M.; Sahadevan, R.
1993-03-01
In recent investigations on nonlinear dynamics, the singularity structure analysis pioneered by Kovalevskaya, Painlevé and contempories, which stresses the meromorphic nature of the solutions of the equations of motion in the complex-time plane, is found to play an increasingly important role. Particularly, soliton equations have been found to be associated with the so-called Painlevé property, which implies that the solutions are free from movable critical points/manifolds. Finite-dimensional integrable dynamical systems have also been found to possess such a property. In this review, after briefly presenting the historical developments and various features of the Painlevé (P) method, we demonstrate how it provides an effective tool in the analysis of nonlinear dynamical systems, starting from simple examples. We apply this method to several important coupled nonlinear oscillators governed by generic Hamiltonians of polynomial type with two, three and arbitrary ( N) degrees of freedom and classify all the P-cases. Sufficient numbers of involutive integrals of motion for each of the P-cases are constructed by employing other direct methods. In particular, we examine the question of integrability from the viewpoint of symmetries, explicitly demonstrate the existence of nontrivial extended Lie symmetries for the P-cases, and obtain the required integrals of motion by direct integration of symmetries. Furthermore, we briefly explain how the singularity structure analysis can be used to understand some of the intrinsic properties of nonintegrability and chaos with special reference to the two-coupled quartic anharmonic oscillators and Henon-Heiles systems.
Quantum mechanics of Drude oscillators with full Coulomb interaction
NASA Astrophysics Data System (ADS)
Sadhukhan, M.; Manby, Frederick R.
2016-09-01
Drude oscillators provide a harmonic description of charge fluctuations and are widely studied as a model system and for ab initio calculations. In the dipole approximation the Hamiltonian describing the interaction of Drudes is quadratic, so it can be diagonalized exactly, but the energy diverges at short range. Here we consider the quantum mechanics of Drude oscillators interacting through the full Coulombic Hamiltonian for which the interaction energy does not have this defect. This protypical model for interactions between matter includes electrostatics, induction, and dispersion. Potential energy curves for rare-gas dimers are very closely matched by Drude correlation energies plus a single exponential function. The exact and accurate results presented here help to delineate between the basic properties of the physical model and the effects that arise from the dipole approximation.
Bifurcations of self-excitation regimes in a Van der Pol oscillator with a nonlinear energy sink
NASA Astrophysics Data System (ADS)
Gendelman, O. V.; Bar, T.
2010-02-01
The paper investigates regimes of self-excitation in a Van der Pol oscillator with an attached nonlinear energy sink (NES). Initial equations are reduced by averaging to a 3D system. The small relative mass of the NES justifies analysis of this averaged system as singularly perturbed with two “slow” and one “super-slow” variable. Such an approach, in turn, provides a complete analytic description of possible response regimes. In addition to almost unperturbed limit cycle oscillations (LCOs), the system can exhibit complete elimination of self-excitation, small-amplitude LCOs as well as excitation of a quasiperiodic strongly modulated response (SMR). In the space of parameters, the latter can be approached by three distinct bifurcation mechanisms: canard explosion, Shil’nikov bifurcation and heteroclinic bifurcation. Some of the above oscillatory regimes can co-exist for the same values of the system parameters. In this case, it is possible to establish the basins of attraction for the co-existing regimes. Direct numeric simulations demonstrate good coincidence with the analytic predictions.
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.
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.
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. PMID:25554054
Parametric Oscillations in Traveling Waves Tubes for Telecommunication Systems
NASA Astrophysics Data System (ADS)
André, Frédéric
2010-03-01
A tentative explanation of oscillations in helix traveling waves tubes (TWT) in the nonlinear regime is proposed here based on a parametric oscillation mechanism. This model explains why the TWT oscillates slightly before saturation and why this type of oscillation occurs at a lower beam current than other types of oscillations in the linear regime.
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
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
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
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.
Observation of Quantum Interference between Separated Mechanical Oscillator Wave Packets
NASA Astrophysics Data System (ADS)
Kienzler, D.; Flühmann, C.; Negnevitsky, V.; Lo, H.-Y.; Marinelli, M.; Nadlinger, D.; Home, J. P.
2016-04-01
We directly observe the quantum interference between two well-separated trapped-ion mechanical oscillator wave packets. The superposed state is created from a spin-motion entangled state using a heralded measurement. Wave packet interference is observed through the energy eigenstate populations. We reconstruct the Wigner function of these states by introducing probe Hamiltonians which measure Fock state populations in displaced and squeezed bases. Squeezed-basis measurements with 8 dB squeezing allow the measurement of interference for Δ α =15.6 , corresponding to a distance of 240 nm between the two superposed wave packets.
Possible physical mechanisms of stochastic oscillations in RF SQUID's
Dmitrenko, I.M.; Konotop, D.A.; Tsoi, G.M.; Shnyrkov, V.I.
1985-03-01
The processes of giant noise generation in RF SQUID's are studied experimentally. It is shown that the appearance of stochastic oscillations is due to different retardation mechanisms in a dynamic system, depending on the characteristics of the Josephson junctions and the external excitation. The retardation times in the SQUID's studied were determined by the recharging of the Josephson-junction capacitance (tau/sub R//sub C/), by quasiparticle relaxation processes (tau/sub epsilon-c/), and by the relaxation time of thermal processes in the junction (tau/sub T/).
Response of a Mechanical Oscillator in Solid 4He
NASA Astrophysics Data System (ADS)
Ahlstrom, S. L.; Bradley, D. I.; Človečko, M.; Fisher, S. N.; Guénault, A. M.; Guise, E. A.; Haley, R. P.; Kolosov, O.; Kumar, M.; McClintock, P. V. E.; Pickett, G. R.; Polturak, E.; Poole, M.; Todoshchenko, I.; Tsepelin, V.; Woods, A. J.
2014-04-01
We present the first measurements of the response of a mechanical oscillator in solid 4He. We use a lithium niobate tuning fork operating in its fundamental resonance mode at a frequency of around 30 kHz. Measurements in solid 4He were performed close to the melting pressure. The tuning fork resonance shows substantial frequency shifts on cooling from around 1.5 K to below 10 mK. The response shows an abrupt change at the bcc-hcp transition. At low temperatures, below around 100 mK, the resonance splits into several overlapping resonances.
Observation of Quantum Interference between Separated Mechanical Oscillator Wave Packets.
Kienzler, D; Flühmann, C; Negnevitsky, V; Lo, H-Y; Marinelli, M; Nadlinger, D; Home, J P
2016-04-01
We directly observe the quantum interference between two well-separated trapped-ion mechanical oscillator wave packets. The superposed state is created from a spin-motion entangled state using a heralded measurement. Wave packet interference is observed through the energy eigenstate populations. We reconstruct the Wigner function of these states by introducing probe Hamiltonians which measure Fock state populations in displaced and squeezed bases. Squeezed-basis measurements with 8 dB squeezing allow the measurement of interference for Δα=15.6, corresponding to a distance of 240 nm between the two superposed wave packets.
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.
Optical mechanical analogy and nonlinear nonholonomic constraints
NASA Astrophysics Data System (ADS)
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.
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.
Geometric Phase of Phase Space Trajectories:Mobius Strip and Nonlinear Oscillators
NASA Astrophysics Data System (ADS)
Balakrishnan, Radha; Satija, Indubala
2005-03-01
We present a gauge invariant formulation of associating a geometric phase with classical phase space trajectories. This geometric phase which depends upon the integrated torsion of the trajectory, bears a close analogy to the generalized Berry phase associated with the time evolution of the quantum wave functions. This topological quantity serves as an order parameter signalling phase transitions including novel geometrical transitions. One of the interesting aspects seen in Duffing and other nonlinear oscillators is the sudden jumps in the geometric phase which is accompanied by the divergence of the local torsion and the vanishing of the local curvature. Intriguingly, the analogous phenomenon was seen in a mobius strip when the ratio of the width to the length of the strip exceeds beyound a critical value.
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.
Induced N2-cooperative phenomenon in an ensemble of the nonlinear coupled oscillators
NASA Astrophysics Data System (ADS)
Tralle, I.; Ziȩba, P.
2014-04-01
In the article the cooperative N2-effect is considered, that is the radiation whose power is ˜N2, where N is the number of emitters which in this case is equal to the number of nonlinear coupled oscillators. They model the electrons moving in a semiconductor structure with grating (micro-undulator). The suggested effect is in a sense similar to Dicke superradiance, however it is not the spontaneous phase coherence arising in the ensemble of two-level atoms interacting via the emitted electromagnetic field, but rather, the result of interplay of two effects. The first one is the 'pumping wave' acting on the electrons and which is the result of undulator field, while the second is the backward effect of radiation which is produced by electrons moving within such micro-undulator. As a result, the specific phase coherence ('synchronization') develops in the ensemble of emitters and they start to generate as a single oscillating charge Ne, while the power of emitted radiation becomes ˜N2. It is very probable, that the effect can be used for the developing of a new semiconductor-based room temperature source of the GHz and THz-radiation.
Razzak, Md Abdur; Alam, Md Shamsul
2016-01-01
Based on a new trial function, an analytical coupled technique (a combination of homotopy perturbation method and variational method) is presented to obtain the approximate frequencies and the corresponding periodic solutions of the free vibration of a conservative oscillator having inertia and static non-linearities. In some of the previous articles, the first and second-order approximations have been determined by the same method of such nonlinear oscillator, but the trial functions have not been satisfied the initial conditions. It seemed to be a big shortcoming of those articles. The new trial function of this paper overcomes aforementioned limitation. The first-order approximation is mainly considered in this paper. The main advantage of this present paper is, the first-order approximation gives better result than other existing second-order harmonic balance methods. The present method is valid for large amplitudes of oscillation. The absolute relative error measures (first-order approximate frequency) in this paper is 0.00 % for large amplitude A = 1000, while the relative error gives two different second-order harmonic balance methods: 10.33 and 3.72 %. Thus the present method is suitable for solving the above-mentioned nonlinear oscillator.
Evolution of adaptation mechanisms: Adaptation energy, stress, and oscillating death.
Gorban, Alexander N; Tyukina, Tatiana A; Smirnova, Elena V; Pokidysheva, Lyudmila I
2016-09-21
In 1938, Selye proposed the notion of adaptation energy and published 'Experimental evidence supporting the conception of adaptation energy.' Adaptation of an animal to different factors appears as the spending of one resource. Adaptation energy is a hypothetical extensive quantity spent for adaptation. This term causes much debate when one takes it literally, as a physical quantity, i.e. a sort of energy. The controversial points of view impede the systematic use of the notion of adaptation energy despite experimental evidence. Nevertheless, the response to many harmful factors often has general non-specific form and we suggest that the mechanisms of physiological adaptation admit a very general and nonspecific description. We aim to demonstrate that Selye׳s adaptation energy is the cornerstone of the top-down approach to modelling of non-specific adaptation processes. We analyze Selye׳s axioms of adaptation energy together with Goldstone׳s modifications and propose a series of models for interpretation of these axioms. Adaptation energy is considered as an internal coordinate on the 'dominant path' in the model of adaptation. The phenomena of 'oscillating death' and 'oscillating remission' are predicted on the base of the dynamical models of adaptation. Natural selection plays a key role in the evolution of mechanisms of physiological adaptation. We use the fitness optimization approach to study of the distribution of resources for neutralization of harmful factors, during adaptation to a multifactor environment, and analyze the optimal strategies for different systems of factors.
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.
Lee, Wai Shing; Ott, Edward; Antonsen, Thomas M
2013-09-01
This paper addresses the behavior of large systems of heterogeneous, globally coupled oscillators each of which is described by the generic Landau-Stuart equation, which incorporates both phase and amplitude dynamics of individual oscillators. One goal of our paper is to investigate the effect of a spread in the amplitude growth parameter of the oscillators and of the effect of a homogeneous nonlinear frequency shift. Both of these effects are of potential relevance to recently reported experiments. Our second goal is to gain further understanding of the macroscopic system dynamics at large coupling strength, and its dependence on the nonlinear frequency shift parameter. It is proven that at large coupling strength, if the nonlinear frequency shift parameter is below a certain value, then there is a unique attractor for which the oscillators all clump at a single amplitude and uniformly rotating phase (we call this a single-cluster "locked state"). Using a combination of analytical and numerical methods, we show that at higher values of the nonlinear frequency shift parameter, the single-cluster locked state attractor continues to exist, but other types of coexisting attractors emerge. These include two-cluster locked states, periodic orbits, chaotic orbits, and quasiperiodic orbits.
Cooperative buckling and the nonlinear mechanics of nematic semiflexible networks
NASA Astrophysics Data System (ADS)
Foucard, L. C.; Price, J. K.; Klug, W. S.; Levine, A. J.
2015-09-01
We review the nonlinear mechanics of cross-linked networks of stiff filaments with a quenched anisotropic (nematic) alignment. A combination of numerical simulations and analytic calculations shows that the broken rotational symmetry of the filament orientational distribution leads to a dramatic nonlinear softening of the network at very small strain (on the order of 0.1%). We argue that one can understand this softening in terms of Euler buckling, i.e. the loss of further load-carrying capacity in compression within the network. With increasing shear strain, this source of geometric nonlinearity appears as heterogeneous nucleation (originating in particularly fragile regions, which may be identified by a linear stability analysis) and subsequently grows into ‘buckling scars’ that eventually spread throughout the system. We develop a simple mean-field model for the nonlinear mechanics of such networks and suggest applications of these ideas to a variety of fiber networks and biopolymer systems.
Nonlinear modal interactions in clamped-clamped mechanical resonators.
Westra, H J R; Poot, M; van der Zant, H S J; Venstra, W J
2010-09-10
A theoretical and experimental investigation is presented on the intermodal coupling between the flexural vibration modes of a single clamped-clamped beam. Nonlinear coupling allows an arbitrary flexural mode to be used as a self-detector for the amplitude of another mode, presenting a method to measure the energy stored in a specific resonance mode. The observed complex nonlinear dynamics are quantitatively captured by a model based on coupling of the modes via the beam extension; the same mechanism is responsible for the well-known Duffing nonlinearity in clamped-clamped beams. PMID:20867605
NASA Astrophysics Data System (ADS)
Elgohary, Tarek Adel Abdelsalam
collocation (RBF-Coll ) is used to address strongly nonlinear dynamical systems and to analyze short as well as long-term responses. The algorithm is compared against, the second order central difference, the classical Runge-Kutta, the adaptive Runge-Kutta-Fehlberg, the Newmark-beta, the Hilber-Hughes-Taylor and the modified Chebyshev-Picard iteration methods in terms of accuracy and computational cost for three types of problems; (1) the unforced highly nonlinear Duffing oscillator, (2) the Duffing oscillator with impact loading and (3) a nonlinear three degrees of freedom (3-DOF) dynamical system. The RBF-Collmethod is further extended for time domain inverse problems addressing fixed time optimal control problems and Lamberts orbital transfer problem. It is shown that this method is very simple, efficient and very accurate in obtaining the solutions. The proposed algorithm is advantageous and has promising applications in solving general nonlinear dynamical systems, optimal control problems and high accuracy orbit propagation in celestial mechanics.
Mode interaction in horses, tea, and other nonlinear oscillators: The universal role of symmetry
NASA Astrophysics Data System (ADS)
van der Weele, Jacobus P.; Banning, Erik J.
2001-09-01
This paper is about mode interaction in systems of coupled nonlinear oscillators. The main ideas are demonstrated by means of a model consisting of two coupled, parametrically driven pendulums. On the basis of this we also discuss mode interaction in the Faraday experiment (as observed by Ciliberto and Gollub) and in running animals. In all these systems the interaction between two modes is seen to take place via a third mode: This interaction mode is a common daughter, born by means of a symmetry breaking bifurcation, of the two interacting modes. Thus, not just any two modes can interact with each other, but only those that are linked (in the system's group-theoretical hierarchy) by a common daughter mode. This is the quintessence of mode interaction. In many cases of interest, the interaction mode is seen to undergo further bifurcations, and this can eventually lead to chaos. These stages correspond to lower and lower levels of symmetry, and the constraints imposed by group theory become less and less restrictive. Indeed, the precise sequence of events during these later stages is determined not so much by group-theoretical stipulations as by the accidental values of the nonlinear terms in the equations of motion.
Nonlinear Geometric Effects in Mechanical Bistable Morphing Structures
NASA Astrophysics Data System (ADS)
Chen, Zi; Guo, Qiaohang; Majidi, Carmel; Chen, Wenzhe; Srolovitz, David J.; Haataja, Mikko P.
2012-09-01
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.
Nonlinear dynamics of a flexible mechanism with impact
NASA Astrophysics Data System (ADS)
Dupac, Mihai; Marghitu, Dan B.
2006-02-01
The nonlinear dynamics of a slider-crank mechanism with a flexible rod is considered in this study. The flexible rod is modeled with lumped masses and periodically impacted by an external flexible sphere. The impact is modeled using a kinematic coefficient of restitution. Nonlinear dynamics tools are applied to analyze the simulated data captured from the connecting rod of the mechanism. The chaotic behavior of the system is analyzed. The stability of the motion is studied using the Lyapunov exponents. The dependence between the Lyapunov exponents and the corresponding angular velocity of the driver link of the mechanism is investigated.
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.
NASA Astrophysics Data System (ADS)
Yang, Kai; Wang, Jun; Yu, Wei
2016-08-01
Large amplitude oscillation shear (LAOS) is used to investigate the yielding and flow behavior of yield stress materials. Considering the problems in determination of the yield stress from the apparent dynamic moduli and relative harmonic intensity using Fourier Transform Rheology, we proposed a new approach based on 2D mechanical correlation spectra (2D-MCS) to quantify the yield stress. We have proved that the nonlinear synchronous self-correlation intensity as functions of stress/strain amplitude can be used to determine the yield stress unambiguously from the change of scaling exponent. The yield stresses from 2D-MCS analysis are well consistent with those from the stress ramp experiments.
Mechanical Properties of a Primary Cilium As Measured by Resonant Oscillation
Resnick, Andrew
2015-01-01
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/rad2; 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. PMID:26153698
Mechanical properties of a primary cilium as measured by resonant oscillation.
Resnick, Andrew
2015-07-01
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.
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.
Enhanced nonlinear interactions in quantum optomechanics via mechanical amplification
NASA Astrophysics Data System (ADS)
Lemonde, Marc-Antoine; Didier, Nicolas; Clerk, Aashish A.
2016-04-01
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.
Intrinsic nonlinearities in the mechanics of hard sphere suspensions.
Kumar, Mansi A; Ewoldt, Randy H; Zukoski, Charles F
2016-09-28
The onset of nonlinear responses in near hard sphere suspensions is characterized as a function of oscillatory frequency and strain amplitude. At low frequencies where the viscous behavior dominates, the onset of nonlinearities is driven by increases in rate of strain. At high deformation frequency, where suspension mechanics is dominated by an elastic response, the nonlinear responses occur when deformation exceeds a characteristic strain. This strain is associated with the transient confinement of particles by nearest neighbors and its volume fraction dependence is through cage parameters derived from the high frequency elastic modulus. The onset of nonlinear responses takes on a universal behavior when deformation frequency is normalized by the characteristic time governing the shift from viscous to elastic behavior indicating that this transition is associated with transient particle localization and is expected to be observed for all volume fractions where pair interactions are important. PMID:27530863
Quantum Magnetomechanics: Ultrahigh-Q-Levitated Mechanical Oscillators
NASA Astrophysics Data System (ADS)
Cirio, M.; Brennen, G. K.; Twamley, J.
2012-10-01
Engineering nanomechanical quantum systems possessing ultralong motional coherence times allows for applications in precision quantum sensing and quantum interfaces, but to achieve ultrahigh motional Q one must work hard to remove all forms of motional noise and heating. We examine a magneto-meso-mechanical quantum system that consists of a 3D arrangement of miniature superconducting loops which is stably levitated in a static inhomogeneous magnetic field. The motional decoherence is predominantly due to loss from induced eddy currents in the magnetized sphere which provides the trapping field ultimately yielding Q˜109 with motional oscillation frequencies of several hundreds of kilohertz. By inductively coupling this levitating object to a nearby driven flux qubit one can cool its motion very close to the ground state and this may permit the generation of macroscopic entangled motional states of multiple clusters.
Electrostatic interactions in micro-electro-mechanical resonant oscillators
NASA Astrophysics Data System (ADS)
Baskaran, Rajashree; Turner, Kimberly L.
2001-11-01
Resonant mode operation is common in many MicroElectroMechanical (MEM) applications including accelerometers, gyroscopes and filters [Kovacs (1998), Nguyen (1999)]. When electrostatic transduction is used in these applications, concerns about cross talk and fringing field effects due to geometry are major issues. In this paper, an electrostatically coupled system is briefly introduced, modeled and the dynamic response due to small parametric (displacement dependant) electrostatic force is analyzed using perturbation methods. The presence of coupled parametric resonance has a very significant effect on the dynamic response. Experimental verification of the occurrence of this phenomenon is also presented here. The coupled oscillator system can also be used as an in situ test device to understand the electrostatic parameters in a system. The method of modeling and analysis presented here is simple, yet captures the dynamic behavior of a system due to a small force. This method can be generalized and will be a useful tool in any resonant MEM system design.
Nonlinear mechanics of soft fibrous networks.
Kabla, A; Mahadevan, L
2007-02-22
Mechanical networks of fibres arise on a range of scales in nature and technology, from the cytoskeleton of a cell to blood clots, from textiles and felts to skin and collageneous tissues. Their collective response is dependent on the individual response of the constituent filaments as well as density, topology and order in the network. Here, we use the example of a low-density synthetic felt of athermal filaments to study the generic features of the mechanical response of such networks including strain stiffening and large effective Poisson ratios. A simple microscopic model allows us to explain these features of our observations, and provides us with a baseline framework to understand active biomechanical networks.
Influence of hydrodynamic thrust bearings on the nonlinear oscillations of high-speed rotors
NASA Astrophysics Data System (ADS)
Chatzisavvas, Ioannis; Boyaci, Aydin; Koutsovasilis, Panagiotis; Schweizer, Bernhard
2016-10-01
This paper investigates the effect of hydrodynamic thrust bearings on the nonlinear vibrations and the bifurcations occurring in rotor/bearing systems. In order to examine the influence of thrust bearings, run-up simulations may be carried out. To be able to perform such run-up calculations, a computationally efficient thrust bearing model is mandatory. Direct discretization of the Reynolds equation for thrust bearings by means of a Finite Element or Finite Difference approach entails rather large simulation times, since in every time-integration step a discretized model of the Reynolds equation has to be solved simultaneously with the rotor model. Implementation of such a coupled rotor/bearing model may be accomplished by a co-simulation approach. Such an approach prevents, however, a thorough analysis of the rotor/bearing system based on extensive parameter studies. A major point of this work is the derivation of a very time-efficient but rather precise model for transient simulations of rotors with hydrodynamic thrust bearings. The presented model makes use of a global Galerkin approach, where the pressure field is approximated by global trial functions. For the considered problem, an analytical evaluation of the relevant integrals is possible. As a consequence, the system of equations of the discretized bearing model is obtained symbolically. In combination with a proper decomposition of the governing system matrix, a numerically efficient implementation can be achieved. Using run-up simulations with the proposed model, the effect of thrust bearings on the bifurcations points as well as on the amplitudes and frequencies of the subsynchronous rotor oscillations is investigated. Especially, the influence of the magnitude of the axial force, the geometry of the thrust bearing and the oil parameters is examined. It is shown that the thrust bearing exerts a large influence on the nonlinear rotor oscillations, especially to those related with the conical mode of the
High-Order Simulation of Non-Linear Oscillations and Shocks in the Solar Atmosphere
NASA Technical Reports Server (NTRS)
Bryson, S.; Kosovichev, A.; Levy, D.
2004-01-01
The solar atmosphere presents a rich source of highly non-linear magneto-hydrodynamic phenomena: strong gradients and forcing terms result in both large shocks and oscillations. The additional requirements of energy balance and initialization in hydrostatic equilibrium compound the challenge of this problem. A wealth of observational data allows us to check the results of our simulations. The problem of simulating the solar atmosphere provides, in addition to an interesting system in its own right, a challenging testbed for high-order shock-capturing methods. We discuss the challenge of simulating solar atmospheric phenomena, concentrating on various high-order central methods ranging from second to fourth order. Our method is based on the central-upwind scheme of Kurganov, Noelle and Petrova, which we extend to high order via various interpolants. We investigate various initial data for our simulations, corresponding to observed conditions in different regions of the solar surface: the normal quiet sun and sunspots. When non-oscillatory using second- and third-order methods, we are able to reproduce non-trivial observational results. In particular we find a correlation between initial data and both the shock speeds and particle oscillation spectra that match observations in the corresponding regions. When using fourth-order WENO interpolants, we find that while the individual shock profiles at any given time appear non-oscillatory, spurious oscillations appear in the fields after long time integrations. The issue of initialization in hydrostatic equilibrium raises difficult issues. Careful treatment of the gravitational source term can reduce violations of hydrostatic equilibrium, but difficulties remain, primarily due to discontinuities in the piecewise-polynomial reconstructions. In the case of the Euler equations in gravity, the use of high-order methods reduces the violation of hydrostatic equilibrium to a sufficiently low level for the above described results
Control mechanisms for a nonlinear model of international relations
Pentek, A.; Kadtke, J.; Lenhart, S.; Protopopescu, V.
1997-07-15
Some issues of control in complex dynamical systems are considered. The authors discuss two control mechanisms, namely: a short range, reactive control based on the chaos control idea and a long-term strategic control based on an optimal control algorithm. They apply these control ideas to simple examples in a discrete nonlinear model of a multi-nation arms race.
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.
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 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
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
ElNady, Khaled; Goda, Ibrahim; Ganghoffer, Jean-François
2016-09-01
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.
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 Kramers equation associated with nonextensive statistical mechanics
NASA Astrophysics Data System (ADS)
Mendes, G. A.; Ribeiro, M. S.; Mendes, R. S.; Lenzi, E. K.; Nobre, F. D.
2015-05-01
Stationary and time-dependent solutions of a nonlinear Kramers equation, as well as its associated nonlinear Fokker-Planck equations, are investigated within the context of Tsallis nonextensive statistical mechanics. Since no general analytical time-dependent solutions are found for such a nonlinear Kramers equation, an ansatz is considered and the corresponding asymptotic behavior is studied and compared with those known for the standard linear Kramers equation. The H-theorem is analyzed for this equation and its connection with Tsallis entropy is investigated. An application is discussed, namely the motion of Hydra cells in two-dimensional cellular aggregates, for which previous measurements have verified q -Gaussian distributions for velocity components and superdiffusion. The present analysis is in quantitative agreement with these experimental results.
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
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.
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.
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)
Ramunno-Johnson, Damien; Strimbu, C. Elliott; Fredrickson, Lea; Kao, Albert; Bozovic, Dolores
2010-03-01
Under in vitro conditions, uncoupled hair bundles of the bullfrog (Rana catesbeiana) sacculus have been shown to exhibit spontaneous oscillations. We used a high-speed complementary metal oxide semiconductor camera to track the movements of hundreds of cells in parallel from dozens of preparations. We found that innate bundle movements exhibit a complex profile with multiple periodicities. Experiments inhibiting the electrical resonance in the cell body show a strong effect on the mechanical oscillations of the hair bundles. This indicates that the electrical oscillation is coupled with the mechanical oscillations of the hair bundles.
Akbarzade, M.; Langari, J.
2011-02-15
In this paper a new approach combining the features of the homotopy concept with variational approach is proposed to find accurate analytical solutions for nonlinear oscillators with and without a fractional power restoring force. Since the first-order approximation leads to very accurate results, comparisons with other results are presented to show the effectiveness of this method. The validity of the method is independent of whether or not there exist small or large parameters in the considered nonlinear equations; the obtained results prove the validity and efficiency of the method, which can be easily extended to other strongly nonlinear problems. At the end we compare our procedure with the optimal homotopy perturbation method.
Anharmonic effects on a phonon-number measurement of a quantum-mesoscopic-mechanical oscillator
Santamore, D.H.; Goan Hsisheng; Milburn, G.J.; Roukes, M.L.
2004-11-01
We generalize a proposal for detecting single-phonon transitions in a single nanoelectromechanical system (NEMS) to include the intrinsic anharmonicity of each mechanical oscillator. In this scheme two NEMS oscillators are coupled via a term quadratic in the amplitude of oscillation for each oscillator. One NEMS oscillator is driven and strongly damped and becomes a transducer for phonon number in the other measured oscillator. We derive the conditions for this measurement scheme to be quantum limited and find a condition on the size of the anharmonicity. We also derive the relation between the phase diffusion back-action noise due to number measurement and the localization time for the measured system to enter a phonon-number eigenstate. We relate both these time scales to the strength of the measured signal, which is an induced current proportional to the position of the read-out oscillator.
Summer North Atlantic Oscillation: decadal change, impact, and possible mechanisms
NASA Astrophysics Data System (ADS)
Sun, J.
2010-12-01
Summer North Atlantic Oscillation: decadal change, impact, and possible mechanisms Jianqi Sun, Huijun Wang, and Wei Yuan Nansen-Zhu International Research Centre (NZC), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China. Email: sunjq@mail.iap.ac.cn It is well known that the North Atlantic Oscillation (NAO) is strong in winter, so most previous studies focused on the NAO in winter time. However, actually the NAO is also one of the teleconnection patterns that have a year-round presence. For example, some studies have indicated that the summer North Atlantic Oscillation (SNAO) is still a dominant pattern over the North Atlantic region. So it is of importance to investigate the SNAO’s variability and influences. Our recent studies revealed that the summer (SNAO) experienced a significant decadal change around the late 1970s, with the southern action center located farther eastward after the late 1970s as compared to before. Such decadal change of the SNAO pattern altered its relationship with the Northern Hemispheric summer climate. In the period before the late 1970s, the connection of the SNAO on the Northern Hemispheric land surface air temperature is weak, but after that time the impact of the SNAO is significantly enhanced. Our further analysis indicated that the decadal change of the SNAO pattern is to some extend attributed to the decadal variability of the Mediterranean-Black Sea (MBS) sea surface temperature (SST). In 1951-1975, the variability of the MBS SST is quite weak, but in 1978-2002 it becomes more active. The active MBS SST can enhance the interaction between the sea and its overlying atmosphere, thus strengthening the activity of the east part of the SNAO southern center after the late 1970s and consequently producing an eastward SNAO southern center shift. This observational analysis result is further confirmed by sensitivity experiments. Besides the MBS SST, the decadal variability of the tropical Atlantic SST
The interplay of nonlinearity and architecture in equilibrium cytoskeletal mechanics.
Wang, Shenshen; Shen, Tongye; Wolynes, Peter G
2011-01-01
The interplay between cytoskeletal architecture and the nonlinearity of the interactions due to bucklable filaments plays a key role in modulating the cell's mechanical stability and affecting its structural rearrangements. We study a model of cytoskeletal structure treating it as an amorphous network of hard centers rigidly cross-linked by nonlinear elastic strings, neglecting the effects of motorization. Using simulations along with a self-consistent phonon method, we show that this minimal model exhibits diverse thermodynamically stable mechanical phases that depend on excluded volume, cross-link concentration, filament length, and stiffness. Within the framework set by the free energy functional formulation and making use of the random first order transition theory of structural glasses, we further estimate the characteristic densities for a kinetic glass transition to occur in this model system. Network connectivity strongly modulates the transition boundaries between various equilibrium phases, as well as the kinetic glass transition density. PMID:21219010
NASA Astrophysics Data System (ADS)
Sharma, S.; Narayan, A.
2001-06-01
The non-linear oscillation of inter-connected satellites system about its equilibrium position in the neighabourhood of main resonance ??=3D 1, under the combined effects of the solar radiation pressure and the dissipative forces of general nature has been discussed. It is found that the oscillation of the system gets disturbed when the frequency of the natural oscillation approaches the resonance frequency.
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
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
Enhanced nonlinear interactions in quantum optomechanics via mechanical amplification
NASA Astrophysics Data System (ADS)
Didier, Nicolas; Lemonde, Marc-Antoine; Clerk, Aashish A.
A key challenge limiting truly quantum behaviour in optomechanical systems is the typically small value of the optomechanical coupling at the single-photon, single-phonon level. We present an approach for exponentially enhancing the single-photon coupling strength in an optomechanical system using only additional linear resources. It allows one to reach the quantum nonlinear regime of optomechanics, where nonlinear effects are observed at the single photon level, even if the bare coupling strength is much smaller than the mechanical frequency and cavity damping rate. 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 setup, 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. Preprint: arXiv:1509.09238.
On the synchronizing mechanisms of tetanically induced hippocampal oscillations.
Bracci, E; Vreugdenhil, M; Hack, S P; Jefferys, J G
1999-09-15
gamma (30-100 Hz) and beta (10-30 Hz) oscillations follow tetanic stimulation in the CA1 region of the rat hippocampal slice. Pyramidal neurons undergo a slow depolarization after the tetanus and generate synchronous action potentials. The slow depolarization was previously attributed to metabotropic glutamate receptor (mGluR) activation. However, we found that this event was mediated by GABA(A) receptors, being blocked by bicuculline (50 microM) and accompanied by a dramatic drop in input resistance. Experiments with NMDA and non-NMDA glutamate receptor antagonists revealed that fast synaptic excitation was not necessary for oscillations. IPSPs were strongly depressed during the oscillations. Instead, synchronization was caused by field effects, as shown by: (1) Action potentials of pyramidal neurons proximal (<200 micrometer) to the stimulation site were often preceded by negative deflections of the intracellular potential that masked a net transmembrane depolarization caused by the population spike. (2) Pyramidal neurons located on the surface of the slice, where field effects are weak, fired repetitively but were not synchronized to the network activity. (3) A moderate decrease (50 mOsm) in artificial CSF (ACSF) osmolality did not affect the slow depolarization but increased oscillation amplitude and duration and recruited previously silent neurons into oscillations. (4) 50 mOsm increase in ACSF osmolality dramatically reduced, or abolished, post-tetanic oscillations. Phasic IPSPs, not detectable in proximal neurons, were present, late in the oscillation, in cells located 200-400 micrometer from the stimulation site and possibly contributed to slowing the rhythm during the gamma to beta transition.
Spintronic Oscillator based on feed-back mechanism
NASA Astrophysics Data System (ADS)
Tulapurkar, Ashwin; Dixit, Dinesh; Konishi, Katsunori; Tomy, C.; Suzuki, Yoshishige
2012-02-01
Nano-scale rf oscillators based on the magnetic tunnel junctions is an active area of research. These oscillators are based on the spin-transfer torque effect, in which a dc current drives the magnetization into precessional motion. Here we present a novel design of a spintronic oscillator which is not based on spin-transfer torque effect. This new oscillator is comprised of a magnetic tunnel junction whose top and bottom contacts are connected to a bias-T. A dc current is passed through the low frequency port of the bias-T and the high frequency port is connected to a ``feed-back'' wire which runs below the MTJ. Any fluctuation in the magnetization direction of the free layer of MTJ, drives ac current through the feed-back wire, which in turn exerts ac magnetic field on the free layer. The feedback wire is oriented such that the ac magnetic field amplifies the magnetization fluctuations for positive value of dc current. For negative value of dc current, the feedback loop suppresses the fluctuations. We find that if the positive dc current passing through the MTJ is more than a critical value, continuous precessing states of the magnetization are possible. Oscillators with better quality factors are possible using the feedback scheme.
From ordinary to discrete quantum mechanics: The Charlier oscillator and its coalgebra symmetry
NASA Astrophysics Data System (ADS)
Latini, D.; Riglioni, D.
2016-10-01
The coalgebraic structure of the harmonic oscillator is used to underline possible connections between continuous and discrete superintegrable models which can be described in terms of SUSY discrete quantum mechanics. A set of 1-parameter algebraic transformations is introduced in order to generate a discrete representation for the coalgebraic harmonic oscillator. This set of transformations is shown to play a role in the generalization of classical orthogonal polynomials to the realm of discrete orthogonal polynomials in the Askey scheme. As an explicit example the connection between Hermite and Charlier oscillators, that share the same coalgebraic structure, is presented and a two-dimensional maximally superintegrable version of the Charlier oscillator is constructed.
NASA Astrophysics Data System (ADS)
Zong, W.; Charpinet, S.; Vauclair, G.; Giammichele, N.; Van Grootel, V.
2016-01-01
Context. The signatures of nonlinear effects affecting stellar oscillations are difficult to observe from ground observatories because of the lack of continuous high-precision photometric data spanning extended enough time baselines. The unprecedented photometric quality and coverage provided by the Kepler spacecraft offers new opportunities to search for these phenomena. Aims: We use the Kepler data accumulated on the pulsating DB white dwarf KIC 08626021 to explore in detail the stability of its oscillation modes, searching, in particular, for evidence of nonlinear behaviors. Methods: We analyze nearly two years of uninterrupted short-cadence data, concentrating on identified triplets that are caused by stellar rotation and that show intriguing behaviors during the course of the observations. Results: We find clear signatures of nonlinear effects that could be attributed to resonant mode coupling mechanisms. These couplings occur between the components of the triplets and can induce different types of behaviors. We first notice that a structure at 3681 μHz, identified as a triplet in previous published studies, is in fact forming a doublet, with the third component being an independent mode. We find that a triplet at 4310 μHz and this doublet at 3681 μHz (most likely the two visible components of an incomplete triplet) have clear periodic frequency and amplitude modulations, which are typical of the so-called intermediate regime of the resonance, with timescales consistent with theoretical expectations. Another triplet at 5073 μHz is likely in a narrow transitory regime in which the amplitudes are modulated while the frequencies are locked. Using nonadiabatic pulsation calculations, based on a model representative of KIC 08626021 to evaluate the linear growth rates of the modes in the triplets, we also provide quantitative information that could be useful for future comparisons with numerical solutions of the amplitude equations. Conclusions: The observed
NASA Astrophysics Data System (ADS)
Donoso, Guillermo; Ladera, Celso L.
2012-11-01
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 first, excited with an ac current, provides the oscillating magnetic driving force on the system. From the magnet-coil interactions, we obtain, analytically, the nonlinear motion equation of the system, found to be a forced and damped cubic Duffing oscillator moving in a quartic potential. The relative strengths of the coefficients of the motion equation can be easily set by varying the coils’ dc and ac currents. We demonstrate, theoretically and experimentally, the nonlinear behaviour of this oscillator, including its oscillation modes and nonlinear resonances, the fold-over effect, the hysteresis and amplitude jumps, and its chaotic behaviour. It is an oscillating system suitable for teaching an advanced experiment in nonlinear dynamics both at senior undergraduate and graduate levels.
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
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.
Sustained mechanical self-oscillations in carbon nanotubes.
Weldon, Jeffrey A; Alemán, Benjamin; Sussman, Allen; Gannett, William; Zettl, Alex K
2010-05-12
The potential size and power benefits of resonant NEMS devices are frequently mitigated by the need for relatively large, high-frequency, high-power electronics. Here we demonstrate controllable, sustained self-oscillations in singly clamped carbon nanotubes operating with a single dc voltage supply, and we develop a model that predicts the required voltage on the basis of the material properties and device geometry. Using this model, we demonstrate for the first time top-down, self-oscillating NEMS devices suitable for large-scale integration.
Single Molecule as a Local Acoustic Detector for Mechanical Oscillators
NASA Astrophysics Data System (ADS)
Tian, Yuxi; Navarro, Pedro; Orrit, Michel
2014-09-01
A single molecule can serve as a nanometer-sized detector of acoustic strain. Such a nanomicrophone has the great advantage that it can be placed very close to acoustic signal sources and high sensitivities can be achieved. We demonstrate this scheme by monitoring the fluorescence intensity of a single dibenzoterrylene molecule in an anthracene crystal attached to an oscillating tuning fork. The characterization of the vibration amplitude and of the detection sensitivity is a first step towards detection and control of nanomechanical oscillators through optical detection and feedback.
Reprint of : Dynamics of coupled vibration modes in a quantum non-linear mechanical resonator
NASA Astrophysics Data System (ADS)
Labadze, G.; Dukalski, M.; Blanter, Ya. M.
2016-08-01
We investigate the behaviour of two non-linearly coupled flexural modes of a doubly clamped suspended beam (nanomechanical resonator). One of the modes is externally driven. We demonstrate that classically, the behavior of the non-driven mode is reminiscent of that of a parametrically driven linear oscillator: it exhibits a threshold behavior, with the amplitude of this mode below the threshold being exactly zero. Quantum-mechanically, we were able to access the dynamics of this mode below the classical parametric threshold. We show that whereas the mean displacement of this mode is still zero, the mean squared displacement is finite and at the threshold corresponds to the occupation number of 1/2. This finite displacement of the non-driven mode can serve as an experimentally verifiable quantum signature of quantum motion.
Gravitational force modulates muscle activity during mechanical oscillation of the tibia in humans.
Chang, Shuo-Hsiu; Dudley-Javoroski, Shauna; Shields, Richard K
2011-10-01
Mechanical oscillation (vibration) is an osteogenic stimulus for bone in animal models and may hold promise as an anti-osteoporosis measure in humans with spinal cord injury (SCI). However, the level of reflex induced muscle contractions associated with various loads (g force) during limb segment oscillation is uncertain. The purpose of this study was to determine whether certain gravitational loads (g forces) at a fixed oscillation frequency (30 Hz) increases muscle reflex activity in individuals with and without SCI. Nine healthy subjects and two individuals with SCI sat with their hip and knee joints at 90° and the foot secured on an oscillation platform. Vertical mechanical oscillations were introduced at 0.3, 0.6, 1.2, 3 and 5 g force for 20 s at 30 Hz. Non-SCI subjects received the oscillation with and without a 5% MVC background contraction. Peak soleus and tibialis anterior (TA) EMG were normalized to M-max. Soleus and TA EMG were <2.5% of M-max in both SCI and non-SCI subjects. The greatest EMG occurred at the highest acceleration (5 g). Low magnitude mechanical oscillation, shown to enhance bone anabolism in animal models, did not elicit high levels of reflex muscle activity in individuals with and without SCI. These findings support the g force modulated background muscle activity during fixed frequency vibration. The magnitude of muscle activity was low and likely does not influence the load during fixed frequency oscillation of the tibia.
Microwave Nano-abacus Electro-mechanical Oscillator
NASA Astrophysics Data System (ADS)
Peng, Haibing; Chang, C. W.; Aloni, S.; Yuzvinsky, T. D.; Zettl, A.
2007-03-01
We describe nanoscale electromechanical oscillators capable of operating in ambient-pressure air at room temperature with unprecedented fundamental resonance frequency of ˜4 GHz. The devices, created from suspended carbon nanotubes loaded abacus-style with inertial metal clamps yielding short effective beam lengths, open windows for immediate practical microwave frequency nanoelectromechanical systems (NEMS) applications.
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…
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.
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
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.
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.
Hopf normal form with SN symmetry and reduction to systems of nonlinearly coupled phase oscillators
NASA Astrophysics Data System (ADS)
Ashwin, Peter; Rodrigues, Ana
2016-06-01
Coupled oscillator models where N oscillators are identical and symmetrically coupled to all others with full permutation symmetry SN are found in a variety of applications. Much, but not all, work on phase descriptions of such systems consider the special case of pairwise coupling between oscillators. In this paper, we show this is restrictive-and we characterize generic multi-way interactions between oscillators that are typically present, except at the very lowest order near a Hopf bifurcation where the oscillations emerge. We examine a network of identical weakly coupled dynamical systems that are close to a supercritical Hopf bifurcation by considering two parameters, ɛ (the strength of coupling) and λ (an unfolding parameter for the Hopf bifurcation). For small enough λ > 0 there is an attractor that is the product of N stable limit cycles; this persists as a normally hyperbolic invariant torus for sufficiently small ɛ > 0. Using equivariant normal form theory, we derive a generic normal form for a system of coupled phase oscillators with SN symmetry. For fixed N and taking the limit 0 < ɛ ≪ λ ≪ 1, we show that the attracting dynamics of the system on the torus can be well approximated by a coupled phase oscillator system that, to lowest order, is the well-known Kuramoto-Sakaguchi system of coupled oscillators. The next order of approximation generically includes terms with up to four interacting phases, regardless of N. Using a normalization that maintains nontrivial interactions in the limit N → ∞, we show that the additional terms can lead to new phenomena in terms of coexistence of two-cluster states with the same phase difference but different cluster size.
Study of nonlinear oscillations due to exciter control using Hopf bifurcation
Abed, E.; Tsolas, N.; Varaiya, P.
1983-01-01
The effect of excitation system parameters on power system stability is studied here. The classical swing equation for a power generator augmented with an exciter is shown to undergo a Hopf bifurcation to periodic solutions. Only unstable oscillations occur for realistic parameter values and characterize the attractor of the stable equilibrium point. Attention is focussed on the global behavior of the oscillations as the critical parameter is varied. The analysis is carred out for a single machine connected to an infinite bus case.
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
Floating Oscillator-Embedded Triboelectric Generator for Versatile Mechanical Energy Harvesting
NASA Astrophysics Data System (ADS)
Seol, Myeong-Lok; Han, Jin-Woo; Jeon, Seung-Bae; Meyyappan, M.; Choi, Yang-Kyu
2015-11-01
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.
Floating Oscillator-Embedded Triboelectric Generator for Versatile Mechanical Energy Harvesting.
Seol, Myeong-Lok; Han, Jin-Woo; Jeon, Seung-Bae; Meyyappan, M; Choi, Yang-Kyu
2015-11-10
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.
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).
BOOK REVIEW: Nonlinear Continuum Mechanics for Finite Element Analysis
NASA Astrophysics Data System (ADS)
Bialek, James M.
1998-05-01
Nonlinear continuum mechanics of solids is a fascinating subject. All the assumptions inherited from an overexposure to linear behaviour and analysis must be re-examined. The standard definitions of strain designed for small deformation linear problems may be totally misleading when finite motion or large deformations are considered. Nonlinear behaviour includes phenomena like `snap-through', where bifurcation theory is applied to engineering design. Capabilities in this field are growing at a fantastic speed; for example, modern automobiles are presently being designed to crumple in the most energy absorbing manner in order to protect the occupants. The combination of nonlinear mechanics and the finite element method is a very important field. Most engineering designs encountered in the fusion effort are strictly limited to small deformation linear theory. In fact, fusion devices are usually kept in the low stress, long life regime that avoids large deformations, nonlinearity and any plastic behaviour. The only aspect of nonlinear continuum solid mechanics about which the fusion community now worries is that rare case where details of the metal forming process must be considered. This text is divided into nine sections: introduction, mathematical preliminaries, kinematics, stress and equilibrium, hyperelasticity, linearized equilibrium equations, discretization and solution, computer implementation and an appendix covering an introduction to large inelastic deformations. The authors have decided to use vector and tensor notation almost exclusively. This means that the usual maze of indicial equations is avoided, but most readers will therefore be stretched considerably to follow the presentation, which quickly proceeds to the heart of nonlinear behaviour in solids. With great speed the reader is led through the material (Lagrangian) and spatial (Eulerian) co-ordinates, the deformation gradient tensor (an example of a two point tensor), the right and left Cauchy
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.
Design optimization of a twist compliant mechanism with nonlinear stiffness
NASA Astrophysics Data System (ADS)
Tummala, Y.; Frecker, M. I.; Wissa, A. A.; Hubbard, J. E., Jr.
2014-10-01
A contact-aided compliant mechanism called a twist compliant mechanism (TCM) is presented in this paper. This mechanism has nonlinear stiffness when it is twisted in both directions along its axis. The inner core of the mechanism is primarily responsible for its flexibility in one twisting direction. The contact surfaces of the cross-members and compliant sectors are primarily responsible for its high stiffness in the opposite direction. A desired twist angle in a given direction can be achieved by tailoring the stiffness of a TCM. The stiffness of a compliant twist mechanism can be tailored by varying thickness of its cross-members, thickness of the core and thickness of its sectors. A multi-objective optimization problem with three objective functions is proposed in this paper, and used to design an optimal TCM with desired twist angle. The objective functions are to minimize the mass and maximum von-Mises stress observed, while minimizing or maximizing the twist angles under specific loading conditions. The multi-objective optimization problem proposed in this paper is solved for an ornithopter flight research platform as a case study, with the goal of using the TCM to achieve passive twisting of the wing during upstroke, while keeping the wing fully extended and rigid during the downstroke. Prototype TCMs have been fabricated using 3D printing and tested. Testing results are also presented in this paper.
Raver, Sylvina M.; Keller, Asaf
2014-01-01
Marijuana use in adolescence, but not adulthood, may permanently impair cognitive functioning and increase the risk of developing schizophrenia. Cortical oscillations are patterns of neural network activity implicated in cognitive processing, and are abnormal in patients with schizophrenia. We have recently reported that cortical oscillations are suppressed in adult mice that were treated, in adolescence but not adulthood, with the cannabinoids WIN55,212-2 (WIN) or Δ9tetrahydrocannabinol (THC). WIN and THC are cannabinoid types 1 and 2 receptor (CB1R & CB2R) agonists, and also have activity at non-cannabinoid receptor targets. However, as acute WIN and THC administration can suppress oscillations through CB1Rs, we hypothesize that a similar mechanism underlies the permanent suppression of oscillations by repeated cannabinoid exposure in adolescence. Here we test the prediction that cannabinoid exposure in adolescence permanently suppresses cortical oscillations by acting through CB1Rs, and that these suppressive effects can be antagonized by a CB1R antagonist. We treated adolescent mice with various cannabinoid compounds, and pharmacologically-evoked oscillations in vitro in adult mice. We find that WIN exposure for six days in early adolescence suppresses oscillations preferentially in adult medial prefrontal cortex (mPFC) via CB1Rs, and that a similar CB1R mechanism accounts for the suppressive effects of long-term (20 day) adolescent THC in adult somatosensory cortex (SCx). Unexpectedly, we also find that CB2Rs may be involved in the suppression of oscillations in both mPFC and SCx by long-term adolescent cannabinoid exposure, and that non-cannabinoid receptors may also contribute to oscillation suppression in adult mPFC. These findings represent a novel attempt to antagonize the effects of adolescent cannabinoid exposure on neural network activity, and reveal the contribution of non-CB1R targets to the suppression of cortical oscillations. PMID:25036610
Entanglement of mechanical oscillators coupled to a nonequilibrium environment
Ludwig, Max; Hammerer, K.; Marquardt, Florian
2010-07-15
Recent experiments aim at cooling nanomechanical resonators to the ground state by coupling them to nonequilibrium environments in order to observe quantum effects such as entanglement. This raises the general question of how such environments affect entanglement. Here we show that there is an optimal dissipation strength for which the entanglement between two coupled oscillators is maximized. Our results are established with the help of a general framework of exact quantum Langevin equations valid for arbitrary bath spectra, in and out of equilibrium. We point out why the commonly employed Lindblad approach fails to give even a qualitatively correct picture.
Stability and decay of Bloch oscillations in the presence of time-dependent nonlinearity
Gaul, Christopher; Dominguez-Adame, Francisco; Diaz, Elena; Lima, Rodrigo P. A.; Mueller, Cord A.
2011-11-15
We consider Bloch oscillations of Bose-Einstein condensates in the presence of a time-modulated s-wave scattering length. Generically, the interaction leads to dephasing and decay of the wave packet. Based on a cyclic-time argument, we find--in addition to the linear Bloch oscillation and a rigid soliton solution--an infinite family of modulations that lead to a periodic time evolution of the wave packet. In order to quantitatively describe the dynamics of Bloch oscillations in the presence of time-modulated interactions, we employ two complementary methods: collective coordinates and the linear stability analysis of an extended wave packet. We provide instructive examples and address the question of robustness against external perturbations.
Han, Lijuan; Neiman, Alexander B.
2010-01-01
We study spontaneous dynamics and signal transduction in a model of active hair bundle mechanics of sensory hair cells. The hair bundle motion is subjected to internal noise resulted from thermal fluctuations and stochastic dynamics of mechano-electrical transduction ion channels. Similar to other studies we found that in the presence of noise the coherence of stochastic oscillations is maximal at a point on the bifurcation diagram away from the Andronov-Hopf bifurcation and is close to the point of maximum sensitivity of the system to weak periodic mechanical perturbations. Despite decoherent effect of noise the stochastic hair bundle oscillations can be synchronized by external periodic force of few pN amplitude in a finite range of control parameters. We then study effects of receptor potential oscillations on mechanics of the hair bundle and show that the hair bundle oscillations can be synchronized by oscillating receptor voltage. Moreover, using a linear model for the receptor potential we show that bi-directional coupling of the hair bundle and the receptor potential results in significant enhancement of the coherence of spontaneous oscillations and of the sensitivity to the external mechanical perturbations. PMID:20481759
NASA Astrophysics Data System (ADS)
Han, Lijuan; Neiman, Alexander B.
2010-04-01
We study spontaneous dynamics and signal transduction in a model of active hair bundle mechanics of sensory hair cells. The hair bundle motion is subjected to internal noise resulted from thermal fluctuations and stochastic dynamics of mechanoelectrical transduction ion channels. Similar to other studies we found that in the presence of noise the coherence of stochastic oscillations is maximal at a point on the bifurcation diagram away from the Andronov-Hopf bifurcation and is close to the point of maximum sensitivity of the system to weak periodic mechanical perturbations. Despite decoherent effect of noise the stochastic hair bundle oscillations can be synchronized by external periodic force of few pN amplitude in a finite range of control parameters. We then study effects of receptor potential oscillations on mechanics of the hair bundle and show that the hair bundle oscillations can be synchronized by oscillating receptor voltage. Moreover, using a linear model for the receptor potential we show that bidirectional coupling of the hair bundle and the receptor potential results in significant enhancement of the coherence of spontaneous oscillations and of the sensitivity to the external mechanical perturbations.
Quantum mechanics of neutrino oscillations - hand waving for pedestrians.
Lipkin, H. J.
1998-12-22
Why Hand Waving? All calculations in books describe oscillations in time. But real experiments don't measure time. Hand waving is used to convert the results of a ''gedanken time experiment'' to the result of a real experiment measuring oscillations in space. Right hand waving gives the right answer; wrong hand waving gives the wrong answer. Many papers use wrong handwaving to get wrong answers. This talk explains how to do it right and also answers the following questions: (1) A neutrino which is a mixture of two mass eigenstates is emitted with muon in the decay of a pion at rest. This is a ''missing mass experiment'' where the muon energy determines the neutrino mass. Why are the two mass states coherent? (2) A neutrino which is a mixture of two mass eigenstates is emitted at time t=0. The two mass eigenstates move with different velocities and arrive at the detector at different times. Why are the two mass states coherent? (3) A neutrino is a mixture of two overlapping wave packets with different masses moving with different velocities. Will the wave packets eventually separate? If yes, when?
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.
NASA Astrophysics Data System (ADS)
Van Gorder, Robert A.
2015-08-01
In this paper, we consider a method for the simple exact analytical solution of autonomous nonlinear oscillator equations. While the approach can be used to solve nonlinear oscillator equations with smooth solutions (and we demonstrate this with an application of the approach to an autonomous Duffing equation), our primary interest will be on solving equations with non-smooth yet continuous solutions. To this end, we consider the second-order pseudo-oscillator equation {yy}\\prime\\prime +1=0 used as a simple model of the path taken by an electron in an electron beam injected into a plasma tube. In recent results of Gadella and Lara, the authors claim the non-existence of periodic solutions to this equation, but actually show that there are no smooth periodic solutions. We show that although there are no smooth solutions to this equation, there does exist a type of continuous periodic solution on the whole problem domain, hence periodic solutions do indeed exist. These periodic solutions can be constructed to have any arbitrary positive period, and the amplitude of these solutions increases as the period is increased. The approach allows one to construct periodic solutions to a variety of nonlinear oscillator equations, even if the solutions are not smooth, and hence could be a useful tool for those interested in physical applications in which nonlinear oscillator models arise.
An exactly solvable model of an oscillator with nonlinear coupling and zeros of Bessel functions
NASA Technical Reports Server (NTRS)
Dodonov, V. V.; Klimov, A. B.
1993-01-01
We consider an oscillator model with nonpolynomial interaction. The model admits exact solutions for two situations: for energy eigenvalues in terms of zeros of Bessel functions, that were considered as functions of the continuous index; and for the corresponding eigenstates in terms of Lommel polynomials.
Numerical analysis of decaying nonlinear oscillations of a viscous liquid drop
Maikov, I. L. Director, L. B.
2008-06-15
An adaptive grid numerical model is developed for simulating the dynamics of a viscous liquid drop whose initial shape is strongly disturbed by an external field. Simulated oscillations of a drop in microgravity and on a horizontal surface are compared with available numerical and experimental results.
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.
Harmonic and anharmonic quantum-mechanical oscillators in noninteger dimensions
NASA Astrophysics Data System (ADS)
Sandev, Trifce; Petreska, Irina; Lenzi, Ervin K.
2014-01-01
We present new results for time-independent solutions for a Schrödinger equation with noninteger dimension by considering different, harmonic and anharmonic, forms for the potential energy. The solutions obtained for these potentials are exact and expressed in terms of the special functions such as Laguerre and Gegenbauer polynomials, associated Legendre functions, and hypergeometric functions. Graphical comparison of the probability density function with the ones for two-dimensional and three-dimensional case is given. We derive the mean values rβsinδθbar for the harmonic oscillator in noninteger dimensions, which may be of interest in the perturbation theory for calculation of energy corrections. We consider anharmonic Kratzer potential energy function and we obtain bound and scattering states. Exact results in case of different forms of θ-dependent potentials are presented. In addition, they can be connected to rich variety of situations which enable us to model anisotropic interactions in real space.
Deterministic nonclassicality for quantum-mechanical oscillators in thermal states
NASA Astrophysics Data System (ADS)
Marek, Petr; Lachman, Lukáš; Slodička, Lukáš; Filip, Radim
2016-07-01
Quantum nonclassicality is the basic building stone for the vast majority of quantum information applications and methods of its generation are at the forefront of research. One of the obstacles any method needs to clear is the looming presence of decoherence and noise which act against the nonclassicality and often erase it completely. In this paper we show that nonclassical states of a quantum harmonic oscillator initially in thermal equilibrium states can be deterministically created by coupling it to a single two-level system. This can be achieved even in the absorption regime in which the two-level system is initially in the ground state. The method is resilient to noise and it may actually benefit from it, as witnessed by the systems with higher thermal energy producing more nonclassical states.
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
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.
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
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.
On classical mechanical systems with non-linear constraints
NASA Astrophysics Data System (ADS)
Terra, Gláucio; Kobayashi, Marcelo H.
2004-03-01
In the present work, we analyze classical mechanical systems with non-linear constraints in the velocities. We prove that the d'Alembert-Chetaev trajectories of a constrained mechanical system satisfy both Gauss' principle of least constraint and Hölder's principle. In the case of a free mechanics, they also satisfy Hertz's principle of least curvature if the constraint manifold is a cone. We show that the Gibbs-Maggi-Appell (GMA) vector field (i.e. the second-order vector field which defines the d'Alembert-Chetaev trajectories) conserves energy for any potential energy if, and only if, the constraint is homogeneous (i.e. if the Liouville vector field is tangent to the constraint manifold). We introduce the Jacobi-Carathéodory metric tensor and prove Jacobi-Carathéodory's theorem assuming that the constraint manifold is a cone. Finally, we present a version of Liouville's theorem on the conservation of volume for the flow of the GMA vector field.
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.
NASA Astrophysics Data System (ADS)
Hüpper, G.; Schöll, E.; Reggiani, L.
1989-12-01
Starting from a Monte Carlo simulation of the microscopic energy and momentum relaxation processes of hot carriers in p-Ge at liquid helium temperatures we derive a set of coupled nonlinear dynamic equations for the mean carrier density, the mean carrier energy, and the electric field. The static current density - field characteristic displays N-shaped negative differential conductivity induced by impact ionization of a shallow acceptor level and optical phonon emission. In the positive differential conductivity regime of this characteristic we find a subcritical Hopf bifurcation and two global bifurcations of self-generated voltage oscillations (collision of two limit cycles, and bifurcation of a limit cycle from a separatrix with critical frequency scaling) and hysteresis between oscillatory and stationary states. Such behavior was not obtained in previous semiconductor models, but is supported by recent experimental findings.
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
Ishimatsu, Kana; Horikawa, Kazuki; Takeda, Hiroyuki
2007-06-01
A unique feature of vertebrate segmentation is its strict periodicity, which is governed by the segmentation clock consisting of numerous cellular oscillators. These cellular oscillators, driven by a negative-feedback loop of Hairy transcription factor, are linked through Notch-dependent intercellular coupling and display the synchronous expression of clock genes. Combining our transplantation experiments in zebrafish with mathematical simulations, we review how the cellular oscillators maintain synchrony and form a robust system that is resistant to the effects of developmental noise such as stochastic gene expression and active cell proliferation. The accumulated evidence indicates that the segmentation clock behaves as a "coupled oscillators," a mechanism that also underlies the synchronous flashing seen in fireflies.
Dynamics of Freely Oscillating and Coupled Hair Cell Bundles under Mechanical Deflection
Fredrickson-Hemsing, Lea; Strimbu, C. Elliott; Roongthumskul, Yuttana; Bozovic, Dolores
2012-01-01
In vitro, attachment to the overlying membrane was found to affect the resting position of the hair cell bundles of the bullfrog sacculus. To assess the effects of such a deflection on mechanically decoupled hair bundles, comparable offsets were imposed on decoupled spontaneously oscillating bundles. Strong modulation was observed in their dynamic state under deflection, with qualitative changes in the oscillation profile, amplitude, and characteristic frequency of oscillation seen in response to stimulus. Large offsets were found to arrest spontaneous oscillation, with subsequent recovery upon reversal of the stimulus. The dynamic state of the hair bundle displayed hysteresis and a dependence on the direction of the imposed offset. The coupled system of hair bundles, with the overlying membrane left on top of the preparation, also exhibited a dependence on offset position, with an increase in the linear response function observed under deflections in the inhibitory direction. PMID:22768934
Dynamics of freely oscillating and coupled hair cell bundles under mechanical deflection.
Fredrickson-Hemsing, Lea; Strimbu, C Elliott; Roongthumskul, Yuttana; Bozovic, Dolores
2012-04-18
In vitro, attachment to the overlying membrane was found to affect the resting position of the hair cell bundles of the bullfrog sacculus. To assess the effects of such a deflection on mechanically decoupled hair bundles, comparable offsets were imposed on decoupled spontaneously oscillating bundles. Strong modulation was observed in their dynamic state under deflection, with qualitative changes in the oscillation profile, amplitude, and characteristic frequency of oscillation seen in response to stimulus. Large offsets were found to arrest spontaneous oscillation, with subsequent recovery upon reversal of the stimulus. The dynamic state of the hair bundle displayed hysteresis and a dependence on the direction of the imposed offset. The coupled system of hair bundles, with the overlying membrane left on top of the preparation, also exhibited a dependence on offset position, with an increase in the linear response function observed under deflections in the inhibitory direction. PMID:22768934
Enhanced interaction between a mechanical oscillator and two coupled resonant electrical circuits
Dmitriev, A. V.; Mitrofanov, V. P.
2014-01-01
This paper reports result of calculation and experimental realization of an electromechanical system that consists of a high-Q mechanical oscillator parametrically coupled in the manner of a capacitive transducer with a radio frequency (RF) circuit, which is in turn inductively coupled with another RF circuit. The system operates in the resolved sideband regime when the mechanical oscillator's frequency is larger than the electrical circuits' bandwidths. Using two coupled RF circuits allowed one to enhance the interaction between them and the mechanical oscillator which is one of flexural vibrational modes of a free-edge circular silicon wafer. Such a coupled electromechanical system can be used as a high-sensitive capacitive vibration sensor. PMID:25173304
NASA Astrophysics Data System (ADS)
Amro, Rami M.; Neiman, Alexander B.
2013-03-01
Sensory hair cells are the first stage in conveying the mechanical stimuli into the electrical signals in auditory and vestibular organs of vertebrates. Experiments showed that hair cells rely on active processes in hair bundles to achieve high selective sensitivity, e.g. due to myosin molecular motors inside stereocilia. In lower vertebrates these active processes result in spontaneous oscillations of hair bundles which can be accompanied by oscillations of the cells' membrane potentials. We use modeling to study how the dynamics of both the membrane potential and the hair bundle interact to produce coherent self-sustained oscillations and how this interaction contributes to the cell's sensitivity to external mechanical perturbations. The model incorporates a mechanical stochastic hair bundle system coupled to a Hodgkin-Huxley type system for the membrane potential. We show that oscillatory regimes result in enhanced sensitivity and selectivity to harmonic stimuli.
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…
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
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 Astrophysics Data System (ADS)
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 Technical Reports Server (NTRS)
Li, Xiao-Fan; 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.
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.
NASA Astrophysics Data System (ADS)
Degenfeld-Schonburg, Peter; Navarrete-Benlloch, Carlos; Hartmann, Michael J.
2015-05-01
Nonlinear quantum optical systems are of paramount relevance for modern quantum technologies, as well as for the study of dissipative phase transitions. Their nonlinear nature makes their theoretical study very challenging and hence they have always served as great motivation to develop new techniques for the analysis of open quantum systems. We apply the recently developed self-consistent projection operator theory to the degenerate optical parametric oscillator to exemplify its general applicability to quantum optical systems. We show that this theory provides an efficient method to calculate the full quantum state of each mode with a high degree of accuracy, even at the critical point. It is equally successful in describing both the stationary limit and the dynamics, including regions of the parameter space where the numerical integration of the full problem is significantly less efficient. We further develop a Gaussian approach consistent with our theory, which yields sensibly better results than the previous Gaussian methods developed for this system, most notably standard linearization techniques.
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.
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.
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
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.
Hamakawa, Hiroshi; Sakai, Hiroaki; Takahashi, Ayuko; Bando, Toru; Date, Hiroshi
2013-01-01
Forced oscillation techniques (FOTs) using sine curved oscillatory waves are used for assessing the lung periphery, but measure only overall respiratory mechanics. Therefore, mathematical models of the respiratory system serve as vehicles to obtain detailed mechanics. Although the simplest model of respiratory mechanics is a simple 3-element series (RIC) model, the constant phase (CP) model is recently used for characterizing respiratory mechanics, which has the advantage of partitioning of respiratory mechanics into airway and tissue components. Meanwhile, FOTs using non-sine curved oscillatory waves are easily applied in patients with severe respiratory diseases because they do not require voluntary apnea. If the latter type of FOTs is as informative as the former, the question arises whether a FOT using non-sine curved oscillatory waves (IOS) could be used to study mechanical properties of the lung periphery. And the CP model should fit the impedance spectra. To answer this, subjects with lymphangioleiomyomatosis (LAM) were recruited as a cohort of patients with lung parenchymal disease. Impedance spectra obtained by the IOS were fitted to the CP and RIC models. Mean values of goodness of fit from the CP and RIC models were 0.978 ± 0.022 and 0.968 ± 0.026, respectively. The extra sum-of-squares F test was used to compare the two mathematical models. The F ratio was 2.37 ± 1.40 and the p-value was 0.29 ± 0.21. Unfortunately, there was no compelling evidence for adopting the CP model for the evaluation of impedance spectra obtained by IOS. This result might relate to the uncertainty of IOS for detecting mechanical properties of the lung periphery.
Hybrid plasmonic nanodevices: Switching mechanism for the nonlinear emission
NASA Astrophysics Data System (ADS)
Bragas, Andrea V.; Singh, Mahi R.
2014-03-01
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.
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.
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.
On the solutions of a nonlinear ‘pseudo’-oscillator equation
NASA Astrophysics Data System (ADS)
Gadella, M.; Lara, L. P.
2014-10-01
The second-order nonlinear equation yy^{\\prime\\prime} +1=0 has been proposed as a simple model to describe the dynamics of electrons in plasma physics. This equation is assumed to have periodic solutions by many authors who argue physical reasons. A great variety of approximate methods have been used in the recent literature in order to detect these periodic solutions. It is the objective of this paper to show that this equation has no periodic solutions whatsoever. In addition, the general solution can be obtained by showing that the equation is equivalent to a planar solvable Hamiltonian system.
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)
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).
Huang, Pu; Zhou, Jingwei; Zhang, Liang; Hou, Dong; Lin, Shaochun; Deng, Wen; Meng, Chao; Duan, Changkui; Ju, Chenyong; Zheng, Xiao; Xue, Fei; Du, Jiangfeng
2016-01-01
Nonlinearity in macroscopic mechanical systems may lead to abundant phenomena for fundamental studies and potential applications. However, it is difficult to generate nonlinearity due to the fact that macroscopic mechanical systems follow Hooke's law and respond linearly to external force, unless strong drive is used. Here we propose and experimentally realize high cubic nonlinear response in a macroscopic mechanical system by exploring the anharmonicity in chemical bonding interactions. We demonstrate the high tunability of nonlinear response by precisely controlling the chemical bonding interaction, and realize, at the single-bond limit, a cubic elastic constant of 1 × 10(20) N m(-3). This enables us to observe the resonator's vibrational bi-states transitions driven by the weak Brownian thermal noise at 6 K. This method can be flexibly applied to a variety of mechanical systems to improve nonlinear responses, and can be used, with further improvements, to explore macroscopic quantum mechanics.
Huang, Pu; Zhou, Jingwei; Zhang, Liang; Hou, Dong; Lin, Shaochun; Deng, Wen; Meng, Chao; Duan, Changkui; Ju, Chenyong; Zheng, Xiao; Xue, Fei; Du, Jiangfeng
2016-01-01
Nonlinearity in macroscopic mechanical systems may lead to abundant phenomena for fundamental studies and potential applications. However, it is difficult to generate nonlinearity due to the fact that macroscopic mechanical systems follow Hooke's law and respond linearly to external force, unless strong drive is used. Here we propose and experimentally realize high cubic nonlinear response in a macroscopic mechanical system by exploring the anharmonicity in chemical bonding interactions. We demonstrate the high tunability of nonlinear response by precisely controlling the chemical bonding interaction, and realize, at the single-bond limit, a cubic elastic constant of 1 × 1020 N m−3. This enables us to observe the resonator's vibrational bi-states transitions driven by the weak Brownian thermal noise at 6 K. This method can be flexibly applied to a variety of mechanical systems to improve nonlinear responses, and can be used, with further improvements, to explore macroscopic quantum mechanics. PMID:27225287
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
Mechanism for intensity-induced chimera states in globally coupled oscillators.
Chandrasekar, V K; Gopal, R; Venkatesan, A; Lakshmanan, M
2014-12-01
We identify the mechanism behind the existence of intensity-induced chimera states in globally coupled oscillators. We find that the effect of intensity in the system is to cause multistability by increasing the number of fixed points. This in turn increases the number of multistable attractors, and we find that their stability is determined by the strength of coupling. This causes the coexistence of different collective states in the system depending upon the initial state. We demonstrate that intensity-induced chimera is generic to both periodic and chaotic systems. We discuss possible applications of our results to real-world systems like the brain and spin torque nano-oscillators.
NASA Astrophysics Data System (ADS)
Karni, O.; Mishra, A. K.; Eisenstein, G.; Reithmaier, J. P.
2015-03-01
We study the interplay between coherent light-matter interactions and nonresonant pulse propagation effects when ultrashort pulses propagate in room-temperature quantum dot (QD) semiconductor optical amplifiers (SOAs). The signatures observed on a pulse envelope after propagating in a transparent SOA, when coherent Rabi oscillations are absent, highlight the contribution of two-photon absorption (TPA), and its accompanying Kerr-like effect, as well as of linear dispersion, to the modification of the pulse complex electric field profile. These effects are incorporated into our previously developed finite-difference time-domain comprehensive model that describes the interaction between the pulses and the QD SOA. The present generalized model is used to investigate the combined effect of coherent and nonresonant phenomena in the gain and absorption regimes of the QD SOA. It confirms that in the QD SOA we examined, linear dispersion in the presence of the Kerr-like effect causes pulse compression, which counteracts the pulse peak suppression due to TPA, and also modifies the patterns which the coherent Rabi oscillations imprint on the pulse envelope under both gain and absorption conditions. The inclusion of these effects leads to a better fit with experiments and to a better understanding of the interplay among the various mechanisms so as to be able to better analyze more complex future experiments of coherent light-matter interaction induced by short pulses propagating along an SOA.
Oscillation of a rotating levitated droplet: Analysis with a mechanical model.
Kitahata, Hiroyuki; Tanaka, Rui; Koyano, Yuki; Matsumoto, Satoshi; Nishinari, Katsuhiro; Watanabe, Tadashi; Hasegawa, Koji; Kanagawa, Tetsuya; Kaneko, Akiko; Abe, Yutaka
2015-12-01
A droplet of millimeter-to-centimeter scale can exhibit electrostatic levitation, and such levitated droplets can be used for the measurement of the surface tension of the liquids by observing the characteristic frequency of oscillatory deformation. In the present study, a simple mechanical model is proposed by considering a single mode of oscillation in the ellipsoidal deformation of a levitated rotating droplet. By measuring the oscillation frequency with respect to the rotational speed and oscillation amplitude, it is expected that the accuracy of the surface tension measurement could be improved. Using the proposed model, the dependences of the characteristic frequency of oscillatory deformation and the averaged aspect ratio are calculated with respect to the rotational angular velocity of a rotating droplet. These dependences are found to be consistent with the experimental observations. PMID:26764771
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.
Notake, Takashi; Nawata, Kouji; Kawamata, Hiroshi; Matsukawa, Takeshi; Qi, Feng; Minamide, Hiroaki
2012-11-01
We developed a difference frequency generation (DFG) source with an organic nonlinear optical crystal of DAST or BNA selectively excited by a dual-wavelength β-BaB(2)O(4) optical parametric oscillator (BBO-OPO). The dual-wavelength BBO-OPO can independently oscillate two lights with different wavelengths from 800 to 1800 nm in a cavity. THz-wave generation by using each organic crystal covers ultrawide range from 1 to 30 THz with inherent intensity dips by crystal absorption modes. The reduced outputs can be improved by switching over the crystals with adequately tuned pump wavelengths of the BBO-OPO.
2012-01-01
Background Collective rhythms of gene regulatory networks have been a subject of considerable interest for biologists and theoreticians, in particular the synchronization of dynamic cells mediated by intercellular communication. Synchronization of a population of synthetic genetic oscillators is an important design in practical applications, because such a population distributed over different host cells needs to exploit molecular phenomena simultaneously in order to emerge a biological phenomenon. However, this synchronization may be corrupted by intrinsic kinetic parameter fluctuations and extrinsic environmental molecular noise. Therefore, robust synchronization is an important design topic in nonlinear stochastic coupled synthetic genetic oscillators with intrinsic kinetic parameter fluctuations and extrinsic molecular noise. Results Initially, the condition for robust synchronization of synthetic genetic oscillators was derived based on Hamilton Jacobi inequality (HJI). We found that if the synchronization robustness can confer enough intrinsic robustness to tolerate intrinsic parameter fluctuation and extrinsic robustness to filter the environmental noise, then robust synchronization of coupled synthetic genetic oscillators is guaranteed. If the synchronization robustness of a population of nonlinear stochastic coupled synthetic genetic oscillators distributed over different host cells could not be maintained, then robust synchronization could be enhanced by external control input through quorum sensing molecules. In order to simplify the analysis and design of robust synchronization of nonlinear stochastic synthetic genetic oscillators, the fuzzy interpolation method was employed to interpolate several local linear stochastic coupled systems to approximate the nonlinear stochastic coupled system so that the HJI-based synchronization design problem could be replaced by a simple linear matrix inequality (LMI)-based design problem, which could be solved with
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.
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. PMID:27066685
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.
Effect of gravity field on the nonequilibrium/nonlinear chemical oscillation reactions
NASA Astrophysics Data System (ADS)
Fujieda, S.; Mori, Y.; Nakazawa, A.; Mogami, Y.
2001-01-01
Biological systems have evolved for a long time under the normal gravity. The Belousov-Zhabotinsky (BZ) reaction is a nonlinear chemical system far from the equilibrium that may be considered as a simplified chemical model of the biological systems so as to study the effect of gravity. The reaction solution is comprised of bromate in sulfuric acid as an oxidizing agent, 1,4-cyclohexanedione as an organic substrate, and ferroin as a metal catalyst. Chemical waves in the BZ reaction-diffusion system are visualized as blue and red patterns of ferriin and ferroin, respectively. After an improvement to the tubular reaction vessels in the experimental setup, the traveling velocity of chemical waves in aqueous solutions was measured in time series under normal gravity, microgravity, hyper-gravity, and normal gravity using the free-fall facility of JAMIC (Japan Microgravity Center), Hokkaido, Japan. Chemical patterns were collected as image data via CCD camera and analyzed by the software of NIH image after digitization. The estimated traveling velocity increased with increasing gravity as expected. It was clear experimentally that the traveling velocity of target patterns in reaction diffusion system was influenced by the effect of convection and correlated closely with the gravity field.
Effect of gravity field on the nonequilibrium/nonlinear chemical oscillation reactions.
Fujieda, S; Mori, Y; Nakazawa, A; Mogami, Y
2001-01-01
Biological systems have evolved for a long time under the normal gravity. The Belousov-Zhabotinsky (BZ) reaction is a nonlinear chemical system far from the equilibrium that may be considered as a simplified chemical model of the biological systems so as to study the effect of gravity. The reaction solution is comprised of bromate in sulfuric acid as an oxidizing agent, 1,4-cyclohexanedione as an organic substrate, and ferroin as a metal catalyst. Chemical waves in the BZ reaction-diffusion system are visualized as blue and red patterns of ferriin and ferroin, respectively. After an improvement to the tubular reaction vessels in the experimental setup, the traveling velocity of chemical waves in aqueous solutions was measured in time series under normal gravity, microgravity, hyper-gravity, and normal gravity using the free-fall facility of JAMIC (Japan Microgravity Center), Hokkaido, Japan. Chemical patterns were collected as image data via CCD camera and analyzed by the software of NIH image after digitization. The estimated traveling velocity increased with increasing gravity as expected. It was clear experimentally that the traveling velocity of target patterns in reaction diffusion system was influenced by the effect of convection and correlated closely with the gravity field.
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.
Simulation of the oscillation regimes of bowed bars: a non-linear modal approach
NASA Astrophysics Data System (ADS)
Inácio, Octávio; Henrique, Luís.; Antunes, José
2003-06-01
It is still a challenge to properly simulate the complex stick-slip behavior of multi-degree-of-freedom systems. In the present paper we investigate the self-excited non-linear responses of bowed bars, using a time-domain modal approach, coupled with an explicit model for the frictional forces, which is able to emulate stick-slip behavior. This computational approach can provide very detailed simulations and is well suited to deal with systems presenting a dispersive behavior. The effects of the bar supporting fixture are included in the model, as well as a velocity-dependent friction coefficient. We present the results of numerical simulations, for representative ranges of the bowing velocity and normal force. Computations have been performed for constant-section aluminum bars, as well as for real vibraphone bars, which display a central undercutting, intended to help tuning the first modes. Our results show limiting values for the normal force FN and bowing velocity ẏbow for which the "musical" self-sustained solutions exist. Beyond this "playability space", double period and even chaotic regimes were found for specific ranges of the input parameters FN and ẏbow. As also displayed by bowed strings, the vibration amplitudes of bowed bars also increase with the bow velocity. However, in contrast to string instruments, bowed bars "slip" during most of the motion cycle. Another important difference is that, in bowed bars, the self-excited motions are dominated by the system's first mode. Our numerical results are qualitatively supported by preliminary experimental results.
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.
Strain Coupling of a Nitrogen-Vacancy Center Spin to a Diamond Mechanical Oscillator
NASA Astrophysics Data System (ADS)
Teissier, J.; Barfuss, A.; Appel, P.; Neu, E.; Maletinsky, P.
2014-07-01
We report on single electronic spins coupled to the motion of mechanical resonators by a novel mechanism based on crystal strain. Our device consists of single-crystal diamond cantilevers with embedded nitrogen-vacancy center spins. Using optically detected electron spin resonance, we determine the unknown spin-strain coupling constants and demonstrate that our system resides well within the resolved sideband regime. We realize coupling strengths exceeding 10 MHz under mechanical driving and show that our system has the potential to reach strong coupling. Our novel hybrid system forms a resource for future experiments on spin-based cantilever cooling and coherent spin-oscillator coupling.
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.
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.
Vincent, Olivier; Roditchev, Ivan; Marmottant, Philippe
2011-01-01
Aquatic species of Utricularia are carnivorous plants living in environments poor in nutrients. Their trapping mechanism has fascinated generations of scientists and is still debated today. It was reported recently that Utricularia traps can fire spontaneously. We show here that these spontaneous firings follow an unexpected diversity of temporal patterns, from "metronomic" traps which fire at fixed time intervals to "random" patterns, displaying more scattered firing times. Some "bursting" traps even combine both aspects, with groups of fast regular firings separated by a variable amount of time. We propose a physical model to understand these very particular behaviors, showing that a trap of Utricularia accomplishes mechanical oscillations, based on continuous pumping and sudden opening of the trap door (buckling). We isolate the key parameters governing these oscillations and discuss the effect of their fluctuations.
Measurement-based control of a mechanical oscillator at its thermal decoherence rate.
Wilson, D J; Sudhir, V; Piro, N; Schilling, R; Ghadimi, A; Kippenberg, T J
2015-08-20
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.
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.
NASA Astrophysics Data System (ADS)
Breznay, Nicholas; Nair, Nityan; Analytis, James; Zhu, Zengwei; Modic, Kimberly; McDonald, Ross
2015-03-01
Recent quantum oscillation studies in cuprate superconductors have allowed for considerable progress in understanding their Fermi surface topography. However, important questions remain about the influence of quantum criticality and competing orders, as well as the universality of these results; in particular quantum oscillation studies to date have been largely confined to a limited range of hole-doped bulk crystal systems. We have observed a field nonlinear Hall effect in superconducting thin films of the cuprate Pr2CuO4, and studied the temperature and magnetic field dependence of this behavior. The Hall effect data are consistent with a simple two-band transport model in this material, and we will interpret them in light of recently observed Shubnikov-de Haas quantum oscillations in these films.
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.
Preuss, J M; Hall, G L; Sly, P D
1999-01-01
The present study has established a method for obtaining low-frequency forced oscillation measurements of lung mechanics in the absence of neuromuscular blockade in the rat. Increasing the ventilation rate of the animals inhibited the spontaneous breathing of the animals for a short period of time; enough to make the low-frequency forced oscillation measurements of lung mechanics without the need for paralysis of the animals. Using this technique, it was possible to show that neuromuscular blockade with pancuronium bromide (0.4 mg/kg iv) resulted in a significant inhibition of methacholine responses in the parenchymal, but not the airway components of the rat lung. In studies where the animals were examined in a repeated manner, there was no significant difference in methacholine responses on day 3 compared with those obtained on day 1. Similarly, in animals that were both challenged with methacholine and lavaged, there was no significant difference in the methacholine responses or in the total and differential cell numbers obtained from the bronchoalveolar lavage fluid. Thus, this study presents a technique for obtaining low-frequency forced oscillation estimates of lung mechanics in non-paralysed rats and allows for repeated measures to be made in the same animals. In addition, this study has demonstrated that neuromuscular blockade has differential effects on methacholine responses in different parts of the lung.
NASA Astrophysics Data System (ADS)
Yang, J. H.; Yang, J.; Kitipornchai, S.
2012-12-01
This paper presents an investigation on the nonlinear dynamic response of piezoelectric cylindrical shells reinforced with boron nitride nanotubes (BNNTs) under a combined axisymmetric electro-thermo-mechanical loading. By employing the classical Donnell shell theory, the von Kármán-Donnell kinematic relationship, and a piezo-elastic constitutive law including thermal effects, the nonlinear governing equations of motion of the shell are derived through the Reissner variational principle. The finite difference method and a time-integration scheme are used to obtain the nonlinear dynamic response of the BNNT-reinforced piezoelectric shell. A parametric study is conducted, showing the effects of geometrically nonlinear deformation, applied voltage, temperature change, mechanical load, BNNT volume fraction and boundary conditions on the nonlinear dynamic response.
A mechanism for ultra-slow oscillations in the cortical default network.
Steyn-Ross, Moira L; Steyn-Ross, D A; Sleigh, J W; Wilson, M T
2011-02-01
When the brain is in its noncognitive "idling" state, functional MRI measurements reveal the activation of default cortical networks whose activity is suppressed during cognitive processing. This default or background mode is characterized by ultra-slow BOLD oscillations (∼0.05 Hz), signaling extremely slow cycling in cortical metabolic demand across distinct cortical regions. Here we describe a model of the cortex which predicts that slow cycling of cortical activity can arise naturally as a result of nonlinear interactions between temporal (Hopf) and spatial (Turing) instabilities. The Hopf instability is triggered by delays in the inhibitory postsynaptic response, while the Turing instability is precipitated by increases in the strength of the gap-junction coupling between interneurons. We comment on possible implications for slow dendritic computation and information processing. PMID:20821063
Yasuda, Masaaki; Takei, Kuniharu; Arie, Takayuki; Akita, Seiji
2016-01-01
Despite the superb intrinsic properties of carbon nanotube mechanical resonators, the quality factors at room temperature are 1,000 or less, even in vacuum, which is much lower than that of mechanical resonators fabricated using a top-down approach. This study demonstrates the improvement of the quality factor and the control of nonlinearity of the mechanical resonance of the cantilevered nanotube by electrostatic interaction. The apparent quality factor of the nanotube supported by insulator is improved drastically from approximately 630 to 3200 at room temperature. Results show that retardation of the electrostatic force induced by the contact resistance between the nanotube and the insulator support improves the quality factor. Finite element method calculation reveals that the nonuniform pileup charge on the insulator support strongly influences the nonlinearity of the resonance. PMID:26935657
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.
Vainshtein mechanism in massive gravity nonlinear sigma models
NASA Astrophysics Data System (ADS)
Aoki, Katsuki; Mizuno, Shuntaro
2016-09-01
We study the stability of the Vainshtein screening solution of massive gravity/bigravity based on the massive nonlinear sigma model as the effective action inside the Vainshtein radius. The effective action is obtained by taking the Λ2 decoupling limit around a curved spacetime. First we derive a general consequence that any Ricci flat Vainshtein screening solution is unstable when we take into account the excitation of the scalar graviton only. This instability suggests that the nonlinear excitation of the scalar graviton is not sufficient to obtain a successful Vainshtein screening in massive gravity/bigravity. Then to see the role of the excitation of the vector graviton, we study perturbations around the static and spherically symmetric solution obtained in bigravity explicitly. As a result, we find that linear excitations of the vector graviton cannot be helpful and the solution still suffers from a ghost and/or a gradient instability for any parameters of the theory for this background.
Self-Sustained Micromechanical Oscillator with Linear Feedback.
Chen, Changyao; Zanette, Damián H; Guest, Jeffrey R; Czaplewski, David A; López, 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 motion, there needs to be an 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 for describing the working principle of the self-sustained oscillations and validate it with experiments performed on a nonlinear microelectromechanical oscillator.
Self-Sustained Micromechanical Oscillator with Linear Feedback
NASA Astrophysics Data System (ADS)
Chen, Changyao; Zanette, Damián H.; Guest, Jeffrey R.; Czaplewski, David A.; López, 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 motion, there needs to be an 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 for describing the working principle of the self-sustained oscillations and validate it with experiments performed on a nonlinear microelectromechanical oscillator.
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.
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
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)
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.
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.
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.
Ma, Pengfei; Zhang, Hanwei; Huang, Long; Wang, Xiaolin; Zhou, Pu; Liu, Zejin
2015-10-01
Ytterbium-Raman cascaded oscillators with linearly polarized output are designed and achieved based on polarization selection loss (PSL) mechanism for the first time. The 1120 nm laser cavity is designed with fully non polarization-maintained (NPM) fiber Bragg gratings (FBGs) and NPM active fiber while the 1080 nm laser cavity is designed based on polarization-maintained (PM) FBGs and PM active fiber. By using PSL mechanism in 1080 nm cavity, even with fully NPM 1120 nm cavity, both linear-polarized 1120 nm and 1080 nm lasers are achieved in the output port of the cascaded oscillators. Based on the new designed cascaded seeds, a high power polarization-maintained Yb-Raman hybrid nonlinear amplifier is established for further power scaling of the 1120 nm laser. In the nonlinear amplifier, only 21-meter-long active fiber and 1.5-meter-long passive fiber is used for power transferring from 1080 nm to 1120 nm. Output power of 1181 W is achieved at central wavelength of 1120 nm with the M(2) factor of <1.2 and polarization-extinction ratio (PER) of 18.2 dB. As far as we known, the output power of this all fiber format is the highest one in 1120 nm with linear polarization. This type of high power Yb-Raman nonlinear amplifier design with linear polarization can be further extended to Yb-Raman amplifying the wavelength range of 1100-1200 nm. PMID:26480163
Nonlinear mechanisms for drift wave saturation and induced particle transport
Dimits, A.M. . Lab. for Plasma Research); Lee, W.W. . Plasma Physics Lab.)
1989-12-01
A detailed theoretical study of the nonlinear dynamics of gyrokinetic particle simulations of electrostatic collisionless and weakly collisional drift waves is presented. In previous studies it was shown that, in the nonlinearly saturated phase of the evolution, the saturation levels and especially the particle fluxes have an unexpected dependence on collisionality. In this paper, the explanations for these collisionality dependences are found to be as follows: The saturation level is determined by a balance between the electron and ion fluxes. The ion flux is small for levels of the potential below an E {times} B-trapping threshold and increases sharply once this threshold is crossed. Due to the presence of resonant electrons, the electron flux has a much smoother dependence on the potential. In the 2-1/2-dimensional ( pseudo-3D'') geometry, the electrons are accelerated away from the resonance as they diffuse spatially, resulting in an inhibition of their diffusion. Collisions and three-dimensional effects can repopulate the resonance thereby increasing the value of the particle flux. 30 refs., 32 figs., 2 tabs.
Nicu, Valentin Paul
2016-08-01
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.
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.
Mori, Shigeo; Katayama, Naomi
2005-02-01
We investigated visual-vestibular interactions in normal humans, where a constant speed of optokinetic stimulation was combined with whole body oscillation of lateral linear acceleration (10 m stroke). The acceleration mode was not sinusoidal, but rectangular (step). The pure optokinetic reflex (reference OKR) and the OKR under combined stimulation (combined OKR) were induced by a random-dot pattern projected onto a hemispherical dome-screen affixed to a chair on a linear accelerator. The translational vestibulo-ocular reflex (tVOR) was determined separately in the dark during acceleration-step oscillation. Since the tVOR was masked by the OKR under combined stimulation, the interaction was assessed as changes in combined-OKR velocity at two segments of opposing acceleration; in other words, tVOR directions identical to (agonistic) and opposite to (antagonistic) the OKR direction. When a moderate optokinetic stimulus-speed of 40 deg/s was combined with a moderate acceleration of 0.3 G (3.0 m/s2) as in Experiment 1 (N=10), the combined-OKR velocity always increased during the agonistic condition, and the motion of the visual pattern was perceived as slow and clear in this segment. On the other hand, during the antagonistic condition, the combined-OKR velocity either remained unchanged or increased moderately, and the motion of the visual pattern was sensed as fast and unclear. Notably, in most subjects, the velocity difference in combined-OKR between the agonistic and antagonistic conditions was around the value of the tVOR velocity. In five of the ten subjects who completed an additional test session with the acceleration level increased from 0.3 to 0.5 G (4.9 m/s2), similar findings were maintained individually, suggesting independent behavior of tVOR. Therefore, we hypothesized that the interaction could be direction-selective; in other words, both tVOR and OKR are additive during the agonistic condition, but tVOR is suppressed during the antagonistic condition
Active stochastic oscillations and amplification of mechanical stimuli in a hair cell model
NASA Astrophysics Data System (ADS)
Han, Lijuan; Neiman, Alexander
2009-03-01
We study signal transduction in spontaneously oscillating hair bundles of an auditory hair cell using a computational model. The effects of intrinsic noise from the Brownian motion of hair bundles and from stochastic fluctuations of transduction ion channels as well as periodic fluctuations of the receptor potential are taken into account. The model shows the explosion of a canard trajectory near the Hopf bifurcation. We have found that the system's gain of weak mechanical stimuli can be greatly enhanced when the system operates slightly beyond the Hopf bifurcation, i.e. in the canard region. The gain can also be optimized by tuning the noise intensity.
Dependence of kink oscillation damping on the amplitude
NASA Astrophysics Data System (ADS)
Goddard, C. R.; Nakariakov, V. M.
2016-05-01
Context. Kink oscillations of coronal loops are one of the most intensively studied oscillatory phenomena in the solar corona. In the large-amplitude rapidly damped regime, these oscillations are observed to have a low quality factor with only a few cycles of oscillation detected before they are damped. The specific mechanism responsible for rapid damping is commonly accepted to be associated with the linear coupling between collective kink oscillations and localised torsional oscillations, the phenomenon of resonant absorption of the kink mode. The role of finite amplitude effects, however, is still not clear. Aims: We investigated the empirical dependence of the kink oscillation damping time and its quality factor, which is defined as the ratio of damping time to oscillation period, on the oscillation amplitude. Methods: We analysed decaying kink oscillation events detected previously with TRACE, SDO/AIA and and STEREO/EUVI in the extreme ultraviolet (EUV) 171 Å band. Results: We found that the ratio of the kink oscillation damping time to the oscillation period systematically decreases with the oscillation amplitude. We approximated the quality factor dependence on the oscillation displacement amplitude via the power-law dependence with the exponent of -1/2, however we stress that this is a by-eye estimate, and a more rigorous estimation of the scaling law requires more accurate measurements and increased statistics. We conclude that damping of kink oscillations of coronal loops depends on the oscillation amplitude, indicating the possible role of non-linear mechanisms for damping.
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.
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.
Simultaneous cooling of coupled mechanical oscillators using whispering gallery mode resonances.
Li, Ying Lia; Millen, James; Barker, P F
2016-01-25
We demonstrate simultaneous center-of-mass cooling of two coupled oscillators, consisting of a microsphere-cantilever and a tapered optical fiber. Excitation of a whispering gallery mode (WGM) of the microsphere, via the evanescent field of the taper, provides a transduction signal that continuously monitors the relative motion between these two microgram objects with a sensitivity of 3 pm. The cavity enhanced optical dipole force is used to provide feedback damping on the motion of the micron-diameter taper, whereas a piezo stack is used to damp the motion of the much larger (up to 180 μm in diameter), heavier (up to 1.5 × 10(-7) kg) and stiffer microsphere-cantilever. In each feedback scheme multiple mechanical modes of each oscillator can be cooled, and mode temperatures below 10 K are reached for the dominant mode, consistent with limits determined by the measurement noise of our system. This represents stabilization on the picometer level and is the first demonstration of using WGM resonances to cool the mechanical modes of both the WGM resonator and its coupling waveguide. PMID:26832520
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.
NASA Astrophysics Data System (ADS)
Bajaj, A. K.; Davies, P.
1994-12-01
The analysis of forced nonlinear response of mechanical and structural systems, subjected to harmonic excitations, is considered in this report. It is shown that the presence of internal resonances on the various linear modes of vibration of the structure can result in quite complex dynamical motions and the motion may not settle down to either a periodic or a sub/super-harmonic response. Internal resonances, which allow for the exchange of energy between the participating modes give rise to beat-like fluctuations in the amplitudes of vibration. The nonlinear amplitude variation is very slow and can be either periodic or chaotic, depending on the level of forcing, damping and the nonlinearity coefficients. The analytical and numerical results are derived for the nonlinear vibrations of a thin rectangular plate, the response of the pendulum vibration absorber, and a double pendulum. Some experimental results of the measured response for a harmonically forced rectangular plate are also presented and compared to analytical predictions.
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 instability in flagellar dynamics: a novel modulation mechanism in sperm migration?
NASA Astrophysics Data System (ADS)
Gadelha, H.; Gaffney, E.; Smith, D.; Kirkman-Brown, J.
2010-11-01
Throughout biology, cells and organisms use flagella and cilia to propel fluid and achieve motility. While the mechanics of flagellum-fluid interaction has been the subject of extensive mathematical studies, these models have been restricted to being geometrically linear or weakly nonlinear. In this talk, we study the effect of geometrical nonlinearity, focusing on the spermatozoon flagellum. For a wide range of physiologically relevant parameters, the nonlinear model predicts that flagellar compression by the internal forces initiates an effective buckling behaviour, leading to a symmetry-breaking bifurcation that causes profound and complicated changes in the waveform and swimming trajectory, as well as the breakdown of the linear theory. The emergent waveform also induces curved swimming in an otherwise symmetric system, with the swimming trajectory being sensitive to head shape - no signalling or asymmetric forces are required. We conclude that non-linear models are essential in understanding the flagellar waveform in migratory human sperm.
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
NASA Astrophysics Data System (ADS)
Vogell, B.; Kampschulte, T.; Rakher, M. T.; Faber, A.; Treutlein, P.; Hammerer, K.; Zoller, P.
2015-04-01
We propose and investigate a hybrid optomechanical system consisting of a micro-mechanical oscillator coupled to the internal states of a distant ensemble of atoms. The interaction between the systems is mediated by a light field which allows the coupling of the two systems in a modular way over long distances. Coupling to internal degrees of freedom of atoms opens up the possibility to employ high-frequency mechanical resonators in the MHz to GHz regime, such as optomechanical crystal structures, and to benefit from the rich toolbox of quantum control over internal atomic states. Previous schemes involving atomic motional states are rather limited in both of these aspects. We derive a full quantum model for the effective coupling including the main sources of decoherence. As an application we show that sympathetic ground-state cooling and strong coupling between the two systems is possible.
Ramunno-Johnson, D; Strimbu, C E; Kao, A; Fredrickson Hemsing, L; Bozovic, D
2010-09-01
Decoupled hair bundles of the bullfrog (Lithobates catesbeianus) sacculus exhibit spontaneous oscillations in vitro. We examine the effect of the somatic electrical circuit upon active hair bundle motility. We found that innate bundle movements exhibit a complex profile with multiple periodicities. Inhibition of somatic ion channels using targeted neurotoxins and modified physiological solutions strongly affects the bundles' mechanical behavior, modifying the amplitude and the temporal characteristics of the oscillation profile. PMID:20566385
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.
Atomic layer deposited alumina (Al2O3) thin films on a high-Q mechanical silicon oscillator
NASA Astrophysics Data System (ADS)
Hahtela, O.; Sievilä, P.; Chekurov, N.; Tittonen, I.
2007-04-01
In this paper, the influence of the atomic layer deposited alumina (Al2O3) thin films on the dynamics of a high-Q mechanical silicon oscillator was experimentally studied. The resonance frequency and Q value of uncoated oscillators used in this work were about f0 = 27 kHz and Q = 100 000 at p < 10-2 mbar and T = 300 K. Deposited alumina film thicknesses varied from 5 to 662 nm. It is demonstrated that the resonance frequency of the mechanical oscillator increases with the film thickness because the added alumina films effectively stiffen the oscillator structure. In addition, it is shown that alumina thin films with thickness up to 100 nm can be deposited on microfabricated mechanical resonant structures without degrading the initially high quality (Q value) of the resonance. The resonance frequency of the silicon oscillator was less sensitive to the changes in ambient temperature with thicker alumina coatings. The reflectivity of silicon at 633 nm was reduced from RSi = 0.35 to RAR = 0.035 by coating the silicon oscillator with an alumina film whose thickness corresponds to the quarter of the optical wavelength serving as a single-layer anti-reflection coating.
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.
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.
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 (Iapp) 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, gM, the persistent Na+ conductance, gNaP, and the cationic h conductance, gh. For gh = 0 and moderate values of gM and gNaP, the model neuron generates STOs, but not MMOs, in response to Iapp injection. STOs transform abruptly to tonic spiking as the current increases. In addition to STOs, MMOs are generated for gh>0 for larger values of Iapp; the Iapp range in which MMOs appear increases linearly with gh. In the MMOs regime, the firing rate increases with Iapp 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 Iapp. 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 whisking amplitude. PMID
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. PMID:26767699
Baldissera, F; Cavallari, P
2001-07-01
The role of kinaesthetic afferences in controlling coupling of voluntary oscillation of the hand and foot, both in-phase and anti-phase, was investigated by modifying the mechanical properties of one of the two segments (the hand) with applied inertial or elastic loads. Loads consisted of a lead disk, rotating coaxially with the wrist (total inertial momentum 15 g m2), or in two symmetrical rubber bands (elasticity, 4 g deg(-1)) connected 5 cm away from the wrist pivot. Experiments were performed on five male and five female subjects. Both the frequency responses of the hand and foot (i.e. the phase relations between the onset of muscular activation in limb extensors and the onset of the related movement) and the inter-limb phase relations (the phase differences between the hand and foot movement cycles and between the onsets of the electromyographic (EMG) activity in hand and foot extensors) were analysed. The hand frequency-response was fitted with a 2nd-order model, allowing us to describe the loaded and unloaded conditions through the changes in the model response. Inertial loading induced an immediate and steep decay in the frequency response, with a clear-cut reduction of the model resonance frequency, while elastic loading shifted the response to the right and upwards. Inter-limb phase relations were only partially affected by inertial loading of the hand. Despite the fact that the load strongly increased the difference between the frequency-responses of the hand and foot, when hand and foot were oscillated in-phase only about half of this difference remained as an increased phase-lag between hand and foot oscillations. The other half was offset by an advance of the contraction of the hand movers with respect to the foot movers. This compensation mechanism was more effective during anti-phase than during in-phase movements. Elastic loading improved inter-limb synchronisation, since it superimposed the hand frequency-response on that of the foot. In this
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.
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.
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 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.
NASA Astrophysics Data System (ADS)
Closa, F.; Gosse, C.; Jullien, L.; Lemarchand, A.
2015-05-01
In order to identify two-step chemical mechanisms, we propose a method based on a small temperature modulation and on the analysis of the concentration oscillations of a single tagged species involved in the first step. The thermokinetic parameters of the first reaction step are first determined. Then, we build test functions that are constant only if the chemical system actually possesses some assumed two-step mechanism. Next, if the test functions plotted using experimental data are actually even, the mechanism is attributed and the obtained constant values provide the rate constants and enthalpy of reaction of the second step. The advantage of the protocol is to use the first step as a probe reaction to reveal the dynamics of the second step, which can hence be relieved of any tagging. The protocol is anticipated to apply to many mechanisms of biological relevance. As far as ligand binding is considered, our approach can address receptor conformational changes or dimerization as well as competition with or modulation by a second partner. The method can also be used to screen libraries of untagged compounds, relying on a tracer whose concentration can be spectroscopically monitored
Comparison of spin transfer mechanisms in three terminal spin-torque-oscillators
NASA Astrophysics Data System (ADS)
Jue, Emilie; Rippard, William; Pufall, Matthew; Evarts, Eric R.; Quantum Electromagnetics Division Team
The manipulation of magnetization by electric current is one of the most active field of spintronics due to its interests for memory and logic applications. This control can be achieved through the transfer of angular momentum via a spin polarized current (the mechanism of spin-transfer torque - STT) or through a direct transfer of angular momentum from the crystal lattice through the spin-orbit interaction (the mechanism of spin-orbit torque - SOT). Over the five past years, SOT gained a lot of attention especially for the new possibilities that it offers for data storage application. However, the quantification and the comparison of both mechanisms' efficiencies remains uncertain. In this work, we compare for the first time the STT and SOT efficiencies in individual devices. For this, we created 3-terminal spin-torque oscillators (STO) composed of spin-valves (SV) on top of a Pt wires. The devices can be excited either by STT or by SOT depending on whether the current is applied through the SV or through the Pt wire. By varying the Pt width and the dimensions of the SV, we tune the SOT and STT and compare their efficiencies. We will discuss the complexity of such a structure and the differences in the magnetization dynamics induced by the different excitation mechanisms.
Digiuni, Simona; Berne-Dedieu, Annik; Martinez-Torres, Cristina; Szecsi, Judit; Bendahmane, Mohammed; Arneodo, Alain; Argoul, Françoise
2015-05-01
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. PMID:25954881
Digiuni, Simona; Berne-Dedieu, Annik; Martinez-Torres, Cristina; Szecsi, Judit; Bendahmane, Mohammed; Arneodo, Alain; Argoul, Françoise
2015-01-01
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. PMID:25954881
NASA Astrophysics Data System (ADS)
Zhang, Lin
2013-05-01
High-gain resonant nonlinear Raman spectrum on trapped cold atoms within a high-finesse optical cavity is simply explained under a nonlinear opto-mechanical mechanism, and a proposal using it to detect frequency of micro-trap is presented. The enhancement of this scattering spectrum is due to a coherent Raman conversion between two different cavity modes mediated by collective vibrations of atoms with nonlinear opto-mechanical couplings. The physical conditions of this technique are roughly estimated on Rubidium atoms, and a simple quantum analysis as well as a multi-body semiclassical simulation on this nonlinear Raman spectrum is conducted.
A biologically plausible mechanism for neuronal coding organized by the phase of alpha oscillations.
Gips, Bart; van der Eerden, Jan P J M; Jensen, Ole
2016-08-01
The visual system receives a wealth of sensory information of which only little is relevant for behaviour. We present a mechanism in which alpha oscillations serve to prioritize different components of visual information. By way of simulated neuronal networks, we show that inhibitory modulation in the alpha range (~ 10 Hz) can serve to temporally segment the visual information to prevent information overload. Coupled excitatory and inhibitory neurons generate a gamma rhythm in which information is segmented and sorted according to excitability in each alpha cycle. Further details are coded by distributed neuronal firing patterns within each gamma cycle. The network model produces coupling between alpha phase and gamma (40-100 Hz) amplitude in the simulated local field potential similar to that observed experimentally in human and animal recordings. PMID:27320148
NASA Astrophysics Data System (ADS)
Liu, Jing; Ren, Zepei; Wang, Cuncheng; Sun, Xingguo
1996-12-01
To make it possible for the thermal wave theory on temperature oscillation (TO) effects in living tissues to be founded on the substantial experimental basis, a series of typical decisive experiments in vivo as well as in artificially simulating constructions were carried out. Conclusions obtained including some other scholars’ animal experimental results all greatly support the thermal wave viewpoint qualitatively. A few experimental facts used not to be easily understood from the classical viewpoint are also well reinterpreted. The revealing on the thermal wave mechanisms of TO in living tissues is a brand new discovery and deep insight into this important thermophysiological phenomenon. It may possibly promote new investigations on the corresponding topics in the field of bioheat transfer science.
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.
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.
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
Nonlinear waves in mechanics and gas dynamics. Final report, 1 Jun 87-30 Sep 90
Liu, T.P.
1990-12-21
The proposer has studied nonlinear hyperbolic-parabolic partial differential equations related to gas dynamics and mechanics. Hyperbolic conservation laws with relaxation are studied with applications to kinetic theory, elasticity with memory and gas flow with thermo-non-equilibrium in mind. Nonlinear waves for the compressible Navier-Stokes equations are studied for their stability and time-asymptotic behavior. The singular behavior of the magnetohydrodynamic shock waves in the small dissipation limits is clarified, and in particular, it is shown that intermediate shocks are stable uniformly with regards to the strength of dissipations only for 2-dimensional model, and not for 3-dimensional model.
Nicu, Valentin Paul
2016-08-01
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.
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. PMID:26117284
Robust energy transfer mechanism via precession resonance in nonlinear turbulent wave systems
NASA Astrophysics Data System (ADS)
Lucas, Dan; Bustamante, Miguel; Quinn, Brenda
2014-11-01
The precise mechanisms by which energy is most efficiently transferred in a turbulent system remain an important open question for the fluid mechanics community. In this talk we present a newly discovered resonance which is found to drive transfers across the spectrum of Fourier modes in a nonlinear wave system. Quadratic nonlinearity results in modes interacting in triads and, by considering the ``truly dynamical degrees of freedom'' (amplitudes and triad phases) and the precessional frequencies of the triads, we show transfers are maximal when the precession resonates with the nonlinear temporal frequencies. This can lead to a collective state of synchronised triads with intense cascades at intermediate nonlinearity; we find greatest transfer between the traditional weak and strong turbulence regimes and discover that this new mechanism is dominant here. We present the effect in a hierarchy of models including a full DNS of the Charney-Hasegawa-Mima equation and confirm analytical predictions. Supported by Science Foundation Ireland (SFI) under Grant Number 12/IP/1491.
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)
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Phillipson, Rebecca; Boyd, Patricia T.; Smale, Alan P.
2016-04-01
The bright low-mass X-ray binary 4U1705-44 exhibits long-term semi-periodic variability with a timescale of several hundred days. The All-Sky Monitor (ASM) aboard the Rossi X-ray Timing Explorer (RXTE) and the Japanese X-ray All-Sky Monitor (MAXI) aboard the International Space Station together have continuously observed the source from December 1995 through the present. The combined ASM-MAXI data provides a continuous time series over fifty times the length of the timescale of interest. The phase space embedding of the flux versus its first derivative shows a strong resemblance to a double-welled nonlinear oscillator. When comparing our time series against well-known nonlinear oscillators, we find that 4U1705-44 exhibits behavior akin to the Duffing oscillator. Topological analysis can help us identify ‘fingerprints’ in the phase space of a system unique to its equations of motion. If such ‘fingerprints’ are the same between two systems, then their equations of motion must be closely related. We therefore found a range of parameters for which the Duffing oscillator closely follows the time evolution of 4U1705-44 and from this range chose 6 different numerical Duffing time series. We can extract low-period, unstable periodic orbits from both the 4U1705-44 and numerical Duffing time series and compare their topological information in phase space, such as their relative rotation rates. We argue that the associated period-1 orbit in 4U1705-44 has a period between 130 and 170 days. The driving periods of our 6 numerical time series correspond to 140 to 175 days. Assigning a logical sequence name to each orbit, the relative rotation rates can be compiled into a unique ‘intertwining’ matrix. The numerical Duffing time series and the 4U1705-44 intertwining matrices are identical, which provides strong evidence that they share the same underlying template. The implications of this equivalence suggests that we can look to the Duffing equation to describe the X
A Brownian energy depot model of the basilar membrane oscillation with a braking mechanism
NASA Astrophysics Data System (ADS)
Zhang, Y.; Kim, C. K.; Lee, K. J. B.; Park, Y.
2009-07-01
High auditory sensitivity, sharp frequency selectivity, and spontaneous otoacoustic emissions are signatures of active amplification of the cochlea. The human ear can also detect very large amplitude sounds without being damaged, as long as the exposed time is not too long. The outer hair cells are believed to be the best candidate for the active force generator of the mammalian cochlea. In this paper, we propose a new model for the basilar membrane oscillation which describes both an active and a protective mechanism by employing an energy depot concept and a critical velocity of the basilar membrane. The compressive response of the basilar membrane at the characteristic frequency and the dynamic response to the stimulation are consistent with the experimental results. Although our model displays a Hopf bifurcation, our braking mechanism results in a hyper-compressive response to intense stimuli which is not generically observed near a Hopf bifurcation. Asymmetry seen in experimental recordings between the onset and the offset of the basilar membrane response to a sound burst is also observed in this model.
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.
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. 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.
2014-01-01
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
NASA Astrophysics Data System (ADS)
Nakagawa, Ryo; Suzuki, Takanao; Shimizu, Hiroshi; Kyoya, Haruki; Nako, Katsuhiro; Hashimoto, Ken-ya
2016-07-01
In this paper, we discuss the generation mechanisms of third-order nonlinearity in surface acoustic wave (SAW) devices on the basis of simulation results, which are obtained by a proposed method for this discussion. First, eight nonlinear terms are introduced to the piezoelectric constitutive equations, and nonlinear stress and electric flux fields are estimated using linear strain and electric fields calculated by a linear analysis, i.e., the coupling of mode simulation. Then, their contributions are embedded as voltage and current sources, respectively, in an equivalent circuit model, and nonlinear signals appearing at external ports are estimated. It is shown that eight coefficients of the nonlinear terms can be determined from a series of experiments carried out at various driving and resulting frequencies. This is because the effect of each nonlinear term on the nonlinear signal outputs changes markedly with the conditions. When the coefficients are determined properly, the simulations agree well with some measurement results under various conditions.
Mechanical stabilities and nonlinear properties of monolayer Gallium selenide under tension
NASA Astrophysics Data System (ADS)
Liu, Gang; Xia, Suxia; Hou, Bin; Gao, Tao; Zhang, Ru
2015-05-01
The mechanical stabilities and nonlinear properties of monolayer Gallium selenide (GaSe) under tension are investigated by using density functional theory (DFT). The ultimate stresses and ultimate strains and the structure evolutions of monolayer GaSe under armchair (AC), zigzag (ZZ) and equiaxial (EQ) tensions are predicted. A thermodynamically rigorous continuum description of nonlinear elastic response is given by expanding the elastic strain energy density in a Taylor series in Lagrangian strain truncated after the fifth-order term. Fourteen nonzero independent elastic constants are determined by least-square fit to the DFT calculations. Pressure-dependent elastic constants (Cij(P)) and pressure derivatives of Cij (P) (C'ij) are also calculated. Calculated values of ultimate stresses and strains and the in-plane Young's modulus are all positive. It proves that monolayer GaSe is mechanically stable.
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.