Nonlinear Electron Waves in Strongly Magnetized Plasmas

DEFF Research Database (Denmark)

Pécseli, Hans; Juul Rasmussen, Jens

1980-01-01

Weakly nonlinear dispersive electron waves in strongly magnetized plasma are considered. A modified nonlinear Schrodinger equation is derived taking into account the effect of particles resonating with the group velocity of the waves (nonlinear Landau damping). The possibility of including the ion...... dynamics in the analysis is also demonstrated. As a particular case the authors investigate nonlinear waves in a strongly magnetized plasma filled wave-guide, where the effects of finite geometry are important. The relevance of this problem to laboratory experiments is discussed....

Nonlinear oscillation regime of electromagnetic disturbances in the equatorial F region

International Nuclear Information System (INIS)

Sazonov, S.V.

1990-01-01

Nonlinear oscillation regime of electromagnetic dicturbances within equatorial ionosphere F-region resulted from Rayleigh-Taylor instability, gradient-drift instability and recombination processes is investigated on the basis of two-liquid quasihydrodynamics equations. It is shown, that at positive linear increment the oscillations are developing in regime with aggregation and are terminated by increment the effect of threshold destabilization, when under certain initial conditions underlgoes oscillation nonlinear swinging, resulting, as well, in bubble formation in contrast to small damping oscillations, is detected

Transport processes in magnetically confined plasmas in the nonlinear regime.

Science.gov (United States)

Sonnino, Giorgio

2006-06-01

A field theory approach to transport phenomena in magnetically confined plasmas is presented. The thermodynamic field theory (TFT), previously developed for treating the generic thermodynamic system out of equilibrium, is applied to plasmas physics. Transport phenomena are treated here as the effect of the field linking the thermodynamic forces with their conjugate flows combined with statistical mechanics. In particular, the Classical and the Pfirsch-Schluter regimes are analyzed by solving the thermodynamic field equations of the TFT in the weak-field approximation. We found that, the TFT does not correct the expressions of the ionic heat fluxes evaluated by the neoclassical theory in these two regimes. On the other hand, the fluxes of matter and electronic energy (heat flow) is further enhanced in the nonlinear Classical and Pfirsch-Schluter regimes. These results seem to be in line with the experimental observations. The complete set of the electronic and ionic transport equations in the nonlinear Banana regime, is also reported. A paper showing the comparison between our theoretic results and the experimental observations in the JET machine is currently in preparation.

Inducing Strong Non-Linearities in a Phonon Trapping Quartz Bulk Acoustic Wave Resonator Coupled to a Superconducting Quantum Interference Device

Directory of Open Access Journals (Sweden)

Maxim Goryachev

2018-04-01

Full Text Available A quartz Bulk Acoustic Wave resonator is designed to coherently trap phonons in such a way that they are well confined and immune to suspension losses so they exhibit extremely high acoustic Q-factors at low temperature, with Q × f products of order 10 18 Hz. In this work we couple such a resonator to a Superconducting Quantum Interference Device (SQUID amplifier and investigate effects in the strong signal regime. Both parallel and series connection topologies of the system are investigated. The study reveals significant non-Duffing response that is associated with the nonlinear characteristics of Josephson junctions. The nonlinearity provides quasi-periodic structure of the spectrum in both incident power and frequency. The result gives an insight into the open loop behaviour of a future Cryogenic Quartz Oscillator in the strong signal regime.

Nonlinear interaction of charged particles with strong laser pulses in a gaseous media

Directory of Open Access Journals (Sweden)

H. K. Avetissian

2007-07-01

Full Text Available The charged particles nonlinear dynamics in the field of a strong electromagnetic wave pulse of finite duration and certain form of the envelope, in the refractive medium with a constant and variable refraction indexes, is investigated by means of numerical integration of the classical relativistic equations of motion. The particle energy dependence on the pulse intensity manifests the nonlinear threshold phenomenon of a particle reflection and capture by actual laser pulses in dielectric-gaseous media that takes place for a plane electromagnetic wave in the induced Cherenkov process. Laser acceleration of the particles in the result of the reflection from the pulse envelope and in the capture regime with the variable refraction index along the pulse propagation direction is investigated.

Nonlinear ion-mixing-mode particle transport in the dissipative trapped electron regime

International Nuclear Information System (INIS)

Ware, A.S.; Terry, P.W.

1993-09-01

The nonlinear particle transport arising from the convection of nonadiabatic electron density by ion temperature gradient driven turbulence is examined for trapped electron collisionality regimes. The renormalized dissipative nonadiabatic trapped electron phase space density response is derived and used to calculate the nonlinear particle flux along with an ansatz for the turbulently broadened frequency spectrum. In the lower temperature end of this regime, trapped electrons are collisional and all components of the quasilinear particle flux are outward (i.e., in the direction of the gradients). Nonlinear effects can alter the phase between the nonadiabatic trapped electron phase space density and the electrostatic potential, producing inward components in the particle flux. Specifically, both turbulent shifting of the peak of the frequency spectrum and nonlinear source terms in the trapped electron response can give rise to inward components. However, in the dissipative regime these terms are small and the trapped electron response remains dominantly laminar. When the trapped electrons are collisionless, there is a temperature threshold above which the electron temperature gradient driven component of the quasilinear particle flux changes sign and becomes inward. For finite amplitude turbulence, however, turbulent broadening of both the electron collisional resonance and the frequency spectrum removes tills threshold., and the temperature gradient driven component remains outward

Transition from linear- to nonlinear-focusing regime in filamentation

Science.gov (United States)

Lim, Khan; Durand, Magali; Baudelet, Matthieu; Richardson, Martin

2014-01-01

Laser filamentation in gases is often carried out in the laboratory with focusing optics to better stabilize the filament, whereas real-world applications of filaments frequently involve collimated or near-collimated beams. It is well documented that geometrical focusing can alter the properties of laser filaments and, consequently, a transition between a collimated and a strongly focused filament is expected. Nevertheless, this transition point has not been identified. Here, we propose an analytical method to determine the transition, and show that it corresponds to an actual shift in the balance of physical mechanisms governing filamentation. In high-NA conditions, filamentation is primarily governed by geometrical focusing and plasma effects, while the Kerr nonlinearity plays a more significant role as NA decreases. We find the transition between the two regimes to be relatively insensitive to the intrinsic laser parameters, and our analysis agrees well with a wide range of parameters found in published literature. PMID:25434678

Analytical solution of strongly nonlinear Duffing oscillators

OpenAIRE

El-Naggar, A.M.; Ismail, G.M.

2016-01-01

In this paper, a new perturbation technique is employed to solve strongly nonlinear Duffing oscillators, in which a new parameter α=α(ε)α=α(ε) is defined such that the value of α is always small regardless of the magnitude of the original parameter εε. Therefore, the strongly nonlinear Duffing oscillators with large parameter ε are transformed into a small parameter system with respect to αα. Approximate solution obtained by the present method is compared with the solution of energy balance m...

Preheating ablation effects on the Rayleigh-Taylor instability in the weakly nonlinear regime

International Nuclear Information System (INIS)

Wang, L. F.; Ye, W. H.; He, X. T.; Sheng, Z. M.; Don, Wai-Sun; Li, Y. J.

2010-01-01

The two-dimensional Rayleigh-Taylor instability (RTI) with and without thermal conduction is investigated by numerical simulation in the weakly nonlinear regime. A preheat model κ(T)=κ SH [1+f(T)] is introduced for the thermal conduction [W. H. Ye, W. Y. Zhang, and X. T. He, Phys. Rev. E 65, 057401 (2002)], where κ SH is the Spitzer-Haerm electron thermal conductivity coefficient and f(T) models the preheating tongue effect in the cold plasma ahead of the ablation front. The preheating ablation effects on the RTI are studied by comparing the RTI with and without thermal conduction with identical density profile relevant to inertial confinement fusion experiments. It is found that the ablation effects strongly influence the mode coupling process, especially with short perturbation wavelength. Overall, the ablation effects stabilize the RTI. First, the linear growth rate is reduced, especially for short perturbation wavelengths and a cutoff wavelength is observed in simulations. Second, the second harmonic generation is reduced for short perturbation wavelengths. Third, the third-order negative feedback to the fundamental mode is strengthened, which plays a stabilization role. Finally, on the contrary, the ablation effects increase the generation of the third harmonic when the perturbation wavelengths are long. Our simulation results indicate that, in the weakly nonlinear regime, the ablation effects are weakened as the perturbation wavelength is increased. Numerical results obtained are in general agreement with the recent weakly nonlinear theories as proposed in [J. Sanz, J. Ramirez, R. Ramis et al., Phys. Rev. Lett. 89, 195002 (2002); J. Garnier, P.-A. Raviart, C. Cherfils-Clerouin et al., Phys. Rev. Lett. 90, 185003 (2003)].

Simulation of weak and strong Langmuir collapse regimes

International Nuclear Information System (INIS)

Hadzievski, L.R.; Skoric, M.M.; Kono, M.; Sato, T.

1998-01-01

In order to check the validity of the self-similar solutions and the existence of weak and strong collapse regimes, direct two dimensional simulation of the time evolution of a Langmuir soliton instability is performed. Simulation is based on the Zakharov model of strong Langmuir turbulence in a weakly magnetized plasma accounting for the full ion dynamics. For parameters considered, agreement with self-similar dynamics of the weak collapse type is found with no evidence of the strong Langmuir collapse. (author)

Transient dynamics of a quantum-dot: From Kondo regime to mixed valence and to empty orbital regimes

Science.gov (United States)

Cheng, YongXi; Li, ZhenHua; Wei, JianHua; Nie, YiHang; Yan, YiJing

2018-04-01

Based on the hierarchical equations of motion approach, we study the time-dependent transport properties of a strongly correlated quantum dot system in the Kondo regime (KR), mixed valence regime (MVR), and empty orbital regime (EOR). We find that the transient current in KR shows the strongest nonlinear response and the most distinct oscillation behaviors. Both behaviors become weaker in MVR and diminish in EOR. To understand the physical insight, we examine also the corresponding dot occupancies and the spectral functions, with their dependence on the Coulomb interaction, temperature, and applied step bias voltage. The above nonlinear and oscillation behaviors could be understood as the interplay between dynamical Kondo resonance and single electron resonant-tunneling.

Nonlinear Plasma Response to Resonant Magnetic Perturbation in Rutherford Regime

Science.gov (United States)

Zhu, Ping; Yan, Xingting; Huang, Wenlong

2017-10-01

Recently a common analytic relation for both the locked mode and the nonlinear plasma response in the Rutherford regime has been developed based on the steady-state solution to the coupled dynamic system of magnetic island evolution and torque balance equations. The analytic relation predicts the threshold and the island size for the full penetration of resonant magnetic perturbation (RMP). It also rigorously proves a screening effect of the equilibrium toroidal flow. In this work, we test the theory by solving for the nonlinear plasma response to a single-helicity RMP of a circular-shaped limiter tokamak equilibrium with a constant toroidal flow, using the initial-value, full MHD simulation code NIMROD. Time evolution of the parallel flow or ``slip frequency'' profile and its asymptotic approach to steady state obtained from the NIMROD simulations qualitatively agree with the theory predictions. Further comparisons are carried out for the saturated island size, the threshold for full mode penetration, as well as the screening effects of equilibrium toroidal flow in order to understand the physics of nonlinear plasma response in the Rutherford regime. Supported by National Magnetic Confinement Fusion Science Program of China Grants 2014GB124002 and 2015GB101004, the 100 Talent Program of the Chinese Academy of Sciences, and U.S. Department of Energy Grants DE-FG02-86ER53218 and DE-FC02-08ER54975.

Analytical solution of strongly nonlinear Duffing oscillators

Directory of Open Access Journals (Sweden)

A.M. El-Naggar

2016-06-01

Full Text Available In this paper, a new perturbation technique is employed to solve strongly nonlinear Duffing oscillators, in which a new parameter α=α(ε is defined such that the value of α is always small regardless of the magnitude of the original parameter ε. Therefore, the strongly nonlinear Duffing oscillators with large parameter ε are transformed into a small parameter system with respect to α. Approximate solution obtained by the present method is compared with the solution of energy balance method, homotopy perturbation method, global error minimization method and lastly numerical solution. We observe from the results that this method is very simple, easy to apply, and gives a very good accuracy not only for small parameter εbut also for large values of ε.

The Cornwall-Norton model in the strong coupling regime

International Nuclear Information System (INIS)

Natale, A.A.

1991-01-01

The Cornwall-Norton model is studied in the strong coupling regime. It is shown that the fermionic self-energy at large momenta behaves as Σ(p) ∼ (m 2 /p) ln (p/m). We verify that in the strong coupling phase the dynamically generated masses of gauge and scalar bosons are of the same order, and the essential features of the model remain intact. (author)

Electrically tunable single-dot nanocavities in the weak and strong coupling regimes

DEFF Research Database (Denmark)

Laucht, Arne; Hofbauer, Felix; Angele, Jacob

2008-01-01

We report the design, fabrication and optical investigation of electrically tunable single quantum dot - photonic crystal defect nanocavities [1] operating in both the weak and strong coupling regimes of the light matter interaction. Unlike previous studies, where the dot-cavity spectral detuning...... of the emitted photons from a single-dot nanocavity in the weak and strong coupling regimes. New information is obtained on the nature of the dot-cavity coupling in the weak coupling regime and electrical control of zero dimensional polaritons is demonstrated for the first time. Vacuum Rabi splittings up to 2g...... electrical readout of the strongly coupled dot-cavity system using photocurrent methods will be discussed. This work is financially supported by the DFG via SFB 631 and by the German Excellence Initiative via the “Nanosystems Initiative Munich (NIM)”....

Coulomb Impurity Problem of Graphene in Strong Coupling Regime in Magnetic Fields.

Science.gov (United States)

Kim, S C; Yang, S-R Eric

2015-10-01

We investigate the Coulomb impurity problem of graphene in strong coupling limit in the presence of magnetic fields. When the strength of the Coulomb potential is sufficiently strong the electron of the lowest energy boundstate of the n = 0 Landau level may fall to the center of the potential. To prevent this spurious effect the Coulomb potential must be regularized. The scaling function for the inverse probability density of this state at the center of the impurity potential is computed in the strong coupling regime. The dependence of the computed scaling function on the regularization parameter changes significantly as the strong coupling regime is approached.

Spectator Effects during Leptogenesis in the Strong Washout Regime

CERN Document Server

Garbrecht, Bjorn

2014-01-01

By including spectator fields into the Boltzmann equations for Leptogenesis, we show that partially equilibrated spectator interactions can have a significant impact on the freeze-out value of the asymmetry in the strong washout regime. The final asymmetry is typically increased, since partially equilibrated spectators "hide" a part of the asymmetry from washout. We study examples with leptonic and non-leptonic spectator processes, assuming thermal initial conditions, and find up to 50% enhanced asymmetries compared to the limit of fully equilibrated spectators. Together with a comprehensive overview of the equilibration temperatures for various Standard Model processes, the numerical results indicate the ranges when the limiting cases of either fully equilibrated or negligible spectator fields are applicable and when they are not. Our findings also indicate an increased sensitivity to initial conditions and finite density corrections even in the strong washout regime.

Phase mixing of transverse oscillations in the linear and nonlinear regimes for IFR relativistic electron beam propagation

International Nuclear Information System (INIS)

Shokair, I.R.

1991-01-01

Phase mixing of transverse oscillations changes the nature of the ion hose instability from an absolute to a convective instability. The stronger the phase mixing, the faster an electron beam reaches equilibrium with the guiding ion channel. This is important for long distance propagation of relativistic electron beams where it is desired that transverse oscillations phase mix within a few betatron wavelengths of injection and subsequently an equilibrium is reached with no further beam emittance growth. In the linear regime phase mixing is well understood and results in asymptotic decay of transverse oscillations as 1/Z 2 for a Gaussian beam and channel system, Z being the axial distance measured in betatron wavelengths. In the nonlinear regime (which is likely mode of propagation for long pulse beams) results of the spread mass model indicate that phase mixing is considerably weaker than in the regime. In this paper we consider this problem of phase mixing in the nonlinear regime. Results of the spread mass model will be shown along with a simple analysis of phase mixing for multiple oscillator models. Particle simulations also indicate that phase mixing is weaker in nonlinear regime than in the linear regime. These results will also be shown. 3 refs., 4 figs

Primordial black holes in linear and non-linear regimes

Energy Technology Data Exchange (ETDEWEB)

Allahyari, Alireza; Abolhasani, Ali Akbar [Department of Physics, Sharif University of Technology, Tehran (Iran, Islamic Republic of); Firouzjaee, Javad T., E-mail: allahyari@physics.sharif.edu, E-mail: j.taghizadeh.f@ipm.ir [School of Astronomy, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of)

2017-06-01

We revisit the formation of primordial black holes (PBHs) in the radiation-dominated era for both linear and non-linear regimes, elaborating on the concept of an apparent horizon. Contrary to the expectation from vacuum models, we argue that in a cosmological setting a density fluctuation with a high density does not always collapse to a black hole. To this end, we first elaborate on the perturbation theory for spherically symmetric space times in the linear regime. Thereby, we introduce two gauges. This allows to introduce a well defined gauge-invariant quantity for the expansion of null geodesics. Using this quantity, we argue that PBHs do not form in the linear regime irrespective of the density of the background. Finally, we consider the formation of PBHs in non-linear regimes, adopting the spherical collapse picture. In this picture, over-densities are modeled by closed FRW models in the radiation-dominated era. The difference of our approach is that we start by finding an exact solution for a closed radiation-dominated universe. This yields exact results for turn-around time and radius. It is important that we take the initial conditions from the linear perturbation theory. Additionally, instead of using uniform Hubble gauge condition, both density and velocity perturbations are admitted in this approach. Thereby, the matching condition will impose an important constraint on the initial velocity perturbations δ {sup h} {sub 0} = −δ{sub 0}/2. This can be extended to higher orders. Using this constraint, we find that the apparent horizon of a PBH forms when δ > 3 at turn-around time. The corrections also appear from the third order. Moreover, a PBH forms when its apparent horizon is outside the sound horizon at the re-entry time. Applying this condition, we infer that the threshold value of the density perturbations at horizon re-entry should be larger than δ {sub th} > 0.7.

Nonlinear charge reduction effect in strongly coupled plasmas

International Nuclear Information System (INIS)

Sarmah, D; Tessarotto, M; Salimullah, M

2006-01-01

The charge reduction effect, produced by the nonlinear Debye screening of high-Z charges occurring in strongly coupled plasmas, is investigated. An analytic asymptotic expression is obtained for the charge reduction factor (f c ) which determines the Debye-Hueckel potential generated by a charged test particle. Its relevant parametric dependencies are analysed and shown to predict a strong charge reduction effect in strongly coupled plasmas

Nonlinear effects in modulated quantum optomechanics

Science.gov (United States)

Yin, Tai-Shuang; Lü, Xin-You; Zheng, Li-Li; Wang, Mei; Li, Sha; Wu, Ying

2017-05-01

The nonlinear quantum regime is crucial for implementing interesting quantum effects, which have wide applications in modern quantum science. Here we propose an effective method to reach the nonlinear quantum regime in a modulated optomechanical system (OMS), which is originally in the weak-coupling regime. The mechanical spring constant and optomechanical interaction are modulated periodically. This leads to the result that the resonant optomechanical interaction can be effectively enhanced into the single-photon strong-coupling regime by the modulation-induced mechanical parametric amplification. Moreover, the amplified phonon noise can be suppressed completely by introducing a squeezed vacuum reservoir, which ultimately leads to the realization of photon blockade in a weakly coupled OMS. The reached nonlinear quantum regime also allows us to engineer the nonclassical states (e.g., Schrödinger cat states) of the cavity field, which are robust against the phonon noise. This work offers an alternative approach to enhance the quantum nonlinearity of an OMS, which should expand the applications of cavity optomechanics in the quantum realm.

Iterative solutions of nonlinear equations with strongly accretive or strongly pseudocontractive maps

International Nuclear Information System (INIS)

Chidume, C.E.

1994-03-01

Let E be a real q-uniformly smooth Banach space. Suppose T is a strongly pseudo-contractive map with open domain D(T) in E. Suppose further that T has a fixed point in D(T). Under various continuity assumptions on T it is proved that each of the Mann iteration process or the Ishikawa iteration method converges strongly to the unique fixed point of T. Related results deal with iterative solutions of nonlinear operator equations involving strongly accretive maps. Explicit error estimates are also provided. (author). 38 refs

Femtosecond nonlinear fiber optics in the ionization regime.

Science.gov (United States)

Hölzer, P; Chang, W; Travers, J C; Nazarkin, A; Nold, J; Joly, N Y; Saleh, M F; Biancalana, F; Russell, P St J

2011-11-11

By using a gas-filled kagome-style photonic crystal fiber, nonlinear fiber optics is studied in the regime of optically induced ionization. The fiber offers low anomalous dispersion over a broad bandwidth and low loss. Sequences of blueshifted pulses are emitted when 65 fs, few-microjoule pulses, corresponding to high-order solitons, are launched into the fiber and undergo self-compression. The experimental results are confirmed by numerical simulations which suggest that free-electron densities of ∼10(17) cm(-3) are achieved at peak intensities of 10(14) W/cm(2) over length scales of several centimeters.

Study of nonlinear optical absorption properties of V{sub 2}O{sub 5} nanoparticles in the femtosecond excitation regime

Energy Technology Data Exchange (ETDEWEB)

Molli, Muralikrishna; Bhat Kademane, Abhijit; Pradhan, Prabin; Sai Muthukumar, V. [Sri Sathya Sai Institute of Higher Learning, Department of Physics, Puttaparthi, Andhra Pradesh (India)

2016-08-15

In this work, we report for the first time, the nonlinear optical absorption properties of vanadium pentoxide (V{sub 2}O{sub 5}) nanoparticles in the femtosecond excitation regime. V{sub 2}O{sub 5} nanoparticles were synthesized through solution combustion technique. The as-synthesized samples were further characterized using XRD, FESEM, EDAX, TEM and UV-visible spectroscopy. X-ray diffraction results revealed the crystalline nature of the nanoparticles. Electron microscopy studies showed the size of the nanoparticles to be ∝200 nm. Open-aperture z-scan technique was employed to study the nonlinear optical absorption behavior of the synthesized samples using a 100-fs laser pulses at 800 nm from a regeneratively amplified Ti: sapphire laser. The mechanism of nonlinear absorption was found to be a three-photon absorption process which was explained using the density of states of V{sub 2}O{sub 5} obtained using density functional theory. These nanoparticles exhibit strong intensity-dependent nonlinear optical absorption and hence could be considered for optical-power-limiting applications. (orig.)

An effective description of dark matter and dark energy in the mildly non-linear regime

Energy Technology Data Exchange (ETDEWEB)

Lewandowski, Matthew; Senatore, Leonardo [Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA 94306 (United States); Maleknejad, Azadeh, E-mail: matthew.lewandowski@cea.fr, E-mail: azade@ipm.ir, E-mail: senatore@stanford.edu [School of Physics, Institute for Research in Fundamental Sciences (IPM), P. Code. 19538-33511, Tehran (Iran, Islamic Republic of)

2017-05-01

In the next few years, we are going to probe the low-redshift universe with unprecedented accuracy. Among the various fruits that this will bear, it will greatly improve our knowledge of the dynamics of dark energy, though for this there is a strong theoretical preference for a cosmological constant. We assume that dark energy is described by the so-called Effective Field Theory of Dark Energy, which assumes that dark energy is the Goldstone boson of time translations. Such a formalism makes it easy to ensure that our signatures are consistent with well-established principles of physics. Since most of the information resides at high wavenumbers, it is important to be able to make predictions at the highest wavenumber that is possible. The Effective Field Theory of Large-Scale Structure (EFTofLSS) is a theoretical framework that has allowed us to make accurate predictions in the mildly non-linear regime. In this paper, we derive the non-linear equations that extend the EFTofLSS to include the effect of dark energy both on the matter fields and on the biased tracers. For the specific case of clustering quintessence, we then perturbatively solve to cubic order the resulting non-linear equations and construct the one-loop power spectrum of the total density contrast.

Relativistic nonlinear electrodynamics the QED vacuum and matter in super-strong radiation fields

CERN Document Server

Avetissian, Hamlet K

2016-01-01

This revised edition of the author’s classic 2006 text offers a comprehensively updated review of the field of relativistic nonlinear electrodynamics. It explores the interaction of strong and super-strong electromagnetic/laser radiation with the electromagnetic quantum vacuum and diverse types of matter – including free charged particles and antiparticles, acceleration beams, plasma and plasmous media.  The appearance of laser sources of relativistic and ultra-relativistic intensities over the last decade has stimulated investigation of a large class of processes under such super-strong radiation fields. Revisions for this second edition reflect these developments and the book includes new chapters on Bremsstrahlung and nonlinear absorption of superintense radiation in plasmas, the nonlinear interaction of relativistic atoms with intense laser radiation, nonlinear interaction of strong laser radiation with Graphene, and relativistic nonlinear phenomena in solid-plasma targets under supershort laser pul...

A Modified Lindstedt–Poincaré Method for a Strongly Nonlinear System with Quadratic and Cubic Nonlinearities

Directory of Open Access Journals (Sweden)

S.H. Chen

1996-01-01

Full Text Available A modified Lindstedt–Poincaré method is presented for extending the range of the validity of perturbation expansion to strongly nonlinear oscillations of a system with quadratic and cubic nonlinearities. Different parameter transformations are introduced to deal with equations with different nonlinear characteristics. All examples show that the efficiency and accuracy of the present method are very good.

Perturbation Solutions of the Quintic Duffing Equation with Strong Nonlinearities

Directory of Open Access Journals (Sweden)

Mehmet Pakdemirli

Full Text Available The quintic Duffing equation with strong nonlinearities is considered. Perturbation solutions are constructed using two different techniques: The classical multiple scales method (MS and the newly developed multiple scales Lindstedt Poincare method (MSLP. The validity criteria for admissible solutions are derived. Both approximate solutions are contrasted with the numerical solutions. It is found that MSLP provides compatible solution with the numerical solution for strong nonlinearities whereas MS solution fail to produce physically acceptable solution for large perturbation parameters.

Regimes of the magnetized Rayleigh endash Taylor instability

International Nuclear Information System (INIS)

Winske, D.

1996-01-01

Hybrid simulations with kinetic ions and massless fluid electrons are used to investigate the linear and nonlinear behavior of the magnetized Rayleigh endash Taylor instability in slab geometry with the plasma subject to a constant gravity. Three regimes are found, which are determined by the magnitude of the complex frequency ω=ω r +iγ. For |ω| i (Ω i = ion gyrofrequency), one finds the typical behavior of the usual fluid regime, namely the development of open-quote open-quote mushroom-head close-quote close-quote spikes and bubbles in the density and a strongly convoluted boundary between the plasma and magnetic field, where the initial gradient is not relaxed much. A second regime, where |ω|∼0.1Ω i , is characterized by the importance of the Hall term. Linearly, the developing flute modes are more finger-like and tilted along the interface; nonlinearly, clump-like structures form, leading to a significant broadening of the interface. The third regime is characterized by unmagnetized ion behavior, with |ω|∼Ω i . Density clumps, rather than flutes, form in the linear stage, while nonlinearly, longer-wavelength modes that resemble those in fluid regime dominate. Finite Larmor radius stabilization of short-wavelength modes is observed in each regime. copyright 1996 American Institute of Physics

BGK-type models in strong reaction and kinetic chemical equilibrium regimes

International Nuclear Information System (INIS)

Monaco, R; Bianchi, M Pandolfi; Soares, A J

2005-01-01

A BGK-type procedure is applied to multi-component gases undergoing chemical reactions of bimolecular type. The relaxation process towards local Maxwellians, depending on mass and numerical densities of each species as well as common velocity and temperature, is investigated in two different cases with respect to chemical regimes. These cases are related to the strong reaction regime characterized by slow reactions, and to the kinetic chemical equilibrium regime where fast reactions take place. The consistency properties of both models are stated in detail. The trend to equilibrium is numerically tested and comparisons for the two regimes are performed within the hydrogen-air and carbon-oxygen reaction mechanism. In the spatial homogeneous case, it is also shown that the thermodynamical equilibrium of the models recovers satisfactorily the asymptotic equilibrium solutions to the reactive Euler equations

Continuous-wave to pulse regimes for a family of passively mode-locked lasers with saturable nonlinearity

Science.gov (United States)

Dikandé, Alain M.; Voma Titafan, J.; Essimbi, B. Z.

2017-10-01

The transition dynamics from continuous-wave to pulse regimes of operation for a generic model of passively mode-locked lasers with saturable absorbers, characterized by an active medium with non-Kerr nonlinearity, are investigated analytically and numerically. The system is described by a complex Ginzburg-Landau equation with a general m:n saturable nonlinearity (i.e {I}m/{(1+{{Γ }}I)}n, where I is the field intensity and m and n are two positive numbers), coupled to a two-level gain equation. An analysis of stability of continuous waves, following the modulational instability approach, provides a global picture of the self-starting dynamics in the system. The analysis reveals two distinct routes depending on values of the couple (m, n), and on the dispersion regime: in the normal dispersion regime, when m = 2 and n is arbitrary, the self-starting requires positive values of the fast saturable absorber and nonlinearity coefficients, but negative values of these two parameters for the family with m = 0. However, when the spectral filter is negative, the laser can self-start for certain values of the input field and the nonlinearity saturation coefficient Γ. The present work provides a general map for the self-starting mechanisms of rare-earth doped figure-eight fiber lasers, as well as Kerr-lens mode-locked solid-state lasers.

Onset of the nonlinear regime in unified dark matter models

International Nuclear Information System (INIS)

Avelino, P.P.; Beca, L.M.G.; Carvalho, J.P.M. de; Martins, C.J.A.P.; Copeland, E.J.

2004-01-01

We discuss the onset of the nonlinear regime in the context of unified dark matter models involving a generalized Chaplygin gas. We show that the transition from dark-matter-like to dark-energy-like behavior will never be smooth. In some regions of space the transition will never take place while in others it may happen sooner or later than naively expected. As a result the linear theory used in previous studies may break down late in the matter dominated era even on large cosmological scales. We study the importance of this effect showing that its magnitude depends on the exact form of the equation of state in the low density regime. We expect that our results will be relevant for other unified dark matter scenarios, particularly those where the quartessence candidate is a perfect fluid

Interface width effect on the classical Rayleigh-Taylor instability in the weakly nonlinear regime

International Nuclear Information System (INIS)

Wang, L. F.; Ye, W. H.; Li, Y. J.

2010-01-01

In this paper, the interface width effects (i.e., the density gradient effects or the density transition layer effects) on the Rayleigh-Taylor instability (RTI) in the weakly nonlinear (WN) regime are investigated by numerical simulation (NS). It is found that the interface width effects dramatically influence the linear growth rate in the linear growth regime and the mode coupling process in the WN growth regime. First, the interface width effects decrease the linear growth rate of the RTI, particularly for the short perturbation wavelengths. Second, the interface width effects suppress (reduce) the third-order feedback to the fundamental mode, which induces the nonlinear saturation amplitude (NSA) to exceed the classical prediction, 0.1λ. The wider the density transition layer is, the larger the NSA is. The NSA in our NS can reach a half of its perturbation wavelength. Finally, the interface width effects suppress the generation and the growth of the second and the third harmonics. The ability to suppress the harmonics' growth increases with the interface width but decreases with the perturbation wavelength. On the whole, in the WN regime, the interface width effects stabilize the RTI, except for an enhancement of the NSA, which is expected to improve the understanding of the formation mechanism for the astrophysical jets, and for the jetlike long spikes in the high energy density physics.

Negative mobility of a Brownian particle: Strong damping regime

Science.gov (United States)

Słapik, A.; Łuczka, J.; Spiechowicz, J.

2018-02-01

We study impact of inertia on directed transport of a Brownian particle under non-equilibrium conditions: the particle moves in a one-dimensional periodic and symmetric potential, is driven by both an unbiased time-periodic force and a constant force, and is coupled to a thermostat of temperature T. Within selected parameter regimes this system exhibits negative mobility, which means that the particle moves in the direction opposite to the direction of the constant force. It is known that in such a setup the inertial term is essential for the emergence of negative mobility and it cannot be detected in the limiting case of overdamped dynamics. We analyse inertial effects and show that negative mobility can be observed even in the strong damping regime. We determine the optimal dimensionless mass for the presence of negative mobility and reveal three mechanisms standing behind this anomaly: deterministic chaotic, thermal noise induced and deterministic non-chaotic. The last origin has never been reported. It may provide guidance to the possibility of observation of negative mobility for strongly damped dynamics which is of fundamental importance from the point of view of biological systems, all of which in situ operate in fluctuating environments.

Propagation of hypergeometric Gaussian beams in strongly nonlocal nonlinear media

Science.gov (United States)

Tang, Bin; Bian, Lirong; Zhou, Xin; Chen, Kai

2018-01-01

Optical vortex beams have attracted lots of interest due to its potential application in image processing, optical trapping and optical communications, etc. In this work, we theoretically and numerically investigated the propagation properties of hypergeometric Gaussian (HyGG) beams in strongly nonlocal nonlinear media. Based on the Snyder-Mitchell model, analytical expressions for propagation of the HyGG beams in strongly nonlocal nonlinear media were obtained. The influence of input power and optical parameters on the evolutions of the beam width and radius of curvature is illustrated, respectively. The results show that the beam width and radius of curvature of the HyGG beams remain invariant, like a soliton when the input power is equal to the critical power. Otherwise, it varies periodically like a breather, which is the result of competition between the beam diffraction and nonlinearity of the medium.

Modified multiple time scale method for solving strongly nonlinear damped forced vibration systems

Science.gov (United States)

Razzak, M. A.; Alam, M. Z.; Sharif, M. N.

2018-03-01

In this paper, modified multiple time scale (MTS) method is employed to solve strongly nonlinear forced vibration systems. The first-order approximation is only considered in order to avoid complexicity. The formulations and the determination of the solution procedure are very easy and straightforward. The classical multiple time scale (MS) and multiple scales Lindstedt-Poincare method (MSLP) do not give desire result for the strongly damped forced vibration systems with strong damping effects. The main aim of this paper is to remove these limitations. Two examples are considered to illustrate the effectiveness and convenience of the present procedure. The approximate external frequencies and the corresponding approximate solutions are determined by the present method. The results give good coincidence with corresponding numerical solution (considered to be exact) and also provide better result than other existing results. For weak nonlinearities with weak damping effect, the absolute relative error measures (first-order approximate external frequency) in this paper is only 0.07% when amplitude A = 1.5 , while the relative error gives MSLP method is surprisingly 28.81%. Furthermore, for strong nonlinearities with strong damping effect, the absolute relative error found in this article is only 0.02%, whereas the relative error obtained by MSLP method is 24.18%. Therefore, the present method is not only valid for weakly nonlinear damped forced systems, but also gives better result for strongly nonlinear systems with both small and strong damping effect.

Strongly nonlinear free vibration of four edges simply supported stiffened plates with geometric imperfections

Energy Technology Data Exchange (ETDEWEB)

Chen, Zhaoting; Wang, Rong Hui; Chen, Li; Dong, Chung Uang [School of Civil Engineering and Transportation, South China University of Technology, Guangzhou (China)

2016-08-15

This article investigated the strongly nonlinear free vibration of four edges simply supported stiffened plates with geometric imperfections. The von Karman nonlinear strain-displacement relationships are applied. The nonlinear vibration of stiffened plate is reduced to a one-degree-of-freedom nonlinear system by assuming mode shapes. The Multiple scales Lindstedt-Poincare method (MSLP) and Modified Lindstedt-Poincare method (MLP) are used to solve the governing equations of vibration. Numerical examples for stiffened plates with different initial geometric imperfections are presented in order to discuss the influences to the strongly nonlinear free vibration of the stiffened plate. The results showed that: the frequency ratio reduced as the initial geometric imperfections of plate increased, which showed that the increase of the initial geometric imperfections of plate can lead to the decrease of nonlinear effect; by comparing the results calculated by MSLP method, using MS method to study strongly nonlinear vibration can lead to serious mistakes.

Scaling of chaos in strongly nonlinear lattices.

Science.gov (United States)

Mulansky, Mario

2014-06-01

Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic observations still remain mostly in the dark. In this work, we numerically analyze the probability of chaos in strongly nonlinear Hamiltonian systems and find different scaling properties depending on the nonlinear structure of the model. We argue that these different scaling laws of chaos have definite consequences for the macroscopic diffusive behavior, as chaos is the microscopic mechanism of diffusion. This is compared with previous results on chaotic diffusion [M. Mulansky and A. Pikovsky, New J. Phys. 15, 053015 (2013)], and a relation between microscopic chaos and macroscopic diffusion is established.

Spectral contents of electron waves under strong Langmuir turbulence

Energy Technology Data Exchange (ETDEWEB)

Alves, Maria Virginia; Dallaqua, Renato Sergio [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil); Prado, Fabio do [Centro Universitario UNIFEI, Itajuba, MG (Brazil); Karfidov, Dmitry Mikhailovich [General Physics Inst., Moscow (Russian Federation)

2003-07-01

Experimental results of electron plasma waves excited in a beam plasma system are presented. Based on our experimental results we determine the transition from the quasi-linear to non-linear regime. We present the space evolution of the electron beam distribution function for both regimes. The spectrum of the electron plasma wave in the non-linear regime shows a component with frequency larger than the plasma frequency besides the plasma frequency itself. We show that the higher frequency component is strongly affected by Landau damping, indicating a dissipation region. The measured experimental power spectrum of this wave shows a dependence on wave number k given by W{sub k} {proportional_to} k{sup -7/2} as theoretically predicted. (author)

Relative Nonlinear Electrodynamics Interaction of Charged Particles with Strong and Super Strong Laser Fields

CERN Document Server

Avetissian, Hamlet

2006-01-01

This book covers a large class of fundamental investigations into Relativistic Nonlinear Electrodynamics. It explores the interaction between charged particles and strong laser fields, mainly concentrating on contemporary problems of x-ray lasers, new type small set-up high-energy accelerators of charged particles, as well as electron-positron pair production from super powerful laser fields of relativistic intensities. It will also discuss nonlinear phenomena of threshold nature that eliminate the concurrent inverse processes in the problems of Laser Accelerator and Free Electron Laser, thus creating new opportunities for solving these problems.

Non-linear regime shifts in Holocene Asian monsoon variability: potential impacts on cultural change and migratory patterns

Science.gov (United States)

Donges, J. F.; Donner, R. V.; Marwan, N.; Breitenbach, S. F. M.; Rehfeld, K.; Kurths, J.

2015-05-01

The Asian monsoon system is an important tipping element in Earth's climate with a large impact on human societies in the past and present. In light of the potentially severe impacts of present and future anthropogenic climate change on Asian hydrology, it is vital to understand the forcing mechanisms of past climatic regime shifts in the Asian monsoon domain. Here we use novel recurrence network analysis techniques for detecting episodes with pronounced non-linear changes in Holocene Asian monsoon dynamics recorded in speleothems from caves distributed throughout the major branches of the Asian monsoon system. A newly developed multi-proxy methodology explicitly considers dating uncertainties with the COPRA (COnstructing Proxy Records from Age models) approach and allows for detection of continental-scale regime shifts in the complexity of monsoon dynamics. Several epochs are characterised by non-linear regime shifts in Asian monsoon variability, including the periods around 8.5-7.9, 5.7-5.0, 4.1-3.7, and 3.0-2.4 ka BP. The timing of these regime shifts is consistent with known episodes of Holocene rapid climate change (RCC) and high-latitude Bond events. Additionally, we observe a previously rarely reported non-linear regime shift around 7.3 ka BP, a timing that matches the typical 1.0-1.5 ky return intervals of Bond events. A detailed review of previously suggested links between Holocene climatic changes in the Asian monsoon domain and the archaeological record indicates that, in addition to previously considered longer-term changes in mean monsoon intensity and other climatic parameters, regime shifts in monsoon complexity might have played an important role as drivers of migration, pronounced cultural changes, and the collapse of ancient human societies.

Dynamics of levitated nanospheres: towards the strong coupling regime

International Nuclear Information System (INIS)

Monteiro, T S; Millen, J; Pender, G A T; Barker, P F; Marquardt, Florian; Chang, D

2013-01-01

The use of levitated nanospheres represents a new paradigm for the optomechanical cooling of a small mechanical oscillator, with the prospect of realizing quantum oscillators with unprecedentedly high quality factors. We investigate the dynamics of this system, especially in the so-called self-trapping regime, where one or more optical fields simultaneously trap and cool the mechanical oscillator. The determining characteristic of this regime is that both the mechanical frequency ω M and single-photon optomechanical coupling strength parameters g are a function of the optical field intensities, in contrast to usual set-ups where ω M and g are constant for the given system. We also measure the characteristic transverse and axial trapping frequencies of different sized silica nanospheres in a simple optical standing wave potential, for spheres of radii r = 20–500 nm, illustrating a protocol for loading single nanospheres into a standing wave optical trap that would be formed by an optical cavity. We use these data to confirm the dependence of the effective optomechanical coupling strength on sphere radius for levitated nanospheres in an optical cavity and discuss the prospects for reaching regimes of strong light–matter coupling. Theoretical semiclassical and quantum displacement noise spectra show that for larger nanospheres with r ∼> 100 nm a range of interesting and novel dynamical regimes can be accessed. These include simultaneous hybridization of the two optical modes with the mechanical modes and parameter regimes where the system is bistable. We show that here, in contrast to typical single-optical mode optomechanical systems, bistabilities are independent of intracavity intensity and can occur for very weak laser driving amplitudes. (paper)

Integrable parameter regimes and stationary states of nonlinearly coupled electromagnetic and ion-acoustic waves

International Nuclear Information System (INIS)

Rao, N.N.

1998-01-01

A systematic analysis of the stationary propagation of nonlinearly coupled electromagnetic and ion-acoustic waves in an unmagnetized plasma via the ponderomotive force is carried out. For small but finite amplitudes, the governing equations have a Hamiltonian structure, but with a kinetic energy term that is not positive definite. The Hamiltonian is similar to the well-known Hacute enon endash Heiles Hamiltonian of nonlinear dynamics, and is completely integrable in three regimes of the allowed parameter space. The corresponding second invariants of motion are also explicitly obtained. The integrable parameter regimes correspond to supersonic values of the Mach number, which characterizes the propagation speed of the coupled waves. On the other hand, in the sub- as well as near-sonic regimes, the coupled mode equations admit different types of exact analytical solutions, which represent nonlinear localized eigenstates of the electromagnetic field trapped in the density cavity due to the ponderomotive potential. While the density cavity has always a single-dip structure, for larger amplitudes it can support higher-order modes having a larger number of nodes in the electromagnetic field. In particular, we show the existence of a new type of localized electromagnetic wave whose field intensity has a triple-hump structure. For typical parameter values, the triple-hump solitons propagate with larger Mach numbers that are closer to the sonic limit than the single- as well as the double-hump solitons, but carry a lesser amount of the electromagnetic field energy. A comparison between the different types of solutions is carried out. The possibility of the existence of trapped electromagnetic modes having a larger number of humps is also discussed. copyright 1998 American Institute of Physics

A method for regulating strong nonlinear vibration energy of the flexible arm

Directory of Open Access Journals (Sweden)

Yushu Bian

2015-07-01

Full Text Available For an oscillating system, large amplitude indicates strong vibration energy. In this article, modal interaction is used as a useful means to regulate strong nonlinear vibration energy of the flexible arm undergoing rigid motion. A method is put forward to migrate and dissipate vibration energy based on modal interaction. By means of multiple-scale perturbation analysis, it is proven that internal resonance can be successfully established between modes of the flexible arm and the vibration absorber. Through examples and analyses, it is verified that this control method is effective in regulating strong vibration energy and can be used to suppress strong nonlinear vibration of the flexible arm undergoing rigid motion.

Effects of nonlinear phase modulation on Bragg scattering in the low-conversion regime

DEFF Research Database (Denmark)

Andersen, Lasse Mejling; Cargill, D. S.; McKinstrie, C. J.

2012-01-01

In this paper, we consider the effects of nonlinear phase modulation on frequency conversion by four-wave mixing (Bragg scattering) in the low-conversion regime. We derive the Green functions for this process using the time-domain collision method, for partial collisions, in which the four fields...... interact at the beginning or the end of the fiber, and complete collisions, in which the four fields interact at the midpoint of the fiber. If the Green function is separable, there is only one output Schmidt mode, which is free from temporal entanglement. We find that nonlinear phase modulation always...... chirps the input and output Schmidt modes and renders the Green function formally nonseparable. However, by pre-chirping the pumps, one can reduce the chirps of the Schmidt modes and enable approximate separability. Thus, even in the presence of nonlinear phase modulation, frequency conversion...

Electronic Maxwell demon in the coherent strong-coupling regime

Science.gov (United States)

Schaller, Gernot; Cerrillo, Javier; Engelhardt, Georg; Strasberg, Philipp

2018-05-01

We consider an external feedback control loop implementing the action of a Maxwell demon. Applying control actions that are conditioned on measurement outcomes, the demon may transport electrons against a bias voltage and thereby effectively converts information into electric power. While the underlying model—a feedback-controlled quantum dot that is coupled to two electronic leads—is well explored in the limit of small tunnel couplings, we can address the strong-coupling regime with a fermionic reaction-coordinate mapping. This exact mapping transforms the setup into a serial triple quantum dot coupled to two leads. We find that a continuous projective measurement of the central dot occupation would lead to a complete suppression of electronic transport due to the quantum Zeno effect. In contrast, by using a microscopic detector model we can implement a weak measurement, which allows for closure of the control loop without transport blockade. Then, in the weak-coupling regime, the energy flows associated with the feedback loop are negligible, and dominantly the information gained in the measurement induces a bound for the generated electric power. In the strong coupling limit, the protocol may require more energy for operating the control loop than electric power produced, such that the whole device is no longer information dominated and can thus not be interpreted as a Maxwell demon.

Study of the Higgs-Yukawa theory in the strong-Yukawa coupling regime

International Nuclear Information System (INIS)

Bulava, John; Gerhold, Philipp; Nagy, Attila; Deutsches Elektronen-Synchrotron; Hou, George W.S.; Smigielski, Brian; Jansen, Karl; Knippschild, Bastian; Univ. of Mainz; Lin, David C.J.; National Centre of Theoretical Sciences, Hsinchu; Nagai, Kei-Ichi; Ogawa, Kenji

2011-12-01

In this article, we present an ongoing lattice study of the Higgs-Yukawa model, in the regime of strong-Yukawa coupling, using overlap fermions. We investigated the phase structure in this regime by computing the Higgs vacuum expectation value, and by exploring the finite-size scaling behaviour of the susceptibility corresponding to the magnetisation. Our preliminary results indicate the existence of a second-order phase transition when the Yukawa coupling becomes large enough, at which the Higgs vacuum expectation value vanishes and the susceptibility diverges. (orig.)

Analog quantum simulation of the Rabi model in the ultra-strong coupling regime.

Science.gov (United States)

Braumüller, Jochen; Marthaler, Michael; Schneider, Andre; Stehli, Alexander; Rotzinger, Hannes; Weides, Martin; Ustinov, Alexey V

2017-10-03

The quantum Rabi model describes the fundamental mechanism of light-matter interaction. It consists of a two-level atom or qubit coupled to a quantized harmonic mode via a transversal interaction. In the weak coupling regime, it reduces to the well-known Jaynes-Cummings model by applying a rotating wave approximation. The rotating wave approximation breaks down in the ultra-strong coupling regime, where the effective coupling strength g is comparable to the energy ω of the bosonic mode, and remarkable features in the system dynamics are revealed. Here we demonstrate an analog quantum simulation of an effective quantum Rabi model in the ultra-strong coupling regime, achieving a relative coupling ratio of g/ω ~ 0.6. The quantum hardware of the simulator is a superconducting circuit embedded in a cQED setup. We observe fast and periodic quantum state collapses and revivals of the initial qubit state, being the most distinct signature of the synthesized model.An analog quantum simulation scheme has been explored with a quantum hardware based on a superconducting circuit. Here the authors investigate the time evolution of the quantum Rabi model at ultra-strong coupling conditions, which is synthesized by slowing down the system dynamics in an effective frame.

Retrieval of high-order susceptibilities of nonlinear metamaterials

International Nuclear Information System (INIS)

Wang Zhi-Yu; Qiu Jin-Peng; Chen Hua; Mo Jiong-Jiong; Yu Fa-Xin

2017-01-01

Active metamaterials embedded with nonlinear elements are able to exhibit strong nonlinearity in microwave regime. However, existing S -parameter based parameter retrieval approaches developed for linear metamaterials do not apply in nonlinear cases. In this paper, a retrieval algorithm of high-order susceptibilities for nonlinear metamaterials is derived. Experimental demonstration shows that, by measuring the power level of each harmonic while sweeping the incident power, high-order susceptibilities of a thin-layer nonlinear metamaterial can be effectively retrieved. The proposedapproach can be widely used in the research of active metamaterials. (paper)

Optical rogue waves generation in a nonlinear metamaterial

Science.gov (United States)

Onana Essama, Bedel Giscard; Atangana, Jacques; Biya-Motto, Frederick; Mokhtari, Bouchra; Cherkaoui Eddeqaqi, Noureddine; Kofane, Timoleon Crepin

2014-11-01

We investigate the behavior of electromagnetic wave which propagates in a metamaterial for negative index regime. The optical pulse propagation is described by the nonlinear Schrödinger equation with cubic-quintic nonlinearities, second- and third-order dispersion effects. The behavior obtained for negative index regime is compared to that observed for positive index regime. The characterization of electromagnetic wave uses some pulse parameters obtained analytically and called collective coordinates such as amplitude, temporal position, width, chirp, frequency shift and phase. Six frequency ranges have been pointed out where a numerical evolution of collective coordinates and their stability are studied under a typical example to verify our analysis. It appears that a robust soliton due to a perfect compensation process between second-order dispersion and cubic-nonlinearity is presented at each frequency range for both negative and positive index regimes. Thereafter, the stability of the soliton pulse and physical conditions leading to optical rogue waves generation are discussed at each frequency range for both regimes, when third-order dispersion and quintic-nonlinearity come into play. We have demonstrated that collective coordinates give much useful information on external and internal behavior of rogue events. Firstly, we determine at what distance begins the internal excitation leading to rogue waves. Secondly, what kind of internal modification and how it modifies the system in order to build-up rogue events. These results lead to a best comprehension of the mechanism of rogue waves generation. So, it clearly appears that the rogue wave behavior strongly depends on nonlinearity strength of distortion, frequency and regime considered.

On the dynamics of Airy beams in nonlinear media with nonlinear losses.

Science.gov (United States)

Ruiz-Jiménez, Carlos; Nóbrega, K Z; Porras, Miguel A

2015-04-06

We investigate on the nonlinear dynamics of Airy beams in a regime where nonlinear losses due to multi-photon absorption are significant. We identify the nonlinear Airy beam (NAB) that preserves the amplitude of the inward Hänkel component as an attractor of the dynamics. This attractor governs also the dynamics of finite-power (apodized) Airy beams, irrespective of the location of the entrance plane in the medium with respect to the Airy waist plane. A soft (linear) input long before the waist, however, strongly speeds up NAB formation and its persistence as a quasi-stationary beam in comparison to an abrupt input at the Airy waist plane, and promotes the formation of a new type of highly dissipative, fully nonlinear Airy beam not described so far.

Strongly nonlinear evolution of low-frequency wave packets in a dispersive plasma

Science.gov (United States)

Vasquez, Bernard J.

1993-01-01

The evolution of strongly nonlinear, strongly modulated wave packets is investigated in a dispersive plasma using a hybrid numerical code. These wave packets have amplitudes exceeding the strength of the external magnetic field, along which they propagate. Alfven (left helicity) wave packets show strong steepening for p Schrodinger (DNLS) equation.

Fitting and forecasting coupled dark energy in the non-linear regime

Energy Technology Data Exchange (ETDEWEB)

Casas, Santiago; Amendola, Luca; Pettorino, Valeria; Vollmer, Adrian [Institut für Theoretische Physik, Ruprecht-Karls-Universität Heidelberg, Philosophenweg 16, Heidelberg, 69120 Germany (Germany); Baldi, Marco, E-mail: casas@thphys.uni-heidelberg.de, E-mail: l.amendola@thphys.uni-heidelberg.de, E-mail: mail@marcobaldi.it, E-mail: v.pettorino@thphys.uni-heidelberg.de, E-mail: vollmer@thphys.uni-heidelberg.de [Dipartimento di Fisica e Astronomia, Alma Mater Studiorum Università di Bologna, viale Berti Pichat, 6/2, Bologna, I-40127 Italy (Italy)

2016-01-01

We consider cosmological models in which dark matter feels a fifth force mediated by the dark energy scalar field, also known as coupled dark energy. Our interest resides in estimating forecasts for future surveys like Euclid when we take into account non-linear effects, relying on new fitting functions that reproduce the non-linear matter power spectrum obtained from N-body simulations. We obtain fitting functions for models in which the dark matter-dark energy coupling is constant. Their validity is demonstrated for all available simulations in the redshift range 0z=–1.6 and wave modes below 0k=1 h/Mpc. These fitting formulas can be used to test the predictions of the model in the non-linear regime without the need for additional computing-intensive N-body simulations. We then use these fitting functions to perform forecasts on the constraining power that future galaxy-redshift surveys like Euclid will have on the coupling parameter, using the Fisher matrix method for galaxy clustering (GC) and weak lensing (WL). We find that by using information in the non-linear power spectrum, and combining the GC and WL probes, we can constrain the dark matter-dark energy coupling constant squared, β{sup 2}, with precision smaller than 4% and all other cosmological parameters better than 1%, which is a considerable improvement of more than an order of magnitude compared to corresponding linear power spectrum forecasts with the same survey specifications.

Fitting and forecasting coupled dark energy in the non-linear regime

International Nuclear Information System (INIS)

Casas, Santiago; Amendola, Luca; Pettorino, Valeria; Vollmer, Adrian; Baldi, Marco

2016-01-01

We consider cosmological models in which dark matter feels a fifth force mediated by the dark energy scalar field, also known as coupled dark energy. Our interest resides in estimating forecasts for future surveys like Euclid when we take into account non-linear effects, relying on new fitting functions that reproduce the non-linear matter power spectrum obtained from N-body simulations. We obtain fitting functions for models in which the dark matter-dark energy coupling is constant. Their validity is demonstrated for all available simulations in the redshift range 0z=–1.6 and wave modes below 0k=1 h/Mpc. These fitting formulas can be used to test the predictions of the model in the non-linear regime without the need for additional computing-intensive N-body simulations. We then use these fitting functions to perform forecasts on the constraining power that future galaxy-redshift surveys like Euclid will have on the coupling parameter, using the Fisher matrix method for galaxy clustering (GC) and weak lensing (WL). We find that by using information in the non-linear power spectrum, and combining the GC and WL probes, we can constrain the dark matter-dark energy coupling constant squared, β 2 , with precision smaller than 4% and all other cosmological parameters better than 1%, which is a considerable improvement of more than an order of magnitude compared to corresponding linear power spectrum forecasts with the same survey specifications

Experimental study of linear and nonlinear regimes of density-driven instabilities induced by CO2 dissolution in water

International Nuclear Information System (INIS)

Outeda, R.; D'Onofrio, A.; El Hasi, C.; Zalts, A.

2014-01-01

Density driven instabilities produced by CO 2 (gas) dissolution in water containing a color indicator were studied in a Hele Shaw cell. The images were analyzed and instability patterns were characterized by mixing zone temporal evolution, dispersion curves, and the growth rate for different CO 2 pressures and different color indicator concentrations. The results obtained from an exhaustive analysis of experimental data show that this system has a different behaviour in the linear regime of the instabilities (when the growth rate has a linear dependence with time), from the nonlinear regime at longer times. At short times using a color indicator to see the evolution of the pattern, the images show that the effects of both the color indicator and CO 2 pressure are of the same order of magnitude: The growth rates are similar and the wave numbers are in the same range (0–30 cm −1 ) when the system is unstable. Although in the linear regime the dynamics is affected similarly by the presence of the indicator and CO 2 pressure, in the nonlinear regime, the influence of the latter is clearly more pronounced than the effects of the color indicator

Nonlinear hydromagnetic Rayleigh-Taylor instability for strong viscous fluids in porous media

CERN Document Server

El-Dib, Y O

2003-01-01

In the present work a weakly nonlinear stability for magnetic fluid is discussed. The research of an interface between two strong viscous homogeneous incompressible fluids through porous medium is investigated theoretically and graphically. The effect of the vertical magnetic field has been demonstrated in this study. The linear form of equation of motion is solved in the light of the nonlinear boundary conditions. The boundary value problem leads to construct nonlinear characteristic equation having complex coefficients in elevation function. The nonlinearity is kept to third-order expansion. The nonlinear characteristic equation leads to derive the well-known nonlinear Schroedinger equation. This equation having complex coefficients of the disturbance amplitude varies in both space and time. Stability criteria have been performed for nonlinear Chanderasekhar dispersion relation including the porous effects. Stability conditions are discussed through the assumption of equal kinematic viscosity. The calculati...

On the properties of two pulses propagating simultaneously in different dispersion regimes in a nonlinear planar waveguide

International Nuclear Information System (INIS)

Pietrzyk, M.E.

1999-02-01

Properties of two pulses propagating simultaneously in different dispersion regimes, anomalous and normal, in a Kerr-type planar waveguide are studied. It is found that the presence of the pulse propagating in normal dispersion regime can cause termination of catastrophic self-focusing of the pulse propagating in anomalous regime. It is also shown that the coupling between pulses can lead to spatio-temporal splitting of the pulse propagating in anomalous dispersion regime, but it does not lead to catastrophic self-focusing of the pulse propagating in normal dispersion regime. For the limiting case when the dispersive term of the pulse propagating in normal dispersion regime can be neglected an indication (based on the variational estimation) to a possibility of a stable self-trapped propagation of both pulses is obtained. This stabilization is similar to the one which was found earlier in media with saturation-type nonlinearity. (author)

Giant X-ray nonlinearities in the kiloelectronvolt regime

International Nuclear Information System (INIS)

Racz, E.; Khan, S.F.; Borisov, A.B.; Poopalasingam, S.; McCorkindale, J.C.; Boguta, J.; Zhao, J.; Ward, S.J.; Longworth, J.W.; Illinois Inst. of Technology, Chicago, IL; Felder, A.E.; Illinois University, Chicago, IL; Rhodes, C.K.; Illinois University, Chicago, IL

2010-01-01

Complete text of publication follows. Copious Xe(M) (∼ 1 keV) and Xe(L) (∼ 4.5 keV) production induced by intense femtosecond 248 nm pulse excitation of Xe clusters is a well established phenomenon. Present studies of the characteristics of Xe(L) amplification in plasma channels have dramatically revealed the presence of very strong nonlinear dispersive and absorptive processes in the x-ray range that are illustrated in Figure 1. The dispersive nonlinearity is illustrated in panels (a) and (b) by the clear action of self-focusing. The corresponding absorptive nonlinearity is shown in panel (c); intense Xe(M) radiation at ∼ 1 keV produces Xe L-shell vacancies that generate corresponding Xe(L) emission, an observation requiring the absorption of a minimum of 5 ∼ 1 keV photons. Since the linear Kramers-Kroenig relation has a nonlinear extension, these two phenomena are in natural alliance. Fig. 1. Simultaneous single-pulse pinhole camera Xe(M) (∼ 1 keV) and Xe(L) (∼ 4.5 keV) images of x-ray production and propagation in a 248 nm driven channel in a Xe cluster medium produced with a 1.4 mm diameter circular nozzle. (a) Characteristic Xe(M) propagation illustrating both copious x-ray production and the self-focusing of the originally annular Xe(M) beam. (b) 3-D view of panel (a) illustrating the collapse of the annular configuration of the Xe(M) beam into a focused axial structure. The self-focusing action is developed in the Xe cluster medium in a region that is not directly excited by the 248 nm pulse. (c) Simultaneously recorded Xe(L) emission that spatially overlaps the image in panel (a). The use of a 7.5 μm thick Ti filter suppresses the Xe(M) signal by a factor of ∼ 10 6 ; hence, only the Xe(L) component is detected. This image demonstrates that sufficiently intense Xe(M) radiation can produce strong Xe(L) emission by a nonlinear coupling. Of particular significance is the Xe(L) production observed at the end of the channel with a maximum spatial

Kolmogorov flow in two dimensional strongly coupled dusty plasma

Energy Technology Data Exchange (ETDEWEB)

Gupta, Akanksha; Ganesh, R., E-mail: ganesh@ipr.res.in; Joy, Ashwin [Institute for Plasma Research, Bhat Gandhinagar, Gujarat 382 428 (India)

2014-07-15

Undriven, incompressible Kolmogorov flow in two dimensional doubly periodic strongly coupled dusty plasma is modelled using generalised hydrodynamics, both in linear and nonlinear regime. A complete stability diagram is obtained for low Reynolds numbers R and for a range of viscoelastic relaxation time τ{sub m} [0 < τ{sub m} < 10]. For the system size considered, using a linear stability analysis, similar to Navier Stokes fluid (τ{sub m} = 0), it is found that for Reynolds number beyond a critical R, say R{sub c}, the Kolmogorov flow becomes unstable. Importantly, it is found that R{sub c} is strongly reduced for increasing values of τ{sub m}. A critical τ{sub m}{sup c} is found above which Kolmogorov flow is unconditionally unstable and becomes independent of Reynolds number. For R < R{sub c}, the neutral stability regime found in Navier Stokes fluid (τ{sub m} = 0) is now found to be a damped regime in viscoelastic fluids, thus changing the fundamental nature of transition of Kolmogorov flow as function of Reynolds number R. A new parallelized nonlinear pseudo spectral code has been developed and is benchmarked against eigen values for Kolmogorov flow obtained from linear analysis. Nonlinear states obtained from the pseudo spectral code exhibit cyclicity and pattern formation in vorticity and viscoelastic oscillations in energy.

Linear and non-linear calculations of the hose instability in the ion-focused regime

International Nuclear Information System (INIS)

Buchanan, H.L.

1982-01-01

A simple model is adopted to study the hose instability of an intense relativistic electron beam in a partially neutralized, low density ion channel (ion focused regime). Equations of motion for the beam and the channel are derived and linearized to obtain an approximate dispersion relation. The non-linear equations of motion are then solved numerically and the results compared to linearized data

Spontaneous dressed-state polarization in the strong driving regime of cavity QED.

Science.gov (United States)

Armen, Michael A; Miller, Anthony E; Mabuchi, Hideo

2009-10-23

We utilize high-bandwidth phase-quadrature homodyne measurement of the light transmitted through a Fabry-Perot cavity, driven strongly and on resonance, to detect excess phase noise induced by a single intracavity atom. We analyze the correlation properties and driving-strength dependence of the atom-induced phase noise to establish that it corresponds to the long-predicted phenomenon of spontaneous dressed-state polarization. Our experiment thus provides a demonstration of cavity quantum electrodynamics in the strong-driving regime in which one atom interacts strongly with a many-photon cavity field to produce novel quantum stochastic behavior.

Existence regimes for the formation of nonlinear dissipative structures in inhomogeneous magnetoplasmas with non-Maxwellian electrons

Science.gov (United States)

Masood, W.; Zahoor, Sara; Gul-e-Ali, Ahmad, Ali

2016-09-01

Nonlinear dissipative structures are studied in one and two dimensions in nonuniform magnetized plasmas with non-Maxwellian electrons. The dissipation is incorporated in the system through ion-neutral collisions. Employing the drift approximation, nonlinear drift waves are derived in 1D, whereas coupled drift-ion acoustic waves are derived in 2D in the weak nonlinearity limit. It is found that the ratio of the diamagnetic drift velocity to the velocity of nonlinear structure determines the nature (compressive or rarefactive) of the shock structure. The upper and lower bounds for velocity of the nonlinear shock structures are also found. It is noticed that the existence regimes for the drift shock waves in one and two dimensions for Cairns distributed electrons are very distinct from those with kappa distributed electrons. Interestingly, it is found that both compressive and rarefactive shock structures could be obtained for the one dimensional drift waves with kappa distributed electrons.

Existence regimes for the formation of nonlinear dissipative structures in inhomogeneous magnetoplasmas with non-Maxwellian electrons

Energy Technology Data Exchange (ETDEWEB)

Masood, W. [COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad (Pakistan); National Centre for Physics, Shahdara Valley Road, Islamabad (Pakistan); Zahoor, Sara [COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad (Pakistan); Gul-e-Ali [Theoretical Plasma Physics Group, Department of Physics, Quaid-i-Azam University, Islamabad 45320 (Pakistan); Ahmad, Ali, E-mail: aliahmad79@hotmail.com [National Centre for Physics, Shahdara Valley Road, Islamabad (Pakistan)

2016-09-15

Nonlinear dissipative structures are studied in one and two dimensions in nonuniform magnetized plasmas with non-Maxwellian electrons. The dissipation is incorporated in the system through ion-neutral collisions. Employing the drift approximation, nonlinear drift waves are derived in 1D, whereas coupled drift-ion acoustic waves are derived in 2D in the weak nonlinearity limit. It is found that the ratio of the diamagnetic drift velocity to the velocity of nonlinear structure determines the nature (compressive or rarefactive) of the shock structure. The upper and lower bounds for velocity of the nonlinear shock structures are also found. It is noticed that the existence regimes for the drift shock waves in one and two dimensions for Cairns distributed electrons are very distinct from those with kappa distributed electrons. Interestingly, it is found that both compressive and rarefactive shock structures could be obtained for the one dimensional drift waves with kappa distributed electrons.

Multi-fluid Approach to High-frequency Waves in Plasmas. III. Nonlinear Regime and Plasma Heating

Science.gov (United States)

Martínez-Gómez, David; Soler, Roberto; Terradas, Jaume

2018-03-01

The multi-fluid modeling of high-frequency waves in partially ionized plasmas has shown that the behavior of magnetohydrodynamic waves in the linear regime is heavily influenced by the collisional interaction between the different species that form the plasma. Here, we go beyond linear theory and study large-amplitude waves in partially ionized plasmas using a nonlinear multi-fluid code. It is known that in fully ionized plasmas, nonlinear Alfvén waves generate density and pressure perturbations. Those nonlinear effects are more pronounced for standing oscillations than for propagating waves. By means of numerical simulations and analytical approximations, we examine how the collisional interaction between ions and neutrals affects the nonlinear evolution. The friction due to collisions dissipates a fraction of the wave energy, which is transformed into heat and consequently raises the temperature of the plasma. As an application, we investigate frictional heating in a plasma with physical conditions akin to those in a quiescent solar prominence.

Electron dynamics in metals and semiconductors in strong THz fields

DEFF Research Database (Denmark)

Jepsen, Peter Uhd

2017-01-01

Semiconductors and metals respond to strong electric fields in a highly nonlinear fashion. Using single-cycle THz field transients it is possible to investigate this response in regimes not accessible by transport-based measurements. Extremely high fields can be applied without material damage...

Nonlinear interaction of strong microwave beam with the ionosphere MINIX rocket experiment

Energy Technology Data Exchange (ETDEWEB)

Kaya, N.; Matsumoto, H.; Miyatake, S.; Kimura, I.; Nagatomo, M.; Obayashi, T.

1986-01-01

A rocket-borne experiment called MINIX was carried out to investigate the nonlinear interaction of a strong microwave energy beam with the ionosphere. The MINIX stands for Microwave-Ionosphere Nonlinear Interaction Experiment and was carried out on August 29, 1983. The objectives of the MINIX is to study possible impacts of the SPS microwave energy beam on the ionosphere such as the Ohmic heating and plasma wave excitation. The experiment showed that the microwave with f = 2.45 GHz nonlinearly excites various electrostatic plasma waves, though no Ohmic heating effects were detected. 4 figures.

Nonlinear interaction of strong microwave beam with the ionosphere MINIX rocket experiment

Science.gov (United States)

Kaya, N.; Matsumoto, H.; Miyatake, S.; Kimura, I.; Nagatomo, M.

A rocket-borne experiment called 'MINIX' was carried out to investigate the nonlinear interaction of a strong microwave energy beam with the ionosphere. The MINIX stands for Microwave-Ionosphere Nonlinear Interaction eXperiment and was carried out on August 29, 1983. The objective of the MINIX is to study possible impacts of the SPS microwave energy beam on the ionosphere, such as the ohmic heating and plasma wave excitation. The experiment showed that the microwave with f = 2.45 GHz nonlinearly excites various electrostatic plasma waves, though no ohmic heating effects were detected.

Nonlinear interaction of strong microwave beam with the ionosphere MINIX rocket experiment

International Nuclear Information System (INIS)

Kaya, N.; Matsumoto, H.; Miyatake, S.; Kimura, I.; Nagatomo, M.; Obayashi, T.

1986-01-01

A rocket-borne experiment called MINIX was carried out to investigate the nonlinear interaction of a strong microwave energy beam with the ionosphere. The MINIX stands for Microwave-Ionosphere Nonlinear Interaction Experiment and was carried out on August 29, 1983. The objectives of the MINIX is to study possible impacts of the SPS microwave energy beam on the ionosphere such as the Ohmic heating and plasma wave excitation. The experiment showed that the microwave with f = 2.45 GHz nonlinearly excites various electrostatic plasma waves, though no Ohmic heating effects were detected. 4 figures

Nonlinear propagation of strong-field THz pulses in doped semiconductors

DEFF Research Database (Denmark)

Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias C.

2012-01-01

We report on nonlinear propagation of single-cycle THz pulses with peak electric fields reaching 300 kV/cm in n-type semiconductors at room temperature. Dramatic THz saturable absorption effects are observed in GaAs, GaP, and Ge, which are caused by the nonlinear electron transport in THz fields....... The semiconductor conductivity, and hence the THz absorption, is modulated due to the acceleration of carriers in strong THz fields, leading to an increase of the effective mass of the electron population, as the electrons are redistributed from the low-momentum, low-effective-mass states to the high-momentum, high...

Advanced data assimilation in strongly nonlinear dynamical systems

Science.gov (United States)

Miller, Robert N.; Ghil, Michael; Gauthiez, Francois

1994-01-01

Advanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence. Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided. Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method--based on an empirical statistical model derived from a Monte Carlo simulation--is formulated, and shown to work very well. Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.

Nonlinear phononics and structural control of strongly correlated materials

Energy Technology Data Exchange (ETDEWEB)

Mankowsky, Roman

2016-01-20

Mid-infrared light pulses can be used to resonantly excite infrared-active vibrational modes for the phase control of strongly correlated materials on subpicosecond timescales. As the energy is transferred directly into atomic motions, dissipation into the electronic system is reduced, allowing for the emergence of unusual low energy collective properties. Light-induced superconductivity, insulator-metal transitions and melting of magnetic order demonstrate the potential of this method. An understanding of the mechanism, by which these transitions are driven, is however missing. The aim of this work is to uncover this process by investigating the nonlinear lattice dynamics induced by the excitation and to elucidate their contribution to the modulation of collective properties of strongly correlated materials. The first signature of nonlinear lattice dynamics was reported in the observation of coherent phonon oscillations, resonant with the excitation of an infrared-active phonon mode in a manganite. This nonlinear phononic coupling can be described within a model, which predicts not only oscillatory coherent phonons dynamics but also directional atomic displacements along the coupled modes on average, which could cause the previously observed transitions. We verified this directional response and quantified the anharmonic coupling constant by tracing the atomic motions in a time-resolved hard X-ray diffraction experiment with sub-picometer spatial and femtosecond temporal resolution. In a subsequent study, we investigated the role of nonlinear lattice dynamics in the emergence of superconductivity far above the equilibrium transition temperature, an intriguing effect found to follow lattice excitation of YBa{sub 2}Cu{sub 3}O{sub 6+x}. By combining density functional theory (DFT) calculations of the anharmonic coupling constants with time-resolved X-ray diffraction experiments, we identified a structural rearrangement, which appears and decays with the same temporal

A novel strong tracking finite-difference extended Kalman filter for nonlinear eye tracking

Institute of Scientific and Technical Information of China (English)

ZHANG ZuTao; ZHANG JiaShu

2009-01-01

Non-Intrusive methods for eye tracking are Important for many applications of vision-based human computer interaction. However, due to the high nonlinearity of eye motion, how to ensure the robust-ness of external interference and accuracy of eye tracking poses the primary obstacle to the integration of eye movements into today's interfaces. In this paper, we present a strong tracking finite-difference extended Kalman filter algorithm, aiming to overcome the difficulty In modeling nonlinear eye tracking. In filtering calculation, strong tracking factor is introduced to modify a priori covariance matrix and im-prove the accuracy of the filter. The filter uses finite-difference method to calculate partial derivatives of nonlinear functions for eye tracking. The latest experimental results show the validity of our method for eye tracking under realistic conditions.

Fixing extensions to general relativity in the nonlinear regime

Science.gov (United States)

Cayuso, Juan; Ortiz, Néstor; Lehner, Luis

2017-10-01

The question of what gravitational theory could supersede General Relativity has been central in theoretical physics for decades. Many disparate alternatives have been proposed motivated by cosmology, quantum gravity and phenomenological angles, and have been subjected to tests derived from cosmological, solar system and pulsar observations typically restricted to linearized regimes. Gravitational waves from compact binaries provide new opportunities to probe these theories in the strongly gravitating/highly dynamical regimes. To this end however, a reliable understanding of the dynamics in such a regime is required. Unfortunately, most of these theories fail to define well posed initial value problems, which prevents at face value from meeting such challenge. In this work, we introduce a consistent program able to remedy this situation. This program is inspired in the approach to "fixing" viscous relativistic hydrodynamics introduced by Israel and Stewart in the late 70's. We illustrate how to implement this approach to control undesirable effects of higher order derivatives in gravity theories and argue how the modified system still captures the true dynamics of the putative underlying theories in 3 +1 dimensions. We sketch the implementation of this idea in a couple of effective theories of gravity, one in the context of Noncommutative Geometry, and one in the context of Chern-Simons modified General Relativity.

On weakly singular and fully nonlinear travelling shallow capillary–gravity waves in the critical regime

Energy Technology Data Exchange (ETDEWEB)

Mitsotakis, Dimitrios, E-mail: dmitsot@gmail.com [Victoria University of Wellington, School of Mathematics, Statistics and Operations Research, PO Box 600, Wellington 6140 (New Zealand); Dutykh, Denys, E-mail: Denys.Dutykh@univ-savoie.fr [LAMA, UMR 5127 CNRS, Université Savoie Mont Blanc, Campus Scientifique, F-73376 Le Bourget-du-Lac Cedex (France); Assylbekuly, Aydar, E-mail: asylbekuly@mail.ru [Khoja Akhmet Yassawi International Kazakh–Turkish University, Faculty of Natural Science, Department of Mathematics, 161200 Turkestan (Kazakhstan); Zhakebayev, Dauren, E-mail: daurjaz@mail.ru [Al-Farabi Kazakh National University, Faculty of Mechanics and Mathematics, Department of Mathematical and Computer Modelling, 050000 Almaty (Kazakhstan)

2017-05-25

In this Letter we consider long capillary–gravity waves described by a fully nonlinear weakly dispersive model. First, using the phase space analysis methods we describe all possible types of localized travelling waves. Then, we especially focus on the critical regime, where the surface tension is exactly balanced by the gravity force. We show that our long wave model with a critical Bond number admits stable travelling wave solutions with a singular crest. These solutions are usually referred to in the literature as peakons or peaked solitary waves. They satisfy the usual speed-amplitude relation, which coincides with Scott–Russel's empirical formula for solitary waves, while their decay rate is the same regardless their amplitude. Moreover, they can be of depression or elevation type independent of their speed. The dynamics of these solutions are studied as well. - Highlights: • A model for long capillary–gravity weakly dispersive and fully nonlinear water waves is derived. • Shallow capillary–gravity waves are classified using phase plane analysis. • Peaked travelling waves are found in the critical regime. • The dynamics of peakons in Serre–Green–Naghdi equations is studied numerically.

Experimental study of linear and nonlinear regimes of density-driven instabilities induced by CO{sub 2} dissolution in water

Energy Technology Data Exchange (ETDEWEB)

Outeda, R.; D' Onofrio, A. [Grupo de Medios Porosos, Facultad de Ingeniería, Universidad de Buenos Aires, Paseo Colón 850, C1063ACV Buenos Aires (Argentina); El Hasi, C.; Zalts, A. [Instituto de Ciencias, Universidad Nacional General Sarmiento, J. M. Gutiérrez 1150, B1613GSX, Los Polvorines, Provincia de Buenos Aires (Argentina)

2014-03-15

Density driven instabilities produced by CO{sub 2} (gas) dissolution in water containing a color indicator were studied in a Hele Shaw cell. The images were analyzed and instability patterns were characterized by mixing zone temporal evolution, dispersion curves, and the growth rate for different CO{sub 2} pressures and different color indicator concentrations. The results obtained from an exhaustive analysis of experimental data show that this system has a different behaviour in the linear regime of the instabilities (when the growth rate has a linear dependence with time), from the nonlinear regime at longer times. At short times using a color indicator to see the evolution of the pattern, the images show that the effects of both the color indicator and CO{sub 2} pressure are of the same order of magnitude: The growth rates are similar and the wave numbers are in the same range (0–30 cm{sup −1}) when the system is unstable. Although in the linear regime the dynamics is affected similarly by the presence of the indicator and CO{sub 2} pressure, in the nonlinear regime, the influence of the latter is clearly more pronounced than the effects of the color indicator.

Nonlinear Single Spin Spectrum Analayzer

Science.gov (United States)

Kotler, Shlomi; Akerman, Nitzan; Glickman, Yinnon; Ozeri, Roee

2014-05-01

Qubits are excellent probes of their environment. When operating in the linear regime, they can be used as linear spectrum analyzers of the noise processes surrounding them. These methods fail for strong non-Gaussian noise where the qubit response is no longer linear. Here we solve the problem of nonlinear spectral analysis, required for strongly coupled environments. Our non-perturbative analytic model shows a nonlinear signal dependence on noise power, resulting in a spectral resolution beyond the Fourier limit as well as frequency mixing. We developed a noise characterization scheme adapted to this non-linearity. We then applied it using a single trapped 88Sr+ ion as the a sensitive probe of strong, non-Gaussian, discrete magnetic field noise. With this method, we attained a ten fold improvement over the standard Fourier limit. Finally, we experimentally compared the performance of equidistant vs. Uhrig modulation schemes for spectral analysis. Phys. Rev. Lett. 110, 110503 (2013), Synopsis at http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.110.110503 Current position: National Institute of Standards and Tehcnology, Boulder, CO.

Laser and Plasma Parameters for Laser Pulse Amplification by Stimulated Brillouin Backscattering in the Strong Coupling Regime

Science.gov (United States)

Gangolf, Thomas; Blecher, Marius; Bolanos, Simon; Lancia, Livia; Marques, Jean-Raphael; Cerchez, Mirela; Prasad, Rajendra; Aurand, Bastian; Loiseau, Pascal; Fuchs, Julien; Willi, Oswald

2017-10-01

In the ongoing quest for novel techniques to obtain ever higher laser powers, plasma amplification has drawn much attention, benefiting from the fact that a plasma can sustain much higher energy densities than a solid state amplifier. As a plasma process, Stimulated Brillouin Backscattering in the strong coupling regime (sc-SBS) can be used to transfer energy from one laser pulse (pump) to another (seed), by a nonlinear ion oscillation forced by the pump laser. Here, we report on experimental results on amplification by sc-SBS using the ARCTURUS Ti:Sapphire multi-beam laser system at the University of Duesseldorf, Germany. Counter-propagating in a supersonic Hydrogen gas jet target, an ultrashort seed pulse with a pulse duration between 30 and 160 fs and an energy between 1 and 12 mJ was amplified by a high-energy pump pulse (1.7 ps, 700 mJ). For some of the measurements, the gas was pre-ionized with a separate laser pulse (780 fs, 460 mJ). Preliminary analysis shows that the amplification was larger for the longer seed pulses, consistent with theoretical predictions.

Laser light triggers increased Raman amplification in the regime of nonlinear Landau damping

International Nuclear Information System (INIS)

Depierreux, S.; Goyon, C.; Masson-Laborde, P.E.; Yahia, V.; Loisel, G.; Labaune, C.

2014-01-01

Stimulated Raman backscattering (SRS) has many unwanted effects in megajoule-scale inertially confined fusion (ICF) plasmas. Moreover, attempts to harness SRS to amplify short laser pulses through backward Raman amplification have achieved limited success. In high temperature fusion plasmas, SRS usually occurs in a kinetic regime where the nonlinear response of the Langmuir wave to the laser drive and its host of complicating factors make it difficult to predict the degree of amplification that can be achieved under given experimental conditions. Here we present experimental evidence of reduced Landau damping with increasing Langmuir wave amplitude and determine its effects on Raman amplification. The threshold for trapping effects to influence the amplification is shown to be very low. Above threshold, the complex SRS dynamics results in increased amplification factors, which partly explains previous ICF experiments. These insights could aid the development of more efficient backward Raman amplification schemes in this regime. (authors)

Sampling strong tracking nonlinear unscented Kalman filter and its application in eye tracking

International Nuclear Information System (INIS)

Zu-Tao, Zhang; Jia-Shu, Zhang

2010-01-01

The unscented Kalman filter is a developed well-known method for nonlinear motion estimation and tracking. However, the standard unscented Kalman filter has the inherent drawbacks, such as numerical instability and much more time spent on calculation in practical applications. In this paper, we present a novel sampling strong tracking nonlinear unscented Kalman filter, aiming to overcome the difficulty in nonlinear eye tracking. In the above proposed filter, the simplified unscented transform sampling strategy with n + 2 sigma points leads to the computational efficiency, and suboptimal fading factor of strong tracking filtering is introduced to improve robustness and accuracy of eye tracking. Compared with the related unscented Kalman filter for eye tracking, the proposed filter has potential advantages in robustness, convergence speed, and tracking accuracy. The final experimental results show the validity of our method for eye tracking under realistic conditions. (classical areas of phenomenology)

Rogue wave train generation in a metamaterial induced by cubic-quintic nonlinearities and second-order dispersion

Science.gov (United States)

Essama, Bedel Giscard Onana; Atangana, Jacques; Frederick, Biya Motto; Mokhtari, Bouchra; Eddeqaqi, Noureddine Cherkaoui; Kofane, Timoleon Crepin

2014-09-01

We investigate the behavior of the electromagnetic wave that propagates in a metamaterial for negative index regime. Second-order dispersion and cubic-quintic nonlinearities are taken into account. The behavior obtained for negative index regime is compared to that observed for absorption regime. The collective coordinates technique is used to characterize the light pulse intensity profile at some frequency ranges. Five frequency ranges have been pointed out. The perfect combination of second-order dispersion and cubic nonlinearity leads to a robust soliton at each frequency range for negative index regime. The soliton peak power progressively decreases for absorption regime. Further, this peak power also decreases with frequency. We show that absorption regime can induce rogue wave trains generation at a specific frequency range. However, this rogue wave trains generation is maintained when the quintic nonlinearity comes into play for negative index regime and amplified for absorption regime at a specific frequency range. It clearly appears that rogue wave behavior strongly depends on the frequency and the regime considered. Furthermore, the stability conditions of the electromagnetic wave have also been discussed at frequency ranges considered for both negative index and absorption regimes.

Nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating embedded in water

Energy Technology Data Exchange (ETDEWEB)

Jiménez, N.; Picó, R. [Instituto de Investigación para la Gestión Integrada de zonas Costeras, Universitat Politècnica de València, Paranimf 1, 46730 Grao de Gandia, València (Spain); Romero-García, V. [LUNAM Université, Université du Maine, LAUM UMR CNRS 6613, Av. O. Messiaen, 72085 Le Mans (France); Garcia-Raffi, L. M. [Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 València (Spain); Staliunas, K. [ICREA, Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Colom, 11, E-08222 Terrassa, Barcelona (Spain)

2015-11-16

We report the nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating immersed in water. In the linear regime, the system presents high focal gain (32 dB), with a narrow beam-width and intense side lobes as it is common in focusing by Fresnel-like lenses. Activating the nonlinearity of the host medium by using high amplitude incident waves, the focusing properties of the lens dramatically change. Theoretical predictions show that the focal gain of the system extraordinary increases in the strongly nonlinear regime (Mach number of 6.1 × 10{sup −4}). Particularly, the harmonic generation is locally activated at the focal spot, and the second harmonic beam is characterized by strongly reduced side-lobes and an excellent beam profile as experiments show in agreement with theory. The results can motivate applications in medical therapy or second harmonic imaging.

Numerical investigation of beam-driven PWFA in quasi-nonlinear regime

International Nuclear Information System (INIS)

Londrillo, P.; Gatti, C.; Ferrario, M.

2014-01-01

In beam-driven Plasma Based Wakefield Acceleration (PWFA), the quasi-nonlinear model has been designed to combine high efficient ‘blowout’ regimes, where cold and overdense driving electron beams form a totally rarefied plasma channel, with low charge beam distribution assuring the excited wakefield preserves relevant linear properties. This scheme can have applications in experimental facilities, like SPARC 150 MeV linac at LNF-INFN laboratories, where low-emittance, low-charge narrow electron beams can be produced to be injected on a preformed plasma channel. Here we present a preliminary numerical investigation of this configuration, using the fully 3D ALaDyn PIC code, as a preparatory work to design optimal conditions for the COMB experimental set-up. Specific numerical tools, having computational and diagnostic advantages in PWFA conditions and checks of the numerical outcomes with analytical results, are also presented and discussed

Effects of intermode nonlinearity and intramode nonlinearity on modulation instability in randomly birefringent two-mode optical fibers

Science.gov (United States)

Li, Jin Hua; Xu, Hui; Sun, Ting Ting; Pei, Shi Xin; Ren, Hai Dong

2018-05-01

We analyze in detail the effects of the intermode nonlinearity (IEMN) and intramode nonlinearity (IRMN) on modulation instability (MI) in randomly birefringent two-mode optical fibers (RB-TMFs). In the anomalous dispersion regime, the MI gain enhances significantly as the IEMN and IRMN coefficients increases. In the normal dispersion regime, MI can be generated without the differential mode group delay (DMGD) effect, as long as the IEMN coefficient between two distinct modes is above a critical value, or the IRMN coefficient inside a mode is below a critical value. This critical IEMN (IRMN) coefficient depends strongly on the given IRMN (IEMN) coefficient and DMGD for a given nonlinear RB-TMF structure, and is independent on the input total power, the power ratio distribution and the group velocity dispersion (GVD) ratio between the two modes. On the other hand, in contrast to the MI band arising from the pure effect of DMGD in the normal dispersion regime, where MI vanishes after a critical total power, the generated MI band under the combined effects of IEMN and IRMN without DMGD exists for any total power and enhances with the total power. The MI analysis is verified numerically by launching perturbed continuous waves (CWs) with wave propagation method.

Spectral transformations in the regime of pulse self-trapping in a nonlinear photonic crystal

International Nuclear Information System (INIS)

Novitsky, Denis V.

2011-01-01

We consider the interaction of a femtosecond light pulse with a one-dimensional photonic crystal with relaxing cubic nonlinearity in the regime of self-trapping. By use of numerical simulations, it is shown that, under certain conditions, the spectra of reflected and transmitted light possess the properties of narrowband (quasimonochromatic) or wideband (continuumlike) radiation. It is remarkable that these spectral features appear due to a significant frequency shift and occur inside a photonic band gap of the structure under investigation.

Resonances of the helium atom in a strong magnetic field

DEFF Research Database (Denmark)

Lühr, Armin Christian; Al-Hujaj, Omar-Alexander; Schmelcher, Peter

2007-01-01

We present an investigation of the resonances of a doubly excited helium atom in a strong magnetic field covering the regime B=0–100  a.u. A full-interaction approach which is based on an anisotropic Gaussian basis set of one-particle functions being nonlinearly optimized for each field strength...

Chimera regimes in a ring of oscillators with local nonlinear interaction

Science.gov (United States)

Shepelev, Igor A.; Zakharova, Anna; Vadivasova, Tatiana E.

2017-03-01

One of important problems concerning chimera states is the conditions of their existence and stability. Until now, it was assumed that chimeras could arise only in ensembles with nonlocal character of interactions. However, this assumption is not exactly right. In some special cases chimeras can be realized for local type of coupling [1-3]. We propose a simple model of ensemble with local coupling when chimeras are realized. This model is a ring of linear oscillators with the local nonlinear unidirectional interaction. Chimera structures in the ring are found using computer simulations for wide area of values of parameters. Diagram of the regimes on plane of control parameters is plotted and scenario of chimera destruction are studied when the parameters are changed.

Strong phase correlations of solitons of nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Litvak, A.G.; Mironov, V.A.; Protogenov, A.P.

1994-06-01

We discuss the possibility to suppress the collapse in the nonlinear 2+1 D Schroedinger equation by using the gauge theory of strong phase correlations. It is shown that invariance relative to q-deformed Hopf algebra with deformation parameter q being the fourth root of unity makes the values of the Chern-Simons term coefficient, k=2, and of the coupling constant, g=1/2, fixed; no collapsing solutions are present at those values. (author). 21 refs

Photon and spin dependence of the resonance line shape in the strong coupling regime

NARCIS (Netherlands)

Miyashita, Seiji; Shirai, Tatsuhiko; Mori, Takashi; De Raedt, Hans; Bertaina, Sylvain; Chiorescu, Irinel

2012-01-01

We study the quantum dynamics of a spin ensemble coupled to cavity photons. Recently, related experimental results have been reported, showing the existence of the strong coupling regime in such systems. We study the eigenenergy distribution of the multi-spin system (following the Tavis-Cummings

Strongly nonlinear theory of rapid solidification near absolute stability

Science.gov (United States)

Kowal, Katarzyna N.; Altieri, Anthony L.; Davis, Stephen H.

2017-10-01

We investigate the nonlinear evolution of the morphological deformation of a solid-liquid interface of a binary melt under rapid solidification conditions near two absolute stability limits. The first of these involves the complete stabilization of the system to cellular instabilities as a result of large enough surface energy. We derive nonlinear evolution equations in several limits in this scenario and investigate the effect of interfacial disequilibrium on the nonlinear deformations that arise. In contrast to the morphological stability problem in equilibrium, in which only cellular instabilities appear and only one absolute stability boundary exists, in disequilibrium the system is prone to oscillatory instabilities and a second absolute stability boundary involving attachment kinetics arises. Large enough attachment kinetics stabilize the oscillatory instabilities. We derive a nonlinear evolution equation to describe the nonlinear development of the solid-liquid interface near this oscillatory absolute stability limit. We find that strong asymmetries develop with time. For uniform oscillations, the evolution equation for the interface reduces to the simple form f''+(βf')2+f =0 , where β is the disequilibrium parameter. Lastly, we investigate a distinguished limit near both absolute stability limits in which the system is prone to both cellular and oscillatory instabilities and derive a nonlinear evolution equation that captures the nonlinear deformations in this limit. Common to all these scenarios is the emergence of larger asymmetries in the resulting shapes of the solid-liquid interface with greater departures from equilibrium and larger morphological numbers. The disturbances additionally sharpen near the oscillatory absolute stability boundary, where the interface becomes deep-rooted. The oscillations are time-periodic only for small-enough initial amplitudes and their frequency depends on a single combination of physical parameters, including the

Nonlinear Principal Component Analysis Using Strong Tracking Filter

Institute of Scientific and Technical Information of China (English)

无

2007-01-01

The paper analyzes the problem of blind source separation (BSS) based on the nonlinear principal component analysis (NPCA) criterion. An adaptive strong tracking filter (STF) based algorithm was developed, which is immune to system model mismatches. Simulations demonstrate that the algorithm converges quickly and has satisfactory steady-state accuracy. The Kalman filtering algorithm and the recursive leastsquares type algorithm are shown to be special cases of the STF algorithm. Since the forgetting factor is adaptively updated by adjustment of the Kalman gain, the STF scheme provides more powerful tracking capability than the Kalman filtering algorithm and recursive least-squares algorithm.

Transition from weak wave turbulence regime to solitonic regime

Science.gov (United States)

Hassani, Roumaissa; Mordant, Nicolas

2017-11-01

The Weak Turbulence Theory (WTT) is a statistical theory describing the interaction of a large ensemble of random waves characterized by very different length scales. For both weak non-linearity and weak dispersion a different regime is predicted where solitons propagate while keeping their shape unchanged. The question under investigation here is which regime between weak turbulence or soliton gas does the system choose ? We report an experimental investigation of wave turbulence at the surface of finite depth water in the gravity-capillary range. We tune the wave dispersion and the level of nonlinearity by modifying the depth of water and the forcing respectively. We use space-time resolved profilometry to reconstruct the deformed surface of water. When decreasing the water depth, we observe a drastic transition between weak turbulence at the weakest forcing and a solitonic regime at stronger forcing. We characterize the transition between both states by studying their Fourier Spectra. We also study the efficiency of energy transfer in the weak turbulence regime. We report a loss of efficiency of angular transfer as the dispersion of the wave is reduced until the system bifurcates into the solitonic regime. This project has recieved funding from the European Research Council (ERC, Grant Agreement No. 647018-WATU).

Optical Control of Mechanical Mode-Coupling within a MoS2 Resonator in the Strong-Coupling Regime.

Science.gov (United States)

Liu, Chang-Hua; Kim, In Soo; Lauhon, Lincoln J

2015-10-14

Two-dimensional (2-D) materials including graphene and transition metal dichalcogenides (TMDs) are an exciting platform for ultrasensitive force and displacement detection in which the strong light-matter coupling is exploited in the optical control of nanomechanical motion. Here we report the optical excitation and displacement detection of a ∼ 3 nm thick MoS2 resonator in the strong-coupling regime, which has not previously been achieved in 2-D materials. Mechanical mode frequencies can be tuned by more than 12% by optical heating, and they exhibit avoided crossings indicative of strong intermode coupling. When the membrane is optically excited at the frequency difference between vibrational modes, normal mode splitting is observed, and the intermode energy exchange rate exceeds the mode decay rate by a factor of 15. Finite element and analytical modeling quantifies the extent of mode softening necessary to control intermode energy exchange in the strong coupling regime.

THREE-POINT PHASE CORRELATIONS: A NEW MEASURE OF NONLINEAR LARGE-SCALE STRUCTURE

Energy Technology Data Exchange (ETDEWEB)

Wolstenhulme, Richard; Bonvin, Camille [Kavli Institute for Cosmology Cambridge and Institute of Astronomy, Madingley Road, Cambridge CB3 OHA (United Kingdom); Obreschkow, Danail [International Centre for Radio Astronomy Research (ICRAR), M468, University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009 (Australia)

2015-05-10

We derive an analytical expression for a novel large-scale structure observable: the line correlation function. The line correlation function, which is constructed from the three-point correlation function of the phase of the density field, is a robust statistical measure allowing the extraction of information in the nonlinear and non-Gaussian regime. We show that, in perturbation theory, the line correlation is sensitive to the coupling kernel F{sub 2}, which governs the nonlinear gravitational evolution of the density field. We compare our analytical expression with results from numerical simulations and find a 1σ agreement for separations r ≳ 30 h{sup −1} Mpc. Fitting formulae for the power spectrum and the nonlinear coupling kernel at small scales allow us to extend our prediction into the strongly nonlinear regime, where we find a 1σ agreement with the simulations for r ≳ 2 h{sup −1} Mpc. We discuss the advantages of the line correlation relative to standard statistical measures like the bispectrum. Unlike the latter, the line correlation is independent of the bias, in the regime where the bias is local and linear. Furthermore, the variance of the line correlation is independent of the Gaussian variance on the modulus of the density field. This suggests that the line correlation can probe more precisely the nonlinear regime of gravity, with less contamination from the power spectrum variance.

Cumulants of heat transfer across nonlinear quantum systems

Science.gov (United States)

Li, Huanan; Agarwalla, Bijay Kumar; Li, Baowen; Wang, Jian-Sheng

2013-12-01

We consider thermal conduction across a general nonlinear phononic junction. Based on two-time observation protocol and the nonequilibrium Green's function method, heat transfer in steady-state regimes is studied, and practical formulas for the calculation of the cumulant generating function are obtained. As an application, the general formalism is used to study anharmonic effects on fluctuation of steady-state heat transfer across a single-site junction with a quartic nonlinear on-site pinning potential. An explicit nonlinear modification to the cumulant generating function exact up to the first order is given, in which the Gallavotti-Cohen fluctuation symmetry is found still valid. Numerically a self-consistent procedure is introduced, which works well for strong nonlinearity.

Critical slowing down associated with regime shifts in the US housing market

Science.gov (United States)

Tan, James Peng Lung; Cheong, Siew Siew Ann

2014-02-01

Complex systems are described by a large number of variables with strong and nonlinear interactions. Such systems frequently undergo regime shifts. Combining insights from bifurcation theory in nonlinear dynamics and the theory of critical transitions in statistical physics, we know that critical slowing down and critical fluctuations occur close to such regime shifts. In this paper, we show how universal precursors expected from such critical transitions can be used to forecast regime shifts in the US housing market. In the housing permit, volume of homes sold and percentage of homes sold for gain data, we detected strong early warning signals associated with a sequence of coupled regime shifts, starting from a Subprime Mortgage Loans transition in 2003-2004 and ending with the Subprime Crisis in 2007-2008. Weaker signals of critical slowing down were also detected in the US housing market data during the 1997-1998 Asian Financial Crisis and the 2000-2001 Technology Bubble Crisis. Backed by various macroeconomic data, we propose a scenario whereby hot money flowing back into the US during the Asian Financial Crisis fueled the Technology Bubble. When the Technology Bubble collapsed in 2000-2001, the hot money then flowed into the US housing market, triggering the Subprime Mortgage Loans transition in 2003-2004 and an ensuing sequence of transitions. We showed how this sequence of couple transitions unfolded in space and in time over the whole of US.

Nonlinear switching dynamics in a photonic-crystal nanocavity

International Nuclear Information System (INIS)

Yu, Yi; Palushani, Evarist; Heuck, Mikkel; Vukovic, Dragana; Peucheret, Christophe; Yvind, Kresten; Mork, Jesper

2014-01-01

We report the experimental observation of nonlinear switching dynamics in an InP photonic crystal nanocavity. Usually, the regime of relatively small cavity perturbations is explored, where the signal transmitted through the cavity follows the temporal variation of the cavity resonance. When the cavity is perturbed by strong pulses, we observe several nonlinear effects, i.e., saturation of the switching contrast, broadening of the switching window, and even initial reduction of the transmission. The effects are analyzed by comparison with nonlinear coupled mode theory and explained in terms of large dynamical variations of the cavity resonance in combination with nonlinear losses. The results provide insight into the nonlinear optical processes that govern the dynamics of nanocavities and are important for applications in optical signal processing, where one wants to optimize the switching contrast.

Nonlinear switching dynamics in a photonic-crystal nanocavity

DEFF Research Database (Denmark)

Yu, Yi; Palushani, Evarist; Heuck, Mikkel

2014-01-01

We report the experimental observation of nonlinear switching dynamics in an InP photonic crystal nanocavity. Usually, the regime of relatively small cavity perturbations is explored, where the signal transmitted through the cavity follows the temporal variation of the cavity resonance. When...... of large dynamical variations of the cavity resonance in combination with nonlinear losses. The results provide insight into the nonlinear optical processes that govern the dynamics of nanocavities and are important for applications in optical signal processing, where one wants to optimize the switching...... the cavity is perturbed by strong pulses, we observe several nonlinear effects, i.e., saturation of the switching contrast, broadening of the switching window, and even initial reduction of the transmission. The effects are analyzed by comparison with nonlinear coupled mode theory and explained in terms...

Geometry effect on energy transfer rate in a coupled-quantum-well structure: nonlinear regime

International Nuclear Information System (INIS)

Salavati-fard, T; Vazifehshenas, T

2014-01-01

We study theoretically the effect of geometry on the energy transfer rate at nonlinear regime in a coupled-quantum-well system using the balance equation approach. To investigate comparatively the effect of both symmetric and asymmetric geometry, different structures are considered. The random phase approximation dynamic dielectric function is employed to include the contributions from both quasiparticle and plasmon excitations. Also, the short-range exchange interaction is taken into account through the Hubbard approximation. Our numerical results show that the energy transfer rate increases by increasing the well thicknesses in symmetric structures. Furthermore, by increasing spatial asymmetry, the energy transfer rate decreases for the electron temperature range of interest. From numerical calculations, it is obtained that the nonlinear energy transfer rate is proportional to the square of electron drift velocity in all structures and also, found that the influence of Hubbard local field correction on the energy transfer rate gets weaker by increasing the strength of applied electric field. (paper)

Nonlinear ionization of many-electron systems over a broad photon-energy range

International Nuclear Information System (INIS)

Karamatskou, Antonia

2015-11-01

Rapid developments in laser technology and, in particular, the advances in the realm of free-electron lasers have initiated tremendous progress in both theoretical and experimental atomic, molecular and optical physics. Owing to high intensities in combination with short pulse durations we can enter the utterly nonlinear regime of light-matter interaction and study the dynamics and features of matter under extreme conditions. The capabilities of X-ray free-electron laser sources have promoted the importance of nonlinear optics also in the X-ray regime. I show in my thesis how we can exploit the nonlinear response regime to reveal hidden information about resonance structures that are not resolved in the weak-field regime. This prospect points to many applications for future investigations of various complex systems with free-electron lasers. In the present thesis the interaction of atomic closed-shell systems with ultrashort and strong laser pulses is investigated. Over a broad photon-energy range the characteristics of the atomic shell are studied with a particular focus on the nonlinear response regime and on electron correlation effects. Several computational extensions of the XCID package for multi-electron dynamics are presented and their applications in various studies are demonstrated; a completely new capability of the numerical method is realized by implementing the calculation of photoelectron spectra and by calculating eigenstates of the many-electron Hamiltonian. The field of study within the present work encompasses (1) the strong-field regime, where the question of the adiabatic character in tunneling ionization is discussed and analyzed, especially for the case of few-cycle pulses; (2) the XUV regime, in which we show for the first time that the collectivity in resonant excitation reveals new information; and (3) the (hard) x-ray regime, which is highly relevant for x-ray free-electron laser experiments, and where we show how important two

Supercritical Nonlinear Vibration of a Fluid-Conveying Pipe Subjected to a Strong External Excitation

Directory of Open Access Journals (Sweden)

Yan-Lei Zhang

2016-01-01

Full Text Available Nonlinear vibration of a fluid-conveying pipe subjected to a transverse external harmonic excitation is investigated in the case with two-to-one internal resonance. The excitation amplitude is in the same magnitude of the transverse displacement. The fluid in the pipes flows in the speed larger than the critical speed so that the straight configuration becomes an unstable equilibrium and two curved configurations bifurcate as stable equilibriums. The motion measured from each of curved equilibrium configurations is governed by a nonlinear integro-partial-differential equation with variable coefficients. The Galerkin method is employed to discretize the governing equation into a gyroscopic system consisting of a set of coupled nonlinear ordinary differential equations. The method of multiple scales is applied to analyze approximately the gyroscopic system. A set of first-order ordinary differential equations governing the modulations of the amplitude and the phase are derived via the method. In the supercritical regime, the subharmonic, superharmonic, and combination resonances are examined in the presence of the 2 : 1 internal resonance. The steady-state responses and their stabilities are determined. The various jump phenomena in the amplitude-frequency response curves are demonstrated. The effects of the viscosity, the excitation amplitude, the nonlinearity, and the flow speed are observed. The analytical results are supported by the numerical integration.

Weak and Strong Order of Convergence of a Semidiscrete Scheme for the Stochastic Nonlinear Schrodinger Equation

International Nuclear Information System (INIS)

Bouard, Anne de; Debussche, Arnaud

2006-01-01

In this article we analyze the error of a semidiscrete scheme for the stochastic nonlinear Schrodinger equation with power nonlinearity. We consider supercritical or subcritical nonlinearity and the equation can be either focusing or defocusing. Allowing sufficient spatial regularity we prove that the numerical scheme has strong order 1/2 in general and order 1 if the noise is additive. Furthermore, we also prove that the weak order is always 1

Nonlinear Response of Strong Nonlinear System Arisen in Polymer Cushion

Directory of Open Access Journals (Sweden)

Jun Wang

2013-01-01

Full Text Available A dynamic model is proposed for a polymer foam-based nonlinear cushioning system. An accurate analytical solution for the nonlinear free vibration of the system is derived by applying He's variational iteration method, and conditions for resonance are obtained, which should be avoided in the cushioning design.

Density-dependent electron scattering in photoexcited GaAs in strongly diffusive regime

DEFF Research Database (Denmark)

Mics, Zoltán; D’Angio, Andrea; Jensen, Søren A.

2013-01-01

In a series of systematic optical pump–terahertz probe experiments, we study the density-dependent electron scattering rate in photoexcited GaAs in the regime of strong carrier diffusion. The terahertz frequency-resolved transient sheet conductivity spectra are perfectly described by the Drude...... model, directly yielding the electron scattering rates. A diffusion model is applied to determine the spatial extent of the photoexcited electron-hole gas at each moment after photoexcitation, yielding the time-dependent electron density, and hence the density-dependent electron scattering time. We find...

The laser proton acceleration in the strong charge separation regime

International Nuclear Information System (INIS)

Nishiuchi, M.; Fukumi, A.; Daido, H.; Li, Z.; Sagisaka, A.; Ogura, K.; Orimo, S.; Kado, M.; Hayashi, Y.; Mori, M.; Bulanov, S.V.; Esirkepov, T.; Nemoto, K.; Oishi, Y.; Nayuki, T.; Fujii, T.; Noda, A.; Iwashita, Y.; Shirai, T.; Nakamura, S.

2006-01-01

We report the experimental results of proton acceleration as well as the simple one-dimensional model which explains our experimental data. The proton acceleration experiment is carried out with a TW short pulse laser irradiated on a tantalum thin-foil target (3 μm thickness) with an intensity of ∼3x10 18 Wcm -2 . Accelerated protons exhibit a typical energy spectrum with two quasi-Maxwellian components with a high energy cut-off. We can successfully explain the higher energy part as well as the cut off energy of the proton spectrum with the simple-one-dimensional model based on the strong charge separation regime, which is the extension of the model proposed originally by [M. Passoni et al., Phys. Rev. E 69 (2004) 026411

The influence of an interfacial heat release on nonlinear convective regimes under the action of an imposed temperature gradient

Energy Technology Data Exchange (ETDEWEB)

Simanovskii, Ilya B, E-mail: cesima@tx.technion.ac.il [Department of Mathematics, Technion—Israel Institute of Technology, 32000 Haifa (Israel)

2016-12-15

The influence of an interfacial heat release on nonlinear convective regimes, developed under the action of an imposed temperature gradient in the 47v2 silicone oil–water system, has been studied. Two types of boundary conditions—periodic boundary conditions and rigid heat-insulated lateral walls—have been considered. Transitions between the flows with different spatial structures have been investigated. It is shown that the presence of an interfacial heat release can change the sequence of bifurcations and can lead to the appearance of new oscillatory regimes. The period-three phase trajectory has been found. (paper)

Optimal explicit strong stability preserving Runge–Kutta methods with high linear order and optimal nonlinear order

KAUST Repository

Gottlieb, Sigal

2015-04-10

High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The search for high order strong stability time-stepping methods with large allowable strong stability coefficient has been an active area of research over the last two decades. This research has shown that explicit SSP Runge-Kutta methods exist only up to fourth order. However, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and this order barrier is lifted: explicit SSP Runge-Kutta methods of any linear order exist. These methods reduce to second order when applied to nonlinear problems. In the current work we aim to find explicit SSP Runge-Kutta methods with large allowable time-step, that feature high linear order and simultaneously have the optimal fourth order nonlinear order. These methods have strong stability coefficients that approach those of the linear methods as the number of stages and the linear order is increased. This work shows that when a high linear order method is desired, it may still be worthwhile to use methods with higher nonlinear order.

Extreme nonlinear energy exchanges in a geometrically nonlinear lattice oscillating in the plane

Science.gov (United States)

Zhang, Zhen; Manevitch, Leonid I.; Smirnov, Valeri; Bergman, Lawrence A.; Vakakis, Alexander F.

2018-01-01

We study the in-plane damped oscillations of a finite lattice of particles coupled by linear springs under distributed harmonic excitation. Strong nonlinearity in this system is generated by geometric effects due to the in-plane stretching of the coupling spring elements. The lattice has a finite number of nonlinear transverse standing waves (termed nonlinear normal modes - NNMs), and an equal number of axial linear modes which are nonlinearly coupled to the transverse ones. Nonlinear interactions between the transverse and axial modes under harmonic excitation give rise to unexpected and extreme nonlinear energy exchanges in the lattice. In particular, we directly excite a transverse NNM by harmonic forcing (causing simulataneous indirect excitation of a corresponding axial linear mode due to nonlinear coupling), and identify three energy transfer mechanisms in the lattice. First, we detect the stable response of the directly excited transverse NNM (despite its instability in the absence of forcing), with simultaneous stability of the indirectly excited axial linear mode. Second, by changing the system and forcing parameters we report extreme nonlinear "energy explosions," whereby, after an initial regime of stability, the directly excited transverse NNM loses stability, leading to abrupt excitation of all transverse and axial modes of the lattice, at all possible wave numbers. This strong instability is triggered by the parametric instability of an indirectly excited axial mode which builds energy until the explosion. This is proved through theoretical analysis. Finally, in other parameter ranges we report intermittent, intense energy transfers from the directly excited transverse NNM to a small set of transverse NNMs with smaller wavelengths, and from the indirectly excited axial mode to a small set of axial modes, but with larger wavelengths. These intermittent energy transfers resemble energy cascades occurring in turbulent flows. Our results show that

Emulating galaxy clustering and galaxy-galaxy lensing into the deeply nonlinear regime: methodology, information, and forecasts

OpenAIRE

Wibking, Benjamin D.; Salcedo, Andrés N.; Weinberg, David H.; Garrison, Lehman H.; Ferrer, Douglas; Tinker, Jeremy; Eisenstein, Daniel; Metchnik, Marc; Pinto, Philip

2017-01-01

The combination of galaxy-galaxy lensing (GGL) with galaxy clustering is one of the most promising routes to determining the amplitude of matter clustering at low redshifts. We show that extending clustering+GGL analyses from the linear regime down to $\\sim 0.5 \\, h^{-1}$ Mpc scales increases their constraining power considerably, even after marginalizing over a flexible model of non-linear galaxy bias. Using a grid of cosmological N-body simulations, we construct a Taylor-expansion emulator ...

A new nonlinear conjugate gradient coefficient under strong Wolfe-Powell line search

Science.gov (United States)

Mohamed, Nur Syarafina; Mamat, Mustafa; Rivaie, Mohd

2017-08-01

A nonlinear conjugate gradient method (CG) plays an important role in solving a large-scale unconstrained optimization problem. This method is widely used due to its simplicity. The method is known to possess sufficient descend condition and global convergence properties. In this paper, a new nonlinear of CG coefficient βk is presented by employing the Strong Wolfe-Powell inexact line search. The new βk performance is tested based on number of iterations and central processing unit (CPU) time by using MATLAB software with Intel Core i7-3470 CPU processor. Numerical experimental results show that the new βk converge rapidly compared to other classical CG method.

Phase locking and quantum statistics in a parametrically driven nonlinear resonator

OpenAIRE

Hovsepyan, G. H.; Shahinyan, A. R.; Chew, Lock Yue; Kryuchkyan, G. Yu.

2016-01-01

We discuss phase-locking phenomena at low-level of quanta for parametrically driven nonlinear Kerr resonator (PDNR) in strong quantum regime. Oscillatory mode of PDNR is created in the process of a degenerate down-conversion of photons under interaction with a train of external Gaussian pulses. We calculate the Wigner functions of cavity mode showing two-fold symmetry in phase space and analyse formation of phase-locked states in the regular as well as the quantum chaotic regime.

Nonlinear gyrokinetic simulations of the I-mode high confinement regime and comparisons with experiment

Energy Technology Data Exchange (ETDEWEB)

White, A. E., E-mail: whitea@mit.edu; Howard, N. T.; Creely, A. J.; Chilenski, M. A.; Greenwald, M.; Hubbard, A. E.; Hughes, J. W.; Marmar, E.; Rice, J. E.; Sierchio, J. M.; Sung, C.; Walk, J. R.; Whyte, D. G. [MIT Plasma Science and Fusion Center, Cambridge, Massachusetts 02139 (United States); Mikkelsen, D. R.; Edlund, E. M.; Kung, C. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08540 (United States); Holland, C. [University of California, San Diego (UCSD) San Diego, California 92093 (United States); Candy, J.; Petty, C. C. [General Atomics, P.O. Box 85608, San Diego, California 92186 (United States); Reinke, M. L. [York University, Heslington, York YO10 5DD (United Kingdom); and others

2015-05-15

For the first time, nonlinear gyrokinetic simulations of I-mode plasmas are performed and compared with experiment. I-mode is a high confinement regime, featuring energy confinement similar to H-mode, but without enhanced particle and impurity particle confinement [D. G. Whyte et al., Nucl. Fusion 50, 105005 (2010)]. As a consequence of the separation between heat and particle transport, I-mode exhibits several favorable characteristics compared to H-mode. The nonlinear gyrokinetic code GYRO [J. Candy and R. E. Waltz, J Comput. Phys. 186, 545 (2003)] is used to explore the effects of E × B shear and profile stiffness in I-mode and compare with L-mode. The nonlinear GYRO simulations show that I-mode core ion temperature and electron temperature profiles are more stiff than L-mode core plasmas. Scans of the input E × B shear in GYRO simulations show that E × B shearing of turbulence is a stronger effect in the core of I-mode than L-mode. The nonlinear simulations match the observed reductions in long wavelength density fluctuation levels across the L-I transition but underestimate the reduction of long wavelength electron temperature fluctuation levels. The comparisons between experiment and gyrokinetic simulations for I-mode suggest that increased E × B shearing of turbulence combined with increased profile stiffness are responsible for the reductions in core turbulence observed in the experiment, and that I-mode resembles H-mode plasmas more than L-mode plasmas with regards to marginal stability and temperature profile stiffness.

Nonlinear properties of gated graphene in a strong electromagnetic field

Energy Technology Data Exchange (ETDEWEB)

Avetisyan, A. A., E-mail: artakav@ysu.am; Djotyan, A. P., E-mail: adjotyan@ysu.am [Yerevan State University, Department of Physics (Armenia); Moulopoulos, K., E-mail: cos@ucy.ac.cy [University of Cyprus, Department of Physics (Cyprus)

2017-03-15

We develop a microscopic theory of a strong electromagnetic field interaction with gated bilayer graphene. Quantum kinetic equations for density matrix are obtained using a tight binding approach within second quantized Hamiltonian in an intense laser field. We show that adiabatically changing the gate potentials with time may produce (at resonant photon energy) a full inversion of the electron population with high density between valence and conduction bands. In the linear regime, excitonic absorption of an electromagnetic radiation in a graphene monolayer with opened energy gap is also studied.

A modified stochastic averaging method on single-degree-of-freedom strongly nonlinear stochastic vibrations

International Nuclear Information System (INIS)

Ge, Gen; Li, ZePeng

2016-01-01

A modified stochastic averaging method on single-degree-of-freedom (SDOF) oscillators under white noise excitations with strongly nonlinearity was proposed. Considering the existing approach dealing with strongly nonlinear SDOFs derived by Zhu and Huang [14, 15] is quite time consuming in calculating the drift coefficient and diffusion coefficients and the expressions of them are considerable long, the so-called He's energy balance method was applied to overcome the minor defect of the Zhu and Huang's method. The modified method can offer more concise approximate expressions of the drift and diffusion coefficients without weakening the accuracy of predicting the responses of the systems too much by giving an averaged frequency beforehand. Three examples, a cubic and quadratic nonlinearity coexisting oscillator, a quadratic nonlinear oscillator under external white noise excitations and an externally excited Duffing–Rayleigh oscillator, were given to illustrate the approach we proposed. The three examples were excited by the Gaussian white noise and the Gaussian colored noise separately. The stationary responses of probability density of amplitudes and energy, together with joint probability density of displacement and velocity are studied to verify the presented approach. The reliability of the systems were also investigated to offer further support. Digital simulations were carried out and the output of that are coincide with the theoretical approximations well.

Strong nonlinear harmonic generation in a PZT/Aluminum resonator

Energy Technology Data Exchange (ETDEWEB)

Parenthoine, D; Haumesser, L; Meulen, F Vander; Tran-Huu-Hue, L-P, E-mail: parenthoine@univ-tours.f [University Francois Rabelais of Tours, U 930 Imagerie et Cerveau, CNRS 2448, ENIVL, rue de la Chocolaterie, BP 3410, 41034 Blois (France)

2009-11-01

In this work, the extentional vibration mode of a coupled PZT/ Aluminum rod resonator is studied experimentally. Geometrical characteristics of the PZT are its 27 mm length and its 4x4 mm{sup 2} cross section area. The excitation voltage consists in sinusoidal bursts in the frequency range (20-80 kHz). Velocity measurements are performed at both ends of this system, using a laser probe. Strong harmonic distortions in the mechanical response (up to -20 dB with respect to the primary wave amplitude) have been observed. The corresponding input levels are far lower than those which are necessary to observe quadratic second harmonic generation in a free PZT resonator. The strong nonlinear effect can be explained as a super-harmonic resonance of the system due to a specific ratio between the eigen frequencies of the two parts of the resonator. Evolution of fundamental and harmonic responses are observed as a function of input levels, highlighting hysteretic behavior.

Three-point phase correlations: A new measure of non-linear large-scale structure

CERN Document Server

Wolstenhulme, Richard; Obreschkow, Danail

2015-01-01

We derive an analytical expression for a novel large-scale structure observable: the line correlation function. The line correlation function, which is constructed from the three-point correlation function of the phase of the density field, is a robust statistical measure allowing the extraction of information in the non-linear and non-Gaussian regime. We show that, in perturbation theory, the line correlation is sensitive to the coupling kernel F_2, which governs the non-linear gravitational evolution of the density field. We compare our analytical expression with results from numerical simulations and find a very good agreement for separations r>20 Mpc/h. Fitting formulae for the power spectrum and the non-linear coupling kernel at small scales allow us to extend our prediction into the strongly non-linear regime. We discuss the advantages of the line correlation relative to standard statistical measures like the bispectrum. Unlike the latter, the line correlation is independent of the linear bias. Furtherm...

Explicit and exact solutions for a generalized long-short wave resonance equations with strong nonlinear term

International Nuclear Information System (INIS)

Shang Yadong

2005-01-01

In this paper, the evolution equations with strong nonlinear term describing the resonance interaction between the long wave and the short wave are studied. Firstly, based on the qualitative theory and bifurcation theory of planar dynamical systems, all of the explicit and exact solutions of solitary waves are obtained by qualitative seeking the homoclinic and heteroclinic orbits for a class of Lienard equations. Then the singular travelling wave solutions, periodic travelling wave solutions of triangle functions type are also obtained on the basis of the relationships between the hyperbolic functions and that between the hyperbolic functions with the triangle functions. The varieties of structure of exact solutions of the generalized long-short wave equation with strong nonlinear term are illustrated. The methods presented here also suitable for obtaining exact solutions of nonlinear wave equations in multidimensions

Strongly nonlinear optical glass fibers from noncentrosymmetric phase-change chalcogenide materials.

Science.gov (United States)

Chung, In; Jang, Joon I; Malliakas, Christos D; Ketterson, John B; Kanatzidis, Mercouri G

2010-01-13

We report that the one-dimensional polar selenophosphate compounds APSe(6) (A = K, Rb), which show crystal-glass phase-change behavior, exhibit strong second harmonic generation (SHG) response in both crystal and glassy forms. The crystalline materials are type-I phase-matchable with SHG coefficients chi((2)) of 151.3 and 149.4 pm V(-1) for K(+) and Rb(+) salts, respectively, which is the highest among phase-matchable nonlinear optical (NLO) materials with band gaps over 1.0 eV. The glass of APSe(6) exhibits comparable SHG intensities to the top infrared NLO material AgGaSe(2) without any poling treatments. APSe(6) exhibit excellent mid-IR transparency. We demonstrate that starting from noncentrosymmetric phase-change materials such as APSe(6) (A = K, Rb), we can obtain optical glass fibers with strong, intrinsic, and temporally stable second-order nonlinear optical (NLO) response. The as-prepared glass fibers exhibit SHG and difference frequency generation (DFG) responses over a wide range of wavelengths. Raman spectroscopy and pair distribution function (PDF) analyses provide further understanding of the local structure in amorphous state of KPSe(6) bulk glass and glass fiber. We propose that this approach can be widely applied to prepare permanent NLO glass from materials that undergo a phase-change process.

Nonlinear Site Response Validation Studies Using KIK-net Strong Motion Data

Science.gov (United States)

Asimaki, D.; Shi, J.

2014-12-01

Earthquake simulations are nowadays producing realistic ground motion time-series in the range of engineering design applications. Of particular significance to engineers are simulations of near-field motions and large magnitude events, for which observations are scarce. With the engineering community slowly adopting the use of simulated ground motions, site response models need to be re-evaluated in terms of their capabilities and limitations to 'translate' the simulated time-series from rock surface output to structural analyses input. In this talk, we evaluate three one-dimensional site response models: linear viscoelastic, equivalent linear and nonlinear. We evaluate the performance of the models by comparing predictions to observations at 30 downhole stations of the Japanese network KIK-Net that have recorded several strong events, including the 2011 Tohoku earthquake. Velocity profiles are used as the only input to all models, while additional parameters such as quality factor, density and nonlinear dynamic soil properties are estimated from empirical correlations. We quantify the differences of ground surface predictions and observations in terms of both seismological and engineering intensity measures, including bias ratios of peak ground response and visual comparisons of elastic spectra, and inelastic to elastic deformation ratio for multiple ductility ratios. We observe that PGV/Vs,30 — as measure of strain— is a better predictor of site nonlinearity than PGA, and that incremental nonlinear analyses are necessary to produce reliable estimates of high-frequency ground motion components at soft sites. We finally discuss the implications of our findings on the parameterization of nonlinear amplification factors in GMPEs, and on the extensive use of equivalent linear analyses in probabilistic seismic hazard procedures.

Propagation dynamics of super-Gaussian beams in fractional Schrödinger equation: from linear to nonlinear regimes.

Science.gov (United States)

Zhang, Lifu; Li, Chuxin; Zhong, Haizhe; Xu, Changwen; Lei, Dajun; Li, Ying; Fan, Dianyuan

2016-06-27

We have investigated the propagation dynamics of super-Gaussian optical beams in fractional Schrödinger equation. We have identified the difference between the propagation dynamics of super-Gaussian beams and that of Gaussian beams. We show that, the linear propagation dynamics of the super-Gaussian beams with order m > 1 undergo an initial compression phase before they split into two sub-beams. The sub-beams with saddle shape separate each other and their interval increases linearly with propagation distance. In the nonlinear regime, the super-Gaussian beams evolve to become a single soliton, breathing soliton or soliton pair depending on the order of super-Gaussian beams, nonlinearity, as well as the Lévy index. In two dimensions, the linear evolution of super-Gaussian beams is similar to that for one dimension case, but the initial compression of the input super-Gaussian beams and the diffraction of the splitting beams are much stronger than that for one dimension case. While the nonlinear propagation of the super-Gaussian beams becomes much more unstable compared with that for the case of one dimension. Our results show the nonlinear effects can be tuned by varying the Lévy index in the fractional Schrödinger equation for a fixed input power.

Magnetic field fluctuations analysis for the ion trap implementation of the quantum Rabi model in the deep strong coupling regime

Science.gov (United States)

Puebla, Ricardo; Casanova, Jorge; Plenio, Martin B.

2018-03-01

The dynamics of the quantum Rabi model (QRM) in the deep strong coupling regime is theoretically analyzed in a trapped-ion set-up. Recognizably, the main hallmark of this regime is the emergence of collapses and revivals, whose faithful observation is hindered under realistic magnetic dephasing noise. Here, we discuss how to attain a faithful implementation of the QRM in the deep strong coupling regime which is robust against magnetic field fluctuations and at the same time provides a large tunability of the simulated parameters. This is achieved by combining standing wave laser configuration with continuous dynamical decoupling. In addition, we study the role that amplitude fluctuations play to correctly attain the QRM using the proposed method. In this manner, the present work further supports the suitability of continuous dynamical decoupling techniques in trapped-ion settings to faithfully realize different interacting dynamics.

Nonlinear undulator tapering in conventional SASE regime at baseline electron beam parameters as a way to optimize the radiation characteristics of the European XFEL

Energy Technology Data Exchange (ETDEWEB)

Serkez, Svitozar; Kocharyan, Vitali; Saldin, Evgeni; Zagorodnov, Igor [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Geloni, Gianluca [European XFEL GmbH, Hamburg (Germany)

2013-09-15

We demonstrate that the output radiation characteristics of the European XFEL sources at nominal operation point can be easily made significantly better than what is currently reported in the TDRs of scientific instruments and X-ray optics. In fact, the output SASE characteristics of the baseline European XFEL have been previously optimized assuming uniform undulators at a nominal operating point of 5 kA peak current, without considering the potential of undulator tapering in the SASE regime. In order to illustrate this point, we analyze the case of an electron bunch with nominal parameters. Based on start-to-end simulations, we demonstrate that nonlinear undulator tapering allows one to achieve up to a tenfold increase in peak power and photon spectral density in the conventional SASE regime, without modification to the baseline design. The FEL code Genesis has been extensively used for these studies. In order to increase our confidence in simulation results, we cross-checked outcomes by reproducing simulations in the deep nonlinear SASE regime with tapered undulator using the code ALICE.

Mathematical structure of Rabi oscillations in the strong coupling regime

International Nuclear Information System (INIS)

Fujii, Kazuyuki

2003-01-01

In this paper, we generalize the Jaynes-Cummings Hamiltonian by making use of some operators based on Lie algebras su(1, 1) and su(2), and study a mathematical structure of Rabi floppings of these models in the strong coupling regime. We show that Rabi frequencies are given by matrix elements of generalized coherent operators (Fujii K 2002 Preprint quant-ph/0202081) under the rotating-wave approximation. In the first half, we make a general review of coherent operators and generalized coherent ones based on Lie algebras su(1, 1) and su(2). In the latter half, we carry out a detailed examination of Frasca (Frasca M 2001 Preprint quant-ph/0111134) and generalize his method, and moreover present some related problems. We also apply our results to the construction of controlled unitary gates in quantum computation. Lastly, we make a brief comment on application to holonomic quantum computation

Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria

International Nuclear Information System (INIS)

Frieman, E.A.; Chen, L.

1981-10-01

A nonlinear gyrokinetic formalism for low-frequency (less than the cyclotron frequency) microscopic electromagnetic perturbations in general magnetic field configurations is developed. The nonlinear equations thus derived are valid in the strong-turbulence regime and contain effects due to finite Larmor radius, plasma inhomogeneities, and magentic field geometries. The specific case of axisymmetric tokamaks is then considered, and a model nonlinear equation is derived for electrostatic drift waves. Also, applying the formalism to the shear Alfven wave heating sceme, it is found that nonlinear ion Landau damping of kinetic shear-Alfven waves is modified, both qualitatively and quantitatively, by the diamagnetic drift effects. In particular, wave energy is found to cascade in wavenumber instead of frequency

The breakdown of the weakly-nonlinear regime for kinetic instabilities

Science.gov (United States)

Sanz-Orozco, David; Berk, Herbert; Wang, Ge

2017-10-01

The evolution of marginally-unstable waves that interact resonantly with populations of energetic particles is governed by a well-known cubic integro-differential equation for the mode amplitude. One of the outcomes predicted by the equation is the so-called ``explosive'' regime, where the amplitude grows indefinitely, eventually taking the equation outside of its domain of validity. Beyond this point, only full Vlasov simulations will accurately describe the evolution of the mode amplitude. In this work, we study the breakdown of the cubic equation in detail. We find that, while the cubic equation is still valid, the distribution function of the energetic particles locally flattens or ``folds'' in phase space. This feature is unexpected in view of the assumptions of the theory that are given in. We also derive fifth-order terms in the wave equation, which not only give us a more accurate description of the marginally-unstable modes, but they also allow us to predict the breakdown of the cubic equation. Our findings allow us to better understand the transition between weakly-nonlinear modes and the long-term chirping modes that ultimately emerge.

Intensity dependent waiting time for strong electron trapping events in speckle stimulated raman scatter

Energy Technology Data Exchange (ETDEWEB)

Rose, Harvey [Los Alamos National Laboratory; Daughton, W [Los Alamos National Laboratory; Yin, L [Los Alamos National Laboratory

2009-01-01

The onset of Stimulated Raman scatter from an intense laser speckle is the simplest experimentally realizable laser-plasma-interaction environment. Despite this data and recent 3D particle simulations, the controlling mechanism at the onset of backscatter in the kinetic regime when strong electron trapping in the daughter Langmuir wave is a dominant nonlinearity is not understood. This paper explores the consequences of assuming that onset is controlled by large thermal fluctuations. A super exponential dependence of mean reflectivity on speckle intensity in the onset regime is predicted.

Strong coupling between coherent gratings due to nonlinear spatial frequency mixing in Bi12SiO20

DEFF Research Database (Denmark)

Andersen, Peter E.; Buchhave, P.; Petersen, Paul Michael

1996-01-01

Nonlinear interactions between multiple coherent photorefractive gratings in Bi12SiO20 are investigated. It is demonstrated that the nonlinear mixing, or cross talk, is strongly influenced by the intensity ration kappa between the two object beams. The diffraction efficiency of a specific grating...... may be increased or strongly decreased depending on kappa. In the limit of a weak reference beam intensity compared to the sum of the object beam intencities, we derive an analytical expression for the cross talk valid for all kappa. Furthermore, we find the value of kappa yielding zero cross talk. We...

Transient thermal effect, nonlinear refraction and nonlinear absorption properties of graphene oxide sheets in dispersion.

Science.gov (United States)

Zhang, Xiao-Liang; Liu, Zhi-Bo; Li, Xiao-Chun; Ma, Qiang; Chen, Xu-Dong; Tian, Jian-Guo; Xu, Yan-Fei; Chen, Yong-Sheng

2013-03-25

The nonlinear refraction (NLR) properties of graphene oxide (GO) in N, N-Dimethylformamide (DMF) was studied in nanosecond, picosecond and femtosecond time regimes by Z-scan technique. Results show that the dispersion of GO in DMF exhibits negative NLR properties in nanosecond time regime, which is mainly attributed to transient thermal effect in the dispersion. The dispersion also exhibits negative NLR in picosecond and femtosecond time regimes, which are arising from sp(2)- hybridized carbon domains and sp(3)- hybridized matrix in GO sheets. To illustrate the relations between NLR and nonlinear absorption (NLA), NLA properties of the dispersion were also studied in nanosecond, picosecond and femtosecond time regimes.

Modeling of Nonlinear Propagation in Multi-layer Biological Tissues for Strong Focused Ultrasound

International Nuclear Information System (INIS)

Ting-Bo, Fan; Zhen-Bo, Liu; Zhe, Zhang; Dong, Zhang; Xiu-Fen, Gong

2009-01-01

A theoretical model of the nonlinear propagation in multi-layered tissues for strong focused ultrasound is proposed. In this model, the spheroidal beam equation (SBE) is utilized to describe the nonlinear sound propagation in each layer tissue, and generalized oblique incidence theory is used to deal with the sound transmission between two layer tissues. Computer simulation is performed on a fat-muscle-liver tissue model under the irradiation of a 1 MHz focused transducer with a large aperture angle of 35°. The results demonstrate that the tissue layer would change the amplitude of sound pressure at the focal region and cause the increase of side petals. (fundamental areas of phenomenology (including applications))

Strong asymmetry for surface modes in nonlinear lattices with long-range coupling

International Nuclear Information System (INIS)

Martinez, Alejandro J.; Vicencio, Rodrigo A.; Molina, Mario I.

2010-01-01

We analyze the formation of localized surface modes on a nonlinear cubic waveguide array in the presence of exponentially decreasing long-range interactions. We find that the long-range coupling induces a strong asymmetry between the focusing and defocusing cases for the topology of the surface modes and also for the minimum power needed to generate them. In particular, for the defocusing case, there is an upper power threshold for exciting staggered modes, which depends strongly on the long-range coupling strength. The power threshold for dynamical excitation of surface modes increases (decreases) with the strength of long-range coupling for the focusing (defocusing) cases. These effects seem to be generic for discrete lattices with long-range interactions.

Response of MDOF strongly nonlinear systems to fractional Gaussian noises

Energy Technology Data Exchange (ETDEWEB)

Deng, Mao-Lin; Zhu, Wei-Qiu, E-mail: wqzhu@zju.edu.cn [Department of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou 310027 (China)

2016-08-15

In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.

Response of MDOF strongly nonlinear systems to fractional Gaussian noises.

Science.gov (United States)

Deng, Mao-Lin; Zhu, Wei-Qiu

2016-08-01

In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.

Response of MDOF strongly nonlinear systems to fractional Gaussian noises

International Nuclear Information System (INIS)

Deng, Mao-Lin; Zhu, Wei-Qiu

2016-01-01

In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.

Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides

DEFF Research Database (Denmark)

Reddy, D. V.; Raymer, M. G.; McKinstrie, C. J.

2013-01-01

in a transparent optical network using temporally orthogonal waveforms to encode different channels. We model the process using coupled-mode equations appropriate for wave mixing in a uniform second-order nonlinear optical medium pumped by a strong laser pulse. We find Green functions describing the process...... in this optimal regime. We also find an operating regime in which high-efficiency frequency conversion without temporal-shape selectivity can be achieved while preserving the shapes of a wide class of input pulses. The results are applicable to both classical and quantum frequency conversion....

Strongly nonlinear electronic transport in Cr-Si composite films

International Nuclear Information System (INIS)

Burkov, A.T.; Vinzelberg, H.; Schumann, J.; Nakama, T.; Yagasaki, K.

2004-01-01

The phase formation, the resistivity and the thermopower of amorphous Cr 0.15 Si 0.85 , and nanocrystalline CrSi 2 -Si thin film composites have been studied. The films were produced by a magnetron sputtering of a composite target onto unheated substrates with subsequent crystallization of the film at high temperatures. As the film composite develops under the heat treatment from the initial amorphous state into the final polycrystalline material, two percolation thresholds were found. At first, the percolating cluster of nanocrystalline CrSi 2 is formed. However, this cluster is destroyed with further annealing due to crystallization and redistribution of Si. The composite films which are close to this insulating threshold reveal a strongly nonlinear conductivity. The conductivity increases with the current by two orders of magnitude

Using strong nonlinearity and high-frequency vibrations to control effective properties of discrete elastic waveguides

DEFF Research Database (Denmark)

Lazarov, Boyan Stefanov; Thomsen, Jon Juel; Snaeland, Sveinn Orri

2008-01-01

The aim of this article is to investigate how highfrequency (HF) excitation, combined with strong nonlinear elastic material behavior, influences the effective material or structural properties for low-frequency excitation and wave propagation. The HF effects are demonstrated on discrete linear s...

A cavity-Cooper pair transistor scheme for investigating quantum optomechanics in the ultra-strong coupling regime

International Nuclear Information System (INIS)

Rimberg, A J; Blencowe, M P; Armour, A D; Nation, P D

2014-01-01

We propose a scheme involving a Cooper pair transistor (CPT) embedded in a superconducting microwave cavity, where the CPT serves as a charge tunable quantum inductor to facilitate ultra-strong coupling between photons in the cavity and a nano- to meso-scale mechanical resonator. The mechanical resonator is capacitively coupled to the CPT, such that mechanical displacements of the resonator cause a shift in the CPT inductance and hence the cavity's resonant frequency. The amplification provided by the CPT is sufficient for the zero point motion of the mechanical resonator alone to cause a significant change in the cavity resonance. Conversely, a single photon in the cavity causes a shift in the mechanical resonator position on the order of its zero point motion. As a result, the cavity-Cooper pair transistor coupled to a mechanical resonator will be able to access a regime in which single photons can affect single phonons and vice versa. Realizing this ultra-strong coupling regime will facilitate the creation of non-classical states of the mechanical resonator, as well as the means to accurately characterize such states by measuring the cavity photon field. (paper)

Stochastic dynamical models for ecological regime shifts

DEFF Research Database (Denmark)

Møller, Jan Kloppenborg; Carstensen, Jacob; Madsen, Henrik

the physical and biological knowledge of the system, and nonlinearities introduced here can generate regime shifts or enhance the probability of regime shifts in the case of stochastic models, typically characterized by a threshold value for the known driver. A simple model for light competition between...... definition and stability of regimes become less subtle. Ecological regime shifts and their modeling must be viewed in a probabilistic manner, particularly if such model results are to be used in ecosystem management....

Microscopic investigations of the terahertz and the extreme nonlinear optical response of semiconductors

Energy Technology Data Exchange (ETDEWEB)

Golde, Daniel

2010-06-22

In the major part of this Thesis, we discuss the linear THz response of semiconductor nanostructures based on a microscopic theory. Here, two different problems are investigated: intersubband transitions in optically excited quantum wells and the THz plasma response of two-dimensional systems. In the latter case, we analyze the response of correlated electron and electron-hole plasmas. Extracting the plasma frequency from the linear response, we find significant deviations from the commonly accepted two-dimensional plasma frequency. Besides analyzing the pure plasma response, we also consider an intermediate regime where the response of the electron-hole plasma consists of a mixture of plasma contributions and excitonic transitions. A quantitative experiment-theory comparison provides novel insights into the behavior of the system at the transition from one regime to the other. The discussion of the intersubband transitions mainly focuses on the coherent superposition of the responses from true THz transitions and the ponderomotively accelerated carriers. We present a simple method to directly identify ponderomotive effects in the linear THz response. Apart from that, the excitonic contributions to intersubband transitions are investigated. The last part of the present Thesis deals with a completely different regime. Here, the extreme nonlinear optical response of low-dimensional semiconductor structures is discussed. Formally, extreme nonlinear optics describes the regime of light-matter interaction where the exciting field is strong enough such that the Rabi frequency is comparable to or larger than the characteristic transition frequency of the investigated system. Here, the Rabi frequency is given by the product of the electrical field strength and the dipole-matrix element of the respective transition. Theoretical investigations have predicted a large number of novel nonlinear effects arising for such strong excitations. Some of them have been observed in

Nonlinear magnetic electron tripolar vortices in streaming plasmas.

Science.gov (United States)

Vranjes, J; Marić, G; Shukla, P K

2000-06-01

Magnetic electron modes in nonuniform magnetized and unmagnetized streaming plasmas, with characteristic frequencies between the ion and electron plasma frequencies and at spatial scales of the order of the collisionless skin depth, are studied. Two coupled equations, for the perturbed (in the case of magnetized plasma) or self-generated (for the unmagnetized plasma case) magnetic field, and the temperature, are solved in the strongly nonlinear regime and stationary traveling solutions in the form of tripolar vortices are found.

The focal boundary value problem for strongly singular higher-order nonlinear functional-differential equations

Czech Academy of Sciences Publication Activity Database

Mukhigulashvili, Sulkhan; Půža, B.

2015-01-01

Roč. 2015, January (2015), s. 17 ISSN 1687-2770 Institutional support: RVO:67985840 Keywords : higher order nonlinear functional-differential equations * two-point right-focal boundary value problem * strong singularity Subject RIV: BA - General Mathematics Impact factor: 0.642, year: 2015 http://link.springer.com/article/10.1186%2Fs13661-014-0277-1

Discrete and mesoscopic regimes of finite-size wave turbulence

International Nuclear Information System (INIS)

L'vov, V. S.; Nazarenko, S.

2010-01-01

Bounding volume results in discreteness of eigenmodes in wave systems. This leads to a depletion or complete loss of wave resonances (three-wave, four-wave, etc.), which has a strong effect on wave turbulence (WT) i.e., on the statistical behavior of broadband sets of weakly nonlinear waves. This paper describes three different regimes of WT realizable for different levels of the wave excitations: discrete, mesoscopic and kinetic WT. Discrete WT comprises chaotic dynamics of interacting wave 'clusters' consisting of discrete (often finite) number of connected resonant wave triads (or quarters). Kinetic WT refers to the infinite-box theory, described by well-known wave-kinetic equations. Mesoscopic WT is a regime in which either the discrete and the kinetic evolutions alternate or when none of these two types is purely realized. We argue that in mesoscopic systems the wave spectrum experiences a sandpile behavior. Importantly, the mesoscopic regime is realized for a broad range of wave amplitudes which typically spans over several orders on magnitude, and not just for a particular intermediate level.

Behavior of Filters and Smoothers for Strongly Nonlinear Dynamics

Science.gov (United States)

Zhu, Yanqui; Cohn, Stephen E.; Todling, Ricardo

1999-01-01

The Kalman filter is the optimal filter in the presence of known gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions. Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz model as well as more realistic models of the means and atmosphere. A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter situations to allow for correct update of the ensemble members. The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to be quite puzzling in that results state estimates are worse than for their filter analogue. In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use the Lorenz model to test and compare the behavior of a variety of implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.

A nonlinear efficient layerwise finite element model for smart piezolaminated composites under strong applied electric field

International Nuclear Information System (INIS)

Kapuria, S; Yaqoob Yasin, M

2013-01-01

In this work, we present an electromechanically coupled efficient layerwise finite element model for the static response of piezoelectric laminated composite and sandwich plates, considering the nonlinear behavior of piezoelectric materials under strong electric field. The nonlinear model is developed consistently using a variational principle, considering a rotationally invariant second order nonlinear constitutive relationship, and full electromechanical coupling. In the piezoelectric layer, the electric potential is approximated to have a quadratic variation across the thickness, as observed from exact three dimensional solutions, and the equipotential condition of electroded piezoelectric surfaces is modeled using the novel concept of an electric node. The results predicted by the nonlinear model compare very well with the experimental data available in the literature. The effect of the piezoelectric nonlinearity on the static response and deflection/stress control is studied for piezoelectric bimorph as well as hybrid laminated plates with isotropic, angle-ply composite and sandwich substrates. For high electric fields, the difference between the nonlinear and linear predictions is large, and cannot be neglected. The error in the prediction of the smeared counterpart of the present theory with the same number of primary displacement unknowns is also examined. (paper)

Electrical control of spontaneous emission and strong coupling for a single quantum dot

DEFF Research Database (Denmark)

Laucht, A.; Hofbauer, F.; Hauke, N.

2009-01-01

We report the design, fabrication and optical investigation of electrically tunable single quantum dots—photonic crystal defect nanocavities operating in both the weak and strong coupling regimes of the light–matter interaction. Unlike previous studies where the dot–cavity spectral detuning...... switchable optical nonlinearity at the single photon level, paving the way towards on-chip dot-based nano-photonic devices that can be integrated with passive optical components....

Variational Boussinesq model for strongly nonlinear dispersive waves

NARCIS (Netherlands)

Lawrence, C.; Adytia, D.; van Groesen, E.

2018-01-01

For wave tank, coastal and oceanic applications, a fully nonlinear Variational Boussinesq model with optimized dispersion is derived and a simple Finite Element implementation is described. Improving a previous weakly nonlinear version, high waves over flat and varying bottom are shown to be

Cosmological N-body simulations with a tree code - Fluctuations in the linear and nonlinear regimes

International Nuclear Information System (INIS)

Suginohara, Tatsushi; Suto, Yasushi; Bouchet, F.R.; Hernquist, L.

1991-01-01

The evolution of gravitational systems is studied numerically in a cosmological context using a hierarchical tree algorithm with fully periodic boundary conditions. The simulations employ 262,144 particles, which are initially distributed according to scale-free power spectra. The subsequent evolution is followed in both flat and open universes. With this large number of particles, the discretized system can accurately model the linear phase. It is shown that the dynamics in the nonlinear regime depends on both the spectral index n and the density parameter Omega. In Omega = 1 universes, the evolution of the two-point correlation function Xi agrees well with similarity solutions for Xi greater than about 100 but its slope is steeper in open models with the same n. 28 refs

Nonlinear parity readout with a microwave photodetector

Science.gov (United States)

Schöndorf, M.; Wilhelm, F. K.

2018-04-01

Robust high-fidelity parity measurement is an important operation in many applications of quantum computing. In this work we show how in a circuit QED architecture, one can measure parity in a single shot at very high contrast by taking advantage of the nonlinear behavior of a strongly driven microwave cavity coupled to one or multiple qubits. We work in a nonlinear dispersive regime treated in an exact dispersive transformation. We show that appropriate tuning of experimental parameters leads to very high contrast in the cavity and therefore to a high-efficiency parity readout with a microwave photon counter or another amplitude detector. These tuning conditions are based on nonlinearity and are hence more robust than previously described linear tuning schemes. In the first part of the paper we show in detail how to achieve this for two-qubit parity measurements and extend this to N qubits in the second part of the paper. We also study the quantum nondemolition character of the protocol.

Fermionic reaction coordinates and their application to an autonomous Maxwell demon in the strong-coupling regime

Science.gov (United States)

Strasberg, Philipp; Schaller, Gernot; Schmidt, Thomas L.; Esposito, Massimiliano

2018-05-01

We establish a theoretical method which goes beyond the weak-coupling and Markovian approximations while remaining intuitive, using a quantum master equation in a larger Hilbert space. The method is applicable to all impurity Hamiltonians tunnel coupled to one (or multiple) baths of free fermions. The accuracy of the method is in principle not limited by the system-bath coupling strength, but rather by the shape of the spectral density and it is especially suited to study situations far away from the wide-band limit. In analogy to the bosonic case, we call it the fermionic reaction coordinate mapping. As an application, we consider a thermoelectric device made of two Coulomb-coupled quantum dots. We pay particular attention to the regime where this device operates as an autonomous Maxwell demon shoveling electrons against the voltage bias thanks to information. Contrary to previous studies, we do not rely on a Markovian weak-coupling description. Our numerical findings reveal that in the regime of strong coupling and non-Markovianity, the Maxwell demon is often doomed to disappear except in a narrow parameter regime of small power output.

A detailed examination of the LWFA in the Self-Guided Nonlinear Blowout Regime for 15-100 Joule Lasers

Science.gov (United States)

Davidson, Asher; Tableman, Adam; Yu, Peicheng; An, Weiming; Tsung, Frank; Mori, Warren; Lu, Wei; Fonseca, Ricardo

2017-10-01

We examine scaling laws for LWFA in the regime nonlinear, self-guided regime in detail using the quasi-3D version of the particle-in-cell code OSIRIS. We find that the scaling laws continue to work well when we fix the normalized laser amplitude while reducing plasma density. It is further found that the energy gain for fixed laser energy can be improved by shortening the pulse length until self-guiding almost no longer occurs and that the energy gain can be optimized by using lasers with asymmetric longitudinal profiles. We find that when optimized, a 15 J laser may yield particle energies as high as 5.3 GeV without the need of any external guiding. Detailed studies for optimizing energy gains from 30 J and 100 J lasers will also presented which indicate that energies in excess of 10 GeV can be possible in the near term without the need for external guiding. This work is supported by the NSF and DOE.

Saturation at Low X and Nonlinear Evolution

International Nuclear Information System (INIS)

Stasto, A.M.

2002-01-01

In this talk the results of the analytical and numerical analysis of the nonlinear Balitsky-Kovchegov equation are presented. The characteristic BFKL diffusion into infrared regime is suppressed by the generation of the saturation scale Q s . We identify the scaling and linear regimes for the solution. We also study the impact of subleading corrections onto the nonlinear evolution. (author)

Using strong nonlinearity and high-frequency vibrations to control effective mechanical stiffness

DEFF Research Database (Denmark)

Thomsen, Jon Juel

2008-01-01

the method of direct separation of motions with results of a modified multiple scales ap-proach, valid also for strong nonlinearity, the stiffening ef-fect is predicted for a generic 1-dof system, and results are tested against numerical simulation and ((it is planned)) laboratory experiments.......High-frequency excitation (HFE) can be used to change the effective stiffness of an elastic structure, and related quanti-ties such as resonance frequencies, wave speed, buckling loads, and equilibrium states. There are basically two ways to do this: By using parametrical HFE (with or without non...

On the physical contributions to the third-order nonlinear optical response in plasmonic nanocomposites

International Nuclear Information System (INIS)

Fernández-Hernández, Roberto Carlos; Gleason-Villagran, Roberto; Rodríguez-Fernández, Luis; Crespo-Sosa, Alejandro; Cheang-Wong, Juan Carlos; López-Suárez, Alejandra; Oliver, Alicia; Reyes-Esqueda, Jorge Alejandro; Torres-Torres, Carlos; Rangel-Rojo, Raúl

2012-01-01

Au and Ag isotropic and anisotropic nanocomposites were prepared using the ion implantation technique. Their optical properties were studied at several wavelengths in the optical range 300–800 nm, across their plasmon resonances. The linear regime was characterized by measuring the absorption spectrum and the third-order nonlinear regime by means of the Z-scan technique using a tunable picosecond pulsed laser system (26 ps). Open-aperture Z-scan traces show a superposition of different optical nonlinear absorption (NLA) processes in the whole range studied. We associate these phenomena with the excitation of inter- and intra-band electronic transitions, which contribute with a positive sign to NLA, and to the formation of hot-electrons, which contribute with opposite sign to NLA. Closed-aperture traces for measuring nonlinear refraction (NLR) show different signs for Au and Ag samples, and a change of sign in Au is found when purely inter-band transitions are excited. In this work, for the appropriate wavelength, it is worth remarking on the free-electron response to the exciting light and its strong contribution to the nonlinear optical properties for low (intra-band) and high (hot-electrons) irradiances. (paper)

Nonlinear Dynamics of Nanomechanical Resonators

Science.gov (United States)

Ramakrishnan, Subramanian; Gulak, Yuiry; Sundaram, Bala; Benaroya, Haym

2007-03-01

Nanoelectromechanical systems (NEMS) offer great promise for many applications including motion and mass sensing. Recent experimental results suggest the importance of nonlinear effects in NEMS, an issue which has not been addressed fully in theory. We report on a nonlinear extension of a recent analytical model by Armour et al [1] for the dynamics of a single-electron transistor (SET) coupled to a nanomechanical resonator. We consider the nonlinear resonator motion in both (a) the Duffing and (b) nonlinear pendulum regimes. The corresponding master equations are derived and solved numerically and we consider moment approximations as well. In the Duffing case with hardening stiffness, we observe that the resonator is damped by the SET at a significantly higher rate. In the cases of softening stiffness and the pendulum, there exist regimes where the SET adds energy to the resonator. To our knowledge, this is the first instance of a single model displaying both negative and positive resonator damping in different dynamical regimes. The implications of the results for SET sensitivity as well as for, as yet unexplained, experimental results will be discussed. 1. Armour et al. Phys.Rev.B (69) 125313 (2004).

Non-linear dynamical classification of short time series of the rössler system in high noise regimes.

Science.gov (United States)

Lainscsek, Claudia; Weyhenmeyer, Jonathan; Hernandez, Manuel E; Poizner, Howard; Sejnowski, Terrence J

2013-01-01

Time series analysis with delay differential equations (DDEs) reveals non-linear properties of the underlying dynamical system and can serve as a non-linear time-domain classification tool. Here global DDE models were used to analyze short segments of simulated time series from a known dynamical system, the Rössler system, in high noise regimes. In a companion paper, we apply the DDE model developed here to classify short segments of encephalographic (EEG) data recorded from patients with Parkinson's disease and healthy subjects. Nine simulated subjects in each of two distinct classes were generated by varying the bifurcation parameter b and keeping the other two parameters (a and c) of the Rössler system fixed. All choices of b were in the chaotic parameter range. We diluted the simulated data using white noise ranging from 10 to -30 dB signal-to-noise ratios (SNR). Structure selection was supervised by selecting the number of terms, delays, and order of non-linearity of the model DDE model that best linearly separated the two classes of data. The distances d from the linear dividing hyperplane was then used to assess the classification performance by computing the area A' under the ROC curve. The selected model was tested on untrained data using repeated random sub-sampling validation. DDEs were able to accurately distinguish the two dynamical conditions, and moreover, to quantify the changes in the dynamics. There was a significant correlation between the dynamical bifurcation parameter b of the simulated data and the classification parameter d from our analysis. This correlation still held for new simulated subjects with new dynamical parameters selected from each of the two dynamical regimes. Furthermore, the correlation was robust to added noise, being significant even when the noise was greater than the signal. We conclude that DDE models may be used as a generalizable and reliable classification tool for even small segments of noisy data.

Nonlinearities in modified gravity cosmology: Signatures of modified gravity in the nonlinear matter power spectrum

International Nuclear Information System (INIS)

Cui Weiguang; Zhang Pengjie; Yang Xiaohu

2010-01-01

A large fraction of cosmological information on dark energy and gravity is encoded in the nonlinear regime. Precision cosmology thus requires precision modeling of nonlinearities in general dark energy and modified gravity models. We modify the Gadget-2 code and run a series of N-body simulations on modified gravity cosmology to study the nonlinearities. The modified gravity model that we investigate in the present paper is characterized by a single parameter ζ, which determines the enhancement of particle acceleration with respect to general relativity (GR), given the identical mass distribution (ζ=1 in GR). The first nonlinear statistics we investigate is the nonlinear matter power spectrum at k < or approx. 3h/Mpc, which is the relevant range for robust weak lensing power spectrum modeling at l < or approx. 2000. In this study, we focus on the relative difference in the nonlinear power spectra at corresponding redshifts where different gravity models have the same linear power spectra. This particular statistics highlights the imprint of modified gravity in the nonlinear regime and the importance of including the nonlinear regime in testing GR. By design, it is less susceptible to the sample variance and numerical artifacts. We adopt a mass assignment method based on wavelet to improve the power spectrum measurement. We run a series of tests to determine the suitable simulation specifications (particle number, box size, and initial redshift). We find that, the nonlinear power spectra can differ by ∼30% for 10% deviation from GR (|ζ-1|=0.1) where the rms density fluctuations reach 10. This large difference, on one hand, shows the richness of information on gravity in the corresponding scales, and on the other hand, invalidates simple extrapolations of some existing fitting formulae to modified gravity cosmology.

Nonlinear dynamics of trions under strong optical excitation in monolayer MoSe2.

Science.gov (United States)

Ye, Jialiang; Yan, Tengfei; Niu, Binghui; Li, Ying; Zhang, Xinhui

2018-02-05

By employing ultrafast transient reflection measurements based on two-color pump-probe spectroscopy, the population and valley polarization dynamics of trions in monolayer MoSe 2 were investigated at relatively high excitation densities under near-resonant excitation. Both the nonlinear dynamic photobleaching of the trion resonance and the redshift of the exciton resonance were found to be responsible for the excitation-energy- and density-dependent transient reflection change as a result of many-body interactions. Furthermore, from the polarization-resolved measurements, it was revealed that the initial fast population and polarization decay process upon strong photoexcitation observed for trions was determined by trion formation, transient phase-space filling and the short valley lifetime of excitons. The results provide a basic understanding of the nonlinear dynamics of population and valley depolarization of trions, as well as exciton-trion correlation in atomically thin MoSe 2 and other transition metal dichalcogenide materials.

IUTAM Symposium on Nonlinear Dynamics for Advanced Technologies and Engineering Design

CERN Document Server

Rega, Giuseppe

2013-01-01

Nonlinear dynamics has been enjoying a vast development for nearly four decades resulting in a range of well established theory, with the potential to significantly enhance performance, effectiveness, reliability and safety of physical systems as well as offering novel technologies and designs. By critically appraising the state-of-the-art, it is now time to develop design criteria and technology for new generation products/processes operating on principles of nonlinear interaction and in the nonlinear regime, leading to more effective, sensitive, accurate, and durable methods than what is currently available. This new approach is expected to radically influence the design, control and exploitation paradigms, in a magnitude of contexts. With a strong emphasis on experimentally calibrated and validated models, contributions by top-level international experts will foster future directions for the development of engineering technologies and design using robust nonlinear dynamics modelling and analysis.  

Strong lensing of a regular black hole with an electrodynamics source

Science.gov (United States)

Manna, Tuhina; Rahaman, Farook; Molla, Sabiruddin; Bhadra, Jhumpa; Shah, Hasrat Hussain

2018-05-01

In this paper we have investigated the gravitational lensing phenomenon in the strong field regime for a regular, charged, static black holes with non-linear electrodynamics source. We have obtained the angle of deflection and compared it to a Schwarzschild black hole and Reissner Nordström black hole with similar properties. We have also done a graphical study of the relativistic image positions and magnifications. We hope that this method may be useful in the detection of non-luminous bodies like this current black hole.

Statistical approach of weakly nonlinear ablative Rayleigh-Taylor instability

International Nuclear Information System (INIS)

Garnier, J.; Masse, L.

2005-01-01

A weakly nonlinear model is proposed for the Rayleigh-Taylor instability in presence of ablation and thermal transport. The nonlinear effects for a single-mode disturbance are computed, included the nonlinear correction to the exponential growth of the fundamental modulation. Mode coupling in the spectrum of a multimode disturbance is thoroughly analyzed by a statistical approach. The exponential growth of the linear regime is shown to be reduced by the nonlinear mode coupling. The saturation amplitude is around 0.1λ for long wavelengths, but higher for short instable wavelengths in the ablative regime

Nonlinear energy transfer and current sheet development in localized Alfvén wavepacket collisions in the strong turbulence limit

Science.gov (United States)

Verniero, J. L.; Howes, G. G.; Klein, K. G.

2018-02-01

In space and astrophysical plasmas, turbulence is responsible for transferring energy from large scales driven by violent events or instabilities, to smaller scales where turbulent energy is ultimately converted into plasma heat by dissipative mechanisms. The nonlinear interaction between counterpropagating Alfvén waves, denoted Alfvén wave collisions, drives this turbulent energy cascade, as recognized by early work with incompressible magnetohydrodynamic (MHD) equations. Recent work employing analytical calculations and nonlinear gyrokinetic simulations of Alfvén wave collisions in an idealized periodic initial state have demonstrated the key properties that strong Alfvén wave collisions mediate effectively the transfer of energy to smaller perpendicular scales and self-consistently generate current sheets. For the more realistic case of the collision between two initially separated Alfvén wavepackets, we use a nonlinear gyrokinetic simulation to show here that these key properties persist: strong Alfvén wavepacket collisions indeed facilitate the perpendicular cascade of energy and give rise to current sheets. Furthermore, the evolution shows that nonlinear interactions occur only while the wavepackets overlap, followed by a clean separation of the wavepackets with straight uniform magnetic fields and the cessation of nonlinear evolution in between collisions, even in the gyrokinetic simulation presented here which resolves dispersive and kinetic effects beyond the reach of the MHD theory.

Tokamak m = 1 magnetohydrodynamic calculations in toroidal geometry using a full set of nonlinear resistive magnetohydrodynamic equations

International Nuclear Information System (INIS)

Charlton, L.A.; Carreras, B.A.; Holmes, J.A.; Lynch, V.E.

1988-01-01

The linear stability and nonlinear evolution of the resistive m = 1 mode in tokamaks is studied using a full set of resistive magnetohydrodynamic (MHD) equations in toroidal geometry. The modification of the linear and nonlinear properties of the mode by a combination of strong toroidal effects and low resistivity is the focus of this work. Linearly there is a transition from resistive kink to resistive tearing behavior as the aspect ratio and resistivity are reduced, and there is a corresponding modification of the nonlinear behavior, including a slowing of the island growth and development of a Rutherford regime, as the tearing regime is approached. In order to study the sensitivity of the stability and evolution to assumptions concerning the equation of state, two sets of full nonlinear resistive MHD equations (a pressure convection set and an incompressible set) are used. Both sets give more stable nonlinear behavior as the aspect ratio is reduced. The pressure convection set shows a transition from a Kadomtsev reconnection at large aspect ratio to a saturation at small aspect ratio. The incompressible set yields Kadomtsev reconnection for all aspect ratios, but with a significant lengthening of the reconnection time and development of a Rutherford regime at an aspect ratio approaching the transition from a resistive kink mode to a tearing mode. The pressure convection set gives an incomplete reconnection similar to that sometimes seen experimentally. The pressure convection set is, however, strictly justified only at high beta

Dynamics of a linear system coupled to a chain of light nonlinear oscillators analyzed through a continuous approximation

Science.gov (United States)

Charlemagne, S.; Ture Savadkoohi, A.; Lamarque, C.-H.

2018-07-01

The continuous approximation is used in this work to describe the dynamics of a nonlinear chain of light oscillators coupled to a linear main system. A general methodology is applied to an example where the chain has local nonlinear restoring forces. The slow invariant manifold is detected at fast time scale. At slow time scale, equilibrium and singular points are sought around this manifold in order to predict periodic regimes and strongly modulated responses of the system. Analytical predictions are in good accordance with numerical results and represent a potent tool for designing nonlinear chains for passive control purposes.

HIGH-PRECISION PREDICTIONS FOR THE ACOUSTIC SCALE IN THE NONLINEAR REGIME

International Nuclear Information System (INIS)

Seo, Hee-Jong; Eckel, Jonathan; Eisenstein, Daniel J.; Mehta, Kushal; Metchnik, Marc; Pinto, Phillip; Xu Xiaoying; Padmanabhan, Nikhil; Takahashi, Ryuichi; White, Martin

2010-01-01

We measure shifts of the acoustic scale due to nonlinear growth and redshift distortions to a high precision using a very large volume of high-force-resolution simulations. We compare results from various sets of simulations that differ in their force, volume, and mass resolution. We find a consistency within 1.5σ for shift values from different simulations and derive shift α(z) - 1 = (0.300 ± 0.015) %[D(z)/D(0)] 2 using our fiducial set. We find a strong correlation with a non-unity slope between shifts in real space and in redshift space and a weak correlation between the initial redshift and low redshift. Density-field reconstruction not only removes the mean shifts and reduces errors on the mean, but also tightens the correlations. After reconstruction, we recover a slope of near unity for the correlation between the real and redshift space and restore a strong correlation between the initial and the low redshifts. We derive propagators and mode-coupling terms from our N-body simulations and compare with the Zel'dovich approximation and the shifts measured from the χ 2 fitting, respectively. We interpret the propagator and the mode-coupling term of a nonlinear density field in the context of an average and a dispersion of its complex Fourier coefficients relative to those of the linear density field; from these two terms, we derive a signal-to-noise ratio of the acoustic peak measurement. We attempt to improve our reconstruction method by implementing 2LPT and iterative operations, but we obtain little improvement. The Fisher matrix estimates of uncertainty in the acoustic scale is tested using 5000 h -3 Gpc 3 of cosmological Particle-Mesh simulations from Takahashi et al. At an expected sample variance level of 1%, the agreement between the Fisher matrix estimates based on Seo and Eisenstein and the N-body results is better than 10%.

Quantitative theory of driven nonlinear brain dynamics.

Science.gov (United States)

Roberts, J A; Robinson, P A

2012-09-01

Strong periodic stimuli such as bright flashing lights evoke nonlinear responses in the brain and interact nonlinearly with ongoing cortical activity, but the underlying mechanisms for these phenomena are poorly understood at present. The dominant features of these experimentally observed dynamics are reproduced by the dynamics of a quantitative neural field model subject to periodic drive. Model power spectra over a range of drive frequencies show agreement with multiple features of experimental measurements, exhibiting nonlinear effects including entrainment over a range of frequencies around the natural alpha frequency f(α), subharmonic entrainment near 2f(α), and harmonic generation. Further analysis of the driven dynamics as a function of the drive parameters reveals rich nonlinear dynamics that is predicted to be observable in future experiments at high drive amplitude, including period doubling, bistable phase-locking, hysteresis, wave mixing, and chaos indicated by positive Lyapunov exponents. Moreover, photosensitive seizures are predicted for physiologically realistic model parameters yielding bistability between healthy and seizure dynamics. These results demonstrate the applicability of neural field models to the new regime of periodically driven nonlinear dynamics, enabling interpretation of experimental data in terms of specific generating mechanisms and providing new tests of the theory. Copyright © 2012 Elsevier Inc. All rights reserved.

Nonlinear dynamics of semiconductors in strong THz electric fields

DEFF Research Database (Denmark)

Tarekegne, Abebe Tilahun

In this thesis, we investigate nonlinear interactions of an intense terahertz (THz) field with semiconductors, in particular the technologically relevant materials silicon and silicon carbide. We reveal the time-resolved dynamics of the nonlinear processes by pump-probe experiments that involve...

Homogenized description and retrieval method of nonlinear metasurfaces

Science.gov (United States)

Liu, Xiaojun; Larouche, Stéphane; Smith, David R.

2018-03-01

A patterned, plasmonic metasurface can strongly scatter incident light, functioning as an extremely low-profile lens, filter, reflector or other optical device. When the metasurface is patterned uniformly, its linear optical properties can be expressed using effective surface electric and magnetic polarizabilities obtained through a homogenization procedure. The homogenized description of a nonlinear metasurface, however, presents challenges both because of the inherent anisotropy of the medium as well as the much larger set of potential wave interactions available, making it challenging to assign effective nonlinear parameters to the otherwise inhomogeneous layer of metamaterial elements. Here we show that a homogenization procedure can be developed to describe nonlinear metasurfaces, which derive their nonlinear response from the enhanced local fields arising within the structured plasmonic elements. With the proposed homogenization procedure, we are able to assign effective nonlinear surface polarization densities to a nonlinear metasurface, and link these densities to the effective nonlinear surface susceptibilities and averaged macroscopic pumping fields across the metasurface. These effective nonlinear surface polarization densities are further linked to macroscopic nonlinear fields through the generalized sheet transition conditions (GSTCs). By inverting the GSTCs, the effective nonlinear surface susceptibilities of the metasurfaces can be solved for, leading to a generalized retrieval method for nonlinear metasurfaces. The application of the homogenization procedure and the GSTCs are demonstrated by retrieving the nonlinear susceptibilities of a SiO2 nonlinear slab. As an example, we investigate a nonlinear metasurface which presents nonlinear magnetoelectric coupling in near infrared regime. The method is expected to apply to any patterned metasurface whose thickness is much smaller than the wavelengths of operation, with inclusions of arbitrary geometry

Tearing mode growth in a regime of weak magnetic shear

International Nuclear Information System (INIS)

Riyopoulos, S.; Hazeltine, R.D.

1987-06-01

The nonlinear growth for the m/n ≥ 2 resistive tearing mode is studied in case when the rational surface q(r 0 ) = m/n falls in a regime of weak magnetic shear, q'(r 0 ) ≅ 0. The island width is determined self-consistently from the nonlinear, zero-helicity component of the perturbed magnetic flux that provides the local shear. It is found that the magnetic perturbation keeps growing exponentially in the nonlinear regime on a hybrid resistive-Alfvenic time scale, while the island width and the vorticity grow on a much slower time scale. Accordingly, much faster release of magnetic energy results for modes growing near minima of hollow q profiles

Approximating the amplitude and form of limit cycles in the weakly nonlinear regime of Lienard systems

International Nuclear Information System (INIS)

Lopez, J.L.; Lopez-Ruiz, R.

2007-01-01

Lienard equations, x+εf(x)x+x=0, with f(x) an even continuous function are considered. In the weak nonlinear regime (ε->0), the number and O(ε 0 ) approximation of the amplitude of limit cycles present in this type of systems, can be obtained by applying a methodology recently proposed by the authors [Lopez-Ruiz R, Lopez JL. Bifurcation curves of limit cycles in some Lienard systems. Int J Bifurcat Chaos 2000;10:971-80]. In the present work, that method is carried forward to higher orders in ε and is embedded in a general recursive algorithm capable to approximate the form of the limit cycles and to correct their amplitudes as an expansion in powers of ε. Several examples showing the application of this scheme are given

The Behavior of Filters and Smoothers for Strongly Nonlinear Dynamics

Science.gov (United States)

Zhu, Yanqiu; Cohn, Stephen E.; Todling, Ricardo

1999-01-01

The Kalman filter is the optimal filter in the presence of known Gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions (e.g., Miller 1994). Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz (1963) model as well as more realistic models of the oceans (Evensen and van Leeuwen 1996) and atmosphere (Houtekamer and Mitchell 1998). A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter equations to allow for correct update of the ensemble members (Burgers 1998). The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to quite puzzling in that results of state estimate are worse than for their filter analogue (Evensen 1997). In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use Lorenz (1963) model to test and compare the behavior of a variety implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.

Understanding of flux-limited behaviors of heat transport in nonlinear regime

Energy Technology Data Exchange (ETDEWEB)

Guo, Yangyu, E-mail: yangyuhguo@gmail.com [Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics and CNMM, Tsinghua University, Beijing 100084 (China); Jou, David, E-mail: david.jou@uab.es [Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Catalonia (Spain); Wang, Moran, E-mail: mrwang@tsinghua.edu [Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics and CNMM, Tsinghua University, Beijing 100084 (China)

2016-01-28

The classical Fourier's law of heat transport breaks down in highly nonequilibrium situations as in nanoscale heat transport, where nonlinear effects become important. The present work is aimed at exploring the flux-limited behaviors based on a categorization of existing nonlinear heat transport models in terms of their theoretical foundations. Different saturation heat fluxes are obtained, whereas the same qualitative variation trend of heat flux versus exerted temperature gradient is got in diverse nonlinear models. The phonon hydrodynamic model is proposed to act as a standard to evaluate other heat flux limiters because of its more rigorous physical foundation. A deeper knowledge is thus achieved about the phenomenological generalized heat transport models. The present work provides deeper understanding and accurate modeling of nonlocal and nonlinear heat transport beyond the diffusive limit. - Highlights: • Exploring flux-limited behaviors based on a categorization of existing nonlinear heat transport models. • Proposing phonon hydrodynamic model as a standard to evaluate heat flux limiters. • Providing accurate modeling of nonlocal and nonlinear heat transport beyond the diffusive limit.

Lasing by driven atoms-cavity system in collective strong coupling regime.

Science.gov (United States)

Sawant, Rahul; Rangwala, S A

2017-09-12

The interaction of laser cooled atoms with resonant light is determined by the natural linewidth of the excited state. An optical cavity is another optically resonant system where the loss from the cavity determines the resonant optical response of the system. The near resonant combination of an optical Fabry-Pérot cavity with laser cooled and trapped atoms couples two distinct optical resonators via light and has great potential for precision measurements and the creation of versatile quantum optics systems. Here we show how driven magneto-optically trapped atoms in collective strong coupling regime with the cavity leads to lasing at a frequency red detuned from the atomic transition. Lasing is demonstrated experimentally by the observation of a lasing threshold accompanied by polarization and spatial mode purity, and line-narrowing in the outcoupled light. Spontaneous emission into the cavity mode by the driven atoms stimulates lasing action, which is capable of operating as a continuous wave laser in steady state, without a seed laser. The system is modeled theoretically, and qualitative agreement with experimentally observed lasing is seen. Our result opens up a range of new measurement possibilities with this system.

Circuit electromechanics with single photon strong coupling

Energy Technology Data Exchange (ETDEWEB)

Xue, Zheng-Yuan, E-mail: zyxue@scnu.edu.cn; Yang, Li-Na [Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, and School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006 (China); Zhou, Jian, E-mail: jianzhou8627@163.com [Department of Electronic Communication Engineering, Anhui Xinhua University, Hefei 230088 (China); Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, and School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006 (China)

2015-07-13

In circuit electromechanics, the coupling strength is usually very small. Here, replacing the capacitor in circuit electromechanics by a superconducting flux qubit, we show that the coupling among the qubit and the two resonators can induce effective electromechanical coupling which can attain the strong coupling regime at the single photon level with feasible experimental parameters. We use dispersive couplings among two resonators and the qubit while the qubit is also driven by an external classical field. These couplings form a three-wave mixing configuration among the three elements where the qubit degree of freedom can be adiabatically eliminated, and thus results in the enhanced coupling between the two resonators. Therefore, our work constitutes the first step towards studying quantum nonlinear effect in circuit electromechanics.

Pressure-anisotropy-induced nonlinearities in the kinetic magnetorotational instability

Science.gov (United States)

Squire, J.; Quataert, E.; Kunz, M. W.

2017-12-01

In collisionless and weakly collisional plasmas, such as hot accretion flows onto compact objects, the magnetorotational instability (MRI) can differ significantly from the standard (collisional) MRI. In particular, pressure anisotropy with respect to the local magnetic-field direction can both change the linear MRI dispersion relation and cause nonlinear modifications to the mode structure and growth rate, even when the field and flow perturbations are very small. This work studies these pressure-anisotropy-induced nonlinearities in the weakly nonlinear, high-ion-beta regime, before the MRI saturates into strong turbulence. Our goal is to better understand how the saturation of the MRI in a low-collisionality plasma might differ from that in the collisional regime. We focus on two key effects: (i) the direct impact of self-induced pressure-anisotropy nonlinearities on the evolution of an MRI mode, and (ii) the influence of pressure anisotropy on the `parasitic instabilities' that are suspected to cause the mode to break up into turbulence. Our main conclusions are: (i) The mirror instability regulates the pressure anisotropy in such a way that the linear MRI in a collisionless plasma is an approximate nonlinear solution once the mode amplitude becomes larger than the background field (just as in magnetohyrodynamics). This implies that differences between the collisionless and collisional MRI become unimportant at large amplitudes. (ii) The break up of large-amplitude MRI modes into turbulence via parasitic instabilities is similar in collisionless and collisional plasmas. Together, these conclusions suggest that the route to magnetorotational turbulence in a collisionless plasma may well be similar to that in a collisional plasma, as suggested by recent kinetic simulations. As a supplement to these findings, we offer guidance for the design of future kinetic simulations of magnetorotational turbulence.

Filamentation and light bullet formation dynamics in solid-state dielectric media with weak, moderate and strong anomalous group velocity dispersion

International Nuclear Information System (INIS)

Gražulevičiūtė, I; Garejev, N; Majus, D; Tamošauskas, G; A Dubietis; Jukna, V

2016-01-01

We present a series of measurements, which characterize filamentation dynamics of intense ultrashort laser pulses in the space–time domain, as captured by means of three-dimensional imaging technique in sapphire and fused silica, in the wavelength range of 1.45–2.25 μm, accessing the regimes of weak, moderate and strong anomalous group velocity dispersion (GVD). In the regime of weak anomalous GVD (at 1.45 μm), pulse splitting into two sub-pulses producing a pair of light bullets with spectrally shifted carrier frequencies in both nonlinear media is observed. In contrast, in the regimes of moderate (at 1.8 μm) and strong (at 2.25 μm) anomalous GVD we observe notably different transient dynamics, which however lead to the formation of a single self-compressed quasistationary light bullet with an universal spatiotemporal shape comprised of an extended ring-shaped periphery and a localized intense core that carries the self-compressed pulse. (paper)

Filamentation and light bullet formation dynamics in solid-state dielectric media with weak, moderate and strong anomalous group velocity dispersion

Science.gov (United States)

Gražulevičiūtė, I.; Garejev, N.; Majus, D.; Jukna, V.; Tamošauskas, G.; Dubietis, A.

2016-02-01

We present a series of measurements, which characterize filamentation dynamics of intense ultrashort laser pulses in the space-time domain, as captured by means of three-dimensional imaging technique in sapphire and fused silica, in the wavelength range of 1.45-2.25 μm, accessing the regimes of weak, moderate and strong anomalous group velocity dispersion (GVD). In the regime of weak anomalous GVD (at 1.45 μm), pulse splitting into two sub-pulses producing a pair of light bullets with spectrally shifted carrier frequencies in both nonlinear media is observed. In contrast, in the regimes of moderate (at 1.8 μm) and strong (at 2.25 μm) anomalous GVD we observe notably different transient dynamics, which however lead to the formation of a single self-compressed quasistationary light bullet with an universal spatiotemporal shape comprised of an extended ring-shaped periphery and a localized intense core that carries the self-compressed pulse.

Blow-Up Analysis for a Quasilinear Degenerate Parabolic Equation with Strongly Nonlinear Source

Directory of Open Access Journals (Sweden)

Pan Zheng

2012-01-01

Full Text Available We investigate the blow-up properties of the positive solution of the Cauchy problem for a quasilinear degenerate parabolic equation with strongly nonlinear source ut=div(|∇um|p−2∇ul+uq,  (x,t∈RN×(0,T, where N≥1, p>2 , and m, l,  q>1, and give a secondary critical exponent on the decay asymptotic behavior of an initial value at infinity for the existence and nonexistence of global solutions of the Cauchy problem. Moreover, under some suitable conditions we prove single-point blow-up for a large class of radial decreasing solutions.

Single-ion nonlinear mechanical oscillator

International Nuclear Information System (INIS)

Akerman, N.; Kotler, S.; Glickman, Y.; Dallal, Y.; Keselman, A.; Ozeri, R.

2010-01-01

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.

Insight into the effect of screw dislocations and oxygen vacancy defects on the optical nonlinear refraction response in chemically grown ZnO/Al2O3 films

Science.gov (United States)

Agrawal, Arpana; Saroj, Rajendra K.; Dar, Tanveer A.; Baraskar, Priyanka; Sen, Pratima; Dhar, Subhabrata

2017-11-01

We report the effect of screw dislocations and oxygen vacancy defects on the optical nonlinear refraction response of ZnO films grown on a sapphire substrate at various oxygen flow rates using the chemical vapor deposition technique. The nonlinear refraction response was investigated in the off-resonant regime using a CW He-Ne laser source to examine the role of the intermediate bandgap states. It has been observed that the structural defects strongly influence the optical nonlinearity in the off-resonant regime. Nonlinearity has been found to improve as the oxygen flow rate is lowered from 2 sccm to 0.3 sccm. From photoluminescence studies, we observe that the enhanced defect density of the electronic defect levels due to the increased concentration of structural defects (with the decrease in the oxygen flow rate) is responsible for this improved optical nonlinearity along with the thermal effect. This suggests that defect engineering is an effective way to tailor the nonlinearity of ZnO films and their utility for optoelectronic device applications.

Density gradient effects in weakly nonlinear ablative Rayleigh-Taylor instability

International Nuclear Information System (INIS)

Wang, L. F.; Ye, W. H.; He, X. T.

2012-01-01

In this research, density gradient effects (i.e., finite thickness of ablation front effects) in ablative Rayleigh-Taylor instability (ARTI), in the presence of preheating within the weakly nonlinear regime, are investigated numerically. We analyze the weak, medium, and strong ablation surfaces which have different isodensity contours, respectively, to study the influences of finite thickness of ablation front on the weakly nonlinear behaviors of ARTI. Linear growth rates, generation coefficients of the second and the third harmonics, and coefficients of the third-order feedback to the fundamental mode are obtained. It is found that the linear growth rate which has a remarkable maximum, is reduced, especially when the perturbation wavelength λ is short and a cut-off perturbation wavelength λ c appears when the perturbation wavelength λ is sufficiently short, where no higher harmonics exists when λ c . The phenomenon of third-order positive feedback to the fundamental mode near the λ c [J. Sanz et al., Phys. Rev. Lett. 89, 195002 (2002); J. Garnier et al., Phys. Rev. Lett. 90, 185003 (2003); J. Garnier and L. Masse, Phys. Plasmas 12, 062707 (2005)] is confirmed in numerical simulations, and the physical mechanism of the third-order positive feedback is qualitatively discussed. Moreover, it is found that generations and growths of the second and the third harmonics are stabilized (suppressed and reduced) by the ablation effect. Meanwhile, the third-order negative feedback to the fundamental mode is also reduced by the ablation effect, and hence, the linear saturation amplitude (typically ∼0.2λ in our simulations) is increased significantly and therefore exceeds the classical prediction 0.1λ, especially for the strong ablation surface with a small perturbation wavelength. Overall, the ablation effect stabilizes the ARTI in the weakly nonlinear regime. Numerical results obtained are in general agreement with the recent weakly nonlinear theories and simulations

Gravitational wave emission from a bounded source: A treatment in the full nonlinear regime

International Nuclear Information System (INIS)

Oliveiral, H.P. de; Damiao Soares, I.

2004-03-01

The dynamics of a bounded gravitational collapsing configuration emitting gravitational waves is studied. The exterior spacetime is described by Robinson-Trautman geometries and have the Schwarzschild black hole as its final gravitational configuration, when the gravitational wave emission ceases. The full nonlinear regime is examined by using the Galerkin method that allows us to reduce the equations governing the dynamics to a finite-dimensional dynamical system, after a proper truncation procedure. Gravitational wave emission patterns from given initial configurations are exhibited for several phases of the collapse and the mass-loss ratio that characterizes the amount of mass extracted by the gravitational wave emission is evaluated. We obtain that the smaller initial mass M init of the configuration, the more rapidly the Schwarzschild solution is attained and a larger fraction of M init is lost in the process of gravitational wave emission. Within all our numerical experiments, the distribution of the mass fraction extracted by gravitational wave emission is shown to satisfy the distribution law of nonextensive statistics and this result is independent of the initial configurations considered. (author)

Semiclassical soliton ensembles for the focusing nonlinear Schrödinger equation

CERN Document Server

Kamvissis, Spyridon; Miller, Peter D

2003-01-01

This book represents the first asymptotic analysis, via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrödinger equation in the semiclassical asymptotic regime. This problem is a key model in nonlinear optical physics and has increasingly important applications in the telecommunications industry. The authors exploit complete integrability to establish pointwise asymptotics for this problem's solution in the semiclassical regime and explicit integration for the underlying nonlinear, elliptic, partial differential equations suspected of governing

Relic dark energy from the trans-Planckian regime

International Nuclear Information System (INIS)

Mersini, Laura; Bastero-Gil, Mar; Kanti, Panagiota

2001-01-01

As yet, there is no underlying fundamental theory for the trans-Planckian regime. There is a need to address the issue of how the observables in our present Universe are affected by processes that may have occurred at super-Planckian energies (referred to as the trans-Planckian regime). Specifically, we focus on the impact the trans-Planckian regime has on two observables: namely, dark energy and the cosmic microwave background radiation (CMBR) spectrum. We model the trans-Planckian regime by introducing a 1-parameter family of smooth non-linear dispersion relations which modify the frequencies at very short distances. A particular feature of the family of dispersion functions chosen is the production of ultralow frequencies at very high momenta k (for k>M P ). We name the range of the ultralow energy modes (of very short distances) that have frequencies equal to or less than the current Hubble rate H 0 as the tail modes. These modes are still frozen today due to the expansion of the Universe. We calculate their energy today and show that the tail provides a strong candidate for the dark energy of the Universe. During inflation, their energy is about 122 to 123 orders of magnitude smaller than the total energy, for any random value of the free parameter in the family of dispersion relations. For this family of dispersions, we present the exact solutions and show that the CMBR spectrum is that of a (nearly) blackbody, and that the adiabatic vacuum is the only choice for the initial conditions

Generalized dispersive wave emission in nonlinear fiber optics.

Science.gov (United States)

Webb, K E; Xu, Y Q; Erkintalo, M; Murdoch, S G

2013-01-15

We show that the emission of dispersive waves in nonlinear fiber optics is not limited to soliton-like pulses propagating in the anomalous dispersion regime. We demonstrate, both numerically and experimentally, that pulses propagating in the normal dispersion regime can excite resonant dispersive radiation across the zero-dispersion wavelength into the anomalous regime.

Destruction of Anderson localization by nonlinearity in kicked rotator at different effective dimensions

International Nuclear Information System (INIS)

Ermann, L; Shepelyansky, D L

2014-01-01

We study numerically the frequency modulated kicked nonlinear rotator with effective dimension d=1,2,3,4. We follow the time evolution of the model up to 10 9 kicks and determine the exponent α of subdiffusive spreading which changes from 0.35 to 0.5 when the dimension changes from d = 1 to 4. All results are obtained in a regime of relatively strong Anderson localization well below the Anderson transition point existing for d = 3, 4. We explain that this variation of the exponent is different from the usual d− dimensional Anderson models with local nonlinearity where α drops with increasing d. We also argue that the renormalization arguments proposed by Cherroret N et al (arXiv:1401.1038) are not valid for this model and the Anderson model with local nonlinearity in d = 3. (paper)

Nonlinear dynamic of interaction of the relativistic electron beam with plasma

International Nuclear Information System (INIS)

Dorofeenko, V.G.; Krasovitskii, V.B.; Osmolovsky, S.I.

1994-01-01

Quasi-transverse instability of thin relativistic electron beam in a dense plasma is studied numerically and analytically in a broad range of the frequency of the beam modulation and external longitudinal magnetic field. It is shown that the nonlinear stage of solution depends on the increment of the instability. It is permitted to classify possible nonlinear solutions and also to determine optimal regimes of the modulation for transport of beam along magnetic field in a plasma without substantial radial divergence. Numerical calculations show, that injection of the bunches with parameters, corresponding nonlinear regime of the beam's instability, in neutrally-charged plasma permits to output on the stationary regime without loss of particles

Transition from weak to strong measurements by nonlinear quantum feedback control

International Nuclear Information System (INIS)

Zhang Jing; Liu Yuxi; Wu Rebing; Li Chunwen; Tarn, Tzyh-Jong

2010-01-01

We find that feedback control may induce 'pseudo'-nonlinear dynamics in a damped harmonic oscillator, whose centroid trajectory in the phase space behaves like a classical nonlinear system. Thus, similar to nonlinear amplifiers (e.g., rf-driven Josephson junctions), feedback control on the harmonic oscillator can induce nonlinear bifurcation, which can be used to amplify small signals and further to measure quantum states of qubits. Using the cavity QED and the circuit QED systems as examples, we show how to apply our method to measuring the states of two-level atoms and superconducting charge qubits.

Experiment of ablative Rayleigh-Taylor instability in a strongly non linear regime on the National Ignition Facility

International Nuclear Information System (INIS)

Casner, A.; Masse, L.; Liberatore, S.; Delorme, B.; Jacquet, L.; Loiseau, P.; Smalyuk, V. A.; Martinez, D.; Remington, B. A.

2012-01-01

As the control of the development of Rayleigh-Taylor-type hydrodynamic instabilities is crucial to achieve efficient implosions on the Laser Megajoule, and as the complexity of these instabilities requires an experimental validation of theoretical models and of the associated numerical simulations, the authors briefly present a proposition of experiments aimed at studying the strongly non linear Rayleigh-Taylor instability on the National Ignition Facility (NIF). This should allow a regime of competition between bubbles to be achieved for the first time in direct attack. They evoke the first experiment performed in March 2013

Breatherlike excitations in discrete lattices with noise and nonlinear damping

DEFF Research Database (Denmark)

Christiansen, Peter Leth; Gaididei, Yuri B.; Johansson, Magnus

1997-01-01

We discuss the stability of highly localized, ''breatherlike,'' excitations in discrete nonlinear lattices under the influence of thermal fluctuations. The particular model considered is the discrete nonlinear Schrodinger equation in the regime of high nonlinearity, where temperature effects...

Features of tuned mass damper behavior under strong earthquakes

Science.gov (United States)

Nesterova, Olga; Uzdin, Alexander; Fedorova, Maria

2018-05-01

Plastic deformations, cracks and destruction of structure members appear in the constructions under strong earthquakes. Therefore constructions are characterized by a nonlinear deformation diagram. Two types of construction non-linearity are considered in the paper. The first type of nonlinearity is elastoplastic one. In this case, plastic deformations occur in the structural elements, and when the element is unloaded, its properties restores. Among such diagrams are the Prandtl diagram, the Prandtl diagram with hardening, the Ramberg-Osgood diagram and others. For systems with such nonlinearity there is an amplitude-frequency characteristic and resonance oscillation frequencies. In this case one can pick up the most dangerous accelerograms for the construction. The second type of nonlinearity is nonlinearity with degrading rigidity and dependence of behavior on the general loading history. The Kirikov-Amankulov model is one of such ones. Its behavior depends on the maximum displacement in the stress history. Such systems do not have gain frequency characteristic and resonance frequency. The period of oscillation of such system is increasing during the system loading, and the system eigen frequency decreases to zero at the time of collapse. In the cases under consideration, when investigating the system with MD behavior, the authors proposed new efficiency criteria. These include the work of plastic deformation forces for the first type of nonlinearity, which determines the possibility of progressive collapse or low cycle fatigue of the structure members. The period of system oscillations and the time to collapse of the structural support members are the criterion for systems with degrading rigidity. In the case of non-linear system behavior, the efficiency of MD application decreases, because the fundamental structure period is reduced because of structure damages and the MD will be rebound from the blanking regime. However, the MD using can significantly reduce

Abrupt climate-independent fire regime changes

Science.gov (United States)

Pausas, Juli G.; Keeley, Jon E.

2014-01-01

Wildfires have played a determining role in distribution, composition and structure of many ecosystems worldwide and climatic changes are widely considered to be a major driver of future fire regime changes. However, forecasting future climatic change induced impacts on fire regimes will require a clearer understanding of other drivers of abrupt fire regime changes. Here, we focus on evidence from different environmental and temporal settings of fire regimes changes that are not directly attributed to climatic changes. We review key cases of these abrupt fire regime changes at different spatial and temporal scales, including those directly driven (i) by fauna, (ii) by invasive plant species, and (iii) by socio-economic and policy changes. All these drivers might generate non-linear effects of landscape changes in fuel structure; that is, they generate fuel changes that can cross thresholds of landscape continuity, and thus drastically change fire activity. Although climatic changes might contribute to some of these changes, there are also many instances that are not primarily linked to climatic shifts. Understanding the mechanism driving fire regime changes should contribute to our ability to better assess future fire regimes.

Hidden regularity for a strongly nonlinear wave equation

International Nuclear Information System (INIS)

Rivera, J.E.M.

1988-08-01

The nonlinear wave equation u''-Δu+f(u)=v in Q=Ωx]0,T[;u(0)=u 0 ,u'(0)=u 1 in Ω; u(x,t)=0 on Σ= Γx]0,T[ where f is a continuous function satisfying, lim |s| sup →+∞ f(s)/s>-∞, and Ω is a bounded domain of R n with smooth boundary Γ, is analysed. It is shown that there exist a solution for the presented nonlinear wave equation that satisfies the regularity condition: |∂u/∂ η|ε L 2 (Σ). Moreover, it is shown that there exist a constant C>0 such that, |∂u/∂ η|≤c{ E(0)+|v| 2 Q }. (author) [pt

Analytical solutions by squeezing to the anisotropic Rabi model in the nonperturbative deep-strong-coupling regime

Science.gov (United States)

Zhang, Yu-Yu; Chen, Xiang-You

2017-12-01

An unexplored nonperturbative deep strong coupling (npDSC) achieved in superconducting circuits has been studied in the anisotropic Rabi model by the generalized squeezing rotating-wave approximation. Energy levels are evaluated analytically from the reformulated Hamiltonian and agree well with numerical ones in a wide range of coupling strength. Such improvement ascribes to deformation effects in the displaced-squeezed state presented by the squeezed momentum variance, which are omitted in previous displaced states. The atom population dynamics confirms the validity of our approach for the npDSC strength. Our approach offers the possibility to explore interesting phenomena analytically in the npDSC regime in qubit-oscillator experiments.

Probing the interatomic potential of solids with strong-field nonlinear phononics

Science.gov (United States)

von Hoegen, A.; Mankowsky, R.; Fechner, M.; Först, M.; Cavalleri, A.

2018-03-01

Nonlinear optical techniques at visible frequencies have long been applied to condensed matter spectroscopy. However, because many important excitations of solids are found at low energies, much can be gained from the extension of nonlinear optics to mid-infrared and terahertz frequencies. For example, the nonlinear excitation of lattice vibrations has enabled the dynamic control of material functions. So far it has only been possible to exploit second-order phonon nonlinearities at terahertz field strengths near one million volts per centimetre. Here we achieve an order-of-magnitude increase in field strength and explore higher-order phonon nonlinearities. We excite up to five harmonics of the A1 (transverse optical) phonon mode in the ferroelectric material lithium niobate. By using ultrashort mid-infrared laser pulses to drive the atoms far from their equilibrium positions, and measuring the large-amplitude atomic trajectories, we can sample the interatomic potential of lithium niobate, providing a benchmark for ab initio calculations for the material. Tomography of the energy surface by high-order nonlinear phononics could benefit many aspects of materials research, including the study of classical and quantum phase transitions.

Near resonant and nonresonant third-order optical nonlinearities of colloidal InP/ZnS quantum dots

Science.gov (United States)

Wang, Y.; Yang, X.; He, T. C.; Gao, Y.; Demir, H. V.; Sun, X. W.; Sun, H. D.

2013-01-01

We have investigated the third-order optical nonlinearities of high-quality colloidal InP/ZnS core-shell quantum dots (QDs) using Z-scan technique with femtosecond pulses. The two-photon absorption cross-sections as high as 6.2 × 103 GM are observed at 800 nm (non-resonant regime) in InP/ZnS QDs with diameter of 2.8 nm, which is even larger than those of CdSe, CdS, and CdTe QDs at similar sizes. Furthermore, both of the 2.2 nm and 2.8 nm-sized InP/ZnS QDs exhibit strong saturable absorption in near resonant regime, which is attributed to large exciton Bohr radius in this material. These results strongly suggest the promising potential of InP/ZnS QDs for widespread applications, especially in two-photon excited bio-imaging and saturable absorbing.

Nonlinearity induced synchronization enhancement in mechanical oscillators

Science.gov (United States)

Czaplewski, David A.; Lopez, Omar; Guest, Jeffrey R.; Antonio, Dario; Arroyo, Sebastian I.; Zanette, Damian H.

2018-05-08

An autonomous oscillator synchronizes to an external harmonic force only when the forcing frequency lies within a certain interval, known as the synchronization range, around the oscillator's natural frequency. Under ordinary conditions, the width of the synchronization range decreases when the oscillation amplitude grows, which constrains synchronized motion of micro- and nano-mechanical resonators to narrow frequency and amplitude bounds. The present invention shows that nonlinearity in the oscillator can be exploited to manifest a regime where the synchronization range increases with an increasing oscillation amplitude. The present invention shows that nonlinearities in specific configurations of oscillator systems, as described herein, are the key determinants of the effect. The present invention presents a new configuration and operation regime that enhances the synchronization of micro- and nano-mechanical oscillators by capitalizing on their intrinsic nonlinear dynamics.

Two-Fluid and Resistive Nonlinear Simulations of Tokamak Equilibrium, Stability, and Reconnection

International Nuclear Information System (INIS)

Jardin, S.; Sovinec, C.; Breslau, J.; Ferraro, N.; Hudson, S.; King, J.; Kruger, S.; Ramos, J.; Schnack, D.

2008-01-01

The NIMROD and M3D/M3D-C1 codes now each have both a resistive MHD and a two-fluid (2F) capability including gyroviscosity and Hall terms. We describe: (1) a nonlinear 3D verification test in the resistive MHD regime in which the two codes are in detailed agreement, (2) new studies that illuminate the effect of two-fluid physics on spontaneous rotation in tokamaks, (3) studies of nonlinear reconnection in regimes of relevance to fusion plasmas with peak nonlinear reconnection rates that are essentially independent of the resistivity, and (4) linear two-fluid tearing mode calculations including electron mass that agree with analytic studies over a wide range of parameter regimes

Initial evolution of nonlinear magnetic islands in high temperature plasmas

International Nuclear Information System (INIS)

Kotschenreuther, M.

1988-06-01

The evolution of nonlinear magnetic islands is computed in the kinetic collisionality regime called the semicollisional regime, which is appropriate to present fusion confinement devices. Realistic effects are included, such as the presence of small external field errors, radial electric fields, and omega. When present simultaneously, these effects can greatly change the stability of small amplitude nonlinear islands. Islands with Δ' > O can sometimes be prevented from growing to macroscopic size; it is also possible to produce moderate mode-number nonlinear instabilities in the plasma edge. Furthermore, island growth can be prevented by application of external fields with suitably chosen amplitude and frequency

Nonlinear Thomson scattering of a relativistically strong tightly focused ultrashort laser pulse

Energy Technology Data Exchange (ETDEWEB)

Vais, O. E.; Bochkarev, S. G., E-mail: bochkar@sci.lebedev.ru; Bychenkov, V. Yu. [Russian Academy of Sciences, Lebedev Physical Institute (Russian Federation)

2016-09-15

The problem of nonlinear Thomson scattering of a relativistically strong linearly polarized ultrashort laser pulse tightly focused into a spot with a diameter of D{sub F} ≳ λ (where λ is the laser wavelength) is solved. The energy, spectral, and angular distributions of radiation generated due to Thomson scattering from test electrons located in the focal region are found. The characteristics of scattered radiation are studied as functions of the tightness of laser focusing and the initial position of test particles relative to the center of the focal region for a given laser pulse energy. It is demonstrated that the ultratight focusing is not optimal for obtaining the brightest and hardest source of secondary electromagnetic radiation. The hardest and shortest radiation pulse is generated when the beam waist diameter is ≃10λ.

Effects of Plasma Shaping on Nonlinear Gyrokinetic Turbulence

Energy Technology Data Exchange (ETDEWEB)

Belli, E. A. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Hammett, G. W. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Dorland, W. [Univ. of Maryland, College Park, MD (United States)

2008-08-01

The effects of flux surface shape on the gyrokinetic stability and transport of tokamak plasmas are studied using the GS2 code [M. Kotschenreuther, G. Rewoldt, and W.M. Tang, Comput. Phys. Commun. 88, 128 (1995); W. Dorland, F. Jenko, M. Kotschenreuther, and B.N. Rogers, Phys. Rev. Lett. 85, 5579 (2000)]. Studies of the scaling of nonlinear turbulence with shaping parameters are performed using analytic equilibria based on interpolations of representative shapes of the Joint European Torus (JET) [P.H. Rebut and B.E. Keen, Fusion Technol. 11, 13 (1987)]. High shaping is found to be a stabilizing influence on both the linear ion-temperature-gradient (ITG) instability and the nonlinear ITG turbulence. For the parameter regime studied here, a scaling of the heat flux with elongation of χ ~ κ^-1.5 or κ^-2.0, depending on the triangularity, is observed at fixed average temperature gradient. While this is not as strong as empirical elongation scalings, it is also found that high shaping results in a larger Dimits upshift of the nonlinear critical temperature gradient due to an enhancement of the Rosenbluth-Hinton residual zonal flows.

Effects of Plasma Shaping on Nonlinear Gyrokinetic Turbulence

International Nuclear Information System (INIS)

E.A. Belli, G.W. Hammett and W. Dorland

2008-01-01

The effects of flux surface shape on the gyrokinetic stability and transport of tokamak plasmas are studied using the GS2 code [M. Kotschenreuther, G. Rewoldt, and W.M. Tang, Comput. Phys. Commun. 88, 128 (1995); W. Dorland, F. Jenko, M. Kotschenreuther, and B.N. Rogers, Phys. Rev. Lett. 85, 5579 (2000)]. Studies of the scaling of nonlinear turbulence with shaping parameters are performed using analytic equilibria based on interpolations of representative shapes of the Joint European Torus (JET) [P.H. Rebut and B.E. Keen, Fusion Technol. 11, 13 (1987)]. High shaping is found to be a stabilizing influence on both the linear ion-temperature-gradient (ITG) instability and the nonlinear ITG turbulence. For the parameter regime studied here, a scaling of the heat flux with elongation of χ ∼ κ -1.5 or κ -2.0 , depending on the triangularity, is observed at fixed average temperature gradient. While this is not as strong as empirical elongation scalings, it is also found that high shaping results in a larger Dimits upshift of the nonlinear critical temperature gradient due to an enhancement of the Rosenbluth-Hinton residual zonal flows

Strong convergence of modified Ishikawa iterations for nonlinear ...

Indian Academy of Sciences (India)

interval [0, 1]. The second iteration process is referred to as Ishikawa's iteration process [11] which is .... Let E be a smooth Banach space with dual E∗ ..... and applications, in: Theory and Applications of Nonlinear Operators of Accretive and.

A multidimensional theory for electron trapping by a plasma wake generated in the bubble regime

International Nuclear Information System (INIS)

Kostyukov, I; Nerush, E; Pukhov, A; Seredov, V

2010-01-01

We present a theory for electron self-injection in nonlinear, multidimensional plasma waves excited by a short laser pulse in the bubble regime or by a short electron beam in the blowout regime. In these regimes, which are typical for electron acceleration in the last impressive experiments, the laser radiation pressure or the electron beam charge pushes out plasma electrons from some region, forming a plasma cavity or a bubble with a huge ion charge. The plasma electrons can be trapped in the bubble and accelerated by the plasma wakefields up to a very high energy. We derive the condition of the electron trapping in the bubble. The developed theory predicts the trapping cross section in terms of the bubble radius and the bubble velocity. It is found that the dynamic bubble deformations observed in the three-dimensional (3D) particle-in-cell (PIC) simulations influence the trapping process significantly. The bubble elongation reduces the gamma-factor of the bubble, thereby strongly enhancing self-injection. The obtained analytical results are in good agreement with the 3D PIC simulations.

Nonlinear response of the quantum Hall system to a strong electromagnetic radiation

International Nuclear Information System (INIS)

Avetissian, H.K.; Mkrtchian, G.F.

2016-01-01

We study nonlinear response of a quantum Hall system in semiconductor-hetero-structures via third harmonic generation process and nonlinear Faraday effect. We demonstrate that Faraday rotation angle and third harmonic radiation intensity have a characteristic Hall plateaus feature. These nonlinear effects remain robust against the significant broadening of Landau levels. We predict realization of an experiment through the observation of the third harmonic signal and Faraday rotation angle, which are within the experimental feasibility. - Highlights: • Nonlinear optical response of a quantum Hall system has specific plateaus feature. • This effect remains robust against the significant broadening of Landau levels. • It can be observed via the third harmonic signal and the nonlinear Faraday effect.

Calculating hadronic properties in strong QCD

International Nuclear Information System (INIS)

Pennington, M.R.

1996-01-01

This talk gives a brief review of the progress that has been made in calculating the properties of hadrons in strong QCD. In keeping with this meeting I will concentrate on those properties that can be studied with electromagnetic probes. Though perturbative QCD is highly successful, it only applies in a limited kinematic regime, where hard scattering occur, and the quarks move in the interaction region as if they are free, pointlike objects. However, the bulk of strong interactions are governed by the long distance regime, where the strong interaction is strong. It is this regime of length scales of the order of a Fermi, that determines the spectrum of light hadrons and their properties. The calculation of these properties requires an understanding of non-perturbative QCD, of confinement and chiral symmetry breaking. (author)

Nonlinearity and nonclassicality in a nanomechanical resonator

Energy Technology Data Exchange (ETDEWEB)

Teklu, Berihu [Clermont Universite, Blaise Pascal University, CNRS, PHOTON-N2, Institut Pascal, Aubiere Cedex (France); Universita degli Studi di Milano, Dipartimento di Fisica, Milano (Italy); Ferraro, Alessandro; Paternostro, Mauro [Queen' s University, Centre for Theoretical Atomic, Molecular, and Optical Physics, School of Mathematics and Physics, Belfast (United Kingdom); Paris, Matteo G.A. [Universita degli Studi di Milano, Dipartimento di Fisica, Milano (Italy)

2015-12-15

We address quantitatively the relationship between the nonlinearity of a mechanical resonator and the nonclassicality of its ground state. In particular, we analyze the nonclassical properties of the nonlinear Duffing oscillator (being driven or not) as a paradigmatic example of a nonlinear nanomechanical resonator. We first discuss how to quantify the nonlinearity of this system and then show that the nonclassicality of the ground state, as measured by the volume occupied by the negative part of the Wigner function, monotonically increases with the nonlinearity in all the working regimes addressed in our study. Our results show quantitatively that nonlinearity is a resource to create nonclassical states in mechanical systems. (orig.)

Current structure of strongly nonlinear interfacial solitary waves

Science.gov (United States)

Semin, Sergey; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim; Churaev, Egor

2015-04-01

The characteristics of highly nonlinear solitary internal waves (solitons) in two-layer flow are computed within the fully nonlinear Navier-Stokes equations with use of numerical model of the Massachusetts Institute of Technology (MITgcm). The verification and adaptation of the model is based on the data from laboratory experiments [Carr & Davies, 2006]. The present paper also compares the results of our calculations with the computations performed in the framework of the fully nonlinear Bergen Ocean Model [Thiem et al, 2011]. The comparison of the computed soliton parameters with the predictions of the weakly nonlinear theory based on the Gardner equation is given. The occurrence of reverse flow in the bottom layer directly behind the soliton is confirmed in numerical simulations. The trajectories of Lagrangian particles in the internal soliton on the surface, on the interface and near the bottom are computed. The results demonstrated completely different trajectories at different depths of the model area. Thus, in the surface layer is observed the largest displacement of Lagrangian particles, which can be more than two and a half times larger than the characteristic width of the soliton. Located at the initial moment along the middle pycnocline fluid particles move along the elongated vertical loop at a distance of not more than one third of the width of the solitary wave. In the bottom layer of the fluid moves in the opposite direction of propagation of the internal wave, but under the influence of the reverse flow, when the bulk of the velocity field of the soliton ceases to influence the trajectory, it moves in the opposite direction. The magnitude of displacement of fluid particles in the bottom layer is not more than the half-width of the solitary wave. 1. Carr, M., and Davies, P.A. The motion of an internal solitary wave of depression over a fixed bottom boundary in a shallow, two-layer fluid. Phys. Fluids, 2006, vol. 18, No. 1, 1 - 10. 2. Thiem, O., Carr

A non-linear theory of strong interactions

International Nuclear Information System (INIS)

Skyrme, T.H.R.

1994-01-01

A non-linear theory of mesons, nucleons and hyperons is proposed. The three independent fields of the usual symmetrical pseudo-scalar pion field are replaced by the three directions of a four-component field vector of constant length, conceived in an Euclidean four-dimensional isotopic spin space. This length provides the universal scaling factor, all other constants being dimensionless; the mass of the meson field is generated by a φ 4 term; this destroys the continuous rotation group in the iso-space, leaving a 'cubic' symmetry group. Classification of states by this group introduces quantum numbers corresponding to isotopic spin and to 'strangeness'; one consequences is that, at least in elementary interactions, charge is only conserved module 4. Furthermore, particle states have not a well-defined parity, but parity is effectively conserved for meson-nucleon interactions. A simplified model, using only two dimensions of space and iso-space, is considered further; the non-linear meson field has solutions with particle character, and an indication is given of the way in which the particle field variables might be introduced as collective co-ordinates describing the dynamics of these particular solutions of the meson field equations, suggesting a unified theory based on the meson field alone. (author). 7 refs

Numerical study of bandwidth effect on stimulated Raman backscattering in nonlinear regime

Science.gov (United States)

Zhou, H. Y.; Xiao, C. Z.; Zou, D. B.; Li, X. Z.; Yin, Y.; Shao, F. Q.; Zhuo, H. B.

2018-06-01

Nonlinear behaviors of stimulated Raman scattering driven by finite bandwidth pumps are studied by one dimensional particle-in-cell simulations. The broad spectral feature of plasma waves and backscattered light reveals the different coupling and growth mechanisms, which lead to the suppression effect before the deep nonlinear stage. It causes nonperiodic plasma wave packets and reduces packet and etching velocities. Based on the negative frequency shift and electron energy distribution, the long-time evolution of instability can be divided into two stages by the relaxation time. It is a critical time after which the alleviation effects of nonlinear frequency shift and hot electrons are replaced by enhancement. Thus, the broadband pump suppresses instability at early time. However, it aggravates in the deep nonlinear stage by lifting the saturation level due to the coupling of the incident pump with each frequency shifted plasma wave. Our simulation results show that the nonlinear effects are valid in a bandwidth range from 2.25% to 3.0%, and the physics are similar within a nearby parameter space.

Effects of delayed nonlinear response on wave packet dynamics in one-dimensional generalized Fibonacci chains

International Nuclear Information System (INIS)

Zhang, Jianxin; Zhang, Zhenjun; Tong, Peiqing

2013-01-01

We investigate the spreading of an initially localized wave packet in one-dimensional generalized Fibonacci (GF) lattices by solving numerically the discrete nonlinear Schrödinger equation (DNLSE) with a delayed cubic nonlinear term. It is found that for short delay time, the wave packet is self-trapping in first class of GF lattices, that is, the second moment grows with time, but the corresponding participation number does not grow. However, both the second moment and the participation number grow with time for large delay time. This illuminates that the wave packet is delocalized. For the second class of GF lattices, the dynamic behaviors of wave packet depend on the strength of on-site potential. For a weak on-site potential, the results are similar to the case of the first class. For a strong on-site potential, both the second moment and the participation number does not grow with time in the regime of short delay time. In the regime of large delay time, both the second moment and the participation number exhibit stair-like growth

Effects of delayed nonlinear response on wave packet dynamics in one-dimensional generalized Fibonacci chains

Energy Technology Data Exchange (ETDEWEB)

Zhang, Jianxin; Zhang, Zhenjun [Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing 210023 (China); Tong, Peiqing, E-mail: pqtong@njnu.edu.cn [Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing 210023 (China); Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems, Nanjing Normal University, Nanjing 210023 (China)

2013-07-15

We investigate the spreading of an initially localized wave packet in one-dimensional generalized Fibonacci (GF) lattices by solving numerically the discrete nonlinear Schrödinger equation (DNLSE) with a delayed cubic nonlinear term. It is found that for short delay time, the wave packet is self-trapping in first class of GF lattices, that is, the second moment grows with time, but the corresponding participation number does not grow. However, both the second moment and the participation number grow with time for large delay time. This illuminates that the wave packet is delocalized. For the second class of GF lattices, the dynamic behaviors of wave packet depend on the strength of on-site potential. For a weak on-site potential, the results are similar to the case of the first class. For a strong on-site potential, both the second moment and the participation number does not grow with time in the regime of short delay time. In the regime of large delay time, both the second moment and the participation number exhibit stair-like growth.

Nonlinear branch-point dynamics of multiarm polystyrene

DEFF Research Database (Denmark)

Nielsen, Jens Kromann; Rasmussen, Henrik K.; Denberg, Martin

2006-01-01

/mol, respectively. The pom-pom was estimated to have 2.5 arms on average, while the estimate is 3.3 for the asymmetric star. The molar mass of each arm is about 27 kg/mol. The melts were characterized in the linear viscoelastic regime and by elongational rheometry in the nonlinear regime. For asymmetric star...

Nonlinear effects in the damping of third-sound pulses

International Nuclear Information System (INIS)

Browne, D.A.

1984-01-01

We show that nonlinearities in the equations of motion for a third-sound pulse in a thick superfluid film lead to the production of short-wavelength solitons. The soliton damping arises from viscous stresses in the film, rather than from coupling to thermal currents in the vapor and the substrate as in the hydrodynamic regime. These solitons are more strongly damped than a long-wavelength third-sound wave and lead to a larger attenuation of the pulse. We show that this mechanism can account for the discrepancy between attenuation calculated theoretically for the long-wavelength limit and the experimentally observed attenuation of low-amplitude third-sound pulses

Nonlinear quantum electrodynamic and electroweak processes in strong laser fields

Energy Technology Data Exchange (ETDEWEB)

Meuren, Sebastian

2015-06-24

Various nonlinear electrodynamic and electroweak processes in strong plane-wave laser fields are considered with an emphasis on short-pulse effects. In particular, the momentum distribution of photoproduced electron-positron pairs is calculated numerically and a semiclassical interpretation of its characteristic features is established. By proving the optical theorem, compact double-integral expressions for the total pair-creation probability are obtained and numerically evaluated. The exponential decay of the photon wave function in a plane wave is included by solving the Schwinger-Dyson equations to leading-order in the quasistatic approximation. In this respect, the polarization operator in a plane wave is investigated and its Ward-Takahashi identity verified. A classical analysis indicates that a photoproduced electron-positron pair recollides for certain initial conditions. The contributions of such recollision processes to the polarization operator are identified and calculated both analytically and numerically. Furthermore, the existence of nontrivial electron-spin dynamics induced by quantum fluctuations is verified for ultra-short laser pulses. Finally, the exchange of weak gauge bosons is considered, which is essential for neutrino-photon interactions. In particular, the axial-vector-vector coupling tensor is calculated and the so-called Adler-Bell-Jackiw (ABJ) anomaly investigated.

Nonlinear atom optics and bright-gap-soliton generation in finite optical lattices

International Nuclear Information System (INIS)

Carusotto, Iacopo; Embriaco, Davide; La Rocca, Giuseppe C.

2002-01-01

We theoretically investigate the transmission dynamics of coherent matter wave pulses across finite optical lattices in both the linear and the nonlinear regimes. The shape and the intensity of the transmitted pulse are found to strongly depend on the parameters of the incident pulse, in particular its velocity and density: a clear physical picture of the main features observed in the numerical simulations is given in terms of the atomic band dispersion in the periodic potential of the optical lattice. Signatures of nonlinear effects due to the atom-atom interaction are discussed in detail, such as atom-optical limiting and atom-optical bistability. For positive scattering lengths, matter waves propagating close to the top of the valence band are shown to be subject to modulational instability. A scheme for the experimental generation of narrow bright gap solitons from a wide Bose-Einstein condensate is proposed: the modulational instability is seeded starting from the strongly modulated density profile of a standing matter wave and the solitonic nature of the generated pulses is checked from their shape and their collisional properties

An improved particle population balance equation in the continuum-slip regime

Directory of Open Access Journals (Sweden)

Xie Mingliang

2016-01-01

Full Text Available An improved moment model is proposed to solve the population balance equation for Brownian coagulation in the continuum-slip regime, and it reduces to a known one in open literature when the non-linear terms in the slip correction factor are ignored. The present model shows same asymptotic behavior as that in the continuum regime.

Formation and propagation of sand dunes: A nonlinear treatment

International Nuclear Information System (INIS)

Eltayeb, I.A.; Hamza, E.A.; Hassan, M.H.A.

1986-06-01

The nonlinear evolutionary equations previously derived for a plane with a rigid lid are here generalized to the free surface model. It is shown that similar equations are obtainable but the coefficients are strongly dependent on the Froude number, F, of the flow. (F is defined as U/(gd) 1/2 , where U is the basic uniform flow, g the gravitational acceleration and d the mean depth of the layer.) When F vanishes, the evolutionary equations reduce to those derived previously for the rigid lid model. The equations possess a dunetrain solution. The stability of this solution is analyzed and found to depend crucially on F. It is found, however, that for all values of F a dunetrain can develop into a solitary dune. The above results apply only when the phase shift δ, originally introduced for the instability of the linear problem, vanishes. For other admissible values of δ, the analysis showed that the neutral solution of the linear theory prevails in the nonlinear regime. (author)

Strong nonlinear photonic responses from microbiologically synthesized tellurium nanocomposites

Science.gov (United States)

Liao, K.-S.; Wang, Jingyuan; Dias, S.; Dewald, J.; Alley, N.J.; Baesman, S.M.; Oremland, R.S.; Blau, W.J.; Curran, S.A.

2010-01-01

A new class of nanomaterials, namely microbiologically-formed nanorods composed of elemental tellurium [Te(0)] that forms unusual nanocomposites when combined with poly(m-phenylenevinylene-co-2,5-dioctoxy-phenylenevinylene) (PmPV) is described. These bio-nanocomposites exhibit excellent broadband optical limiting at 532 and 1064 nm. Nonlinear scattering, originating from the laser induced solvent bubbles and microplasmas, is responsible for this nonlinear behavior. The use of bacterially-formed Te(0) when combined with an organic chemical host (e.g., PmPV) is a new green method of nanoparticle syntheses. This opens the possibilities of using unique, biologically synthesized materials to advance future nanoelectronic and nanophotonic applications. ?? 2009 Elsevier B.V. All rights reserved.

Thermalization and confinement in strongly coupled gauge theories

Directory of Open Access Journals (Sweden)

Ishii Takaaki

2016-01-01

Full Text Available Quantum field theories of strongly interacting matter sometimes have a useful holographic description in terms of the variables of a gravitational theory in higher dimensions. This duality maps time dependent physics in the gauge theory to time dependent solutions of the Einstein equations in the gravity theory. In order to better understand the process by which “real world” theories such as QCD behave out of thermodynamic equilibrium, we study time dependent perturbations to states in a model of a confining, strongly coupled gauge theory via holography. Operationally, this involves solving a set of non-linear Einstein equations supplemented with specific time dependent boundary conditions. The resulting solutions allow one to comment on the timescale by which the perturbed states thermalize, as well as to quantify the properties of the final state as a function of the perturbation parameters. We comment on the influence of the dual gauge theory’s confinement scale on these results, as well as the appearance of a previously anticipated universal scaling regime in the “abrupt quench” limit.

Coupling of tt̄ and γγ with a strongly interacting Electroweak Symmetry Breaking Sector

Directory of Open Access Journals (Sweden)

Delgado Rafael L.

2017-01-01

Full Text Available We report the coupling of an external γγ or tt̄ state to a strongly interacting EWSBS satisfying unitarity. We exploit perturbation theory for those coupling of the external state, whereas the EWSBS is taken as strongly interacting. We use a modified version of the IAM unitarization procedure to model such a strongly interacting regime. The matrix elements VLVL → VLVL, VLVL ↔ hh, hh → hh, VLVL ↔ {γγ, tt̄}, hh ↔ {γγ, tt̄} are all computed to NLO in perturbation theory with the Nonlinear Effective Field Theory of the EWSBS, within the Equivalence Theorem. This allows us to describe resonances of the electroweak sector that may be found at the LHC and their effect on other channels such as γγ or tt̄ where they may be discovered.

Utilizing strongly absorbing materials for low-loss surface-wave nonlinear optics

Science.gov (United States)

Grosse, Nicolai B.; Franz, Philipp; Heckmann, Jan; Pufahl, Karsten; Woggon, Ulrike

2018-04-01

Optical media endowed with large nonlinear susceptibilities are highly prized for their employment in frequency conversion and the generation of nonclassical states of light. Although the presence of an optical resonance can greatly increase the nonlinear response (e.g., in epsilon-near-zero materials), the non-negligible increase in linear absorption often precludes the application of such materials in nonlinear optics. Absorbing materials prepared as thin films, however, can support a low-loss surface wave: the long-range surface exciton polariton (LRSEP). Its propagation lifetime increases with greater intrinsic absorption and reduced film thickness, provided that the film is embedded in a transparent medium (symmetric cladding). We explore LRSEP propagation in a molybdenum film by way of a prism-coupling configuration. Our observations show that excitation of the LRSEP mode leads to a dramatic increase in the yield of second-harmonic generation. This implies that the LRSEP mode is an effective vehicle for utilizing the nonlinear response of absorbing materials.

Nonlinear growth of strongly unstable tearing modes

International Nuclear Information System (INIS)

Waelbroeck, F.L.

1993-11-01

Rutherford's theory of the tearing instability is extended to cases where current nonlinearities are important, such as long wavelength modes in current slabs and the m = 1 instability in tokamaks with moderately large aspect-ratios. Of particular interest is the possibility that the associated magnetic islands, as a result of secondary instabilities, have a singular response to the Ohmic diffusion of the current. A family of islands is used to test this possibility; it is found that the response remains bounded

Infrared reduction, an efficient method to control the non-linear optical property of graphene oxide in femtosecond regime

Science.gov (United States)

Bhattacharya, S.; Maiti, R.; Saha, S.; Das, A. C.; Mondal, S.; Ray, S. K.; Bhaktha, S. B. N.; Datta, P. K.

2016-04-01

Graphene Oxide (GO) has been prepared by modified Hummers method and it has been reduced using an IR bulb (800-2000 nm). Both as grown GO and reduced graphene oxide (RGO) have been characterized using Raman spectroscopy and X-ray photoelectron spectroscopy (XPS). Raman spectra shows well documented Dband and G-band for both the samples while blue shift of G-band confirms chemical functionalization of graphene with different oxygen functional group. The XPS result shows that the as-prepared GO contains 52% of sp2 hybridized carbon due to the C=C bonds and 33% of carbon atoms due to the C-O bonds. As for RGO, increment of the atomic % of the sp2 hybridized carbon atom to 83% and rapid decrease in atomic % of C=O bonds confirm an efficient reduction with infrared radiation. UV-Visible absorption spectrum also confirms increment of conjugation with increased reduction. Non-linear optical properties of both GO and RGO are measured using single beam open aperture Z-Scan technique in femtosecond regime. Intensity dependent nonlinear phenomena are observed. Depending upon the intensity, both saturable absorption and two photon absorption contribute to the non-linearity of both the samples. Saturation dominates at low intensity (~ 127 GW/cm2) while two photon absorption become prominent at higher intensities (from 217 GW/cm2 to 302 GW/cm2). We have calculated the two-photon absorption co-efficient and saturation intensity for both the samples. The value of two photon absorption co-efficient (for GO~ 0.0022-0.0037 cm/GW and for RGO~ 0.0128-0.0143 cm/GW) and the saturation intensity (for GO~57 GW/cm2 and for RGO~ 194GW/cm2) is increased with reduction. Increase in two photon absorption coefficient with increasing intensity can also suggest that there may be multi-photon absorption is taking place.

Nonlinear periodic wavetrains in thin liquid films falling on a uniformly heated horizontal plate

Science.gov (United States)

Issokolo, Remi J. Noumana; Dikandé, Alain M.

2018-05-01

A thin liquid film falling on a uniformly heated horizontal plate spreads into fingering ripples that can display a complex dynamics ranging from continuous waves, nonlinear spatially localized periodic wave patterns (i.e., rivulet structures) to modulated nonlinear wavetrain structures. Some of these structures have been observed experimentally; however, conditions under which they form are still not well understood. In this work, we examine profiles of nonlinear wave patterns formed by a thin liquid film falling on a uniformly heated horizontal plate. For this purpose, the Benney model is considered assuming a uniform temperature distribution along the film propagation on the horizontal surface. It is shown that for strong surface tension but a relatively small Biot number, spatially localized periodic-wave structures can be analytically obtained by solving the governing equation under appropriate conditions. In the regime of weak nonlinearity, a multiple-scale expansion combined with the reductive perturbation method leads to a complex Ginzburg-Landau equation: the solutions of which are modulated periodic pulse trains which amplitude and width and period are expressed in terms of characteristic parameters of the model.

Transmutation of skyrmions to half-solitons driven by the nonlinear optical spin Hall effect.

Science.gov (United States)

Flayac, H; Solnyshkov, D D; Shelykh, I A; Malpuech, G

2013-01-04

We show that the spin domains, generated in the linear optical spin Hall effect by the analog of spin-orbit interaction for exciton polaritons, are associated with the formation of a Skyrmion lattice. In the nonlinear regime, the spin anisotropy of the polariton-polariton interactions results in a spatial compression of the domains and in a transmutation of the Skyrmions into oblique half-solitons. This phase transition is associated with both the focusing of the spin currents and the emergence of a strongly anisotropic emission pattern.

Nonlinear optics quantum computing with circuit QED.

Science.gov (United States)

Adhikari, Prabin; Hafezi, Mohammad; Taylor, J M

2013-02-08

One approach to quantum information processing is to use photons as quantum bits and rely on linear optical elements for most operations. However, some optical nonlinearity is necessary to enable universal quantum computing. Here, we suggest a circuit-QED approach to nonlinear optics quantum computing in the microwave regime, including a deterministic two-photon phase gate. Our specific example uses a hybrid quantum system comprising a LC resonator coupled to a superconducting flux qubit to implement a nonlinear coupling. Compared to the self-Kerr nonlinearity, we find that our approach has improved tolerance to noise in the qubit while maintaining fast operation.

A strain-hardening bi-power law for the nonlinear behaviour of biological soft tissues.

Science.gov (United States)

Nicolle, S; Vezin, P; Palierne, J-F

2010-03-22

Biological soft tissues exhibit a strongly nonlinear viscoelastic behaviour. Among parenchymous tissues, kidney and liver remain less studied than brain, and a first goal of this study is to report additional material properties of kidney and liver tissues in oscillatory shear and constant shear rate tests. Results show that the liver tissue is more compliant but more strain hardening than kidney. A wealth of multi-parameter mathematical models has been proposed for describing the mechanical behaviour of soft tissues. A second purpose of this work is to develop a new constitutive law capable of predicting our experimental data in the both linear and nonlinear viscoelastic regime with as few parameters as possible. We propose a nonlinear strain-hardening fractional derivative model in which six parameters allow fitting the viscoelastic behaviour of kidney and liver tissues for strains ranging from 0.01 to 1 and strain rates from 0.0151 s(-1) to 0.7s(-1). Copyright (c) 2009 Elsevier Ltd. All rights reserved.

Performance emulation and parameter estimation for nonlinear fibre-optic links

DEFF Research Database (Denmark)

Piels, Molly; Porto da Silva, Edson; Zibar, Darko

2016-01-01

Fibre-optic communication systems, especially when operating in the nonlinear regime, generally do not perform exactly as theory would predict. A number of methods for data-based evaluation of nonlinear fibre-optic link parameters, both for accurate performance emulation and optimization...

Entangled plasmon generation in nonlinear spaser system under the action of external magnetic field

Science.gov (United States)

Gubin, M. Yu.; Shesterikov, A. V.; Karpov, S. N.; Prokhorov, A. V.

2018-02-01

The present paper theoretically investigates features of quantum dynamics for localized plasmons in three-particle or four-particle spaser systems consisting of metal nanoparticles and semiconductor quantum dots. In the framework of the mean field approximation, the conditions for the observation of stable stationary regimes for single-particle plasmons in spaser systems are revealed, and realization of these regimes is discussed. The strong dipole-dipole interaction between adjacent nanoparticles for the four-particle spaser system is investigated. We show that this interaction can lead to the decreasing of the autocorrelation function values for plasmons. The generation of entangled plasmons in a three-particle spaser system with nonlinear plasmon-exciton interaction is predicted. The use of an external magnetic field is proposed for control of the cross correlations between plasmons in the three-particle spaser system.

Strongly interacting photons and atoms

International Nuclear Information System (INIS)

Alge, W.

1999-05-01

This thesis contains the main results of the research topics I have pursued during the my PhD studies at the University of Innsbruck and partly in collaboration with the Institut d' Optique in Orsay, France. It is divided into three parts. The first and largest part discusses the possibility of using strong standing waves as a tool to cool and trap neutral atoms in optical cavities. This is very important in the field of nonlinear optics where several successful experiments with cold atoms in cavities have been performed recently. A discussion of the optical parametric oscillator in a regime where the nonlinearity dominates the evolution is the topic of the second part. We investigated mainly the statistical properties of the cavity output of the three interactive cavity modes. Very recently a system has been proposed which promises fantastic properties. It should exhibit a giant Kerr nonlinearity with negligible absorption thus leading to a photonic turnstile device based on cold atoms in cavity. We have shown that this model suffers from overly simplistic assumptions and developed several more comprehensive approaches to study the behavior of this system. Apart from the division into three parts of different contents the thesis is divided into publications, supplements and invisible stuff. The intention of the supplements is to reach researchers which work in related areas and provide them with more detailed information about the concepts and the numerical tools we used. It is written especially for diploma and PhD students to give them a chance to use the third part of our work which is actually the largest one. They consist of a large number of computer programs we wrote to investigate the behavior of the systems in parameter regions where no hope exists to solve the equations analytically. (author)

Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor-Couette flow

Science.gov (United States)

Mamatsashvili, G.; Stefani, F.; Guseva, A.; Avila, M.

2018-01-01

Magnetorotational instability (MRI) is one of the fundamental processes in astrophysics, driving angular momentum transport and mass accretion in a wide variety of cosmic objects. Despite much theoretical/numerical and experimental efforts over the last decades, its saturation mechanism and amplitude, which sets the angular momentum transport rate, remains not well understood, especially in the limit of high resistivity, or small magnetic Prandtl numbers typical to interiors (dead zones) of protoplanetary disks, liquid cores of planets and liquid metals in laboratory. Using direct numerical simulations, in this paper we investigate the nonlinear development and saturation properties of the helical magnetorotational instability (HMRI)—a relative of the standard MRI—in a magnetized Taylor-Couette flow at very low magnetic Prandtl number (correspondingly at low magnetic Reynolds number) relevant to liquid metals. For simplicity, the ratio of azimuthal field to axial field is kept fixed. From the linear theory of HMRI, it is known that the Elsasser number, or interaction parameter determines its growth rate and plays a special role in the dynamics. We show that this parameter is also important in the nonlinear problem. By increasing its value, a sudden transition from weakly nonlinear, where the system is slightly above the linear stability threshold, to strongly nonlinear, or turbulent regime occurs. We calculate the azimuthal and axial energy spectra corresponding to these two regimes and show that they differ qualitatively. Remarkably, the nonlinear state remains in all cases nearly axisymmetric suggesting that this HMRI-driven turbulence is quasi two-dimensional in nature. Although the contribution of non-axisymmetric modes increases moderately with the Elsasser number, their total energy remains much smaller than that of the axisymmetric ones.

Microresonators for Nonlinear Quantum Optics

Science.gov (United States)

Vernon, Zachary

In this thesis I study in detail the quantum dynamics of several nonlinear optical processes in microresonator systems. A Heisenberg-picture input-output formalism is developed from first principles that includes the effects of scattering losses and independent quality factors and coupling ratios for different resonances. The task of calculating the device output is then reduced to solving a set of driven, damped, ordinary differential equations for the resonator mode operators alone. This theoretical framework is used to study photon pair generation via spontaneous four-wave mixing in the weakly pumped regime, on which the effects of scattering losses are appraised. A more strongly driven regime is studied for continuous wave pumps, demonstrating when self- and cross-phase modulation and multi-photon pair generation become important, and their effects on the spectral and power scaling properties of the system are examined; A detuning strategy is presented that compensates for some of these effects. The results of the weak-pump regime are applied to study microresonator-based heralded single photon sources. The impact of scattering losses is studied, revealing that typical systems suffer from low heralding efficiency due to these losses. A technique to improve heralding efficiency is presented through over-coupling the resonator-channel system, and a resultant trade-off between heralding rate and heralding efficiency is uncovered. Limitations to the spectral purity of the heralded single photon output for conventional microresonator systems are also analysed, and a more sophisticated coupling scheme presented to overcome the upper bound for spectral purity of 93% that exists in typical systems, permitting the generation of single photons with spectral purity arbitrarily close to 100% without spectral filtering or sophisticated phase-matching techniques. The theory of quantum frequency conversion in microresonators using four-wave mixing is then developed in detail

Probing different regimes of strong field light-matter interaction with semiconductor quantum dots and few cavity photons

Science.gov (United States)

Hargart, F.; Roy-Choudhury, K.; John, T.; Portalupi, S. L.; Schneider, C.; Höfling, S.; Kamp, M.; Hughes, S.; Michler, P.

2016-12-01

In this work we present an extensive experimental and theoretical investigation of different regimes of strong field light-matter interaction for cavity-driven quantum dot (QD) cavity systems. The electric field enhancement inside a high-Q micropillar cavity facilitates exceptionally strong interaction with few cavity photons, enabling the simultaneous investigation for a wide range of QD-laser detuning. In case of a resonant drive, the formation of dressed states and a Mollow triplet sideband splitting of up to 45 μeV is measured for a mean cavity photon number ≤slant 1. In the asymptotic limit of the linear AC Stark effect we systematically investigate the power and detuning dependence of more than 400 QDs. Some QD-cavity systems exhibit an unexpected anomalous Stark shift, which can be explained by an extended dressed 4-level QD model. We provide a detailed analysis of the QD-cavity systems properties enabling this novel effect. The experimental results are successfully reproduced using a polaron master equation approach for the QD-cavity system, which includes the driving laser field, exciton-cavity and exciton-phonon interactions.

Phenomenological modeling of nonlinear holograms based on metallic geometric metasurfaces.

Science.gov (United States)

Ye, Weimin; Li, Xin; Liu, Juan; Zhang, Shuang

2016-10-31

Benefiting from efficient local phase and amplitude control at the subwavelength scale, metasurfaces offer a new platform for computer generated holography with high spatial resolution. Three-dimensional and high efficient holograms have been realized by metasurfaces constituted by subwavelength meta-atoms with spatially varying geometries or orientations. Metasurfaces have been recently extended to the nonlinear optical regime to generate holographic images in harmonic generation waves. Thus far, there has been no vector field simulation of nonlinear metasurface holograms because of the tremendous computational challenge in numerically calculating the collective nonlinear responses of the large number of different subwavelength meta-atoms in a hologram. Here, we propose a general phenomenological method to model nonlinear metasurface holograms based on the assumption that every meta-atom could be described by a localized nonlinear polarizability tensor. Applied to geometric nonlinear metasurfaces, we numerically model the holographic images formed by the second-harmonic waves of different spins. We show that, in contrast to the metasurface holograms operating in the linear optical regime, the wavelength of incident fundamental light should be slightly detuned from the fundamental resonant wavelength to optimize the efficiency and quality of nonlinear holographic images. The proposed modeling provides a general method to simulate nonlinear optical devices based on metallic metasurfaces.

Regime shifts in mean-variance efficient frontiers: some international evidence

OpenAIRE

Massimo Guidolin; Federica Ria

2010-01-01

Regime switching models have been assuming a central role in financial applications because of their well-known ability to capture the presence of rich non-linear patterns in the joint distribution of asset returns. This paper examines how the presence of regimes in means, variances, and correlations of asset returns translates into explicit dynamics of the Markowitz mean-variance frontier. In particular, the paper shows both theoretically and through an application to international equity po...

Optimal conditions for the generation of the third harmonic of focused radiation in a self-interaction regime

International Nuclear Information System (INIS)

Kulagin, I A; Usmanov, T

1998-01-01

A method developed for the analysis of the interaction of wave beams in a self-interaction regime is used to determine the changes in the optimal conditions for third-harmonic generation with changes in the degree of focusing of the fundamental-frequency radiation in isotropic media. Conditions under which a redistribution of the intensities and phases of the interacting wave beams reduces the efficiency of third-harmonic generation are identified. It is shown that, under strong focusing conditions, there may be additional extrema in the dependence of the intensity of the harmonic on the density of the medium. (nonlinear optical phenomena)

Pattern formation due to non-linear vortex diffusion

Science.gov (United States)

Wijngaarden, Rinke J.; Surdeanu, R.; Huijbregtse, J. M.; Rector, J. H.; Dam, B.; Einfeld, J.; Wördenweber, R.; Griessen, R.

Penetration of magnetic flux in YBa 2Cu 3O 7 superconducting thin films in an external magnetic field is visualized using a magneto-optic technique. A variety of flux patterns due to non-linear vortex diffusion is observed: (1) Roughening of the flux front with scaling exponents identical to those observed in burning paper including two distinct regimes where respectively spatial disorder and temporal disorder dominate. In the latter regime Kardar-Parisi-Zhang behavior is found. (2) Fractal penetration of flux with Hausdorff dimension depending on the critical current anisotropy. (3) Penetration as ‘flux-rivers’. (4) The occurrence of commensurate and incommensurate channels in films with anti-dots as predicted in numerical simulations by Reichhardt, Olson and Nori. It is shown that most of the observed behavior is related to the non-linear diffusion of vortices by comparison with simulations of the non-linear diffusion equation appropriate for vortices.

Dynamics of electron wave packet in a disordered chain with delayed nonlinear response

International Nuclear Information System (INIS)

Zhu Hongjun; Xiong Shijie

2010-01-01

We investigate the dynamics of one electron wave packet in a linear chain with random on-site energies and a nonadiabatic electron-phonon interaction which is described by a delayed cubic nonlinear term in the time-dependent Schroedinger equation. We show that in the regime where the wave packet is delocalized in the case with only the delayed nonlinearity, the wave packet becomes localized when the disorder is added and the localization is enhanced by increasing the disorder. In the regime where the self-trapping phenomenon occurs in the case with only the delayed nonlinearity, by adding the disorder the general dynamical features of the wave packet do not change if the nonlinearity parameter is small, but the dynamics shows the subdiffusive behavior if the nonlinearity parameter is large. The numerical results demonstrate complicated wave packet dynamics of systems with both the disorder and nonlinearity.

Nonlinear drift tearing mode. Strong mode of excitation and stabilization mechanisms

International Nuclear Information System (INIS)

Galeev, A.A.; Zelenyj, L.M.; Kuznetsova, M.M.

1985-01-01

A nonlinear theory of magnetic disturbance development in collisionless configurations with magnetic field shear is considered. The instability evolution is investigated with account for the dynamics of ions and potential electric fields which determine the mode stabilization. It has been found that the drift tearing mode possesses metastable properties: in a nonlinear mode even the growth of linearly stable disturbances of the finite amplitude is possible

Electron dynamics with radiation and nonlinear wigglers

International Nuclear Information System (INIS)

Jowett, J.M.

1986-06-01

The physics of electron motion in storage rings is described by supplementing the Hamiltonian equations of motion with fluctuating radiation reaction forces to describe the effects of synchrotron radiation. This leads to a description of radiation damping and quantum diffusion in single-particle phase-space by means of Fokker-Planck equations. For practical purposes, most storage rings remain in the regime of linear damping and diffusion; this is discussed in some detail with examples, concentrating on longitudinal phase space. However special devices such as nonlinear wigglers may permit the new generation of very large rings to go beyond this into regimes of nonlinear damping. It is shown how a special combined-function wiggler can be used to modify the energy distribution and current profile of electron bunches

Doping dependent nonlinear Hall effect in SmFeAsO1-xFx

International Nuclear Information System (INIS)

Riggs, Scott C; Kemper, J B; Stegen, Z; Boebinger, G S; McDonald, R D; Balakirev, F F; Kohama, Y; Migliori, A; Chen, H; Liu, R H; Chen, X H

2009-01-01

We report the Hall resistivity, ρ xy , of polycrystalline SmFeAsO 1-x F x for four different fluorine concentrations from the onset of superconductivity through the collapse of the structural phase transition. For the two more highly doped samples, ρ xy is linear in magnetic field up to 50 T with only weak temperature dependence, reminiscent of a simple Fermi liquid. For the lightly doped samples with x xy (H) being both nonlinear in magnetic field and strongly temperature-dependent even though the Hall angle is small. The onset temperature for this nonlinear regime is in the vicinity of the structural phase (SPT)/magnetic ordering (MO) transitions. The temperature dependence of the Hall resistivity is consistent with a thermal activation of carriers across an energy gap. The evolution of the energy gap with doping is reported. (fast track communication)

Topological approximation of the nonlinear Anderson model

Science.gov (United States)

Milovanov, Alexander V.; Iomin, Alexander

2014-06-01

We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrödinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance overlap in phase space, ranging from a fully developed chaos involving Lévy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that the quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on the infinite Cayley tree (Bethe lattice). It is found in the vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t →+∞. The second moment of the associated probability distribution grows with time as a power law ∝ tα, with the exponent α =1/3 exactly. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to the details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of "stripes" propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the

Evidence for a bubble-competition regime in indirectly driven ablative Rayleigh-Taylor instability experiments on the NIF.

Science.gov (United States)

Martinez, D A; Smalyuk, V A; Kane, J O; Casner, A; Liberatore, S; Masse, L P

2015-05-29

We investigate on the National Ignition Facility the ablative Rayleigh-Taylor instability in the transition from weakly nonlinear to highly nonlinear regimes. A planar plastic package with preimposed two-dimensional broadband modulations is accelerated for up to 12 ns by the x-ray drive of a gas-filled Au radiation cavity with a radiative temperature plateau at 175 eV. This extended tailored drive allows a distance traveled in excess of 1 mm for a 130  μm thick foil. Measurements of the modulation optical density performed by x-ray radiography show that a bubble-merger regime for the Rayleigh-Taylor instability at an ablation front is achieved for the first time in indirect drive. The mutimode modulation amplitudes are in the nonlinear regime, grow beyond the Haan multimode saturation level, evolve toward the longer wavelengths, and show insensitivity to the initial conditions.

Nonlinear optical response of some Graphene oxide and Graphene fluoride derivatives

OpenAIRE

Liaros Nikolaos; Orfanos Ioannis; Papadakis Ioannis; Couris Stelios

2016-01-01

The nonlinear optical properties of two graphene derivatives, graphene oxide and graphene fluoride, are investigated by means of the Z-scan technique employing 35 ps and 4 ns, visible (532 nm) laser excitation. Both derivatives were found to exhibit significant third-order nonlinear optical response at both excitation regimes, with the nonlinear absorption being relatively stronger and concealing the presence of nonlinear refraction under ns excitation, while ps excita...

Relationship Between the Parameters of the Linear and Nonlinear Wave Generation Stages in a Magnetospheric Cyclotron Maser in the Backward-Wave Oscillator Regime

Science.gov (United States)

Demekhov, A. G.

2017-03-01

By using numerical simulations we generalize certain relationships between the parameters of quasimonochromatic whistler-mode waves generated at the linear and nonlinear stages of the cyclotron instability in the backward-wave oscillator regime. One of these relationships is between the wave amplitude at the nonlinear stage and the linear growth rate of the cyclotron instability. It was obtained analytically by V.Yu.Trakhtengerts (1984) for a uniform medium under the assumption of constant frequency and amplitude of the generated wave. We show that a similar relationship also holds for the signals generated in a nonuniform magnetic field and having a discrete structure in the form of short wave packets (elements) with fast frequency drift inside each element. We also generalize the formula for the linear growth rate of absolute cyclotron instability in a nonuniform medium and analyze the relationship between the frequency drift rate in the discrete elements and the wave amplitude. These relationships are important for analyzing the links between the parameters of chorus emissions in the Earth's and planetary magnetospheres and the characteristics of the energetic charged particles generating these signals.

Coexistence of Multiple Nonlinear States in a Tristable Passive Kerr Resonator

Science.gov (United States)

Anderson, Miles; Wang, Yadong; Leo, François; Coen, Stéphane; Erkintalo, Miro; Murdoch, Stuart G.

2017-07-01

Passive Kerr cavities driven by coherent laser fields display a rich landscape of nonlinear physics, including bistability, pattern formation, and localized dissipative structures (solitons). Their conceptual simplicity has for several decades offered an unprecedented window into nonlinear cavity dynamics, providing insights into numerous systems and applications ranging from all-optical memory devices to microresonator frequency combs. Yet despite the decades of study, a recent theoretical work has surprisingly alluded to an entirely new and unexplored paradigm in the regime where nonlinearly tilted cavity resonances overlap with one another [T. Hansson and S. Wabnitz, J. Opt. Soc. Am. B 32, 1259 (2015), 10.1364/JOSAB.32.001259]. We use synchronously driven fiber ring resonators to experimentally access this regime and observe the rise of new nonlinear dissipative states. Specifically, we observe, for the first time to the best of our knowledge, the stable coexistence of temporal Kerr cavity solitons and extended modulation instability (Turing) patterns, and perform real-time measurements that unveil the dynamics of the ensuing nonlinear structure. When operating in the regime of continuous wave tristability, we further observe the coexistence of two distinct cavity soliton states, one of which can be identified as a "super" cavity soliton, as predicted by Hansson and Wabnitz. Our experimental findings are in excellent agreement with theoretical analyses and numerical simulations of the infinite-dimensional Ikeda map that governs the cavity dynamics. The results from our work reveal that experimental systems can support complex combinations of distinct nonlinear states, and they could have practical implications to future microresonator-based frequency comb sources.

Rayleigh-Taylor growth measurements of three-dimensional modulations in a nonlinear regime

International Nuclear Information System (INIS)

Smalyuk, V.A.; Sadot, O.; Betti, R.; Goncharov, V.N.; Delettrez, J.A.; Meyerhofer, D.D.; Regan, S.P.; Sangster, T.C.; Shvarts, D.

2006-01-01

An understanding of the nonlinear evolution of Rayleigh-Taylor (RT) instability is essential in inertial confinement fusion and astrophysics. The nonlinear RT growth of three-dimensional (3-D) broadband nonuniformities was measured near saturation levels using x-ray radiography in planar foils accelerated by laser light. The initial 3-D target modulations were seeded by laser nonuniformities and subsequently amplified by the RT instability. The measured modulation Fourier spectra and nonlinear growth velocities are in excellent agreement with those predicted by Haan's model [S. Haan, Phys. Rev. A 39, 5812 (1989)]. These spectra and growth velocities are insensitive to initial conditions. In a real-space analysis, the bubble merger was quantified by a self-similar evolution of bubble size distributions, in agreement with the Alon-Oron-Shvarts theoretical predictions [D. Oron et al. Phys. Plasmas 8, 2883 (2001)

REGIME SWITCHING DETERMINANTS OF SOVEREIGN CDS SPREADS: EVIDENCE FROM TURKEY

Directory of Open Access Journals (Sweden)

Umurcan Polat

2017-12-01

Full Text Available In this study, it is assessed the main determinants of sovereign CDS spreads in Turkey from January 2006 to December 2015. Before delving into the nonlinear Markov regime-switching model estimation, a conventional one-state linear model is estimated answering to what extent the sovereign credit risk is affected in between global and country-specific market variables and by credit ratings announcement changes. In broad strokes, the regime-switching analysis reveals that among domestic variables, it is the foreign exchange rate that affects the sovereign credit risk more in more volatile periods and among global variables, the indicators standing for global volatility risk premiums and international liquidity primarily influence the changes in the sovereign CDS spread in turbulent regimes whereas proxies for global risk free rate are significant more in tranquil regimes.

Second sound in a two-dimensional Bose gas: From the weakly to the strongly interacting regime

Science.gov (United States)

Ota, Miki; Stringari, Sandro

2018-03-01

Using Landau's theory of two-fluid hydrodynamics, we investigate first and second sounds propagating in a two-dimensional (2D) Bose gas. We study the temperature and interaction dependence of both sound modes and show that their behavior exhibits a deep qualitative change as the gas evolves from the weakly interacting to the strongly interacting regime. Special emphasis is placed on the jump of both sounds at the Berezinskii-Kosterlitz-Thouless transition, caused by the discontinuity of the superfluid density. We find that the excitation of second sound through a density perturbation becomes weaker and weaker as the interaction strength increases as a consequence of the decrease in the thermal expansion coefficient. Our results could be relevant for future experiments on the propagation of sound on the Bose-Einstein condensate (BEC) side of the BCS-BEC crossover of a 2D superfluid Fermi gas.

Strong coupling of collection of emitters on hyperbolic meta-material

Science.gov (United States)

Biehs, Svend-Age; Xu, Chenran; Agarwal, Girish S.

2018-04-01

Recently, considerable effort has been devoted to the realization of a strong coupling regime of the radiation matter interaction in the context of an emitter at a meta surface. The strong interaction is well realized in cavity quantum electrodynamics, which also show that strong coupling is much easier to realize using a collection of emitters. Keeping this in mind, we study if emitters on a hyperbolic meta materials can yield a strong coupling regime. We show that strong coupling can be realized for densities of emitters exceeding a critical value. A way to detect strong coupling between emitters and hyperbolic metamaterials is to use the Kretschman-Raether configuration. The strong coupling appears as the splitting of the reflectivity dip. In the weak coupling regime, the dip position shifts. The shift and splitting can be used to sense active molecules at surfaces.

Design and implementation plan for indirect-drive highly nonlinear ablative Rayleigh-Taylor instability experiments on the National Ignition Facility

International Nuclear Information System (INIS)

Casner, A.; Masse, L.; Delorme, B.; Jacquet, L.; Liberatore, S.; Smalyuk, V.; Martinez, D.; Seugling, R.; Park, H.S.; Remington, B.A.; Moore, A.; Igumenshev, I.; Chicanne, C.

2013-01-01

In the context of National Ignition Facility Basic Science program we propose to study on the NIF ablative Rayleigh-Taylor (RT) instability in transition from weakly nonlinear to highly nonlinear regimes. Based on the analogy between flame front and ablation front, highly nonlinear RT instability measurements at the ablation front can provide important insights into the initial deflagration stage of thermonuclear supernovae of type Ia. NIF provides a unique platform to study the rich physics of nonlinear and turbulent mixing flows in High Energy Density plasmas because it can accelerate targets over much larger distances and longer time periods than previously achieved on the NOVA and OMEGA lasers. In one shot, growth of RT modulations can be measured from the weakly nonlinear stage near nonlinear saturation levels to the highly nonlinear bubble-competition, bubble-merger regimes and perhaps into a turbulent-like regime. The role of ablation on highly-nonlinear RT instability evolution will be comprehensively studied by varying ablation velocity using indirect and direct-drive platforms. We present a detailed hydro-code design of the indirect-drive platform and discuss the implementation plan for these experiments which only use NIF diagnostics already qualified. (authors)

Nonlinear Magnus-induced dynamics and Shapiro spikes for ac and dc driven skyrmions on periodic quasi-one-dimensional substrates

Science.gov (United States)

Reichhardt, Charles; Reichhardt, Cynthia J. Olson

We numerically examine skyrmions interacting with a periodic quasi-one-dimensional substrate. When we drive the skyrmions perpendicular to the substrate periodicity direction, a rich variety of nonlinear Magnus-induced effects arise, in contrast to an overdamped system that shows only a linear velocity-force curve for this geometry. The skyrmion velocity-force curve is strongly nonlinear and we observe a Magnus-induced speed-up effect when the pinning causes the Magnus velocity response to align with the dissipative response. At higher applied drives these components decouple, resulting in strong negative differential conductivity. For skyrmions under combined ac and dc driving, we find a new class of phase locking phenomena in which the velocity-force curves contain a series of what we call Shapiro spikes, distinct from the Shapiro steps observed in overdamped systems. There are also regimes in which the skyrmion moves in the direction opposite to the applied dc drive to give negative mobility.

BRIEF COMMUNICATIONS: Strong reflection of a series of pulses from a four-wave mirror with thermal nonlinearity under parametric feedback conditions

Science.gov (United States)

Barashkov, M. S.; Bel'dyugin, Igor'M.; Zolotarev, M. V.; Kruzhilin, Yu I.; Krymskiĭ, M. I.; Oshkin, S. P.; Starkov, G. S.; Umnov, A. F.; Kharchenko, M. A.

1989-04-01

A four-wave mirror exhibiting a thermal nonlinearity was used in a study of the interaction of concurrent waves under parametric feedback conditions in the presence of a nonreciprocal element. Strong reflection of a series of pulses of ~ 300 ns duration from a neodymium glass laser was demonstrated: the maximum reflection coefficient was in excess of 30. An analysis was made of the quality of the radiation reflected from this four-mirror parametric feedback system. A considerable reduction was observed in the steady-state threshold for the operation of this mirror with a thermal nonlinearity when the angles of convergence of the interacting beams were small compared with the case of head-on collision of the waves.

Engineering light emission of two-dimensional materials in both the weak and strong coupling regimes

Science.gov (United States)

Brotons-Gisbert, Mauro; Martínez-Pastor, Juan P.; Ballesteros, Guillem C.; Gerardot, Brian D.; Sánchez-Royo, Juan F.

2018-01-01

Two-dimensional (2D) materials have promising applications in optoelectronics, photonics, and quantum technologies. However, their intrinsically low light absorption limits their performance, and potential devices must be accurately engineered for optimal operation. Here, we apply a transfer matrix-based source-term method to optimize light absorption and emission in 2D materials and related devices in weak and strong coupling regimes. The implemented analytical model accurately accounts for experimental results reported for representative 2D materials such as graphene and MoS2. The model has been extended to propose structures to optimize light emission by exciton recombination in MoS2 single layers, light extraction from arbitrarily oriented dipole monolayers, and single-photon emission in 2D materials. Also, it has been successfully applied to retrieve exciton-cavity interaction parameters from MoS2 microcavity experiments. The present model appears as a powerful and versatile tool for the design of new optoelectronic devices based on 2D semiconductors such as quantum light sources and polariton lasers.

Nonlinear features of the longitudinal instability for high-current machines

International Nuclear Information System (INIS)

Hofmann, I.; Boine-Frankenheim, O.

1999-01-01

We present results from experiments at the GSI machines as well as computer simulation for space charge dominated coasting beams (below transition). It is found that for the high-current machines presently under discussion the actual challenge lies in the nonlinear regime. Experiments are in good agreement with theory and simulation in the linear regime; for the nonlinear regime and long-time evolution rsp. saturation our experimental results show good agreement in some aspects, like wave steepening. To analyze the final momentum distribution we still depend on simulation, which shows that the behavior differs substantially, depending on whether the working point in the impedance plane lies close to the real (resistive dominated) or imaginary (space charge dominated) axis, or in between. For the space-charge-dominated regime (Re Z<< Im Z) it is found by computer simulation that for currents far above the Keil-Schnell threshold self-stabilization occurs by formation of a momentum tail, hence linear instability criteria can be practically ignored. It is shown here that the global impedance distribution is of crucial importance

Comparison between measured and predicted turbulence frequency spectra in ITG and TEM regimes

Science.gov (United States)

Citrin, J.; Arnichand, H.; Bernardo, J.; Bourdelle, C.; Garbet, X.; Jenko, F.; Hacquin, S.; Pueschel, M. J.; Sabot, R.

2017-06-01

The observation of distinct peaks in tokamak core reflectometry measurements—named quasi-coherent-modes (QCMs)—are identified as a signature of trapped-electron-mode (TEM) turbulence (Arnichand et al 2016 Plasma Phys. Control. Fusion 58 014037). This phenomenon is investigated with detailed linear and nonlinear gyrokinetic simulations using the Gene code. A Tore-Supra density scan is studied, which traverses through a linear (LOC) to saturated (SOC) ohmic confinement transition. The LOC and SOC phases are both simulated separately. In the LOC phase, where QCMs are observed, TEMs are robustly predicted unstable in linear studies. In the later SOC phase, where QCMs are no longer observed, ion-temperature-gradient (ITG) modes are identified. In nonlinear simulations, in the ITG (SOC) phase, a broadband spectrum is seen. In the TEM (LOC) phase, a clear emergence of a peak at the TEM frequencies is seen. This is due to reduced nonlinear frequency broadening of the underlying linear modes in the TEM regime compared with the ITG regime. A synthetic diagnostic of the nonlinearly simulated frequency spectra reproduces the features observed in the reflectometry measurements. These results support the identification of core QCMs as an experimental marker for TEM turbulence.

Selection Criteria in Regime Switching Conditional Volatility Models

Directory of Open Access Journals (Sweden)

Thomas Chuffart

2015-05-01

Full Text Available A large number of nonlinear conditional heteroskedastic models have been proposed in the literature. Model selection is crucial to any statistical data analysis. In this article, we investigate whether the most commonly used selection criteria lead to choice of the right specification in a regime switching framework. We focus on two types of models: the Logistic Smooth Transition GARCH and the Markov-Switching GARCH models. Simulation experiments reveal that information criteria and loss functions can lead to misspecification ; BIC sometimes indicates the wrong regime switching framework. Depending on the Data Generating Process used in the experiments, great care is needed when choosing a criterion.

Realization and optical characterisation of micro-cavities in strong coupling regime using self-assembled multi-quantum wells structure of 2D perovskites

International Nuclear Information System (INIS)

Lanty, Gaetan

2011-01-01

The research work which is reported in this manuscript focuses on 2D perovskites and their use to obtain micro-cavities working in the strong coupling regime. Perovskite structure forms a multi-quantum wells in which the excitonic states have a high oscillator strength and a large binding energy (a few 100 MeV) due to quantum and dielectric confinement effects. A first axis of this work was to collect information on the excitonic properties of these materials. On a particular perovskite (PEPI), we performed photoluminescence and pump-probe measurements, which seem to suggest the existence, under high excitation density, a process of Auger recombination of excitons. A second research axis was to put in cavity thin layers of some perovskites. With PEPI and PEPC perovskites, we have shown that the realization of micro-cavities with a quality factor of the order of ten is sufficient to obtain at room temperature, the strong coupling regime in absorption and emission with Rabi splitting up to 220 MeV. A bottleneck effect has been clearly demonstrated for the PEPI microcavity. We have also shown that perovskites could be associated with inorganic semiconductors in 'hybrid' micro-cavities. According Agranovich et al., these micro-cavities could present polariton lasing with lower quality factors. To this end, the ZnO/MFMPB association seems particularly promising. (author)

Nonlinear optical spectroscopy of isotropic and anisotropic metallic nanocomposites

Energy Technology Data Exchange (ETDEWEB)

Fernandez-Hernandez, R C; Gleason-Villagran, R; Cheang-Wong, J C; Crespo-Sosa, A; Rodriguez-Fernandez, L; Lopez-Suarez, A; Oliver, A; Reyes-Esqueda, J A [Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Mexico, D. F. 04510 (Mexico); Torres-Torres, C [Seccion de Estudios de Posgrado e Investigacion, ESIME-Zacatenco, Instituto Politecnico Nacional, Mexico, D. F. 07338 (Mexico); Rangel-Rojo, R, E-mail: reyes@fisica.unam.mx [CICESE/Depto. de Optica, A.P. 360, Ensenada, B. C. 22860 (Mexico)

2011-01-01

In this work, we studied the nonlinear absorption and refraction of isotropic and anisotropic metallic nanocomposites, which consist of Au and Ag nanoparticles (NPs) embedded in matrices of SiO{sub 2}. We performed this study at different wavelengths using the Z-scan technique in the picosecond regime. The wavelengths were selected accordingly to the absorption spectra of the nanocomposites, choosing wavelengths into the inter- and intra-band transitions regions, including the surface plasmon (SP) resonance, as well as in the transparent region. For the anisotropic nanocomposites, the polarization and the incident angle were varied in order to evaluate the different components of the third order susceptibility tensor, {chi}{sup (3)}. We observed dramatic changes of sign for both, nonlinear refraction and absorption, when passing from Au to Ag and/or varying the wave length. The results accentuate the importance of the hot-electrons contribution to the nonlinear optical response at this temporal regime, when compared to inter-band and intra-band transitions contributions.

Nonlinear optical spectroscopy of isotropic and anisotropic metallic nanocomposites

International Nuclear Information System (INIS)

Fernandez-Hernandez, R C; Gleason-Villagran, R; Cheang-Wong, J C; Crespo-Sosa, A; Rodriguez-Fernandez, L; Lopez-Suarez, A; Oliver, A; Reyes-Esqueda, J A; Torres-Torres, C; Rangel-Rojo, R

2011-01-01

In this work, we studied the nonlinear absorption and refraction of isotropic and anisotropic metallic nanocomposites, which consist of Au and Ag nanoparticles (NPs) embedded in matrices of SiO 2 . We performed this study at different wavelengths using the Z-scan technique in the picosecond regime. The wavelengths were selected accordingly to the absorption spectra of the nanocomposites, choosing wavelengths into the inter- and intra-band transitions regions, including the surface plasmon (SP) resonance, as well as in the transparent region. For the anisotropic nanocomposites, the polarization and the incident angle were varied in order to evaluate the different components of the third order susceptibility tensor, χ (3) . We observed dramatic changes of sign for both, nonlinear refraction and absorption, when passing from Au to Ag and/or varying the wave length. The results accentuate the importance of the hot-electrons contribution to the nonlinear optical response at this temporal regime, when compared to inter-band and intra-band transitions contributions.

Nonlinear dynamics of a coherent polariton-biexciton system

International Nuclear Information System (INIS)

Nguyen Trung Dan; Vo Tinh

1994-08-01

The nonlinear dynamics of a coherent interacting polariton-biexciton system in optically excited semiconductors is investigated. We consider the case when two macroscopically coherent modes - a lower branch polariton and a biexciton existing simultaneously in a direct-gap semiconductor. The conditions for exhibiting optical bistability in stationary regime are obtained. Numerical simulation for the nonlinear dynamics equations of the system is also carried out. (author). 16 refs, 4 figs

Coexistence of Multiple Nonlinear States in a Tristable Passive Kerr Resonator

Directory of Open Access Journals (Sweden)

Miles Anderson

2017-08-01

Full Text Available Passive Kerr cavities driven by coherent laser fields display a rich landscape of nonlinear physics, including bistability, pattern formation, and localized dissipative structures (solitons. Their conceptual simplicity has for several decades offered an unprecedented window into nonlinear cavity dynamics, providing insights into numerous systems and applications ranging from all-optical memory devices to microresonator frequency combs. Yet despite the decades of study, a recent theoretical work has surprisingly alluded to an entirely new and unexplored paradigm in the regime where nonlinearly tilted cavity resonances overlap with one another [T. Hansson and S. Wabnitz, J. Opt. Soc. Am. B 32, 1259 (2015JOBPDE0740-322410.1364/JOSAB.32.001259]. We use synchronously driven fiber ring resonators to experimentally access this regime and observe the rise of new nonlinear dissipative states. Specifically, we observe, for the first time to the best of our knowledge, the stable coexistence of temporal Kerr cavity solitons and extended modulation instability (Turing patterns, and perform real-time measurements that unveil the dynamics of the ensuing nonlinear structure. When operating in the regime of continuous wave tristability, we further observe the coexistence of two distinct cavity soliton states, one of which can be identified as a “super” cavity soliton, as predicted by Hansson and Wabnitz. Our experimental findings are in excellent agreement with theoretical analyses and numerical simulations of the infinite-dimensional Ikeda map that governs the cavity dynamics. The results from our work reveal that experimental systems can support complex combinations of distinct nonlinear states, and they could have practical implications to future microresonator-based frequency comb sources.

Vibration mitigation of a bridge cable using a nonlinear energy sink: design and experiment

Directory of Open Access Journals (Sweden)

Weiss Mathieu

2015-01-01

Full Text Available This work deals with the design and experiment of a cubic nonlinear energy sink (NES for horizontal vibration mitigation of a bridge cable. Modal analysis of horizontal linear modes of the cable is experimentally performed using accelerometers and displacement sensors. A theoretical simplified 2-dof model of the coupled cable-NES system is used to analytically design the NES by mean of multi-time scale systems behaviours and detection its invariant manifold, equilibrium and singular points which stand for periodic and strongly modulated regimes, respectively. Numerical integration is used to confirm the efficiency of the designed NES for the system under step release excitation. Then, the prototype system is built using geometrical cubic nonlinearity as the potential of the NES. Efficiency of the prototype system for mitigation of horizontal vibrations of the cable under for step release and forced excitations is experimentally demonstrated.

Multiphase Weakly Nonlinear Geometric Optics for Schrödinger Equations

KAUST Repository

Carles, Ré mi; Dumas, Eric; Sparber, Christof

2010-01-01

We describe and rigorously justify the nonlinear interaction of highly oscillatory waves in nonlinear Schrödinger equations, posed on Euclidean space or on the torus. Our scaling corresponds to a weakly nonlinear regime where the nonlinearity affects the leading order amplitude of the solution, but does not alter the rapid oscillations. We consider initial states which are superpositions of slowly modulated plane waves, and use the framework of Wiener algebras. A detailed analysis of the corresponding nonlinear wave mixing phenomena is given, including a geometric interpretation of the resonance structure for cubic nonlinearities. As an application, we recover and extend some instability results for the nonlinear Schrödinger equation on the torus in negative order Sobolev spaces. © 2010 Society for Industrial and Applied Mathematics.

Cosmological leverage from the matter power spectrum in the presence of baryon and nonlinear effects

International Nuclear Information System (INIS)

Bielefeld, Jannis; Huterer, Dragan; Linder, Eric V.

2015-01-01

We investigate how the use of higher wavenumbers (smaller scales) in the galaxy clustering power spectrum influences cosmological constraints. We take into account uncertainties from nonlinear density fluctuations, (scale dependent) galaxy bias, and baryonic effects. Allowing for substantially model independent uncertainties through separate fit parameters in each wavenumber bin that also allow for the redshift evolution, we quantify strong gains in dark energy and neutrino mass leverage with increasing maximum wavenumber, despite marginalizing over numerous (up to 125) extra fit parameters. The leverage is due to not only an increased number of modes but, more significantly, breaking of degeneracies beyond the linear regime

Nonlinear harmonic generation and proposed experimental verification in SASE FELs

CERN Document Server

Freund, H P; Milton, S V

2000-01-01

Recently, a 3D, polychromatic, nonlinear simulation code was developed to study the growth of nonlinear harmonics in self-amplified spontaneous emission (SASE) free-electron lasers (FELs). The simulation was applied to the parameters for each stage of the Advanced Photon Source (APS) SASE FEL, intended for operation in the visible, UV, and short UV wavelength regimes, respectively, to study the presence of nonlinear harmonic generation. Significant nonlinear harmonic growth is seen. Here, a discussion of the code development, the APS SASE FEL, the simulations and results, and, finally, the proposed experimental procedure for verification of such nonlinear harmonic generation at the APS SASE FEL will be given.

Radiation-reaction effects in the quantum regime

International Nuclear Information System (INIS)

Neitz, Norman

2014-01-01

In this work the influence of radiation reaction on the interaction of an electron bunch with a strong laser field is studied including nonlinear and quantum effects. This venture is motivated by two technological developments: On the one hand, the tremendous increase in available laser intensities and, on the other hand, the significant advancements in electron acceleration technology. Considering a regime where radiation reaction effects are caused by the incoherent emission of several photons, a kinetic approach is developed to describe the dynamics of electrons and photons via distribution functions. Whereas classical electrodynamics, employing the Landau-Lifshitz equation, predicts a narrowing of the energy distribution of the electron beam, the analysis in this work reveals the opposite effect in case that quantum effects become significant. The spreading of the electrons' energy distribution is shown to be caused by the intrinsic stochastic nature of photon emission. In order to explain quantitatively the discrepancy between classical and quantum radiation reaction, the final electron distribution as computed in our quantum treatment is demonstrated to depend on the laser's envelope shape and its duration at a given total laser fluence. On the contrary, the classical analysis does not exhibit such a dependency. Finally, the kinetic approach is extended to allow for the inclusion of pair creation by photons emitted during the scattering. This facilitates a conclusive investigation of the nonlinear coupled dynamics of all particles involved in the interaction, i.e., electrons in the initial bunch, photons and electron-positron pairs produced during the scattering.

Extreme Nonlinear Optics An Introduction

CERN Document Server

Wegener, Martin

2005-01-01

Following the birth of the laser in 1960, the field of "nonlinear optics" rapidly emerged. Today, laser intensities and pulse durations are readily available, for which the concepts and approximations of traditional nonlinear optics no longer apply. In this regime of "extreme nonlinear optics," a large variety of novel and unusual effects arise, for example frequency doubling in inversion symmetric materials or high-harmonic generation in gases, which can lead to attosecond electromagnetic pulses or pulse trains. Other examples of "extreme nonlinear optics" cover diverse areas such as solid-state physics, atomic physics, relativistic free electrons in a vacuum and even the vacuum itself. This book starts with an introduction to the field based primarily on extensions of two famous textbook examples, namely the Lorentz oscillator model and the Drude model. Here the level of sophistication should be accessible to any undergraduate physics student. Many graphical illustrations and examples are given. The followi...

Nonlinear single-spin spectrum analyzer.

Science.gov (United States)

Kotler, Shlomi; Akerman, Nitzan; Glickman, Yinnon; Ozeri, Roee

2013-03-15

Qubits have been used as linear spectrum analyzers of their environments. Here we solve the problem of nonlinear spectral analysis, required for discrete noise induced by a strongly coupled environment. Our nonperturbative analytical model shows a nonlinear signal dependence on noise power, resulting in a spectral resolution beyond the Fourier limit as well as frequency mixing. We develop a noise characterization scheme adapted to this nonlinearity. We then apply it using a single trapped ion as a sensitive probe of strong, non-Gaussian, discrete magnetic field noise. Finally, we experimentally compared the performance of equidistant vs Uhrig modulation schemes for spectral analysis.

Nonlinear transport behavior of low dimensional electron systems

Science.gov (United States)

Zhang, Jingqiao

The nonlinear behavior of low-dimensional electron systems attracts a great deal of attention for its fundamental interest as well as for potentially important applications in nanoelectronics. In response to microwave radiation and dc bias, strongly nonlinear electron transport that gives rise to unusual electron states has been reported in two-dimensional systems of electrons in high magnetic fields. There has also been great interest in the nonlinear response of quantum ballistic constrictions, where the effects of quantum interference, spatial dispersion and electron-electron interactions play crucial roles. In this thesis, experimental results of the research of low dimensional electron gas systems are presented. The first nonlinear phenomena were observed in samples of highly mobile two dimensional electrons in GaAs heavily doped quantum wells at different magnitudes of DC and AC (10 KHz to 20 GHz) excitations. We found that in the DC excitation regime the differential resistance oscillates with the DC current and external magnetic field, similar behavior was observed earlier in AlGaAs/GaAs heterostructures [C.L. Yang et al. ]. At external AC excitations the resistance is found to be also oscillating as a function of the magnetic field. However the form of the oscillations is considerably different from the DC case. We show that at frequencies below 100 KHz the difference is a result of a specific average of the DC differential resistance during the period of the external AC excitations. Secondly, in similar samples, strong suppression of the resistance by the electric field is observed in magnetic fields at which the Landau quantization of electron motion occurs. The phenomenon survives at high temperatures at which the Shubnikov de Haas oscillations are absent. The scale of the electric fields essential for the effect, is found to be proportional to temperature in the low temperature limit. We suggest that the strong reduction of the longitudinal resistance

Nonlinearities in the quantum measurement process of superconducting qubits

Energy Technology Data Exchange (ETDEWEB)

Serban, Ioana

2008-05-15

The work described in this thesis focuses on the investigation of decoherence and measurement backaction, on the theoretical description of measurement schemes and their improvement. The study presented here is centered around quantum computing implementations using superconducting devices and most important, the Josephson effect. The measured system is invariantly a qubit, i. e. a two-level system. The objective is to study detectors with increasing nonlinearity, e. g. coupling of the qubit to the frequency a driven oscillator, or to the bifurcation amplifier, to determine the performance and backaction of the detector on the measured system and to investigate the importance of a strong qubit-detector coupling for the achievement of a quantum non-demolition type of detection. The first part gives a very basic introduction to quantum information, briefly reviews some of the most promising physical implementations of a quantum computer before focusing on the superconducting devices. The second part presents a series of studies of different qubit measurements, describing the backaction of the measurement onto the measured system and the internal dynamics of the detector. Methodology adapted from quantum optics and chemical physics (master equations, phase-space analysis etc.) combined with the representation of a complex environment yielded a tool capable of describing a nonlinear, non-Markovian environment, which couples arbitrarily strongly to the measured system. This is described in chapter 3. Chapter 4 focuses on the backaction on the qubit and presents novel insights into the qubit dephasing in the strong coupling regime. Chapter 5 uses basically the same system and technical tools to explore the potential of a fast, strong, indirect measurement, and determine how close such a detection would ideally come to the quantum non-demolition regime. Chapter 6 focuses on the internal dynamics of a strongly driven Josephson junction. The analytical results are based on

Nonlinearities in the quantum measurement process of superconducting qubits

International Nuclear Information System (INIS)

Serban, Ioana

2008-05-01

The work described in this thesis focuses on the investigation of decoherence and measurement backaction, on the theoretical description of measurement schemes and their improvement. The study presented here is centered around quantum computing implementations using superconducting devices and most important, the Josephson effect. The measured system is invariantly a qubit, i. e. a two-level system. The objective is to study detectors with increasing nonlinearity, e. g. coupling of the qubit to the frequency a driven oscillator, or to the bifurcation amplifier, to determine the performance and backaction of the detector on the measured system and to investigate the importance of a strong qubit-detector coupling for the achievement of a quantum non-demolition type of detection. The first part gives a very basic introduction to quantum information, briefly reviews some of the most promising physical implementations of a quantum computer before focusing on the superconducting devices. The second part presents a series of studies of different qubit measurements, describing the backaction of the measurement onto the measured system and the internal dynamics of the detector. Methodology adapted from quantum optics and chemical physics (master equations, phase-space analysis etc.) combined with the representation of a complex environment yielded a tool capable of describing a nonlinear, non-Markovian environment, which couples arbitrarily strongly to the measured system. This is described in chapter 3. Chapter 4 focuses on the backaction on the qubit and presents novel insights into the qubit dephasing in the strong coupling regime. Chapter 5 uses basically the same system and technical tools to explore the potential of a fast, strong, indirect measurement, and determine how close such a detection would ideally come to the quantum non-demolition regime. Chapter 6 focuses on the internal dynamics of a strongly driven Josephson junction. The analytical results are based on

Nonlinear dynamics of resistive electrostatic drift waves

DEFF Research Database (Denmark)

Korsholm, Søren Bang; Michelsen, Poul; Pécseli, H.L.

1999-01-01

The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which is pertur......The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which...... polarity, i.e. a pair of electrostatic convective cells....

Nonlinear peculiar-velocity analysis and PCA

Energy Technology Data Exchange (ETDEWEB)

Dekel, A. [and others

2001-02-20

We allow for nonlinear effects in the likelihood analysis of peculiar velocities, and obtain {approximately}35%-lower values for the cosmological density parameter and for the amplitude of mass-density fluctuations. The power spectrum in the linear regime is assumed to be of the flat {Lambda}CDM model (h = 0:65, n = 1) with only {Omega}{sub m} free. Since the likelihood is driven by the nonlinear regime, we break the power spectrum at k{sub b} {approximately} 0.2 (h{sup {minus}1} Mpc){sup {minus}1} and fit a two-parameter power-law at k > k{sub b} . This allows for an unbiased fit in the linear regime. Tests using improved mock catalogs demonstrate a reduced bias and a better fit. We find for the Mark III and SFI data {Omega}{sub m} = 0.35 {+-} 0.09 with {sigma}{sub 8}{Omega}P{sub m}{sup 0.6} = 0.55 {+-} 0.10 (90% errors). When allowing deviations from {Lambda}CDM, we find an indication for a wiggle in the power spectrum in the form of an excess near k {approximately} 0.05 and a deficiency at k {approximately} 0.1 (h{sup {minus}1} Mpc){sup {minus}1}--a cold flow which may be related to a feature indicated from redshift surveys and the second peak in the CMB anisotropy. A {chi}{sup 2} test applied to principal modes demonstrates that the nonlinear procedure improves the goodness of fit. The Principal Component Analysis (PCA) helps identifying spatial features of the data and fine-tuning the theoretical and error models. We address the potential for optimal data compression using PCA.

LINKING TESTS OF GRAVITY ON ALL SCALES: FROM THE STRONG-FIELD REGIME TO COSMOLOGY

Energy Technology Data Exchange (ETDEWEB)

Baker, Tessa [Astrophysics, Denys Wilkinson Building, Keble Road, University of Oxford, Oxford, OX1 3RH (United Kingdom); Psaltis, Dimitrios [Astronomy Department, University of Arizona, 933 North Cherry Avenue., Tucson, AZ 85721 (United States); Skordis, Constantinos, E-mail: tessa.baker@astro.ox.ac.uk, E-mail: dpsaltis@email.arizona.edu, E-mail: skordis@ucy.ac.cy [School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD (United Kingdom)

2015-03-20

The current effort to test general relativity (GR) employs multiple disparate formalisms for different observables, obscuring the relations between laboratory, astrophysical, and cosmological constraints. To remedy this situation, we develop a parameter space for comparing tests of gravity on all scales in the universe. In particular, we present new methods for linking cosmological large-scale structure, the cosmic microwave background, and gravitational waves with classic PPN tests of gravity. Diagrams of this gravitational parameter space reveal a noticeable untested regime. The untested window, which separates small-scale systems from the troubled cosmological regime, could potentially hide the onset of corrections to GR.

Quantitative comparison of electron temperature fluctuations to nonlinear gyrokinetic simulations in C-Mod Ohmic L-mode discharges

Energy Technology Data Exchange (ETDEWEB)

Sung, C., E-mail: csung@physics.ucla.edu [University of California, Los Angeles, Los Angeles, California 90095 (United States); White, A. E.; Greenwald, M.; Howard, N. T. [Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); Mikkelsen, D. R.; Churchill, R. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States); Holland, C. [University of California, San Diego, La Jolla, California 92093 (United States); Theiler, C. [Ecole Polytechnique Fédérale de Lausanne, SPC, Lausanne 1015 (Switzerland)

2016-04-15

Long wavelength turbulent electron temperature fluctuations (k{sub y}ρ{sub s} < 0.3) are measured in the outer core region (r/a > 0.8) of Ohmic L-mode plasmas at Alcator C-Mod [E. S. Marmar et al., Nucl. Fusion 49, 104014 (2009)] with a correlation electron cyclotron emission diagnostic. The relative amplitude and frequency spectrum of the fluctuations are compared quantitatively with nonlinear gyrokinetic simulations using the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] in two different confinement regimes: linear Ohmic confinement (LOC) regime and saturated Ohmic confinement (SOC) regime. When comparing experiment with nonlinear simulations, it is found that local, electrostatic ion-scale simulations (k{sub y}ρ{sub s} ≲ 1.7) performed at r/a ∼ 0.85 reproduce the experimental ion heat flux levels, electron temperature fluctuation levels, and frequency spectra within experimental error bars. In contrast, the electron heat flux is robustly under-predicted and cannot be recovered by using scans of the simulation inputs within error bars or by using global simulations. If both the ion heat flux and the measured temperature fluctuations are attributed predominantly to long-wavelength turbulence, then under-prediction of electron heat flux strongly suggests that electron scale turbulence is important for transport in C-Mod Ohmic L-mode discharges. In addition, no evidence is found from linear or nonlinear simulations for a clear transition from trapped electron mode to ion temperature gradient turbulence across the LOC/SOC transition, and also there is no evidence in these Ohmic L-mode plasmas of the “Transport Shortfall” [C. Holland et al., Phys. Plasmas 16, 052301 (2009)].

Designs for highly nonlinear ablative Rayleigh-Taylor experiments on the National Ignition Facility

International Nuclear Information System (INIS)

Casner, A.; Masse, L.; Liberatore, S.; Jacquet, L.; Loiseau, P.; Poujade, O.; Smalyuk, V. A.; Bradley, D. K.; Park, H. S.; Remington, B. A.; Igumenshchev, I.; Chicanne, C.

2012-01-01

We present two designs relevant to ablative Rayleigh-Taylor instability in transition from weakly nonlinear to highly nonlinear regimes at the National Ignition Facility [E. I. Moses, J. Phys.: Conf. Ser. 112, 012003 (2008)]. The sensitivity of nonlinear Rayleigh-Taylor instability physics to ablation velocity is addressed with targets driven by indirect drive, with stronger ablative stabilization, and by direct drive, with weaker ablative stabilization. The indirect drive design demonstrates the potential to reach a two-dimensional bubble-merger regime with a 20 ns duration drive at moderate radiation temperature. The direct drive design achieves a 3 to 5 times increased acceleration distance for the sample in comparison to previous experiments allowing at least 2 more bubble generations when starting from a three-dimensional broadband spectrum.

Designs for highly nonlinear ablative Rayleigh-Taylor experiments on the National Ignition Facility

Energy Technology Data Exchange (ETDEWEB)

Casner, A.; Masse, L.; Liberatore, S.; Jacquet, L.; Loiseau, P.; Poujade, O. [CEA, DAM, DIF, F-91297 Arpajon (France); Smalyuk, V. A.; Bradley, D. K.; Park, H. S.; Remington, B. A. [Lawrence Livermore National Laboratory, Livermore, California 94550 (United States); Igumenshchev, I. [Laboratory of Laser Energetics, University of Rochester, Rochester, New York 14623-1299 (United States); Chicanne, C. [CEA, DAM, VALDUC, F-21120 Is-sur-Tille (France)

2012-08-15

We present two designs relevant to ablative Rayleigh-Taylor instability in transition from weakly nonlinear to highly nonlinear regimes at the National Ignition Facility [E. I. Moses, J. Phys.: Conf. Ser. 112, 012003 (2008)]. The sensitivity of nonlinear Rayleigh-Taylor instability physics to ablation velocity is addressed with targets driven by indirect drive, with stronger ablative stabilization, and by direct drive, with weaker ablative stabilization. The indirect drive design demonstrates the potential to reach a two-dimensional bubble-merger regime with a 20 ns duration drive at moderate radiation temperature. The direct drive design achieves a 3 to 5 times increased acceleration distance for the sample in comparison to previous experiments allowing at least 2 more bubble generations when starting from a three-dimensional broadband spectrum.

Fourier imaging of non-linear structure formation

Energy Technology Data Exchange (ETDEWEB)

Brandbyge, Jacob; Hannestad, Steen, E-mail: jacobb@phys.au.dk, E-mail: sth@phys.au.dk [Department of Physics and Astronomy, University of Aarhus, Ny Munkegade 120, DK-8000 Aarhus C (Denmark)

2017-04-01

We perform a Fourier space decomposition of the dynamics of non-linear cosmological structure formation in ΛCDM models. From N -body simulations involving only cold dark matter we calculate 3-dimensional non-linear density, velocity divergence and vorticity Fourier realizations, and use these to calculate the fully non-linear mode coupling integrals in the corresponding fluid equations. Our approach allows for a reconstruction of the amount of mode coupling between any two wavenumbers as a function of redshift. With our Fourier decomposition method we identify the transfer of power from larger to smaller scales, the stable clustering regime, the scale where vorticity becomes important, and the suppression of the non-linear divergence power spectrum as compared to linear theory. Our results can be used to improve and calibrate semi-analytical structure formation models.

Fourier imaging of non-linear structure formation

International Nuclear Information System (INIS)

Brandbyge, Jacob; Hannestad, Steen

2017-01-01

We perform a Fourier space decomposition of the dynamics of non-linear cosmological structure formation in ΛCDM models. From N -body simulations involving only cold dark matter we calculate 3-dimensional non-linear density, velocity divergence and vorticity Fourier realizations, and use these to calculate the fully non-linear mode coupling integrals in the corresponding fluid equations. Our approach allows for a reconstruction of the amount of mode coupling between any two wavenumbers as a function of redshift. With our Fourier decomposition method we identify the transfer of power from larger to smaller scales, the stable clustering regime, the scale where vorticity becomes important, and the suppression of the non-linear divergence power spectrum as compared to linear theory. Our results can be used to improve and calibrate semi-analytical structure formation models.

Nonlinear normal vibration modes in the dynamics of nonlinear elastic systems

International Nuclear Information System (INIS)

Mikhlin, Yu V; Perepelkin, N V; Klimenko, A A; Harutyunyan, E

2012-01-01

Nonlinear normal modes (NNMs) are a generalization of the linear normal vibrations. By the Kauderer-Rosenberg concept in the regime of the NNM all position coordinates are single-values functions of some selected position coordinate. By the Shaw-Pierre concept, the NNM is such a regime when all generalized coordinates and velocities are univalent functions of a couple of dominant (active) phase variables. The NNMs approach is used in some applied problems. In particular, the Kauderer-Rosenberg NNMs are analyzed in the dynamics of some pendulum systems. The NNMs of forced vibrations are investigated in a rotor system with an isotropic-elastic shaft. A combination of the Shaw-Pierre NNMs and the Rauscher method is used to construct the forced NNMs and the frequency responses in the rotor dynamics.

Effects of toroidal coupling on the non-linear evolution of tearing modes and on the stochastisation of the magnetic field topology in plasmas

International Nuclear Information System (INIS)

Edery, D.; Pellat, R.; Soule, J.L.

1981-01-01

The resistive MHD equations have been handled in toroidal geometry following the tokamak ordering, in order to obtain a simplified set of non-linear equations. This system of equations is compact, closed, consistent and exact to the first two orders in the expansion in the inverse aspect ratio. Studies of the non-linear evolution of tearing modes in the real geometry of tokamak discharges are now in progress, and quite significant results have been obtained from the numerical code REVE of Fontenay based on our above model. From the analytical results, strong linear coupling between neighbouring modes is expected as is demonstrated by the numerical results in the linear, and non-linear regimes. Moreover, coupling exhibits a stochastic structure of the magnetic field lines, the threshold of which is seen to be easily computed by a simple analytical criterion. (orig.)

Polarization Nonlinear Optics of Quadratically Nonlinear Azopolymers

International Nuclear Information System (INIS)

Konorov, S.O.; Akimov, D.A.; Ivanov, A.A.; Petrov, A.N.; Alfimov, M.V.; Yakimanskii, A.V.; Smirnov, N.N.; Ivanova, V.N.; Kudryavtsev, V.V.; Podshivalov, A.A.; Sokolova, I.M.; Zheltikov, A.M.

2005-01-01

The polarization properties of second harmonic and sum-frequency signals generated by femtosecond laser pulses in films of polymers containing covalent groups of an azobenzothiazole chromophore polarized by an external electric field are investigated. It is shown that the methods of polarization nonlinear optics make it possible to determine the structure of oriented molecular dipoles and reveal important properties of the motion of collectivized πelectrons in organic molecules with strong optical nonlinearities. The polarization measurements show that the tensor of quadratic nonlinear optical susceptibility of chromophore fragments oriented by an external field in macromolecules of the noted azopolymers has a degenerate form. This is indicative of a predominantly one-dimensional character of motion of collectivized π electrons along an extended group of atoms in such molecules

Comparison of the effect of annular and solid electron beams on linear and nonlinear traveling wave tube

Directory of Open Access Journals (Sweden)

F. Sheykhe

Full Text Available The present paper, compares the effect of the annular and solid electron beam on the efficiency of linear and nonlinear TWTs. To do this, first we introduce four different geometric structure of the beam-helix. Then, we calculate the output power of each structure, in linear and nonlinear modes, at different frequencies using the numerical solution of the mathematical equations of the multi-frequency Eulerian model. Now, plot the output power in terms of distance for each structure at different frequencies and compare them. In a linear tube, the effect of annular beams on the output power is better than the solid beam, while this affects the frequency in nonlinear tubes. It is shown that in linear regime the power increase linearly with frequency but for nonlinear regimes is nonlinear. Keywords: Annular beam, Solid beam, Circuit power, Nonlinear, Traveling wave tube, Helix

Dispersive regime of the Jaynes–Cummings and Rabi lattice

International Nuclear Information System (INIS)

Zhu, Guanyu; Koch, Jens; Schmidt, Sebastian

2013-01-01

Photon-based strongly correlated lattice models like the Jaynes–Cummings and Rabi lattices differ from their more conventional relatives like the Bose–Hubbard model by the presence of an additional tunable parameter: the frequency detuning between the pseudo-spin degree of freedom and the harmonic mode frequency on each site. Whenever this detuning is large compared to relevant coupling strengths, the system is said to be in the dispersive regime. The physics of this regime is well-understood at the level of a single Jaynes–Cummings or Rabi site. Here, we extend the theoretical description of the dispersive regime to lattices with many sites, for both strong and ultra-strong coupling. We discuss the nature and spatial range of the resulting qubit–qubit and photon–photon coupling, demonstrate the emergence of photon-pairing and squeezing and illustrate our results by exact diagonalization of the Rabi dimer. (paper)

Strong quasi-particle tunneling study in the paired quantum Hall states

OpenAIRE

Nomura, Kentaro; Yoshioka, Daijiro

2001-01-01

The quasi-particle tunneling phenomena in the paired fractional quantum Hall states are studied. A single point-contact system is first considered. Because of relevancy of the quasi-particle tunneling term, the strong tunneling regime should be investigated. Using the instanton method it is shown that the strong quasi-particle tunneling regime is described as the weak electron tunneling regime effectively. Expanding to the network model the paired quantum Hall liquid to insulator transition i...

The natural sediment regime in rivers: broadening the foundation for ecosystem management

Science.gov (United States)

Wohl, Ellen E.; Bledsoe, Brian P.; Jacobson, Robert B.; Poff, N. LeRoy; Rathburn, Sara L.; Walters, David M.; Wilcox, Andrew C.

2015-01-01

Water and sediment inputs are fundamental drivers of river ecosystems, but river management tends to emphasize flow regime at the expense of sediment regime. In an effort to frame a more inclusive paradigm for river management, we discuss sediment inputs, transport, and storage within river systems; interactions among water, sediment, and valley context; and the need to broaden the natural flow regime concept. Explicitly incorporating sediment is challenging, because sediment is supplied, transported, and stored by nonlinear and episodic processes operating at different temporal and spatial scales than water and because sediment regimes have been highly altered by humans. Nevertheless, managing for a desired balance between sediment supply and transport capacity is not only tractable, given current geomorphic process knowledge, but also essential because of the importance of sediment regimes to aquatic and riparian ecosystems, the physical template of which depends on sediment-driven river structure and function.

Nonlinear MHD dynamo operating at equipartition

DEFF Research Database (Denmark)

Archontis, V.; Dorch, Bertil; Nordlund, Åke

2007-01-01

Context.We present results from non linear MHD dynamo experiments with a three-dimensional steady and smooth flow that drives fast dynamo action in the kinematic regime. In the saturation regime, the system yields strong magnetic fields, which undergo transitions between an energy-equipartition a......Context.We present results from non linear MHD dynamo experiments with a three-dimensional steady and smooth flow that drives fast dynamo action in the kinematic regime. In the saturation regime, the system yields strong magnetic fields, which undergo transitions between an energy......, and that it can saturate at a level significantly higher than intermittent turbulent dynamos, namely at energy equipartition, for high values of the magnetic and fluid Reynolds numbers. The equipartition solution however does not remain time-independent during the simulation but exhibits a much more intricate...

Nonlinear relativistic plasma resonance: Renormalization group approach

Energy Technology Data Exchange (ETDEWEB)

Metelskii, I. I., E-mail: metelski@lebedev.ru [Russian Academy of Sciences, Lebedev Physical Institute (Russian Federation); Kovalev, V. F., E-mail: vfkvvfkv@gmail.com [Dukhov All-Russian Research Institute of Automatics (Russian Federation); Bychenkov, V. Yu., E-mail: bychenk@lebedev.ru [Russian Academy of Sciences, Lebedev Physical Institute (Russian Federation)

2017-02-15

An analytical solution to the nonlinear set of equations describing the electron dynamics and electric field structure in the vicinity of the critical density in a nonuniform plasma is constructed using the renormalization group approach with allowance for relativistic effects of electron motion. It is demonstrated that the obtained solution describes two regimes of plasma oscillations in the vicinity of the plasma resonance— stationary and nonstationary. For the stationary regime, the spatiotemporal and spectral characteristics of the resonantly enhanced electric field are investigated in detail and the effect of the relativistic nonlinearity on the spatial localization of the energy of the plasma relativistic field is considered. The applicability limits of the obtained solution, which are determined by the conditions of plasma wave breaking in the vicinity of the resonance, are established and analyzed in detail for typical laser and plasma parameters. The applicability limits of the earlier developed nonrelativistic theories are refined.

Footprints of electron correlation in strong-field double ionization of Kr close to the sequential-ionization regime

Science.gov (United States)

Li, Xiaokai; Wang, Chuncheng; Yuan, Zongqiang; Ye, Difa; Ma, Pan; Hu, Wenhui; Luo, Sizuo; Fu, Libin; Ding, Dajun

2017-09-01

By combining kinematically complete measurements and a semiclassical Monte Carlo simulation we study the correlated-electron dynamics in the strong-field double ionization of Kr. Interestingly, we find that, as we step into the sequential-ionization regime, there are still signatures of correlation in the two-electron joint momentum spectrum and, more intriguingly, the scaling law of the high-energy tail is completely different from early predictions on the low-Z atom (He). These experimental observations are well reproduced by our generalized semiclassical model adapting a Green-Sellin-Zachor potential. It is revealed that the competition between the screening effect of inner-shell electrons and the Coulomb focusing of nuclei leads to a non-inverse-square central force, which twists the returned electron trajectory at the vicinity of the parent core and thus significantly increases the probability of hard recollisions between two electrons. Our results might have promising applications ranging from accurately retrieving atomic structures to simulating celestial phenomena in the laboratory.

A nonlinear equation for ionic diffusion in a strong binary electrolyte

Science.gov (United States)

Ghosal, Sandip; Chen, Zhen

2010-01-01

The problem of the one-dimensional electro-diffusion of ions in a strong binary electrolyte is considered. The mathematical description, known as the Poisson–Nernst–Planck (PNP) system, consists of a diffusion equation for each species augmented by transport owing to a self-consistent electrostatic field determined by the Poisson equation. This description is also relevant to other important problems in physics, such as electron and hole diffusion across semiconductor junctions and the diffusion of ions in plasmas. If concentrations do not vary appreciably over distances of the order of the Debye length, the Poisson equation can be replaced by the condition of local charge neutrality first introduced by Planck. It can then be shown that both species diffuse at the same rate with a common diffusivity that is intermediate between that of the slow and fast species (ambipolar diffusion). Here, we derive a more general theory by exploiting the ratio of the Debye length to a characteristic length scale as a small asymptotic parameter. It is shown that the concentration of either species may be described by a nonlinear partial differential equation that provides a better approximation than the classical linear equation for ambipolar diffusion, but reduces to it in the appropriate limit. PMID:21818176

Field dependent transition to the non-linear regime in magnetic hyperthermia experiments: Comparison between maghemite, copper, zinc, nickel and cobalt ferrite nanoparticles of similar sizes

Directory of Open Access Journals (Sweden)

E. L. Verde

2012-09-01

Full Text Available Further advances in magnetic hyperthermia might be limited by biological constraints, such as using sufficiently low frequencies and low field amplitudes to inhibit harmful eddy currents inside the patient's body. These incite the need to optimize the heating efficiency of the nanoparticles, referred to as the specific absorption rate (SAR. Among the several properties currently under research, one of particular importance is the transition from the linear to the non-linear regime that takes place as the field amplitude is increased, an aspect where the magnetic anisotropy is expected to play a fundamental role. In this paper we investigate the heating properties of cobalt ferrite and maghemite nanoparticles under the influence of a 500 kHz sinusoidal magnetic field with varying amplitude, up to 134 Oe. The particles were characterized by TEM, XRD, FMR and VSM, from which most relevant morphological, structural and magnetic properties were inferred. Both materials have similar size distributions and saturation magnetization, but strikingly different magnetic anisotropies. From magnetic hyperthermia experiments we found that, while at low fields maghemite is the best nanomaterial for hyperthermia applications, above a critical field, close to the transition from the linear to the non-linear regime, cobalt ferrite becomes more efficient. The results were also analyzed with respect to the energy conversion efficiency and compared with dynamic hysteresis simulations. Additional analysis with nickel, zinc and copper-ferrite nanoparticles of similar sizes confirmed the importance of the magnetic anisotropy and the damping factor. Further, the analysis of the characterization parameters suggested core-shell nanostructures, probably due to a surface passivation process during the nanoparticle synthesis. Finally, we discussed the effect of particle-particle interactions and its consequences, in particular regarding discrepancies between estimated

Quantum Information Processing using Nonlinear Optical Effects

DEFF Research Database (Denmark)

Andersen, Lasse Mejling

This PhD thesis treats applications of nonlinear optical effects for quantum information processing. The two main applications are four-wave mixing in the form of Bragg scattering (BS) for quantum-state-preserving frequency conversion, and sum-frequency generation (SFG) in second-order nonlinear......-chirping the pumps. In the high-conversion regime without the effects of NPM, exact Green functions for BS are derived. In this limit, separability is possible for conversion efficiencies up to 60 %. However, the system still allows for selective frequency conversion as well as re-shaping of the output. One way...

The Whitham approach to dispersive shocks in systems with cubic–quintic nonlinearities

KAUST Repository

Crosta, M

2012-09-12

By employing a rigorous approach based on the Whitham modulation theory, we investigate dispersive shock waves arising in a high-order nonlinear Schrödinger equation with competing cubic and quintic nonlinear responses. This model finds important applications in both nonlinear optics and Bose–Einstein condensates. Our theory predicts the formation of dispersive shocks with totally controllable properties, encompassing both steering and compression effects. Numerical simulations confirm these results perfectly. Quite remarkably, shock tuning can be achieved in the regime of a very small high order, i.e. quintic, nonlinearity.

The Whitham approach to dispersive shocks in systems with cubic–quintic nonlinearities

KAUST Repository

Crosta, M; Trillo, S; Fratalocchi, Andrea

2012-01-01

By employing a rigorous approach based on the Whitham modulation theory, we investigate dispersive shock waves arising in a high-order nonlinear Schrödinger equation with competing cubic and quintic nonlinear responses. This model finds important applications in both nonlinear optics and Bose–Einstein condensates. Our theory predicts the formation of dispersive shocks with totally controllable properties, encompassing both steering and compression effects. Numerical simulations confirm these results perfectly. Quite remarkably, shock tuning can be achieved in the regime of a very small high order, i.e. quintic, nonlinearity.

Nonlinear left-handed transmission line metamaterials

International Nuclear Information System (INIS)

Kozyrev, A B; Weide, D W van der

2008-01-01

Metamaterials, exhibiting simultaneously negative permittivity ε and permeability μ, more commonly referred to as left-handed metamaterials (LHMs) and also known as negative-index materials, have received substantial attention in the scientific and engineering communities [1]. Most studies of LHMs (and electromagnetic metamaterials in general) have been in the linear regime of wave propagation and have already inspired new types of microwave circuits and devices. The results of these studies have already been the subject of numerous reviews and books. This review covers a less explored but rapidly developing area of investigation involving media that combine nonlinearity (dependence of the permittivity and permeability on the magnitude of the propagating field) with the anomalous dispersion exhibited by LHM. The nonlinear phenomena in such media will be considered on the example of a model system: the nonlinear left-handed transmission line. These nonlinear phenomena include parametric generation and amplification, harmonic and subharmonic generation as well as modulational instabilities and envelope solitons. (topical review)

Nonlinear approaches in engineering applications 2

CERN Document Server

Jazar, Reza N

2013-01-01

Provides updated principles and applications of the nonlinear approaches in solving engineering and physics problems Demonstrates how nonlinear approaches may open avenues to better, safer, cheaper systems with less energy consumption Has a strong emphasis on the application, physical meaning, and methodologies of nonlinear approaches in different engineering and science problems

Impulse position control algorithms for nonlinear systems

Energy Technology Data Exchange (ETDEWEB)

Sesekin, A. N., E-mail: sesekin@list.ru [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002 (Russian Federation); Institute of Mathematics and Mechanics, Ural Division of Russian Academy of Sciences, 16 S. Kovalevskaya, Ekaterinburg, 620990 (Russian Federation); Nepp, A. N., E-mail: anepp@urfu.ru [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002 (Russian Federation)

2015-11-30

The article is devoted to the formalization and description of impulse-sliding regime in nonlinear dynamical systems that arise in the application of impulse position controls of a special kind. The concept of trajectory impulse-sliding regime formalized as some limiting network element Euler polygons generated by a discrete approximation of the impulse position control This paper differs from the previously published papers in that it uses a definition of solutions of systems with impulse controls, it based on the closure of the set of smooth solutions in the space of functions of bounded variation. The need for the study of such regimes is the fact that they often arise when parry disturbances acting on technical or economic control system.

Impulse position control algorithms for nonlinear systems

Science.gov (United States)

Sesekin, A. N.; Nepp, A. N.

2015-11-01

The article is devoted to the formalization and description of impulse-sliding regime in nonlinear dynamical systems that arise in the application of impulse position controls of a special kind. The concept of trajectory impulse-sliding regime formalized as some limiting network element Euler polygons generated by a discrete approximation of the impulse position control This paper differs from the previously published papers in that it uses a definition of solutions of systems with impulse controls, it based on the closure of the set of smooth solutions in the space of functions of bounded variation. The need for the study of such regimes is the fact that they often arise when parry disturbances acting on technical or economic control system.

Determination of the onset nonlinearity hydrodynamic characteristics at two-phase flow in parallel vertical channels

International Nuclear Information System (INIS)

Jovic, V.; Afgan, N.; Jovic, L.; Spasojevic, D.

1993-01-01

The paper presents results of the experimental and theoretical analyses of linear and nonlinear characteristics of adiabatic two-phase water-air flow in vertical parallel channels. Regime character changes and linear to nonlinear dynamic characteristics transfer conditions were defined. (author)

Turbulent regimes in the tokamak scrape-off layer

International Nuclear Information System (INIS)

Mosetto, A.

2014-01-01

The tokamak scrape-off layer (SOL) is the plasma region characterized by open field lines that start and end on the vessel walls. The plasma dynamics in the SOL plays a crucial role in determining the overall performance of a tokamak, since it controls the plasma-wall interactions, being responsible of exhausting the tokamak power, it regulates the overall plasma confinement, and it governs the plasma refueling and the removal of fusion ashes. Scrape-off layer physics is intrinsically non-linear and characterized by phenomena that occur on a wide range of spatio-temporal scales. Free energy sources drive a number of unstable modes that develop into turbulence and lead to transport of particles and heat across the magnetic field lines. Depending on the driving instability, different SOL turbulent regimes can be identified. As the SOL turbulent regimes determine the plasma confinement properties and the SOL width (and, consequently, the power flux on the vessel wall, for example), it is of crucial importance to understand which turbulent regimes are active in the SOL, under which conditions they develop, and which are the main properties of the associated turbulent transport. In the present thesis we define the SOL turbulent regimes, and we provide a framework to identify them, given the operational SOL parameters. Our study is based on the drift-reduced Braginskii equations and it is focused on a limited tokamak SOL configuration. We first describe the main SOL linear instabilities, such as the inertial and resistive branches of the drift waves, the resistive, inertial and ideal branches of the ballooning modes, and the ion temperature gradient mode. Then, we find the SOL turbulent regimes depending on the instability driving turbulent transport, assuming that turbulence saturates when the radial gradient associated to the pressure fluctuations is comparable to the equilibrium one. Our methodology for the turbulent regime identification is supported by the analysis

3D Relativistic Magnetohydrodynamic Simulations of Current-Driven Instability. 1; Instability of a Static Column

Science.gov (United States)

Mizuno, Yosuke; Lyubarsky, Yuri; ishikawa, Ken-Ichi; Hardee, Philip E.

2010-01-01

We have investigated the development of current-driven (CD) kink instability through three-dimensional relativistic MHD simulations. A static force-free equilibrium helical magnetic configuration is considered in order to study the influence of the initial configuration on the linear and nonlinear evolution of the instability. We found that the initial configuration is strongly distorted but not disrupted by the kink instability. The instability develops as predicted by linear theory. In the non-linear regime the kink amplitude continues to increase up to the terminal simulation time, albeit at different rates, for all but one simulation. The growth rate and nonlinear evolution of the CD kink instability depends moderately on the density profile and strongly on the magnetic pitch profile. The growth rate of the kink mode is reduced in the linear regime by an increase in the magnetic pitch with radius and the non-linear regime is reached at a later time than for constant helical pitch. On the other hand, the growth rate of the kink mode is increased in the linear regime by a decrease in the magnetic pitch with radius and reaches the non-linear regime sooner than the case with constant magnetic pitch. Kink amplitude growth in the non-linear regime for decreasing magnetic pitch leads to a slender helically twisted column wrapped by magnetic field. On the other hand, kink amplitude growth in the non-linear regime nearly ceases for increasing magnetic pitch.

THREE-DIMENSIONAL RELATIVISTIC MAGNETOHYDRODYNAMIC SIMULATIONS OF CURRENT-DRIVEN INSTABILITY. I. INSTABILITY OF A STATIC COLUMN

International Nuclear Information System (INIS)

Mizuno, Yosuke; Nishikawa, Ken-Ichi; Lyubarsky, Yuri; Hardee, Philip E.

2009-01-01

We have investigated the development of current-driven (CD) kink instability through three-dimensional relativistic magnetohydrodynamic simulations. A static force-free equilibrium helical magnetic configuration is considered in order to study the influence of the initial configuration on the linear and nonlinear evolution of the instability. We found that the initial configuration is strongly distorted but not disrupted by the kink instability. The instability develops as predicted by linear theory. In the nonlinear regime, the kink amplitude continues to increase up to the terminal simulation time, albeit at different rates, for all but one simulation. The growth rate and nonlinear evolution of the CD kink instability depend moderately on the density profile and strongly on the magnetic pitch profile. The growth rate of the kink mode is reduced in the linear regime by an increase in the magnetic pitch with radius and reaches the nonlinear regime at a later time than the case with constant helical pitch. On the other hand, the growth rate of the kink mode is increased in the linear regime by a decrease in the magnetic pitch with radius and reaches the nonlinear regime sooner than the case with constant magnetic pitch. Kink amplitude growth in the nonlinear regime for decreasing magnetic pitch leads to a slender helically twisted column wrapped by magnetic field. On the other hand, kink amplitude growth in the nonlinear regime nearly ceases for increasing magnetic pitch.

Stabilizing strongly correlated photon fluids with non-Markovian reservoirs

Science.gov (United States)

Lebreuilly, José; Biella, Alberto; Storme, Florent; Rossini, Davide; Fazio, Rosario; Ciuti, Cristiano; Carusotto, Iacopo

2017-09-01

We introduce a frequency-dependent incoherent pump scheme with a square-shaped spectrum as a way to study strongly correlated photons in arrays of coupled nonlinear resonators. This scheme can be implemented via a reservoir of population-inverted two-level emitters with a broad distribution of transition frequencies. Our proposal is predicted to stabilize a nonequilibrium steady state sharing important features with a zero-temperature equilibrium state with a tunable chemical potential. We confirm the efficiency of our proposal for the Bose-Hubbard model by computing numerically the steady state for finite system sizes: first, we predict the occurrence of a sequence of incompressible Mott-insulator-like states with arbitrary integer densities presenting strong robustness against tunneling and losses. Secondly, for stronger tunneling amplitudes or noninteger densities, the system enters a coherent regime analogous to the superfluid state. In addition to an overall agreement with the zero-temperature equilibrium state, exotic nonequilibrium processes leading to a finite entropy generation are pointed out in specific regions of parameter space. The equilibrium ground state is shown to be recovered by adding frequency-dependent losses. The promise of this improved scheme in view of quantum simulation of the zero-temperature many-body physics is highlighted.

Polynomially decaying transmission for the nonlinear schrodinger equation in a random medium

International Nuclear Information System (INIS)

Devillard, P.; Sovillard, B.

1986-01-01

This is the first study of one the transmission problems associate to the nonlinear Schrodinger equation with a random potential. We show that for almost every realization of the medium the rate of transmission vanishes when increasing the size of the medium; however, whereas it decays exponentially in the linear regime, it decays polynomially in the nonlinear one

Controller Design of Complex System Based on Nonlinear Strength

Directory of Open Access Journals (Sweden)

Rongjun Mu

2015-01-01

Full Text Available This paper presents a new idea of controller design for complex systems. The nonlinearity index method was first developed for error propagation of nonlinear system. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of the system model. The algorithm of nonlinearity index according to engineering application is first proposed in this paper. Applying this method on nonlinear systems is an effective way to measure the nonlinear strength of dynamics model over the full flight envelope. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of system model. According to the different nonlinear strength of dynamical model, the control system is designed. The simulation time of dynamical complex system is selected by the maximum value of dynamic nonlinearity indices. Take a missile as example; dynamical system and control characteristic of missile are simulated. The simulation results show that the method is correct and appropriate.

Nonlinear absorption dynamics using field-induced surface hopping: zinc porphyrin in water.

Science.gov (United States)

Röhr, Merle I S; Petersen, Jens; Wohlgemuth, Matthias; Bonačić-Koutecký, Vlasta; Mitrić, Roland

2013-05-10

We wish to present the application of our field-induced surface-hopping (FISH) method to simulate nonlinear absorption dynamics induced by strong nonresonant laser fields. We provide a systematic comparison of the FISH approach with exact quantum dynamics simulations on a multistate model system and demonstrate that FISH allows for accurate simulations of nonlinear excitation processes including multiphoton electronic transitions. In particular, two different approaches for simulating two-photon transitions are compared. The first approach is essentially exact and involves the solution of the time-dependent Schrödinger equation in an extended manifold of excited states, while in the second one only transiently populated nonessential states are replaced by an effective quadratic coupling term, and dynamics is performed in a considerably smaller manifold of states. We illustrate the applicability of our method to complex molecular systems by simulating the linear and nonlinear laser-driven dynamics in zinc (Zn) porphyrin in the gas phase and in water. For this purpose, the FISH approach is connected with the quantum mechanical-molecular mechanical approach (QM/MM) which is generally applicable to large classes of complex systems. Our findings that multiphoton absorption and dynamics increase the population of higher excited states of Zn porphyrin in the nonlinear regime, in particular in solution, provides a means for manipulating excited-state properties, such as transient absorption dynamics and electronic relaxation. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Strong Tracking Filter for Nonlinear Systems with Randomly Delayed Measurements and Correlated Noises

Directory of Open Access Journals (Sweden)

Hongtao Yang

2018-01-01

Full Text Available This paper proposes a novel strong tracking filter (STF, which is suitable for dealing with the filtering problem of nonlinear systems when the following cases occur: that is, the constructed model does not match the actual system, the measurements have the one-step random delay, and the process and measurement noises are correlated at the same epoch. Firstly, a framework of decoupling filter (DF based on equivalent model transformation is derived. Further, according to the framework of DF, a new extended Kalman filtering (EKF algorithm via using first-order linearization approximation is developed. Secondly, the computational process of the suboptimal fading factor is derived on the basis of the extended orthogonality principle (EOP. Thirdly, the ultimate form of the proposed STF is obtained by introducing the suboptimal fading factor into the above EKF algorithm. The proposed STF can automatically tune the suboptimal fading factor on the basis of the residuals between available and predicted measurements and further the gain matrices of the proposed STF tune online to improve the filtering performance. Finally, the effectiveness of the proposed STF has been proved through numerical simulation experiments.

Experimental verification of a bridge-shaped, nonlinear vibration energy harvester

Energy Technology Data Exchange (ETDEWEB)

Gafforelli, Giacomo, E-mail: giacomo.gafforelli@polimi.it; Corigliano, Alberto [Department of Civil and Environmental Engineering, Politecnico di Milano, Milano, 20133 (Italy); Xu, Ruize; Kim, Sang-Gook [Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)

2014-11-17

This paper reports a comprehensive modeling and experimental characterization of a bridge shaped nonlinear energy harvester. A doubly clamped beam at large deflection requires stretching strain in addition to the bending strain to be geometrically compatible, which stiffens the beam as the beam deflects and transforms the dynamics to a nonlinear regime. The Duffing mode non-linear resonance widens the frequency bandwidth significantly at higher frequencies than the linear resonant frequency. The modeling includes a nonlinear measure of strain coupled with piezoelectric constitutive equations which end up in nonlinear coupling terms in the equations of motion. The main result supports that the power generation is bounded by the mechanical damping for both linear and nonlinear harvesters. Modeling also shows the power generation is over a wider bandwidth in the nonlinear case. A prototype is manufactured and tested to measure the power generation at different load resistances and acceleration amplitudes. The prototype shows a nonlinear behavior with well-matched experimental data to the modeling.

Nonlinear dynamics of semiclassical coherent states in periodic potentials

International Nuclear Information System (INIS)

Carles, Rémi; Sparber, Christof

2012-01-01

We consider nonlinear Schrödinger equations with either local or nonlocal nonlinearities. In addition, we include periodic potentials as used, for example, in matter wave experiments in optical lattices. By considering the corresponding semiclassical scaling regime, we construct asymptotic solutions, which are concentrated both in space and in frequency around the effective semiclassical phase-space flow induced by Bloch’s spectral problem. The dynamics of these generalized coherent states is governed by a nonlinear Schrödinger model with effective mass. In the case of nonlocal nonlinearities, we establish a novel averaging-type result in the critical case. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)

Non-reciprocity in nonlinear elastodynamics

Science.gov (United States)

Blanchard, Antoine; Sapsis, Themistoklis P.; Vakakis, Alexander F.

2018-01-01

Reciprocity is a fundamental property of linear time-invariant (LTI) acoustic waveguides governed by self-adjoint operators with symmetric Green's functions. The break of reciprocity in LTI elastodynamics is only possible through the break of time reversal symmetry on the micro-level, and this can be achieved by imposing external biases, adding nonlinearities or allowing for time-varying system properties. We present a Volterra-series based asymptotic analysis for studying spatial non-reciprocity in a class of one-dimensional (1D), time-invariant elastic systems with weak stiffness nonlinearities. We show that nonlinearity is neither necessary nor sufficient for breaking reciprocity in this class of systems; rather, it depends on the boundary conditions, the symmetries of the governing linear and nonlinear operators, and the choice of the spatial points where the non-reciprocity criterion is tested. Extension of the analysis to higher dimensions and time-varying systems is straightforward from a mathematical point of view (but not in terms of new non-reciprocal physical phenomena), whereas the connection of non-reciprocity and time irreversibility can be studied as well. Finally, we show that suitably defined non-reciprocity measures enable optimization, and can provide physical understanding of the nonlinear effects in the dynamics, enabling one to establish regimes of "maximum nonlinearity." We highlight the theoretical developments by means of a numerical example.

Nonlinearity management in higher dimensions

International Nuclear Information System (INIS)

Kevrekidis, P G; Pelinovsky, D E; Stefanov, A

2006-01-01

In the present paper, we revisit nonlinearity management of the time-periodic nonlinear Schroedinger equation and the related averaging procedure. By means of rigorous estimates, we show that the averaged nonlinear Schroedinger equation does not blow up in the higher dimensional case so long as the corresponding solution remains smooth. In particular, we show that the H 1 norm remains bounded, in contrast with the usual blow-up mechanism for the focusing Schroedinger equation. This conclusion agrees with earlier works in the case of strong nonlinearity management but contradicts those in the case of weak nonlinearity management. The apparent discrepancy is explained by the divergence of the averaging procedure in the limit of weak nonlinearity management

Collapse of nonlinear Langmuir waves

International Nuclear Information System (INIS)

Malkin, V.M.

1986-01-01

The dispersion of sufficiently intensive Langmuir waves is determined by intrinsic (electron) nonlinearity. During Langmuir collapse the wave energy density required for the appearance of electron nonlinearity is attained, generally speaking, prior to the development of dissipative processes. Up to now, the effect of electron nonlinearity on the collapse dynamics and spectrum of strong Langmuir turbulence ( which may be very appreciable ) has not been studied extensively because of the difficulty of describing nonlinear Langmuir waves. In the present paper the positive determinacy of the electron nonlinear hamiltonian is proven, the increment of modulation instability of a nonlinear Langmuir wave cluster localized in a cavity is calculated, and the universal law of their collapse is found

Nonlinear reflection of shock shear waves in soft elastic media.

Science.gov (United States)

Pinton, Gianmarco; Coulouvrat, François; Gennisson, Jean-Luc; Tanter, Mickaël

2010-02-01

For fluids, the theoretical investigation of shock wave reflection has a good agreement with experiments when the incident shock Mach number is large. But when it is small, theory predicts that Mach reflections are physically unrealistic, which contradicts experimental evidence. This von Neumann paradox is investigated for shear shock waves in soft elastic solids with theory and simulations. The nonlinear elastic wave equation is approximated by a paraxial wave equation with a cubic nonlinear term. This equation is solved numerically with finite differences and the Godunov scheme. Three reflection regimes are observed. Theory is developed for shock propagation by applying the Rankine-Hugoniot relations and entropic constraints. A characteristic parameter relating diffraction and non-linearity is introduced and its theoretical values are shown to match numerical observations. The numerical solution is then applied to von Neumann reflection, where curved reflected and Mach shocks are observed. Finally, the case of weak von Neumann reflection, where there is no reflected shock, is examined. The smooth but non-monotonic transition between these three reflection regimes, from linear Snell-Descartes to perfect grazing case, provides a solution to the acoustical von Neumann paradox for the shear wave equation. This transition is similar to the quadratic non-linearity in fluids.

Fatigue damage evaluation of austenitic stainless steel using nonlinear ultrasonic waves in low cycle regime

Energy Technology Data Exchange (ETDEWEB)

Zhang, Jianfeng; Xuan, Fu-Zhen, E-mail: fzxuan@ecust.edu.cn [MOE Key Laboratory of Pressurized System and Safety, School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai 200237 (China)

2014-05-28

The interrupted low cycle fatigue test of austenitic stainless steel was conducted and the dislocation structure and fatigue damage was evaluated subsequently by using both transmission electron microscope and nonlinear ultrasonic wave techniques. A “mountain shape” correlation between the nonlinear acoustic parameter and the fatigue life fraction was achieved. This was ascribed to the generation and evolution of planar dislocation structure and nonplanar dislocation structure such as veins, walls, and cells. The “mountain shape” correlation was interpreted successfully by the combined contribution of dislocation monopole and dipole with an internal-stress dependent term of acoustic nonlinearity.

Parametric autoresonant excitation of the nonlinear Schrödinger equation.

Science.gov (United States)

Friedland, L; Shagalov, A G

2016-10-01

Parametric excitation of autoresonant solutions of the nonlinear Schrodinger (NLS) equation by a chirped frequency traveling wave is discussed. Fully nonlinear theory of the process is developed based on Whitham's averaged variational principle and its predictions verified in numerical simulations. The weakly nonlinear limit of the theory is used to find the threshold on the amplitude of the driving wave for entering the autoresonant regime. It is shown that above the threshold, a flat (spatially independent) NLS solution can be fully converted into a traveling wave. A simplified, few spatial harmonics expansion approach is also developed for studying this nonlinear mode conversion process, allowing interpretation as autoresonant interaction within triads of spatial harmonics.

Wave propagation in a strongly nonlinear locally resonant granular crystal

Science.gov (United States)

Vorotnikov, K.; Starosvetsky, Y.; Theocharis, G.; Kevrekidis, P. G.

2018-02-01

In this work, we study the wave propagation in a recently proposed acoustic structure, the locally resonant granular crystal. This structure is composed of a one-dimensional granular crystal of hollow spherical particles in contact, containing linear resonators. The relevant model is presented and examined through a combination of analytical approximations (based on ODE and nonlinear map analysis) and of numerical results. The generic dynamics of the system involves a degradation of the well-known traveling pulse of the standard Hertzian chain of elastic beads. Nevertheless, the present system is richer, in that as the primary pulse decays, secondary ones emerge and eventually interfere with it creating modulated wavetrains. Remarkably, upon suitable choices of parameters, this interference "distills" a weakly nonlocal solitary wave (a "nanopteron"). This motivates the consideration of such nonlinear structures through a separate Fourier space technique, whose results suggest the existence of such entities not only with a single-side tail, but also with periodic tails on both ends. These tails are found to oscillate with the intrinsic oscillation frequency of the out-of-phase motion between the outer hollow bead and its internal linear attachment.

Complex nonlinear dynamics in the limit of weak coupling of a system of microcantilevers connected by a geometrically nonlinear tunable nanomembrane.

Science.gov (United States)

Jeong, Bongwon; Cho, Hanna; Keum, Hohyun; Kim, Seok; Michael McFarland, D; Bergman, Lawrence A; King, William P; Vakakis, Alexander F

2014-11-21

Intentional utilization of geometric nonlinearity in micro/nanomechanical resonators provides a breakthrough to overcome the narrow bandwidth limitation of linear dynamic systems. In past works, implementation of intentional geometric nonlinearity to an otherwise linear nano/micromechanical resonator has been successfully achieved by local modification of the system through nonlinear attachments of nanoscale size, such as nanotubes and nanowires. However, the conventional fabrication method involving manual integration of nanoscale components produced a low yield rate in these systems. In the present work, we employed a transfer-printing assembly technique to reliably integrate a silicon nanomembrane as a nonlinear coupling component onto a linear dynamic system with two discrete microcantilevers. The dynamics of the developed system was modeled analytically and investigated experimentally as the coupling strength was finely tuned via FIB post-processing. The transition from the linear to the nonlinear dynamic regime with gradual change in the coupling strength was experimentally studied. In addition, we observed for the weakly coupled system that oscillation was asynchronous in the vicinity of the resonance, thus exhibiting a nonlinear complex mode. We conjectured that the emergence of this nonlinear complex mode could be attributed to the nonlinear damping arising from the attached nanomembrane.

Frontiers of plasma physics. III. The implications of nonlinearity

International Nuclear Information System (INIS)

Bardwell, S.

1977-01-01

In the first two articles of this series, Bardwell reviewed the experimental evidence that points to an inherent nonlinear quality in plasmas. Evidence from strongly turbulent plasmas, where the energy in the plasma's collective motions is comparable to the energy in random motion, leads to the speculation that high energy-density plasmas can provide insight into previously inaccessible regimes of physical behavior. Both laboratory and astrophysical plasmas show a marked tendency to generate self-ordered, large-scale structures; islands of self-generated magnetic field, circulation cells, vortices, and filaments are among the most remarkable of these. These self-ordered phenomena, Bardwell reports, challenge in a fundamental way the conceptual tools of physics as they are presently understood. In part two of this series, Bardwell draws on the connection between linearity and entropy, a topic also examined in Levitt's companion piece in the September 1976 FEF Newsletter, to conclude that these difficulties in plasma physics stem from the invalid extension of contemporary physics, which is basically linear, to high-energy density regimes of a plasma; contemporary physics in these cases is inapplicable. Readers without a background in mathematics should not be deterred by the mathematical formalism in the last section of the article; the text can be understood without a detailed mastery of the mathematical formulae

Turbulent transport regimes and the scrape-off layer heat flux width

Science.gov (United States)

Myra, J. R.; D'Ippolito, D. A.; Russell, D. A.

2015-04-01

Understanding the responsible mechanisms and resulting scaling of the scrape-off layer (SOL) heat flux width is important for predicting viable operating regimes in future tokamaks and for seeking possible mitigation schemes. In this paper, we present a qualitative and conceptual framework for understanding various regimes of edge/SOL turbulence and the role of turbulent transport as the mechanism for establishing the SOL heat flux width. Relevant considerations include the type and spectral characteristics of underlying instabilities, the location of the gradient drive relative to the SOL, the nonlinear saturation mechanism, and the parallel heat transport regime. We find a heat flux width scaling with major radius R that is generally positive, consistent with the previous findings [Connor et al., Nucl. Fusion 39, 169 (1999)]. The possible relationship of turbulence mechanisms to the neoclassical orbit width or heuristic drift mechanism in core energy confinement regimes known as low (L) mode and high (H) mode is considered, together with implications for the future experiments.

Turbulent transport regimes and the scrape-off layer heat flux width

International Nuclear Information System (INIS)

Myra, J. R.; D'Ippolito, D. A.; Russell, D. A.

2015-01-01

Understanding the responsible mechanisms and resulting scaling of the scrape-off layer (SOL) heat flux width is important for predicting viable operating regimes in future tokamaks and for seeking possible mitigation schemes. In this paper, we present a qualitative and conceptual framework for understanding various regimes of edge/SOL turbulence and the role of turbulent transport as the mechanism for establishing the SOL heat flux width. Relevant considerations include the type and spectral characteristics of underlying instabilities, the location of the gradient drive relative to the SOL, the nonlinear saturation mechanism, and the parallel heat transport regime. We find a heat flux width scaling with major radius R that is generally positive, consistent with the previous findings [Connor et al., Nucl. Fusion 39, 169 (1999)]. The possible relationship of turbulence mechanisms to the neoclassical orbit width or heuristic drift mechanism in core energy confinement regimes known as low (L) mode and high (H) mode is considered, together with implications for the future experiments

Nonlinear Physics of Plasmas

CERN Document Server

Kono, Mitsuo

2010-01-01

A nonlinearity is one of the most important notions in modern physics. A plasma is rich in nonlinearities and provides a variety of behaviors inherent to instabilities, coherent wave structures and turbulence. The book covers the basic concepts and mathematical methods, necessary to comprehend nonlinear problems widely encountered in contemporary plasmas, but also in other fields of physics and current research on self-organized structures and magnetized plasma turbulence. The analyses make use of strongly nonlinear models solved by analytical techniques backed by extensive simulations and available experiments. The text is written for senior undergraduates, graduate students, lecturers and researchers in laboratory, space and fusion plasmas.

Nonlinear silicon photonics

Science.gov (United States)

Borghi, M.; Castellan, C.; Signorini, S.; Trenti, A.; Pavesi, L.

2017-09-01

Silicon photonics is a technology based on fabricating integrated optical circuits by using the same paradigms as the dominant electronics industry. After twenty years of fervid development, silicon photonics is entering the market with low cost, high performance and mass-manufacturable optical devices. Until now, most silicon photonic devices have been based on linear optical effects, despite the many phenomenologies associated with nonlinear optics in both bulk materials and integrated waveguides. Silicon and silicon-based materials have strong optical nonlinearities which are enhanced in integrated devices by the small cross-section of the high-index contrast silicon waveguides or photonic crystals. Here the photons are made to strongly interact with the medium where they propagate. This is the central argument of nonlinear silicon photonics. It is the aim of this review to describe the state-of-the-art in the field. Starting from the basic nonlinearities in a silicon waveguide or in optical resonator geometries, many phenomena and applications are described—including frequency generation, frequency conversion, frequency-comb generation, supercontinuum generation, soliton formation, temporal imaging and time lensing, Raman lasing, and comb spectroscopy. Emerging quantum photonics applications, such as entangled photon sources, heralded single-photon sources and integrated quantum photonic circuits are also addressed at the end of this review.

Nonlinear behaviors of a bounded electron beam-plasma system

International Nuclear Information System (INIS)

Iizuka, Satoru; Saeki, Koichi; Sato, Noriyoshi; Hatta, Yoshisuke

1985-01-01

Nonlinear developments of a bounded electron beam-plasma system including stationary electrons are investigated experimentally. A stable double layer is formed as a result of ion trapping in a growing negative potential dip induced by the Pierce instability above the current regime of the Buneman instability. In the in-between regime of the Buneman and Pierce instabilities, energetic ions are observed. This effective ion heating is caused by ion detrapping due to double-layer disruption, being consistent with computer simulation. (author)

Nonlinear dynamics and stability of boiling water reactors: qualitative and quantitative analyses

International Nuclear Information System (INIS)

March-Leuba, J.; Cacuci, D.G.; Perez, R.B.

1985-01-01

A phenomenological model has been developed to simulate the qualitative behavior of boiling water reactors (BWRs) in the nonlinear regime under deterministic and stochastic excitations. After the linear stability threshold is crossed, limit cycle oscillations appear due to interactions between two unstable equilibrium points and the phase-space trajectories. This limit cycle becomes unstable when the feedback gain exceeds a certain critical value. Subsequent limit cycle instabilities produce a cascade of period-doubling bifurcations that leads to a periodic pulsed behavior. Under stochastic excitations, BWRs exhibit a single characteristic resonance, at approx.0.5 Hz, in the linear regime. By contrast, this work shows that harmonics of this characteristic frequency appear in the nonlinear regime. Furthermore, this work also demonstrates that amplitudes of the limit cycle oscillations do not depend on the variance of the stochastic excitation and remain bounded at all times. A physical model of nonlinear BWR dynamics has also been developed and employed to calculate the amplitude of limit cycle oscillations and their effects on fuel integrity over a wide range of operating conditions in the Vermont Yankee reactor. These calculations have confirmed that, beyond the threshold for linear stability, the reactor's state variable undergo limit cycle oscillations

Probing nonlinear electrodynamics in slowly rotating spacetimes through neutrino astrophysics

OpenAIRE

Cuesta, Herman J. Mosquera; Lambiase, Gaetano; Pereira, Jonas P.

2017-01-01

Huge electromagnetic fields are known to be present during the late stages of the dynamics of supernovae. Thus, when dealing with electrodynamics in this context, the possibility may arise to probe nonlinear theories (generalizations of the Maxwellian electromagnetism). We firstly solve Einstein field equations minimally coupled to an arbitrary (current-free) nonlinear Lagrangian of electrodynamics (NLED) in the slow rotation regime $a\\ll M$ (black hole's mass), up to first order in $a/M$. We...

Strong gravity and supersymmetry

International Nuclear Information System (INIS)

Chamseddine, Ali H.; Salam, A.; Strathdee, J.

1977-11-01

A supersymmetric theory is constructed for a strong f plus a weak g graviton, together with their accompanying massive gravitinos, by gaugin the gradel 0Sp(2,2,1)x 0Sp(2,2,1) structure. The mixing term between f and g fields, which makes the strong graviton massive, can be introduced through a spontaneous symmetry-breaking mechanism implemented in this note by constructing a non-linear realization of the symmetry group

Low-dimensional chaotic attractors in drift wave turbulence

International Nuclear Information System (INIS)

Persson, M.; Nordman, H.

1991-01-01

Simulation results of toroidal η i -mode turbulence are analyzed using mathematical tools of nonlinear dynamics. Low-dimensional chaotic attractors are found in the strongly nonlinear regime while in the weakly interacting regime the dynamics is high dimensional. In both regimes, the solutions are found to display sensitive dependence on initial conditions, characterized by a positive largest Liapunov exponent. (au)

Inverse chaos synchronization in linearly and nonlinearly coupled systems with multiple time-delays

International Nuclear Information System (INIS)

Shahverdiev, E.M.; Hashimov, R.H.; Nuriev, R.A.; Hashimova, L.H.; Huseynova, E.M.; Shore, K.A.

2005-04-01

We report on inverse chaos synchronization between two unidirectionally linearly and nonlinearly coupled chaotic systems with multiple time-delays and find the existence and stability conditions for different synchronization regimes. We also study the effect of parameter mismatches on synchonization regimes. The method is tested on the famous Ikeda model. Numerical simulations fully support the analytical approach. (author)

A bimodal temom model for particle Brownian coagulation in the continuum-slip regime

Directory of Open Access Journals (Sweden)

He Qing

2016-01-01

Full Text Available In this paper, a bimodal Taylor-series expansion moment of method is proposed to deal with Brownian coagulation in the continuum-slip regime, where the non-linear terms in the Cunningham correction factor is approximated by Taylor-series expansion technology. The results show that both the number concentration and volume fraction decrease with time in the smaller mode due to the intra and inter coagulation, and the asymptotic behavior of the larger mode is as same as that in the continuum regime.

Nonlinear focal shift beyond the geometrical focus in moderately focused acoustic beams.

Science.gov (United States)

Camarena, Francisco; Adrián-Martínez, Silvia; Jiménez, Noé; Sánchez-Morcillo, Víctor

2013-08-01

The phenomenon of the displacement of the position along the axis of the pressure, intensity, and radiation force maxima of focused acoustic beams under increasing driving voltages (nonlinear focal shift) is studied for the case of a moderately focused beam. The theoretical and experimental results show the existence of this shift along the axis when the initial pressure in the transducer increases until the acoustic field reaches the fully developed nonlinear regime of propagation. Experimental data show that at high amplitudes and for moderate focusing, the position of the on-axis pressure maximum and radiation force maximum can surpass the geometrical focal length. On the contrary, the on-axis pressure minimum approaches the transducer under increasing driving voltages, increasing the distance between the positive and negative peak pressure in the beam. These results are in agreement with numerical KZK model predictions and the existed data of other authors and can be explained according to the effect of self-refraction characteristic of the nonlinear regime of propagation.

Neutrino Astrophysics in Slowly Rotating Spacetimes Permeated by Nonlinear Electrodynamics Fields

Science.gov (United States)

Mosquera Cuesta, Herman J.

2017-02-01

Many theoretical and astrophysical arguments involve consideration of the effects of super strong electromagnetic fields and the rotation during the late stages of core-collapse supernovae. In what follows, we solve Einstein field equations that are minimally coupled to an arbitrary (current-free) Born-Infeld nonlinear Lagrangian L(F,G) of electrodynamics (NLED) in the slow rotation regime a ≪ r+ (outer horizon size), up to first order in a/r. We cross-check the physical properties of such NLED spacetime w.r.t. against the Maxwell one. A study case on both neutrino flavor ({ν }e\\to {ν }μ ,{ν }τ ) oscillations and flavor+helicity (spin) flip ({ν }e\\to {\\overline{ν }}μ ,τ ) gyroscopic precession proves that in the spacetime of a slowly rotating nonlinear charged black hole (RNCBH), the neutrino dynamics translates into a positive enhancement of the r-process (reduction of the electron fraction Ye < 0.5). Consequently, it guarantees successful hyperluminous core-collapse supernova explosions due to the enlargement of the number and amount of decaying nuclide species. This posits that, as far as the whole luminosity is concerned, hypernovae will be a proof of the formation of astrophysical RNCBH.

Octave-Spanning Mid-IR Supercontinuum Generation with Ultrafast Cascaded Nonlinearities

DEFF Research Database (Denmark)

Zhou, Binbin; Guo, Hairun; Liu, Xing

2014-01-01

An octave-spanning mid-IR supercontinuum is observed experimentally using ultrafast cascaded nonlinearities in an LiInS2 quadratic nonlinear crystal pumped with 70 fs energetic mid-IR pulses and cut for strongly phase-mismatched second-harmonic generation.......An octave-spanning mid-IR supercontinuum is observed experimentally using ultrafast cascaded nonlinearities in an LiInS2 quadratic nonlinear crystal pumped with 70 fs energetic mid-IR pulses and cut for strongly phase-mismatched second-harmonic generation....

Nonlinear response time-dependent density functional theory combined with the effective fragment potential method

Energy Technology Data Exchange (ETDEWEB)

Zahariev, Federico; Gordon, Mark S., E-mail: mark@si.msg.chem.iastate.edu [Department of Chemistry, Iowa State University, Ames, Iowa 50011 (United States)

2014-05-14

This work presents an extension of the linear response TDDFT/EFP method to the nonlinear-response regime together with the implementation of nonlinear-response TDDFT/EFP in the quantum-chemistry computer package GAMESS. Included in the new method is the ability to calculate the two-photon absorption cross section and to incorporate solvent effects via the EFP method. The nonlinear-response TDDFT/EFP method is able to make correct qualitative predictions for both gas phase values and aqueous solvent shifts of several important nonlinear properties.

Nonlinear optical studies in semiconductor-doped glasses under ...

Indian Academy of Sciences (India)

Abstract. Nonlinear optical studies in semiconductor-doped glasses (SDGs) are per- formed under femtosecond laser pulse excitation. Z-scan experiments with 800 nm wave- length pulses are used to excite SDG samples in the resonance and non-resonance regimes. Schott colour glass filter OG 515 shows stronger ...

Propagation of transition fronts in nonlinear chains with non-degenerate on-site potentials

Science.gov (United States)

Shiroky, I. B.; Gendelman, O. V.

2018-02-01

We address the problem of transition front propagation in chains with a bi-stable nondegenerate on-site potential and a nonlinear gradient coupling. For generic nonlinear coupling, one encounters a special regime of transitions, characterized by extremely narrow fronts, far supersonic velocities of the front propagation, and long waves in the oscillatory tail. This regime can be qualitatively associated with a shock wave. The front propagation can be described with the help of a simple reduced-order model; the latter delivers a kinetic law, which is almost not sensitive to the fine details of the on-site potential. Besides, it is possible to predict all main characteristics of the transition front, including its velocity, as well as the frequency and the amplitude of the oscillatory tail. Numerical results are in good agreement with the analytical predictions. The suggested approach allows one to consider the effects of an external pre-load, the next-nearest-neighbor coupling and the on-site damping. When the damping is moderate, it is possible to consider the shock propagation in the damped chain as a perturbation of the undamped dynamics. This approach yields reasonable predictions. When the damping is high, the transition front enters a completely different asymptotic regime of a subsonic kink. The gradient nonlinearity generically turns negligible, and the propagating front converges to the regime described by a simple exact solution for a continuous model with linear coupling.

Topology optimization of nonlinear optical devices

DEFF Research Database (Denmark)

Jensen, Jakob Søndergaard

2011-01-01

This paper considers the design of nonlinear photonic devices. The nonlinearity stems from a nonlinear material model with a permittivity that depends on the local time-averaged intensity of the electric field. A finite element model is developed for time-harmonic wave propagation and an incremen......This paper considers the design of nonlinear photonic devices. The nonlinearity stems from a nonlinear material model with a permittivity that depends on the local time-averaged intensity of the electric field. A finite element model is developed for time-harmonic wave propagation...... limiter. Here, air, a linear and a nonlinear material are distributed so that the wave transmission displays a strong sensitivity to the amplitude of the incoming wave....

Flow over an obstruction with the generation of nonlinear waves on the free surface: Limiting regimes

International Nuclear Information System (INIS)

Maklakov, D.V.

1995-01-01

A numerical-analytic method of calculating a subcritical flow over an obstruction is proposed. This method is based on the identification of the asymptotics of the behavior of a wave train in unknown functions. The method makes it possible to calculate both steep and long waves. The effectiveness of the method is demonstrated for the problem of flow over a vortex. The concept of the limiting flow regime as a regime with the maximum value of the perturbation parameter for which steady flow still persists is introduced. Various types of the limiting regimes obtained in the calculations are analyzed

A Nonlinear Modal Aeroelastic Solver for FUN3D

Science.gov (United States)

Goldman, Benjamin D.; Bartels, Robert E.; Biedron, Robert T.; Scott, Robert C.

2016-01-01

A nonlinear structural solver has been implemented internally within the NASA FUN3D computational fluid dynamics code, allowing for some new aeroelastic capabilities. Using a modal representation of the structure, a set of differential or differential-algebraic equations are derived for general thin structures with geometric nonlinearities. ODEPACK and LAPACK routines are linked with FUN3D, and the nonlinear equations are solved at each CFD time step. The existing predictor-corrector method is retained, whereby the structural solution is updated after mesh deformation. The nonlinear solver is validated using a test case for a flexible aeroshell at transonic, supersonic, and hypersonic flow conditions. Agreement with linear theory is seen for the static aeroelastic solutions at relatively low dynamic pressures, but structural nonlinearities limit deformation amplitudes at high dynamic pressures. No flutter was found at any of the tested trajectory points, though LCO may be possible in the transonic regime.

Nonlinear fibre optics overview

DEFF Research Database (Denmark)

Travers, J. C.; Frosz, Michael Henoch; Dudley, J. M.

2010-01-01

The optical fiber based supercontinuum source has recently become a significant scientific and commercial success, with applications ranging from frequency comb production to advanced medical imaging. This one-of-a-kind book explains the theory of fiber supercontinuum broadening, describes......, provides a background to the associated nonlinear optical processes, treats the generation mechanisms from continuous wave to femtosecond pulse pump regimes and highlights the diverse applications. A full discussion of numerical methods and comprehensive computer code are also provided, enabling readers...

Nonlinear temporal modulation of pulsar radioemission

International Nuclear Information System (INIS)

Chian, A.C.-L.

1984-01-01

A nonlinear theory is discussed for self-modulation of pulsar radio pulses. A nonlinear Schroedinger equation is derived for strong electromagnetic waves propagating in an electron-positron plasma. The nonlinearities arising from wave intensity induced relativistic particle mass variation may excite the modulational instability of circularly and linearly polarized pulsar radiation. The resulting wave envelopes can take the form of periodic wave trains or solitons. These nonlinear stationary wave forms may account for the formation of pulsar microstructures. (Author) [pt

DETERMINANTS OF FOREIGN DIRECT INVESTMENT IN NIGERIA: A MARKOV REGIME-SWITCHING APPROACH

Directory of Open Access Journals (Sweden)

Akinlo A. Enisan

2017-04-01

Full Text Available Several studies have analyzed the movement of foreign direct investment in Nigeria using linear approach. In contrast with all existing studies in Nigeria, this paper runs several non linear FDI equations where the main determinants of FDI are determined using Markov- Regime Switching Model (MSMs. The approach enables us to observe structural changes, where exist, in FDI equations through time. Asides, where FDI regression equation is truly nonlinear, MSMs fit data better than the linear models. The paper adopts maximum likelihood methodology of Markov-Regime Model (MSM to identify possible structural changes in level and/or trends and possible changes in parameters of independent variables through the transition probabilities. The results show that FDI process in Nigeria is governed by two different regimes and a shift from one regime to another regime depends on transition probabilities. The results show that the main determinants of FDI are GDP growth, macro instability, financial development, exchange rate, inflation and discount rate. This implies liberalization that stems inflation and enhance the value of domestic currency will attract more FDI into the country.

Nonlinearities and noise in micromechanical resonators: From understanding to characterization and design tools

Science.gov (United States)

Polunin, Pavel M.

In this work we consider several nonlinearity-based and/or noise-related phenomena that have been recently observed in micro-electromechanical vibratory systems. The main goals are to closely examine these phenomena, develop an understanding of their underlying physics, derive techniques for characterizing parameters in relevant mathematical models, and determine ways to improve the performance of specific classes of micro-electromechanical systems (MEMS) used in applications. The general perspective of this work is based on the fact that nonlinearity and noise represent integral parts of the models needed to describe the response of these systems, and the focus is on situations where these generally undesirable features can be utilized or accounted for in design. We consider three different, but related, topics in this general area. The first topic uses the slowly varying states in a rotating frame of reference where we analyze the stationary probability distribution of a nonlinear parametrically-driven resonator subjected to Poisson pulses and thermal noise. We show that Poisson pulses with low pulse rates, as compared with the resonator decay rate, cause a power-law divergence of the probability density at the resonator equilibrium in both the underdamped (overdamped) regimes, in which the response does (does not) spiral in the rotating frame. We have also found that the shape of the probability distribution away from the equilibrium position is qualitatively different for the overdamped and underdamped cases. In particular, in the overdamped regime, the form of the secondary singularity in the probability distribution depends strongly on the reference phase of the resonator response and the pulse modulation phase, while in the underdamped regime several singular peaks occur in the distribution, and their locations are determined by the resonator frequency and decay rate in the rotating frame. Finally, we show that even weak Gaussian noise smoothens out the

Strong nonlinearity-induced correlations for counterpropagating photons scattering on a two-level emitter

DEFF Research Database (Denmark)

Nysteen, Anders; McCutcheon, Dara; Mørk, Jesper

2015-01-01

We analytically treat the scattering of two counterpropagating photons on a two-level emitter embedded in an optical waveguide. We find that the nonlinearity of the emitter can give rise to significant pulse-dependent directional correlations in the scattered photonic state, which could be quanti......We analytically treat the scattering of two counterpropagating photons on a two-level emitter embedded in an optical waveguide. We find that the nonlinearity of the emitter can give rise to significant pulse-dependent directional correlations in the scattered photonic state, which could...

Influence of magnetic flutter on tearing growth in linear and nonlinear theory

Science.gov (United States)

Kreifels, L.; Hornsby, W. A.; Weikl, A.; Peeters, A. G.

2018-06-01

Recent simulations of tearing modes in turbulent regimes show an unexpected enhancement in the growth rate. In this paper the effect is investigated analytically. The enhancement is linked to the influence of turbulent magnetic flutter, which is modelled by diffusion terms in magnetohydrodynamics (MHD) momentum balance and Ohm’s law. Expressions for the linear growth rate as well as the island width in nonlinear theory for small amplitudes are derived. The results indicate an enhanced linear growth rate and a larger linear layer width compared with resistive MHD. Also the island width in the nonlinear regime grows faster in the diffusive model. These observations correspond well to simulations in which the effect of turbulence on the magnetic island width and tearing mode growth is analyzed.

Nonlinear evolution of MHD instabilities

International Nuclear Information System (INIS)

Bateman, G.; Hicks, H.R.; Wooten, J.W.; Dory, R.A.

1975-01-01

A 3-D nonlinear MHD computer code was used to study the time evolution of internal instabilities. Velocity vortex cells are observed to persist into the nonlinear evolution. Pressure and density profiles convect around these cells for a weak localized instability, or convect into the wall for a strong instability. (U.S.)

Extremely broadband, on-chip optical nonreciprocity enabled by mimicking nonlinear anti-adiabatic quantum jumps near exceptional points.

Science.gov (United States)

Choi, Youngsun; Hahn, Choloong; Yoon, Jae Woong; Song, Seok Ho; Berini, Pierre

2017-01-20

Time-asymmetric state-evolution properties while encircling an exceptional point are presently of great interest in search of new principles for controlling atomic and optical systems. Here, we show that encircling-an-exceptional-point interactions that are essentially reciprocal in the linear interaction regime make a plausible nonlinear integrated optical device architecture highly nonreciprocal over an extremely broad spectrum. In the proposed strategy, we describe an experimentally realizable coupled-waveguide structure that supports an encircling-an-exceptional-point parametric evolution under the influence of a gain saturation nonlinearity. Using an intuitive time-dependent Hamiltonian and rigorous numerical computations, we demonstrate strictly nonreciprocal optical transmission with a forward-to-backward transmission ratio exceeding 10 dB and high forward transmission efficiency (∼100%) persisting over an extremely broad bandwidth approaching 100 THz. This predicted performance strongly encourages experimental realization of the proposed concept to establish a practical on-chip optical nonreciprocal element for ultra-short laser pulses and broadband high-density optical signal processing.

Nonlinearity and fractional integration in the US dollar/euro exchange rate

Directory of Open Access Journals (Sweden)

Kiran Burcu

2012-01-01

Full Text Available This paper examines the nonlinear behavior and the fractional integration property of the US dollar/euro exchange rate over the period from January 1999 to August 2010 by extending the procedure of Peter M. Robinson (1994 to the case of nonlinearity. First, using the approach developed by Mehmet Caner and Bruce E. Hansen (2001, we investigate the possible presence of nonlinearity in the series through the estimation of a two-regime threshold autoregressive model. After finding nonlinearity, we also allow for disturbances to be fractionally integrated based on the different versions of Robinson (1994 tests. The findings show that the US dollar/euro exchange rate follows a stationary process with a weak evidence for long memory.

Nonlinear Weibel Instability and Turbulence in Strong Collisionless Shocks

International Nuclear Information System (INIS)

Medvedev, Mikhail M.

2008-01-01

This research project was devoted to studies of collisionless shocks, their properties, microphysics and plasma physics of underlying phenomena, such as Weibel instability and generation of small-scale fields at shocks, particle acceleration and transport in the generated random fields, radiation mechanisms from these fields in application to astrophysical phenomena and laboratory experiments (e.g., laser-plasma and beam-plasma interactions, the fast ignition and inertial confinement, etc.). Thus, this study is highly relevant to astrophysical sciences, the inertial confinement program and, in particular, the Fast Ignition concept, etc. It makes valuable contributions to the shock physics, nonlinear plasma theory, as well as to the basic plasma science, in general

Strong correlation effects on surfaces of topological insulators via holography

Science.gov (United States)

Seo, Yunseok; Song, Geunho; Sin, Sang-Jin

2017-07-01

We investigate the effects of strong correlation on the surface state of a topological insulator (TI). We argue that electrons in the regime of crossover from weak antilocalization to weak localization are strongly correlated, and calculate the magnetotransport coefficients of TIs using the gauge-gravity principle. Then, we examine the magnetoconductivity (MC) formula and find excellent agreement with the data of chrome-doped Bi2Te3 in the crossover regime. We also find that the cusplike peak in MC at low doping is absent, which is natural since quasiparticles disappear due to the strong correlation.

Single-temporal-mode photon generation beyond the low-power regime

DEFF Research Database (Denmark)

McKinstrie, C. J.; Christensen, Jesper Bjerge; Rottwitt, Karsten

2017-01-01

Nondegenerate four-wave mixing in a strongly-birefringent fiber generates signal and idler photons that are associated with only one pair of temporal modes, for a wide range of pump powers. Nonlinear phase modulation degrades the heralded-signal purity only slightly.......Nondegenerate four-wave mixing in a strongly-birefringent fiber generates signal and idler photons that are associated with only one pair of temporal modes, for a wide range of pump powers. Nonlinear phase modulation degrades the heralded-signal purity only slightly....

Single-photon blockade in a hybrid cavity-optomechanical system via third-order nonlinearity

Science.gov (United States)

Sarma, Bijita; Sarma, Amarendra K.

2018-04-01

Photon statistics in a weakly driven optomechanical cavity, with Kerr-type nonlinearity, are analyzed both analytically and numerically. The single-photon blockade effect is demonstrated via calculations of the zero-time-delay second-order correlation function g (2)(0). The analytical results obtained by solving the Schrödinger equation are in complete conformity with the results obtained through numerical solution of the quantum master equation. A systematic study on the parameter regime for observing photon blockade in the weak coupling regime is reported. The parameter regime where the photon blockade is not realizable due to the combined effect of nonlinearities owing to the optomechanical coupling and the Kerr-effect is demonstrated. The experimental feasibility with state-of-the-art device parameters is discussed and it is observed that photon blockade could be generated at the telecommunication wavelength. An elaborate analysis of the thermal effects on photon antibunching is presented. The system is found to be robust against pure dephasing-induced decoherences and thermal phonon number fluctuations.

Spread F bubbles - Nonlinear Rayleigh-Taylor mode in two dimensions

Science.gov (United States)

Hudson, M. K.

1978-01-01

The paper discusses long-wavelength developed bottomside spread F which has been attributed to the Rayleigh-Taylor instability. The nonlinear saturation amplitude and the k spectrum of the inertia-dominated Rayleigh-Taylor instability is found in two directions: east-west and vertical. As in the collisional case (Chaturvedi and Ossakow, 1977), the dominant nonlinearity is found to be two-dimensional. It is found that the linearly most unstable modes, which are primarily horizontal, saturate by the nonlinear generation of vertical spatial harmonics. The harmonics are damped by diffusion or recombination. The resulting amplitude spectrum indicates that bubbles are vertically elongated in both inertial and collisional regimes.

Evidence for bifurcation and universal chaotic behavior in nonlinear semiconducting devices

International Nuclear Information System (INIS)

Testa, J.; Perez, J.; Jeffries, C.

1982-01-01

Bifurcations, chaos, and extensive periodic windows in the chaotic regime are observed for a driven LRC circuit, the capacitive element being a nonlinear varactor diode. Measurements include power spectral analysis; real time amplitude data; phase portraits; and a bifurcation diagram, obtained by sampling methods. The effects of added external noise are studied. These data yield experimental determinations of several of the universal numbers predicted to characterize nonlinear systems having this route to chaos

Nonlinear Theory of Nonparaxial Laser Pulse Propagation in Plasma Channels

International Nuclear Information System (INIS)

Esarey, E.; Schroeder, C. B.; Shadwick, B. A.; Wurtele, J. S.; Leemans, W. P.

2000-01-01

Nonparaxial propagation of ultrashort, high-power laser pulses in plasma channels is examined. In the adiabatic limit, pulse energy conservation, nonlinear group velocity, damped betatron oscillations, self-steepening, self-phase modulation, and shock formation are analyzed. In the nonadiabatic limit, the coupling of forward Raman scattering (FRS) and the self-modulation instability (SMI) is analyzed and growth rates are derived, including regimes of reduced growth. The SMI is found to dominate FRS in most regimes of interest. (c) 2000 The American Physical Society

Third-order optical nonlinearities in bulk and fs-laser inscribed waveguides in strengthened alkali aluminosilcate glass

Science.gov (United States)

Almeida, Gustavo F. B.; Almeida, Juliana M. P.; Martins, Renato J.; De Boni, Leonardo; Arnold, Craig B.; Mendonca, Cleber R.

2018-01-01

The development of advanced photonics devices requires materials with large optical nonlinearities, fast response times and high optical transparency, while at the same time allowing for the micro/nano-processing needed for integrated photonics. In this context, glasses have been receiving considerable attention given their relevant optical properties which can be specifically tailored by compositional control. Corning Gorilla® Glass (strengthened alkali aluminosilicate glass) is well-known for its use as a protective screen in mobile devices, and has attracted interest as a potential candidate for optical devices. Therefore, it is crucial not only to expand the knowledge on the fabrication of waveguides in Gorilla Glass under different regimes, but also to determine its nonlinear optical response, both using fs-laser pulses. Thus, this paper reports, for the first time, characterization of the third-order optical nonlinearities of Gorilla Glass, as well as linear and nonlinear characterization of waveguide written with femtosecond pulses under the low repetition rate regime (1 kHz).

Anti-Weak Localization Measurements in the Ballistic Regime

Science.gov (United States)

Jayathilaka, Dilhani; Dedigama, Aruna; Murphy, Sheena; Edirisooriya, Madhavie; Goel, Niti; Mishima, Tetsuya; Santos, Michael; Mullen, Kieran

2007-03-01

Anti-weak localization dominates at low fields in systems in which spin-orbit coupling is strong. The experimental results are well described by theory [1] in low mobility systems in which the magnetic length (lB) is greater than the mean free path; however high mobility systems with strong spin-orbit interactions, such the InSb based two dimensional systems (2DESs) examined here, are not in this diffusive regime. A recently developed theory [2] addresses both the diffusive and ballistic regimes taking into account both the backscattered and non-backscattered contributions to the conductivity. We will discuss the agreement of the new theory to measurements of InSb 2DESs prepared with both strong Dresselhaus and Rashba effects. [1] S.V. Iordanskii, Yu B. Lyanda-Geller, and G.E. Pikus, JETP Lett. 60, 206 (1994). [2] L.E. Golub, Phys. Rev. B. 71, 235310 (2005).

Nonlinear dynamics between linear and impact limits

CERN Document Server

Pilipchuk, Valery N; Wriggers, Peter

2010-01-01

This book examines nonlinear dynamic analyses based on the existence of strongly nonlinear but simple counterparts to the linear models and tools. Discusses possible application to periodic elastic structures with non-smooth or discontinuous characteristics.

Nonlinear viscous vortex motion in two-dimensional Josephson-junction arrays

International Nuclear Information System (INIS)

Hagenaars, T.J.; Tiesinga, P.H.E.; van Himbergen, J.E.; Jose, J.V.

1994-01-01

When a vortex in a two-dimensional Josephson-junction array is driven by a constant external current it may move as a particle in a viscous medium. Here we study the nature of this viscous motion. We model the junctions in a square array as resistively and capacitively shunted Josephson junctions and carry out numerical calculations of the current-voltage characteristics. We find that the current-voltage characteristics in the damped regime are well described by a model with a nonlinear viscous force of the form F D =η(y)y=[A/(1+By]y, where y is the vortex velocity, η(y) is the velocity-dependent viscosity, and A and B are constants for a fixed value of the Stewart-McCumber parameter. This result is found to apply also for triangular lattices in the overdamped regime. Further qualitative understanding of the nature of the nonlinear friction on the vortex motion is obtained from a graphic analysis of the microscopic vortex dynamics in the array. The consequences of having this type of nonlinear friction law are discussed and compared to previous theoretical and experimental studies

Numerical study of fractional nonlinear Schrodinger equations

KAUST Repository

Klein, Christian

2014-10-08

Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By an appropriate choice of the dispersive exponent, both mass and energy sub- and supercritical regimes can be identified. This allows us to study the possibility of finite time blow-up versus global existence, the nature of the blow-up, the stability and instability of nonlinear ground states and the long-time dynamics of solutions. The latter is also studied in a semiclassical setting. Moreover, we numerically construct ground state solutions of the fractional nonlinear Schrödinger equation.

Kondo and mixed-valence regimes in multilevel quantum dots

International Nuclear Information System (INIS)

Chudnovskiy, A. L.; Ulloa, S. E.

2001-01-01

We investigate the dependence of the ground state of a multilevel quantum dot on the coupling to an external fermionic system and on the interactions in the dot. As the coupling to the external system increases, the rearrangement of the effective energy levels in the dot signals the transition from the Kondo regime to a mixed-valence (MV) regime. The MV regime in a two-level dot is characterized by an intrinsic mixing of the levels in the dot, resulting in nonperturbative subtunneling and supertunneling phenomena that strongly influence the Kondo effect

Valuing a gas-fired power plant: A comparison of ordinary linear models, regime-switching approaches, and models with stochastic volatility

International Nuclear Information System (INIS)

Heydari, Somayeh; Siddiqui, Afzal

2010-01-01

Energy prices are often highly volatile with unexpected spikes. Capturing these sudden spikes may lead to more informed decision-making in energy investments, such as valuing gas-fired power plants, than ignoring them. In this paper, non-linear regime-switching models and models with mean-reverting stochastic volatility are compared with ordinary linear models. The study is performed using UK electricity and natural gas daily spot prices and suggests that with the aim of valuing a gas-fired power plant with and without operational flexibility, non-linear models with stochastic volatility, specifically for logarithms of electricity prices, provide better out-of-sample forecasts than both linear models and regime-switching models.

Flow regime analysis for fluid injection into a confined aquifer: implications for CO2 sequestration

Science.gov (United States)

Guo, B.; Zheng, Z.; Celia, M. A.; Stone, H.

2015-12-01

Carbon dioxide injection into a confined saline aquifer may be modeled as an axisymmetric two-phase flow problem. Assuming the two fluids segregate in the vertical direction due to strong buoyancy, and neglecting capillary pressure and miscibility, the lubrication approximation leads to a nonlinear advection-diffusion equation that describes the evolution of the sharp fluid-fluid interface. The flow behaviors in the system are controlled by two dimensionless groups: M, the viscosity ratio of the displaced fluid relative to injected fluid, and Γ , the gravity number, which represents the relative importance of buoyancy and fluid injection. Four different analytical solutions can be derived as the asymptotic approximations, representing specific values of the parameter pairs. The four solutions correspond to: (1) Γ 1; and (4) Γ >> 1, any M values. The first two of these solutions are new, while the third corresponds to the solution of Nordbotten and Celia (2006) for confined injections and the fourth corresponds to the solution of (Lyle et al., 2005) for gravity currents in an unconfined aquifer. Overall, the various axisymmetric flows can be summarized in a Γ-M regime diagram with five distinct dynamic behaviors including the four asymptotic regimes and an intermediate regime (Fig. 1). Data from a number of CO2 injection sites around the world can be used to compute the two dimensionless groups Γ and M associated with each injection. When plotted on the regime diagram, these values show the flow behavior for each injection and how the values vary from site to site. For all the CO2 injections, M is always larger than 1, while Γ can range from 0.01 up to 100. The pairs of (Γ, M) with lower Γ values correspond to solution (3), while the ones with higher Γ values can move up to the intermediate regime and the flow regime for solution (4). The higher values of Γ correspond to pilot-scale injections with low injection rates; most industrial-scale injection

NONLINEAR REFLECTION PROCESS OF LINEARLY POLARIZED, BROADBAND ALFVÉN WAVES IN THE FAST SOLAR WIND

Energy Technology Data Exchange (ETDEWEB)

Shoda, M.; Yokoyama, T., E-mail: shoda@eps.s.u-tokyo.ac.jp [Department of Earth and Planetary Science, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033 (Japan)

2016-04-01

Using one-dimensional numerical simulations, we study the elementary process of Alfvén wave reflection in a uniform medium, including nonlinear effects. In the linear regime, Alfvén wave reflection is triggered only by the inhomogeneity of the medium, whereas in the nonlinear regime, it can occur via nonlinear wave–wave interactions. Such nonlinear reflection (backscattering) is typified by decay instability. In most studies of decay instabilities, the initial condition has been a circularly polarized Alfvén wave. In this study we consider a linearly polarized Alfvén wave, which drives density fluctuations by its magnetic pressure force. For generality, we also assume a broadband wave with a red-noise spectrum. In the data analysis, we decompose the fluctuations into characteristic variables using local eigenvectors, thus revealing the behaviors of the individual modes. Different from the circular-polarization case, we find that the wave steepening produces a new energy channel from the parent Alfvén wave to the backscattered one. Such nonlinear reflection explains the observed increasing energy ratio of the sunward to the anti-sunward Alfvénic fluctuations in the solar wind with distance against the dynamical alignment effect.

A Review of Critical Conditions for the Onset of Nonlinear Fluid Flow in Rock Fractures

Directory of Open Access Journals (Sweden)

Liyuan Yu

2017-01-01

Full Text Available Selecting appropriate governing equations for fluid flow in fractured rock masses is of special importance for estimating the permeability of rock fracture networks. When the flow velocity is small, the flow is in the linear regime and obeys the cubic law, whereas when the flow velocity is large, the flow is in the nonlinear regime and should be simulated by solving the complex Navier-Stokes equations. The critical conditions such as critical Reynolds number and critical hydraulic gradient are commonly defined in the previous works to quantify the onset of nonlinear fluid flow. This study reviews the simplifications of governing equations from the Navier-Stokes equations, Stokes equation, and Reynold equation to the cubic law and reviews the evolutions of critical Reynolds number and critical hydraulic gradient for fluid flow in rock fractures and fracture networks, considering the influences of shear displacement, normal stress and/or confining pressure, fracture surface roughness, aperture, and number of intersections. This review provides a reference for the engineers and hydrogeologists especially the beginners to thoroughly understand the nonlinear flow regimes/mechanisms within complex fractured rock masses.

Energy transfer in coupled nonlinear phononic waveguides: transition from wandering breather to nonlinear self-trapping

International Nuclear Information System (INIS)

Kosevich, Y A; Manevitch, L I; Savin, A V

2007-01-01

We consider, both analytically and numerically, the dynamics of stationary and slowly-moving breathers (localized short-wavelength excitations) in two weakly coupled nonlinear oscillator chains (nonlinear phononic waveguides). We show that there are two qualitatively different dynamical regimes of the coupled breathers: the oscillatory exchange of the low-amplitude breather between the phononic waveguides (wandering breather), and one-waveguide-localization (nonlinear self-trapping) of the high-amplitude breather. We also show that phase-coherent dynamics of the coupled breathers in two weakly linked nonlinear phononic waveguides has a profound analogy, and is described by a similar pair of equations, to the tunnelling quantum dynamics of two weakly linked Bose-Einstein condensates in a symmetric double-well potential (single bosonic Josephson junction). The exchange of phonon energy and excitations between the coupled phononic waveguides takes on the role which the exchange of atoms via quantum tunnelling plays in the case of the coupled condensates. On the basis of this analogy, we predict a new tunnelling mode of the coupled Bose-Einstein condensates in a single bosonic Josephson junction in which their relative phase oscillates around π/2. The dynamics of relative phase of two weakly linked Bose-Einstein condensates can be studied by means of interference, while the dynamics of the exchange of lattice excitations in coupled nonlinear phononic waveguides can be observed by means of light scattering

Nonequilibrium and Nonlinear Dynamics in Geomaterials I : The Low Strain Regime

OpenAIRE

Pasqualini, Donatella; Heitmann, Katrin; TenCate, James A.; Habib, Salman; Higdon, David; Johnson, Paul A.

2006-01-01

Members of a wide class of geomaterials are known to display complex and fascinating nonlinear and nonequilibrium dynamical behaviors over a wide range of bulk strains, down to surprisingly low values, e.g., 10^{-7}. In this paper we investigate two sandstones, Berea and Fontainebleau, and characterize their behavior under the influence of very small external forces via carefully controlled resonant bar experiments. By reducing environmental effects due to temperature and humidity variations,...

Arbitrary-ratio power splitter based on nonlinear multimode interference coupler

International Nuclear Information System (INIS)

Tajaldini, Mehdi; Jafri, Mohd Zubir Mat

2015-01-01

We propose an ultra-compact multimode interference (MMI) power splitter based on nonlinear effects from simulations using nonlinear modal propagation analysis (NMPA) cooperation with finite difference Method (FDM) to access free choice of splitting ratio. Conventional multimode interference power splitter could only obtain a few discrete ratios. The power splitting ratio may be adjusted continuously while the input set power is varying by a tunable laser. In fact, using an ultra- compact MMI with a simple structure that is launched by a tunable nonlinear input fulfills the problem of arbitrary-ratio in integrated photonics circuits. Silicon on insulator (SOI) is used as the offered material due to the high contrast refractive index and Centro symmetric properties. The high-resolution images at the end of the multimode waveguide in the simulated power splitter have a high power balance, whereas access to a free choice of splitting ratio is not possible under the linear regime in the proposed length range except changes in the dimension for any ratio. The compact dimensions and ideal performance of the device are established according to optimized parameters. The proposed regime can be extended to the design of M×N arbitrary power splitters ratio for programmable logic devices in all optical digital signal processing. The results of this study indicate that nonlinear modal propagation analysis solves the miniaturization problem for all-optical devices based on MMI couplers to achieve multiple functions in a compact planar integrated circuit and also overcomes the limitations of previously proposed methods for nonlinear MMI

Arbitrary-ratio power splitter based on nonlinear multimode interference coupler

Energy Technology Data Exchange (ETDEWEB)

Tajaldini, Mehdi [School of Physics, Universiti Sains Malaysia, 11800 Pulau Pinang (Malaysia); Young Researchers and Elite Club, Baft Branch, Islamic Azad University, Baft (Iran, Islamic Republic of); Jafri, Mohd Zubir Mat [School of Physics, Universiti Sains Malaysia, 11800 Pulau Pinang (Malaysia)

2015-04-24

We propose an ultra-compact multimode interference (MMI) power splitter based on nonlinear effects from simulations using nonlinear modal propagation analysis (NMPA) cooperation with finite difference Method (FDM) to access free choice of splitting ratio. Conventional multimode interference power splitter could only obtain a few discrete ratios. The power splitting ratio may be adjusted continuously while the input set power is varying by a tunable laser. In fact, using an ultra- compact MMI with a simple structure that is launched by a tunable nonlinear input fulfills the problem of arbitrary-ratio in integrated photonics circuits. Silicon on insulator (SOI) is used as the offered material due to the high contrast refractive index and Centro symmetric properties. The high-resolution images at the end of the multimode waveguide in the simulated power splitter have a high power balance, whereas access to a free choice of splitting ratio is not possible under the linear regime in the proposed length range except changes in the dimension for any ratio. The compact dimensions and ideal performance of the device are established according to optimized parameters. The proposed regime can be extended to the design of M×N arbitrary power splitters ratio for programmable logic devices in all optical digital signal processing. The results of this study indicate that nonlinear modal propagation analysis solves the miniaturization problem for all-optical devices based on MMI couplers to achieve multiple functions in a compact planar integrated circuit and also overcomes the limitations of previously proposed methods for nonlinear MMI.

Sulfur passivation of semi-insulating GaAs: Transition from Coulomb blockade to weak localization regime

Energy Technology Data Exchange (ETDEWEB)

Bagraev, N. T., E-mail: Bagraev@mail.ioffe.ru [Ioffe Institute (Russian Federation); Chaikina, E. I. [Centro de Investigacion Cientifica y de Educacion Superior de Ensenada, Division de Fisica Aplicada (Mexico); Danilovskii, E. Yu.; Gets, D. S.; Klyachkin, L. E.; L’vova, T. V.; Malyarenko, A. M. [Ioffe Institute (Russian Federation)

2016-04-15

The sulfur passivation of the semi-insulating GaAs bulk (SI GaAs) grown in an excess phase of arsenic is used to observe the transition from the Coulomb blockade to the weak localization regime at room temperature. The I–V characteristics of the SI GaAs device reveal nonlinear behavior that appears to be evidence of the Coulomb blockade process as well as the Coulomb oscillations. The sulfur passivation of the SI GaAs device surface results in enormous transformation of the I–V characteristics that demonstrate the strong increase of the resistance and Coulomb blockade regime is replaced by the electron tunneling processes. The results obtained are analyzed within frameworks of disordering SI GaAs surface that is caused by inhomogeneous distribution of the donor and acceptor anti-site defects which affects the conditions of quantum- mechanical tunneling. Weak localization processes caused by the preservation of the Fermi level pinning are demonstrated by measuring the negative magnetoresistance in weak magnetic fields at room temperature. Finally, the studies of the magnetoresistance at higher magnetic fields reveal the h/2e Aharonov–Altshuler–Spivak oscillations with the complicated behavior due to possible statistical mismatch of the interference paths in the presence of different microdefects.

Laser Theory for Optomechanics: Limit Cycles in the Quantum Regime

Directory of Open Access Journals (Sweden)

Niels Lörch

2014-01-01

Full Text Available Optomechanical systems can exhibit self-sustained limit cycles where the quantum state of the mechanical resonator possesses nonclassical characteristics such as a strongly negative Wigner density, as was shown recently in a numerical study by Qian et al. [Phys. Rev. Lett. 109, 253601 (2012]. Here, we derive a Fokker-Planck equation describing mechanical limit cycles in the quantum regime that correctly reproduces the numerically observed nonclassical features. The derivation starts from the standard optomechanical master equation and is based on techniques borrowed from the laser theory due to Haake and Lewenstein. We compare our analytical model with numerical solutions of the master equation based on Monte Carlo simulations and find very good agreement over a wide and so far unexplored regime of system parameters. As one main conclusion, we predict negative Wigner functions to be observable even for surprisingly classical parameters, i.e., outside the single-photon strong-coupling regime, for strong cavity drive and rather large limit-cycle amplitudes. The approach taken here provides a natural starting point for further studies of quantum effects in optomechanics.

Nonlinear amplitude dynamics in flagellar beating.

Science.gov (United States)

Oriola, David; Gadêlha, Hermes; Casademunt, Jaume

2017-03-01

The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating.

Nonlinear optical control of Josephson coupling in cuprates

Energy Technology Data Exchange (ETDEWEB)

Casandruc, Eliza

2017-03-15

In High-T{sub C} cuprates superconducting Cu-O planes alternate with insulating layers along the crystallographic c-axis, making the materials equivalent to Josephson junctions connected in series. The most intriguing consequence is that the out-of-plane superconducting transport occurs via Cooper pairs tunneling across the insulating layers and can be predicted by the Josephson tunneling equations. Nonlinear interaction between light fields and the superconducting carriers serves as a powerful dynamical probe of cuprates, while offering opportunities for controlling them in an analogous fashion to other stimuli such as pressure and magnetic fields. The main goal of this thesis work is to use intense transient light fields to control the interlayer superconducting transport on ultrafast time scales. This was achieved by tuning the wavelength of such light pulses to completely different ranges, in order to either directly excite Josephson Plasma Waves in the nonlinear regime, or efficiently melt the competing charge and spin order phase, which in certain cuprates quenches the Josephson tunneling at equilibrium. In a first study, I have utilized strong field terahertz transients with frequencies tuned to the Josephson plasma resonance (JPR) to coherently control the c-axis superconducting transport. The Josephson relations have a cubic nonlinearity which is exploited to achieve two related, albeit slightly different, phenomena. Depending on the driving pulse, solitonic breathers were excited with narrow-band multi-cycle pulses in La{sub 1.84}Sr{sub 0.16}CuO{sub 4} while broad-band half-cycle pulses were employed to achieve a parametric amplification of Josephson Plasma Waves in La{sub 1.905}Ba{sub 0.095}CuO{sub 4}. These experiments are supported by extensive modeling, showing exceptional agreement. A comprehensive study illustrates the strong enhancement of the nonlinear effects near the JPR frequency. Then, I turned to investigate the competition between

Entanglement and Other Nonclassical Properties of Two Two-Level Atoms Interacting with a Two-Mode Binomial Field: Constant and Intensity-Dependent Coupling Regimes

International Nuclear Information System (INIS)

Tavassoly, M.K.; Hekmatara, H.

2015-01-01

In this paper, we consider the interaction between two two-level atoms and a two-mode binomial field with a general intensity-dependent coupling regime. The outlined dynamical problem has explicit analytical solution, by which we can evaluate a few of its physical features of interest. To achieve the purpose of the paper, after choosing a particular nonlinearity function, we investigate the quantum statistics, atomic population inversion and at last the linear entropy of the atom-field system which is a good measure for the degree of entanglement. In detail, the effects of binomial field parameters, in addition to different initial atomic states on the temporal behavior of the mentioned quantities have been analyzed. The results show that, the values of binomial field parameters and the initial state of the two atoms influence on the nonclassical effects in the obtained states through which one can tune the nonclassicality criteria appropriately. Setting intensity-dependent coupling function equal to 1 reduces the results to the constant coupling case. By comparing the latter case with the nonlinear regime, we will observe that the nonlinearity disappears the pattern of collapse-revival phenomenon in the evolution of Mandel parameter and population inversion (which can be seen in the linear case with constant coupling), however, more typical collapse-revivals will be appeared for the cross-correlation function in the nonlinear case. Finally, in both linear and nonlinear regime, the entropy remains less than (but close to) 0.5. In other words the particular chosen nonlinearity does not critically affect on the entropy of the system. (paper)

Linear and nonlinear Biot waves in a noncohesive granular medium slab: transfer function, self-action, second harmonic generation.

Science.gov (United States)

Legland, J-B; Tournat, V; Dazel, O; Novak, A; Gusev, V

2012-06-01

Experimental results are reported on second harmonic generation and self-action in a noncohesive granular medium supporting wave energy propagation both in the solid frame and in the saturating fluid. The acoustic transfer function of the probed granular slab can be separated into two main frequency regions: a low frequency region where the wave propagation is controlled by the solid skeleton elastic properties, and a higher frequency region where the behavior is dominantly due to the air saturating the beads. Experimental results agree well with a recently developed nonlinear Biot wave model applied to granular media. The linear transfer function, second harmonic generation, and self-action effect are studied as a function of bead diameter, compaction step, excitation amplitude, and frequency. This parametric study allows one to isolate different propagation regimes involving a range of described and interpreted linear and nonlinear processes that are encountered in granular media experiments. In particular, a theoretical interpretation is proposed for the observed strong self-action effect.

Stable boundary-layer regimes at dome C, Antarctica : observation and analysis

NARCIS (Netherlands)

Vignon, E.; van de Wiel, B.J.H.; van Hooijdonk, I.G.S.; Genthon, C.; van der Linden, S.J.A.; van Hooft, J.A.; Baas, P.; Maurel, W.; Traullé, O.; Casasanta, G.

2017-01-01

Investigation of meteorological measurements along a 45 m tower at Dome C on the high East Antarctic Plateau revealed two distinct stable boundary layer (SBL) regimes at this location. The first regime is characterized by strong winds and continuous turbulence. It results in full vertical coupling

A phenomenological constitutive model for the nonlinear viscoelastic responses of biodegradable polymers

KAUST Repository

Khan, Kamran; El Sayed, Tamer S.

2012-01-01

We formulate a constitutive framework for biodegradable polymers that accounts for nonlinear viscous behavior under regimes with large deformation. The generalized Maxwell model is used to represent the degraded viscoelastic response of a polymer

Calculation of Nonlinear Thermoelectric Coefficients of InAs1-xSbx Using Monte Carlo Method

Energy Technology Data Exchange (ETDEWEB)

Sadeghian, RB; Bahk, JH; Bian, ZX; Shakouri, A

2011-12-28

It was found that the nonlinear Peltier effect could take place and increase the cooling power density when a lightly doped thermoelectric material is under a large electrical field. This effect is due to the Seebeck coefficient enhancement from an electron distribution far from equilibrium. In the nonequilibrium transport regime, the solution of the Boltzmann transport equation in the relaxation-time approximation ceases to apply. The Monte Carlo method, on the other hand, proves to be a capable tool for simulation of semiconductor devices at small scales as well as thermoelectric effects with local nonequilibrium charge distribution. InAs1-xSb is a favorable thermoelectric material for nonlinear operation owing to its high mobility inherited from the binary compounds InSb and InAs. In this work we report simulation results on the nonlinear Peltier power of InAs1-xSb at low doping levels, at room temperature and at low temperatures. The thermoelectric power factor in nonlinear operation is compared with the maximum value that can be achieved with optimal doping in the linear transport regime.

Nonlinear effects and conversion efficiency of free electron laser in compton regime

International Nuclear Information System (INIS)

Taguchi, Toshihiro; Mima, Kunioki; Mochizuki, Takayasu

1980-01-01

Nonlinear evolutions of free electron laser are analyzed by using quasi-linear theory. By the analysis, the energy conversion rates and the spectral width of the emitted radiations are calculated self-consistently. Moreover, it is found that the energy conversion rate is remarkably improved, when a RF field is applied to reaccelerate electron beam. (author)

Strongly nonlinear nonhomogeneous elliptic unilateral problems with L^1 data and no sign conditions

Directory of Open Access Journals (Sweden)

Elhoussine Azroul

2012-05-01

Full Text Available In this article, we prove the existence of solutions to unilateral problems involving nonlinear operators of the form: $$ Au+H(x,u,abla u=f $$ where $A$ is a Leray Lions operator from $W_0^{1,p(x}(Omega$ into its dual $W^{-1,p'(x}(Omega$ and $H(x,s,xi$ is the nonlinear term satisfying some growth condition but no sign condition. The right hand side $f$ belong to $L^1(Omega$.

Microscopic origin of nonlinear non-affine deformation in metallic glasses

NARCIS (Netherlands)

Zaccone, A.; Schall, P.; Terentjev, E.M.

2014-01-01

The atomic theory of elasticity of amorphous solids, based on the nonaffine response formalism, is extended into the nonlinear stress-strain regime by coupling with the underlying irreversible many-body dynamics. The latter is implemented in compact analytical form using a qualitative method for the

Climate change and future fire regimes: Examples from California

Science.gov (United States)

Keeley, Jon E.; Syphard, Alexandra D.

2016-01-01

Climate and weather have long been noted as playing key roles in wildfire activity, and global warming is expected to exacerbate fire impacts on natural and urban ecosystems. Predicting future fire regimes requires an understanding of how temperature and precipitation interact to control fire activity. Inevitably this requires historical analyses that relate annual burning to climate variation. Fuel structure plays a critical role in determining which climatic parameters are most influential on fire activity, and here, by focusing on the diversity of ecosystems in California, we illustrate some principles that need to be recognized in predicting future fire regimes. Spatial scale of analysis is important in that large heterogeneous landscapes may not fully capture accurate relationships between climate and fires. Within climatically homogeneous subregions, montane forested landscapes show strong relationships between annual fluctuations in temperature and precipitation with area burned; however, this is strongly seasonal dependent; e.g., winter temperatures have very little or no effect but spring and summer temperatures are critical. Climate models that predict future seasonal temperature changes are needed to improve fire regime projections. Climate does not appear to be a major determinant of fire activity on all landscapes. Lower elevations and lower latitudes show little or no increase in fire activity with hotter and drier conditions. On these landscapes climate is not usually limiting to fires but these vegetation types are ignition-limited. Moreover, because they are closely juxtaposed with human habitations, fire regimes are more strongly controlled by other direct anthropogenic impacts. Predicting future fire regimes is not rocket science; it is far more complicated than that. Climate change is not relevant to some landscapes, but where climate is relevant, the relationship will change due to direct climate effects on vegetation trajectories, as well as

Climate Change and Future Fire Regimes: Examples from California

Directory of Open Access Journals (Sweden)

Jon E. Keeley

2016-08-01

Full Text Available Climate and weather have long been noted as playing key roles in wildfire activity, and global warming is expected to exacerbate fire impacts on natural and urban ecosystems. Predicting future fire regimes requires an understanding of how temperature and precipitation interact to control fire activity. Inevitably this requires historical analyses that relate annual burning to climate variation. Fuel structure plays a critical role in determining which climatic parameters are most influential on fire activity, and here, by focusing on the diversity of ecosystems in California, we illustrate some principles that need to be recognized in predicting future fire regimes. Spatial scale of analysis is important in that large heterogeneous landscapes may not fully capture accurate relationships between climate and fires. Within climatically homogeneous subregions, montane forested landscapes show strong relationships between annual fluctuations in temperature and precipitation with area burned; however, this is strongly seasonal dependent; e.g., winter temperatures have very little or no effect but spring and summer temperatures are critical. Climate models that predict future seasonal temperature changes are needed to improve fire regime projections. Climate does not appear to be a major determinant of fire activity on all landscapes. Lower elevations and lower latitudes show little or no increase in fire activity with hotter and drier conditions. On these landscapes climate is not usually limiting to fires but these vegetation types are ignition-limited. Moreover, because they are closely juxtaposed with human habitations, fire regimes are more strongly controlled by other direct anthropogenic impacts. Predicting future fire regimes is not rocket science; it is far more complicated than that. Climate change is not relevant to some landscapes, but where climate is relevant, the relationship will change due to direct climate effects on vegetation

Journal Afrika Statistika ISSN 0852-0305 Nonlinear wavelet ...

African Journals Online (AJOL)

mator; Nonparametric regression; Strong mixing condition. ... In this paper we consider the right censorship model and we introduce a new nonlinear ... provide excellent selective review article on nonlinear wavelet methods in nonparametric.

Effect of the scrape-off layer in AORSA full wave simulations of fast wave minority, mid/high harmonic, and helicon heating regimes

Energy Technology Data Exchange (ETDEWEB)

Bertelli, N., E-mail: nbertell@pppl.gov; Gerhardt, S.; Hosea, J. C.; LeBlanc, B.; Perkins, R. J.; Phillips, C. K.; Taylor, G.; Valeo, E. J.; Wilson, J. R. [Princeton Plasma Physics Laboratory, Princeton, NJ 08543 (United States); Jaeger, E. F. [XCEL Engineering Inc., Oak Ridge, TN 37830 (United States); Lau, C.; Blazevski, D.; Green, D. L.; Berry, L.; Ryan, P. M. [Oak Ridge National Laboratory, Oak Ridge, TN 37831-6169 (United States); Bonoli, P. T.; Wright, J. C. [MIT Plasma Science and Fusion Center, Cambridge, MA 02139 (United States); Pinsker, R. I.; Prater, R. [General Atomics, PO Box 85608, San Diego, CA 92186-5608 (United States); Qin, C. M. [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); and others

2015-12-10

Several experiments on different machines and in different fast wave (FW) heating regimes, such as hydrogen minority heating and high harmonic fast waves, have found strong interactions between radio-frequency (RF) waves and the scrape-off layer (SOL) region. This paper examines the propagation and the power loss in the SOL by using the full wave code AORSA, in which the edge plasma beyond the last closed flux surface (LCFS) is included in the solution domain and a collisional damping parameter is used as a proxy to represent the real, and most likely nonlinear, damping processes. 3D AORSA results for the National Spherical Torus eXperiment (NSTX), where a full antenna spectrum is reconstructed, are shown, confirming the same behavior found for a single toroidal mode results in Bertelli et al, Nucl. Fusion, 54 083004, 2014, namely, a strong transition to higher SOL power losses (driven by the RF field) when the FW cut-off is moved away from in front of the antenna by increasing the edge density. Additionally, full wave simulations have been extended to “conventional” tokamaks with higher aspect ratios, such as the DIII-D, Alcator C-Mod, and EAST devices. DIII-D results show similar behavior found in NSTX and NSTX-U, consistent with previous DIII-D experimental observations. In contrast, a different behavior has been found for Alcator C-Mod and EAST, which operate in the minority heating regime unlike NSTX/NSTX-U and DIII-D, which operate in the mid/high harmonic regime. A substantial discussion of some of the main aspects, such as (i) the pitch angle of the magnetic field; (ii) minority heating vs. mid/high harmonic regimes is presented showing the different behavior of the RF field in the SOL region for NSTX-U scenarios with different plasma current. Finally, the preliminary results of the impact of the SOL region on the evaluation of the helicon current drive efficiency in DIII-D is presented for the first time and briefly compared with the different regimes

Terahertz semiconductor nonlinear optics

DEFF Research Database (Denmark)

Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias

2013-01-01

In this proceedings we describe our recent results on semiconductor nonlinear optics, investigated using single-cycle THz pulses. We demonstrate the nonlinear absorption and self-phase modulation of strong-field THz pulses in doped semiconductors, using n-GaAs as a model system. The THz...... nonlinearity in doped semiconductors originates from the near-instantaneous heating of free electrons in the ponderomotive potential created by electric field of the THz pulse, leading to ultrafast increase of electron effective mass by intervalley scattering. Modification of effective mass in turn leads...... to a decrease of plasma frequency in semiconductor and produces a substantial modification of THz-range material dielectric function, described by the Drude model. As a result, the nonlinearity of both absorption coefficient and refractive index of the semiconductor is observed. In particular we demonstrate...

All-fiber nonlinearity- and dispersion-managed dissipative soliton nanotube mode-locked laser

Energy Technology Data Exchange (ETDEWEB)

Zhang, Z. [Department of Physics, Bilkent University, 06800 Ankara (Turkey); Nanjing University of Posts and Communications, Nanjing 210003 (China); Popa, D., E-mail: dp387@cam.ac.uk; Wittwer, V. J.; Milana, S.; Hasan, T.; Jiang, Z.; Ferrari, A. C. [Cambridge Graphene Centre, University of Cambridge, Cambridge CB3 0FA (United Kingdom); Ilday, F. Ö. [Department of Physics, Bilkent University, 06800 Ankara (Turkey); Department of Electrical and Electronics Engineering, Bilkent University, 06800 Ankara (Turkey)

2015-12-14

We report dissipative soliton generation from an Yb-doped all-fiber nonlinearity- and dispersion-managed nanotube mode-locked laser. A simple all-fiber ring cavity exploits a photonic crystal fiber for both nonlinearity enhancement and dispersion compensation. The laser generates stable dissipative solitons with large linear chirp in the net normal dispersion regime. Pulses that are 8.7 ps long are externally compressed to 118 fs, outperforming current nanotube-based Yb-doped fiber laser designs.

TESTING NONLINEAR INFLATION CONVERGENCE FOR THE CENTRAL AFRICAN ECONOMIC AND MONETARY COMMUNITY

Directory of Open Access Journals (Sweden)

Emmanuel Anoruo

2014-01-01

Full Text Available This paper uses nonlinear unit root testing procedures to examine the issue of inflation convergence for the Central African Economic and Monetary Community (CEMAC member states including Cameron, Central African Republic, Chad, Equatorial Guinea, Gabon and the Republic of Congo. The results from nonlinear STAR unit root tests suggest that inflation differentials for the sample countries are nonlinear and mean reverting processes. These results provide evidence of inflation convergence among countries within CEMAC. The finding of inflation convergence indicates the feasibility of a common monetary policy and/or inflation targeting regime within CEMAC.

A study of discrete nonlinear systems

International Nuclear Information System (INIS)

Dhillon, H.S.

2001-04-01

An investigation of various spatially discrete time-independent nonlinear models was undertaken. These models are generically applicable to many different physical systems including electron-phonon interactions in solids, magnetic multilayers, layered superconductors and classical lattice systems. To characterise the possible magnetic structures created on magnetic multilayers a model has been formulated and studied. The Euler-Lagrange equation for this model is a discrete version of the Sine-Gordon equation. Solutions of this equation are generated by applying the methods of Chaotic Dynamics - treating the space variable associated with the layer number as a discrete time variable. The states found indicate periodic, quasiperiodic and chaotic structures. Analytic solutions to the discrete nonlinear Schroedinger Equation (DNSE) with cubic nonlinearity are presented in the strong coupling limit. Using these as a starting point, a procedure is developed to determine the wave function and the energy eigenvalue for moderate coupling. The energy eigenvalues of the different structures of the wave function are found to be in excellent agreement with the exact strong coupling result. The solutions to the DNSE indicate commensurate and incommensurate spatial structures associated with different localisation patterns of the wave function. The states which arise may be fractal, periodic, quasiperiodic or chaotic. This work is then extended to solve a first order discrete nonlinear equation. The exact solutions for both the first and second order discrete nonlinear equations with cubic nonlinearity suggests that this method of studying discrete nonlinear equations may be applied to solve discrete equations with any order difference and cubic nonlinearity. (author)

Nonlinear optical interactions in silicon waveguides

Directory of Open Access Journals (Sweden)

Kuyken B.

2017-03-01

Full Text Available The strong nonlinear response of silicon photonic nanowire waveguides allows for the integration of nonlinear optical functions on a chip. However, the detrimental nonlinear optical absorption in silicon at telecom wavelengths limits the efficiency of many such experiments. In this review, several approaches are proposed and demonstrated to overcome this fundamental issue. By using the proposed methods, we demonstrate amongst others supercontinuum generation, frequency comb generation, a parametric optical amplifier, and a parametric optical oscillator.

Numerical Analysis of Strongly Nonlinear Oscillation Systems using He's Max-Min Method

DEFF Research Database (Denmark)

Babazadeh, H; Domairry, G; Barari, Amin

2011-01-01

Nonlinear functions are crucial points and terms in engineering problems. Actual and physical problems can be solved by solving and processing such functions. Thus, most scientists and engineers focus on solving these equations. This paper presents a novel method called the max-min method...

Multifractal regime transition in a modified minority game model

International Nuclear Information System (INIS)

Crepaldi, Antonio F.; Rodrigues Neto, Camilo; Ferreira, Fernando F.; Francisco, Gerson

2009-01-01

The search for more realistic modeling of financial time series reveals several stylized facts of real markets. In this work we focus on the multifractal properties found in price and index signals. Although the usual minority game (MG) models do not exhibit multifractality, we study here one of its variants that does. We show that the nonsynchronous MG models in the nonergodic phase is multifractal and in this sense, together with other stylized facts, constitute a better modeling tool. Using the structure function (SF) approach we detected the stationary and the scaling range of the time series generated by the MG model and, from the linear (non-linear) behavior of the SF we identified the fractal (multifractal) regimes. Finally, using the wavelet transform modulus maxima (WTMM) technique we obtained its multifractal spectrum width for different dynamical regimes.

Direct numerical simulation of a compressible boundary-layer flow past an isolated three-dimensional hump in a high-speed subsonic regime

Science.gov (United States)

De Grazia, D.; Moxey, D.; Sherwin, S. J.; Kravtsova, M. A.; Ruban, A. I.

2018-02-01

In this paper we study the boundary-layer separation produced in a high-speed subsonic boundary layer by a small wall roughness. Specifically, we present a direct numerical simulation (DNS) of a two-dimensional boundary-layer flow over a flat plate encountering a three-dimensional Gaussian-shaped hump. This work was motivated by the lack of DNS data of boundary-layer flows past roughness elements in a similar regime which is typical of civil aviation. The Mach and Reynolds numbers are chosen to be relevant for aeronautical applications when considering small imperfections at the leading edge of wings. We analyze different heights of the hump: The smaller heights result in a weakly nonlinear regime, while the larger result in a fully nonlinear regime with an increasing laminar separation bubble arising downstream of the roughness element and the formation of a pair of streamwise counterrotating vortices which appear to support themselves.

Hall effect in hopping regime

International Nuclear Information System (INIS)

Avdonin, A.; Skupiński, P.; Grasza, K.

2016-01-01

A simple description of the Hall effect in the hopping regime of conductivity in semiconductors is presented. Expressions for the Hall coefficient and Hall mobility are derived by considering averaged equilibrium electron transport in a single triangle of localization sites in a magnetic field. Dependence of the Hall coefficient is analyzed in a wide range of temperature and magnetic field values. Our theoretical result is applied to our experimental data on temperature dependence of Hall effect and Hall mobility in ZnO. - Highlights: • Expressions for Hall coefficient and mobility for hopping conductivity are derived. • Theoretical result is compared with experimental curves measured on ZnO. • Simultaneous action of free and hopping conduction channels is considered. • Non-linearity of hopping Hall coefficient is predicted.

Hall effect in hopping regime

Energy Technology Data Exchange (ETDEWEB)

Avdonin, A., E-mail: avdonin@ifpan.edu.pl [Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa (Poland); Skupiński, P. [Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa (Poland); Grasza, K. [Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa (Poland); Institute of Electronic Materials Technology, ul. Wólczyńska 133, 01-919 Warszawa (Poland)

2016-02-15

A simple description of the Hall effect in the hopping regime of conductivity in semiconductors is presented. Expressions for the Hall coefficient and Hall mobility are derived by considering averaged equilibrium electron transport in a single triangle of localization sites in a magnetic field. Dependence of the Hall coefficient is analyzed in a wide range of temperature and magnetic field values. Our theoretical result is applied to our experimental data on temperature dependence of Hall effect and Hall mobility in ZnO. - Highlights: • Expressions for Hall coefficient and mobility for hopping conductivity are derived. • Theoretical result is compared with experimental curves measured on ZnO. • Simultaneous action of free and hopping conduction channels is considered. • Non-linearity of hopping Hall coefficient is predicted.

Regime switches in the risk-return trade-off

OpenAIRE

Marcellino, Massimiliano; Ghysels, Eric; Guerin, Pierre

2014-01-01

This paper deals with the estimation of the risk-return trade-off. We use a MIDAS model for the conditional variance and allow for possible switches in the risk-return relation through a Markov-switching specification. We find strong evidence for regime changes in the risk-return relation. This finding is robust to a large range of specifications. In the first regime characterized by low ex-post returns and high volatility, the risk-return relation is reversed, whereas the intuitive positive ...

Application of a modified rational harmonic balance method for a class of strongly nonlinear oscillators

International Nuclear Information System (INIS)

Belendez, A.; Gimeno, E.; Alvarez, M.L.; Mendez, D.I.; Hernandez, A.

2008-01-01

An analytical approximate technique for conservative nonlinear oscillators is proposed. This method is a modification of the rational harmonic balance method in which analytical approximate solutions have rational form. This approach gives us the frequency of the motion as a function of the amplitude of oscillation. We find that this method works very well for the whole range of parameters, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. The most significant features of this method are its simplicity and its excellent accuracy for the whole range of oscillation amplitude values and the results reveal that this technique is very effective and convenient for solving conservative truly nonlinear oscillatory systems with complex nonlinearities

Nonlinearity in nanomechanical cantilevers

DEFF Research Database (Denmark)

Villanueva Torrijo, Luis Guillermo; Karabalin, R. B.; Matheny, M. H.

2013-01-01

Euler-Bernoulli beam theory is widely used to successfully predict the linear dynamics of micro-and nanocantilever beams. However, its capacity to characterize the nonlinear dynamics of these devices has not yet been rigorously assessed, despite its use in nanoelectromechanical systems developmen....... These findings underscore the delicate balance between inertial and geometric nonlinear effects in the fundamental mode, and strongly motivate further work to develop theories beyond the Euler-Bernoulli approximation. DOI: 10.1103/PhysRevB.87.024304...

Nonlinear spin wave coupling in adjacent magnonic crystals

Energy Technology Data Exchange (ETDEWEB)

Sadovnikov, A. V., E-mail: sadovnikovav@gmail.com; Nikitov, S. A. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation); Kotel' nikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow 125009 (Russian Federation); Beginin, E. N.; Morozova, M. A.; Sharaevskii, Yu. P.; Grishin, S. V.; Sheshukova, S. E. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation)

2016-07-25

We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.

Nonlinear spin wave coupling in adjacent magnonic crystals

International Nuclear Information System (INIS)

Sadovnikov, A. V.; Nikitov, S. A.; Beginin, E. N.; Morozova, M. A.; Sharaevskii, Yu. P.; Grishin, S. V.; Sheshukova, S. E.

2016-01-01

We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.

Nonlinear Optics: Principles and Applications

DEFF Research Database (Denmark)

Rottwitt, Karsten; Tidemand-Lichtenberg, Peter

of applications, Nonlinear Optics: Principles and Applications effectively bridges physics and mathematics with relevant applied material for real-world use. The book progresses naturally from fundamental aspects to illustrative examples, and presents a strong theoretical foundation that equips the reader...... and matter, this text focuses on the physical understanding of nonlinear optics, and explores optical material response functions in the time and frequency domain....

Shock compression of strongly correlated oxides: A liquid-regime equation of state for cerium(IV) oxide

Science.gov (United States)

Weck, Philippe F.; Cochrane, Kyle R.; Root, Seth; Lane, J. Matthew D.; Shulenburger, Luke; Carpenter, John H.; Sjostrom, Travis; Mattsson, Thomas R.; Vogler, Tracy J.

2018-03-01

The shock Hugoniot for full-density and porous CeO2 was investigated in the liquid regime using ab initio molecular dynamics (AIMD) simulations with Erpenbeck's approach based on the Rankine-Hugoniot jump conditions. The phase space was sampled by carrying out NVT simulations for isotherms between 6000 and 100 000 K and densities ranging from ρ =2.5 to 20 g /cm3 . The impact of on-site Coulomb interaction corrections +U on the equation of state (EOS) obtained from AIMD simulations was assessed by direct comparison with results from standard density functional theory simulations. Classical molecular dynamics (CMD) simulations were also performed to model atomic-scale shock compression of larger porous CeO2 models. Results from AIMD and CMD compression simulations compare favorably with Z-machine shock data to 525 GPa and gas-gun data to 109 GPa for porous CeO2 samples. Using results from AIMD simulations, an accurate liquid-regime Mie-Grüneisen EOS was built for CeO2. In addition, a revised multiphase SESAME-type EOS was constrained using AIMD results and experimental data generated in this work. This study demonstrates the necessity of acquiring data in the porous regime to increase the reliability of existing analytical EOS models.

Ishikawa iteration process for nonlinear Lipschitz strongly accretive mappings

International Nuclear Information System (INIS)

Chidume, C.E.; Osilike, M.O.

1994-05-01

Let E=L p , p≥2 and let T:E→ E be a Lipschitzian and strongly accretive mapping. Let S:E → E be defined by Sx=f-Tx+x. It is proved that under suitable conditions on the real sequences {α n } ∞ n=0 and {β n } ∞ n=0 , the iteration process, x 0 is an element of E, x n+1 =(1-α n ) x n +α n S[(1-β n ) x n +β n Sx n ], n≥0, converges strongly to the unique solution of Tx=f. A related result deals with the iterative approximation of fixed points for Lipschitz strongly pseudocontractive mappings in E. A consequence of our results gives an affirmative answer to a problem posed by one of the authors in 1990. (J. Math. Anal. Appl. 151, 2 (1990) p. 460). (author). 36 refs

Ultrafast nonlinear dynamics of thin gold films due to an intrinsic delayed nonlinearity

Science.gov (United States)

Bache, Morten; Lavrinenko, Andrei V.

2017-09-01

Using long-range surface plasmon polaritons light can propagate in metal nano-scale waveguides for ultracompact opto-electronic devices. Gold is an important material for plasmonic waveguides, but although its linear optical properties are fairly well understood, the nonlinear response is still under investigation. We consider the propagation of pulses in ultrathin gold strip waveguides, modeled by the nonlinear Schrödinger equation. The nonlinear response of gold is accounted for by the two-temperature model, revealing it as a delayed nonlinearity intrinsic in gold. The consequence is that the measured nonlinearities are strongly dependent on pulse duration. This issue has so far only been addressed phenomenologically, but we provide an accurate estimate of the quantitative connection as well as a phenomenological theory to understand the enhanced nonlinear response as the gold thickness is reduced. In comparison with previous works, the analytical model for the power-loss equation has been improved, and can be applied now to cases with a high laser peak power. We show new fits to experimental data from the literature and provide updated values for the real and imaginary parts of the nonlinear susceptibility of gold for various pulse durations and gold layer thicknesses. Our simulations show that the nonlinear loss is inhibiting efficient nonlinear interaction with low-power laser pulses. We therefore propose to design waveguides suitable for the mid-IR, where the ponderomotive instantaneous nonlinearity can dominate over the delayed hot-electron nonlinearity and provide a suitable plasmonics platform for efficient ultrafast nonlinear optics.

Bright and dark solitons in the normal dispersion regime of inhomogeneous optical fibers: Soliton interaction and soliton control

International Nuclear Information System (INIS)

Liu Wenjun; Tian Bo; Xu Tao; Sun Kun; Jiang Yan

2010-01-01

Symbolically investigated in this paper is a nonlinear Schroedinger equation with the varying dispersion and nonlinearity for the propagation of optical pulses in the normal dispersion regime of inhomogeneous optical fibers. With the aid of the Hirota method, analytic one- and two-soliton solutions are obtained. Relevant properties of physical and optical interest are illustrated. Different from the previous results, both the bright and dark solitons are hereby derived in the normal dispersion regime of the inhomogeneous optical fibers. Moreover, different dispersion profiles of the dispersion-decreasing fibers can be used to realize the soliton control. Finally, soliton interaction is discussed with the soliton control confirmed to have no influence on the interaction. The results might be of certain value for the study of the signal generator and soliton control.

A nonlinear beam model to describe the postbuckling of wide neo-Hookean beams

Science.gov (United States)

Lubbers, Luuk A.; van Hecke, Martin; Coulais, Corentin

2017-09-01

Wide beams can exhibit subcritical buckling, i.e. the slope of the force-displacement curve can become negative in the postbuckling regime. In this paper, we capture this intriguing behaviour by constructing a 1D nonlinear beam model, where the central ingredient is the nonlinearity in the stress-strain relation of the beams constitutive material. First, we present experimental and numerical evidence of a transition to subcritical buckling for wide neo-Hookean hyperelastic beams, when their width-to-length ratio exceeds a critical value of 12%. Second, we construct an effective 1D energy density by combining the Mindlin-Reissner kinematics with a nonlinearity in the stress-strain relation. Finally, we establish and solve the governing beam equations to analytically determine the slope of the force-displacement curve in the postbuckling regime. We find, without any adjustable parameters, excellent agreement between the 1D theory, experiments and simulations. Our work extends the understanding of the postbuckling of structures made of wide elastic beams and opens up avenues for the reverse-engineering of instabilities in soft and metamaterials.

Stirring Strongly Coupled Plasma

CERN Document Server

Fadafan, Kazem Bitaghsir; Rajagopal, Krishna; Wiedemann, Urs Achim

2009-01-01

We determine the energy it takes to move a test quark along a circle of radius L with angular frequency w through the strongly coupled plasma of N=4 supersymmetric Yang-Mills (SYM) theory. We find that for most values of L and w the energy deposited by stirring the plasma in this way is governed either by the drag force acting on a test quark moving through the plasma in a straight line with speed v=Lw or by the energy radiated by a quark in circular motion in the absence of any plasma, whichever is larger. There is a continuous crossover from the drag-dominated regime to the radiation-dominated regime. In the crossover regime we find evidence for significant destructive interference between energy loss due to drag and that due to radiation as if in vacuum. The rotating quark thus serves as a model system in which the relative strength of, and interplay between, two different mechanisms of parton energy loss is accessible via a controlled classical gravity calculation. We close by speculating on the implicati...

Nonlinear elasticity in resonance experiments

Science.gov (United States)

Li, Xun; Sens-Schönfelder, Christoph; Snieder, Roel

2018-04-01

Resonant bar experiments have revealed that dynamic deformation induces nonlinearity in rocks. These experiments produce resonance curves that represent the response amplitude as a function of the driving frequency. We propose a model to reproduce the resonance curves with observed features that include (a) the log-time recovery of the resonant frequency after the deformation ends (slow dynamics), (b) the asymmetry in the direction of the driving frequency, (c) the difference between resonance curves with the driving frequency that is swept upward and downward, and (d) the presence of a "cliff" segment to the left of the resonant peak under the condition of strong nonlinearity. The model is based on a feedback cycle where the effect of softening (nonlinearity) feeds back to the deformation. This model provides a unified interpretation of both the nonlinearity and slow dynamics in resonance experiments. We further show that the asymmetry of the resonance curve is caused by the softening, which is documented by the decrease of the resonant frequency during the deformation; the cliff segment of the resonance curve is linked to a bifurcation that involves a steep change of the response amplitude when the driving frequency is changed. With weak nonlinearity, the difference between the upward- and downward-sweeping curves depends on slow dynamics; a sufficiently slow frequency sweep eliminates this up-down difference. With strong nonlinearity, the up-down difference results from both the slow dynamics and bifurcation; however, the presence of the bifurcation maintains the respective part of the up-down difference, regardless of the sweep rate.

Numerical studies on the electromagnetic properties of the nonlinear Lorentz Computational model for the dielectric media

International Nuclear Information System (INIS)

Abe, H.; Okuda, H.

1994-06-01

We study linear and nonlinear properties of a new computer simulation model developed to study the propagation of electromagnetic waves in a dielectric medium in the linear and nonlinear regimes. The model is constructed by combining a microscopic model used in the semi-classical approximation for the dielectric media and the particle model developed for the plasma simulations. It is shown that the model may be useful for studying linear and nonlinear wave propagation in the dielectric media

Fluid flows of mixed regimes in porous media

Science.gov (United States)

Celik, Emine; Hoang, Luan; Ibragimov, Akif; Kieu, Thinh

2017-02-01

In porous media, there are three known regimes of fluid flows, namely, pre-Darcy, Darcy, and post-Darcy. Because of their different natures, these are usually treated separately in the literature. To study complex flows when all three regimes may be present in different portions of a same domain, we use a single equation of motion to unify them. Several scenarios and models are then considered for slightly compressible fluids. A nonlinear parabolic equation for the pressure is derived, which is degenerate when the pressure gradient is either small or large. We estimate the pressure and its gradient for all time in terms of initial and boundary data. We also obtain their particular bounds for large time which depend on the asymptotic behavior of the boundary data but not on the initial one. Moreover, the continuous dependence of the solutions on initial and boundary data and the structural stability for the equation are established.

Seasonality of fire weather strongly influences fire regimes in South Florida savanna-grassland landscapes.

Directory of Open Access Journals (Sweden)

William J Platt

Full Text Available Fire seasonality, an important characteristic of fire regimes, commonly is delineated using seasons based on single weather variables (rainfall or temperature. We used nonparametric cluster analyses of a 17-year (1993-2009 data set of weather variables that influence likelihoods and spread of fires (relative humidity, air temperature, solar radiation, wind speed, soil moisture to explore seasonality of fire in pine savanna-grassland landscapes at the Avon Park Air Force Range in southern Florida. A four-variable, three-season model explained more variation within fire weather variables than models with more seasons. The three-season model also delineated intra-annual timing of fire more accurately than a conventional rainfall-based two-season model. Two seasons coincided roughly with dry and wet seasons based on rainfall. The third season, which we labeled the fire season, occurred between dry and wet seasons and was characterized by fire-promoting conditions present annually: drought, intense solar radiation, low humidity, and warm air temperatures. Fine fuels consisting of variable combinations of pyrogenic pine needles, abundant C4 grasses, and flammable shrubs, coupled with low soil moisture, and lightning ignitions early in the fire season facilitate natural landscape-scale wildfires that burn uplands and across wetlands. We related our three season model to fires with different ignition sources (lightning, military missions, and prescribed fires over a 13-year period with fire records (1997-2009. Largest wildfires originate from lightning and military ignitions that occur within the early fire season substantially prior to the peak of lightning strikes in the wet season. Prescribed ignitions, in contrast, largely occur outside the fire season. Our delineation of a pronounced fire season provides insight into the extent to which different human-derived fire regimes mimic lightning fire regimes. Delineation of a fire season associated with

Seasonality of Fire Weather Strongly Influences Fire Regimes in South Florida Savanna-Grassland Landscapes

Science.gov (United States)

Platt, William J.; Orzell, Steve L.; Slocum, Matthew G.

2015-01-01

Fire seasonality, an important characteristic of fire regimes, commonly is delineated using seasons based on single weather variables (rainfall or temperature). We used nonparametric cluster analyses of a 17-year (1993–2009) data set of weather variables that influence likelihoods and spread of fires (relative humidity, air temperature, solar radiation, wind speed, soil moisture) to explore seasonality of fire in pine savanna-grassland landscapes at the Avon Park Air Force Range in southern Florida. A four-variable, three-season model explained more variation within fire weather variables than models with more seasons. The three-season model also delineated intra-annual timing of fire more accurately than a conventional rainfall-based two-season model. Two seasons coincided roughly with dry and wet seasons based on rainfall. The third season, which we labeled the fire season, occurred between dry and wet seasons and was characterized by fire-promoting conditions present annually: drought, intense solar radiation, low humidity, and warm air temperatures. Fine fuels consisting of variable combinations of pyrogenic pine needles, abundant C4 grasses, and flammable shrubs, coupled with low soil moisture, and lightning ignitions early in the fire season facilitate natural landscape-scale wildfires that burn uplands and across wetlands. We related our three season model to fires with different ignition sources (lightning, military missions, and prescribed fires) over a 13-year period with fire records (1997–2009). Largest wildfires originate from lightning and military ignitions that occur within the early fire season substantially prior to the peak of lightning strikes in the wet season. Prescribed ignitions, in contrast, largely occur outside the fire season. Our delineation of a pronounced fire season provides insight into the extent to which different human-derived fire regimes mimic lightning fire regimes. Delineation of a fire season associated with timing of

Nonlinear Dynamics of Silicon Nanowire Resonator Considering Nonlocal Effect.

Science.gov (United States)

Jin, Leisheng; Li, Lijie

2017-12-01

In this work, nonlinear dynamics of silicon nanowire resonator considering nonlocal effect has been investigated. For the first time, dynamical parameters (e.g., resonant frequency, Duffing coefficient, and the damping ratio) that directly influence the nonlinear dynamics of the nanostructure have been derived. Subsequently, by calculating their response with the varied nonlocal coefficient, it is unveiled that the nonlocal effect makes more obvious impacts at the starting range (from zero to a small value), while the impact of nonlocal effect becomes weaker when the nonlocal term reaches to a certain threshold value. Furthermore, to characterize the role played by nonlocal effect in exerting influence on nonlinear behaviors such as bifurcation and chaos (typical phenomena in nonlinear dynamics of nanoscale devices), we have calculated the Lyapunov exponents and bifurcation diagram with and without nonlocal effect, and results shows the nonlocal effect causes the most significant effect as the device is at resonance. This work advances the development of nanowire resonators that are working beyond linear regime.

Spin and wavelength multiplexed nonlinear metasurface holography

Science.gov (United States)

Ye, Weimin; Zeuner, Franziska; Li, Xin; Reineke, Bernhard; He, Shan; Qiu, Cheng-Wei; Liu, Juan; Wang, Yongtian; Zhang, Shuang; Zentgraf, Thomas

2016-06-01

Metasurfaces, as the ultrathin version of metamaterials, have caught growing attention due to their superior capability in controlling the phase, amplitude and polarization states of light. Among various types of metasurfaces, geometric metasurface that encodes a geometric or Pancharatnam-Berry phase into the orientation angle of the constituent meta-atoms has shown great potential in controlling light in both linear and nonlinear optical regimes. The robust and dispersionless nature of the geometric phase simplifies the wave manipulation tremendously. Benefitting from the continuous phase control, metasurface holography has exhibited advantages over conventional depth controlled holography with discretized phase levels. Here we report on spin and wavelength multiplexed nonlinear metasurface holography, which allows construction of multiple target holographic images carried independently by the fundamental and harmonic generation waves of different spins. The nonlinear holograms provide independent, nondispersive and crosstalk-free post-selective channels for holographic multiplexing and multidimensional optical data storages, anti-counterfeiting, and optical encryption.

Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations

International Nuclear Information System (INIS)

Udaltsov, Vladimir S.; Goedgebuer, Jean-Pierre; Larger, Laurent; Cuenot, Jean-Baptiste; Levy, Pascal; Rhodes, William T.

2003-01-01

We report that signal encoding with high-dimensional chaos produced by delayed feedback systems with a strong nonlinearity can be broken. We describe the procedure and illustrate the method with chaotic waveforms obtained from a strongly nonlinear optical system that we used previously to demonstrate signal encryption/decryption with chaos in wavelength. The method can be extended to any systems ruled by nonlinear time-delayed differential equations

Turbulent transport regimes and the SOL heat flux width

Science.gov (United States)

Myra, J. R.; D'Ippolito, D. A.; Russell, D. A.

2014-10-01

Understanding the responsible mechanisms and resulting scaling of the scrape-off layer (SOL) heat flux width is important for predicting viable operating regimes in future tokamaks, and for seeking possible mitigation schemes. Simulation and theory results using reduced edge/SOL turbulence models have produced SOL widths and scalings in reasonable accord with experiments in many cases. In this work, we attempt to qualitatively and conceptually understand various regimes of edge/SOL turbulence and the role of turbulent transport in establishing the SOL heat flux width. Relevant considerations include the type and spectral characteristics of underlying instabilities, the location of the gradient drive relative to the SOL, the nonlinear saturation mechanism, and the parallel heat transport regime. Recent SOLT turbulence code results are employed to understand the roles of these considerations and to develop analytical scalings. We find a heat flux width scaling with major radius R that is generally positive, consistent with older results reviewed in. The possible relationship of turbulence mechanisms to the heuristic drift mechanism is considered, together with implications for future experiments. Work supported by US DOE grant DE-FG02-97ER54392.

Nonlinear Electromagnetic Stabilization of Plasma Microturbulence

Science.gov (United States)

Whelan, G. G.; Pueschel, M. J.; Terry, P. W.

2018-04-01

The physical causes for the strong stabilizing effect of finite plasma β on ion-temperature-gradient-driven turbulence, which far exceeds quasilinear estimates, are identified from nonlinear gyrokinetic simulations. The primary contribution stems from a resonance of frequencies in the dominant nonlinear interaction between the unstable mode, the stable mode, and zonal flows, which maximizes the triplet correlation time and therefore the energy transfer efficiency. A modification to mixing-length transport estimates is constructed, which reproduces nonlinear heat fluxes throughout the examined β range.

NONLINEAR OPTICAL PHENOMENA: Self-reflection effect in semiconductors in a two-pulse regime

Science.gov (United States)

Khadzhi, P. I.; Nad'kin, L. Yu

2004-12-01

Peculiarities of reflection at the end face of a semi-infinite semiconductor in a two-pulse regime are studied. The reflection functions behave in a complex and ambiguous manner governed by the amplitudes of the fields of incident pulses. The possibility of a complete bleaching of the medium for the field in the M-band is predicted.

Probe-controlled soliton frequency shift in the regime of optical event horizon.

Science.gov (United States)

Gu, Jie; Guo, Hairun; Wang, Shaofei; Zeng, Xianglong

2015-08-24

In optical analogy of the event horizon, temporal pulse collision and mutual interactions are mainly between an intense solitary wave (soliton) and a dispersive probe wave. In such a regime, here we numerically investigate the probe-controlled soliton frequency shift as well as the soliton self-compression. In particular, in the dispersion landscape with multiple zero dispersion wavelengths, bi-directional soliton spectral tunneling effects is possible. Moreover, we propose a mid-infrared soliton self-compression to the generation of few-cycle ultrashort pulses, in a bulk of quadratic nonlinear crystals in contrast to optical fibers or cubic nonlinear media, which could contribute to the community with a simple and flexible method to experimental implementations.

Proceedings of the workshop on nonlinear MHD and extended MHD

International Nuclear Information System (INIS)

1998-01-01

Nonlinear MHD simulations have proven their value in interpreting experimental results over the years. As magnetic fusion experiments reach higher performance regimes, more sophisticated experimental diagnostics coupled with ever expanding computer capabilities have increased both the need for and the feasibility of nonlinear global simulations using models more realistic than regular ideal and resistive MHD. Such extended-MHD nonlinear simulations have already begun to produce useful results. These studies are expected to lead to ever more comprehensive simulation models in the future and to play a vital role in fully understanding fusion plasmas. Topics include the following: (1) current state of nonlinear MHD and extended-MHD simulations; (2) comparisons to experimental data; (3) discussions between experimentalists and theorists; (4) /equations for extended-MHD models, kinetic-based closures; and (5) paths toward more comprehensive simulation models, etc. Selected papers have been indexed separately for inclusion in the Energy Science and Technology Database

Proceedings of the workshop on nonlinear MHD and extended MHD

Energy Technology Data Exchange (ETDEWEB)

NONE

1998-12-01

Nonlinear MHD simulations have proven their value in interpreting experimental results over the years. As magnetic fusion experiments reach higher performance regimes, more sophisticated experimental diagnostics coupled with ever expanding computer capabilities have increased both the need for and the feasibility of nonlinear global simulations using models more realistic than regular ideal and resistive MHD. Such extended-MHD nonlinear simulations have already begun to produce useful results. These studies are expected to lead to ever more comprehensive simulation models in the future and to play a vital role in fully understanding fusion plasmas. Topics include the following: (1) current state of nonlinear MHD and extended-MHD simulations; (2) comparisons to experimental data; (3) discussions between experimentalists and theorists; (4) /equations for extended-MHD models, kinetic-based closures; and (5) paths toward more comprehensive simulation models, etc. Selected papers have been indexed separately for inclusion in the Energy Science and Technology Database.

Photoinduced Electron Transfer in the Strong Coupling Regime: Waveguide-Plasmon Polaritons.

Science.gov (United States)

Zeng, Peng; Cadusch, Jasper; Chakraborty, Debadi; Smith, Trevor A; Roberts, Ann; Sader, John E; Davis, Timothy J; Gómez, Daniel E

2016-04-13

Reversible exchange of photons between a material and an optical cavity can lead to the formation of hybrid light-matter states where material properties such as the work function [ Hutchison et al. Adv. Mater. 2013 , 25 , 2481 - 2485 ], chemical reactivity [ Hutchison et al. Angew. Chem., Int. Ed. 2012 , 51 , 1592 - 1596 ], ultrafast energy relaxation [ Salomon et al. Angew. Chem., Int. Ed. 2009 , 48 , 8748 - 8751 ; Gomez et al. J. Phys. Chem. B 2013 , 117 , 4340 - 4346 ], and electrical conductivity [ Orgiu et al. Nat. Mater. 2015 , 14 , 1123 - 1129 ] of matter differ significantly to those of the same material in the absence of strong interactions with the electromagnetic fields. Here we show that strong light-matter coupling between confined photons on a semiconductor waveguide and localized plasmon resonances on metal nanowires modifies the efficiency of the photoinduced charge-transfer rate of plasmonic derived (hot) electrons into accepting states in the semiconductor material. Ultrafast spectroscopy measurements reveal a strong correlation between the amplitude of the transient signals, attributed to electrons residing in the semiconductor and the hybridization of waveguide and plasmon excitations.

Probing the ionization wave packet and recollision dynamics with an elliptically polarized strong laser field in the nondipole regime

Science.gov (United States)

Maurer, J.; Willenberg, B.; Daněk, J.; Mayer, B. W.; Phillips, C. R.; Gallmann, L.; Klaiber, M.; Hatsagortsyan, K. Z.; Keitel, C. H.; Keller, U.

2018-01-01

We explore ionization and rescattering in strong mid-infrared laser fields in the nondipole regime over the full range of polarization ellipticity. In three-dimensional photoelectron momentum distributions (3D PMDs) measured with velocity map imaging spectroscopy, we observe the appearance of a sharp ridge structure along the major polarization axis. Within a certain range of ellipticity, the electrons in this ridge are clearly separated from the two lobes that commonly appear in the PMD with elliptically polarized laser fields. In contrast to the well-known lobes of direct electrons, the sharp ridge is created by Coulomb focusing of the softly recolliding electrons. These ridge electrons are directly related to a counterintuitive shift of the PMD peak opposite to the laser beam propagation direction when the dipole approximation breaks down. The ellipticity-dependent 3D PMDs give access to different ionization and recollision dynamics with appropriate filters in the momentum space. For example, we can extract information about the spread of the initial wave packet and the Coulomb momentum transfer of the rescattering electrons.

Influence of earthquake strong motion duration on nonlinear structural response

International Nuclear Information System (INIS)

Meskouris, K.

1983-01-01

The effects of motion duration on nonlinear structural response of high-rise, moment resisting frames are studied by subjecting shear beam models of a 10- and a 5-story frame to a series of synthetic accelerograms, all matching the same NEWMARK/HALL design spectrum. Two different hysteretic laws are used for the story springs, and calculations are carried out for target ductility values of 2 and 4. Maximum ductilities reached and energy-based damage indicators (maximum seismically input energy, hysteretically dissipated energy) are evaluated and correlated with the motion characteristics. A reasonable extrapolative determination of structural response characteristics based on these indicators seems possible. (orig.)

Envisioning, quantifying, and managing thermal regimes on river networks

Science.gov (United States)

Steel, E. Ashley; Beechie, Timothy J.; Torgersen, Christian E.; Fullerton, Aimee H.

2017-01-01

Water temperatures fluctuate in time and space, creating diverse thermal regimes on river networks. Temporal variability in these thermal landscapes has important biological and ecological consequences because of nonlinearities in physiological reactions; spatial diversity in thermal landscapes provides aquatic organisms with options to maximize growth and survival. However, human activities and climate change threaten to alter the dynamics of riverine thermal regimes. New data and tools can identify particular facets of the thermal landscape that describe ecological and management concerns and that are linked to human actions. The emerging complexity of thermal landscapes demands innovations in communication, opens the door to exciting research opportunities on the human impacts to and biological consequences of thermal variability, suggests improvements in monitoring programs to better capture empirical patterns, provides a framework for suites of actions to restore and protect the natural processes that drive thermal complexity, and indicates opportunities for better managing thermal landscapes.

Electrophoresis in strong electric fields.

Science.gov (United States)

Barany, Sandor

2009-01-01

Two kinds of non-linear electrophoresis (ef) that can be detected in strong electric fields (several hundred V/cm) are considered. The first ("classical" non-linear ef) is due to the interaction of the outer field with field-induced ionic charges in the electric double layer (EDL) under conditions, when field-induced variations of electrolyte concentration remain to be small comparatively to its equilibrium value. According to the Shilov theory, the non-linear component of the electrophoretic velocity for dielectric particles is proportional to the cubic power of the applied field strength (cubic electrophoresis) and to the second power of the particles radius; it is independent of the zeta-potential but is determined by the surface conductivity of particles. The second one, the so-called "superfast electrophoresis" is connected with the interaction of a strong outer field with a secondary diffuse layer of counterions (space charge) that is induced outside the primary (classical) diffuse EDL by the external field itself because of concentration polarization. The Dukhin-Mishchuk theory of "superfast electrophoresis" predicts quadratic dependence of the electrophoretic velocity of unipolar (ionically or electronically) conducting particles on the external field gradient and linear dependence on the particle's size in strong electric fields. These are in sharp contrast to the laws of classical electrophoresis (no dependence of V(ef) on the particle's size and linear dependence on the electric field gradient). A new method to measure the ef velocity of particles in strong electric fields is developed that is based on separation of the effects of sedimentation and electrophoresis using videoimaging and a new flowcell and use of short electric pulses. To test the "classical" non-linear electrophoresis, we have measured the ef velocity of non-conducting polystyrene, aluminium-oxide and (semiconductor) graphite particles as well as Saccharomice cerevisiae yeast cells as a

Nonreciprocity in the dynamics of coupled oscillators with nonlinearity, asymmetry, and scale hierarchy

Science.gov (United States)

Moore, Keegan J.; Bunyan, Jonathan; Tawfick, Sameh; Gendelman, Oleg V.; Li, Shuangbao; Leamy, Michael; Vakakis, Alexander F.

2018-01-01

In linear time-invariant dynamical and acoustical systems, reciprocity holds by the Onsager-Casimir principle of microscopic reversibility, and this can be broken only by odd external biases, nonlinearities, or time-dependent properties. A concept is proposed in this work for breaking dynamic reciprocity based on irreversible nonlinear energy transfers from large to small scales in a system with nonlinear hierarchical internal structure, asymmetry, and intentional strong stiffness nonlinearity. The resulting nonreciprocal large-to-small scale energy transfers mimic analogous nonlinear energy transfer cascades that occur in nature (e.g., in turbulent flows), and are caused by the strong frequency-energy dependence of the essentially nonlinear small-scale components of the system considered. The theoretical part of this work is mainly based on action-angle transformations, followed by direct numerical simulations of the resulting system of nonlinear coupled oscillators. The experimental part considers a system with two scales—a linear large-scale oscillator coupled to a small scale by a nonlinear spring—and validates the theoretical findings demonstrating nonreciprocal large-to-small scale energy transfer. The proposed study promotes a paradigm for designing nonreciprocal acoustic materials harnessing strong nonlinearity, which in a future application will be implemented in designing lattices incorporating nonlinear hierarchical internal structures, asymmetry, and scale mixing.

What occurs in the fragile-to-strong liquid transition regime?

DEFF Research Database (Denmark)

Yue, Yuanzheng; Hu, L.N.

The slow dynamics of glass-forming liquids is a complex subject of the condensed matter science. But the fragile-to-strong transition, which was observed not long ago [Ito, et al, Nature 1999], makes this subject even more complex since it is extremely challenging to directly probe the structural...

Flat super-continuum generation based on normal dispersion nonlinear photonic crystal fibre

DEFF Research Database (Denmark)

Chow, K.K.; Takushima, Y.; Lin, C.

2006-01-01

Flat super-continuum generation spanning over the whole telecommunication band using a passively modelocked fibre laser source at 1550 nm together with a dispersion-flattened nonlinear photoinc crystal fibre is demonstrated. Since the pulses propagate in the normal dispersion regime of the fibre...

Periodic wavetrains for systems of coupled nonlinear Schrödinger ...

Indian Academy of Sciences (India)

Exact, periodic wavetrains for systems of coupled nonlinear Schrödinger equations are obtained by the Hirota bilinear method and theta functions identities. Both the bright and dark soliton regimes are treated, and the solutions involve products of elliptic functions. The validity of these solutions is verified independently by a ...

Double shock dynamics induced by the saturation of defocusing nonlinearities

KAUST Repository

Crosta, Matteo

2012-01-01

We show that the saturation of defocusing nonlinearities leads to qualitative changes in the onset of wave breaking, determining double shock formation whose regularization occurs in terms of antidark solitons. In a given material, the crossover between different regimes can be controlled by changing the input intensity. © 2012 Optical Society of America.

The determination of capital controls: Which role do exchange rate regimes play?

OpenAIRE

von Hagen, Jürgen; Zhou, Jizhong

2003-01-01

This paper investigates the role of exchange rate regime choices in the determination of capital controls in transition economies. We first use a simultaneous equations model to allow direct interactions between decisions on capital controls and on exchange rate regimes. We find that exchange rate regime choices strongly influence the imposition or removal of capital controls, but the feed-back effect is weak. We further estimate a single equation model for capital controls with exchange rate...

Nonlinear interplay of TEM and ITG turbulence and its effect on transport

Science.gov (United States)

Merz, F.; Jenko, F.

2010-05-01

The dominant source of anomalous transport in fusion plasmas on ion scales is turbulence driven by trapped electron modes (TEMs) and ion temperature gradient (ITG) modes. While the individual properties of each of these two instabilities and the corresponding microturbulence have been examined in detail in the past, the effects of a coexistence of the two modes and the phenomena of transitions between the TEM and ITG dominated regimes are not well studied. In many experimental situations, the temperature and density gradients support both microinstabilities simultaneously, so that transitional regimes are important for a detailed understanding of fusion plasmas. In this paper, this issue is addressed, using the gyrokinetic code GENE for a detailed investigation of the dominant and subdominant linear instabilities and the corresponding nonlinear system. A simple quasilinear model based on eigenvalue computations is presented which is shown to reproduce important features of the nonlinear TEM-ITG transition.

Pulse interactions in a quantum dot waveguide in the regime of electromagnetically Induced transparency

DEFF Research Database (Denmark)

Nielsen, Per; Nielsen, Henri; Mørk, Jesper

2006-01-01

The interaction of optical pulses in a quantum dot waveguide in the slow-light regime is investigated. Dipole oscillations lead to strong interactions between the two pulses, implying a minimum pulse separation for optical buffer applications.......The interaction of optical pulses in a quantum dot waveguide in the slow-light regime is investigated. Dipole oscillations lead to strong interactions between the two pulses, implying a minimum pulse separation for optical buffer applications....

The legacy of large regime shifts in shallow lakes.

Science.gov (United States)

Ramstack Hobbs, Joy M; Hobbs, William O; Edlund, Mark B; Zimmer, Kyle D; Theissen, Kevin M; Hoidal, Natalie; Domine, Leah M; Hanson, Mark A; Herwig, Brian R; Cotner, James B

2016-12-01

Ecological shifts in shallow lakes from clear-water macrophyte-dominated to turbid-water phytoplankton-dominated are generally thought of as rapid short-term transitions. Diatom remains in sediment records from shallow lakes in the Prairie Pothole Region of North America provide new evidence that the long-term ecological stability of these lakes is defined by the legacy of large regime shifts. We examine the modern and historical stability of 11 shallow lakes. Currently, four of the lakes are in a clear-water state, three are consistently turbid-water, and four have been observed to change state from year to year (transitional). Lake sediment records spanning the past 150-200 yr suggest that (1) the diatom assemblage is characteristic of either clear or turbid lakes, (2) prior to significant landscape alteration, all of the lakes existed in a regime of a stable clear-water state, (3) lakes that are currently classified as turbid or transitional have experienced one strong regime shift over the past 150-200 yr and have since remained in a regime where turbid-water predominates, and (4) top-down impacts to the lake food-web from fish introductions appear to be the dominant driver of strong regime shifts and not increased nutrient availability. Based on our findings we demonstrate a method that could be used by lake managers to identify lakes that have an ecological history close to the clear-turbid regime threshold; such lakes might more easily be returned to a clear-water state through biomanipulation. The unfortunate reality is that many of these lakes are now part of a managed landscape and will likely require continued intervention. © 2016 by the Ecological Society of America.

Efficient Market Hypothesis in South Africa: Evidence from Linear and Nonlinear Unit Root Tests

Directory of Open Access Journals (Sweden)

Andrew Phiri

2015-12-01

Full Text Available This study investigates the weak form efficient market hypothesis (EMH for five generalized stock indices in the Johannesburg Stock Exchange (JSE using weekly data collected from 31st January 2000 to 16th December 2014. In particular, we test for weak form market efficiency using a battery of linear and nonlinear unit root testing procedures comprising of the classical augmented Dickey-Fuller (ADF tests, the two-regime threshold autoregressive (TAR unit root tests described in Enders and Granger (1998 as well as the three-regime unit root tests described in Bec, Salem, and Carrasco (2004. Based on our empirical analysis, we are able to demonstrate that whilst the linear unit root tests advocate for unit roots within the time series, the nonlinear unit root tests suggest that most stock indices are threshold stationary processes. These results bridge two opposing contentions obtained from previous studies by concluding that under a linear framework the JSE stock indices offer support in favour of weak form market efficiency whereas when nonlinearity is accounted for, a majority of the indices violate the weak form EMH.

Dynamics of a photorefractive response and competition of nonlinear processes in self-pumping double phase-conjugate mirrors

International Nuclear Information System (INIS)

Mogaddam, Mehran Wahdani; Shuvalov, Vladimir V

2005-01-01

The dynamics of formation of a nonlinear response of a double phase-conjugate (PC) BaTiO 3 mirror is calculated. It is shown that because of competition between processes of different types (related to the presence of several PC channels, the local and nonlocal components of the photorefractive nonlinearity), the transient and dynamic lasing regimes for this mirror can be substantially different. It is found that the development of lasing begins with the successive formation and phasing of dynamic holograms of two different types (two PC channels). It is shown that even under optimal conditions, the lasing regime is not stationary due to competition between processes of different types, and the parameters of output fields fluctuate in time in a nontrivial way (due to the presence of the in-phase and out-of-phase components). Several scenarios of transition to the dynamic chaos are described. (nonlinear optical phenomena)

Dynamic nonlinear elasticity in geo materials

International Nuclear Information System (INIS)

Ostrovsky, L.A.; Johnson, P.A.

2001-01-01

The nonlinear elastic behaviour of earth materials is an extremely rich topic, one that has broad implications to earth and materials sciences, including strong ground motion, rock physics, nondestructive evaluation and materials science. The mechanical properties of rock appear to place it in a broader class of materials, it can be named the Structural nonlinear elasticity class (also Mesoscopic/nano scale elasticity, or MS/NSE class). These terms are in contrast to materials that display classical, Atomic Elasticity, such as most fluids and monocrystalline solids. The difference between these two categories of materials is both in intensity and origin of their nonlinear response. The nonlinearity of atomic elastic materials is due to the atomic/molecular lattice anharmonicity. The latter is relatively small because the intermolecular forces are extremely strong. In contrast, the materials considered below contain small soft features that it is called the bond system (cracks, grain contacts, dislocations, etc.) within a hard matrix and relaxation (slow dynamical effects) are characteristic, non of which appear in atomic elastic materials. The research begins with a brief historical background from nonlinear acoustics to the recent developments in rock nonlinearity. This is followed by an overview of some representative laboratory measurements which serve as primary indicators of nonlinear behaviour, followed by theoretical development, and finally, mention a variety of observations of nonlinearity under field conditions and applications to nondestructive testing of materials. The goal is not to survey all papers published in the are but to demonstrate some experimental and theoretical results and ideas that will the reader to become oriented in this broad and rapidly growing area bridging macro-, meso- and microscale (nano scale) phenomena in physics, materials science, and geophysics

Nonlinear Dynamics in Gene Regulation Promote Robustness and Evolvability of Gene Expression Levels.

Science.gov (United States)

Steinacher, Arno; Bates, Declan G; Akman, Ozgur E; Soyer, Orkun S

2016-01-01

Cellular phenotypes underpinned by regulatory networks need to respond to evolutionary pressures to allow adaptation, but at the same time be robust to perturbations. This creates a conflict in which mutations affecting regulatory networks must both generate variance but also be tolerated at the phenotype level. Here, we perform mathematical analyses and simulations of regulatory networks to better understand the potential trade-off between robustness and evolvability. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics, through the creation of regions presenting sudden changes in phenotype with small changes in genotype. For genotypes embedding low levels of nonlinearity, robustness and evolvability correlate negatively and almost perfectly. By contrast, genotypes embedding nonlinear dynamics allow expression levels to be robust to small perturbations, while generating high diversity (evolvability) under larger perturbations. Thus, nonlinearity breaks the robustness-evolvability trade-off in gene expression levels by allowing disparate responses to different mutations. Using analytical derivations of robustness and system sensitivity, we show that these findings extend to a large class of gene regulatory network architectures and also hold for experimentally observed parameter regimes. Further, the effect of nonlinearity on the robustness-evolvability trade-off is ensured as long as key parameters of the system display specific relations irrespective of their absolute values. We find that within this parameter regime genotypes display low and noisy expression levels. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics. Our results provide a possible solution to the robustness-evolvability trade-off, suggest an explanation for

Nonlinear Dynamics in Gene Regulation Promote Robustness and Evolvability of Gene Expression Levels.

Directory of Open Access Journals (Sweden)

Arno Steinacher

Full Text Available Cellular phenotypes underpinned by regulatory networks need to respond to evolutionary pressures to allow adaptation, but at the same time be robust to perturbations. This creates a conflict in which mutations affecting regulatory networks must both generate variance but also be tolerated at the phenotype level. Here, we perform mathematical analyses and simulations of regulatory networks to better understand the potential trade-off between robustness and evolvability. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics, through the creation of regions presenting sudden changes in phenotype with small changes in genotype. For genotypes embedding low levels of nonlinearity, robustness and evolvability correlate negatively and almost perfectly. By contrast, genotypes embedding nonlinear dynamics allow expression levels to be robust to small perturbations, while generating high diversity (evolvability under larger perturbations. Thus, nonlinearity breaks the robustness-evolvability trade-off in gene expression levels by allowing disparate responses to different mutations. Using analytical derivations of robustness and system sensitivity, we show that these findings extend to a large class of gene regulatory network architectures and also hold for experimentally observed parameter regimes. Further, the effect of nonlinearity on the robustness-evolvability trade-off is ensured as long as key parameters of the system display specific relations irrespective of their absolute values. We find that within this parameter regime genotypes display low and noisy expression levels. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics. Our results provide a possible solution to the robustness-evolvability trade-off, suggest

NUMERICAL MODELING AND DYNAMIC SIMULATIONS OF NONLINEAR AEROTHERMOELASTIC OF A DOUBLE-WEDGE LIFTING SURFACE

Directory of Open Access Journals (Sweden)

ARIF A. EBRAHEEM AL-QASSAR

2008-12-01

Full Text Available The design of the re-entry space vehicles and high-speed aircrafts requires special attention to the nonlinear thermoelastic and aerodynamic instabilities of their structural components. The thermal effects are important since temperature environment influences significantly the static and dynamic behaviors of flight structures in supersonic/hypersonic regimes. To contribute to the understanding of dynamic behavior of these “hot” structures, a double-wedge lifting surface with combined freeplay and cubic stiffening structural nonlinearities in both plunging and pitching degrees-of-freedom operating in supersonic/hypersonic flight speed regimes has been analyzed. A third order Piston Theory Aerodynamics is used to evaluate the applied nonlinear unsteady aerodynamic loads. The loss of torsional stiffness that may be incurred by lifting surfaces subjected to axial stresses induced by aerodynamic heating is also considered. The aerodynamic heating effect is estimated based on the adiabatic wall temperature due to high speed airstreams. Modelling issues as well as simulation results have been presented and pertinent conclusions outlined. It is highlighted that a serious loss of torsional stiffness may induce the dynamic instability of the lifting surfaces. The influence of various parameters such as flight condition, thickness ratio, freeplays and pitching stiffness nonlinearity are also discussed.