The Gouy phase shift in nonlinear interactions of waves
Lastzka, Nico; Schnabel, Roman
2007-06-01
We theoretically analyze the influence of the Gouy phase shift on the nonlinear interaction between waves of different frequencies. We focus on χ(2)interaction of optical fields, e.g. through birefringent crystals, and show that focussing, stronger than suggested by the Boyd-Kleinman factor, can further improve nonlinear processes. An increased value of 3.32 for the optimal focussing parameter for a single pass process is found. The new value builds on the compensation of the Gouy phase shift by a spatially varying, instead constant, wave vector phase mismatch. We analyze the single-ended, singly resonant standing wave nonlinear cavity and show that in this case the Gouy phase shift leads to an additional phase during backreflection. Our numerical simulations may explain ill-understood experimental observations in such devices.
Nonlinear Phase Control and Anomalous Phase Matching in Plasmonic Metasurfaces
Almeida, Euclides; Prior, Yehiam
2015-01-01
Metasurfaces, and in particular those containing plasmonic-based metallic elements, constitute a particularly attractive set of materials. By means of modern nanolithographic fabrication techniques, flat, ultrathin optical elements may be constructed. However, in spite of their strong optical nonlinearities, plasmonic metasurfaces have so far been investigated mostly in the linear regime. Here we introduce full nonlinear phase control over plasmonic elements in metasurfaces. We show that for nonlinear interactions in a phase-gradient nonlinear metasurface a new anomalous nonlinear phase matching condition prevails, which is the nonlinear analog of the generalized Snell law demonstrated for linear metasurfaces. This phase matching condition is very different from the other known phase matching schemes. The subwavelength phase control of optical nonlinearities provides a foundation for the design of flat nonlinear optical elements based on metasurfaces. Our demonstrated flat nonlinear elements (i.e. lenses) act...
Hu, Kun; Peng, C. K.; Huang, Norden E.; Wu, Zhaohua; Lipsitz, Lewis A.; Cavallerano, Jerry; Novak, Vera
2008-04-01
Cerebral autoregulation is an important mechanism that involves dilatation and constriction in arterioles to maintain relatively stable cerebral blood flow in response to changes of systemic blood pressure. Traditional assessments of autoregulation focus on the changes of cerebral blood flow velocity in response to large blood pressure fluctuations induced by interventions. This approach is not feasible for patients with impaired autoregulation or cardiovascular regulation. Here we propose a newly developed technique-the multimodal pressure-flow (MMPF) analysis, which assesses autoregulation by quantifying nonlinear phase interactions between spontaneous oscillations in blood pressure and flow velocity during resting conditions. We show that cerebral autoregulation in healthy subjects can be characterized by specific phase shifts between spontaneous blood pressure and flow velocity oscillations, and the phase shifts are significantly reduced in diabetic subjects. Smaller phase shifts between oscillations in the two variables indicate more passive dependence of blood flow velocity on blood pressure, thus suggesting impaired cerebral autoregulation. Moreover, the reduction of the phase shifts in diabetes is observed not only in previously-recognized effective region of cerebral autoregulation (type 2 diabetes mellitus alters cerebral blood flow regulation over a wide frequency range and that this alteration can be reliably assessed from spontaneous oscillations in blood pressure and blood flow velocity during resting conditions. We also show that the MMPF method has better performance than traditional approaches based on Fourier transform, and is more suitable for the quantification of nonlinear phase interactions between nonstationary biological signals such as blood pressure and blood flow.
Berger, N. K.; Zhukov, E. A.; Novokhatskiĭ, V. V.
1984-04-01
The use of a semiconductor-metal phase transition for wavefront reversal of laser radiation was proposed. An investigation was made of nonlinear reflection of CO2 laser radiation at a phase transition in VO2. A three-wave interaction on a VO2 surface was achieved using low-power cw and pulsed CO2 lasers. In the first case, the intensity reflection coefficient was 0.5% for a reference wave intensity of 0.9 W/cm2 and in the second case, it was 42% for a threshold reference wave energy density of 0.6-0.8 mJ/cm2.
Nonlinear interaction of infrared waves on a VO2 surface at a semiconductor-metal phase transition
Berger, N. K.; Zhukov, E. A.; Novokhatskii, V. V.
1984-04-01
Nonlinear interactions (including wavefront reversal) of light from CW or pulsed 10.6-micron CO2 lasers at the semiconductor-metal phase transition in a VO2 film are investigated experimentally. The results are presented in graphs and characterized in detail. The intensity reflection coefficients of the three-wave interactions are found to be 0.5 percent for a CW reference wave of intensity 900 mW/sq cm and 42 percent for a pulsed reference wave of threshold density 600-800 microjoule/sq cm.
Nonlinear phased array imaging
Croxford, Anthony J.; Cheng, Jingwei; Potter, Jack N.
2016-04-01
A technique is presented for imaging acoustic nonlinearity within a specimen using ultrasonic phased arrays. Acoustic nonlinearity is measured by evaluating the difference in energy of the transmission bandwidth within the diffuse field produced through different focusing modes. The two different modes being classical beam forming, where delays are applied to different element of a phased array to physically focus the energy at a single location (parallel firing) and focusing in post processing, whereby one element at a time is fired and a focused image produced in post processing (sequential firing). Although these two approaches are linearly equivalent the difference in physical displacement within the specimen leads to differences in nonlinear effects. These differences are localized to the areas where the amplitude is different, essentially confining the differences to the focal point. Direct measurement at the focal point are however difficult to make. In order to measure this the diffuse field is used. It is a statistical property of the diffuse field that it represents the total energy in the system. If the energy in the diffuse field for both the sequential and parallel firing case is measured then the difference between these, within the input signal bandwidth, is largely due to differences at the focal spot. This difference therefore gives a localized measurement of where energy is moving out of the transmission bandwidth due to nonlinear effects. This technique is used to image fatigue cracks and other damage types undetectable with conventional linear ultrasonic measurements.
Phase retrieval using nonlinear diversity.
Lu, Chien-Hung; Barsi, Christopher; Williams, Matthew O; Kutz, J Nathan; Fleischer, Jason W
2013-04-01
We extend the Gerchberg-Saxton algorithm to phase retrieval in a nonlinear system. Using a tunable photorefractive crystal, we experimentally demonstrate the noninterferometric technique by reconstructing an unknown phase object from optical intensity measurements taken at different nonlinear strengths.
Lo, Men-Tzung; Novak, Vera; Peng, C-K; Liu, Yanhui; Hu, Kun
2009-06-01
Phase interactions among signals of physical and physiological systems can provide useful information about the underlying control mechanisms of the systems. Physical and biological recordings are often noisy and exhibit nonstationarities that can affect the estimation of phase interactions. We systematically studied effects of nonstationarities on two phase analyses including (i) the widely used transfer function analysis (TFA) that is based on Fourier decomposition and (ii) the recently proposed multimodal pressure flow (MMPF) analysis that is based on Hilbert-Huang transform (HHT)-an advanced nonlinear decomposition algorithm. We considered three types of nonstationarities that are often presented in physical and physiological signals: (i) missing segments of data, (ii) linear and step-function trends embedded in data, and (iii) multiple chaotic oscillatory components at different frequencies in data. By generating two coupled oscillatory signals with an assigned phase shift, we quantify the change in the estimated phase shift after imposing artificial nonstationarities into the oscillatory signals. We found that all three types of nonstationarities affect the performances of the Fourier-based and the HHT-based phase analyses, introducing bias and random errors in the estimation of the phase shift between two oscillatory signals. We also provided examples of nonstationarities in real physiological data (cerebral blood flow and blood pressure) and showed how nonstationarities can complicate result interpretation. Furthermore, we propose certain strategies that can be implemented in the TFA and the MMPF methods to reduce the effects of nonstationarities, thus improving the performances of the two methods.
2009-01-01
Phase interactions among signals of physical and physiological systems can provide useful information about the underlying control mechanisms of the systems. Physical and biological recordings are often noisy and exhibit nonstationarities that can affect the estimation of phase interactions. We systematically studied effects of nonstationarities on two phase analyses including (i) the widely used transfer function analysis (TFA) that is based on Fourier decomposition and (ii) the recently pro...
Nonlinear Light-Matter Interactions in Metamaterials
O'Brien, Kevin Patrick
Metamaterials possess extraordinary linear optical properties never observed in natural materials such as a negative refractive index, enabling exciting applications such as super resolution imaging and cloaking. In this thesis, we explore the equally extraordinary nonlinear properties of metamaterials. Nonlinear optics, the study of light-matter interactions where the optical fields are strong enough to change material properties, has fundamental importance to physics, chemistry, and material science as a non-destructive probe of material properties and has important technological applications such as entangled photon generation and frequency conversion. Due to their ability to manipulate both linear and nonlinear light matter interactions through sub-wavelength structuring, metamaterials are a promising direction for both fundamental and applied nonlinear optics research. We perform the first experiments on nonlinear propagation in bulk zero and negative index optical metamaterials and demonstrate that a zero index material can phase match four wave mixing processes in ways not possible in finite index materials. In addition, we demonstrate the ability of nonlinear scattering theory to describe the geometry dependence of second and third harmonic generation in plasmonic nanostructures. As an application of nonlinear metamaterials, we propose a phase matching technique called "resonant phase matching" to increase the gain and bandwidth of Josephson junction traveling wave parametric amplifiers. With collaborators, we demonstrate a best in class amplifier for superconducting qubit readout--over 20 dB gain with near quantum limited noise performance with a bandwidth and dynamic range an order of magnitude larger than alternative devices. In conclusion, we have demonstrated several ways in which nonlinear metamaterials surpass their natural counterparts. We look forward to the future of the field where nonlinear and quantum metamaterials will enable further new
Nonlinear phase noise in coherent optical OFDM transmission systems.
Zhu, Xianming; Kumar, Shiva
2010-03-29
We derive an analytical formula to estimate the variance of nonlinear phase noise caused by the interaction of amplified spontaneous emission (ASE) noise with fiber nonlinearity such as self-phase modulation (SPM), cross-phase modulation (XPM), and four-wave mixing (FWM) in coherent orthogonal frequency division multiplexing (OFDM) systems. The analytical results agree very well with numerical simulations, enabling the study of the nonlinear penalties in long-haul coherent OFDM systems without extensive numerical simulation. Our results show that the nonlinear phase noise induced by FWM is significantly larger than that induced by SPM and XPM, which is in contrast to traditional WDM systems where ASE-FWM interaction is negligible in quasi-linear systems. We also found that fiber chromatic dispersion can reduce the nonlinear phase noise. The variance of the total phase noise increases linearly with the bit rate, and does not depend significantly on the number of subcarriers for systems with moderate fiber chromatic dispersion.
VARIANCE OF NONLINEAR PHASE NOISE IN FIBER-OPTIC SYSTEM
RANJU KANWAR; SAMEKSHA BHASKAR
2013-01-01
In communication system, the noise process must be known, in order to compute the system performance. The nonlinear effects act as strong perturbation in long- haul system. This perturbation effects the signal, when interact with amplitude noise, and results in random motion of the phase of the signal. Based on the perturbation theory, the variance of nonlinear phase noise contaminated by both self- and cross-phase modulation, is derived analytically for phase-shift- keying system. Through th...
Berry phase in a generalized nonlinear two-level system
Institute of Scientific and Technical Information of China (English)
Liu Ji-Bing; Li Jia-Hua; Song Pei-Jun; Li Wei-Bin
2008-01-01
In this paper,we investigate the behaviour of the geometric phase of a more generalized nonlinear system composed of an effective two-level system interacting with a single-mode quantized cavity field.Both the field nonlinearity and the atom-field coupling nonlinearity are considered.We find that the geometric phase depends on whether the index k is an odd number or an even number in the resonant case.In addition,we also find that the geometric phase may be easily observed when the field nonlinearity is not considered.The fractional statistical phenomenon appears in this system if the strong nonlinear atom-field coupling is considered.We have also investigated the geometric phase of an effective two-level system interacting with a two-mode quantized cavity field.
Interaction nonlinearity in asphalt binders
Motamed, Arash; Bhasin, Amit; Liechti, Kenneth M.
2012-05-01
Asphalt mixtures are complex composites that comprise aggregate, asphalt binder, and air. Several research studies have shown that the mechanical behavior of the asphalt mixture is strongly influenced by the matrix, i.e. the asphalt binder. Characterization and a thorough understanding of the binder behavior is the first and crucial step towards developing an accurate constitutive model for the composite. Accurate constitutive models for the constituent materials are critical to ensure accurate performance predictions at a material and structural level using micromechanics. This paper presents the findings from a systematic investigation into the nature of the linear and nonlinear response of asphalt binders subjected to different types of loading using the Dynamic Shear Rheometer (DSR). Laboratory test data show that a compressive normal force is generated in an axially constrained specimen subjected to torsional shear. This paper investigates the source of this normal force and demonstrates that the asphalt binder can dilate when subjected to shear loads. This paper also presents the findings from a study conducted to investigate the source of the nonlinearity in the asphalt binder. Test results demonstrate that the application of cyclic shear loads results in the development of a normal force and a concomitant reduction in the dynamic shear modulus. This form of nonlinear response is referred to as an "interaction nonlinearity". A combination of experimental and analytical tools is used to demonstrate and verify the presence of this interaction nonlinearity in asphalt binders. The findings from this study highlight the importance of modeling the mechanical behavior of asphalt binders based on the overall stress state of the material.
Nonlinear Interaction of Waves in Geomaterials
Ostrovsky, L. A.
2009-05-01
Progress of 1990s - 2000s in studying vibroacoustic nonlinearities in geomaterials is largely related to experiments in resonance samples of rock and soils. It is now a common knowledge that many such materials are very strongly nonlinear, and they are characterized by hysteresis in the dependence between the stress and strain tensors, as well as by nonlinear relaxation ("slow time"). Elastic wave propagation in such media has many peculiarities; for example, third harmonic amplitude is a quadratic (not cubic as in classical solids) function of the main harmonic amplitude, and average wave velocity is linearly (not quadratically as usual) dependent on amplitude. The mechanisms of these peculiarities are related to complex structure of a material typically consisting of two phases: a hard matrix and relatively soft inclusions such as microcracks and grain contacts. Although most informative experimental results have been obtained in rock in the form of resonant bars, few theoretical models are yet available to describe and calculate waves interacting in such samples. In this presentation, a brief overview of structural vibroacoustic nonlinearities in rock is given first. Then, a simple but rather general approach to the description of wave interaction in solid resonators is developed based on accounting for resonance nonlinear perturbations which are cumulating from period to period. In particular, the similarity and the differences between traveling waves and counter-propagating waves are analyzed for materials with different stress-strain dependences. These data can be used for solving an inverse problem, i.e. characterizing nonlinear properties of a geomaterial by its measured vibroacoustic parameters. References: 1. L. Ostrovsky and P. Johnson, Riv. Nuovo Chimento, v. 24, 1-46, 2007 (a review); 2. L. Ostrovsky, J. Acoust. Soc. Amer., v. 116, 3348-3353, 2004.
Nonlinear Ultrasonic Phased Array Imaging
Potter, J. N.; Croxford, A. J.; Wilcox, P. D.
2014-10-01
This Letter reports a technique for the imaging of acoustic nonlinearity. By contrasting the energy of the diffuse field produced through the focusing of an ultrasonic array by delayed parallel element transmission with that produced by postprocessing of sequential transmission data, acoustic nonlinearity local to the focal point is measured. Spatially isolated wave distortion is inferred without requiring interrogation of the wave at the inspection point, thereby allowing nonlinear imaging through depth.
Nonlinear ultrasonic phased array imaging
Potter, J N; Croxford, A.J.; Wilcox, P. D.
2014-01-01
This Letter reports a technique for the imaging of acoustic nonlinearity. By contrasting the energy of the diffuse field produced through the focusing of an ultrasonic array by delayed parallel element transmission with that produced by postprocessing of sequential transmission data, acoustic nonlinearity local to the focal point is measured. Spatially isolated wave distortion is inferred without requiring interrogation of the wave at the inspection point, thereby allowing nonlinear imaging t...
Nonlinear ultrasonic phased array imaging.
Potter, J N; Croxford, A J; Wilcox, P D
2014-10-03
This Letter reports a technique for the imaging of acoustic nonlinearity. By contrasting the energy of the diffuse field produced through the focusing of an ultrasonic array by delayed parallel element transmission with that produced by postprocessing of sequential transmission data, acoustic nonlinearity local to the focal point is measured. Spatially isolated wave distortion is inferred without requiring interrogation of the wave at the inspection point, thereby allowing nonlinear imaging through depth.
Interactive optomechanical coupling with nonlinear polaritonic systems
Bobrovska, N; Liew, T C H; Kyriienko, O
2016-01-01
We study a system of interacting matter quasiparticles strongly coupled to photons inside an optomechanical cavity. The resulting normal modes of the system are represented by hybrid polaritonic quasiparticles, which acquire effective nonlinearity. Its strength is influenced by the presence of the mechanical mode and depends on the resonance frequency of the cavity. This leads to an interactive type of optomechanical coupling, being distinct from the previously studied dispersive and dissipative couplings in optomechanical systems. The emergent interactive coupling is shown to generate effective optical nonlinearity terms of high order, being quartic in the polariton number. We consider particular systems of exciton-polaritons and dipolaritons, and show that the induced effective optical nonlinearity due to the interactive coupling can exceed in magnitude the strength of Kerr nonlinear terms, such as those arising from polariton-polariton interactions. As applications, we show that the higher order terms give...
Nonlinear science an interactive Mathematica notebook
Campbell, David K; Tanury, Thomas A
2012-01-01
This interactive Mathematica(TM) notebook provides a ready-made tool by which users can undertake their own mathematical experiments and explore the behavior of non-linear systems, from chaos in low-dimensional maps and coupled ordinary differential equations to solitons and coherent structures in nonlinear partial differential equations and "intrisic localized modes" and "discrete breathers" in extended lattice systems.
VARIANCE OF NONLINEAR PHASE NOISE IN FIBER-OPTIC SYSTEM
Directory of Open Access Journals (Sweden)
RANJU KANWAR
2013-04-01
Full Text Available In communication system, the noise process must be known, in order to compute the system performance. The nonlinear effects act as strong perturbation in long- haul system. This perturbation effects the signal, when interact with amplitude noise, and results in random motion of the phase of the signal. Based on the perturbation theory, the variance of nonlinear phase noise contaminated by both self- and cross-phase modulation, is derived analytically for phase-shift- keying system. Through this work, it is investigated that for longer transmission distance, 40-Gb/s systems are more sensitive to nonlinear phase noise as compared to 50-Gb/s systems. Also, when transmitting the data through the fiber optic link, bit errors are produced due to various effects such as noise from optical amplifiers and nonlinearity occurring in fiber. On the basis of the simulation results , we have compared the bit error rate based on 8-PSK with theoretical results, and result shows that in real time approach, the bit error rate is high for the same signal to noise ratio. MATLAB software is used to validate the analytical expressions for the variance of nonlinear phase noise.
Kinetic equation for nonlinear resonant wave-particle interaction
Artemyev, A. V.; Neishtadt, A. I.; Vasiliev, A. A.; Mourenas, D.
2016-09-01
We investigate the nonlinear resonant wave-particle interactions including the effects of particle (phase) trapping, detrapping, and scattering by high-amplitude coherent waves. After deriving the relationship between probability of trapping and velocity of particle drift induced by nonlinear scattering (phase bunching), we substitute this relation and other characteristic equations of wave-particle interaction into a kinetic equation for the particle distribution function. The final equation has the form of a Fokker-Planck equation with peculiar advection and collision terms. This equation fully describes the evolution of particle momentum distribution due to particle diffusion, nonlinear drift, and fast transport in phase-space via trapping. Solutions of the obtained kinetic equation are compared with results of test particle simulations.
Colloquium: Nonlinear Collective Interactions in Dense Plasmas
Shukla, P K
2010-01-01
The current understanding of some important collective processes in dense quantum plasmas is presented. After reviewing the basic properties of dense quantum plasmas with degenerate electrons, we present model equations (e.g. the quantum hydrodynamic and effective nonlinear Schr\\"odinger-Poisson equations) that describe collective nonlinear phenomena at nanoscales. The effects of the electron degeneracy arise due to Heisenberg's uncertainty principle and Pauli's exclusion principle for overlapping electron wave functions that result in a nonlinear quantum electron pressure and tunneling/diffusion of electrons through a nonlinear quantum Bohm potential. Since degenerate electrons have $1/2-$spin due to their Fermionic nature, there also appear a spin electron current and a spin force acting on the electrons due to the Bohr magnetization. The present nonlinear equations do not include strong electron correlations and electron-exchange interactions. The quantum effects caused by the electron degeneracy produce n...
Soil-structure interaction including nonlinear soil
Gicev, Vlado
2008-01-01
There are two types of models of soil-structure system depending upon the rigidity of foundation: models with rigid and models with flexible foundation. Main features of the soil-structure interaction phenomenon: -wave scattering, -radiation damping, -reduction of the system frequencies. In this presentation, the influence of interaction on the development of nonlinear zones in the soil is studied.
Symmetry, phase modulation and nonlinear waves
Bridges, Thomas J
2017-01-01
Nonlinear waves are pervasive in nature, but are often elusive when they are modelled and analysed. This book develops a natural approach to the problem based on phase modulation. It is both an elaboration of the use of phase modulation for the study of nonlinear waves and a compendium of background results in mathematics, such as Hamiltonian systems, symplectic geometry, conservation laws, Noether theory, Lagrangian field theory and analysis, all of which combine to generate the new theory of phase modulation. While the build-up of theory can be intensive, the resulting emergent partial differential equations are relatively simple. A key outcome of the theory is that the coefficients in the emergent modulation equations are universal and easy to calculate. This book gives several examples of the implications in the theory of fluid mechanics and points to a wide range of new applications.
Nonlinear wave interactions in quantum magnetoplasmas
Shukla, P K; Marklund, M; Stenflo, L
2006-01-01
Nonlinear interactions involving electrostatic upper-hybrid (UH), ion-cyclotron (IC), lower-hybrid (LH), and Alfven waves in quantum magnetoplasmas are considered. For this purpose, the quantum hydrodynamical equations are used to derive the governing equations for nonlinearly coupled UH, IC, LH, and Alfven waves. The equations are then Fourier analyzed to obtain nonlinear dispersion relations, which admit both decay and modulational instabilities of the UH waves at quantum scales. The growth rates of the instabilities are presented. They can be useful in applications of our work to diagnostics in laboratory and astrophysical settings.
Tunable Resonators for Nonlinear Modal Interactions
Ramini, Abdallah
2016-10-04
Understanding the various mechanisms of nonlinear mode coupling in micro and nano resonators has become an imminent necessity for their successful implementation in practical applications. However, consistent, repeatable, and flexible experimental procedures to produce nonlinear mode coupling are lacking, and hence research into well-controlled experimental conditions is crucial. Here, we demonstrate well-controlled and repeatable experiments to study nonlinear mode coupling among micro and nano beam resonators. Such experimental approach can be applied to other micro and nano structures to help study their nonlinear interactions and exploit them for higher sensitive and less noisy responses. Using electrothermal tuning and electrostatic excitation, we demonstrate three different kinds of nonlinear interactions among the first and third bending modes of vibrations of slightly curved beams (arches): two-one internal resonance, three-one internal resonance, and mode veering (near crossing). The experimental procedure is repeatable, highly flexible, do not require special or precise fabrication, and is conducted in air and at room temperature. This approach can be applied to other micro and nano structures, which come naturally curved due to fabrication imperfections, such as CNTs, and hence lays the foundation to deeply investigate the nonlinear mode coupling in these structures in a consistent way.
Tunable Resonators for Nonlinear Modal Interactions
Ramini, Abdallah H.; Hajjaj, Amal Z.; Younis, Mohammad I.
2016-10-01
Understanding the various mechanisms of nonlinear mode coupling in micro and nano resonators has become an imminent necessity for their successful implementation in practical applications. However, consistent, repeatable, and flexible experimental procedures to produce nonlinear mode coupling are lacking, and hence research into well-controlled experimental conditions is crucial. Here, we demonstrate well-controlled and repeatable experiments to study nonlinear mode coupling among micro and nano beam resonators. Such experimental approach can be applied to other micro and nano structures to help study their nonlinear interactions and exploit them for higher sensitive and less noisy responses. Using electrothermal tuning and electrostatic excitation, we demonstrate three different kinds of nonlinear interactions among the first and third bending modes of vibrations of slightly curved beams (arches): two-one internal resonance, three-one internal resonance, and mode veering (near crossing). The experimental procedure is repeatable, highly flexible, do not require special or precise fabrication, and is conducted in air and at room temperature. This approach can be applied to other micro and nano structures, which come naturally curved due to fabrication imperfections, such as CNTs, and hence lays the foundation to deeply investigate the nonlinear mode coupling in these structures in a consistent way.
Nonlinear waves in strongly interacting relativistic fluids
Fogaça, D A; Filho, L G Ferreira
2013-01-01
During the past decades the study of strongly interacting fluids experienced a tremendous progress. In the relativistic heavy ion accelerators, specially the RHIC and LHC colliders, it became possible to study not only fluids made of hadronic matter but also fluids of quarks and gluons. Part of the physics program of these machines is the observation of waves in this strongly interacting medium. From the theoretical point of view, these waves are often treated with li-nearized hydrodynamics. In this text we review the attempts to go beyond linearization. We show how to use the Reductive Perturbation Method to expand the equations of (ideal and viscous) relativistic hydrodynamics to obtain nonlinear wave equations. These nonlinear wave equations govern the evolution of energy density perturbations (in hot quark gluon plasma) or baryon density perturbations (in cold quark gluon plasma and nuclear matter). Different nonlinear wave equations, such as the breaking wave, Korteweg-de Vries and Burgers equations, are...
Nonlinear dynamics of interacting populations
Bazykin, Alexander D
1998-01-01
This book contains a systematic study of ecological communities of two or three interacting populations. Starting from the Lotka-Volterra system, various regulating factors are considered, such as rates of birth and death, predation and competition. The different factors can have a stabilizing or a destabilizing effect on the community, and their interplay leads to increasingly complicated behavior. Studying and understanding this path to greater dynamical complexity of ecological systems constitutes the backbone of this book. On the mathematical side, the tool of choice is the qualitative the
Nonlinear interactions for massive spin-2 fields
Schmidt-May, Angnis
2016-01-01
We give a basic introduction to ghost-free nonlinear theories involving massive spin-2 fields, focussing on bimetric theory. After motivating the construction of such models from field theoretical considerations, we review the linear theories for massive and massless spin-2 fluctuations propagating on maximally symmetric backgrounds. The structure of general nonlinear spin-2 interactions is explained before we specialise to the ghost-free case. We review the maximally symmetric solutions of bimetric theory, its mass spectrum and the parameter limit which brings the theory close to general relativity. Finally we discuss applications of bimetric theory to cosmology with particular emphasis on the role of the general relativity limit.
Beam Combining by Phase Transition Nonlinear Media
1990-02-01
use the Redlich Kwong equation of state for the media we consider. This equation of state can be written RT a p - -b -FT(p.-’ + b)p ; 2-I M (2-1) where...as ac 3 dg-A7 C VA/\\CIIJT (6) The Redlich - Kwong equation of state; i.e., _ RT T-1/2 v-P v(v+P) (7) can be used to compute aP/lT, where the relevant...practical the application of nonlinear phase conjugate techniques to the beam combining of multiple lasers with a coherence characteristic of a
Phase reduction approach to synchronisation of nonlinear oscillators
Nakao, Hiroya
2016-04-01
Systems of dynamical elements exhibiting spontaneous rhythms are found in various fields of science and engineering, including physics, chemistry, biology, physiology, and mechanical and electrical engineering. Such dynamical elements are often modelled as nonlinear limit-cycle oscillators. In this article, we briefly review phase reduction theory, which is a simple and powerful method for analysing the synchronisation properties of limit-cycle oscillators exhibiting rhythmic dynamics. Through phase reduction theory, we can systematically simplify the nonlinear multi-dimensional differential equations describing a limit-cycle oscillator to a one-dimensional phase equation, which is much easier to analyse. Classical applications of this theory, i.e. the phase locking of an oscillator to a periodic external forcing and the mutual synchronisation of interacting oscillators, are explained. Further, more recent applications of this theory to the synchronisation of non-interacting oscillators induced by common noise and the dynamics of coupled oscillators on complex networks are discussed. We also comment on some recent advances in phase reduction theory for noise-driven oscillators and rhythmic spatiotemporal patterns.
Non-Linear Dynamics and Fundamental Interactions
Khanna, Faqir
2006-01-01
The book is directed to researchers and graduate students pursuing an advanced degree. It provides details of techniques directed towards solving problems in non-linear dynamics and chos that are, in general, not amenable to a perturbative treatment. The consideration of fundamental interactions is a prime example where non-perturbative techniques are needed. Extension of these techniques to finite temperature problems is considered. At present these ideas are primarily used in a perturbative context. However, non-perturbative techniques have been considered in some specific cases. Experts in the field on non-linear dynamics and chaos and fundamental interactions elaborate the techniques and provide a critical look at the present status and explore future directions that may be fruitful. The text of the main talks will be very useful to young graduate students who are starting their studies in these areas.
Phase reduction theory for hybrid nonlinear oscillators
Shirasaka, Sho; Kurebayashi, Wataru; Nakao, Hiroya
2017-01-01
Hybrid dynamical systems characterized by discrete switching of smooth dynamics have been used to model various rhythmic phenomena. However, the phase reduction theory, a fundamental framework for analyzing the synchronization of limit-cycle oscillations in rhythmic systems, has mostly been restricted to smooth dynamical systems. Here we develop a general phase reduction theory for weakly perturbed limit cycles in hybrid dynamical systems that facilitates analysis, control, and optimization of nonlinear oscillators whose smooth models are unavailable or intractable. On the basis of the generalized theory, we analyze injection locking of hybrid limit-cycle oscillators by periodic forcing and reveal their characteristic synchronization properties, such as ultrafast and robust entrainment to the periodic forcing and logarithmic scaling at the synchronization transition. We also illustrate the theory by analyzing the synchronization dynamics of a simple physical model of biped locomotion.
Nonlinear interactions between gravity waves and tides
Institute of Scientific and Technical Information of China (English)
LIU Xiao; XU JiYao; MA RuiPing
2007-01-01
In this study, we present the nonlinear interactions between gravity waves (GWs) and tides by using the 2D numerical model for the nonlinear propagation of GWs in the compressible atmosphere. During the propagation in the tidal background, GWs become instable in three regions, that is z = 75-85 km, z =90-110 km and z= 115-130 km. The vertical wavelength firstly varies gradually from the initial 12 km to 27 km. Then the newly generated longer waves are gradually compressed. The longer and shorter waves occur in the regions where GWs propagate in the reverse and the same direction of the horizontal mean wind respectively. In addition, GWs can propagate above the main breaking region (90-110 km). During GWs propagation, not only the mean wind is accelerated, but also the amplitude of tide is amplified. Especially, after GWs become instable, this amplified effect to the tidal amplitude is much obvious.
Nonlinear interactions between gravity waves and tides
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this study, we present the nonlinear interactions between gravity waves (GWs) and tides by using the 2D numerical model for the nonlinear propagation of GWs in the compressible atmosphere. During the propagation in the tidal background, GWs become instable in three regions, that is z = 75―85 km, z = 90―110 km and z = 115―130 km. The vertical wavelength firstly varies gradually from the initial 12 km to 27 km. Then the newly generated longer waves are gradually compressed. The longer and shorter waves occur in the regions where GWs propagate in the reverse and the same direction of the hori-zontal mean wind respectively. In addition, GWs can propagate above the main breaking region (90—110 km). During GWs propagation, not only the mean wind is accelerated, but also the amplitude of tide is amplified. Especially, after GWs become instable, this amplified effect to the tidal amplitude is much obvious.
Nonlinear Electromagnetic Interactions in Energetic Materials
Wood, M A; Moore, D S
2016-01-01
We study the scattering of electromagnetic waves in anisotropic energetic materials. Nonlinear light-matter interactions in molecular crystals result in frequency-conversion and polarization changes. Applied electromagnetic fields of moderate intensity can induce these nonlinear effects without triggering chemical decomposition, offering a mechanism for non-ionizing identification of explosives. We use molecular dynamics simulations to compute such two-dimensional Raman spectra in the terahertz range for planar slabs made of PETN and ammonium nitrate. We discuss third-harmonic generation and polarization-conversion processes in such materials. These observed far-field spectral features of the reflected or transmitted light may serve as an alternative tool for stand-off explosive detection.
Nonlinear shallow ocean-wave soliton interactions on flat beaches.
Ablowitz, Mark J; Baldwin, Douglas E
2012-09-01
Ocean waves are complex and often turbulent. While most ocean-wave interactions are essentially linear, sometimes two or more waves interact in a nonlinear way. For example, two or more waves can interact and yield waves that are much taller than the sum of the original wave heights. Most of these shallow-water nonlinear interactions look like an X or a Y or two connected Ys; at other times, several lines appear on each side of the interaction region. It was thought that such nonlinear interactions are rare events: they are not. Here we report that such nonlinear interactions occur every day, close to low tide, on two flat beaches that are about 2000 km apart. These interactions are closely related to the analytic, soliton solutions of a widely studied multidimensional nonlinear wave equation. On a much larger scale, tsunami waves can merge in similar ways.
Nonlinear processes in the strong wave-plasma interaction
Pegoraro, Francesco; Califano, Francesco; Attico, Nicola; Bulanov, Sergei
2000-10-01
Nonlinear interactions in hot laboratory and/or astrophysical plasmas are a very efficient mechanism able to transfer the energy from the large to the small spatial scales of the system. As a result, kinetic processes are excited and play a key role in the plasma dynamics since the typical fluid dissipative length scales (where the nonlinear cascade is stopped) are (much) smaller then the kinetic length scales. Then, the key point is the role of the kinetic effects in the global plasma dynamics, i.e. whether the kinetic effects remains confined to the small scales of the system or whether there is a significant feedback on the large scales. Here we will address this problem by discussing the nonlinear kinetic evolution of the electromagnetic beam plasma instability where phase space vortices, as well as large scale vortex like magnetic structures in the physical space, are generated by wave - particle interactions. The role and influence of kinetic effects on the large scale plasma dynamics will be also discussed by addressing the problem of collisionless magnetic reconection.
Complex Nonlinearity Chaos, Phase Transitions, Topology Change and Path Integrals
Ivancevic, Vladimir G
2008-01-01
Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to th...
Holographic paramagnetism-ferromagnetism phase transition with the nonlinear electrodynamics
Zhang, Cheng-Yuan; Zhang, Ya-Nan; Wang, Huan-Yu; Wu, Meng-Meng
2016-01-01
In the probe limit, we investigate the nonlinear electrodynamical effects of the both exponential form and the logarithmic form on the holographic paramagnetism-ferromagnetism phase transition in the background of a Schwarzschild-AdS black hole spacetime. Moreover, by comparing the exponential form of nonlinear electrodynamics with the logarithmic form of nonlinear electrodynamics and the Born-Infeld nonlinear electrodynamics which has been presented in Ref.~\\cite{Wu:2016uyj}, we find that the higher nonlinear electrodynamics correction makes the critical temperature smaller and the magnetic moment harder form in the case without external field. Furthermore, the increase of nonlinear parameter b will result in extending the period of the external magnetic field. Especially, the effect of the exponential form of nonlinear electrodynamics on the periodicity of hysteresis loop is more noticeable.
Exotic quantum phase transitions of strongly interacting topological insulators
Slagle, Kevin; You, Yi-Zhuang; Xu, Cenke
2015-03-01
Using determinant quantum Monte Carlo simulations, we demonstrate that an extended Hubbard model on a bilayer honeycomb lattice has two novel quantum phase transitions. The first is a quantum phase transition between the weakly interacting gapless Dirac fermion phase and a strongly interacting fully gapped and symmetric trivial phase, which cannot be described by the standard Gross-Neveu model. The second is a quantum critical point between a quantum spin Hall insulator with spin Sz conservation and the previously mentioned strongly interacting fully gapped phase. At the latter quantum critical point the single-particle excitations remain gapped, while spin and charge gaps both close. We argue that the first quantum phase transition is related to the Z16 classification of the topological superconductor 3He-B phase with interactions, while the second quantum phase transition is a topological phase transition described by a bosonic O (4 ) nonlinear sigma model field theory with a Θ term.
Harmonic Phase Response of Nonlinear Radar Targets
2015-10-01
to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT...of an improvised explosive device (IED). Previous nonlinear radar systems detect targets via transmission of a single frequency ω, stepping...electronically nonlinear components, such as transistors, diodes , and semiconductors. While many circuit devices, such as amplifiers, mixers, and
Dark Spatial Soliton Interaction in Nonlinear Kerr Medium
Institute of Scientific and Technical Information of China (English)
LuchuanWANG; QinliangFAN
1998-01-01
The dark spatial soliton interaction in nonlinear Kerr medium has been studied in this paper.The problem has been solved by the use of the slowly varying envelope approximation in solving coupled nonlinear Schroedinger equations.The perturbation nature of dark spatial soliton interaction has been described and some of their key properties has been discussed as well in the paper.
Anomalous interaction of nonlocal solitons in media with competing nonlinearities
DEFF Research Database (Denmark)
Esbensen, B. K.; Bache, Morten; Bang, Ole
2012-01-01
We theoretically investigate properties of individual bright spatial solitons and their interaction in nonlocal media with competing focusing and defocusing nonlinearities. We consider the general case with both nonlinear responses characterized by different strengths and degrees of nonlocality. We...... and interaction of solitons using numerical simulations of the full model of beam propagation. The numerical simulations fully confirm our analytical results....
Subwavelength nonlinear phase control and anomalous phase matching in plasmonic metasurfaces
Almeida, Euclides; Shalem, Guy; Prior, Yehiam
2016-01-01
Metasurfaces, and in particular those containing plasmonic-based metallic elements, constitute an attractive set of materials with a potential for replacing standard bulky optical elements. In recent years, increasing attention has been focused on their nonlinear optical properties, particularly in the context of second and third harmonic generation and beam steering by phase gratings. Here, we harness the full phase control enabled by subwavelength plasmonic elements to demonstrate a unique metasurface phase matching that is required for efficient nonlinear processes. We discuss the difference between scattering by a grating and by subwavelength phase-gradient elements. We show that for such interfaces an anomalous phase-matching condition prevails, which is the nonlinear analogue of the generalized Snell's law. The subwavelength phase control of optical nonlinearities paves the way for the design of ultrathin, flat nonlinear optical elements. We demonstrate nonlinear metasurface lenses, which act both as generators and as manipulators of the frequency-converted signal.
Phase Relation of Harmonics in Nonlinear Focused Ultrasound
Institute of Scientific and Technical Information of China (English)
Zhe-Fan Peng; Wei-Jun Lin; Shi-Lei Liu; Chang Su; Hai-Lan Zhang; Xiu-Ming Wang
2016-01-01
The phase relation of harmonics in high-intensity focused ultrasound is investigated numerically and experimentally.The nonlinear Westervelt equation is solved to model nonlinear focused sound field by using the finite difference time domain method.Experimental waveforms are measured by a robust needle hydrophone.Then the relative phase quantity is introduced and obtained by using the zero-phase filter.The results show that the nth harmonic relative phase quantity is approximately (n-1)π/3 at geometric center and increases along the axial direction.Moreover,the relative phase quantity decreases with the increase of source amplitude.This phase relation gives an explanation of some nonlinear phenomena such as the discrepancy of positive and negative pressure.
Nonlinear optical interactions in silicon waveguides
Kuyken, B.; Leo, F.; Clemmen, S.; Dave, U.; Van Laer, R.; Ideguchi, T.; Zhao, H.; Liu, X.; Safioui, J.; Coen, S.; Gorza, S. P.; Selvaraja, S. K.; Massar, S.; Osgood, R. M.; Verheyen, P.; Van Campenhout, J.; Baets, R.; Green, W. M. J.; Roelkens, G.
2017-03-01
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.
Extra phase noise from thermal fluctuations in nonlinear optical crystals
DEFF Research Database (Denmark)
César, J. E. S.; Coelho, A.S.; Cassemiro, K.N.
2009-01-01
We show theoretically and experimentally that scattered light by thermal phonons inside a second-order nonlinear crystal is the source of additional phase noise observed in optical parametric oscillators. This additional phase noise reduces the quantum correlations and has hitherto hindered the d...... the direct production of multipartite entanglement in a single nonlinear optical system. We cooled the nonlinear crystal and observed a reduction in the extra noise. Our treatment of this noise can be successfully applied to different systems in the literature....
Soliton pair generation in the interactions of Airy and nonlinear accelerating beams
Zhang, Yiqi; Wu, Zhenkun; Zheng, Huaibin; Lu, Keqing; Li, Yuanyuan; Zhang, Yanpeng
2013-01-01
We investigate numerically the interactions of two in-phase and out-of-phase Airy beams and nonlinear accelerating beams in Kerr and saturable nonlinear media, in one transverse dimension. We find that bound and unbound soliton pairs, as well as single solitons, can form in such interactions. If the interval between two incident beams is large relative to the width of their first lobes, the generated soliton pairs just propagate individually and do not interact. However, if the interval is comparable to the widths of the maximum lobes, the pairs interact and display varied behavior. In the in-phase case, they attract each other and exhibit stable bound, oscillating, and unbound states, after shedding some radiation initially. In the out-of-phase case, they repel each other and after an initial interaction, fly away as individual solitons. While the incident beams display acceleration, the solitons or soliton pairs generated from those beams do not.
Thermodynamics of Phase Transitions of a Kerr Nonlinear Blackbody
Institute of Scientific and Technical Information of China (English)
CHENG Ze
2008-01-01
We study the thermodynamics of phase transitions of a blackbody whose interior is filled by a Kerr nonlinear crystal. There is a transition temperature To, above which the Kerr nonlinear blackbody is in the normal thermal radiation state, and below which it is in the squeezed thermal radiation state. At To, the Gibbs free energy of the two phases is continuous but the entropy density of the two phases is discontinuous. Hence, there is a jump in the entropy density and this leads to a latent heat density. The photon system undergoes a first-order phase transition from the normal to the squeezed thermal radiation state.
Phase mixing and nonlinearity in geodesic acoustic modes
Energy Technology Data Exchange (ETDEWEB)
Hung, C. P.; Hassam, A. B. [University of Maryland at College Park, College Park, Maryland 20742 (United States)
2013-09-15
Phase mixing and nonlinear resonance detuning of geodesic acoustic modes in a tokamak plasma are examined. Geodesic acoustic modes (GAMs) are tokamak normal modes with oscillations in poloidal flow constrained to lie within flux surfaces. The mode frequency is sonic, dependent on the local flux surface temperature. Consequently, mode oscillations between flux surfaces get rapidly out of phase, resulting in enhanced damping from the phase mixing. Damping rates are shown to scale as the negative 1/3 power of the large viscous Reynolds number. The effect of convective nonlinearities on the normal modes is also studied. The system of nonlinear GAM equations is shown to resemble the Duffing oscillator, which predicts resonance detuning of the oscillator. Resonant amplification is shown to be suppressed nonlinearly. All analyses are verified by numerical simulation. The findings are applied to a recently proposed GAM excitation experiment on the DIII-D tokamak.
Phased-array sources based on nonlinear metamaterial nanocavities.
Wolf, Omri; Campione, Salvatore; Benz, Alexander; Ravikumar, Arvind P; Liu, Sheng; Luk, Ting S; Kadlec, Emil A; Shaner, Eric A; Klem, John F; Sinclair, Michael B; Brener, Igal
2015-07-01
Coherent superposition of light from subwavelength sources is an attractive prospect for the manipulation of the direction, shape and polarization of optical beams. This phenomenon constitutes the basis of phased arrays, commonly used at microwave and radio frequencies. Here we propose a new concept for phased-array sources at infrared frequencies based on metamaterial nanocavities coupled to a highly nonlinear semiconductor heterostructure. Optical pumping of the nanocavity induces a localized, phase-locked, nonlinear resonant polarization that acts as a source feed for a higher-order resonance of the nanocavity. Varying the nanocavity design enables the production of beams with arbitrary shape and polarization. As an example, we demonstrate two second harmonic phased-array sources that perform two optical functions at the second harmonic wavelength (∼5 μm): a beam splitter and a polarizing beam splitter. Proper design of the nanocavity and nonlinear heterostructure will enable such phased arrays to span most of the infrared spectrum.
Nonlinear Landau-Zener tunneling in quantum phase space
Energy Technology Data Exchange (ETDEWEB)
Trimborn, F [Institut fuer theoretische Physik, Leibniz Universitaet Hannover, D-30167 Hannover (Germany); Witthaut, D [QUANTOP, Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen (Denmark); Kegel, V; Korsch, H J, E-mail: friederike.trimborn@itp.uni-hannover.d [Fachbereich Physik, TU Kaiserslautern, D-67663 Kaiserslautern (Germany)
2010-05-15
We present a detailed analysis of the Landau-Zener problem for an interacting Bose-Einstein condensate in a time-varying double-well trap, especially focusing on the relation between the full many-particle problem and the mean-field approximation. Due to the nonlinear self-interaction a dynamical instability occurs, which leads to a breakdown of adiabaticity and thus fundamentally alters the dynamics. It is shown that essentially all the features of the Landau-Zener problem including the depletion of the condensate mode can be already understood within a semiclassical phase-space picture. In particular, this treatment resolves the formerly imputed incommutability of the adiabatic and semiclassical limits. The possibility of exploiting Landau-Zener sweeps to generate squeezed states for spectroscopic tasks is analyzed in detail. Moreover, we study the influence of phase noise and propose a Landau-Zener sweep as a sensitive yet readily implementable probe for decoherence, since the noise has significant effect on the transition rate for slow parameter variations.
Nonlinear Landau-Zener tunneling in quantum phase space
Trimborn, F; Kegel, V; Korsch, H J; 10.1088/1367-2630/12/5/053010
2010-01-01
We present a detailed analysis of the Landau-Zener problem for an interacting Bose-Einstein condensate in a time-varying double-well trap, especially focussing on the relation between the full many-particle problem and the mean-field approximation. Due to the nonlinear self-interaction a dynamical instability occurs, which leads to a breakdown of adiabaticity condition and thus fundamentally alters the dynamics. It is shown that essentially all features of the Landau-Zener problem including the depletion of the condensate mode can be already understood within a semiclassical phase space picture. In particular, this treatment resolves the formerly imputed incommutability of the adiabatic and semiclassical limits. The possibility to exploit Landau-Zener sweeps to generate squeezed states for spectroscopic tasks is analysed in detail. Moreover, we study the influence of phase noise and propose a Landau-Zener sweep as a sensitive, yet readily implementable probe for decoherence, since this has a significant effec...
Interacting Weyl fermions: Phases, phase transitions, and global phase diagram
Roy, Bitan; Goswami, Pallab; Juričić, Vladimir
2017-05-01
We study the effects of short-range interactions on a generalized three-dimensional Weyl semimetal, where the band touching points act as the (anti)monopoles of Abelian Berry curvature of strength n . We show that any local interaction has a negative scaling dimension -2 /n . Consequently, all Weyl semimetals are stable against weak short-range interactions. For sufficiently strong interactions, we demonstrate that the Weyl semimetal either undergoes a first-order transition into a band insulator or a continuous transition into a symmetry breaking phase. A translational symmetry breaking axion insulator and a rotational symmetry breaking semimetal are two prominent candidates for the broken symmetry phase. At the one-loop order, the correlation length exponent for continuous transitions is ν =n /2 , indicating their non-Gaussian nature for any n >1 . We also discuss the scaling of the thermodynamic and transport quantities in general Weyl semimetals as well as inside broken symmetry phases.
Phase sensitivity in deformed-state superposition considering nonlinear phase shifts
Berrada, K.
2016-07-01
We study the problem of the phase estimation for the deformation-state superposition (DSS) under perfect and lossy (due to a dissipative interaction of DSS with their environment) regimes. The study is also devoted to the phase enhancement of the quantum states resulting from a generalized non-linearity of the phase shifts, both without and with losses. We find that such a kind of superposition can give the smallest variance in the phase parameter in comparison with usual Schrödinger cat states in different order of non-linearity even if for a larger average number of photons. Due to the significance of how a system is quantum correlated with its environment in the construction of a scalable quantum computer, the entanglement between the DSS and its environment is investigated during the dissipation. We show that partial entanglement trapping occurs during the dynamics depending on the kind of deformation and mean photon number. These features make the DSS with a larger average number of photons a good candidate for implementation of schemes of quantum optics and information with high precision.
Two-dimensional simulations of nonlinear beam-plasma interaction in isotropic and magnetized plasmas
Timofeev, I V
2012-01-01
Nonlinear interaction of a low density electron beam with a uniform plasma is studied using two-dimensional particle-in-cell (PIC) simulations. We focus on formation of coherent phase space structures in the case, when a wide two-dimensional wave spectrum is driven unstable, and we also study how nonlinear evolution of these structures is affected by the external magnetic field. In the case of isotropic plasma, nonlinear buildup of filamentation modes due to the combined effects of two-stream and oblique instabilities is found to exist and growth mechanisms of secondary instabilities destroying the BGK--type nonlinear wave are identified. In the weak magnetic field, the energy of beam-excited plasma waves at the nonlinear stage of beam-plasma interaction goes predominantly to the short-wavelength upper-hybrid waves propagating parallel to the magnetic field, whereas in the strong magnetic field the spectral energy is transferred to the electrostatic whistlers with oblique propagation.
DEFF Research Database (Denmark)
Guo, Hairun; Zeng, Xianglong; Zhou, Binbin
2013-01-01
We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic...
Interacting Weyl fermions: Phases, phase transitions and global phase diagram
Roy, Bitan; Juricic, Vladimir
2016-01-01
We study the effects of short-range interactions on a generalized three-dimensional Weyl semimetal, where the band touching points act as the (anti)monopoles of Abelian Berry curvature of strength $n$. We show that any local interaction has a \\emph{negative} scaling dimension $-2/n$. Consequently all Weyl semimetals are stable against weak short-range interactions. For sufficiently strong interactions, we demonstrate that the Weyl semimetal either undergoes a first order transition into a band insulator or a continuous transition into a symmetry breaking phase. A translational symmetry breaking axion insulator and a rotational symmetry breaking semimetal are two prominent candidates for the broken symmetry phase. At one loop level, the correlation length exponent for continuous transitions is $\
Probabilistic approach to nonlinear wave-particle resonant interaction
Artemyev, A. V.; Neishtadt, A. I.; Vasiliev, A. A.; Mourenas, D.
2017-02-01
In this paper we provide a theoretical model describing the evolution of the charged-particle distribution function in a system with nonlinear wave-particle interactions. Considering a system with strong electrostatic waves propagating in an inhomogeneous magnetic field, we demonstrate that individual particle motion can be characterized by the probability of trapping into the resonance with the wave and by the efficiency of scattering at resonance. These characteristics, being derived for a particular plasma system, can be used to construct a kinetic equation (or generalized Fokker-Planck equation) modeling the long-term evolution of the particle distribution. In this equation, effects of charged-particle trapping and transport in phase space are simulated with a nonlocal operator. We demonstrate that solutions of the derived kinetic equations agree with results of test-particle tracing. The applicability of the proposed approach for the description of space and laboratory plasma systems is also discussed.
Inverse problem for multi-body interaction of nonlinear waves
Marruzzo, Alessia; Antenucci, Fabrizio; Pagnani, Andrea; Leuzzi, Luca
2016-01-01
The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we test two methods based on pseudolikelihood, respectively with regularization and with decimation, to determine the coupling constants from sets of measured configurations. We test statistical inference predictions for increasing number of sampled configurations and for an externally tunable {\\em temperature}-like parameter mimicing real data noise and helping minimization procedures. Analyzed models with phasors and rotors are generalizations of problems of real-valued spherical problems (e.g., density fluctuations), discrete spins (Ising and vectorial Potts) or finite number of states (standard Potts): inference methods presented here can, then, be straightforward applied to a large class of inverse problems.
Nonlinear Transformation of Orbital Angular Momentum through Quasi-phase Matching
Shao, Guang-hao; Chen, Jin-hui; Xu, Fei; Lu, Yan-qing
2013-01-01
We propose and investigate the quasi-phase matched (QPM) nonlinear optical frequency conversion of optical vortices in periodically poled Lithium Niobate (PPLN). Laguerre-Gaussian (LG) modes are used to represent the orbital angular momentum (OAM) states, characterized with the azimuthal and radial indices. Typical three-wave nonlinear interactions among the involved OAM modes are studied with the help of coupling wave equations. Being different from normal QPM process where the energy and quasi-momentum conservations are satisfied, both of the azimuthal and radial indices of the OAM states keep constant in most of the cases. However, abnormal change of the radial index is observed when there is asynchronous nonlinear conversion in different parts of the beams. The QPM nonlinear evolution of fractional OAM states is also discussed showing some interesting properties. In comparison with the traditional birefringent phase matching (BPM), the QPM technique avoids the undesired walk-off effect to reserve high-qua...
Stiripentol kinetics in epilepsy: nonlinearity and interactions.
Levy, R H; Loiseau, P; Guyot, M; Blehaut, H M; Tor, J; Moreland, T A
1984-11-01
Stiripentol kinetics during oral therapy were assessed in six patients with epilepsy who were receiving other antiepileptic drugs. Steady-state levels at 600, 1200, and 2400 mg/day increased in a nonlinear fashion, indicating Michaelis-Menten kinetics. Oral clearance of stiripentol at 600 mg/day was 41.5 +/- 23.4 l/day/kg (mean +/- SD), greater than that at 1200 mg/day (20.3 +/- 8.8 l/day/kg; P less than 0.05) or 2400 mg/day (8.5 +/- 3.8 l/day/kg; P less than 0.01). The apparent in vivo Michaelis-Menten parameters were determined from three mean steady-state concentrations. The average velocity of conversion of stiripentol to its metabolites (Vm), Michaelis constant (Km), and the ratio Vm/Km were 49.3 +/- 13.1 mg/day/kg, 1.35 +/- 1.08 mg/l, and 50.2 +/- 27.5 l/day/kg. Stiripentol reduced the elimination clearances of concomitant antiepileptic drugs. Phenytoin clearance was reduced in all five subjects who received this drug, from a mean control of 29.5 +/- 13.4 l/day to 18.5 +/- 4.6 l/day at a stiripentol dose of 1200 mg/day (P = 0.05) and to 6.48 +/- 2.59 l/day at 2400 mg/day (P less than 0.01). Stiripentol reduced the clearance of carbamazepine in one subject from a control value of 209 l/day to 128 l/day (1200 mg/day) and 61 l/day (2400 mg/day). Stiripentol reduced phenobarbital clearance in two subjects from 3.8 and 5.1 l/day to 2.3 and 3.4 l/day (2400 mg/day). The Michaelis-Menten kinetics of stiripentol, as well as its interactions with other antiepileptic drugs, have important implications in the designing of controlled clinical trials.
Ocean wave nonlinearity and phase couplings
Digital Repository Service at National Institute of Oceanography (India)
Varkey, M.J.
Bispectrum of a swell dominated sea state is computed using Fourier coefficients from an original record and from simulated Fourier coefficients using pseudorandom (uniform) phase spectrum. The differences in the bispectra clearly bring out...
Sudarshanam, V. S.; Claus, Richard O.
1993-03-01
A new cylindrical coil configuration for polyvinylidene flouride (PVF2) film based fiber optic phase modulator is studied for the frequency response and nonlinearity of phase shift at the resonance frequency. This configuration, hitherto unapproached for PVF2 film modulators, offers resonance at well defined, controllable and higher frequencies than possible for the flat-strip configuration. Two versions of this configuration are presented that differ strongly in both the resonance frequency and the phase shift nonlinearity coefficient.
Non-Linearly Interacting Ghost Dark Energy in Brans-Dicke Cosmology
Ebrahimi, E
2016-01-01
In this paper we extend the form of interaction term into the non-linear regime in the ghost dark energy model. A general form of non-linear interaction term is presented and cosmic dynamic equations are obtained. Next, the model is detailed for two special choice of the non-linear interaction term. According to this the universe transits at suitable time ($z\\sim 0.8$) from deceleration to acceleration phase which alleviate the coincidence problem. Squared sound speed analysis revealed that for one class of non-linear interaction term $v_s^2$ can gets positive. This point is an impact of the non-linear interaction term and we never find such behavior in non interacting and linearly interacting ghost dark energy models. Also statefinder parameters are introduced for this model and we found that for one class the model meets the $\\Lambda CDM$ while in the second choice although the model approaches the $\\Lambda CDM$ but never touch that.
Phase space analysis of some interacting Chaplygin gas models
Energy Technology Data Exchange (ETDEWEB)
Khurshudyan, M. [Academy of Sciences of Armenia, Institute for Physical Research, Ashtarak (Armenia); Tomsk State University of Control Systems and Radioelectronics, Laboratory for Theoretical Cosmology, Tomsk (Russian Federation); Tomsk State Pedagogical University, Department of Theoretical Physics, Tomsk (Russian Federation); Myrzakulov, R. [Eurasian National University, Eurasian International Center for Theoretical Physics, Astana (Kazakhstan)
2017-02-15
In this paper we discuss a phase space analysis of various interacting Chaplygin gas models in general relativity. Linear and nonlinear sign changeable interactions are considered. For each case appropriate late time attractors of field equations are found. The Chaplygin gas is one of the dark fluids actively considered in modern cosmology due to the fact that it is a joint model of dark energy and dark matter. (orig.)
Solidification of ternary systems with a nonlinear phase diagram
Alexandrov, D. V.; Dubovoi, G. Yu.; Malygin, A. P.; Nizovtseva, I. G.; Toropova, L. V.
2017-02-01
The directional solidification of a ternary system with an extended phase transition region is theoretically studied. A mathematical model is developed to describe quasi-stationary solidification, and its analytical solution is constructed with allowance for a nonlinear liquidus line equation. A deviation of the liquidus equation from a linear function is shown to result in a substantial change in the solidification parameters.
Nonlinear interaction of meta-atoms through optical coupling
Energy Technology Data Exchange (ETDEWEB)
Slobozhanyuk, A. P.; Kapitanova, P. V.; Filonov, D. S.; Belov, P. A. [National Research University of Information Technologies, Mechanics and Optics (ITMO), St. Petersburg 197101 (Russian Federation); Powell, D. A. [Nonlinear Physics Centre and Centre for Ultrahigh-bandwidth Devices for Optical Systems (CUDOS), Australian National University, Canberra, ACT 0200 (Australia); Shadrivov, I. V.; Kivshar, Yu. S. [National Research University of Information Technologies, Mechanics and Optics (ITMO), St. Petersburg 197101 (Russian Federation); Nonlinear Physics Centre and Centre for Ultrahigh-bandwidth Devices for Optical Systems (CUDOS), Australian National University, Canberra, ACT 0200 (Australia); Lapine, M., E-mail: mlapine@physics.usyd.edu.au [National Research University of Information Technologies, Mechanics and Optics (ITMO), St. Petersburg 197101 (Russian Federation); Centre for Ultrahigh-bandwidth Devices for Optical Systems (CUDOS), School of Physics, University of Sydney, New South Wales 2006 (Australia); McPhedran, R. C. [Centre for Ultrahigh-bandwidth Devices for Optical Systems (CUDOS), School of Physics, University of Sydney, New South Wales 2006 (Australia)
2014-01-06
We propose and experimentally demonstrate a multi-frequency nonlinear coupling mechanism between split-ring resonators. We engineer the coupling between two microwave resonators through optical interaction, whilst suppressing the direct electromagnetic coupling. This allows for a power-dependent interaction between the otherwise independent resonators, opening interesting opportunities to address applications in signal processing, filtering, directional coupling, and electromagnetic compatibility.
Inverse problem for multi-body interaction of nonlinear waves.
Marruzzo, Alessia; Tyagi, Payal; Antenucci, Fabrizio; Pagnani, Andrea; Leuzzi, Luca
2017-06-14
The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we test two methods based on pseudolikelihood, respectively with regularization and with decimation, to determine the coupling constants from sets of measured configurations. We test statistical inference predictions for increasing number of sampled configurations and for an externally tunable temperature-like parameter mimicing real data noise and helping minimization procedures. Analyzed models with phasors and rotors are generalizations of problems of real-valued spherical problems (e.g., density fluctuations), discrete spins (Ising and vectorial Potts) or finite number of states (standard Potts): inference methods presented here can, then, be straightforward applied to a large class of inverse problems. The high versatility of the exposed techniques also concerns the number of expected interactions: results are presented for different graph topologies, ranging from sparse to dense graphs.
Inference of a nonlinear stochastic model of the cardiorespiratory interaction
Smelyanskiy, V N; Stefanovska, A; McClintock, P V E
2005-01-01
A new technique is introduced to reconstruct a nonlinear stochastic model of the cardiorespiratory interaction. Its inferential framework uses a set of polynomial basis functions representing the nonlinear force governing the system oscillations. The strength and direction of coupling, and the noise intensity are simultaneously inferred from a univariate blood pressure signal, monitored in a clinical environment. The technique does not require extensive global optimization and it is applicable to a wide range of complex dynamical systems subject to noise.
Phase-selective entrainment of nonlinear oscillator ensembles
Zlotnik, Anatoly; Nagao, Raphael; Kiss, István Z.; Li-Shin, Jr.
2016-03-01
The ability to organize and finely manipulate the hierarchy and timing of dynamic processes is important for understanding and influencing brain functions, sleep and metabolic cycles, and many other natural phenomena. However, establishing spatiotemporal structures in biological oscillator ensembles is a challenging task that requires controlling large collections of complex nonlinear dynamical units. In this report, we present a method to design entrainment signals that create stable phase patterns in ensembles of heterogeneous nonlinear oscillators without using state feedback information. We demonstrate the approach using experiments with electrochemical reactions on multielectrode arrays, in which we selectively assign ensemble subgroups into spatiotemporal patterns with multiple phase clusters. The experimentally confirmed mechanism elucidates the connection between the phases and natural frequencies of a collection of dynamical elements, the spatial and temporal information that is encoded within this ensemble, and how external signals can be used to retrieve this information.
Tavassoli, Vahid
This thesis studies and mathematically models nonlinear interactions among channels of modern high bit rate (amplitude/) phase modulated optical systems. First, phase modulated analogue systems are studied and a differential receiving method is suggested with experimental validation. The main focus of the rest of the thesis is on digital advanced modulation format systems. Cross-talk due to fiber Kerr nonlinearity in two-format hybrid systems as well as 16-QAM systems is mathematically modelled and verified by simulation for different system parameters. A comparative study of differential receivers and coherent receivers is also given for hybrid systems. The model is based on mathematically proven assumptions and provides an intuitive analytical understanding of nonlinear cross-talk in such systems.
Parametric interaction and intensification of nonlinear Kelvin waves
Novotryasov, Vadim
2008-01-01
Observational evidence is presented for nonlinear interaction between mesoscale internal Kelvin waves at the tidal -- $\\omega_t$ or the inertial -- $\\omega_i$ frequency and oscillations of synoptic -- $\\Omega $ frequency of the background coastal current of Japan/East Sea. Enhanced coastal currents at the sum -- $\\omega_+ $ and dif -- $\\omega_-$ frequencies: $\\omega_\\pm =\\omega_{t,i}\\pm \\Omega$ have properties of propagating Kelvin waves suggesting permanent energy exchange from the synoptic band to the mesoscale $\\omega_\\pm $ band. The interaction may be responsible for the greater than predicted intensification, steepen and break of boundary trapped and equatorially trapped Kelvin waves, which can affect El Ni\\~{n}o. The problem on the parametric interaction of the nonlinear Kelvin wave at the frequency $\\omega $ and the low-frequency narrow-band nose with representative frequency $\\Omega\\ll\\omega $ is investigated with the theory of nonlinear week dispersion waves.
Fardad, Shima; Mills, Matthew S; Zhang, Peng; Man, Weining; Chen, Zhigang; Christodoulides, D N
2013-09-15
We demonstrate optical interactions between stable self-trapped optical beams in soft-matter systems with pre-engineered saturable self-focusing optical nonlinearities. Our experiments, carried out in dilute suspensions of particles with negative polarizabilities, show that optical beam interactions can vary from attractive to repulsive, or can display an energy exchange depending on the initial relative phases. The corresponding observations are in good agreement with theoretical predictions.
Nonlinear two-dimensional terahertz photon echo and rotational spectroscopy in the gas phase
Lu, Jian; Hwang, Harold Y; Ofori-Okai, Benjamin K; Fleischer, Sharly; Nelson, Keith A
2016-01-01
Ultrafast two-dimensional spectroscopy utilizes correlated multiple light-matter interactions for retrieving dynamic features that may otherwise be hidden under the linear spectrum. Its extension to the terahertz regime of the electromagnetic spectrum, where a rich variety of material degrees of freedom reside, remains an experimental challenge. Here we report ultrafast two-dimensional terahertz spectroscopy of gas-phase molecular rotors at room temperature. Using time-delayed terahertz pulse pairs, we observe photon echoes and other nonlinear signals resulting from molecular dipole orientation induced by three terahertz field-dipole interactions. The nonlinear time-domain orientation signals are mapped into the frequency domain in two-dimensional rotational spectra which reveal J-state-resolved nonlinear rotational dynamics. The approach enables direct observation of correlated rotational transitions and may reveal rotational coupling and relaxation pathways in the ground electronic and vibrational state.
Saito, Shinji; Miyoshi, Yoshizumi; Seki, Kanako
2016-07-01
Wave-particle interactions with whistler chorus waves are believed to provide a primary acceleration for electrons in the outer radiation belt. Previous models for flux enhancement of the radiation belt have assumed the stochastic process as a diffusion manner of successive random-phase interactions, but physical mechanisms for the acceleration are not fully incorporated in these models because of the lack of a nonlinear scattering process. Here we report rapid increase in relativistic electron flux by using an innovative computer simulation model that incorporates not only diffusive process but also nonlinear scattering processes. The simulations show that three types of scattering simultaneously occur, which are diffusive, phase trapping, and phase bunching. It is found that the phase trapping is the most efficient mechanism to produce the MeV electrons rapidly in the scattering processes. The electrons are accelerated from 400 keV to over 1 MeV in time scale less than 60 s. On the other hand, as the phase trapping is suppressed by the breaking of relative phase angle between waves and gyrating electrons during the interaction, the increase of electron flux at MeV energy is clearly reduced. Our simulations conclude that the phase-trapping process causes a significant effect for the increase in relativistic electron flux and suggest that a quasi-linear diffusion model is not always valid to fully describe the relativistic electron acceleration.
Using genetic programming to discover nonlinear variable interactions.
Westbury, Chris; Buchanan, Lori; Sanderson, Michael; Rhemtulla, Mijke; Phillips, Leah
2003-05-01
Psychology has to deal with many interacting variables. The analyses usually used to uncover such relationships have many constraints that limit their utility. We briefly discuss these and describe recent work that uses genetic programming to evolve equations to combine variables in nonlinear ways in a number of different domains. We focus on four studies of interactions from lexical access experiments and psychometric problems. In all cases, genetic programming described nonlinear combinations of items in a manner that was subsequently independently verified. We discuss the general implications of genetic programming and related computational methods for multivariate problems in psychology.
Alkhalifah, Tariq Ali
2012-09-25
Traveltime inversion focuses on the geometrical features of the waveform (traveltimes), which is generally smooth, and thus, tends to provide averaged (smoothed) information of the model. On other hand, general waveform inversion uses additional elements of the wavefield including amplitudes to extract higher resolution information, but this comes at the cost of introducing non-linearity to the inversion operator, complicating the convergence process. We use unwrapped phase-based objective functions in waveform inversion as a link between the two general types of inversions in a domain in which such contributions to the inversion process can be easily identified and controlled. The instantaneous traveltime is a measure of the average traveltime of the energy in a trace as a function of frequency. It unwraps the phase of wavefields yielding far less non-linearity in the objective function than that experienced with conventional wavefields, yet it still holds most of the critical wavefield information in its frequency dependency. However, it suffers from non-linearity introduced by the model (or reflectivity), as reflections from independent events in our model interact with each other. Unwrapping the phase of such a model can mitigate this non-linearity as well. Specifically, a simple modification to the inverted domain (or model), can reduce the effect of the model-induced non-linearity and, thus, make the inversion more convergent. Simple numerical examples demonstrate these assertions.
Effects of noise on the phase dynamics of nonlinear oscillators
Daffertshofer, A.
1998-07-01
Various properties of human rhythmic movements have been successfully modeled using nonlinear oscillators. However, despite some extensions towards stochastical differential equations, these models do not comprise different statistical features that can be explained by nondynamical statistics. For instance, one observes certain lag one serial correlation functions for consecutive periods during periodic motion. This work aims at an extension of dynamical descriptions in terms of stochastically forced nonlinear oscillators such as ξ¨+ω20ξ=n(ξ,ξ˙)+q(ξ,ξ˙)Ψ(t), where the nonlinear function n(ξ,ξ˙) generates a limit cycle and Ψ(t) denotes colored noise that is multiplied via q(ξ,ξ˙). Nonlinear self-excited systems have been frequently investigated, particularly emphasizing stability properties and amplitude evolution. Thus, one can focus on the effects of noise on the frequency or phase dynamics that can be analyzed by use of time-dependent Fokker-Planck equations. It can be shown that noise multiplied via polynoms of arbitrary finite order cannot generate the desired period correlation but predominantly results in phase diffusion. The system is extended in terms of forced oscillators in order to find a minimal model producing the required error correction.
Nonlinear Phase Noise Compensation in Experimental WDM Systems with 256QAM
DEFF Research Database (Denmark)
Yankov, Metodi Plamenov; Da Ros, Francesco; Porto da Silva, Edson
2016-01-01
Nonlinear phase noise (NLPN) is studied in an experimental wavelength division multiplexed (WDM) system operating at 256QAM. Extremely narrow linewidth lasers (phase part of the nonlinear noise in a Raman amplified link. Based...
Nariyuki, Y; Nariyuki, Yasuhiro; Hada, Tohru
2006-01-01
Nonlinear relations among frequencies and phases in modulational instability of circularly polarized Alfven waves are discussed, within the context of one dimensional, dissipation-less, unforced fluid system. We show that generation of phase coherence is a natural consequence of the modulational instability of Alfven waves. Furthermore, we quantitatively evaluate intensity of wave-wave interaction by using bi-coherence, and also by computing energy flow among wave modes, and demonstrate that the energy flow is directly related to the phase coherence generation.
Phase locking and quantum statistics in a parametrically driven nonlinear resonator
Hovsepyan, G. H.; Shahinyan, A. R.; Chew, Lock Yue; Kryuchkyan, G. Yu.
2016-04-01
We discuss phase-locking phenomenon at low-level of quanta and quantum statistics for parametrically driven nonlinear Kerr resonator (PDNR). 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 distribution of photon-number states, the second-order correlation function of photons, the Wigner functions of cavity mode showing two-fold symmetry in phase space, and we analyze formation of phase-locked states in the regular as well as the quantum chaotic regime of the PDNR.
A Geometrically Nonlinear Phase Field Theory of Brittle Fracture
2014-10-01
tension. Int J Fract Mech 4:257–266 Voyiadjis G, Mozaffari N (2013) Nonlocal damage model using the phase field method: theory and applications. Int J... model of fracture. Computer simula- tions enable descriptions of fracture in brittle solids under complex loading conditions and for nonlinear and...Simple models based on the notion of theo- retical strength (Gilman1960;Clayton 2009, 2010) can provide insight into directionality of fracture
Interactions between nonlinear spur gear dynamics and surface wear
Ding, Huali; Kahraman, Ahmet
2007-11-01
In this study, two different dynamic models, a finite elements-based deformable-body model and a simplified discrete model, and a surface wear model are combined to study the interaction between gear surface wear and gear dynamic response. The proposed dynamic gear wear model includes the influence of worn surface profiles on dynamic tooth forces and transmission error as well as the influence of dynamic tooth forces on wear profiles. This paper first introduces the nonlinear dynamic models that include gear backlash and time-varying gear mesh stiffness, and a wear model separately. It presents a comparison to experiments for validation of the dynamic models. The dynamic models are combined with the wear model to study the interaction of surface wear and dynamic behavior in both linear and nonlinear response regimes. At the end, several sets of simulation results are used to demonstrate the two-way relationship between nonlinear gear dynamics and surface wear.
Nonlinear lepton-photon interactions in external background fields
Energy Technology Data Exchange (ETDEWEB)
Akal, Ibrahim [DESY, Hamburg (Germany). Theory Group; Moortgat-Pick, Gudrid [DESY, Hamburg (Germany). Theory Group; Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2016-02-09
Nonlinear phenomena of lepton-photon interactions in external backgrounds with a generalised periodic plane-wave geometry are studied. We discuss nonlinear Compton scattering in head-on lepton-photon collisions extended properly to beyond the soft-photon regime. In addition, our results are applied to stimulated lepton-antilepton pair production in photon collisions with unrestricted energies. Derivations are considered semi-classically based on unperturbed fermionic Volkov representations encoding the full interaction with the background field. Closed expressions for total probabilities considering S-matrix elements have been derived. The general formula is applied to Compton scattering by an electron propagating in an external laser-like background. We obtain additive contributions in the extended unconstrained result which turns out to be stringently required in the highly nonlinear regime. A detailed comparison of contributing harmonics is discussed for various field parameters.
Nonlinear dynamic theory for photorefractive phase hologram formation
Kim, D. M.; Shah, R. R.; Rabson, T. A.; Tittle, F. K.
1976-01-01
A nonlinear dynamic theory is developed for the formation of photorefractive volume phase holograms. A feedback mechanism existing between the photogenerated field and free-electron density, treated explicitly, yields the growth and saturation of the space-charge field in a time scale characterized by the coupling strength between them. The expression for the field reduces in the short-time limit to previous theories and approaches in the long-time limit the internal or photovoltaic field. Additionally, the phase of the space charge field is shown to be time-dependent.
An Agent Interaction Based Method for Nonlinear Process Plan Scheduling
Institute of Scientific and Technical Information of China (English)
GAO Qinglu; WU Bo; GUO Guang
2006-01-01
This article puts forward a scheduling method for nonlinear process plan shop floor. Task allocation and load balance are realized by bidding mechanism. Though the agent interaction process, the execution of tasks is determined and the coherence of manufacturing decision is verified. The employment of heuristic index can help to optimize the system performance.
Non-Linear Interactive Stories in Computer Games
DEFF Research Database (Denmark)
Bangsø, Olav; Jensen, Ole Guttorm; Kocka, Tomas
2003-01-01
The paper introduces non-linear interactive stories (NOLIST) as a means to generate varied and interesting stories for computer games automatically. We give a compact representation of a NOLIST based on the specification of atomic stories, and show how to build an object-oriented Bayesian network...
Phase stabilization of Kerr frequency comb internally without nonlinear optical interferometry
Huang, S -W; Yang, J; Yu, M; Kwong, D -L; Wong, C W
2016-01-01
Optical frequency comb (OFC) technology has been the cornerstone for scientific breakthroughs such as precision frequency metrology, redefinition of time, extreme light-matter interaction, and attosecond sciences. While the current mode-locked laser-based OFC has had great success in extending the scientific frontier, its use in real-world applications beyond the laboratory setting remains an unsolved challenge. Microresonator-based OFCs, or Kerr frequency comb, have recently emerged as a candidate solution to the challenge because of their preferable size, weight, and power consumption (SWaP). On the other hand, the current phase stabilization technology requires either external optical references or power-demanding nonlinear processes, overturning the SWaP benefit of Kerr frequency combs. Introducing a new concept in phase control, here we report an internally phase stabilized Kerr frequency comb without the need of any optical references or nonlinear processes. We describe the comb generation analytically ...
Institute of Scientific and Technical Information of China (English)
Hamed Farokhi; Mergen H Ghayesh
2016-01-01
This paper analyses the modal interactions in the nonlinear, size-dependent dynamics of geometrically imper-fect microplates. Based on the modified couple stress theory, the equations of motion for the in-plane and out-of-plane motions are obtained employing the von Kármán plate theory as well as Kirchhoff ’s hypotheses by means of the Lagrange equations. The equations of motions are solved using the pseudo-arclength continuation technique and direct time-integration method. The system parameters are tuned to the values associated with modal interactions, and then non-linear resonant responses and energy transfer are analysed. Nonlinear motion characteristics are shown in the form of frequency-response and force-response curves, time histo-ries, phase-plane portraits, and fast Fourier transforms.
Nonlinear interaction of waves in boundary-layer flows
Nayfeh, A. H.; Bozatli, A. N.
1979-01-01
First-order nonlinear interactions of Tollmien-Schlichting waves of different frequencies and initial amplitudes in boundary-layer flows are analyzed by using the method of multiple scales. For the case of two waves, a strong nonlinear interaction exists if one of the frequencies w2 is twice the other frequency w1. Numerical results for flow past a flat plate show that this interaction mechanism is strongly destabilizing even in regions where either the fundamental or its harmonic is damped in the absence of the interaction. For the case of three waves, a strong nonlinear interaction exists when w3 = w2- w1. This combination resonance causes the amplitude of the wave with the difference frequency w3 to multiply many times in magnitude in a short distance even if it is damped in the absence of the interaction. The initial amplitudes play a dominant role in determining the changes in the amplitudes of the waves in both of these mechanisms.
Analysis of linear and nonlinear genotype × environment interaction
Directory of Open Access Journals (Sweden)
Rong-Cai eYang
2014-07-01
Full Text Available The usual analysis of genotype × environment interaction (GxE is based on the linear regression of genotypic performance on environmental changes (e.g., classic stability analysis. This linear model may often lead to lumping together of the nonlinear responses to the whole range of environmental changes from suboptimal and superoptimal conditions, thereby lowering the power of detecting GxE variation. On the other hand, the GxE is present when the magnitude of the genetic effect differs across the range of environmental conditions regardless of whether the response to environmental changes is linear or nonlinear. The objectives of this study are: (i explore the use of four commonly used nonlinear functions (logistic, parabola, normal and Cauchy functions for modeling nonlinear genotypic responses to environmental changes and (ii to investigate the difference in the magnitude of estimated genetic effects under different environmental conditions. The use of nonlinear functions was illustrated through the analysis of one data set taken from barley cultivar trials in Alberta, Canada (Data A and the examination of change in effect sizes is through the analysis another data set taken from the North America Barley Genome Mapping Project (Data B. The analysis of Data A showed that the Cauchy function captured an average of >40% of total GxE variation whereas the logistic function captured less GxE variation than the linear function. The analysis of Data B showed that genotypic responses were largely linear and that strong QTL × environment interaction existed as the positions, sizes and directions of QTL detected differed in poor vs. good environments. We conclude that (i the nonlinear functions should be considered when analyzing multi-environmental trials with a wide range of environmental variation and (ii QTL × environment interaction can arise from the difference in effect sizes across environments.
Nonlinear interaction of electromagnetic field with quantum plasma
Latyshev, A V
2014-01-01
The analysis of nonlinear interaction of transversal electromagnetic field with quantum collisionless plasma is carried out. Formulas for calculation electric current in quantum collisionless plasma at any temperature are deduced. It has appeared, that the nonlinearity account leads to occurrence of the longitudinal electric current directed along a wave vector. This second current is orthogonal to the known transversal classical current, received at the classical linear analysis. The case of degenerate electronic plasma is considered. It is shown, that for degenerate plasmas the electric current is calculated under the formula, not containing quadratures.
Nonlinear interaction of two waves in boundary-layer flows
Nayfeh, A. H.; Bozatli, A. N.
1980-01-01
First-order nonlinear interactions of Tollmien-Schlichting waves of different frequencies and initial amplitudes in boundary-layer flows are analyzed using the method of multiple scales. Numerical results for flow past a flat plate show that the spatial detuning wipes out resonant interactions unless the initial amplitudes are very large. Thus, a wave having a moderate amplitude has little influence on its subharmonic although it has a strong influence on its second harmonic. Moreover, two waves having moderate amplitudes have a strong influence on their difference frequency. The results show that the difference frequency can be very unstable when generated by the nonlinear interaction, even though it may be stable when introduced by itself in the boundary layer.
Nonlinear interactions isolated through scale synthesis in experimental wall turbulence
Duvvuri, Subrahmanyam; McKeon, Beverley
2016-07-01
An experimental investigation of nonlinear scale interactions in a forced turbulent boundary layer is presented here. A dynamic wall perturbation mechanism was used to externally force two distinct large-scale synthetic modes with well-defined spatial and temporal wave numbers in a fully turbulent flow. The focus is on characterizing the nonlinear flow response at triadically consistent wave numbers that arises from the direct interactions of the two synthetic modes. These experimental results isolate triadic scale interactions in wall turbulence in a unique fashion, and provide the ability to explore the dynamics of scale coupling in a systematic and detailed manner. The ideas advanced here are intended to contribute towards modeling efforts of high-Reynolds-number wall turbulence.
Generalized Ghost Dark Energy with Non-Linear Interaction
Ebrahimi, E; Mehrabi, A; Movahed, S M S
2016-01-01
In this paper we investigate ghost dark energy model in the presence of non-linear interaction between dark energy and dark matter. The functional form of dark energy density in the generalized ghost dark energy (GGDE) model is $\\rho_D\\equiv f(H, H^2)$ with coefficient of $H^2$ represented by $\\zeta$ and the model contains three free parameters as $\\Omega_D, \\zeta$ and $b^2$ (the coupling coefficient of interactions). We propose three kinds of non-linear interaction terms and discuss the behavior of equation of state, deceleration and dark energy density parameters of the model. We also find the squared sound speed and search for signs of stability of the model. To compare the interacting GGDE model with observational data sets, we use more recent observational outcomes, namely SNIa, gamma-ray bursts, baryonic acoustic oscillation and the most relevant CMB parameters including, the position of acoustic peaks, shift parameters and redshift to recombination. For GGDE with the first non-linear interaction, the j...
Optimization of the Phase Advance Between RHIC Interaction Points
Tomas, Rogelio
2005-01-01
We consider the scenario of having two identical Interaction Points (IPs) in the Relativistic Heavy Ion Collider (RHIC). The strengths of beam-beam resonances strongly depend on the phase advance between these two IPs and therefore certain phase advances could improve beam lifetime and luminosity. We compute the dynamic aperture as function of the phase advance between these IPs to find the optimum settings. The beam-beam interaction is treated in the weak-strong approximation and a complete non-linear model of the lattice is used. For the current RHIC proton working point (0.69,0.685) the design lattice is found to have the optimum phase advance. However this is not the case for other working points.
Nonlinear wave-wave interactions and wedge waves
Institute of Scientific and Technical Information of China (English)
Ray Q.Lin; Will Perrie
2005-01-01
A tetrad mechanism for exciting long waves,for example edge waves,is described based on nonlinear resonant wave-wave interactions.In this mechanism,resonant interactions pass energy to an edge wave,from the three participating gravity waves.The estimated action flux into the edge wave can be orders of magnitude greater than the transfer fluxes derived from other competing mechanisms,such as triad interactions.Moreover,the numerical results show that the actual transfer rates into the edge wave from the three participating gravity waves are two-to three- orders of magnitude greater than bottom friction.
Contactless nonlinear optics mediated by long-range Rydberg interactions
Busche, Hannes; Huillery, Paul; Ball, Simon W.; Ilieva, Teodora; Jones, Matthew P. A.; Adams, Charles S.
2017-07-01
In conventional nonlinear optics, linear quantum optics, and cavity quantum electrodynamics to create effective photon-photon interactions photons must have, at one time, interacted with matter inside a common medium. In contrast, in Rydberg quantum optics, optical photons are coherently and reversibly mapped onto collective atomic Rydberg excitations, giving rise to dipole-mediated effective photon-photon interactions that are long range. Consequently, a spatial overlap between the light modes is no longer required. We demonstrate such a contactless coupling between photons stored as collective Rydberg excitations in spatially separate optical media. The potential induced by each photon modifies the retrieval mode of its neighbour, leading to correlations between them. We measure these correlations as a function of interaction strength, distance and storage time, demonstrating an effective interaction between photons separated by 15 times their wavelength. Contactless effective photon-photon interactions are relevant for scalable multichannel photonic devices and the study of strongly correlated many-body dynamics using light.
Frequency-domain nonlinear optics in two-dimensionally patterned quasi-phase-matching media
Phillips, C R; Gallmann, L; Keller, U
2015-01-01
Advances in the amplification and manipulation of ultrashort laser pulses has led to revolutions in several areas. Examples include chirped pulse amplification for generating high peak-power lasers, power-scalable amplification techniques, pulse shaping via modulation of spatially-dispersed laser pulses, and efficient frequency-mixing in quasi-phase-matched nonlinear crystals to access new spectral regions. In this work, we introduce and demonstrate a new platform for nonlinear optics which has the potential to combine all of these separate functionalities (pulse amplification, frequency transfer, and pulse shaping) into a single monolithic device. Moreover, our approach simultaneously offers solutions to the performance-limiting issues in the conventionally-used techniques, and supports scaling in power and bandwidth of the laser source. The approach is based on two-dimensional patterning of quasi-phase-matching gratings combined with optical parametric interactions involving spatially dispersed laser pulses...
Photonics linear and nonlinear interactions of laser light and matter
Menzel, R
2007-01-01
This book covers the fundamental properties and the description of single photons and light beams, experimentally and theoretically. It explains the essentials of linear interactions and most nonlinear interactions between light and matter in both the transparent and absorbing cases. It also provides a basic understanding of modern quantum optics and lasers, as well as the principles of nonlinear optical spectroscopy. It is self-consistent and enriched by a large number of calculated illustrations, examples, and descriptive tables. Graduate students in physics and electrical engineering, as well as other sciences, will find this book a thorough introduction to the field, while for lecturers and scientists it is a rich source of useful information and a ready-to-hand reference. The new edition has been thoroughly expanded and revised in all sections
Impact of nonlinear effective interactions on GFT quantum gravity condensates
Pithis, Andreas G A; Tomov, Petar
2016-01-01
We present the numerical analysis of effectively interacting Group Field Theory (GFT) models in the context of the GFT quantum gravity condensate analogue of the Gross-Pitaevskii equation for real Bose-Einstein condensates including combinatorially local interaction terms. Thus we go beyond the usually considered construction for free models. More precisely, considering such interactions in a weak regime, we find solutions for which the expectation value of the number operator N is finite, as in the free case. When tuning the interaction to the strongly nonlinear regime, however, we obtain solutions for which N grows and eventually blows up, which is reminiscent of what one observes for real Bose-Einstein condensates, where a strong interaction regime can only be realized at high density. This behaviour suggests the breakdown of the Bogoliubov ansatz for quantum gravity condensates and the need for non-Fock representations to describe the system when the condensate constituents are strongly correlated. Furthe...
Nonlinear Interaction of Transversal Modes in a CO2 Laser
Lopez-Ruiz, Ricardo; Mindlin, G. B.; Perez-Garcia, C.; Tredicce, J. R.
2002-01-01
We show the possibility of achieving experimentally a Takens-Bogdanov bifurcation for the nonlinear interaction of two transverse modes ($l = \\pm 1$) in a $CO_2$ laser. The system has a basic O(2) symmetry which is perturbed by some symmetry-breaking effects that still preserve the $Z_2$ symmetry. The pattern dynamics near this codimension two bifurcation under such symmetries is described. This dynamics changes drastically when the laser properties are modified.
Nonlinear mechanisms to Rogue events in the process of interaction between optical filaments
Kovachev, L M
2015-01-01
We investigate two types of nonlinear interaction between collinear femtosecond laser pulses with power slightly above the critical for self-focusing $P_{cr}$. In the first case we study energy exchange between filaments. The model describes this process through degenerate four-photon parametric mixing (FPPM) scheme and requests initial phase difference between the waves. When there are no initial phase difference between the pulses, the FPPM process does not work. In this case it is obtained the second type of interaction as merging between two, three or four filaments in a single filament with higher power. It is found that in the second case the interflow between the filaments has potential of interaction due to cross-phase modulation (CPM).
Chaitanya, N Apurv; Banerji, J; Samanta, G K
2016-01-01
Hollow Gaussian beams (HGB) are a special class of doughnut shaped beams that do not carry orbital angular momentum (OAM). Such beams have a wide range of applications in many fields including atomic optics, bio-photonics, atmospheric science, and plasma physics. Till date, these beams have been generated using linear optical elements. Here, we show a new way of generating HGBs by three-wave mixing in a nonlinear crystal. Based on nonlinear interaction of photons having OAM and conservation of OAM in nonlinear processes, we experimentally generated ultrafast HGBs of order as high as 6 and power >180 mW at 355 nm. This generic concept can be extended to any wavelength, timescales (continuous-wave and ultrafast) and any orders. We show that the removal of azimuthal phase of vortices does not produce Gaussian beam. We also propose a new and only method to characterize the order of the HGBs.
Chaitanya, N. Apurv; Jabir, M. V.; Banerji, J.; Samanta, G. K.
2016-09-01
Hollow Gaussian beams (HGB) are a special class of doughnut shaped beams that do not carry orbital angular momentum (OAM). Such beams have a wide range of applications in many fields including atomic optics, bio-photonics, atmospheric science, and plasma physics. Till date, these beams have been generated using linear optical elements. Here, we show a new way of generating HGBs by three-wave mixing in a nonlinear crystal. Based on nonlinear interaction of photons having OAM and conservation of OAM in nonlinear processes, we experimentally generated ultrafast HGBs of order as high as 6 and power >180 mW at 355 nm. This generic concept can be extended to any wavelength, timescales (continuous-wave and ultrafast) and any orders. We show that the removal of azimuthal phase of vortices does not produce Gaussian beam. We also propose a new and only method to characterize the order of the HGBs.
Nonlinear dynamics of wind waves: multifractal phase/time effects
Directory of Open Access Journals (Sweden)
R. H. Mellen
1994-01-01
Full Text Available In addition to the bispectral coherence method, phase/time analysis of analytic signals is another promising avenue for the investigation of phase effects in wind waves. Frequency spectra of phase fluctuations obtained from both sea and laboratory experiments follow an F-β power law over several decades, suggesting that a fractal description is appropriate. However, many similar natural phenomena have been shown to be multifractal. Universal multifractals are quantified by two additional parameters: the Lévy index 0 α 2 for the type of multifractal and the co-dimension 0 C1 1 for intermittence. The three parameters are a full statistical measure the nonlinear dynamics. Analysis of laboratory flume data is reported here and the results indicate that the phase fluctuations are 'hard multifractal' (α > 1. The actual estimate is close to the limiting value α = 2, which is consistent with Kolmogorov's lognormal model for turbulent fluctuations. Implications for radar and sonar backscattering from the sea surface are briefly considered.
Nonlinear clustering during the BEC dark matter phase transition
Energy Technology Data Exchange (ETDEWEB)
Freitas, Rodolfo C. de, E-mail: rodolfo.camargo@pq.cnpq.br [Universidade Federal do Espírito Santo, Av. Fernando Ferrari, Goiabeiras, Vitória (Brazil); Instituto Federal de Educação, Ciência e Tecnologia do Espírito Santo, Avenida Vitória 1729, Jucutuquara, Vitória (Brazil); Velten, Hermano, E-mail: velten@pq.cnpq.br [Universidade Federal do Espírito Santo, Av. Fernando Ferrari, Goiabeiras, Vitória (Brazil); UMR 7332, CPT, Aix Marseille Université, 13288, Marseille (France)
2015-12-16
Spherical collapse of the Bose–Einstein condensate (BEC) dark matter model is studied in the Thomas–Fermi approximation. The evolution of the overdensity of the collapsed region and its expansion rate are calculated for two scenarios. We consider the case of a sharp phase transition (which happens when the critical temperature is reached) from the normal dark matter state to the condensate one and the case of a smooth first order phase transition where there is a continuous conversion of “normal” dark matter to the BEC phase. We present numerical results for the physics of the collapse for a wide range of the model’s space parameter, i.e. the mass of the scalar particle m{sub χ} and the scattering length l{sub s}. We show the dependence of the transition redshift on m{sub χ} and l{sub s}. Since small scales collapse earlier and eventually before the BEC phase transition, the evolution of collapsing halos in this limit is indeed the same in both the CDM and the BEC models. Differences are expected to appear only on the largest astrophysical scales. However, we argue that the BEC model is almost indistinguishable from the usual dark matter scenario concerning the evolution of nonlinear perturbations above typical clusters scales, i.e., ≳10{sup 14}M{sub ⊙}. This provides an analytical confirmation for recent results from cosmological numerical simulations (Schive et al., Nat Phys 10:496, 2014)
Nonlinear transient and chaotic interactions in disc brake squeal
Oberst, S.; Lai, J. C. S.
2015-04-01
In automotive disc-brake squeal, most numerical studies have been focussed on the prediction of unstable vibration modes in the frequency domain using the complex eigenvalue analysis. However, the magnitude of the positive real part of a complex eigenvalue is an unreliable indicator of squeal occurrence. Although nonlinearities have been shown to play a significant role in brake squeal, transient nonlinear time domain analyses have rarely been applied owing to high computational costs. Here the complex eigenvalue analysis, the direct steady-state analysis and the transient nonlinear time domain analysis are applied to an isotropic pad-on-disc finite element model representing a simple model of a brake system. While in this investigation, in-plane pad-mode instabilities are not detected by the complex eigenvalue analysis, the dissipated energy obtained by the direct steady-state analysis of the model subjected to harmonic contact pressure excitation is negative at frequencies of pad modes, indicating a potential for instabilities. Transient nonlinear time domain analysis of the pad and disc dynamics reveal that in-plane pad vibrations excite a dominant out-of-plane disc mode. For intermittently chaotic pad motion, the disc dynamics is quasi-periodic; and for chaotic motion of the pad, a toroidal attractor is found for the disc's out-of-plane motion. Nonlinear interactions between the pad and the disc highlight that different parts in a brake system display different dynamic behaviour and need to be analysed separately. The type II intermittency route to chaos could be the cause for the experimentally observed instantaneous mode squeal.
Fluid transport due to nonlinear fluid-structure interaction
Energy Technology Data Exchange (ETDEWEB)
Soendergaard Jensen, J.
1996-08-01
This work considers nonlinear fluid-structure interaction for a vibrating pipe containing fluid. Transverse pipe vibrations will force the fluid to move relative to the pipe creating uni-directional fluid flow towards the pipe end. The fluid flow induced affects the damping and the stiffness of the pipe. The behavior of the system in response to lateral resonant base excitation is analyzed numerically mode of vibration seems to be most effective for high mean fluid speed, whereas higher modes of vibration can be used to transport fluid with the same fluid speed but with smaller magnitude of pipe vibrations. The effect of the nonlinear geometrical terms is analyzed and these terms are shown to affect the response for higher modes of vibration. Experimental investigations show good agreement with theoretical predictions. (au) 16 refs.
Fluid transport due to nonlinear fluid-structure interaction
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard
1997-01-01
This work considers nonlinear fluid-structure interaction for a vibrating pipe containing fluid. Transverse pipe vibrations will force the fluid to move relative to the pipe creating unidirectional fluid flow towards the pipe end. The fluid flow induced affects the damping and the stiffness...... of the pipe. The behavior of the system in response to lateral resonant base excitation is analysed numerically and by the use of a perturbation method (multiple scales). Exciting the pipe in the fundamental mode of vibration seems to be most effective for transferring energy from the shaker to the fluid......, whereas higher modes of vibration can be used to transport fluid with pipe vibrations of smaller amplitude. The effect of the nonlinear geometrical terms is analysed and these terms are shown to affect the response for higher modes of vibration. Experimental investigations show good agreement...
Institute of Scientific and Technical Information of China (English)
XU Guang; QIAN Liejia; WANG Tao; FAN Dianyuan; LI Fuming
2004-01-01
It is shown that the cascaded fifth-order nonlinear phase shifts will increase with energy loss in the cascaded processes. Essentially different from the multi-photon absorption accompanied with inherent material nonlinearities, the loss of fundamental wave in a cascaded process is controllable and suppressible. By introducing difference frequencies generated from the reaction between the fundamental and its second harmonic after the cascaded processes, the fundamental wave can be free of energy loss, while the large cascaded fifth-order nonlinear phase shift is maintained.
Nonlinear interaction of axisymmetric circulation and nonaxisymmetric disturbances in hurricanes
Institute of Scientific and Technical Information of China (English)
LUO Zhexian
2004-01-01
The nonlinear interaction of axisymmetric circulation and nonaxisymmetric disturbances in hurricanes is numerically studied with a quasigeostrophic barotropic model of a higher resolution. It is pointed out that the interaction may be divided into two categories. In the first category, nonaxisymmetric disturbances decay, the coordinate locus of maximum relative vorticity ζmax is seemingly unordered, and the central pressure of hurricane rises; while in the second one, nonaxisymmetric disturbances develop, the locus of ζmax shows an ordered limit cycle pattern, and the central pressure falls remarkably. A succinct criterion is given to judge which category the interaction belongs to, i.e. the vortex beta Rossby number at the initial time Rβ 1 to the developing one. Finally, practical applications of theoretical results of the rotational adaptation process presented by Zeng and numerical results in this paper to the hurricane intensity prediction in China are also discussed.
The quasi-equilibrium phase of nonlinear chains
Indian Academy of Sciences (India)
T R Krishna Mohan; Surajit Sen
2005-03-01
We show that time evolution initiated via kinetic energy perturbations in conservative, discrete, spring-mass chains with purely nonlinear, non-integrable, algebraic potentials of the form ( − +1 ∼ $(_{} − _{+1})^{2}$, ≥ 2 and an integer, occurs via discrete solitary waves (DSWs) and discrete antisolitary waves (DASWs). Presence of reflecting and periodic boundaries in the system leads to collisions between the DSWs and DASWs. Such collisions lead to the breakage and subsequent reformation of (different) DSWs and DASWs. Our calculations show that the system eventually reaches a stable `quasi-equilibrium' phase that appears to be independent of initial conditions, possesses Gaussian velocity distribution, and has a higher mean kinetic energy and larger range of kinetic energy fluctuations as compared to the pure harmonic system with = 1; the latter indicates possible violation of equipartition.
Advanced nonlinear control of three phase series active power filter
Directory of Open Access Journals (Sweden)
Abouelmahjoub Y.
2014-01-01
Full Text Available The problem of controlling three-phase series active power filter (TPSAPF is addressed in this paper in presence of the perturbations in the voltages of the electrical supply network. The control objective of the TPSAPF is twofold: (i compensation of all voltage perturbations (voltage harmonics, voltage unbalance and voltage sags, (ii regulation of the DC bus voltage of the inverter. A controller formed by two nonlinear regulators is designed, using the Backstepping technique, to provide the above compensation. The regulation of the DC bus voltage of the inverter is ensured by the use of a diode bridge rectifier which its output is in parallel with the DC bus capacitor. The Analysis of controller performances is illustrated by numerical simulation in Matlab/Simulink environment.
Nonlinear clustering during the BEC dark matter phase transition
Energy Technology Data Exchange (ETDEWEB)
Freitas, Rodolfo C. de [Universidade Federal do Espirito Santo, Vitoria (Brazil); Ciencia e Tecnologia do Espirito Santo, Instituto Federal de Educacao, Vitoria (Brazil); Velten, Hermano [Universidade Federal do Espirito Santo, Vitoria (Brazil); Aix Marseille Universite, UMR 7332, CPT, Marseille (France)
2015-12-15
Spherical collapse of the Bose-Einstein condensate (BEC) dark matter model is studied in the Thomas-Fermi approximation. The evolution of the overdensity of the collapsed region and its expansion rate are calculated for two scenarios. We consider the case of a sharp phase transition (which happens when the critical temperature is reached) from the normal dark matter state to the condensate one and the case of a smooth first order phase transition where there is a continuous conversion of ''normal'' dark matter to the BEC phase. We present numerical results for the physics of the collapse for a wide range of the model's space parameter, i.e. the mass of the scalar particle m{sub χ} and the scattering length l{sub s}. We show the dependence of the transition redshift on m{sub χ} and l{sub s}. Since small scales collapse earlier and eventually before the BEC phase transition, the evolution of collapsing halos in this limit is indeed the same in both the CDM and the BEC models. Differences are expected to appear only on the largest astrophysical scales. However, we argue that the BEC model is almost indistinguishable from the usual dark matter scenario concerning the evolution of nonlinear perturbations above typical clusters scales, i.e., >or similar 10{sup 14}M{sub s}un. This provides an analytical confirmation for recent results from cosmological numerical simulations (Schive et al., Nat Phys 10:496, 2014). (orig.)
Quantum nonlinear optics with single photons enabled by strongly interacting atoms
DEFF Research Database (Denmark)
Peyronel, Thibault; Firstenberg, Ofer; Liang, Qi Yu
2012-01-01
The realization of strong nonlinear interactions between individual light quanta (photons) is a long-standing goal in optical science and engineering, being of both fundamental and technological significance. In conventional optical materials, the nonlinearity at light powers corresponding...
Dimensional Hierarchy of Fermionic Interacting Topological Phases
Queiroz, Raquel; Khalaf, Eslam; Stern, Ady
2016-11-01
We present a dimensional reduction argument to derive the classification reduction of fermionic symmetry protected topological phases in the presence of interactions. The dimensional reduction proceeds by relating the topological character of a d -dimensional system to the number of zero-energy bound states localized at zero-dimensional topological defects present at its surface. This correspondence leads to a general condition for symmetry preserving interactions that render the system topologically trivial, and allows us to explicitly write a quartic interaction to this end. Our reduction shows that all phases with topological invariant smaller than n are topologically distinct, thereby reducing the noninteracting Z classification to Zn.
Dimensional Hierarchy of Fermionic Interacting Topological Phases.
Queiroz, Raquel; Khalaf, Eslam; Stern, Ady
2016-11-11
We present a dimensional reduction argument to derive the classification reduction of fermionic symmetry protected topological phases in the presence of interactions. The dimensional reduction proceeds by relating the topological character of a d-dimensional system to the number of zero-energy bound states localized at zero-dimensional topological defects present at its surface. This correspondence leads to a general condition for symmetry preserving interactions that render the system topologically trivial, and allows us to explicitly write a quartic interaction to this end. Our reduction shows that all phases with topological invariant smaller than n are topologically distinct, thereby reducing the noninteracting Z classification to Z_{n}.
Coupling fluid-structure interaction with phase-field fracture
Wick, Thomas
2016-12-01
In this work, a concept for coupling fluid-structure interaction with brittle fracture in elasticity is proposed. The fluid-structure interaction problem is modeled in terms of the arbitrary Lagrangian-Eulerian technique and couples the isothermal, incompressible Navier-Stokes equations with nonlinear elastodynamics using the Saint-Venant Kirchhoff solid model. The brittle fracture model is based on a phase-field approach for cracks in elasticity and pressurized elastic solids. In order to derive a common framework, the phase-field approach is re-formulated in Lagrangian coordinates to combine it with fluid-structure interaction. A crack irreversibility condition, that is mathematically characterized as an inequality constraint in time, is enforced with the help of an augmented Lagrangian iteration. The resulting problem is highly nonlinear and solved with a modified Newton method (e.g., error-oriented) that specifically allows for a temporary increase of the residuals. The proposed framework is substantiated with several numerical tests. In these examples, computational stability in space and time is shown for several goal functionals, which demonstrates reliability of numerical modeling and algorithmic techniques. But also current limitations such as the necessity of using solid damping are addressed.
Switching Correlation and Noise Level in Pr3+:YSO Crystal via Dressing Nonlinear Phase
Irfan Ahmed; Zhaoyang Zhang; Feng Wen; Da Zhang; Changbiao Li; Ruimin Wang; Yanpeng Zhang
2016-01-01
We propose and experimentally demonstrate that the intensity noise correlation and the noise level of intensity-difference and intensity-sum in Stokes and anti-Stokes channel can be well controlled by the relative nonlinear phase in spontaneous parametric four-wave mixing process. By modulating the relative nonlinear phase, including self-phase modulation and cross-phase modulation, switching the correlation into anti-correlation and the relative intensity noise level between the intensity-di...
A Scanning Hologram Recorded by Phase Conjugate Property of Nonlinear Crystals
DEFF Research Database (Denmark)
Zi-Liang, Ping; Dalsgaard, Erik
1996-01-01
A methode of recording a scanning hologram with phase conjugate property of nonlinear crystal is provided. The principle of recording, setup and experiments are given.......A methode of recording a scanning hologram with phase conjugate property of nonlinear crystal is provided. The principle of recording, setup and experiments are given....
A look to nonlinear interacting Ghost dark energy cosmology
Khurshudyan, Martiros
2016-07-01
In this paper, we organize a look to nonlinear interacting Ghost dark energy cosmology involving a discussion on the thermodynamics of the Ghost dark energy, when the universe is bounded via the Hubble horizon. One of the ways to study a dark energy model, is to reconstruct thermodynamics of it. Ghost dark energy is one of the models of the dark energy which has an explicitly given energy density as a function of the Hubble parameter. There is an active discussion towards various cosmological scenarios, where the Ghost dark energy interacts with the pressureless cold dark matter (CDM). Recently, various models of the varying Ghost dark energy has been suggested, too. To have a comprehensive understanding of suggested models, we will discuss behavior of the cosmological parameters on parameter-redshift z plane. Some discussion on Om and statefinder hierarchy analysis of these models is presented. Moreover, up to our knowledge, suggested forms of interaction between the Ghost dark energy and cold dark matter (CDM) are new, therefore, within obtained results, we provide new contribution to previously discussed models available in the literature. Our study demonstrates that the forms of the interactions considered in the Ghost dark energy cosmology are not exotic and the justification of this is due to the recent observational data.
Nonlinear wave dynamics near phase transition in PT-symmetric localized potentials
Nixon, Sean; Yang, Jianke
2016-09-01
Nonlinear wave propagation in parity-time symmetric localized potentials is investigated analytically near a phase-transition point where a pair of real eigenvalues of the potential coalesce and bifurcate into the complex plane. Necessary conditions for a phase transition to occur are derived based on a generalization of the Krein signature. Using the multi-scale perturbation analysis, a reduced nonlinear ordinary differential equation (ODE) is derived for the amplitude of localized solutions near phase transition. Above the phase transition, this ODE predicts a family of stable solitons not bifurcating from linear (infinitesimal) modes under a certain sign of nonlinearity. In addition, it predicts periodically-oscillating nonlinear modes away from solitons. Under the opposite sign of nonlinearity, it predicts unbounded growth of solutions. Below the phase transition, solution dynamics is predicted as well. All analytical results are compared to direct computations of the full system and good agreement is observed.
Nonlinear wave dynamics near phase transition in $\\mathcal{PT}$-symmetric localized potentials
Nixon, Sean
2015-01-01
Nonlinear wave propagation in parity-time ($\\mathcal{PT}$) symmetric localized potentials is investigated analytically near a phase-transition point where a pair of real eigenvalues of the potential coalesce and bifurcate into the complex plane. Necessary conditions for phase transition to occur are derived based on a generalization of the Krein signature. Using multi-scale perturbation analysis, a reduced nonlinear ODE model is derived for the amplitude of localized solutions near phase transition. Above phase transition, this ODE model predicts a family of stable solitons not bifurcating from linear (infinitesimal) modes under a certain sign of nonlinearity. In addition, it predicts periodically-oscillating nonlinear modes away from solitons. Under the opposite sign of nonlinearity, it predicts unbounded growth of solutions. Below phase transition, solution dynamics is predicted as well. All analytical results are compared to direct computations of the full system and good agreement is observed.
Energy Technology Data Exchange (ETDEWEB)
Khorashadizadeh, S. M., E-mail: smkhorashadi@birjand.ac.ir; Taheri Boroujeni, S. [Physics Department, University of Birjand, Birjand (Iran, Islamic Republic of); Niknam, A. R. [Laser and Plasma Research Institute, Shahid Beheshti University, G.C., Tehran (Iran, Islamic Republic of)
2015-11-15
In this paper, we have investigated the nonlinear interaction between high-frequency surface plasmons and low-frequency ion oscillations in a semi-bounded collisional quantum plasma. By coupling the nonlinear Schrodinger equation and quantum hydrodynamic model, and taking into account the ponderomotive force, the dispersion equation is obtained. By solving this equation, it is shown that there is a modulational instability in the system, and collisions and quantum forces play significant roles on this instability. The quantum tunneling increases the phase and group velocities of the modulated waves and collisions increase the growth rate of the modulational instability. It is also shown that the effect of quantum forces and collisions is more significant in high modulated wavenumber regions.
Characterizing the nonlinear interaction of S- and P-waves in a rock sample
Gallot, Thomas; Szabo, Thomas L; Brown, Stephen; Burns, Daniel; Fehler, Michael
2014-01-01
The nonlinear elastic response of rocks is known to be caused by the rocks' microstructure, particularly cracks and fluids. This paper presents a method for characterizing the nonlinearity of rocks in a laboratory scale experiment with a unique configuration. This configuration has been designed to open up the possibility the nonlinear characterization of rocks as an imaging tool in a field scenario. The nonlinear interaction of two traveling waves: a low-amplitude 500 kHz P-wave probe and a high-amplitude 50 kHz S-wave pump has been studied on a room-dry 15 x 15x 3 cm slab of Berea sandstone. Changes in the arrival time of the P-wave probe as it passes through the perturbation created by the traveling S-wave pump were recorded. Waveforms were time gated to simulate a semi-infinite medium. The shear wave phase relative to the P-wave probe signal was varied with resultant changes in the P-wave probe arrival time of up to 100 ns, corresponding to a change in elastic properties of 0.2%. In order to estimate the ...
Energy Technology Data Exchange (ETDEWEB)
Itasse, Maxime, E-mail: Maxime.Itasse@onera.fr; Brazier, Jean-Philippe, E-mail: Jean-Philippe.Brazier@onera.fr; Léon, Olivier, E-mail: Olivier.Leon@onera.fr; Casalis, Grégoire, E-mail: Gregoire.Casalis@onera.fr [Onera - The French Aerospace Lab, F-31055 Toulouse (France)
2015-08-15
Nonlinear evolution of disturbances in an axisymmetric, high subsonic, high Reynolds number hot jet with forced eigenmodes is studied using the Parabolized Stability Equations (PSE) approach to understand how modes interact with one another. Both frequency and azimuthal harmonic interactions are analyzed by setting up one or two modes at higher initial amplitudes and various phases. While single mode excitation leads to harmonic growth and jet noise amplification, controlling the evolution of a specific mode has been made possible by forcing two modes (m{sub 1}, n{sub 1}), (m{sub 2}, n{sub 2}), such that the difference in azimuth and in frequency matches the desired “target” mode (m{sub 1} − m{sub 2}, n{sub 1} − n{sub 2}). A careful setup of the initial amplitudes and phases of the forced modes, defined as the “killer” modes, has allowed the minimizing of the initially dominant instability in the near pressure field, as well as its estimated radiated noise with a 15 dB loss. Although an increase of the overall sound pressure has been found in the range of azimuth and frequency analyzed, the present paper reveals the possibility to make the initially dominant instability ineffective acoustically using nonlinear interactions with forced eigenmodes.
Unity through nonlinearity: a unimodal coral-nutrient interaction.
Gil, Michael A
2013-08-01
The magnitude and direction of biological effects of environmental disturbances can vary considerably, especially among studies that use presence/absence manipulations. Because nonlinearities (e.g., humped relationships) are common in biological systems, this heterogeneity in effects may arise if systems are similar in their responses but specific studies use few (e.g., two) levels, or a narrow range, of a factor. To test whether nonlinearity can explain heterogeneous responses to a common environmental disturbance, I examined the effect of nutrient enrichment on coral growth, which has been previously shown using simple (e.g., two-level) manipulations to yield positive, negative, or neutral responses. I subjected corals (Porites) to a nutrient gradient in situ for 28 days. Coral growth rate increased (2.4-fold) then decreased (2.7-fold) with enrichment, returning to near-ambient values at the highest nutrient levels. This unimodal response could explain disparities among past findings and provides a compelling case for using regression designs to understand heterogeneity within ecological interactions.
Nonlinear phase noise mitigation in phase-sensitive amplified transmission systems.
Olsson, Samuel L I; Karlsson, Magnus; Andrekson, Peter A
2015-05-04
We investigate the impact of in-line amplifier noise in transmission systems amplified by two-mode phase-sensitive amplifiers (PSAs) and present the first experimental demonstration of nonlinear phase noise (NLPN) mitigation in a modulation format independent PSA-amplified transmission system. The NLPN mitigation capability is attributed to the correlated noise on the signal and idler waves at the input of the transmission span. We study a single-span system with noise loading in the transmitter but the results are expected to be applicable also in multi-span systems. The experimental investigation is supported by numerical simulations showing excellent agreement with the experiments. In addition to demonstrating NLPN mitigation we also present a record high sensitivity receiver, enabled by low-noise PSA-amplification, requiring only 4.1 photons per bit to obtain a bit error ratio (BER) of 1 × 10(-3) with 10 GBd quadrature phase-shift keying (QPSK) data.
Gravitational Waves from the Phase Transition of a Non-linearly Realised Electroweak Gauge Symmetry
Kobakhidze, Archil; Yue, Jason
2016-01-01
Within the Standard Model with non-linearly realised electroweak symmetry, the LHC Higgs boson may reside in a singlet representation of the gauge group. Several new interactions are then allowed, including anomalous Higgs self-couplings, which may drive the electroweak phase transition to be strongly first-order. In this paper we investigate the cosmological electroweak phase transition in a simplified model with an anomalous Higgs cubic self- coupling. We look at the feasibility of detecting gravitational waves produced during such a transition in the early universe by future space-based experiments. We find that for the range of relatively large cubic couplings, $111~{\\rm GeV}~ \\lesssim |\\kappa| \\lesssim 118~{\\rm GeV}$, $\\sim $mHz frequency gravitational waves can be observed by eLISA, while BBO will potentially be able to detect waves in a wider frequency range, $0.1-10~$mHz.
On a class of nonlinear dispersive-dissipative interactions
Energy Technology Data Exchange (ETDEWEB)
Rosenau, P. [Tel Aviv Univ. (Israel). School of Mathematical Sciences
1997-07-29
The authors study the prototypical, genuinely nonlinear, equation; u{sub t} + a(u{sup m}){sub x} + (u{sup n}){sub xxx} = {mu}(u{sup k}){sub xx}, a, {mu} = consts., which encompasses a wide variety of dissipative-dispersive interactions. The parametric surface k = (m + n)/2 separates diffusion dominated from dissipation dominated phenomena. On this surface dissipative and dispersive effects are in detailed balance for all amplitudes. In particular, the m = n + 2 = k + 1 subclass can be transformed into a form free of convection and dissipation making it accessible to theoretical studies. Both bounded and unbounded oscillations are found and certain exact solutions are presented. When a = (2{mu}3/){sup 2} the map yields a linear equation; rational, periodic and aperiodic solutions are constructed.
Nonlinear dynamic susceptibilities of interacting and noninteracting magnetic nanoparticles
Joensson, P; García-Palacios, J L; Svedlindh, P
2000-01-01
The linear and cubic dynamic susceptibilities of solid dispersions of nanosized maghemite gamma-Fe sub 2 O sub 3 particles have been measured for three samples with a volume concentration of magnetic particles ranging from 0.3% to 17%, in order to study the effect of dipole-dipole interactions. Significant differences between the dynamic response of the samples are observed. While the linear and cubic dynamic susceptibilities of the most dilute sample compare reasonably well with the corresponding expressions proposed by Raikher and Stepanov for noninteracting particles, the nonlinear dynamic response of the most concentrated sample exhibits at low temperatures similar features as observed in a Ag(11 at% Mn) spin glass.
New holographic dark energy model with non-linear interaction
Oliveros, A
2014-01-01
In this paper the cosmological evolution of a holographic dark energy model with a non-linear interaction between the dark energy and dark matter components in a FRW type flat universe is analysed. In this context, the deceleration parameter $q$ and the equation state $w_{\\Lambda}$ are obtained. We found that, as the square of the speed of sound remains positive, the model is stable under perturbations since early times; it also shows that the evolution of the matter and dark energy densities are of the same order for a long period of time, avoiding the so--called coincidence problem. We have also made the correspondence of the model with the dark energy densities and pressures for the quintessence and tachyon fields. From this correspondence we have reconstructed the potential of scalar fields and their dynamics.
On a class of nonlinear dispersive-dissipative interactions
Energy Technology Data Exchange (ETDEWEB)
Rosenau, P. [Tel Aviv Univ. (Israel). School of Mathematical Sciences
1997-07-29
The authors study the prototypical, genuinely nonlinear, equation; u{sub t} + a(u{sup m}){sub x} + (u{sup n}){sub xxx} = {mu}(u{sup k}){sub xx}, a, {mu} = consts., which encompasses a wide variety of dissipative-dispersive interactions. The parametric surface k = (m + n)/2 separates diffusion dominated from dissipation dominated phenomena. On this surface dissipative and dispersive effects are in detailed balance for all amplitudes. In particular, the m = n + 2 = k + 1 subclass can be transformed into a form free of convection and dissipation making it accessible to theoretical studies. Both bounded and unbounded oscillations are found and certain exact solutions are presented. When a = (2{mu}3/){sup 2} the map yields a linear equation; rational, periodic and aperiodic solutions are constructed.
Nonlinear laser-plasma interaction in magnetized liner inertial fusion
Geissel, Matthias; Awe, T. J.; Bliss, D. E.; Campbell, M. E.; Gomez, M. R.; Harding, E.; Harvey-Thompson, A. J.; Hansen, S. B.; Jennings, C.; Kimmel, M. W.; Knapp, P.; Lewis, S. M.; McBride, R. D.; Peterson, K.; Schollmeier, M.; Scoglietti, D. J.; Sefkow, A. B.; Shores, J. E.; Sinars, D. B.; Slutz, S. A.; Smith, I. C.; Speas, C. S.; Vesey, R. A.; Porter, J. L.
2016-03-01
Sandia National Laboratories is pursuing a variation of Magneto-Inertial Fusion called Magnetized Liner Inertial Fusion, or MagLIF. The MagLIF approach requires magnetization of the deuterium fuel, which is accomplished by an initial external B-Field and laser-driven pre-heat. While magnetization is crucial to the concept, it is challenging to couple sufficient energy to the fuel, since laser-plasma instabilities exist, and a compromise between laser spot size, laser entrance window thickness, and fuel density must be found. Nonlinear processes in laser plasma interaction, or laser-plasma instabilities (LPI), complicate the deposition of laser energy by enhanced absorption, backscatter, filamentation and beam-spray. Key LPI processes are determined, and mitigation methods are discussed. Results with and without improvement measures are presented.
Flight Dynamic Simulation with Nonlinear Aeroelastic Interaction using the ROM-ROM Procedure Project
National Aeronautics and Space Administration — ZONA Technology, Inc. (ZONA) proposes to develop an integrated flight dynamics simulation capability with nonlinear aeroelastic interactions by combining a flight...
Flight Dynamic Simulation with Nonlinear Aeroelastic Interaction using the ROM-ROM Procedure Project
National Aeronautics and Space Administration — ZONA Technology, Inc. proposes to develop an integrated flight dynamics simulation capability with nonlinear aeroelastic interactions by combining a flight dynamics...
Topological charge algebra of optical vortices in nonlinear interactions.
Zhdanova, Alexandra A; Shutova, Mariia; Bahari, Aysan; Zhi, Miaochan; Sokolov, Alexei V
2015-12-28
We investigate the transfer of orbital angular momentum among multiple beams involved in a coherent Raman interaction. We use a liquid crystal light modulator to shape pump and Stokes beams into optical vortices with various integer values of topological charge, and cross them in a Raman-active crystal to produce multiple Stokes and anti-Stokes sidebands. We measure the resultant vortex charges using a tilted-lens technique. We verify that in every case the generated beams' topological charges obey a simple relationship, resulting from angular momentum conservation for created and annihilated photons, or equivalently, from phase-matching considerations for multiple interacting beams.
Arditi, Tal; Granot, Er'el; Sternklar, Shmuel
2007-09-15
Brillouin amplification with counterpropagating modulated pump and Stokes light leads to nonlinear modulation-phase shifts of the interacting intensity waves. This is due to a partial transformation of the nonmodulated light component at the input into modulated light at the output as a result of a mixing process with the counterpropagating modulated component of the pump and results in an advance or delay of the input modulation. This occurs for interactions over less than half of a modulation wavelength. Milliwatts of power in a kilometer of standard single-mode fiber give significant tunability of the modulation phase.
Phase transformations, stability, and materials interactions
Energy Technology Data Exchange (ETDEWEB)
Morris, J.W. Jr.; Brewer, L.; Cost, J.R.; Shewmon, P.
1977-07-01
The proceedings of the Materials Sciences Workshop on Phase Transformations, Stability, and Materials Interactions are divided into sections according to the following topics: (I) workshop scope and priorities; (II) study group reports--ERDA mission needs; (III) study group reports--technical area research priorities. (SDF)
Characterizing the nonlinear interaction of S- and P-waves in a rock sample
Gallot, Thomas; Malcolm, Alison; Szabo, Thomas L.; Brown, Stephen; Burns, Daniel; Fehler, Michael
2015-01-01
The nonlinear elastic response of rocks is known to be caused by the rocks' microstructure, particularly cracks and fluids. This paper presents a method for characterizing the nonlinearity of rocks in a laboratory scale experiment with a unique configuration. This configuration has been designed to open up the possibility of using the nonlinear characterization of rocks as an imaging tool in the field. In our experiment, we study the nonlinear interaction of two traveling waves: a low-amplitude 500 kHz P-wave probe and a high-amplitude 50 kHz S-wave pump in a room-dry 15 × 15 × 3 cm slab of Berea sandstone. Changes in the arrival time of the P-wave probe as it passes through the perturbation created by the traveling S-wave pump were recorded. Waveforms were time gated to simulate a semi-infinite medium. The shear wave phase relative to the P-wave probe signal was varied with resultant changes in the P-wave probe arrival time of up to 100 ns, corresponding to a change in elastic properties of 0.2%. In order to estimate the strain in our sample, we also measured the particle velocity at the sample surface to scale a finite difference linear elastic simulation to estimate the complex strain field in the sample, on the order of 10-6, induced by the S-wave pump. We derived a fourth order elastic model to relate the changes in elasticity to the pump strain components. We recover quadratic and cubic nonlinear parameters: β ˜ = - 872 and δ ˜ = - 1.1 × 10 10 , respectively, at room-temperature and when particle motions of the pump and probe waves are aligned. Temperature fluctuations are correlated to changes in the recovered values of β ˜ and δ ˜ , and we find that the nonlinear parameter changes when the particle motions are orthogonal. No evidence of slow dynamics was seen in our measurements. The same experimental configuration, when applied to Lucite and aluminum, produced no measurable nonlinear effects. In summary, a method of selectively determining the
Nonlinear neutrino-photon interactions inside strong laser pulses
Meuren, Sebastian; Di Piazza, Antonino
2015-01-01
Even though neutrinos are neutral particles and interact only via the exchange of weak gauge bosons, charged leptons and quarks can mediate a coupling to the photon field beyond tree level. Inside a relativistically strong laser field nonlinear effects in the laser amplitude can play an important role, as electrons and positrons interact nonperturbatively with the coherent part of the photon field. Here, we calculate for the first time the leading-order contribution to the axial-vector--vector current-coupling tensor inside an arbitrary plane-wave laser field (which is taken into account exactly by employing the Furry picture). The current-coupling tensor appears in the calculation of various electroweak processes inside strong laser fields like photon emission or trident electron-positron pair production by a neutrino. Moreover, as we will see below, the axial-vector--vector current-coupling tensor contains the Adler-Bell-Jackiw (ABJ) anomaly. This occurrence renders the current-coupling tensor also interest...
Texture segmentation via nonlinear interactions among Gabor feature pairs
Tang, Hak W.; Srinivasan, Venugopal; Ong, Sim-Heng
1995-01-01
Segmentation of an image based on texture can be performed by a set of N Gabor filters that uniformly covers the spatial frequency domain. The filter outputs that characterize the frequency and orientation content of the intensity distribution in the vicinity of a pixel constitute an N-element feature vector. As an alternative to the computationally intensive procedure of segmentation based on the N-element vectors generated at each pixel, we propose an algorithm for selecting a pair of filters that provides maximum discrimination between two textures constituting the object and its surroundings in an image. Images filtered by the selected filters are nonlinearity transformed to produce two feature maps. The feature maps are smoothed by an intercompetitive and intracooperative interaction process between them. These interactions have proven to be much superior to simple Gaussian filtering in reducing the effects of spatial variability of feature maps. A segmented binary image is then generated by a pixel-by-pixel comparison of the two maps. Results of experiments involving several texture combinations show that this procedure is capable of producing clean segmentation.
eta/s and the phase transition of the Non-Linear Sigma Model
Dobado, Antonio; Torres-Rincon, Juan M
2008-01-01
We present a calculation of eta/s for the meson gas (zero baryon number) within unitarized NLO chiral perturbation theory and confirm the observation that eta/s decreases towards the possible phase transition to a quark-gluon plasma/liquid. The value is however somewhat higher than previously estimated in LO chiPT. We then study the behavior of the viscosity over entropy density across the known second order phase transition in the Non-Linear Sigma Model, and establish that it has indeed a minimum that, within calculational uncertainties, can be identified with the phase transition. Finally we examine the case of atomic Argon gas to check the discontinuity of eta/s across a first order phase transition. Our results reinforce the possibility of employing the KSS number to pin down the phase transition and critical point to a cross-over in strongly interacting nuclear matter between the hadron gas and the quark and gluon plasma/liquid.
Gauge interactions and topological phases of matter
Tachikawa, Yuji; Yonekura, Kazuya
2016-09-01
We study the effects of strongly coupled gauge interactions on the properties of the topological phases of matter. In particular, we discuss fermionic systems with three spatial dimensions, protected by time-reversal symmetry. We first derive a sufficient condition for the introduction of a dynamical Yang-Mills field to preserve the topological phase of matter, and then show how the massless pions capture in the infrared the topological properties of the fermions in the ultraviolet. Finally, we use the S-duality of calligraphy">N=2 supersymmetric SU(2) gauge theory with N=4 flavors to show that the ν=16 phase of Majorana fermions can be continuously connected to the trivial ν=0 phase.
Nonlinear interactions of electromagnetic waves with the auroral ionosphere
Wong, Alfred Y.
1999-09-01
The ionosphere provides us with an opportunity to perform plasma experiments in an environment with long confinement times, very large-scale lengths, and no confining walls. The auroral ionosphere with its nearly vertical magnetic field geometry is uniquely endowed with large amount of free energy from electron and ion precipitation along the magnetic field and mega-ampere current across the magnetic field. To take advantage of this giant outdoor laboratory, two facilities HAARP and HIPAS, with frequencies ranging from the radio to optical bands, are now available for active probing of and interaction with this interesting region. The ponderomotive pressures from the self-consistent wave fields have produced significant local perturbations of density and particle distributions at heights where the incident EM frequency matches a plasma resonance. This paper will review theory and experiments covering the nonlinear phenomena of parametric decay instability to wave collapse processes. At HF frequencies plasma lenses can be created by preconditioning pulses to focus what is a normally divergent beam into a high-intensity spot to further enhance nonlinear phenomena. At optical wavelengths a large rotating liquid metal mirror is used to focus laser pulses up to a given height. Such laser pulses are tuned to the same wavelengths of selected atomic and molecular resonances, with resulting large scattering cross sections. Ongoing experiments on dual-site experiments and excitation of ELF waves will be presented. The connection of such basic studies to environmental applications will be discussed. Such applications include the global communication using ELF waves, the ozone depletion and remediation and the control of atmospheric CO2 through the use of ion cyclotron resonant heating.
Nonlinear Dynamics of Cantilever-Sample Interactions in Atomic Force Microscopy
Cantrell, John H.; Cantrell, Sean A.
2010-01-01
The interaction of the cantilever tip of an atomic force microscope (AFM) with the sample surface is obtained by treating the cantilever and sample as independent systems coupled by a nonlinear force acting between the cantilever tip and a volume element of the sample surface. The volume element is subjected to a restoring force from the remainder of the sample that provides dynamical equilibrium for the combined systems. The model accounts for the positions on the cantilever of the cantilever tip, laser probe, and excitation force (if any) via a basis set of set of orthogonal functions that may be generalized to account for arbitrary cantilever shapes. The basis set is extended to include nonlinear cantilever modes. The model leads to a pair of coupled nonlinear differential equations that are solved analytically using a matrix iteration procedure. The effects of oscillatory excitation forces applied either to the cantilever or to the sample surface (or to both) are obtained from the solution set and applied to the to the assessment of phase and amplitude signals generated by various acoustic-atomic force microscope (A-AFM) modalities. The influence of bistable cantilever modes of on AFM signal generation is discussed. The effects on the cantilever-sample surface dynamics of subsurface features embedded in the sample that are perturbed by surface-generated oscillatory excitation forces and carried to the cantilever via wave propagation are accounted by the Bolef-Miller propagating wave model. Expressions pertaining to signal generation and image contrast in A-AFM are obtained and applied to amplitude modulation (intermittent contact) atomic force microscopy and resonant difference-frequency atomic force ultrasonic microscopy (RDF-AFUM). The influence of phase accumulation in A-AFM on image contrast is discussed, as is the effect of hard contact and maximum nonlinearity regimes of A-AFM operation.
Nonlinear Pulse Compression and Reshaping Using Cross-Phase Modulation in a Dispersion-Shifted Fiber
Institute of Scientific and Technical Information of China (English)
S.; W.; Chan; K.; K.; Chow; C.; Shu
2003-01-01
Nonlinear pulse compression has been demonstrated by cross-phase modulation in a dispersion-shifted fiber. The output is obtained from filtering of the broadened optical spectrum and a pulse width reduction from 61 to 28 ps is achieved.
Elsaesser, Thomas; Reimann, Klaus; Woerner, Michael
2015-06-01
Intense terahertz (THz) electric field transients with amplitudes up to several megavolts/centimeter and novel multidimensional techniques are the key ingredients of nonlinear THz spectroscopy, a new area of basic research. Both nonlinear light-matter interactions including the non-perturbative regime and THz driven charge transport give new insight into the character and dynamics of low-energy excitations of condensed matter and into quantum kinetic phenomena. This article provides an overview of recent progress in this field, combining an account of technological developments with selected prototype results for liquids and solids. The potential of nonlinear THz methods for future studies of low-frequency excitations of condensed-phase molecular systems is discussed as well.
Nonlinear Wave-Currents interactions in shallow water
Lannes, David
2015-01-01
We study here the propagation of long waves in the presence of vorticity. In the irrotational framework, the Green-Naghdi equations (also called Serre or fully nonlinear Boussinesq equations) are the standard model for the propagation of such waves. These equations couple the surface elevation to the vertically averaged horizontal velocity and are therefore independent of the vertical variable. In the presence of vorticity, the dependence on the vertical variable cannot be removed from the vorticity equation but it was however shown in [?] that the motion of the waves could be described using an extended Green-Naghdi system. In this paper we propose an analysis of these equations, and show that they can be used to get some new insight into wave-current interactions. We show in particular that solitary waves may have a drastically different behavior in the presence of vorticity and show the existence of solitary waves of maximal amplitude with a peak at their crest, whose angle depends on the vorticity. We als...
Asymmetrically pumped Bragg scattering with the effects of nonlinear phase modulation
DEFF Research Database (Denmark)
Andersen, Lasse Mejling; Friis, Søren Michael Mørk; Reddy, Dileep V.
2014-01-01
We derive exact solutions to asymmetrically pumped Bragg scattering with nonlinear phase-modulation (NPM) and show that this setup allows for the frequency conversion of many temporal modes, while reducing the effects due to NPM.......We derive exact solutions to asymmetrically pumped Bragg scattering with nonlinear phase-modulation (NPM) and show that this setup allows for the frequency conversion of many temporal modes, while reducing the effects due to NPM....
A WEAKLY NONLINEAR WATER WAVE MODEL TAKING INTO ACCOUNT DISPERSION OF WAVE PHASE VELOCITY
Institute of Scientific and Technical Information of China (English)
李瑞杰; 李东永
2002-01-01
This paper presents a weakly nonlinear water wave model using a mild slope equation and a new explicit formulation which takes into account dispersion of wave phase velocity, approximates Hedges' (1987) nonlinear dispersion relationship, and accords well with the original empirical formula. Comparison of the calculating results with those obtained from the experimental data and those obtained from linear wave theory showed that the present water wave model considering the dispersion of phase velocity is rational and in good agreement with experiment data.
Extended phase space of Black Holes in Lovelock gravity with nonlinear electrodynamics
Hendi, S H; Panah, B Eslam
2015-01-01
In this paper, we consider Lovelock gravity in presence of two Born-Infeld types of nonlinear electrodynamics and study their thermodynamical behavior. We extend the phase space by considering cosmological constant as a thermodynamical pressure. We obtain critical values of pressure, volume and temperature and investigate the effects of both the Lovelock gravity and the nonlinear electrodynamics on these values. We plot $P-v$, $T-v$ and $G-T$ diagrams to study the phase transition of these thermodynamical systems. We show that power of the nonlinearity and gravity have opposite effects. We also show how considering cosmological constant, nonlinearity and Lovelock parameters as thermodynamical variables will modify Smarr formula and first law of thermodynamics. In addition, we study the behavior of universal ratio of $\\frac{P_{c}v_{c}}{T_{c}}$ for different values of nonlinearity power of electrodynamics as well as the Lovelock coefficients.
Switching Correlation and Noise Level in Pr(3+):YSO Crystal via Dressing Nonlinear Phase.
Ahmed, Irfan; Zhang, Zhaoyang; Wen, Feng; Zhang, Da; Li, Changbiao; Wang, Ruimin; Zhang, Yanpeng
2016-09-21
We propose and experimentally demonstrate that the intensity noise correlation and the noise level of intensity-difference and intensity-sum in Stokes and anti-Stokes channel can be well controlled by the relative nonlinear phase in spontaneous parametric four-wave mixing process. By modulating the relative nonlinear phase, including self-phase modulation and cross-phase modulation, switching the correlation into anti-correlation and the relative intensity noise level between the intensity-difference and intensity-sum are realized. We also show that the variation tendencies of the relative intensity noise level and the corresponding intensity fluctuations correlation are in accordance with each other.
Nonlinear modal interactions in parity-time (${\\cal PT}$) symmetric lasers
Ge, Li
2016-01-01
Parity-time ($\\cal PT$) symmetric lasers have attracted considerable attention lately due to their promising applications and intriguing properties, such as free spectral range doubling and single-mode lasing. In this work we discuss nonlinear modal interactions in these laser systems under steady state conditions, and we demonstrate that several gain clamping scenarios can occur for lasing operation in the $\\cal PT$-symmetric and $\\cal PT$-broken phases. In particular, we show that, depending on the system's design and the external pump profile, its operation in the nonlinear regime falls into two different categories: in one the system is frozen in the $\\cal PT$ phase space as the applied gain increases, while in the other the system is pulled towards its exceptional point. These features are first illustrated by a coupled mode formalism and later verified by employing the Steady-state Ab-initio Laser Theory (SALT). Our findings shine light on the robustness of single-mode operation in these lasers against ...
Cantrell, John H., Jr.; Cantrell, Sean A.
2008-01-01
A comprehensive analytical model of the interaction of the cantilever tip of the atomic force microscope (AFM) with the sample surface is developed that accounts for the nonlinearity of the tip-surface interaction force. The interaction is modeled as a nonlinear spring coupled at opposite ends to linear springs representing cantilever and sample surface oscillators. The model leads to a pair of coupled nonlinear differential equations that are solved analytically using a standard iteration procedure. Solutions are obtained for the phase and amplitude signals generated by various acoustic-atomic force microscope (A-AFM) techniques including force modulation microscopy, atomic force acoustic microscopy, ultrasonic force microscopy, heterodyne force microscopy, resonant difference-frequency atomic force ultrasonic microscopy (RDF-AFUM), and the commonly used intermittent contact mode (TappingMode) generally available on AFMs. The solutions are used to obtain a quantitative measure of image contrast resulting from variations in the Young modulus of the sample for the amplitude and phase images generated by the A-AFM techniques. Application of the model to RDF-AFUM and intermittent soft contact phase images of LaRC-cp2 polyimide polymer is discussed. The model predicts variations in the Young modulus of the material of 24 percent from the RDF-AFUM image and 18 percent from the intermittent soft contact image. Both predictions are in good agreement with the literature value of 21 percent obtained from independent, macroscopic measurements of sheet polymer material.
Nonlinear effects in the torsional adjustment of interacting DNA.
Kornyshev, A A; Wynveen, A
2004-04-01
DNA molecules in solution, having negatively charged phosphates and countercations readsorbed on its surface, possess a distinct charge separation motif to interact electrostatically. If their double-helical structure were ideal, duplexes in parallel juxtaposition could choose azimuthal alignment providing attraction, or at least a reduction of repulsion, between them. But duplexes are not perfect staircases and the distortions of their helical structure correlate with their base pair texts. If the patterns of distortions on the opposing molecules are uncorrelated, the mismatch will accumulate as a random walk and attraction vanishes. Based on this idea, a model of recognition of homologous sequences has been proposed [A. A. Kornyshev and S. Leikin, Phys. Rev. Lett. 86, 3666 (2001)]. But DNA has torsional elasticity. How will this help to relax a mismatch between the charge distributions on two nonhomologous DNA's? In the same work, the solution of this problem has been mapped onto a frustrated sine Gordon equation in a nonlocal random field (where the latter represents a pattern of twist angle distortions on the opposing molecules), but the results had been obtained in the limit of torsionally rigid molecules. In the present paper, by solving this equation numerically, we find a strongly nonlinear relaxation mechanism which utilizes static kink-soliton modes triggered by the "random field." In the range of parameters where the solitons do not emerge, we find good agreement with the results of a variational study [A. G. Cherstvy, A. A. Kornyshev, and S. Leikin, J. Phys. Chem. B (to be published)]. We reproduce the first-order transitions in the interaxial separation dependence, but detect also second-order or weak first-order transitions for shorter duplexes. The recognition energy between two nonhomologous DNA sequences is calculated as a function of interaxial separation and the length of juxtaposition. The soliton-caused kinky length dependence is discussed in
Nonlinear effects in the torsional adjustment of interacting DNA
Kornyshev, A. A.; Wynveen, A.
2004-04-01
DNA molecules in solution, having negatively charged phosphates and countercations readsorbed on its surface, possess a distinct charge separation motif to interact electrostatically. If their double-helical structure were ideal, duplexes in parallel juxtaposition could choose azimuthal alignment providing attraction, or at least a reduction of repulsion, between them. But duplexes are not perfect staircases and the distortions of their helical structure correlate with their base pair texts. If the patterns of distortions on the opposing molecules are uncorrelated, the mismatch will accumulate as a random walk and attraction vanishes. Based on this idea, a model of recognition of homologous sequences has been proposed [A. A. Kornyshev and S. Leikin, Phys. Rev. Lett. 86, 3666 (2001)]. But DNA has torsional elasticity. How will this help to relax a mismatch between the charge distributions on two nonhomologous DNA’s? In the same work, the solution of this problem has been mapped onto a frustrated sine Gordon equation in a nonlocal random field (where the latter represents a pattern of twist angle distortions on the opposing molecules), but the results had been obtained in the limit of torsionally rigid molecules. In the present paper, by solving this equation numerically, we find a strongly nonlinear relaxation mechanism which utilizes static kink-soliton modes triggered by the “random field.” In the range of parameters where the solitons do not emerge, we find good agreement with the results of a variational study [A. G. Cherstvy, A. A. Kornyshev, and S. Leikin, J. Phys. Chem. B (to be published)]. We reproduce the first-order transitions in the interaxial separation dependence, but detect also second-order or weak first-order transitions for shorter duplexes. The recognition energy between two nonhomologous DNA sequences is calculated as a function of interaxial separation and the length of juxtaposition. The soliton-caused kinky length dependence is
Negative Kerr Nonlinearity of Graphene as seen via Chirped-Pulse-Pumped Self-Phase Modulation
Vermeulen, Nathalie; Castelló-Lurbe, David; Cheng, JinLuo; Pasternak, Iwona; Krajewska, Aleksandra; Ciuk, Tymoteusz; Strupinski, Wlodek; Thienpont, Hugo; Van Erps, Jürgen
2016-10-01
We experimentally demonstrate a negative Kerr nonlinearity for quasiundoped graphene. Hereto, we introduce the method of chirped-pulse-pumped self-phase modulation and apply it to graphene-covered silicon waveguides at telecom wavelengths. The extracted Kerr-nonlinear index for graphene equals n2 ,gr=-10-13 m2 /W . Whereas the sign of n2 ,gr turns out to be negative in contrast to what has been assumed so far, its magnitude is in correspondence with that observed in earlier experiments. Graphene's negative Kerr nonlinearity strongly impacts how graphene should be exploited for enhancing the nonlinear response of photonic (integrated) devices exhibiting a positive nonlinearity. It also opens up the possibility of using graphene to annihilate unwanted nonlinear effects in such devices, to develop unexplored approaches for establishing Kerr processes, and to extend the scope of the "periodic poling" method often used for second-order nonlinearities towards third-order Kerr processes. Because of the generic nature of the chirped-pulse-pumped self-phase modulation method, it will allow fully characterizing the Kerr nonlinearity of essentially any novel (2D) material.
Cain, A. B.; Thompson, M. W.
1986-01-01
The growth of the momentum thickness and the modal disturbance energies are examined to study the nature and onset of nonlinearity in a temporally growing free shear layer. A shooting technique is used to find solutions to the linearized eigenvalue problem, and pseudospectral weakly nonlinear simulations of this flow are obtained for comparison. The roll-up of a fundamental disturbance follows linear theory predictions even with a 20 percent disturbance amplitude. A weak nonlinear interaction of the disturbance creates a finite-amplitude mean shear stress which dominates the growth of the layer momentum thickness, and the disturbance growth rate changes until the fundamental disturbance dominates. The fundamental then becomes an energy source for the harmonic, resulting in an increase in the growth rate of the subharmonic over the linear prediction even when the fundamental has no energy to give. Also considered are phase relations and the wall influence.
A NUMERICAL METHOD FOR SIMULATING NONLINEAR FLUID-RIGID STRUCTURE INTERACTION PROBLEMS
Institute of Scientific and Technical Information of China (English)
XingJ.T; PriceW.G; ChenY.G
2005-01-01
A numerical method for simulating nonlinear fluid-rigid structure interaction problems is developed. The structure is assumed to undergo large rigid body motions and the fluid flow is governed by nonlinear, viscous or non-viscous, field equations with nonlinear boundary conditions applied to the free surface and fluid-solid interaction interfaces. An Arbitrary-Lagrangian-Eulerian (ALE) mesh system is used to construct the numerical model. A multi-block numerical scheme of study is adopted allowing for the relative motion between moving overset grids, which are independent of one another. This provides a convenient method to overcome the difficulties in matching fluid meshes with large solid motions. Nonlinear numerical equations describing nonlinear fluid-solid interaction dynamics are derived through a numerical discretization scheme of study. A coupling iteration process is used to solve these numerical equations. Numerical examples are presented to demonstrate applications of the model developed.
Lavrov, Roman; Peil, Michael; Jacquot, Maxime; Larger, Laurent; Udaltsov, Vladimir; Dudley, John
2009-08-01
We demonstrate experimentally how nonlinear optical phase dynamics can be generated with an electro-optic delay oscillator. The presented architecture consists of a linear phase modulator, followed by a delay line, and a differential phase-shift keying demodulator (DPSK-d). The latter represents the nonlinear element of the oscillator effecting a nonlinear transformation. This nonlinearity is considered as nonlocal in time since it is ruled by an intrinsic differential delay, which is significantly greater than the typical phase variations. To study the effect of this specific nonlinearity, we characterize the dynamics in terms of the dependence of the relevant feedback gain parameter. Our results reveal the occurrence of regular GHz oscillations (approximately half of the DPSK-d free spectral range), as well as a pronounced broadband phase-chaotic dynamics. Beyond this, the observed dynamical phenomena offer potential for applications in the field of microwave photonics and, in particular, for the realization of novel chaos communication systems. High quality and broadband phase-chaos synchronization is also reported with an emitter-receiver pair of the setup.
DEFF Research Database (Denmark)
Bang, Ole; Graversen, T. W.; Clausen, Carl A. Balslev
2000-01-01
Quasi-phase-matching gratings induces Kerr effects in quadratic nonlinear materials. We show analytically and confirm numerically how modulating the grating changes the effective quadratic and cubic nonlinearities and allows for multi-wavelength second-harmonic generation....
Indian Academy of Sciences (India)
R Ganapathy; V C Kuriakose
2002-04-01
We obtain conditions for the occurrence of cross-phase modulational instability in the normal dispersion regime for the coupled higher order nonlinear Schrödinger equation with higher order dispersion and nonlinear terms.
Nonlinear infragravity–wave interactions on a gently sloping laboratory beach
De Bakker, A.T.M.; Herbers, T.H.C.; Smit, P.B.; Tissier, M.F.S.; Ruessink, B.G.
2015-01-01
A high-resolution dataset of three irregular wave conditions collected on a gently sloping laboratory beach is analyzed to study nonlinear energy transfers involving infragravity frequencies. This study uses bispectral analysis to identify the dominant, nonlinear interactions and estimate energy tra
Nonlinear infragravity-wave interactions on a gently sloping laboratory beach
de Bakker, A. T M; Herbers, T. H C; Smit, P. B.; Tissier, M. F S; Ruessink, B. G.
2015-01-01
A high-resolution dataset of three irregular wave conditions collected on a gently sloping laboratory beach is analyzed to study nonlinear energy transfers involving infragravity frequencies. This study uses bispectral analysis to identify the dominant, nonlinear interactions and estimate energy tra
Beach steepness effects on nonlinear infragravity-wave interactions : A numerical study
de Bakker, A. T M; Tissier, M. F S; Ruessink, B. G.
2016-01-01
The numerical model SWASH is used to investigate nonlinear energy transfers between waves for a diverse set of beach profiles and wave conditions, with a specific focus on infragravity waves. We use bispectral analysis to study the nonlinear triad interactions, and estimate energy transfers to deter
DEFF Research Database (Denmark)
Hu, Hao; Jopson, R. M.; Dinu, M.;
2013-01-01
We demonstrate compensation of fiber nonlinearities using optical phase conjugation of an 8-chamiel WDM 32-Gbaud PDM QPSK signal. Conjugating phase every 600 km in a fiber loop enabled a 6000 km transmission over True Wave fiber. © 2013 Optical Society of America....
DEFF Research Database (Denmark)
Bang, Ole; Corney, Joel Frederick
2001-01-01
In continuous-wave operation asymmetric induced nonlinearities induce an intensity-dependent phase mismatch that implies a nonzero so-called separatrix intensity, the crossing of which changes the one-period phase shift of the fundamental by Pi , with obvious use in switching applications.We deri...
Low-Complexity Tracking of Laser and Nonlinear Phase Noise in WDM Optical Fiber Systems
DEFF Research Database (Denmark)
Yankov, Metodi Plamenov; Fehenberger, Tobias; Barletta, Luca;
2015-01-01
In this paper, the wavelength division multiplexed (WDM) fiber optic channel is considered. It is shown that for ideal distributed Raman amplification (IDRA), the Wiener process model is suitable for the non-linear phase noise due to cross phase modulation from neighboring channels. Based...
On the theory of ternary melt crystallization with a non-linear phase diagram
Toropova, L. V.; Dubovoi, G. Yu; Alexandrov, D. V.
2017-04-01
The present study is concerned with a theoretical analysis of unidirectional solidification process of ternary melts in the presence of a phase transition (mushy) layer. A new analytical solution of heat and mass transfer equations describing the steady-state crystallization scenario is found with allowance for a non-linear liquidus equation. The model under consideration takes into account the presence of two phase transition layers, namely, the primary and cotectic mushy regions. We demonstrate that the phase diagram nonlinearity leads to substantial changes of analytical solutions.
Tholerus, Emmi; Hellsten, Torbjörn
2016-01-01
FOXTAIL is a new hybrid magnetohydrodynamic-kinetic code used to describe interactions between energetic particles and Alfv\\'en eigenmodes in tokamaks with realistic geometries. The code simulates the nonlinear dynamics of the amplitudes of individual eigenmodes and of a set of discrete markers in five-dimensional phase space representing the energetic particle distribution. Action-angle coordinates of the equilibrium system are used for efficient tracing of energetic particles, and the particle acceleration by the wave fields of the eigenmodes is Fourier decomposed in the same angles. The eigenmodes are described using temporally constant eigenfunctions with dynamic complex amplitudes. Possible applications of the code are presented, e.g., making a quantitative validity evaluation of the one-dimensional bump-on-tail approximation of the system. Expected effects of the fulfillment of the Chirikov criterion in two-mode scenarios have also been verified.
Nonlinear light behaviors near phase transition in non-parity-time-symmetric complex waveguides
Nixon, Sean
2016-01-01
Many classes of non-parity-time (PT) symmetric waveguides with arbitrary gain and loss distributions still possess all-real linear spectrum or exhibit phase transition. In this article, nonlinear light behaviors in these complex waveguides are probed analytically near a phase transition. Using multi-scale perturbation methods, a nonlinear ordinary differential equation (ODE) is derived for the light's amplitude evolution. This ODE predicts that the first class of these non-PT-symmetric waveguides support continuous families of solitons and robust amplitude-oscillating solutions both above and below phase transition, in close analogy with PT-symmetric systems. For the other classes of waveguides, the light's intensity always amplifies under the effect of nonlinearity even if the waveguide is below phase transition. These analytical predictions are confirmed by direct computations of the full system.
Wei, Xile; Lu, Meili; Wang, Jiang; Tsang, K. M.; Deng, Bin; Che, Yanqiu
2010-05-01
We consider the assumption of existence of the general nonlinear internal model that is introduced in the design of robust output regulators for a class of minimum-phase nonlinear systems with rth degree (r ≥ 2). The robust output regulation problem can be converted into a robust stabilisation problem of an augmented system consisting of the given plant and a high-gain nonlinear internal model, perfectly reproducing the bounded including not only periodic but also nonperiodic exogenous signal from a nonlinear system, which satisfies some general immersion assumption. The state feedback controller is designed to guarantee the asymptotic convergence of system errors to zero manifold. Furthermore, the proposed scheme makes use of output feedback dynamic controller that only processes information from the regulated output error by using high-gain observer to robustly estimate the derivatives of the regulated output error. The stabilisation analysis of the resulting closed-loop systems leads to regional as well as semi-global robust output regulation achieved for some appointed initial condition in the state space, for all possible values of the uncertain parameter vector and the exogenous signal, ranging over an arbitrary compact set.
Mukamel, Shaul
2016-07-01
Nonlinear spectroscopy signals detected by fluorescence from dilute samples of N non-interacting molecules are usually adequately described by simply multiplying the single molecule response by N. We show that signals that scale with higher powers of N are generated by the joint detection of several particles. This can be accomplished by phase sensitive detection such as phase cycling, photo-acoustic modulation, or by Hanbury-Brown Twiss photon coincidence. Such measurements can dissect the ensemble according to the number of excited particles.
Optical frequency conversion in quasi-phase-matched stacks of nonlinear crystals
Rustagi, K. C.; Mehendale, S. C.; Meenakshi, S.
1982-06-01
The paper presents a quantitative theory of nonlinear frequency conversion in stacks of crystals in which the phase mismatch due to dispersion is compensated by changing the sign of the nonlinear coupling coefficient in successive crystals. The effects of systematic and random departures in crystal lengths are studied with emphasis on the evolution of the relative phase. It is shown that with the appropriate choice of the signs of the nonlinear coupling coefficient in various crystals, high efficiency frequency conversion should be possible using almost any sufficiently large set of nonlinear crystals. In addition, the theory of second harmonic generation in periodic stacks and in rotating twinned crystals of zinc-blend structure is described.
Nonlinear dynamics of phase space zonal structures and energetic particle physics in fusion plasmas
Zonca, Fulvio; Briguglio, Sergio; Fogaccia, Giuliana; Vlad, Gregorio; Wang, Xin
2014-01-01
A general theoretical framework for investigating nonlinear dynamics of phase space zonal structures is presented in this work. It is then, more specifically, applied to the limit where the nonlinear evolution time scale is smaller or comparable to the wave-particle trapping period. In this limit, both theoretical and numerical simulation studies show that non-adiabatic frequency chirping and phase locking could lead to secular resonant particle transport on meso- or macro-scales. The interplay between mode structures and resonant particles then provides the crucial ingredient to properly understand and analyze the nonlinear dynamics of Alfv\\'en wave instabilities excited by non-perturbative energetic particles in burning fusion plasmas. Analogies with autoresonance in nonlinear dynamics and with superradiance in free electron lasers are also briefly discussed.
Understanding and Ameliorating Non-Linear Phase and Amplitude Responses in AMCW Lidar
Directory of Open Access Journals (Sweden)
John P. Godbaz
2011-12-01
Full Text Available Amplitude modulated continuous wave (AMCW lidar systems commonly suffer from non-linear phase and amplitude responses due to a number of known factors such as aliasing and multipath inteference. In order to produce useful range and intensity information it is necessary to remove these perturbations from the measurements. We review the known causes of non-linearity, namely aliasing, temporal variation in correlation waveform shape and mixed pixels/multipath inteference. We also introduce other sources of non-linearity, including crosstalk, modulation waveform envelope decay and non-circularly symmetric noise statistics, that have been ignored in the literature. An experimental study is conducted to evaluate techniques for mitigation of non-linearity, and it is found that harmonic cancellation provides a significant improvement in phase and amplitude linearity.
Nonlinear dynamics of wave packets in PT-symmetric optical lattices near the phase transition point
Nixon, Sean; Yang, Jianke
2012-01-01
Nonlinear dynamics of wave packets in PT-symmetric optical lattices near the phase-transition point are analytically studied. A nonlinear Klein-Gordon equation is derived for the envelope of these wave packets. A variety of novel phenomena known to exist in this envelope equation are shown to also exist in the full equation including wave blowup, periodic bound states and solitary wave solutions.
Possible second-order nonlinear interactions of plane waves in an elastic solid
Korneev, V.A.; Demcenko, A.
2014-01-01
There exist ten possible nonlinear elastic wave interactions for an isotropic solid described by three constants of the third order. All other possible interactions out of 54 combinations (triplets) of interacting and resulting waves are prohibited, because of restrictions of various kinds. The cons
Wu, Ya-Bo; Zhang, Cheng-Yuan; Lu, Jian-Bo; Hu, Mu-Hong; Chai, Yun-Tian
2017-04-01
We numerically investigate the holographic paramagnetism-ferromagnetism phase transition in the 4-dimensional Lifshitz spacetime in the presence of three kinds of typical Born-Infeld-like nonlinear electrodynamics. Concretely, in the probe limit, we thoroughly discuss the effects of the nonlinear parameter b and the dynamical exponent z on the critical temperature, magnetic moment and hysteresis loop. The results show that the exponential form of nonlinear electrodynamics correction makes the critical temperature smaller and the magnetic moment harder to form with the absent external field for a constant nonlinear parameter b comparing it with the logarithmic form of nonlinear electrodynamics and the Born-Infeld nonlinear electrodynamics, especially for the case of larger dynamical exponent z. Moreover, the increase of nonlinear parameter b (for the fixed z) or dynamical exponent z (for the fixed b) will result in extending the period of the external magnetic field. Particularly, the effect of the exponential form of nonlinear electrodynamics on the periodicity of hysteresis loop is more noteworthy.
Advanced Seismic Fragility Modeling using Nonlinear Soil-Structure Interaction Analysis
Energy Technology Data Exchange (ETDEWEB)
Bolisetti, Chandu [Idaho National Lab. (INL), Idaho Falls, ID (United States); Coleman, Justin [Idaho National Lab. (INL), Idaho Falls, ID (United States); Talaat, Mohamed [Simpson-Gupertz & Heger, Waltham, MA (United States); Hashimoto, Philip [Simpson-Gupertz & Heger, Waltham, MA (United States)
2015-09-01
The goal of this effort is to compare the seismic fragilities of a nuclear power plant system obtained by a traditional seismic probabilistic risk assessment (SPRA) and an advanced SPRA that utilizes Nonlinear Soil-Structure Interaction (NLSSI) analysis. Soil-structure interaction (SSI) response analysis for a traditional SPRA involves the linear analysis, which ignores geometric nonlinearities (i.e., soil and structure are glued together and the soil material undergoes tension when the structure uplifts). The NLSSI analysis will consider geometric nonlinearities.
High-order finite difference solution for 3D nonlinear wave-structure interaction
DEFF Research Database (Denmark)
Ducrozet, Guillaume; Bingham, Harry B.; Engsig-Karup, Allan Peter;
2010-01-01
This contribution presents our recent progress on developing an efficient fully-nonlinear potential flow model for simulating 3D wave-wave and wave-structure interaction over arbitrary depths (i.e. in coastal and offshore environment). The model is based on a high-order finite difference scheme...... OceanWave3D presented in [1, 2]. A nonlinear decomposition of the solution into incident and scattered fields is used to increase the efficiency of the wave-structure interaction problem resolution. Application of the method to the diffraction of nonlinear waves around a fixed, bottom mounted circular...
Advanced Phase noise modeling techniques of nonlinear microwave devices
Prigent, M.; J. C. Nallatamby; R. Quere
2004-01-01
In this paper we present a coherent set of tools allowing an accurate and predictive design of low phase noise oscillators. Advanced phase noise modelling techniques in non linear microwave devices must be supported by a proven combination of the following : - Electrical modeling of low-frequency noise of semiconductor devices, oriented to circuit CAD . The local noise sources will be either cyclostationary noise sources or quasistationary noise sources. - Theoretic...
DEFF Research Database (Denmark)
Peucheret, Christophe; Da Ros, Francesco; Vukovic, Dragana;
- compatible fabrication process, degrees of freedom in dispersion engineering, and high nonlinear coecient. However, the detrimental eect of free-carrier absorption induced by two-photon absorp- tion has so far prevented them from being used for the demonstration of phase-sensitive processing. Thanks...
Cui, Junning; He, Zhangqiang; Jiu, Yuanwei; Tan, Jiubin; Sun, Tao
2016-09-01
The demand for minimal cyclic nonlinearity error in laser interferometry is increasing as a result of advanced scientific research projects. Research shows that the quadrature phase error is the main effect that introduces cyclic nonlinearity error, and polarization-mixing cross talk during beam splitting is the main error source that causes the quadrature phase error. In this paper, a new homodyne quadrature laser interferometer configuration based on nonpolarization beam splitting and balanced interference between two circularly polarized laser beams is proposed. Theoretical modeling indicates that the polarization-mixing cross talk is elaborately avoided through nonpolarizing and Wollaston beam splitting, with a minimum number of quadrature phase error sources involved. Experimental results show that the cyclic nonlinearity error of the interferometer is up to 0.6 nm (peak-to-valley value) without any correction and can be further suppressed to 0.2 nm with a simple gain and offset correction method.
Nonlinear Zeno dynamics due to atomic interactions in Bose–Einstein condensate
Energy Technology Data Exchange (ETDEWEB)
Navarro, V.G.; Shchesnovich, V.S., E-mail: valery@ufabc.edu.br
2014-12-01
We show that nonlinear interactions induce both the Zeno and anti-Zeno effects in the generalized Bose–Josephson model (with the on-site interactions and the second-order tunneling) describing Bose–Einstein condensate in double-well trap subject to particle removal from one of the wells. We find that the on-site interactions induce only the Zeno effect, which appears at long evolution times, whereas the second-order tunneling leads to a strong decay of the atomic population at short evolution times, reminiscent of the anti-Zeno effect, and destroys the nonlinear Zeno effect due to the on-site interactions at long times.
Signal-to-noise-ratio analysis for nonlinear N-ary phase filters.
Miller, Paul C
2007-09-01
The problem of recognizing targets in nonoverlapping clutter using nonlinear N-ary phase filters is addressed. Using mathematical analysis, expressions were derived for an N-ary phase filter and the intensity variance of an optical correlator output. The N-ary phase filter was shown to consist of an infinite sum of harmonic terms whose periodicity was determined by N. For the intensity variance, it was found that under certain conditions the variance was minimized due to a previously undiscovered phase quadrature effect. Comparison showed that optimal real filters produced greater signal-to-noise-ratio values than the continuous phase versions as a consequence of this effect.
Axion-induced birefringence effects in laser driven nonlinear vacuum interaction
Villalba-Chávez, Selym
2013-01-01
The propagation of a probe electromagnetic field through a counterpropagating strong plane wave is investigated. The effects of the electromagnetic field-(pseudo)scalar axion field interaction and of the self-interaction of the electromagnetic field mediated by virtual electron-positron pairs in the effective Lagrangian approach are included. First, we show that if the strong field is circularly polarized, contrary to the leading-order nonlinear QED effects, the axion-photon interaction induces a chiral-like birefringence and a dichroism in the vacuum. The latter effect is explained by evoking the conservation of the total angular momentum along the common propagation direction of probe and the strong wave, which allows for real axion production only for probe and strong fields with the same helicity. Moreover, in the case of ultra-short strong pulses, it is shown that the absorption coefficients of probe photons depend on the form of the pulse and, in particular, on the carrier-envelope phase of the strong b...
Nonlinear dynamics of electrons interacting with oblique whistler mode chorus in the magnetosphere
Hsieh, Yi-Kai; Omura, Yoshiharu
2017-01-01
We perform test particle simulations for relativistic electrons interacting with a whistler mode chorus packet propagating at oblique angles. By confirming that the energy transport of oblique lower band chorus is nearly along the ambient magnetic field, we apply the gyroaveraging method in calculating equations of motion of electrons. We trace evolution of a delta function of relativistic electrons in a phase space of kinetic energy and equatorial pitch angle and obtain numerical Green's functions of the chorus wave-particle interactions. Examining the Green's functions in a wide range of kinetic energies, we find that Landau resonance can accelerate MeV electrons efficiently and that higher nth resonances such as n =- 1 and n = 2 also contribute to acceleration of electrons at high equatorial pitch angles (˜70°) and high energies (˜2 MeV). We investigate the rate of energy gain of the cyclotron resonance acceleration and the Landau resonance acceleration and find that the perpendicular component of wave electric field dominates both accelerations for MeV electrons. Furthermore, the proximity between the parallel components of Vp and Vg of oblique whistler mode waves and the nonlinear trapping condition make the interaction time of Landau resonance much longer than that of n = 1 cyclotron resonance, resulting in efficient acceleration of MeV electrons.
Nonlinear optics with phase-controlled pulses in the sub-two-cycle regime.
Morgner, U; Ell, R; Metzler, G; Schibli, T R; Kärtner, F X; Fujimoto, J G; Haus, H A; Ippen, E P
2001-06-11
Nonlinear optical effects due to the phase between carrier and envelope are observed with 5 fs pulses from a Kerr-lens mode-locked Ti:sapphire laser. These sub-two-cycle pulses with octave spanning spectra are the shortest pulses ever generated directly from a laser oscillator. Detection of the carrier-envelope phase slip is made possible by simply focusing the short pulses directly from the oscillator into a BBO crystal. As a further example of nonlinear optics with such short pulses, the interference between second- and third-harmonic components is also demonstrated.
Enhanced linear and nonlinear optical phase response of AlGaAs microring resonators.
Heebner, John E; Lepeshkin, Nick N; Schweinsberg, Aaron; Wicks, G W; Boyd, Robert W; Grover, Rohit; Ho, P T
2004-04-01
We have constructed and characterized several optical microring resonators with scale sizes of the order of 10 microm. These devices are intended to serve as building blocks for engineerable linear and nonlinear photonic media. Light is guided vertically by an epitaxially grown structure and transversely by deeply etched air-clad sidewalls. We report on the spectral phase transfer characteristics of such resonators. We also report the observation of a pi-rad Kerr nonlinear phase shift accumulated in a single compact ring resonator evidenced by all-optical switching between output ports of a resonator-enhanced Mach-Zehnder interferometer.
Enhanced nonlinear spectral compression in fiber by external sinusoidal phase modulation
Boscolo, S.; Mouradian, L. Kh; Finot, C.
2016-10-01
We propose a new, simple approach to enhance the spectral compression process arising from nonlinear pulse propagation in an optical fiber. We numerically show that an additional sinusoidal temporal phase modulation of the pulse enables efficient reduction of the intensity level of the side lobes in the spectrum that are produced by the mismatch between the initial linear negative chirp of the pulse and the self-phase modulation-induced nonlinear positive chirp. Remarkable increase of both the extent of spectrum narrowing and the quality of the compressed spectrum is afforded by the proposed approach across a wide range of experimentally accessible parameters.
Directory of Open Access Journals (Sweden)
A.G. Sereda
2015-06-01
Full Text Available Purpose. Theoretical justification and engineering of induction motors heat protection method from overload currents taking into account nonlinear distortion of the phase current and implementation as a microprocessor device functioning algorithm. Methodology. To solve the problem used the theory of the representing complex harmonic oscillations analog signals expansion into the oscillation spectrum forming elementary harmonic components in order to compare their properties by applying the theory of discrete signals and systems, as well as methods of spectral analysis and discrete signals filtering. The harmonic analysis versatility is that any periodic signal may be synthesized from harmonic oscillation of certain amplitude, frequency and initial phase. A mathematical model for determining the phase current harmonic content of power supply networks with isolated neutral and non-linear loads types and, as a consequence, the distortion of sinusoidal phase current change is developed by multiplying the analog current in time dependency on the grate delta-function with different sampling intervals, in which the use of simple and widely used in relay protection units, in particular electronic overcurrent relays, mathematical operations of integration squares instantaneous current allows the most in harmony with the mathematical tools to build other network protection types. Findings. The necessity to increase the sensitivity of the induction motors heat protection from overload currents taking into account nonlinear distortion of the phase currents is proved. By nonlinear distortion harmonic analysis of the phase currents the motor protection reliability increasing provided by taking into account the higher harmonic components of the phase currents, which causes to additional losses and heating of the stator winding. It uses the simplest and widely used in protective relaying mathematical apparatus determining of most significant higher harmonics
Rapidly Activated Dynamic Phase Transitions in Nonlinear Solids
1993-02-15
I Form Approv# edAD -A263 601 AiENTA11ON PAGE- f____________18 1. AGENCY USE ONLY (Lea"e blaWk 12. REPORT DATE 13. REPORT TYPE AND OATES COVEREO Feb...phase transforming media during high energy impact. Conversion of mechanical energy to thermal ener- gy has been studied by means of an extended theory...and Phase Structures in General Media , R. Fosdick, E. Dunn & M. Slemrod eds., IMA volume series, Springer- Verlag. Song, J. and T. L. Pence (1992
On phase transitions of the Potts model with three competing interactions on Cayley tree
Directory of Open Access Journals (Sweden)
S. Temir
2011-06-01
Full Text Available In the present paper we study a phase transition problem for the Potts model with three competing interactions, the nearest neighbors, the second neighbors and triples of neighbors and non-zero external field on Cayley tree of order two. We prove that for some parameter values of the model there is phase transition. We reduce the problem of describing by limiting Gibbs measures to the problem of solving a system of nonlinear functional equations. We extend the results obtained by Ganikhodjaev and Rozikov [Math. Phys. Anal. Geom., 2009, vol. 12, No. 2, 141-156] on phase transition for the Ising model to the Potts model setting.
Negative Kerr nonlinearity of graphene as seen via chirped-pulse-pumped self-phase modulation
Vermeulen, Nathalie; Cheng, JinLuo; Pasternak, Iwona; Krajewska, Aleksandra; Ciuk, Tymoteusz; Strupinski, Wlodek; Thienpont, Hugo; Van Erps, Jurgen
2016-01-01
We experimentally demonstrate a negative Kerr nonlinearity for quasi-undoped graphene. Hereto, we introduce the method of chirped-pulse-pumped self-phase modulation and apply it to graphene-covered silicon waveguides at telecom wavelengths. The extracted Kerr-nonlinear index for graphene equals n2,gr = -10^(-13) m^2/W. Whereas the sign of n2,gr turns out to be negative in contrast to what has been assumed so far, its magnitude is in correspondence with that observed in earlier experiments. Graphene's negative Kerr nonlinearity strongly impacts how graphene should be exploited for enhancing the nonlinear response of photonic (integrated) devices exhibiting a positive nonlinearity. It also opens up the possibility of using graphene to annihilate unwanted nonlinear effects in such devices, to develop unexplored approaches for establishing Kerr processes, and to extend the scope of the "periodic poling" method often used for second-order nonlinearities towards third-order Kerr processes. Because of the generic na...
Nonlinear supercoherent states and geometric phases for the supersymmetric harmonic oscillator
Díaz-Bautista, Erik
2016-01-01
Nonlinear supercoherent states, which are eigenstates of nonlinear deformations of the Kornbluth-Zypman annihilation operator for the supersymmetric harmonic oscillator, will be studied. They turn out to be expressed in terms of nonlinear coherent states, associated to the corresponding deformations of the standard annihilation operator. We will discuss as well the Heisenberg uncertainty relation for a special particular case, in order to compare our results with those obtained for the Kornbluth-Zypman linear supercoherent states. As the supersymmetric harmonic oscillator executes an evolution loop, such that the evolution operator becomes the identity at a certain time, thus the linear and nonlinear supercoherent states turn out to be cyclic and the corresponding geometric phases will be evaluated.
Time-varying interaction leads to amplitude death in coupled nonlinear oscillators
Indian Academy of Sciences (India)
Awadhesh Prasad
2013-09-01
A new form of time-varying interaction in coupled oscillators is introduced. In this interaction, each individual oscillator has always time-independent self-feedback while its interaction with other oscillators are modulated with time-varying function. This interaction gives rise to a phenomenon called amplitude death even in diffusively coupled identical oscillators. The nonlinear variation of the locus of bifurcation point is shown. Results are illustrated with Landau–Stuart (LS) and Rössler oscillators.
Naseri, Tayebeh; Moradi, Ronak
2017-01-01
Some optical properties including the linear and nonlinear susceptibility and electromagnetically induced phase grating (EIG) in graphene under Raman excitation is studied. A single-layer graphene nanostructure driven by coherent and incoherent fields is investigated theoretically. It is revealed that by adjusting the amplitude of control and incoherent fields, the linear and nonlinear absorption as well as Kerr nonlinearity of the medium can be optimized. It is realized that the enhanced Kerr nonlinearity can occur with zero linear absorption and nonlinear amplification. Furthermore, it should be noted that EIG in graphene is studied for the first time. The results indicate that the diffraction efficiency of the phase grating is dramatically enhanced by controlling the amplitude of coherent and incoherent fields, and an efficient electromagnetically induced phase grating can be obtained. A novel result shows a considerable improvement of the intensity of higher-order diffractions and switching between different orders of grating via incoherent pumping field. Therefore, this model can be used in real experiments for the development of new types of nanoelectronic devices used for the realization of all-optical switching processes.
Nonlinear phased analysis of reinforced concrete tunnels under fire exposure
Lilliu, G.; Meda, A.
2013-01-01
Fire analysis of precast segmental tunnels involves several problems, mainly related to the soil-structure interaction during fire exposure, coupled with material degradation. Temperature increase in the tunnel is the cause of thermal expansion of the lining, which is resisted by the soil pressure.
Nonlinear phased analysis of reinforced concrete tunnels under fire exposure
Lilliu, G.; Meda, A.
2013-01-01
Fire analysis of precast segmental tunnels involves several problems, mainly related to the soil-structure interaction during fire exposure, coupled with material degradation. Temperature increase in the tunnel is the cause of thermal expansion of the lining, which is resisted by the soil pressure.
Correction of Phase Distortion by Nonlinear Optical Techniques
1979-03-01
switch (such as a thyratron ) transfers a fixed voltage (and charge) onto the electrooptical electrodes via a capacitor precharged to a voltage...maximum gain, valid for any distri- bution of incident-wave amplitudes and phases. We apply this theory to several models in a rectangular waveguide...We next use (41) to calculate r for a fairly general da» of pump beams. VIII. MODEL CALCULATION OP NONCONJUGATEO POWER FRACTION We calculate
Directory of Open Access Journals (Sweden)
S. I. Samsudin
2014-01-01
Full Text Available The wastewater treatment plant (WWTP is highly known with the nonlinearity of the control parameters, thus it is difficult to be controlled. In this paper, the enhancement of nonlinear PI controller (ENon-PI to compensate the nonlinearity of the activated sludge WWTP is proposed. The ENon-PI controller is designed by cascading a sector-bounded nonlinear gain to linear PI controller. The rate variation of the nonlinear gain kn is automatically updated based on adaptive interaction algorithm. Initiative to simplify the ENon-PI control structure by adapting kn has been proved by significant improvement under various dynamic influents. More than 30% of integral square error and 14% of integral absolute error are reduced compared to benchmark PI for DO control and nitrate in nitrogen removal control. Better average effluent qualities, less number of effluent violations, and lower aeration energy consumption resulted.
Luo, Dehai; Cha, Jing; Zhong, Linhao; Dai, Aiguo
2014-05-01
In this paper, a nonlinear multi-scale interaction (NMI) model is used to propose an eddy-blocking matching (EBM) mechanism to account for how synoptic eddies reinforce or suppress a blocking flow. It is shown that the spatial structure of the eddy vorticity forcing (EVF) arising from upstream synoptic eddies determines whether an incipient block can grow into a meandering blocking flow through its interaction with the transient synoptic eddies from the west. Under certain conditions, the EVF exhibits a low-frequency oscillation on timescales of 2-3 weeks. During the EVF phase with a negative-over- positive dipole structure, a blocking event can be resonantly excited through the transport of eddy energy into the incipient block by the EVF. As the EVF changes into an opposite phase, the blocking decays. The NMI model produces life cycles of blocking events that resemble observations. Moreover, it is shown that the eddy north-south straining is a response of the eddies to a dipole- or Ω-type block. In our model, as in observations, two synoptic anticyclones (cyclones) can attract and merge with one another as the blocking intensifies, but only when the feedback of the blocking on the eddies is included. Thus, we attribute the eddy straining and associated vortex interaction to the feedback of the intensified blocking on synoptic eddies. The results illustrate the concomitant nature of the eddy deformation, whose role as a PV source for the blocking flow becomes important only during the mature stage of a block. Our EBM mechanism suggests that an incipient block flow is amplified (or suppressed) under certain conditions by the EVF coming from the upstream of the blocking region.
Rajput, Sudheesh K; Nishchal, Naveen K
2014-01-20
We propose a novel nonlinear image-encryption scheme based on a Gerchberg-Saxton (G-S) phase-retrieval algorithm in the Fresnel transform domain. The decryption process can be performed using conventional double random phase encoding (DRPE) architecture. The encryption is realized by applying G-S phase-retrieval algorithm twice, which generates two asymmetric keys from intermediate phases. The asymmetric keys are generated in such a way that decryption is possible optically with a conventional DRPE method. Due to the asymmetric nature of the keys, the proposed encryption process is nonlinear and offers enhanced security. The cryptanalysis has been carried out, which proves the robustness of proposed scheme against known-plaintext, chosen-plaintext, and special attacks. A simple optical setup for decryption has also been suggested. Results of computer simulation support the idea of the proposed cryptosystem.
Mode interaction in horses, tea, and other nonlinear oscillators: the universal role of symmetry
Weele, van der Jacobus P.; Banning, Erik J.
2001-01-01
This paper is about mode interaction in systems of coupled nonlinear oscillators. The main ideas are demonstrated by means of a model consisting of two coupled, parametrically driven pendulums. On the basis of this we also discuss mode interaction in the Faraday experiment (as observed by Ciliberto
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Johansson, M.
1998-01-01
The dynamics of discrete two-dimensional nonlinear Schrodinger models with long-range dispersive interactions is investigated. In particular, we focus on the cases where the dispersion arises from a dipole-dipole interaction, assuming the dipole moments at each lattice site to be aligned either...
The Nonlinear Interaction Process in the Wave Assimilation Model and Its Experiments
Institute of Scientific and Technical Information of China (English)
杨永增; 纪永刚; 袁业立
2003-01-01
This paper presents a composite interaction formula based on the discrete-interactionoperator of wave-wave nonlinear interaction for deriving its adjoint source function in the wave assimilation model. Assimilation experiments were performed using the significant wave heights observed by the TOPES/POSEIDON satellite, and the gradient distribution in the physical space wasalso analyzed preliminarily.
The dynamics of interacting nonlinearities governing long wavelength driftwave turbulence
Energy Technology Data Exchange (ETDEWEB)
Newman, D.E.
1993-09-01
Because of the ubiquitous nature of turbulence and the vast array of different systems which have turbulent solutions, the study of turbulence is an area of active research. Much present day understanding of turbulence is rooted in the well established properties of homogeneous Navier-Stokes turbulence, which, due to its relative simplicity, allows for approximate analytic solutions. This work examines a group of turbulent systems with marked differences from Navier-Stokes turbulence, and attempts to quantify some of their properties. This group of systems represents a variety of drift wave fluctuations believed to be of fundamental importance in laboratory fusion devices. From extensive simulation of simple local fluid models of long wavelength drift wave turbulence in tokamaks, a reasonably complete picture of the basic properties of spectral transfer and saturation has emerged. These studies indicate that many conventional notions concerning directions of cascades, locality and isotropy of transfer, frequencies of fluctuations, and stationarity of saturation are not valid for moderate to long wavelengths. In particular, spectral energy transfer at long wavelengths is dominated by the E {times} B nonlinearity, which carries energy to short scale in a manner that is highly nonlocal and anisotropic. In marked contrast to the canonical self-similar cascade dynamics of Kolmogorov, energy is efficiently passed between modes separated by the entire spectrum range in a correlation time. At short wavelengths, transfer is dominated by the polarization drift nonlinearity. While the standard dual cascade applies in this subrange, it is found that finite spectrum size can produce cascades that are reverse directed and are nonconservative in enstrophy and energy similarity ranges. In regions where both nonlinearities are important, cross-coupling between the nolinearities gives rise to large no frequency shifts as well as changes in the spectral dynamics.
Ulku, Huseyin Arda
2015-02-01
An explicit marching on-in-time (MOT) based time domain electric field volume integral equation (TDVIE) solver for characterizing electromagnetic wave interactions on scatterers with nonlinear material properties is proposed. Discretization of the unknown electric field intensity and flux density is carried out by half and full Schaubert-Wilton-Glisson basis functions, respectively. Coupled system of spatially discretized TDVIE and the nonlinear constitutive relation between the field intensity and the flux density is integrated in time to compute the samples of the unknowns. An explicit PE(CE)m scheme is used for this purpose. Explicitness allows for \\'easy\\' incorporation of the nonlinearity as a function only to be evaluated on the right hand side of the coupled system of equations. A numerical example that demonstrates the applicability of the proposed MOT scheme to analyzing electromagnetic interactions on Kerr-nonlinear scatterers is presented. © 2015 IEEE.
Fluid transport due to nonlinear fluid-structure interaction
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard
1997-01-01
of the pipe. The behavior of the system in response to lateral resonant base excitation is analysed numerically and by the use of a perturbation method (multiple scales). Exciting the pipe in the fundamental mode of vibration seems to be most effective for transferring energy from the shaker to the fluid......, whereas higher modes of vibration can be used to transport fluid with pipe vibrations of smaller amplitude. The effect of the nonlinear geometrical terms is analysed and these terms are shown to affect the response for higher modes of vibration. Experimental investigations show good agreement...
Frequency and Phase Noise in Non-Linear Microwave Oscillator Circuits
Tannous, C.
2003-01-01
We have developed a new methodology and a time-domain software package for the estimation of the oscillation frequency and the phase noise spectrum of non-linear noisy microwave circuits based on the direct integration of the system of stochastic differential equations representing the circuit. Our theoretical evaluations can be used in order to make detailed comparisons with the experimental measurements of phase noise spectra in selected oscillating circuits.
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...
Effects of nonlinear phase modulation on low-conversion four-wave mixing Bragg scattering
DEFF Research Database (Denmark)
Andersen, Lasse Mejling; McKinstrie, C. J.; Rottwitt, Karsten
We consider the effects of nonlinear phase modulation (NPM) on frequency converseon by Bragg scattering. Previously we found that arbitrary mode reshaping without temporal entanglement (separability) was possible. When NPM is included, the modes are chirped and the separability is no longer compl...
Deng, Linhua
2015-07-01
Three nonlinear analysis techniques, including cross-recurrence plot, line of synchronization, and cross-wavelet transform, are proposed to estimate the coherent phase vibrations of nonlinear and non-stationary time series. The case study utilizes the monthly averages of sunspot areas during the time interval from May 1874 to August 2014. The following prominent results are found: (1) the phase-leading hemisphere of long-term sunspot areas has changed twice in the past 140 years, indicating that the hemispheric imbalances and apparent phase differences on both hemispheres are a prevalent behavior and are not anomalous; (2) the alternating regularity of hemispheric asynchronism exhibits a cyclical pattern of 4.5+3.5 cycles, and the magnetic flux excess in a certain hemisphere during the ascending branch of a cycle can be taken as an indication of the phase-leading hemisphere in this cycle. We firmly believe that powerful nonlinear approaches are more advanced than classical linear methods when they are combined to determine the dynamic complexity of nonlinear physical systems.
Knoester, Jasper; Mukamel, Shaul
1990-01-01
A general scheme is presented for calculating the nonlinear optical response in condensed phases that provides a unified picture of excitons, polaritons, retardation, and local-field effects in crystals and in disordered systems. A fully microscopic starting point is taken by considering the evoluti
Experimental Study of Nonlinear Phase Noise and its Impact on WDM Systems with DP-256QAM
DEFF Research Database (Denmark)
Yankov, Metodi Plamenov; Da Ros, Francesco; Porto da Silva, Edson
2016-01-01
A probabilistic method for mitigating the phase noise component of the non-linear interference in WDM systems with Raman amplification is experimentally demonstrated. The achieved gains increase with distance and are comparable to the gains of single-channel digital back-propagation....
The Nonlinear Interaction of Two-Crossed Focussed Ultrasonic Beams in the Presence of Turbulence
1988-06-10
in water or any fluid medium can be obtained by the vibration of a solid body in the fluid, such as the vibration of a vocal chord or guitar string . In... physical phenomenon due to the nonlinearity of sound arises from the interaction of two sound beams. Nonlinear acoustic theory predictions by Westervelt in...known experimental data for the turbulent velocity field. Goals of this research include mapping out the turbulence and studying the physical
A MATLAB Function for Plotting Phase Planes Interactively
Forsman, Krister
1992-01-01
A MATLAB-function serving as a sort of graphical interface to the MATLAB ODE-solver ode45 is presented. The main use of it is to facilitate phase plane analysis of nonlinear 2-D systems via simulation. The numerical integration of the system is mouse-operated via the ginput-function. After each choice of initial value a simulation is made and plotted in the phase plane.
Nonlinear Interactions of Dispersion-managed Soliton in OTDM Systems
Institute of Scientific and Technical Information of China (English)
CAI Ju; MAO Yu; LU Hui; ZHANG Li-na; YANG Xiang-lin
2003-01-01
The dispersion-managed soliton (DMS) transmission model of dispersion-managed systems is established,and the intrachannel DMS interactions equation is obtained.The impact of soliton interactions on DMS systems are numerically investigated.Finally,the relationships of the collision length changing with map strength are revealed.
Institute of Scientific and Technical Information of China (English)
Abhijit Sinha; Sourangshu Mukhopadhyay
2004-01-01
In optical soliton propagation through a single mode optical fiber,it is established that self-phase mod ulation is maintained by the third order non-linearity of the silica-based glass material of the fiber.In this paper we show that the fifth order non-linearity has also some contribution in frequency variation of self-phase modulation.
Band-phase-randomized Surrogates to assess nonlinearity in non-stationary time series
Guarin, Diego; Orozco, Alvaro
2011-01-01
Testing for nonlinearity is one of the most important preprocessing steps in nonlinear time series analysis. Typically, this is done by means of the linear surrogate data methods. But it is a known fact that the validity of the results heavily depends on the stationarity of the time series. Since most physiological signals are non-stationary, it is easy to falsely detect nonlinearity using the linear surrogate data methods. In this document, we propose a methodology to extend the procedure for generating constrained surrogate time series in order to assess nonlinearity in non-stationary data. The method is based on the band-phase-randomized surrogates, which consists (contrary to the linear surrogate data methods) in randomizing only a portion of the Fourier phases in the high frequency band. Analysis of simulated time series showed that in comparison to the linear surrogate data method, our method is able to discriminate between linear stationarity, linear non-stationary and nonlinear time series. When apply...
Phase mixing versus nonlinear advection in drift-kinetic plasma turbulence
Schekochihin, A. A.; Parker, J. T.; Highcock, E. G.; Dellar, P. J.; Dorland, W.; Hammett, G. W.
2016-04-01
> A scaling theory of long-wavelength electrostatic turbulence in a magnetised, weakly collisional plasma (e.g. drift-wave turbulence driven by ion temperature gradients) is proposed, with account taken both of the nonlinear advection of the perturbed particle distribution by fluctuating flows and of its phase mixing, which is caused by the streaming of the particles along the mean magnetic field and, in a linear problem, would lead to Landau damping. It is found that it is possible to construct a consistent theory in which very little free energy leaks into high velocity moments of the distribution function, rendering the turbulent cascade in the energetically relevant part of the wavenumber space essentially fluid-like. The velocity-space spectra of free energy expressed in terms of Hermite-moment orders are steep power laws and so the free-energy content of the phase space does not diverge at infinitesimal collisionality (while it does for a linear problem); collisional heating due to long-wavelength perturbations vanishes in this limit (also in contrast with the linear problem, in which it occurs at the finite rate equal to the Landau damping rate). The ability of the free energy to stay in the low velocity moments of the distribution function is facilitated by the `anti-phase-mixing' effect, whose presence in the nonlinear system is due to the stochastic version of the plasma echo (the advecting velocity couples the phase-mixing and anti-phase-mixing perturbations). The partitioning of the wavenumber space between the (energetically dominant) region where this is the case and the region where linear phase mixing wins its competition with nonlinear advection is governed by the `critical balance' between linear and nonlinear time scales (which for high Hermite moments splits into two thresholds, one demarcating the wavenumber region where phase mixing predominates, the other where plasma echo does).
Possible second-order nonlinear interactions of plane waves in an elastic solid.
Korneev, V A; Demčenko, A
2014-02-01
There exist ten possible nonlinear elastic wave interactions for an isotropic solid described by three constants of the third order. All other possible interactions out of 54 combinations (triplets) of interacting and resulting waves are prohibited, because of restrictions of various kinds. The considered waves include longitudinal and two shear waves polarized in the interacting plane and orthogonal to it. The amplitudes of scattered waves have simple analytical forms, which can be used for experimental setup and design. The analytic results are verified by comparison with numerical solutions of initial equations. Amplitude coefficients for all ten interactions are computed as functions of frequency for polyvinyl chloride, together with interaction and scattering angles. The nonlinear equation of motion is put into a general vector form and can be used for any coordinate system.
Simulations of Energetic Particles Interacting with Nonlinear Anisotropic Dynamical Turbulence
Heusen, Martin
2016-01-01
We investigate test-particle diffusion in dynamical turbulence based on a numerical approach presented before. For the turbulence we employ the nonlinear anisotropic dynamical turbulence model which takes into account wave propagation effects as well as damping effects. We compute numerically diffusion coefficients of energetic particles along and across the mean magnetic field. We focus on turbulence and particle parameters which should be relevant for the solar system and compare our findings with different interplanetary observations. We vary different parameters such as the dissipation range spectral index, the ratio of the turbulence bendover scales, and the magnetic field strength in order to explore the relevance of the different parameters. We show that the bendover scales as well as the magnetic field ratio have a strong influence on diffusion coefficients whereas the influence of the dissipation range spectral index is weak. The best agreement with solar wind observations can be found for equal bend...
Chaotic saddles in nonlinear modulational interactions in a plasma
Energy Technology Data Exchange (ETDEWEB)
Miranda, Rodrigo A. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), Sao Jose dos Campos, SP 12228-900 (Brazil); National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, Sao Jose dos Campos, SP 12227-010 (Brazil); University of Brasilia (UnB), Gama Campus, and Plasma Physics Laboratory, Institute of Physics, Brasilia, DF 70910-900 (Brazil); Rempel, Erico L. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), Sao Jose dos Campos, SP 12228-900 (Brazil); National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, Sao Jose dos Campos, SP 12227-010 (Brazil); Chian, Abraham C.-L. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), Sao Jose dos Campos, SP 12228-900 (Brazil); National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, Sao Jose dos Campos, SP 12227-010 (Brazil); Observatoire de Paris, LESIA, CNRS, 92195 Meudon (France)
2012-11-15
A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a function of the damping rates in a two-parameter space, and identify shrimp-shaped self-similar structures in the parameter space. By varying the damping rate of the low-frequency wave, we construct bifurcation diagrams and focus on a saddle-node bifurcation and an interior crisis associated with a periodic window. We detect chaotic saddles and their stable and unstable manifolds, and demonstrate how the connection between two chaotic saddles via coupling unstable periodic orbits can result in a crisis-induced intermittency. The relevance of this work for the understanding of modulational processes observed in plasmas and fluids is discussed.
Chaotic saddles in nonlinear modulational interactions in a plasma
Miranda, Rodrigo A; Chian, Abraham C -L
2012-01-01
A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a function of the damping rates in a two-parameter space, and identify shrimp-shaped self-similar structures in the parameter space. By varying the damping rate of the low-frequency wave, we construct bifurcation diagrams and focus on a saddle-node bifurcation and an interior crisis associated with a periodic window. We detect chaotic saddles and their stable and unstable manifolds, and demonstrate how the connection between two chaotic saddles via coupling unstable periodic orbits can result in a crisis-induced intermittency. The relevance of this work for the understanding of modulational processes observed in plasmas and fluids is discussed.
Interactive Classroom Graphics--Simulating Non-Linear Arrhenius Plots.
Ben-Zion, M.; Hoz, S.
1980-01-01
Describes two simulation programs using an interactive graphic display terminal that were developed for a course in physical organic chemistry. Demonstrates the energetic conditions that give rise to deviations from linearity in the Arrhenius equation. (CS)
AxiSketcher: Interactive Nonlinear Axis Mapping of Visualizations through User Drawings.
Kwon, Bum Chul; Kim, Hannah; Wall, Emily; Choo, Jaegul; Park, Haesun; Endert, Alex
2017-01-01
Visual analytics techniques help users explore high-dimensional data. However, it is often challenging for users to express their domain knowledge in order to steer the underlying data model, especially when they have little attribute-level knowledge. Furthermore, users' complex, high-level domain knowledge, compared to low-level attributes, posits even greater challenges. To overcome these challenges, we introduce a technique to interpret a user's drawings with an interactive, nonlinear axis mapping approach called AxiSketcher. This technique enables users to impose their domain knowledge on a visualization by allowing interaction with data entries rather than with data attributes. The proposed interaction is performed through directly sketching lines over the visualization. Using this technique, users can draw lines over selected data points, and the system forms the axes that represent a nonlinear, weighted combination of multidimensional attributes. In this paper, we describe our techniques in three areas: 1) the design space of sketching methods for eliciting users' nonlinear domain knowledge; 2) the underlying model that translates users' input, extracts patterns behind the selected data points, and results in nonlinear axes reflecting users' complex intent; and 3) the interactive visualization for viewing, assessing, and reconstructing the newly formed, nonlinear axes.
Otten, Daniel; Rubbert, Sebastian; Ulrich, Jascha; Hassler, Fabian
2016-09-01
Josephson junctions are the most prominent nondissipative and at the same time nonlinear elements in superconducting circuits allowing Cooper pairs to tunnel coherently between two superconductors separated by a tunneling barrier. Due to this, physical systems involving Josephson junctions show highly complex behavior and interesting novel phenomena. Here, we consider an infinite one-dimensional chain of superconducting islands where neighboring islands are coupled by capacitances. We study the effect of Josephson junctions shunting each island to a common ground superconductor. We treat the system in the regime where the Josephson energy exceeds the capacitive coupling between the islands. For the case of two offset charges on two distinct islands, we calculate the interaction energy of these charges mediated by quantum phase slips due to the Josephson nonlinearities. We treat the phase slips in an instanton approximation and map the problem onto a classical partition function of interacting particles. Using the Mayer cluster expansion, we find that the interaction potential of the offset charges decays with a universal inverse-square power-law behavior.
Zhu, Chengjie; Huang, Guoxiang
2011-11-07
We study linear and nonlinear propagations of probe and signal pulses in a multiple quantum-well structure with a four-level, double Λ-type configuration. We show that slow, mutually matched group velocities and giant Kerr nonlinearity of the probe and the signal pulses may be achieved with nearly vanishing optical absorption. Based on these properties we demonstrate that two-qubit quantum polarization phase gates can be constructed and highly entangled photon pairs may be produced. In addition, we show that coupled slow-light soliton pairs with very low generation power can be realized in the system.
Sharing of nonlinear load in parallel-connected three-phase converters
DEFF Research Database (Denmark)
Borup, Uffe; Blaabjerg, Frede; Enjeti, Prasad N.
2001-01-01
In this paper, a new control method is presented which enables equal sharing of linear and nonlinear loads in three-phase power converters connected in parallel, without communication between the converters. The paper focuses on solving the problem that arises when two converters with harmonic...... compensation are connected in parallel. Without the new solution, they are normally not able to distinguish the harmonic currents that flow to the load and harmonic currents that circulate between the converters. Analysis and experimental results on two 90-kVA 400-Hz converters in parallel are presented....... The results show that both linear and nonlinear loads can be shared equally by the proposed concept....
Observation of spectral self-imaging by nonlinear parabolic cross-phase modulation.
Lei, Lei; Huh, Jeonghyun; Cortés, Luis Romero; Maram, Reza; Wetzel, Benjamin; Duchesne, David; Morandotti, Roberto; Azaña, José
2015-11-15
We report an experimental demonstration of spectral self-imaging on a periodic frequency comb induced by a nonlinear all-optical process, i.e., parabolic cross-phase modulation in a highly nonlinear fiber. The comb free spectral range is reconfigured by simply tuning the temporal period of the pump parabolic pulse train. In particular, undistorted FSR divisions by factors of 2 and 3 are successfully performed on a 10 GHz frequency comb, realizing new frequency combs with an FSR of 5 and 3.3 GHz, respectively. The pump power requirement associated to the SSI phenomena is also shown to be significantly relaxed by the use of dark parabolic pulses.
Tamma, Kumar K.; Railkar, Sudhir B.
1988-01-01
The present paper describes the applicability of hybrid transfinite element modeling/analysis formulations for nonlinear heat conduction problems involving phase change. The methodology is based on application of transform approaches and classical Galerkin schemes with finite element formulations to maintain the modeling versatility and numerical features for computational analysis. In addition, in conjunction with the above, the effects due to latent heat are modeled using enthalpy formulations to enable a physically realistic approximation to be dealt computationally for materials exhibiting phase change within a narrow band of temperatures. Pertinent details of the approach and computational scheme adapted are described in technical detail. Numerical test cases of comparative nature are presented to demonstrate the applicability of the proposed formulations for numerical modeling/analysis of nonlinear heat conduction problems involving phase change.
Energy Technology Data Exchange (ETDEWEB)
Lin Jaeyuh [Chang Jung Univ., Tainan (Taiwan, Province of China); Chen Hantaw [National Cheng Kung Univ., Tainan (Taiwan, Province of China). Dept. of Mechanical Engineering
1997-09-01
A hybrid numerical scheme combining the Laplace transform and control-volume methods is presented to solve nonlinear two-dimensional phase-change problems with the irregular geometry. The Laplace transform method is applied to deal with the time domain, and then the control-volume method is used to discretize the transformed system in the space domain. Nonlinear terms induced by the temperature-dependent thermal properties are linearized by using the Taylor series approximation. Control-volume meshes in the solid and liquid regions during simulations are generated by using the discrete transfinite mapping method. The location of the phase-change interface and the isothermal distributions are determined. Comparison of these results with previous results shows that the present numerical scheme has good accuracy for two-dimensional phase-change problems. (orig.). With 10 figs.
Multichannel nonlinear distortion compensation using optical phase conjugation in a silicon nanowire
DEFF Research Database (Denmark)
Vukovic, Dragana; Schoerder, Jochen; Da Ros, Francesco
2015-01-01
silicon nanowire. A clear improvement in Q-factor is shown after 800-km transmission with high span input power when comparing the system with and without the optical phase conjugation module. The influence of OSNR degradation introduced by the silicon nanowire is analysed by comparing transmission......We experimentally demonstrate compensation of nonlinear distortion caused by the Kerr effect in a 3 x 32-Gbaud quadrature phase-shift keying (QPSK) wavelength-division multiplexing (WDM) transmission system. We use optical phase conjugation (OPC) produced by four-wave mixing (FWM) in a 7-mm long...... systems of three different lengths. This is the first demonstration of nonlinear compensation using a silicon nanowire. (C)2015 Optical Society of America...
A Nonlinear-Phase, Model-Based Human Detector for Radar (Preprint)
2010-06-01
characterization techniques cannot be applied. Note that the Fourier transform implements a linear- phase filter yielding a peak response...history of a human target can be highly nonlinear, resulting in an inherent SNR loss when matched filtered with a linear- phase filter , such as the FFT...filter with a linear phase filter , which may be expressed as TNjNj ee )1(121 LINw , (9) where i and are generalized
Pump induced normal mode splittings in phase conjugation in a Kerr nonlinear waveguide
Indian Academy of Sciences (India)
S Dutta Gupta
2000-03-01
Phase conjugation in a Kerr nonlinear waveguide is studied with counter-propagating normally incident pumps and a probe beam at an arbitrary angle of incidence. Detailed numerical results for the specular and phase conjugated reﬂectivities are obtained with full account of pump depletion. For sufﬁcient strengths of the pump a normal mode splitting is demonstrated in both the specular and the phase conjugated reﬂectivities of the probe wave. The splitting is explained in terms of a simple model under undepleted pump approximation.
Yao, Weiping; Jing, Jiliang
2016-08-01
We study the holographic entanglement entropy in metal/superconductor phase transition with exponential nonlinear electrodynamics (ENE) in four and five dimensional spacetimes. We find that the holographic entanglement entropy is powerful tool in studying the properties of the holographic phase transition. For the operator , we show that the entanglement entropy in 4-dimensional spacetime decreases in metal phase but changes non-monotonously in superconducting phase with the increase of the ENE parameter. Interestingly, the change of the entanglement entropy in 5-dimensional spacetime for the two phases is monotonous as the ENE factor alters. For the operator , we note that the behavior of entanglement entropy in four and five dimensional spacetimes changes monotonously for the two phases as we tune the strength of the ENE. Furthermore, for both operators, the entanglement entropy in four or five dimensional black hole increases with the increase of the width of the region.
DEFF Research Database (Denmark)
Rasmussen, Kim; Christiansen, Peter Leth; Johansson, Magnus
1998-01-01
A one-dimensional discrete nonlinear Schrodinger (DNLS) model with the power dependence, r(-s) on the distance r, of dispersive interactions is proposed. The stationary states of the system are studied both analytically and numerically. Two kinds of trial functions, exp-like and sech-like are exp......A one-dimensional discrete nonlinear Schrodinger (DNLS) model with the power dependence, r(-s) on the distance r, of dispersive interactions is proposed. The stationary states of the system are studied both analytically and numerically. Two kinds of trial functions, exp-like and sech...
Nonlinear interaction of impulsive gravitational waves for the vacuum Einstein equations
Luk, Jonathan
2013-01-01
In this paper, we study the problem of the nonlinear interaction of impulsive gravitational waves for the Einstein vacuum equations. The problem is studied in the context of a characteristic initial value problem with data given on two null hypersurfaces and containing curvature delta singularities. We establish an existence and uniqueness result for the spacetime arising from such data and show that the resulting spacetime represents the interaction of two impulsive gravitational waves germinating from the initial singularities. In the spacetime, the curvature delta singularities propagate along 3-dimensional null hypersurfaces intersecting to the future of the data. To the past of the intersection, the spacetime can be thought of as containing two independent, non-interacting impulsive gravitational waves and the intersection represents the first instance of their nonlinear interaction. Our analysis extends to the region past their first interaction and shows that the spacetime still remains smooth away fro...
Efficient supercontinuum generation in quadratic nonlinear waveguides without quasi-phase matching
Guo, Hairun; Steinert, Michael; Setzpfandt, Frank; Pertsch, Thomas; Chung, Hung-ping; Chen, Yen-Hung; Bache, Morten
2014-01-01
Efficient supercontinuum generation (SCG) requires excitation of solitons at the pump laser wavelength. Quadratic nonlinear waveguides may support an effective self-defocusing nonlinearity so solitons can directly be generated at common ultrafast laser wavelengths without any waveguide dispersion engineering. We here experimentally demonstrate efficient SCG in a standard lithium niobate (LN) waveguide without using quasi-phase matching (QPM). By using femtosecond pumps with wavelengths in the $1.25-1.5 \\mu\\rm m$ range, where LN has normal dispersion and thus supports self-defocusing solitons, octave-spanning SCG is observed. An optimized mid-IR waveguide design is expected to support even broader spectra. The QPM-free design reduces production complexity, allows longer waveguides, limits undesired spectral resonances and effectively allows using nonlinear crystals where QPM is inefficient or impossible. This result is important for mid-IR SCG, where QPM-free self-defocusing waveguides in common mid-IR nonline...
Numerical method of studying nonlinear interactions between long waves and multiple short waves
Institute of Scientific and Technical Information of China (English)
Xie Tao; Kuang Hai-Lan; William Perrie; Zou Guang-Hui; Nan Cheng-Feng; He Chao; Shen Tao; Chen Wei
2009-01-01
Although the nonlinear interactions between a single short gravity wave and a long wave can be solved analytically,the solution is less tractable in more general cases involving multiple short waves.In this work we present a numerical method of studying nonlinear interactions between a long wave and multiple short harmonic waves in infinitely deep water.Specifically,this method is applied to the calculation of the temporal and spatial evolutions of the surface elevations in which a given long wave interacts with several short harmonic waves.Another important application of our method is to quantitatively analyse the nonlinear interactions between an arbitrary short wave train and another short wave train.From simulation results,we obtain that the mechanism for the nonlinear interactions between one short wave train and another short wave train(expressed as wave train 2)leads to the energy focusing of the other short wave train(expressed as wave train 31.This mechanism Occurs on wave components with a narrow frequency bandwidth,whose frequencies are near that of wave train 3.
You, Yi-Zhuang; Bi, Zhen; Mao, Dan; Xu, Cenke
2016-03-01
We propose a series of simple two-dimensional (2D) lattice interacting fermion models that we demonstrate at low energy describe bosonic symmetry-protected topological (SPT) states and quantum phase transitions between them. This is because due to interaction, the fermions are gapped both at the boundary of the SPT states and at the bulk quantum phase transition, thus these models at low energy can be described completely by bosonic degrees of freedom. We show that the bulk of these models is described by a Sp (N ) principal chiral model with a topological Θ term, whose boundary is described by a Sp (N ) principal chiral model with a Wess-Zumino-Witten term at level 1. The quantum phase transition between SPT states in the bulk is tuned by a particular interaction term, which corresponds to tuning Θ in the field theory, and the phase transition occurs at Θ =π . The simplest version of these models with N =1 is equivalent to the familiar O(4) nonlinear sigma model (NLSM) with a topological term, whose boundary is a (1 +1 )D conformal field theory with central charge c =1 . After breaking the O(4) symmetry to its subgroups, this model can be viewed as bosonic SPT states with U(1), or Z2 symmetries, etc. All of these fermion models, including the bulk quantum phase transitions, can be simulated with the determinant quantum Monte Carlo method without the sign problem. Recent numerical results strongly suggest that the quantum disordered phase of the O(4) NLSM with precisely Θ =π is a stable (2 +1 )D conformal field theory with gapless bosonic modes.
Phase Structure of the Non-Linear σ-MODEL with Oscillator Representation Method
Mishchenko, Yuriy; Ji, Chueng-R.
2004-03-01
Non-Linear σ-model plays an important role in many areas of theoretical physics. Been initially uintended as a simple model for chiral symmetry breaking, this model exhibits such nontrivial effects as spontaneous symmetry breaking, asymptotic freedom and sometimes is considered as an effective field theory for QCD. Besides, non-linear σ-model can be related to the strong-coupling limit of O(N) ϕ4-theory, continuous limit of N-dim. system of quantum spins, fermion gas and many others and takes important place in undertanding of how symmetries are realized in quantum field theories. Because of this variety of connections, theoretical study of the critical properties of σ-model is interesting and important. Oscillator representation method is a theoretical tool for studying the phase structure of simple QFT models. It is formulated in the framework of the canonical quantization and is based on the view of the unitary non-equivalent representations as possible phases of a QFT model. Successfull application of the ORM to ϕ4 and ϕ6 theories in 1+1 and 2+1 dimensions motivates its study in more complicated models such as non-linear σ-model. In our talk we introduce ORM, establish its connections with variational approach in QFT. We then present results of ORM in non-linear σ-model and try to interprete them from the variational point of view. Finally, we point out possible directions for further research in this area.
Nonlinear instability and chaos in plasma wave-wave interactions. II. Numerical methods and results
Energy Technology Data Exchange (ETDEWEB)
Kueny, C.S.; Morrison, P.J.
1995-05-01
In Part I of this work and Physics of Plasmas, June 1995, the behavior of linearly stable, integrable systems of waves in a simple plasma model was described using a Hamiltonian formulation. It was shown that explosive instability arises from nonlinear coupling between modes of positive and negative energy, with well-defined threshold amplitudes depending on the physical parameters. In this concluding paper, the nonintegrable case is treated numerically. Several sets of waves are considered, comprising systems of two and three degrees of freedom. The time evolution is modelled with an explicit symplectic integration algorithm derived using Lie algebraic methods. When initial wave amplitudes are large enough to support two-wave decay interactions, strongly chaotic motion destroys the separatrix bounding the stable region for explosive triplets. Phase space orbits then experience diffusive growth to amplitudes that are sufficient for explosive instability, thus effectively reducing the threshold amplitude. For initial amplitudes too small to drive decay instability, small perturbations might still grow to arbitrary size via Arnold diffusion. Numerical experiments do not show diffusion in this case, although the actual diffusion rate is probably underestimated due to the simplicity of the model.
Shukla, P K; Eliasson, B
2007-08-31
We consider nonlinear interactions between intense circularly polarized electromagnetic (CPEM) waves and electron plasma oscillations (EPOs) in a dense quantum plasma, taking into account the electron density response in the presence of the relativistic ponderomotive force and mass increase in the CPEM wave fields. The dynamics of the CPEM waves and EPOs is governed by the two coupled nonlinear Schrödinger equations and Poisson's equation. The nonlinear equations admit the modulational instability of an intense CPEM pump wave against EPOs, leading to the formation and trapping of localized CPEM wave pipes in the electron density hole that is associated with a positive potential distribution in our dense plasma. The relevance of our investigation to the next generation intense laser-solid density plasma interaction experiments is discussed.
Nonlinear theory of laser-induced dipolar interactions in arbitrary geometry
Shahmoon, Ephraim
2013-01-01
Polarizable dipoles, such as atoms, molecules or nanoparticles, subject to laser radiation, may attract or repel each other. We derive a general formalism in which such laser-induced dipole-dipole interactions (LIDDI) in any geometry and for any laser strength are described in terms of the resonant dipole-dipole interaction (RDDI) between dipoles dressed by the laser. Our expressions provide a physically clear and technically simple route towards the analysis of LIDDI in a general geometry. This approach can treat both mechanical and internal-state interactions between the dipoles. Our general results reveal LIDDI effects due to nonlinear dipole-laser interactions, unaccounted for by previous treatments of LIDDI. We discuss, via several simple approaches, the origin of these nonlinear effects and their absence in previous works.
Nonlinear gravity-wave interactions in stratified turbulence
Remmel, Mark; Sukhatme, Jai; Smith, Leslie M.
2014-04-01
To investigate the dynamics of gravity waves in stratified Boussinesq flows, a model is derived that consists of all three-gravity-wave-mode interactions (the GGG model), excluding interactions involving the vortical mode. The GGG model is a natural extension of weak turbulence theory that accounts for exact three-gravity-wave resonances. The model is examined numerically by means of random, large-scale, high-frequency forcing. An immediate observation is a robust growth of the so-called vertically sheared horizontal flow (VSHF). In addition, there is a forward transfer of energy and equilibration of the nonzero-frequency (sometimes called "fast") gravity-wave modes. These results show that gravity-wave-mode interactions by themselves are capable of systematic interscale energy transfer in a stratified fluid. Comparing numerical simulations of the GGG model and the full Boussinesq system, for the range of Froude numbers ( Fr) considered (0.05 ≤ Fr ≤ 1), in both systems the VSHF is hardest to resolve. When adequately resolved, VSHF growth is more vigorous in the GGG model. Furthermore, a VSHF is observed to form in milder stratification scenarios in the GGG model than the full Boussinesq system. Finally, fully three-dimensional nonzero-frequency gravity-wave modes equilibrate in both systems and their scaling with vertical wavenumber follows similar power-laws. The slopes of the power-laws obtained depend on Fr and approach -2 (from above) at Fr = 0.05, which is the strongest stratification that can be properly resolved with our computational resources.
Three-wave interaction in two-component quadratic nonlinear lattices
DEFF Research Database (Denmark)
Konotop, V. V.; Cunha, M. D.; Christiansen, Peter Leth
1999-01-01
We investigate a two-component lattice with a quadratic nonlinearity and find with the multiple scale technique that integrable three-wave interaction takes place between plane wave solutions when these fulfill resonance conditions. We demonstrate that. energy conversion and pulse propagation kno...
Knoester, Jasper; Mukamel, Shaul
1989-01-01
Reduced equations of motion for material and radiation field variables in a molecular crystal are presented that allow us to calculate linear- and nonlinear-optical susceptibilities, accounting in a systematic way for intermolecular interactions. These equations are derived starting from the multipo
Interaction of Tangent Conormal Waves for Higher-Order Nonlinear Strictly Hyperbolic Equations
Institute of Scientific and Technical Information of China (English)
尹会成; 仇庆久
1994-01-01
In this paper we deal with the interaction of three conormal waves for a class of third-order nonlinear strictly hyperbolic equations, in which two conormal waves are tangent. By the same argument, we may also discuss the similar problem for equation system of compressible fluid flow and obtain similar conclusions.
Towards Ultrafast Communications: Nonlinear Coupling Dynamics and Light-Semiconductor Interaction
Wang, W.
2007-01-01
This thesis deals with some specific problems concerning the processing of ultrashort optical pulses and their interaction with semiconductors. It includes the investigation of the ultrashort optical pulse propagation and coupling dynamics in the nonlinear coupled waveguide, and the coherent and in
Kelava, Augustin; Werner, Christina S.; Schermelleh-Engel, Karin; Moosbrugger, Helfried; Zapf, Dieter; Ma, Yue; Cham, Heining; Aiken, Leona S.; West, Stephen G.
2011-01-01
Interaction and quadratic effects in latent variable models have to date only rarely been tested in practice. Traditional product indicator approaches need to create product indicators (e.g., x[superscript 2] [subscript 1], x[subscript 1]x[subscript 4]) to serve as indicators of each nonlinear latent construct. These approaches require the use of…
Interaction-induced effects in the nonlinear coherent response of quantum-well excitons
DEFF Research Database (Denmark)
Wagner, Hans Peter; Schätz, A.; Langbein, Wolfgang Werner;
1999-01-01
Interaction-induced processes are studied using the third-order nonlinear polarization created in polarization-dependent four-wave-mixing experiments (FWM) on a ZnSe single quantum well. We discuss their influence by a comparison of the experimental FWM with calculations based on extended optical...
Towards Ultrafast Communications: Nonlinear Coupling Dynamics and Light-Semiconductor Interaction
Wang, W.
2007-01-01
This thesis deals with some specific problems concerning the processing of ultrashort optical pulses and their interaction with semiconductors. It includes the investigation of the ultrashort optical pulse propagation and coupling dynamics in the nonlinear coupled waveguide, and the coherent and
Management of the orbital angular momentum of vortex beams in a quadratic nonlinear interaction
Bovino, Fabio A; Bertolotti, Mario; Sibilia, Concita
2011-01-01
Light intensity control of the orbital angular momentum of the fundamental beam in a quadratic nonlinear process is theoretically and numerically presented. In particular we analyzed a seeded second harmonic generation process in presence of orbital angular momentum of the interacting beams due both to on axis and off axis optical vortices. Examples are proposed and discussed.
Soliton-potential interaction in the Nonlinear Klein-Gordon Model
Saadatmand, Danial
2011-01-01
Interaction of solitons with external potentials in nonlinear Klein-Gordon field theory is investigated using an improved model. Presented model is constructed with a better approximation for adding the potential to the lagrangian through the metric of background space-time. The results of the model are compared with the another model and the differences are discussed.
A two-phase free boundary problem for a nonlinear diffusion-convection equation
Energy Technology Data Exchange (ETDEWEB)
De Lillo, S; Lupo, G [Dipartimento di Matematica e Informatica, Universita degli Studi di Perugia, Via Vanvitelli 1, 06123 Perugia (Italy)], E-mail: silvana.delillo@pg.infn.it
2008-04-11
A two-phase free boundary problem associated with a diffusion-convection equation is considered. The problem is reduced to a system of nonlinear integral equations, which admits a unique solution for small times. The system admits an explicit two-component solution corresponding to a two-component shock wave of the Burgers equation. The stability of such a solution is also discussed.
A Phase Field Model of Deformation Twinning: Nonlinear Theory and Numerical Simulations
2011-03-01
anisotropic elastic constants. The present phase field method does not enable resolution of atomic details of defect structures afforded by quantum or...multiple twins, following the theory in Appendix B. 6. Conclusions A nonlinear theory has been developed to address mechani - cal twinning. The general...Mag. A 63 (1991) 1001–1012. [25] A. Paxton, P. Gumbsch, M. Methfessel, A quantum mechanical calculation of the theoretical strength of metals, Phil. Mag
Numerical method for nonlinear two-phase displacement problem and its application
Institute of Scientific and Technical Information of China (English)
YUAN Yi-rang; LIANG Dong; RUI Hong-xing; DU Ning; WANG Wen-qia
2008-01-01
For the three-dimensional nonlinear two-phase displacement problem, the modified upwind finite difference fractional steps schemes were put forward. Some techniques, such as calculus of variations, induction hypothesis, decomposition of high order difference operators, the theory of prior estimates and techniques were used. Optimal order estimates were derived for the error in the approximation solution. These methods have been successfully used to predict the consequences of seawater intrusion and protection projects.
Nonlinear neutrino-photon interactions inside strong laser pulses
Energy Technology Data Exchange (ETDEWEB)
Meuren, Sebastian; Keitel, Christoph H.; Di Piazza, Antonino [Max-Planck-Institut fuer Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg (Germany)
2016-07-01
As different neutrino mass eigenstates exist, only the lightest neutrino is absolutely stable. However, due to the small phase space and the GIM suppression mechanism the radiative neutrino lifetime is much larger than the age of the universe. Interestingly, the photon-emission probability by a neutrino is drastically increased in the presence of an external background field. Therefore, it is natural to ask the question whether this so-called ''electromagnetic catalysis'' could be studied in an laboratory experiment using existing and upcoming laser facilities. To shed light on this question, we derive the vector-axialvector coupling tensor in the presence of an arbitrary plane-wave background field, which is needed for the calculation of the radiative neutrino decay. Furthermore, we study the Adler-Bell-Jackiw anomaly associated with this object in detail.
Interaction of Lyapunov vectors in the formulation of the nonlinear extension of the Kalman filter.
Palatella, Luigi; Trevisan, Anna
2015-04-01
When applied to strongly nonlinear chaotic dynamics the extended Kalman filter (EKF) is prone to divergence due to the difficulty of correctly forecasting the forecast error probability density function. In operational forecasting applications ensemble Kalman filters circumvent this problem with empirical procedures such as covariance inflation. This paper presents an extension of the EKF that includes nonlinear terms in the evolution of the forecast error estimate. This is achieved starting from a particular square-root implementation of the EKF with assimilation confined in the unstable subspace (EKF-AUS), that is, the span of the Lyapunov vectors with non-negative exponents. When the error evolution is nonlinear, the space where it is confined is no more restricted to the unstable and neutral subspace causing filter divergence. The algorithm presented here, denominated EKF-AUS-NL, includes the nonlinear terms in the error dynamics: These result from the nonlinear interaction among the leading Lyapunov vectors and account for all directions where the error growth may take place. Numerical results show that with the nonlinear terms included, filter divergence can be avoided. We test the algorithm on the Lorenz96 model, showing very promising results.
Backward phase-matching for nonlinear optical generation in negative-index materials
Lan, Shoufeng; Kang, Lei; Schoen, David T.; Rodrigues, Sean P.; Cui, Yonghao; Brongersma, Mark L.; Cai, Wenshan
2015-08-01
Metamaterials have enabled the realization of unconventional electromagnetic properties not found in nature, which provokes us to rethink the established rules of optics in both the linear and nonlinear regimes. One of the most intriguing phenomena in nonlinear metamaterials is `backward phase-matching', which describes counter-propagating fundamental and harmonic waves in a negative-index medium. Predicted nearly a decade ago, this process is still awaiting a definitive experimental confirmation at optical frequencies. Here, we report optical measurements showing backward phase-matching by exploiting two distinct modes in a nonlinear plasmonic waveguide, where the real parts of the mode refractive indices are 3.4 and -3.4 for the fundamental and the harmonic waves respectively. The observed peak conversion efficiency at the excitation wavelength of ~780 nm indicates the fulfilment of the phase-matching condition of k2ω = 2kω and n2ω = -nω, where the coherent harmonic wave emerges along a direction opposite to that of the incoming fundamental light.
LINEAR AND NONLINEAR AERODYNAMIC THEORY OF INTERACTION BETWEEN FLEXIBLE LONG STRUCTURE AND WIND
Institute of Scientific and Technical Information of China (English)
徐旭; 曹志远
2001-01-01
In light of the characteristics of the interactions between flexible structure and wind in three directions, and based on the rational mechanical section-model of structure, a new aerodynamic force model is accepted, i. e. the coefficients of three component forces are the functions of the instantaneous attack angle and rotational speed Ci = Ci(β(t),θ),(i = D, L, M). So, a new method to formulate the linear and nonlinear aerodynamic items of wind and structure interacting has been put forward in accordance with "strip theory"and modified "quasi-static theory ", and then the linear and nonlinear coupled theory of super-slender structure for civil engineering analyzing are converged in one model. For the linear aerodynamic-force parts, the semi-analytical expressions of the items so-called "flutter derivatives" corresponding to the one in the classic equations have been given here,and so have the nonlinear parts. The study of the stability of nonlinear aerodynamic-coupled torsional vibration of the old Tacoma bridge shows that the form and results of the nonlinear control equation in rotational direction are in agreement with that of V. F. Bohm's.
Hida, Kazuo
2016-12-01
A series of symmetry-protected topological (SPT) and trivial spin-gap phases in the spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain with alternating next-nearest-neighbour interaction are investigated using two kinds of entanglement spectra defined by different divisions of the whole chain. In case one of the next-nearest-neighbor interactions vanishes, the model reduces to the Δ-chain in which a series of spin-gap phases are found, as shown in J. Phys. Soc. Jpn. 77, 044707 (2008). From the degeneracy of the entanglement spectra, these phases are identified as the SPT and trivial phases. It is found that the ground-state phase boundaries are insensitive to the strength of the alternation in the next-nearest-neighbor interaction. These results are consistent with the analysis based on the nonlinear σ model and exact solution on the ferromagnetic-nonmagnetic phase boundary.
Nonlinear Interactions within the D-Region Ionosphere
Moore, Robert
2016-07-01
This paper highlights the best results obtained during D-region modification experiments performed by the University of Florida at the High-frequency Active Auroral Research Program (HAARP) observatory between 2007 and 2014. Over this period, we saw a tremendous improvement in ELF/VLF wave generation efficiency. We identified methods to characterize ambient and modified ionospheric properties and to discern and quantify specific types of interactions. We have demonstrated several important implications of HF cross-modulation effects, including "Doppler Spoofing" on HF radio waves. Throughout this talk, observations are compared with the predictions of an ionospheric HF heating model to provide context and guidance for future D-region modification experiments.
Phase disruption as a new design paradigm for optimizing the nonlinear-optical response
Lytel, Rick; Kuzyk, Mark G
2015-01-01
The intrinsic optical nonlinearities of quasi-one dimensional structures, including conjugated chain polymers and nanowires, are shown to be dramatically enhanced by the judicious placement of a side group or wire of sufficiently short length to create a large phase disruption in the dominant eigenfunctions along the main path of probability current. Phase disruption is proposed as a new general principle for the design of molecules, nanowires and any quasi-1D quantum system with large intrinsic response and does not require charge donors-acceptors at the ends.
Phase Diagrams of Strongly Interacting Theories
DEFF Research Database (Denmark)
Sannino, Francesco
2010-01-01
We summarize the phase diagrams of SU, SO and Sp gauge theories as function of the number of flavors, colors, and matter representation as well as the ones of phenomenologically relevant chiral gauge theories such as the Bars-Yankielowicz and the generalized Georgi-Glashow models. We finally repo...
Interharmonic modulation products as a means to quantify nonlinear D-region interactions
Moore, Robert
Experimental observations performed during dual beam ionospheric HF heating experiments at the High frequency Active Auroral Research Program (HAARP) HF transmitter in Gakona, Alaska are used to quantify the relative importance of specific nonlinear interactions that occur within the D region ionosphere. During these experiments, HAARP broadcast two amplitude modulated HF beams whose center frequencies were separated by less than 20 kHz. One beam was sinusoidally modulated at 500 Hz while the second beam was sinusoidally modulated using a 1-7 kHz linear frequency-time chirp. ELF/VLF observations performed at two different locations (3 and 98 km from HAARP) provide clear evidence of strong interactions between all field components of the two HF beams in the form of low and high order interharmonic modulation products. From a theoretical standpoint, the observed interharmonic modulation products could be produced by several different nonlinearities. The two primary nonlinearities take the form of wave-medium interactions (i.e., cross modulation), wherein the ionospheric conductivity modulation produced by one signal crosses onto the other signal via collision frequency modification, and wave-wave interactions, wherein the conduction current associated with one wave mixes with the electric field of the other wave to produce electron temperature oscillations. We are able to separate and quantify these two different nonlinearities, and we conclude that the wave-wave interactions dominate the wave-medium interactions by a factor of two. These results are of great importance for the modeling of transioinospheric radio wave propagation, in that both the wave-wave and the wave-medium interactions could be responsible for a significant amount of anomalous absorption.
Low-Complexity Tracking of Laser and Nonlinear Phase Noise in WDM Optical Fiber Systems
DEFF Research Database (Denmark)
Yankov, Metodi Plamenov; Fehenberger, Tobias; Barletta, Luca
2015-01-01
In this paper, the wavelength division multiplexed (WDM) fiber optic channel is considered. It is shown that for ideal distributed Raman amplification (IDRA), the Wiener process model is suitable for the non-linear phase noise due to cross phase modulation from neighboring channels. Based...... compared to previous trellis-based approaches, which require numerical integration. Further, the proposed method performs very well in low-to-moderate signal-to-noise ratio (SNR), where standard decision directed (DD) methods, especially for high-order modulation, fail. The proposed algorithm does not rely...... on this model, a phase noise tracking algorithm is presented. We approximate the distribution of the phase noise at each time instant by a mixture of Tikhonov distributions, and derive a closed form expression for the posterior probabilities of the input symbols. This reduces the complexity dramatically...
Nonlinear interaction of two trapped-mode resonances in a bilayer "fish-scale" metamaterial
Tuz, Vladimir R; Mladyonov, Pavel L; Prosvirnin, Sergey L; Novitsky, Andrey V
2014-01-01
We report on a bistable light transmission through a bilayer "fish-scale" (meander-line) metamaterial. It is demonstrated that an all-optical switching may be achieved nearly the frequency of the high-quality-factor Fano-shaped trapped-mode resonance excitation. The nonlinear interaction of two closely spaced trapped-mode resonances in the bilayer structure composed with a Kerr-type nonlinear dielectric slab is analyzed in both frequency and time domains. It is demonstrated that these two resonances react differently on the applied intense light which leads to destination of a multistable transmission.
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.
Shen, Yanfeng; Cesnik, Carlos E. S.
2016-04-01
This paper presents a parallelized modeling technique for the efficient simulation of nonlinear ultrasonics introduced by the wave interaction with fatigue cracks. The elastodynamic wave equations with contact effects are formulated using an explicit Local Interaction Simulation Approach (LISA). The LISA formulation is extended to capture the contact-impact phenomena during the wave damage interaction based on the penalty method. A Coulomb friction model is integrated into the computation procedure to capture the stick-slip contact shear motion. The LISA procedure is coded using the Compute Unified Device Architecture (CUDA), which enables the highly parallelized supercomputing on powerful graphic cards. Both the explicit contact formulation and the parallel feature facilitates LISA's superb computational efficiency over the conventional finite element method (FEM). The theoretical formulations based on the penalty method is introduced and a guideline for the proper choice of the contact stiffness is given. The convergence behavior of the solution under various contact stiffness values is examined. A numerical benchmark problem is used to investigate the new LISA formulation and results are compared with a conventional contact finite element solution. Various nonlinear ultrasonic phenomena are successfully captured using this contact LISA formulation, including the generation of nonlinear higher harmonic responses. Nonlinear mode conversion of guided waves at fatigue cracks is also studied.
Shen, Yanfeng
2017-04-01
This paper presents a numerical investigation of the nonlinear interactions between multimodal guided waves and delamination in composite structures. The elastodynamic wave equations for anisotropic composite laminate were formulated using an explicit Local Interaction Simulation Approach (LISA). The contact dynamics was modeled using the penalty method. In order to capture the stick-slip contact motion, a Coulomb friction law was integrated into the computation procedure. A random gap function was defined for the contact pairs to model distributed initial closures or openings to approximate the nature of rough delamination interfaces. The LISA procedure was coded using the Compute Unified Device Architecture (CUDA), which enables the highly parallelized computation on powerful graphic cards. Several guided wave modes centered at various frequencies were investigated as the incident wave. Numerical case studies of different delamination locations across the thickness were carried out. The capability of different wave modes at various frequencies to trigger the Contact Acoustic Nonlinearity (CAN) was studied. The correlation between the delamination size and the signal nonlinearity was also investigated. Furthermore, the influence from the roughness of the delamination interfaces was discussed as well. The numerical investigation shows that the nonlinear features of wave delamination interactions can enhance the evaluation capability of guided wave Structural Health Monitoring (SHM) system. This paper finishes with discussion, concluding remarks, and suggestions for future work.
Statistical analysis of nonlinear wave interactions in simulated Langmuir turbulence data
Directory of Open Access Journals (Sweden)
J. Soucek
Full Text Available We present a statistical analysis of strong turbulence of Langmuir and ion-sound waves resulting from beam-plasma interaction. The analysis is carried out on data sets produced by a numerical simulation of one-dimensional Zakharov’s equations. The nonlinear wave interactions are studied using two different approaches: high-order spectra and Volterra models. These methods were applied to identify two and three wave processes in the data, and the Volterra model was furthermore employed to evaluate the direction and magnitude of energy transfer between the wave modes in the case of Langmuir wave decay. We demonstrate that these methods allow one to determine the relative importance of strongly and weakly turbulent processes. The statistical validity of the results was thoroughly tested using surrogated data set analysis.
Key words. Space plasma physics (wave-wave interactions; experimental and mathematical techniques; nonlinear phenomena
On the acoustic director interaction in the smectic A phase
Perlo, Josefina; Aguirre, Luis E.; Revelli, Jorge; Anoardo, Esteban
2007-12-01
A model was previously proposed for the interaction energy between an acoustic field and the local nematic director. The consistency of this model was verified through nuclear magnetic relaxation and optical experiments. The model was later extended to the smectic A phase, despite the fact that the smectic essence of the problem was never included in the interaction process. In this work we investigate details of this interaction through the inclusion of elemental features of the smectic phase. We show that the acoustic-director interaction can be enhanced if the external acoustic field matches an eigenmode of the smectic system.
Integrability and Quantum Phase Transitions in Interacting Boson Models
Dukelsky, J; García-Ramos, J E; Pittel, S
2003-01-01
The exact solution of the boson pairing hamiltonian given by Richardson in the sixties is used to study the phenomena of level crossings and quantum phase transitions in the integrable regions of the sd and sdg interacting boson models.
Berry phases for interacting spins in composite environments
Yang, Da-Bao; Chen, Jing-Ling
2012-01-01
Due to the potential application in quantum information process, geometric phase of interacting system arouse many interests. Some physicists concentrate on the system in pure classical envi- ronment, while others study the system in pure quantized environment. So a natural question is asked: how about an interacting system in composite environments made up of both classical and quantized field. In this letter, we analyze a quantum system composed of two interacting spins, of which one is in classical magnetic field and the other is in quantized field. First, classical magnetic field driven Berry phases for the whole system and subsystem are studied. The effect of couplings between particles and photon on these phases are analyzed. In comparison with the dynamical quantized field, We find that even a static quantized field in its vacuum state can also have an effect on Berry phase. Second, quantized field driven Berry phases for the whole system and sub- system are formulated, including both one and two mode ...
Energy Technology Data Exchange (ETDEWEB)
Bhaumik, Lopamudra, E-mail: lbhaumi2@illinois.edu [University of Illinois at Urbana-Champaign (United States); Raychowdhury, Prishati, E-mail: prishati@iitk.ac.in [Indian Institute of Technology Kanpur (India)
2013-12-15
Highlights: • Seismic response analysis of an internal shearwall of a reactor is done. • Incremental dynamic analysis is performed with 30 recorded ground motions. • Equivalent viscous damping increases up to twice when nonlinear SSI is considered. • Roof drift demand increases up to 25% upon consideration of foundation nonlinearity. • Base shear, base moment and ductility reduce up to 62%, 40%, and 35%, respectively. - Abstract: This study focuses on the seismic response analysis of an internal shearwall of a typical Indian reactor resting on a medium dense sandy silty soil, incorporating the nonlinear behavior of the soil-foundation interface. The modeling is done in an open-source finite element framework, OpenSees, where the soil-structure interaction (SSI) is modeled using a Beam-on-Nonlinear-Winkler-Foundation (BNWF) approach. Static pushover analysis and cyclic analysis are performed followed by an incremental dynamic analysis (IDA) with 30 recorded ground motions. For performing IDA, the spectral acceleration of each motion corresponding to the fundamental period, S{sub a}(T{sub 1})is incremented from 0.1 g to 1.0 g with an increment step of 0.1 g. It is observed from the cyclic analysis that the equivalent viscous damping of the system increases upto twice upon incorporation of inelastic SSI. The IDA results demonstrate that the average peak base shear, base moment and displacement ductility demand reduces as much as 62%, 40%, and 35%, respectively, whereas the roof drift demand increases up to 25% upon consideration of foundation nonlinearity for the highest intensity motion. These observations indicate the need of critical consideration of nonlinear soil-structure interaction as any deficient modeling of the same may lead to an inaccurate estimation of the seismic demands of the structure.
DEFF Research Database (Denmark)
Zeng, Xianglong; Guo, Hairun; Zhou, Binbin
2012-01-01
In few-cycle soliton generation with large compression factors using cascaded nonlinearities the pulse quality can be improved by engineering quasi-phase-matching structures. The soliton-induced mid-IR optical Cherenkov wave is also enhanced.......In few-cycle soliton generation with large compression factors using cascaded nonlinearities the pulse quality can be improved by engineering quasi-phase-matching structures. The soliton-induced mid-IR optical Cherenkov wave is also enhanced....
Scalerandi, Marco; Agostini, Valentina; Delsanto, Pier Paolo; Van Den Abeele, Koen; Johnson, Paul A
2003-06-01
Recent studies show that a broad category of materials share "nonclassical" nonlinear elastic behavior much different from "classical" (Landau-type) nonlinearity. Manifestations of "nonclassical" nonlinearity include stress-strain hysteresis and discrete memory in quasistatic experiments, and specific dependencies of the harmonic amplitudes with respect to the drive amplitude in dynamic wave experiments, which are remarkably different from those predicted by the classical theory. These materials have in common soft "bond" elements, where the elastic nonlinearity originates, contained in hard matter (e.g., a rock sample). The bond system normally comprises a small fraction of the total material volume, and can be localized (e.g., a crack in a solid) or distributed, as in a rock. In this paper a model is presented in which the soft elements are treated as hysteretic or reversible elastic units connected in a one-dimensional lattice to elastic elements (grains), which make up the hard matrix. Calculations are performed in the framework of the local interaction simulation approach (LISA). Experimental observations are well predicted by the model, which is now ready both for basic investigations about the physical origins of nonlinear elasticity and for applications to material damage diagnostics.
Evaluation of self-interaction parameters from binary phase diagrams
Energy Technology Data Exchange (ETDEWEB)
Ellison, T. L.
1977-10-01
The feasibility of calculating Wagner self-interaction parameters from binary phase diagrams was examined. The self-interaction parameters of 22 non-ferrous liquid solutions were calculated utilizing an equation based on the equality of the chemical potentials of a component in two equilibrium phases. Utilization of the equation requires the evaluation of the first and second derivatives of various liquidus and solidus data at infinite dilution of the solute component. Several numerical methods for evaluating the derivatives of tabular data were examined. A method involving power series curve fitting and subsequent differentiation of the power series was found to be the most suitable for the interaction parameter calculations. Comparison of the calculated self-interaction parameters with values obtained from thermodynamic measurements indicates that the Wagner self-interaction parameter can be successfully calculated from binary phase diagrams.
Measurement of nonlinear coefficient and phase matching characteristics of AgGaS sub 2
Energy Technology Data Exchange (ETDEWEB)
Canarelli, P.; Benko, Z.; Hielscher, A.H.; Curl, R.F.; Tittle, F.K. (Dept. of Electrical and Computer Engineering, Rice Quantum Inst., Rice Univ., Houston, TX (US))
1992-01-01
This paper reports on a nonlinear optical characteristics of AgGaS{sub 2} that were investigated by measuring visible parametric fluorescence with a pump wavelength of 600 nm. A value of d{sub 36}(AgGaS{sub 2}) = 31 {plus minus} 5 10{sup {minus}12} m/V for the nonlinear coefficient was determined. The temperature dependence of phase matching up to 100{degrees}C was studied. A significant temperature effect, although much smaller than the LiNbO{sub 3}, was found and results in a change in the infrared difference frequency generated of {approximately}0.6 cm{sup {minus}1} {center dot} {degrees}C{sup {minus}1}.
Wave–vortex interactions in the nonlinear Schrödinger equation
Energy Technology Data Exchange (ETDEWEB)
Guo, Yuan, E-mail: yuanguo@cims.nyu.edu; Bühler, Oliver [Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States)
2014-02-15
This is a theoretical study of wave–vortex interaction effects in the two-dimensional nonlinear Schrödinger equation, which is a useful conceptual model for the limiting dynamics of superfluid quantum condensates at zero temperature. The particular wave–vortex interaction effects are associated with the scattering and refraction of small-scale linear waves by the straining flows induced by quantized point vortices and, crucially, with the concomitant nonlinear back-reaction, the remote recoil, that these scattered waves exert on the vortices. Our detailed model is a narrow, slowly varying wavetrain of small-amplitude waves refracted by one or two vortices. Weak interactions are studied using a suitable perturbation method in which the nonlinear recoil force on the vortex then arises at second order in wave amplitude, and is computed in terms of a Magnus-type force expression for both finite and infinite wavetrains. In the case of an infinite wavetrain, an explicit asymptotic formula for the scattering angle is also derived and cross-checked against numerical ray tracing. Finally, under suitable conditions a wavetrain can be so strongly refracted that it collapses all the way onto a zero-size point vortex. This is a strong wave–vortex interaction by definition. The conditions for such a collapse are derived and the validity of ray tracing theory during the singular collapse is investigated.
Pitch glide effect induced by a nonlinear string-barrier interaction
Kartofelev, Dmitri; Stulov, Anatoli; Välimäki, Vesa
2015-10-01
Interactions of a vibrating string with its supports and other spatially distributed barriers play a significant role in the physics of many stringed musical instruments. It is well known that the tone of the string vibrations is determined by the string supports, and that the boundary conditions of the string termination may cause a short-lasting initial fundamental frequency shifting. Generally, this phenomenon is associated with the nonlinear modulation of the stiff string tension. The aim of this paper is to study the initial frequency glide phenomenon that is induced only by the string-barrier interaction, apart from other possible physical causes, and without the interfering effects of dissipation and dispersion. From a numerical simulation perspective, this highly nonlinear problem may present various difficulties, not the least of which is the risk of numerical instability. We propose a numerically stable and a purely kinematic model of the string-barrier interaction, which is based on the travelling wave solution of the ideal string vibration. The model is capable of reproducing the motion of the vibrating string exhibiting the initial fundamental frequency glide, which is caused solely by the complex nonlinear interaction of the string with its termination. The results presented in this paper can expand our knowledge and understanding of the timbre evolution and the physical principles of sound generation of numerous stringed instruments, such as lutes called the tambura, sitar and biwa.
Yang, Haijian
2016-07-26
Fully implicit methods are drawing more attention in scientific and engineering applications due to the allowance of large time steps in extreme-scale simulations. When using a fully implicit method to solve two-phase flow problems in porous media, one major challenge is the solution of the resultant nonlinear system at each time step. To solve such nonlinear systems, traditional nonlinear iterative methods, such as the class of the Newton methods, often fail to achieve the desired convergent rate due to the high nonlinearity of the system and/or the violation of the boundedness requirement of the saturation. In the paper, we reformulate the two-phase model as a variational inequality that naturally ensures the physical feasibility of the saturation variable. The variational inequality is then solved by an active-set reduced-space method with a nonlinear elimination preconditioner to remove the high nonlinear components that often causes the failure of the nonlinear iteration for convergence. To validate the effectiveness of the proposed method, we compare it with the classical implicit pressure-explicit saturation method for two-phase flow problems with strong heterogeneity. The numerical results show that our nonlinear solver overcomes the often severe limits on the time step associated with existing methods, results in superior convergence performance, and achieves reduction in the total computing time by more than one order of magnitude.
Nonlinear wave-particle interactions in the outer radiation belts: Van Allen Probes results
Agapitov, Oleksiy; Mozer, Forrest; Artemyev, Anton; Drake, James; Vasko, Ivan
2016-10-01
Huge numbers of different nonlinear structures (double layers, electron holes, non-linear whistlers, etc. referred to as Time Domain Structures - TDS) have been observed by the electric field experiment on board the Van Allen Probes. A large part of the observed non-linear structures are associated with whistler waves and some of them can be directly driven by whistlers. Observations of electron velocity distributions and chorus waves by the Van Allen Probe B provided long-lasting signatures of electron Landau resonant interactions with oblique chorus waves in the outer radiation belt. In the inhomogeneous geomagnetic field, such resonant interactions then lead to the formation of a plateau in the parallel (with respect to the geomagnetic field) velocity distribution due to trapping of electrons into the wave effective potential. The feedback from trapped particles provides steepening of parallel electric field and development of TDS seeded from initial whistler structure (well explained in terms of Particle-In-Cell model). The decoupling of the whistler wave and the nonlinear electrostatic component is shown in PIC simulation in the inhomogeneous magnetic field system and are observed by the Van Allen Probes in the radiation belts.
Interactions between time-varying mesh stiffness and clearance non-linearities in a geared system
Kahraman, A.; Singh, R.
1991-04-01
Frequency response characteristics of a non-linear geared rotor-bearing system with time-varying mesh stiffness k h( overlinet) are examined in this paper. First, the single-degree-of-freedom spur gear pair model with backlash is extended to include sinusoidal or periodic mesh stiffness k h( overlinet) . Second, a three-degree-of-freedom model with k h( overlinet) and clearance non-lineariries associated with gear backlash and rolling element bearings, as excited by the static transmission error overlinee( overlinet) under a mean torque load, is developed. The governing equations are solved using digital simulation technique and only the primary resonances are studied. Resonances of the corresponding linear time-varying system associated with parametric and external excitations are identified using the method of multiple scales and digital simulation. Interactions between the mesh stiffness variation and clearance non-linearities have been investigated; a strong interaction between time-varying mesh stiffness k h( overlinet) and gear backlash is found, whereas the coupling between k h( overlinet) and bearing non-linearities is weak. Finally, our time-varying non-linear formulations yield reasonably good predictions when compared with the benchmark experimental results available in the literature.
Harmonic Propagation and Interaction Evaluation between Small-Scale Wind Farms and Nonlinear Loads
Directory of Open Access Journals (Sweden)
Cheng-Xiong Mao
2013-07-01
Full Text Available Distributed generation is a flexible and effective way to utilize renewable energy. The dispersed generators are quite close to the load, and pose some power quality problems such as harmonic current emissions. This paper focuses on the harmonic propagation and interaction between a small-scale wind farm and nonlinear loads in the distribution grid. Firstly, by setting the wind turbines as P – Q(V nodes, the paper discusses the expanding Newton-Raphson power flow method for the wind farm. Then the generalized gamma mixture models are proposed to study the non-characteristic harmonic propagation of the wind farm, which are based on Gaussian mixture models, improved phasor clustering and generalized Gamma models. After the integration of the small-scale wind farm, harmonic emissions of nonlinear loads will become random and fluctuating due to the non-stationary wind power. Furthermore, in this paper the harmonic coupled admittance matrix model of nonlinear loads combined with a wind farm is deduced by rigorous formulas. Then the harmonic propagation and interaction between a real wind farm and nonlinear loads are analyzed by the harmonic coupled admittance matrix and generalized gamma mixture models. Finally, the proposed models and methods are verified through the corresponding simulation models in MATLAB/SIMULINK and PSCAD/EMTDC.
Gyroid phase of fluids with spherically symmetric competing interactions.
Edelmann, Markus; Roth, Roland
2016-06-01
We study the phase diagram of a fluid with spherically symmetric competing pair interactions that consist of a short-ranged attraction and a longer-ranged repulsion in addition to a hard core. To this end we perform free minimizations of three-dimensional triple periodic structures within the framework of classical density functional theory. We compare our results to those from Landau theory. Our main finding is that the double gyroid phase can exist as a thermodynamically stable phase.
Nonlinear Phase Distortion in a Ti:Sapphire Optical Amplifier for Optical Stochastic Cooling
Energy Technology Data Exchange (ETDEWEB)
Andorf, Matthew [NICADD, DeKalb; Lebedev, Valeri [Fermilab; Piot, Philippe [NICADD, DeKalb; Ruan, Jinhao [Fermilab
2016-06-01
Optical Stochastic Cooling (OSC) has been considered for future high-luminosity colliders as it offers much faster cooling time in comparison to the micro-wave stochastic cooling. The OSC technique relies on collecting and amplifying a broadband optical signal from a pickup undulator and feeding the amplified signal back to the beam. It creates a corrective kick in a kicker undulator. Owing to its superb gain qualities and broadband amplification features, Titanium:Sapphire medium has been considered as a gain medium for the optical amplifier (OA) needed in the OSC*. A limiting factor for any OA used in OSC is the possibility of nonlinear phase distortions. In this paper we experimentally measure phase distortions by inserting a single-pass OA into one leg of a Mach-Zehnder interferometer. The measurement results are used to estimate the reduction of the corrective kick a particle would receive due to these phase distortions in the kicker undulator.
Subharmonic phase clusters in the complex Ginzburg-Landau equation with nonlinear global coupling.
García-Morales, Vladimir; Orlov, Alexander; Krischer, Katharina
2010-12-01
A wide variety of subharmonic n -phase cluster patterns was observed in experiments with spatially extended chemical and electrochemical oscillators. These patterns cannot be captured with a phase model. We demonstrate that the introduction of a nonlinear global coupling (NGC) in the complex Ginzburg-Landau equation has subharmonic cluster pattern solutions in wide parameter ranges. The NGC introduces a conservation law for the oscillatory state of the homogeneous mode, which describes the strong oscillations of the mean field in the experiments. We show that the NGC causes a pronounced 2:1 self-resonance on any spatial inhomogeneity, leading to two-phase subharmonic clustering, as well as additional higher resonances. Nonequilibrium Ising-Bloch transitions occur as the coupling strength is varied.
Non-linear clustering during the BEC dark matter phase transition
de Freitas, Rodolfo C
2015-01-01
Spherical collapse of the Bose-Einstein Condensate (BEC) dark matter model is studied. The evolution of perturbed quantities like the density of the collapsed region and its expansion rate are calculated for two scenarios. Firstly, we consider the case of a sharp phase transition (which happens when the critical temperature is reached) from the normal dark matter state to the condensate one. In the second case studied we consider a smooth first order phase transition where there is a continuous conversion of "normal" dark matter to the BEC phase. We calculate in detail the perturbative quantities at nonlinear level presenting numerical results for the physics of the collapse for a wide range of the model's space parameter. The model is properly compared to the standard dark matter scenario.
Miksovsky, J.; Raidl, A.
Time delays phase space reconstruction represents one of useful tools of nonlinear time series analysis, enabling number of applications. Its utilization requires the value of time delay to be known, as well as the value of embedding dimension. There are sev- eral methods how to estimate both these parameters. Typically, time delay is computed first, followed by embedding dimension. Our presented approach is slightly different - we reconstructed phase space for various combinations of mentioned parameters and used it for prediction by means of the nearest neighbours in the phase space. Then some measure of prediction's success was computed (correlation or RMSE, e.g.). The position of its global maximum (minimum) should indicate the suitable combination of time delay and embedding dimension. Several meteorological (particularly clima- tological) time series were used for the computations. We have also created a MS- Windows based program in order to implement this approach - its basic features will be presented as well.
Mao, Heng; Zhao, Dazun
2009-03-16
A modified Levenberg-Marquardt (MLM) algorithm is proposed to substitute for modified G-S (MGS) algorithm in some situations of phase-diverse phase retrieval wavefront sensing (WFS), such as the obstructed pupil, in which the second derivative information is specifically employed to eliminate the local minimum stagnation. Experiments have been performed to validate MLM algorithm in WFS accuracy (less than lambda/30 RMS) referring to ZYGO interferometer results and in WFS repeatability (less than lambda/200 RMS), even the dynamic range is more than 7 lambda PV. Moreover, experiments have shown the MLM algorithm is superior to the MGS algorithm both in WFS accuracy and repeatability.
Directory of Open Access Journals (Sweden)
M. Simić
2014-06-01
Full Text Available This paper describes the realization of a three-phase transformer model based on a non-linear open-circuit characteristic. The proposed model is based on the fact that in case of a star connection with a neutral wire on the primary windings for all three phases, the applied voltage presents phase voltage and line (phase currents are magnetization currents. These variables are available for measuring and it is easy to obtain three non-linear open circuit characteristics. The results of simulations and a comparison with references and experimental results verified this approach.
Phase diagram and entanglement of two interacting topological Kitaev chains
Herviou, Loïc; Mora, Christophe; Le Hur, Karyn
2016-04-01
A superconducting wire described by a p -wave pairing and a Kitaev Hamiltonian exhibits Majorana fermions at its edges and is topologically protected by symmetry. We consider two Kitaev wires (chains) coupled by a Coulomb-type interaction and study the complete phase diagram using analytical and numerical techniques. A topological superconducting phase with four Majorana fermions occurs until moderate interactions between chains. For large interactions, both repulsive and attractive, by analogy with the Hubbard model, we identify Mott phases with Ising-type magnetic order. For repulsive interactions, the Ising antiferromagnetic order favors the occurrence of orbital currents spontaneously breaking time-reversal symmetry. By strongly varying the chemical potentials of the two chains, quantum phase transitions towards fully polarized (empty or full) fermionic chains occur. In the Kitaev model, the quantum critical point separating the topological superconducting phase and the polarized phase belongs to the universality class of the critical Ising model in two dimensions. When increasing the Coulomb interaction between chains, then we identify an additional phase corresponding to two critical Ising theories (or two chains of Majorana fermions). We confirm the existence of such a phase from exact mappings and from the concept of bipartite fluctuations. We show the existence of negative logarithmic corrections in the bipartite fluctuations, as a reminiscence of the quantum critical point in the Kitaev model. Other entanglement probes such as bipartite entropy and entanglement spectrum are also used to characterize the phase diagram. The limit of large interactions can be reached in an equivalent setup of ultracold atoms and Josephson junctions.
Continuum Random Phase Approximation with finite-range interactions
Energy Technology Data Exchange (ETDEWEB)
Co' , Giampaolo [Universita del Salento, Dipartimento di Fisica ' ' E. De Giorgi' ' , Lecce (Italy); INFN, Sezione di Lecce, Lecce (Italy); De Donno, Viviana [Universita del Salento, Dipartimento di Fisica ' ' E. De Giorgi' ' , Lecce (Italy); Anguiano, Marta; Lallena, Antonio M. [Universidad de Granada, Departamento de Fisica Atomica, Molecular y Nuclear, Granada (Spain)
2016-05-15
We rewrite the Random Phase Approximation secular equations in a form which allows the treatment of the continuum part of the single-particle spectrum without approximations. Within this formalism finite-range interactions can be used without restrictions. We present some results, obtained with Gogny interactions, where the role of the continuum is relevant. (orig.)
Ulku, Huseyin Arda
2014-07-06
Effects of material nonlinearities on electromagnetic field interactions become dominant as field amplitudes increase. A typical example is observed in plasmonics, where highly localized fields “activate” Kerr nonlinearities. Naturally, time domain solvers are the method of choice when it comes simulating these nonlinear effects. Oftentimes, finite difference time domain (FDTD) method is used for this purpose. This is simply due to the fact that explicitness of the FDTD renders the implementation easier and the material nonlinearity can be easily accounted for using an auxiliary differential equation (J.H. Green and A. Taflove, Opt. Express, 14(18), 8305-8310, 2006). On the other hand, explicit marching on-in-time (MOT)-based time domain integral equation (TDIE) solvers have never been used for the same purpose even though they offer several advantages over FDTD (E. Michielssen, et al., ECCOMAS CFD, The Netherlands, Sep. 5-8, 2006). This is because explicit MOT solvers have never been stabilized until not so long ago. Recently an explicit but stable MOT scheme has been proposed for solving the time domain surface magnetic field integral equation (H.A. Ulku, et al., IEEE Trans. Antennas Propag., 61(8), 4120-4131, 2013) and later it has been extended for the time domain volume electric field integral equation (TDVEFIE) (S. B. Sayed, et al., Pr. Electromagn. Res. S., 378, Stockholm, 2013). This explicit MOT scheme uses predictor-corrector updates together with successive over relaxation during time marching to stabilize the solution even when time step is as large as in the implicit counterpart. In this work, an explicit MOT-TDVEFIE solver is proposed for analyzing electromagnetic wave interactions on scatterers exhibiting Kerr nonlinearity. Nonlinearity is accounted for using the constitutive relation between the electric field intensity and flux density. Then, this relation and the TDVEFIE are discretized together by expanding the intensity and flux - sing half
Role of Convective Cells in Nonlinear Interaction of Kinetic Alfven Waves
Luk, Onnie
The convective cells are observed in the auroral ionosphere and they could play an important role in the nonlinear interaction of Alfven waves and disrupt the kinetic Alfven wave (KAW) turbulence. Zonal fields, which are analogous to convective cells, are generated by microturbulence and regulate microturbulence inside toroidally confined plasmas. It is important to understand the role of convective cells in the nonlinear interaction of KAW leading to perpendicular cascade of spectral energy. A nonlinear gyrokinetic particle simulation has been developed to study the perpendicular spectral cascade of kinetic Alfven wave. However, convective cells were excluded in the study. In this thesis project, we have modified the formulation to implement the convective cells to study their role in the nonlinear interactions of KAW. This thesis contains detail description of the code formulation and convergence tests performed, and the simulation results on the role of convective cells in the nonlinear interactions of KAW. In the single KAW pump wave simulations, we observed the pump wave energy cascades to waves with shorter wavelengths, with three of them as dominant daughter waves. Convective cells are among those dominant daughter waves and they enhance the rate of energy transfer from pump to daughter waves. When zonal fields are present, the growth rates of the dominant daughter waves are doubled. The convective cell (zonal flow) of the zonal fields is shown to play a major role in the nonlinear wave interaction, while the linear zonal vector potential has little effects. The growth rates of the daughter waves linearly depends on the pump wave amplitude and the square of perpendicular wavenumber. On the other hand, the growth rates do not depend on the parallel wavenumber in the limit where the parallel wavenumber is much smaller than the perpendicular wavenumber. The nonlinear wave interactions with various perpendicular wavenumbers are also studied in this work. When
Complete elimination of nonlinear light-matter interactions with broadband ultrafast laser pulses
DEFF Research Database (Denmark)
Shu, Chuan-Cun; Dong, Daoyi; Petersen, Ian R.
2017-01-01
nonlinear interactions of ultrafast laser pulses with quantum systems. That is, a completely linear response of the system with respect to the spectral energy density of the incident light at the transition frequency can be obtained for all transition probabilities between 0 and 100% in multilevel quantum......The absorption of a single photon that excites a quantum system from a low to a high energy level is an elementary process of light-matter interaction, and a route towards realizing pure single-photon absorption has both fundamental and practical implications in quantum technology. Due to nonlinear...... optical effects, however, the probability of pure single-photon absorption is usually very low, which is particularly pertinent in the case of strong ultrafast laser pulses with broad bandwidth. Here we demonstrate theoretically a counterintuitive coherent single-photon absorption scheme by eliminating...
Numerical simulation of nonlinear long waves interacting with arrays of emergent cylinders
Zainali, Amir; Weiss, Robert; Irish, Jennifer L; Yang, Yongqian
2016-01-01
We presented numerical simulation of long waves, interacting with arrays of emergent cylinders inside regularly spaced patches, representing discontinues patchy coastal vegetation. We employed the fully nonlinear and weakly dispersive Serre-Green-Naghdi equations (SGN) until the breaking process starts, while we changed the governing equations to nonlinear shallow water equations (NSW) at the vicinity of the breaking-wave peak and during the runup stage. We modeled the cylinders as physical boundaries rather than approximating them as macro-roughness friction. We showed that the cylinders provide protection for the areas behind them. However they might also cause amplification in local water depth in those areas. The presented results are extensively validated against the existing numerical and experimental data. Our results demonstrate the capability and reliability of our model in simulating wave interaction with emergent cylinders.
Modelling of Nonlinear Dynamic of Mechanic Systems with the Force Tribological Interaction
Directory of Open Access Journals (Sweden)
K.A. Nuzhdin
2015-09-01
Full Text Available This paper considers the mechanisms with different structure: tribometric device and a mechanism for handling of optical glasses. In the first device, the movement of the upper platform is due to a reciprocating friction interaction. In the second device, the processing of the optical element or group of elements occurs due to the rotational motion. Modelling of the dynamic of these systems with Matlab/Simmechanic allowed carrying out the analysis of dynamic of mechanisms, considering nonlinearity tribological interactions for these systems. The article shows that using of the computer models can effectively carry out the selection of the control parameters to create the desired mode of operation, as well as to investigate the behaviour of systems with nonlinear parameters and processes of self-oscillations. The organization of the managed self-oscillation process is realized to create the relevant high-performance manufacturing, for example, for the processing of optical glasses.
The effect of crack orientation on the nonlinear interaction of a P wave with an S wave
TenCate, J. A.; Malcolm, A. E.; Feng, X.; Fehler, M. C.
2016-06-01
Cracks, joints, fluids, and other pore-scale structures have long been hypothesized to be the cause of the large elastic nonlinearity observed in rocks. It is difficult to definitively say which pore-scale features are most important, however, because of the difficulty in isolating the source of the nonlinear interaction. In this work, we focus on the influence of cracks on the recorded nonlinear signal and in particular on how the orientation of microcracks changes the strength of the nonlinear interaction. We do this by studying the effect of orientation on the measurements in a rock with anisotropy correlated with the presence and alignment of microcracks. We measure the nonlinear response via the traveltime delay induced in a low-amplitude P wave probe by a high-amplitude S wave pump. We find evidence that crack orientation has a significant effect on the nonlinear signal.
Many-body fits of phase-equivalent effective interactions
Johnson, Calvin W
2010-01-01
In many-body theory it is often useful to renormalize short-distance, high-momentum components of an interaction via unitary transformations. Such transformations preserve the on-shell physical observables of the two-body system (mostly phase-shifts, hence unitarily-connected effective interactions are often called phase-equivalent), while modifying off-shell T-matrix elements influential in many-body systems. In this paper I lay out a general and systematic approach for controlling the off-shell behavior of an effective interaction, which can be adjusted to many-body properties, and present an application to trapped fermions at the unitary
Exact thermodynamics and phase diagram of integrable t-J model with chiral interaction
Tavares, T. S.; Ribeiro, G. A. P.
2016-09-01
We study the phase diagram and finite temperature properties of an integrable generalization of the one-dimensional super-symmetric t-J model containing interactions explicitly breaking parity-time reversal (PT) symmetries. To this purpose, we apply the quantum transfer matrix method which results in a finite set of non-linear integral equations. We obtain numerical solutions to these equations leading to results for thermodynamic quantities as a function of temperature, magnetic field, particle density and staggering parameter. Studying the maxima lines of entropy at low but non zero temperature reveals the phase diagram of the model. There are ten different phases which we may classify in terms of the qualitative behaviour of auxiliary functions, closely related to the dressed energy functions.
Wavenumber resonance in nonlinear wave interactions in the wake of a flat plate
Davila, Jose Benigno
The spatial traits of nonlinear wave interactions in transitioning flow in the symmetric wake of a flat plate were studied. The study combines the use of hot wire anemometry and digital analysis techniques for extracting frequency and wavenumber information from velocity fluctuation time series measurements. The linear spatial coherence was computed from velocity fluctuation data in order to determine if the frequency modes behave as waves, that is, spatially coherent fluctuations with a well defined dispersion relation. A new method was used to compute the mode triad wavenumber mismatch. The results were used to determine to what extent wavenumber resonance is present among quadratically interacting frequency resonant modes, as predicted by resonant wave interaction theory. The results show that, in the early part of the transition, instability modes interact nonlinearity to generate spatially coherent modes at frequencies above the instability range. Quadratically interacting, frequency resonant mode triads involve the transfer of energy to the harmonics of the fundamental instability exhibit good wavenumber resonance, as predicted by resonant wave interaction theory.
Plasmon beams interaction at interface between metal and dielectric with saturable Kerr nonlinearity
Energy Technology Data Exchange (ETDEWEB)
Ignatyeva, Daria O.; Sukhorukov, Anatoly P. [Lomonosov Moscow State University, Moscow (Russian Federation)
2012-12-15
We present a novel theory of surface plasmon polariton interaction on the surface of dielectric with saturable Kerr nonlinearity. The effect of the total internal reflection of a weak signal plasmon beam from a high-power reference beam is discussed. Both ray and wave theories are used to describe signal propagation. The effect of the signal tunneling through the narrow inhomogeneity induced by the reference beam is considered. (orig.)
Interaction-based nonlinear quantum metrology with a cold atomic ensemble
2014-01-01
In this manuscript we present an experimental and theoretical investigation of quantum-noise-limited measurement by nonlinear interferometry, or from another perspective, quantum-noise-limited interaction-based measurement. The experimental work is performed using a polarization-based quantum interface between propagating light pulses and cold rubidium-87 atoms trapped in an optical dipole trap. We first review the theory of quantum metrology and estimation theory, and we describe theor...
Model-order reduction of nonlinear models of electromagnetic phased-array hyperthermia.
Kowalski, Marc E; Jin, Jian-Ming
2003-11-01
A method based on the Karhunen-Loéve (KL) transform is proposed for the reduction of large-scale, nonlinear ordinary differential equations such as those arising from the finite difference modeling of biological heat transfer. The method of snapshots is used to expedite computation of the required quantities in the KL procedure. Guidelines are presented and validated for snapshot selection and resultant basis series truncation, emphasizing the special physical features of the electromagnetic phased-array heat transfer physics. Applications to fast temperature prediction are presented.
DEFF Research Database (Denmark)
Andersen, Lasse Mejling; McKinstrie, C. J.; Rottwitt, Karsten
2013-01-01
Recently, we solved the coupled-mode equations for Bragg scattering (BS) in the low- and high-conversion regimes, but without the effects of nonlinear phase modulation (NPM). We now present solutions and Green functions in the low-conversion regime that include NPM. We find that NPM does not change...... are still possible, even when the effects of NPM are included. Finally, the effects of using different input signals are considered, and we conclude that using the natural input modes of the system drastically increases the efficiency. © (2013) COPYRIGHT Society of Photo-Optical Instrumentation Engineers...
Energy Technology Data Exchange (ETDEWEB)
Kumar, Manoj [Department of Physics and Astrophysics, University of Delhi, Delhi 110007 (India); Lahon, Siddhartha, E-mail: sid.lahon@gmail.com [Department of Physics and Astrophysics, University of Delhi, Delhi 110007 (India); Department of Physics, Kirori Mal College, University of Delhi, Delhi 110007 (India); Jha, Pradip Kumar [Department of Physics and Astrophysics, University of Delhi, Delhi 110007 (India); Department of Physics, DDU College, University of Delhi, Delhi 110007 (India); Gumber, Sukirti; Mohan, Man [Department of Physics and Astrophysics, University of Delhi, Delhi 110007 (India)
2014-04-01
Here we have investigated the influence of external electric field and magnetic field on the nonlinear optical rectification of a parabolic confinement wire in the presence of Rashba spin–orbit interaction. We have used density matrix formulation for obtaining optical properties within the effective mass approximation. The results are presented as a function of quantum wire radius, electric field, magnetic field, Rashba spin–orbit interaction strength and photon energy. Our results indicate an increase of electric field gives the red-shift of the peak positions of nonlinear optical rectification. The role of confinement strength and spin–orbit interaction strength as control parameters on this nonlinear property have been demonstrated.
Towards the biaxial nematic phase via specific intermolecular interactions
Omnes, L
2001-01-01
The work described in this thesis has been focussed on the search of an elusive liquid crystal phase, known as the biaxial nematic phase. Indeed, despite nearly thirty years of intense research, no-one has been able to characterise unambiguously a biaxial nematic phase in a low-molar-mass thermotropic system. Our research is based on the concept of molecular biaxiality as distinct from shape biaxiality. Thus, we are seeking to design palladium complexes where specific intermolecular interactions could exist. Therefore, a few original synthetic strategies were developed to tackle the challenge of discovering the biaxial nematic phase
Energy Technology Data Exchange (ETDEWEB)
Chirkin, A S [Physics Department, M V Lomonosov Moscow State University, Vorob' evy Gory, 119899 Moscow (Russian Federation)
2002-06-01
The results of quantum analysis of the light generated by consecutive and simultaneous quasi-phase-matched (QPM) wave interactions in periodically poled nonlinear crystals (PPNCs) are presented. In the case of the consecutive interactions of waves with multiple frequencies {omega}, 2{omega} and 3{omega}, the parametric amplification at low-frequency pumping is investigated. Generation of the quadrature-squeezed light at frequencies {omega} and 3{omega} in the 2{omega} frequency pumping field, the photon statistics and correlation as well as the entanglement properties for photons produced at different frequencies are studied. In the case of simultaneous QPM spontaneous parametric down-conversion processes in single PPNC, the main attention is paid to obtaining the polarization-entangled states at the collinear geometry of the wave interaction.
Teitelbaum, H.; Vial, F.; Manson, A. H.; Giraldez, R.; Masseboeuf, M.
1989-01-01
Many years of measurements obtained using French meteor radars at Garchy (latitude 47 N) and Montpazier (latitude 44 N) are used to show the existence of an 8 hour oscillation. Some examples of the structure of this wave are displayed and compared with measurements performed at Saskatoon (latitude 52 N) and Budrio (latitude 45 N). This wave can be interpreted as the solar driven terdiurnal tide, or as the result of the nonlinear interaction between the diurnal and semidiurnal tides. Both hypotheses are tested with numerical models. Incidentally, the possible existence of a 24 hour wave resulting from this interaction is also studied.
Beta-functions of non-linear $\\sigma$-models for disordered and interacting electron systems
Dell'Anna, Luca
2016-01-01
We provide and study complete sets of one-loop renormalization group equations, calculated at all orders in the interaction parameters, of several Finkel'stein non-linear $\\sigma$-models, the effective field theories describing the diffusive quantum fluctuations in correlated disordered systems. We consider different cases according to the presence of certain symmetries induced by the original random Hamiltonians, and we show that, for interacting systems, the Cartan's classification of symmetry classes is not enough to uniquely determine their scaling behaviors.
Topological phases and transport properties of screened interacting quantum wires
Xu, Hengyi; Xiong, Ye; Wang, Jun
2016-10-01
We study theoretically the effects of long-range and on-site Coulomb interactions on the topological phases and transport properties of spin-orbit-coupled quasi-one-dimensional quantum wires imposed on a s-wave superconductor. The distributions of the electrostatic potential and charge density are calculated self-consistently within the Hartree approximation. Due to the finite width of the wires and charge repulsion, the potential and density distribute inhomogeneously in the transverse direction and tend to accumulate along the lateral edges where the hard-wall confinement is assumed. This result has profound effects on the topological phases and the differential conductance of the interacting quantum wires and their hybrid junctions with superconductors. Coulomb interactions renormalize the gate voltage and alter the topological phases strongly by enhancing the topological regimes and producing jagged boundaries. Moreover, the multicritical points connecting different topological phases are modified remarkably in striking contrast to the predictions of the two-band model. We further suggest the possible non-magnetic topological phase transitions manipulated externally with the aid of long-range interactions. Finally, the transport properties of normal-superconductor junctions are further examined, in particular, the impacts of Coulomb interactions on the zero-bias peaks related to the Majorana fermions and near zero-energy peaks.
Bartelmann, Matthias; Berg, Daniel; Kozlikin, Elena; Lilow, Robert; Viermann, Celia
2014-01-01
We calculate the power spectrum of density fluctuations in the statistical non-equilibrium field theory for classical, microscopic degrees of freedom to first order in the interaction potential. We specialise our result to cosmology by choosing appropriate initial conditions and propagators and show that the non-linear growth of the density power spectrum found in numerical simulations of cosmic structure evolution is reproduced well to redshift zero and for arbitrary wave numbers. The main difference of our approach to ordinary cosmological perturbation theory is that we do not perturb a dynamical equation for the density contrast. Rather, we transport the initial phase-space distribution of a canonical particle ensemble forward in time and extract any collective information from it at the time needed. Since even small perturbations of particle trajectories can lead to large fluctuations in density, our approach allows to reach high density contrast already at first order in the perturbations of the particle...
Observation and output adaptive tracking for a class of nonlinear non-minimum phase systems
Bartolini, G.; Estrada, A.; Punta, E.
2016-09-01
In this paper, the output tracking problem for a class of systems with unstable zero dynamics is addressed. The state is assumed not measurable. The output of the dynamical system to be controlled has to track a signal, which is the sum of a known number of sinusoids with unknown frequencies, amplitudes and phases. The non-minimum phase nature of the considered systems prevents the direct tracking by standard sliding mode methods, which are known to generate unstable behaviours of the internal dynamics. The proposed method relies on the availability of a flat output and its time derivatives which are functions of the unavailable state; therefore, a nonlinear observer is needed. Due to the uncertainty in the frequencies and in the parameters defining the relationship between the output of the system and the flat states, adaptive indirect methods are applied.
Phase quadrature discrimination based on three-pump four-wave mixing in nonlinear optical fibers.
Baillot, Maxime; Gay, Mathilde; Peucheret, Christophe; Michel, Joindot; Chartier, Thierry
2016-11-14
We theoretically and experimentally study the principle of phase-sensitive frequency conversion in a highly-nonlinear fiber using three pump waves. This mechanism, originally demonstrated with four continuous-wave pumps and a signal wave, is based on four-wave mixing and enables to convert the two quadrature components of the signal to different frequencies. In this work, we derive a set of two simple equations to describe this mechanism and find analytic solutions. We show that only three pumps are required, instead of four as originally proposed. We give simple relations to determine the initial conditions for the power levels and the phases of the pumps. To validate this approach, we perform an experimental demonstration of the three-pump scheme and find excellent agreement with the theory.
Institute of Scientific and Technical Information of China (English)
YU You-Bin
2008-01-01
The electron-phonon interaction influences on linear and nonlinear optical absorption in cylindrical quantum wires (CQW) with an infinite confining potential are investigated. The optical absorption coefficients are obtained by using the compact-density-matrix approach and iterative method, and the numerical results are presented for GaAs CQW. The results show that the electron-phonon interaction makes a distinct influence on optical absorption in CQW. The electron-phonon interaction on the wave functions of electron dominates the values of absorption coefficients and the correction of the electron-phonon effect on the energies of the electron makes the absorption peaks blue shift and become wider. Moreover, the electron-phonon interaction influence on optical absorption with an infinite confining potential is different from that with a finite confining potential.
Institute of Scientific and Technical Information of China (English)
李蔚; 梅君瑶; 韩庆生; 王腾
2009-01-01
The analytical expression of bit error probability in a balanced differential phase-shift keying(DPSK) optical receiver considering nonlinear phase noise and EDFA ASE noise is given,which is very useful to estimate the performance of DPSK balanced and unbalanced receiver in optical communication system.Through analysis,if only nonlinear phase noise is considered,both the balance and unbalanced receivers have the same performances.But if adding the ASE noise of EDFA,the balanced receiver is better.
Sheykhi, A.; Naeimipour, F.; Zebarjad, S. M.
2015-06-01
Considering the Lagrangian of the logarithmic nonlinear electrodynamics in the presence of a scalar dilaton field, we obtain a new class of topological black hole solutions of Einstein-dilaton gravity with two Liouville-type dilaton potentials. Black hole horizons and cosmological horizons, in these spacetimes, can be a two-dimensional positive, zero, or negative constant curvature surface. We find that the behavior of the electric field crucially depends on the dilaton coupling constant α . For small α , the electric field diverges near the origin, although its divergency is weaker than the linear Maxwell field. However, with increasing α , the behavior of the electric field, near the origin, approaches to that of the Maxwell field. We also study casual structure, asymptotic behavior, and physical properties of the solutions. We find that, depending on the model parameters, the topological dilaton black holes may have one or two horizons, and even in some cases we encounter a naked singularity without horizon. We compute the conserved and thermodynamic quantities of the spacetime and investigate that these quantities satisfy the first law of thermodynamics. We also probe thermal stability in the canonical and grand canonical ensembles and disclose the effects of the dilaton field as well as nonlinear parameter on the thermal stability of the solutions. Finally, we investigate thermodynamical geometry of the obtained solutions by introducing a new metric and studying the phase transition points due to the divergency of the Ricci scalar. We find that the dilaton field affects the phase transition points of the system.
Phases of 4D Scalar-tensor black holes coupled to Born-Infeld nonlinear electrodynamics
Stefanov, Ivan Zh; Todorov, Michail D
2007-01-01
Recent results show that when non-linear electrodynamics is considered the no-scalar-hair theorems in the scalar-tensor theories (STT) of gravity, which are valid for the cases of neutral black holes and charged black holes in the Maxwell electrodynamics, can be circumvented. What is even more, in the present work, we find new non-unique, numerical solutions describing charged black holes coupled to non-linear electrodynamics in a special class of scalar-tensor theories. One of the phases has a trivial scalar field and coincides with the corresponding solution in General Relativity. The other four phases that we find are characterized by the value of the scalar field charge. The causal structure and some aspects of the stability of the solutions have also been studied. For the scalar-tensor theories considered, the black holes have a single, non-degenerate horizon, i.e., their causal structure resembles that of the Schwarzschild black hole. The thermodynamic analysis of the stability of the solutions indicate...
Directory of Open Access Journals (Sweden)
James Sae Siew
2015-01-01
Full Text Available Rail turnouts are built to enable flexibility in the rail network as they allow for vehicles to switch between various tracks, therefore maximizing the utilisation of existing rail infrastructure. In general, railway turnouts are a safety-critical and expensive feature to a rail system as they suffer aggressive operational loads, in comparison to a plain rail track, and thus require frequent monitoring and maintenance. In practice, great consideration is given to the dynamic interaction between the turnouts components as a failed component may have adverse effects on the performance of neighbouring components. This paper presents a nonlinear 3D finite element (FE model, taking into account the nonlinearities of materials, in order to evaluate the interaction and behaviour of turnout components. Using ABAQUS, the finite element model was developed to simulate standard concrete bearers with 60 kg/m rail and with a tangential turnout radius of 250 m. The turnout structure is supported by a ballast layer, which is represented by a nonlinearly deformable tensionless solid. The numerical studies firstly demonstrate the importance of load transfer mechanisms in the failure modes of the turnout components. The outcome will lead to a better design and maintenance of railway turnouts, improving public safety and operational reliability.
Interactive cell segmentation based on phase contrast optics.
Su, Hang; Su, Zhou; Zheng, Shibao; Yang, Hua; Wei, Sha
2014-01-01
Cell segmentation in phase contrast microscopy images lays a crucial foundation for numerous subsequent computer-aided cell image analysis, but it encounters many unsolved challenges due to image qualities and artifacts caused by phase contrast optics. Addressing the unsolved challenges, the authors propose an interactive cell segmentation scheme over phase retardation features. After partitioning the images into phase homogeneous atoms, human annotations are propagated to unlabeled atoms over an affinity graph that is learned based on discrimination analysis. Then, an active query strategy is proposed for which the most informative unlabeled atom is selected for annotation, which is also propagated to the other unlabeled atoms. Cell segmentation converges to quality results after several rounds of interactions involving both the user's intentions and characteristics of image features. Experimental results demonstrate that cells with different optical properties are well segmented via the proposed approach.
Energy Technology Data Exchange (ETDEWEB)
Spears, Robert Edward [Idaho National Lab. (INL), Idaho Falls, ID (United States); Coleman, Justin Leigh [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2015-09-01
Currently the Department of Energy (DOE) and the nuclear industry perform seismic soil-structure interaction (SSI) analysis using equivalent linear numerical analysis tools. For lower levels of ground motion, these tools should produce reasonable in-structure response values for evaluation of existing and new facilities. For larger levels of ground motion these tools likely overestimate the in-structure response (and therefore structural demand) since they do not consider geometric nonlinearities (such as gaping and sliding between the soil and structure) and are limited in the ability to model nonlinear soil behavior. The current equivalent linear SSI (SASSI) analysis approach either joins the soil and structure together in both tension and compression or releases the soil from the structure for both tension and compression. It also makes linear approximations for material nonlinearities and generalizes energy absorption with viscous damping. This produces the potential for inaccurately establishing where the structural concerns exist and/or inaccurately establishing the amplitude of the in-structure responses. Seismic hazard curves at nuclear facilities have continued to increase over the years as more information has been developed on seismic sources (i.e. faults), additional information gathered on seismic events, and additional research performed to determine local site effects. Seismic hazard curves are used to develop design basis earthquakes (DBE) that are used to evaluate nuclear facility response. As the seismic hazard curves increase, the input ground motions (DBE’s) used to numerically evaluation nuclear facility response increase causing larger in-structure response. As ground motions increase so does the importance of including nonlinear effects in numerical SSI models. To include material nonlinearity in the soil and geometric nonlinearity using contact (gaping and sliding) it is necessary to develop a nonlinear time domain methodology. This
Chitgarha, Mohammad Reza; Khaleghi, Salman; Ziyadi, Morteza; Mohajerin-Ariaei, Amirhossein; Almaiman, Ahmed; Daab, Wajih; Rogawski, Devora; Tur, Moshe; Touch, Joseph D; Langrock, Carsten; Fejer, Martin M; Willner, Alan E
2014-05-15
We propose and demonstrate an all-optical phase noise reduction scheme that uses optical nonlinear mixing and tunable optical delays to suppress the low-speed phase noise induced by laser linewidth. By utilizing the phase conjugate copy of the original signal and two narrow-linewidth optical pumps, the phase noise induced by laser linewidth can be reduced by a factor of ∼5 for a laser with 500-MHz phase noise bandwidth. The error-vector-magnitude can be improved from ∼30% to ∼14% for the same laser linewidth for 40-Gbit/s quadrature phase shift keying signal.
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The nonlinear dynamic behavior of a rubbing rotor system was studied with a mathematical model established with the eccentricity and interaction between bending and torsional vibrations taken into consideration.The nonlinear vibrational response of a rubbing rotor was analyzed using numerical integral,spectroscopic analysis and Poince mapping method,which made it possible to have better understanding of the vibrational characteristics of partial rubbing and complete circular rubbing rotors.The numerical results reveal the response of torsional vibration mainly takes a form of suporchronous motion,and its frequency decreases as the rotational speed increases when partial rubbing occurs,and the response of torsional vibration is synchronous when complete circular rubbing occurs.The comparison of the dynamics of rubbing rotors with and without the interaction between bending and torsional vibrations shows the interaction between bending and torsional vibrations advances the rotational speed,at which the response of bending vibration changes from a synchronous motion into a quasi-periodic motion,and the interaction between bending and torsional vibrations reduces stability of the rubbing rotor.
Institute of Scientific and Technical Information of China (English)
Xie Ru-Sheng; Fan Wen-Bin; Lu Ming; Zhao You-Yuan
2007-01-01
This paper reports that the nonlinear refractive index of a novel organic optical storage film doped azodiphenylamine polymer is measured by using the Z-scan technique. The nonlinear refractive index up to 3.7 ×10-6 cm2/W induced by thermo-optical effect is obtained. It indicates that the sample has excellent optical nonlinear properties. The physical mechanism of the great nonlinear optical effect is analysed and the optical conjugate characteristic is also discussed with degenerate four-wave-mixing. The phase conjugate wave diffracted from the formative refractive index grating in the sample is acquired and its equivalent reflectivity reaches about 22%. On this basis,the reflective wave phase-conjugated mirror system was designed, and the image aberration experienced in propagation in the storage experiment is corrected by using the system.
Latyshev, A V
2014-01-01
The analysis of nonlinear interaction of transversal electromagnetic field with quantum collisionless plasma is carried out. Formulas for calculation electric current in quantum collisionless plasma at any temperature are deduced. It has appeared, that the nonlinearity account leads to occurrence of the longitudinal electric current directed along a wave vector. This second current is orthogonal to the known transversal classical current, received at the classical linear analysis. The case of degenerate electronic plasma is considered. The concept of longitudinal-transversal conductivity is entered. The graphic analysis of the real and imaginary parts of dimensionless coefficient of longitudinal-transversal conductivity is made. It is shown, that for degenerate plasmas the electric current is calculated under the formula, not containing quadratures. In this formula we have allocated known Kohn's singularities (W. Kohn, 1959).
On Nonlinear Self-interaction of Geodesic Acoustic Mode Driven By Energetic Particles
Energy Technology Data Exchange (ETDEWEB)
G.Y. Fu
2010-10-01
It is shown that nonlinear self-interaction of energetic particle-driven Geodesic Acoustic Mode does not generate a second harmonic in radial electric field using the fluid model. However, kinetic effects of energetic particles can induce a second harmonic in the radial electric field. A formula for the second order plasma density perturbation is derived. It is shown that a second harmonic of plasma density perturbation is generated by the convective nonlinearity of both thermal plasma and energetic particles. Near the midplane of a tokamak, the second order plasma density perturbation (the sum of second harmonic and zero frequency sideband) is negative on the low field side with its size comparable to the main harmonic at low fluctuation level. These analytic predictions are consistent with the recent experimental observation in DIII-D.
On Nonlinear Self-interaction of Geodesic Acoustic Mode Driven by Energetic Particles
Energy Technology Data Exchange (ETDEWEB)
G. Y. Fu
2010-06-04
It is shown that nonlinear self-interaction of energetic particle-driven Geodesic Acoustic Mode does not generate a second harmonic in radial electric field using the fluid model. However, kinetic effects of energetic particles can induce a second harmonic in the radial electric field. A formula for the second order plasma density perturbation is derived. It is shown that a second harmonic of plasma density perturbation is generated by the convective nonlinearity of both thermal plasma and energetic particles. Near the midplane of a tokamak, the second order plasma density perturbation (the sum of second harmonic and zero frequency sideband) is negative on the low field side with its size comparable to the main harmonic at low uctuation level. These analytic predictions are consistent with the recent experimental observation in DIII-D.
Phase diagram and critical end point for strongly interacting quarks.
Qin, Si-xue; Chang, Lei; Chen, Huan; Liu, Yu-xin; Roberts, Craig D
2011-04-29
We introduce a method based on chiral susceptibility, which enables one to draw a phase diagram in the chemical-potential-temperature plane for strongly interacting quarks whose interactions are described by any reasonable gap equation, even if the diagrammatic content of the quark-gluon vertex is unknown. We locate a critical end point at (μ(E),T(E))∼(1.0,0.9)T(c), where T(c) is the critical temperature for chiral-symmetry restoration at μ=0, and find that a domain of phase coexistence opens at the critical end point whose area increases as a confinement length scale grows.
2015-09-30
Interaction of Surface Gravity Waves with Nonlinear Internal Gravity Waves Lian Shen St. Anthony Falls Laboratory and Department of Mechanical...on studying surface gravity wave evolution and spectrum in the presence of surface currents caused by strongly nonlinear internal solitary waves...interaction of surface and internal gravity waves in the South China Sea. We will seek answers to the following questions: 1) How does the wind-wave
Nonlinear analysis of gas-water/oil-water two-phase flow in complex networks
Gao, Zhong-Ke; Wang, Wen-Xu
2014-01-01
Understanding the dynamics of multi-phase flows has been a challenge in the fields of nonlinear dynamics and fluid mechanics. This chapter reviews our work on two-phase flow dynamics in combination with complex network theory. We systematically carried out gas-water/oil-water two-phase flow experiments for measuring the time series of flow signals which is studied in terms of the mapping from time series to complex networks. Three network mapping methods were proposed for the analysis and identification of flow patterns, i.e. Flow Pattern Complex Network (FPCN), Fluid Dynamic Complex Network (FDCN) and Fluid Structure Complex Network (FSCN). Through detecting the community structure of FPCN based on K-means clustering, distinct flow patterns can be successfully distinguished and identified. A number of FDCN’s under different flow conditions were constructed in order to reveal the dynamical characteristics of two-phase flows. The FDCNs exhibit universal power-law degree distributions. The power-law exponent ...
The effects of phase advances between interaction points
Energy Technology Data Exchange (ETDEWEB)
Luo, Y. [Brookhaven National Lab. (BNL), Upton, NY (United States); Tepekian, S. [Brookhaven National Lab. (BNL), Upton, NY (United States); Fischer, W. [Brookhaven National Lab. (BNL), Upton, NY (United States); Gu, X. [Brookhaven National Lab. (BNL), Upton, NY (United States); Trbojevic, D. [Brookhaven National Lab. (BNL), Upton, NY (United States)
2011-03-01
In this note we perform simulation studies to investigate the effects of betatron phase advances between the beam-beam interaction points on half-integer resonance driving term, second order chromaticty and dynamic aperture in RHIC. The betatron phase advances are adjusted with artificial matrices inserted in the middle of arcs. The lattices for the 2011 RHIC polarized proton (p-p) run and 2010 RHIC Au-Au runs are used. We also scan the phase advances between IP8 and the electron lens for the proposed Blue ring lattice with head-on beam-beam compensation.
Hydration, phase separation and nonlinear rheology of temperature-sensitive water-soluble polymers.
Tanaka, Fumihiko; Koga, Tsuyoshi; Kaneda, Isamu; Winnik, Françoise M
2011-07-20
The collapse of a poly(N-isopropylacrylamide) (PNIPAM) chain upon heating and the phase diagrams of aqueous PNIPAM solutions with a very flat lower critical solution temperature (LCST) phase separation line are theoretically studied on the basis of cooperative dehydration (simultaneous dissociation of bound water molecules in a group of correlated sequence), and compared with the experimental observation of temperature-induced coil-globule transition by light scattering methods. The transition becomes sharper with the cooperativity parameter σ of hydration. The reentrant coil-globule-coil transition and cononsolvency in a mixed solvent of water and methanol are also studied from the viewpoint of competitive hydrogen bonds between polymer-water and polymer-methanol. The downward shift of the cloud-point curves (LCST cononsolvency) with the mol fraction of methanol due to the competition is calculated and compared with the experimental data. Aqueous solutions of hydrophobically modified PNIPAM carrying short alkyl chains at both chain ends (telechelic PNIPAM) are theoretically and experimentally studied. The LCST of these solutions is found to shift downward along the sol-gel transition curve as a result of end-chain association (association-induced phase separation), and separate from the coil-globule transition line. Associated structures in the solution, such as flower micelles, mesoglobules, and higher fractal assembly, are studied by ultra small-angle neutron scattering with theoretical modeling of the scattering function. Dynamic-mechanical modulus, nonlinear stationary viscosity, and stress build-up in start-up shear flows of the associated networks are studied on the basis of the affine and non-affine transient network theory. The molecular conditions for thickening, strain hardening, and stress overshoot are found in terms of the nonlinear amplitude A of the chain tension and the tension-dissociation coupling constant g.
Phase transitions in simplified models with long-range interactions
Rocha Filho, T. M.; Amato, M. A.; Mello, B. A.; Figueiredo, A.
2011-10-01
We study the origin of phase transitions in several simplified models with long-range interactions. For the self-gravitating ring model, we are unable to observe a possible phase transition predicted by Nardini and Casetti [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.80.060103 80, 060103R (2009).] from an energy landscape analysis. Instead we observe a sharp, although without any nonanalyticity, change from a core-halo to a core-only configuration in the spatial distribution functions for low energies. By introducing a different class of solvable simplified models without any critical points in the potential energy we show that a behavior similar to the thermodynamics of the ring model is obtained, with a first-order phase transition from an almost homogeneous high-energy phase to a clustered phase and the same core-halo to core configuration transition at lower energies. We discuss the origin of these features for the simplified models and show that the first-order phase transition comes from the maximization of the entropy of the system as a function of energy and an order parameter, as previously discussed by Hahn and Kastner [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.72.056134 72, 056134 (2005); Eur. Phys. J. BEPJBFY1434-602810.1140/epjb/e2006-00100-7 50, 311 (2006)], which seems to be the main mechanism causing phase transitions in long-range interacting systems.
Institute of Scientific and Technical Information of China (English)
Lu Jun
2004-01-01
The stationary-state nonlinear Schr(o)dinger equation, which models the dilute-gas Bose-Einstein condensate, is introduced within the framework of the quantum phase-space representation established by Torres-Vega and Frederick.The exact solutions of equation are obtained in the phase space, by means of the wave-mechanics method. The the phase space eigenfunctions. The eigenfunction with a hypersecant part is discussed as an example.
Directory of Open Access Journals (Sweden)
Matías A Goldin
Full Text Available The nature of telencephalic control over premotor and motor circuits is debated. Hypotheses range from complete usurping of downstream circuitry to highly interactive mechanisms of control. We show theoretically and experimentally, that telencephalic song motor control in canaries is consistent with a highly interactive strategy. As predicted from a theoretical model of respiratory control, mild cooling of a forebrain nucleus (HVC led to song stretching, but further cooling caused progressive restructuring of song, consistent with the hypothesis that respiratory gestures are subharmonic responses to a timescale present in the output of HVC. This interaction between a life-sustaining motor function (respiration and telencephalic song motor control suggests a more general mechanism of how nonlinear integration of evolutionarily new brain structures into existing circuitry gives rise to diverse, new behavior.
Mean Field Limit of Interacting Filaments and Vector Valued Non-linear PDEs
Bessaih, Hakima; Coghi, Michele; Flandoli, Franco
2017-03-01
Families of N interacting curves are considered, with long range, mean field type, interaction. They generalize models based on classical interacting point particles to models based on curves. In this new set-up, a mean field result is proven, as N→ ∞. The limit PDE is vector valued and, in the limit, each curve interacts with a mean field solution of the PDE. This target is reached by a careful formulation of curves and weak solutions of the PDE which makes use of 1-currents and their topologies. The main results are based on the analysis of a nonlinear Lagrangian-type flow equation. Most of the results are deterministic; as a by-product, when the initial conditions are given by families of independent random curves, we prove a propagation of chaos result. The results are local in time for general interaction kernel, global in time under some additional restriction. Our main motivation is the approximation of 3D-inviscid flow dynamics by the interacting dynamics of a large number of vortex filaments, as observed in certain turbulent fluids; in this respect, the present paper is restricted to smoothed interaction kernels, instead of the true Biot-Savart kernel.
Interaction of dispersed cubic phases with blood components
DEFF Research Database (Denmark)
Bode, J C; Kuntsche, Judith; Funari, S S;
2013-01-01
The interaction of aqueous nanoparticle dispersions, e.g. based on monoolein/poloxamer 407, with blood components is an important topic concerning especially the parenteral way of administration. Therefore, the influence of human and porcine plasma on dispersed cubic phases was investigated...
Feedback control of an interacting Bose-Einstein condensate using phase-contrast imaging
Szigeti, Stuart S; Carvalho, Andre R R; Hope, Joseph J
2010-01-01
The linewidth of an atom laser is limited by density fluctuations in the Bose-Einstein condensate (BEC) from which the atom laser beam is outcoupled. In this paper we show that a stable spatial mode for an interacting BEC can be generated using a realistic control scheme that includes the effects of the measurement backaction. This model extends the feedback theory, based on a phase-contrast imaging setup, presented in \\cite{Szigeti:2009}. In particular, it is applicable to a BEC with large interatomic interactions and solves the problem of inadequacy of the mean-field (coherent state) approximation by utilising a fixed number state approximation. Our numerical analysis shows the control to be more effective for a condensate with a large nonlinearity.
Feedback control of an interacting Bose-Einstein condensate using phase-contrast imaging
Szigeti, S. S.; Hush, M. R.; Carvalho, A. R. R.; Hope, J. J.
2010-10-01
The linewidth of an atom laser is limited by density fluctuations in the Bose-Einstein condensate (BEC) from which the atom laser beam is outcoupled. In this paper we show that a stable spatial mode for an interacting BEC can be generated using a realistic control scheme that includes the effects of the measurement backaction. This model extends the feedback theory, based on a phase-contrast imaging setup, presented by Szigeti, Hush, Carvalho, and Hope [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.80.013614 80, 013614 (2009)]. In particular, it is applicable to a BEC with large interatomic interactions and solves the problem of inadequacy of the mean-field (coherent state) approximation by utilizing a fixed number state approximation. Our numerical analysis shows the control to be more effective for a condensate with a large nonlinearity.
Separable interactions and liquid 3He : V. Phase diagram in the presence of a Hubbard interaction
Capel, H.W.; Nijhoff, F.W.; Breems, A. den
1986-01-01
A comparison is made between the various extrema of the Landau expansion of liquid 3He derived in a previous paper. As an application the phase diagram is investigated in the presence of an external magnetic field assuming that the Hubbard interaction is small as compared to the pairing interaction
ALE Fractional Step Finite Element Method for Fluid-Structure Nonlinear Interaction Problem
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A computational procedure is developed to solve the problems of coupled motion of a structure and a viscous incompressible fluid. In order to incorporate the effect of the moving surface of the structure as well as the free surface motion, the arbitrary Lagrangian-Eulerian formulation is employed as the basis of the finite element spatial discretization. For numerical integration in time, the fraction step method is used. This method is useful because one can use the same linear interpolation function for both velocity and pressure. The method is applied to the nonlinear interaction of a structure and a tuned liquid damper. All computations are performed with a personal computer.
Tang, H. T.; Hofmann, R.; Yee, G.; Vaughan, D. K.
1980-01-01
Transient, nonlinear soil-structure interaction simulations of an Electric Power Research Institute, SIMQUAKE experiment were performed using the large strain, time domain STEALTH 2D code and a cyclic, kinematically hardening cap soil model. Results from the STEALTH simulations were compared to identical simulations performed with the TRANAL code and indicate relatively good agreement between all the STEALTH and TRANAL calculations. The differences that are seen can probably be attributed to: (1) large (STEALTH) vs. small (TRANAL) strain formulation and/or (2) grid discretization differences.
Pressure and phase equilibria in interacting active brownian spheres.
Solon, Alexandre P; Stenhammar, Joakim; Wittkowski, Raphael; Kardar, Mehran; Kafri, Yariv; Cates, Michael E; Tailleur, Julien
2015-05-15
We derive a microscopic expression for the mechanical pressure P in a system of spherical active Brownian particles at density ρ. Our exact result relates P, defined as the force per unit area on a bounding wall, to bulk correlation functions evaluated far away from the wall. It shows that (i) P(ρ) is a state function, independent of the particle-wall interaction; (ii) interactions contribute two terms to P, one encoding the slow-down that drives motility-induced phase separation, and the other a direct contribution well known for passive systems; and (iii) P is equal in coexisting phases. We discuss the consequences of these results for the motility-induced phase separation of active Brownian particles and show that the densities at coexistence do not satisfy a Maxwell construction on P.
Modeling the macroscopic behavior of two-phase nonlinear composites by infinite-rank laminates
Idiart, Martín I.
A new approach is proposed for estimating the macroscopic behavior of two-phase nonlinear composites with random, particulate microstructures. The central idea is to model composites by sequentially laminated constructions of infinite rank whose macroscopic behavior can be determined exactly. The resulting estimates incorporate microstructural information up to the two-point correlation functions, and require the solution to a Hamilton-Jacobi equation with the inclusion concentration and the macroscopic fields playing the role of 'time' and 'spatial' variables, respectively. Because they are realizable, by construction, these estimates are guaranteed to be convex, to satisfy all pertinent bounds, to exhibit no duality gap, and to be exact to second order in the heterogeneity contrast. Sample results are provided for two- and three-dimensional power-law composites, and are compared with other homogenization estimates, as well as with numerical simulations available from the literature. The estimates are found to give physically sensible predictions for all the cases considered, even for extreme values of the nonlinearity and heterogeneity contrast. Interestingly, in the case of isotropic porous materials under hydrostatic loadings, the estimates agree exactly with standard Gurson-type models for viscoplastic porous media.
Guo, Tieding; Kang, Houjun; Wang, Lianhua; Zhao, Yueyu
2016-12-01
Cable dynamics under ideal longitudinal support motions/excitations assumes that the support's mass, stiffness and mechanical energy are infinite. However, for many long/slender support structures, their finite mass and stiffness should be taken into account and the cable-support dynamic interactions should be modelled and evaluated. These moving supports are non-ideal support excitations, deserving a proper coupling analysis. For systems with a large support/cable mass ratio, using the multiple scale method and asymptotic approximations, a cable-support coupled reduced model, with both cable's geometric nonlinearity and cable-support coupling nonlinearity included, is established asymptotically and validated numerically in this paper. Based upon the reduced model, cable's nonlinear responses under non-ideal support excitations(and also the coupled responses) are found, with stability and bifurcation characteristics determined. By finding the modifications caused by the support/cable mass ratio, boundary damping, and internal detuning, full investigations into coupling-induced dynamic effects on the cable are conducted. Finally, the approximate analytical results based on the reduced model are verified by numerical results from the original full model.
Nonlinear interaction of instability waves and vortex-pairing noise in axisymmetric subsonic jets
Yang, Hai-Hua; Zhou, Lin; Zhang, Xing-Chen; Wan, Zhen-Hua; Sun, De-Jun
2016-10-01
A direct simulation with selected inflow forcing is performed for an accurate description of the jet flow field and far-field noise. The effects of the Mach number and heating on the acoustic field are studied in detail. The beam patterns and acoustic intensities are both varied as the change of the Mach number and temperature. The decomposition of the source terms of the Lilley-Goldstein (L-G) equation shows that the momentum and thermodynamic components lead to distinctly different beam patterns. Significant cancellation is found between the momentum and thermodynamic components at low polar angles for the isothermal jet and large polar angles for the hot jet. The cancellation leads to the minimum values of the far-field sound. Based on linear parabolized stability equation solutions, the nonlinear interaction model for sound prediction is built in combination with the L-G equation. The dominant beam patterns and their original locations predicted by the nonlinear model are in good agreement with the direct simulation results, and the predictions of sound pressure level (SPL) by the nonlinear model are relatively reasonable.
149.8 nm, the shortest wavelength generated by phase matching in nonlinear crystals
Nakazato, Tomoharu; Ito, Isao; Kobayashi, Yohei; Wang, Xiaoyang; Chen, Chuangtian; Watanabe, Shuntaro
2017-02-01
Narrow band light sources in the vacuum ultraviolet (VUV) region are attractive for photo lithography and high resolution photoelectron spectroscopy. Phase matching is essential to generate high power VUV lights by using a narrow band, low peak intensity and nanosecond pump source. In this research, sum frequency mixing has been demonstrated below 150 nm in KBe2BO3F2 by using the fundamental with its fourth harmonic of a 6 kHz Ti:sapphire laser. The laser system we have developed in this research, consists of a Ti:sapphire laser system and a frequency conversion stage. We generated 149.8-nm radiation, which is the shortest wavelength ever obtained to our knowledge by phase matching in nonlinear crystals. The fifth harmonic output powers were 3.6 μW at 149.8 nm and 110 μW at 154.0 nm, respectively. The phase matching angles measured from 149.8 nm to 158.1 nm are larger by 3-4 degrees than those expected from the existing Sellmeier equation. The optical transmission spectra of some KBBF crystals were measured by the spectrophotometer. The transmittance near the absorption edge supports the generation of coherent radiation below 150 nm. The improvement of a prism-coupled device contributed to the generation of coherent radiation below 150 nm. Another reason for the present break through to the shorter wavelength is the use of the short pulse driving source compared with our previous research.
Nonlinear response and dynamical transitions in a phase-field crystal model for adsorbed overlayers
Energy Technology Data Exchange (ETDEWEB)
Ramos, J A P [Departamento de Ciencias Exatas, Universidade Estadual do Sudoeste da Bahia, 45000-000 Vitoria da Conquista, BA (Brazil); Granato, E [Laboratorio Associado de Sensores e Materiais, Instituto Nacional de Pesquisas Espaciais, 12245-970 Sao Jose dos Campos, SP (Brazil); Ying, S C; Ala-Nissila, T [Department of Physics, PO Box 1843, Brown University, Providence, RI 02912-1843 (United States); Achim, C V [Department of Applied Physics, Aalto University School of Science and Technology, PO Box 11000, FI-00076 Aalto, Espoo (Finland); Elder, K R, E-mail: Jorge@las.inpe.b [Department of Physics, Oakland University, Rochester, Michigan 48309-4487 (United States)
2010-09-01
The nonlinear response and sliding friction behavior of a phase-field crystal model for driven adsorbed atomic layers is determined numerically. The model describes the layer as a continuous density field coupled to the pinning potential of the substrate and under an external driving force. Dynamical equations which take into account both thermal fluctuations and inertial effects are used for numerical simulations of commensurate and incommensurate layers. At low temperatures, the velocity response of an initially commensurate layer shows hysteresis with dynamical melting and freezing transitions at different critical forces. The main features of the sliding friction behavior are similar to the results obtained previously from molecular dynamics simulations of particle models. However, the dynamical transitions correspond to nucleations of stripes rather than closed domains.
THE NONLINEAR BEHAVIOR OF INTERFACE BETWEEN TWO-PHASE SHEAR FLOW WITH LARGE DENSITY RATIOS
Institute of Scientific and Technical Information of China (English)
DONG Yu-hong
2006-01-01
The Navier-Stokes equations for the two-dimensional incompressible flow are used to investigate the effects of the Reynolds number and the Weber number on the behavior of interface between liquid-gas shear flow.In the present study, the density ratios are fixed at approximately 100-103.The interface between the two phases is resolved using the level-set approach.The Reynolds number and the Weber number, based on the gas, are selected as 400-10000 and 40-5000, respectively.In the past, simulations reappeared the amplitude of interface growth predicted by viscous Orr-Sommerfeld linear theory, verifying the applicability and accuracy of the numerical method over a wide range of density and viscosity ratios; now, the simulations show that the nonlinear development of ligament elongated structures and resulted in the subsequent breakup of the heavier fluid into drops.
Hendi, S H; Panah, B Eslam
2016-01-01
In this paper, we take into account the black hole solutions of Einstein gravity in the presence of logarithmic and exponential forms of nonlinear electrodynamics. At first, we consider the cosmological constant as a dynamic pressure to study the analogy of the black hole solutions with the Van der Waals liquid--gas system in the extended phase space. We plot $P-V$, $T-V$ and $G-T$ diagrams and investigate the phase transition of adS black holes in the canonical ensemble. Moreover, we discuss about the effect of nonlinear electrodynamics on the the critical values and the universal ratio $P_{c}v_{c}/T_{c}$.
Three-photon interactions and spin exchange in a quantum nonlinear medium
Cantu, Sergio; Liang, Qi-Yu; Thompson, Jeff; Nicholson, Travis; Venkatramani, Aditya; Gullans, Michael; Gorshkov, Alexey; Choi, Soonwon; Lukin, Mikhail; Vuletic, Vladan
2016-05-01
Robust quantum gates for photonic qubits are a longstanding goal of quantum information science. One promising approach to achieve this goal requires strong nonlinear interactions between single photons, which is impossible with conventional optical media. We realize these interactions with electromagnetically induced transparency (EIT), and strongly interacting Rydberg states to mediate strong interactions between photons. Operating in the dispersive regime of EIT, we have recently shown that two photons propagating in our system can bind into a photonic molecule. Extending these two-photon experiments to many-body physics would lead to exotic phenomena like photon crystallization. To that end, we have scaled up our two-photon measurements to three-photon experiments. We are now able to discern signatures of three-photon molecules from a variety of two- and three-photon interactions. Three-photon bound states manifest as an increase in photon bunching in g (3) correlation measurements. We also present a recent observation of coherent spin exchange interactions in Rydberg EIT.
Nucleon-alpha particle interactions from inversion of scattering phase shifts
Energy Technology Data Exchange (ETDEWEB)
Alexander, N.; Amos, K.; Apagyi, B.; Lun, D.R.
1996-03-01
Scattering amplitudes have been extracted from (elastic scattering) neutron-alpha (n-{alpha}) differential cross sections below threshold using the constraint that the scattering function is unitary. Real phase shifts have been obtained therefrom. A modification to the Newton iteration method has been used to solve the nonlinear equation that specifies the phase of the scattering amplitude in terms of the complete (0 to 180 deg) cross section since the condition for a unique and convergent solution by an exact iterated fixed point method, the `Martin` condition, is not satisfied. The results compare well with those found using standard optical model search procedures. Those optical model phase shifts, from both n - {alpha} and p - {alpha} (proton-alpha) calculations in which spin-orbit effects were included, were used in the second phase of this study, namely to determine the scattering potentials by inversion of that phase shift data. A modified Newton-Sabatier scheme to solve the inverse scattering problem has been used to obtain inversion potentials (both central and spin-orbit) for nucleon energies in the range 1 to 24 MeV. The inversion interactions differ noticeably from the Woods-Saxon forms used to give the input phase shifts. Not only do those inversion potentials when used in Schroedinger equations reproduce the starting phase shifts but they are also very smooth, decay rapidly, and are as feasible as the optical model potentials of others to be the local form for interactions deduced by folding realistic two-nucleon g matrices with the density matrix elements of the alpha particle. 23 refs., 8 tabs., 9 figs.
Institute of Scientific and Technical Information of China (English)
邓英尔; 刘慈群
2003-01-01
A mathematical model of two-phase fluid nonlinear flow in the direction ofnormal of ellipse through low-permeability porous media was established according to anonlinear flow law expressed in a continuous function with three parameters, a massconservation law and a concept of turbulent ellipses. A solution to the model was obtainedby using a finite difference method and an extrapolation method. Formulas of calculatingdevelopment index not only before but also after water breaks through an oil well in thecondition of two-phase fluid nonlinear flow in the media were derived. An example wasdiscussed. Water saturation distribution was presented. The moving law of drainage frontwas found. Laws of change of pressure difference with time were recognized. Results showthat there is much difference of water saturation distribution between nonlinear flow andlinear flow; that drainage front by water moves faster, water breaks through sooner and theindex gets worse because of the nonlinear flow ; and that dimensionless pressure differencegets larger at the same dimensionless time and difficulty of oil development becomes biggerby the nonlinear flow . Thus, it is necessary that influence of nonlinear flow on developmentindexes of the oil fields be taken into account. The results provide water-floodingdevelopment of the oil fields with scientific basis.
Schmidt, Bruno E; Ernotte, Guilmot; Clerici, Matteo; Morandotti, Roberto; Ibrahim, Heide; Legare, Francois
2016-01-01
In the framework of linear optics, light fields do not interact with each other in a medium. Yet, when their field amplitude becomes comparable to the electron binding energies of matter, the nonlinear motion of these electrons emits new dipole radiation whose amplitude, frequency and phase differ from the incoming fields. Such high fields are typically achieved with ultra-short, femtosecond (1fs = 10-15 sec.) laser pulses containing very broad frequency spectra. Here, the matter not only couples incoming and outgoing fields but also causes different spectral components to interact and mix through a convolution process. In this contribution, we describe how frequency domain nonlinear optics overcomes the shortcomings arising from this convolution in conventional time domain nonlinear optics1. We generate light fields with previously inaccessible properties because the uncontrolled coupling of amplitudes and phases is turned off. For example, arbitrary phase functions are transferred linearly to the second har...
Characterization of topological phases in models of interacting fermions
Energy Technology Data Exchange (ETDEWEB)
Motruk, Johannes
2016-05-25
The concept of topology in condensed matter physics has led to the discovery of rich and exotic physics in recent years. Especially when strong correlations are included, phenomenons such as fractionalization and anyonic particle statistics can arise. In this thesis, we study several systems hosting topological phases of interacting fermions. In the first part, we consider one-dimensional systems of parafermions, which are generalizations of Majorana fermions, in the presence of a Z{sub N} charge symmetry. We classify the symmetry-protected topological (SPT) phases that can occur in these systems using the projective representations of the symmetries and find a finite number of distinct phases depending on the prime factorization of N. The different phases exhibit characteristic degeneracies in their entanglement spectrum (ES). Apart from these SPT phases, we report the occurrence of parafermion condensate phases for certain values of N. When including an additional Z{sub N} symmetry, we find a non-Abelian group structure under the addition of phases. In the second part of the thesis, we focus on two-dimensional lattice models of spinless fermions. First, we demonstrate the detection of a fractional Chern insulator (FCI) phase in the Haldane honeycomb model on an infinite cylinder by means of the density-matrix renormalization group (DMRG). We report the calculation of several quantities characterizing the topological order of the state, i.e., (i) the Hall conductivity, (ii) the spectral flow and level counting in the ES, (iii) the topological entanglement entropy, and (iv) the charge and topological spin of the quasiparticles. Since we have access to sufficiently large system sizes without band projection with DMRG, we are in addition able to investigate the transition from a metal to the FCI at small interactions which we find to be of first order. In a further study, we consider a time-reversal symmetric model on the honeycomb lattice where a Chern insulator (CI
Song, Yong-Won; Yamashita, Shinji; Goh, Chee S.; Set, Sze Y.
2007-01-01
We demonstrate a novel passive mode-locking scheme for pulsed lasers enhanced by the interaction of carbon nanotubes (CNTs) with the evanescent field of propagating light in a D-shaped optical fiber. The scheme features all-fiber operation as well as a long lateral interaction length, which guarantees a strong nonlinear effect from the nanotubes. Mode locking is achieved with less than 30% of the CNTs compared with the amount of nanotubes used for conventional schemes. Our method also ensures the preservation of the original morphology of the individual CNTs. The demonstrated pulsed laser with our CNT mode locker has a repetition rate of 5.88 MHz and a temporal pulse width of 470 fs.
Song, Yong-Won; Yamashita, Shinji; Goh, Chee S; Set, Sze Y
2007-01-15
We demonstrate a novel passive mode-locking scheme for pulsed lasers enhanced by the interaction of carbon nanotubes (CNTs) with the evanescent field of propagating light in a D-shaped optical fiber. The scheme features all-fiber operation as well as a long lateral interaction length, which guarantees a strong nonlinear effect from the nanotubes. Mode locking is achieved with less than 30% of the CNTs compared with the amount of nanotubes used for conventional schemes. Our method also ensures the preservation of the original morphology of the individual CNTs. The demonstrated pulsed laser with our CNT mode locker has a repetition rate of 5.88 MHz and a temporal pulse width of 470 fs.
Chimera regimes in a ring of oscillators with local nonlinear interaction
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.
Discrete and continuum links to a nonlinear coupled transport problem of interacting populations
Duong, M. H.; Muntean, A.; Richardson, O. M.
2017-02-01
We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind are inspired by the dynamics of pedestrian flows in open spaces and are intimately connected to cross-diffusion and thermo-diffusion problems holding a variational structure. The tools we use include a suitable structure of the relative entropy controlling TV-norms, the construction of Lyapunov functionals and particular closed-form solutions to nonlinear transport equations, a hydrodynamics limiting procedure due to Philipowski, as well as the construction of numerical approximates to both the continuum limit problem in 2D and to the original interacting particle systems.
Three-state interactions determine the second-order nonlinear optical response
Perez-Moreno, Javier
2016-01-01
Using the sum-rules, the sum-over-states expression for the diagonal term of first hyperpolarizability can be expressed as the sum of three-state interaction terms. We study the behavior of a generic three-state term to show that is possible to tune the contribution of resonant terms by tuning the spectrum of the molecule. When extrapolated to the off-resonance regime, the three-state interaction terms are shown to behave in a similar manner as the three-level model used to derive the fundamental limits. We finally show that most results derived using the three-level ansatz are general, and apply to molecules where more than three levels contribute to the second-order nonlinear response or/and far from optimization.
A non-linear analytic stress model for the analysis on the stress interaction between TSVs
Directory of Open Access Journals (Sweden)
Ming-Han Liao
2015-06-01
Full Text Available Thermo-elastic strain is induced by through silicon vias (TSV due to the difference of thermal expansion coefficients between the copper (∼18 ppm/◦C and silicon (∼2.8 ppm/◦C when the structure is exposed to a thermal budget in the three dimensional integrated circuit (3DIC process. These thermal expansion stresses are high enough to induce the delamination on the interfaces between the copper, silicon, and isolated dielectric. A compact analytic model for the strain field induced by different layouts of thermal copper filled TSVs with the linear superposition principle is found to result in large errors due to the strong stress interaction between TSVs. In this work, a nonlinear stress analytic model with different TSV layouts is demonstrated by the finite element method and Mohr’s circle analysis. The stress characteristics are also measured by the atomic force microscope-raman technique at a nanometer level resolution. This nonlinear stress model for the strong interactions between TSVs results in an electron mobility change ~2-6% smaller than that resulting from a model that only considers the linear stress superposition principle.
Berry Phase Physics in Free and Interacting Fermionic Systems
Chen, Jing-Yuan
2016-01-01
Berry phase plays an important role in many non-trivial phenomena over a broad range of many-body systems. In this thesis we focus on the Berry phase due to the change of the particles' momenta, and study its effects in free and interacting fermionic systems. We start with reviewing the semi-classical kinetic theory with Berry phase for a non-interacting ensemble of fermions -- a Berry Fermi gas -- which might be far-from-equilibrium. We particularly review the famous Berry phase contribution to the anomalous Hall current. We then provide a concrete and general path integral derivation for the semi-classical theory. Then we turn to the specific example of Weyl fermion, which exhibits the profound quantum phenomenon of chiral anomaly; we review how this quantum effect, and its closely related chiral magnetic effect and chiral vortical effect, arise from Berry phase in the semi-classical kinetic theory. We also discuss how Lorentz symmetry in the kinetic theory of Weyl fermion, seemly violated by the Berry phas...
Weak intermolecular interactions in gas-phase NMR
Garbacz, Piotr; Jackowski, Karol; Moszynski, Robert; Jaszunski, Michal
2011-01-01
Gas-phase NMR spectra demonstrating the effect of weak intermolecular forces on the NMR shielding constants of the interacting species are reported. We analyse the interaction of the molecular hydrogen isotopomers with He, Ne, and Ar, and the interaction in the He-CO_2 dimer. The same effects are studied for all these systems in the ab initio calculations. The comparison of the experimental and computed shielding constants is shown to depend strongly on the treatment of the bulk susceptibility effects, which determine in practice the pressure dependence of the experimental values. Best agreement of the results is obtained when the bulk susceptibility correction in rare gas solvents is evaluated from the analysis of the He-rare gas interactions, and when the shielding of deuterium in D_2-rare gas systems is considered.
Performance analysis of an all-optical OFDM system in presence of non-linear phase noise.
Hmood, Jassim K; Harun, Sulaiman W; Emami, Siamak D; Khodaei, Amin; Noordin, Kamarul A; Ahmad, Harith; Shalaby, Hossam M H
2015-02-23
The potential for higher spectral efficiency has increased the interest in all-optical orthogonal frequency division multiplexing (OFDM) systems. However, the sensitivity of all-optical OFDM to fiber non-linearity, which causes nonlinear phase noise, is still a major concern. In this paper, an analytical model for estimating the phase noise due to self-phase modulation (SPM), cross-phase modulation (XPM), and four-wave mixing (FWM) in an all-optical OFDM system is presented. The phase noise versus power, distance, and number of subcarriers is evaluated by implementing the mathematical model using Matlab. In order to verify the results, an all-optical OFDM system, that uses coupler-based inverse fast Fourier transform/fast Fourier transform without any nonlinear compensation, is demonstrated by numerical simulation. The system employs 29 subcarriers; each subcarrier is modulated by a 4-QAM or 16-QAM format with a symbol rate of 25 Gsymbol/s. The results indicate that the phase variance due to FWM is dominant over those induced by either SPM or XPM. It is also shown that the minimum phase noise occurs at -3 dBm and -1 dBm for 4-QAM and 16-QAM, respectively. Finally, the error vector magnitude (EVM) versus subcarrier power and symbol rate is quantified using both simulation and the analytical model. It turns out that both EVM results are in good agreement with each other.
A phase insensitive all-optical router based on nonlinear lenslike planar waveguides.
Mateo, Eduardo; Liñares, Jesús
2005-05-02
We present the design of an all-optical router based on the properties of both propagation and interaction of Gaussian beams in lenslike planar guides. Variational results of single co- and counterpropagation are derived and used to design three integrated optical devices, that is, a header extraction device, an optical bistable device and a data routing device, which perform an ultrafast, phase-insensitive and fiber compatible routing operation in the optical domain.
Jumps and bi-stability in the phase-gain characteristics of a nonlinear parametric amplifier
DEFF Research Database (Denmark)
Neumeyer, Stefan; van de Looij, Ruud; Thomsen, Jon Juel
2014-01-01
This work experimentally investigates the impact of nonlinearity on macromechanical parametric amplification. For a strong cubic stiffness nonlinearity we observe jumps in gain (ratio of steady-state vibration amplitude of the externally and parametrically excited system, to vibration amplitude...
Complete modulational-instability gain spectrum of nonlinear quasi-phase-matching gratings
DEFF Research Database (Denmark)
Corney, Joel F.; Bang, Ole
2004-01-01
We consider plane waves propagating in quadratic nonlinear slab waveguides with nonlinear quasi-phasematching gratings. We predict analytically and verify numerically the complete gain spectrum for transverse modulational instability, including hitherto undescribed higher-order gain bands....
Phase mixing vs. nonlinear advection in drift-kinetic plasma turbulence
Schekochihin, A A; Highcock, E G; Dellar, P J; Dorland, W; Hammett, G W
2015-01-01
A scaling theory of long-wavelength electrostatic turbulence in a magnetised, weakly collisional plasma (e.g., drift-wave turbulence driven by temperature gradients) is proposed, with account taken both of the nonlinear advection of the perturbed particle distribution by fluctuating ExB flows and of its phase mixing, which is caused by the streaming of the particles along the mean magnetic field and, in a linear problem, would lead to Landau damping. A consistent theory is constructed in which very little free energy leaks into high velocity moments of the distribution, rendering the turbulent cascade in the energetically relevant part of the wave-number space essentially fluid-like. The velocity-space spectra of free energy expressed in terms of Hermite-moment orders are steep power laws and so the free-energy content of the phase space does not diverge at infinitesimal collisionality (while it does for a linear problem); collisional heating due to long-wavelength perturbations vanishes in this limit (also i...
Phase-referenced nonlinear spectroscopy of the α-quartz/water interface
Ohno, Paul E.; Saslow, Sarah A.; Wang, Hong-Fei; Geiger, Franz M.; Eisenthal, Kenneth B.
2016-12-01
Probing the polarization of water molecules at charged interfaces by second harmonic generation spectroscopy has been heretofore limited to isotropic materials. Here we report non-resonant nonlinear optical measurements at the interface of anisotropic z-cut α-quartz and water under conditions of dynamically changing ionic strength and bulk solution pH. We find that the product of the third-order susceptibility and the interfacial potential, χ(3) × Φ(0), is given by (χ1(3)-iχ2(3)) × Φ(0), and that the interference between this product and the second-order susceptibility of bulk quartz depends on the rotation angle of α-quartz around the z axis. Our experiments show that this newly identified term, iχ(3) × Φ(0), which is out of phase from the surface terms, is of bulk origin. The possibility of internally phase referencing the interfacial response for the interfacial orientation analysis of species or materials in contact with α-quartz is discussed along with the implications for conditions of resonance enhancement.
Crystal growth of an organic non-linear optical material from the vapour phase
Hou, W
1999-01-01
Due to the potential applications of organic non-linear optical materials in the areas of optical processing and communication, the investigation of the crystal growth of new organic NLO materials has been an active field for the last 20 years. For such uses it is necessary to produce single crystals of high quality and perfection, free of strain and defects. When crystals are grown from the solution and the melt, solvent and the decomposition component in the melt can introduce impurities and imperfection to the as-grown crystals. For crystals grown from vapour phase, in the absence of the solvent, this cannot occur and the method promises to yield single crystals of higher quality. Despite this attraction, little attention has been paid to the vapour phase growth of organic NLO crystals. It was with this in mind that the following investigation was carried out. Using Methyl p-hydroxybenzoate (p-MHB), a potential organic NLO material, a comparison investigation was made of its crystal growth from both the va...
Experimental nonlinear beam dynamics studies with turn- by-turn phase space monitors
Terebilo, Andrei Gennadyevich
1999-10-01
This thesis presents an experimental study of single particle and collective beam dynamics undertaken by the author in SPEAR electron storage ring. The technique used for measurement consists of exciting transverse oscillations of a bunch circulating in the ring with a fast kicker and observing the center of mass oscillations every turn for several thousand turns. The goal of this study was to develop new applications of the turn-by-turn technique to accelerator diagnostics. One innovation introduced is the use of a collective mode of the beam motion as a phase space probe. When in this mode the bunch behaves similar to a macroparticle and oscillates coherently. It is possible to control the growth/damping rate of this oscillation by adjusting the accelerator parameters. Another new tool proposed is the analysis of phase space trajectories in the time-frequency domain. This technique makes it possible to conduct nonlinear dynamics experiments such as observation of high order resonances in the frequency map and single-kick measurement of the tune dependence on the amplitude of oscillations.
Long-term wave growth and its linear and nonlinear interactions with wind fluctuations
Directory of Open Access Journals (Sweden)
Z. Ge
2008-05-01
Full Text Available Following Ge and Liu (2007, the simultaneously recorded time series of wave elevation and wind velocity are examined for long-term (on Lavrenov's τ_{4}-scale or 3 to 6 h linear and nonlinear interactions between the wind fluctuations and the wave field. Over such long times the detected interaction patterns should reveal general characteristics for the wave growth process. The time series are divided into three episodes, each approximately 1.33 h long, to represent three sequential stages of wave growth. The classic Fourier-domain spectral and bispectral analyses are used to identify the linear and quadratic interactions between the waves and the wind fluctuations as well as between different components of the wave field.
The results show clearly that as the wave field grows the linear interaction becomes enhanced and covers wider range of frequencies. Two different wave-induced components of the wind fluctuations are identified. These components, one at around 0.4 Hz and the other at around 0.15 to 0.2 Hz, are generated and supported by both linear and quadratic wind-wave interactions probably through the distortions of the waves to the wind field. The fact that the higher-frequency wave-induced component always stays with the equilibrium range of the wave spectrum around 0.4 Hz and the lower-frequency one tends to move with the downshifting of the primary peak of the wave spectrum defines the partition of the primary peak and the equilibrium range of the wave spectrum, a characteristic that could not be revealed by short-time wavelet-based analyses in Ge and Liu (2007. Furthermore, these two wave-induced peaks of the wind spectrum appear to have different patterns of feedback to the wave field. The quadratic wave-wave interactions also are assessed using the auto-bispectrum and are found to be especially active during the first and the third episodes. Such directly detected wind-wave interactions, both linear and
Quantum phases of a chain of strongly interacting anyons
Finch, Peter E.; Frahm, Holger; Lewerenz, Marius; Milsted, Ashley; Osborne, Tobias J.
2014-08-01
Quantum gates for the manipulation of topological qubits rely on interactions between non-Abelian anyonic quasiparticles. We study the collective behavior of systems of anyons arising from such interactions. In particular, we study the effect of favoring different fusion channels of the screened Majorana spins appearing in the recently proposed topological Kondo effect. Based on the numerical solution of a chain of SO(5)2 anyons we identify two critical phases whose low-energy behavior is characterized by conformal field theories with central charges c =1 and c =8/7, respectively. Our results are complemented by exact results for special values of the coupling constants which provide additional information about the corresponding phase transitions.
Energy Technology Data Exchange (ETDEWEB)
Trezza, M.; Cirillo, C.; Sabatino, P.; Carapella, G.; Attanasio, C. [CNR-SPIN Salerno and Dipartimento di Fisica “E. R. Caianiello”, Università degli Studi di Salerno, Fisciano I-84084 (Italy); Prischepa, S. L. [Belarusian State University of Informatics and Radioelectronics, P. Browka 6, Minsk 220013 (Belarus)
2013-12-16
We report on the transport properties of an array of N∼30 interconnected Nb nanowires, grown by sputtering on robust porous Si substrates. The analyzed system exhibits a broad resistive transition in zero magnetic field, H, and highly nonlinear V(I) characteristics as a function of H, which can be both consistently described by quantum tunneling of phase slips.
Phase diagram of strong interactions in an external magnetic field
Mizher, Ana Julia; Chernodub, M N
2011-01-01
We obtain the phase diagram of strong interactions in the presence of a magnetic field within the linear sigma model coupled to quarks and to the Polyakov loop, and show that the chiral and deconfinement lines can split. We also study the behavior of the chiral condensate in this magnetic environment and find an approximately linear dependence on the external field, in accordance with lattice data.
Directory of Open Access Journals (Sweden)
C. M. Huang
2006-12-01
Full Text Available To quantitatively study the effects of nonlinear interactions on tide structure, a nonlinear numerical tidal model is developed, and the reliability and convergence of the adopted algorithm and coding are checked by numerical experiments. Under the same conditions as those employed by the GSWM-00 (Global Scale Wave Model 2000, our model provides the nonlinear quasi-steady solution of the migrating semidiurnal tide, which differs from the GSWM-00 result (the linear steady solution in the MLT region, especially above 100 km. Additionally, their amplitude difference displays a remarkable month-to-month variation, and its significant magnitudes occur during the month with strong semidiurnal tide. A quantitative analysis suggests that the main cause for the amplitude difference is that the initial migrating 12-h tide will interact with the mean flow as well as the nonlinearity-excited 6-h tide, and subsequently yield a new 12-h tidal part. Furthermore, our simulations also show that the mean flow/tidal interaction will significantly alter the background wind and temperature fields. The large magnitudes of the tidal amplitude difference and the background alteration indicate that the nonlinear processes involved in tidal propagations should be comprehensively considered in the description of global atmospheric dynamics in the MLT region. The comparisons among our simulations, the GSWMs and some observations of tides suggest that the nonlinearity-induced tidal structure variation could be a possible mechanism to account for some discrepancies between the GSWMs and the observations.
He, Yuan-Yao; Wu, Han-Qing; You, Yi-Zhuang; Xu, Cenke; Meng, Zi Yang; Lu, Zhong-Yi
2016-03-01
It is expected that the interplay between nontrivial band topology and strong electron correlation will lead to very rich physics. Thus a controlled study of the competition between topology and correlation is of great interest. Here, employing large-scale quantum Monte Carlo simulations, we provide a concrete example of the Kane-Mele-Hubbard model on an AA-stacking bilayer honeycomb lattice with interlayer antiferromagnetic interaction. Our simulation identified several different phases: a quantum spin Hall insulator (QSH), an x y -plane antiferromagnetic Mott insulator, and an interlayer dimer-singlet insulator. Most importantly, a bona fide topological phase transition between the QSH and the dimer-singlet insulators, purely driven by the interlayer antiferromagnetic interaction, is found. At the transition, the spin and charge gap of the system close while the single-particle excitations remain gapped, which means that this transition has no mean-field analog and it can be viewed as a transition between bosonic symmetry-protected topological (SPT) states. At one special point, this transition is described by a (2 +1 )d O (4 ) nonlinear sigma model with exact S O (4 ) symmetry and a topological term at exactly Θ =π . The relevance of this work towards more general interacting SPT states is discussed.
Bona fide interaction-driven topological phase transition in correlated SPT states
Meng, Zi Yang; He, Yuan-Yao; Wu, Han-Qing; You, Yi-Zhuang; Xu, Cenke; Lu, Zhong-Yi
It is expected the interplay between non-trivial band topology and strong electron correlation will lead to very rich physics. Thus a controlled study of the competition between topology and correlation is of great interest. Here, employing large-scale quantum Monte Carlo simulations, we provide a concrete example of the Kane-Mele-Hubbard model on an AA stacking bilayer honeycomb lattice with inter-layer antiferromagnetic interaction. Our simulation identified several different phases: a quantum spin-Hall insulator (QSH), a xy-plane antiferromagnetic Mott insulator (xy-AFM) and an inter-layer dimer-singlet insulator (dimer-singlet). Most importantly, a bona fide topological phase transition between the QSH and the dimer-singlet insulators, purely driven by the inter-layer antiferromagnetic interaction is found. At the transition, the spin and charge gap of the system close while the single-particle excitations remain gapped, which means that this transition has no mean field analogue and it can be viewed as a transition between bosonic SPT states. At one special point, this transition is described by a (2+1)d O(4) nonlinear sigma model with exact SO(4) symmetry, and a topological term at theta=p. Relevance of this work towards more general interacting SPT states is discussed.
Phase relations of triadic scale interactions in turbulent flows
Duvvuri, Subrahmanyam; McKeon, Beverley
2014-11-01
The quadratic nature of non-linearity in the Navier-Stokes (NS) equations dictates the coupling between scales in a turbulent flow to be of triadic form. An understanding of the triadic coupling affords good insights into the dynamics of turbulence, as demonstrated by Sharma & McKeon (J. Fluid Mech., 2013) through analysis of the NS resolvent operator; a set of three triadically consistent spatio-temporal modes was shown to produce complex structures such as modulating packets of hairpin vortices observed in wall-bounded turbulent flows. Here we interpret Skewness (Sk) of velocity fluctuations and the Amplitude Modulation coefficient (Ram), proposed by Mathis, Hutchins & Marusic (J. Fluid Mech., 2009), to be a measure of the large- and small-scale phase relationship. Through a simple decomposition of scales, both Sk and Ram are shown to be amplitude weighted (and normalized) measures of phase between scales that have direct triadic coupling. An analytical relationship is established between the two quantities and the result is demonstrated using experimental data from canonical and dynamically forced turbulent boundary layers presented in Duvvuri and McKeon (AIAA 2014-2883). The support of AFOSR (Grant No. FA 9550-12-1-0469) and Resnick Institute Graduate Research Fellowship (S.D.) is gratefully acknowledged.
Li, Hua; Wu, Tao
2016-10-01
A diffuse-interface model is presented in this paper for simulation of the evolution of phase transition between the liquid solution and solid gel states for physical hydrogel with nonlinear deformation. The present domain covers the gel and solution states as well as a diffuse interface between them. They are indicated by the crosslink density in such a way that the solution phase is identified as the state when the crosslink density is small, while the gel as the state if the crosslink density becomes large. In this work, a novel order parameter is thus defined as the crosslink density, which is homogeneous in each distinct phase and smoothly varies over the interface from one phase to another. In this model, the constitutive equations, imposed on the two distinct phases and the interface, are formulated by the second law of thermodynamics, which are in the same form as those derived by a different approach. The present constitutive equations include a novel Ginzburg-Landau type of free energy with a double-well profile, which accounts for the effect of crosslink density. The present governing equations include the equilibrium of forces, the conservations of mass and energy, and an additional kinetic equation imposed for phase transition, in which nonlinear deformation is considered. The equilibrium state is investigated numerically, where two stable phases are observed in the free energy profile. As case studies, a spherically symmetrical solution-gel phase transition is simulated numerically for analysis of the phase transition of physical hydrogel.
Interaction of in-phase and out-of-phase flexible filament in fish schooling
Ud Din, Emad; Sung, Hyung
2011-11-01
Fish schooling is not merely a social behavior; schooling improves the efficiency of movement within the fluid environment. Inspired by the schooling from a hydrodynamic perspective, a group of aquatic animals is modeled as a collection of individuals arranged in a combination of tandem and side-by-side (diamond) formation. The downstream bodies are strongly influenced by the vortices shed by the upstream body shown by vortex-vortex and vortex-body interactions. Trailing fish takes advantage of this flow pattern for energy economy. To investigate the interactions between flexible bodies and vortices, in the present study three flexible flags in viscous flow are solved by numerical simulation using an improved version of the immersed boundary method for in-phase and out-of-phase filaments. The drag coefficient of the downstream filaments drops even below the value of a single flag. Such drag variations are influenced by the interactions between vortices shed by the upstream flexible body and vortices surrounding the downstream filaments. Interaction of the flexible flags is investigated as a function of the gap distance between flags and different bending coefficients, for in-phase and out-of-phase cases at intermediate Reynolds numbers. This study was supported by the Creative Research Initiatives of NRF/MEST (No. 2011-0000423) of Korea.
Fluid-structure interaction for nonlinear response of shells conveying pulsatile flow
Tubaldi, Eleonora; Amabili, Marco; Païdoussis, Michael P.
2016-06-01
Circular cylindrical shells with flexible boundary conditions conveying pulsatile flow and subjected to pulsatile pressure are investigated. The equations of motion are obtained based on the nonlinear Novozhilov shell theory via Lagrangian approach. The flow is set in motion by a pulsatile pressure gradient. The fluid is modeled as a Newtonian pulsatile flow and it is formulated using a hybrid model that contains the unsteady effects obtained from the linear potential flow theory and the pulsatile viscous effects obtained from the unsteady time-averaged Navier-Stokes equations. A numerical bifurcation analysis employs a refined reduced order model to investigate the dynamic behavior. The case of shells containing quiescent fluid subjected to the action of a pulsatile transmural pressure is also addressed. Geometrically nonlinear vibration response to pulsatile flow and transmural pressure are here presented via frequency-response curves and time histories. The vibrations involving both a driven mode and a companion mode, which appear due to the axial symmetry, are also investigated. This theoretical framework represents a pioneering study that could be of great interest for biomedical applications. In particular, in the future, a more refined model of the one here presented will possibly be applied to reproduce the dynamic behavior of vascular prostheses used for repairing and replacing damaged and diseased thoracic aorta in cases of aneurysm, dissection or coarctation. For this purpose, a pulsatile time-dependent blood flow model is here considered by applying physiological waveforms of velocity and pressure during the heart beating period. This study provides, for the first time in literature, a fully coupled fluid-structure interaction model with deep insights in the nonlinear vibrations of circular cylindrical shells subjected to pulsatile pressure and pulsatile flow.
Rate of non-linearity in DMS aerosol-cloud-climate interactions
Directory of Open Access Journals (Sweden)
M. A. Thomas
2011-11-01
Full Text Available The degree of non-linearity in DMS-cloud-climate interactions is assessed using the ECHAM5-HAMMOZ model by taking into account end-to-end aerosol chemistry-cloud microphysics link. The evaluation is made over the Southern oceans in austral summer, a region of minimal anthropogenic influence. In this study, we compare the DMS-derived changes in the aerosol and cloud microphysical properties between a baseline simulation with the ocean DMS emissions from a prescribed climatology, and a scenario where the DMS emissions are doubled. Our results show that doubling the DMS emissions in the current climate results in a non-linear response in atmospheric DMS burden and subsequently, in SO_{2} and H_{2}SO_{4} burdens due to inadequate OH oxidation. The aerosol optical depth increases by only ~20 % in the 30° S–75° S belt in the SH summer months. This increases the vertically integrated cloud droplet number concentrations (CDNC by 25 %. Since the vertically integrated liquid water vapor is constant in our model simulations, an increase in CDNC leads to a reduction in cloud droplet radius of 3.4 % over the Southern oceans in summer. The equivalent increase in cloud liquid water path is 10.7 %. The above changes in cloud microphysical properties result in a change in global annual mean radiative forcing at the TOA of −1.4 W m^{−2}. The results suggest that the DMS-cloud microphysics link is highly non-linear. This has implications for future studies investigating the DMS-cloud climate feedbacks in a warming world and for studies evaluating geoengineering options to counteract warming by modulating low level marine clouds.
Kumar, P; Kumar, Dinesh; Rai, K N
2016-08-01
In this article, a non-linear dual-phase-lag (DPL) bio-heat transfer model based on temperature dependent metabolic heat generation rate is derived to analyze the heat transfer phenomena in living tissues during thermal ablation treatment. The numerical solution of the present non-linear problem has been done by finite element Runge-Kutta (4,5) method which combines the essence of Runge-Kutta (4,5) method together with finite difference scheme. Our study demonstrates that at the thermal ablation position temperature predicted by non-linear and linear DPL models show significant differences. A comparison has been made among non-linear DPL, thermal wave and Pennes model and it has been found that non-linear DPL and thermal wave bio-heat model show almost same nature whereas non-linear Pennes model shows significantly different temperature profile at the initial stage of thermal ablation treatment. The effect of Fourier number and Vernotte number (relaxation Fourier number) on temperature profile in presence and absence of externally applied heat source has been studied in detail and it has been observed that the presence of externally applied heat source term highly affects the efficiency of thermal treatment method.
Kharitonov, Maxim; Juergens, Stefan; Trauzettel, Björn
2016-07-01
We consider a class of quantum Hall topological insulators: topologically nontrivial states with zero Chern number at finite magnetic field, in which the counterpropagating edge states are protected by a symmetry (spatial or spin) other than time-reversal. HgTe-type heterostructures and graphene are among the relevant systems. We study the effect of electron interactions on the topological properties of the system. We particularly focus on the vicinity of the topological phase transition, marked by the crossing of two Landau levels, where the system is a strongly interacting quantum Hall ferromagnet. We analyze the edge properties using the formalism of the nonlinear σ -model. We establish the symmetry requirement for the topological protection in this interacting system: effective continuous U(1) symmetry with respect to uniaxial isospin rotations must be preserved. If U(1) symmetry is preserved, the topologically nontrivial phase persists; its edge is a helical Luttinger liquid with highly tunable effective interactions. We obtain explicit analytical expressions for the parameters of the Luttinger liquid in the quantum-Hall-ferromagnet regime. However, U(1) symmetry may be broken, either spontaneously or by U(1)-asymmetric interactions. In either case, interaction-induced transitions occur to the respective topologically trivial phases with gapped edge charge excitations.
Nonlinear gauge interactions: a possible solution to the "measurement problem" in quantum mechanics
Hansson, Johan
2010-01-01
Two fundamental, and unsolved problems in physics are: i) the resolution of the "measurement problem" in quantum mechanics ii) the quantization of strongly nonlinear (nonabelian) gauge theories. The aim of this paper is to suggest that these two problems might be linked, and that a mutual, simultaneous solution to both might exist. We propose that the mechanism responsible for the "collapse of the wave function" in quantum mechanics is the nonlinearities already present in the theory via nonabelian gauge interactions. Unlike all other models of spontaneous collapse, our proposal is, to the best of our knowledge, the only one which does not introduce any new elements into the theory. A possible experimental test of the model would be to compare the coherence lengths - here defined as the distance over which quantum mechanical superposition is still valid - for, \\textit{e.g}, electrons and photons in a double-slit experiment. The electrons should have a finite coherence length, while photons should have a much ...
Detection of phase and lag synchrony as an adaptive measure of asymmetric neuronal interactions
Zochowski, Michal
2006-03-01
Asymmetric temporal interdependencies between individual neurons and their populations are though to underlie learning and memory formation and can provide information about direction of information transfer in neural systems. We have developed an adaptive measure that detects asymmetries in phase and lag synchrony between activities of individual neurons of synchronized networks. In the first part of the talk I will discuss the properties of the measure on network models of coupled non-linear oscillators and show progression of rapid transitions in temporal patterning in such networks as a function of their topology. In the second part of the talk I will present its application in analysis of normal and pathological neural activity: detection of evolving asymmetry in interactions of hippocampal neurons in freely behaving rats, and characterization of dynamical progression of synchronous seizure-like activity recorded from intact rat hippocampus.
The ''phase velocity'' of nonlinear plasma waves in the laser beat-wave accelerator
Energy Technology Data Exchange (ETDEWEB)
Spence, W.L.
1985-04-01
A calculational scheme for beat-wave accelerators is introduced that includes all orders in velocity and in plasma density, and additionally accounts for the influence of plasma nonlinearities on the wave's phase velocity. The main assumption is that the laser frequencies are very large compared to the plasma frequency - under which it is possible to sum up all orders of forward Raman scattering. It is found that the nonlinear plasma wave does not have simply a single phase velocity, but that the beat-wave which drives it is usefully described by a non-local ''effective phase velocity'' function. A time-space domain approach is followed. (LEW)
Indian Academy of Sciences (India)
S Lakshmi; Swapan K Pati
2003-10-01
We consider an interacting one-dimensional molecular wire attached to two metal electrodes on either side of it. The electrostatic potential profile across the wire-electrode interface has been deduced solving the Schrodinger and Poisson equations self-consistently. Since the Poisson distribution crucially depends on charge densities, we have considered different Hamiltonian parameters to model the nanoscale wire. We find that for very weak electron correlations, the potential gradient is almost zero in the middle of the wire but are large near the chain ends. However, for strong correlations, the potential is essentially a ramp function. The nonlinear current, obtained from the scattering formalism, is found to be less with the ramp potential than for weak correlations. Some of the interesting features in current-voltage characteristics have been explained using one-electron formalism and instabilities in the system.
Interactions between impurities and breather-pairs in a nonlinear lattice
Lin, Han; Chen, Weizhong; Lu, Lei; Wei, Rongjue
2003-09-01
Based on the Frenkel-Kontorova (FK) model with a δ-impurity, this Letter investigates the interactions between impurities and breather-pairs in a nonlinear pendulum chain driven by a vertical vibration. The numerical results show that a long impurity in pendulum length can absorb more energy into the chain and upgrade the energy level of the breather-pair, when the driving frequency is slight lower than that of parametric resonance of the perfect pendulums, while a short one plays a counteractive role. As the chain is driven at a higher frequency, the effect of impurities turns reverse, which shows a clear symmetry and equivalency between long and short impurities. The main results including the effect and the symmetry of impurities generalize the conclusion on the single breather to the breather-pair.
Interactions between impurities and breather-pairs in a nonlinear lattice
Energy Technology Data Exchange (ETDEWEB)
Lin Han; Chen Weizhong; Lu Lei; Wei Rongjue
2003-09-15
Based on the Frenkel-Kontorova (FK) model with a {delta}-impurity, this Letter investigates the interactions between impurities and breather-pairs in a nonlinear pendulum chain driven by a vertical vibration. The numerical results show that a long impurity in pendulum length can absorb more energy into the chain and upgrade the energy level of the breather-pair, when the driving frequency is slight lower than that of parametric resonance of the perfect pendulums, while a short one plays a counteractive role. As the chain is driven at a higher frequency, the effect of impurities turns reverse, which shows a clear symmetry and equivalency between long and short impurities. The main results including the effect and the symmetry of impurities generalize the conclusion on the single breather to the breather-pair.
Directory of Open Access Journals (Sweden)
Etienne Thoret
2016-06-01
Full Text Available In this paper, a flexible control strategy for a synthesis model dedicated to nonlinear friction phenomena is proposed. This model enables to synthesize different types of sound sources, such as creaky doors, singing glasses, squeaking wet plates or bowed strings. Based on the perceptual stance that a sound is perceived as the result of an action on an object we propose a genuine source/filter synthesis approach that enables to elude physical constraints induced by the coupling between the interacting objects. This approach makes it possible to independently control and freely combine the action and the object. Different implementations and applications related to computer animation, gesture learning for rehabilitation and expert gestures are presented at the end of this paper.
Linear and nonlinear interactions between the earth tide and a tectonically stressed earth
Beaumont, C.
1978-01-01
In the vincinity of earthquake focal regions, conditions may not be equal. Crustal rocks stressed to more than approximately 0.6 of their failure strength exhibit material properties over and above that of linear elasticity. Interactions between the earth tide and crustal rocks that are under high tectonic stress are discussed in terms of simple phenomenological models. In particular, the difference between a nonlinear elastic model of dilatancy and a dilatancy model that exhibits hysteresis is noted. It is concluded that the small changes in stress produced by the earth tide act as a probe of the properties of crustal rocks. Observations of earth tide tilts and strains in such high stress zones may, therefore, provide keys to the constitutive properties and the tectonic stress rate tensor of these zones.
Trautmann, L.; Rabenstein, R.
2004-12-01
The functional transformation method (FTM) is a well-established mathematical method for accurate simulations of multidimensional physical systems from various fields of science, including optics, heat and mass transfer, electrical engineering, and acoustics. This paper applies the FTM to real-time simulations of transversal vibrating strings. First, a physical model of a transversal vibrating lossy and dispersive string is derived. Afterwards, this model is solved with the FTM for two cases: the ideally linearly vibrating string and the string interacting nonlinearly with the frets. It is shown that accurate and stable simulations can be achieved with the discretization of the continuous solution at audio rate. Both simulations can also be performed with a multirate approach with only minor degradations of the simulation accuracy but with preservation of stability. This saves almost 80% of the computational cost for the simulation of a six-string guitar and therefore it is in the range of the computational cost for digital waveguide simulations.
Non-linear interactions in a cosmological background in the DGP braneworld
Koyama, K; Koyama, Kazuya; Silva, Fabio P
2007-01-01
We study quasi-static perturbations in a cosmological background in the Dvali-Gabadadze-Porrati (DGP) braneworld model. We identify the Vainshtein radius at which the non-linear interactions of the brane bending mode become important in a cosmological background. The Vainshtein radius in the early universe is much smaller than the one in the Minkowski background, but in a self-accelerating universe it is the same as the Minkowski background. Our result shows that the perturbative approach is applicable beyond the Vainshtein radius for weak gravity by taking into account the second order effects of the brane bending mode. The linearised cosmological perturbations are shown to be smoothly matched to the solutions inside the Vainshtein radius. We emphasize the importance of imposing a regularity condition in the bulk by solving the 5D perturbations and we highlight the problem of ad hoc assumptions on the bulk gravity that lead to different conclusions.
Transition waves and nonlinear interactions in the near wake of a circular cylinder
Institute of Scientific and Technical Information of China (English)
凌国灿; Allen T.Chwang; 牛家玉; 王冬(女菱)
1997-01-01
Transition waves and interactions between two kinds of instability-vortex shedding and transition wave in the near wake of a circular cylinder in the Reynolds number range 3 000-10 000 are studied by a domain decomposition hybrid numerical method.Based on high resolution power spectral analyses for velocity new results on the Reynolds-number dependence of the transition wave frequency,i.e.ft/fa~Re0.87 are obtained.The new predictions are in good agreement with the experimental results of Wei and Smith but different from Braza’s prediction and some early experimental results ft/fa-Re0.5 given by Bloor et al.The multi-interactions between two kinds of vortex are clearly visualized numerically.The strong nonlinear interactions between the two independent frequencies (ft,fa) leading to spectra broadening to form the coupling mfs±nft are predicted and analyzed numerically,and the characteristics of the transition are described.Longitudinal variations of the transition wave and its coupling are reported.Deta
Comparative Study of Controllers for a Variable Area MIMO Interacting NonLinear System
Directory of Open Access Journals (Sweden)
Priya Chandrasekar
2014-03-01
Full Text Available Most of the industrial processes are basically Multi Input Multi Output (MIMO system. In this paper a new combination of Spherical Conical Interacting Tank System (SCITS which is a variable area nonlinear MIMO system is considered for study and various control algorithms based on Ziegler Nichol’s tuning method, Hagglund Astrom Robust tuning method, Fractional Order (FO control and Passivity Based Control (PBC are used and compared for the level control of spherical tank system and conical tank system connected with interaction. Transfer function matrix of the system is obtained experimentally from the open loop response of the system. The designed controllers are tested for servo and regulatory operations. The controllers are compared in terms of time domain specification and performance index criterion. From the analysis of the simulation results, it is seen that FO controller gives improved performance when compared to conventional Integer Order (IO controller and overall Passivity Based Controller (PBCr gives improved performance comparatively for spherical conical interacting MIMO system.
Interaction model between capsule robot and intestine based on nonlinear viscoelasticity.
Zhang, Cheng; Liu, Hao; Tan, Renjia; Li, Hongyi
2014-03-01
Active capsule endoscope could also be called capsule robot, has been developed from laboratory research to clinical application. However, the system still has defects, such as poor controllability and failing to realize automatic checks. The imperfection of the interaction model between capsule robot and intestine is one of the dominating reasons causing the above problems. A model is hoped to be established for the control method of the capsule robot in this article. It is established based on nonlinear viscoelasticity. The interaction force of the model consists of environmental resistance, viscous resistance and Coulomb friction. The parameters of the model are identified by experimental investigation. Different methods are used in the experiment to obtain different values of the same parameter at different velocities. The model is proved to be valid by experimental verification. The achievement in this article is the attempted perfection of an interaction model. It is hoped that the model can optimize the control method of the capsule robot in the future.
Rury, Aaron S.
2016-06-01
This study reports experimental, computational, and theoretical evidence for a previously unobserved coherent phonon-phonon interaction in an organic solid that can be described by the application of Fano's analysis to a case without the presence of a continuum. Using Raman spectroscopy of the hydrogen-bonded charge-transfer material quinhydrone, two peaks appear near 700 cm-1 we assign as phonons whose position and line-shape asymmetry depend on the sample temperature and light scattering excitation energy. Density functional theory calculations find two nearly degenerate phonons possessing frequencies near the values found in experiment that share similar atomic motion out of the aromatic plane of electron donor and acceptor molecules of quinhydrone. Further analytical modeling of the steady-state light scattering process using the Peierls-Hubbard Hamiltonian and time-dependent perturbation theory motivates assignment of the physical origin of the asymmetric features of each peak's line shape to an interaction between two discrete phonons via nonlinear electron-phonon coupling. In the context of analytical model results, characteristics of the experimental spectra upon 2.33 eV excitation of the Raman scattering process are used to qualify the temperature dependence of the magnitude of this coupling in the valence band of quinhydrone. These results broaden the range of phonon-phonon interactions in materials in general while also highlighting the rich physics and fundamental attributes specific to organic solids that may determine their applicability in next generation electronics and photonics technologies.
Phase diagram of interacting spinless fermions on the honeycomb lattice
Capponi, Sylvain
2017-02-01
Fermions hopping on a hexagonal lattice represent one of the most active research fields in condensed matter since the discovery of graphene in 2004 and its numerous applications. Another exciting aspect of the interplay between geometry and quantum mechanical effects is given by the Haldane model (Haldane 1988 Phys. Rev. Lett. 61 2015), where spinless fermions experiencing a certain flux pattern on the honeycomb lattice leads to the stabilization of a topological phase of matter, distinct from a Mott insulator and nowadays dubbed Chern insulator. In this context, it is crucial to understand the role of interactions and this review will describe recent results that have been obtained for a minimal model, namely spinless fermions with nearest and next-nearest neighbour density-density interactions on the honeycomb lattice at half-filling. Topics addressed include an introduction of the minimal model and a discussion of the possible instabilities of the Dirac semimetal, a presentation of various theoretical and numerical approaches, and a summary of the results with a particular emphasis on the stability or not of some exotic quantum phases such as charge ordered ones (similar to Wigner crystals) and spontaneous Chern insulator phases.
Electronic dynamics under effect of a nonlinear Morse interaction and a static electric field
Ranciaro Neto, A.; de Moura, F. A. B. F.
2016-11-01
Considering non-interacting electrons in a one-dimension alloy in which atoms are coupled by a Morse potential, we study the system dynamics in the presence of a static electric field. Calculations are performed assuming a quantum mechanical treatment for the electronic transport and a classical Hamiltonian model for the lattice vibrations. We report numerical evidence of the existence of a soliton-electron pair, even when the electric field is turned on, and we offer a description of how the existence of such a phase depends on the magnitude of the electric field and the electron-phonon interaction.
Resonant nonlinear interactions between atmospheric waves in the polar summer mesopause region
Institute of Scientific and Technical Information of China (English)
LIU; Renqiang; (刘仁强); YI; Fan; (易帆)
2003-01-01
Data obtained from the mobile SOUSY VHF radar at And(ya/Norway in summer 1987 have been used to study the nonlinear interactions between planetary waves, tides and gravity waves in the polar mesosphere, and the instability of background atmosphere above the mesopause. It is observed that 35-h planetary wave, diurnal, semidiurnal and terdiurnal tides are the prominent perturbations in the Lomb-Scargle spectra of the zonal wind component. By inspecting the frequency combinations, several triads are identified. By bispectral analysis it is shown that most bispectral peaks stand for quadratic coupling between tidal harmonics or between tide and planetary or gravity wave, and the height dependence of bispectral peaks reflects the variation of wave-wave interactions. Above the mesopause, the occurrence heights of the maximum L-S power spectral peaks corresponding to the prominent wave components tend to increase with their frequencies. This may result from the process in which two low frequency waves interact to generate a high frequency wave. Intensities of the planetary wave and tides increase gradually, arrive at their maxima, and then decay quickly in turn with increasing height. This kind of scene correlates with a "chain" of wave-wave resonant interactions that shifts with height from lower frequency segment to higher frequency segment. By instability analysis, it is observed that above the mesopause, the Richardson number becomes smaller and smaller with height, implying that the turbulent motion grows stronger and stronger and accordingly the background atmosphere more and more instable. It is suggested that the wave-wave sum resonant interaction and the wave dissipation due to instability are two dominant dynamical processes that occur in the mesopause region. The former invokes the energy transfer from lower frequency waves to higher frequency waves. The latter results in the heating of the atmosphere and accelerating of the background flow.
Cosmic flows and the expansion of the Local Universe from nonlinear phase-space reconstructions
Hess, Steffen
2014-01-01
We investigate the impact of cosmic flows and density perturbations on Hubble constant $H_0$ measurements using nonlinear phase-space reconstructions of the Local Universe (LU). We rely on a set of 25 N-body simulations which are constrained to resemble the LU within distances of about 90 Mpc/h. These have been randomly extended up to volumes enclosing distances of 360 Mpc/h with augmented Lagrangian perturbation theory (=750 simulations), accounting in this way for effects from from larger scales ($\\sigma_{\\rm large}=134$ km/s). We report on Local Group (LG) speed reconstructions, which are compatible with those derived from the CMB-dipole: $|v_{\\rm LG}|=685\\pm137$ km/s. The direction $(l,b)=(260.5\\pm 13.3,39.1\\pm 10.4)^\\circ$ is found to be compatible with observations. We use the CMB-dipole information to estimate the missing large scale bulk flow component, indicating that we miss a closely perpendicular flow with a magnitude corresponding to $1.4 \\sigma_{\\rm large}$. Considering this, our bulk flow estim...
Collapse of optical wave arrested by cross-phase modulation in nonlinear metamaterials
Zhang, Jinggui; Li, Ying; Xiang, Yuanjiang; Lei, Dajun; Zhang, Lifu
2016-03-01
In this article, we put forward a novel strategy to realize the management of wave collapse through designing probe-pump configuration where probe wave is assumed to propagate in the positive-index region of metamaterials (MMs), while pump wave is assumed to propagate in the negative-index region. We disclose that cross-phase modulation (XPM) in MMs as a new physical mechanism that can be used to arrest the collapse of probe wave in the positive-index region by copropagating it together with pump wave in the negative-index region. Further, we observe that pump wave will evolve into a ring while probe wave will develop a side lob in the wings during the course of coupled waves propagation, different from the corresponding counterpart in the ordinary positive-index materials (OMs) where they simultaneously exhibit the catastrophic self-focusing behavior. Meanwhile, we also discuss how to control the collapse of probe wave by adjusting intensity-detuned pump wave. Our analysis is performed by directly numerically solving the coupled nonlinear Schrödinger equations, as well as using the variational approximation, both showing consistent results. The finding demonstrates XPM as a specific physical mechanism in MMs can provide us unique opportunities unattainable in OMs to manipulate self-focusing of high-power laser.
Supercontinuum generation in quadratic nonlinear waveguides without quasi-phase matching
DEFF Research Database (Denmark)
Guo, Hairun; Zhou, Binbin; Steinert, Michael
2015-01-01
bandwidths (even octave spanning), together with other experimental data, indicate that negative nonlinearity solitons are indeed excited, which is backed up by numerical simulations. The QPM-free design reduces production complexity, extends the maximum waveguide length, and limits undesired spectral...... resonances. Finally, nonlinear crystals can be used where QPM is inefficient or impossible, which is important for mid-IR SCG. QPM-free waveguides in mid-IR nonlinear crystals can support negative nonlinearity solitons, as these waveguides have a normal dispersion at the emission wavelengths of mid...
Antolín, Pablo; Zhang, Nan; Goicolea, José M.; Xia, He; Astiz, Miguel Á.; Oliva, Javier
2013-03-01
In this work models with nonlinear wheel-rail contact forces are considered for analysing the dynamic interaction between high speed trains and bridges, in order to study dynamic effects both in the bridge and in the vehicles resulting from the coupling. Nonlinear contact models may be necessary for evaluating the stability and the safety of running traffic in situations such as vehicle overturn when the train is crossing a bridge under strong lateral winds or when an earthquake occurs. For studying the coupled dynamic response of trains and bridges, models of multibody dynamics are used for vehicles and the finite element method for structures. Special relevance is given here to the consideration of contact interaction forces between railway vehicles and the track. Four different interaction models are compared in this work: (1) a model where the vehicle wheelset is considered to be rigidly coupled to the track; (2) a staggered uncoupled method in which vehicle and structure are analysed separately; (3) a linear contact model in which lateral relative displacements between rails and train wheels are allowed, assuming biconic wheel and rail profiles and linear Kalker theory for tangential contact; (4) a nonlinear model in which realistic wheel and rail profiles, Hertz's nonlinear theory for normal contact and Kalker's nonlinear theory for tangential contact are used. The different models are applied and compared to experimental measurements for a test case of a high-speed train in China.
Phase transitions in the $sdg$ interacting boson model
Van Isacker, P; Zerguine, S
2009-01-01
A geometric analysis of the $sdg$ interacting boson model is performed. A coherent-state is used in terms of three types of deformation: axial quadrupole ($\\beta_2$), axial hexadecapole ($\\beta_4$) and triaxial ($\\gamma_2$). The phase-transitional structure is established for a schematic $sdg$ hamiltonian which is intermediate between four dynamical symmetries of U(15), namely the spherical ${\\rm U}(5)\\otimes{\\rm U}(9)$, the (prolate and oblate) deformed ${\\rm SU}_\\pm(3)$ and the $\\gamma_2$-soft SO(15) limits. For realistic choices of the hamiltonian parameters the resulting phase diagram has properties close to what is obtained in the $sd$ version of the model and, in particular, no transition towards a stable triaxial shape is found.
Institute of Scientific and Technical Information of China (English)
Hongwei Li⁎; Junpeng Liu; Yunlong Zhou; Bin Sun
2016-01-01
Gas–liquid two-phase flow is complex and has uncertainty in phase interfaces, which make the two-phase flow look very complicated. Even though the flow behavior (e.g. coalescence, crushing and separation) of single bubble or bubble groups in the liquid phase looks random, combining some established character-istics and methodologies can find regularities among the randomness. In order to excavate the nonlinear dynamic characteristics of gas–liquid two-phase flow, the authors developed an improved matrix pencil (IMP) method to analyze the pressure difference signals of the two-phase flow. This paper elucidates the influence of signal length on MP calculation results and the anti-noise-interference ability of the MP method. An IMP algorithm was applied to the fluctuation signals of gas–liquid two-phase flow to extract the mode frequency and damping ratio, which were combined with the component energy index (CEI) en-tropy to identify the different flow patterns. It is also found that frequency, damping ratio, CEI entropy and stability diagram together not only identify flow patterns, but also provide a new way to examine and un-derstand the evolution mechanism of physical dynamics embedded in flow patterns. Combining these characteristics and methods, the evolution of the nonlinear dynamic physical behavior of gas bubbles is revealed.
Directory of Open Access Journals (Sweden)
T McMillen
2008-08-01
Full Text Available Locomotion provides superb examples of cooperation among neuromuscular systems, environmental reaction forces, and sensory feedback. As part of a program to understand the neuromechanics of locomotion, here we construct a model of anguilliform (eel-like swimming in slender fishes. Building on a continuum mechanical representation of the body as an viscoelastic rod, actuated by a traveling wave of preferred curvature and subject to hydrodynamic reaction forces, we incorporate a new version of a calcium release and muscle force model, fitted to data from the lamprey Ichthyomyzon unicuspis, that interactively generates the curvature wave. We use the model to investigate the source of the difference in speeds observed between electromyographic waves of muscle activation and mechanical waves of body curvature, concluding that it is due to a combination of passive viscoelastic and geometric properties of the body and active muscle properties. Moreover, we find that nonlinear force dependence on muscle length and shortening velocity may reduce the work done by the swimming muscles in steady swimming.
Nguyen, Vu A.; Palo, Scott E.; Lieberman, Ruth S.; Forbes, Jeffrey M.; Ortland, David A.; Siskind, David E.
2016-07-01
Theory and past observations have provided evidence that atmospheric tides and other global-scale waves interact nonlinearly to produce additional secondary waves throughout the space-atmosphere interaction region. However, few studies have investigated the generation region of nonlinearly generated secondary waves, and as a result, the manifestation and impacts of these waves are still poorly understood. This study focuses on the nonlinear interaction between the quasi 2 day wave (2dayW3) and the migrating diurnal tide (DW1), two of the largest global-scale waves in the atmosphere. The fundamental goals of this effort are to characterize the forcing region of the secondary waves and to understand how it relates to their manifestation on a global scale. First, the Fast Fourier Synoptic Mapping method is applied to Thermosphere Ionosphere Mesosphere Energetics and Dynamics-Sounding of the Atmosphere using Broadband Emission Radiometry satellite observations to provide new evidence of secondary waves. These results show that secondary waves are only significant above 80 km. The nonlinear forcing for each secondary wave is then computed by extracting short-term primary wave information from a reanalysis model. The estimated nonlinear forcing quantities are used to force a linearized tidal model in order to calculate numerical secondary wave responses. Model results show that the secondary waves are significant from the upper mesosphere to the middle thermosphere, highlighting the implications for the atmosphere-space weather coupling. The study also concludes that the secondary wave response is most sensitive to the nonlinear forcing occurring in the lower and middle mesosphere and not coincident with the regions of strongest nonlinear forcing.
Wahlstrand, J K; McCole, E T; Cheng, Y -H; Palastro, J P; Levis, R J; Milchberg, H M
2013-01-01
Nonlinear optics experiments measuring phase shifts induced in a weak probe pulse by a strong pump pulse must account for coherent effects that only occur when the pump and probe pulses are temporally overlapped. It is well known that a weak probe beam experiences a greater phase shift from a strong pump beam than the pump beam induces on itself. The physical mechanism behind the enhanced phase shift is diffraction of pump light into the probe direction by a nonlinear refractive index grating produced by interference between the two beams. For an instantaneous third-order response, the effect of the grating is to simply double the probe phase shift, but when delayed nonlinearities are considered, the effect is more complex. A comprehensive treatment is given for both degenerate and nondegenerate pump-probe experiments in noble and diatomic gases. Results of numerical calculations are compared to a recent transient birefringence measurement [Loriot et al., Opt. Express 17, 13429 (2009)] and a recent spectral i...
Dey, Prasenjit
understanding the basic unexplored science as well as creating technological developments. The dephasing dynamics in semiconductors typically occur in the picosecond to femtosecond timescale, thus the use of ultrafast laser spectroscopy is a potential route to probe such excitonic responses. The focus of this dissertation is two-fold: firstly, to develop the necessary instrumentation to accurately probe the aforementioned parameters and secondly, to explore the quantum dynamics and the underlying many-body interactions in different layered semiconducting materials. A custom-built multidimensional optical non-linear spectrometer was developed in order to perform two-dimensional spectroscopic (2DFT) measurements. The advantages of this technique are multifaceted compared to regular one-dimensional and non-linear incoherent techniques. 2DFT technique is based on an enhanced version of Four wave mixing experiments. This powerful tool is capable of identifying the resonant coupling, probing the coherent pathways, unambiguously extracting the homogeneous linewidth in the presence of inhomogeneity and decomposing a complex spectra into real and imaginary parts. It is not possible to uncover such crucial features by employing one dimensional non-linear technique. Monolayers as well as bulk TMDs and group III-VI bulk layered materials are explored in this dissertation. The exciton quantum dynamics is explored with three pulse four-wave mixing whereas the phase sensitive measurements are obtained by employing two-dimensional Fourier transform spectroscopy. Temperature and excitation density dependent 2DFT experiments unfold the information associated with the many-body interactions in the layered semiconducting samples.
Energy Technology Data Exchange (ETDEWEB)
Reena Mary, A P; Anantharaman, M R [Department of Physics, Cochin University of Science and Technology, Cochin 682 022 (India); Suchand Sandeep, C S; Philip, Reji [Light and Matter Physics Group, Raman Research Institute, Sadashivanagar, Bangalore-560080 (India); Narayanan, T N; Moloney, Padraig; Ajayan, P M, E-mail: reji@rri.res.in, E-mail: mraiyer@yahoo.com [Department of Mechanical Engineering and Materials Science, Rice University, Houston, TX-77005 (United States)
2011-09-16
Oxide free stable metallic nanofluids have the potential for various applications such as in thermal management and inkjet printing apart from being a candidate system for fundamental studies. A stable suspension of nickel nanoparticles of {approx} 5 nm size has been realized by a modified two-step synthesis route. Structural characterization by x-ray diffraction and transmission electron microscopy shows that the nanoparticles are metallic and are phase pure. The nanoparticles exhibited superparamagnetic properties. The magneto-optical transmission properties of the nickel nanofluid (Ni-F) were investigated by linear optical dichroism measurements. The magnetic field dependent light transmission studies exhibited a polarization dependent optical absorption, known as optical dichroism, indicating that the nanoparticles suspended in the fluid are non-interacting and superparamagnetic in nature. The nonlinear optical limiting properties of Ni-F under high input optical fluence were then analyzed by an open aperture z-scan technique. The Ni-F exhibits a saturable absorption at moderate laser intensities while effective two-photon absorption is evident at higher intensities. The Ni-F appears to be a unique material for various optical devices such as field modulated gratings and optical switches which can be controlled by an external magnetic field.
Energy Technology Data Exchange (ETDEWEB)
Ye, Jinwu, E-mail: jy306@ccs.msstate.edu [Beijing Key Laboratory for Terahertz Spectroscopy and Imaging, Key Laboratory of Terahertz Optoelectronics, Ministry of Education, Department of Physics, Capital Normal University, Beijing 100048 (China); Department of Physics and Astronomy, Mississippi State University, P.O. Box 5167, MS 39762 (United States); Chen, Yan, E-mail: yanchen99@gmail.com [Department of Physics, Surface Physics Laboratory (National Key Laboratory) and Lab of Advanced Materials, Fudan University, Shanghai (China)
2013-04-11
logarithmic corrections). Excitation spectra of all these insulating phases and supersolid phases are also studied. Implications on QMC simulations with both nearest neighbor and next nearest neighbor interactions in both lattices are given. Some possible intrinsic problems of the DOF in identifying the insulating phases are also pointed out.
Akhbari, Mahsa; Shamsollahi, Mohammad B; Jutten, Christian; Armoundas, Antonis A; Sayadi, Omid
2016-02-01
In this paper we propose an efficient method for denoising and extracting fiducial point (FP) of ECG signals. The method is based on a nonlinear dynamic model which uses Gaussian functions to model ECG waveforms. For estimating the model parameters, we use an extended Kalman filter (EKF). In this framework called EKF25, all the parameters of Gaussian functions as well as the ECG waveforms (P-wave, QRS complex and T-wave) in the ECG dynamical model, are considered as state variables. In this paper, the dynamic time warping method is used to estimate the nonlinear ECG phase observation. We compare this new approach with linear phase observation models. Using linear and nonlinear EKF25 for ECG denoising and nonlinear EKF25 for fiducial point extraction and ECG interval analysis are the main contributions of this paper. Performance comparison with other EKF-based techniques shows that the proposed method results in higher output SNR with an average SNR improvement of 12 dB for an input SNR of -8 dB. To evaluate the FP extraction performance, we compare the proposed method with a method based on partially collapsed Gibbs sampler and an established EKF-based method. The mean absolute error and the root mean square error of all FPs, across all databases are 14 ms and 22 ms, respectively, for our proposed method, with an advantage when using a nonlinear phase observation. These errors are significantly smaller than errors obtained with other methods. For ECG interval analysis, with an absolute mean error and a root mean square error of about 22 ms and 29 ms, the proposed method achieves better accuracy and smaller variability with respect to other methods.
2013-11-18
capability to realistic ocean environments. REFERENCES 1. Dysthe, K.B. 1979 Note on a modification to the nonlinear schrodinger equation for...wave turbulence. Phy. Rev. Lett. 98, 94503. 3. Trulsen,K.and Dysthe,K.B. 1996 A modified nonlinear Schrodinger equation for broader bandwidth
Analytical expressions for Z-scan with arbitrary phase change in thin nonlocal nonlinear media.
Ortega, A Balbuena; Carrasco, M L Arroyo; Otero, M M Méndez; Lara, E Reynoso; Ramírez, E V García; Castillo, M D Iturbe
2014-11-17
Analytical expressions for the normalized transmittance of a thin material with simultaneous nonlocal nonlinear change in refraction and absorption are reported. Gaussian decomposition method was used to obtain the formulas that are adequate for any magnitude of the nonlinear changes. Particular cases of no locality are compared with the local case. Experimental results are reproduced (fitted) with the founded expressions.
Optimal bipedal interactions with dynamic terrain: synthesis and analysis via nonlinear programming
Hubicki, Christian; Goldman, Daniel; Ames, Aaron
In terrestrial locomotion, gait dynamics and motor control behaviors are tuned to interact efficiently and stably with the dynamics of the terrain (i.e. terradynamics). This controlled interaction must be particularly thoughtful in bipeds, as their reduced contact points render them highly susceptible to falls. While bipedalism under rigid terrain assumptions is well-studied, insights for two-legged locomotion on soft terrain, such as sand and dirt, are comparatively sparse. We seek an understanding of how biological bipeds stably and economically negotiate granular media, with an eye toward imbuing those abilities in bipedal robots. We present a trajectory optimization method for controlled systems subject to granular intrusion. By formulating a large-scale nonlinear program (NLP) with reduced-order resistive force theory (RFT) models and jamming cone dynamics, the optimized motions are informed and shaped by the dynamics of the terrain. Using a variant of direct collocation methods, we can express all optimization objectives and constraints in closed-form, resulting in rapid solving by standard NLP solvers, such as IPOPT. We employ this tool to analyze emergent features of bipedal locomotion in granular media, with an eye toward robotic implementation.
Neurosurgery Simulation Using Non-linear Finite Element Modeling and Haptic Interaction.
Lee, Huai-Ping; Audette, Michel; Joldes, Grand Roman; Enquobahrie, Andinet
2012-02-23
Real-time surgical simulation is becoming an important component of surgical training. To meet the real-time requirement, however, the accuracy of the biomechancial modeling of soft tissue is often compromised due to computing resource constraints. Furthermore, haptic integration presents an additional challenge with its requirement for a high update rate. As a result, most real-time surgical simulation systems employ a linear elasticity model, simplified numerical methods such as the boundary element method or spring-particle systems, and coarse volumetric meshes. However, these systems are not clinically realistic. We present here an ongoing work aimed at developing an efficient and physically realistic neurosurgery simulator using a non-linear finite element method (FEM) with haptic interaction. Real-time finite element analysis is achieved by utilizing the total Lagrangian explicit dynamic (TLED) formulation and GPU acceleration of per-node and per-element operations. We employ a virtual coupling method for separating deformable body simulation and collision detection from haptic rendering, which needs to be updated at a much higher rate than the visual simulation. The system provides accurate biomechancial modeling of soft tissue while retaining a real-time performance with haptic interaction. However, our experiments showed that the stability of the simulator depends heavily on the material property of the tissue and the speed of colliding objects. Hence, additional efforts including dynamic relaxation are required to improve the stability of the system.
The neurochemical mobile with non-linear interaction matrix: an exploratory computational model.
Qi, Z; Fieni, D; Tretter, F; Voit, E O
2013-05-01
Several years ago, the "neurochemical mobile" was introduced as a visual tool for explaining the different balances between neurotransmitters in the brain and their role in mental disorders. Here we complement this concept with a non-linear computational systems model representing the direct and indirect interactions between neurotransmitters, as they have been described in the "neurochemical interaction matrix." The model is constructed within the framework of biochemical systems theory, which facilitates the mapping of numerically ill-characterized systems into a mathematical and computational construct that permits a variety of analyses. Simulations show how short- and long-term perturbations in any of the neurotransmitters migrate through the entire system, thereby affecting the balances within the mobile. In cases of short-term alterations, transients are of particular interest, whereas long-term changes shed light on persistently altered, allostatic states, which in mental diseases and sleep disorders could be due to a combination of unfavorable factors, resulting from a specific genetic predisposition, epigenetic effects, disease, or the repeated use of drugs, such as opioids and amphetamines.
The late Universe with non-linear interaction in the dark sector: the coincidence problem
Bouhmadi-López, Mariam; Zhuk, Alexander
2016-01-01
We study the Universe at the late stage of its evolution and deep inside the cell of uniformity. At such a scale the Universe is highly inhomogeneous and filled with discretely distributed inhomogeneities in the form of galaxies and groups of galaxies. As a matter source, we consider dark matter (DM) and dark energy (DE) with a non-linear interaction $Q = 3\\mathcal{H}\\gamma \\overline\\varepsilon_{\\mathrm{DE}} \\overline\\varepsilon_{\\mathrm{DM}} / (\\overline\\varepsilon_{\\mathrm{DE}} + \\overline\\varepsilon_{\\mathrm{DM}})$, where $\\gamma$ is a constant. We assume that DM is pressureless and DE has a constant equation of state parameter $w$. In the considered model, the energy densities of the dark sector components present a scaling behaviour with $\\overline\\varepsilon_{\\mathrm{DM}} / \\overline\\varepsilon_{\\mathrm{DE}} \\sim \\left({a_0} / {a} \\right)^{-3(w+\\gamma)}$. We investigate the possibility that the perturbations of DM and DE, which are interacting among themselves, could be coupled to the galaxies with the ...
Neurosurgery simulation using non-linear finite element modeling and haptic interaction
Lee, Huai-Ping; Audette, Michel; Joldes, Grand R.; Enquobahrie, Andinet
2012-02-01
Real-time surgical simulation is becoming an important component of surgical training. To meet the realtime requirement, however, the accuracy of the biomechancial modeling of soft tissue is often compromised due to computing resource constraints. Furthermore, haptic integration presents an additional challenge with its requirement for a high update rate. As a result, most real-time surgical simulation systems employ a linear elasticity model, simplified numerical methods such as the boundary element method or spring-particle systems, and coarse volumetric meshes. However, these systems are not clinically realistic. We present here an ongoing work aimed at developing an efficient and physically realistic neurosurgery simulator using a non-linear finite element method (FEM) with haptic interaction. Real-time finite element analysis is achieved by utilizing the total Lagrangian explicit dynamic (TLED) formulation and GPU acceleration of per-node and per-element operations. We employ a virtual coupling method for separating deformable body simulation and collision detection from haptic rendering, which needs to be updated at a much higher rate than the visual simulation. The system provides accurate biomechancial modeling of soft tissue while retaining a real-time performance with haptic interaction. However, our experiments showed that the stability of the simulator depends heavily on the material property of the tissue and the speed of colliding objects. Hence, additional efforts including dynamic relaxation are required to improve the stability of the system.
DEFF Research Database (Denmark)
Castaldi, P J; Demeo, D L; Hersh, C P;
2010-01-01
with COPD. Using data from the Alpha-1 Antitrypsin Genetic Modifiers Study, the accuracy and power of two different approaches to model smoking were compared by performing a simulation study of a genetic variant with a range of gene-by-smoking interaction effects. Results Non-linear relationships between...
Institute of Scientific and Technical Information of China (English)
兰朝凤; 李凤臣; 陈欢; 卢迪; 杨德森; 张梦
2015-01-01
Based on the Burgers equation and Manley-Rowe equation, the derivation about nonlinear interaction of the acoustic waves has been done in this paper. After nonlinear interaction among the low-frequency weak waves and the pump wave, the analytical solutions of acoustic waves’ amplitude in the field are deduced. The relationship between normalized energy of high-frequency and the change of acoustic energy before and after the nonlinear interaction of the acoustic waves is analyzed. The experimental results about the changes of the acoustic energy are presented. The study shows that new frequencies are generated and the energies of the low-frequency are modulated in a long term by the pump waves, which leads the energies of the low-frequency acoustic waves to change in the pulse trend in the process of the nonlinear interaction of the acoustic waves. The increase and decrease of the energies of the low-frequency are observed under certain typical conditions, which lays a foundation for practical engineering applications.
Steffen, T; Tanimura, Y
2000-01-01
The quantum Fokker-Planck equation is derived for a system nonlinearly coupled to a harmonic oscillator bath. The system-bath interaction is assumed to be linear in the bath coordinates but quadratic in the system coordinate. The relaxation induced dynamics of a harmonic system are investigated by s
Sapsis, T.; Dijkstra, H.A.
2013-01-01
In this paper the authors study the interactions of additive noise and nonlinear dynamics in a quasi-geostrophicmodel of the double-gyre wind-driven ocean circulation. The recently developed framework of dynamically orthogonal field theory is used to determine the statistics of the flows that arise
Electrostatic interactions between particles through heterogeneous fluid phases.
Kang, Dong Woo; Lee, Mina; Kim, Kyung Hak; Xia, Ming; Im, Sang Hyuk; Park, Bum Jun
2017-09-27
We investigated the electrostatic interactions between particles acting through heterogeneous fluid phases. An oil lens system floating on the surface of water was used to trap particles at different fluid-fluid interfaces. The inner particles are located at the centrosymmetrically curved oil-water interface inside the oil lens while satellite particles are located at the curved air-water interface, separated by a particular distance from the triple phase boundary. The satellite particles are likely to be captured in an energy minimum state due to electrostatic repulsions by the inner particles balanced with the gravity-induced potential energy. As the size of the oil lens decreases upon evaporation, the satellite particles escape from the gravitational confinement at a critical moment. The self-potential values of the inner particles and the satellite particles were calculated by employing an energy balance and the experimentally obtained geometric parameter values. It was found that the self-potential values of the inner particles decrease as oil evaporates over time and that the magnitude of the self-potential of the satellite particles is a hundred times larger than that of the inner particles. These results demonstrate significant effects of the thickness and shape of the nonpolar superphase on the electrostatic interactions between the particles trapped at different fluid-fluid interfaces.
Astra, Egon; Olsson, Samuel L I; Eliasson, Henrik; Andrekson, Peter A
2017-06-12
We present an investigation of dispersion map optimization for two-span single-channel 28 GBaud QPSK transmission systems with phase-sensitive amplifiers (PSAs). In experiments, when the PSA link is operated in a highly nonlinear regime, a 1.4 dB error vector magnitude (EVM) improvement is achieved compared to a one-span optimized dispersion map link due to improved nonlinearity mitigation. The two-span optimized dispersion map of a PSA link differs from the optimized dispersion map of a dispersion managed phase-insensitive amplifier (PIA) link. Simulations show that the performance of the two-span dispersion map optimized PSA link does not improve by residual dispersion optimization. Further, by using the two-span optimized dispersion maps repeatedly in a long-haul PSA link instead of one-span optimized maps, the maximum transmission reach can be improved 1.5 times.
Fluid-structure interaction of complex bodies in two-phase flows on locally refined grids
Angelidis, Dionysios; Shen, Lian; Sotiropoulos, Fotis
2016-11-01
Many real-life flow problems in engineering applications involve fluid-structure interaction (FSI) of arbitrarily complex geometries interacting with free surface flows. Despite the recent significant computational advances, conventional numerical methods are inefficient to resolve the prevailing complex dynamics due to the inherent large disparity of spatial and temporal scales that emerge in the air/water phases of the flow and around rigid bodies. To this end, the new generation 3D, unsteady, unstructured Cartesian incompressible flow solver, developed at the Saint Anthony Falls Laboratory (SAFL), is integrated with a FSI immersed boundary method and is coupled with the level-set formulation. The predictive capabilities of our method to simulate non-linear free surface phenomena, with low computational cost, are significantly improved by locally refining the computational grid in the vicinity of solid boundaries and around the free surface interface. We simulate three-dimensional complex flows involving complex rigid bodies interacting with a free surface both with prescribed body motion and coupled FSI and we investigate breaking wave events. In all the cases, very good agreement with benchmark data is found. This material is based upon work supported by the National Science Foundation (CBET-1509071).
Topological Phases of Interacting Bosons on the Kagome Lattice
Roychowdhury, Krishanu; Bhattacharjee, Subhro; Pollmann, Frank
2015-03-01
We consider an extended Hubbard model of hard core bosons including nearest-neighbour hopping and long range repulsive interactions on a kagome lattice. The system is an insulator at commensurate fillings of 1/6, 1/3 and 1/2 and can be mapped to different dimer models on the triangular lattice (depending on the filling). We focus on the filling of 1/3, which transforms to a fully packed loop (FPL) model, and derive the full phase diagram in the low-energy subspace. Similar to the quantum dimer model and easy-axis kagome antiferromagnetic model studied before, we find an extended region of a gapped Z2 liquid with vison excitations. The gauge fluctuations, responsible for the vison modes, are dictated by the action of an even Ising gauge theory. In the ordered phase, where the vison gap closes, we observe a 3-fold rotationally symmetric loop ordering and present the critical theory for the amplitude fluctuations of the condensed modes. We also speculate the phase diagram for the fermionic counterpart of the model at all the above mentioned fractional fillings.
Hendi, S H; Momennia, M
2015-01-01
In this paper, we consider quadratic Maxwell invariant as a correction to the Maxwell theory and study thermodynamic behavior of the black holes in Einstein (EN) and Gauss-Bonnet (GB) gravities. We consider cosmological constant as a thermodynamic pressure to extend phase space. Next, we obtain critical values in case of variation of nonlinearity and GB parameters. We generalized the study by considering the effects of dimensionality on critical values and make comparisons between our models with their special sub classes.
The two-phase issue in the O(n) non-linear $\\sigma$-model: A Monte Carlo study
Alles, B.; Buonanno, A.; Cella, G.
1996-01-01
We have performed a high statistics Monte Carlo simulation to investigate whether the two-dimensional O(n) non-linear sigma models are asymptotically free or they show a Kosterlitz- Thouless-like phase transition. We have calculated the mass gap and the magnetic susceptibility in the O(8) model with standard action and the O(3) model with Symanzik action. Our results for O(8) support the asymptotic freedom scenario.
Jaishankar, Aditya; Wee, May; Matia-Merino, Lara; Goh, Kelvin K T; McKinley, Gareth H
2015-06-05
Mamaku gum is a polysaccharide extracted from the fronds of the black tree fern found in New Zealand. The cooked pith has traditionally been used for various medicinal purposes and as a food source by the Maori people of New Zealand. It has potential applications as a thickener in the food industry and as a palliative for patients with dysphagia. Studies on the shear rheology of Mamaku gum have revealed that the gum exhibits shear thickening at a critical shear rate due to a transition from intra- to inter-molecular chain interactions upon shear-induced chain elongation. In this paper, we demonstrate that these interactions are primarily due to hydrogen bonding. We perform extensional rheology on mixtures of Mamaku gum and urea (a known disruptor of hydrogen bonds) to quantify the nature of these interactions. Capillary Breakup Extensional Rheometry (CaBER) performed on the pure Mamaku gum solutions yield plateau values of the Trouton ratio as high as ∼10(4), showing that the viscoelasticity of the gum in uniaxial elongation is much higher than in shear. For all Mamaku concentrations tested, the extensional viscosity decreases upon increasing urea concentration. Furthermore, the relaxation time decreases exponentially with increasing urea concentration. This exponential relationship is independent of the Mamaku concentration, and is identical to the relationships between urea concentration and characteristic timescales measured in nonlinear shear rheology. We show using the sticky reptation model for polymers with multiple sticker groups along the backbone how such a relationship is consistent with a linear decrease in the free energy for hydrogen bond dissociation. We then demonstrate that a time-concentration superposition principle can be used to collapse the viscoelastic properties of the Mamaku-gum/urea mixtures. Copyright © 2015 Elsevier Ltd. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Molin, B. [Ecole Generaliste d' Ingenieurs de Marseille, 13 (France)
2006-03-15
At first approximation, the study of wave interaction with fixed or floating bodies is carried out within a linear frame. However nonlinear effects are numerous and they have diverse origins: mechanical nonlinearities, variation in time of the wetted part of the hull, viscous phenomena (flow separation), nonlinear free surface equations. We focus here on the latter type of nonlinearities. Two different approaches are described, both being based on potential flow theory. Practical applications are given for two basic geometries: a vertical cylinder and a vertical plate, perpendicular to the wave direction. In the first approach, one proceeds through successive approximations, based on a perturbation series development. The first-order of approximation coincides with the linear theory. The main interest of the second-order of approximation, well mastered nowadays, is that it yields excitation loads in an enlarged frequency domain, encompassing most of the natural frequencies of the system considered. At third-order the complexity of the equations becomes dissuasive and few researchers have ventured there. We suggest that third-order (or tertiary) interactions, between incoming waves and reflected waves by the structure, can play a very important role, overlooked so far, in phenomena such as run-up or green water. In the second approach one integrates in time and space the nonlinear equations of the initial boundary value problem, with the free surface equations being exactly satisfied. In this way one obtains numerical equivalents of the physical wave-tanks. They are briefly described and some illustrative results are given. (authors)
Energy Technology Data Exchange (ETDEWEB)
Bai, Xiao-Dong; Ai, Qing; Zhang, Mei; Xiong, Jun, E-mail: junxiong@bnu.edu.cn; Yang, Guo-Jian; Deng, Fu-Guo
2015-09-15
We investigate the stability and phase transition of localized modes in Bose–Einstein Condensates (BECs) in an optical lattice with the discrete nonlinear Schrödinger model by considering both two- and three-body interactions. We find that there are three types of localized modes, bright discrete breather (DB), discrete kink (DK), and multi-breather (MUB). Moreover, both two- and three-body on-site repulsive interactions can stabilize DB, while on-site attractive three-body interactions destabilize it. There is a critical value for the three-body interaction with which both DK and MUB become the most stable ones. We give analytically the energy thresholds for the destabilization of localized states and find that they are unstable (stable) when the total energy of the system is higher (lower) than the thresholds. The stability and dynamics characters of DB and MUB are general for extended lattice systems. Our result is useful for the blocking, filtering, and transfer of the norm in nonlinear lattices for BECs with both two- and three-body interactions.
Loures, Cristian Redondo; Biancalana, Fabio
2014-01-01
We study the influence of third-harmonic generation (THG) and negative frequency polarization terms in the self-phase modulation (SPM) of short and intense pulses in Kerr media. We find that THG induces additional symmetric lobes in the SPM process. The amplitude of these new sidebands are greatly enhanced by the contributions of the negative frequency Kerr (NFK) term and the shock operator. We compare our theoretical predictions based on the analytical nonlinear phase with simulations carried out by using the full unidirectional pulse propagation equation (UPPE).
DEFF Research Database (Denmark)
Liu, Xing; Zhou, Binbin; Guo, Hairun;
2015-01-01
in a quadratic nonlinear crystal (beta-barium borate) in the normal dispersion regime due to cascaded (phase-mismatched) second-harmonic generation, and the mid-IR converted wave is formed in the anomalous dispersion regime between. lambda = 2.2-2.4 mu m as a resonant dispersive wave. This process relies...... on nondegenerate four-wave mixing mediated by an effective negative cross-phase modulation term caused by cascaded soliton-probe sum-frequency generation. (C) 2015 Optical Society of America...
Energy Technology Data Exchange (ETDEWEB)
Camporeale, Enrico, E-mail: e.camporeale@cwi.nl [Center for Mathematics and Computer Science (CWI), 1098 XG Amsterdam (Netherlands); Zimbardo, Gaetano [Department of Physics, University of Calabria, Ponte P. Bucci, Cubo 31C, I-87036 Rende (Italy)
2015-09-15
We present a self-consistent Particle-in-Cell simulation of the resonant interactions between anisotropic energetic electrons and a population of whistler waves, with parameters relevant to the Earth's radiation belt. By tracking PIC particles and comparing with test-particle simulations, we emphasize the importance of including nonlinear effects and time evolution in the modeling of wave-particle interactions, which are excluded in the resonant limit of quasi-linear theory routinely used in radiation belt studies. In particular, we show that pitch angle diffusion is enhanced during the linear growth phase, and it rapidly saturates well before a single bounce period. This calls into question the widely used bounce average performed in most radiation belt diffusion calculations. Furthermore, we discuss how the saturation is related to the fact that the domain in which the particles pitch angle diffuses is bounded, and to the well-known problem of 90° diffusion barrier.
Camporeale, Enrico
2014-01-01
We present self-consistent Particle-in-Cell simulations of the resonant interactions between anisotropic energetic electrons and a population of whistler waves, with parameters relevant to the Earth's radiation belt. By tracking PIC particles, and comparing with test-particles simulations we emphasize the importance of including nonlinear effects and time evolution in the modeling of wave-particle interactions, which are excluded in the resonant limit of quasi-linear theory routinely used in radiation belt studies. In particular we show that pitch angle diffusion is enhanced during the linear growth phase, and it rapidly saturates. We discuss how the saturation is related to the fact that the domain in which the particles' pitch angle diffuse is bounded, and to the well-known problem of $90^\\circ$ diffusion barrier.
H-infinity control for cascade minimum-phase switched nonlinear systems
Institute of Scientific and Technical Information of China (English)
Shengzhi ZHAO; Jun ZHAO
2005-01-01
This paper is concerned with the H-infinity control problem for a class of cascade switched nonlinear systems.Each switched system in this class is composed of a zero-input asymptotically stable nonlinear part,which is also a switched system,and a linearizable part which is controllable.Conditions under which the H-infinity control problem is solvable under arbitrary switching law and under some designed switching law are derived respectively.The nonlinear state feedback and switching law are designed.We exploit the structural characteristics of the switched nonlinear systems to construct common Lyapunov functions for arbitrary switching and to find a single Lyapunov function for designed switching law.The proposed methods do not rely on the solutions of Hamilton-Jacobi inequalities.
1986-12-05
nonlinear oscillators described by a Duffing equation (e.g., a mass on a nonlinear spring,. The period-doubling transition to chaos is perhaps the more...resonance tube to exhibit characteristics similar to those of a mass-nonlinear spring oscillator . When driven hard, a hard spring oscillator , for example...same results was performed a bit later at the Naval Postgraduate School (NPS) by Ruff [30]. Coupled oscillators The work Breazeale began was taken up
Foster, J. C.; Erickson, P. J.; Omura, Y.; Baker, D. N.; Kletzing, C. A.; Claudepierre, S. G.
2017-01-01
Prompt recovery of MeV (millions of electron Volts) electron populations in the poststorm core of the outer terrestrial radiation belt involves local acceleration of a seed population of energetic electrons in interactions with VLF chorus waves. Electron interactions during the generation of VLF rising tones are strongly nonlinear, such that a fraction of the relativistic electrons at resonant energies are trapped by waves, leading to significant nonadiabatic energy exchange. Through detailed examination of VLF chorus and electron fluxes observed by Van Allen Probes, we investigate the efficiency of nonlinear processes for acceleration of electrons to MeV energies. We find through subpacket analysis of chorus waveforms that electrons with initial energy of hundreds of keV to 3 MeV can be accelerated by 50 keV-200 keV in resonant interactions with a single VLF rising tone on a time scale of 10-100 ms.
DEFF Research Database (Denmark)
Da Ros, Francesco; Dalgaard, Kjeld; Lei, Lei
2013-01-01
A phase-sensitive four-wave mixing (FWM) scheme enabling the simultaneous conversion of the two orthogonal quadratures of an optical signal to different wavelengths is demonstrated for the first time under dynamic operation using a highly nonlinear optical fiber (HNLF) as the nonlinear medium....... The scheme is first optimized with respect to the power levels and phases of the four phase-coherent pumps. The successful modulation and wavelength conversion of the two complex quadratures of a quadrature phase-shift keying (QPSK) signal to two binary phase-shift keying (BPSK) signals is then demonstrated...
DEFF Research Database (Denmark)
Deng, Lei; Pang, Xiaodan; Tafur Monroy, Idelfonso
2014-01-01
We propose a nonlinearity and phase noise tolerant orthogonal frequency division multiplexing (OFDM) W-band signal over fiber system based on phase modulation and photonic heterodyne up-conversion techniques. By heterodyne mixing the phase-modulated optical OFDM signal with a free-running laser...... in the photodiode, the constant envelope OFDM W-band wireless signal is obtained to suppress the nonlinear impairments. Moreover, the phase noises of the beating lasers appear as additive terms to the desired signal, and could be easily filtered out without complex phase noise estimation and compensation algorithms...
Energy Technology Data Exchange (ETDEWEB)
Gandomzadeh, Ali
2011-02-08
The interaction of the soil with the structure has been largely explored the assumption of material and geometrical linearity of the soil. Nevertheless, for moderate or strong seismic events, the maximum shear strain can easily reach the elastic limit of the soil behavior. Considering soil-structure interaction, the nonlinear effects may change the soil stiffness at the base of the structure and therefore energy dissipation into the soil. Consequently, ignoring the nonlinear characteristics of the dynamic soil-structure interaction (DSSI) this phenomenon could lead to erroneous predictions of structural response. The goal of this work is to implement a fully nonlinear constitutive model for soils into a numerical code in order to investigate the effect of soil nonlinearity on dynamic soil structure interaction. Moreover, different issues are taken into account such as the effect of confining stress on the shear modulus of the soil, initial static condition, contact elements in the soil-structure interface, etc. During this work, a simple absorbing layer method based on a Rayleigh/Caughey damping formulation, which is often already available in existing Finite Element softwares, is also presented. The stability conditions of the wave propagation problems are studied and it is shown that the linear and nonlinear behavior are very different when dealing with numerical dispersion. It is shown that the 10 points per wavelength rule, recommended in the literature for the elastic media is not sufficient for the nonlinear case. The implemented model is first numerically verified by comparing the results with other known numerical codes. Afterward, a parametric study is carried out for different types of structures and various soil profiles to characterize nonlinear effects. Different features of the DSSI are compared to the linear case: modification of the amplitude and frequency content of the waves propagated into the soil, fundamental frequency, energy dissipation in
Interaction of stress and phase transformations during thermochemical surface engineering
DEFF Research Database (Denmark)
Jespersen, Freja Nygaard
Low temperature nitriding of austenitic stainless steel causes a surface zone of expanded austenite, which improves the wear resistance of the stainless steel while preserving the stainless behavior. During nitriding huge residual stresses are introduced in the treated zone, arising from the volume...... expansion that accompanies the dissolution of high nitrogen contents in expanded austenite. An intriguing phenomenon during low-temperature nitriding, is that the residual stresses evoked by dissolution of nitrogen in the solid state, affect the thermodynamics and the diffusion kinetics of nitrogen...... dissolution. The present project is devoted to understanding the mutual interaction of stresses and phase transformations during thermochemical surface engineering by combining numerical modelling with experimental materials science. The modelling was done by combining solid mechanics with thermodynamics...
Strongly Interacting Fermions and Phases of the Casimir Effect
Flachi, Antonino
2013-01-01
With the intent of exploring how the interplay between boundary effects and chiral symmetry breaking may alter the thermodynamical behavior of a system of strongly interacting fermions, we study the Casimir effect for the set-up of two parallel layers using a four-fermion effective field theory at zero density. This system reveals a number of interesting features. While for infinitely large separation (no boundaries), chiral symmetry is broken/restored via a second order phase transition, in the opposite case of small (and, in general, finite) separation the transition becomes first order, rendering effects of finite size, for the present set-up, similar to those of a chemical potential. Appropriately moving on the separation--temperature plane, it is possible to generate a peculiar behavior in the temperature dependence of the thermodynamic potential and of the condensate, compensating thermal with geometrical variations. A behavior similar to what we find here has been predicted to occur in bilayer graphene...
Elenchezhiyan, M; Prakash, J
2015-09-01
In this work, state estimation schemes for non-linear hybrid dynamic systems subjected to stochastic state disturbances and random errors in measurements using interacting multiple-model (IMM) algorithms are formulated. In order to compute both discrete modes and continuous state estimates of a hybrid dynamic system either an IMM extended Kalman filter (IMM-EKF) or an IMM based derivative-free Kalman filters is proposed in this study. The efficacy of the proposed IMM based state estimation schemes is demonstrated by conducting Monte-Carlo simulation studies on the two-tank hybrid system and switched non-isothermal continuous stirred tank reactor system. Extensive simulation studies reveal that the proposed IMM based state estimation schemes are able to generate fairly accurate continuous state estimates and discrete modes. In the presence and absence of sensor bias, the simulation studies reveal that the proposed IMM unscented Kalman filter (IMM-UKF) based simultaneous state and parameter estimation scheme outperforms multiple-model UKF (MM-UKF) based simultaneous state and parameter estimation scheme.
Directory of Open Access Journals (Sweden)
R. Rabenstein
2004-06-01
Full Text Available The functional transformation method (FTM is a well-established mathematical method for accurate simulations of multidimensional physical systems from various fields of science, including optics, heat and mass transfer, electrical engineering, and acoustics. This paper applies the FTM to real-time simulations of transversal vibrating strings. First, a physical model of a transversal vibrating lossy and dispersive string is derived. Afterwards, this model is solved with the FTM for two cases: the ideally linearly vibrating string and the string interacting nonlinearly with the frets. It is shown that accurate and stable simulations can be achieved with the discretization of the continuous solution at audio rate. Both simulations can also be performed with a multirate approach with only minor degradations of the simulation accuracy but with preservation of stability. This saves almost 80% of the computational cost for the simulation of a six-string guitar and therefore it is in the range of the computational cost for digital waveguide simulations.
Vučićević, Katarina; Jovanović, Marija; Golubović, Bojana; Kovačević, Sandra Vezmar; Miljković, Branislava; Martinović, Žarko; Prostran, Milica
2015-02-01
The present study aimed to establish population pharmacokinetic model for phenobarbital (PB), examining and quantifying the magnitude of PB interactions with other antiepileptic drugs concomitantly used and to demonstrate its use for individualization of PB dosing regimen in adult epileptic patients. In total 205 PB concentrations were obtained during routine clinical monitoring of 136 adult epilepsy patients. PB steady state concentrations were measured by homogeneous enzyme immunoassay. Nonlinear mixed effects modelling (NONMEM) was applied for data analyses and evaluation of the final model. According to the final population model, significant determinant of apparent PB clearance (CL/F) was daily dose of concomitantly given valproic acid (VPA). Typical value of PB CL/F for final model was estimated at 0.314 l/h. Based on the final model, co-therapy with usual VPA dose of 1000 mg/day, resulted in PB CL/F average decrease of about 25 %, while 2000 mg/day leads to an average 50 % decrease in PB CL/F. Developed population PB model may be used in estimating individual CL/F for adult epileptic patients and could be applied for individualizing dosing regimen taking into account dose-dependent effect of concomitantly given VPA.
Nagatomo, Makoto; Kaya, Nobuyuki; Matsumoto, Hiroshi
The Microwave Ionosphere Nonlinear Interaction Experiment (MINIX) is a sounding rocket experiment to study possible effects of strong microwave fields in case it is used for energy transmission from the Solar Power Satellite (SPS) upon the Earth's atmosphere. Its secondary objective is to develop high power microwave technology for space use. Two rocket-borne magnetrons were used to emit 2.45 GHz microwave in order to make a simulated condition of power transmission from an SPS to a ground station. Sounding of the environment radiated by microwave was conducted by the diagnostic package onboard the daughter unit which was separated slowly from the mother unit. The main design drivers of this experiment were to build such high power equipments in a standard type of sounding rocket, to keep the cost within the budget and to perform a series of experiments without complete loss of the mission. The key technology for this experiment is a rocket-borne magnetron and high voltage converter. Location of position of the daughter unit relative to the mother unit was a difficult requirement for a spin-stabilized rocket. These problems were solved by application of such a low cost commercial products as a magnetron for microwave oven and a video tape recorder and camera.
The late Universe with non-linear interaction in the dark sector: The coincidence problem
Bouhmadi-López, Mariam; Morais, João; Zhuk, Alexander
2016-12-01
We study the Universe at the late stage of its evolution and deep inside the cell of uniformity. At such a scale the Universe is highly inhomogeneous and filled with discretely distributed inhomogeneities in the form of galaxies and groups of galaxies. As a matter source, we consider dark matter (DM) and dark energy (DE) with a non-linear interaction Q = 3 HγεbarDEεbarDM /(εbarDE +εbarDM) , where γ is a constant. We assume that DM is pressureless and DE has a constant equation of state parameter w. In the considered model, the energy densities of the dark sector components present a scaling behaviour with εbarDM /εbarDE ∼(a0 / a) - 3(w + γ). We investigate the possibility that the perturbations of DM and DE, which are interacting among themselves, could be coupled to the galaxies with the former being concentrated around them. To carry our analysis, we consider the theory of scalar perturbations (within the mechanical approach), and obtain the sets of parameters (w , γ) which do not contradict it. We conclude that two sets: (w = - 2 / 3 , γ = 1 / 3) and (w = - 1 , γ = 1 / 3) are of special interest. First, the energy densities of DM and DE on these cases are concentrated around galaxies confirming that they are coupled fluids. Second, we show that for both of them, the coincidence problem is less severe than in the standard ΛCDM. Third, the set (w = - 1 , γ = 1 / 3) is within the observational constraints. Finally, we also obtain an expression for the gravitational potential in the considered model.
Zhang, Guoqiang; Yan, Zhenya; Wen, Xiao-Yong; Chen, Yong
2017-04-01
We investigate the defocusing coupled nonlinear Schrödinger equations from a 3 ×3 Lax pair. The Darboux transformations with the nonzero plane-wave solutions are presented to derive the newly localized wave solutions including dark-dark and bright-dark solitons, breather-breather solutions, and different types of new vector rogue wave solutions, as well as interactions between distinct types of localized wave solutions. Moreover, we analyze these solutions by means of parameters modulation. Finally, the perturbed wave propagations of some obtained solutions are explored by means of systematic simulations, which demonstrates that nearly stable and strongly unstable solutions. Our research results could constitute a significant contribution to explore the distinct nonlinear waves (e.g., dark solitons, breather solutions, and rogue wave solutions) dynamics of the coupled system in related fields such as nonlinear optics, plasma physics, oceanography, and Bose-Einstein condensates.
DEFF Research Database (Denmark)
Da Ros, Francesco; Marco Calabrese, Pachito; Kang, Ning;
2013-01-01
Phase-sensitive processes exploiting FWM in an HNLF allow simultaneously converting two orthogonal quadratures of an optical signal to different wavelengths. Conversion efficiencies to two 90°-phase-shifted idlers exceeding 10dB of phase-sensitive extinction ratio are obtained experimentally....
Energy Technology Data Exchange (ETDEWEB)
Angelin Jeba, K.; Latha, M. M., E-mail: lathaisaac@yahoo.com [Department of Physics, Women' s Christian College, Nagercoil 629 001 (India); Jain, Sudhir R. [Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai 400085 (India)
2015-11-15
The nonlinear dynamics of intra- and inter-spine interaction models of alpha-helical proteins is investigated by proposing a Hamiltonian using the first quantized operators. Hamilton's equations of motion are derived, and the dynamics is studied by constructing the trajectories and phase space plots in both cases. The phase space plots display a chaotic behaviour in the dynamics, which opens questions about the relationship between the chaos and exciton-exciton and exciton-phonon interactions. This is verified by plotting the Lyapunov characteristic exponent curves.
Angelin Jeba, K; Latha, M M; Jain, Sudhir R
2015-11-01
The nonlinear dynamics of intra- and inter-spine interaction models of alpha-helical proteins is investigated by proposing a Hamiltonian using the first quantized operators. Hamilton's equations of motion are derived, and the dynamics is studied by constructing the trajectories and phase space plots in both cases. The phase space plots display a chaotic behaviour in the dynamics, which opens questions about the relationship between the chaos and exciton-exciton and exciton-phonon interactions. This is verified by plotting the Lyapunov characteristic exponent curves.
Halladay, Kate; Good, Peter
2016-11-01
We present a detailed analysis of mechanisms underlying the evapotranspiration response to increased {CO}_2 in HadGEM2-ES, focussed on western Amazonia. We use three simulations from CMIP5 in which atmospheric {CO}_2 increases at 1% per year reaching approximately four times pre-industrial levels after 140 years. Using 3-hourly data, we found that evapotranspiration (ET) change was dominated by decreased stomatal conductance (g_s ), and to a lesser extent by decreased canopy water and increased moisture gradient (specific humidity difference between surface and near-surface). There were large, non-linear decreases in ET in the simulation in which radiative and physiological forcings could interact. This non-linearity arises from non-linearity in the conductance term (includes aerodynamic and stomatal resistance and partitioning between the two, which is determined by canopy water availability), the moisture gradient, and negative correlation between these two terms. The conductance term is non-linear because GPP responds non-linearly to temperature and GPP is the dominant control on g_s in HadGEM2-ES. In addition, canopy water declines, mainly due to increases in potential evaporation, which further decrease the conductance term. The moisture gradient responds non-linearly owing to the non-linear response of temperature to {CO}_2 increases, which increases the Bowen ratio. Moisture gradient increases resulting from ET decline increase ET and thus constitute a negative feedback. This analysis highlights the importance of the g_s parametrisation in determining the ET response and the potential differences between offline and online simulations owing to feedbacks on ET via the atmosphere, some of which would not occur in an offline simulation.
Jiang, Y; Poggiolini, P; Forghieri, F
2014-01-01
We accurately characterize nonlinear phase noise in uncompensated coherent optical systems. We find that, though present, its impact on system performance is typically negligible in a wide range of practical system scenarios.
DEFF Research Database (Denmark)
Hu, Hao; Jopson, R. M.; Gnauck, A. H.;
2016-01-01
We demonstrate compensation of fiber nonlinearities using repeated optical phase conjugation (OPC) in a WDM system with eight 32-Gbaud PDM 16-QAM channels, showing improved performance over a single mid-span OPC and no OPC....
DEFF Research Database (Denmark)
Da Ros, Francesco; Sackey, I.; Jazayerifar, M.
2015-01-01
Kerr nonlinearity compensation by optical phase conjugation is demonstrated in a WDM PDM 16-QAM system. Improved received signal quality is reported for both dispersion-compensated and dispersion-uncompensated transmission and a comparison with digital backpropagation is provided....
Phase Diagram and Phase Separation of a Trapped Interacting Bose-Fermi Gas Mixture
Institute of Scientific and Technical Information of China (English)
MA Yong-Li
2004-01-01
@@ In six different regimes for a spatial phase diagram of a trapped interacting Bose-Fermi gas mixture at low temperatures, we present the conditions for the spatial demixing and separation of bosons and fermions. Starting from a semiclassically thermodynamic model for the local density functional of thermal bosons and fermions,the explicit analytical expressions for the fugacities of bosons and fermions are derived in different regimes by means of a first-order perturbation method in a local-density approximation. The critical values of the fermionboson interaction strength as a function of the fractional composition of fermions have a general feature: increase,extreme and decrease with increasing the fermionic composition slightly above Bose-Einstein critical temperature.
Builes-Jaramillo, Alejandro; Marwan, Norbert; Poveda, Germán; Kurths, Jürgen
2017-07-01
We study the physical processes involved in the potential influence of Amazon (AM) hydroclimatology over the Tropical North Atlantic (TNA) Sea Surface Temperatures (SST) at interannual timescales, by analyzing time series of the precipitation index (P-E) over AM, as well as the surface atmospheric pressure gradient between both regions, and TNA SSTs. We use a recurrence joint probability based analysis that accounts for the lagged nonlinear dependency between time series, which also allows quantifying the statistical significance, based on a twin surrogates technique of the recurrence analysis. By means of such nonlinear dependence analysis we find that at interannual timescales AM hydrology influences future states of the TNA SSTs from 0 to 2 months later with a 90-95% statistical confidence. It also unveils the existence of two-way feedback mechanisms between the variables involved in the processes: (1) precipitation over AM leads the atmospheric pressure gradient between TNA and AM from 0 to 2 month lags, (2) the pressure gradient leads the trade zonal winds over the TNA from 0 to 3 months and from 7 to 12 months, (3) the zonal winds lead the SSTs from 0 to 3 months, and (4) the SSTs lead precipitation over AM by 1 month lag. The analyses were made for time series spanning from 1979 to 2008, and for extreme precipitation events in the AM during the years 1999, 2005, 2009 and 2010. We also evaluated the monthly mean conditions of the relevant variables during the extreme AM droughts of 1963, 1980, 1983, 1997, 1998, 2005, and 2010, and also during the floods of 1989, 1999, and 2009. Our results confirm that the Amazon River basin acts as a land surface-atmosphere bridge that links the Tropical Pacific and TNA SSTs at interannual timescales. The identified mutual interactions between TNA and AM are of paramount importance for a deeper understanding of AM hydroclimatology but also of a suite of oceanic and atmospheric phenomena over the TNA, including recently
Nonlinearity Role in Long-Term Interaction of the Ocean Gravity Waves
2012-09-30
the Nonlinear Schrodinger equation and its exact solutions. Numerical simulations of the fully nonlinear Euler equation have also been performed in... Schrodinger breathers, Proceedings of ECMWF Workshop on "Ocean Waves" - 25 to 27 June 2012 [published] • Onorato, M. and Proment, D.; Approximate rogue wave
A Non-smooth Nonlinear Conjugate Gradient Method for Interactive Contact Force Problems
DEFF Research Database (Denmark)
Silcowitz, Morten; Niebe, Sarah Maria; Erleben, Kenny
2010-01-01
of a nonlinear complementarity problem (NCP), which can be solved using an iterative splitting method, such as the projected Gauss–Seidel (PGS) method. We present a novel method for solving the NCP problem by applying a Fletcher–Reeves type nonlinear nonsmooth conjugate gradient (NNCG) type method. We analyze...
Tawfik, Walid
2016-08-01
A source of white-light radiation that generates few-cycle pulses with controlled peak power values has been developed. These ultrafast pulses have been observed by spectral broadening of 32 fs pulses through nonlinear self-phase modulation in a neon-filled hollow-fiber then compressed with a pair of chirped mirrors for dispersion compensation. The observed pulses reached transform-limited duration of 5.77 fs and their peak power values varied from 57 GW up to 104 GW at repetition rate of 1 kHz. Moreover, the applied method is used for a direct tuning of the peak power of the output pulses through varying the chirping of the input pulses at different neon pressures. The observed results may give an opportunity to control the ultrafast interaction dynamics on the femtosecond time scale and facilitate the regeneration of attosecond pulses.
Stoller, Patrick C.; Kim, Beop-Min; Rubenchik, Alexander M.; Reiser, Karen M.; Da Silva, Luiz B.
2001-05-01
The measurement of the second order nonlinear susceptibility of collagen in various biological tissues has potential applications in the detection of structural changes which are related to different pathological conditions. We investigate second harmonic generation in a rat-tail tendon, a highly organized collagen structure consisting of parallel fibers. Using an electro-optic modulator and a quarter-wave plate, we modulate the linear polarization of an ultra-short pulse laser beam that is used to measure second harmonic generation in a confocal microscopy setup. Phase-sensitive detection of the generated signal, coupled with a simple model of the collagen protein structures, allows us to measure a parameter (gamma) related to nonlinear susceptibility and to determine the relative orientation of the structures. Our preliminary results indicate that it may be possible to use this parameter to characterize the structure.
Energy Technology Data Exchange (ETDEWEB)
Stoller, P; Kim, B-M; Rubenchik, A M; Reiser, K M; Da Silva, L B
2001-03-03
The measurement of the second order nonlinear susceptibility of collagen in various biological tissues has potential applications in the detection of structural changes which are related to different pathological conditions. We investigate second harmonic generation in rat-tail tendon, a highly organized collagen structure consisting of parallel fibers. Using an electro-optic modulator and a quarter-wave plate, we modulate the linear polarization of an ultra-short pulse laser beam that is used to measure second harmonic generation (SHG) in a confocal microscopy setup. Phase-sensitive detection of the generated signal, coupled with a simple model of the collagen protein structures, allows us to measure a parameter {gamma} related to nonlinear susceptibility and to determine the relative orientation of the structures. Our preliminary results indicate that it may be possible to use this parameter to characterize the structure.
Institute of Scientific and Technical Information of China (English)
Mehran Vahdani Moghaddam; Zeynab Chenari; Hamid Latifi; Vladimir Vladimirovich Shuvalov; Konestantin Valentinovich Rudenko
2008-01-01
@@ We deal with computer simulation of a transient process in a self-pumped phase conjugate plane-curve loop mirror based on BaTiO3. In optimal circumstances the nonlinear reflectivity and fidelity of such a mirror respectively achieve 0.80-0.90 and 0.95-0.98. The generation of conjugate wave-front occurs due to scattering from the dynamic hologram which is produced in the region of self-intersection of forward and backward beams. In such a model the scenario of passing to unstable generation regimes is similar to the self-pumped phase conjugate plane-plane loop mirror and substantially differs from a single-crystal double phase conjugate mirror.
Institute of Scientific and Technical Information of China (English)
赵应桥; 朱鹤元; 刘建华; 孙迭篪; 李富铭
1997-01-01
A time-resolved cross-phase modulation method combined with a modified nonlinear Schrodinger equation is used to study the effects of nonlinear response time on the propagation of ultrashort pulses in nonlinear dispersion media. Evolution of cross-phase modulation spectrum with the different time delay between the probe pulse and pump pulse is simulated using split-step Fourier method. It is shown that both normal self-frequency-shift-red-shift and abnormal self-frequency-shift-blue-shift can occur in the frequency domain for the probe pulse, and a satisfactory theoretical interpretation is given.
Zimmermann, Claudia; Schaaf, Wolfgang
2010-05-01
In the initial phase of soil formation interactions between solid and liquid phases and processes like mineral weathering, formation of reactive surfaces and accumulation of organic matter play a decisive role in developing soil properties. As part of the Transregional Collaborative Research Centre (SFB/TRR 38) 'Patterns and processes of initial ecosystem development' in an artificial catchment, these interactions are studied at the catchment 'Chicken Creek' (Gerwin et al. 2009). To link the interactions between soil solid phase and soil solution at the micro-scale with observed processes at the catchment scale, microcosm experiments under controlled laboratory conditions were carried out. Main objectives were to determine the transformation processes of C and N from litter decomposition within the gaseous, liquid and solid phase, the interaction with mineral surfaces and its role for the establishment of biogeochemical cycles. The microcosm experiments were established in a climate chamber at constant 10 ° C. In total 48 soil columns (diameter: 14.4 cm; height: 30 cm) were filled with two different quaternary substrates (sand and loamy sand) representing the textural variation within the catchment at a bulk density of 1.4-1.5 g*cm-3. The columns were automatically irrigated four times a day with 6.6 ml each (corresponding to 600 mm*yr-1). The gaseous phase in the headspace of the microcosms was analysed continuously for CO2 and N2O contents. C and N transformation processes were studied using 13C and 15N labelled litter of two different plant species occurring at the catchment (Lotus corniculatus, Calamagrostis epigejos) that was incorporated into the microcosm surface. All treatments including a control ran with four replicates over a period of 40 weeks. Two additional microcosms act as pure litter controls where substrate was replaced by glass pearls. Litter and substrate were analysed before and after the experiment. Percolate was continuously collected and
DEFF Research Database (Denmark)
Deng, Lei; Pang, Xiaodan; Zhang, Xu
2013-01-01
We report on the transmission of 8 Gb/s 0 dB PAPR 16QAM-OFDM W-band (75-110 GHz) signals over 22.8km SMF without phase noise compensation by using a phase modulator in the optical heterodyne up-convertor.......We report on the transmission of 8 Gb/s 0 dB PAPR 16QAM-OFDM W-band (75-110 GHz) signals over 22.8km SMF without phase noise compensation by using a phase modulator in the optical heterodyne up-convertor....
Mizuta, Yo; Nagasawa, Minoru; Ohtani, Morimasa; Yamashita, Mikio
2005-12-01
A numerical approach called Fourier direct method (FDM) is applied to nonlinear propagation of optical pulses with the central wavelength 800 nm, the width 2.67-12.00 fs, and the peak power 25-6870 kW in a fused-silica fiber. Bidirectional propagation, delayed Raman response, nonlinear dispersion (self-steepening, core dispersion), as well as correct linear dispersion are incorporated into “bidirectional propagation equations” which are derived directly from Maxwell’s equations. These equations are solved for forward and backward waves, instead of the electric-field envelope as in the nonlinear Schrödinger equation (NLSE). They are integrated as multidimensional simultaneous evolution equations evolved in space. We investigate, both theoretically and numerically, the validity and the limitation of assumptions and approximations used for deriving the NLSE. Also, the accuracy and the efficiency of the FDM are compared quantitatively with those of the finite-difference time-domain numerical approach. The time-domain size 500 fs and the number of grid points in time 2048 are chosen to investigate numerically intensity spectra, spectral phases, and temporal electric-field profiles up to the propagation distance 1.0 mm. On the intensity spectrum of a few-optical-cycle pulses, the self-steepening, core dispersion, and the delayed Raman response appear as dominant, middle, and slight effects, respectively. The delayed Raman response and the core dispersion reduce the effective nonlinearity. Correct linear dispersion is important since it affects the intensity spectrum sensitively. For the compression of femtosecond optical pulses by the complete phase compensation, the shortness and the pulse quality of compressed pulses are remarkably improved by the intense initial peak power rather than by the short initial pulse width or by the propagation distance longer than 0.1 mm. They will be compressed as short as 0.3 fs below the damage threshold of fused-silica fiber 6
Testik, Firat Yener
An experimental and theoretical study has been conducted to obtain a fundamental understanding of the dynamics of the sand, water and a solid object interaction as progressive gravity waves impinge on a sloping beach. Aside from obvious scientific interest, this exceedingly complex physical problem is important for naval applications, related to the behavior of disk/cylindrical shaped objects (mines) in the coastal waters. To address this problem, it was divided into a set of simpler basic problems. To begin, nonlinear progressive waves were investigated experimentally in a wave tank for the case of a rigid (impermeable) sloping bottom. Parameterizations for wave characteristics were proposed and compared with the experiments. In parallel, a numerical wave tank model (NWT) was calibrated using experimental data from a single run, and wave field in the wave tank was simulated numerically for the selected experiments. Subsequently, a layer of sand was placed on the slope and bottom topography evolution processes (ripple and sandbar dynamics, bottom topography relaxation under variable wave forcing, etc.) were investigated experimentally. Models for those processes were developed and verified by experimental measurements. Flow over a circular cylinder placed horizontally on a plane wall was also studied. The far-flow field of the cylinder placed in the wave tank was investigated experimentally and numerical results from the NWT simulations were compared with the experimental data. In the mean time, the near-flow velocity/vorticity field around a short cylinder under steady and oscillatory flow was studied in a towing tank. Horseshoe vortex formation and periodic shedding were documented and explained. With the understanding gained through the aforementioned studies, dynamics and burial/scour around the bottom objects in the wave tank were studied. Possible scenarios on the behavior of the disk-shaped objects were identified and explained. Scour around 3D cylindrical
Study of Nonlinear Interaction and Turbulence of Alfven Waves in LAPD Experiments
Energy Technology Data Exchange (ETDEWEB)
Boldyrev, Stanislav; Perez, Jean Carlos
2013-11-29
The complete project had two major goals — investigate MHD turbulence generated by counterpropagating Alfven modes, and study such processes in the LAPD device. In order to study MHD turbulence in numerical simulations, two codes have been used: full MHD, and reduced MHD developed specialy for this project. Quantitative numerical results are obtained through high-resolution simulations of strong MHD turbulence, performed through the 2010 DOE INCITE allocation. We addressed the questions of the spectrum of turbulence, its universality, and the value of the so-called Kolmogorov constant (the normalization coefficient of the spectrum). In these simulations we measured with unprecedented accuracy the energy spectra of magnetic and velocity fluctuations. We also studied the so-called residual energy, that is, the difference between kinetic and magnetic energies in turbulent fluctuations. In our analytic work we explained generation of residual energy in weak MHD turbulence, in the process of random collisions of counterpropagating Alfven waves. We then generalized these results for the case of strong MHD turbulence. The developed model explained generation of residual energy is strong MHD turbulence, and verified the results in numerical simulations. We then analyzed the imbalanced case, where more Alfven waves propagate in one direction. We found that spectral properties of the residual energy are similar for both balanced and imbalanced cases. We then compared strong MHD turbulence observed in the solar wind with turbulence generated in numerical simulations. Nonlinear interaction of Alfv´en waves has been studied in the upgraded Large Plasma Device (LAPD). We have simulated the collision of the Alfven modes in the settings close to the experiment. We have created a train of wave packets with the apltitudes closed to those observed n the experiment, and allowed them to collide. We then saw the generation of the second harmonic, resembling that observed in the
Guo, Bang-Xing; Gao, Zhan-Jie; Lin, Ji
2016-12-01
The consistent tanh expansion (CTE) method is applied to the (2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explicitly given, such as the bright soliton-periodic wave interaction solution, variational amplitude periodic wave solution, and kink-periodic wave interaction solution. We also obtain the bright soliton solution, kind bright soliton solution, double well dark soliton solution and kink-bright soliton interaction solution by using Painlevé truncated expansion method. And we investigate interactive properties of solitons and periodic waves. Supported by the National Natural Science Foundation of Zhejiang Province under Grant No. LZ15A050001 and the National Natural Science Foundation of China under Grant No. 11675164
Energy Technology Data Exchange (ETDEWEB)
Sentman, L.H.; Nayfeh, M.H.
1983-12-01
This research is an integrated theoretical and experimental investigation of the nonlinear interactions which may occur between the chemical kinetics, the fluid dynamics and the unstable resonator of a continuous wave fluid flow laser. The objectives of this grant were to measure the frequency and amplitude of the time dependent pulsations in the power spectral output which have been predicted to occur in cw chemical lasers employing unstable resonators to extract power.
2015-09-30
1 A multiscale nested modeling framework to simulate the interaction of surface gravity waves with nonlinear internal gravity waves...Minnesota LONG-TERM GOALS Our long-term goal is to develop a multiscale nested modeling framework that simulates, with the finest resolution...frameworks such as the proposed HYCOM-LZSNFS-SUNTANS-LES nested model are crucial for understanding multiscale processes that are unresolved, and hence
DEFF Research Database (Denmark)
Sayed, Karim El; Birkedal, Dan; Vadim, Lyssenko;
1997-01-01
of the exciton line in the FWM spectrum and in the decay of the time-resolved FWM signal in real time are governed by the intrinsic excitonic dephasing rate. It is shown that for pulse durations of similar to 100 fs (for GaAs quantum wells) this behavior can be explained as the influence of the Coulomb exchange...... interaction, while for even shorter pulses this behavior is dominantly caused by nonlinear polarization decay....
Three-Phase Grid-Connected of Photovoltaic Generator Using Nonlinear Control
DEFF Research Database (Denmark)
Yahya, A.; El Fadil, H.; Guerrero, Josep M.
2014-01-01
of PV panels, ii) guaranteeing a power factor unit in the side of the grid, iii) ensuring the global asymptotic stability of the closed loop system. Based on the nonlinear model of the whole system, the controller is carried out using a Lyapunov approach. It is formally shown, using a theoretical...
Vilardy, Juan M.; Millán, María S.; Pérez-Cabré, Elisabet
2017-02-01
A novel nonlinear image encryption scheme based on a fully phase nonzero-order joint transform correlator architecture (JTC) in the Gyrator domain (GD) is proposed. In this encryption scheme, the two non-overlapping data distributions of the input plane of the JTC are fully encoded in phase and this input plane is transformed using the Gyrator transform (GT); the intensity distribution captured in the GD represents a new definition of the joint Gyrator power distribution (JGPD). The JGPD is modified by two nonlinear operations with the purpose of retrieving the encrypted image, with enhancement of the decrypted signal quality and improvement of the overall security. There are three keys used in the encryption scheme, two random phase masks and the rotation angle of the GT, which are all necessary for a proper decryption. Decryption is highly sensitivity to changes of the rotation angle of the GT as well as to little changes in other parameters or keys. The proposed encryption scheme in the GD still preserves the shift-invariance properties originated in the JTC-based encryption in the Fourier domain. The proposed encryption scheme is more resistant to brute force attacks, chosen-plaintext attacks, known-plaintext attacks, and ciphertext-only attacks, as they have been introduced in the cryptanalysis of the JTC-based encryption system. Numerical results are presented and discussed in order to verify and analyze the feasibility and validity of the novel encryption-decryption scheme.
A nonlinear Schroedinger equation with two symmetric point interactions in one dimension
Energy Technology Data Exchange (ETDEWEB)
Kovarik, Hynek [Dipartimento di Matematica, Politecnico di Torino, Torino (Italy); Sacchetti, Andrea [Facolta di Scienze, Universita di Modena e Reggio Emilia, Modena (Italy)], E-mail: Hynek.Kovarik@polito.it, E-mail: Andrea.Sacchetti@unimore.it
2010-04-16
We consider a time-dependent one-dimensional nonlinear Schroedinger equation with a symmetric double-well potential represented by two Dirac's {delta}. Among our results we give an explicit formula for the integral kernel of the unitary semigroup associated with the linear part of the Hamiltonian. Then we establish the corresponding Strichartz-type estimate and we prove local existence and uniqueness of the solution to the original nonlinear probl0008.
Echeikh, Hamdi; Trabelsi, Ramzi; Iqbal, Atif; Bianchi, Nicola; Mimouni, Mohamed Fouizi
2016-11-01
In this paper non-linear backstepping control (BSC) is employed for high performance five-phase induction motor drive for low speed operation. The traditional control approaches such as direct torque control and indirect rotor field oriented control introduces stability problem at low speed. The proposed BSC is shown to offer stable operation in the sense of Lyapunov and high dynamics at low speed. Experimental results are provided to present the proprieties of the proposed approach at low speed in terms of stability, torque ripple, desired control performance, achievable dynamics and complexity of implementation etc. Copyright © 2016. Published by Elsevier Ltd.
Pathak, A
2006-01-01
Interaction of intense laser beam with an inversion symmetric third order nonlinear medium is modeled as a quartic anharmonic oscillator. A first order operator solution of the model Hamiltonian is used to study the possibilities of generation of higher order nonclassical states. It is found that the higher order squeezed and higher order antibunched states can be produced by this interaction. It is also shown that the higher order nonclassical states may appear separately, i.e. a higher order antibunched state is not essentially higher order squeezed state and vice versa.
Yang, Houwen; Wang, Bo; Wang, Junhua; Li, Xiaofang; Liu, Zhaojun; Cheng, Wenyong
2017-03-01
We demonstrated an ultraviolet laser at 355 nm using a type-I and a type-II phase-matching nonlinear optical crystal of LiB3O5 (LBO). A method of adjusting temperature for compensation is presented. The crystal temperature is controlled by proportional integral derivative (PID) thermal controllers with a ±0.01 °C resolution. The value of wave vector mismatch, distance of light propagation in nonlinear crystals, effective nonlinear coefficient, theoretical analysis and calculation of conversion efficiency versus temperature are discussed. The experimental results show that the average output power of the 355 nm laser is 1.24 W with the pump power of 13.33 W, when the repetition frequency is 15 kHz. The pulse duration is 9.8 ns, and the beam quality factors are of Mx2 = 1.8, My2 = 1.7. The conversion efficiency from 808 nm to 355 nm laser is 9.3%, which nearly reaches the optimum value reported so far and is limited by the wavelength mismatch between the pumping and absorbing lasers. The 355 nm output power instability of the laser device is 0.45% in 2 h. A compact no-water-cooling ultraviolet laser with high stability and high efficiency is obtained.
Institute of Scientific and Technical Information of China (English)
Xianqiong Zhong; Anping Xiang
2007-01-01
@@ The synthetic effects of group-velocity mismatch and cubic-quintic nonlinearity on cross-phase modulation induced modulation instability in loss single-mode optical fibers have been numerically investigated. The results show that the quintic nonlinearity plays a role similar to the case of neglecting the group-velocity mismatch in modifying the modulation instability, namely, the positive and negative quintic nonlinearities can still enhance and weaken the modulation instability, respectively. The group-velocity mismatch can considerably change the gain spectrum of modulation instability in terms of its shape, peak value, and position. In the normal dispersion regime, with the increase of the group-velocity mismatch parameter,the gain spectrum widens and then narrows, shifts to higher frequencies, and the peak value gets higher before approaching a saturable value. In the abnormal dispersion regime, two separated spectra may occur when the group-velocity mismatch is taken into account. With the increase of the group-velocity mismatch parameter, the peak value of the gain spectrum gets higher and shorter before tending to a saturable value for the first and second spectral regimes, respectively.
DEFF Research Database (Denmark)
Rasmussen, Anders Rønne; Sørensen, Mads Peter; Gaididei, Yuri Borisovich
2011-01-01
A wave equation including nonlinear terms up to the second order for a thermoviscous Newtonian fluid is proposed. In the lossless case this equation results from an expansion to third order of the Lagrangian for the fundamental non-dissipative fluid dynamical equations. Thus it preserves...
Energy Technology Data Exchange (ETDEWEB)
Solberg, Jerome M., E-mail: solberg2@llnl.gov [Methods Development Group, Lawrence Livermore Nat’l Lab, P.O. Box 808, Mailstop L-125, Livermore, CA 94550 (United States); Hossain, Quazi, E-mail: hossain1@llnl.gov [Structural and Applied Mechanics Group, Lawrence Livermore Nat’l Lab, P.O. Box 808, Mailstop L-129, Livermore, CA 94550 (United States); Mseis, George, E-mail: george.mseis@gmail.com [Structural and Applied Mechanics Group, Lawrence Livermore Nat’l Lab, P.O. Box 808, Mailstop L-129, Livermore, CA 94550 (United States)
2016-08-01
Highlights: • Derived modified version of Bielak’s SSI method for nonlinear time-domain analysis. • Utilized a Ramberg–Osgood material with parameters that can be fit to EPRI data. • Matched vertically propagating shear wave results from CARES. • Applied this technique to a representative SMR, compared well with SASSI. • The technique is extensible to other material models and nonlinear effects. - Abstract: A generalized time-domain method for soil–structure interaction analysis is developed, based upon an extension of the work of the domain reduction method of Bielak et al. The methodology is combined with the use of a simple hysteretic soil model based upon the Ramberg–Osgood formulation and applied to a notional Small Modular Reactor. These benchmark results compare well (with some caveats) with those obtained by using the industry-standard frequency-domain code SASSI. The methodology provides a path forward for investigation of other sources of nonlinearity, including those associated with the use of more physically-realistic material models incorporating pore-pressure effects, gap opening/closing, the effect of nonlinear structural elements, and 3D seismic inputs.
Blackman, Karin; Perret, Laurent
2016-09-01
In the present work, a boundary layer developing over a rough-wall consisting of staggered cubes with a plan area packing density, λp = 25%, is studied within a wind tunnel using combined particle image velocimetry and hot-wire anemometry to investigate the non-linear interactions between large-scale momentum regions and small-scale structures induced by the presence of the roughness. Due to the highly turbulent nature of the roughness sub-layer and measurement equipment limitations, temporally resolved flow measurements are not feasible, making the conventional filtering methods used for triple decomposition unsuitable for the present work. Thus, multi-time delay linear stochastic estimation is used to decompose the flow into large-scales and small-scales. Analysis of the scale-decomposed skewness of the turbulent velocity (u') shows a significant contribution of the non-linear term uL ' uS ' 2 ¯ , which represents the influence of the large-scales ( uL ' ) onto the small-scales ( uS ' ). It is shown that this non-linear influence of the large-scale momentum regions occurs with all three components of velocity in a similar manner. Finally, through two-point spatio-temporal correlation analysis, it is shown quantitatively that large-scale momentum regions influence small-scale structures throughout the boundary layer through a non-linear top-down mechanism.