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.
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.
NASA Astrophysics Data System (ADS)
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).
NASA Astrophysics Data System (ADS)
Hagedorn, P.
The mathematical pendulum is used to provide a survey of free and forced oscillations in damped and undamped systems. This simple model is employed to present illustrations for and comparisons between the various approximation schemes. A summary of the Liapunov stability theory is provided. The first and the second method of Liapunov are explained for autonomous as well as for nonautonomous systems. Here, a basic familiarity with the theory of linear oscillations is assumed. La Salle's theorem about the stability of invariant domains is explained in terms of illustrative examples. Self-excited oscillations are examined, taking into account such oscillations in mechanical and electrical systems, analytical approximation methods for the computation of self-excited oscillations, analytical criteria for the existence of limit cycles, forced oscillations in self-excited systems, and self-excited oscillations in systems with several degrees of freedom. Attention is given to Hamiltonian systems and an introduction to the theory of optimal control is provided.
Nonlinear 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. PMID:27250151
NASA Astrophysics Data System (ADS)
Chowdhury, A.; Yeo, I.; Tsvirkun, V.; Raineri, F.; Beaudoin, G.; Sagnes, I.; Raj, R.; Robert-Philip, I.; Braive, R.
2016-04-01
We investigate the non-linear mechanical dynamics of a nano-optomechanical mirror formed by a suspended membrane pierced by a photonic crystal. By applying to the mirror a periodic electrostatic force induced by interdigitated electrodes integrated below the membrane, we evidence superharmonic resonances of our nano-electro-mechanical system; the constant phase shift of the oscillator across the resonance tongues is observed on the onset of principal harmonic and subharmonic excitation regimes.
Nonlinear nanomechanical oscillators for ultrasensitive inertial detection
Datskos, Panagiotis George; Lavrik, Nickolay V
2013-08-13
A system for ultrasensitive mass and/or force detection of this invention includes a mechanical oscillator driven to oscillate in a nonlinear regime. The mechanical oscillator includes a piezoelectric base with at least one cantilever resonator etched into the piezoelectric base. The cantilever resonator is preferably a nonlinear resonator which is driven to oscillate with a frequency and an amplitude. The system of this invention detects an amplitude collapse of the cantilever resonator at a bifurcation frequency as the cantilever resonator stimulated over a frequency range. As mass and/or force is introduced to the cantilever resonator, the bifurcation frequency shifts along a frequency axis in proportion to the added mass.
Oscillation quenching mechanisms: Amplitude vs. oscillation death
NASA Astrophysics Data System (ADS)
Koseska, Aneta; Volkov, Evgeny; Kurths, Jürgen
2013-10-01
Oscillation quenching constitutes a fundamental emergent phenomenon in systems of coupled nonlinear oscillators. Its importance for various natural and man-made systems, ranging from climate, lasers, chemistry and a wide range of biological oscillators can be projected from two main aspects: (i) suppression of oscillations as a regulator of certain pathological cases and (ii) a general control mechanism for technical systems. We distinguish two structurally distinct oscillation quenching types: oscillation (OD) and amplitude death (AD) phenomena. In this review we aim to set clear boundaries between these two very different oscillation quenching manifestations and demonstrate the importance for their correct identification from the aspect of theory as well as of applications. Moreover, we pay special attention to the physiological interpretation of OD and AD in a large class of biological systems, further underlying their different properties. Several open issues and challenges that await further resolving are also highlighted.
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…
Phased array beamforming using nonlinear oscillators
NASA Astrophysics Data System (ADS)
Gabbay, Michael; Larsen, Michael L.; Tsimring, Lev S.
2004-10-01
We describe a concept in which an array of coupled nonlinear oscillators is used for beamforming in phased array receivers. The signal that each sensing element receives, beam steered by time delays, is input to a nonlinear oscillator. The nonlinear oscillators for each element are in turn coupled to each other. For incident signals sufficiently close to the steering angle, the oscillator array will synchronize to the forcing signal whereas more obliquely incident signals will not induce synchronization. The beam pattern that results can show a narrower mainlobe and lower sidelobes than the equivalent conventional linear beamformer. We present a theoretical analysis to explain the beam pattern of the nonlinear oscillator array.
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
2014-01-01
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
Coupled Oscillator Model for Nonlinear Gravitational Perturbations
NASA Astrophysics Data System (ADS)
Yang, Huan; Zhang, Fan; Green, Stephen; Lehner, Luis
2015-04-01
Motivated by the fluid/gravity correspondence, we introduce a new method for characterizing nonlinear gravitational interactions. Namely we map the nonlinear perturbative form of the Einstein's equation to the equations of motion of a series of nonlinearly-coupled harmonic oscillators. These oscillators correspond to the quasinormal modes of the background spacetime. We demonstrate the mechanics and the utility of this formalism with an asymptotically AdS black-brane spacetime, where the equations of motion for the oscillators are shown to be equivalent to the Navier-Stokes equation for the boundary fluid in the mode-expansion picture. We thereby expand on the explicit correspondence connecting the fluid and gravity sides for this particular physical set-up. Perhaps more importantly, we expect this formalism to remain valid in more general spacetimes, including those without a fluid/gravity correspondence. In other words, although born out of the correspondence, the formalism survives independently of it and has a much wider range of applicability.
Coupled oscillator model for nonlinear gravitational perturbations
NASA Astrophysics Data System (ADS)
Yang, Huan; Zhang, Fan; Green, Stephen R.; Lehner, Luis
2015-04-01
Motivated by the gravity-fluid correspondence, we introduce a new method for characterizing nonlinear gravitational interactions. Namely we map the nonlinear perturbative form of the Einstein equation to the equations of motion of a collection of nonlinearly coupled harmonic oscillators. These oscillators correspond to the quasinormal or normal modes of the background spacetime. We demonstrate the mechanics and the utility of this formalism within the context of perturbed asymptotically anti-de Sitter black brane spacetimes. We confirm in this case that the boundary fluid dynamics are equivalent to those of the hydrodynamic quasinormal modes of the bulk spacetime. We expect this formalism to remain valid in more general spacetimes, including those without a fluid dual. In other words, although born out of the gravity-fluid correspondence, the formalism is fully independent and it has a much wider range of applicability. In particular, as this formalism inspires an especially transparent physical intuition, we expect its introduction to simplify the often highly technical analytical exploration of nonlinear gravitational dynamics.
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.
NASA Astrophysics Data System (ADS)
Ghalambaz, Mohammad; Ghalambaz, Mehdi; Edalatifar, Mohammad
2016-03-01
The energy balance method is utilized to analyze the oscillation of a nonlinear nanoelectro-mechanical system resonator. The resonator comprises an electrode, which is embedded between two substrates. Two types of clamped-clamped and cantilever nano-resonators are studied. The effects of the van der Waals attractions, Casimir force, the small size, the fringing field, the mid-plane stretching, and the axial load are taken into account. The governing partial differential equation of the resonator is reduced using the Galerkin method. The energy method is applied to obtain an analytical solution without considering any linearization or small parameter. The results of the present study are compared with the results available in the literature. In addition, the results of the present analytical solution are compared with the Runge-Kutta numerical results. An excellent agreement between the present analytical solution, numerical solution, and the results available in the literature was found. The influences of the van der Waals force, Casimir force, size effect, and fringing field effect on the oscillation frequency of resonators are studied. The results indicate that the presence of the intermolecular forces (van der Waals), Casimir force, and fringing field effect decreases the oscillation frequency of the resonator. In contrast, the presence of the size effect increases the oscillation frequency of the resonator.
Forced oscillations with linear and nonlinear damping
NASA Astrophysics Data System (ADS)
Li, Aijun; Ma, Li; Keene, David; Klingel, Joshua; Payne, Marvin; Wang, Xiao-jun
2016-01-01
A general solution is derived for the differential equations of forced oscillatory motion with both linear damping ( ˜v ) and nonlinear damping ( ˜v2 ). Experiments with forced oscillators are performed using a flat metal plate with a drag force due to eddy currents and a flat piece of stiffened cardboard with a drag force due to air resistance serving as the linear and nonlinear damping, respectively. Resonance of forced oscillations for different damping forces and quality factors is demonstrated. The experimental measurements and theoretical calculations are in good agreement, and damping constants are determined.
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…
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 gas oscillations in pipes. I - Theory.
NASA Technical Reports Server (NTRS)
Jimenez, J.
1973-01-01
The problem of forced acoustic oscillations in a pipe is studied theoretically. The oscillations are produced by a moving piston in one end of the pipe, while a variety of boundary conditions ranging from a completely closed to a completely open mouth at the other end are considered. The linear theory predicts large amplitudes near resonance and that nonlinear effects become crucially important. By expanding the equations of motion in a series in the Mach number, both the amplitude and waveform of the oscillation are predicted there. In both the open- and closed-end cases the need for shock waves in some range of parameters is found. The amplitude of the oscillation is different for the two cases, however, being proportional to the square root of the piston amplitude in the closed-end case and to the cube root for the open end.
Nonlinear gas oscillations in pipes. II - Experiment
NASA Technical Reports Server (NTRS)
Sturtevant, B.
1974-01-01
The problem of forced acoustic oscillations in a pipe was experimentally investigated, taking into account the response of both open and closed tubes to near-resonant excitation by large amplitude oscillations of a piston at one end of the tube. Attention was given to the effect of the orifice area on shock waves. By comparing the experimental results with nonlinear theory, wave reflection coefficients of the orifice plates were determined at both closed-tube and open-tube resonant frequencies. This approach can even be used when the terminating elements are subjected to intense periodic pressure pulses.
Limit cycles in nonlinear excitation of clusters of classical oscillators
NASA Astrophysics Data System (ADS)
De Lauro, E.; De Martino, S.; Falanga, M.; Ixaru, L. Gr.
2009-10-01
In this paper we develop a numerical procedure for detecting the existence of limit cycles in nonlinear excitation of clusters of classical harmonic oscillators. Our technique is able to compute also the main parameters of a limit cycle, that is the amplitudes and the period. The numerical method, based on the propagation matrix formalism, is transparent and easy to apply. It may find application in various areas where nonlinear excitations are involved, e.g., sound and mechanic vibrations in musical instruments, ground vibrations in volcanic areas, and sea tides.
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network
Goto, Hayato
2016-01-01
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence. PMID:26899997
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network
NASA Astrophysics Data System (ADS)
Goto, Hayato
2016-02-01
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network.
Goto, Hayato
2016-01-01
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
Phase-selective entrainment of nonlinear oscillator ensembles
NASA Astrophysics Data System (ADS)
Zlotnik, Anatoly; Nagao, Raphael; Kiss, István Z.; Li-Shin, Jr.
2016-03-01
The ability to organize and finely manipulate the hierarchy and timing of dynamic processes is important for understanding and influencing brain functions, sleep and metabolic cycles, and many other natural phenomena. However, establishing spatiotemporal structures in biological oscillator ensembles is a challenging task that requires controlling large collections of complex nonlinear dynamical units. In this report, we present a method to design entrainment signals that create stable phase patterns in ensembles of heterogeneous nonlinear oscillators without using state feedback information. We demonstrate the approach using experiments with electrochemical reactions on multielectrode arrays, in which we selectively assign ensemble subgroups into spatiotemporal patterns with multiple phase clusters. The experimentally confirmed mechanism elucidates the connection between the phases and natural frequencies of a collection of dynamical elements, the spatial and temporal information that is encoded within this ensemble, and how external signals can be used to retrieve this information.
Phase-selective entrainment of nonlinear oscillator ensembles
Zlotnik, Anatoly V.; Nagao, Raphael; Kiss, Istvan Z.; 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
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
Accurate numerical solutions of conservative nonlinear oscillators
NASA Astrophysics Data System (ADS)
Khan, Najeeb Alam; Nasir Uddin, Khan; Nadeem Alam, Khan
2014-12-01
The objective of this paper is to present an investigation to analyze the vibration of a conservative nonlinear oscillator in the form u" + lambda u + u^(2n-1) + (1 + epsilon^2 u^(4m))^(1/2) = 0 for any arbitrary power of n and m. This method converts the differential equation to sets of algebraic equations and solve numerically. We have presented for three different cases: a higher order Duffing equation, an equation with irrational restoring force and a plasma physics equation. It is also found that the method is valid for any arbitrary order of n and m. Comparisons have been made with the results found in the literature the method gives accurate results.
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.
Nonlinear lower-hybrid oscillations in cold plasma
Maity, Chandan; Chakrabarti, Nikhil
2010-08-15
In a fluid description nonlinear lower-hybrid oscillation have been studied in a cold quasineutral magnetized plasma using Lagrangian variables. An exact analytical solution with nontrivial space and time dependence is obtained. The solution demonstrates that under well defined initial and boundary conditions the amplitude of the oscillations increases due to nonlinearity and then comes back to its initial condition again. These solutions indicate a class of nonlinear transient structures in magnetized plasma.
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.
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
Multifrequency synthesis using two coupled nonlinear oscillator arrays.
Palacios, Antonio; Carretero-González, Ricardo; Longhini, Patrick; Renz, Norbert; In, Visarath; Kho, Andy; Neff, Joseph D; Meadows, Brian K; Bulsara, Adi R
2005-08-01
We illustrate a scheme that exploits the theory of symmetry-breaking bifurcations for generating a spatio-temporal pattern in which one of two interconnected arrays, each with N Van der Pol oscillators, oscillates at N times the frequency of the other. A bifurcation analysis demonstrates that this type of frequency generation cannot be realized without the mutual interaction between the two arrays. It is also demonstrated that the mechanism for generating these frequencies between the two arrays is different from that of a master-slave interaction, a synchronization effect, or that of subharmonic and ultraharmonic solutions generated by forced systems. This kind of frequency generation scheme can find applications in the developed field of nonlinear antenna and radar systems. PMID:16196688
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.
Nonlinear oscillation behavior of a driven gyrotron backward-wave oscillator
Yeh, Y. S.; Jhou, J. N.; Huang, J. M.; Shiao, J. L.; Wu, Z. Q.; Chang, T. H.; Fan, C. T.; Chiu, C. C.; Hung, C. L.
2010-11-15
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…
Oscillation theorems for second order nonlinear forced differential equations.
Salhin, Ambarka A; Din, Ummul Khair Salma; Ahmad, Rokiah Rozita; Noorani, Mohd Salmi Md
2014-01-01
In this paper, a class of second order forced nonlinear differential equation is considered and several new oscillation theorems are obtained. Our results generalize and improve those known ones in the literature. PMID:25077054
Kerr-lens-mediated dynamics of two nonlinearly coupled mode-locked laser oscillators
NASA Astrophysics Data System (ADS)
Wu, Song; Smith, Sandra L.; Fork, Richard L.
1992-02-01
The dynamics of two nonlinearly coupled femtosecond oscillators are investigated for the case where two distinct nonlinear mechanisms are balanced to determine the temporal relationship and properties of the pulses in the two oscillators. In the time domain the shared bleaching of a common absorber creates an attractive mechanism for the pulses, while interactive Kerr lens deflections create a repulsive mechanism. The interplay of these two mechanisms causes a variety of dynamical behaviors, including pulse synchronization, pulse duration switching, and a latching type of amplitude bistability.
Zang, Xiao-Fei; Jiang, Chun; Zhu, Hai-Bin
2009-09-01
We study nonlinear dynamics of classical electromagnetic wave propagation in a one-dimensional nonlinear periodic photonic structure. It is found that the period of Rabi oscillations can be modulated by the relatively weak nonlinearity (2V0/gamma>1). When nonlinearity is relatively strong compared to the strength of resonant coupling (2V0/gamma<1), Rabi oscillations is suppressed and the system shows a dynamical behavior, i.e., energy localizes in one mode rather than full oscillation between two degenerated modes. Phase plane analysis is applied to explain these dynamical phenomena. PMID:19905235
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.
Electromagnetic radiation due to nonlinear oscillations of a charged drop
NASA Astrophysics Data System (ADS)
Shiryaeva, S. O.; Grigor'ev, A. N.; Kolbneva, N. Yu.
2016-03-01
The nonlinear oscillations of a spherical charged drop are asymptotically analyzed under the conditions of a multimode initial deformation of its equilibrium shape. It is found that if the spectrum of initially excited modes contains two adjacent modes, the translation mode of oscillations is excited among others. In this case, the center of the drop's charge oscillates about the equilibrium position, generating a dipole electromagnetic radiation. It is shown that the intensity of this radiation is many orders of magnitude higher than the intensity of the drop's radiation, which arises in calculations of the first order of smallness and is related to the drop's charged surface oscillations.
Hopf bifurcation with dihedral group symmetry - Coupled nonlinear oscillators
NASA Technical Reports Server (NTRS)
Golubitsky, Martin; Stewart, Ian
1986-01-01
The theory of Hopf bifurcation with symmetry developed by Golubitsky and Stewart (1985) is applied to systems of ODEs having the symmetries of a regular polygon, that is, whose symmetry group is dihedral. The existence and stability of symmetry-breaking branches of periodic solutions are considered. In particular, these results are applied to a general system of n nonlinear oscillators coupled symmetrically in a ring, and the generic oscillation patterns are described. It is found that the symmetry can force some oscillators to have twice the frequency of others. The case of four oscillators has exceptional features.
Relaxation Oscillations as a Mechanism of Abrupt Climate Change
NASA Astrophysics Data System (ADS)
Marchal, O.; Jackson, C.; Nilsson, J.; Paul, A.; Stocker, T.
2007-12-01
Climate variability at the millennial time scale is difficult to rationalize, as the frequency 0.001 1/yr falls near the middle of a wide gap in the spectrum of external forcing on the climate system (between the low-frequency orbital components and the high-frequency tidal components). This situation prompted interest in the possibility for the climate system to undergo self-sustained or self-excited oscillations. Our contribution will comprise two parts. First, we will review elements from the theory of non-linear vibrations that provide a framework for the discussion of the fundamental mechanisms responsible for millennial-scale climate variability. Particular emphasis will be put on the self-sustained oscillations that occur in physical systems with one degree of freedom. In such systems self-sustained oscillations arise from the nonlinear dependence of the damping force on velocity. In the limit of very large nonlinearity, the oscillator stores energy for a relatively long period of time and releases this energy in a relatively short time, i.e., the oscillations are strongly asymmetric (relaxation oscillations). Second, we will examine the self-sustained oscillations of the meridional overturning circulation simulated by an ocean circulation model when subject to large freshwater forcing (salt addition at low latitudes and salt extraction at high latitudes). A scaling analysis provides evidence that these oscillations can be fundamentally interpreted as relaxation oscillations : the model ocean stores potential energy in the form of an unstable vertical temperature gradient for a relatively long period of time (phase of reduced MOC) and converts this potential energy into kinetic energy (phase of intense MOC) when the unstable vertical temperature gradient dominates the stable vertical salinity gradient in the density stratification. The merits and weaknesses of the hypothesis of relaxation oscillations as a mechanism of abrupt climate change will be discussed.
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.
Nonlinear oscillations of inviscid free drops
NASA Technical Reports Server (NTRS)
Patzek, T. W.; Benner, R. E., Jr.; Basaran, O. A.; Scriven, L. E.
1991-01-01
The present analysis of free liquid drops' inviscid oscillations proceeds through solution of Bernoulli's equation to obtain the free surface shape and of Laplace's equation for the velocity potential field. Results thus obtained encompass drop-shape sequences, pressure distributions, particle paths, and the temporal evolution of kinetic and surface energies; accuracy is verified by the near-constant drop volume and total energy, as well as the diminutiveness of mass and momentum fluxes across drop surfaces. Further insight into the nature of oscillations is provided by Fourier power spectrum analyses of mode interactions and frequency shifts.
Lebrun, R; Jenkins, A; Dussaux, A; Locatelli, N; Tsunegi, S; Grimaldi, E; Kubota, H; Bortolotti, P; Yakushiji, K; Grollier, J; Fukushima, A; Yuasa, S; Cros, V
2015-07-01
We investigate experimentally the synchronization of vortex based spin transfer nano-oscillators to an external rf current whose frequency is at multiple integers, as well as at an integer fraction, of the oscillator frequency. Through a theoretical study of the locking mechanism, we highlight the crucial role of both the symmetries of the spin torques and the nonlinear properties of the oscillator in understanding the phase locking mechanism. In the locking regime, we report a phase noise reduction down to -90 dBc/Hz at 1 kHz offset frequency. Our demonstration that the phase noise of these nanoscale nonlinear oscillators can be tuned and eventually lessened, represents a key achievement for targeted radio frequency applications using spin torque devices. PMID:26182117
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. PMID:21405932
Nonlinearly driven oscillations in the gyrotron traveling-wave amplifier
Chiu, C. C.; Pao, K. F.; Yan, Y. C.; Chu, K. R.; Barnett, L. R.; Luhmann, N. C. Jr.
2008-12-15
By delivering unprecedented power and gain, the gyrotron traveling-wave amplifier (gyro-TWT) offers great promise for advanced millimeter wave radars. However, the underlying physics of this complex nonlinear system is yet to be fully elucidated. Here, we report a new phenomenon in the form of nonlinearly driven oscillations. A zero-drive stable gyro-TWT is shown to be susceptible to a considerably reduced dynamic range at the band edge, followed by a sudden transition into driven oscillations and then a hysteresis effect. An analysis of this unexpected behavior and its physical interpretation are presented.
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.
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. PMID:24580292
On the nonlinear dissipative dynamics of weakly overdamped oscillators
Brezhnev, Yu. V.; Sazonov, S. V.
2014-11-15
We consider the motion of weakly overdamped linear oscillators. Weak overdamping of an oscillator is defined as a slight excess of the damping decrement over its natural frequency. Exact solutions are obtained for a certain relation between the decrement and the natural frequency and qualitatively different regimes of motion are analyzed. The threshold conditions corresponding to changes of regimes are established; one-component models with an arbitrary degree of nonlinearity are analyzed, and quadratic and cubic nonlinearities are considered in detail. If the nonlinearity in a multicomponent model is determined by a homogeneous function, transformations of the Kummer-Liouville type can be reduced to an autonomous system of second-order differential equations in the case when the relation between the decrement and the natural frequency has been established. Some integrable multicomponent models with quadratic and cubic nonlinearities are analyzed.
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.
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
Relativistic effects on nonlinear lower hybrid oscillations in cold plasma
Maity, Chandan; Chakrabarti, Nikhil
2011-04-15
Nonlinear lower hybrid mode in a quasineutral magnetized plasma is analyzed in one space dimension using Lagrangian coordinates. In a cold fluid, we treat electron fluid relativistically, whereas ion fluid nonrelativistically. The homotopy perturbation method is employed to obtain the nonlinear solution which also finds the frequency-amplitude relationship for the lower hybrid mode. The solution indicates that the amplitude of oscillation increases due to the weak relativistic effects. The appearance of density spikes is not ruled out in a magnetized plasma.
Multisynchronization of chaotic oscillators via nonlinear observer approach.
Aguilar-López, Ricardo; Martínez-Guerra, Rafael; Mata-Machuca, Juan L
2014-01-01
The goal of this work is to synchronize a class of chaotic oscillators in a master-slave scheme, under different initial conditions, considering several slaves systems. The Chen oscillator is employed as a benchmark model and a nonlinear observer is proposed to reach synchronicity between the master and the slaves' oscillators. The proposed observer contains a proportional and integral form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Numerical experiments were carried out to show the operation of the considered methodology. PMID:24578671
Multisynchronization of Chaotic Oscillators via Nonlinear Observer Approach
Aguilar-López, Ricardo; Martínez-Guerra, Rafael; Mata-Machuca, Juan L.
2014-01-01
The goal of this work is to synchronize a class of chaotic oscillators in a master-slave scheme, under different initial conditions, considering several slaves systems. The Chen oscillator is employed as a benchmark model and a nonlinear observer is proposed to reach synchronicity between the master and the slaves' oscillators. The proposed observer contains a proportional and integral form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Numerical experiments were carried out to show the operation of the considered methodology. PMID:24578671
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.
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…
Phase and amplitude dynamics of nonlinearly coupled oscillators
NASA Astrophysics Data System (ADS)
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.
Nonlinear Oscillations and Bifurcations in Silicon Photonic Microresonators
NASA Astrophysics Data System (ADS)
Abrams, Daniel M.; Slawik, Alex; Srinivasan, Kartik
2014-03-01
Silicon microdisks are optical resonators that can exhibit surprising nonlinear behavior. We present a new analysis of the dynamics of these resonators elucidating the mathematical origin of spontaneous oscillations and deriving predictions for observed phenomena such as a frequency comb spectrum with MHz-scale repetition rate. We test predictions through laboratory experiment and numerical simulation.
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.
A novel smooth and discontinuous oscillator with strong irrational nonlinearities
NASA Astrophysics Data System (ADS)
Han, YanWei; Cao, QingJie; Chen, YuShu; Wiercigroch, Marian
2012-10-01
In this paper, we propose a novel nonlinear oscillator with strong irrational nonlinearities having smooth and discontinuous characteristics depending on the values of a smoothness parameter. The oscillator is similar to the SD oscillator, originally introduced in Phys Rev E 69(2006). The equilibrium stability and the complex bifurcations of the unperturbed system are investigated. The bifurcation sets of the equilibria in parameter space are constructed to demonstrate transitions in the multiple well dynamics for both smooth and discontinuous regimes. The Melnikov method is employed to obtain the analytical criteria of chaotic thresholds for the singular closed orbits of homoclinic, homo-heteroclinic, cuspidal heteroclinic and tangent homoclinic orbits of the perturbed system.
An exactly solvable three-dimensional nonlinear quantum oscillator
Schulze-Halberg, A.; Morris, J. R.
2013-11-15
Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dependent mass. This system is the generalization of the corresponding one-dimensional system, which has been the focus of recent attention. In contrast to other approaches, we are able to obtain solutions in terms of special functions, without a reliance upon a Rodrigues-type of formula. The wave functions of the quantum oscillator have the familiar spherical harmonic solutions for the angular part. For the s-states of the system, the radial equation accepts solutions that have been recently found for the one-dimensional nonlinear quantum oscillator, given in terms of associated Legendre functions, along with a constant shift in the energy eigenvalues. Radial solutions are obtained for all angular momentum states, along with the complete energy spectrum of the bound states.
NASA Astrophysics Data System (ADS)
Zega, V.; Nitzan, S.; Li, M.; Ahn, C. H.; Ng, E.; Hong, V.; Yang, Y.; Kenny, T.; Corigliano, A.; Horsley, D. A.
2015-06-01
This work investigates the closed-loop operation of microelectromechanical oscillators in the presence of both cubic (Duffing) nonlinearities and parametric amplification. We present a theoretical model for this system that enables us to predict oscillation amplitude and instability and experimentally verify it using a silicon disk resonator with a quality factor (Q) of 85 000 and a natural frequency of 251 kHz. We determine that, contrary to previous understanding gained from analyzing the open-loop system, the presence of cubic nonlinearities does not limit the maximum stable oscillation amplitude if the resonator is operated in a closed loop. In addition, the stability and amplitude behavior predicted by our theoretical model are independent of the presence or severity of cubic nonlinearities, or on drive amplitude.
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.
Suppressing nonlinear resonances in an impact oscillator using SMAs
NASA Astrophysics Data System (ADS)
Sitnikova, Elena; Pavlovskaia, Ekaterina; Ing, James; Wiercigroch, Marian
2012-07-01
In this paper, we study the resonant responses of an impact oscillator with a one sided SMA motion constraint operating in the pseudoelastic regime. The effectiveness of the SMA restraint in suppressing nonlinear resonances of the impact oscillator is assessed by comparing the dynamic responses of the impact oscillator with SMA and elastic restraints. It is shown that the hysteretic behaviour of the SMA restraint provides an overall vibration reduction in the resonant frequency ranges. Due to the softening behaviour of the SMA element, the resonant frequencies for the SMA oscillator were found to be lower than for the oscillator with an elastic restraint. At each resonance, a single periodic response for the oscillator with the elastic restraint corresponds to two co-existing periodic responses of the SMA oscillator. While at the first resonance peak the emergence of one of the co-existing responses is associated with the hardening effect of the SMA restraint when the pseudoelastic force varies over a complete transformation cycle, at higher frequency resonances incomplete phase transformations in the SMA were detected for both responses. The experimental study undertaken verified the response-modification effects predicted by the numerical analysis conducted under the isothermal approximation. The experimental results showed a good quantitative correspondence with the mathematical modelling.
Nonlinear saturation of thermoacoustic oscillations in annular combustion chambers
NASA Astrophysics Data System (ADS)
Ghirardo, Giulio; Juniper, Matthew
2014-11-01
Continuous combustion systems such as aeroplane engines can experience self-sustained pressure oscillations, called thermoacoustic oscillations. Quite often the combustion chamber is rotationally symmetric and confined between inner and outer walls, with a fixed number of burners equispaced along the annulus, at the chamber inlet. We focus on thermoacoustic oscillations in the azimuthal direction, and discuss the nonlinear saturation of the system towards 2 types of solutions: standing waves (with velocity and pressure nodes fixed in time and in space) and spinning waves (rotating waves, in clockwise or anti-clockwise direction). We neglect the effect of the transverse velocity oscillating in the azimuthal direction in the combustion chamber, and focus the model on the nonlinear effect that the longitudinal velocity, just upstream of each burner, has on the fluctuating heat-release response in the chamber. We present a low-order analytical framework to discuss the stability of the 2 types of solutions. We discuss how the stability and amplitudes of the 2 solutions depend on: 1) the acoustic damping in the system; 2) the number of injectors equispaced in the annulus; 3) the nonlinear response of the flames.
Nonlinear magnetotransport theory and Hall induced resistance oscillations in graphene.
Gutiérrez-Jáuregui, R; Torres, M
2014-06-11
The quantum oscillations of nonlinear magnetoresistance in graphene that occur in response to a dc current bias are investigated. We present a theoretical model for the nonlinear magnetotransport of graphene carriers. The model is based on the exact solution of the effective Dirac equation in crossed electric and magnetic fields, while the effects of randomly distributed impurities are perturbatively added. To compute the nonlinear current effects, we develop a covariant formulation of the migration center theory. The current is calculated for short- and large-range scatterers. The analysis of the differential resistivity in the large magnetic field region, shows that the extrema of the Shubnikov de Hass oscillations invert when the dc currents exceed a threshold value. These results are in good agreement with experimental observations. In the small magnetic field regime, corresponding to large filling factors, the existence of Hall induced resistance oscillations are predicted for ultra clean graphene samples. These oscillations originate from Landau-Zener tunneling between Landau levels, that are tilted by the strong electric Hall field. PMID:24827913
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.
NASA Astrophysics Data System (ADS)
Domany, E.; Gendelman, O. V.
2013-10-01
The paper considers dynamics of Van der Pol-Duffing (VdPD) oscillator with attached nonlinear energy sink. Due to a cubic nonlinearity of the VdPD oscillator, a frequency of oscillations near the unstable origin strongly differs from the frequency of limit cycle oscillations (LCO). The paper demonstrates that, despite the strong nonlinearity of the model system, one can efficiently describe the dynamics with a combination of averaging and multiple scales methods. Global structure of possible response regimes is revealed. It is also demonstrated that the nonlinear energy sink can efficiently control and mitigate the undesired LCOs in this system.
Nonlinear oscillator metamaterial model: numerical and experimental verification.
Poutrina, E; Huang, D; Urzhumov, Y; Smith, D R
2011-04-25
We verify numerically and experimentally the accuracy of an analytical model used to derive the effective nonlinear susceptibilities of a varactor-loaded split ring resonator (VLSRR) magnetic medium. For the numerical validation, a nonlinear oscillator model for the effective magnetization of the metamaterial is applied in conjunction with Maxwell equations and the two sets of equations solved numerically in the time-domain. The computed second harmonic generation (SHG) from a slab of a nonlinear material is then compared with the analytical model. The computed SHG is in excellent agreement with that predicted by the analytical model, both in terms of magnitude and spectral characteristics. Moreover, experimental measurements of the power transmitted through a fabricated VLSRR metamaterial at several power levels are also in agreement with the model, illustrating that the effective medium techniques associated with metamaterials can accurately be transitioned to nonlinear systems. PMID:21643082
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.
Nonlinear electrostatic oscillations in a sharp plasma interface
Haas, F.; Shukla, P. K.
2009-11-10
We revisit a generalized nonlinear Schroedinger equation derived by Stenflo and Gradov, describing electrostatic oscillations in a sharp plasma interface. A Madelung decomposition is used to deduce a Sagdeev potential associated to an autonomous one-dimensional Hamiltonian system, whose solutions are all periodic. A conservation law preventing singularities (under suitable boundary conditions and initial wave profile) is derived. In the particular case where some of the nonlinearities can be neglected, the model is shown to be equivalent to the free-particle Schroedinger equation.
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
An application of integral inequality to second order nonlinear oscillation
NASA Astrophysics Data System (ADS)
Kwong, Man Kam; Wong, James S. W.
A simple result concerning integral inequalities enables us to give an alternative proof of Waltman's theorem: lim t → ∞ ∝ t0a( s) ds = ∞ implies oscillation of the second order nonlinear equation y″( t) + a( t) f( y( t)) = 0; to prove an analog of Wintner's theorem that relates the nonoscillation of the second order nonlinear equations to the existence of solutions of some integral equations, assuming that lim t → ∞ ∝ t0a( s) ds exists; and to give an alternative proof and to extend a result of Butler. An often used condition on the coefficient a( t) is given a more familiar equivalent form and an oscillation criterion involving this condition is established.
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
Enhanced vibration energy harvesting using nonlinear oscillations
NASA Astrophysics Data System (ADS)
Engel, Emily; Wei, Jiaying; Lee, Christopher L.
2015-05-01
Results for the design and testing of an electromagnetic device that converts ambient mechanical vibration into electricity are presented. The design of the device is based on an L-shaped beam structure which is tuned so that the first two natural frequencies have a near two-to-one ratio which is referred to as an internal resonance or autoparametic condition. It is shown that in contrast to single degree-of-freedom, linear-dynamics-based vibration harvesters which convert energy in a very narrow frequency band the prototype can generate power over an extended frequency range when subject to harmonic, base displacement excitation.
Nonlinear optics of Bloch oscillating electrons in semiconductor superlattices
NASA Astrophysics Data System (ADS)
Ghosh, Avik
A quantum particle in a periodic potential can exhibit rich dynamics in a driving field. In particular, Bloch oscillation of electrons in a superlattice leads to optical properties that are nonlinear functions of the input fields. In a DC field, we analyze the coupling of Bloch oscillations in a superlattice with plasmons and longitudinal optical (LO) phonons, modelled by a pendulum linearly coupled to an oscillator. In the absence of LO phonons, the pendulum equation predicts a sharp transition from plasma oscillations to Bloch oscillations at a critical density or electric field. Resonant Bloch-phonon coupling enhances the phonon amplitude and generates sidebands, but produces no gap in the Bloch-phonon spectrum. Our predictions qualitatively agree with recent experimental results. Considerably more dramatic is the response of charges to an oscillatory incident field. In an AC field, the resonance between the external frequency and the Bloch oscillation frequency set by the field amplitude makes the optical response a nonlinear function of the field amplitude. At certain discrete values of the AC amplitude the electron is dynamically localized, whereupon the total current density decreases drastically while the power dissipated is maximized. The THz reflection coefficient vanishes at dynamic localization, and thus oscillates with varying AC field amplitude inside the superlattice. At high doping, the nonlinear transformation between the fields inside and outside the superlattice leads furthermore to multistability in the optical properties as a function of the incident field. Similar oscillations and multistability exist for third harmonic power generated by a set of superlattices fabricated into a quasi-optical array. The generated power can be optimized by bringing the harmonics into Fabry-Perot resonance with the substrate. We compare our predictions with recent experimental results for a quasi-optical array. Combining a mixture of DC and AC fields leads to
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
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 0.416η(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
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.
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
PT-symmetric dimer of coupled nonlinear oscillators
NASA Astrophysics Data System (ADS)
Cuevas, Jesús; Kevrekidis, Panayotis G.; Saxena, Avadh; Khare, Avinash
2013-09-01
We provide a systematic analysis of a prototypical nonlinear oscillator system respecting PT symmetry i.e., one of them has gain and the other an equal and opposite amount of loss. Starting from the linear limit of the system, we extend considerations to the nonlinear case for both soft and hard cubic nonlinearities identifying symmetric and antisymmetric breather solutions, as well as symmetry-breaking variants thereof. We propose a reduction of the system to a Schrödinger-type PT-symmetric dimer, whose detailed earlier understanding can explain many of the phenomena observed herein, including the PT phase transition. Nevertheless, there are also significant parametric as well as phenomenological potential differences between the two models and we discuss where these arise and where they are most pronounced. Finally, we also provide examples of the evolution dynamics of the different states in their regimes of instability.
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.
Hazledine, Saul; Sun, Jongho; Wysham, Derin; Downie, J. Allan; Oldroyd, Giles E. D.; Morris, Richard J.
2009-01-01
Legume plants form beneficial symbiotic interactions with nitrogen fixing bacteria (called rhizobia), with the rhizobia being accommodated in unique structures on the roots of the host plant. The legume/rhizobial symbiosis is responsible for a significant proportion of the global biologically available nitrogen. The initiation of this symbiosis is governed by a characteristic calcium oscillation within the plant root hair cells and this signal is activated by the rhizobia. Recent analyses on calcium time series data have suggested that stochastic effects have a large role to play in defining the nature of the oscillations. The use of multiple nonlinear time series techniques, however, suggests an alternative interpretation, namely deterministic chaos. We provide an extensive, nonlinear time series analysis on the nature of this calcium oscillation response. We build up evidence through a series of techniques that test for determinism, quantify linear and nonlinear components, and measure the local divergence of the system. Chaos is common in nature and it seems plausible that properties of chaotic dynamics might be exploited by biological systems to control processes within the cell. Systems possessing chaotic control mechanisms are more robust in the sense that the enhanced flexibility allows more rapid response to environmental changes with less energetic costs. The desired behaviour could be most efficiently targeted in this manner, supporting some intriguing speculations about nonlinear mechanisms in biological signaling. PMID:19675679
Coupled nonlinear oscillation and stability evolution of viscoelastic dielectric elastomers.
Zhang, Junshi; Chen, Hualing; Li, Bo; McCoul, David; Pei, Qibing
2015-10-14
This article describes the development of an analytical model to study the coupled nonlinear oscillation and stability evolution of viscoelastic dielectric elastomers (DEs) under non-equibiaxial tensile forces by utilizing the method of virtual work. Numerically calculated results are employed to predict this nonlinear dynamic behavior. The resonant frequency (where the amplitude-frequency response curve peaks) and the amplitude-frequency response of the deformation in both in-plane directions are tuned by varying the values of tensile force. The oscillation response in the two in-plane directions exhibits strong nonlinearity and coupling with each other, and is tuned by the changing tensile forces under a specific excitation frequency. By varying the values of tensile forces, the dynamic viscoelastic creep in a certain in-plane direction can be eliminated. Phase diagrams and Poincaré maps under several values of tensile forces are utilized to study the stability evolution of the DE system under non-equibiaxial tensile forces. PMID:26287474
Nonlinear Oscillations, Noise and Chaos in Neural Delayed Feedback.
NASA Astrophysics Data System (ADS)
Longtin, Andre
Bifurcations and complex oscillations in the human pupil light reflex (PLR) are studied. Autonomous pupil area oscillations are produced by substituting electronically controllable nonlinear feedback for the normal negative feedback of this reflex. A physiologically sound theoretical framework in which to study pupillary oscillations is developed. The model, framed as a delay-differential equation (DDE), agrees quantitatively with the simpler periodic behaviors and qualitatively with the complex behaviors. Much of the aperiodicity in the data can be ascribed to noise and transients rather than to chaos. The critical behavior of the PLR at oscillation onset is different with piecewise constant rather than smooth negative feedback. In the former, relative fluctuations in period are larger than those in amplitude, and vice versa in the latter. Properties of the time solutions and densities of a stochastic DDE are used to explain this experimental result. The Hopf bifurcation in this system is postponed by both additive and multiplicative colored noise. Theoretical insight into the behavior of stationary densities of DDE's and the origin of the postponement is given, and implications for analyzing bifurcations in neural delayed feedback systems are discussed.
Observation of chaotic dynamics of coupled nonlinear oscillators
NASA Astrophysics Data System (ADS)
van Buskirk, R.; Jeffries, C.
1985-05-01
Experimental data are employed as bases for theoretically modelling the behavior of a finite number of driven nonlinear coupled oscillators. Attention is focused on Si p-n junction resonators exposed to an external inductance. A junction oscillator displays period doubling, Hopf figuracions to quasi-periodicity, entrainment horns and breakup of the invariant torus. Calculated and measured data are compared, with favorable results, by means of Poincare' sections, bifurcation diagrams and parameter phase space diagrams for the drive voltage and frequency. Fractal dimensions 2.03 and 2.33 are expressed in Poincare' sections to illustrate the behavior of single and dual coupled resonators which experience a breakup of the strange attractor.
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.
A nonlinear dynamic model of relaxation oscillations in tokamaks
NASA Astrophysics Data System (ADS)
Thyagaraja, A.; Haas, F. A.; Harvey, D. J.
1999-06-01
Tokamaks exhibit several types of relaxation oscillations such as sawteeth, fishbones and Edge Localized Modes (ELMs) under appropriate conditions. Several authors have introduced model nonlinear dynamic systems with a small number of degrees of freedom which can illustrate the generic characteristics of such oscillations. In these models, one focuses on physically "relevant" degrees of freedom, without attempting to simulate all the myriad details of the fundamentally nonlinear tokamak phenomena. Such degrees of freedom often involve the plasma macroscopic quantities such as pressure or density and also some measure of the plasma turbulence, which is thought to control transport. In addition, "coherent" modes may be involved in the dynamics of relaxation, as well as radial electric fields, sheared flows, etc. In the present work, an extension of an earlier sawtooth model (which involved only two degrees of freedom) due to the authors is presented. The dynamical consequences of a pressure-driven "coherent" mode, which interacts with the turbulence in a specific manner, are investigated. Varying only the two parameters related to the coherent mode, the bifurcation properties of the system have been studied. These turn out to be remarkably rich and varied and qualitatively similar to the behavior found experimentally in actual tokamaks. The dynamic model presented involves only continuous nonlinearities and is the simplest known to the authors that can yield features such as sawteeth, "compound sawteeth" with partial crashes, "monster" sawteeth, metastability, intermittency, chaos, periodic and "grassy" ELMing in appropriate regions of parameter space. The results suggest that linear stability analysis of systems, while useful in elucidating instability drives, can be misleading in understanding the dynamics of nonlinear systems over time scales much longer than linear growth times and states far from stable equilibria.
Frequency Response and Gap Tuning for Nonlinear Electrical Oscillator Networks
Bhat, Harish S.; Vaz, Garnet J.
2013-01-01
We study nonlinear electrical oscillator networks, the smallest example of which consists of a voltage-dependent capacitor, an inductor, and a resistor driven by a pure tone source. By allowing the network topology to be that of any connected graph, such circuits generalize spatially discrete nonlinear transmission lines/lattices that have proven useful in high-frequency analog devices. For such networks, we develop two algorithms to compute the steady-state response when a subset of nodes are driven at the same fixed frequency. The algorithms we devise are orders of magnitude more accurate and efficient than stepping towards the steady-state using a standard numerical integrator. We seek to enhance a given network's nonlinear behavior by altering the eigenvalues of the graph Laplacian, i.e., the resonances of the linearized system. We develop a Newton-type method that solves for the network inductances such that the graph Laplacian achieves a desired set of eigenvalues; this method enables one to move the eigenvalues while keeping the network topology fixed. Running numerical experiments using three different random graph models, we show that shrinking the gap between the graph Laplacian's first two eigenvalues dramatically improves a network's ability to (i) transfer energy to higher harmonics, and (ii) generate large-amplitude signals. Our results shed light on the relationship between a network's structure, encoded by the graph Laplacian, and its function, defined in this case by the presence of strongly nonlinear effects in the frequency response. PMID:24223751
Chimera states in mechanical oscillator networks
Martens, Erik Andreas; Thutupalli, Shashi; Fourrière, Antoine; Hallatschek, Oskar
2013-01-01
The synchronization of coupled oscillators is a fascinating manifestation of self-organization that nature uses to orchestrate essential processes of life, such as the beating of the heart. Although it was long thought that synchrony and disorder were mutually exclusive steady states for a network of identical oscillators, numerous theoretical studies in recent years have revealed the intriguing possibility of “chimera states,” in which the symmetry of the oscillator population is broken into a synchronous part and an asynchronous part. However, a striking lack of empirical evidence raises the question of whether chimeras are indeed characteristic of natural systems. This calls for a palpable realization of chimera states without any fine-tuning, from which physical mechanisms underlying their emergence can be uncovered. Here, we devise a simple experiment with mechanical oscillators coupled in a hierarchical network to show that chimeras emerge naturally from a competition between two antagonistic synchronization patterns. We identify a wide spectrum of complex states, encompassing and extending the set of previously described chimeras. Our mathematical model shows that the self-organization observed in our experiments is controlled by elementary dynamical equations from mechanics that are ubiquitous in many natural and technological systems. The symmetry-breaking mechanism revealed by our experiments may thus be prevalent in systems exhibiting collective behavior, such as power grids, optomechanical crystals, or cells communicating via quorum sensing in microbial populations. PMID:23759743
Nonlinear oscillation of pathological vocal folds during vocalization
NASA Astrophysics Data System (ADS)
Wan, Ni; Peng, DanDan; Sun, Min; Zhang, Dong
2013-07-01
The extended two-mass model is adopted to analyze the nonlinear oscillation of pathological vocal folds during vocalization. Redundant tissue or area in laryngeal patients is modeled as a massless rigid connected to the upper mass of the vocal folds, and a parameter Q is introduced to represent the change of glottal configurations and tension imbalance between the left and right sides of vocal folds. Numerical simulations demonstrate that the pathological vocal-fold decreases the threshold of Q to generate nonlinear vocal oscillation, indicating the improvement of the sensitivity of vocal folds to asymmetries and enhancing the coupling between two sides. Furthermore, the pathological vocal-fold can lower the fundamental frequency and eliminate high-order harmonics, For example, the fundamental frequency decreases from 119.94 Hz to 84.95 Hz when Q=0.58 and the sub-glottal pressure 1450 Pa. However, there are no prominent effects on the amplitudes of sub-harmonic and low-order harmonics.
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.
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 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.
Modified semi-classical methods for nonlinear quantum oscillations problems
Moncrief, Vincent; Marini, Antonella; Maitra, Rachel
2012-10-15
We develop a modified semi-classical approach to the approximate solution of Schroedinger's equation for certain nonlinear quantum oscillations problems. In our approach, at lowest order, the Hamilton-Jacobi equation of the conventional semi-classical formalism is replaced by an inverted-potential-vanishing-energy variant thereof. With suitable smoothness, convexity and coercivity properties imposed on its potential energy function, we prove, using methods drawn from the calculus of variations together with the (Banach space) implicit function theorem, the existence of a global, smooth 'fundamental solution' to this equation. Higher order quantum corrections thereto, for both ground and excited states, can then be computed through the integration of associated systems of linear transport equations, derived from Schroedinger's equation, and formal expansions for the corresponding energy eigenvalues obtained therefrom by imposing the natural demand for smoothness on the (successively computed) quantum corrections to the eigenfunctions. For the special case of linear oscillators our expansions naturally truncate, reproducing the well-known exact solutions for the energy eigenfunctions and eigenvalues. As an explicit application of our methods to computable nonlinear problems, we calculate a number of terms in the corresponding expansions for the one-dimensional anharmonic oscillators of quartic, sectic, octic, and dectic types and compare the results obtained with those of conventional Rayleigh/Schroedinger perturbation theory. To the orders considered (and, conjecturally, to all orders) our eigenvalue expansions agree with those of Rayleigh/Schroedinger theory whereas our wave functions more accurately capture the more-rapid-than-gaussian decay known to hold for the exact solutions to these problems. For the quartic oscillator in particular our results strongly suggest that both the ground state energy eigenvalue expansion and its associated wave function expansion
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.
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
Spectral properties of a confined nonlinear quantum oscillator in one and three dimensions
Schulze-Halberg, Axel; Gordon, Christopher R.
2013-04-15
We analyze the spectral behaviour of a nonlinear quantum oscillator model under confinement. The underlying potential is given by a harmonic oscillator interaction plus a nonlinear term that can be weakened or strengthened through a parameter. Numerical eigenvalues of the model in one and three dimensions are presented. The asymptotic behaviour of the eigenvalues for confinement relaxation and for vanishing nonlinear term in the potential is investigated. Our findings are compared with existing results.
NASA Astrophysics Data System (ADS)
Simanovskii, I. B.; Viviani, A.; Dubois, F.; -C., Legros J.
2011-02-01
The nonlinear development of oscillatory instability under the joint action of buoyant and thermocapillary effects in a multilayer system, is investigated. The nonlinear convective regimes are studied by the finite difference method. Two different types of boundary conditions - periodic boundary conditions and rigid heat-insulated lateral walls, are considered. It is found that in the case of periodic boundary conditions, the competition of both mechanisms of instability may lead to the development of specific types of flow: buoyant-thermocapillary traveling wave and pulsating traveling wave. In the case of rigid heat-insulated boundaries, various types of nonlinear flows - symmetric and asymmetric oscillations, have been found.
Solar atmospheric dynamics. II - Nonlinear models of the photospheric and chromospheric oscillations
NASA Technical Reports Server (NTRS)
Leibacher, J.; Gouttebroze, P.; Stein, R. F.
1982-01-01
The one-dimensional, nonlinear dynamics of the solar atmosphere is investigated, and models of the observed photospheric (300 s) and chromospheric (200 s) oscillations are described. These are resonances of acoustic wave cavities formed by the variation of the temperature and ionization between the subphotospheric, hydrogen convection zone and the chromosphere-corona transition region. The dependence of the oscillations upon the excitation and boundary conditions leads to the conclusion that for the observed amplitudes, the modes are independently excited and, as trapped modes, transport little if any mechanical flux. In the upper photosphere and lower chromosphere, where the two modes have comparable energy density, interference between them leads to apparent vertical phase delays which might be interpreted as evidence of an energy flux.
The probabilistic solution of stochastic oscillators with even nonlinearity under poisson excitation
NASA Astrophysics Data System (ADS)
Guo, Siu-Siu; Er, Guo-Kang
2012-06-01
The probabilistic solutions of nonlinear stochastic oscillators with even nonlinearity driven by Poisson white noise are investigated in this paper. The stationary probability density function (PDF) of the oscillator responses governed by the reduced Fokker-Planck-Kolmogorov equation is obtained with exponentialpolynomial closure (EPC) method. Different types of nonlinear oscillators are considered. Monte Carlo simulation is conducted to examine the effectiveness and accuracy of the EPC method in this case. It is found that the PDF solutions obtained with EPC agree well with those obtained with Monte Carlo simulation, especially in the tail regions of the PDFs of oscillator responses. Numerical analysis shows that the mean of displacement is nonzero and the PDF of displacement is nonsymmetric about its mean when there is even nonlinearity in displacement in the oscillator. Numerical analysis further shows that the mean of velocity always equals zero and the PDF of velocity is symmetrically distributed about its mean.
Methods of stability analysis in nonlinear mechanics
Warnock, R.L.; Ruth, R.D.; Gabella, W.; Ecklund, K.
1989-01-01
We review our recent work on methods to study stability in nonlinear mechanics, especially for the problems of particle accelerators, and compare our ideals to those of other authors. We emphasize methods that (1) show promise as practical design tools, (2) are effective when the nonlinearity is large, and (3) have a strong theoretical basis. 24 refs., 2 figs., 2 tabs.
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.}
Nonequilibrium / nonlinear chemical oscillation in the virtual absence of gravity.
Fujieda, S; Mogami, Y; Moriyasu, K; Mori, Y
1999-01-01
The Belousov-Zhabotinsky (BZ) reactions were used as typical examples of a nonlinear system far from equilibrium in connection with biological evolution. The virtual absence of gravity in the present work was given from the free-fall facility of Japan Microgravity Center (JAMIC) in Hokkaido. The reaction solution of BZ reaction was composed of bromate in sulfuric acid, 1,4-cyclohexanedione and ferroin to visualize the time development of patterns of chemical oscillations in the reaction-diffusion system. It is a bubble-free constitution in the aging of the reaction. Therefore, the setup constructed to collect image data via CCD cameras was simplified. The operation sequences of necessary devices were comprised of simple solid state relays which were started by a command from the operation room of JAMIC. The propagation profile of chemical patterns under microgravity of 10(-5) g was collected as image data for 9.8 s, and processed by a software of STM-STS2. In the aqueous solutions, propagation velocity of chemical patterns under microgravity was decreased to 80.9 % of that under normal gravity, owing to suppression of convection. On the other hand, in gel matrix, gravity did not influence the propagation velocity. PMID:11712549
Nonequilibrium / nonlinear chemical oscillation in the virtual absence of gravity
NASA Astrophysics Data System (ADS)
Fujieda, S.; Mogami, Y.; Moriyasu, K.; Mori, Y.
1999-01-01
The Belousov-Zhabotinsky (BZ) reactions were used as typical examples of a nonlinear system far from equilibrium in connection with biological evolution. The virtual absence of gravity in the present work was given from the free-fall facility of Japan Microgravity Center (JAMIC) in Hokkaido. The reaction solution of BZ reaction was composed of bromate in sulfuric acid, 1,4-cyclohexanedione and ferroin to visualize the time development of patterns of chemical oscillations in the reaction-diffusion system. It is a bubble-free constitution in the aging of the reaction. Therefore, the setup constructed to collect image data via CCD cameras was simplified. The operation sequences of necessary devices were comprised of simple solid state relays which were started by a command from the operation room of JAMIC. The propagation profile of chemical patterns under microgravity of 10-5 g was collected as image data for 9.8 s, and processed by a software of STM-STS2. In the aqueous solutions, propagation velocity of chemical patterns under microgravity was decreased to 80.9 % of that under normal gravity, owing to suppression of convection. On the other hand, in gel matrix, gravity did not influence the propagation velocity.
Spontaneous mechanical oscillations: implications for developing organisms.
Kruse, Karsten; Riveline, Daniel
2011-01-01
Major transformations of cells during embryonic development are traditionally associated with the activation or inhibition of genes and with protein modifications. The contributions of mechanical properties intrinsic to the matter an organism is made of, however, are often overlooked. The emerging field "physics of living matter" is addressing active material properties of the cytoskeleton and tissues like the spontaneous generation of stress, which may lead to shape changes and tissue flows, and their implications for embryonic development. Here, we discuss spontaneous mechanical oscillations to present some basic elements for understanding this physics, and we illustrate its application to developing embryos. We highlight the role of state diagrams to quantitatively probe the significance of the corresponding physical concepts for understanding development. PMID:21501749
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Lamarque, C.-H.; Ture Savadkoohi, A.; Naudan, M.
2013-09-01
The concept of energy exchange between coupled oscillators can be endowed for wide variety of applications such as control and energy harvesting. It has been proved that by coupling an essential nonlinear oscillator (cubic nonlinearity) to a main system (mostly linear), the latter system can be controlled in a one way and almost irreversible manner. The phenomenon is called energy pumping and the coupled nonlinear system is named as nonlinear energy sink (NES). The process of energy transfer from the main system to the nonlinear smooth or non-smooth attachment at different scales of time can present several scenarios: It can be attracted to periodic behaviors which present low or high energy levels for the main system and/or to quasi-periodic responses of two oscillators by persistent bifurcations between their stable zones. In this paper we analyze multi-scale dynamics of two attached oscillators: a Bouc-Wen type in general (in particular: a Dahl type and a modified hysteresis system) and a NES (nonsmooth and cubic). The system behavior at fast and first slow times scales by detecting its invariant manifold, its fixed points and singularities will be analyzed. Analytical developments will be accompanied by some numerical examples for systems that present quasi-periodic responses. The endowed Bouc-Wen models correspond to the hysteretic behavior of materials or structures. This paper is clearly connected with the dynamics of systems with hysteresis and nonlinear dynamics based energy harvesting.
An experimental study on synchronization of nonlinear oscillators with Huygens' coupling
NASA Astrophysics Data System (ADS)
Peña-Ramírez, J.; Fey, R. H. B.; Nijmeijer, H.
In this experimental study, phase synchronization is studied in pairs of nonlinear oscillators coupled through a movable support. In particular, the dynamics of two discontinuous mass-spring-damper oscillators and the dynamics of the classical Huygens' pendulum clocks are considered. In both systems the individual oscillators are self-sustained. It is shown that in both cases, the oscillators exhibit in-phase and anti-phase synchronization. All experiments are executed on a new experimental setup consisting of two controllable mass-spring-damper oscillators coupled through an elastically supported rigid bar. The results suggest, that the synchronized motion observed by Christiaan Huygens around 1650 in a pair of pendulum clocks mounted on a flexible support, in many cases can also be observed when the pendulum clocks are replaced by other self-sustained nonlinear oscillators.
Hot Fluids and Nonlinear Quantum Mechanics
NASA Astrophysics Data System (ADS)
Mahajan, Swadesh M.; Asenjo, Felipe A.
2015-05-01
A hot relativistic fluid is viewed as a collection of quantum objects that represent interacting elementary particles. We present a conceptual framework for deriving nonlinear equations of motion obeyed by these hypothesized objects. A uniform phenomenological prescription, to affect the quantum transition from a corresponding classical system, is invoked to derive the nonlinear Schrödinger, Klein-Gordon, and Pauli-Schrödinger and Feynman-GellMaan equations. It is expected that the emergent hypothetical nonlinear quantum mechanics would advance, in a fundamental way, both the conceptual understanding and computational abilities, particularly, in the field of extremely high energy-density physics.
Nonlinear optomechanical measurement of mechanical motion.
Brawley, G A; Vanner, M R; Larsen, P E; Schmid, S; Boisen, A; Bowen, W P
2016-01-01
Precision measurement of nonlinear observables is an important goal in all facets of quantum optics. This allows measurement-based non-classical state preparation, which has been applied to great success in various physical systems, and provides a route for quantum information processing with otherwise linear interactions. In cavity optomechanics much progress has been made using linear interactions and measurement, but observation of nonlinear mechanical degrees-of-freedom remains outstanding. Here we report the observation of displacement-squared thermal motion of a micro-mechanical resonator by exploiting the intrinsic nonlinearity of the radiation-pressure interaction. Using this measurement we generate bimodal mechanical states of motion with separations and feature sizes well below 100 pm. Future improvements to this approach will allow the preparation of quantum superposition states, which can be used to experimentally explore collapse models of the wavefunction and the potential for mechanical-resonator-based quantum information and metrology applications. PMID:26996234
Nonlinear 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
Vibrational spectroscopy of a harmonic oscillator system nonlinearly coupled to a heat bath
NASA Astrophysics Data System (ADS)
Kato, Tsuyoshi; Tanimura, Yoshitaka
2002-10-01
Vibrational relaxation of a harmonic oscillator nonlinearly coupled to a heat bath is investigated by the Gaussian-Markovian quantum Fokker-Planck equation approach. The system-bath interaction is assumed to be linear in the bath coordinate, but linear plus square in the system coordinate modeling the elastic and inelastic relaxation mechanisms. Interplay of the two relaxation processes induced by the linear-linear and square-linear interactions in Raman or infrared spectra is discussed for various system-bath couplings, temperatures, and correlation times for the bath fluctuations. The one-quantum coherence state created through the interaction with the pump laser pulse relaxes through different pathways in accordance with the mechanisms of the system-bath interactions. Relations between the present theory, Redfield theory, and stochastic theory are also discussed.
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).
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.
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
Donko, Z.; Schulze, J.; Czarnetzki, U.; Luggenhoelscher, D.
2009-03-30
At low pressures, nonlinear self-excited plasma series resonance (PSR) oscillations are known to drastically enhance electron heating in geometrically asymmetric capacitively coupled radio frequency discharges by nonlinear electron resonance heating (NERH). Here we demonstrate via particle-in-cell simulations that high-frequency PSR oscillations can also be excited in geometrically symmetric discharges if the driving voltage waveform makes the discharge electrically asymmetric. This can be achieved by a dual-frequency (f+2f) excitation, when PSR oscillations and NERH are turned on and off depending on the electrical discharge asymmetry, controlled by the phase difference of the driving frequencies.
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.
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.
Limit cycle oscillation of missile control fin with structural non-linearity
NASA Astrophysics Data System (ADS)
Bae, J. S.; Lee, I.
2004-01-01
Non-linear aeroelastic characteristics of a deployable missile control fin with structural non-linearity are investigated. A deployable missile control fin is modelled as a two-dimensional typical section model. Doublet-point method is used for the calculation of supersonic unsteady aerodynamic forces, and aerodynamic forces are approximated by using the minimum-state approximation. For non-linear flutter analysis structural non-linearity is represented by an asymmetric bilinear spring and is linearized by using the describing function method. The linear and non-linear flutter analyses indicate that the flutter characteristics are significantly dependent on the frequency ratio. From the non-linear flutter analysis, various types of limit cycle oscillations are observed in a wide range of air speeds below or above the linear divergent flutter boundary. The non-linear flutter characteristics and the non-linear aeroelastic responses are investigated.
Nonlinear NDE of Concrete Mechanical Properties
NASA Astrophysics Data System (ADS)
Shkolnik, Iosif E.
2006-05-01
Obtained theoretical relationship shows that the strength of concrete increases if the nonlinear parameter decreases. Experimental data proved that modulus of elasticity, ultrasound pulse velocity and nonlinear parameter are independent characteristics of concrete. Two nondestructive patent methods based on the measurement of resonant frequency shift and phase shift are described. These nonlinear nondestructive methods can be used when conventional acoustic methods are not applicable for evaluating strength of concrete. The relationship between static and dynamic modulus is obtained from the thermofluctuation theory and nonlinear equation of state of concrete. Corresponding relationship shows that the ratio of the static to the dynamic modulus of elasticity depends on the strength of concrete, its temperature, ratio and rate of loading, and that dynamic modulus is greater than static modulus of elasticity. Comparative study illustrates substantial agreement between obtained relationships and existing experimental results as well as general equations given in standards. Presented data illustrate the potential of the nonlinear approach, and indicate a new direction for nonlinear nondestructive methods of evaluating mechanical properties of concrete.
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 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.
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).
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. PMID:26901575
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 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.
Low-nonlinearity spin-torque oscillations driven by ferromagnetic nanocontacts
NASA Astrophysics Data System (ADS)
Al-Mahdawi, Muftah; Toda, Yusuke; Shiokawa, Yohei; Sahashi, Masashi
2016-01-01
Spin-torque oscillators are strong candidates as nanoscale microwave generators and detectors. However, because of large amplitude-phase coupling (nonlinearity), phase noise is enhanced over other linear autooscillators. One way to reduce nonlinearity is to use ferromagnetic layers as a resonator and excite them at localized spots, making a resonator-excitor pair. We investigated the excitation of oscillations in dipole-coupled ferromagnetic layers, driven by localized current at ferromagnetic nanocontacts. Oscillations possessed properties of optical-mode spin waves and at low field (≈200 Oe) had high frequency (15 GHz), a moderate precession amplitude (2∘-3∘), and a narrow spectral linewidth (<3 MHz) due to localized excitation at nanocontacts. Micromagnetic simulation showed emission of the resonator's characteristic optical-mode spin waves from disturbances generated by domain-wall oscillations at nanocontacts.
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.
Mechanical analogy of the nonlinear dynamics of a driven unstable mode near marginal stability
NASA Astrophysics Data System (ADS)
Zaleśny, J.; Marczyński, S.; Lisak, M.; Anderson, D.; Gałkowski, A.; Berczyński, P.; Berczyński, S.; Rogowski, R.
2009-02-01
The universal integrodifferential model equation derived by Berk et al. [Phys. Rev. Lett. 76, 1256 (1996)] for studying the nonlinear evolution of unstable modes driven by kinetic wave particle resonances near the instability threshold is reduced to a differential equation and next as a further simplification to a nonlinear oscillator equation. This mechanical analogy properly reproduces most of the essential physics of the system and allows an understanding of the qualitative features of the theory of Berk et al.
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.
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.
Aperiodic behaviour of a non-linear oscillator.
NASA Technical Reports Server (NTRS)
Baker, N. H.; Moore, D. W.; Spiegel, E. A.
1971-01-01
The aperiodic behavior of the solution of the equation of motion derived previously (1966) when considering a model thermomechanical oscillator is examined. Periodic solutions of this equation are studied numerically and analytically. Conditions for the instability of the solutions are determined. This instability seems to be the cause of the observed aperiodicity.
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.
Remote synchronization of amplitudes across an experimental ring of non-linear oscillators
NASA Astrophysics Data System (ADS)
Minati, Ludovico
2015-12-01
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.
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.
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.
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.
Self-organized escape of oscillator chains in nonlinear potentials.
Hennig, D; Fugmann, S; Schimansky-Geier, L; Hänggi, P
2007-10-01
We present the noise-free escape of a chain of linearly interacting units from a metastable state over a cubic on-site potential barrier. The underlying dynamics is conservative and purely deterministic. The mutual interplay between nonlinearity and harmonic interactions causes an initially uniform lattice state to become unstable, leading to an energy redistribution with strong localization. As a result, a spontaneously emerging localized mode grows into a critical nucleus. By surpassing this transition state, the nonlinear chain manages a self-organized, deterministic barrier crossing. Most strikingly, these noise-free, collective nonlinear escape events proceed generally by far faster than transitions assisted by thermal noise when the ratio between the average energy supplied per unit in the chain and the potential barrier energy assumes small values. PMID:17994939
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.
Diffeomorphism groups and nonlinear quantum mechanics
NASA Astrophysics Data System (ADS)
Goldin, Gerald A.
2012-02-01
This talk is dedicated to my friend and collaborator, Prof. Dr. Heinz-Dietrich Doebner, on the occasion of his 80th birthday. I shall review some highlights of the approach we have taken in deriving and interpreting an interesting class of nonlinear time-evolution equations for quantum-mechanical wave functions, with few equations; more detail may be found in the references. Then I shall comment on the corresponding hydrodynamical description.
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.
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.
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.…
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.
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.
Frequency multiplying optoelectronic oscillator based on nonlinearly-coupled double loops.
Xu, Wei; Jin, Tao; Chi, Hao
2013-12-30
We propose and demonstrate a frequency multiplying optoelectronic oscillator with nonlinearly-coupled double loops based on two cascaded Mach-Zehnder modulators, to generate high frequency microwave signals using only low-frequency devices. We find the final oscillation modes are only determined by the length of the master oscillation loop. Frequency multiplying signals are generated via nonlinearly-coupled double loops, the output of one loop being used to modulate the other. In the experiments, microwave signals at 10 GHz with -121 dBc/Hz phase noise at 10 kHz offset and 20 GHz with -112.8 dBc/Hz phase noise at 10 kHz offset are generated. Meanwhile, their side-mode suppression ratios are also evaluated and the maximum ratio of 70 dB is obtained. PMID:24514845
Non-linear shape oscillations of rising drops and bubbles: Experiments and simulations
NASA Astrophysics Data System (ADS)
Lalanne, Benjamin; Abi Chebel, Nicolas; Vejražka, Jiří; Tanguy, Sébastien; Masbernat, Olivier; Risso, Frédéric
2015-12-01
This paper focuses on shape-oscillations of a gas bubble or a liquid drop rising in another liquid. The bubble/drop is initially attached to a capillary and is released by a sudden motion of that capillary, resulting in the rise of the bubble/drop along with the oscillations of its shape. Such experimental conditions make difficult the interpretation of the oscillation dynamics with regard to the standard linear theory of oscillation because (i) amplitude of deformation is large enough to induce nonlinearities, (ii) the rising motion may be coupled with the oscillation dynamics, and (iii) clean conditions without residual surfactants may not be achieved. These differences with the theory are addressed by comparing experimental observation with numerical simulation. Simulations are carried out using Level-Set and Ghost-Fluid methods with clean interfaces. The effect of the rising motion is investigated by performing simulations under different gravity conditions. Using a decomposition of the bubble/drop shape into a series of spherical harmonics, experimental and numerical time evolutions of their amplitudes are compared. Due to large oscillation amplitude, non-linear couplings between the modes are evidenced from both experimental and numerical signals; modes of lower frequency influence modes of higher frequency, whereas the reverse is not observed. Nevertheless, the dominant frequency and overall damping rate of the first five modes are in good agreement with the linear theory. Effect of the rising motion on the oscillations is globally negligible, provided the mean shape of the oscillation remains close to a sphere. In the drop case, despite the residual interface contamination evidenced by a reduction in the terminal velocity, the oscillation dynamics is shown to be unaltered compared to that of a clean drop.
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.
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. 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
A quantum quasi-harmonic nonlinear oscillator with an isotonic term
Rañada, Manuel F.
2014-08-01
The properties of a nonlinear oscillator with an additional term k{sub g}/x², characterizing the isotonic oscillator, are studied. The nonlinearity affects to both the kinetic term and the potential and combines two nonlinearities associated to two parameters, κ and k{sub g}, in such a way that for κ = 0 all the characteristics of the standard isotonic system are recovered. The first part is devoted to the classical system and the second part to the quantum system. This is a problem of quantization of a system with position-dependent mass of the form m(x) = 1/(1 − κx²), with a κ-dependent non-polynomial rational potential and with an additional isotonic term. The Schrödinger equation is exactly solved and the (κ, k{sub g})-dependent wave functions and bound state energies are explicitly obtained for both κ < 0 and κ > 0.
Integrable nonlinear parity-time-symmetric optical oscillator
NASA Astrophysics Data System (ADS)
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.
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.
Observation of Nonclassical Radiation Pressure Forces on a Mechanical Oscillator
NASA Astrophysics Data System (ADS)
Clark, Jeremy; Lecocq, Florent; Simmonds, Raymond; Aumentado, Jose; Teufel, John
Squeezed states of light are known to be useful for enhancing mechanical displacement sensing since they can be tailored to reduce the ``photon counting noise'' that limits the measurement's noise floor. On the other hand, recent experiments in cavity optomechanics have reached measurement regimes where an interrogating light field exerts radiation pressure noise on a mechanical oscillator. One outstanding challenge has been to explore the intersection between such experiments. I will present data obtained using a superconducting cavity optomechanical system wherein a mechanical oscillator is driven by nonclassical radiation pressure imparted by squeezed microwave fields. JBC acknowledges the NRC for financial support.
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.
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
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.
Effects of multiple structural nonlinearities on limit cycle oscillation of missile control fin
NASA Astrophysics Data System (ADS)
Seo, Young-Jin; Lee, Seung-Jun; Bae, Jae-Sung; Lee, In
2011-05-01
Aeroelastic analyses are performed for a 2-D typical section model with multiple nonlinearities. The differences between a system with multiple nonlinearities in its pitch and plunge spring and a system with a single nonlinearity in its pitch are thoroughly investigated. The unsteady supersonic aerodynamic forces are calculated by the doublet point method (DPM). The iterative V-g method is used for a multiple-nonlinear aeroelastic analysis in the frequency domain and the freeplay nonlinearity is linearized using a describing function method. In the time domain, the DPM unsteady aerodynamic forces, which are based on a function of the reduced frequency, are approximated by the minimum state approximation method. Consequently, multiple structural nonlinearities in the 2-D typical wing section model are influenced by the pitch to plunge frequency ratio. This result is important in that it demonstrates that the flutter speed is closely connected with the frequency ratio, considering that both pitch and plunge nonlinearities result in a higher flutter speed boundary than a conventional aeroelastic system with only one pitch nonlinearity. Furthermore, the gap size of the freeplay affects the amplitude of the limit cycle oscillation (LCO) to gap size ratio.
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.
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. PMID:27300883
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
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.
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.
Cold atoms coupled with mechanical oscillators
NASA Astrophysics Data System (ADS)
Valencia, Jose; Montoya, Cris; Ranjit, Gambhir; Geraci, Andrew; Eardley, Matt; Kitching, John
2015-05-01
Mechanical resonators can be used to probe and manipulate atomic spins with nanometer spatial resolution and single-spin sensitivity, ultimately enabling new approaches in neutral-atom quantum computation, quantum simulation, or precision sensing. We describe our experiment that manipulates the spin of trapped, cold Rb atoms using magnetic material on a cantilever. Cold atoms can also be used as a coolant for mechanical resonators: we estimate that ground state cooling of an optically trapped nano-sphere is achievable when starting at room temperature, by sympathetic cooling of a cold atomic gas optically coupled to the nanoparticle.
NASA Astrophysics Data System (ADS)
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.
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)
Kurkin, S. A.; Koronovski, A. A.; Hramov, A. E.
2009-08-01
Results are presented from a numerical study of the effect of an external magnetic field on the conditions and mechanisms for the formation of a virtual cathode in a relativistic electron beam. Characteristic features of the nonlinear dynamics of an electron beam with a virtual cathode are considered when the external magnetic field is varied. Various mechanisms are investigated by which the virtual cathode oscillations become chaotic and their spectrum becomes a multifrequency spectrum, thereby complicating the dynamics of the vircator system. A general mechanism for chaotization of the oscillations of a virtual cathode in a vircator system is revealed: the electron structures that form in an electron beam interact by means of a common space charge field to give rise to additional internal feedback. That the oscillations of a virtual cathode change from the chaotic to the periodic regime is due to the suppression of the mechanism for forming secondary electron structures.
NASA Astrophysics Data System (ADS)
Yang, Xiaofan; Zheng, Zhongquan Charlie
2010-04-01
Nonlinear responses to a transversely oscillating cylinder in the wake of a stationary upstream cylinder are studied theoretically by using an immersed-boundary method at Re=100. Response states are investigated in the three flow regimes for a tandem-cylinder system: the "vortex suppression" regime, the critical spacing regime, and the "vortex formation" regime. When the downstream cylinder is forced to oscillate at a fixed frequency and amplitude, the response state of flow around the two cylinders varies with different spacing between the two cylinders, while in the same flow regime, the response state can change with the oscillating frequency and amplitude of the downstream cylinder. Based on velocity phase portraits, each of the nonlinear response states can be categorized into one of the three states in the order of increasing chaotic levels: lock-in, transitional, or quasiperiodic. These states can also be correlated with velocity spectral behaviors. The discussions are conducted using near-wake velocity phase portraits, spectral analyses, and related vorticity fields. A general trend in the bifurcation diagrams of frequency spacing shows the smaller the spacing, frequency, or amplitude, the less chaotic the response state of the system and more likely the downstream and upstream wakes are in the same response state. The system is not locked-in in any case when the spacing between the cylinders is larger than the critical spacing. The near-wake velocity spectral behaviors correspond to the nonlinear response states, with narrow-banded peaks shown at the oscillation frequency and its harmonics in the lock-in cases. High frequency harmonic peaks, caused by interactions between the upstream wake and the downstream oscillating cylinder, are reduced in the near-wake velocity spectra of the upstream cylinder when the spacing increases.
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.
Spontaneous oscillations in a nonlinear delayed-feedback shunting model of the pupil light reflex
NASA Astrophysics Data System (ADS)
Bressloff, P. C.; Wood, C. V.
1998-09-01
We analyze spontaneous oscillations in a second-order delayed-feedback shunting model of the pupil light reflex. This model describes in a simple fashion the nonlinear effects of both the iris and retinal parts of the reflex pathway. In the case of smooth negative feedback, linear stability analysis is used to determine the conditions for a Hopf bifurcation in the pupil area as a function of various neurophysiological parameters of the system such as the time delay and the strength of neural connections. We also investigate oscillation onset in the case of piecewise negative feedback and obtain an analytical expression for the period of oscillations. Finally, complex periodic behavior is shown to arise in the presence of mixed feedback.
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
NASA Astrophysics Data System (ADS)
Zheng, Z.; Yang, Xiaofan
2008-11-01
Nonlinear responses to a transversely oscillating cylinder in the wake of a stationary upstream cylinder are studied theoretically by using an immersed-boundary method. It is found that flow around the two cylinders varies with different spacing between the two cylinders and the oscillation frequency of the downstream cylinder. As known in a stationary tandem-cylinder system, there exist the ``vortex suppression regime'' (VS) and the ``vortex formation regime'' (VF). These two regimes are divided by a critical spacing. When the downstream cylinder is forced to oscillate at a fixed amplitude but different frequency, different flow patterns appear in each of the regime. On the other hand, at the same oscillating frequency but different spacing, the response state (lock-in, transient or non-lock-in) changes. While each state has periodic or quasi-periodic behaviors, nonlinear responses appear. All of the analyses are based on vorticity contours, time histories of the velocities in the near wake regions, spectral analyses, and related phase portraits.
NASA Astrophysics Data System (ADS)
Kim, B.; Williams, D. R.
1998-11-01
The instantaneous pressure distribution was measured around the azimuth of a circular cylinder undergoing forced oscillations. The forcing direction was either in-line or cross-flow to produce symmetric or antisymmetric disturbances, respectively. The fluctuating lift and drag coefficients were computed from the pressure distributions. Combination modes appear in the spectrum of the surface pressure signals when the forcing frequency is different from the von Karman vortex shedding frequency, fo. The spatial symmetry of the sum and difference modes depends on the direction of the cylinder oscillation, and is predictable with a simple set of symmetry relations representative of quadratic nonlinear interaction. As a result, cross-flow oscillations channel energy into the fluctuating drag component through the combination modes, while in-line oscillations affect the fluctuating lift. The second harmonic (3 fo) commonly seen in flow-induced vibrations is the result of the nonlinear interaction between the fundamental and its first harmonic. By the symmetry relations, the 3 fo mode necessarily appears in the fluctuating lift spectrum.
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.
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.
NASA Astrophysics Data System (ADS)
Harko, Tiberiu; Liang, Shi-Dong
2016-06-01
We investigate the connection between the linear harmonic oscillator equation and some classes of second order nonlinear ordinary differential equations of Li\\'enard and generalized Li\\'enard type, which physically describe important oscillator systems. By using a method inspired by quantum mechanics, and which consist on the deformation of the phase space coordinates of the harmonic oscillator, we generalize the equation of motion of the classical linear harmonic oscillator to several classes of strongly non-linear differential equations. The first integrals, and a number of exact solutions of the corresponding equations are explicitly obtained. The devised method can be further generalized to derive explicit general solutions of nonlinear second order differential equations unrelated to the harmonic oscillator. Applications of the obtained results for the study of the travelling wave solutions of the reaction-convection-diffusion equations, and of the large amplitude free vibrations of a uniform cantilever beam are also presented.
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.)
A generator with nonlinear spring oscillator to provide vibrations of multi-frequency
NASA Astrophysics Data System (ADS)
Yang, Bin; Liu, Jingquan; Tang, Gang; Luo, Jiangbo; Yang, Chunsheng; Li, Yigui
2011-11-01
A piezoelectric generator with nonlinear spring oscillator is proposed to provide multiple resonant modes for operation and improve conversion efficiency. In order to scavenge the vibration energy of multiple frequencies from a certain vibration source, two types of nonlinear springs have been employed and tested. The maximum output power of 5, 17.83, and 23.39 μW for the nonlinear spring of 8.3 N/m with 1 g acceleration has been obtained under the resonant frequency of 89, 104, and 130 Hz, respectively. Its total output power of 46.22 μW is obviously larger than the one of 28.35 μW for traditional second-order spring-mass linear system.
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. PMID:17931024
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 Schroedinger 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.
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. 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
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.
NASA Astrophysics Data System (ADS)
Kato, Tsuyoshi; Tanimura, Yoshitaka
2004-01-01
Multidimensional vibrational response functions of a harmonic oscillator are reconsidered by assuming nonlinear system-bath couplings. In addition to a standard linear-linear (LL) system-bath interaction, we consider a square-linear (SL) interaction. The LL interaction causes the vibrational energy relaxation, while the SL interaction is mainly responsible for the vibrational phase relaxation. The dynamics of the relevant system are investigated by the numerical integration of the Gaussian-Markovian Fokker-Planck equation under the condition of strong couplings with a colored noise bath, where the conventional perturbative approach cannot be applied. The response functions for the fifth-order nonresonant Raman and the third-order infrared (or equivalently the second-order infrared and the seventh-order nonresonant Raman) spectra are calculated under the various combinations of the LL and the SL coupling strengths. Calculated two-dimensional response functions demonstrate that those spectroscopic techniques are very sensitive to the mechanism of the system-bath couplings and the correlation time of the bath fluctuation. We discuss the primary optical transition pathways involved to elucidate the corresponding spectroscopic features and to relate them to the microscopic sources of the vibrational nonlinearity induced by the system-bath interactions. Optical pathways for the fifth-order Raman spectroscopies from an "anisotropic" medium were newly found in this study, which were not predicted by the weak system-bath coupling theory or the standard Brownian harmonic oscillator model.
Kato, Tsuyoshi; Tanimura, Yoshitaka
2004-01-01
Multidimensional vibrational response functions of a harmonic oscillator are reconsidered by assuming nonlinear system-bath couplings. In addition to a standard linear-linear (LL) system-bath interaction, we consider a square-linear (SL) interaction. The LL interaction causes the vibrational energy relaxation, while the SL interaction is mainly responsible for the vibrational phase relaxation. The dynamics of the relevant system are investigated by the numerical integration of the Gaussian-Markovian Fokker-Planck equation under the condition of strong couplings with a colored noise bath, where the conventional perturbative approach cannot be applied. The response functions for the fifth-order nonresonant Raman and the third-order infrared (or equivalently the second-order infrared and the seventh-order nonresonant Raman) spectra are calculated under the various combinations of the LL and the SL coupling strengths. Calculated two-dimensional response functions demonstrate that those spectroscopic techniques are very sensitive to the mechanism of the system-bath couplings and the correlation time of the bath fluctuation. We discuss the primary optical transition pathways involved to elucidate the corresponding spectroscopic features and to relate them to the microscopic sources of the vibrational nonlinearity induced by the system-bath interactions. Optical pathways for the fifth-order Raman spectroscopies from an "anisotropic" medium were newly found in this study, which were not predicted by the weak system-bath coupling theory or the standard Brownian harmonic oscillator model. PMID:15267286
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.
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
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.
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.
Phase-noise reduction in surface wave oscillators by using nonlinear sustaining amplifiers.
Avramov, Ivan D
2006-04-01
Nonlinear sustaining amplifier operation has been investigated and applied to high-power negative resistance oscillators (NRO), using single-port surface transverse wave (STW) resonators, and single-transistor sustaining amplifiers for feedback-loop STW oscillators (FLSO) stabilized with two-port STW devices. In all cases, self-limiting, silicon (Si)-bipolar sustaining amplifiers that operate in the highly nonlinear AB-, B-, or C-class modes are implemented. Phase-noise reduction is based on the assumption that a sustaining amplifier, operating in one of these modes, uses current limiting and remains cut off over a significant portion of the wave period. Therefore, it does not generate 1/f noise over the cut-off portion of the radio frequency (RF) cycle, and this reduces the close-in oscillator phase noise significantly. The proposed method has been found to provide phase-noise levels in the -111 to -119 dBc/Hz range at 1 KHz carrier offset in 915 MHz C-class power NRO and FLSO generating up to 23 dBm of RF-power at RF versus dc (RF/dc) efficiencies exceeding 40%. C-class amplifier design techniques are used for adequate matching and high RF/dc efficiency. PMID:16615574
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.
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
Deterministic escape dynamics of two-dimensional coupled nonlinear oscillator chains.
Fugmann, S; Hennig, D; Schimansky-Geier, L; Hänggi, P
2008-06-01
We consider the deterministic escape dynamics of a chain of coupled oscillators under microcanonical conditions from a metastable state over a cubic potential barrier. The underlying dynamics is conservative and noise free. We introduce a two-dimensional chain model and assume that neighboring units are coupled by Morse springs. It is found that, starting from a homogeneous lattice state, due to the nonlinearity of the external potential the system self-promotes an instability of its initial preparation and initiates complex lattice dynamics leading to the formation of localized large amplitude breathers, evolving in the direction of barrier crossing, accompanied by global oscillations of the chain transverse to the barrier. A few chain units accumulate locally sufficient energy to cross the barrier. Eventually the metastable state is left and either these particles dissociate or pull the remaining chain over the barrier. We show this escape for both linear rodlike and coil-like configurations of the chain in two dimensions. PMID:18643245
NASA Astrophysics Data System (ADS)
Manevitch, Leonid I.; Kovaleva, Agnessa; Sigalov, Grigori
2016-03-01
In this paper we study the effect of nonstationary energy localization in a nonlinear conservative resonant system of two weakly coupled oscillators. This effect is alternative to the well-known stationary energy localization associated with the existence of localized normal modes and resulting from a local topological transformation of the phase portraits of the system. In this work we show that nonstationary energy localization results from a global transformation of the phase portrait. A key to solving the problem is the introduction of the concept of limiting phase trajectories (LPTs) corresponding to maximum possible energy exchange between the oscillators. We present two scenarios of nonstationary energy localization under the condition of 1:1 resonance. It is demonstrated that the conditions of nonstationary localization determine the conditions of efficient targeted energy transfer in a generating dynamical system. A possible extension to multi-particle systems is briefly discussed.
Effect of asymmetry parameter on the dynamical states of nonlocally coupled nonlinear oscillators
NASA Astrophysics Data System (ADS)
Gopal, R.; Chandrasekar, V. K.; Senthilkumar, D. V.; Venkatesan, A.; Lakshmanan, M.
2015-06-01
We show that coexisting domains of coherent and incoherent oscillations can be induced in an ensemble of any identical nonlinear dynamical systems using nonlocal rotational matrix coupling with an asymmetry parameter. Further, a chimera is shown to emerge in a wide range of the asymmetry parameter in contrast to near π/2 values of it employed in earlier works. We have also corroborated our results using the strength of incoherence in the frequency domain (Sω) and in the amplitude domain (S ), thereby distinguishing the frequency and amplitude chimeras. The robust nature of the asymmetry parameter in inducing chimeras in any generic dynamical system is established using ensembles of identical Rössler oscillators, Lorenz systems, and Hindmarsh-Rose neurons in their chaotic regimes.
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.
Respiratory mechanics studied by forced oscillations during artificial ventilation.
Peslin, R; Felicio da Silva, J; Duvivier, C; Chabot, F
1993-06-01
Potential advantages of the forced oscillation technique over other methods for monitoring total respiratory mechanics during artificial ventilation are that it does not require patient relaxation, and that additional information may be derived from the frequency dependence of the real (Re) and imaginary (Im) parts of respiratory impedance. We wanted to assess feasibility and usefulness of the forced oscillation technique in this setting and therefore used the approach in 17 intubated patients, mechanically ventilated for acute respiratory failure. Sinusoidal pressure oscillations at 5, 10 and 20 Hz were applied at the airway opening, using a specially devised loudspeaker-type generator placed in parallel with the ventilator. Real and imaginary parts were corrected for the flow-dependent impedance of the endotracheal tube; they usually exhibited large variations during the respiratory cycle, and were computed separately for the inspiratory and expiratory phases. In many instances the real part was larger during inspiration, probably due to the larger respiratory flow, and decreased with increasing frequency. The imaginary part of respiratory impedance usually increased with increasing frequency during expiration, as expected for a predominately elastic system, but often varied little, or even decreased, with increasing frequency during inspiration. In most patients, the data were inconsistent with the usual resistance-inertance-compliance model. A much better fit was obtained with a model featuring central airways and a peripheral pathway in parallel with bronchial compliance. The results obtained with the latter model suggest that dynamic airway compression occurred during passive expiration in a number of patients. We conclude that the use of forced oscillation is relatively easy to implement during mechanical ventilation, that it allows the study of respiratory mechanics at various points in the respiratory cycle, and may help in detecting expiratory flow
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)
Randrianandrasana, Michel F.; Wei, Xueyong; Lowe, David
2011-07-01
Future sensor arrays will be composed of interacting nonlinear components with complex behaviours with no known analytic solutions. This paper provides a preliminary insight into the expected behaviour through numerical and analytical analysis. Specifically, the complex behaviour of a periodically driven nonlinear Duffing resonator coupled elastically to a van der Pol oscillator is investigated as a building block in a 2D lattice of such units with local connectivity. An analytic treatment of the 2-device unit is provided through a two-time-scales approach and the stability of the complex dynamic motion is analysed. The pattern formation characteristics of a 2D lattice composed of these units coupled together through nearest neighbour interactions is analysed numerically for parameters appropriate to a physical realisation through MEMS devices. The emergent patterns of global and cluster synchronisation are investigated with respect to system parameters and lattice size.
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.
Forced oscillation assessment of respiratory mechanics in ventilated patients
Navajas, Daniel; Farré, Ramon
2001-01-01
The forced oscillation technique (FOT) is a method for non-invasively assessing respiratory mechanics that is applicable both in paralysed and non-paralysed patients. As the FOT requires a minimal modification of the conventional ventilation setting and does not interfere with the ventilation protocol, the technique is potentially useful to monitor patient mechanics during invasive and noninvasive ventilation. FOT allows the assessment of the respiratory system linearity by measuring resistance and reactance at different lung volumes or end-expiratory pressures. Moreover, FOT allows the physician to track the changes in patient mechanics along the ventilation cycle. Applying FOT at different frequencies may allow the physician to interpret patient mechanics in terms of models with pathophysiological interest. The current methodological and technical experience make possible the implementation of portable and compact computerised FOT systems specifically addressed to its application in the mechanical ventilation setting. PMID:11178220
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
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. PMID:27575123
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.
Partial synchronization in networks of non-linearly coupled oscillators: The Deserter Hubs Model
NASA Astrophysics Data System (ADS)
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.
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.
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.
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. PMID:27104686
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.
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.
NASA Astrophysics Data System (ADS)
Michiels, Wim; Nijmeijer, Henk
2009-09-01
We consider the synchronization problem of an arbitrary number of coupled nonlinear oscillators with delays in the interconnections. The network topology is described by a directed graph. Unlike the conventional approach of deriving directly sufficient synchronization conditions, the approach of the paper starts from an exact stability analysis in a (gain, delay) parameter space of a synchronized equilibrium and extracts insights from an analysis of its bifurcations and from the corresponding emerging behavior. Instrumental to this analysis a factorization of the characteristic equation is employed that not only facilitates the analysis and reduces computational cost but also allows to determine the precise role of the individual agents and the topology of the network in the (in)stability mechanisms. The study provides an algorithm to perform a stability and bifurcation analysis of synchronized equilibria. Furthermore, it reveals fundamental limitations to synchronization and it explains under which conditions on the topology of the network and on the characteristics of the coupling the systems are expected to synchronize. In the second part of the paper the results are applied to coupled Lorenz systems. The main results show that for sufficiently large coupling gains, delay-coupled Lorenz systems exhibit a generic behavior that does not depend on the number of systems and the topology of the network, as long as some basic assumptions are satisfied, including the strong connectivity of the graph. Here the linearized stability analysis is strengthened by a nonlinear stability analysis which confirms the predictions based on the linearized stability and bifurcation analysis. This illustrates the usefulness of the exact linearized analysis in a situation where a direct nonlinear stability analysis is not possible or where it yields conservative conditions from which it is hard to get qualitative insights in the synchronization mechanisms and their scaling properties
Two-oscillator model of trapped-modes interaction in a nonlinear bilayer fish-scale metamaterial
NASA Astrophysics Data System (ADS)
Tuz, Vladimir R.; Kochetov, Bogdan A.; Kochetova, Lyudmila A.; Mladyonov, Pavel L.; Prosvirnin, Sergey L.
2015-02-01
We discuss a similarity between resonant oscillations in two nonlinear systems; namely, a chain of coupled Duffing oscillators and a bilayer fish-scale metamaterial. In such systems two different resonant states arise which differ in their spectral lines. The spectral line of the first resonant state has a Lorentzian form, whereas the second one has a Fano form. This difference leads to a specific nonlinear response of the systems which manifests itself in the appearance of closed loops in spectral lines and bending and overlapping of resonant curves. Conditions for achieving bistability and multistability are determined.
NASA Astrophysics Data System (ADS)
Kengne, Jacques; Kenmogne, Fabien
2014-12-01
The nonlinear dynamics of fourth-order Silva-Young type chaotic oscillators with flat power spectrum recently introduced by Tamaseviciute and collaborators is considered. In this type of oscillators, a pair of semiconductor diodes in an anti-parallel connection acts as the nonlinear component necessary for generating chaotic oscillations. Based on the Shockley diode equation and an appropriate selection of the state variables, a smooth mathematical model (involving hyperbolic sine and cosine functions) is derived for a better description of both the regular and chaotic dynamics of the system. The complex behavior of the oscillator is characterized in terms of its parameters by using time series, bifurcation diagrams, Lyapunov exponents' plots, Poincaré sections, and frequency spectra. It is shown that the onset of chaos is achieved via the classical period-doubling and symmetry restoring crisis scenarios. Some PSPICE simulations of the nonlinear dynamics of the oscillator are presented in order to confirm the ability of the proposed mathematical model to accurately describe/predict both the regular and chaotic behaviors of the oscillator.
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. PMID:25554054
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.
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
SEACAS Theory Manuals: Part II. Nonlinear Continuum Mechanics
Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.
1998-09-01
This report summarizes the key continuum mechanics concepts required for the systematic prescription and numerical solution of finite deformation solid mechanics problems. Topics surveyed include measures of deformation appropriate for media undergoing large deformations, stress measures appropriate for such problems, balance laws and their role in nonlinear continuum mechanics, the role of frame indifference in description of large deformation response, and the extension of these theories to encompass two dimensional idealizations, structural idealizations, and rigid body behavior. There are three companion reports that describe the problem formulation, constitutive modeling, and finite element technology for nonlinear continuum mechanics systems.
NASA Astrophysics Data System (ADS)
Taghipour, Javad; Dardel, Morteza
2015-10-01
Steady state dynamical behavior of two degrees of freedom (DOF) system composed of a harmonically excited nonlinear oscillator coupled with a single DOF nonlinear energy sink (NES) is studied in comparison with the behavior of a system consisting of a nonlinear oscillator coupled with a two-DOF NES subjected to external harmonic excitation. First, an optimized set of parameters was obtained using optimization for the two-DOF system. Results show that the system with one NES has low robustness to the changes of the parameters and external force. By adding a degree of freedom to the first system, the steady state behavior of the resulting three-DOF system was investigated. Conclusions illustrated that increasing the degrees of freedom of the NES would increase the robustness of the system to the changes in system parameters and amplitude of external force.
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. PMID:26801872
NASA Astrophysics Data System (ADS)
Hoefer, Mark A.
This thesis examines nonlinear wave phenomena, in two physical systems: a Bose-Einstein condensate (BEC) and thin film ferromagnets where the magnetization dynamics are excited by the spin momentum transfer (SMT) effect. In the first system, shock waves generated by steep gradients in the BEC wavefunction are shown to be of the disperse type. Asymptotic and averaging methods are used to determine shock speeds and structure in one spatial dimension. These results are compared with multidimensional numerical simulations and experiment showing good, qualitative agreement. In the second system, a model of magnetization dynamics due to SMT is presented. Using this model, nonlinear oscillating modes---nano-oscillators---are found numerically and analytically using perturbative methods. These results compare well with experiment. A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, e.g. traveling fronts with steep gradients. However, the governing Gross-Pitaevskii (GP) equation that describes the mean field of a BEC admits no dissipation hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave (DSW). Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical 1D dissipative and dispersive shock problem shows significant differences in shock structure and shock front speed. Numerical results associated with laboratory experiments show that three and two-dimensional approximations are in excellent agreement and one dimensional approximations are in qualitative agreement. The interaction of two DSWs is investigated analytically and numerically. Using one dimensional DSW theory it is argued
Fast physical and pseudo random number generation based on a nonlinear optoelectronic oscillator
NASA Astrophysics Data System (ADS)
Mu, Penghua; Pan, Wei; Xiang, Shuiying; Li, Nianqiang; Liu, Xinkai; Zou, Xihua
2015-08-01
High speed random number generation (RNG) utilizing a nonlinear optoelectronic oscillator (OEO) is explored experimentally. It has been found that by simply adjusting either the injected optical power or the gain of the modulator driver, low complexity dynamics such as square wave, and more complex dynamics including fully developed chaos can be experimentally achieved. More importantly, physical RNG based on high-speed-oscilloscope measurements and pseudo RNG based on post-processing are implemented in this paper. The generated bit sequences pass all the standard statistical random tests, indicating that fast physical and pseudo RNG could be achieved based on the same OEO entropy source. Our results could provide further insight into the implementation of RNG based on chaotic optical systems.
Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators
NASA Astrophysics Data System (ADS)
Duanmu, M.; Whitaker, N.; Kevrekidis, P. G.; Vainchtein, A.; Rubin, J. E.
2016-06-01
Motivated by earlier studies of artificial perceptions of light called phosphenes, we analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model problem in its co-traveling frame and systematically obtain the corresponding traveling waves in one spatial dimension. Direct numerical simulations as well as linear stability analysis are employed to reveal the parameter regions where the traveling waves are stable, and these waves are, in turn, connected to the standing waves analyzed in earlier work. We also consider a two-dimensional extension of the model and demonstrate the robust evolution and stability of planar fronts. Our simulations also suggest the radial fronts tend to either annihilate or expand and flatten out, depending on the phase value inside and the parameter regime. Finally, we observe that solutions that initially feature two symmetric fronts with bulged centers evolve in qualitative agreement with experimental observations of phosphenes.
NASA Technical Reports Server (NTRS)
Smith, J. W.; Edwards, J. W.
1980-01-01
Analysis of a longitudinal pilot-induced oscillation (PIO) experienced just prior to touchdown on the final flight of the space shuttle's approach landing tests indicated that the source of the problem was a combination of poor basic handling qualities aggravated by time delays through the digital flight control computer and rate limiting of the elevator actuators due to high pilot gain. A nonlinear PIO suppression (PIOS) filter was designed and developed to alleviate the vehicle's PIO tendencies by reducing the gain in the command path. From analytical and simulator studies it was shown that the PIOS filter, in an adaptive fashion, can attenuate the command path gain without adding phase lag to the system. With the pitch attitude loop of a simulated shuttle model closed, the PIOS filter increased the gain margin by a factor of about two.
NASA Astrophysics Data System (ADS)
Yasunobu, Tsuyoshi; Otobe, Yumiko; Kashimura, Hideo
2013-04-01
When the underexpanded supersonic jet impinges on the obstacle, it is well known that the self-induced flow oscillation occurs. This oscillation depends on the pressure ratio in the flowfield, the position of an obstacle and is related with the noise problems of aeronautical and other industrial engineering. The characteristic and the mechanism of self-induced flow oscillation, have to be clarified to control various noise problems. But, it seems that the characteristics of the oscillated flowfield and the mechanism of an oscillation have to be more cleared to control the oscillation. This paper aims to clarify the effect of the pressure ratio and the obstacle position and the mechanism of self-induced flow oscillation by numerical analysis and experiment, when the underexpanded supersonic jet impinges on the cylindrical body. From the result of this study, it is clear that occurrence of the self-induced flow oscillation depends on the pressure balance in the flowfield.
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.
On nonlinear effects in fracture mechanics.
NASA Technical Reports Server (NTRS)
Liebowitz, H.; Eftis, J.
1971-01-01
Linear elastic treatment of fracture is considered applicable for net section stress up to about 0.8 the uniaxial tensile yield stress. Crack front plastic yield is still small enough to be viewed and treated as a small perturbation to the local crack front elastic stress field. Assuming these same circumstances and adopting the same point of view, an approach is presented for incorporating the nonlinear effects of small scale crack front plastic yield and slow crack extension in determination of the energy release rate and fracture toughness. Deviation from linearity of the load-displacement record in a fracture toughness test offers a quantifiable measure of these effects and is used to calculate the energy release rate. Fracture toughness values for one-eight inch thick 7075-T6 center cracked aluminum sheet are compared with uncorrected values and with values obtained by the Irwin method of plasticity correction.
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.
Multifractal analysis of nonlinear complexity of sacral skin blood flow oscillations in older adults
Liao, Fuyuan; Struck, Bryan D.; MacRobert, Margo
2011-01-01
The objective of this study was to investigate the relationship between cutaneous vasodilatory function and nonlinear complexity of blood flow oscillations (BFO) in older people. A non-painful fast local heating protocol was applied to the sacral skin in 20 older subjects with various vasodilatory functions. Laser Doppler flowmetry was used to measure skin blood oscillations. The complexity of the characteristic frequencies (i.e., metabolic (0.0095–0.02 Hz), neurogenic (0.02–0.05 Hz), myogenic (0.05–0.15 Hz), respiratory (0.15–0.4 Hz), and cardiac (0.4–2 Hz)) of BFO was quantified using the multifractal detrended fluctuation analysis. Compared with the 65–75 years group, the complexity of metabolic BFO in the 75–85 years group was significantly lower at the baseline (P < 0.05) and the second peak (P < 0.001). Compared with baseline BFO, subjects in the 65–75 years group had a significant increase in the complexity of metabolic BFO (P < 0.01) in response to local heating; while subjects in the 75–85 years group did not. Our findings support the use of multifractal analysis to assess aging-related microvascular dysfunction. PMID:21487818
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.
A mechanical memory with a dc modulation of nonlinear resonance
NASA Astrophysics Data System (ADS)
Noh, Hyunho; Shim, Seung-Bo; Jung, Minkyung; Khim, Zheong G.; Kim, Jinhee
2010-07-01
We present a mechanical memory device based on dynamic motion of a nanoelectromechanical (NEM) resonator. The NEM resonator exhibits clear nonlinear resonance characteristics which can be controlled by the dc bias voltage. For memory operations, the NEM resonator is driven to the nonlinear resonance region, and binary values are assigned to the two allowed states on the bifurcation branch. The transition between memory states is achieved by modulating the nonlinear resonance characteristics with dc bias voltage. Our device works at room temperature and modest vacuum conditions with a maximum operation frequency of about 5 kHz.
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
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)
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.
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. PMID:27119060
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. PMID:25636380
NASA Astrophysics Data System (ADS)
Fidler, Andrew F.; Engel, Gregory S.
2013-10-01
We present a theory for a bath model in which we approximate the adiabatic nuclear potential surfaces on the ground and excited electronic states by displaced harmonic oscillators that differ in curvature. Calculations of the linear and third-order optical response functions employ an effective short-time approximation coupled with the cumulant expansion. In general, all orders of correlation contribute to the optical response, indicating that the solvation process cannot be described as Gaussian within the model. Calculations of the linear absorption and fluorescence spectra resulting from the theory reveal a stronger temperature dependence of the Stokes shift along with a general asymmetry between absorption and fluorescence line shapes, resulting purely from the difference in the phonon side band. We discuss strategies for controlling spectral tuning and energy-transfer dynamics through the manipulation of the excited-state and ground-state curvature. Calculations of the nonlinear response also provide insights into the dynamics of the system-bath interactions and reveal that multidimensional spectroscopies are sensitive to a difference in curvature between the ground- and excited-state adiabatic surfaces. This extension allows for the elucidation of short-time dynamics of dephasing that are accessible in nonlinear spectroscopic methods.
Mode-coupling mechanisms in nanocontact spin-torque oscillators
NASA Astrophysics Data System (ADS)
Iacocca, Ezio; Dürrenfeld, Philipp; Heinonen, Olle; Åkerman, Johan; Dumas, Randy K.
2015-03-01
Spin-torque oscillators (STOs) are devices that allow for the excitation of a variety of magnetodynamical modes at the nanoscale. Depending on both external conditions and intrinsic magnetic properties, STOs can exhibit regimes of mode hopping and even mode coexistence. Whereas mode hopping has been extensively studied in STOs patterned as nanopillars, coexistence has been only recently observed for localized modes in nanocontact STOs (NC-STOs), where the current is confined to flow through a NC fabricated on an extended pseudo spin valve. By means of electrical characterization and a multimode STO theory, we investigate the physical origin of the mode-coupling mechanisms favoring coexistence. Two coupling mechanisms are identified: (i) magnon-mediated scattering and (ii) intermode interactions. These mechanisms can be physically disentangled by fabricating devices where the NCs have an elliptical cross section. The generation power and linewidth from such devices are found to be in good qualitative agreement with the theoretical predictions, as well as provide evidence of the dominant mode-coupling mechanisms.
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.
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.
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.
Cloning in nonlinear Hamiltonian quantum and hybrid mechanics
NASA Astrophysics Data System (ADS)
Arsenović, D.; Burić, N.; Popović, D. B.; Radonjić, M.; Prvanović, S.
2014-10-01
The possibility of state cloning is analyzed in two types of generalizations of quantum mechanics with nonlinear evolution. It is first shown that nonlinear Hamiltonian quantum mechanics does not admit cloning without the cloning machine. It is then demonstrated that the addition of the cloning machine, treated as a quantum or as a classical system, makes cloning possible by nonlinear Hamiltonian evolution. However, a special type of quantum-classical theory, known as the mean-field Hamiltonian hybrid mechanics, does not admit cloning by natural evolution. The latter represents an example of a theory where it appears to be possible to communicate between two quantum systems at superluminal speed, but at the same time it is impossible to clone quantum pure states.
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.
OSCILLATION MECHANICS OF THE RESPIRATORY SYSTEM: APPLICATIONS TO LUNG DISEASE
Kaczka, David W.; Dellacá, Raffaele L.
2011-01-01
Since its introduction in the 1950s, the forced oscillation technique (FOT) and the measurement of respiratory impedance have evolved into powerful tools for the assessment of various mechanical phenomena in the mammalian lung during health and disease. In this review, we highlight the most recent developments in instrumentation, signal processing, and modeling relevant to FOT measurements. We demonstrate how FOT provides unparalleled information on the mechanical status of the respiratory system compared to more widely-used pulmonary function tests. The concept of mechanical impedance is reviewed, as well as the various measurement techniques used to acquire such data. Emphasis is placed on the analysis of lower, physiologic frequency ranges (typically less than 10 Hz) that are most sensitive to normal physical processes as well as pathologic structural alterations. Various inverse modeling approaches used to interpret alterations in impedance are also discussed, specifically in the context of three common respiratory diseases: asthma, chronic obstructive pulmonary disease, and acute lung injury. Finally, we speculate on the potential role for FOT in the clinical arena. PMID:22011237
Mechanical phase matching of birefringent non-linear crystals.
Deyra, Loïc; Balembois, François; Guilbaud, André; Villeval, Philippe; Georges, Patrick
2014-09-22
Second-order nonlinear processes such as second harmonic generation or parametric amplification have found numerous applications in the scientific and industrial world, from micromachining to petawatt laser facilities. These nonlinear interactions are mostly carried out in birefringent crystals because of their low cost and the possibility to operate at high powers Phase-matching configurations in birefringent crystals are determined by their refractive indexes. Here, we show that an important mechanical stress can be used to significantly change the phase-matching properties of a birefringent crystal. As an example, we demonstrate the shift of second harmonic non-critical phase matching wavelength of LiB3O5 (LBO) crystal at room temperature from 1200 nm to 1120 nm by applying compressive forces up to 100 MPa. We believe that this mechanical phase matching can be used as an additional degree of freedom to optimize nonlinear optical frequency mixing geometries. PMID:25321800
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.
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.
New Facts on the Nature of Gravitational Force And Nonlinear Oscillations of Space
NASA Astrophysics Data System (ADS)
Kursunoglu, Behram N.
2002-07-01
This paper discusses the letters received by this author from Albert Einstein, Erwin Schrodinger, and Paul Adrian Maurice Dirac, about fifty years ago which comment on my nonsymmetrical generalization of Einstein's general relativistic theory of gravitation. The writing of this paper, because of the dates of the letters, seems to have been delayed by half a century. Of the three versions of the nonsymmetrical theory (Einstein, Schrodinger and Kursunoglu Theories) my own paper contains results obtained as solutions of Generalized Theory of Gravitation field equations. In this paper it is shown that the field equations yield space nonlinear oscillations; a quartet of gravitational forces, quintessence, and replace Einstein's Cosmological Constant by two invariant parameters r0 and q related according to r02 q2 = c4/2G, where r0 is a length varying between zero and infinity and where q2 has the dimensions of energy density. These parameters govern the expansion of the universe with increasing acceleration and their existence yield four different solutions at each space-time point.
Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators
Duanmu, M.; Whitaker, N.; Kevrekidis, P. G.; 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
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.
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.
He, Qingbo Xu, Yanyan; Lu, Siliang; Dai, Daoyi
2014-04-28
This Letter reports an out-of-resonance vibro-acoustic modulation (VAM) effect in nonlinear ultrasonic evaluation of a microcracked cantilever beam. We design a model to involve the microcracked cantilever beam in a nonlinear oscillator system whose dynamics is introduced to extend the operating vibration excitation band of the VAM out of resonance. The prototype model exhibits an effective bandwidth four times that of the traditional linear model. The reported VAM effect allows efficiently enhancing the detection, localization, and imaging of various types of microcracks in solid materials at out-of-resonance vibration excitation frequencies.
The Two-Capacitor Problem Revisited: A Mechanical Harmonic Oscillator Model Approach
ERIC Educational Resources Information Center
Lee, Keeyung
2009-01-01
The well-known two-capacitor problem, in which exactly half the stored energy disappears when a charged capacitor is connected to an identical capacitor, is discussed based on the mechanical harmonic oscillator model approach. In the mechanical harmonic oscillator model, it is shown first that "exactly half" the work done by a constant applied…
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 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
The use of normal forms for analysing nonlinear mechanical vibrations.
Neild, Simon A; Champneys, Alan R; Wagg, David J; Hill, Thomas L; Cammarano, Andrea
2015-09-28
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
Nonlinear Kramers equation associated with nonextensive statistical mechanics.
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. PMID:26066118
NASA Astrophysics Data System (ADS)
Bourland, F. J.; Haberman, Richard; Kath, William L.
1991-08-01
Strongly nonlinear oscillators under slowly varying perturbations (not necessarily Hamiltonian) are analyzed by putting the equations into the standard form for the method of averaging. By using the usual near-identity transformations, energy-angle (and equivalent action-angle) equations are derived using the properties of strongly nonlinear oscillators. By introducing a perturbation expansion, a differential equation for the phase shift is derived and shown to agree with earlier results obtained by Bourland and Haberman using the multiple scale perturbation method. The slowly varying phase shift is used (by necessity) to determine the boundary of the basin of attraction for competing stable equilibria, even though these averaged equations are known not to be valid near a separatrix (unperturbed homoclinic orbit).
A nonlinear generalized continuum approach for electro-mechanical coupling
NASA Astrophysics Data System (ADS)
Skatulla, S.; Arockiarajan, A.; Sansour, C.
2008-07-01
Electro-active polymers (EAP) are "smart materials" whose mechanical properties may be changed significantly by the application of electric field. Hence, these materials can serve as actuators in electro-mechanical systems, artificial muscles, etc. In this paper, we provide a generalized continuum framework basis for the characterization of the nonlinear electroelastic properties of these materials. This approach introduces new strain and stress measures which lead to the formulation of a corresponding generalized variational principle. The theory is then completed by Dirichlet boundary conditions for the displacement field and the electric potential and then derivatives normal to the boundary. The basic idea behind this generalized continuum framework is the consideration of a micro- and a macro-space which together span the generalized space. All quantities including the constitutive law for the electro-mechanically coupled nonlinear hyperelasticity are defined in the generalized space. Numerical examples are presented to demonstrate the numerical accuracy of the implemented formulation using the mesh free method.
Are nonlinear discrete cellular automata compatible with quantum mechanics?
NASA Astrophysics Data System (ADS)
Elze, Hans-Thomas
2015-07-01
We consider discrete and integer-valued cellular automata (CA). A particular class of which comprises “Hamiltonian CA” with equations of motion that bear similarities to Hamilton's equations, while they present discrete updating rules. The dynamics is linear, quite similar to unitary evolution described by the Schrödinger equation. This has been essential in our construction of an invertible map between such CA and continuous quantum mechanical models, which incorporate a fundamental discreteness scale. Based on Shannon's sampling theory, it leads, for example, to a one-to-one relation between quantum mechanical and CA conservation laws. The important issue of linearity of the theory is examined here by incorporating higher-order nonlinearities into the underlying action. These produce inconsistent nonlocal (in time) effects when trying to describe continuously such nonlinear CA. Therefore, in the present framework, only linear CA and local quantum mechanical dynamics are compatible.
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.
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.
Dynamics and synchronization of nonlinear oscillators with time delay: A study with fiber lasers
NASA Astrophysics Data System (ADS)
Franz, Anthony Lawrence
The effect of time delay on nonlinear oscillators is an important problem in the study of dynamical systems. Erbium-doped fiber ring lasers have an internal time scale set by the length of the laser's electromagnetic cavity. Long cavities allow thousands of modes to experience gain making it very difficult to model the lasers. We examine the effect of adding external time delays through feedback and coupling. In the first experiment an external time delay is added to a laser by adding a feedback loop to the cavity. These delay times are varied over four orders of magnitude by changing the length of fiber in the feedback loop. The laser intensity dynamics are examined using time series, power spectra, time delay embeddings, and spatiotemporal representations. We apply Karhunen-Loeve (KL) decomposition on the spatiotemporal representations and use the Shannon entropy as calculated from the KL eigenvalue spectra as a measure of the complexity of the dynamics. For long delays we find that the complexity increases as expected, but also that the fluctuation size increases. In the second experiment two lasers are mutually coupled together with a coupling time delay that is varied over four orders of magnitude. The analysis is repeated and we find the surprising result that the dynamical complexity decreases for short coupling delays as compared to the uncoupled lasers. Measurements of the optical spectra indicate a narrowing of the spectra indicating that the simplification in dynamics could be due to the reduction in the number of electromagnetic modes experiencing gain. The fluctuation size increases for all delay times and is largest when the internal and external time delays match. Lag-synchrony is also observed for the mutually coupled lasers. Recent modeling using Ikeda ring oscillators showed that stable isochronal synchrony could be achieved if a third drive laser was unidirectionally coupled with enough strength. We experimentally find that increasing the
Some observations on the mechanics of oscillation of ultrasonic files.
Ahmad, M
1990-02-01
The resonant characteristics of ultrasonic files driven by the Cavi-Endo unit were examined. The investigation was carried out by evaluating the pattern of oscillation and the power emitted by the ultrasonic files. It was observed that the files oscillated in a sinusoidal fashion, exhibiting a standing wave pattern along the file. The power emitted was found to be directly proportional to the flexibility of the file. Such behaviour is typical of a system that exhibits resonance. PMID:2202589
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
Nonlinear fracture mechanics. Volume 1. Time-dependent fracture
Saxena, A.; Landes, J.D.; Bassani, J.L.
1989-01-01
Various papers on time-dependent fracture in nonlinear fracture mechanics are presented. Individual subjects considered include: numerical study of non-steady-state creep at stationary crack tips, crack growth in small-scale creep, growth of macroscopic cracks by void coalescence under extensive creeping conditions, creep embrittlement susceptibility and creep crack growth behavior in low-alloy steels, and experimental determination of the high-temperature crack growth behavior of Incoloy 800H. Also discussed are: three-dimensional transient analysis of a dynamically loaded three-point-bend ductile fracture specimen, experimental study of the validity of a Delta J criterion for fatigue crack growth, combined-mode low-cycle fatigue crack growth under torsional loading, fatigue crack-tip mechanics in 7075-T6 aluminum alloy from high-sensitivity displacement field measurements, and nonlinear fracture of concrete and ceramics.
Enhanced nonlinear interactions in quantum optomechanics via mechanical amplification
Lemonde, Marc-Antoine; Didier, Nicolas; Clerk, Aashish A.
2016-01-01
The quantum nonlinear regime of optomechanics is reached when nonlinear effects of the radiation pressure interaction are observed at the single-photon level. This requires couplings larger than the mechanical frequency and cavity-damping rate, and is difficult to achieve experimentally. Here we show how to exponentially enhance the single-photon optomechanical coupling strength using only additional linear resources. Our method is based on using a large-amplitude, strongly detuned mechanical parametric drive to amplify mechanical zero-point fluctuations and hence enhance the radiation pressure interaction. It has the further benefit of allowing time-dependent control, enabling pulsed schemes. For a two-cavity optomechanical set-up, we show that our scheme generates photon blockade for experimentally accessible parameters, and even makes the production of photonic states with negative Wigner functions possible. We discuss how our method is an example of a more general strategy for enhancing boson-mediated two-particle interactions and nonlinearities. PMID:27108814
Nonlinear Mechanisms of Lesion Formation by High Intensity Focused Ultrasound
NASA Astrophysics Data System (ADS)
Khokhlova, V. A.; Bailey, M. R.; Reed, J.; Canney, M. S.; Kaczkowski, P. J.; Crum, L. A.
2006-05-01
Nonlinear mechanisms of lesion formation by high intensity focused ultrasound (HIFU) were investigated experimentally and numerically in a transparent polyacrylamide gel phantom. Numerical predictions were made with a finite-amplitude acoustic propagation model. A 2-MHz transducer of 42-mm diameter and 44.5-mm radius of curvature was operated above the cavitation threshold of the gel phantom at various peak acoustic powers and duty cycles. Acoustic waveforms were recorded in the gel by a fiber optic hydrophone. Bubble activity was detected actively by B-mode diagnostic imaging, passively by a remote focused hydrophone, and optically by CCD and high-speed cameras. Elevated static pressure was applied to suppress bubble activity and increase the boiling temperature, thus isolating the pure effect of acoustic nonlinearity. In overpressure experiment performed at 32 W acoustic power, both cavitation and nonlinear ultrasound propagation accelerated lesion inception and growth, but acoustic nonlinearity, which led to shock formation, played the dominant role. Rapid localized heating, particularly by increased absorption in the shocked wave, led to boiling and then to proximal growth and migration of the lesion even at low overpressure. At 90W acoustic power, boiling was observed and predicted in less than 50 ms.
Nonequilibrium Statistical Mechanics of Weakly Stochastically Perturbed System of Oscillators
NASA Astrophysics Data System (ADS)
Dymov, Andrey
2016-07-01
We consider a finite region of a $d$-dimensional lattice, $d\\in\\mathbb{N}$, of weakly coupled harmonic oscillators. The coupling is provided by a nearest-neighbour potential (harmonic or not) of size $\\varepsilon$. Each oscillator weakly interacts by force of order $\\varepsilon$ with its own stochastic Langevin thermostat of arbitrary positive temperature. We investigate limiting as $\\varepsilon\\rightarrow 0$ behaviour of solutions of the system and of the local energy of oscillators on long-time intervals of order $\\varepsilon^{-1}$ and in a stationary regime. We show that it is governed by an effective equation which is a dissipative SDE with nondegenerate diffusion. Next we assume that the interaction potential is of size $\\varepsilon\\lambda$, where $\\lambda$ is another small parameter, independent from $\\varepsilon$. Solutions corresponding to this scaling describe small low temperature oscillations. We prove that in a stationary regime, under the limit $\\varepsilon\\rightarrow 0$, the main order in $\\lambda$ of the averaged Hamiltonian energy flow is proportional to the gradient of temperature. We show that the coefficient of proportionality, which we call the conductivity, admits a representation through stationary space-time correlations of the energy flow. Most of the results and convergences we obtain are uniform with respect to the number of oscillators in the system.
NASA Astrophysics Data System (ADS)
Sammis, C. G.; Dolan, J. F.; Smith, S. W.
2003-12-01
There is mounting paleoseismological evidence that large earthquakes on a given fault network tend to occur in temporal clusters. Examples include the southern San Andreas system in the Imperial Valley (Rockwell et al., in prep, 2003), the Eastern California Shear Zone (Rockwell et al., BSSA, 2000), the Garlock system (Dawson et al, in prep., 2003) and the Los Angeles area (Dolan et al., in prep., 2003). This last study has also found evidence that clusters within the Los Angeles area tend to be anti-correlated with similar clusters in the Eastern California shear zone and on the Garlock fault. This clustering behavior is expected if large earthquakes behave as coupled non-linear relaxation oscillators. As a simplest case, we consider two identical faults which are loaded at constant strain rate and which fail at a prescribed stress threshold. Each thus produces the saw-tooth stress strain curve characteristic of a relaxation oscillator. The faults are non-linear oscillators because we assume the stress-strain curve is non-linear, having the negative curvature typical of laboratory experiments and regional damage mechanics models (Ben-Zion and Lyakhovsky, 2002). The two faults are coupled by symmetric stress transfer, in that we assume each fault either increases or decrease the Coulomb stress on the other by an equal amount. We find that events on the two faults phase-lock either in phase if the Coulomb stress transfer is positive or 180 degrees out of phase if the transfer is negative. This phase-lock is driven by the non-linear stress-strain relation. When a fault is close to failure, the increment of stress transfer causes a larger increment in strain. Since time is linked to strain through the assumption of constant strain rate loading, the time shift of the impending event is larger the nearer a fault is to failure. For a positive stress transfer, this shortens the interval and leads to in-phase locking. For a negative stress transfer, the interval is
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.
NASA Astrophysics Data System (ADS)
Harlow, Jennifer Wightman
In the past several years, the field of optomechanics has progressed from proof-of-principle experiments to the realization of mechanical oscillators and measurements in the quantum regime. Mechanical oscillators are of great interest because they can have small dissipation rates, can couple to many different systems of interest, and are the fundamental elements of ultrasensitive force detectors. Coupling these mechanical oscillators to microwave or optical fields provides a two-fold advantage. Firstly, information about mechanical position can be encoded in the interrogating field, enabling sensitive readout of the mechanical oscillator. Secondly, the radiation pressure force of that field can be used to control the state of the mechanical oscillator. Including a high-quality microwave or optical cavity enhances both of these effects, as the field strength is resonantly increased. The major questions in the field of optomechanics in the last several years have dealt with using mechanical oscillators for ultrasensitive measurements and as tools for quantum information. Both of these goals have the prerequisite that we be able to read out the motion of the mechanical oscillator in a quantum efficient manner. To that end, we developed a nearly shot-noise limited microwave interferometer capable of measuring mechanical motion with an imprecision below that at the standard quantum limit. This achievement is not only a critical improvement for the electromechanical experiments we do, but is also an important tool for any experiment that encodes the information of interest in microwave fields. In order to use mechanical oscillators as tools for quantum information, the mechanical oscillator must also be cooled into the quantum regime and fully controllable by the interrogating fields. To this end, we used the radiation pressure of microwave fields to cool our macroscopic mechanical oscillator to less than one phonon. We also demonstrated coherent transfer between
Probing wave function collapse models with a classically driven mechanical oscillator
NASA Astrophysics Data System (ADS)
Ho, Melvyn; Lafont, Ambroise; Sangouard, Nicolas; Sekatski, Pavel
2016-03-01
We show that the interaction of a pulsed laser light with a mechanical oscillator through the radiation pressure results in an opto-mechanical entangled state in which the photon number is correlated with the oscillator position. Interestingly, the mechanical oscillator can be delocalized over a large range of positions when driven by an intense laser light. This provides a simple yet sensitive method to probe hypothetical post-quantum theories including an explicit wave function collapse model, like the Diosi & Penrose model. We propose an entanglement witness to reveal the quantum nature of this opto-mechanical state as well as an optical technique to record the decoherence of the mechanical oscillator. We also report on a detailed feasibility study giving the experimental challenges that need to be overcome in order to confirm or rule out predictions from explicit wave function collapse models.
Zolotoverkh, I I; Kamysheva, A A; Kravtsov, N V; Lariontsev, E G; Firsov, V V; Chekina, S N
2008-10-31
Nonlinear phenomena appearing in a solid-state ring laser upon approaching the period-doubling bifurcation point of self-modulation oscillations and inside the doubling region are studied theoretically and experimentally. The bifurcation appears due to the parametric interaction of self-modulation oscillations of the first kind with relaxation oscillations. It is found that the bifurcation diagrams, time dependences of the intensities and power spectrum can significantly differ for counterpropagating waves because of the amplitude nonreciprocity of the ring resonator and the inequality of the moduli of the feedback coefficients. It is shown that when the self-modulation period is doubled, the widths of spectral peaks corresponding the self-modulation frequency and the fundamental relaxation frequency decrease. Noise precursors of doubling bifurcation are studied. It is found that the distance between the peaks of noise precursors increases with increasing the noise intensity. It is demonstrated experimentally that the noise modulation leads to the bifurcation point displacement, which increases with increasing the noise. (nonlinear optical phenomena)
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.
Mechanical signaling via nonlinear wavefront propagation in a mechanically excitable medium.
Idema, Timon; Liu, Andrea J
2014-06-01
Models that invoke nonlinear wavefront propagation in a chemically excitable medium are rife in the biological literature. Indeed, the idea that wavefront propagation can serve as a signaling mechanism has often been invoked to explain synchronization of developmental processes. In this paper we suggest a kind of signaling based not on diffusion of a chemical species but on the propagation of mechanical stress. We construct a theoretical approach to describe mechanical signaling as a nonlinear wavefront propagation problem and study its dependence on key variables such as the effective elasticity and damping of the medium. PMID:25019816
Mechanical signaling via nonlinear wavefront propagation in a mechanically excitable medium
NASA Astrophysics Data System (ADS)
Idema, Timon; Liu, Andrea J.
2014-06-01
Models that invoke nonlinear wavefront propagation in a chemically excitable medium are rife in the biological literature. Indeed, the idea that wavefront propagation can serve as a signaling mechanism has often been invoked to explain synchronization of developmental processes. In this paper we suggest a kind of signaling based not on diffusion of a chemical species but on the propagation of mechanical stress. We construct a theoretical approach to describe mechanical signaling as a nonlinear wavefront propagation problem and study its dependence on key variables such as the effective elasticity and damping of the medium.
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
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…
Development of drive mechanism for an oscillating airfoil
NASA Technical Reports Server (NTRS)
Sticht, Clifford D.
1988-01-01
The design and development of an in-draft wind tunnel test section which will be used to study the dynamic stall of airfoils oscillating in pitch is described. The hardware developed comprises a spanned airfoil between schleiren windows, a four bar linkage, flywheels, a drive system and a test section structure.
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.
Gravitational force modulates muscle activity during mechanical oscillation of the tibia in humans
Chang, Shuo-Hsiu; Dudley-Javoroski, Shauna; Shields, Richard K.
2012-01-01
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 5g force for 20 seconds 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 (5g). 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. PMID:21708472
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
Feedback as a mechanism for the resurrection of oscillations from death states
NASA Astrophysics Data System (ADS)
Chandrasekar, V. K.; Karthiga, S.; Lakshmanan, M.
2015-07-01
The quenching of oscillations in interacting systems leads to several unwanted situations, which necessitate a suitable remedy to overcome the quenching. In this connection, this work addresses a mechanism that can resurrect oscillations in a typical situation. Through both numerical and analytical studies, we show that the candidate which is capable of resurrecting oscillations is nothing but the feedback, the one which is profoundly used in dynamical control and in biotherapies. Even in the case of a rather general system, we demonstrate analytically the applicability of the technique over one of the oscillation quenched states called amplitude death states. We also discuss some of the features of this mechanism such as adaptability of the technique with the feedback of only a few of the oscillators.
Balachandran, R.; Dowling, A.P.; Mastorakos, E.; Ayoola, B.O.; Kaminski, C.F.
2005-10-01
This paper describes an experimental investigation of acoustically forced lean premixed turbulent bluff-body-stabilised flames in an enclosure short enough so that no coupling of the combustor downstream acoustics occurred for the frequencies studied here, which allows an unambiguous examination of the flame response to inlet velocity fluctuations. Special emphasis was placed on the amplitude dependence of this response. Measurements of the heat release rate were performed with OH{sup *} and CH{sup *} chemiluminescence, planar laser-induced fluorescence (PLIF) of OH from which the flame surface density (FSD) was computed, and simultaneous CH{sub 2}O and OH PLIF imaging from which the local heat release rate (RX) was estimated. The global heat release measured with chemiluminescence and that integrated from the local FSD measurements were in close agreement, while a comparison between FSD and high-resolution RX imaging also showed good agreement. This suggests that estimates of the flame area are sufficient to determine heat release rate for this flow. The heat release response became nonlinear after inlet velocity amplitudes of around 15% of the bulk velocity. This value depended on the forcing frequency and the equivalence ratio. The nonlinearity was found to occur when the shear layers rolled up into vortices. The vortices induced by the inlet velocity fluctuations not only generated flame area when the flame wrapped around them, but also caused cusps and even large-scale flame annihilation events, as observed in time-resolved OH PLIF images. Such events occurred when parts of the flame stabilised on the inner shear layer close to the recirculation zone collapsed on parts of the flame stabilised on the outer recirculation zone, a phenomenon that was made more prominent with increasing forcing amplitude. A further nonlinearity occurred at high amplitudes and at some equivalence ratios, where a significant leakage of energy to higher harmonics was observed, but the
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.
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.
A dynamical instability as a driving mechanism for stellar oscillations
NASA Astrophysics Data System (ADS)
Auvergne, M.; Baglin, A.
1985-01-01
Nonlinear effects in some cases lead to overstable pseudo periodic, irregular or even chaotic motions in dynamical systems, where catastrophic ones (i.e. dynamical instabilities) are expected from the linear theory. In a rough approximation, the motion of an ionization zone in a star is described by a simple nonlinear differential equation. This equation, analogous to the one obtained by Moore and Spiegel (1966) in the treatment of radiating convective elements, exhibits behaviours sensitive to small perturbations due to the competition between several equilibrium configurations: a dynamically unstable one, and two stable ones. Astrophysical applications to Miras and white dwarfs are tentatively proposed.
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.
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.
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. PMID:23320977
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
2015-01-01
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
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
Optimization of an ultra low-phase noise sapphire--SiGe HBT oscillator using nonlinear CAD.
Cibiel, Gilles; Régis, Myrianne; Llopis, Olivier; Rennane, Abdelali; Bary, Laurent; Plana, Robert; Kersalé, Yann; Giordano, Vincent
2004-01-01
In this paper, the electrical and noise performances of a 0.8 microm silicon germanium (SiGe) transistor optimized for the design of low phase-noise circuits are described. A nonlinear model developed for the transistor and its use for the design of a low-phase noise C band sapphire resonator oscillator are also reported. The best measured phase noise (at ambient temperature) is -138 dBc/Hz at 1 kHz offset from a 4.85 GHz carrier frequency, with a loaded QL factor of 75,000. PMID:14995014
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.
Testing Spontaneous Wave-Function Collapse Models on Classical Mechanical Oscillators
NASA Astrophysics Data System (ADS)
Diósi, Lajos
2015-02-01
We show that the heating effect of spontaneous wave-function collapse models implies an experimentally significant increment Δ Tsp of equilibrium temperature in a mechanical oscillator. The obtained new form Δ Tsp is linear in the oscillator's relaxation time τ and independent of the mass. The oscillator can be in a classical thermal state, also the effect Δ Tsp is classical for a wide range of frequencies and quality factors. We note that the test of Δ Tsp does not necessitate quantum state monitoring just tomography. In both the gravity-related and the continuous spontaneous localization models the strong-effect edge of their parameter range can be challenged in existing experiments on classical oscillators. For the continuous spontaneous localization theory, the conjectured highest collapse rate parameter values become immediately constrained by evidences from current experiments on extreme slow-ring-down oscillators.
Testing spontaneous wave-function collapse models on classical mechanical oscillators.
Diósi, Lajos
2015-02-01
We show that the heating effect of spontaneous wave-function collapse models implies an experimentally significant increment ΔT(sp) of equilibrium temperature in a mechanical oscillator. The obtained new form ΔT(sp) is linear in the oscillator's relaxation time τ and independent of the mass. The oscillator can be in a classical thermal state, also the effect ΔT(sp) is classical for a wide range of frequencies and quality factors. We note that the test of ΔT(sp) does not necessitate quantum state monitoring just tomography. In both the gravity-related and the continuous spontaneous localization models the strong-effect edge of their parameter range can be challenged in existing experiments on classical oscillators. For the continuous spontaneous localization theory, the conjectured highest collapse rate parameter values become immediately constrained by evidences from current experiments on extreme slow-ring-down oscillators. PMID:25699424
Nonlinear whistler-mode Chorus Amplification: a lasing mechanism
NASA Astrophysics Data System (ADS)
Soto-chavez, A.; Bhattacharjee, A.
2013-12-01
A mechanism for chorus wave amplification is presented. We show [1] that the whistler-mode chorus dynamical equations can be put in a form similar to the ones describing the physics of Free-electron lasers (underscoring the well known observational fact that the intensity of whistler-mode chorus demand a quasi-coherent mechanism [2]). We solve these dynamical equations numerically in the nonlinear regime [3]. In this regime our numerical results exhibit strong amplitude modulation and particle trapping, consistent with observations and numerical results previously obtained in the literature. Finally, our model gives simplified analytical expressions of wave growth rate in terms of a few measurable plasma parameters that can be used by observers without further simplification. 1. A. R. Soto-Chavez et al. Phys. Plasmas, 19, 010701, (2012). 2. P. A. Isenberg et al. J. Geophys. Res., 87, 1495, (1982). 3. A. R. Soto-Chavez and A. Bhattacharjee, JGR, (2013) submitted.
Stochastic resonance in a nonlinear mechanical vibration isolation system
NASA Astrophysics Data System (ADS)
Lu, Zeqi; Chen, Li-Qun; Brennan, Michael J.; Yang, Tiejun; Ding, Hu; Liu, Zhigang
2016-05-01
This paper concerns the effect that a stochastic resonance can have on a vibration isolation system. Rather than reducing the transmitted force, it is shown that it is possible to significantly mask the component of the force transmitted though the isolator, when the system is excited harmonically. This can be achieved by adding a very low intensity of random noise to the harmonic excitation force. The nonlinear mechanical vibration isolation system used in the study consists of a vertical linear spring in parallel with two horizontal springs, which are configured so that the potential energy of the system has a double-well. Prior to the analytical and numerical study, an experiment to demonstrate stochastic resonance in a mechanical system is described.
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
Raver, Sylvina M; Keller, Asaf
2014-11-01
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 with the cannabinoids WIN55,212-2 (WIN) or Δ(9)tetrahydrocannabinol (THC) in adolescence, but not adulthood. WIN and THC are cannabinoid-1 (CB1R) and 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 local field potentials (LFPs) in vitro in adults. 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
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?
Damped Mechanical Oscillator: Experiment and Detailed Energy Analysis
NASA Astrophysics Data System (ADS)
Corridoni, Tommaso; D'Anna, Michele; Fuchs, Hans
2014-02-01
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 characterized by ripples, which can easily be demonstrated by using a dynamic modeling approach.8 In this note we consider an oscillator consisting of a cart running on a horizontal track, two springs, and a damping device created with magnets and a metal plate attached to the cart (Fig. 1). Using sensors and data-acquisition software,9 we measure kinematic quantities and three forces: those of the springs on the cart and, separately, the force between magnets and the plate. A detailed analysis of the energy exchanges between the cart and the interacting parts is obtained. In particular, we show that only the energy exchanges with the magnets are affected by dissipative processes while over a suitable time interval the net energy exchanged between cart and springs equals zero.
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
Predicting the Highly Nonlinear Mechanical Properties of Polymeric Materials
NASA Astrophysics Data System (ADS)
Porter, David
2009-06-01
Over the past few years, we have developed models that calculate the highly nonlinear mechanical properties of polymers as a function of temperature, strain and strain rate from their molecular and morphological structure. A review of these models is presented here, with emphasis on combining the fundamental aspects of molecular physics that dictate these properties and the pragmatic need to make realistic predictions for our customers; the designer of new materials and the engineers who use these materials. The models calculate the highly nonlinear mechanical properties of polymers as a function of temperature, strain and strain rate from their molecular structure. The model is based upon the premise that mechanical properties are a direct consequence of energy stored and energy dissipated during deformation of a material. This premise is transformed into a consistent set of structure-property relations for the equation of state, EoS, and the engineering constitutive relations in a polymer by quantifying energy storage and loss at the molecular level of interactions between characteristic groups of atoms in a polymer. These relations are derived from a simple volumetric mean field Lennard-Jones potential function for the potential energy of intermolecular interactions in a polymer. First, properties such as temperature-volume relations and glass transition temperature are calculated directly from the potential function. Then, the `shock' EoS is derived simply by differentiating the potential function with respect to volume, assuming that the molecules cannot relax in the time scales of the deformation. The energy components are then used to predict the dynamic mechanical spectrum of a polymer in terms of temperature and rate. This can be transformed directly into the highly nonlinear stress-strain relations through yield. The constitutive relations are formulated as a set of analytical equations that predict properties directly in terms of a small set of
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.
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.
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.
NASA Astrophysics Data System (ADS)
Bhardwaj, R.; Bhatnagar, K. B.
1995-12-01
The rotational motion of a satellite in a circular orbit under the influence of magnetic torque is being studied. The present paper deals with the non-resonance and resonance cases. By using Melnikov's method, the authors have shown that the equation of motion is non-integrable. Taking the magnetic torque perturbation to be small (ɛ ≪ 1) and using BKM method, it is observed that the amplitude of the oscillation remains constant up to the second order of approximation. The main resonance has been shown to exist. The analysis regarding the stability near the resonance frequency shows that discontinuity occurs in the amplitude of the oscillation at a frequency of the external periodic force which is less than the frequency of the natural oscillation.
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.
Statistical mechanics of the nonlinear Schrödinger equation
NASA Astrophysics Data System (ADS)
Lebowitz, Joel L.; Rose, Harvey A.; Speer, Eugene R.
1988-02-01
We investigate the statistical mechanics of a complex field ø whose dynamics is governed by the nonlinear Schrödinger equation. Such fields describe, in suitable idealizations, Langmuir waves in a plasma, a propagating laser field in a nonlinear medium, and other phenomena. Their Hamiltonian H(φ ) = int_Ω {[1/2|nabla φ |^2 - (1/p) |φ |^p ] dx} is unbounded below and the system will, under certain conditions, develop (self-focusing) singularities in a finite time. We show that, when Ω is the circle and the L 2 norm of the field (which is conserved by the dynamics) is bounded by N, the Gibbs measure υ obtained is absolutely continuous with respect to Wiener measure and normalizable if and only if p and N are such that classical solutions exist for all time—no collapse of the solitons. This measure is essentially the same as that of a one-dimensional version of the more realisitc Zakharov model of coupled Langmuir and ion acoustic waves in a plasma. We also obtain some properties of the Gibbs state, by both analytic and numerical methods, as N and the temperature are varied.
Non-Linear Dynamics of AN ELASTO-PLASTIC Oscillator with Kinematic and Isotropic Hardening
NASA Astrophysics Data System (ADS)
Savi, M. A.; Pacheco, P. M. C. L.
1997-10-01
This contribution reports on a dynamic analysis of an elasto-plastic oscillator. Kinematic and isotropic hardening are considered. The equations of motion have five state variable associated with complementary conditions. System dynamics is treated by performing a split in phase space in two parts. This split is suggested by an analysis of the equations of motion near equilibrium points and permits conclusions about high dimensional dynamical system by analyzing subspaces with lower dimension. This physical consideration is in close agreement with the operator split technique used for the numerical solution. Some numerical results are shown for free and forced vibrations of the oscillator with kinematic, isotropic and kinematic/isotropic hardening.
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.
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. PMID:26821264
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.
On Galilean invariance and nonlinearity in electrodynamics and quantum mechanics
NASA Astrophysics Data System (ADS)
Goldin, Gerald A.; Shtelen, Vladimir M.
2001-02-01
Recent experimental results such as those on slow light heighten interest in nonlinear Maxwell theories. We obtain Galilei covariant equations for electromagnetism by allowing special nonlinearities in the constitutive equations only, keeping Maxwell's equations unchanged. Combining these with linear or nonlinear Schrödinger equations, e.g., as proposed by Doebner and Goldin, yields a consistent, nonlinear, Galilean Schrödinger-Maxwell electrodynamics.
Numerical computation of nonlinear normal modes in mechanical engineering
NASA Astrophysics Data System (ADS)
Renson, L.; Kerschen, G.; Cochelin, B.
2016-03-01
This paper reviews the recent advances in computational methods for nonlinear normal modes (NNMs). Different algorithms for the computation of undamped and damped NNMs are presented, and their respective advantages and limitations are discussed. The methods are illustrated using various applications ranging from low-dimensional weakly nonlinear systems to strongly nonlinear industrial structures.
The Slow Oscillation in Cortical and Thalamic Networks: Mechanisms and Functions
Neske, Garrett T.
2016-01-01
During even the most quiescent behavioral periods, the cortex and thalamus express rich spontaneous activity in the form of slow (<1 Hz), synchronous network state transitions. Throughout this so-called slow oscillation, cortical and thalamic neurons fluctuate between periods of intense synaptic activity (Up states) and almost complete silence (Down states). The two decades since the original characterization of the slow oscillation in the cortex and thalamus have seen considerable advances in deciphering the cellular and network mechanisms associated with this pervasive phenomenon. There are, nevertheless, many questions regarding the slow oscillation that await more thorough illumination, particularly the mechanisms by which Up states initiate and terminate, the functional role of the rhythmic activity cycles in unconscious or minimally conscious states, and the precise relation between Up states and the activated states associated with waking behavior. Given the substantial advances in multineuronal recording and imaging methods in both in vivo and in vitro preparations, the time is ripe to take stock of our current understanding of the slow oscillation and pave the way for future investigations of its mechanisms and functions. My aim in this Review is to provide a comprehensive account of the mechanisms and functions of the slow oscillation, and to suggest avenues for further exploration. PMID:26834569
Suppression of nonlinear oscillations in combustors with partial length acoustic liners
NASA Technical Reports Server (NTRS)
Espander, W. R.; Mitchell, C. E.; Baer, M. R.
1975-01-01
An analytical model is formulated for a three-dimensional nonlinear stability problem in a rocket motor combustion chamber. The chamber is modeled as a right circular cylinder with a short (multi-orifice) nozzle, and an acoustic linear covering an arbitrary portion of the cylindrical periphery. The combustion is concentrated at the injector and the gas flow field is characterized by a mean Mach number. The unsteady combustion processes are formulated using the Crocco time lag model. The resulting equations are solved using a Green's function method combined with numerical evaluation techniques. The influence of acoustic liners on the nonlinear waveforms is predicted. Nonlinear stability limits and regions where triggering is possible are also predicted for both lined and unlined combustors in terms of the combustion parameters.
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.
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
A Realtime Active Feedback Control System For Coupled Nonlinear Chemical Oscillators
NASA Astrophysics Data System (ADS)
Tompkins, Nathan; Fraden, Seth
2012-02-01
We study the manipulation and control of oscillatory networks. As a model system we use an emulsion of Belousov-Zhabotinsky (BZ) oscillators packed on a hexagonal lattice. Each drop is observed and perturbed by a Programmable Illumination Microscope (PIM). The PIM allows us to track individual BZ oscillators, calculate the phase and order parameters of every drop, and selectively perturb specific drops with photo illumination, all in realtime. To date we have determined the native attractor patterns for drops in 1D arrays and 2D hexagonal packing as a function of coupling strength as well as determined methods to move the system from one attractor basin to another. Current work involves implementing these attractor control methods with our experimental system and future work will likely include implementing a model neural network for use with photo controllable BZ emulsions.
Switching mechanism of sensor-motor coordination through an oscillator network model.
Funato, Tetsuro; Kurabayashi, Daisuke; Nara, Masahito; Aonuma, Hitoshi
2008-06-01
Insects have small brains, but their behavior is highly adaptive; this leads us to conclude that their brains possess a simple adaptation mechanism. This paper focuses on the pheromone processing of crickets, varying their aggression depending on their global neural connection, and proposes a behavior selection mechanism that can be controlled by network transformation. The controller is composed of an oscillator network, and its behavior is decided by the synchrony of organic oscillations. Furthermore, every network component corresponds to a certain brain module. A model is realized by using an analog circuit, and it is applied to a simple robot that displays the behavior of a real insect. PMID:18558540
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.
NASA Astrophysics Data System (ADS)
King, J. R. C.; Ziolkowski, A. M.; Ruffert, M.
2015-03-01
We have developed a new boundary condition for finite volume simulations of oscillating bubbles. Our method uses an approximation to the motion outside the domain, based on the solution at the domain boundary. We then use this approximation to apply boundary conditions by defining incoming characteristic waves at the domain boundary. Our boundary condition is applicable in regions where the motion is close to spherically symmetric. We have tested our method on a range of one- and two-dimensional test cases. Results show good agreement with previous studies. The method allows simulations of oscillating bubbles for long run times (5 ×105 time steps with a CFL number of 0.8) on highly truncated domains, in which the boundary condition may be applied within 0.1% of the maximum bubble radius. Conservation errors due to the boundary conditions are found to be of the order of 0.1% after 105 time steps. The method significantly reduces the computational cost of fixed grid finite volume simulations of oscillating bubbles. Two-dimensional results demonstrate that highly asymmetric bubble features, such as surface instabilities and the formation of jets, may be captured on a small domain using this boundary condition.
Nonlinear oscillations of a sessile drop on a hydrophobic surface induced by ac electrowetting
NASA Astrophysics Data System (ADS)
Lee, Joohee; Park, Jun Kwon; Hong, Jiwoo; Lee, Sang Joon; Kang, Kwan Hyoung; Hwang, Hyung Ju
2014-09-01
We examine the nature of ac electrowetting (EW)-driven axisymmetric oscillations of a sessile water drop on a dielectric substrate. In ac EW, small-amplitude oscillations of a drop differ from the Rayleigh linear modes of freely oscillating drops. In this paper, we demonstrate that changes in the time-averaged contact angle of the sessile drop attributed to the presence of an electric field and a solid substrate mainly caused this discrepancy. We combine the domain perturbation method with the Lindsted-Poincaré method to derive an asymptotic formula for resonant frequency. Theoretical analysis shows that the resonant frequency is a function of the time-averaged contact angle. Each mode of the resonance frequency is a linear function of ɛ1, which is the magnitude of the cosine of the time-averaged contact angle. The most dominant mode in this study, that is, the fundamental mode n =2, decreases linearly with ɛ1. The results of the theoretical model are compared with those of both the experiments and numerical simulations. The average resonant frequency deviation between the perturbation solutions and numerical simulations is 4.3%, whereas that between the perturbation solutions and the experiments is 1.8%.
Gottschall, Thomas; Meyer, Tobias; Schmitt, Michael; Popp, Jürgen; Limpert, Jens; Tünnermann, Andreas
2015-09-01
A novel concept for an optical parametric oscillator based on four-wave mixing (FOPO) in an optical fiber is presented. This setup has the ability of generating highly chirped signal and idler pulses with compressed pulse durations below 600 fs and pulse energies of up to 250 nJ. At a fixed pump wavelength of 1040 nm, the emerging signal and idler wavelengths can be easily tuned between 867 to 918 nm and 1200 to 1300 nm, respectively, only by altering the cavity length. With compressed peak powers >100 kW and a repetition rate of only 785 kHz, this source provides tunable intense ultra-short pulses at moderate average powers. This setup constitutes a stable, simple and in many ways superior alternative to bulk state-of-the-art OPO light converters for demanding biomedical applications and non-linear microspectroscopy. PMID:26368487
NASA Astrophysics Data System (ADS)
Li, Zhen-Bo; Tang, Jia-Shi; Cai, Ping
2014-12-01
An intrinsic extension of Padé approximation method, called the generalized Padé approximation method, is proposed based on the classic Padé approximation theorem. According to the proposed method, the numerator and denominator of Padé approximant are extended from polynomial functions to a series composed of any kind of function, which means that the generalized Padé approximant is not limited to some forms, but can be constructed in different forms in solving different problems. Thus, many existing modifications of Padé approximation method can be considered to be the special cases of the proposed method. For solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators, two novel kinds of generalized Padé approximants are constructed. Then, some examples are given to show the validity of the present method. To show the accuracy of the method, all solutions obtained in this paper are compared with those of the Runge—Kutta method.
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.
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.
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 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 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.
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.
NASA Astrophysics Data System (ADS)
Meister, S.; Mecklenburg, M.; Gramich, V.; Stockburger, J. T.; Ankerhold, J.; Kubala, B.
2015-11-01
Motivated by recent experiments in which a voltage-biased Josephson junction is placed in series with a resonator, the classical dynamics of the circuit is studied in various domains of parameter space. This problem can be mapped onto the dissipative motion of a single degree of freedom in a nonlinear time-dependent potential, where in contrast to conventional settings the nonlinearity appears in the driving while the static potential is purely harmonic. For long times the system approaches steady states which are analyzed in the underdamped regime over the full range of driving parameters including the fundamental resonance as well as higher harmonics and subharmonics. Observables such as the dc-Josephson current and the radiated microwave power give direct information about the underlying dynamics covering phenomena such as bifurcations, irregular motion, and up- and down-conversion. Due to their tunability, present and future setups provide versatile platforms to explore the changeover from linear response to strongly nonlinear behavior in driven dissipative systems under well defined conditions.
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…
Tu, Hung-Ya; Chen, Yu-Jiun; McQuiston, Adam R; Chiao, Chuan-Chin; Chen, Ching-Kang
2015-01-01
It has been shown in rd1 and rd10 models of photoreceptor degeneration (PD) that inner retinal neurons display spontaneous and rhythmic activities. Furthermore, the rhythmic activity has been shown to require the gap junction protein connexin 36, which is likely located in AII amacrine cells (AII-ACs). In the present study, an autosomal dominant PD model called rhoΔCTA, whose rods overexpress a C-terminally truncated mutant rhodopsin and degenerate with a rate similar to that of rd1, was used to investigate the generality and mechanisms of heightened inner retinal activity following PD. To fluorescently identify cholinergic starburst amacrine cells (SACs), the rhoΔCTA mouse was introduced into a combined ChAT-IRES-Cre and Ai9 background. In this mouse, we observed excitatory postsynaptic current (EPSC) oscillation and non-rhythmic inhibitory postsynaptic current (IPSC) in both ON- and OFF-SACs. The IPSCs were more noticeable in OFF- than in ON-SACs. Similar to reported retinal ganglion cell (RGC) oscillation in rd1 mice, EPSC oscillation was synaptically driven by glutamate and sensitive to blockade of NaV channels and gap junctions. These data suggest that akin to rd1 mice, AII-AC is a prominent oscillator in rhoΔCTA mice. Surprisingly, OFF-SAC but not ON-SAC EPSC oscillation could readily be enhanced by GABAergic blockade. More importantly, weakening the AII-AC gap junction network by activating retinal dopamine receptors abolished oscillations in ON-SACs but not in OFF-SACs. Furthermore, the latter persisted in the presence of flupirtine, an M-type potassium channel activator recently reported to dampen intrinsic AII-AC bursting. These data suggest the existence of a novel oscillation mechanism in mice with PD. PMID:26793064
Tu, Hung-Ya; Chen, Yu-Jiun; McQuiston, Adam R.; Chiao, Chuan-Chin; Chen, Ching-Kang
2016-01-01
It has been shown in rd1 and rd10 models of photoreceptor degeneration (PD) that inner retinal neurons display spontaneous and rhythmic activities. Furthermore, the rhythmic activity has been shown to require the gap junction protein connexin 36, which is likely located in AII amacrine cells (AII-ACs). In the present study, an autosomal dominant PD model called rhoΔCTA, whose rods overexpress a C-terminally truncated mutant rhodopsin and degenerate with a rate similar to that of rd1, was used to investigate the generality and mechanisms of heightened inner retinal activity following PD. To fluorescently identify cholinergic starburst amacrine cells (SACs), the rhoΔCTA mouse was introduced into a combined ChAT-IRES-Cre and Ai9 background. In this mouse, we observed excitatory postsynaptic current (EPSC) oscillation and non-rhythmic inhibitory postsynaptic current (IPSC) in both ON- and OFF-SACs. The IPSCs were more noticeable in OFF- than in ON-SACs. Similar to reported retinal ganglion cell (RGC) oscillation in rd1 mice, EPSC oscillation was synaptically driven by glutamate and sensitive to blockade of NaV channels and gap junctions. These data suggest that akin to rd1 mice, AII-AC is a prominent oscillator in rhoΔCTA mice. Surprisingly, OFF-SAC but not ON-SAC EPSC oscillation could readily be enhanced by GABAergic blockade. More importantly, weakening the AII-AC gap junction network by activating retinal dopamine receptors abolished oscillations in ON-SACs but not in OFF-SACs. Furthermore, the latter persisted in the presence of flupirtine, an M-type potassium channel activator recently reported to dampen intrinsic AII-AC bursting. These data suggest the existence of a novel oscillation mechanism in mice with PD. PMID:26793064
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
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).
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)
Mechanical oscillator with optical cavity read-out for high sensitivity force detection
NASA Astrophysics Data System (ADS)
Michels, Thomas; Miao, Houxun; Srinivasan, Kartik; Zou, Jie; Rangelow, Ivo W.; Aksyuk, Vladimir
2013-03-01
Incorporating cavity optomechanics into micro and nano-scale electro mechanical systems (MEMS, NEMS) is a topic of high interest since it enables measurement of mechanical motion near the fundamental limits of precision imposed by quantum mechanics. We have developed an on-chip cavity optomechanical transducer platform that combines high bandwidth and sensitivity near the standard quantum limit with compactness, robustness, small size, and potential for low cost batch fabrication inherent in MEMS. We present a novel MEMS transducer with a fiber pigtailed on-chip Si microdisk optical cavity used to readout the motion of a mechanical oscillator probe. The SiN torsional oscillator can be excited by an electrical signal supplied to an integrated thermal actuator. The oscillator is evanescently coupled to a high-Q whispering gallery mode of the optical cavity and the motion is detected by measuring the resonance frequency shift of the mode. One side of the oscillator probe overhangs the edge of the chip, where it can be easily coupled to a variety of off-chip samples and physical systems of interest. A 10 um long probe is currently designed to have a stiffness of 1 N/m to 3 N/m and a resonance frequency of 100 kHz to 500 kHz, while the design can be easily and broadly tailored for specific sensing applications.
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. PMID:26396646
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.
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.
Non-linear saturation mechanism of electron temperature gradient modes
Tokluoglu, E. K.; Sokolov, V.; Sen, A. K.
2012-10-15
The electron temperature gradient (ETG) mode is a very plausible candidate to explain the large electron particle transport and thermal conduction. Production and identification of slab ETG modes and measurement electron transport have been already reported [X. Wei, V. Sokolov, and A. K. Sen, Phys. Plasmas 17, 042108 (2010); V. Sokolov and A. K. Sen, Phys. Rev. Lett. (2011)]. Now, we develop a theoretical model of non-linear saturation mechanism of ETG mode based on the three wave coupling of an unstable high frequency ETG mode with a damped ETG radial harmonic and a damped ion acoustic (IA) mode. Bicoherence analysis of Columbia linear machine (CLM) data show coupling between ETG modes ({approx}2.4 MHz) and a low frequency mode ({approx}50 kHz). The large damping drive of the ETG radial harmonic accompanied by the smaller but finite damping of the IA mode presents an energy sink for the unstable ETG mode, thus causing saturation. This model predicts a saturation level of {approx}10% and agrees with the observed levels of ETG modes in the CLM.
NASA Astrophysics Data System (ADS)
Josephine Usha, R.; Sagayaraj, P.; Joseph, V.
2014-12-01
The highly efficient nonlinear optical single crystal of manganese mercury thiocyanate has been grown from slow evaporation solvent technique. The second harmonic generation and optical transmittance of the grown crystal are studied by Kurtz and Perry powder technique and spectroscopic absorbance spectrum. Mechanical behaviour is analyzed using Vickers microhardness test. The dielectric response of the grown crystal is studied as a function of the temperature and the results are discussed. Further, electronic properties such as plasma energy, Penngap, Fermi energy and electronic polarizability are evaluated. Third order nonlinear optical studies are performed using by single beam Z-scan technique using Nd:YAG laser and parameters such as nonlinear refractive index n2, absorption co-efficient β and nonlinear optical susceptibility χ(3) are evaluated for the grown crystal. The surface of the grown crystal is analyzed with field emission scanning electron microscope and atomic force microscope analyses.
Josephine Usha, R; Sagayaraj, P; Joseph, V
2014-12-10
The highly efficient nonlinear optical single crystal of manganese mercury thiocyanate has been grown from slow evaporation solvent technique. The second harmonic generation and optical transmittance of the grown crystal are studied by Kurtz and Perry powder technique and spectroscopic absorbance spectrum. Mechanical behaviour is analyzed using Vickers microhardness test. The dielectric response of the grown crystal is studied as a function of the temperature and the results are discussed. Further, electronic properties such as plasma energy, Penngap, Fermi energy and electronic polarizability are evaluated. Third order nonlinear optical studies are performed using by single beam Z-scan technique using Nd:YAG laser and parameters such as nonlinear refractive index n2, absorption co-efficient β and nonlinear optical susceptibility χ((3)) are evaluated for the grown crystal. The surface of the grown crystal is analyzed with field emission scanning electron microscope and atomic force microscope analyses. PMID:24945865
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
Armitage, C.A.; Mastorakos, E.; Cant, R.S.; Balachandran, R.
2006-08-15
Acoustically forced lean premixed turbulent bluff-body stabilized flames are investigated using turbulent combustion CFD. The calculations simulate aspects of the experimental investigation by Balachandran et al. [R. Balachandran, B. Ayoola, C. Kaminski, A. Dowling, E. Mastorakos, Combust. Flame 143 (2005) 37-55] and focus on the amplitude dependence of the flame response. For the frequencies of interest in this investigation an unsteady Reynolds-averaged Navier-Stokes (URANS) approach is appropriate. The combustion is represented using a modified laminar flamelet approach with an algebraic representation of the flame surface density. The predictions are compared with flame surface density (FSD) and OH* chemiluminescence measurements. In the experiments the response of the flame has been quantified by means of a number of single-frequency, amplitude-dependent transfer functions. The predicted flame shape and position are in good agreement with the experiment. The dynamic response of the flame to inlet velocity forcing is also well captured by the calculations. At moderate frequencies nonlinear behavior of the transfer functions is observed as the forcing amplitude is increased. In the experiments this nonlinearity was attributed in part to the rollup of the reacting shear layer into vortices and in part to the collision of the inner and outer flame sheets. This transition to nonlinearity is also observed in the transfer functions obtained from the predictions. Furthermore, the vortex shedding and flame-sheet collapse may be seen in snapshots of the predicted flow field taken throughout the forcing cycle. The URANS methodology successfully predicts the behavior of the forced premixed turbulent flames and captures the effects of saturation in the transfer function of the response of the heat release to velocity fluctuations. (author)
NASA Astrophysics Data System (ADS)
Weisberg, H.; Glenn, J. W.
1980-03-01
Nonlinear effects in resonant slow extraction from a synchrotron are such that a displacement in angle by means of a thin septum deflector can result in a displacement in position an integral number of betatron wavelengths downstream. This fact is exploited in the choice of location for an electrostatic septum to improve the extraction efficiency of the Brookhaven AGS. A curved septum, operating at 80 kV cm -1, is used. The extraction efficiency is measured by a loss monitor technique. The measured efficiency is 97%, compared with 85% without the electrostatic septum.
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
NASA Astrophysics Data System (ADS)
Huang, Pu; Zhou, Jingwei; Zhang, Liang; Hou, Dong; Lin, Shaochun; Deng, Wen; Meng, Chao; Duan, Changkui; Ju, Chenyong; Zheng, Xiao; Xue, Fei; Du, Jiangfeng
2016-05-01
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.
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. PMID:27225287
On the analysis of labyrinth seal flow induced vibration by Oscillating Fluid Mechanics Method
NASA Astrophysics Data System (ADS)
Chen, Zuoyi; Jing, Youhao; Sun, Yongzhong
1994-12-01
A numerical model and a solution method to analyze the labyrinth seal flow induced vibration by Oscillating Fluid Mechanics Method (OFMM) are presented in this paper, including the basic equations and solution procedure to determine the oscillating velocity, pressure and the dynamic characteristic coefficients of Labyrinth seal such as the stiffness coefficients and damping coefficients. The results show that this method has the advantages of both less time consuming and high accuracy. In addition, it can be applied to the field diagnosis of the vibration of the axis of turbomachinery system.
Brinkmann, Maximilian; Janfrüchte, Sarah; Hellwig, Tim; Dobner, Sven; Fallnich, Carsten
2016-05-15
We present a fiber-based optical parametric oscillator (FOPO) pumped by a fiber-coupled laser diode. The FOPO consisted of a photonic crystal fiber to convert the pump pulses via four-wave mixing and a dispersive resonator formed by a single-mode fiber. Via dispersion filtering, output pulses with a bandwidth of about 3 nm, a temporal duration of about 8 ps and a pulse energy of up to 22 nJ could be generated. By changing the repetition frequency of the pump laser diode by about ±1 kHz, the wavelength of the output pulses could be tuned between 1130 and 1310 nm within 8 μs, without the need to change the length of the resonator. Therewith, the FOPO should especially be suited for hyperspectral imaging, while its all-electronic control constitutes a promising approach to a turnkey and alignment-free light source. PMID:27176960
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
Heulitt, Mark J; Jones, Stacie M; Holt, Shirley J; Thurman, Tracy L; Jo, Chan-Hee; Simpson, Pippa M
2008-09-01
The ability to successfully intubate the trachea of rats repeatedly over time, recover them, and perform repeated measures of changes in respiratory mechanics is important. The authors performed experiments utilizing 2 groups of rats at various ages in their development. Rats in the single-measurement group were studied at 1 age only. Rats in the repeated-measurement group were studied at each age point over time. Measurements of respiratory mechanics were made utilizing a forced-oscillation technique. We found no differences in respiratory mechanics between the 2 groups. Our results demonstrate that developing rats can be studied longitudinally to illustrate maturational changes in respiratory mechanics. PMID:18716927
An acoustic levitation technique for the study of nonlinear oscillations of gas bubbles in liquids
NASA Astrophysics Data System (ADS)
Young, D. A.; Crum, L. A.
1983-08-01
A technique of acoustic levitation was developed for the study of individual gas bubbles in a liquid. Isopropyl alcohol and a mixture of glycerine and water (33-1/3% glycerine by volume) were the two liquids used in this research. Bubbles were levitated near the acoustic pressure antinode of an acoustic wave in the range of 20-22 kHz. Measurements were made of the levitation number as a function of the normalized radius of the bubbles. The levitation number is the ratio of the hydrostatic pressure gradient to the acoustic pressure gradient. These values were then compared to a nonlinear theory. Results were very much in agreement except for the region near the n=2 harmonic. An explanation for the discrepancy between theory and experiment appears to lie in the polytropic exponent associated with the gas in the interior of the bubble.
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.
Nonlinear oscillations of compact stars in the vicinity of the maximum mass configuration
NASA Astrophysics Data System (ADS)
Brillante, A.; Mishustin, I. N.
2015-07-01
We solve the dynamical GR equations for the spherically symmetric evolution of compact stars in the vicinity of the maximum mass, for which instability sets in according to linear perturbation theory. The calculations are done with the analytical Zeldovich-like EOS P=a≤ft(ρ-ρ_0\\right) and with the TM1 parametrisation of the RMF model. The initial configurations for the dynamical calculations are represented by spherical stars with equilibrium density profile, which are perturbed by either i) an artificially added inward velocity field proportional to the radial coordinate, or ii) a rarefaction corresponding to a static and expanded star. These configurations are evolved using a one-dimensional GR hydro code for ideal and barotropic fluids. Depending on the initial conditions we obtain either stable oscillations or the collapse to a black hole. The minimal amplitude of the perturbation, needed to trigger gravitational collapse is evaluated. The approximate independence of this energy on the type of perturbation is pointed out. At the threshold we find type-I critical behaviour for all stellar models considered and discuss the dependence of the time scaling exponent on the baryon mass and EOS.
NASA Astrophysics Data System (ADS)
Liu, Ya; Ma, Yongting; Bhattacharya, Amitabh; Kuksenok, Olga; He, Ximin; Aizenberg, Joanna; Balazs, Anna
2013-11-01
In biomimetics, designing an effective ``catch and release'' device for the selective removal of target species from the surrounding solution is critical for developing autonomous sensors and sorters. Using computational simulation, we model an array of oscillating fins that are tethered on the floor of a microchannel and immersed in a binary-fluid stream. During the oscillation, the fins with the specific chemical wetting reach the upper fluid when they are upright and are entirely within the lower stream when they are tilted. We introduce specific adhesive interactions between the fins and particulates in the solution and determine conditions where the oscillating fins can selectively bind (``catch'') target nanoparticles within the upper fluid stream and then release these particles into the lower stream. We isolate the effects of chemical wetting on the fins (e.g., wetting contact angle between fins and fluid) and mechanical parameters (e.g., frequency of fins' oscillations) that lead to the efficient extraction of target species from the upper stream and placement into the lower fluid. Our understanding provides fundamental insights into the system's complex dynamics and mechanism for detection, separation, and purification of multi-component mixtures.
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.
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. PMID:23187402
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
Neural mechanisms of evoked oscillations: stability and interaction with transient events.
Moratti, Stephan; Clementz, Brett A; Gao, Yuan; Ortiz, Tomás; Keil, Andreas
2007-12-01
There is increasing evidence that early event-related potentials are a result of phase alignment of ongoing background oscillations of the electroencephalogram rather than additive amplitude modulation. Steady state visual-evoked potentials (ssVEPs) can be recorded using an intensity modulated stimulus, resulting in an evoked brain response at a known frequency, i.e. the stimulation frequency. Given this property, the ssVEP is ideally suited for examining the relationship between single-trial fluctuations in phase/amplitude and the evoked brain potential resulting from averaging across trials. To address this issue, the current study investigated the contribution of single trial power and intertrial phase locking to ssVEP generation by presenting a peripheral flicker. Further, transient stimuli were presented during flicker and at three increasing latency lags following flicker offset to examine (1) to what extent a stimulus can disturb the ssVEP oscillation and (2) how phase alignment during P1-N1-P2 time windows is affected during presence of evoked oscillations. The former assessment evaluates the stability of ssVEPs and the latter the phase alignment processes to transient stimuli under experimentally induced background oscillations. We observed that ssVEPs are a result of phase alignment rather than single trial amplitude modulation. In addition, ssVEP oscillations were not disturbed by transient stimuli. Finally, phase alignment in P1-N1-P2 time windows was distorted during and shortly after steady state stimulation. We conclude that ssVEPs represent strongly phase locked oscillations sharing the same generation mechanisms as early evoked potentials. PMID:17274017
Cavity-mediated coupling of mechanical oscillators limited by quantum back-action
NASA Astrophysics Data System (ADS)
Spethmann, Nicolas; Kohler, Jonathan; Schreppler, Sydney; Buchmann, Lukas; Stamper-Kurn, Dan M.
2016-01-01
A complex quantum system can be constructed by coupling simple elements. For example, trapped-ion or superconducting quantum bits may be coupled by Coulomb interactions, mediated by the exchange of virtual photons. Alternatively, quantum objects can be made to emit and exchange real photons, providing either unidirectional coupling in cascaded geometries, or bidirectional coupling that is particularly strong when both objects are placed within a common electromagnetic resonator. However, in such an open system, the capacity of a coupling channel to convey quantum information or generate entanglement may be compromised by photon loss. Here, we realize phase-coherent interactions between two addressable, spatially separated, near-ground-state mechanical oscillators within a driven optical cavity. We observe the quantum back-action noise imparted by the optical coupling resulting in correlated mechanical fluctuations of the two oscillators. Our results illustrate challenges and opportunities of coupling quantum objects with light for applications of quantum cavity optomechanics.
The Bogoliubov-de Gennes system, the AKNS hierarchy, and nonlinear quantum mechanical supersymmetry
Correa, Francisco; Dunne, Gerald V.; Plyushchay, Mikhail S.
2009-12-15
We show that the Ginzburg-Landau expansion of the grand potential for the Bogoliubov-de Gennes Hamiltonian is determined by the integrable nonlinear equations of the AKNS hierarchy, and that this provides the natural mathematical framework for a hidden nonlinear quantum mechanical supersymmetry underlying the dynamics.
Measurement-based control of a mechanical oscillator at its thermal decoherence rate
NASA Astrophysics Data System (ADS)
Wilson, D. J.; Sudhir, V.; Piro, N.; Schilling, R.; Ghadimi, A.; Kippenberg, T. J.
2015-08-01
In real-time quantum feedback protocols, the record of a continuous measurement is used to stabilize a desired quantum state. Recent years have seen successful applications of these protocols in a variety of well-isolated micro-systems, including microwave photons and superconducting qubits. However, stabilizing the quantum state of a tangibly massive object, such as a mechanical oscillator, remains very challenging: the main obstacle is environmental decoherence, which places stringent requirements on the timescale in which the state must be measured. Here we describe a position sensor that is capable of resolving the zero-point motion of a solid-state, 4.3-megahertz nanomechanical oscillator in the timescale of its thermal decoherence, a basic requirement for real-time (Markovian) quantum feedback control tasks, such as ground-state preparation. The sensor is based on evanescent optomechanical coupling to a high-Q microcavity, and achieves an imprecision four orders of magnitude below that at the standard quantum limit for a weak continuous position measurement--a 100-fold improvement over previous reports--while maintaining an imprecision-back-action product that is within a factor of five of the Heisenberg uncertainty limit. As a demonstration of its utility, we use the measurement as an error signal with which to feedback cool the oscillator. Using radiation pressure as an actuator, the oscillator is cold damped with high efficiency: from a cryogenic-bath temperature of 4.4 kelvin to an effective value of 1.1 +/- 0.1 millikelvin, corresponding to a mean phonon number of 5.3 +/- 0.6 (that is, a ground-state probability of 16 per cent). Our results set a new benchmark for the performance of a linear position sensor, and signal the emergence of mechanical oscillators as practical subjects for measurement-based quantum control.
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.
Breuer; Huber; Petruccione
2000-05-01
The dynamics of periodically driven quantum systems coupled to a thermal environment is investigated. The interaction of the system with the external coherent driving field is taken into account exactly by making use of the Floquet picture. Treating the coupling to the environment within the Born-Markov approximation one finds a Pauli-type master equation for the diagonal elements of the reduced density matrix in the Floquet representation. The stationary solution of the latter yields a quasistationary, time-periodic density matrix which describes the long-time behavior of the system. Taking the example of a periodically driven particle in a box, the stationary solution is determined numerically for a wide range of driving amplitudes and temperatures. It is found that the quasistationary distribution differs substantially from a Boltzmann-type distribution at the temperature of the environment. For large driving fields it exhibits a plateau region describing a nearly constant population of a certain number of Floquet states. This number of Floquet states turns out to be nearly independent of the temperature. The plateau region is sharply separated from an exponential tail of the stationary distribution which expresses a canonical Boltzmann-type distribution over the mean energies of the Floquet states. These results are explained in terms of the structure of the matrix of transition rates for the dissipative quantum system. Investigating the corresponding classical, nonlinear Hamiltonian system, one finds that in the semiclassical range essential features of the quasistationary distribution can be understood from the structure of the underlying classical phase space. PMID:11031530
Martens, S; Hennig, D; Fugmann, S; Schimansky-Geier, L
2008-10-01
We study the Langevin dynamics of a two-dimensional discrete oscillator chain absorbed on a periodic substrate and subjected to an external localized point force. Going beyond the commonly used harmonic bead-spring model, we consider a nonlinear Morse interaction between the next-nearest neighbors. We focus interest on the activation of directed motion instigated by thermal fluctuations and the localized point force. In this context the local transition states are identified and the corresponding activation energies are calculated. It is found that the transport of the chain in point force direction is determined by stepwise escapes of a single unit or segments of the chain due to the existence of multiple locally stable attractors. The nonvanishing net current of the chain is quantitatively assessed by the value of the mobility of the center of mass. It turns out that the latter as a function of the ratio of the competing length scales of the system, that is the period of the substrate potential and the equilibrium distance between two chain units, shows a resonance behavior. More precisely there exists a set of optimal parameter values maximizing the mobility. Interestingly, the phenomenon of negative resistance is found, i.e., the mobility possesses a minimum at a finite value of the strength of the thermal fluctuations for a given overcritical external driving force. PMID:18999393
NASA Astrophysics Data System (ADS)
Popov, Pavel; Sideris, Athanasios; Sirignano, William
2014-11-01
We examine the non-linear dynamics of the transverse modes of combustion-driven acoustic instability in a liquid-propellant rocket engine. Triggering can occur, whereby small perturbations from mean conditions decay, while larger disturbances grow to a limit-cycle of amplitude that may compare to the mean pressure. For a deterministic perturbation, the system is also deterministic, computed by coupled finite-volume solvers at low computational cost for a single realization. The randomness of the triggering disturbance is captured by treating the injector flow rates, local pressure disturbances, and sudden acceleration of the entire combustion chamber as random variables. The combustor chamber with its many sub-fields resulting from many injector ports may be viewed as a multi-scale complex system wherein the developing acoustic oscillation is the emergent structure. Numerical simulation of the resulting stochastic PDE system is performed using the polynomial chaos expansion method. The overall probability of unstable growth is assessed in different regions of the parameter space. We address, in particular, the seven-injector, rectangular Purdue University experimental combustion chamber. In addition to the novel geometry, new features include disturbances caused by engine acceleration and unsteady thruster nozzle flow.
NASA Astrophysics Data System (ADS)
Liu, Ya; Kuksenok, Olga; Bhattacharya, Amitabh; Ma, Yongting; He, Ximin; Aizenberg4, Joanna; Balazs, Anna
2014-03-01
In biomimetics, designing an effective ``catch and release'' device for the selective removal of target species from the surrounding solution is critical for developing autonomous sensors and sorters. Using computer simulations, we model an array of oscillating fins that are tethered on the floor of a microchannel and immersed in a mixture of binary fluid stream and binary nanoparticles. During the oscillation, the fins with the specific chemical wetting reach the upper fluid when they are upright and are entirely immersed within the lower stream when they are tilted. We introduce specific interaction between the fins and particulates in the solution and determine conditions where the oscillating fins can selectively ?catch? target nanoparticles within the upper fluid stream and then release these particles into the lower stream. We isolate the effects of wetting contact angle between fins and fluid and the mode of fins' oscillations that lead to the efficient extraction of target species from the upper stream and their placement into the lower fluid. These studies provide fundamental insights into the system's complex dynamics and mechanism for detection, separation, and purification of multi-component mixtures.
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.
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.
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)
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.
NASA Astrophysics Data System (ADS)
Yasuda, Masaaki; Takei, Kuniharu; Arie, Takayuki; Akita, Seiji
2016-03-01
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.
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
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
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.
Jing, Da; Baik, Andrew D.; Lu, X. Lucas; Zhou, Bin; Lai, Xiaohan; Wang, Liyun; Luo, Erping; Guo, X. Edward
2014-01-01
Osteocytes have been hypothesized to be the major mechanosensors in bone. How in situ osteocytes respond to mechanical stimuli is still unclear because of technical difficulties. In vitro studies have shown that osteocytes exhibited unique calcium (Ca2+) oscillations to fluid shear. However, whether this mechanotransduction phenomenon holds for in situ osteocytes embedded within a mineralized bone matrix under dynamic loading remains unknown. Using a novel synchronized loading/imaging technique, we successfully visualized in real time and quantified Ca2+ responses in osteocytes and bone surface cells in situ under controlled dynamic loading on intact mouse tibia. The resultant fluid-induced shear stress on the osteocyte in the lacunocanalicular system (LCS) was also quantified. Osteocytes, but not surface cells, displayed repetitive Ca2+ spikes in response to dynamic loading, with spike frequency and magnitude dependent on load magnitude, tissue strain, and shear stress in the LCS. The Ca2+ oscillations were significantly reduced by endoplasmic reticulum (ER) depletion and P2 purinergic receptor (P2R)/phospholipase C (PLC) inhibition. This study provides direct evidence that osteocytes respond to in situ mechanical loading by Ca2+ oscillations, which are dependent on the P2R/PLC/inositol trisphosphate/ER pathway. This study develops a novel approach in skeletal mechanobiology and also advances our fundamental knowledge of bone mechanotransduction.—Jing, D., Baik, A. D., Lu, X. L., Zhou, B., Lai, X., Wang, L., Luo, E., Guo, X. E. In situ intracellular calcium oscillations in osteocytes in intact mouse long bones under dynamic mechanical loading. PMID:24347610
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.
NASA Astrophysics Data System (ADS)
Castellanos-Gomez, A.
2013-01-01
A simple strobe setup with the potential to study higher-order eigenmodes and multifrequency oscillations in micromechanical resonators is described. It requires standard equipment, commonly found in many laboratories, and it can thus be employed for public demonstrations of mechanical resonances. Moreover, the work presented here can be used by undergraduate students and/or teachers to prepare practical work in laboratory courses at physics or engineering universities. The dynamics of a micromachined cantilever is analysed as an example. In fact, using our stroboscopic setup, the first and second flexural eigenmodes, as well as a multifrequency oscillation composed by a superposition of both modes, have been successfully filmed with a conventional optical microscope equipped with a digital camera.
NASA Astrophysics Data System (ADS)
Sudhir, Vivishek; Wilson, Dalziel; Schilling, Ryan; Schuetz, Hendrik; Nunnenkamp, Andreas; Kippenberg, Tobias
Measurement-based feedback provides an avenue to study the delicate interplay between the quantum correlations established during the process of measurement, and their progressive obfuscation when exposed to uncorrelated noise in the form of fundamental quantum fluctuations in the feedback path. Here we demonstrate this tradeoff using a feedback strategy whose objective is to cool a nano-mechanical oscillator close to its ground state. The correlations established due to the measurement are revealed in the appearance of motional sideband asymmetry. The latter, faithfully measured using an optical heterodyne interferometer with an imprecision ~17 dB below that at the standard quantum limit, increases to 6% as the oscillator is feedback cooled to an occupation of 15 phonons. Further increase in the gain of the feedback loop leads to a decrease in the asymmetry. This is due to the addition of unavoidable quantum fluctuations in a feedback amplifier - photon shot-noise amplified by a homodyne detector in our case.
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. PMID:27419587
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.
The electrical soliton oscillator
NASA Astrophysics Data System (ADS)
Ricketts, David Shawn
Solitons are a special class of pulse-shaped waves that propagate in nonlinear dispersive media while maintaining their spatial confinement. They are found throughout nature where the proper balance between nonlinearity and dispersion is achieved. Examples of the soliton phenomena include shallow water waves, vibrations in a nonlinear spring-mass lattice, acoustic waves in plasma, and optical pulses in fiber optic cable. In electronics, the nonlinear transmission line (NLTL) serves as a nonlinear dispersive medium that propagates voltage solitons. Electrical solitons on the NLTL have been actively investigated over the last 40 years, particularly in the microwave domain, for sharp pulse generation applications and for high-speed RF and microwave sampling applications. In these past studies the NLTL has been predominantly used as a 2-port system where a high-frequency input is required to generate a sharp soliton output through a transient process. One meaningful extension of the past 2-port NLTL works would be to construct a 1-port self-sustained electrical soliton oscillator by properly combining the NLTL with an amplifier (positive active feedback). Such an oscillator would self-start by growing from ambient noise to produce a train of periodic soliton pulses in steady-state, and hence would make a self-contained soliton generator not requiring an external high-frequency input. While such a circuit may offer a new direction in the field of electrical pulse generation, there has not been a robust electrical soliton oscillator reported to date to the best of our knowledge. In this thesis we introduce the first robust electrical soliton oscillator, which is able to self-generate a stable, periodic train of electrical solitons. This new oscillator is made possible by combining the NLTL with a unique nonlinear amplifier that is able to "tame" the unruly dynamics of the NLTL. The principle contribution of this thesis is the identification of the key instability
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.
NASA Astrophysics Data System (ADS)
Liu, J. Y.
Experimental scientists have indicated that an in-phase relationship between measurements of ionospheric Doppler velocity oscillations and ULF pulsations in the northward component of the geomagnetic field on the ground results from the compressional mechanism. A careful study of the theoretical models developed previously, however, shows that in low and middle geomagnetic latitudes, owing to the compressional mechanism the ionospheric Doppler velocity oscillations lead the ULF pulsations in the northward component of the geomagnetic field at ground level by 90 deg.
Stationary and uniformly accelerated states in nonlinear quantum mechanics
NASA Astrophysics Data System (ADS)
Plastino, A. R.; Souza, A. M. C.; Nobre, F. D.; Tsallis, C.
2014-12-01
We consider two kinds of solutions of a recently proposed field theory leading to a nonlinear Schrödinger equation exhibiting solitonlike solutions of the power-law form eqi (k x -w t ), involving the q exponential function naturally arising within nonextensive thermostatistics [eqz≡[1+(1 -q ) z ] 1 /(1 -q ) , with e1z=ez ]. These fundamental solutions behave like free particles, satisfying p =ℏ k , E =ℏ ω , and E =p2/2 m (1 ≤q <2 ) . Here we introduce two additional types of exact, analytical solutions of the aforementioned field theory. As a first step we extend the theory to situations involving a potential energy term, thus going beyond the previous treatment concerning solely the free-particle dynamics. Then we consider both bound, stationary states associated with a confining potential and also time-evolving states corresponding to a linear potential function. These types of solutions might be relevant for physical applications of the present nonlinear generalized Schrödinger equation. In particular, the stationary solution obtained shows an increase in the probability for finding the particle localized around a certain position of the well as one increases q in the interval 1 ≤q <2 , which should be appropriate for physical systems where one finds a low-energy particle localized inside a confining potential.
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
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.
Parametric and nonparametric nonlinear system identification of lung tissue strip mechanics.
Yuan, H; Westwick, D T; Ingenito, E P; Lutchen, K R; Suki, B
1999-01-01
Lung parenchyma is a soft biological material composed of many interacting elements such as the interstitial cells, extracellular collagen-elastin fiber network, and proteoglycan ground substance. The mechanical behavior of this delicate structure is complex showing several mild but distinct types of nonlinearities and a fractal-like long memory stress relaxation characterized by a power-law function. To characterize tissue nonlinearity in the presence of such long memory, we investigated the robustness and predictive ability of several nonlinear system identification techniques on stress-strain data obtained from lung tissue strips with various input wave forms. We found that in general, for a mildly nonlinear system with long memory, a nonparametric nonlinear system identification in the frequency domain is preferred over time-domain techniques. More importantly, if a suitable parametric nonlinear model is available that captures the long memory of the system with only a few parameters, high predictive ability with substantially increased robustness can be achieved. The results provide evidence that the first-order kernel of the stress-strain relationship is consistent with a fractal-type long memory stress relaxation and the nonlinearity can be described as a Wiener-type nonlinear structure for displacements mimicking tidal breathing. PMID:10468239
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.
Within-Breath Analysis of Respiratory Mechanics in Asthmatic Patients by Forced Oscillation
Veiga, Juliana; Lopes, Agnaldo José; Jansen, José Manoel; de Melo, Pedro Lopes
2009-01-01
INTRODUCTION: The within-breath analysis of respiratory mechanics by the monofrequency Forced Oscillation Technique (mFOT) is of great interest in both physiopathology studies and the diagnosis of respiratory diseases. However, there are limited data on the use of this technique in the analysis of asthma. This study evaluates within-breath mechanics of asthmatic individuals and the contribution of the mFOT in the asthma diagnosis. METHODS: Twenty-two healthy and twenty-two asthmatic subjects, including patients with mild (n=8), moderate (n=8), and severe (n=6) obstruction, were studied. Forced Oscillation Technique data were interpreted using the mean respiratory impedance (Zt), the impedance during inspiration (Zi), expiration (Ze), at the beginning of inspiration (Zii), and at expiration (Zie). The peak-to-peak impedance (Zpp) was also calculated by the subtraction of Zii from Zie. Receiver operating characteristic curves were used to determine the sensitivity (Se) and specificity (Sp) of m Forced Oscillation Technique parameters in identifying asthma. RESULTS: Respiratory impedance values were significantly higher in asthmatics: Zt (p<0.001), Zi (p<0.001), Ze (p<0.001), Zii (p<0.001), Zie (p<0.001), and Zpp (p<0.003). The best parameters for detecting asthma were Zi, Zii, and Zie (Se=90.9%, Sp=90.9%), followed by Zt and Ze. These results are in close agreement with recently published theories and pathophysiological fundamentals. CONCLUSIONS: mFOT permits a non-invasive and detailed analysis in different phases of the respiratory cycle, providing parameters that are adequate for the diagnosis of asthma with high accuracy. These results confirm the high clinical and scientific potential of this methodology in the evaluation of asthmatic patients. PMID:19606241
NASA Astrophysics Data System (ADS)
Molz, F. J.; Faybishenko, B.; Jenkins, E. W.
2012-12-01
Mass and energy fluxes within the soil-plant-atmosphere continuum are highly coupled and inherently nonlinear. The main focus of this presentation is to demonstrate the results of numerical modeling of a system of 4 coupled, nonlinear ordinary differential equations (ODEs), which are used to describe the long-term, rhizosphere processes of soil microbial dynamics, including the competition between nitrogen-fixing bacteria and those unable to fix nitrogen, along with substrate concentration (nutrient supply) and oxygen concentration. Modeling results demonstrate the synchronized patterns of temporal oscillations of competing microbial populations, which are affected by carbon and oxygen concentrations. The temporal dynamics and amplitude of the root exudation process serve as a driving force for microbial and geochemical phenomena, and lead to the development of the Gompetzian dynamics, synchronized oscillations, and phase-space attractors of microbial populations and carbon and oxygen concentrations. The nonlinear dynamic analysis of time series concentrations from the solution of the ODEs was used to identify several types of phase-space attractors, which appear to be dependent on the parameters of the exudation function and Monod kinetic parameters. This phase space analysis was conducted by means of assessing the global and local embedding dimensions, correlation time, capacity and correlation dimensions, and Lyapunov exponents of the calculated model variables defining the phase space. Such results can be used for planning experimental and theoretical studies of biogeochemical processes in the fields of plant nutrition, phyto- and bio-remediation, and other ecological areas.
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.
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
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.
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
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.
Dupont, Geneviève; Combettes, Laurent; Bird, Gary S.; Putney, James W.
2011-01-01
Calcium signaling results from a complex interplay between activation and inactivation of intracellular and extracellular calcium permeable channels. This complexity is obvious from the pattern of calcium signals observed with modest, physiological concentrations of calcium-mobilizing agonists, which typically present as sequential regenerative discharges of stored calcium, a process referred to as calcium oscillations. In this review, we discuss recent advances in understanding the underlying mechanism of calcium oscillations through the power of mathematical modeling. We also summarize recent findings on the role of calcium entry through store-operated channels in sustaining calcium oscillations and in the mechanism by which calcium oscillations couple to downstream effectors. PMID:21421924
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
Oscillating Permanent Magnets.
ERIC Educational Resources Information Center
Michaelis, M. M.; Haines, C. M.
1989-01-01
Describes several ways to partially levitate permanent magnets. Computes field line geometries and oscillation frequencies. Provides several diagrams illustrating the mechanism of the oscillation. (YP)
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
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.
Nonlinear Inelastic Mechanical Behavior Of Epoxy Resin Polymeric Materials
NASA Astrophysics Data System (ADS)
Yekani Fard, Masoud
Polymer and polymer matrix composites (PMCs) materials are being used extensively in different civil and mechanical engineering applications. The behavior of the epoxy resin polymers under different types of loading conditions has to be understood before the mechanical behavior of Polymer Matrix Composites (PMCs) can be accurately predicted. In many structural applications, PMC structures are subjected to large flexural loadings, examples include repair of structures against earthquake and engine fan cases. Therefore it is important to characterize and model the flexural mechanical behavior of epoxy resin materials. In this thesis, a comprehensive research effort was undertaken combining experiments and theoretical modeling to investigate the mechanical behavior of epoxy resins subject to different loading conditions. Epoxy resin E 863 was tested at different strain rates. Samples with dog-bone geometry were used in the tension tests. Small sized cubic, prismatic, and cylindrical samples were used in compression tests. Flexural tests were conducted on samples with different sizes and loading conditions. Strains were measured using the digital image correlation (DIC) technique, extensometers, strain gauges, and actuators. Effects of triaxiality state of stress were studied. Cubic, prismatic, and cylindrical compression samples undergo stress drop at yield, but it was found that only cubic samples experience strain hardening before failure. Characteristic points of tensile and compressive stress strain relation and load deflection curve in flexure were measured and their variations with strain rate studied. Two different stress strain models were used to investigate the effect of out-of-plane loading on the uniaxial stress strain response of the epoxy resin material. The first model is a strain softening with plastic flow for tension and compression. The influence of softening localization on material behavior was investigated using the DIC system. It was found that
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.
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.
NASA Astrophysics Data System (ADS)
Aoi, Shinya; Yamashita, Tsuyoshi; Tsuchiya, Kazuo
2011-06-01
We investigated the dynamics of quadrupedal locomotion by constructing a simple quadruped model that consists of a body mechanical model and an oscillator network model. The quadruped model has front and rear bodies connected by a waist joint with a torsional spring and damper system and four limbs controlled by command signals from the oscillator network model. The simulation results reveal that the quadruped model produces various gait patterns through dynamic interactions among the body mechanical system, the oscillator network system, and the environment. They also show that it undergoes a gait transition induced by changes in the waist joint stiffness and the walking speed. In addition, the gait pattern transition exhibits a hysteresis similar to that observed in human and animal locomotion. We examined the hysteresis mechanism from a dynamic viewpoint.
NASA Astrophysics Data System (ADS)
Aerts, J. R. M.; Dirckx, J. J. J.; Pintelon, R.
2008-06-01
Recently, a measurement set-up was presented to detect small nonlinear distortions in the vibration of acoustically driven mechanical systems. A speaker generates a specially designed multisine excitation signal that drives the vibration of a test object. The generated sound pressure is measured with a probe microphone in front of the test object, and an heterodyne vibrometer measures the corresponding vibration. Due to the high degree of linearity of the heterodyne technique, very small nonlinear distortions can be detected. In this paper the set-up is used to verify whether small nonlinear distortions are present in the vibration of the middle ear system, which is classically considered to be a completely linear system. In vitro measurements on the right ear of an adult male gerbil proved that nonlinear distortions are present in the vibration of the tympanic membrane. Similar results were seen in measurements on the left ear. The influence of post-mortem changes on the nonlinear behaviour of the middle ear was verified in a number of successive measurements. These indicated that the nonlinear behaviour of the middle ear decreases in time.
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
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.
Piezoeletric and Mechanical properties of Non-linear Optical Manganese Mercury thiocyanate (MMTC)
NASA Astrophysics Data System (ADS)
Kumar, Santhosh R.; Korah, Ignatius; Chandralingam, S.; kumar, Binay; George, Sijosh; Joseph, Ginson P.
2011-07-01
Single crystasls of the coordination complex non-linear optical crystal material, MMTC with dimensions of 12×8×6 mm3 were grown from aqueous solutions by slow evaporation technique. The mechanical properties and piezoelectric properties of the crystals were studied.
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.
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
Wharton, A. M.; Sekar Iyengar, A. N.; Janaki, M. S.
2013-02-15
Hilbert Huang transform (HHT) based time series analysis was carried out on nonlinear floating potential fluctuations obtained from hollow cathode glow discharge plasma in the presence of anode glow. HHT was used to obtain contour plots and the presence of nonlinearity was studied. Frequency shift with time, which is a typical nonlinear behaviour, was detected from the contour plots. Various plasma parameters were measured and the concepts of correlation coefficients and the physical contribution of each intrinsic mode function have been discussed. Physically important quantities such as instantaneous energy and their uses in studying physical phenomena such as intermittency and non-stationary data have also been discussed.
Nicu, Valentin Paul
2016-08-01
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. PMID:27453052
A brief review on nonlinear modeling methods and applications of compliant mechanisms
NASA Astrophysics Data System (ADS)
Hao, Guangbo; Yu, Jingjun; Li, Haiyang
2016-05-01
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.
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.
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.
2015-01-01
Acute lymphoid leukemia is a common type of blood cancer and chemotherapy is the initial treatment of choice. Quantifying the effect of a chemotherapeutic drug at the cellular level plays an important role in the process of the treatment. In this study, an oscillating optical tweezer was employed to characterize the frequency-dependent mechanical properties of Jurkat cells exposed to the chemotherapeutic agent, artesunate (ART). A motion equation for a bead bound to a cell was applied to describe the mechanical characteristics of the cell cytoskeleton. By comparing between the modeling results and experimental results from the optical tweezer, the stiffness and viscosity of the Jurkat cells before and after the ART treatment were obtained. The results demonstrate a weak power-law dependency of cell stiffness with frequency. Furthermore, the stiffness and viscosity were increased after the treatment. Therefore, the cytoskeleton cell stiffness as the well as power-law coefficient can provide a useful insight into the chemo-mechanical relationship of drug treated cancer cells and may serve as another tool for evaluating therapeutic performance quantitatively. PMID:25928073
Hervás, C; Toledo, R; Silva, M
2001-01-01
The suitability of pruned computational neural networks (CNNs) for resolving nonlinear multicomponent systems involving synergistic effects by use of oscillating chemical reaction-based methods implemented using the analyte pulse perturbation technique is demonstrated. The CNN input data used for this purpose are estimates provided by the Levenberg-Marquardt method in the form of a three-parameter Gaussian curve associated with the singular profile obtained when the oscillating system is perturbed by an analyte mixture. The performance of the proposed method was assessed by applying it to the resolution of mixtures of pyrogallol and gallic acid based on their perturbating effect on a classical oscillating chemical system, viz. the Belousov-Zhabotinskyi reaction. A straightforward network topology (3:3:2, with 18 connections after pruning) allowed the resolution of mixtures of the two analytes in concentration ratios from 1:7 to 6:2 with a standard error of prediction for the testing set of 4.01 and 8.98% for pyrogallol and gallic acid, respectively. The reduced dimensions of the selected CNN architecture allowed a mathematical transformation of the input vector into the output one that can be easily implemented via software. Finally, the suitability of response surface analysis as an alternative to CNNs was also tested. The results were poor (relative errors were high), which confirms that properly selected pruned CNNs are effective tools for solving the analytical problem addressed in this work. PMID:11500128
Alvarado-Rojas, C; Huberfeld, G; Baulac, M; Clemenceau, S; Charpier, S; Miles, R; Menendez de la Prida, L; Le Van Quyen, M
2015-01-01
Transient high-frequency oscillations (150-600 Hz) in local field potential generated by human hippocampal and parahippocampal areas have been related to both physiological and pathological processes. The cellular basis and effects of normal and abnormal forms of high-frequency oscillations (HFO) has been controversial. Here, we searched for HFOs in slices of the subiculum prepared from human hippocampal tissue resected for treatment of pharmacoresistant epilepsy. HFOs occurred spontaneously in extracellular field potentials during interictal discharges (IID) and also during pharmacologically induced preictal discharges (PID) preceding ictal-like events. While most of these events might be considered pathological since they invaded the fast ripple band (>250 Hz), others were spectrally similar to physiological ripples (150-250 Hz). Do similar cellular mechanisms underly IID-ripples and PID-ripples? Are ripple-like oscillations a valid proxy of epileptogenesis in human TLE? With combined intra- or juxta-cellular and extracellular recordings, we showed that, despite overlapping spectral components, ripple-like IID and PID oscillations were associated with different cellular and synaptic mechanisms. IID-ripples were associated with rhythmic GABAergic and glutamatergic synaptic potentials with moderate neuronal firing. In contrast, PID-ripples were associated with depolarizing synaptic inputs frequently reaching the threshold for bursting in most cells. Thus ripple-like oscillations (100-250 Hz) in the human epileptic hippocampus are associated with different mechanisms for synchrony reflecting distinct dynamic changes in inhibition and excitation during interictal and pre-ictal states. PMID:25448920
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.
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
McNaughton, Brandon H.
2007-12-01
The nonlinear rotation of a magnetic particle, suspended in a viscous fluid, occurs when a driving magnetic field, used to rotate the magnetic particle, exceeds some critical frequency. This type of rotational dynamics depends on physical parameters, such as the particle's magnetic moment, the external magnetic field, and the rotational drag that the particle experiences. Therefore, by studying the rotational dynamics of a magnetic particle, a variety of physical properties can be measured on the microscale and nanoscale. Accordingly, this thesis gives a detailed theoretical analysis for measurements of (1) local magnetic fields, (2) magnetic particle characteristics, (3) viscosity and (4) chemical binding, along with their corresponding experimental demonstrations. The idea of combining physical measurements with chemical sensors is also discussed. One of the most promising applications for nonlinear magnetic oscillators---that result from changes in drag---is for the fluid-based detection of single biological agents. This application was demonstrated using a particle to mimic a bacteria and also with Escherichia coli, where an easily measurable change in the nonlinear rotation frequency was made in both cases. This concept can be extended to study of single bacterial growth dynamics with potential applications for antibiotic susceptibility measurements.
NASA Astrophysics Data System (ADS)
Conti, Livia; De Gregorio, Paolo; Bonaldi, Michele; Borrielli, Antonio; Crivellari, Michele; Karapetyan, Gagik; Poli, Charles; Serra, Enrico; Thakur, Ram-Krishna; Rondoni, Lamberto
2012-06-01
We study experimentally, numerically, and theoretically the elastic response of mechanical resonators along which the temperature is not uniform, as a consequence of the onset of steady-state thermal gradients. Two experimental setups and designs are employed, both using low-loss materials. In both cases, we monitor the resonance frequencies of specific modes of vibration, as they vary along with variations of temperatures and of temperature differences. In one case, we consider the first longitudinal mode of vibration of an aluminum alloy resonator; in the other case, we consider the antisymmetric torsion modes of a silicon resonator. By defining the average temperature as the volume-weighted mean of the temperatures of the respective elastic sections, we find out that the elastic response of an object depends solely on it, regardless of whether a thermal gradient exists and, up to 10% imbalance, regardless of its magnitude. The numerical model employs a chain of anharmonic oscillators, with first- and second-neighbor interactions and temperature profiles satisfying Fourier's Law to a good degree. Its analysis confirms, for the most part, the experimental findings and it is explained theoretically from a statistical mechanics perspective with a loose notion of local equilibrium.
Comb-drive micro-electro-mechanical systems oscillators for low temperature experiments.
González, M; Zheng, P; Garcell, E; Lee, Y; Chan, H B
2013-02-01
We have designed and characterized micro-electro-mechanical systems (MEMS) for applications at low temperatures. The mechanical resonators were fabricated using a surface micromachining process. The devices consist of a pair of parallel plates with a well defined gap. The top plate can be actuated for shear motion relative to the bottom fixed plate through a set of comb-drive electrodes. Details on the operation and fabrication of the devices are discussed. The geometry was chosen to study the transport properties of the fluid entrained in the gap. An atomic force microscopy study was performed in order to characterize the surface. A full characterization of their resonance properties in air and at room temperature was conducted as a function of pressure, from 10 mTorr to 760 Torr, ranging from a highly rarefied gas to a hydrodynamic regime. We demonstrate the operation of our resonator at low temperatures immersed in superfluid (4)He and in the normal and superfluid states of (3)He down to 0.3 mK. These MEMS oscillators show potential for use in a wide range of low temperature experiments, in particular, to probe novel phenomena in quantum fluids. PMID:23464242
Mori, Kazutaka; Shirai, Toshihiro; Mikamo, Masashi; Shishido, Yuichiro; Akita, Takefumi; Morita, Satoru; Asada, Kazuhiro; Fujii, Masato; Hozumi, Hironao; Suda, Takafumi; Chida, Kingo
2013-01-15
The coexistence of emphysema and pulmonary fibrosis is known as combined pulmonary fibrosis and emphysema (CPFE). The aim of this study was to compare the lung mechanics measured by multi-frequency forced oscillation technique (FOT) among patients with CPFE, interstitial pneumonia (IP), and chronic obstructive pulmonary disease (COPD). FOT and pulmonary function tests were performed in 41 patients with CPFE, 47 with IP, and 86 with COPD. Whole-breath resistance at 20 Hz was significantly lower in patients with CPFE than in those with IP or COPD, irrespective of the severity of airflow limitation. Within-breath analyses of resistance revealed no difference among the 3 groups; however, the difference between inspiratory and expiratory phases of reactance at 5 Hz, which reflects expiratory flow limitation, in patients with CPFE was significantly higher than in those with IP and lower than in those with COPD. In conclusion, both emphysema and fibrosis affect lung mechanics in CPFE, leading to different findings from IP or COPD alone. PMID:23117106
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
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
Mechanisms underlying very-low-frequency RR-interval oscillations in humans
NASA Technical Reports Server (NTRS)
Taylor, J. A.; Carr, D. L.; Myers, C. W.; Eckberg, D. L.
1998-01-01
BACKGROUND: Survival of post-myocardial infarction patients is related inversely to their levels of very-low-frequency (0.003 to 0.03 Hz) RR-interval variability. The physiological basis for such oscillations is unclear. In our study, we used blocking drugs to evaluate potential contributions of sympathetic and vagal mechanisms and the renin-angiotensin-aldosterone system to very-low-frequency RR-interval variability in 10 young healthy subjects. METHODS AND RESULTS: We recorded RR intervals and arterial pressures during three separate sessions, with the patient in supine and 40 degree upright tilt positions, during 20-minute frequency (0.25 Hz) and tidal volume-controlled breathing after intravenous injections: saline (control), atenolol (0.2 mg/kg, beta-adrenergic blockade), atropine sulfate (0.04 mg/kg, parasympathetic blockade), atenolol and atropine (complete autonomic blockade), and enalaprilat (0.02 mg/kg, ACE blockade). We integrated fast Fourier transform RR-interval spectral power at very low (0.003 to 0.03 Hz), low (0.05 to 0. 15 Hz), and respiratory (0.2 to 0.3 Hz) frequencies. Beta-adrenergic blockade had no significant effect on very-low- or low-frequency RR-interval power but increased respiratory frequency power 2-fold. ACE blockade had no significant effect on low or respiratory frequency RR-interval power but modestly (approximately 21%) increased very-low-frequency power in the supine (but not upright tilt) position (P<0.05). The most profound effects were exerted by parasympathetic blockade: Atropine, given alone or with atenolol, abolished nearly all RR-interval variability and decreased very-low-frequency variability by 92%. CONCLUSIONS: Although very-low-frequency heart period rhythms are influenced by the renin-angiotensin-aldosterone system, as low and respiratory frequency RR-interval rhythms, they depend primarily on the presence of parasympathetic outflow. Therefore the prognostic value of very-low-frequency heart period oscillations may
NASA Astrophysics Data System (ADS)
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 mechanics of the organ of Corti caused by Deiters cells.
Böhnke, F; Arnold, W
1998-10-01
Though the organ of Corti (OC) has been an object of experimental and theoretical hearing research, open questions remain concerning the processing of acoustic signals by the cochlea where the OC is located. Today there is extensive knowledge about single parts of the organ but a lack of understanding as to how these elements act together. One of the reasons for this is the missing analysis of the mechanics of the OC in three dimensions. In order to fill this gap, we have analyzed a short section (0.06 mm) of the basilar membrane including the OC and evaluated its nonlinear finite element model numerically. The Deiters cells are idealized as thin elastic beams with a comparably low modulus of elasticity of actin. Therefore, they show nonlinear mechanical behavior generating additional frequency components with two-tone stimulation. PMID:9775536
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.
Identification of Nonlinear Micron-Level Mechanics for a Precision Deployable Joint
NASA Technical Reports Server (NTRS)
Bullock, S. J.; Peterson, L. D.
1994-01-01
The experimental identification of micron-level nonlinear joint mechanics and dynamics for a pin-clevis joint used in a precision, adaptive, deployable space structure are investigated. The force-state mapping method is used to identify the behavior of the joint under a preload. The results of applying a single tension-compression cycle to the joint under a tensile preload are presented. The observed micron-level behavior is highly nonlinear and involves all six rigid body motion degrees-of-freedom of the joint. it is also suggests that at micron levels of motion modelling of the joint mechanics and dynamics must include the interactions between all internal components, such as the pin, bushings, and the joint node.
NASA Astrophysics Data System (ADS)
Levine, Alex
Transiently cross linked networks of semiflexible filaments make up the principal structural component of the cell -- the cytoskeleton. This intracellular network, along with molecular motors, forms the basis for cellular control of morphology and force generation. In this talk, I report on investigations of the effect of transiently bound cross linkers on the structure and mechanics of semiflexible networks. Specifically, I address the role of Casimir or fluctuation-induced interactions between cross linkers in the formation of filament bundles. I report on the linear viscoelasticity of transiently cross-linked networks of bundles. Finally, I discuss the nonlinear mechanical response of such networks, where applied stress induces a persistent structural rearrangement of the network that can dramatically alter its nonlinear response to stresses subsequently applied.
NASA Astrophysics Data System (ADS)
Biradar, N. S.; Raman, R.
2012-09-01
Hot cracking studies on autogenous AA2014 T6 TIG welds were carried out. Significant cracking was observed during linear and circular welding test (CWT) on 4-mm-thick plates. Weld metal grain structure and amount of liquid distribution during the terminal stages of solidification were the key cause for hot cracking in aluminum welds. Square-wave AC TIG welding with transverse mechanical arc oscillation (TMAO) was employed to study the cracking behavior during linear and CWT. TMAO welds with amplitude = 0.9 mm and frequency = 0.5 Hz showed significant reduction in cracking tendency. The increase in cracking resistance in the arc-oscillated weld was attributed to grain refinement and improved weld bead morphology, which improved the weld metal ductility and uniformity, respectively, of residual tensile stresses that developed during welding. The obtained results were comparable to those of reported favorable results of electromagnetic arc oscillation.
Cheng, Yu; Muroski, Megan E; Petit, Dorothée C M C; Mansell, Rhodri; Vemulkar, Tarun; Morshed, Ramin A; Han, Yu; Balyasnikova, Irina V; Horbinski, Craig M; Huang, Xinlei; Zhang, Lingjiao; Cowburn, Russell P; Lesniak, Maciej S
2016-02-10
Magnetic particles that can be precisely controlled under a magnetic field and transduce energy from the applied field open the way for innovative cancer treatment. Although these particles represent an area of active development for drug delivery and magnetic hyperthermia, the in vivo anti-tumor effect under a low-frequency magnetic field using magnetic particles has not yet been demonstrated. To-date, induced cancer cell death via the oscillation of nanoparticles under a low-frequency magnetic field has only been observed in vitro. In this report, we demonstrate the successful use of spin-vortex, disk-shaped permalloy magnetic particles in a low-frequency, rotating magnetic field for the in vitro and in vivo destruction of glioma cells. The internalized nanomagnets align themselves to the plane of the rotating magnetic field, creating a strong mechanical force which damages the cancer cell structure inducing programmed cell death. In vivo, the magnetic field treatment successfully reduces brain tumor size and increases the survival rate of mice bearing intracranial glioma xenografts, without adverse side effects. This study demonstrates a novel approach of controlling magnetic particles for treating malignant glioma that should be applicable to treat a wide range of cancers. PMID:26708022
NASA Astrophysics Data System (ADS)
Chen, Chun-Wei; Khoo, Iam Choon; Zhao, Shuo; Lin, Tsung-Hsien; Ho, Tsung-Jui
2015-10-01
We have investigated the mechanisms responsible for nonlinear optical processes occurring in azobenzene-doped blue phase liquid crystals (BPLC), which exhibit two thermodynamically stable BPs: BPI and BPII. In coherent two wave-mixing experiments, a slow (minutes) and a fast (few milliseconds) side diffractions are observed. The underlying mechanisms were disclosed by monitoring the dynamics of grating formation and relaxation as well as by some supplementary experiments. We found the photothermal indexing and dye/LC intermolecular torque leading to lattice distortion to be the dominant mechanisms for the observed nonlinear response in BPLC. Moreover, the response time of the nonlinear optical process varied with operating phase. The rise time of the thermal indexing process was in good agreement with our findings on the temperature dependence of BP refractive index: τ(ISO) > τ(BPI) > τ(BPII). The relaxation time of the torque-induced lattice distortion was analogue to its electrostriction counterpart: τ'(BPI) > τ'(BPII). In a separate experiment, lattice swelling with selective reflection of <110> direction changed from green to red was also observed. This was attributable to the isomerization-induced change in cholesteric pitch, which directly affects the lattice spacing. The phenomenon was confirmed by measuring the optical rotatory power of the BPLC.
Bossé, Dominick; Beaulieu, Alexandre; Avoine, Olivier; Micheau, Philippe; Praud, Jean-Paul; Walti, Hervé
2010-08-01
This study aimed to implement low-frequency forced oscillation technique (LFFOT) in neonatal total liquid ventilation (TLV) and to provide the first insight into respiratory impedance under this new modality of ventilation. Thirteen newborn lambs, weighing 2.5 + or - 0.4 kg (mean + or - SD), were premedicated, intubated, anesthetized, and then placed under TLV using a specially design liquid ventilator and a perfluorocarbon. The respiratory mechanics measurements protocol was started immediately after TLV initiation. Three blocks of measurements were first performed: one during initial respiratory system adaptation to TLV, followed by two other series during steady-state conditions. Lambs were then divided into two groups before undergoing another three blocks of measurements: the first group received a 10-min intravenous infusion of salbutamol (1.5 microg x kg(-1) x min(-1)) after continuous infusion of methacholine (9 microg x kg(-1) x min(-1)), while the second group of lambs was chest strapped. Respiratory impedance was measured using serial single-frequency tests at frequencies ranging between 0.05 and 2 Hz and then fitted with a constant-phase model. Harmonic test signals of 0.2 Hz were also launched every 10 min throughout the measurement protocol. Airway resistance and inertance were starkly increased in TLV compared with gas ventilation, with a resonant frequency < or = 1.2 Hz. Resistance of 0.2 Hz and reactance were sensitive to bronchoconstriction and dilation, as well as during compliance reduction. We report successful implementation of LFFOT to neonatal TLV and present the first insight into respiratory impedance under this new modality of ventilation. We show that LFFOT is an effective tool to track respiratory mechanics under TLV. PMID:20538848
NASA Astrophysics Data System (ADS)
Pérez-Molina, Manuel; Pérez-Polo, Manuel F.
2014-10-01
This paper analyzes a controlled servomechanism with feedback and a cubic nonlinearity by means of the Bogdanov-Takens and Andronov-Poincaré-Hopf bifurcations, from which steady-state, self-oscillating and chaotic behaviors will be investigated using the center manifold theorem. The system controller is formed by a Proportional plus Integral plus Derivative action (PID) that allows to stabilize and drive to a prescribed set point a body connected to the shaft of a DC motor. The Bogdanov-Takens bifurcation is analyzed through the second Lyapunov stability method and the harmonic-balance method, whereas the first Lyapunov value is used for the Andronov-Poincaré-Hopf bifurcation. On the basis of the results deduced from the bifurcation analysis, we show a procedure to select the parameters of the PID controller so that an arbitrary steady-state position of the servomechanism can be reached even in presence of noise. We also show how chaotic behavior can be obtained by applying a harmonical external torque to the device in self-oscillating regime. The advantage of achieving chaotic behavior is that it can be used so that the system reaches a set point inside a strange attractor with a small control effort. The analytical calculations have been verified through detailed numerical simulations.
Nonlinear instability in flagellar dynamics: a novel modulation mechanism in sperm migration?
Gadêlha, H.; Gaffney, E. A.; Smith, D. J.; Kirkman-Brown, J. C.
2010-01-01
Throughout biology, cells and organisms use flagella and cilia to propel fluid and achieve motility. The beating of these organelles, and the corresponding ability to sense, respond to and modulate this beat is central to many processes in health and disease. 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, despite the high curvatures observed physiologically. 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 nonlinear models are essential in understanding the flagellar waveform in migratory human sperm; these models will also be invaluable in understanding motile flagella and cilia in other systems. PMID:20462879
Dynamic Analysis of Flexible Slider-Crank Mechanisms with Non-Linear Finite Element Method
NASA Astrophysics Data System (ADS)
CHEN, J.-S.; HUANG, C.-L.
2001-09-01
Previous research in finite element formulation of flexible mechanisms usually neglected high order terms in the strain-energy function. In particular, the quartic term of the displacement gradient is always neglected due to the common belief that it is not important in the dynamic analysis. In this paper, we show that this physical intuition is not always valid. By retaining all the high order terms in the strain-energy function the equations of motion naturally become non-linear, which can then be solved by the Newmark method. In the low-speed range it is found that the dynamic responses predicted by non-linear and linear approaches indeed make no significant difference. However, when the rotation speed increases up to about one-fifth of the fundamental bending natural frequency of the connecting rod, simplified approaches begin to incur noticeable error. Specifically, for a connecting rod with a slenderness ratio of 0·01 the conventional simplified approaches overestimate the vibration amplitude almost 10-fold when the rotation speed is comparable to the fundamental natural frequency of the connecting rod. Therefore, non-linear finite element formulation taking into account the complete non-linear strain is needed in analyzing high-speed flexible mechnisms with slender links.
NASA Astrophysics Data System (ADS)
Yasumura, Kevin Youl
In 1986 the atomic force microscope (AFM) was invented by Binnig, Quate, and Gerber. Cantilever based force microscopy has been used in a wide range of fields including the study of biological samples, data storage media, and microelectronics. These AFM-based imaging techniques typically measure forces in the piconewton (10-12 N) range. Recent developments in microcantilever fabrication and optical fiber displacement sensors have allowed for the construction of force microscope systems that are capable of measuring forces in the attonewton (10-18 N) range. Applications such as magnetic resonance force microscopy (MRFM) require the cantilevers used to have subattonewton force resolution in order to eventually detect single nuclear spins. It is believed that improvements in cantilever and experimental design will allow for improved force resolution. A fundamental limit to the detection of small forces is thermomechanical noise. The thermal noise force limit, via the fluctuation dissipation theorem, is directly related to the amount of mechanical energy dissipation in the cantilever-based force sensor. Work has therefore been focused on developing an understanding of which mechanisms are limiting the force resolution of these microcantilever oscillators. Arrays of silicon nitride, single-crystal silicon, and polysilicon cantilevers have been fabricated and studied. By measuring the dependence of Q on cantilever material, geometry, and surface treatments, significant insight into the dissipation mechanisms has been obtained. For submicron thick cantilevers, Q is found to decrease with decreasing cantilever thickness, indicative of surface loss mechanisms. For single-crystal silicon cantilevers, significant increase in room temperature Q is obtained after 700 C heat treatment in either N 2 or forming gas. Thermoelastic dissipation is not a factor for submicron thick cantilevers, but is shown to be significant for silicon nitride cantilevers as thin as 2.3 um. At low