Two-component vector solitons in defocusing Kerr-type media with spatially modulated nonlinearity
Zhong, Wei-Ping; Belić, Milivoj
2014-12-15
We present a class of exact solutions to the coupled (2+1)-dimensional nonlinear Schrödinger equation with spatially modulated nonlinearity and a special external potential, which describe the evolution of two-component vector solitons in defocusing Kerr-type media. We find a robust soliton solution, constructed with the help of Whittaker functions. For specific choices of the topological charge, the radial mode number and the modulation depth, the solitons may exist in various forms, such as the half-moon, necklace-ring, and sawtooth vortex-ring patterns. Our results show that the profile of such solitons can be effectively controlled by the topological charge, the radial mode number, and the modulation depth. - Highlights: • Two-component vector soliton clusters in defocusing Kerr-type media are reported. • These soliton clusters are constructed with the help of Whittaker functions. • The half-moon, necklace-ring and vortex-ring patterns are found. • The profile of these solitons can be effectively controlled by three soliton parameters.
Liu, Ye; Zhou, Fei; Mao, Qinghe
2013-10-01
In this article, an analytical theory to describe the nonlinear dynamic response characteristics of a typical SPP waveguide-cavity structure formed by a Kerr-type standing-wave cavity side-coupling to a metal-insulator-metal (MIM) waveguide is proposed by combining the temporal coupled mode theory and the Kerr nonlinearity. With the analytical theory, the optical bistability with the hysteresis behavior is successfully predicted, and the optical bistability evolutions and its dynamic physical mechanism are also phenomenologically analyzed. Moreover, the influence of the quality factors Q₀ and Q₁ on the first-turnning point (FTP) power of optical bistability and the bistable region width, the approaches to decrease the FTP power and to broaden the bistable region are also discussed in detail with our analytical theory. This work can help us understand the physical mechanism of the nonlinear dynamical response at nanoscale, and may be useful to design nonlinear nanophotonic systems for applications in ultra-compact all-optical devices and storages.
Nonlinear ring resonator: spatial pattern generation
NASA Astrophysics Data System (ADS)
Ivanov, Vladimir Y.; Lachinova, Svetlana L.; Irochnikov, Nikita G.
2000-03-01
We consider theoretically spatial pattern formation processes in a unidirectional ring cavity with thin layer of Kerr-type nonlinear medium. Our method is based on studying of two coupled equations. The first is a partial differential equation for temporal dynamics of phase modulation of light wave in the medium. It describes nonlinear interaction in the Kerr-type lice. The second is a free propagation equation for the intracavity field complex amplitude. It involves diffraction effects of light wave in the cavity.
Nonlinear long-range plasmonic waveguides
Degiron, Aloyse; Smith, David R.
2010-09-15
We report on plasmonic waveguides made of a thin metal stripe surrounded on one or both sides by a Kerr nonlinear medium. Using an iterative numerical method, we investigate the stationary long-range plasmons that exist for self-focusing and self-defocusing Kerr-type nonlinearities. The solutions are similar to the well-known case of infinitely wide nonlinear waveguides - they are strongly power-dependent and can experience symmetry-breaking bifurcations under appropriate conditions.
He, G S; Xu, G C; Cui, Y; Prasad, P N
1993-08-20
The spectral superbroadening behavior of forward coherent radiation from a 10-cm-long liquid-filled cell is investigated by using an ultrashort (∼0.5 ps) and intense (∼10 GW/cm(2)) laser pulse as the pump source. Five different transparent liquids (heavy water, water, carbon tetrachloride, benzene, and carbon disulfide) have been studied with a special experimental design that can distinguish the predominant contributions from the various possible mechanisms. Under the same pump condition, a very wide and symmetrical superbroadening (continuum) is observed on both the Stokes and the anti-Stokes side of the pump line for non-Kerr-type liquids such as heavy water and water, whereas only a red-shifted spectral broadening can be observed on the Stokes side for Kerr-type liquids such as carbon disulfide and benzene. For an explanation of the latter behavior, the dominant contributions from stimulated Rayleigh-Kerr and Raman-Kerr scattering are proposed.
Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium.
Xiong, Hao; Si, Liu-Gang; Yang, Xiaoxue; Wu, Ying
2015-01-01
A simple but highly efficient approach for dealing with the problem of cylindrical electromagnetic waves propagation in a nonlinear medium is proposed based on an exact solution proposed recently. We derive an analytical explicit formula, which exhibiting rich interesting nonlinear effects, to describe the propagation of any amount of cylindrical electromagnetic waves in a nonlinear medium. The results obtained by using the present method are accurately concordant with the results of using traditional coupled-wave equations. As an example of application, we discuss how a third wave affects the sum- and difference-frequency generation of two waves propagation in the nonlinear medium.
Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium
Xiong, Hao; Si, Liu-Gang; Yang, Xiaoxue; Wu, Ying
2015-01-01
A simple but highly efficient approach for dealing with the problem of cylindrical electromagnetic waves propagation in a nonlinear medium is proposed based on an exact solution proposed recently. We derive an analytical explicit formula, which exhibiting rich interesting nonlinear effects, to describe the propagation of any amount of cylindrical electromagnetic waves in a nonlinear medium. The results obtained by using the present method are accurately concordant with the results of using traditional coupled-wave equations. As an example of application, we discuss how a third wave affects the sum- and difference-frequency generation of two waves propagation in the nonlinear medium. PMID:26073066
Wave propagation in elastic medium with heterogeneous quadratic nonlinearity
Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin
2011-06-23
This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter {beta} when the nonlinearity distribution in the layer is a stochastic process.
NASA Astrophysics Data System (ADS)
Zhang, Lida; Evers, Jörg
2016-09-01
Nonlinear and nonlocal effects are discussed in the interaction of laser fields with thermal Rydberg atoms in an electromagnetically induced transparency configuration. We assume that the system's steady state adiabatically follows the time variation in the dipole-dipole interactions due to the atomic motion and use a continuum description for the atomic medium. Based on these approximations, we obtain an analytical form for the nonlocal nonlinear atomic response of the thermal medium and study it for different parameter cases. We further propose a generalized model to describe the modulational instability (MI) in absorptive nonlinear media, in order to understand the propagation dynamics in the thermal Rydberg medium. Interestingly, this model predicts that at short propagation distances, each wave component exhibits the MI effect in absorptive nonlinear media, unlike in the purely dispersive case.
Nonlinear site response in medium magnitude earthquakes near Parkfield, California
Rubinstein, Justin L.
2011-01-01
Careful analysis of strong-motion recordings of 13 medium magnitude earthquakes (3.7 ≤ M ≤ 6.5) in the Parkfield, California, area shows that very modest levels of shaking (approximately 3.5% of the acceleration of gravity) can produce observable changes in site response. Specifically, I observe a drop and subsequent recovery of the resonant frequency at sites that are part of the USGS Parkfield dense seismograph array (UPSAR) and Turkey Flat array. While further work is necessary to fully eliminate other models, given that these frequency shifts correlate with the strength of shaking at the Turkey Flat array and only appear for the strongest shaking levels at UPSAR, the most plausible explanation for them is that they are a result of nonlinear site response. Assuming this to be true, the observation of nonlinear site response in small (M M 6.5 San Simeon earthquake and the 2004 M 6 Parkfield earthquake).
Strongly interacting photons in a quantum nonlinear medium
NASA Astrophysics Data System (ADS)
Peyronel, Thibault
2014-05-01
Photons are fast and robust carriers of information but their lack of mutual interactions hinders their use in quantum information protocols. Interactions can be mediated by nonlinear media, and optical nonlinearities at the single photon level are a long-standing goal of quantum optical science. By coherently coupling slowly propagating photons to Rydberg states in a dense cold atomic gas, we create a single-pass medium with large photon-photon interactions. We first demonstrate that combining electromagnetically induced transparency techniques with the Rydberg blockade effect leads to strong dissipative interactions between individual photons. As a result, the simultaneous propagation of photons is suppressed in an otherwise transparent medium, and coherent laser pulses are converted into single photons. We subsequently explore the regime of coherent interactions, where simultaneously propagating photons acquire a large conditional phase-shift and become entangled. In this regime, the photons behave as massive particles exerting an attractive force onto each other and their evolution is governed by the existence of a photonic bound-state. This work paves the way for cavity-free deterministic optical quantum gates and quantum many-body physics with light.
NASA Astrophysics Data System (ADS)
Trofimov, Vyacheslav A.; Lysak, T. M.
2016-05-01
We demonstrate a new possibility of a soliton velocity control at its propagation in a nonlinear layered structure (1D photonic crystal) which is placed in a nonlinear ambient medium. Nonlinear response of the ambient medium, as well as the PhC layers, is cubic. At the initial time moment, a soliton is spread over a few layers of PhC. Then, soliton propagates across the layered structure because of the initial wave-vector direction presence for the laser beam. The soliton reaches the PhC faces and reflects from them or passes through the face. As a nonlinear medium surrounds the PhC, the laser beam obtains additional impulse after interaction with this medium and accelerates (or slows down or stops near the PhC face). Nonlinear response of the ambient medium can be additionally created by another laser beam which shines near the PhC faces.
Nonlinear self-adjointness and conservation laws for a porous medium equation with absorption
NASA Astrophysics Data System (ADS)
Gandarias, M. L.; Bruzón, M. S.
2013-10-01
We give conditions for a general porous medium equation to be nonlinear self-adjoint. By using the property of nonlinear self-adjointness we construct some conservation laws associated with classical and nonclassical generators of a porous medium equation with absorption.
Rigorous calculation of nonlinear parameters in graphene-comprising waveguides
NASA Astrophysics Data System (ADS)
Chatzidimitriou, Dimitrios; Pitilakis, Alexandros; Kriezis, Emmanouil E.
2015-07-01
We describe a rigorous formalism for the calculation of the nonlinear parameter of arbitrary three-dimensional nanophotonic graphene-comprising waveguides. Graphene is naturally implemented as a zero-thickness conductive sheet, modeled solely by complex linear and nonlinear surface conductivity tensors, whose values are extracted from theoretical models. This representation is compared to the more commonly employed equivalent bulk-medium representation and is found superior. We numerically calculate the nonlinear parameters of several optical waveguide archetypes overlaid with infinite graphene monolayers, including silicon-wire and plasmonic metal-slot and metal-stripe configurations. The metal-slot configuration offers the most promising performance for Kerr-type nonlinear applications. Finally, we apply the same formalism to probe the potential of graphene nanoribbon waveguide nonlinearity in the terahertz band.
Fresnel drag of light by a moving nonlinear and nanostructured dielectric medium
Peiponen, Kai-Erik; Gornov, Evgeny
2007-12-15
The Fresnel drag is viewed in the frame of nonlinear and/or nanostructured uniformly moving media. It is shown that in the case of intense light pulse interaction with an optically nonlinear medium the relativistic frequency chirp due to self-phase modulation is smaller than in the rest frame. In the case of light interaction with optically linear or nonlinear nanostructured medium the Fresnel drag depends on the effective refractive index of the medium. While the nanostructures are in a liquid matrix the drag can be controlled by the fill fraction of the inclusions. As an example the Fresnel drag for optically linear Bruggeman liquid is considered.
Propagation of femtosecond pulse with self-similar shape in medium with nonlinear absorption
NASA Astrophysics Data System (ADS)
Trofimov, Vyacheslav A.; Zakharova, Irina G.
2015-05-01
We investigate the propagation of laser pulse with self-similar shape in homogeneous medium with various mechanisms of nonlinear absorption: multi-photon absorption or resonant nonlinearity under detuning the frequency, corresponding to energy transition, from the current frequency of wave packet, or nonlinear absorption with its saturation. Both types of sign for frequency detuning are considered. This results in appearance of a refractive index grating which induced a laser pulse self-action. We analyze also the influence of the laser pulse self-modulation due to cubic nonlinearity on existence of the laser pulse propagation mode with self-similar shape. We develop an analytical solution of the corresponding nonlinear eigenfunction problem for laser pulse propagation in medium with nonlinear absorption. This solution is confirmed by computer simulation of the eigenfunction problem for Schrödinger equation with considered nonlinearity. This mode of laser pulse propagation is very important for powerful TW laser pulse propagating in glass.
On the spectral-spatial instability of a light wave in a medium with cubic nonlinearity
Afanas'ev, Anatolii A; Volkov, V M
2003-11-30
Based on the analysis of frequency-nondegenerate four-photon parametric scattering, the spectral-angular dependences of the increments of perturbing modes are obtained in the field of an intense light wave propagating in a medium with cubic nonlinearity. (nonlinear optical phenomena)
Nonlinear effective-medium theory of disordered spring networks.
Sheinman, M; Broedersz, C P; MacKintosh, F C
2012-02-01
Disordered soft materials, such as fibrous networks in biological contexts, exhibit a nonlinear elastic response. We study such nonlinear behavior with a minimal model for networks on lattice geometries with simple Hookian elements with disordered spring constant. By developing a mean-field approach to calculate the differential elastic bulk modulus for the macroscopic network response of such networks under large isotropic deformations, we provide insight into the origins of the strain stiffening and softening behavior of these systems. We find that the nonlinear mechanics depends only weakly on the lattice geometry and is governed by the average network connectivity. In particular, the nonlinear response is controlled by the isostatic connectivity, which depends strongly on the applied strain. Our predictions for the strain dependence of the isostatic point as well as the strain-dependent differential bulk modulus agree well with numerical results in both two and three dimensions. In addition, by using a mapping between the disordered network and a regular network with random forces, we calculate the nonaffine fluctuations of the deformation field and compare them to the numerical results. Finally, we discuss the limitations and implications of the developed theory.
Nonlinear effective-medium theory of disordered spring networks.
Sheinman, M; Broedersz, C P; MacKintosh, F C
2012-02-01
Disordered soft materials, such as fibrous networks in biological contexts, exhibit a nonlinear elastic response. We study such nonlinear behavior with a minimal model for networks on lattice geometries with simple Hookian elements with disordered spring constant. By developing a mean-field approach to calculate the differential elastic bulk modulus for the macroscopic network response of such networks under large isotropic deformations, we provide insight into the origins of the strain stiffening and softening behavior of these systems. We find that the nonlinear mechanics depends only weakly on the lattice geometry and is governed by the average network connectivity. In particular, the nonlinear response is controlled by the isostatic connectivity, which depends strongly on the applied strain. Our predictions for the strain dependence of the isostatic point as well as the strain-dependent differential bulk modulus agree well with numerical results in both two and three dimensions. In addition, by using a mapping between the disordered network and a regular network with random forces, we calculate the nonaffine fluctuations of the deformation field and compare them to the numerical results. Finally, we discuss the limitations and implications of the developed theory. PMID:22463230
Self-similar pulse-shape mode for femtosecond pulse propagation in medium with resonant nonlinearity
NASA Astrophysics Data System (ADS)
Trofimov, Vyacheslav A.; Zakharova, Irina G.; Konar, Swapan
2014-05-01
We investigate the mode of laser pulse propagation in homogeneous medium with resonant nonlinearity, at which the shape of pulse is self-similar one along some distance of propagation. We take into account a laser pulse frequency detuning from resonant frequency. Both types of sign for frequency detuning are considered. This results in appearance of a refractive index grating which induced self-action of a laser pulse. I certain cases we develop analytical solution of corresponding nonlinear eigenfunction problem of laser pulse propagation in medium for multi-photon resonance. This solution is confirmed by computer simulation of an eigenfunction problem for Schrödinger equation with considered nonlinearity. Using computer simulation, one shows a validity of existence of such kind of laser pulse propagation in a medium with resonant nonlinear response.
NASA Astrophysics Data System (ADS)
Gulyaev, A. V.; Tikhonova, O. V.
2010-05-01
The propagation of ultrashort few-cycle laser pulses through a quantum nonlinear medium with resonant properties is studied using the method of slowly varying amplitudes with allowance for dispersion effects. A self-consistent system of nonlinear wave equation for the evolution of laser field and the nonstationary Schrödinger equation that determines the material polarization response is numerically solved. Specific features of the propagation of laser pulse caused by a relatively large spectral width and the nonadiabatic character of the laser pulse are established. The rise of the slowly dumping polarization at the eigenfrequency of the medium and the consequent stretching of the laser pulse are observed. The role of the resonant absorption of the laser energy in the medium is analyzed. The nonlinear spectral broadening is demonstrated for the laser pulse propagating through the medium.
Phase conjugate mirror system consisting of a rod amplifier and a nonlinear medium
NASA Astrophysics Data System (ADS)
Lee, Hak K.; Lee, Sang-Soo
1990-07-01
The phase conjugate (PC) mirror system consisting of a rod amplifier and a nonlinear medium is presented and the theoretical analysis of the enhanced PC wave in the system is derived by taking into account of the overlap of the probe and counterpropagating PC wave in the amplifier. In order to examine experimentally the enhanced PC reflectivity in degenerate four wave mixing (DFWM) an amplifier is placed in the probe beam path. Experimental result of maximal R/R 90. 25 is obtained where R and R are PC reflectivities in the absence and presence of the amplifier respectively. The experimental results agree within 5 with the theoretical values. 1. THEORETICAL ANALYSIS Schematic digram of the PC mirror system consisting of an amplifier and a nonlinear medium is shown in Fig. 1. The phase distortion 4 is due to several effects such as inhomogemous pumping stress gain saturation thermal leasing and self-focusing/defocusing in the amplifier. 1 The amplifier is palced near the nonlinear medium so that the changes in phase (4) and gain (g) are negligible during the round trip time. Considering phase conjugation at the nonlinear medium the output signal SA8 over the input probe bA. is expressed as 8A ge+/ (ge14''A) J where R is PC reflectivity of nonlinear medium. There is no phase distortion term in output signal. Thus we obtain the following expression for the signal 6M photons/ 2
Nonlinear Interaction of Light with Transversely Moving Medium
NASA Astrophysics Data System (ADS)
Tabiryan, N. V.; Nersisyan, S. R.; Warenghem, M.
1996-10-01
Interaction of a light beam with matter reveals extreme sensitivity to transverse motions. Spatio-temporal delocalization of interaction and diffusive transport of light-induced perturbations is revealed through a new family of diffraction patterns. The response of the medium to the transverse motion of the light enhances near the second order phase transition point. The phenomenon has large application potential for the study of motions that are beyond the power of Doppler-effect-based methods, and suggests fundamental problems about critical processes with nonstationary influences.
Optical polarization multistability in reflection in a semi-infinite isotropic nonlinear Kerr medium
NASA Astrophysics Data System (ADS)
Singh, D. K.; Prakash, H.
2012-03-01
We study nonlinear interaction of counter-propagating plane light waves in a semi-infinite isotropic lossless nonlinear Kerr medium and report existence of several regions of optical-polarization-multistability. The counter-propagating waves may be produced by normal reflection of an incident beam by a mirror in the nonlinear Kerr medium. We obtain nonlinear coupled differential equations for Stokes parameters of the two beams and solve them following the method of Prakash et al. [Mod. Phys. Lett. B 14, 47 (2000)] and the boundary conditions at the mirror. We find that, for the same incident intensity and for the same polarization state of the incident beam, output beam may exist in several stable polarization states.
The propagation of a nonlinear sound wave in an unconsolidated granular medium
NASA Astrophysics Data System (ADS)
Naugolnykh, K. A.; Esipov, I. B.
2005-11-01
The propagation of a high-intensity sound wave in an unconsolidated medium is considered. Dissipation effects are taken into account on the basis of Buckingham’s theory of a relaxation mechanism of sound attenuation in a saturated sediment. The nonlinear evolution equation for the relaxing medium is obtained, and the solutions of this equation are analyzed. The second-harmonic generation in such a medium decays, as does the linear sound wave of the same frequency. The stationary weak shock profile has a specific form due to relaxation effects.
Optical-soliton and chaotic motions in a nonlocal nonlinear medium
NASA Astrophysics Data System (ADS)
Zhen, Hui-Ling; Tian, Bo; Xie, Xi-Yang; Liu, Lei
2016-05-01
The coupled equations for the incoherent optical spatial solitons in a nonlocal nonlinear medium is studied analytically. With the soliton solutions hereby obtained via the symbolic computation, the optical-soliton motion in the nonlocal nonlinear medium is studied: ? is inversely related to ?, ?, and ?, while ? is positively related to ? and ?, but ? is independent of ?, with ? as the slowly varying amplitude of the beam, ? as the refractive index change, ? as the beam intensity distribution, ? as the frequency of the propagating beam, and ? as the unperturbed refractive index. Head-on and overtaking interactions are observed, and head-on interaction is transformed into an overtaking one with ? increasing. Bound-state interaction is displayed, and with ? increasing, the period of ? decreases, while that of ? increases. Considering the external forces in the nonlocal nonlinear medium, we explore the chaotic motions in the nonlinear nonlocal medium, including effects of the external forces on such motions. It is seen that when ? and ?, the two-dimensional attractors with stretching-and-folding structures are exhibited, and the developed chaos occurs, where ? and ? are the amplitudes of external forces, c is the speed of light in vacuum. Such chaotic motions are weakened with ?, ?, ?, and ? increasing, or with ? decreasing, where ? and ? represent the frequencies of external forces.
Localized states and their stability in an anharmonic medium with a nonlinear defect
Gerasimchuk, I. V.
2015-10-15
A comprehensive analysis of soliton states localized near a plane defect (a defect layer) possessing nonlinear properties is carried out within a quasiclassical approach for different signs of nonlinearity of the medium and different characters of interaction of elementary excitations of the medium with the defect. A quantum interpretation is given to these nonlinear localized modes as a bound state of a large number of elementary excitations. The domains of existence of such states are determined, and their properties are analyzed as a function of the character of interaction of elementary excitations between each other and with the defect. A full analysis of the stability of all the localized states with respect to small perturbations of amplitude and phase is carried out analytically, and the frequency of small oscillations of the state localized on the defect is determined.
NASA Astrophysics Data System (ADS)
Adhikari, S. K.
2016-09-01
We consider the statics and dynamics of a stable, mobile three-dimensional (3D) spatiotemporal light bullet in a cubic-quintic nonlinear medium with a focusing cubic nonlinearity above a critical value and any defocusing quintic nonlinearity. The 3D light bullet can propagate with a constant velocity in any direction. Stability of the light bullet under a small perturbation is established numerically. We consider frontal collision between two light bullets with different relative velocities. At large velocities the collision is elastic with the bullets emerge after collision with practically no distortion. At small velocities two bullets coalesce to form a bullet molecule. At a small range of intermediate velocities the localized bullets could form a single entity which expands indefinitely, leading to a destruction of the bullets after collision. The present study is based on an analytic Lagrange variational approximation and a full numerical solution of the 3D nonlinear Schrödinger equation.
NASA Astrophysics Data System (ADS)
Shirgina, N. V.; Korobov, A. I.; Kokshaiskii, A. I.
2013-09-01
We have studied the influence of external static (pressure) and dynamic (caused by an elastic wave with a finite amplitude) actions on the linear and nonlinear elastic properties of a granulated unconsolidated medium, which was simulated by steel spheres with diameters of 2 and 4 mm. We have analyzed the equation of state for such a medium taking into account the presence of weakly and strongly deformed contacts between individual spheres. We have obtained expressions for the elasticity coefficient and second- and third-order nonlinear elastic parameters, and we have experimentally studied the influence of external static pressure on their values. We have measured the dependence of the velocity of elastic waves on external static pressure and the probing signal amplitude. In the studied medium, a number of structural phase transitions were observed, related to rearrangement of the packing of spheres, which were caused by both static and dynamic actions. The structural phase transition was accompanied by an anomalous change in the nonlinear elastic parameters of the medium and the velocity of elastic waves. We have analyzed the results based on the Hertz theory of contact interaction.
Propagation of the quasimonochromatic signal through medium having non-linear dispersion
Galkin, Y.
1996-12-31
Tunable Diode Laser Absorption Spectroscopy (TDLAS) fulfill the requirements for trace gas analysis, for the measurement of concentrations of most atmospheric pollutants, and is increasingly being used to measure pollutants. The medium non-linear dispersion influence for complex form of quasimonochromatic signal propagating through environment is described. It is shown, that a non-linear dispersion disturbs both a real amplitude and an imaginary phase of signal. The proofs are adduced for AM-signal. The results of a computer simulation of a process corroborate the theoretical conclusions. Noted effects may be important for the signal propagating within spectral absorption line at the TDLS.
Submodels of model of nonlinear diffusion in the inhomogeneous medium involving absorption
Chirkunov, Yu. A.
2015-10-15
We study the five-parameter model, describing the process of nonlinear diffusion in an inhomogeneous medium in the presence of absorption, for which the differential equation of the model admits a continuous Lie group of transformations, acting on the set of its solutions. We found six submodels of the original model of nonlinear diffusion, with different symmetry properties. Of these six submodels, the five submodels with transient absorption, for which the absorption coefficient depends on time according to a power law, represent the greatest interest with a mathematical point of view and with the point of view of physical applications. For each of these nonlinear submodels, we obtained formulas for producing new solutions that contain arbitrary constants, and we found all invariant submodels. All essentially distinct invariant solutions describing these invariant submodels are found in an explicit form or are reduced to finding the solution of nonlinear integral equations. The presence of the arbitrary constants in the integral equations that determine these solutions provide new opportunities for analytical and numerical study of boundary value problems for the received submodels and, thus, for the original model of nonlinear diffusion. For the received invariant submodels, we studied diffusion processes for which at the initial moment of the time at a fixed point is specified as a concentration and its gradient or as a concentration and its velocity. Solving of boundary value problems describing these processes is reduced to the solving of nonlinear integral equations. We established the existence and uniqueness of solutions of these boundary value problems under some additional conditions. The obtained results can be used to study the diffusion of substances, diffusion of conduction electrons and other particles, diffusion of physical fields and propagation of heat in inhomogeneous medium, and also to study a turbulence (Leith model, differential
NASA Astrophysics Data System (ADS)
Gallot, T.; Fehler, M. C.; Brown, S. R.; Buns, D.; Szabo, T.; Malcolm, A. E.
2013-12-01
The nonlinear mechanical behavior of rocks is a well known phenomenon at a laboratory scale and has been observed during earthquakes, slow slip events, volcanic activity, reservoir fracturing, etc. he present work explores the possibility of measuring nonlinear parameters in a semi-infinite medium. Contrary to existing methods that rely on vibrating a sample at a fixed resonant frequency, a pulsed wave is used to create a high amplitude perturbation (the pump) responsible for the nonlinear response. At the same time, a low amplitude wave probes the material to measure changes in elastic properties. Laboratory experiments have been performed in rocks (berea sandstones) to explore the possibility of using such a method for Earth imaging. The strain created by the pump (a shear wave in the tens of kHz), is on the order of a microstrain and is measured by laser vibrometry and extrapolated to the whole sample by a finite difference simulation. A compressional pulse (in the hundreds of kHz range) probes the 15-cm size sample. The variation in time of flight is related to a change in elasticity as described as a function of the strain through quadratic and cubic nonlinearities. Those nonlinear coefficients are shown to be sensitive to several environmental parameters such as temperature, humidity, and also physical properties such as the amplitude of the strain and the relative orientation of the pump and the probing wave. Experimental set-up: a P-wave transducer generates an ultrasonic pulse at 500 kHz recorded by an identical transducer after propagation through the sample. The medium is then perturbed with a S-wave transducer on the top of the sample at 50 kHz .
Nonlinear dynamics of a gas bubble in an incompressible elastic medium.
Emelianov, Stanislav Y; Hamilton, Mark F; Ilinskii, Yurii A; Zabolotskaya, Evgenia A
2004-02-01
A nonlinear model in the form of the Rayleigh-Plesset equation is developed for a gas bubble in an essentially incompressible elastic medium such as a tissue or rubberlike medium. Two constitutive laws for the elastic medium are considered: the Mooney potential, and Landau's expansion of the strain energy density. These two constitutive laws are compared at quadratic order to obtain a relation between their respective elastic constants. Attention is devoted to the relative importance of shear stress on the bubble dynamics, allowing for the equilibrium gas pressure in the bubble to differ substantially from the pressure at infinity. The model for the bubble motion is approximated to quadratic order to assess the importance of shear stress in the surrounding medium relative to that of the gas pressure in the bubble. Relations are derived for the value of the shear wave speed at which the two contributions are comparable, which provide an assessment of when shear stress in the surrounding medium must be taken into account when modeling bubble dynamics.
Some models of propagation of extremely short electromagnetic pulses in a nonlinear medium
Maimistov, Andrei I
2000-04-30
Some cases of model media considered in this paper allow analytical solutions to nonlinear wave equations to be found and the time dependence of the electric field strength to be determined in the explicit form for arbitrarily short electromagnetic pulses. Our analysis does not employ any assumptions concerning a harmonic carrier wave or the variation rate of the field in such pulses. The class of models considered includes two-level resonance and quasi-resonance systems. Nonresonance media are analysed in terms of models of anharmonic oscillators - the Duffing and Lorentz models. In most cases, only particular solutions describing the stationary propagation of a video pulse (a unipolar transient of the electric field or a pulse including a small number of oscillations of the electric field around zero) can be found. These solutions correspond to sufficiently strong electromagnetic fields when the dispersion inherent in the medium is suppressed by nonlinear processes. (invited paper)
NASA Astrophysics Data System (ADS)
Chew, J. V. L.; Sulaiman, J.
2016-06-01
This paper considers Newton-MSOR iterative method for solving 1D nonlinear porous medium equation (PME). The basic concept of proposed iterative method is derived from a combination of one step nonlinear iterative method which known as Newton method with Modified Successive Over Relaxation (MSOR) method. The reliability of Newton-MSOR to obtain approximate solution for several PME problems is compared with Newton-Gauss-Seidel (Newton-GS) and Newton-Successive Over Relaxation (Newton-SOR). In this paper, the formulation and implementation of these three iterative methods have also been presented. From four examples of PME problems, numerical results showed that Newton-MSOR method requires lesser number of iterations and computational time as compared with Newton-GS and Newton-SOR methods.
Nonlinear instability of an Oldroyd elastico-viscous magnetic nanofluid saturated in a porous medium
NASA Astrophysics Data System (ADS)
Moatimid, Galal M.; Alali, Elham M. M.; Ali, Hoda S. M.
2014-09-01
Through viscoelastic potential theory, a Kelvin-Helmholtz instability of two semi-infinite fluid layers, of Oldroydian viscoelastic magnetic nanofluids (MNF), is investigated. The system is saturated by porous medium through two semi-infinite fluid layers. The Oldroyd B model is utilized to describe the rheological behavior of viscoelastic MNF. The system is influenced by uniform oblique magnetic field that acts at the surface of separation. The model is used for the MNF incorporated the effects of uniform basic streaming and viscoelasticity. Therefore, a mathematical simplification must be considered. A linear stability analysis, based upon the normal modes analysis, is utilized to find out the solutions of the equations of motion. The onset criterion of stability is derived; analytically and graphs have been plotted by giving numerical values to the various parameters. These graphs depict the stability characteristics. Regions of stability and instability are identified and discussed in some depth. Some previous studies are recovered upon appropriate data choices. The stability criterion in case of ignoring the relaxation stress times is also derived. To relax the mathematical manipulation of the nonlinear approach, the linearity of the equations of motion is taken into account in correspondence with the nonlinear boundary conditions. Taylor's theory is adopted to expand the governing nonlinear characteristic equation according to of the multiple time scales technique. This analysis leads to the well-known Ginzburg-Landau equation, which governs the stability criteria. The stability criteria are achieved theoretically. To simplify the mathematical manipulation, a special case is considered to achieve the numerical estimations. The influence of orientation of the magnetic fields on the stability configuration, in linear as well as nonlinear approaches, makes a dual role for the magnetic field strength in the stability graphs. Stability diagram is plotted for
Nonlinear instability of an Oldroyd elastico–viscous magnetic nanofluid saturated in a porous medium
Moatimid, Galal M.; Alali, Elham M. M. Ali, Hoda S. M.
2014-09-15
Through viscoelastic potential theory, a Kelvin-Helmholtz instability of two semi-infinite fluid layers, of Oldroydian viscoelastic magnetic nanofluids (MNF), is investigated. The system is saturated by porous medium through two semi-infinite fluid layers. The Oldroyd B model is utilized to describe the rheological behavior of viscoelastic MNF. The system is influenced by uniform oblique magnetic field that acts at the surface of separation. The model is used for the MNF incorporated the effects of uniform basic streaming and viscoelasticity. Therefore, a mathematical simplification must be considered. A linear stability analysis, based upon the normal modes analysis, is utilized to find out the solutions of the equations of motion. The onset criterion of stability is derived; analytically and graphs have been plotted by giving numerical values to the various parameters. These graphs depict the stability characteristics. Regions of stability and instability are identified and discussed in some depth. Some previous studies are recovered upon appropriate data choices. The stability criterion in case of ignoring the relaxation stress times is also derived. To relax the mathematical manipulation of the nonlinear approach, the linearity of the equations of motion is taken into account in correspondence with the nonlinear boundary conditions. Taylor's theory is adopted to expand the governing nonlinear characteristic equation according to of the multiple time scales technique. This analysis leads to the well-known Ginzburg–Landau equation, which governs the stability criteria. The stability criteria are achieved theoretically. To simplify the mathematical manipulation, a special case is considered to achieve the numerical estimations. The influence of orientation of the magnetic fields on the stability configuration, in linear as well as nonlinear approaches, makes a dual role for the magnetic field strength in the stability graphs. Stability diagram is plotted for
NASA Astrophysics Data System (ADS)
Bhattacharyya, S.; De, Simanta
2016-09-01
The impact of the solid polarization of a charged dielectric particle in gel electrophoresis is studied without imposing a weak-field or a thin Debye length assumption. The electric polarization of a dielectric particle due to an external electric field creates a non-uniform surface charge density, which in turn creates a non-uniform Debye layer at the solid-gel interface. The solid polarization of the particle, the polarization of the double layer, and the electro-osmosis of mobile ions within the hydrogel medium create a nonlinear effect on the electrophoresis. We have incorporated those nonlinear effects by considering the electrokinetics governed by the Stokes-Brinkman-Nernst-Planck-Poisson equations. We have computed the governing nonlinear coupled set of equations numerically by adopting a finite volume based iterative algorithm. Our numerical method is tested for accuracy by comparing with several existing results on free-solution electrophoresis as well as results based on the Debye-Hückel approximation. Our computed result shows that the electrophoretic velocity decreases with the rise of the particle dielectric permittivity constant and attains a saturation limit at large values of permittivity. A significant impact of the solid polarization is found in gel electrophoresis compared to the free-solution electrophoresis.
Seismic demand evaluation of medium ductility RC moment frames using nonlinear procedures
NASA Astrophysics Data System (ADS)
Ghaffarzadeh, Hosein; Talebian, Nima; Kohandel, Roya
2013-09-01
Performance-based earthquake engineering is a recent focus of research that has resulted in widely developed design methodologies due to its ability to realistically simulate structural response characteristics. Precise prediction of seismic demands is a key component of performance-based design methodologies. This paper presents a seismic demand evaluation of reinforced concrete moment frames with medium ductility. The accuracy of utilizing simplified nonlinear static analysis is assessed by comparison against the results of time history analysis on a number of frames. Displacement profiles, drift demand and maximum plastic rotation were computed to assess seismic demands. Estimated seismic demands were compared to acceptance criteria in FEMA 356. The results indicate that these frames have sufficient capacity to resist interstory drifts that are greater than the limit value.
Convection and reaction in a diffusive boundary layer in a porous medium: Nonlinear dynamics
NASA Astrophysics Data System (ADS)
Andres, Jeanne Therese H.; Cardoso, Silvana S. S.
2012-09-01
We study numerically the nonlinear interactions between chemical reaction and convective fingering in a diffusive boundary layer in a porous medium. The reaction enhances stability by consuming a solute that is unstably distributed in a gravitational field. We show that chemical reaction profoundly changes the dynamics of the system, by introducing a steady state, shortening the evolution time, and altering the spatial patterns of velocity and concentration of solute. In the presence of weak reaction, finger growth and merger occur effectively, driving strong convective currents in a thick layer of solute. However, as the reaction becomes stronger, finger growth is inhibited, tip-splitting is enhanced and the layer of solute becomes much thinner. Convection enhances the mass flux of solute consumed by reaction in the boundary layer but has a diminishing effect as reaction strength increases. This nonlinear behavior has striking differences to the density fingering of traveling reaction fronts, for which stronger chemical kinetics result in more effective finger merger owing to an increase in the speed of the front. In a boundary layer, a strong stabilizing effect of reaction can maintain a long-term state of convection in isolated fingers of wavelength comparable to that at onset of instability.
NASA Astrophysics Data System (ADS)
Pikichyan, H. V.
2016-06-01
It is shown that for the nonlinear boundary value problem of determining the radiation field inside a one-dimensional anisotropic medium illuminated from outside at its boundaries on both sides, the formulas for adding layers in semilinear systems of differential equations for radiative transfer, invariant embedding, and total Ambartsumyan invariance can be used to reduce the equations for the problem to separable equations with initial conditions. The fields travelling to the left and right are thereby found independently of one another. In addition, when one of them has been determined, the other can be found directly using an explicit expression. A general equivalence property of operators with respect to a certain mathematical form, expression, or functional is formulated mathematically. New equations, referred to as kinetic equations of equivalency, are derived from the mutual equivalence of the differential operators of the Boltzmann kinetic equation (the equations of radiative transfer) and the functional equation of the Ambartsumian's complete invariance. Besides separability, these new equations also have the property of linearity. Formulas are also introduced for special problems of single sided illumination of a medium that in this case serve as supplementary information in the initial conditions for formulating Cauchy problems.
Position-momentum-entangled photon pairs in nonlinear waveguides and transmission lines
NASA Astrophysics Data System (ADS)
Sherkunov, Y.; Whittaker, David M.; Fal'ko, Vladimir
2016-04-01
We analyze the correlation properties of light in nonlinear waveguides and transmission lines, predict the position-momentum realization of the Einstein-Podolsky-Rosen paradox for photon pairs in Kerr-type nonlinear photonic circuits, and we show how two-photon entangled states can be generated and detected.
Kitsak, M A; Kitsak, A I
2008-04-30
The cross modulation method of transformation of the spatial coherence of low-power pulsed laser radiation in a nonlinear medium is proposed. The method is realised experimentally in a multimode optical fibre. The estimates of the degree of spatial coherence of radiation subjected to the phase cross modulation demonstrated the high efficiency of this radiation decorrelation mechanism. (control of laser radiation parameters)
Varray, François; Ramalli, Alessandro; Cachard, Christian; Tortoli, Piero; Basset, Olivier
2011-07-01
The simulation of nonlinear propagation of ultrasound waves is typically based on the Kuznetsov-Zabolotskaya- Khokhlov equation. A set of simulators has been proposed in the literature but none of them takes into account a possible spatial 3-D variation of the nonlinear parameter in the investigated medium. This paper proposes a generalization of the angular spectrum method (GASM) including the spatial variation of the nonlinear parameter. The proposed method computes the evolution of the fundamental and second-harmonic waves in four dimensions (spatial 3-D and time). For validation purposes, the one-way fields produced by the GASM are first compared with those produced by established reference simulators and with experimental one-way fields in media with a homogeneous nonlinear parameter. The same simulations are repeated for media having an axial variation of the nonlinear parameter. The mean errors estimated in the focal region are less than 4.0% for the fundamental and 5.4% for the second harmonic in all cases. Finally, the fundamental and second-harmonic fields simulated for media having nonlinear parameter variations in the axial, lateral, and elevation directions, which cannot be simulated with other currently available methods, are presented. The new approach is also shown to yield a reduction in computation time by a factor of 13 with respect to the standard nonlinear simulator.
NASA Astrophysics Data System (ADS)
Ahmad, Harith; Hassan, Nor Ahya; Aidit, Siti Nabila; Tiu, Zian Cheak
2016-07-01
The applications of graphene thin film as a nonlinear medium and stabilizer to generate a stable multi-wavelength is proposed and demonstrated. A 50 m long highly nonlinear photonic crystal fiber (PCF) is incorporated into the cavity to achieve unstable multi-wavelength based on nonlinear polarization rotation (NPR) effect. By introducing the graphene thin film into the cavity, a stable multi-wavelength oscillation is obtained. The laser generates more than 7 lasings with constant spacing of 0.47 nm. The output is highly stable with power fluctuation of less than 3 dB within a period of 30 min. The multi-wavelength EDFL exhibits a tunability from the center wavelength of 1550 nm to 1560 nm.
NASA Technical Reports Server (NTRS)
Lobashov, A. A.; Mostepanenko, V. M.
1993-01-01
The theory of quantum effects in nonlinear dielectric media is developed. The nonlinear dielectric media is influenced by an external pumping field. The diagonalization of the Hamiltonian of a quantized field is obtained by the canonical Bogoliubov transformations. The transformations allow us to obtain the general expressions for the number of created photons and for the degree of squeezing. In the case of a plane pumping wave, for example, the results are calculated by using the zero order of the secular perturbation theory, with small parameters characterizing the medium nonlinearity. The Heisenberg equations of motion are obtained for non-stationary case and a commonly used Hamiltonian is derived from the first principles of quantum electrodynamics.
NASA Astrophysics Data System (ADS)
Sharma, Rajesh; Bhargava, Rama
2015-07-01
In this article, the two-dimensional boundary layer problem of Hiemenz flow (two-dimensional flow of a fluid near a stagnation point) of an incompressible micropolar fluid towards a nonlinear stretching surface placed in a porous medium in the presence of transverse magnetic field is examined. The resulting nonlinear differential equations governing the problem have been transformed by a similarity transformation into a system of nonlinear ordinary differential equations which are solved numerically by the Element Free Galerkin method. The influence of various parameters on the velocity, microrotation, temperature, and concentration is shown. Some of the results are compared with the Finite Element Method. Finally, validation of the numerical results is demonstrated for local skin friction ? for hydrodynamic micropolar fluid flow on a linearly stretching surface.
On shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients.
Abdel-Gawad, Hamdy I; Osman, Mohamed
2015-07-01
In this paper, we studied the progression of shallow water waves relevant to the variable coefficient Korteweg-de Vries (vcKdV) equation. We investigated two kinds of cases: when the dispersion and nonlinearity coefficients are proportional, and when they are not linearly dependent. In the first case, it was shown that the progressive waves have some geometric structures as in the case of KdV equation with constant coefficients but the waves travel with time dependent speed. In the second case, the wave structure is maintained when the nonlinearity balances the dispersion. Otherwise, water waves collapse. The objectives of the study are to find a wide class of exact solutions by using the extended unified method and to present a new algorithm for treating the coupled nonlinear PDE's.
On shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients
Abdel-Gawad, Hamdy I.; Osman, Mohamed
2014-01-01
In this paper, we studied the progression of shallow water waves relevant to the variable coefficient Korteweg–de Vries (vcKdV) equation. We investigated two kinds of cases: when the dispersion and nonlinearity coefficients are proportional, and when they are not linearly dependent. In the first case, it was shown that the progressive waves have some geometric structures as in the case of KdV equation with constant coefficients but the waves travel with time dependent speed. In the second case, the wave structure is maintained when the nonlinearity balances the dispersion. Otherwise, water waves collapse. The objectives of the study are to find a wide class of exact solutions by using the extended unified method and to present a new algorithm for treating the coupled nonlinear PDE’s. PMID:26199750
On shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients.
Abdel-Gawad, Hamdy I; Osman, Mohamed
2015-07-01
In this paper, we studied the progression of shallow water waves relevant to the variable coefficient Korteweg-de Vries (vcKdV) equation. We investigated two kinds of cases: when the dispersion and nonlinearity coefficients are proportional, and when they are not linearly dependent. In the first case, it was shown that the progressive waves have some geometric structures as in the case of KdV equation with constant coefficients but the waves travel with time dependent speed. In the second case, the wave structure is maintained when the nonlinearity balances the dispersion. Otherwise, water waves collapse. The objectives of the study are to find a wide class of exact solutions by using the extended unified method and to present a new algorithm for treating the coupled nonlinear PDE's. PMID:26199750
NASA Astrophysics Data System (ADS)
Kamada, Kenji; Satoh, Kazuyuki; Tanaka, Yoshito
2016-09-01
Optical recording by a single shot of an 8 ns laser pulse in a dye-doped holographic polymeric medium was demonstrated with a peak power as low as 71 W at a wavelength of 402 nm. Nonlinear absorption triggered by two-photon absorption and enhanced by the succeeding process allows high-speed recording corresponding to 125 Mbps (3.4 times the recording speed of a Blu-ray Disc). The preformed holographic grating in the medium enhanced the readout signal through diffraction, resulting in a signal-to-noise ratio of about 15 dB. The recording capacity was estimated at ca. 80 GB/side for 100 µm/side by recording 20 layers, but that of over TB/side class would be possible for optical optimization. Theoretically, it can be improved to 10 TB/side for 800 µm/side by recording 400 layers.
Propagation of Weakly Guided Waves in a Kerr Nonlinear Medium using a Perturbation Approach
Dacles-Mariani, J; Rodrigue, G
2004-10-06
The equations are represented in a simplified format with only a few leading terms needed in the expansion. The set of equations are then solved numerically using vector finite element method. To validate the algorithm, they analyzed a two-dimensional rectangular waveguide consisting of a linear core and nonlinear identical cladding. The exact nonlinear solutions for three different modes of propagations, TE0, TE1, and TE2 modes are generated and compared with the computed solutions. Next, they investigate the effect of a more intense monochromatic field on the propagation of a 'weak' optical field in a fully three-dimensional cylindrical waveguide.
Nonlinear shear wave in a non Newtonian visco-elastic medium
Banerjee, D.; Janaki, M. S.; Chakrabarti, N.
2012-06-15
An analysis of nonlinear transverse shear wave has been carried out on non-Newtonian viscoelastic liquid using generalized hydrodynamic model. The nonlinear viscoelastic behavior is introduced through velocity shear dependence of viscosity coefficient by well known Carreau-Bird model. The dynamical feature of this shear wave leads to the celebrated Fermi-Pasta-Ulam problem. Numerical solution has been obtained which shows that initial periodic solutions reoccur after passing through several patterns of periodic waves. A possible explanation for this periodic solution is given by constructing modified Korteweg de Vries equation. This model has application from laboratory to astrophysical plasmas as well as in biological systems.
Makarov, V A; Petnikova, V M; Rudenko, K V; Shuvalov, V V
2015-01-31
The adiabatic approximation is used to obtain an analytical solution to a nonintegrable problem of propagation of a plane elliptically polarised light wave with zero mean amplitudes of orthogonal circularly polarised field components through an isotropic gyrotropic medium with local and nonlocal components of Kerr nonlinearity and second-order group velocity dispersion. We describe the aperiodic evolution of bound (attributable to the medium nonlinearity) paired states, which are responsible for the propagation of two orthogonal polarisation components – cnoidal waves with significantly different periods. (nonlinear optical phenomena)
Tensor of the nonlinear polarizability of anisotropic medium and ``local'' field method
NASA Astrophysics Data System (ADS)
Lavric, V. V.; Ovander, L. N.; Shunyakov, V. T.
1983-08-01
The nonlinear polarizability tensor (NPT) for a molecular crystal of arbitrary symmetry has been obtained within the framework of polariton theory. Use of the Göppert-Mayer unitary transformation for the Hamiltonian of the crystal plus quantized electromagnetic field system made it possible to represent finally the result for the NPT in a compact form and to compare with results of semiphenomenological calculation of the NPT and to go out of the framework of the Gaitler-London approximation.
Light steering of Air-Gaussian beam in Nonlocal Nonlinear Medium
NASA Astrophysics Data System (ADS)
Chen, Ran; Zhang, Xiaping
2016-07-01
With a nonlocal model, we investigate the propagation dynamics of a single Airy-Gaussian (AiG) beam and their interaction in one-dimensional condition by means of direct numerical simulations. With the split-step Fourier method, numerical results show that nonlocality can support periodic intensity distribution of AiG beams leading to the formation of stable bound states. Espesically, by tuning the phase difference between the two beams, we can steer the centre of the bound AiG beams in nonlocal nonlinear media.
Polarization-dependent colored conical emission in a quadratically nonlinear medium
NASA Astrophysics Data System (ADS)
Bi, Jie; Zhou, Lina; Zheng, Anshou; Lv, Tao; Xiang, Dong
2012-07-01
Both supercontinuum conical emission (SCCE) and blue-green conical emission (CE) by means of second harmonic generation (SHG) were observed alternately in a β-barium borate (BBO) crystal induced by femtosecond laser pulses with vertical polarization state. Three theoretical models were analyzed to interpret the angular beam of SCCE. The experimental conical angles with different wavelengths in BBO crystal and BK-7 glass can be explained well by nonlinear X-wave model and Cerenkov type phase matching model other than four-wave mixing (FWM) model.
Three-dimensional spinning solitons in the cubic-quintic nonlinear medium.
Mihalache, D; Mazilu, D; Crasovan, L C; Malomed, B A; Lederer, F
2000-06-01
We find one-parameter families of three-dimensional spatiotemporal bright vortex solitons (doughnuts, or spinning light bullets), in bulk dispersive cubic-quintic optically nonlinear media. The spinning solitons display a symmetry-breaking azimuthal instability, which leads to breakup of the spinning soliton into a set of fragments, each being a stable nonspinning light bullet. However, in some cases the instability is developing so slowly that the spinning light bullets may be regarded as virtually stable ones, from the standpoint of an experiment with finite-size samples.
Breathing as a low frequency wave propagation in nonlinear elastic permeable medium
NASA Astrophysics Data System (ADS)
Kyriakou, Elizabeth; McKenzie, David R.; Suchowerska, Natalka; Fulton, Roger R.
2007-05-01
Breathing can be regarded as a type of low frequency wave propagation. Unlike sound propagation in open air, in breathing, the air compressibility is not as important as the flow of air, and to a first approximation the air can be regarded as incompressible. We have developed a one-dimensional analytical description of wave motion in a metamaterial consisting of a porous elastic medium contained within chambers, separated by plates with orifices representing the minor airways. The metamaterial is placed within a cylinder with impermeable sides representing the thorax, driven at one end by a piston representing the diaphragm. The incompressible air is able to escape from the top of the cylinder. The solutions to the wave equation have characteristics that depend on the values of permeability (defined by the size of the orifice in the plates), the Young's modulus of the elastic medium and the density of lung tissue. A ‘normal' regime is identified in which the strain of the medium near the diaphragm is large and the strain at the top of the cylinder near the outlet is small. An ‘abnormal' regime is also identified in which the opposite applies. A rapid transition between the two regimes can be caused by changing the parameters representing the lung tissue. This transition may represent the onset of a disease state such as asthma.
Bobylev, Yu. B.; Kuzelev, M. V.
2012-06-15
A nonlinear quantum theory of stimulated Cherenkov radiation of transverse electromagnetic waves from a low-density relativistic electron beam in an isotropic dielectric medium is presented. A quantum model based on the Klein-Gordon equation is used. The growth rates of beam instabilities caused by the effect of stimulated Cherenkov radiation have been determined in the linear approximation. Mechanisms of the nonlinear saturation of relativistic quantum Cherenkov beam instabilities have been analyzed and the corresponding analytical solutions have been obtained.
Nonlinear Stress/Strain Behavior of a Synthetic Porous Medium at Seismic Frequencies
NASA Astrophysics Data System (ADS)
Roberts, P. M.; Ibrahim, R. H.
2008-12-01
Laboratory experiments on porous core samples have shown that seismic-band (100 Hz or less) mechanical, axial stress/strain cycling of the porous matrix can influence the transport behavior of fluids and suspended particles during steady-state fluid flow through the cores. In conjunction with these stimulated transport experiments, measurements of the applied dynamic axial stress/strain were made to investigate the nonlinear mechanical response of porous media for a poorly explored range of frequencies from 1 to 40 Hz. A unique core-holder apparatus that applies low-frequency mechanical stress/strain to 2.54-cm-diameter porous samples during constant-rate fluid flow was used for these experiments. Applied stress was measured with a load cell in series with the source and porous sample, and the resulting strain was measured with an LVDT attached to the core face. A synthetic porous system consisting of packed 1-mm-diameter glass beads was used to investigate both stress/strain and stimulated mass-transport behavior under idealized conditions. The bead pack was placed in a rubber sleeve and static confining stresses of 2.4 MPa radial and 1.7 MPa axial were applied to the sample. Sinusoidal stress oscillations were applied to the sample at 1 to 40 Hz over a range of RMS stress amplitude from 37 to 275 kPa. Dynamic stress/strain was measured before and after the core was saturated with deionized water. The slope of the linear portion of each stress/strain hysteresis loop was used to estimate Young's modulus as a function of frequency and amplitude for both the dry and wet sample. The modulus was observed to increase after the dry sample was saturated. For both dry and wet cases, the modulus decreased with increasing dynamic RMS stress amplitude at a constant frequency of 23 Hz. At constant RMS stress amplitude, the modulus increased with increasing frequency for the wet sample but remained constant for the dry sample. The observed nonlinear behavior of Young's modulus
NASA Astrophysics Data System (ADS)
Zhang, Jitao; He, Wei; Zhang, Ming; Zhao, Hongmei; Yang, Qian; Guo, Shuting; Wang, Xiaolei; Zheng, Xiaowan; Cao, Lingzhi
2015-09-01
A broadband current-sensing device with frequency-conversion mechanism consisting of Terfenol-D/Pb(Zr.Ti)O3 (PZT)/Terfenol-D magnetoelectric laminate and Fe73.5Cu1Nb3Si13.5B9 nanocrystalline flux concentrator is fabricated and characterized. For the purpose of acquiring resonance-enhanced sensitivity within broad bandwidth, a frequency-modulation mechanism is introduced into the presented device through the nonlinearity of field-dependence giant magnetostrictive materials. The presented configuration provides a solution to monitor the weak currents and achieves resonance-enhanced sensitivity of 178.4 mV/A at power-line frequency, which exhibits ˜3.86 times higher than that of direct output at power-line frequency of 50 Hz. Experimental results demonstrate that a weak step-change input current of 1 mA can be clearly distinguished by the output amplitude or phase. This miniature current-sensing device provides a promising application in power-line weak current measurement.
Zhang, Jitao; He, Wei; Zhang, Ming; Zhao, Hongmei; Yang, Qian; Guo, Shuting; Wang, Xiaolei; Zheng, Xiaowan; Cao, Lingzhi
2015-09-01
A broadband current-sensing device with frequency-conversion mechanism consisting of Terfenol-D/Pb(Zr.Ti)O3 (PZT)/Terfenol-D magnetoelectric laminate and Fe73.5Cu1Nb3Si13.5B9 nanocrystalline flux concentrator is fabricated and characterized. For the purpose of acquiring resonance-enhanced sensitivity within broad bandwidth, a frequency-modulation mechanism is introduced into the presented device through the nonlinearity of field-dependence giant magnetostrictive materials. The presented configuration provides a solution to monitor the weak currents and achieves resonance-enhanced sensitivity of 178.4 mV/A at power-line frequency, which exhibits ∼3.86 times higher than that of direct output at power-line frequency of 50 Hz. Experimental results demonstrate that a weak step-change input current of 1 mA can be clearly distinguished by the output amplitude or phase. This miniature current-sensing device provides a promising application in power-line weak current measurement.
Makarov, V A; Petnikova, V M; Potravkin, N N; Shuvalov, V V
2014-02-28
Using the linearization method, we obtain approximate solutions to a one-dimensional nonintegrable problem of propagation of elliptically polarised light waves in an isotropic gyrotropic medium with local and nonlocal components of the Kerr nonlinearity and group-velocity dispersion. The consistent evolution of two orthogonal circularly polarised components of the field is described analytically in the case when their phases vary linearly during propagation. The conditions are determined for the excitation of waves with a regular and 'chaotic' change in the polarisation state. The character of the corresponding nonlinear solutions, i.e., periodic analogues of multisoliton complexes, is analysed. (nonlinear optical phenomena)
Eliminating material constraints for nonlinearity with plasmonic metamaterials
Neira, Andres D.; Olivier, Nicolas; Nasir, Mazhar E.; Dickson, Wayne; Wurtz, Gregory A.; Zayats, Anatoly V.
2015-01-01
Nonlinear optical materials comprise the foundation of modern photonics, offering functionalities ranging from ultrafast lasers to optical switching, harmonic and soliton generation. Optical nonlinearities are typically strong near the electronic resonances of a material and thus provide limited tuneability for practical use. Here we show that in plasmonic nanorod metamaterials, the Kerr-type nonlinearity is not limited by the nonlinear properties of the constituents. Compared with gold's nonlinearity, the measured nonlinear absorption and refraction demonstrate more than two orders of magnitude enhancement over a broad spectral range that can be engineered via geometrical parameters. Depending on the metamaterial's effective plasma frequency, either a focusing or defocusing nonlinearity is observed. The ability to obtain strong and fast optical nonlinearities in a given spectral range makes these metamaterials a flexible platform for the development of low-intensity nonlinear applications. PMID:26195182
NASA Astrophysics Data System (ADS)
RamReddy, Chetteti; Pradeepa, Teegala
2016-05-01
Based on the nonlinear variation of density with temperature (NDT) in the buoyancy term, the mixed convection flow along a vertical plate of a micropolar fluid saturated porous medium is considered. In addition, the effect of homogeneous-heterogeneous reaction and convective boundary condition has been taken into account. Using lie scaling group transformations, the similarity representation is attained for the system of partial differential equations, prior to being solved by a spectral quasilinearization method. The results show that in the presence of aiding and opposing flow situations, both the species concentration and mass transfer rate decreases when the strength of homogeneous and heterogeneous reaction parameters are enhanced.
Vu, Cung Khac; Nihei, Kurt; Johnson, Paul A.; Guyer, Robert; Ten Cate, James A.; Le Bas, Pierre-Yves; Larmat, Carene S.
2015-12-29
A method and system includes generating a first coded acoustic signal including pulses each having a modulated signal at a central frequency; and a second coded acoustic signal each pulse of which includes a modulated signal a central frequency of which is a fraction d of the central frequency of the modulated signal for the corresponding pulse in the first plurality of pulses. A receiver detects a third signal generated by a non-linear mixing process in the mixing zone and the signal is processed to extract the third signal to obtain an emulated micro-seismic event signal occurring at the mixing zone; and to characterize properties of the medium or creating a 3D image of the properties of the medium, or both, based on the emulated micro-seismic event signal.
Volkova, E. A.; Popov, A. M. Tikhonova, O. V.
2013-03-15
The nonlinear polarization response of a quantum system modeling a silver atom in the field of high-intensity radiation in the IR and UV spectral ranges has been studied by direct numerical integration of a nonstationary Schroedinger equation. The domains of applicability of perturbation theory and polarization expansion in powers of the field intensity are determined. The contribution of excited atoms and electrons in a continuum to the atomic polarization response at the field frequency, which arises due to the radiation-induced excitation and photoionization processes, is analyzed. Features of the nonlinear response to an external field under conditions of atom stabilization are considered.
Optical nonlinearities in plasmonic metamaterials (Conference Presentation)
NASA Astrophysics Data System (ADS)
Zayats, Anatoly V.
2016-04-01
Metals exhibit strong and fast nonlinearities making metallic, plasmonic, structures very promising for ultrafast all-optical applications at low light intensities. Combining metallic nanostructures in metamaterials provides additional functionalities via prospect of precise engineering of spectral response and dispersion. From this point of view, hyperbolic metamaterials, in particular those based on plasmonic nanorod arrays, provide wealth of exciting possibilities in nonlinear optics offering designed linear and nonlinear properties, polarization control, spontaneous emission control and many others. Experiments and modeling have already demonstrated very strong Kerr-nonlinear response and its ultrafast recovery due to the nonlocal nature of the plasmonic mode of the metamaterial, so that small changes in the permittivity of the metallic component under the excitation modify the nonlocal response that in turn leads to strong changes of the metamaterial transmission. In this talk, we will discuss experimental studies and numerical modeling of second- and third-order nonlinear optical processes in hyperbolic metamaterials based on metallic nanorods and other plasmonic systems where coupling between the resonances plays important role in defining nonlinear response. Second-harmonic generation and ultrafast Kerr-type nonlinearity originating from metallic component of the metamaterial will be considered, including nonlinear magneto-optical effects. Nonlinear optical response of stand-alone as well as integrated metamaterial components will be presented. Some of the examples to be discussed include nonlinear polarization control, nonlinear metamaterial integrated in silicon photonic circuitry and second-harmonic generation, including magneto-optical effects.
NASA Astrophysics Data System (ADS)
Almaev, R. Kh; Suvorov, A. A.
1993-09-01
We investigate the statistical characteristics of the phase of a wave propagating along a ranging path that includes a phase-conjugate mirror through a medium whose complex permittivity ɛ varies randomly. We obtain expressions for the mean change and variance of fluctuations in the phase of a plane wave. We show that phase fluctuations caused by the random changes of the imaginary part of ɛ are not canceled by the phase-conjugate mirror. We obtain conditions for the appearance of enhanced backward scattering in comparison with the mean phase and variance of phase fluctuations for the reflected wave in this absorbing, randomly inhomogeneous medium.
Higher-order nonlinear effects in a Josephson parametric amplifier
NASA Astrophysics Data System (ADS)
Kochetov, Bogdan A.; Fedorov, Arkady
2015-12-01
Nonlinearity of the current-phase relationship of a Josephson junction is the key resource for a Josephson parametric amplifier (JPA) as well as for a Josephson traveling-wave parametric amplifier, the only devices in which the quantum limit for added noise has so far been approached at microwave frequencies. A standard approach to describe JPA takes into account only the lowest order (cubic) nonlinearity resulting in a Duffing-like oscillator equation of motion or in a Kerr-type nonlinearity term in the Hamiltonian. In this paper we derive the quantum expression for the gain of JPA including all orders of the Josephson junction nonlinearity in the linear response regime. We then analyze gain saturation effect for stronger signals within a semiclassical approach. Our results reveal nonlinear effects of higher orders and their implications for operation of a JPA.
NASA Astrophysics Data System (ADS)
Sun, Wen-Rong; Tian, Bo; Xie, Xi-Yang; Chai, Jun; Jiang, Yan
2016-10-01
High-order rogue waves of the coupled nonlinear Schrödinger equations with negative coherent coupling, which describe the propagation of orthogonally polarized optical waves in an isotropic medium, are reported in this paper. Key point lies in the introduction of a limit process in the Darboux transformation, with which we obtain a family of the first- and second-order rational solutions for the purpose of modelling the rogue waves. We observe that the double-hump rogue wave in the course of evolution turns into the one-hump rogue wave, and that the dark rogue wave with four valleys in the course of evolution turns into the bright rogue wave. It is found that the second-order rogue wave can split up, giving birth to the multiple rogue waves.
NASA Astrophysics Data System (ADS)
Anwar Bég, O.; Zueco, J.; Takhar, H. S.; Bég, T. A.; Sajid, A.
2009-11-01
A boundary-layer model is described for the two-dimensional nonlinear transient thermal convection heat and mass transfer in an optically-thick fluid in a Darcian porous medium adjacent to an impulsively started vertical surface, in the presence of significant thermal radiation and buoyancy forces in an (X∗,Y∗,t∗) coordinate system. An algebraic approximation is employed to simplify the integro-differential equation of radiative transfer for unidirectional flux normal to the plate into the boundary-layer regime, by incorporating this flux term in the energy conservation equation. The conservation equations are non-dimensionalized into an (X,Y,T) coordinate system and solved using the Network Simulation Method (NSM), a robust numerical technique which demonstrates high efficiency and accuracy. The transient variation of non-dimensional streamwise velocity component (u) and temperature (T) and concentration (C) functions is computed for various selected values of Stark number (radiation-conduction interaction parameter) and Darcy number. Transient velocity (u) and steady-state local skin friction (τX) are also studied for various thermal Grashof number (Gr), species Grashof number (Gm), Schmidt number (Sc) and Stark number (N) values. These computations for the infinite permeability case (Da → ∞) are compared with previous finite difference solutions [Prasad et al. Int J Therm Sci 2007;46(12):1251-8] and shown to be in excellent agreement. An increase in Darcy number is seen to accelerate the flow and boost velocity. A decrease in Stark number (corresponding to an increase in thermal radiation heat transfer contribution) is shown to increase the velocity values. Temperature function is observed to fall in value with a rise in Da and increase with decrease in N (corresponding to an increase in thermal radiation heat transfer contribution). Applications of the study include rocket combustion chambers, astrophysical flows, spacecraft thermal fluid dynamics in
NASA Astrophysics Data System (ADS)
Grigoriev, K. S.; Makarov, V. A.; Perezhogin, I. A.
2016-01-01
For the first time we have obtained the analytical expressions describing the spatial distribution of the polarization of a second harmonic beam’s light field reflected from the surface of an isotropic gyrotropic medium in the case when a normally incident fundamental beam contains a polarization singularity of an arbitrary type. The contribution of bulk and surface responses of the nonlinear medium in the formation of the lines of circular polarization in the second harmonic beam were analyzed. The relation between topological characteristics and polarization states of the singularities in the incident and reflected beams was established.
Improved nonlinear slot waveguides using dielectric buffer layers: properties of TM waves.
Elsawy, Mahmoud M R; Renversez, Gilles
2016-04-01
We propose an improved version of the symmetric metal slot waveguides with a Kerr-type nonlinear dielectric core adding linear dielectric buffer layers between the metal regions and the core. Using a finite element method to compute the stationary nonlinear modes, we provide the full phase diagrams of its main transverse magnetic modes as a function of the total power, buffer layer, and core thicknesses that are more complex than the ones of the simple nonlinear metal slot. We show that these modes can exhibit spatial transitions toward specific modes of the new structure as a function of power. We also demonstrate that, for the main modes, the losses are reduced compared to the previous structures, and that they can now decrease with power. Finally, we describe the stability properties of the main stationary solutions using nonlinear FDTD simulations. PMID:27192282
NASA Astrophysics Data System (ADS)
Hristov, Jordan
2016-03-01
Closed form approximate solutions to nonlinear heat (mass) diffusion equation with power-law nonlinearity of the thermal (mass) diffusivity have been developed by the integral-balance method avoiding the commonly used linearization by the Kirchhoff transformation. The main improvement of the solution is based on the double-integration technique and a new approach to the space derivative. Solutions to Dirichlet and Neumann boundary condition problems have been developed and benchmarked against exact numerical and approximate analytical solutions available in the literature.
NASA Astrophysics Data System (ADS)
McGurn, Arthur R.
2013-10-01
The barrier transmission characteristics of a one-dimensional chain of optically linear split-ring resonators (SRRs) containing a barrier composed of optically nonlinear split-ring resonators are studied. (This is an analogy to the quantum mechanical problem of the resonant transmission of a particle through a finite barrier potential.) The SRRs are idealized as inductor-resistor-capacitor-equivalent resonator circuits where the capacitance is either from a linear dielectric medium (optically linear SRRs) or from a Kerr-type nonlinear dielectric medium (optically nonlinear SRRs). The SRRs are arrayed in a one-dimensional chain and interact with one another through weak nearest-neighbor mutually inductive couplings. The transmission maxima of the SRR barrier problem are studied as they are located in a two-dimensional parameter space characterizing the linear mutually inductive coupling and the nonlinear Kerr dielectric of the SRRs of the barrier. The result is a two-dimensional map giving the conditions for the existence of the resonant-barrier modes that are excited in the transmission process. The various lines of transmission maxima in the two-dimensional plot are associated with different types of resonant excitations in the barrier. The map is similar to one recently made in McGurn [Phys. Rev. BPRBMDO0163-182910.1103/PhysRevB.77.115105 77, 115105 (2008)] for the resonant-transmission modes of a nonlinear barrier in a photonic crystal waveguide. The SRR problem, however, is quite different from the photonic crystal problem as the nonlinear difference equations of the two systems are different in the nature of their nonlinear interactions. Consequently, the results for the two systems are briefly compared. The transmission maxima of the SRR system occur along lines in the two-dimensional plot, which are associated with modes resonantly excited in the barrier. These lines of resonant modes either originate as a simple evolution from the resonant modes of the
NASA Technical Reports Server (NTRS)
Dede, Christopher J.
1990-01-01
Claims and rebuttals that hypermedia (the associative, nonlinear interconnection of multimedia materials) is a fundamentally innovative means of thinking and communicating are described. This representational architecture has many advantages that make it a major advance over other media; however, it also has several intrinsic problems that severly limits its effectiveness as a medium. These advantages and limits in applications are discussed.
Ding, Yujie J
2010-01-15
Owing to strong coupling between transverse-optical phonons and high-frequency terahertz waves in zinc-blende semiconductors, second-order nonlinear coefficients can be dramatically enhanced within the forbidden band of the polariton resonance. However, linear absorption in this regime is also dramatically increased. We show that transverse-pumping geometry can be exploited for achieving an efficient terahertz generation at the polariton resonance. Our estimates illustrate that pump powers as low as 100 mW are sufficient for causing the significant depletion of the pump beams.
NASA Astrophysics Data System (ADS)
Sadhu, Arunangshu; Sarkar, Somenath
2016-05-01
We report a simple and straightforward approximate analysis to investigate the effect of Kerr type nonlinear optical processes in sub-wavelength diameter step index optical fibers based on Marcuse method in single mode region. Optimum core diameters of such fibers, predicted by us, together with relevant core nonlinearity coefficient and effective area are seen to be compatible with the analytical values indicating the validity of this novel application of the elegant approximate method. However, the corresponding values, obtained by earlier variational method, show larger discrepancy with analytical findings in comparison with ours. Also, maximum enhancement of nonlinear processes within single mode region, confirming almost the analytical method, assures less diffraction. Formulations, coupled with simplicity and novelty of the present analysis, should find wide use by system users and experimentalists in this emerging area.
Ullah, Imran; Bhattacharyya, Krishnendu; Shafie, Sharidan; Khan, Ilyas
2016-01-01
Numerical results are presented for the effect of first order chemical reaction and thermal radiation on mixed convection flow of Casson fluid in the presence of magnetic field. The flow is generated due to unsteady nonlinearly stretching sheet placed inside a porous medium. Convective conditions on wall temperature and wall concentration are also employed in the investigation. The governing partial differential equations are converted to ordinary differential equations using suitable transformations and then solved numerically via Keller-box method. It is noticed that fluid velocity rises with increase in radiation parameter in the case of assisting flow and is opposite in the case of opposing fluid while radiation parameter has no effect on fluid velocity in the forced convection. It is also seen that fluid velocity and concentration enhances in the case of generative chemical reaction whereas both profiles reduces in the case of destructive chemical reaction. Further, increase in local unsteadiness parameter reduces fluid velocity, temperature and concentration. Over all the effects of physical parameters on fluid velocity, temperature and concentration distribution as well as on the wall shear stress, heat and mass transfer rates are discussed in detail. PMID:27776174
Filamentation with nonlinear Bessel vortices.
Jukna, V; Milián, C; Xie, C; Itina, T; Dudley, J; Courvoisier, F; Couairon, A
2014-10-20
We present a new type of ring-shaped filaments featured by stationary nonlinear high-order Bessel solutions to the laser beam propagation equation. Two different regimes are identified by direct numerical simulations of the nonlinear propagation of axicon focused Gaussian beams carrying helicity in a Kerr medium with multiphoton absorption: the stable nonlinear propagation regime corresponds to a slow beam reshaping into one of the stationary nonlinear high-order Bessel solutions, called nonlinear Bessel vortices. The region of existence of nonlinear Bessel vortices is found semi-analytically. The influence of the Kerr nonlinearity and nonlinear losses on the beam shape is presented. Direct numerical simulations highlight the role of attractors played by nonlinear Bessel vortices in the stable propagation regime. Large input powers or small cone angles lead to the unstable propagation regime where nonlinear Bessel vortices break up into an helical multiple filament pattern or a more irregular structure. Nonlinear Bessel vortices are shown to be sufficiently intense to generate a ring-shaped filamentary ionized channel in the medium which is foreseen as opening the way to novel applications in laser material processing of transparent dielectrics. PMID:25401574
NASA Astrophysics Data System (ADS)
McLaughlin, David W.
1994-01-01
The principal investigator, together with two post-doctoral fellows, several graduate students, and colleagues, has applied the modern mathematical theory of nonlinear waves to problems in nonlinear optics. Projects included the interaction of laser light with nematic liquid crystals, propagation through random nonlinear media, cross polarization instabilities and optical shocks for propagation along nonlinear optical fibers, and the dynamics of bistable optical switches coupled through both diffusion and diffraction. In the first project the extremely strong nonlinear response of a CW laser beam in a nematic liquid crystal medium produced striking undulation and filamentation of the CW beam which was observed experimentally and explained theoretically. In the second project the interaction of randomness with nonlinearity was investigated, as well as an effective randomness due to the simultaneous presence of many nonlinear instabilities. In the polarization problems theoretical hyperbolic structure (instabilities and homoclinic orbits) in the coupled nonlinear Schroedinger (NLS) equations was identified and used to explain cross polarization instabilities in both the focusing and defocusing cases, as well as to describe optical shocking phenomena. For the coupled bistable optical switches, a numerical code was carefully developed in two spatial and one temporal dimensions. The code was used to study the decay of temporal transients to 'on-off' steady states in a geometry which includes forward and backward longitudinal propagation, together with one dimensional transverse coupling of both electromagnetic diffraction and carrier diffusion.
Improved nonlinear plasmonic slot waveguide: a full study
NASA Astrophysics Data System (ADS)
Elsawy, Mahmoud M. R.; Nazabal, Virginie; Chauvet, Mathieu; Renversez, Gilles
2016-04-01
We present a full study of an improved nonlinear plasmonic slot waveguides (NPSWs) in which buffer linear dielectric layers are added between the Kerr type nonlinear dielectric core and the two semi-infinite metal regions. Our approach computes the stationary solutions using the fixed power algorithm, in which for a given structure the wave power is an input parameter and the outputs are the propagation constant and the corresponding field components. For TM polarized waves, the inclusion of these supplementary layers have two consequences. First, they reduced the overall losses. Secondly, they modify the types of solutions that propagate in the NPSWs adding new profiles enlarging the possibilities offered by these nonlinear waveguides. In addition to the symmetric linear plasmonic profile obtained in the simple plasmonic structure with linear core such that its effective index is above the linear core refractive index, we obtained a new field profile which is more localized in the core with an effective index below the core linear refractive index. In the nonlinear case, if the effective index of the symmetric linear mode is above the core linear refractive index, the mode field profiles now exhibit a spatial transition from a plasmonic type profile to a solitonic type one. Our structure also provides longer propagation length due to the decrease of the losses compared to the simple nonlinear slot waveguide and exhibits, for well-chosen refractive index or thickness of the buffer layer, a spatial transition of its main modes that can be controlled by the power. We provide a full phase diagram of the TM wave operating regimes of these improved NPSWs. The stability of the main TM modes is then demonstrated numerically using the FDTD. We also demonstrate the existence of TE waves for both linear and nonlinear cases (for some configurations) in which the maximum intensity is located in the middle of the waveguide. We indicate the bifurcation of the nonlinear
TOPICAL REVIEW: Nonlinear photonic crystals: III. Cubic nonlinearity
NASA Astrophysics Data System (ADS)
Babin, Anatoli; Figotin, Alexander
2003-10-01
Weakly nonlinear interactions between wavepackets in a lossless periodic dielectric medium are studied based on the classical Maxwell equations with a cubic nonlinearity. We consider nonlinear processes such that: (i) the amplitude of the wave component due to the nonlinearity does not exceed the amplitude of its linear component; (ii) the spatial range of a probing wavepacket is much smaller than the dimension of the medium sample, and it is not too small compared with the dimension of the primitive cell. These nonlinear processes are naturally described in terms of the cubic interaction phase function based on the dispersion relations of the underlying linear periodic medium. It turns out that only a few quadruplets of modes have significant nonlinear interactions. They are singled out by a system of selection rules including the group velocity, frequency and phase matching conditions. It turns out that the intrinsic symmetries of the cubic interaction phase stemming from assumed inversion symmetry of the dispersion relations play a significant role in the cubic nonlinear interactions. We also study canonical forms of the cubic interaction phase leading to a complete quantitative classification of all possible significant cubic interactions. The classification is ultimately based on a universal system of indices reflecting the intensity of nonlinear interactions.
Photon correlations in a two-site nonlinear cavity system under coherent drive and dissipation
Ferretti, Sara; Andreani, Lucio Claudio; Tuereci, Hakan E.; Gerace, Dario
2010-07-15
We calculate the normalized second-order correlation function for a system of two tunnel-coupled photonic resonators, each one exhibiting a single-photon nonlinearity of the Kerr type. We employ a full quantum formulation: The master equation for the model, which takes into account both a coherent continuous drive and radiative as well as nonradiative dissipation channels, is solved analytically in steady state through a perturbative approach, and the results are compared to exact numerical simulations. The degree of second-order coherence displays values between 0 and 1, and divides the diagram identified by the two energy scales of the system - the tunneling and the nonlinear Kerr interaction - into two distinct regions separated by a crossover. When the tunneling term dominates over the nonlinear one, the system state is delocalized over both cavities, and the emitted light is coherent. In the opposite limit, photon blockade sets in, and the system shows an insulatorlike state with photons locked on each cavity, identified by antibunching of emitted light.
NASA Astrophysics Data System (ADS)
H, R. Baghshahi; M, K. Tavassoly; A, Behjat
2014-07-01
The interaction between a two-level atom and a single-mode field in the k-photon Jaynes—Cummings model (JCM) in the presence of the Stark shift and a Kerr medium is studied. All terms in the Hamiltonian, such as the single-mode field, its interaction with the atom, the contribution of the Stark shift and the Kerr medium effects are considered to be f-deformed. In particular, the effect of the initial state of the radiation field on the dynamical evolution of some physical properties such as atomic inversion and entropy squeezing are investigated by considering different initial field states (coherent, squeezed and thermal states).
Nonlinear optics and nonlinear dynamics
NASA Astrophysics Data System (ADS)
Chen, C. H.
1990-08-01
The author was invited by the Institute of Atomic and Molecular Sciences, Academia Sinica, in Taiwan to give six lectures on nonlinear optics. The participants included graduate students, postdoctoral fellows, research staff, and professors from several research organizations and universities. Extensive discussion followed each lecture. Since both the Photophysics Group at Oak Ridge National Laboratory (ORNL) and Institute of Atomic and Molecular Sciences in Taiwan have been actively participating in nonlinear optics research, the discussions are very beneficial to ORNL programs. The author also visited several laboratories at IAMS to exchange research ideas on nonlinear optics.
Wave propagation in ordered, disordered, and nonlinear photonic band gap materials
Lidorikis, Elefterios
1999-12-10
Photonic band gap materials are artificial dielectric structures that give the promise of molding and controlling the flow of optical light the same way semiconductors mold and control the electric current flow. In this dissertation the author studied two areas of photonic band gap materials. The first area is focused on the properties of one-dimensional PBG materials doped with Kerr-type nonlinear material, while, the second area is focused on the mechanisms responsible for the gap formation as well as other properties of two-dimensional PBG materials. He first studied, in Chapter 2, the general adequacy of an approximate structure model in which the nonlinearity is assumed to be concentrated in equally-spaced very thin layers, or 6-functions, while the rest of the space is linear. This model had been used before, but its range of validity and the physical reasons for its limitations were not quite clear yet. He performed an extensive examination of many aspects of the model's nonlinear response and comparison against more realistic models with finite-width nonlinear layers, and found that the d-function model is quite adequate, capturing the essential features in the transmission characteristics. The author found one exception, coming from the deficiency of processing a rigid bottom band edge, i.e. the upper edge of the gaps is always independent of the refraction index contrast. This causes the model to miss-predict that there are no soliton solutions for a positive Kerr-coefficient, something known to be untrue.
Golubkov, A A; Makarov, Vladimir A
2011-06-30
We have proved for the first time and proposed an algorithm of unique spatial profile reconstruction of the components {chi}-circumflex {sup (3)}{sub yyyy} of complex tensors {chi}-circumflex {sup (3)}(z, {omega}', {omega}', -{omega}, {omega}) and {chi}-circumflex {sup (3)}(z, 2{omega}{+-}{omega}', {+-}{omega}', {omega}, {omega}), describing four-photon interaction of light waves in a one-dimensionally inhomogeneous plate, whose medium has a symmetry plane m{sub y} that is perpendicular to its surface. For the media with an additional symmetry axis 2{sub z}, 4{sub z}, 6{sub z} or {infinity}{sub z} that is perpendicular to the plate surface, the proposed method can be used to reconstruct about one-fifth of all independent components of the above tensors. (nonlinear optical phenomena)
Modeling of active and passive nonlinear metamaterials
NASA Astrophysics Data System (ADS)
Colestock, Patrick L.; Reiten, Matthew T.; O'Hara, John F.
2012-11-01
We develop general results for nonlinear metamaterials based on simple circuit models that reflect the elementary nonlinear behavior of the medium. In particular, we consider both active and passive nonlinearities which can lead to gain, harmonic generation and a variety of nonlinear waves depending on circuit parameters and signal amplitude. We show that the medium can exhibit a phase transition to a synchronized state and derive conditions for the transformation based on a widely used multiple time scale approach that leads to the well-known Complex Ginzburg-Landau equation. Further, we examine the variety of nonlinear waves that can exist in such systems, and we present numerical results for both active and passive metamaterial cases.
Diffraction from an edge in a self-focusing medium.
Wan, Wenjie; Dylov, Dmitry V; Barsi, Christopher; Fleischer, Jason W
2010-08-15
We experimentally demonstrate diffraction from a straight edge in a medium with self-focusing nonlinearity. Diffraction into the shadow region is suppressed with increasing nonlinearity, but mode coupling leads to excitations and traveling waves on the high-intensity side. Theoretically, we interpret these modulations as spatially dispersive shock waves with negative pressure.
In, Visarath; Longhini, Patrick; Kho, Andy; Neff, Joseph D; Leung, Daniel; Liu, Norman; Meadows, Brian K; Gordon, Frank; Bulsara, Adi R; Palacios, Antonio
2012-12-01
The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz.
Some aspects of the comparison between optics and nonlinear acoustics
NASA Technical Reports Server (NTRS)
Perrin, B.
1980-01-01
Some results concerning nonlinear acoustics deduced from a comparison of nonlinear processes in optics and acoustics are discussed. An aspect of nonlinearity in acoustics connected with the dimensionality of the medium of propagation is emphasized and illustrated by the proof of static instability of an ideal linear solid. In addition a phenomenon, which can be called acoustical rectification by analogy with nonlinear optics, is propounded to measure the third order elastic constants. Its experimental consequences are predicted in a particular case.
ERIC Educational Resources Information Center
Seider, Warren D.; Ungar, Lyle H.
1987-01-01
Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…
Interstellar medium simulations
NASA Astrophysics Data System (ADS)
Breitschwerdt, D.; de Avillez, M. A.; Feige, J.; Dettbarn, C.
2012-06-01
In this review we critically assess numerical simulations of the interstellar medium (ISM), and argue that 3D high resolution calculations are the most promising method to determine the structure of the interstellar gas and follow its evolution well into the nonlinear regime. Based on a Riemann solver adaptive mesh refinement code, we present a model, which fulfills the basic requirements of running it sufficiently long in order to erase memory effects of the initial conditions, set up a disk-halo fountain flow cycle, for converging solutions with increasing mesh refinement. We obtain the following results: (i) in a supernova driven ISM, high Reynolds number turbulence generates structures on all scales, (ii) the volume filling factor of the hot gas is substantially reduced due to the fountain flow, (iii) gas clouds are transient shock compressed layers, (iv) more than half of the gas mass resides in thermally unstable regimes, (v) O VI is distributed in patchy mixing layers, with the derived column densities being in agreement with FUSE and Copernicus observations, (vi) the electron density distribution up to distances of 8 kpc in the disk is consistent with pulsar dispersion measure observations, provided that the electron and ionization structure are not in equilibrium, (vii) the interstellar cooling function depends both on space and time (and not only on temperature and metallicity), (viii) the Local Bubble has been produced by 14-20 supernovae about 14 Myr ago, exploding in a moving group on its path through the local ISM, (ix) the nearest supernova explosion to Earth occurred 2.2 {×} 106 yr ago at a distance of {˜} 85 pc, in agreement with measurements of the radionuclide 60Fe found in the ferromanganese crust on the ocean floor.
Evaluation of radiation damage using nonlinear ultrasound
Matlack, K. H.; Wall, J. J.; Kim, J.-Y.; Qu, J.; Jacobs, L. J.; Viehrig, H.-W.
2012-03-01
Nonlinear ultrasound was used to monitor radiation damage in two reactor pressure vessel (RPV) steels. The microstructural changes associated with radiation damage include changes in dislocation density and the formation of precipitates, and nonlinear ultrasonic waves are known to be sensitive to such changes. Six samples each of two different RPV steels were previously irradiated in the Rheinsberg power reactor to two fluence levels, up to 10{sup 20} n/cm{sup 2} (E > 1 MeV). Longitudinal waves were used to measure the acoustic nonlinearity in these samples, and the results show a clear increase in the measured acoustic nonlinearity from the unirradiated state to the medium dose, and then a decrease from medium dose to high dose.
NASA Astrophysics Data System (ADS)
Ranjbar, Monireh; Bahari, Ali
2016-09-01
Four-wave mixing in propagation of cylindrical waves in a homogeneous nonlinear optical media has been investigated theoretically. An explicit analytical expression which contains all the main nonlinear optical effects, including third harmonic generation, sum and difference frequency generation has been obtained. A comparison between sum frequency efficiency for exact and approximation expression in a homogeneous nonlinear medium has been done. The effect of increasing the nonlinear optical coefficient (χeff(3)) and increasing the frequency difference between two adjacent waves (Δ ω) , on the efficiency of sum frequency generation in homogeneous media has been investigated.
Polarization renormalization due to nonlinear optical generation
NASA Astrophysics Data System (ADS)
Wynne, J. J.
1984-02-01
A classical Maxwellian analysis of the reduction of multiphoton excitation associated with the coherent third-harmonic generation of electromagnetic waves propagating in nonlinear media is presented. The approach of Bloembergen and Pershan (1962) is followed, making no use of quantum-mechanical description and considering the total electric polarization (the sum of the medium's linear response and the nonlinear source polarization) at the generated frequency. It is demonstrated that this method successfully explains the experimental results of Aron and Johnson (1977), Miller et al. (1980), Glownia and Sander (1982), and Faisal et al. (1977) by analyzing the relationship of the total and nonlinear polarization components.
Quasicompactons in inverted nonlinear photonic crystals
Li Yongyao; Malomed, Boris A.; Wu Jianxiong; Pang Wei; Wang Sicong; Zhou Jianying
2011-10-15
We study large-amplitude one-dimensional solitary waves in photonic crystals featuring competition between linear and nonlinear lattices, with minima of the linear potential coinciding with maxima of the nonlinear pseudopotential, and vice versa (inverted nonlinear photonic crystals, INPCs), in the case of the saturable self-focusing nonlinearity. Such crystals were recently fabricated using a mixture of SU-8 and Rhodamine-B optical materials. By means of numerical methods and analytical approximations, we find that large-amplitude solitons are broad sharply localized stable pulses (quasicompactons, QCs). With the increase of the total power, P, the QC's centroid performs multiple switchings between minima and maxima of the linear potential. Unlike cubic INPCs, the large-amplitude solitons are mobile in the medium with the saturable nonlinearity. The threshold value of the kick necessary to set the soliton in motion is found as a function of P. Collisions between moving QCs are considered too.
Large nonlocal nonlinear optical response of castor oil
NASA Astrophysics Data System (ADS)
Souza, Rogério F.; Alencar, Márcio A. R. C.; Meneghetti, Mario R.; Hickmann, Jandir M.
2009-09-01
The nonlocal nonlinearity of castor oil was investigated using the Z-scan technique in the CW regime at 514 nm and in femtosecond regime at 810 nm. Large negative nonlinear refractive indexes of thermal origin, thermo-optical coefficients and degree of nonlocality were obtained for both laser excitation wavelengths. The results indicate that the electronic part of the nonlinear refractive index and nonlinear absorption were negligible. Our results suggest that castor oil is promising candidate as a nonlinear medium for several nonlocal optical applications, such as in spatial soliton propagation, as well as a dispersant agent in the measurement of absorptive properties of nanoparticles.
Nonlinear common-path interferometer: an image processor.
Treviño-Palacios, Carlos Gerardo; Iturbe-Castillo, Marcelo David; Sánchez-de-la-Llave, David; Ramos-García, Ruben; Olivos-Pérez, Luis Ignacio
2003-09-01
A single-lens optical setup with a nonlinear medium placed in its geometrical focal plane is used to contrast a phase disturbance. This setup blends the robustness of phase-contrast methods with an optical nonlinear intensity-dependent medium and the usefulness of traditional interferometric techniques. We show that the ratio of the total illumination area to the phase-object area determines an adequate phase-disturbance contrast. PMID:12962385
NASA Astrophysics Data System (ADS)
Sengupta, Parijat; Bellotti, Enrico
2016-09-01
We study the optical behavior of an arrangement in which the interface between a linear and non-linear dielectric media is covered by an embedded mono-layer of transition metal dichalcogenides (TMDC). The optical behavior is qualitatively obtained through transmission and reflection coefficients which are a function of the third order non-linear susceptibility of the Kerr-type dielectric and the inter-band optical conductivity of the TMDC mono-layer. The inter-band optical conductivity of the TMDC mono-layer is calculated using the Kubo formalism from the linear response theory. In particular, we theoretically demonstrate that the optical response of this structure can be switched between the total internal reflection and a normal transmission regime by controlling the intensity of the incident radiation. The reflection and transmission functions are shown to be amenable to further control by altering the inter-band optical conductivity of the embedded TMDC mono-layer. The optical conductivity is directly related to its energy dispersion. We specifically choose two TMDC mono-layers, MoS2 and WSe2, which have nearly identical dispersion parameters apart from a much stronger spin-orbit coupling in the latter. The stronger spin-orbit coupling in WSe2 does not significantly alter the inter-band optical conductivity to manifest as an enhanced reflection spectrum. However, we find that application of an external perturbation such as strain could be effectively used to modulate the overall optical response. We conclude by discussing briefly the phenomenon of optical bistability which arises in materials exhibiting optical non-linearity via an intensity-dependent refractive index.
Light steering in a strongly nonlocal nonlinear medium
Ouyang Shigen; Hu Wei; Guo Qi
2007-11-15
With a strongly nonlocal model, we present an analytical solution of the coherent interaction of two Gaussian beams with an arbitrary phase difference and arbitrary incident angles. Numerical simulations show that the analytical solution can describe the interaction of two Gaussian beams very well in the strongly nonlocal case. It is theoretically shown that one can steer lights in strongly nonlocal media by tuning the incident conditions of coherently interacting beams like the phase difference between beams and their relative amplitude.
New Nonlinear Multigrid Analysis
NASA Technical Reports Server (NTRS)
Xie, Dexuan
1996-01-01
The nonlinear multigrid is an efficient algorithm for solving the system of nonlinear equations arising from the numerical discretization of nonlinear elliptic boundary problems. In this paper, we present a new nonlinear multigrid analysis as an extension of the linear multigrid theory presented by Bramble. In particular, we prove the convergence of the nonlinear V-cycle method for a class of mildly nonlinear second order elliptic boundary value problems which do not have full elliptic regularity.
Stokowski, Stanley E.
1989-01-01
A laser medium is particularly useful in high average power solid state lasers. The laser medium includes a chormium dopant and preferably neodymium ions as codopant, and is primarily a gadolinium scandium gallium garnet, or an analog thereof. Divalent cations inhibit spiral morphology as large boules from which the laser medium is derived are grown, and a source of ions convertible between a trivalent state and a tetravalent state at a low ionization energy are in the laser medium to reduce an absorption coefficient at about one micron wavelength otherwise caused by the divalent cations. These divalent cations and convertible ions are dispersed in the laser medium. Preferred convertible ions are provided from titanium or cerium sources.
Stokowski, S.E.
1987-10-20
A laser medium is particularly useful in high average power solid state lasers. The laser medium includes a chromium dopant and preferably neodymium ions as codopant, and is primarily a gadolinium scandium gallium garnet, or an analog thereof. Divalent cations inhibit spiral morphology as large boules from which the laser medium is derived are grown, and a source of ions convertible between a trivalent state and a tetravalent state at a low ionization energy are in the laser medium to reduce an absorption coefficient at about one micron wavelength otherwise caused by the divalent cations. These divalent cations and convertible ions are dispersed in the laser medium. Preferred convertible ions are provided from titanium or cerium sources.
NEW NONLINEAR ACOUSTIC TECHNIQUES FOR NDE
J. A. TENCATE
2000-09-01
Acoustic nonlinearity in a medium may occur as a result of a variety of mechanisms. Some of the more common nonlinear effects may come from: (1) one or several cracks, volumetrically distributed due to age or fatigue or single disbonds or delamination; (2) imperfect grain-to-grain contacts, e.g., materials like concretes that are cemented together and have less than perfect bonds; (3) hard parts in a soft matrix, e.g., extreme duty materials like tungsten/copper alloys; or (4) atomic-scale nonlinearities. Nonlinear effects that arise from the first two mechanisms are considerably larger than the last two; thus, we have focused considerable attention on these. The most pervasive nonlinear measure of damage today is a second harmonic measurement. We show that for many cases of interest to NDE, a second harmonic measurement may not be the best choice. We examine the manifestations of nonlinearity in (nonlinear) materials with cracks and/or imperfect bonds and illustrate their applicability to NDE. For example, nonlinear resonance frequency shifts measured at increasing drive levels correlate strongly with the amount of ASR (alkali-silica reaction) damage of concrete cores. Memory effects (slow dynamics) also seem to correlate with the amount of damage.
[Nonlinear magnetohydrodynamics
Not Available
1994-01-01
Resistive MHD equilibrium, even for small resistivity, differs greatly from ideal equilibrium, as do the dynamical consequences of its instabilities. The requirement, imposed by Faraday`s law, that time independent magnetic fields imply curl-free electric fields, greatly restricts the electric fields allowed inside a finite-resistivity plasma. If there is no flow and the implications of the Ohm`s law are taken into account (and they need not be, for ideal equilibria), the electric field must equal the resistivity times the current density. The vanishing of the divergence of the current density then provides a partial differential equation which, together with boundary conditions, uniquely determines the scalar potential, the electric field, and the current density, for any given resistivity profile. The situation parallels closely that of driven shear flows in hydrodynamics, in that while dissipative steady states are somewhat more complex than ideal ones, there are vastly fewer of them to consider. Seen in this light, the vast majority of ideal MHD equilibria are just irrelevant, incapable of being set up in the first place. The steady state whose stability thresholds and nonlinear behavior needs to be investigated ceases to be an arbitrary ad hoc exercise dependent upon the whim of the investigator, but is determined by boundary conditions and choice of resistivity profile.
Measuring Acoustic Nonlinearity by Collinear Mixing Waves
NASA Astrophysics Data System (ADS)
Liu, M.; Tang, G.; Jacobs, L. J.; Qu, J.
2011-06-01
It is well known that the acoustic nonlinearity parameter β is correlated to fatigue damage in metallic materials. Various methods have been developed to measure β. One of the most often used methods is the harmonic generation technique, in which β is obtained by measuring the magnitude of the second order harmonic waves. An inherent weakness of this method is the difficulty in distinguishing material nonlinearity from the nonlinearity of the measurement system. In this paper, we demonstrate the possibility of using collinear mixing waves to measure β. The wave mixing method is based on the interaction between two incident waves in a nonlinear medium. Under certain conditions, such interactions generate a third wave of different frequency. This generated third wave is also called resonant wave, because its amplitude is unbounded if the medium has no attenuation. Such resonant waves are less sensitive to the nonlinearity of the measurement system, and have the potential to identify the source location of the nonlinearity. In this work, we used a longitudinal wave and a shear wave as the incident waves. The resonant shear wave is measured experimentally on samples made of aluminum and steel, respectively. Numerical simulations of the tests were also performed using a finite difference method.
Conservations laws for a porous medium equation through nonclassical generators
NASA Astrophysics Data System (ADS)
Gandarias, M. L.
2014-02-01
In Ibragimov (2007) [13] a general theorem on conservation laws was proved. In Gandarias (2011) and Ibragimov (2011) [7,15] the concepts of self-adjoint and quasi self-adjoint equations were generalized and the definitions of weak self-adjoint equations and nonlinearly self-adjoint equations were introduced. In this paper, we find the subclasses of nonlinearly self-adjoint porous medium equations. By using the property of nonlinear self-adjointness, we construct some conservation laws associated with classical and nonclassical generators of the differential equation.
Nonlinear Talbot effect of rogue waves.
Zhang, Yiqi; Belić, Milivoj R; Zheng, Huaibin; Chen, Haixia; Li, Changbiao; Song, Jianping; Zhang, Yanpeng
2014-03-01
Akhmediev and Kuznetsov-Ma breathers are rogue wave solutions of the nonlinear Schrödinger equation (NLSE). Talbot effect (TE) is an image recurrence phenomenon in the diffraction of light waves. We report the nonlinear TE of rogue waves in a cubic medium. It is different from the linear TE, in that the wave propagates in a NL medium and is an eigenmode of NLSE. Periodic rogue waves impinging on a NL medium exhibit recurrent behavior, but only at the TE length and at the half-TE length with a π-phase shift; the fractional TE is absent. The NL TE is the result of the NL interference of the lobes of rogue wave breathers. This interaction is related to the transverse period and intensity of breathers, in that the bigger the period and the higher the intensity, the shorter the TE length.
Linear and nonlinear light bullets: recent developments
NASA Astrophysics Data System (ADS)
Mihalache, Dumitru
2013-06-01
The spatiotemporal optical solitons (alias nonlinear "light bullets") are nondiffracting and nondispersing wave packets propagating in nonlinear optical media. The three-dimensional spatiotemporal solitons are localized (self-guided) in two transverse (spatial) dimensions and in the direction of propagation due to the balance of anomalous group-velocity dispersion of the medium in which they form and nonlinear self-phase modulation. The formation of fully threedimensional spatiotemporal optical solitons in two-dimensional photonic lattices was reported in recent experiments. Also, linear light bullets, which are robust and versatile localized wave packets combining Bessel beams in the transverse plane with temporal Airy pulses have been reported experimentally. A brief up-to-date survey of recent theoretical and experimental studies of the formation, stability and robustness of linear and nonlinear light bullets in various physical settings is given.
Nonlinear Diffusion and Transient Osmosis
NASA Astrophysics Data System (ADS)
Akira, Igarashi; Lamberto, Rondoni; Antonio, Botrugno; Marco, Pizzi
2011-08-01
We investigate both analytically and numerically the concentration dynamics of a solution in two containers connected by a narrow and short channel, in which diffusion obeys a porous medium equation. We also consider the variation of the pressure in the containers due to the flow of matter in the channel. In particular, we identify a phenomenon, which depends on the transport of matter across nano-porous membranes, which we call “transient osmosis". We find that nonlinear diffusion of the porous medium equation type allows numerous different osmotic-like phenomena, which are not present in the case of ordinary Fickian diffusion. Experimental results suggest one possible candidate for transiently osmotic processes.
Coda wave interferometry for estimating nonlinear behavior in seismic velocity.
Snieder, Roel; Grêt, Alexandre; Douma, Huub; Scales, John
2002-03-22
In coda wave interferometry, one records multiply scattered waves at a limited number of receivers to infer changes in the medium over time. With this technique, we have determined the nonlinear dependence of the seismic velocity in granite on temperature and the associated acoustic emissions. This technique can be used in warning mode, to detect the presence of temporal changes in the medium, or in diagnostic mode, where the temporal change in the medium is quantified.
Nonlinear propagation and control of acoustic waves in phononic superlattices
NASA Astrophysics Data System (ADS)
Jiménez, Noé; Mehrem, Ahmed; Picó, Rubén; García-Raffi, Lluís M.; Sánchez-Morcillo, Víctor J.
2016-05-01
The propagation of intense acoustic waves in a one-dimensional phononic crystal is studied. The medium consists in a structured fluid, formed by a periodic array of fluid layers with alternating linear acoustic properties and quadratic nonlinearity coefficient. The spacing between layers is of the order of the wavelength, therefore Bragg effects such as band gaps appear. We show that the interplay between strong dispersion and nonlinearity leads to new scenarios of wave propagation. The classical waveform distortion process typical of intense acoustic waves in homogeneous media can be strongly altered when nonlinearly generated harmonics lie inside or close to band gaps. This allows the possibility of engineer a medium in order to get a particular waveform. Examples of this include the design of media with effective (e.g., cubic) nonlinearities, or extremely linear media (where distortion can be canceled). The presented ideas open a way towards the control of acoustic wave propagation in nonlinear regime. xml:lang="fr"
Mean dyadic Green's function for a two layer random medium
NASA Technical Reports Server (NTRS)
Zuniga, M. A.
1981-01-01
The mean dyadic Green's function for a two-layer random medium with arbitrary three-dimensional correlation functions has been obtained with the zeroth-order solution to the Dyson equation by applying the nonlinear approximation. The propagation of the coherent wave in the random medium is similar to that in an anisotropic medium with different propagation constants for the characteristic transverse electric and transverse magnetic polarizations. In the limit of a laminar structure, two propagation constants for each polarization are found to exist.
Instability of evaporation fronts in the interstellar medium
Kim, Jeong-Gyu; Kim, Woong-Tae E-mail: wkim@astro.snu.ac.kr
2013-12-10
The neutral component of the interstellar medium is segregated into the cold neutral medium (CNM) and warm neutral medium (WNM) as a result of thermal instability. It was found that a plane-parallel CNM-WNM evaporation interface, across which the CNM undergoes thermal expansion, is linearly unstable to corrugational disturbances, in complete analogy with the Darrieus-Landau instability (DLI) of terrestrial flames. We perform a full linear stability analysis as well as nonlinear hydrodynamic simulations of the DLI of such evaporation fronts in the presence of thermal conduction. We find that the DLI is suppressed at short length scales by conduction. The length and time scales of the fastest growing mode are inversely proportional to the evaporation flow speed of the CNM and its square, respectively. In the nonlinear stage, the DLI saturates to a steady state where the front deforms to a finger-like shape protruding toward the WNM, without generating turbulence. The evaporation rate at nonlinear saturation is larger than the initial plane-parallel value by a factor of ∼2.4 when the equilibrium thermal pressure is 1800 k {sub B} cm{sup –3} K. The degrees of front deformation and evaporation-rate enhancement at nonlinear saturation are determined primarily by the density ratio between the CNM and WNM. We demonstrate that the Field length in the thermally unstable medium should be resolved by at least four grid points to obtain reliable numerical outcomes involving thermal instability.
Theory and design of nonlinear metamaterials
NASA Astrophysics Data System (ADS)
Rose, Alec Daniel
and oscillators. By applying this set of tools and knowledge to microwave metamaterials, I experimentally confirm several novel nonlinear phenomena. Most notably, I construct a backward wave nonlinear medium from varactor-loaded split ring resonators loaded in a rectangular waveguide, capable of generating second-harmonic opposite to conventional nonlinear materials with a conversion efficiency as high as 1.5%. In addition, I confirm nonlinear magnetoelectric coupling in two dual gap varactor-loaded split ring resonator metamaterials through measurement of the amplitude and phase of the second-harmonic generated in the forward and backward directions from a thin slab. I then use the presence of simultaneous nonlinearities in such metamaterials to observe nonlinear interference, manifest as unidirectional difference frequency generation with contrasts of 6 and 12 dB in the forward and backward directions, respectively. Finally, I apply these principles and intuition to several plasmonic platforms with the goal of achieving similar enhancements and configurations at optical frequencies. Using the example of fluorescence enhancement in optical patch antennas, I develop a semi-classical numerical model for the calculation of field-induced enhancements to both excitation and spontaneous emission rates of an embedded fluorophore, showing qualitative agreement with experimental results, with enhancement factors of more than 30,000. Throughout these series of works, I emphasize the indispensability of effective design and retrieval tools in understanding and optimizing both metamaterials and plasmonic systems. Ultimately, when weighed against the disadvantages in fabrication and optical losses, the results presented here provide a context for the application of nonlinear metamaterials within three distinct areas where a competitive advantage over conventional materials might be obtained: fundamental science demonstrations, linear and nonlinear anisotropy engineering, and
NASA Astrophysics Data System (ADS)
Lauterborn, Werner; Kurz, Thomas; Akhatov, Iskander
At high sound intensities or long propagation distances at
Nonlinear model of elastic field sources
NASA Astrophysics Data System (ADS)
Lev, B. I.; Zagorodny, A. G.
2016-09-01
A general concept of the long-range elastic interactions in continuous medium is proposed. The interaction is determined as a consequence of symmetry breaking of the elastic field distribution produced by the topological defect as isolated inclusions. It is proposed to treat topological defects as the source of elastic field that can be described in terms of this field. The source is considered as a nonlinear object which determines the effective charge of the field at large distances in the linear theory. The models of the nonlinear source are proposed.
Combined optical solitons with parabolic law nonlinearity and spatio-temporal dispersion
NASA Astrophysics Data System (ADS)
Zhou, Qin; Zhu, Qiuping
2015-03-01
In this work, combined optical solitons are constructed in a weakly nonlocal nonlinear medium. The spatio-temporal dispersion (STD), parabolic law nonlinearity, detuning, nonlinear dispersion as well as inter-modal dispersion are taken into account. The integration tool that is applied is the complex envelope function ansatz. The influences of different parameters on dynamical behavior of combined optical solitons are discussed. The results are useful in describing the propagation of combined optical solitons with STD and parabolic law nonlinearity.
Nonlinear Hysteretic Torsional Waves
NASA Astrophysics Data System (ADS)
Cabaret, J.; Béquin, P.; Theocharis, G.; Andreev, V.; Gusev, V. E.; Tournat, V.
2015-07-01
We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters.
Tomlin, R.
1990-01-27
A nonlinear oscillator design was imported from Cornell modified, and built for the purpose of simulating the chaotic states of a forced pendulum. Similar circuits have been investigated in the recent nonlinear explosion.
NASA Technical Reports Server (NTRS)
Gange, Robert Allen (Inventor)
1977-01-01
A holographic recording medium comprising a conductive substrate, a photoconductive layer and an electrically alterable layer of a linear, low molecular weight hydrocarbon polymer has improved fatigue resistance. An acrylic barrier layer can be interposed between the photoconductive and electrically alterable layers.
The function of nonlinear phenomena in meerkat alarm calls.
Townsend, Simon W; Manser, Marta B
2011-02-23
Nonlinear vocal phenomena are a ubiquitous feature of human and non-human animal vocalizations. Although we understand how these complex acoustic intrusions are generated, it is not clear whether they function adaptively for the animals producing them. One explanation is that nonlinearities make calls more unpredictable, increasing behavioural responses and ultimately reducing the chances of habituation to these call types. Meerkats (Suricata suricatta) exhibit nonlinear subharmonics in their predator alarm calls. We specifically tested the 'unpredictability hypothesis' by playing back naturally occurring nonlinear and linear medium-urgency alarm call bouts. Results indicate that subjects responded more strongly and foraged less after hearing nonlinear alarm calls. We argue that these findings support the unpredictability hypothesis and suggest this is the first study in animals or humans to show that nonlinear vocal phenomena function adaptively.
The function of nonlinear phenomena in meerkat alarm calls.
Townsend, Simon W; Manser, Marta B
2011-02-23
Nonlinear vocal phenomena are a ubiquitous feature of human and non-human animal vocalizations. Although we understand how these complex acoustic intrusions are generated, it is not clear whether they function adaptively for the animals producing them. One explanation is that nonlinearities make calls more unpredictable, increasing behavioural responses and ultimately reducing the chances of habituation to these call types. Meerkats (Suricata suricatta) exhibit nonlinear subharmonics in their predator alarm calls. We specifically tested the 'unpredictability hypothesis' by playing back naturally occurring nonlinear and linear medium-urgency alarm call bouts. Results indicate that subjects responded more strongly and foraged less after hearing nonlinear alarm calls. We argue that these findings support the unpredictability hypothesis and suggest this is the first study in animals or humans to show that nonlinear vocal phenomena function adaptively. PMID:20659926
Towards the nonlinear acousto-magneto-plasmonics
NASA Astrophysics Data System (ADS)
Temnov, Vasily V.; Razdolski, Ilya; Pezeril, Thomas; Makarov, Denys; Seletskiy, Denis; Melnikov, Alexey; Nelson, Keith A.
2016-09-01
We review the recent progress in experimental and theoretical research of interactions between the acoustic, magnetic and plasmonic transients in hybrid metal-ferromagnet multilayer structures excited by ultrashort laser pulses. The main focus is on understanding the nonlinear aspects of the acoustic dynamics in materials as well as the peculiarities in the nonlinear optical and magneto-optical response. For example, the nonlinear optical detection is illustrated in detail by probing the static magneto-optical second harmonic generation in gold–cobalt–silver trilayer structures in Kretschmann geometry. Furthermore, we show experimentally how the nonlinear reshaping of giant ultrashort acoustic pulses propagating in gold can be quantified by time-resolved plasmonic interferometry and how these ultrashort optical pulses dynamically modulate the optical nonlinearities. An effective medium approximation for the optical properties of hybrid multilayers enables the understanding of novel optical detection techniques. In the discussion we also highlight recent works on the nonlinear magneto-elastic interactions, and strain-induced effects in semiconductor quantum dots.
Towards the nonlinear acousto-magneto-plasmonics
NASA Astrophysics Data System (ADS)
Temnov, Vasily V.; Razdolski, Ilya; Pezeril, Thomas; Makarov, Denys; Seletskiy, Denis; Melnikov, Alexey; Nelson, Keith A.
2016-09-01
We review the recent progress in experimental and theoretical research of interactions between the acoustic, magnetic and plasmonic transients in hybrid metal-ferromagnet multilayer structures excited by ultrashort laser pulses. The main focus is on understanding the nonlinear aspects of the acoustic dynamics in materials as well as the peculiarities in the nonlinear optical and magneto-optical response. For example, the nonlinear optical detection is illustrated in detail by probing the static magneto-optical second harmonic generation in gold-cobalt-silver trilayer structures in Kretschmann geometry. Furthermore, we show experimentally how the nonlinear reshaping of giant ultrashort acoustic pulses propagating in gold can be quantified by time-resolved plasmonic interferometry and how these ultrashort optical pulses dynamically modulate the optical nonlinearities. An effective medium approximation for the optical properties of hybrid multilayers enables the understanding of novel optical detection techniques. In the discussion we also highlight recent works on the nonlinear magneto-elastic interactions, and strain-induced effects in semiconductor quantum dots.
NASA Astrophysics Data System (ADS)
Karpov, S. V.; Kodirov, M. K.; Ryasnyansky, A. I.; Slabko, V. V.
2001-10-01
The relation between the degree of aggregation of silver hydrosols and their nonlinear refractive index n2 is studied experimentally. It is found that the sign of n2 at a wavelength of 1.064 μm changes with increasing the aggregation degree, which corresponds to the replacing of self-focusing by self-defocusing. The observed effects are explained based on the analysis of a change in nonlinear dispersion of the medium, taking into account the interaction between phases and the photochromic effects, which are typical for colloidal structures with fractal geometry. It is shown that the change in the sign of the nonlinear refractive index of hydrosols upon irradiation by laser pulses of duration of less than 10-7 s is caused by the perturbation of resonances of silver and water and by the competition between Kerr nonlinear polarisations involving these resonances.
Nonlinear quantum optics mediated by Rydberg interactions
NASA Astrophysics Data System (ADS)
Firstenberg, O.; Adams, C. S.; Hofferberth, S.
2016-08-01
By mapping the strong interaction between Rydberg excitations in ultra-cold atomic ensembles onto single photons via electromagnetically induced transparency, it is now possible to realize a medium which exhibits a strong optical nonlinearity at the level of individual photons. We review the theoretical concepts and the experimental state-of-the-art of this exciting new field, and discuss first applications in the field of all-optical quantum information processing.
Liquid chromatographic extraction medium
Horwitz, E. Philip; Dietz, Mark L.
1994-01-01
A method and apparatus for extracting strontium and technetium values from biological, industrial and environmental sample solutions using a chromatographic column is described. An extractant medium for the column is prepared by generating a solution of a diluent containing a Crown ether and dispersing the solution on a resin substrate material. The sample solution is highly acidic and is introduced directed to the chromatographic column and strontium or technetium is eluted using deionized water.
Liquid chromatographic extraction medium
Horwitz, E.P.; Dietz, M.L.
1994-09-13
A method and apparatus are disclosed for extracting strontium and technetium values from biological, industrial and environmental sample solutions using a chromatographic column. An extractant medium for the column is prepared by generating a solution of a diluent containing a Crown ether and dispersing the solution on a resin substrate material. The sample solution is highly acidic and is introduced directed to the chromatographic column and strontium or technetium is eluted using deionized water. 1 fig.
Nonlinear noise waves in soft biological tissues
NASA Astrophysics Data System (ADS)
Rudenko, O. V.; Gurbatov, S. N.; Demin, I. Yu.
2013-09-01
The study of intense waves in soft biological tissues is necessary both for diagnostics and therapeutic aims. Tissue represents an inherited medium with frequency-dependent dissipative properties, in which waves are described by nonlinear integro-differential equations. The equations for such waves are well known. Their group analysis has been performed, and a number of exact solutions have been found. However, statistical problems for nonlinear waves in tissues have hardly been studied. As well, for medical applications, both intense noise waves and waves with fluctuating parameters can be used. In addition, statistical solutions are simpler in structure than regular solutions; they are useful for understanding the physics of processes. Below a general approach is described for solving nonlinear statistical problems applied to the considered mathematical models of biological tissues. We have calculated the dependences of the intensities of the narrowband noise harmonics on distance. For wideband noise, we have calculated the dependence of the spectral integral intensity on distance. In all cases, wave attenuation is determined both by the specific dissipative properties of the tissue and the nonlinearity of the medium.
Fractal dimension and nonlinear dynamical processes
NASA Astrophysics Data System (ADS)
McCarty, Robert C.; Lindley, John P.
1993-11-01
Mandelbrot, Falconer and others have demonstrated the existence of dimensionally invariant geometrical properties of non-linear dynamical processes known as fractals. Barnsley defines fractal geometry as an extension of classical geometry. Such an extension, however, is not mathematically trivial Of specific interest to those engaged in signal processing is the potential use of fractal geometry to facilitate the analysis of non-linear signal processes often referred to as non-linear time series. Fractal geometry has been used in the modeling of non- linear time series represented by radar signals in the presence of ground clutter or interference generated by spatially distributed reflections around the target or a radar system. It was recognized by Mandelbrot that the fractal geometries represented by man-made objects had different dimensions than the geometries of the familiar objects that abound in nature such as leaves, clouds, ferns, trees, etc. The invariant dimensional property of non-linear processes suggests that in the case of acoustic signals (active or passive) generated within a dispersive medium such as the ocean environment, there exists much rich structure that will aid in the detection and classification of various objects, man-made or natural, within the medium.
On the Doppler effect for light from orbiting sources in Kerr-type metrics
NASA Astrophysics Data System (ADS)
Cisneros, S.; Goedecke, G.; Beetle, C.; Engelhardt, M.
2015-04-01
A formula is derived for the combined motional and gravitational Doppler effect in general stationary axisymmetric metrics for a photon emitted parallel or antiparallel to the assumed circular orbital motion of its source. The same formula is derived by both the eikonal approximation and Killing vector approaches to elucidate connections between observational astronomy and modern relativity. The formula yields expected results in the limits of a moving or stationary source in the exterior Kerr and Schwarzschild metrics and is useful for broad range astrophysical analyses.
QCL-based nonlinear sensing of independent targets dynamics.
Mezzapesa, F P; Columbo, L L; Dabbicco, M; Brambilla, M; Scamarcio, G
2014-03-10
We demonstrate a common-path interferometer to measure the independent displacement of multiple targets through nonlinear frequency mixing in a quantum-cascade laser (QCL). The sensing system exploits the unique stability of QCLs under strong optical feedback to access the intrinsic nonlinearity of the active medium. The experimental results using an external dual cavity are in excellent agreement with the numerical simulations based on the Lang-Kobayashi equations.
NASA Astrophysics Data System (ADS)
Ferlet, Roger
Substantial progress in the field of the Local Interstellar Medium has been largely due to recent launches of space missions, mostly in the UV and X-ray domains, but also to ground-based observations, mainly in high resolution spectroscopy. However, a clear gap seems to remain between the wealth of new data and the theoretical understanding. This paper gives an overview of some observational aspects, with no attempt of completeness or doing justice to all the people involved in the field. As progress rarely evolves in straight paths, we can expect that our present picture of the solar system surroundings is not definitive.
Exact propagating nonlinear singular disturbances in strongly coupled dusty plasmas
Das, Amita; Tiwari, Sanat Kumar; Kaw, Predhiman; Sen, Abhijit
2014-08-15
The dynamical response of the strongly coupled dusty plasma medium has recently been described by utilizing the Generalized Hydrodynamic (GHD) model equations. The GHD equations capture the visco-elastic properties of the medium and have been successful in predicting a host of phenomena (e.g., existence of novel transverse shear waves in the fluid medium, modification of longitudinal wave dispersion by elastic effects, etc.) which have found experimental confirmation. In this paper, the nonlinear longitudinal response of the medium governed by GHD equations in strong coupling limit is discussed analytically. The structure of the equations rules out the balance between dispersion and nonlinearity, thereby, forbidding soliton formation. However, a host of new varieties of nonlinear solutions are found to exist, which have singular spatial profiles and yet have conservative properties. For instance, existence of novel conservative shock structures with zero strength is demonstrated, waves whose breaking produces no dissipation in the medium are observed, propagating solutions which produce cusp like singularities can exist and so on. It is suggested that simulations and experiments should look for these novel nonlinear structures in the large amplitude strong coupling limit of longitudinal disturbances in dusty plasmas.
NASA Astrophysics Data System (ADS)
Hausmann, B. J. M.; Bulu, I.; Venkataraman, V.; Deotare, P.; Lončar, M.
2014-05-01
Despite progress towards integrated diamond photonics, studies of optical nonlinearities in diamond have been limited to Raman scattering in bulk samples. Diamond nonlinear photonics, however, could enable efficient, in situ frequency conversion of single photons emitted by diamond's colour centres, as well as stable and high-power frequency microcombs operating at new wavelengths. Both of these applications depend crucially on efficient four-wave mixing processes enabled by diamond's third-order nonlinearity. Here, we have realized a diamond nonlinear photonics platform by demonstrating optical parametric oscillation via four-wave mixing using single-crystal ultrahigh-quality-factor (1 × 106) diamond ring resonators operating at telecom wavelengths. Threshold powers as low as 20 mW are measured, and up to 20 new wavelengths are generated from a single-frequency pump laser. We also report the first measurement of the nonlinear refractive index due to the third-order nonlinearity in diamond at telecom wavelengths.
Nonlinear rotordynamics analysis
NASA Technical Reports Server (NTRS)
Day, W. B.
1985-01-01
The special nonlinearities of the Jeffcott equations in rotordynamics are examined. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot firing ground testing. Deadband, side force and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency is defined and used to develop the solutions of the nonlinear Jeffcott equations as asympotic expansions. This nonlinear natural frequency which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies. Numerical solutions are included for comparison with the analysis. Also, nonlinear frequency-response tables are made for a typical range of values.
Stationary nonlinear Airy beams
Lotti, A.; Faccio, D.; Couairon, A.; Papazoglou, D. G.; Panagiotopoulos, P.; Tzortzakis, S.; Abdollahpour, D.
2011-08-15
We demonstrate the existence of an additional class of stationary accelerating Airy wave forms that exist in the presence of third-order (Kerr) nonlinearity and nonlinear losses. Numerical simulations and experiments, in agreement with the analytical model, highlight how these stationary solutions sustain the nonlinear evolution of Airy beams. The generic nature of the Airy solution allows extension of these results to other settings, and a variety of applications are suggested.
Interactive Workshop Discusses Nonlinear Waves and Chaos
NASA Astrophysics Data System (ADS)
Tsurutani, Bruce; Morales, George; Passot, Thierry
2010-07-01
Eighth International Nonlinear Wave Workshop; La Jolla, California, 1-5 March 2010; Nonlinear waves and chaos were the focus of a weeklong series of informal and interactive discussions at the Eighth International Nonlinear Wave Workshop (NWW8), held in California. The workshop gathered nonlinear plasma and water wave experts from the United States, France, Czech Republic, Germany, Greece, Holland, India, and Japan. Attendees were from the fields of space, laboratory, and fusion plasma physics, astrophysics, and applied mathematics. Special focus was placed on nonlinear waves and turbulence in the terrestrial environment as well as in the interstellar medium from observational, laboratory, and theoretical perspectives. Discussions covered temperature anisotropies and related instabilities, the properties and origin of the so-called dissipation range, and various coherent structures of electromagnetic as well as electrostatic nature. Reconnection and shocks were also topics of discussion, as were properties of magnetospheric whistler and chorus waves. Examples and analysis techniques for superdiffusion and subdiffusion were identified. On this last topic, a good exchange of ideas and results occurred between a water wave expert and a plasma expert, with the rest of the audience listening intently.
DENSE MEDIUM CYCLONE OPTIMIZATON
Gerald H. Luttrell; Chris J. Barbee; Peter J. Bethell; Chris J. Wood
2005-06-30
Dense medium cyclones (DMCs) are known to be efficient, high-tonnage devices suitable for upgrading particles in the 50 to 0.5 mm size range. This versatile separator, which uses centrifugal forces to enhance the separation of fine particles that cannot be upgraded in static dense medium separators, can be found in most modern coal plants and in a variety of mineral plants treating iron ore, dolomite, diamonds, potash and lead-zinc ores. Due to the high tonnage, a small increase in DMC efficiency can have a large impact on plant profitability. Unfortunately, the knowledge base required to properly design and operate DMCs has been seriously eroded during the past several decades. In an attempt to correct this problem, a set of engineering tools have been developed to allow producers to improve the efficiency of their DMC circuits. These tools include (1) low-cost density tracers that can be used by plant operators to rapidly assess DMC performance, (2) mathematical process models that can be used to predict the influence of changes in operating and design variables on DMC performance, and (3) an expert advisor system that provides plant operators with a user-friendly interface for evaluating, optimizing and trouble-shooting DMC circuits. The field data required to develop these tools was collected by conducting detailed sampling and evaluation programs at several industrial plant sites. These data were used to demonstrate the technical, economic and environmental benefits that can be realized through the application of these engineering tools.
Enhancement of the Sagnac effect due to nonlinearly induced nonreciprocity
NASA Astrophysics Data System (ADS)
Kaplan, A. E.; Meystre, P.
1981-12-01
A novel method is proposed for enhancing the Sagnac effect through the use of a nonlinear ring interferometer. The proposed method takes advantage of the nonlinearly induced nonreciprocity of counterpropagating waves caused by the formation of an index grating in the nonlinear medium. The enhancement of the Sagnac effect could find applications in cases where high sensitivity is required, e.g. in optical tests of general relativity. The measurement of the enhancement factor also provides a novel spectroscopic method for analyzing nonlocal interactions (nonreciprocal Sagnac spectroscopy).
Organic nonlinear optical materials
NASA Technical Reports Server (NTRS)
Umegaki, S.
1987-01-01
Recently, it became clear that organic compounds with delocalized pi electrons show a great nonlinear optical response. Especially, secondary nonlinear optical constants of more than 2 digits were often seen in the molecular level compared to the existing inorganic crystals such as LiNbO3. The crystallization was continuously tried. Organic nonlinear optical crystals have a new future as materials for use in the applied physics such as photomodulation, optical frequency transformation, opto-bistabilization, and phase conjugation optics. Organic nonlinear optical materials, e.g., urea, O2NC6H4NH2, I, II, are reviewed with 50 references.
Nonlinear optics at interfaces
Chen, C.K.
1980-12-01
Two aspects of surface nonlinear optics are explored in this thesis. The first part is a theoretical and experimental study of nonlinear intraction of surface plasmons and bulk photons at metal-dielectric interfaces. The second part is a demonstration and study of surface enhanced second harmonic generation at rough metal surfaces. A general formulation for nonlinear interaction of surface plasmons at metal-dielectric interfaces is presented and applied to both second and third order nonlinear processes. Experimental results for coherent second and third harmonic generation by surface plasmons and surface coherent antiStokes Raman spectroscopy (CARS) are shown to be in good agreement with the theory.
Optical vortex interaction and generation via nonlinear wave mixing
Lenzini, F.; Residori, S.; Bortolozzo, U.; Arecchi, F. T.
2011-12-15
Optical vortex beams are made to interact via degenerate two-wave mixing in a Kerr-like nonlinear medium. Vortex mixing is shown to occur inside the medium, leading to exchange of topological charge and cascaded generation of vortex beams. A mean-field model is developed and is shown to account for the selection rules of the topological charges observed after the wave-mixing process. Fractional charges are demonstrated to follow the same rules as for integer charges.
Time-reversed wave mixing in nonlinear optics.
Zheng, Yuanlin; Ren, Huaijin; Wan, Wenjie; Chen, Xianfeng
2013-11-19
Time-reversal symmetry is important to optics. Optical processes can run in a forward or backward direction through time when such symmetry is preserved. In linear optics, a time-reversed process of laser emission can enable total absorption of coherent light fields inside an optical cavity of loss by time-reversing the original gain medium. Nonlinearity, however, can often destroy such symmetry in nonlinear optics, making it difficult to study time-reversal symmetry with nonlinear optical wave mixings. Here we demonstrate time-reversed wave mixings for optical second harmonic generation (SHG) and optical parametric amplification (OPA) by exploring this well-known but underappreciated symmetry in nonlinear optics. This allows us to observe the annihilation of coherent beams. Our study offers new avenues for flexible control in nonlinear optics and has potential applications in efficient wavelength conversion, all-optical computing.
Nonlinear refraction of silver hydrosols during their aggregation
Karpov, S V; Kodirov, M K; Ryasnyansky, A I; Slabko, V V
2001-10-31
The relation between the degree of aggregation of silver hydrosols and their nonlinear refractive index n{sub 2} is studied experimentally. It is found that the sign of n{sub 2} at a wavelength of 1.064 {mu}m changes with increasing the aggregation degree, which corresponds to the replacing of self-focusing by self-defocusing. The observed effects are explained based on the analysis of a change in nonlinear dispersion of the medium, taking into account the interaction between phases and the photochromic effects, which are typical for colloidal structures with fractal geometry. It is shown that the change in the sign of the nonlinear refractive index of hydrosols upon irradiation by laser pulses of duration of less than 10{sup -7} s is caused by the perturbation of resonances of silver and water and by the competition between Kerr nonlinear polarisations involving these resonances. (nonlinear optical phenomena and devices)
Necklace beam generation in nonlinear colloidal engineered media.
Silahli, Salih Z; Walasik, Wiktor; Litchinitser, Natalia M
2015-12-15
Modulational instability is a phenomenon that reveals itself as the exponential growth of weak perturbations in the presence of an intense pump beam propagating in a nonlinear medium. It plays a key role in such nonlinear optical processes as supercontinuum generation, light filamentation, rogue waves, and ring (or necklace) beam formation. To date, a majority of studies of these phenomena have focused on light-matter interactions in self-focusing Kerr media existing in nature. However, a large and tunable nonlinear response of a colloidal suspension can be tailored at will by judiciously engineering the optical polarizability. Here, we analytically and numerically show the possibility of necklace beam generation originating from spatial modulational instability of vortex beams in engineered soft-matter nonlinear media with different types of exponential nonlinearity. PMID:26670494
Nonlinear scattering of acoustic waves by vibrating obstacles
NASA Astrophysics Data System (ADS)
Piquette, J. C.
1983-06-01
The problem of the generation of sum- and difference-frequency waves produced via the scattering of an acoustic wave by an obstacle whose surface vibrates harmonically was studied both theoretically and experimentally. The theoretical approach involved solving the nonlinear wave equation, subject to appropriate boundary conditions, by the use of a perturbation expansion of the fields and a Green's function method. In addition to ordinary rigid-body scattering, Censor predicted nongrowing waves at frequencies equal to the sum and to the difference of the frequencies of the primary waves. The solution to the nonlinear wave equation also yields scattered waves at the sum and difference frequencies. However, the nonlinearity of the medium causes these waves to grow with increasing distance from the scatter's surface and, after a very small distance, dominate those predicted by Censor. The simple-source formulation of the second-order nonlinear wave equation for a lossless fluid medium has been derived for arbitrary primary wave fields. This equation was used to solve the problem of nonlinear scattering of acoustic waves by a vibrating obstacle for three geometries: (1) a plane-wave scattering by a vibrating plane, (2) cylindrical-wave scattering by a vibrating cylinder, and (3) plane-wave scattering by a vibrating cylinder. Successful experimental validation of the theory was inhibited by previously unexpected levels of nonlinearity in the hydrophones used. Such high levels of hydrophone nonlinearity appeared in hydrophones that, by their geometry of construction, were expected to be fairly linear.
Nonlinear Coherent Structures, Microbursts and Turbulence
NASA Astrophysics Data System (ADS)
Lakhina, G. S.
2015-12-01
Nonlinear waves are found everywhere, in fluids, atmosphere, laboratory, space and astrophysical plasmas. The interplay of nonlinear effects, dispersion and dissipation in the medium can lead to a variety of nonlinear waves and turbulence. Two cases of coherent nonlinear waves: chorus and electrostatic solitary waves (ESWs) and their impact on modifying the plasma medium are discussed. Chorus is a right-hand, circularly-polarized electromagnetic plane wave. Dayside chorus is a bursty emission composed of rising frequency "elements" with duration of ~0.1 to 1.0 s. Each element is composed of coherent subelements with durations of ~1 to 100 ms or more. The cyclotron resonant interaction between energetic electrons and the coherent chorus waves is studied. An expression for the pitch angle transport due to this interaction is derived considering a Gaussian distribution for the time duration of the chorus elements. The rapid pitch scattering can provide an explanation for the ionospheric microbursts of ~0.1 to 0.5 s in bremsstrahlung x-rays formed by ~10-100 keV precipitating electrons. On the other hand, the ESWs are observed in the electric field component parallel to the background magnetic field, and are usually bipolar or tripolar. Generation of coherent ESWs has been explained in terms of nonlinear fluid models of ion- and electron-acoustic solitons and double layers (DLs) based on Sagdeev pseudopotential technique. Fast Fourier transform of electron- and ion-acoustic solitons/DLs produces broadband wave spectra which can explain the properties of the electrostatic turbulence observed in the magnetosheath and plasma sheet boundary layer, and in the solar wind, respectively.
Nonlinear Optics and Applications
NASA Technical Reports Server (NTRS)
Abdeldayem, Hossin A. (Editor); Frazier, Donald O. (Editor)
2007-01-01
Nonlinear optics is the result of laser beam interaction with materials and started with the advent of lasers in the early 1960s. The field is growing daily and plays a major role in emerging photonic technology. Nonlinear optics play a major role in many of the optical applications such as optical signal processing, optical computers, ultrafast switches, ultra-short pulsed lasers, sensors, laser amplifiers, and many others. This special review volume on Nonlinear Optics and Applications is intended for those who want to be aware of the most recent technology. This book presents a survey of the recent advances of nonlinear optical applications. Emphasis will be on novel devices and materials, switching technology, optical computing, and important experimental results. Recent developments in topics which are of historical interest to researchers, and in the same time of potential use in the fields of all-optical communication and computing technologies, are also included. Additionally, a few new related topics which might provoke discussion are presented. The book includes chapters on nonlinear optics and applications; the nonlinear Schrodinger and associated equations that model spatio-temporal propagation; the supercontinuum light source; wideband ultrashort pulse fiber laser sources; lattice fabrication as well as their linear and nonlinear light guiding properties; the second-order EO effect (Pockels), the third-order (Kerr) and thermo-optical effects in optical waveguides and their applications in optical communication; and, the effect of magnetic field and its role in nonlinear optics, among other chapters.
Nonlinearly realized extended supergravity
Izawa, K.-I.; Nakai, Y.; Takahashi, Ryo
2010-10-01
We provide a nonlinear realization of supergravity with an arbitrary number of supersymmetries by means of coset construction. The number of gravitino degrees of freedom counts the number of supersymmetries, which will possibly be probed in future experiments. We also consider Goldstino embedding in the construction to discuss the relation to nonlinear realizations with rigid supersymmetries.
Friction and nonlinear dynamics
NASA Astrophysics Data System (ADS)
Manini, N.; Braun, O. M.; Tosatti, E.; Guerra, R.; Vanossi, A.
2016-07-01
The nonlinear dynamics associated with sliding friction forms a broad interdisciplinary research field that involves complex dynamical processes and patterns covering a broad range of time and length scales. Progress in experimental techniques and computational resources has stimulated the development of more refined and accurate mathematical and numerical models, capable of capturing many of the essentially nonlinear phenomena involved in friction.
NASA Technical Reports Server (NTRS)
Sheen, Jyh-Jong; Bishop, Robert H.
1992-01-01
The feedback linearization technique is applied to the problem of spacecraft attitude control and momentum management with control moment gyros (CMGs). The feedback linearization consists of a coordinate transformation, which transforms the system to a companion form, and a nonlinear feedback control law to cancel the nonlinear dynamics resulting in a linear equivalent model. Pole placement techniques are then used to place the closed-loop poles. The coordinate transformation proposed here evolves from three output functions of relative degree four, three, and two, respectively. The nonlinear feedback control law is presented. Stability in a neighborhood of a controllable torque equilibrium attitude (TEA) is guaranteed and this fact is demonstrated by the simulation results. An investigation of the nonlinear control law shows that singularities exist in the state space outside the neighborhood of the controllable TEA. The nonlinear control law is simplified by a standard linearization technique and it is shown that the linearized nonlinear controller provides a natural way to select control gains for the multiple-input, multiple-output system. Simulation results using the linearized nonlinear controller show good performance relative to the nonlinear controller in the neighborhood of the TEA.
Lasers for nonlinear microscopy.
Wise, Frank
2013-03-01
Various versions of nonlinear microscopy are revolutionizing the life sciences, almost all of which are made possible because of the development of ultrafast lasers. In this article, the main properties and technical features of short-pulse lasers used in nonlinear microscopy are summarized. Recent research results on fiber lasers that will impact future instruments are also discussed.
NASA Astrophysics Data System (ADS)
Solookinejad, G.
2016-09-01
In this study, the linear and nonlinear susceptibility of a single-layer graphene nanostructure driven by a weak probe light and an elliptical polarized coupling field is discussed theoretically. The Landau levels of graphene can be separated in infrared or terahertz regions under the strong magnetic field. Therefore, by using the density matrix formalism in quantum optic, the linear and nonlinear susceptibility of the medium can be derived. It is demonstrated that by adjusting the elliptical parameter, one can manipulate the linear and nonlinear absorption as well as Kerr nonlinearity of the medium. It is realized that the enhanced Kerr nonlinearity can be possible with zero linear absorption and nonlinear amplification at some values of elliptical parameter. Our results may be having potential applications in quantum information science based on Nano scales devices.
NASA Technical Reports Server (NTRS)
Hunt, L. R.; Whitney, Paul
1987-01-01
A technique for identifying nonlinear systems was introduced, beginning with a single input-single output system. Assuming the system is initially at rest, the first kernel (first convolution integral in the continuous case or first convolution sum in the discrete case) was calculated. A controllable and observable linear realization was then obtained in a particular canonical form. The actual nonlinear system was probed with an appropriate input (or inputs) and the output (or outputs) determined. For the linear system, the input was computed that produces the same output. In the difference between the inputs to the nonlinear and linear systems, basic information was found about the nonlinear system. There is an interesting class of nonlinear systems for which this type of identification scheme should prove to be accurate.
Influence of Kerr-like medium on the dynamics of a two-mode Raman coupled model
NASA Astrophysics Data System (ADS)
Singh, Sudha; Gilhare, Karuna
2016-08-01
We study the quantum dynamics of an effective two-level atom interacting with two modes via Raman process inside an ideal cavity in the presence of Kerr non-linearity. The cavity modes interact both with the atom as well as the Kerr-like medium. The unitary transformation method presented here, not only solves the time-dependent problem, but also provides the eigensolutions of the interacting Hamiltonian at the same time. We study the atomic-population dynamics and the dynamics of the photon statistics in the two cavity modes. The influence of the Kerr-like medium on the statistics of the field is explored and it is observed that Kerr medium introduces antibunching in mode 1 and this effect is enhanced by a stronger interaction with the non-linear medium. In the high non-linear coupling regime anticorrelated beam become correlated. Kerr medium also introduces non-classical correlation between the two modes.
Model of optical nonlinearity of air in the mid-IR wavelength range
Geints, Yu E; Zemlyanov, A A
2014-09-30
A model of optical nonlinearity of air (atmospheric nitrogen and oxygen) is developed. This model can be used to calculate numerically the propagation of radiation with a wavelength close to 10 μm. It takes into account the electronic Kerr effect, higher order nonlinearities, ionisation of a gas medium by electron impact, and pulse group-velocity dispersion. The applicability limits of the Drude approximation for calculating the impact-ionisation rate are also considered. (nonlinear optical phenomena)
Abe, H.; Okuda, H.
1994-06-01
We study linear and nonlinear properties of a new computer simulation model developed to study the propagation of electromagnetic waves in a dielectric medium in the linear and nonlinear regimes. The model is constructed by combining a microscopic model used in the semi-classical approximation for the dielectric media and the particle model developed for the plasma simulations. It is shown that the model may be useful for studying linear and nonlinear wave propagation in the dielectric media.
Reflection of a Gaussian beam from a nonlinear interface.
Marcuse, D
1980-09-15
A numerical analysis of the reflection of a two dimensional Gaussian beam from the interface between a linear and a nonlinear medium is presented. The refractive index of the nonlinear medium is a function of the intensity of the radiation field, having a smaller value than the linear refractive index for zero field intensity. The Gaussian beam is incident from the linear medium and suffers total reflection at low intensity. At sufficiently high intensity nonlinear effects are observed. Above a threshold value the incident beam breaks up into a reflected wave and a surface wave. Once the beam is sufficiently strong for a surface wave to form, its interaction with the boundary becomes surprisingly independent of field intensity; but for very strong fields the reflectivity is increased at the expense of the surface wave. A very different behavior is observed when the refractive index is constrained to remain below a certain maximum value. Now the field detaches itself from the surface and penetrates into the nonlinear medium forming one or more distinct beams. The plane wave theory predicts the existence of hysteresis so that two different solutions should exist for the same physical parameters. A second solution was indeed found in one case with constrained refractive index, but its validity is somewhat uncertain at this time.
OPCPA modeling using YCOB as the non-linear crystal
NASA Astrophysics Data System (ADS)
Pires, Hugo; Cardoso, Luis; Wemans, João; João, Celso; Figueira, Gonçalo
2010-04-01
In this work, we evaluate numerically the performance of the nonlinear crystal yttrium calcium oxyborate (YCOB) as the gain medium in a noncollinear, angularly dispersed beam OPCPA configuration, and compare it to other well-studied crystals. In particular, we study its use in the context of an ultrahigh peak and average power amplifier setup. Possible bandwidths are assessed.
Zweig, George
2016-05-01
An earlier paper characterizing the linear mechanical response of the organ of Corti [J. Acoust. Soc. Am. 138, 1102-1121 (2015)] is extended to the nonlinear domain. Assuming the existence of nonlinear oscillators nonlocally coupled through the pressure they help create, the oscillator equations are derived and examined when the stimuli are modulated tones and clicks. The nonlinearities are constrained by the requirements of oscillator stability and the invariance of zero crossings in the click response to changes in click amplitude. The nonlinear oscillator equations for tones are solved in terms of the fluid pressure that drives them, and its time derivative, presumably a proxy for forces created by outer hair cells. The pressure equation is reduced to quadrature, the integrand depending on the oscillators' responses. The resulting nonlocally coupled nonlinear equations for the pressure, and oscillator amplitudes and phases, are solved numerically in terms of the fluid pressure at the stapes. Methods for determining the nonlinear damping directly from measurements are described. Once the oscillators have been characterized from their tone and click responses, the mechanical response of the cochlea to natural sounds may be computed numerically. Signal processing inspired by cochlear mechanics opens up a new area of nonlocal nonlinear time-frequency analysis.
Zweig, George
2016-05-01
An earlier paper characterizing the linear mechanical response of the organ of Corti [J. Acoust. Soc. Am. 138, 1102-1121 (2015)] is extended to the nonlinear domain. Assuming the existence of nonlinear oscillators nonlocally coupled through the pressure they help create, the oscillator equations are derived and examined when the stimuli are modulated tones and clicks. The nonlinearities are constrained by the requirements of oscillator stability and the invariance of zero crossings in the click response to changes in click amplitude. The nonlinear oscillator equations for tones are solved in terms of the fluid pressure that drives them, and its time derivative, presumably a proxy for forces created by outer hair cells. The pressure equation is reduced to quadrature, the integrand depending on the oscillators' responses. The resulting nonlocally coupled nonlinear equations for the pressure, and oscillator amplitudes and phases, are solved numerically in terms of the fluid pressure at the stapes. Methods for determining the nonlinear damping directly from measurements are described. Once the oscillators have been characterized from their tone and click responses, the mechanical response of the cochlea to natural sounds may be computed numerically. Signal processing inspired by cochlear mechanics opens up a new area of nonlocal nonlinear time-frequency analysis. PMID:27250151
New approaches to nonlinear diffractive field propagation.
Christopher, P T; Parker, K J
1991-07-01
In many domains of acoustic field propagation, such as medical ultrasound imaging, lithotripsy shock treatment, and underwater sonar, a realistic calculation of beam patterns requires treatment of the effects of diffraction from finite sources. Also, the mechanisms of loss and nonlinear effects within the medium are typically nonnegligible. The combination of diffraction, attenuation, and nonlinear effects has been treated by a number of formulations and numerical techniques. A novel model that incrementally propagates the field of baffled planar sources with substeps that account for the physics of diffraction, attenuation, and nonlinearity is presented. The model accounts for the effect of refraction and reflection (but not multiple reflections) in the case of propagation through multiple, parallel layers of fluid medium. An implementation of the model for axis symmetric sources has been developed. In one substep of the implementation, a new discrete Hankel transform is used with spatial transform techniques to propagate the field over a short distance with diffraction and attenuation. In the other substep, the temporal frequency domain solution to Burgers' equation is implemented to account for the nonlinear accretion and depletion of harmonics. This approach yields a computationally efficient procedure for calculating beam patterns from a baffled planar, axially symmetric source under conditions ranging from quasilinear through shock. The model is not restricted by the usual parabolic wave approximation and the field's directionality is explicitly accounted for at each point. Useage of a harmonic-limiting scheme allows the model to propagate some previously intractable high-intensity nonlinear fields. Results of the model are shown to be in excellent agreement with measurements performed on the nonlinear field of an unfocused 2.25-MHz piston source, even in the near field where the established parabolic wave approximation model fails. Next, the model is used to
Nonlinear pulse propagation: a time-transformation approach.
Xiao, Yuzhe; Agrawal, Govind P; Maywar, Drew N
2012-04-01
We present a time-transformation approach for studying the propagation of optical pulses inside a nonlinear medium. Unlike the conventional way of solving for the slowly varying amplitude of an optical pulse, our new approach maps directly the input electric field to the output one, without making the slowly varying envelope approximation. Conceptually, the time-transformation approach shows that the effect of propagation through a nonlinear medium is to change the relative spacing and duration of various temporal slices of the pulse. These temporal changes manifest as self-phase modulation in the spectral domain and self-steepening in the temporal domain. Our approach agrees with the generalized nonlinear Schrödinger equation for 100 fs pulses and the finite-difference time-domain solution of Maxwell's equations for two-cycle pulses, while producing results 20 and 50 times faster, respectively.
Nonlinear ordinary difference equations
NASA Technical Reports Server (NTRS)
Caughey, T. K.
1979-01-01
Future space vehicles will be relatively large and flexible, and active control will be necessary to maintain geometrical configuration. While the stresses and strains in these space vehicles are not expected to be excessively large, their cumulative effects will cause significant geometrical nonlinearities to appear in the equations of motion, in addition to the nonlinearities caused by material properties. Since the only effective tool for the analysis of such large complex structures is the digital computer, it will be necessary to gain a better understanding of the nonlinear ordinary difference equations which result from the time discretization of the semidiscrete equations of motion for such structures.
Martin, G; McGarel, S
2001-01-01
A mill is a mechanical device that grinds mined or processed material into small particles. The process is known to display significant deadtime, and, more notably, severe nonlinear behavior. Over the past 25 years attempts at continuous mill control have met varying degrees of failure, mainly due to model mismatch caused by changes in the mill process gains. This paper describes an on-line control application on a closed-circuit cement mill that uses nonlinear model predictive control technology. The nonlinear gains for the control model are calculated on-line from a neural network model of the process.
Multipole nonlinearity of metamaterials
Petschulat, J.; Chipouline, A.; Tuennermann, A.; Pertsch, T.; Menzel, C.; Rockstuhl, C.; Lederer, F.
2009-12-15
We report on the linear and nonlinear optical response of metamaterials evoked by first- and second-order multipoles. The analytical ground on which our approach is based permits for new insights into the functionality of metamaterials. For the sake of clarity we focus here on a key geometry, namely, the split-ring resonator, although the introduced formalism can be applied to arbitrary structures. We derive the equations that describe linear and nonlinear light propagation where special emphasis is put on second-harmonic generation. This contribution basically aims at stretching versatile and existing concepts to describe light propagation in nonlinear media toward the realm of metamaterials.
NASA Astrophysics Data System (ADS)
Verweij, Martin D.; Demi, Libertario; van Dongen, Koen W. A.
2012-09-01
The Iterative Nonlinear Contrast Source (INCS) method is a full-wave method for the accurate computation of wide-angle, pulsed, nonlinear ultrasound fields appearing in, e.g., medical echoscopy. The method is based on the Westervelt equation and considers the occurring nonlinear term as a distributed contrast source that operates in a linear background medium. This formulation leads to an integral equation, which is solved in an iterative way. The original INCS method uses a Neumann scheme to successively approximate the nonlinear wave field in homogeneous, lossless, nonlinear media. To cope with attenuative and/or inhomogeneous nonlinear media, additional contrast sources may be introduced. Since these deteriorate the convergence rate of the Neumann scheme, more advanced iterative solution schemes like Bi-CGSTAB are required. To overcome the difficulty that such schemes only apply to linear integral equations, the nonlinear contrast source is linearized, at the cost of a significant systematic error in the fourth and higher harmonics. In this paper, a strategy is proposed in which the relevant iterative solution scheme is restarted with an updated version of the linearized contrast source. Results demonstrate the effectiveness of this strategy in eliminating the systematic error. In addition, it is shown that the same approach also improves the convergence rate in case of nonlinear propagation in media with attenuation.
Nonlinear optomechanical pressure
NASA Astrophysics Data System (ADS)
Conti, Claudio; Boyd, Robert
2014-03-01
A transparent material exhibits ultrafast optical nonlinearity and is subject to optical pressure if irradiated by a laser beam. However, the effect of nonlinearity on optical pressure is often overlooked, even if a nonlinear optical pressure may be potentially employed in many applications, such as optical manipulation, biophysics, cavity optomechanics, quantum optics, and optical tractors, and is relevant in fundamental problems such as the Abraham-Minkoswky dilemma or the Casimir effect. Here, we show that an ultrafast nonlinear polarization gives indeed a contribution to the optical pressure that also is negative in certain spectral ranges; the theoretical analysis is confirmed by first-principles simulations. An order-of-magnitude estimate shows that the effect can be observable by measuring the deflection of a membrane made by graphene.
NASA Technical Reports Server (NTRS)
1984-01-01
Nonlinear structural analysis techniques for engine structures and components are addressed. The finite element method and boundary element method are discussed in terms of stress and structural analyses of shells, plates, and laminates.
Library for Nonlinear Optimization
2001-10-09
OPT++ is a C++ object-oriented library for nonlinear optimization. This incorporates an improved implementation of an existing capability and two new algorithmic capabilities based on existing journal articles and freely available software.
Nonlinear Dynamics in Cardiology
Krogh-Madsen, Trine; Christini, David J.
2013-01-01
The dynamics of many cardiac arrhythmias, as well as the nature of transitions between different heart rhythms, have long been considered evidence of nonlinear phenomena playing a direct role in cardiac arrhythmogenesis. In most types of cardiac disease, the pathology develops slowly and gradually, often over many years. In contrast, arrhythmias often occur suddenly. In nonlinear systems, sudden changes in qualitative dynamics can, counter-intuitively, result from a gradual change in a system parameter –this is known as a bifurcation. Here, we review how nonlinearities in cardiac electrophysiology influence normal and abnormal rhythms and how bifurcations change the dynamics. In particular, we focus on the many recent developments in computational modeling at the cellular level focused on intracellular calcium dynamics. We discuss two areas where recent experimental and modeling work have suggested the importance of nonlinearities in calcium dynamics: repolarization alternans and pacemaker cell automaticity. PMID:22524390
Nonlinear Refractive Properties
NASA Technical Reports Server (NTRS)
Vikram, Chandra S.; Witherow, William K.
2001-01-01
Using nonlinear refractive properties of a salt-water solution at two wavelengths, numerical analysis has been performed to extract temperature and concentration from interferometric fringe data. The theoretical study, using a commercially available equation solving software, starts with critical fringe counting needs and the role of nonlinear refractive properties in such measurements. Finally, methodology of the analysis, codes, fringe counting accuracy needs, etc. is described in detail.
Photon Number-Phase Uncertainty Relation in the Evolution of the Field in a Kerr-Like Medium
NASA Technical Reports Server (NTRS)
Fan, An-Fu; Sun, Nian-Chun
1996-01-01
A model of a single-mode field, initially prepared in a coherent state, coupled to a two-level atom surrounded by a nonlinear Kerr-like medium contained inside a very good quality cavity is considered. We derive the photon number-phase uncertainty relation in the evolution of the field for a weak and strong nonlinear coupling respectively, within the Hermitian phase operator formalism of Pegg and Barnett, and discuss the effects of nonlinear coupling of the Kerr-like medium on photon number-phase uncertainty relation of the field.
Numerical studies of the nonlinear properties of composites
NASA Astrophysics Data System (ADS)
Zhang, X.; Stroud, D.
1994-01-01
Using both numerical and analytical techniques, we investigate various ways to enhance the cubic nonlinear susceptibility χe of a composite material. We start from the exact relation χe =tsumipiχi<(E.E)2>i,lin/ E40, where χi and pi are the cubic nonlinear susceptibility and volume fraction of the ith component, E0 is the applied electric field, and
Nonlinear systems in medicine.
Higgins, John P.
2002-01-01
Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states. PMID:14580107
NASA Astrophysics Data System (ADS)
Yang, Qianli; Pitkow, Xaq
2015-03-01
Most interesting natural sensory stimuli are encoded in the brain in a form that can only be decoded nonlinearly. But despite being a core function of the brain, nonlinear population codes are rarely studied and poorly understood. Interestingly, the few existing models of nonlinear codes are inconsistent with known architectural features of the brain. In particular, these codes have information content that scales with the size of the cortical population, even if that violates the data processing inequality by exceeding the amount of information entering the sensory system. Here we provide a valid theory of nonlinear population codes by generalizing recent work on information-limiting correlations in linear population codes. Although these generalized, nonlinear information-limiting correlations bound the performance of any decoder, they also make decoding more robust to suboptimal computation, allowing many suboptimal decoders to achieve nearly the same efficiency as an optimal decoder. Although these correlations are extremely difficult to measure directly, particularly for nonlinear codes, we provide a simple, practical test by which one can use choice-related activity in small populations of neurons to determine whether decoding is suboptimal or optimal and limited by correlated noise. We conclude by describing an example computation in the vestibular system where this theory applies. QY and XP was supported by a grant from the McNair foundation.
New medium licensed for campylobacter
Technology Transfer Automated Retrieval System (TEKTRAN)
A medium, “Campy-Cefex”, has been licensed by the ARS Office of Technology Transfer with Becton Dickinson (No. 1412-002) and Neogen (No. 1412-001) based on patent No. 5,891,709, “Campy-Cefex Selective and Differential Medium for Campylobacter” by Dr. Norman Stern of the Poultry Microbiological Safet...
Nonlinear optical studies of organic monolayers
Shen, Y.R.
1988-02-01
Second-order nonlinear optical effects are forbidden in a medium with inversion symmetry, but are necessarily allowed at a surface where the inversion summary is broken. They are often sufficiently strong so that a submonolayer perturbation of the surface can be readily detected. They can therefore be used as effective tools to study monolayers adsorbed at various interfaces. We discuss here a number of recent experiments in which optical second harmonic generation (SHG) and sum-frequency generation (SFG) are employed to probe and characterize organic monolayers. 15 refs., 5 figs.
Superfluid light in bulk nonlinear media.
Carusotto, Iacopo
2014-09-01
We review how the paraxial approximation naturally leads to a hydrodynamic description of light propagation in a bulk Kerr nonlinear medium in terms of a wave equation analogous to the Gross-Pitaevskii equation for the order parameter of a superfluid. The main features of the many-body collective dynamics of the fluid of light in this propagating geometry are discussed: generation and observation of Bogoliubov sound waves in the fluid of light is first described. Experimentally accessible manifestations of superfluidity are then highlighted. Perspectives in view of realizing analogue models of gravity are finally given. PMID:25197252
Nonlinear wave propagation in strongly coupled dusty plasmas
Veeresha, B. M.; Tiwari, S. K.; Sen, A.; Kaw, P. K.; Das, A.
2010-03-15
The nonlinear propagation of low-frequency waves in a strongly coupled dusty plasma medium is studied theoretically in the framework of the phenomenological generalized hydrodynamic (GH) model. A set of simplified model nonlinear equations are derived from the original nonlinear integrodifferential form of the GH model by employing an appropriate physical ansatz. Using standard perturbation techniques characteristic evolution equations for finite small amplitude waves are then obtained in various propagation regimes. The influence of viscoelastic properties arising from dust correlation contributions on the nature of nonlinear solutions is discussed. The modulational stability of dust acoustic waves to parallel perturbation is also examined and it is shown that dust compressibility contributions influenced by the Coulomb coupling effects introduce significant modification in the threshold and range of the instability domain.
Electrically controlled nonlinear generation of light with plasmonics.
Cai, Wenshan; Vasudev, Alok P; Brongersma, Mark L
2011-09-23
Plasmonics provides a route to develop ultracompact optical devices on a chip by using extreme light concentration and the ability to perform simultaneous electrical and optical functions. These properties also make plasmonics an ideal candidate for dynamically controlling nonlinear optical interactions at the nanoscale. We demonstrate electrically tunable harmonic generation of light from a plasmonic nanocavity filled with a nonlinear medium. The metals that define the cavity also serve as electrodes that can generate high direct current electric fields across the nonlinear material. A fundamental wave at 1.56 micrometers was frequency doubled and modulated in intensity by applying a moderate external voltage to the electrodes, yielding a voltage-dependent nonlinear generation with a normalized magnitude of ~7% per volt.
Kim, Kihong; Phung, D K; Rotermund, F; Lim, H
2008-01-21
We develop a generalized version of the invariant imbedding method, which allows us to solve the electromagnetic wave equations in arbitrarily inhomogeneous stratified media where both the dielectric permittivity and magnetic permeability depend on the strengths of the electric and magnetic fields, in a numerically accurate and efficient manner. We apply our method to a uniform nonlinear slab and find that in the presence of strong external radiation, an initially uniform medium of positive refractive index can spontaneously change into a highly inhomogeneous medium where regions of positive or negative refractive index as well as metallic regions appear. We also study the wave transmission properties of periodic nonlinear media and the influence of nonlinearity on the mode conversion phenomena in inhomogeneous plasmas. We argue that our theory is very useful in the study of the optical properties of a variety of nonlinear media including nonlinear negative index media fabricated using wires and split-ring resonators.
Nonlinearity assessment of ASL F900 resistance thermometry bridges
NASA Astrophysics Data System (ADS)
Joung, W.; Gam, K. S.; Yang, I.; Kim, Y. G.
2013-09-01
Despite the importance of resistance bridges in thermometry as fundamental instruments measuring resistance ratios of SPRTs, an accurate assessment of their nonlinearity and investigation of their behavior under various operating conditions have not been investigated much. Among various methods for nonlinearity assessment, a Hamon-type resistance network known to be RBC (resistance bridge calibrator) is widely used. However, due to finite temperature coefficients of base resistors used in the RBC, the evaluated nonlinearity of the resistance bridges under normal operating environment have been in doubt. In this work, to accurately evaluate the nonlinearity of the resistance thermometry bridge, an air medium thermostatted chamber having peak-to-peak temperature stability of around 0.1 °C was devised, and using this chamber, the nonlinearity of the resistance bridges at KRISS (two ASL F900s) was assessed. In addition to this, the behavior of the resistance bridge in terms of the nonlinearity was thoroughly investigated under different operating conditions of various gain and bandwidth combinations. The results showed that the resistance thermometry bridge marked the minimum nonlinearity of 11 ppb at 105 gain and 0.1 Hz bandwidth, and showed noticeable dependence on the gain.
The Wave Processes in the Media Having Inelastic Hysteresis with Saturation of The Nonlinear Loss
NASA Astrophysics Data System (ADS)
Nazarov, V. E.; Kiyashko, S. B.
2016-07-01
We study theoretically the nonlinear wave processes during excitation of a longitudinal harmonic wave in an unbounded medium and the rod resonator with inelastic hysteresis and saturation of the amplitude-dependent loss. The nonlinear-wave characteristics in such systems, namely, the amplitude-dependent loss, variation in the wave-propagation velocity, the resonant-frequency shift, and the higher-harmonic amplitudes are determined. The results of the theoretical and experimental studies of nonlinear effects in the rod resonator of annealed polycrystalline copper are compared. The effective parameters of the hysteretic nonlinearity of this metal are evaluated.
Effective medium method for sound propagation in a soft medium containing air bubbles.
Liang, Bin; Zou, Xinye; Cheng, Jianchun
2008-09-01
An effective medium method (EMM) is developed to investigate the nonlinear propagation of acoustic waves for soft media containing air bubbles, which accounts for the effects of weak compressibility, viscosity, surrounding pressure, surface tension, and encapsulating shells. Based on the dynamics model of an individual bubble that has included these effects, the EMM is presented by employing a simple perturbation approach to "homogenize" the bubbly soft media. The equations describing the fundamental and the second harmonic waves are derived that applies to three-dimensional cases, and then solved in a one-dimensional case to obtain the effective acoustical parameters of a longitudinal wave. The EMM is compared with the previous theories in three representative cases regarded as simple models of significant practical applications. The results show that the EMM agrees well with the previous theories and can incorporate the additional effects, which may notably affect the accuracy of the results. The limitations of the EMM are also identified and stated.
Nonlinear optomechanics with graphene
NASA Astrophysics Data System (ADS)
Shaffer, Airlia; Patil, Yogesh Sharad; Cheung, Hil F. H.; Wang, Ke; Vengalattore, Mukund
2016-05-01
To date, studies of cavity optomechanics have been limited to exploiting the linear interactions between the light and mechanics. However, investigations of quantum signal transduction, quantum enhanced metrology and manybody physics with optomechanics each require strong, nonlinear interactions. Graphene nanomembranes are an exciting prospect for realizing such studies due to their inherently nonlinear nature and low mass. We fabricate large graphene nanomembranes and study their mechanical and optical properties. By using dark ground imaging techniques, we correlate their eigenmode shapes with the measured dissipation. We study their hysteretic response present even at low driving amplitudes, and their nonlinear dissipation. Finally, we discuss ongoing efforts to use these resonators for studies of quantum optomechanics and force sensing. This work is supported by the DARPA QuASAR program through a Grant from the ARO.
Monheit, G D
2001-07-01
The combination medium-depth chemical peel (Jessner's solution +35% TCA) has been accepted as a safe, reliable, and effective method for the treatment of moderate photoaging skin. This article discusses the procedure in detail, including postoperative considerations. PMID:11599398
An improved holographic recording medium
NASA Technical Reports Server (NTRS)
Gange, R. A.
1973-01-01
Solid, linear chain hydrocarbons with molecular weight ranging from about 300 to 2000 can serve as long-lived recording medium in optical memory system. Suitable recording hydrocarbons include microcrystalline waxes and low molecular weight polymers or ethylene.
Engineered nonlinear lattices.
Clausen, C B; Christiansen, P L; Torner, L; Gaididei, Y B
1999-11-01
We show that with the quasi-phase-matching technique it is possible to fabricate stripes of nonlinearity that trap and guide light like waveguides. We investigate an array of such stripes and find that when the stripes are sufficiently narrow, the beam dynamics is governed by a quadratic nonlinear discrete equation. The proposed structure therefore provides an experimental setting for exploring discrete effects in a controlled manner. In particular, we show propagation of breathers that are eventually trapped by discreteness. When the stripes are wide the beams evolve in a structure we term a quasilattice, which interpolates between a lattice system and a continuous system. PMID:11970457
Nonlinear aerodynamic wing design
NASA Technical Reports Server (NTRS)
Bonner, Ellwood
1985-01-01
The applicability of new nonlinear theoretical techniques is demonstrated for supersonic wing design. The new technology was utilized to define outboard panels for an existing advanced tactical fighter model. Mach 1.6 maneuver point design and multi-operating point compromise surfaces were developed and tested. High aerodynamic efficiency was achieved at the design conditions. A corollary result was that only modest supersonic penalties were incurred to meet multiple aerodynamic requirements. The nonlinear potential analysis of a practical configuration arrangement correlated well with experimental data.
Nonlinear trajectory navigation
NASA Astrophysics Data System (ADS)
Park, Sang H.
Trajectory navigation entails the solution of many different problems that arise due to uncertain knowledge of the spacecraft state, including orbit prediction, correction maneuver design, and trajectory estimation. In practice, these problems are usually solved based on an assumption that linear dynamical models sufficiently approximate the local trajectory dynamics and their associated statistics. However, astrodynamics problems are nonlinear in general and linear spacecraft dynamics models can fail to characterize the true trajectory dynamics when the system is subject to a highly unstable environment or when mapped over a long time period. This limits the performance of traditional navigation techniques and can make it difficult to perform precision analysis or robust navigation. This dissertation presents an alternate method for spacecraft trajectory navigation based on a nonlinear local trajectory model and their statistics in an analytic framework. For a given reference trajectory, we first solve for the higher order Taylor series terms that describe the localized nonlinear motion and develop an analytic expression for the relative solution flow. We then discuss the nonlinear dynamical mapping of a spacecraft's probability density function by solving the Fokker-Planck equation for a deterministic system. From this result we derive an analytic method for orbit uncertainty propagation which can replicate Monte-Carlo simulations with the benefit of added flexibility in initial orbit statistics. Using this approach, we introduce the concept of the statistically correct trajectory where we directly incorporate statistical information about an orbit state into the trajectory design process. As an extension of this concept, we define a nonlinear statistical targeting method where we solve for a correction maneuver which intercepts the desired target on average. Then we apply our results to a Bayesian filtering problem to obtain a general filtering algorithm for
Nonlinear and quantum optics near nanoparticles
NASA Astrophysics Data System (ADS)
Dhayal, Suman
We study the behavior of electric fields in and around dielectric and metal nanoparticles, and prepare the ground for their applications to a variety of systems viz. photovoltaics, imaging and detection techniques, and molecular spectroscopy. We exploit the property of nanoparticles being able to focus the radiation field into small regions and study some of the interesting nonlinear, and quantum coherence and interference phenomena near them. The traditional approach to study the nonlinear light-matter interactions involves the use of the slowly varying amplitude approximation (SVAA) as it simplifies the theoretical analysis. However, SVVA cannot be used for systems which are of the order of the wavelength of the light. We use the exact solutions of the Maxwell's equations to obtain the fields created due to metal and dielectric nanoparticles, and study nonlinear and quantum optical phenomena near these nanoparticles. We begin with the theoretical description of the electromagnetic fields created due to the nonlinear wavemixing process, namely, second-order nonlinearity in an nonlinear sphere. The phase-matching condition has been revisited in such particles and we found that it is not satisfied in the sphere. We have suggested a way to obtain optimal conditions for any type and size of material medium. We have also studied the modifications of the electromagnetic fields in a collection of nanoparticles due to strong near field nonlinear interactions using the generalized Mie theory for the case of many particles applicable in photovoltaics (PV). We also consider quantum coherence phenomena such as modification of dark states, stimulated Raman adiabatic passage (STIRAP), optical pumping in 4-level atoms near nanoparticles by using rotating wave approximation to describe the Hamiltonian of the atomic system. We also considered the behavior of atomic and the averaged atomic polarization in 7-level atoms near nanoparticles. This could be used as a prototype to study
Femtosecond Fiber Lasers Based on Dissipative Processes for Nonlinear Microscopy
Wise, Frank W.
2012-01-01
Recent progress in the development of femtosecond-pulse fiber lasers with parameters appropriate for nonlinear microscopy is reviewed. Pulse-shaping in lasers with only normal-dispersion components is briefly described, and the performance of the resulting lasers is summarized. Fiber lasers based on the formation of dissipative solitons now offer performance competitive with that of solid-state lasers, but with the benefits of the fiber medium. Lasers based on self-similar pulse evolution in the gain section of a laser also offer a combination of short pulse duration and high pulse energy that will be attractive for applications in nonlinear bioimaging. PMID:23869163
Femtosecond Fiber Lasers Based on Dissipative Processes for Nonlinear Microscopy.
Wise, Frank W
2012-01-01
Recent progress in the development of femtosecond-pulse fiber lasers with parameters appropriate for nonlinear microscopy is reviewed. Pulse-shaping in lasers with only normal-dispersion components is briefly described, and the performance of the resulting lasers is summarized. Fiber lasers based on the formation of dissipative solitons now offer performance competitive with that of solid-state lasers, but with the benefits of the fiber medium. Lasers based on self-similar pulse evolution in the gain section of a laser also offer a combination of short pulse duration and high pulse energy that will be attractive for applications in nonlinear bioimaging.
Nondegenerate two-beam coupling in Kerr nonlinear photonic crystals.
Xie, Ping; Zhang, Zhao-Qing
2005-09-01
We show that the energy-transfer efficiency by nondegenerate two-beam coupling in a one-dimensional Kerr-nonlinear superlattice can be enhanced by several orders of magnitude as compared with that in a homogeneous medium of the same nonlinearity and length. This significant enhancement utilizes the strong localized field at the band-edge state, two-frequency localized state, or defect state. Due to the intensity-induced index modulation, the bistability is observed, and because of the energy transfer between different wavelength components, the tristability behavior is induced.
Variational principle for nonlinear wave propagation in dissipative systems.
Dierckx, Hans; Verschelde, Henri
2016-02-01
The dynamics of many natural systems is dominated by nonlinear waves propagating through the medium. We show that in any extended system that supports nonlinear wave fronts with positive surface tension, the asymptotic wave-front dynamics can be formulated as a gradient system, even when the underlying evolution equations for the field variables cannot be written as a gradient system. The variational potential is simply given by a linear combination of the occupied volume and surface area of the wave front and changes monotonically over time. PMID:26986334
Variational principle for nonlinear wave propagation in dissipative systems.
Dierckx, Hans; Verschelde, Henri
2016-02-01
The dynamics of many natural systems is dominated by nonlinear waves propagating through the medium. We show that in any extended system that supports nonlinear wave fronts with positive surface tension, the asymptotic wave-front dynamics can be formulated as a gradient system, even when the underlying evolution equations for the field variables cannot be written as a gradient system. The variational potential is simply given by a linear combination of the occupied volume and surface area of the wave front and changes monotonically over time.
Some nonlinear problems in the manipulation of beams
Sessler, A.M.
1990-10-01
An overview is given of nonlinear problems that arise in the manipulation of beams. Beams can be made of material particles or photons, can be intense or dilute, can be energetic or not, and they can be propagating in vacuum or in a medium. The nonlinear aspects of the motion are different in each case, and this diversity of behavior is categorized. Many examples are given, which serves to illustrate the categorization and, furthermore, display the richness of behavior encountered in the physics of beams. 25 refs., 5 figs.
Probing material nonlinearity at various depths by time reversal mirrors
Payan, C.; Ulrich, T. J.; Le Bas, P. Y.; Remillieux, M. C.; Griffa, M.; Schuetz, P.; Saleh, T. A.
2014-04-07
In this Letter, the time reversal mirror is used to focus elastic energy at a prescribed location and to analyze the amplitude dependence of the focus signal, thus providing the nonlinearity of the medium. By varying the frequency content of the focused waveforms, the technique can be used to probe the surface, by penetrating to a depth defined by the wavelength of the focused waves. The validity of this concept is shown in the presence of gradual and distributed damage in concrete by comparing actual results with a reference nonlinear measurement and X ray tomography images.
Variational principle for nonlinear wave propagation in dissipative systems
NASA Astrophysics Data System (ADS)
Dierckx, Hans; Verschelde, Henri
2016-02-01
The dynamics of many natural systems is dominated by nonlinear waves propagating through the medium. We show that in any extended system that supports nonlinear wave fronts with positive surface tension, the asymptotic wave-front dynamics can be formulated as a gradient system, even when the underlying evolution equations for the field variables cannot be written as a gradient system. The variational potential is simply given by a linear combination of the occupied volume and surface area of the wave front and changes monotonically over time.
Slow and fast light propagation in nonlinear Kerr media.
NASA Astrophysics Data System (ADS)
Yang, Qiguang; Ma, Seongmin; Wang, Huitian; Jung, S. S.
2005-04-01
Sub- and superluminal propagation of light pulse in Kerr materials has been investigated. Group velocities as slow as much less than 1 millimeter per second to as fast as negative several hundreds meters per second can be easily obtained in Kerr medium, which possesses large nonlinear refractive index and long relaxation time, such as Cr doped Alexandrite, Ruby, and GdAlO3. The physical mechanism is the strong highly dispersive coupling between different frequency components of the pulse. The new mechanism of slowing down pulses as well as producing superluminal pulses enlarges the very specific materials to all kinds of nonlinear optical materials.
Microwave remote sensing of a two-layer random medium
NASA Technical Reports Server (NTRS)
Tsang, L.; Kong, J. A.
1976-01-01
A two-variable expansion technique is used to solve for the mean Green's. function from the Dyson equation under the nonlinear approximation. The Bethe-Salpeter equation then gives rise to a set of modified radiative transfer (MRT) equations which accommodate coherent effects essential to bounded media. It is found that the nonlinear approximation, instead of the more popular bilocal approximation, should be used for the case of bounded media. The two approximations yield identical results for unbounded media. The MRT equations are then solved for a two-layer random medium. The MRT equations give rise to simple and useful solutions which are applicable to both active and passive microwave remote sensing.
NASA Astrophysics Data System (ADS)
Tsia, Kevin K.; Jalali, Bahram
2010-05-01
An intriguing optical property of silicon is that it exhibits a large third-order optical nonlinearity, with orders-ofmagnitude larger than that of silica glass in the telecommunication band. This allows efficient nonlinear optical interaction at relatively low power levels in a small footprint. Indeed, we have witnessed a stunning progress in harnessing the Raman and Kerr effects in silicon as the mechanisms for enabling chip-scale optical amplification, lasing, and wavelength conversion - functions that until recently were perceived to be beyond the reach of silicon. With all the continuous efforts developing novel techniques, nonlinear silicon photonics is expected to be able to reach even beyond the prior achievements. Instead of providing a comprehensive overview of this field, this manuscript highlights a number of new branches of nonlinear silicon photonics, which have not been fully recognized in the past. In particular, they are two-photon photovoltaic effect, mid-wave infrared (MWIR) silicon photonics, broadband Raman effects, inverse Raman scattering, and periodically-poled silicon (PePSi). These novel effects and techniques could create a new paradigm for silicon photonics and extend its utility beyond the traditionally anticipated applications.
Intramolecular and nonlinear dynamics
Davis, M.J.
1993-12-01
Research in this program focuses on three interconnected areas. The first involves the study of intramolecular dynamics, particularly of highly excited systems. The second area involves the use of nonlinear dynamics as a tool for the study of molecular dynamics and complex kinetics. The third area is the study of the classical/quantum correspondence for highly excited systems, particularly systems exhibiting classical chaos.
Generalized Nonlinear Yule Models
NASA Astrophysics Data System (ADS)
Lansky, Petr; Polito, Federico; Sacerdote, Laura
2016-10-01
With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.
Callen, J. D.
2002-11-04
The primary efforts this year have focused on exploring the nonlinear evolution of localized interchange instabilities, some extensions of neoclassical tearing mode theory, and developing a model for the dynamic electrical conductivity in a bumpy cylinder magnetic field. In addition, we have vigorously participated in the computationally-focused NIMROD and CEMM projects.
Universal nonlinear entanglement witnesses
Kotowski, Marcin; Kotowski, Michal
2010-06-15
We give a universal recipe for constructing nonlinear entanglement witnesses able to detect nonclassical correlations in arbitrary systems of distinguishable and/or identical particles for an arbitrary number of constituents. The constructed witnesses are expressed in terms of expectation values of observables. As such, they are, at least in principle, measurable in experiments.
Nonlinear growing neutrino cosmology
NASA Astrophysics Data System (ADS)
Ayaita, Youness; Baldi, Marco; Führer, Florian; Puchwein, Ewald; Wetterich, Christof
2016-03-01
The energy scale of dark energy, ˜2 ×10-3 eV , is a long way off compared to all known fundamental scales—except for the neutrino masses. If dark energy is dynamical and couples to neutrinos, this is no longer a coincidence. The time at which dark energy starts to behave as an effective cosmological constant can be linked to the time at which the cosmic neutrinos become nonrelativistic. This naturally places the onset of the Universe's accelerated expansion in recent cosmic history, addressing the why-now problem of dark energy. We show that these mechanisms indeed work in the growing neutrino quintessence model—even if the fully nonlinear structure formation and backreaction are taken into account, which were previously suspected of spoiling the cosmological evolution. The attractive force between neutrinos arising from their coupling to dark energy grows as large as 106 times the gravitational strength. This induces very rapid dynamics of neutrino fluctuations which are nonlinear at redshift z ≈2 . Nevertheless, a nonlinear stabilization phenomenon ensures only mildly nonlinear oscillating neutrino overdensities with a large-scale gravitational potential substantially smaller than that of cold dark matter perturbations. Depending on model parameters, the signals of large-scale neutrino lumps may render the cosmic neutrino background observable.
Teaching the Nonlinear Pendulum.
ERIC Educational Resources Information Center
Zheng, T. F.; And Others
1994-01-01
Emphasizes two aspects for a calculus-based physics course: applying calculus and numerical integral methods to determine the theoretical period of a pendulum with nonlinear motion, and achieving theoretical and experimental results by using "MathCad" software and a microcomputer-based laboratory (MBL) system. (MVL)
Nonlinear Theory and Breakdown
NASA Technical Reports Server (NTRS)
Smith, Frank
2007-01-01
The main points of recent theoretical and computational studies on boundary-layer transition and turbulence are to be highlighted. The work is based on high Reynolds numbers and attention is drawn to nonlinear interactions, breakdowns and scales. The research focuses in particular on truly nonlinear theories, i.e. those for which the mean-flow profile is completely altered from its original state. There appear to be three such theories dealing with unsteady nonlinear pressure-displacement interactions (I), with vortex/wave interactions (II), and with Euler-scale flows (III). Specific recent findings noted for these three, and in quantitative agreement with experiments, are the following. Nonlinear finite-time break-ups occur in I, leading to sublayer eruption and vortex formation; here the theory agrees with experiments (Nishioka) regarding the first spike. II gives rise to finite-distance blowup of displacement thickness, then interaction and break-up as above; this theory agrees with experiments (Klebanoff, Nishioka) on the formation of three-dimensional streets. III leads to the prediction of turbulent boundary-layer micro-scale, displacement-and stress-sublayer-thicknesses.
Three-point bounds for the overall properties of a nonlinear composite dielectric
NASA Astrophysics Data System (ADS)
Talbot, D. R. S.; Willis, J. R.
1996-08-01
The Hashin-Shtrikman methodology for nonlinear composite problems relies on the use of a comparison medium and in many of the examples studied so far the comparison medium has been taken to be homogeneous. A related approach originated by P. Ponte Castaneda employs a comparison medium which is itself a linear composite with the same microgeometry as the nonlinear composite. When the method is applicable, the bounds for the nonlinear problem then involve bounds for the energy of the linear comparison composite which could include, for example, three-point information about the microstructure of the composite. It is, however, only possible to obtain at most one bound using a linear comparison material. A recent approach involves the use of a nonlinear comparison medium and trial fields with the property of bounded mean oscillation. In this paper the approach is extended by using a nonlinear comparison composite so that both upper and lower bounds can be obtained which incorporate three-point information. The development is in the context of bounding the properties of nonlinear dielectric composites, although it has wider application.
Regularity for the porous medium equation with variable exponent: The singular case
NASA Astrophysics Data System (ADS)
Henriques, Eurica
We extend to the singular case the results of [E. Henriques, J.M. Urbano, Intrinsic scaling for PDEs with an exponential nonlinearity, Indiana Univ. Math. J. 55 (5) (2006) 1701-1721] concerning the regularity of weak solutions of the porous medium equation with variable exponent. The method of intrinsic scaling is used to show that local weak solutions are locally continuous.
Westdickenberg, Michael; Wilkening, Jon
2008-12-10
We introduce variational particle schemes for the porous medium equation and the system of isentropic Euler equations in one space dimension. The methods are motivated by the interpretation of each of these partial differential equations as a 'steepest descent' on a suitable abstract manifold. We show that our methods capture very well the nonlinear features of the flows.
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.
Schwartz, Sylvain; Feugnet, Gilles; Pocholle, Jean-Paul; Gutty, Francois; Bouyer, Philippe
2008-05-09
We report fine-tuning of nonlinear interactions in a solid-state ring laser gyroscope by vibrating the gain medium along the cavity axis. We demonstrate both experimentally and theoretically that nonlinear interactions vanish for some values of the vibration parameters, leading to quasi-ideal rotation sensing. We eventually point out that our conclusions can be mapped onto other subfields of physics such as ring-shaped superfluid configurations, where nonlinear interactions could be tuned by using Feshbach resonance.
Garnier, Josselin; Picozzi, Antonio
2010-03-15
This article presents a unified kinetic formulation of partially coherent nonlinear optical waves propagating in a noninstantaneous response Kerr medium. We derive a kinetic equation that combines the weak Langmuir turbulence kinetic equation and a Vlasov-like equation within a general framework: It describes the evolution of the spectrum of a random field that exhibits a quasistationary statistics in the presence of a noninstantaneous nonlinear response. The kinetic equation sheds new light on the dynamics of partially coherent nonlinear waves and allows for a qualitative interpretation of the interplay between the noninstantaneous nonlinearity and the nonstationary statistics of the incoherent field. It is shown that the incoherent modulational instability of a random nonlinear wave can be suppressed by the noninstantaneous nonlinear response. Moreover, incoherent modulational instability can prevent the generation of spectral incoherent solitons.
On fluid flow in a heterogeneous medium under nonisothermal conditions
D.W., Vasco
2010-11-01
An asymptotic technique, valid in the presence of smoothly-varying heterogeneity, provides explicit expressions for the velocity of a propagating pressure and temperature disturbance. The governing equations contain nonlinear terms due to the presence of temperature-dependent coefficients and due to the advection of fluids with differing temperatures. Two cases give well-defined expressions in terms of the parameters of the porous medium: the uncoupled propagation of a pressure disturbance and the propagation of a fully coupled temperature and pressure disturbance. The velocity of the coupled disturbance or front, depends upon the medium parameters and upon the change in temperature and pressure across the front. For uncoupled flow, the semi-analytic expression for the front velocity reduces to that associated with a linear diffusion equation. A comparison of the asymptotic travel time estimates with calculations from a numerical simulator indicates reasonably good agreement for both uncoupled and coupled disturbances.
Oscillatory motion of a viscous fluid in a porous medium
Siraev, R. R.
2015-08-15
An oscillatory flow of an incompressible fluid in a saturated porous medium in the presence of a solid inclusion has been theoretically studied. Unsteady filtration has been described by the Brinkman–Forchheimer equation, where inertial effects and terms with acceleration characteristic of high filtration rates and the presence of pulsations are taken into account. The convective part of the acceleration is responsible for nonlinear effects near macroinhomogeneities. These effects can play a noticeable role in unsteady flows in the porous medium, as is shown for the problem of a solid ball streamed by an oscillatory flow having a given velocity at infinity. The results indicate that a secondary averaged flow appears in the case of high frequencies and cannot be described by Darcy’s or Forchheimer’s filtration laws.
Cubication of Conservative Nonlinear Oscillators
ERIC Educational Resources Information Center
Belendez, Augusto; Alvarez, Mariela L.; Fernandez, Elena; Pascual, Immaculada
2009-01-01
A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear…
Control of Group Velocity via Spontaneous Generated Coherence and Kerr Nonlinearity
NASA Astrophysics Data System (ADS)
Hazrat, Ali; Iftikhar, Ahmad; Ziauddin
2014-09-01
A four-level N-type atomic medium is considered to study the effect of spontaneous generated coherence (SGC) and Kerr nonlinearity on light pulse propagation. A light pulse is propagating inside the medium where each atom follows four-level N-type atom-field configuration of rubidium (85Rb) atom. The atom-field interaction leads to electromagnetically induced transparency (EIT) process. The atom-field interaction is accompanied by normal dispersion and in the presence of SGC and Kerr nonlinearity the dispersion property of the proposed atomic medium is modified, which leads to enhancement of positive group index of the medium. The enhancement of positive group index then leads to slow group velocity inside the medium. A more slow group velocity is also investigated by incorporated the collective effect of SGC and Kerr nonlinearity. The control of group velocity inside a four-level N-type atomic medium via collective effect of SGC and Kerr nonlinearity is the major part of this work.
Four-photon homoclinic instabilities in nonlinear highly birefringent media
De Angelis, C.; Santagiustina, M. ); Trillo, S. )
1995-01-01
We investigate the nonlinear dynamics of a nonconventional (i.e., pumped by a mixed-mode wave) modulational instability in a highly birefringent nonlinear dispersive medium. We find that the depleted regime of propagation beyond the linearized stage can be described analytically in a proper region of the parameter space. In this case the governing coupled nonlinear Schroedinger equations, which are not integrable, are reduced to an integrable one-dimensional nonlinear oscillator that rules the propagation of the pump wave and a single sideband pair. This approach permits us to predict the existence of stable and unstable manifolds of time-periodic solutions of the coupled nonlinear Schroedinger equations. The nonlinear dynamics governed by these equations mimics the period-doubling instabilities associated with the homoclinic separatrices in the reduced phase space. Moreover, our approach is also capable of describing the onset of spatial chaos that occurs when the parameter values are such that the additional degree of freedom represented by the conjugated sidebands becomes effective.
Quantification and prediction of rare events in nonlinear waves
NASA Astrophysics Data System (ADS)
Sapsis, Themistoklis; Cousins, Will; Mohamad, Mustafa
2014-11-01
The scope of this work is the quantification and prediction of rare events characterized by extreme intensity, in nonlinear dispersive models that simulate water waves. In particular we are interested for the understanding and the short-term prediction of rogue waves in the ocean and to this end, we consider 1-dimensional nonlinear models of the NLS type. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A stochastic analysis of the Gabor coefficients reveals i) the low-dimensionality of the intermittent structures, ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as iii) the critical scales (or Gabor coefficients) where a critical energy can trigger the formation of an extreme event. The unstable character of these critical localized modes is analysed directly through the system equation and it is shown that it is defined as the result of the system nonlinearity and the wave dissipation (that mimics wave breaking). These unstable modes are randomly triggered through the dispersive ``heat bath'' of random waves that propagate in the nonlinear medium. Using these properties we formulate low-dimensional functionals of these Gabor coefficients that allow for the prediction of extreme event well before the strongly nonlinear interactions begin to occur. The prediction window is further enhanced by the combination of the developed scheme with traditional filtering schemes.
A FORTRAN program for calculating nonlinear seismic ground response
Joyner, William B.
1977-01-01
The program described here was designed for calculating the nonlinear seismic response of a system of horizontal soil layers underlain by a semi-infinite elastic medium representing bedrock. Excitation is a vertically incident shear wave in the underlying medium. The nonlinear hysteretic behavior of the soil is represented by a model consisting of simple linear springs and Coulomb friction elements arranged as shown. A boundary condition is used which takes account of finite rigidity in the elastic substratum. The computations are performed by an explicit finite-difference scheme that proceeds step by step in space and time. A brief program description is provided here with instructions for preparing the input and a source listing. A more detailed discussion of the method is presented elsewhere as is the description of a different program employing implicit integration.
Properties of the nuclear medium.
Baldo, M; Burgio, G F
2012-02-01
We review our knowledge on the properties of the nuclear medium that have been studied, over many years, on the basis of many-body theory, laboratory experiments and astrophysical observations. Throughout the presentation particular emphasis is placed on the possible relationship and links between the nuclear medium and the structure of nuclei, including the limitations of such an approach. First we consider the realm of phenomenological laboratory data and astrophysical observations and the hints they can give on the characteristics that the nuclear medium should possess. The analysis is based on phenomenological models, that however have a strong basis on physical intuition and an impressive success. More microscopic models are also considered, and it is shown that they are able to give invaluable information on the nuclear medium, in particular on its equation of state. The interplay between laboratory experiments and astrophysical observations is particularly stressed, and it is shown how their complementarity enormously enriches our insights into the structure of the nuclear medium. We then introduce the nucleon-nucleon interaction and the microscopic many-body theory of nuclear matter, with a critical discussion about the different approaches and their results. The Landau-Fermi liquid theory is introduced and briefly discussed, and it is shown how fruitful it can be in discussing the macroscopic and low-energy properties of the nuclear medium. As an illustrative example, we discuss neutron matter at very low density, and it is shown how it can be treated within the many-body theory. The general bulk properties of the nuclear medium are reviewed to indicate at which stage of our knowledge we stand, taking into account the most recent developments both in theory and experiments. A section is dedicated to the pairing problem. The connection with nuclear structure is then discussed, on the basis of the energy density functional method. The possibility of linking
Properties of the nuclear medium
NASA Astrophysics Data System (ADS)
Baldo, M.; Burgio, G. F.
2012-02-01
We review our knowledge on the properties of the nuclear medium that have been studied, over many years, on the basis of many-body theory, laboratory experiments and astrophysical observations. Throughout the presentation particular emphasis is placed on the possible relationship and links between the nuclear medium and the structure of nuclei, including the limitations of such an approach. First we consider the realm of phenomenological laboratory data and astrophysical observations and the hints they can give on the characteristics that the nuclear medium should possess. The analysis is based on phenomenological models, that however have a strong basis on physical intuition and an impressive success. More microscopic models are also considered, and it is shown that they are able to give invaluable information on the nuclear medium, in particular on its equation of state. The interplay between laboratory experiments and astrophysical observations is particularly stressed, and it is shown how their complementarity enormously enriches our insights into the structure of the nuclear medium. We then introduce the nucleon-nucleon interaction and the microscopic many-body theory of nuclear matter, with a critical discussion about the different approaches and their results. The Landau-Fermi liquid theory is introduced and briefly discussed, and it is shown how fruitful it can be in discussing the macroscopic and low-energy properties of the nuclear medium. As an illustrative example, we discuss neutron matter at very low density, and it is shown how it can be treated within the many-body theory. The general bulk properties of the nuclear medium are reviewed to indicate at which stage of our knowledge we stand, taking into account the most recent developments both in theory and experiments. A section is dedicated to the pairing problem. The connection with nuclear structure is then discussed, on the basis of the energy density functional method. The possibility of linking
Electromagnetic wave scattering in a two-layer anisotropic random medium
NASA Technical Reports Server (NTRS)
Lee, J. K.; Kong, J. A.
1985-01-01
For electromagnetic wave propagation and scattering in an anisotropic random medium, the Dyson equation for the mean field and the Bethe-Salpeter equation for the correlation or the covariance of the field were derived. With the random permittivity expressed in a general anisotropic form, the bilocal and the nonlinear approximations are employed to solve the Dyson equation, and the ladder approximation to solve the Bethe-Salpeter equation. The mean dyadic Green's function for a two-layer anisotropic random medium with arbitrary three-dimensional correlation functions has been investigated with the zeroth-order solutions to the Dyson equation under the nonlinear approximation. The effective propagation constants are calculated for the four characteristic waves associated with the coherent vector fields, propagating in an anisotropic random-medium layer, which are the ordinary and extraordinary waves with upward- and downward-propagating vectors.
Kavitha, L.; Saravanan, M.; Srividya, B.; Gopi, D.
2011-12-15
We investigate the nature of propagation of electromagnetic waves (EMWs) in an antiferromagnetic medium with Dzyaloshinsky-Moriya (DM) interaction environment. The interplay of bilinear and DM exchange spin coupling with the magnetic field component of the EMW has been studied by solving Maxwell's equations coupled with a nonlinear spin equation for the magnetization of the medium. We made a nonuniform expansion of the magnetization and magnetic field along the direction of propagation of EMW, in the framework of reductive perturbation method, and the dynamics of the system is found to be governed by a generalized derivative nonlinear Schroedinger (DNLS) equation. We employ the Jacobi-elliptic function method to solve the DNLS equation, and the electromagnetic wave propagation in an antiferromagnetic medium is governed by the breatherlike spatially and temporally coherent localized modes under the influence of DM interaction parameter.
Influence of the medium's dimensionality on defect-mediated turbulence.
St-Yves, Ghislain; Davidsen, Jörn
2015-03-01
Spatiotemporal chaos in oscillatory and excitable media is often characterized by the presence of phase singularities called defects. Understanding such defect-mediated turbulence and its dependence on the dimensionality of a given system is an important challenge in nonlinear dynamics. This is especially true in the context of ventricular fibrillation in the heart, where the importance of the thickness of the ventricular wall is contentious. Here, we study defect-mediated turbulence arising in two different regimes in a conceptual model of excitable media and investigate how the statistical character of the turbulence changes if the thickness of the medium is changed from (quasi-) two- dimensional to three dimensional. We find that the thickness of the medium does not have a significant influence in, far from onset, fully developed turbulence while there is a clear transition if the system is close to a spiral instability. We provide clear evidence that the observed transition and change in the mechanism that drives the turbulent behavior is purely a consequence of the dimensionality of the medium. Using filament tracking, we further show that the statistical properties in the three-dimensional medium are different from those in turbulent regimes arising from filament instabilities like the negative line tension instability. Simulations also show that the presence of this unique three-dimensional turbulent dynamics is not model specific. PMID:25871191
Influence of the medium's dimensionality on defect-mediated turbulence
NASA Astrophysics Data System (ADS)
St-Yves, Ghislain; Davidsen, Jörn
2015-03-01
Spatiotemporal chaos in oscillatory and excitable media is often characterized by the presence of phase singularities called defects. Understanding such defect-mediated turbulence and its dependence on the dimensionality of a given system is an important challenge in nonlinear dynamics. This is especially true in the context of ventricular fibrillation in the heart, where the importance of the thickness of the ventricular wall is contentious. Here, we study defect-mediated turbulence arising in two different regimes in a conceptual model of excitable media and investigate how the statistical character of the turbulence changes if the thickness of the medium is changed from (quasi-) two- dimensional to three dimensional. We find that the thickness of the medium does not have a significant influence in, far from onset, fully developed turbulence while there is a clear transition if the system is close to a spiral instability. We provide clear evidence that the observed transition and change in the mechanism that drives the turbulent behavior is purely a consequence of the dimensionality of the medium. Using filament tracking, we further show that the statistical properties in the three-dimensional medium are different from those in turbulent regimes arising from filament instabilities like the negative line tension instability. Simulations also show that the presence of this unique three-dimensional turbulent dynamics is not model specific.
Nonlinear Polarimetric Microscopy for Biomedical Imaging
NASA Astrophysics Data System (ADS)
Samim, Masood
A framework for the nonlinear optical polarimetry and polarimetric microscopy is developed. Mathematical equations are derived in terms of linear and nonlinear Stokes Mueller formalism, which comprehensively characterize the polarization properties of the incoming and outgoing radiations, and provide structural information about the organization of the investigated materials. The algebraic formalism developed in this thesis simplifies many predictions for a nonlinear polarimetry study and provides an intuitive understanding of various polarization properties for radiations and the intervening medium. For polarimetric microscopy experiments, a custom fast-scanning differential polarization microscope is developed, which is also capable of real-time three-dimensional imaging. The setup is equipped with a pair of high-speed resonant and galvanometric scanning mirrors, and supplemented by advanced adaptive optics and data acquisition modules. The scanning mirrors when combined with the adaptive optics deformable mirror enable fast 3D imaging. Deformable membrane mirrors and genetic algorithm optimization routines are employed to improve the imaging conditions including correcting the optical aberrations, maximizing signal intensities, and minimizing point-spread-functions of the focal volume. A field-programmable-gate array (FPGA) chip is exploited to rapidly acquire and process the multidimensional data. Using the nonlinear optical polarimetry framework and the home-built polarization microscope, a few biologically important tissues are measured and analyzed to gain insight as to their structure and dynamics. The structure and distribution of muscle sarcomere myosins, connective tissue collagen, carbohydrate-rich starch, and fruit fly eye retinal molecules are characterized with revealing polarization studies. In each case, using the theoretical framework, polarization sensitive data are analyzed to decipher the molecular orientations and nonlinear optical
Nonlinear metamaterials for holography.
Almeida, Euclides; Bitton, Ora; Prior, Yehiam
2016-01-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three-dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years, it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multilayer metamaterial holograms. A background free image is formed at a new frequency-the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analysed and prospects for future device applications are discussed. PMID:27545581
Nonlinear metamaterials for holography
NASA Astrophysics Data System (ADS)
Almeida, Euclides; Bitton, Ora; Prior, Yehiam
2016-08-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three-dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years, it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multilayer metamaterial holograms. A background free image is formed at a new frequency--the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analysed and prospects for future device applications are discussed.
Nonlinear Photonics 2014: introduction.
Akhmediev, N; Kartashov, Yaroslav
2015-01-12
International Conference "Nonlinear Photonics-2014" took place in Barcelona, Spain on July 27-31, 2014. It was a part of the "Advanced Photonics Congress" which is becoming a traditional notable event in the world of photonics. The current focus issue of Optics Express contains contributions from the participants of the Conference and the Congress. The articles in this focus issue by no means represent the total number of the congress contributions (around 400). However, it demonstrates wide range of topics covered at the event. The next conference of this series is to be held in 2016 in Australia, which is the home of many researchers working in the field of photonics in general and nonlinear photonics in particular.
Nonlinear metamaterials for holography
Almeida, Euclides; Bitton, Ora
2016-01-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three-dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years, it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multilayer metamaterial holograms. A background free image is formed at a new frequency—the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analysed and prospects for future device applications are discussed. PMID:27545581
Nonlinear differential equations
Dresner, L.
1988-01-01
This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.
Nonlinear terahertz superconducting plasmonics
Wu, Jingbo; Liang, Lanju; Jin, Biaobing E-mail: tonouchi@ile.osaka-u.ac.jp Kang, Lin; Xu, Weiwei; Chen, Jian; Wu, Peiheng E-mail: tonouchi@ile.osaka-u.ac.jp; Zhang, Caihong; Kawayama, Iwao; Murakami, Hironaru; Tonouchi, Masayoshi E-mail: tonouchi@ile.osaka-u.ac.jp; Wang, Huabing
2014-10-20
Nonlinear terahertz (THz) transmission through subwavelength hole array in superconducting niobium nitride (NbN) film is experimentally investigated using intense THz pulses. The good agreement between the measurement and numerical simulations indicates that the field strength dependent transmission mainly arises from the nonlinear properties of the superconducting film. Under weak THz pulses, the transmission peak can be tuned over a frequency range of 145 GHz which is attributed to the high kinetic inductance of 50 nm-thick NbN film. Utilizing the THz pump-THz probe spectroscopy, we study the dynamic process of transmission spectra and demonstrate that the transition time of such superconducting plasmonic device is within 5 ps.
Nonlinear chiral transport phenomena
NASA Astrophysics Data System (ADS)
Chen, Jiunn-Wei; Ishii, Takeaki; Pu, Shi; Yamamoto, Naoki
2016-06-01
We study the nonlinear responses of relativistic chiral matter to the external fields such as the electric field E , gradients of temperature and chemical potential, ∇T and ∇μ . Using the kinetic theory with Berry curvature corrections under the relaxation time approximation, we compute the transport coefficients of possible new electric currents that are forbidden in usual chirally symmetric matter but are allowed in chirally asymmetric matter by parity. In particular, we find a new type of electric current proportional to ∇μ ×E due to the interplay between the effects of the Berry curvature and collisions. We also derive an analog of the "Wiedemann-Franz" law specific for anomalous nonlinear transport in relativistic chiral matter.
Optothermal nonlinearity of silica aerogel
NASA Astrophysics Data System (ADS)
Braidotti, Maria Chiara; Gentilini, Silvia; Fleming, Adam; Samuels, Michiel C.; Di Falco, Andrea; Conti, Claudio
2016-07-01
We report on the characterization of silica aerogel thermal optical nonlinearity, obtained by z-scan technique. The results show that typical silica aerogels have nonlinear optical coefficient similar to that of glass (≃10-12 m2/W), with negligible optical nonlinear absorption. The nonlinear coefficient can be increased to values in the range of 10-10 m2/W by embedding an absorbing dye in the aerogel. This value is one order of magnitude higher than that observed in the pure dye and in typical highly nonlinear materials like liquid crystals.
Nonlinear Generalized Hydrodynamic Wave Equations in Strongly Coupled Dusty Plasmas
Veeresha, B. M.; Sen, A.; Kaw, P. K.
2008-09-07
A set of nonlinear equations for the study of low frequency waves in a strongly coupled dusty plasma medium is derived using the phenomenological generalized hydrodynamic (GH) model and is used to study the modulational stability of dust acoustic waves to parallel perturbations. Dust compressibility contributions arising from strong Coulomb coupling effects are found to introduce significant modifications in the threshold and range of the instability domain.
Acoustic field distribution of sawtooth wave with nonlinear SBE model
Liu, Xiaozhou Zhang, Lue; Wang, Xiangda; Gong, Xiufen
2015-10-28
For precise prediction of the acoustic field distribution of extracorporeal shock wave lithotripsy with an ellipsoid transducer, the nonlinear spheroidal beam equations (SBE) are employed to model acoustic wave propagation in medium. To solve the SBE model with frequency domain algorithm, boundary conditions are obtained for monochromatic and sawtooth waves based on the phase compensation. In numerical analysis, the influence of sinusoidal wave and sawtooth wave on axial pressure distributions are investigated.
Exact and explicit solitary wave solutions to some nonlinear equations
Jiefang Zhang
1996-08-01
Exact and explicit solitary wave solutions are obtained for some physically interesting nonlinear evolutions and wave equations in physics and other fields by using a special transformation. These equations include the KdV-Burgers equation, the MKdV-Burgers equation, the combined KdV-MKdV equation, the Newell-Whitehead equation, the dissipative {Phi}{sup 4}-model equation, the generalized Fisher equation, and the elastic-medium wave equation.
Leitão, J C; Miotto, J M; Gerlach, M; Altmann, E G
2016-07-01
One of the most celebrated findings in complex systems in the last decade is that different indexes y (e.g. patents) scale nonlinearly with the population x of the cities in which they appear, i.e. y∼x (β) ,β≠1. More recently, the generality of this finding has been questioned in studies that used new databases and different definitions of city boundaries. In this paper, we investigate the existence of nonlinear scaling, using a probabilistic framework in which fluctuations are accounted for explicitly. In particular, we show that this allows not only to (i) estimate β and confidence intervals, but also to (ii) quantify the evidence in favour of β≠1 and (iii) test the hypothesis that the observations are compatible with the nonlinear scaling. We employ this framework to compare five different models to 15 different datasets and we find that the answers to points (i)-(iii) crucially depend on the fluctuations contained in the data, on how they are modelled, and on the fact that the city sizes are heavy-tailed distributed. PMID:27493764
2016-01-01
One of the most celebrated findings in complex systems in the last decade is that different indexes y (e.g. patents) scale nonlinearly with the population x of the cities in which they appear, i.e. y∼xβ,β≠1. More recently, the generality of this finding has been questioned in studies that used new databases and different definitions of city boundaries. In this paper, we investigate the existence of nonlinear scaling, using a probabilistic framework in which fluctuations are accounted for explicitly. In particular, we show that this allows not only to (i) estimate β and confidence intervals, but also to (ii) quantify the evidence in favour of β≠1 and (iii) test the hypothesis that the observations are compatible with the nonlinear scaling. We employ this framework to compare five different models to 15 different datasets and we find that the answers to points (i)–(iii) crucially depend on the fluctuations contained in the data, on how they are modelled, and on the fact that the city sizes are heavy-tailed distributed. PMID:27493764
Ultrafast Thermal Nonlinearity
Khurgin, Jacob B.; Sun, Greg; Chen, Wei Ting; Tsai, Wei-Yi; Tsai, Din Ping
2015-01-01
Third order nonlinear optical phenomena explored in the last half century have been predicted to find wide range of applications in many walks of life, such as all-optical switching, routing, and others, yet this promise has not been fulfilled primarily because the strength of nonlinear effects is too low when they are to occur on the picosecond scale required in today’s signal processing applications. The strongest of the third-order nonlinearities, engendered by thermal effects, is considered to be too slow for the above applications. In this work we show that when optical fields are concentrated into the volumes on the scale of few tens of nanometers, the speed of the thermo-optical effects approaches picosecond scale. Such a sub-diffraction limit concentration of field can be accomplished with the use of plasmonic effects in metal nanoparticles impregnating the thermo-optic dielectric (e.g. amorphous Si) and leads to phase shifts sufficient for all optical switching on ultrafast scale. PMID:26644322
Duck, F
2010-01-01
The propagation of acoustic waves is a fundamentally non-linear process, and only waves with infinitesimally small amplitudes may be described by linear expressions. In practice, all ultrasound propagation is associated with a progressive distortion in the acoustic waveform and the generation of frequency harmonics. At the frequencies and amplitudes used for medical diagnostic scanning, the waveform distortion can result in the formation of acoustic shocks, excess deposition of energy, and acoustic saturation. These effects occur most strongly when ultrasound propagates within liquids with comparatively low acoustic attenuation, such as water, amniotic fluid, or urine. Attenuation by soft tissues limits but does not extinguish these non-linear effects. Harmonics may be used to create tissue harmonic images. These offer improvements over conventional B-mode images in spatial resolution and, more significantly, in the suppression of acoustic clutter and side-lobe artefacts. The quantity B/A has promise as a parameter for tissue characterization, but methods for imaging B/A have shown only limited success. Standard methods for the prediction of tissue in-situ exposure from acoustic measurements in water, whether for regulatory purposes, for safety assessment, or for planning therapeutic regimes, may be in error because of unaccounted non-linear losses. Biological effects mechanisms are altered by finite-amplitude effects. PMID:20349813
Nonlinearity without superluminality
NASA Astrophysics Data System (ADS)
Kent, Adrian
2005-07-01
Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signaling. As Czachor, Gisin, and Polchinski pointed out, this is not generally true of general nonlinear modifications of the Schrödinger equation. Excluding superluminal signaling has thus been taken to rule out most nonlinear versions of quantum theory. The no-superluminal-signaling constraint has also been used for alternative derivations of the optimal fidelities attainable for imperfect quantum cloning and other operations. These results apply to theories satisfying the rule that their predictions for widely separated and slowly moving entangled systems can be approximated by nonrelativistic equations of motion with respect to a preferred time coordinate. This paper describes a natural way in which this rule might fail to hold. In particular, it is shown that quantum readout devices which display the values of localized pure states need not allow superluminal signaling, provided that the devices display the values of the states of entangled subsystems as defined in a nonstandard, although natural, way. It follows that any locally defined nonlinear evolution of pure states can be made consistent with Minkowski causality.
Nonlinearity without superluminality
Kent, Adrian
2005-07-15
Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signaling. As Czachor, Gisin, and Polchinski pointed out, this is not generally true of general nonlinear modifications of the Schroedinger equation. Excluding superluminal signaling has thus been taken to rule out most nonlinear versions of quantum theory. The no-superluminal-signaling constraint has also been used for alternative derivations of the optimal fidelities attainable for imperfect quantum cloning and other operations. These results apply to theories satisfying the rule that their predictions for widely separated and slowly moving entangled systems can be approximated by nonrelativistic equations of motion with respect to a preferred time coordinate. This paper describes a natural way in which this rule might fail to hold. In particular, it is shown that quantum readout devices which display the values of localized pure states need not allow superluminal signaling, provided that the devices display the values of the states of entangled subsystems as defined in a nonstandard, although natural, way. It follows that any locally defined nonlinear evolution of pure states can be made consistent with Minkowski causality.
Nonlinear gyrokinetic equations
Dubin, D.H.E.; Krommes, J.A.; Oberman, C.; Lee, W.W.
1983-03-01
Nonlinear gyrokinetic equations are derived from a systematic Hamiltonian theory. The derivation employs Lie transforms and a noncanonical perturbation theory first used by Littlejohn for the simpler problem of asymptotically small gyroradius. For definiteness, we emphasize the limit of electrostatic fluctuations in slab geometry; however, there is a straight-forward generalization to arbitrary field geometry and electromagnetic perturbations. An energy invariant for the nonlinear system is derived, and various of its limits are considered. The weak turbulence theory of the equations is examined. In particular, the wave kinetic equation of Galeev and Sagdeev is derived from an asystematic truncation of the equations, implying that this equation fails to consider all gyrokinetic effects. The equations are simplified for the case of small but finite gyroradius and put in a form suitable for efficient computer simulation. Although it is possible to derive the Terry-Horton and Hasegawa-Mima equations as limiting cases of our theory, several new nonlinear terms absent from conventional theories appear and are discussed.
NASA Astrophysics Data System (ADS)
Ciampa, Francesco; Meo, Michele
2012-04-01
In this research work, an imaging method of the nonlinear signature in a reverberant complex anisotropic structure with hysteretic behaviour is reported. The proposed technique relies on a combination of phase symmetry analysis with frequency modulation excitation and nonlinear time reversal, and it is applied to a number of waveforms containing the nonlinear impulse responses of the medium. Phase symmetry analysis was used to characterize the third order nonlinearity of the structure due to delamination and cracks, by exploiting its invariant properties with the phase angle of the input waveforms. Then, a "virtual" reciprocal time reversal imaging process, using only two sensors in pitch-catch mode, was used to "illuminate" the damage. Taking advantage of multiple linear scattering, this methodology allows achieving the optimal focalization at the nonlinear source by a compensation of the distortion effects in a dissipative medium. The robustness of this technique was experimentally demonstrated on a damaged sandwich panel undergone to low-velocity impact loading. The nonlinear source was retrieved with a high level of accuracy with little computational time (less than 1 sec). Its minimal processing requirements make this method a valid alternative to the traditional nonlinear elastic wave spectroscopy techniques for materials showing either classical or non-classical nonlinear behaviour.
Research in nonlinear structural and solid mechanics
NASA Technical Reports Server (NTRS)
Mccomb, H. G., Jr. (Compiler); Noor, A. K. (Compiler)
1980-01-01
Nonlinear analysis of building structures and numerical solution of nonlinear algebraic equations and Newton's method are discussed. Other topics include: nonlinear interaction problems; solution procedures for nonlinear problems; crash dynamics and advanced nonlinear applications; material characterization, contact problems, and inelastic response; and formulation aspects and special software for nonlinear analysis.
Nonlinear Aharonov-Bohm Scattering by Optical Vortices
Neshev, Dragomir; Nepomnyashchy, Alexander; Kivshar, Yuri S.
2001-07-23
We study linear and nonlinear wave scattering by an optical vortex in a self-defocusing nonlinear Kerr medium. In the linear case, we find a splitting of a plane-wave front at the vortex proportional to its circulation, similar to what occurs in the scattered wave of electrons for the Aharonov-Bohm effect. For larger wave amplitudes, we study analytically and numerically the scattering of a dark-soliton stripe (a nonlinear analog of a small-amplitude wave packet) by a vortex and observe a significant asymmetry of the scattered wave. Subsequently, a wave-front splitting of the scattered wave develops into transverse modulational instability, ''unzipping'' the stripe into trains of vortices with opposite charges.
Development of Analog Nonlinear Materials Using Varactor Loaded Split-ring Resonator Metamaterials
NASA Astrophysics Data System (ADS)
Huang, Da
As research in electromagnetics has expanded, it has given rise to the examination of metamaterials, which possess nontrivial electromagnetic material properties such as engineered permittivity and permeability. Aside from their application in the microwave industry, metamaterials have been associated with novel phenomena since their invention, including sub-wavelength focusing in negative refractive index slabs, evanescent wave amplification in negative index media, and invisibility cloaking and its demonstration at microwave frequency with controlled material properties in space. Effective medium theory plays a key role in the development and application of metamaterials, simplifying the electromagnetic analysis of complex engineered metamaterial composites. Any metamaterial composite can be treated as a homogeneous or inhomogeneous medium, while every unit structure in the composite is represented by its permittivity and permeability tensor. Hence, studying an electromagnetic wave's interaction with complex composites is equivalent to studying the interaction between the wave and an artificial material. This dissertation first examines the application of a magnetic metamaterial lens in wireless power transfer (WPT) technology, which is proposed to enhance the mutual coupling between two magnetic dipoles in the system. I examine and investigate the boundary effect in the finite sized magnetic metamaterial lens using a numerical simulator. I propose to implement an anisotropic and indefinite lens in a WPT system to simplify the lens design and relax the lens dimension requirements. The numerical results agree with the analytical model proposed by Smith et al. in 2011, where lenses are assumed to be infinitely large. By manipulating the microwave properties of a magnetic metamaterial, the nonlinear properties come into the scope of this research. I chose split-ring resonators (SRR) loaded with varactors to develop nonlinear metamaterials. Analogous to linear
Identification of nonlinear boundary effects using nonlinear normal modes
NASA Astrophysics Data System (ADS)
Ahmadian, Hamid; Zamani, Arash
2009-08-01
Local nonlinear effects due to micro-slip/slap introduced in boundaries of structures have dominant influence on their lower modal model. This paper studies these effects by experimentally observing the behavior of a clamped-free beam structure with local nonlinearities due to micro-slip at the clamped end. The structure is excited near one of its resonance frequencies and recorded responses are employed to identify the nonlinear effects at the boundary. The nonlinear response of structure is defined using an amplitude-dependent nonlinear normal mode identified from measured responses. A new method for reconstructing nonlinear normal mode is represented in this paper by relating the nonlinear normal mode to the clamped end displacement-dependent stiffness parameters using an eigensensitivity analysis. Solution of obtained equations results equivalent stiffness models at different vibration amplitudes and the corresponding nonlinear normal mode is identified. The approach results nonlinear modes with efficient capabilities in predicting dynamical behavior of the structure at different loading conditions. To evaluate the efficiency of the identified model, the structure is excited at higher excitation load levels than those employed in identification procedures and the observed responses are compared with the predictions of the model at the corresponding input force levels. The predictions are in good agreement with the observed behavior indicating success of identification procedure in capturing the physical merits involve in the boundary local nonlinearities.
Coherent-incoherent phenomena in nonlinear optics and imaging
NASA Astrophysics Data System (ADS)
Dylov, Dmitry V.
While the majority of modern experimentation in optics and optical technology relies on pure and highly coherent sources, the light encountered in nature is of inferior quality. The low-quality, or noisy, light creates problems in nonlinear signal processing, as the random, multi-mode distribution inhibits phase matching and wave mixing. In this dissertation, we will discover new incoherent phenomena using nonlinear optics and characterize many fundamental, and useful, features pertinent to waves with inferior coherence. The first part of the thesis will be devoted to a new theory describing the nonlinear propagation of statistical light. The essence of the theory is to represent incoherent light as a gas of particles (speckles) that can interact collectively via nonlinearity, effectively forming a photonic plasma. We carried out a set of basic plasma-like experiments in optics and showed that this representation is valid and promising. Experiments were conducted using a nonlinear photorefractive crystal and basic phenomena such as modulation and bump-on-tail instabilities, optical turbulence, etc., were observed. In the second part of the thesis, we will apply this plasma formalism to the recovery and amplification of weak, noise-hidden images. The signal fidelity will be shown to improve by exploiting signal-noise interaction in the nonlinear medium. This new, dynamical type of stochastic resonance (a process in which signal can grow at expense of the noise) is treated as an equivalent beam-plasma instability, allowing an analytical characterization of the resonance as a function of coupling strength, noise statistics, modal content of the signal and wavelength. The theory also suggests an exponential limit to the amount of information transmissible in nonlinear communications systems. The results link the fields of optics, plasma and information theory, and pave the way for a variety of nonlinear, instability-driven imaging techniques.
Application of time reversal acoustics focusing for nonlinear imaging ms
NASA Astrophysics Data System (ADS)
Sarvazyan, Armen; Sutin, Alexander
2001-05-01
Time reversal acoustic (TRA) focusing of ultrasound appears to be an effective tool for nonlinear imaging in industrial and medical applications because of its ability to efficiently concentrate ultrasonic energy (close to diffraction limit) in heterogeneous media. In this study, we used two TRA systems to focus ultrasonic beams with different frequencies in coinciding focal points, thus causing the generation of ultrasonic waves with combination frequencies. Measurements of the intensity of these combination frequency waves provide information on the nonlinear parameter of medium in the focal region. Synchronized stirring of two TRA focused beams enables obtaining 3-D acoustic nonlinearity images of the object. Each of the TRA systems employed an aluminum resonator with piezotransducers glued to its facet. One of the free facets of each resonator was submerged into a water tank and served as a virtual phased array capable of ultrasound focusing and beam steering. To mimic a medium with spatially varying acoustical nonlinearity a simplest model such as a microbubble column in water was used. Microbubbles were generated by electrolysis of water using a needle electrode. An order of magnitude increase of the sum frequency component was observed when the ultrasound beams were focused in the area with bubbles.
Flow regimes for fluid injection into a confined porous medium
Zheng, Zhong; Guo, Bo; Christov, Ivan C.; Celia, Michael A.; Stone, Howard A.
2015-02-24
We report theoretical and numerical studies of the flow behaviour when a fluid is injected into a confined porous medium saturated with another fluid of different density and viscosity. For a two-dimensional configuration with point source injection, a nonlinear convection–diffusion equation is derived to describe the time evolution of the fluid–fluid interface. In the early time period, the fluid motion is mainly driven by the buoyancy force and the governing equation is reduced to a nonlinear diffusion equation with a well-known self-similar solution. In the late time period, the fluid flow is mainly driven by the injection, and the governing equation is approximated by a nonlinear hyperbolic equation that determines the global spreading rate; a shock solution is obtained when the injected fluid is more viscous than the displaced fluid, whereas a rarefaction wave solution is found when the injected fluid is less viscous. In the late time period, we also obtain analytical solutions including the diffusive term associated with the buoyancy effects (for an injected fluid with a viscosity higher than or equal to that of the displaced fluid), which provide the structure of the moving front. Numerical simulations of the convection–diffusion equation are performed; the various analytical solutions are verified as appropriate asymptotic limits, and the transition processes between the individual limits are demonstrated.
Flow regimes for fluid injection into a confined porous medium
Zheng, Zhong; Guo, Bo; Christov, Ivan C.; Celia, Michael A.; Stone, Howard A.
2015-02-24
We report theoretical and numerical studies of the flow behaviour when a fluid is injected into a confined porous medium saturated with another fluid of different density and viscosity. For a two-dimensional configuration with point source injection, a nonlinear convection–diffusion equation is derived to describe the time evolution of the fluid–fluid interface. In the early time period, the fluid motion is mainly driven by the buoyancy force and the governing equation is reduced to a nonlinear diffusion equation with a well-known self-similar solution. In the late time period, the fluid flow is mainly driven by the injection, and the governingmore » equation is approximated by a nonlinear hyperbolic equation that determines the global spreading rate; a shock solution is obtained when the injected fluid is more viscous than the displaced fluid, whereas a rarefaction wave solution is found when the injected fluid is less viscous. In the late time period, we also obtain analytical solutions including the diffusive term associated with the buoyancy effects (for an injected fluid with a viscosity higher than or equal to that of the displaced fluid), which provide the structure of the moving front. Numerical simulations of the convection–diffusion equation are performed; the various analytical solutions are verified as appropriate asymptotic limits, and the transition processes between the individual limits are demonstrated.« less
Frequency domain nonlinear optics
NASA Astrophysics Data System (ADS)
Legare, Francois
2016-05-01
The universal dilemma of gain narrowing occurring in fs amplifiers prevents ultra-high power lasers from delivering few-cycle pulses. This problem is overcome by a new amplification concept: Frequency domain Optical Parametric Amplification - FOPA. It enables simultaneous up-scaling of peak power and amplified spectral bandwidth and can be performed at any wavelength range of conventional amplification schemes, however, with the capability to amplify single cycles of light. The key idea for amplification of octave-spanning spectra without loss of spectral bandwidth is to amplify the broad spectrum ``slice by slice'' in the frequency domain, i.e. in the Fourier plane of a 4f-setup. The striking advantages of this scheme, are its capability to amplify (more than) one octave of bandwidth without shorting the corresponding pulse duration. This is because ultrabroadband phase matching is not defined by the properties of the nonlinear crystal employed but the number of crystals employed. In the same manner, to increase the output energy one simply has to increase the spectral extension in the Fourier plane and to add one more crystal. Thus, increasing pulse energy and shortening its duration accompany each other. A proof of principle experiment was carried out at ALLS on the sub-two cycle IR beam line and yielded record breaking performance in the field of few-cycle IR lasers. 100 μJ two-cycle pulses from a hollow core fibre compression setup were amplified to 1.43mJ without distorting spatial or temporal properties. Pulse duration at the input of FOPA and after FOPA remains the same. Recently, we have started upgrading this system to be pumped by 250 mJ to reach 40 mJ two-cycle IR few-cycle pulses and latest results will be presented at the conference. Furthermore, the extension of the concept of FOPA to other nonlinear optical processes will be discussed. Frequency domain nonlinear optics.
Evolution of the ring Airy Gaussian beams with a spiral phase in the Kerr medium
NASA Astrophysics Data System (ADS)
Chen, Bo; Chen, Chidao; Peng, Xi; Peng, Yulian; Zhou, Meiling; Deng, Dongmei; Guo, Hong
2016-05-01
Nonlinear optical phenomena are of great practical interest in optics. The evolution of ring Airy Gaussian beams with a spiral phase in the nonlinear Kerr medium is investigated using the nonlinear Schrödinger equation. Numerical simulations indicate that the distribution factor b can influence the formation of the ring Airy Gaussian beams. Results show that the beams can be oscillating, and the light filament can be achieved under appropriate laser input power. On the other hand, the evolution of the ring Airy Gaussian beams with a spiral phase in the nonlinear Kerr medium can be implemented, and the numerical simulations of the holographic generation of the ring Airy Gaussian vortex beams propagated in the medium demonstrate that the vortex can be preserved along the propagation. The Poynting vector shows that the energy flow of the ring Airy Gaussian beams flows in the opposite direction on both sides of the focus plane; however, for beams with a spiral phase, the flow direction remains the same; the energy flow can rotate in opposite directions on both sides of the focal plane.
Nonlinear magnetohydrodynamics from gravity
NASA Astrophysics Data System (ADS)
Hansen, James; Kraus, Per
2009-04-01
We apply the recently established connection between nonlinear fluid dynamics and AdS gravity to the case of the dyonic black brane in AdS4. This yields the equations of fluid dynamics for a 2+1 dimensional charged fluid in a background magnetic field. We construct the gravity solution to second order in the derivative expansion. From this we find the fluid dynamical stress tensor and charge current to second and third order in derivatives respectively, along with values for the associated transport coefficients.
Optical correlator tracking nonlinearity
NASA Astrophysics Data System (ADS)
Gregory, Don A.; Kirsch, James C.; Johnson, John L.
1987-01-01
A limitation observed in the tracking ability of optical correlators is reported. It is shown by calculations that an inherent nonlinearity exists in many optical correlator configurations, with the problem manifesting itself in a mismatch of the input scene with the position of the correlation signal. Results indicate that some care must be given to the selection of components and their configuration in constructing an optical correlator which exhibits true translational invariance. An input test scene is shown along with the correlation spot and cross hairs from a contrast detector; the offset is apparent.
Nonlinear methods for communications
NASA Astrophysics Data System (ADS)
1992-08-01
An innovative communication system has been developed. This system has the potential for improved secure communication for covert operations. By modulating data on the chaotic signal used to synchronize two nonlinear systems, they have created a Low Probability of Intercept (LPI) communications system. The researchers derived the equations which govern the system, made models of the system, and performed numerical simulations to test these models. The theoretical and numerical studies of this system have been validated by experiment. A recent design improvement has led to a system that synchronizes at 0 db Signal-to-Noise. This development holds the promise of a Low Probability of Detection (LPD) system.
Linear and nonlinear optical response of spherical anisotropic semiconductor microcrystallites
NASA Astrophysics Data System (ADS)
Ramaniah, Lavanya M.; Nair, Selvakumar V.; Rustagi, Kailash C.
1989-12-01
We present a phenomenological theory of the linear and nonlinear optical properties associated with the Fröhlich resonances of an optically anisotropic, spherical semiconductor crystallite. Using the Maxwell-Garnett approach, we calculate the effective dielectric function of a composite medium containing such crystallites. To study the effect of anisotropy, we take CdS and CdSe quantum dots as examples for the inclusions, and use a two-resonance model for the dielectric function. Even for randomly oriented inclusions, the Fröhlich resonances split as a result of anisotropic local-field corrections. At higher laser intensities, absorption saturation leads to bistability or tristability in the optical response of individual crystallites, while the response of the composite medium with randomly oriented inclusions shows multistability, with many intermediate branches. The nonlinear response of such a composite medium also exhibits a new kind of orientation-induced broadening of resonances. We also find that tristability is possible in another kind of inhomogeneous material, viz., a composite medium containing two types of isotropic spherical crystallites.
Medium Modification of Vector Mesons
Chaden Djalali, Michael Paolone, Dennis Weygand, Michael H. Wood, Rakhsha Nasseripour
2011-03-01
The theory of the strong interaction, Quantum Chromodynamics (QCD), has been remarkably successful in describing high-energy and short-distance-scale experiments involving quarks and gluons. However, applying QCD to low energy and large-distance scale experiments has been a major challenge. Various QCD-inspired models predict a partial restoration of chiral symmetry in nuclear matter with modifications of the properties of hadrons from their free-space values. Measurable changes such as a shift in mass and/or a change of width are predicted at normal nuclear density. Photoproduction of vector mesons off nuclei have been performed at different laboratories. The properties of the ρ, ω and φ mesons are investigated either directly by measuring their mass spectra or indirectly through transparency ratios. The latest results regarding medium modifications of the vector mesons in the nuclear medium will be discussed.
Medium modifications with recoil polarization
Brand, J.F.J. van den; Ent, R.
1994-04-01
The authors show that the virtual Compton scattering process allows for a precise study of the off-shell electron-nucleon vertex. In a separable model, they show the sensitivity to new unconstrained structure functions of the nucleon, beyond the usual Dirac and Pauli form factors. In addition, they show the sensitivity to bound nucleon form factors using the reaction 4He({rvec e},e{prime},{rvec p}){sup 3}H. A nucleon embedded in a nucleus represents a complex system. Firstly, the bound nucleon is necessarily off-shell and in principle a complete understanding of the dynamical structure of the nucleon is required in order to calculate its off-shell electromagnetic interaction. Secondly, one faces the possibility of genuine medium effects, such as for example quark-exchange contributions. Furthermore, the electromagnetic coupling to the bound nucleon is dependent on the nuclear dynamics through the self-energy of the nucleon in the nuclear medium.
Rashidian Vaziri, Mohammad Reza
2013-07-10
In this paper, the Z-scan theory for nonlocal nonlinear media has been further developed when nonlinear absorption and nonlinear refraction appear simultaneously. To this end, the nonlinear photoinduced phase shift between the impinging and outgoing Gaussian beams from a nonlocal nonlinear sample has been generalized. It is shown that this kind of phase shift will reduce correctly to its known counterpart for the case of pure refractive nonlinearity. Using this generalized form of phase shift, the basic formulas for closed- and open-aperture beam transmittances in the far field have been provided, and a simple procedure for interpreting the Z-scan results has been proposed. In this procedure, by separately performing open- and closed-aperture Z-scan experiments and using the represented relations for the far-field transmittances, one can measure the nonlinear absorption coefficient and nonlinear index of refraction as well as the order of nonlocality. Theoretically, it is shown that when the absorptive nonlinearity is present in addition to the refractive nonlinearity, the sample nonlocal response can noticeably suppress the peak and enhance the valley of the Z-scan closed-aperture transmittance curves, which is due to the nonlocal action's ability to change the beam transverse dimensions.
Nonlinear refraction in vitreous humor.
Rockwell, B A; Roach, W P; Rogers, M E; Mayo, M W; Toth, C A; Cain, C P; Noojin, G D
1993-11-01
We extend the application of the z-scan technique to determine the nonlinear refractive index (n(2)) for human and rabbit vitreous humor, water, and physiological saline. In these measurements there were nonlinear contributions to the measured signal from the aqueous samples and the quartz cell that held the sample. Measurements were made with 60-ps pulses at 532 nm. To our knowledge, this is the first measurement of the nonlinear refractive properties of biological material. PMID:19829406
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.
T. MILONNI; G. CSANAK; ET AL
1999-07-01
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at Los Alamos National Laboratory (LANL). The project objectives were to explore theoretically various aspects of nonlinear atom optics effects in cold-atom waves and traps. During the project a major development occurred the observation, by as many as a dozen experimental groups, of Bose-Einstein condensation (BEC) in cold-atom traps. This stimulated us to focus our attention on those aspects of nonlinear atom optics relating to BEC, in addition to continuing our work on a nonequilibrium formalism for dealing with the interaction of an electromagnetic field with multi-level atomic systems, allowing for macroscopic coherence effects such as BEC. Studies of several problems in BEC physics have been completed or are near completion, including the suggested use of external electric fields to modify the nature of the interatomic interaction in cold-atom traps; properties of two-phase condensates; and molecular loss processes associated with BEC experiments involving a so-called Feshbach resonance.
Improved nonlinear prediction method
NASA Astrophysics Data System (ADS)
Adenan, Nur Hamiza; Md Noorani, Mohd Salmi
2014-06-01
The analysis and prediction of time series data have been addressed by researchers. Many techniques have been developed to be applied in various areas, such as weather forecasting, financial markets and hydrological phenomena involving data that are contaminated by noise. Therefore, various techniques to improve the method have been introduced to analyze and predict time series data. In respect of the importance of analysis and the accuracy of the prediction result, a study was undertaken to test the effectiveness of the improved nonlinear prediction method for data that contain noise. The improved nonlinear prediction method involves the formation of composite serial data based on the successive differences of the time series. Then, the phase space reconstruction was performed on the composite data (one-dimensional) to reconstruct a number of space dimensions. Finally the local linear approximation method was employed to make a prediction based on the phase space. This improved method was tested with data series Logistics that contain 0%, 5%, 10%, 20% and 30% of noise. The results show that by using the improved method, the predictions were found to be in close agreement with the observed ones. The correlation coefficient was close to one when the improved method was applied on data with up to 10% noise. Thus, an improvement to analyze data with noise without involving any noise reduction method was introduced to predict the time series data.
Nonlinear Attitude Filtering Methods
NASA Technical Reports Server (NTRS)
Markley, F. Landis; Crassidis, John L.; Cheng, Yang
2005-01-01
This paper provides a survey of modern nonlinear filtering methods for attitude estimation. Early applications relied mostly on the extended Kalman filter for attitude estimation. Since these applications, several new approaches have been developed that have proven to be superior to the extended Kalman filter. Several of these approaches maintain the basic structure of the extended Kalman filter, but employ various modifications in order to provide better convergence or improve other performance characteristics. Examples of such approaches include: filter QUEST, extended QUEST, the super-iterated extended Kalman filter, the interlaced extended Kalman filter, and the second-order Kalman filter. Filters that propagate and update a discrete set of sigma points rather than using linearized equations for the mean and covariance are also reviewed. A two-step approach is discussed with a first-step state that linearizes the measurement model and an iterative second step to recover the desired attitude states. These approaches are all based on the Gaussian assumption that the probability density function is adequately specified by its mean and covariance. Other approaches that do not require this assumption are reviewed, including particle filters and a Bayesian filter based on a non-Gaussian, finite-parameter probability density function on SO(3). Finally, the predictive filter, nonlinear observers and adaptive approaches are shown. The strengths and weaknesses of the various approaches are discussed.
Electromagnetic scattering from nonlinear anisotropic cylinders. I - Fundamental frequency
NASA Astrophysics Data System (ADS)
Hasan, Moh'd. A.; Uslenghi, P. L. E.
1990-04-01
The solution of the problem of electromagnetic scattering of obliquely incident plane waves by homogeneous, nonlinear anisotropic cylindrical structures is obtained. The medium of the scatterer is characterized by Volterra-type integrals for the electric and magnetic flux density vectors D and B, respectively. The nonlinear problem is solved using the perturbation method. The effects of nonlinearities on the field properties both inside and outside the scatterer, together with the effect on the radar cross section, are investigated for the fundamental frequency components. To demonstrate the validity of the approach, the results obtained by the perturbation method are compared with those obtained using the plane wave representation method of Censor (1983), where the iteration method is used to solve the resulting dispersion equation. The results are in very good agreement in both amplitude and phase of the fields for the case of very weak nonlinearity. When the relative magnitude of the nonlinear component of the permittivity is increased, the iteration method shows a faster divergence of the phase from the linear phase.
Nonlinear regional warming with increasing CO2 concentrations
NASA Astrophysics Data System (ADS)
Good, Peter; Lowe, Jason A.; Andrews, Timothy; Wiltshire, Andrew; Chadwick, Robin; Ridley, Jeff K.; Menary, Matthew B.; Bouttes, Nathaelle; Dufresne, Jean Louis; Gregory, Jonathan M.; Schaller, Nathalie; Shiogama, Hideo
2015-02-01
When considering adaptation measures and global climate mitigation goals, stakeholders need regional-scale climate projections, including the range of plausible warming rates. To assist these stakeholders, it is important to understand whether some locations may see disproportionately high or low warming from additional forcing above targets such as 2 K (ref. ). There is a need to narrow uncertainty in this nonlinear warming, which requires understanding how climate changes as forcings increase from medium to high levels. However, quantifying and understanding regional nonlinear processes is challenging. Here we show that regional-scale warming can be strongly superlinear to successive CO2 doublings, using five different climate models. Ensemble-mean warming is superlinear over most land locations. Further, the inter-model spread tends to be amplified at higher forcing levels, as nonlinearities grow--especially when considering changes per kelvin of global warming. Regional nonlinearities in surface warming arise from nonlinearities in global-mean radiative balance, the Atlantic meridional overturning circulation, surface snow/ice cover and evapotranspiration. For robust adaptation and mitigation advice, therefore, potentially avoidable climate change (the difference between business-as-usual and mitigation scenarios) and unavoidable climate change (change under strong mitigation scenarios) may need different analysis methods.
Non-linear calibration models for near infrared spectroscopy.
Ni, Wangdong; Nørgaard, Lars; Mørup, Morten
2014-02-27
Different calibration techniques are available for spectroscopic applications that show nonlinear behavior. This comprehensive comparative study presents a comparison of different nonlinear calibration techniques: kernel PLS (KPLS), support vector machines (SVM), least-squares SVM (LS-SVM), relevance vector machines (RVM), Gaussian process regression (GPR), artificial neural network (ANN), and Bayesian ANN (BANN). In this comparison, partial least squares (PLS) regression is used as a linear benchmark, while the relationship of the methods is considered in terms of traditional calibration by ridge regression (RR). The performance of the different methods is demonstrated by their practical applications using three real-life near infrared (NIR) data sets. Different aspects of the various approaches including computational time, model interpretability, potential over-fitting using the non-linear models on linear problems, robustness to small or medium sample sets, and robustness to pre-processing, are discussed. The results suggest that GPR and BANN are powerful and promising methods for handling linear as well as nonlinear systems, even when the data sets are moderately small. The LS-SVM is also attractive due to its good predictive performance for both linear and nonlinear calibrations.
Using nonlinear kernels in seismic tomography: go beyond gradient methods
NASA Astrophysics Data System (ADS)
Wu, R.
2013-05-01
In quasi-linear inversion, a nonlinear problem is typically solved iteratively and at each step the nonlinear problem is linearized through the use of a linear functional derivative, the Fréchet derivative. Higher order terms generally are assumed to be insignificant and neglected. The linearization approach leads to the popular gradient method of seismic inversion. However, for the real Earth, the wave equation (and the real wave propagation) is strongly nonlinear with respect to the medium parameter perturbations. Therefore, the quasi-linear inversion may have a serious convergence problem for strong perturbations. In this presentation I will compare the convergence properties of the Taylor-Fréchet series and the renormalized Fréchet series, the De Wolf approximation, and illustrate the improved convergence property with numerical examples. I'll also discuss the application of nonlinear partial derivative to least-square waveform inversion. References: Bonnans, J., Gilbert, J., Lemarechal, C. and Sagastizabal, C., 2006, Numirical optmization, Springer. Wu, R.S. and Y. Zheng, 2012. Nonlinear Fréchet derivative and its De Wolf approximation, Expanded Abstracts of Society of Exploration Gephysicists, SI 8.1.
Comparison of Medium Frequency Burst Generation Theories
NASA Astrophysics Data System (ADS)
Bunch, N. L.; Labelle, J. W.; Weatherwax, A. T.; Yoon, P. H.
2009-12-01
Auroral Medium Frequency (MF) burst is a naturally occurring spontaneous impulsive radio emission observed at ground level between 800 and 4500 kHz. MF burst has been shown to be associated with auroral substorm onset, commonly observed coincidentally with auroral roar and hiss, with typical durations of a few minutes, amplitudes of ~10-14 V^2 /m^2 Hz, and measured to be left hand polarized. Despite several suggested theories, the exact generation mechanism for MF burst still remains a mystery. Recent experimental findings combined with a discussion of normal wave modes available in the auroral ionosphere allow us to constrain potential modes of generation. Normal modes available in the auroral ionosphere (Omega_ce = ~800-1600 kHz, omega_pe = ~100-6000 kHz between 100 and 1000 km altitude) include R-X, L-O, Z (L-X), Langmuir-upper hybrid, electron cyclotron, electron acoustic, and electron cyclotron sound. Each mode is considered in light of experimental evidence, including accessibility to the L-O mode for propagation to ground with left hand polarization, and requirements for excitation by an auroral electron beam (100-10s of keV). A linear mode conversion process is also preferred over non-linear due to their inefficiency. Specific scenarios include: mode conversion of Langmuir waves at a range of altitudes on either the top or bottom side F-region, short wavelength (thermal branch) Langmuir waves, electron acoustic waves, electron cyclotron sound waves, direct generation of the L mode, and refraction and conversion of Z / upper hybrid waves - similar to that of auroral roar.
Latorre-Ossa, Heldmuth; Gennisson, Jean-Luc; De Brosses, Emilie; Tanter, Mickaël
2012-04-01
The study of new tissue mechanical properties such as shear nonlinearity could lead to better tissue characterization and clinical diagnosis. This work proposes a method combining static elastography and shear wave elastography to derive the nonlinear shear modulus by applying the acoustoelasticity theory in quasi-incompressible soft solids. Results demonstrate that by applying a moderate static stress at the surface of the investigated medium, and by following the quantitative evolution of its shear modulus, it is possible to accurately and quantitatively recover the local Landau (A) coefficient characterizing the shear nonlinearity of soft tissues.
An exact approach to intensity analysis of optical pulses in nonlinear meta-materials
NASA Astrophysics Data System (ADS)
Nanda, Lipsa
2016-05-01
The nonlinear pulse propagation has been analytically studied by solving the nonlinear Schrödinger's equation (NLSE) in bulk media exhibiting frequency dependent dielectric permittivity(ɛ) and magnetic permeability(μ). The exact solutions obtained are shown to be of trigonometric & localized types. The analytical and simulation based method has been further extended to investigate the intensity distribution in a nonlinear meta-material which behaves as a negative refractive medium (NRM), where both ɛ and μ are shown to be dispersive and negative in nature.
Small amplitude nonlinear electron acoustic solitary waves in weakly magnetized plasma
Dutta, Manjistha; Khan, Manoranjan; Ghosh, Samiran; Roychoudhury, Rajkumar; Chakrabarti, Nikhil
2013-01-15
Nonlinear propagation of electron acoustic waves in homogeneous, dispersive plasma medium with two temperature electron species is studied in presence of externally applied magnetic field. The linear dispersion relation is found to be modified by the externally applied magnetic field. Lagrangian transformation technique is applied to carry out nonlinear analysis. For small amplitude limit, a modified KdV equation is obtained, the modification arising due to presence of magnetic field. For weakly magnetized plasma, the modified KdV equation possesses stable solitary solutions with speed and amplitude increasing temporally. The solutions are valid upto some finite time period beyond which the nonlinear wave tends to wave breaking.
Problems in nonlinear resistive MHD
Turnbull, A.D.; Strait, E.J.; La Haye, R.J.; Chu, M.S.; Miller, R.L.
1998-12-31
Two experimentally relevant problems can relatively easily be tackled by nonlinear MHD codes. Both problems require plasma rotation in addition to the nonlinear mode coupling and full geometry already incorporated into the codes, but no additional physics seems to be crucial. These problems discussed here are: (1) nonlinear coupling and interaction of multiple MHD modes near the B limit and (2) nonlinear coupling of the m/n = 1/1 sawtooth mode with higher n gongs and development of seed islands outside q = 1.
Nonlinear ptychographic coherent diffractive imaging.
Odstrcil, M; Baksh, P; Gawith, C; Vrcelj, R; Frey, J G; Brocklesby, W S
2016-09-01
Ptychographic Coherent diffractive imaging (PCDI) is a significant advance in imaging allowing the measurement of the full electric field at a sample without use of any imaging optics. So far it has been confined solely to imaging of linear optical responses. In this paper we show that because of the coherence-preserving nature of nonlinear optical interactions, PCDI can be generalised to nonlinear optical imaging. We demonstrate second harmonic generation PCDI, directly revealing phase information about the nonlinear coefficients, and showing the general applicability of PCDI to nonlinear interactions. PMID:27607631
Effects of gravity and nonlinearity on the waves in the granular chain.
Hong, J; Xu, A
2001-06-01
The solitary signal observed in a horizontal granular chain changes its speed and form due to gravity in a vertical chain. We find that all the propagating signals in a vertical chain follow power laws in depth for propagating speed, grain velocity, amplitude, and width. This stems from the power-law type changing of elastic properties in a medium under gravity. The propagation may be separated into two types according to the behavior of the power-law exponents, depending on the strength of the nonlinearity. We show that the power-law exponents are constants in the strength of the impulse in the weakly nonlinear regime, while they depend on the strength of the impulse in the strongly nonlinear regime. We derive power-law exponents for the weakly nonlinear regime analytically and try to understand the behaviors of the strongly nonlinear regime through analytical treatment. PMID:11415095
Nonlinear light-matter interactions in engineered optical media
NASA Astrophysics Data System (ADS)
Litchinitser, Natalia
In this talk, we consider fundamental optical phenomena at the interface of nonlinear and singular optics in artificial media, including theoretical and experimental studies of linear and nonlinear light-matter interactions of vector and singular optical beams in metamaterials. We show that unique optical properties of metamaterials open unlimited prospects to ``engineer'' light itself. Thanks to their ability to manipulate both electric and magnetic field components, metamaterials open new degrees of freedom for tailoring complex polarization states and orbital angular momentum (OAM) of light. We will discuss several approaches to structured light manipulation on the nanoscale using metal-dielectric, all-dielectric and hyperbolic metamaterials. These new functionalities, including polarization and OAM conversion, beam magnification and de-magnification, and sub-wavelength imaging using novel non-resonant hyperlens are likely to enable a new generation of on-chip or all-fiber structured light applications. The emergence of metamaterials also has a strong potential to enable a plethora of novel nonlinear light-matter interactions and even new nonlinear materials. In particular, nonlinear focusing and defocusing effects are of paramount importance for manipulation of the minimum focusing spot size of structured light beams necessary for nanoscale trapping, manipulation, and fundamental spectroscopic studies. Colloidal suspensions offer as a promising platform for engineering polarizibilities and realization of large and tunable nonlinearities. We will present our recent studies of the phenomenon of spatial modulational instability leading to laser beam filamentation in an engineered soft-matter nonlinear medium. Finally, we introduce so-called virtual hyperbolic metamaterials formed by an array of plasma channels in air as a result of self-focusing of an intense laser pulse, and show that such structure can be used to manipulate microwave beams in a free space. This
Hong, Ming; Su, Zhongqing; Wang, Qiang; Cheng, Li; Qing, Xinlin
2014-03-01
A dedicated modeling technique for comprehending nonlinear characteristics of ultrasonic waves traversing in a fatigued medium was developed, based on a retrofitted constitutive relation of the medium by considering the nonlinearities originated from material, fatigue damage, as well as the "breathing" motion of fatigue cracks. Piezoelectric wafers, for exciting and acquiring ultrasonic waves, were integrated in the model. The extracted nonlinearities were calibrated by virtue of an acoustic nonlinearity parameter. The modeling technique was validated experimentally, and the results showed satisfactory consistency in between, both revealing: the developed modeling approach is able to faithfully simulate fatigue crack-incurred nonlinearities manifested in ultrasonic waves; a cumulative growth of the acoustic nonlinearity parameter with increasing wave propagation distance exists; such a parameter acquired via a sensing path is nonlinearly related to the offset distance from the fatigue crack to that sensing path; and neither the incidence angle of the probing wave nor the length of the sensing path impacts on the parameter significantly. This study has yielded a quantitative characterization strategy for fatigue cracks using embeddable piezoelectric sensor networks, facilitating deployment of structural health monitoring which is capable of identifying small-scale damage at an embryo stage and surveilling its growth continuously.
2D Self-Similar Profile for Laser Beam Propagation in Medium with Saturating Multi-Photon Absorption
NASA Astrophysics Data System (ADS)
Trofimov, Vyacheslav A.; Lysak, Tatiana M.; Zakharova, Irina G.
2016-02-01
We study a self-similar mode of 2D laser beam propagation in media with multiphoton absorption (MA) taking into account a resonant nonlinearity and nonlinear absorption saturating. An analytical solution of the corresponding equations describing the problems under consideration is derived using an eigenvalue problem method generalization for soliton- like solution finding. The developed solution is used as incident beam profile and phase front for computer simulation of the 2D laser beam propagation. In particular, we demonstrate numerically that the laser beam propagation in a self-similar mode occurs within a certain distance, which depends on medium properties. Under certain relations between the nonlinear absorption and resonant nonlinearity, and cubic nonlinear response, we observe the super long distance of the beam propagation without any beam profile distributions.
Dislocation nonlinearity and nonlinear wave processes in polycrystals with dislocations
NASA Astrophysics Data System (ADS)
Nazarov, V. E.
2016-09-01
Based on the modification of the linear part of the Granato-Lücke dislocation theory of absorption, the equation of state of polycrystalline solids with dissipative and reactive nonlinearity has been derived. The nonlinear effects of the interaction and self-action of longitudinal elastic waves in such media have been theoretically studied.
Coherent transmission of an ultrasonic shock wave through a multiple scattering medium
NASA Astrophysics Data System (ADS)
Viard, Nicolas; Giammarinaro, Bruno; Derode, Arnaud; Barrière, Christophe
2013-08-01
We report measurements of the transmitted coherent (ensemble-averaged) wave resulting from the interaction of an ultrasonic shock wave with a two-dimensional random medium. Despite multiple scattering, the coherent waveform clearly shows the steepening that is typical of nonlinear harmonic generation. This is taken advantage of to measure the elastic mean free path and group velocity over a broad frequency range (2-15 MHz) in only one experiment. Experimental results are found to be in good agreement with a linear theoretical model taking into account spatial correlations between scatterers. These results show that nonlinearity and multiple scattering are both present, yet uncoupled.
Level set methods to compute minimal surfaces in a medium with exclusions (voids).
Walsh, Timothy Francis; Chopp, David; Torres, Monica
2003-06-01
In T1, periodic minimal surfaces in a medium with exclusions (voids) are constructed and in this paper we present two algorithms for computing these minimal surfaces. The two algorithms use evolution of level sets by mean curvature. The first algorithm solves the governing nonlinear PDE directly and enforces numerically an orthogonality condition that the surfaces satisfy when they meet the boundaries of the exclusions. The second algorithm involves h-adaptive finite element approximations of a linear convection-diffusion equation, which has been shown to linearize the governing nonlinear PDE for weighted mean curvature flow.
Galaxy formation in an intergalactic medium dominated by explosions
NASA Technical Reports Server (NTRS)
Ostriker, J. P.; Cowie, L. L.
1981-01-01
The evolution of galaxies in an intergalactic medium dominated by explosions of star systems is considered analogously to star formation by nonlinearly interacting processes in the interstellar medium. Conditions for the existence of a hydrodynamic instability by which galaxy formation leads to more galaxy formation due to the propagation of the energy released at the death of massive stars are examined, and it is shown that such an explosive amplification is possible at redshifts less than about 5 and stellar system masses between 10 to the 8th and 10 to the 12th solar masses. Explosions before a redshift of about 5 are found to lead primarily to the formation of massive stars rather than galaxies, while those at a redshift close to 5 will result in objects of normal galactic scale. The model also predicts a dusty interstellar medium preventing the detection of objects of redshift greater than 3, numbers and luminosities of protogalaxies comparable to present observations, unvirialized groups of galaxies lying on two-dimensional surfaces, and a significant number of black holes in the mass range 1000-10,000 solar masses.
NASA Astrophysics Data System (ADS)
Etemadpour, R.; Sepehri Javan, N.; Dorranian, D.
2016-05-01
The nonlinear dynamics of a circularly polarized laser pulse propagating in the magnetized plasmas whose constituents are superthermal ions and mixed nonthermal high-energy tail electrons is studied theoretically. A nonlinear equation which describes the dynamics of the slowly varying amplitude is obtained using a relativistic two-fluid model. Based on this nonlinear equation and taking into account some nonlinear phenomena such as modulational instability, self-focusing and soliton formation are investigated. Effect of the magnetized plasma with superthermal ions and mixed nonthermal high-energy tail electrons on these phenomena is considered. It is shown that the nonthermality and superthermality of particles can substantially change the nonlinearity of medium.
A Heterogeneous Medium Analytical Benchmark
Ganapol, B.D.
1999-09-27
A benchmark, called benchmark BLUE, has been developed for one-group neutral particle (neutron or photon) transport in a one-dimensional sub-critical heterogeneous plane parallel medium with surface illumination. General anisotropic scattering is accommodated through the Green's Function Method (GFM). Numerical Fourier transform inversion is used to generate the required Green's functions which are kernels to coupled integral equations that give the exiting angular fluxes. The interior scalar flux is then obtained through quadrature. A compound iterative procedure for quadrature order and slab surface source convergence provides highly accurate benchmark qualities (4- to 5- places of accuracy) results.
Medium Effects in Parton Distributions
William Detmold, Huey-Wen Lin
2011-12-01
A defining experiment of high-energy physics in the 1980s was that of the EMC collaboration where it was first observed that parton distributions in nuclei are non-trivially related to those in the proton. This result implies that the presence of the nuclear medium plays an important role and an understanding of this from QCD has been an important goal ever since Here we investigate analogous, but technically simpler, effects in QCD and examine how the lowest moment of the pion parton distribution is modified by the presence of a Bose-condensed gas of pions or kaons.
Multimodal Nonlinear Optical Microscopy
Yue, Shuhua; Slipchenko, Mikhail N.; Cheng, Ji-Xin
2013-01-01
Because each nonlinear optical (NLO) imaging modality is sensitive to specific molecules or structures, multimodal NLO imaging capitalizes the potential of NLO microscopy for studies of complex biological tissues. The coupling of multiphoton fluorescence, second harmonic generation, and coherent anti-Stokes Raman scattering (CARS) has allowed investigation of a broad range of biological questions concerning lipid metabolism, cancer development, cardiovascular disease, and skin biology. Moreover, recent research shows the great potential of using CARS microscope as a platform to develop more advanced NLO modalities such as electronic-resonance-enhanced four-wave mixing, stimulated Raman scattering, and pump-probe microscopy. This article reviews the various approaches developed for realization of multimodal NLO imaging as well as developments of new NLO modalities on a CARS microscope. Applications to various aspects of biological and biomedical research are discussed. PMID:24353747
Nonlinear integrable ion traps
Nagaitsev, S.; Danilov, V.; /SNS Project, Oak Ridge
2011-10-01
Quadrupole ion traps can be transformed into nonlinear traps with integrable motion by adding special electrostatic potentials. This can be done with both stationary potentials (electrostatic plus a uniform magnetic field) and with time-dependent electric potentials. These potentials are chosen such that the single particle Hamilton-Jacobi equations of motion are separable in some coordinate systems. The electrostatic potentials have several free adjustable parameters allowing for a quadrupole trap to be transformed into, for example, a double-well or a toroidal-well system. The particle motion remains regular, non-chaotic, integrable in quadratures, and stable for a wide range of parameters. We present two examples of how to realize such a system in case of a time-independent (the Penning trap) as well as a time-dependent (the Paul trap) configuration.
Spherically symmetric nonlinear structures
NASA Astrophysics Data System (ADS)
Calzetta, Esteban A.; Kandus, Alejandra
1997-02-01
We present an analytical method to extract observational predictions about the nonlinear evolution of perturbations in a Tolman universe. We assume no a priori profile for them. We solve perturbatively a Hamilton-Jacobi equation for a timelike geodesic and obtain the null one as a limiting case in two situations: for an observer located in the center of symmetry and for a noncentered one. In the first case we find expressions to evaluate the density contrast and the number count and luminosity distance versus redshift relationships up to second order in the perturbations. In the second situation we calculate the CMBR anisotropies at large angular scales produced by the density contrast and by the asymmetry of the observer's location, up to first order in the perturbations. We develop our argument in such a way that the formulas are valid for any shape of the primordial spectrum.
Nonlinearities in vegetation functioning
NASA Astrophysics Data System (ADS)
Ceballos-Núñez, Verónika; Müller, Markus; Metzler, Holger; Sierra, Carlos
2016-04-01
Given the current drastic changes in climate and atmospheric CO2 concentrations, and the role of vegetation in the global carbon cycle, there is increasing attention to the carbon allocation component in biosphere terrestrial models. Improving the representation of C allocation in models could be the key to having better predictions of the fate of C once it enters the vegetation and is partitioned to C pools of different residence times. C allocation has often been modeled using systems of ordinary differential equations, and it has been hypothesized that most models can be generalized with a specific form of a linear dynamical system. However, several studies have highlighted discrepancies between empirical observations and model predictions, attributing these differences to problems with model structure. Although efforts have been made to compare different models, the outcome of these qualitative assessments has been a conceptual categorization of them. In this contribution, we introduce a new effort to identify the main properties of groups of models by studying their mathematical structure. For this purpose, we performed a literature research of the relevant models of carbon allocation in vegetation and developed a database with their representation in symbolic mathematics. We used the Python package SymPy for symbolic mathematics as a common language and manipulated the models to calculate their Jacobian matrix at fixed points and their eigenvalues, among other mathematical analyses. Our preliminary results show a tendency of inverse proportionality between model complexity and size of time/space scale; complex interactions between the variables controlling carbon allocation in vegetation tend to operate at shorter time/space scales, and vice-versa. Most importantly, we found that although the linear structure is common, other structures with non-linearities have been also proposed. We, therefore, propose a new General Model that can accommodate these
Adaptive nonlinear flight control
NASA Astrophysics Data System (ADS)
Rysdyk, Rolf Theoduor
1998-08-01
Research under supervision of Dr. Calise and Dr. Prasad at the Georgia Institute of Technology, School of Aerospace Engineering. has demonstrated the applicability of an adaptive controller architecture. The architecture successfully combines model inversion control with adaptive neural network (NN) compensation to cancel the inversion error. The tiltrotor aircraft provides a specifically interesting control design challenge. The tiltrotor aircraft is capable of converting from stable responsive fixed wing flight to unstable sluggish hover in helicopter configuration. It is desirable to provide the pilot with consistency in handling qualities through a conversion from fixed wing flight to hover. The linear model inversion architecture was adapted by providing frequency separation in the command filter and the error-dynamics, while not exiting the actuator modes. This design of the architecture provides for a model following setup with guaranteed performance. This in turn allowed for convenient implementation of guaranteed handling qualities. A rigorous proof of boundedness is presented making use of compact sets and the LaSalle-Yoshizawa theorem. The analysis allows for the addition of the e-modification which guarantees boundedness of the NN weights in the absence of persistent excitation. The controller is demonstrated on the Generic Tiltrotor Simulator of Bell-Textron and NASA Ames R.C. The model inversion implementation is robustified with respect to unmodeled input dynamics, by adding dynamic nonlinear damping. A proof of boundedness of signals in the system is included. The effectiveness of the robustification is also demonstrated on the XV-15 tiltrotor. The SHL Perceptron NN provides a more powerful application, based on the universal approximation property of this type of NN. The SHL NN based architecture is also robustified with the dynamic nonlinear damping. A proof of boundedness extends the SHL NN augmentation with robustness to unmodeled actuator
Linearization of Conservative Nonlinear Oscillators
ERIC Educational Resources Information Center
Belendez, A.; Alvarez, M. L.; Fernandez, E.; Pascual, I.
2009-01-01
A linearization method of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force which allows us to obtain a frequency-amplitude relation which is valid not only for small but also for large amplitudes and, sometimes, for…
Nonlinear diffusion and superconducting hysteresis
Mayergoyz, I.D.
1996-12-31
Nonlinear diffusion of electromagnetic fields in superconductors with ideal and gradual resistive transitions is studied. Analytical results obtained for linear and nonlinear polarizations of electromagnetic fields are reported. These results lead to various extensions of the critical state model for superconducting hysteresis.
Passive linearization of nonlinear resonances
NASA Astrophysics Data System (ADS)
Habib, G.; Grappasonni, C.; Kerschen, G.
2016-07-01
The objective of this paper is to demonstrate that the addition of properly tuned nonlinearities to a nonlinear system can increase the range over which a specific resonance responds linearly. Specifically, we seek to enforce two important properties of linear systems, namely, the force-displacement proportionality and the invariance of resonance frequencies. Numerical simulations and experiments are used to validate the theoretical findings.
Solving Nonlinear Coupled Differential Equations
NASA Technical Reports Server (NTRS)
Mitchell, L.; David, J.
1986-01-01
Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.
How Does the Medium Affect the Message?
ERIC Educational Resources Information Center
Dommermuth, William P.
1974-01-01
This experimental comparison of the advertising effectiveness of television, movies, radio, and print finds no support for McLuhan's idea that television is a "cool" medium and movies are a "hot" medium. (RB)
Nonlinear Oscillators in Space Physics
NASA Technical Reports Server (NTRS)
Lester,Daniel; Thronson, Harley
2011-01-01
We discuss dynamical systems that produce an oscillation without an external time dependent source. Numerical results are presented for nonlinear oscillators in the Em1h's atmosphere, foremost the quasi-biennial oscillation (QBOl. These fluid dynamical oscillators, like the solar dynamo, have in common that one of the variables in a governing equation is strongly nonlinear and that the nonlinearity, to first order, has particular form. of 3rd or odd power. It is shown that this form of nonlinearity can produce the fundamental li'equency of the internal oscillation. which has a period that is favored by the dynamical condition of the fluid. The fundamental frequency maintains the oscillation, with no energy input to the system at that particular frequency. Nonlinearities of 2nd or even power could not maintain the oscillation.
Properties of Nonlinear Dynamo Waves
NASA Technical Reports Server (NTRS)
Tobias, S. M.
1997-01-01
Dynamo theory offers the most promising explanation of the generation of the sun's magnetic cycle. Mean field electrodynamics has provided the platform for linear and nonlinear models of solar dynamos. However, the nonlinearities included are (necessarily) arbitrarily imposed in these models. This paper conducts a systematic survey of the role of nonlinearities in the dynamo process, by considering the behaviour of dynamo waves in the nonlinear regime. It is demonstrated that only by considering realistic nonlinearities that are non-local in space and time can modulation of the basic dynamo wave he achieved. Moreover, this modulation is greatest when there is a large separation of timescales provided by including a low magnetic Prandtl number in the equation for the velocity perturbations.
Gravitational lensing in plasmic medium
Bisnovatyi-Kogan, G. S. Tsupko, O. Yu.
2015-07-15
The influence of plasma on different effects of gravitational lensing is reviewed. Using the Hamiltonian approach for geometrical optics in a medium in the presence of gravity, an exact formula for the photon deflection angle by a black hole (or another body with a Schwarzschild metric) embedded in plasma with a spherically symmetric density distribution is derived. The deflection angle in this case is determined by the mutual combination of different factors: gravity, dispersion, and refraction. While the effects of deflection by the gravity in vacuum and the refractive deflection in a nonhomogeneous medium are well known, the new effect is that, in the case of a homogeneous plasma, in the absence of refractive deflection, the gravitational deflection differs from the vacuum deflection and depends on the photon frequency. In the presence of a plasma nonhomogeneity, the chromatic refractive deflection also occurs, so the presence of plasma always makes gravitational lensing chromatic. In particular, the presence of plasma leads to different angular positions of the same image if it is observed at different wavelengths. It is discussed in detail how to apply the presented formulas for the calculation of the deflection angle in different situations. Gravitational lensing in plasma beyond the weak deflection approximation is also considered.
Gravitational lensing in plasmic medium
NASA Astrophysics Data System (ADS)
Bisnovatyi-Kogan, G. S.; Tsupko, O. Yu.
2015-07-01
The influence of plasma on different effects of gravitational lensing is reviewed. Using the Hamiltonian approach for geometrical optics in a medium in the presence of gravity, an exact formula for the photon deflection angle by a black hole (or another body with a Schwarzschild metric) embedded in plasma with a spherically symmetric density distribution is derived. The deflection angle in this case is determined by the mutual combination of different factors: gravity, dispersion, and refraction. While the effects of deflection by the gravity in vacuum and the refractive deflection in a nonhomogeneous medium are well known, the new effect is that, in the case of a homogeneous plasma, in the absence of refractive deflection, the gravitational deflection differs from the vacuum deflection and depends on the photon frequency. In the presence of a plasma nonhomogeneity, the chromatic refractive deflection also occurs, so the presence of plasma always makes gravitational lensing chromatic. In particular, the presence of plasma leads to different angular positions of the same image if it is observed at different wavelengths. It is discussed in detail how to apply the presented formulas for the calculation of the deflection angle in different situations. Gravitational lensing in plasma beyond the weak deflection approximation is also considered.
Visco-elastic fluid simulations of coherent structures in strongly coupled dusty plasma medium
Singh Dharodi, Vikram; Kumar Tiwari, Sanat; Das, Amita
2014-07-15
A generalized hydrodynamic model depicting the behaviour of visco-elastic fluids has often been invoked to explore the behaviour of a strongly coupled dusty plasma medium below their crystallization limit. The model has been successful in describing the collective normal modes of the strongly coupled dusty plasma medium observed experimentally. The paper focuses on the study of nonlinear dynamical characteristic features of this model. Specifically, the evolution of coherent vorticity patches is being investigated here within the framework of this model. A comparison with Newtonian fluids and molecular dynamics simulations treating the dust species interacting through the Yukawa potential has also been presented.
On modeling center of foot pressure distortion through a medium.
Betker, Aimee L; Moussavi, Zahra M K; Szturm, Tony
2005-03-01
. A nonlinear mathematical model is proposed which describes COP distortion through a medium such as a sponge. Although the values for the model parameters determined were for a particular sponge, this study suggests that a neural network plant identification model may be applied to any medium other than the sponge; the information can then be used to determine how the balance control model is affected given the sensory information received.
Vassiliadis, P.; Kalapothaki, V.; Mavrommati, C.; Trichopoulos, D.
1984-01-01
The Rappaport-Vassiliadis enrichment medium (RV medium) in 10 ml quantities (RV/43 degrees C, 10 ml) inoculated with 0.1 ml of pre-enrichment medium (P medium) was found more efficient in the isolation of salmonellae from 409 pre-enriched samples (mainly meat products), than the original Rappaport medium incubated at 43 degrees C (R/43 degrees C) and the RV medium in 5 ml quantities (RV/43 degrees C, 5 ml) inoculated with 0.01 ml of P medium (P less than 0.001, in both instances). Therefore, the inoculum from pre-enriched foods should not be less than 0.1 ml in 10 ml of RV medium. The RV/43 degrees, 10 ml was also better (P less than 0.01) in detecting samples containing salmonellas than the original Rappaport medium incubated at 37 degrees C (R/37 degrees C, 10 ml) and the modification R25 of R medium incubated at 37 degrees C. The R25 modification was used in 10 ml quantities (R25/37 degrees C, 10 ml) inoculated with 0.1 ml of P medium and in 5 ml quantities (R25/37 degrees, 5 ml) inoculated with 0.01 ml of P medium. The last two R25 procedures were of the same efficiency in isolating salmonellas from meat products. PMID:6747286
Code of Federal Regulations, 2014 CFR
2014-10-01
... 49 Transportation 3 2014-10-01 2014-10-01 false Test medium. 195.306 Section 195.306... PIPELINE Pressure Testing § 195.306 Test medium. (a) Except as provided in paragraphs (b), (c), and (d) of this section, water must be used as the test medium. (b) Except for offshore pipelines,...
Code of Federal Regulations, 2012 CFR
2012-10-01
... 49 Transportation 3 2012-10-01 2012-10-01 false Test medium. 195.306 Section 195.306... PIPELINE Pressure Testing § 195.306 Test medium. (a) Except as provided in paragraphs (b), (c), and (d) of this section, water must be used as the test medium. (b) Except for offshore pipelines,...
Code of Federal Regulations, 2011 CFR
2011-10-01
... 49 Transportation 3 2011-10-01 2011-10-01 false Test medium. 195.306 Section 195.306... PIPELINE Pressure Testing § 195.306 Test medium. (a) Except as provided in paragraphs (b), (c), and (d) of this section, water must be used as the test medium. (b) Except for offshore pipelines,...
Code of Federal Regulations, 2013 CFR
2013-10-01
... 49 Transportation 3 2013-10-01 2013-10-01 false Test medium. 195.306 Section 195.306... PIPELINE Pressure Testing § 195.306 Test medium. (a) Except as provided in paragraphs (b), (c), and (d) of this section, water must be used as the test medium. (b) Except for offshore pipelines,...
27 CFR 19.914 - Medium plants.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Medium plants. 19.914 Section 19.914 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT... Medium plants. Any person wishing to establish a medium plant shall make application for and obtain...
Code of Federal Regulations, 2010 CFR
2010-10-01
... 49 Transportation 3 2010-10-01 2010-10-01 false Test medium. 195.306 Section 195.306... PIPELINE Pressure Testing § 195.306 Test medium. (a) Except as provided in paragraphs (b), (c), and (d) of this section, water must be used as the test medium. (b) Except for offshore pipelines,...
Nonlinear optical whispering gallery mode resonators
NASA Technical Reports Server (NTRS)
Ilchenko, Vladimir (Inventor); Matsko, Andrey B. (Inventor); Savchenkov, Anatoliy (Inventor); Maleki, Lutfollah (Inventor)
2005-01-01
Whispering gallery mode (WGM) optical resonators comprising nonlinear optical materials, where the nonlinear optical material of a WGM resonator includes a plurality of sectors within the optical resonator and nonlinear coefficients of two adjacent sectors are oppositely poled.
Layer contributions to the nonlinear acoustic radiation from stratified media.
Vander Meulen, François; Haumesser, Lionel
2016-12-01
This study presents the thorough investigation of the second harmonic generation scenario in a three fluid layer system. An emphasis is on the evaluation of the nonlinear parameter B/A in each layer from remote measurements. A theoretical approach of the propagation of a finite amplitude acoustic wave in a multilayered medium is developed. In the frame of the KZK equation, the weak nonlinearity of the media, attenuation and diffraction effects are computed for the fundamental and second harmonic waves propagating back and forth in each of the layers of the system. The model uses a gaussian expansion to describe the beam propagation in order to quantitatively evaluate the contribution of each part of the system (layers and interfaces) to its nonlinearity. The model is validated through measurements on a water/aluminum/water system. Transmission as well as reflection configurations are studied. Good agreement is found between the theoretical results and the experimental data. The analysis of the second harmonic field sources measured by the transducers from outside the stratified medium highlights the factors that favor the cumulative effects.
Doppler effects in the propagation of a few-cycle pulse through a dense medium.
Chen, Yue-Yue; Feng, Xun-Li; Liu, Chengpu
2015-06-29
This numerical study demonstrates that Doppler redshift exists in the reflected spectrum of a few-cycle pulse, propagating through a dense medium. It manifests itself in two different forms, a sharp low-frequency spike (LFS) located at the red edge of the reflected spectrum and a relatively broader redshift near the carrier frequency. With the variation of the laser and medium parameters, the dominant reflection mechanism changes between bulk generation of backwards propagation waves and nonlinear reflection near the front face. This leads to the manifestation of Doppler effect changing accordingly between the two different forms. This study unifies the physical mechanism behind the LFS and dynamic nonlinear optical skin effect, which enriches the theoretical explanation of the spectral redshift of few-cycle pulse propagation beyond the intrapulse four-wave mixing. PMID:26191713
NASA Astrophysics Data System (ADS)
Sutin, A. M.; Johnson, P. A.
2005-04-01
This paper presents the second part of the review of Nonlinear Elastic Wave Spectroscopy (NEWS) in NDE, and describe two different methods of nonlinear NDE that provide not only damage detection but location as well. Nonlinear Wave Modulation Spectroscopy is based on the application of an ultrasonic probe signal modulated by a low frequency vibration. Damage location can be obtained by application of Impulse Modulation Techniques that exploit the modulation of a short pulse reflected from a damage feature (e.g. crack) by low frequency vibration. Nonlinear Time Reversed Acoustic methods provide the means to focus acoustic energy to any point in a solid. In combination, we are applying the focusing properties of TRA and the nonlinear properties of cracks to locate them.
Collapse arresting in an inhomogeneous quintic nonlinear Schrödinger model.
Gaididei, Y B; Schjødt-Eriksen, J; Christiansen, P L
1999-10-01
Collapse of (1+1)-dimensional beams in the inhomogeneous one-dimensional quintic nonlinear Schrödinger equation is analyzed both numerically and analytically. It is shown that in the vicinity of a narrow attractive inhomogeneity, the collapse of beams in which the homogeneous medium would blow up may be delayed and even arrested. PMID:11970353
Self-sustained pulsations of light in a nonlinear thin-film system
Paulau, P.V.; Loiko, N.A.
2005-07-15
The propagation of light through the system composed of two thin films with resonant nonlinearity has been considered. Conditions for the multistability and Hopf bifurcations have been found. Two kinds of self-sustained pulsations including Rabi oscillations have been distinguished. A possible experimental observation of the effects described using quantum-confined semiconductor structures as a resonant medium has been discussed.
Cross-polarized wave generation by effective cubic nonlinear optical interaction.
Petrov, G I; Albert, O; Etchepare, J; Saltiel, S M
2001-03-15
A new cubic nonlinear optical effect in which a linearly polarized wave propagating in a single quadratic medium is converted into a wave that is cross polarized to the input wave is observed in BBO crystal. The effect is explained by cascading of two different second-order processes: second-harmonic generation and difference frequency mixing.
NASA Astrophysics Data System (ADS)
Rozanov, N. N.; Kiselev, Al. S.; Kiselev, An. S.
2008-08-01
Self-reflection of pulses of intense laser radiation from an inhomogeneity induced by them in a medium with fast optical nonlinearity is analyzed. The reflected radiation is characterized by a considerable Doppler shift and by a signal magnitude that is sufficient for experimental detection.
Sintered composite medium and filter
Bergman, Werner
1987-01-01
A particulate filter medium is formed of a sintered composite of 0.5 micron diameter quartz fibers and 2 micron diameter stainless steel fibers. A preferred composition is about 40 vol. % quartz and about 60 vol. % stainless steel fibers. The media is sintered at about 1100.degree. C. to bond the stainless steel fibers into a cage network which holds the quartz fibers. High filter efficiency and low flow resistance are provided by the smaller quartz fibers. High strength is provided by the stainless steel fibers. The resulting media has a high efficiency and low pressure drop similar to the standard HEPA media, with tensile strength at least four times greater, and a maximum operating temperature of about 550.degree. C. The invention also includes methods to form the composite media and a HEPA filter utilizing the composite media. The filter media can be used to filter particles in both liquids and gases.
Medium consumption in holographic memories.
Ayres, Mark R; McLeod, Robert R
2009-07-01
The dynamic range of holographic storage media is traditionally characterized in terms of M/#. However, this is a system parameter that assumes simple, uniform plane-wave holograms. Realistic architectures violate this assumption so that M/# measured with plane waves cannot be used to predict system diffraction efficiency. Thus, there currently is no systematic method predicting signal strength and medium consumption for holographic storage architectures a priori. We define a new material parameter, the modulation integral, M(I), and show how this may be used for dynamic range budgeting and diffraction efficiency prediction in complex storage systems. The method is illustrated by applying it to two architectures, collinear and angle polytopic, in order to estimate the M/# required for achieving a target storage density in the presence of empirical optical scatter noise.
Theory of interstellar medium diagnostics
NASA Technical Reports Server (NTRS)
Fahr, H. J.
1983-01-01
The theoretical interpretation of observed interplanetary resonance luminescence patterns is used as one of the must promising methods to determine the state of the local interstellar medium (LISM). However, these methods lead to discrepant results that would be hard to understand in the framework of any physical LISM scenario. Assuming that the observational data are reliable, two possibilities which could help to resolve these discrepancies are discussed: (1) the current modeling of resonance luminescence patterns is unsatisfactory and has to be improved, and (2) the extrapolated interstellar parameters are not indicative of the unperturbed LISM state, but rather designate an intermediate state attained in the outer regions of the solar system. It is shown that a quantitative treatment of the neutral gas-plasma interaction effects in the interface between the heliospheric and the interstellar plasmas is of major importance for the correct understanding of the whole complex.
On the linear properties of the nonlinear radiative transfer problem
NASA Astrophysics Data System (ADS)
Pikichyan, H. V.
2016-11-01
In this report, we further expose the assertions made in nonlinear problem of reflection/transmission of radiation from a scattering/absorbing one-dimensional anisotropic medium of finite geometrical thickness, when both of its boundaries are illuminated by intense monochromatic radiative beams. The new conceptual element of well-defined, so-called, linear images is noteworthy. They admit a probabilistic interpretation. In the framework of nonlinear problem of reflection/transmission of radiation, we derive solution which is similar to linear case. That is, the solution is reduced to the linear combination of linear images. By virtue of the physical meaning, these functions describe the reflectivity and transmittance of the medium for a single photon or their beam of unit intensity, incident on one of the boundaries of the layer. Thereby the medium in real regime is still under the bilateral illumination by external exciting radiation of arbitrary intensity. To determine the linear images, we exploit three well known methods of (i) adding of layers, (ii) its limiting form, described by differential equations of invariant imbedding, and (iii) a transition to the, so-called, functional equations of the "Ambartsumyan's complete invariance".
Nonlinear natural engine: Model for thermodynamic processes in mesoscale systems
Wheatley, John; Buchanan, D. S.; Swift, G. W.; Migliori, A.; Hofler, T.
1985-01-01
To develop intuition on the possible application of concepts from thermodynamic heat engines to mesoscale systems, we have constructed and studied a model thermoacoustic heat engine. The model consists of a chain of coupled nonlinear acoustic vibrators in which the primary thermodynamic medium is argon gas, the secondary thermodynamic medium is constituted by solids bounding the gas, and frequencies are ca. 3 × 102 Hz. The nonlinear elements are the necks, made flexible by means of an oil-loaded DuPont Kapton film, of Helmholtz resonators. When the primary medium is driven uniformly by an acoustic driver at a frequency somewhat below the low-amplitude resonant frequency and at a high enough driving amplitude, stationary localized or solitary states appear irreversibly on the chain. These are characterized by a higher vibrational amplitude than that in surrounding vibrators, where the amplitude can decrease; by the appearance of deep subharmonics of the drive frequency, corresponding to driven low-frequency vibrations of the Kapton film-oil systems; and by the pumping of heat toward the localized states. Possible implications of these results for mesoscale systems consisting of chains of molecular vibrators are then discussed. Images PMID:16593625
Diffusion Solution of the Equation of Magnetic Induction in a Moving Medium
NASA Astrophysics Data System (ADS)
Lasukov, V. V.; Malik, Kh. K.; Moldovanova, E. A.; Abdrashitova, M. O.; Gorbacheva, E. S.; Rozhkova, S. V.
2016-09-01
It is shown that there exist solutions for which the linear differential equations of physics are transformed into nonlinear equations. The corresponding diffusion Maxwellian solution of the equation of magnetic induction in a moving medium can be used to describe the emergence and subsequent evolution of the magnetic fields of the Earth, Sun, and other planets and stars. If the magnetic viscosity is complex, the evolution of the magnetic induction is cyclic, in which case the magnetic induction can change sign.
Nonlinear evolution of Airy-like beams generated by modulated waveguide arrays.
Cao, Zheng; Tan, Qinggui; Li, Xiaojun; Qi, Xinyuan
2016-08-20
We numerically study the formation of modulated waveguide generated Airy-like beams and their subsequent evolution in homogeneous medium. The results show that the Airy-like beams could be generated from narrow Gaussian beams propagating in one-dimensional transverse separation modulated unbent, cosine bent, or logarithm bent waveguide arrays, respectively. The waveguide-generated Airy-like beams maintain their characteristics when propagating without nonlinearity or under the self-defocusing nonlinearity in homogeneous medium, while the beams are distorted under the self-focusing nonlinearity. The deformation depends on the waveguide bending and the outgoing angles of the Airy-like beams. Our results provide a new way to generate and manipulate the Airy-like beam.
BRST Structure of Nonlinear Superalgebras
NASA Astrophysics Data System (ADS)
Asorey, M.; Lavrov, P. M.; Radchenko, O. V.; Sugamoto, A.
In this paper we analyze the structure of the BRST charge of nonlinear superalgebras. We consider quadratic nonlinear superalgebras where a commutator (in terms of (super-)Poisson brackets) of the generators is a quadratic polynomial of the generators. We find the explicit form of the BRST charge up to cubic order in Faddeev-Popov ghost fields for arbitrary quadratic nonlinear superalgebras. We point out the existence of constraints on structure constants of the superalgebra when the nilpotent BRST charge is quadratic in Faddeev-Popov ghost fields. The general results are illustrated by simple examples of superalgebras.
Intrinsic Negative Mass from Nonlinearity
NASA Astrophysics Data System (ADS)
Di Mei, F.; Caramazza, P.; Pierangeli, D.; Di Domenico, G.; Ilan, H.; Agranat, A. J.; Di Porto, P.; DelRe, E.
2016-04-01
We propose and provide experimental evidence of a mechanism able to support negative intrinsic effective mass. The idea is to use a shape-sensitive nonlinearity to change the sign of the mass in the leading linear propagation equation. Intrinsic negative-mass dynamics is reported for light beams in a ferroelectric crystal substrate, where the diffusive photorefractive nonlinearity leads to a negative-mass Schrödinger equation. The signature of inverted dynamics is the observation of beams repelled from strongly guiding integrated waveguides irrespective of wavelength and intensity and suggests shape-sensitive nonlinearity as a basic mechanism leading to intrinsic negative mass.
Dissipative nonlinear dynamics in holography
NASA Astrophysics Data System (ADS)
Basu, Pallab; Ghosh, Archisman
2014-02-01
We look at the response of a nonlinearly coupled scalar field in an asymptotically AdS black brane geometry and find a behavior very similar to that of known dissipative nonlinear systems like the chaotic pendulum. Transition to chaos proceeds through a series of period-doubling bifurcations. The presence of dissipation, crucial to this behavior, arises naturally in a black hole background from the ingoing conditions imposed at the horizon. AdS/CFT translates our solution to a chaotic response of O, the operator dual to the scalar field. Our setup can also be used to study quenchlike behavior in strongly coupled nonlinear systems.
Design and evaluation of a fast Fourier transform-based nonlinear dielectric spectrometer
NASA Astrophysics Data System (ADS)
Treo, Ernesto F.; Felice, Carmelo J.
2009-11-01
Nonlinear dielectric spectroscopy of micro-organism is carried out by applying a moderate electrical field to an aqueous sample through two metal electrodes. Several ad hoc nonlinear spectrometers were proposed in the literature. However, these designs barely compensated the nonlinear distortion derived from the electrode-electrolyte interfaces (EEI). Moreover, the contribution of the suspension is masked by the effect of the nonlinearity introduced by the electrode contacts. Conversely, the nonlinear capability of a commercial tetrapolar analyzer has not been fully investigated. In this paper a new nonlinear tetrapolar spectrometer is proposed based on a commercial linear apparatus and ad hoc control and signal processing software. The system was evaluated with discrete electronic phantoms and showed that it can measure nonlinear properties of aqueous suspension independently of the presence of EEI (ANOVA test, p >0.001). It was also tested with real aqueous samples. The harmonics observed in the current that circulates through the sample reveals useful information about the transfer function of the sample. The total harmonic distortion was computed for linear mediums. Values lower than -60 dB suggest that the system has enough capability to perform nonlinear microbiological analysis. Design specifications, sources of interference, and equipment's limitations are discussed.
NASA Technical Reports Server (NTRS)
Meyer, George
1997-01-01
The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of way points through which the aircraft trajectory must pass. The way points typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory which satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multi-dimensional, multi-axis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of possible operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordinatization, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions must be smooth. The guidance algorithm is based on the inversion of the pure feedback approximations, which is followed by iterative corrections for the effects of zero dynamics. The paper describes the structure and modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.
NASA Technical Reports Server (NTRS)
Meyer, George; Null, Cynthia H. (Technical Monitor)
1996-01-01
The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of way points through which the aircraft trajectory must pass. The way points typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory which satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multi-dimensional, multi-axis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of possible operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordination, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions must be smooth. The guidance algorithm is based on the inversion of the pure feedback approximations, which is followed by iterative corrections for the effects of zero dynamics. The paper describes the structure and modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.
Nonlinear Frequency Compression
Scollie, Susan; Glista, Danielle; Seelisch, Andreas
2013-01-01
Frequency lowering technologies offer an alternative amplification solution for severe to profound high frequency hearing losses. While frequency lowering technologies may improve audibility of high frequency sounds, the very nature of this processing can affect the perceived sound quality. This article reports the results from two studies that investigated the impact of a nonlinear frequency compression (NFC) algorithm on perceived sound quality. In the first study, the cutoff frequency and compression ratio parameters of the NFC algorithm were varied, and their effect on the speech quality was measured subjectively with 12 normal hearing adults, 12 normal hearing children, 13 hearing impaired adults, and 9 hearing impaired children. In the second study, 12 normal hearing and 8 hearing impaired adult listeners rated the quality of speech in quiet, speech in noise, and music after processing with a different set of NFC parameters. Results showed that the cutoff frequency parameter had more impact on sound quality ratings than the compression ratio, and that the hearing impaired adults were more tolerant to increased frequency compression than normal hearing adults. No statistically significant differences were found in the sound quality ratings of speech-in-noise and music stimuli processed through various NFC settings by hearing impaired listeners. These findings suggest that there may be an acceptable range of NFC settings for hearing impaired individuals where sound quality is not adversely affected. These results may assist an Audiologist in clinical NFC hearing aid fittings for achieving a balance between high frequency audibility and sound quality. PMID:23539261
Nonlinear vibrational microscopy
Holtom, Gary R.; Xie, Xiaoliang Sunney; Zumbusch, Andreas
2000-01-01
The present invention is a method and apparatus for microscopic vibrational imaging using coherent Anti-Stokes Raman Scattering or Sum Frequency Generation. Microscopic imaging with a vibrational spectroscopic contrast is achieved by generating signals in a nonlinear optical process and spatially resolved detection of the signals. The spatial resolution is attained by minimizing the spot size of the optical interrogation beams on the sample. Minimizing the spot size relies upon a. directing at least two substantially co-axial laser beams (interrogation beams) through a microscope objective providing a focal spot on the sample; b. collecting a signal beam together with a residual beam from the at least two co-axial laser beams after passing through the sample; c. removing the residual beam; and d. detecting the signal beam thereby creating said pixel. The method has significantly higher spatial resolution then IR microscopy and higher sensitivity than spontaneous Raman microscopy with much lower average excitation powers. CARS and SFG microscopy does not rely on the presence of fluorophores, but retains the resolution and three-dimensional sectioning capability of confocal and two-photon fluorescence microscopy. Complementary to these techniques, CARS and SFG microscopy provides a contrast mechanism based on vibrational spectroscopy. This vibrational contrast mechanism, combined with an unprecedented high sensitivity at a tolerable laser power level, provides a new approach for microscopic investigations of chemical and biological samples.
Ohnuma, S.
1984-03-01
Two approximations are made, one essential and the other not so essential but convenient to keep the analytical treatment manageable: (1) Only one nonlinear resonance is considered at a time so that the treatment is best suited when the tune is close to one resonance only. To improve this approximation, one must go to the next order which involves a canonical transformation of dynamical variables. Analytical treatment of more than one resonance is not possible for general cases. (2) In the formalism using the action-angle variables, the Hamiltonian can have terms which are independent of the angle variables. These terms are called phase-independent terms or shear terms. The tune is then a function of the oscillation amplitudes. In the lowest-order treatment, the (4N)-pole components but not the (4N + 2)-pole components contribute to this dependence. In deriving the resonance width analytically, one ignores these terms in the Hamiltonian for the sake of simplicity. If these are retained, one needs at least three extra parameters and the analytical treatment becomes rather unwieldy.
Macroscopic view of light pressure on a continuous medium
NASA Astrophysics Data System (ADS)
Gorkunov, M. V.; Kondratov, A. V.
2013-07-01
The ambiguity of the macroscopic description of light pressure on a continuous medium originates from the uncertainty of dividing the energy-momentum tensor of electromagnetically excited matter into a material and field parts or, equivalently, the total acting force into pressure and deformation terms. We show that, although there exists a continuum of formally correct formulations, one can adopt the appropriate form of the macroscopic field stress tensor that allows a unified description of pressure during elementary light-matter interactions, such as reflection, refraction, absorption, and nonlinear conversion. The derived simple expressions for the pressure force are compatible with the polariton momentum ℏk. The corresponding relation for the electromagnetic momentum density generalizes Rytov's definition for right-handed and left-handed frequency dispersive media.
Medium-Based Design: Extending a Medium to Create an Exploratory Learning Environment
ERIC Educational Resources Information Center
Rick, Jochen; Lamberty, K. K.
2005-01-01
This article introduces "medium-based" design -- an approach to creating "exploratory learning environments" using the method of "extending a medium". First, the characteristics of exploratory learning environments and medium-based design are described and grounded in related work. Particular attention is given to "extending a medium" --…
Nonlinear resonances and antiresonances of a forced sonic vacuum
Pozharskiy, D.; Zhang, Y.; Williams, M. O.; McFarland, D. M.; Kevrekidis, P. G.; Vakakis, A. F.; Kevrekidis, I. G.
2015-12-23
We consider a harmonically driven acoustic medium in the form of a (finite length) highly nonlinear granular crystal with an amplitude- and frequency-dependent boundary drive. Despite the absence of a linear spectrum in the system, we identify resonant periodic propagation whereby the crystal responds at integer multiples of the drive period and observe that this can lead to local maxima of transmitted force at its fixed boundary. In addition, we identify and discuss minima of the transmitted force (“antiresonances”) between these resonances. Representative one-parameter complex bifurcation diagrams involve period doublings and Neimark-Sacker bifurcations as well as multiple isolas (e.g., ofmore » period-3, -4, or -5 solutions entrained by the forcing). We combine them in a more detailed, two-parameter bifurcation diagram describing the stability of such responses to both frequency and amplitude variations of the drive. This picture supports a notion of a (purely) “nonlinear spectrum” in a system which allows no sound wave propagation (due to zero sound speed: the so-called sonic vacuum). As a result, we rationalize this behavior in terms of purely nonlinear building blocks: apparent traveling and standing nonlinear waves.« less
Nonlinear resonances and antiresonances of a forced sonic vacuum
NASA Astrophysics Data System (ADS)
Pozharskiy, D.; Zhang, Y.; Williams, M. O.; McFarland, D. M.; Kevrekidis, P. G.; Vakakis, A. F.; Kevrekidis, I. G.
2015-12-01
We consider a harmonically driven acoustic medium in the form of a (finite length) highly nonlinear granular crystal with an amplitude- and frequency-dependent boundary drive. Despite the absence of a linear spectrum in the system, we identify resonant periodic propagation whereby the crystal responds at integer multiples of the drive period and observe that this can lead to local maxima of transmitted force at its fixed boundary. In addition, we identify and discuss minima of the transmitted force ("antiresonances") between these resonances. Representative one-parameter complex bifurcation diagrams involve period doublings and Neimark-Sacker bifurcations as well as multiple isolas (e.g., of period-3, -4, or -5 solutions entrained by the forcing). We combine them in a more detailed, two-parameter bifurcation diagram describing the stability of such responses to both frequency and amplitude variations of the drive. This picture supports a notion of a (purely) "nonlinear spectrum" in a system which allows no sound wave propagation (due to zero sound speed: the so-called sonic vacuum). We rationalize this behavior in terms of purely nonlinear building blocks: apparent traveling and standing nonlinear waves.
Time-reversal of nonlinear waves: Applicability and limitations
NASA Astrophysics Data System (ADS)
Ducrozet, G.; Fink, M.; Chabchoub, A.
2016-09-01
Time-reversal (TR) refocusing of waves is one of the fundamental principles in wave physics. Using the TR approach, time-reversal mirrors can physically create a time-reversed wave that exactly refocus back, in space and time, to its original source regardless of the complexity of the medium as if time were going backward. Laboratory experiments have proved that this approach can be applied not only in acoustics and electromagnetism, but also in the field of linear and nonlinear water waves. Studying the range of validity and limitations of the TR approach may determine and quantify its range of applicability in hydrodynamics. In this context, we report a numerical study of hydrodynamic time-reversal using a unidirectional numerical wave tank, implemented by the nonlinear high-order spectral method, known to accurately model the physical processes at play, beyond physical laboratory restrictions. The applicability of the TR approach is assessed over a variety of hydrodynamic localized and pulsating structures' configurations, pointing out the importance of high-order dispersive and particularly nonlinear effects in the refocusing of hydrodynamic stationary envelope solitons and breathers. We expect that the results may motivate similar experiments in other nonlinear dispersive media and encourage several applications with particular emphasis on the field of ocean engineering.
Nonlinear resonances and antiresonances of a forced sonic vacuum
Pozharskiy, D.; Zhang, Y.; Williams, M. O.; McFarland, D. M.; Kevrekidis, P. G.; Vakakis, A. F.; Kevrekidis, I. G.
2015-12-23
We consider a harmonically driven acoustic medium in the form of a (finite length) highly nonlinear granular crystal with an amplitude- and frequency-dependent boundary drive. Despite the absence of a linear spectrum in the system, we identify resonant periodic propagation whereby the crystal responds at integer multiples of the drive period and observe that this can lead to local maxima of transmitted force at its fixed boundary. In addition, we identify and discuss minima of the transmitted force (“antiresonances”) between these resonances. Representative one-parameter complex bifurcation diagrams involve period doublings and Neimark-Sacker bifurcations as well as multiple isolas (e.g., of period-3, -4, or -5 solutions entrained by the forcing). We combine them in a more detailed, two-parameter bifurcation diagram describing the stability of such responses to both frequency and amplitude variations of the drive. This picture supports a notion of a (purely) “nonlinear spectrum” in a system which allows no sound wave propagation (due to zero sound speed: the so-called sonic vacuum). As a result, we rationalize this behavior in terms of purely nonlinear building blocks: apparent traveling and standing nonlinear waves.
Nonlinearity-induced PT-symmetry without material gain
NASA Astrophysics Data System (ADS)
Miri, Mohammad-Ali; Alù, Andrea
2016-06-01
Parity-time symmetry has raised a great deal of attention in optics in recent years, yet its application has been so far hindered by the stringent requirements on coherent gain balanced with loss. In this paper, we show that the conditions to enable parity and time symmetry can be simultaneously satisfied for a pair of modes with mixed frequencies interacting in a nonlinear medium, without requiring the presence of material gain. First, we consider a guided wave structure with second order nonlinearity and we derive the PT-symmetric Hamiltonian that governs the interaction of two waves of mixed frequencies when accompanied by a high intensity pump beam at the sum frequency. We also extend the results to an array of coupled nonlinear waveguide channels. It is shown that the evolution dynamics of the low-frequency waves is associated with a periodic PT-symmetric lattice while the phase of the pump beams can be utilized as a control parameter to modify the gain and loss distribution, thus realizing different PT lattices by design. Our results suggest that nonlinear wave mixing processes can form a rich platform to realize PT-symmetric Hamiltonians of arbitrary dimensions in optical systems, without requiring material gain.
Nonlinear acoustics in cicada mating calls enhance sound propagation.
Hughes, Derke R; Nuttall, Albert H; Katz, Richard A; Carter, G Clifford
2009-02-01
An analysis of cicada mating calls, measured in field experiments, indicates that the very high levels of acoustic energy radiated by this relatively small insect are mainly attributed to the nonlinear characteristics of the signal. The cicada emits one of the loudest sounds in all of the insect population with a sound production system occupying a physical space typically less than 3 cc. The sounds made by tymbals are amplified by the hollow abdomen, functioning as a tuned resonator, but models of the signal based solely on linear techniques do not fully account for a sound radiation capability that is so disproportionate to the insect's size. The nonlinear behavior of the cicada signal is demonstrated by combining the mutual information and surrogate data techniques; the results obtained indicate decorrelation when the phase-randomized and non-phase-randomized data separate. The Volterra expansion technique is used to fit the nonlinearity in the insect's call. The second-order Volterra estimate provides further evidence that the cicada mating calls are dominated by nonlinear characteristics and also suggests that the medium contributes to the cicada's efficient sound propagation. Application of the same principles has the potential to improve radiated sound levels for sonar applications.
Nonlinear resonances and antiresonances of a forced sonic vacuum.
Pozharskiy, D; Zhang, Y; Williams, M O; McFarland, D M; Kevrekidis, P G; Vakakis, A F; Kevrekidis, I G
2015-12-01
We consider a harmonically driven acoustic medium in the form of a (finite length) highly nonlinear granular crystal with an amplitude- and frequency-dependent boundary drive. Despite the absence of a linear spectrum in the system, we identify resonant periodic propagation whereby the crystal responds at integer multiples of the drive period and observe that this can lead to local maxima of transmitted force at its fixed boundary. In addition, we identify and discuss minima of the transmitted force ("antiresonances") between these resonances. Representative one-parameter complex bifurcation diagrams involve period doublings and Neimark-Sacker bifurcations as well as multiple isolas (e.g., of period-3, -4, or -5 solutions entrained by the forcing). We combine them in a more detailed, two-parameter bifurcation diagram describing the stability of such responses to both frequency and amplitude variations of the drive. This picture supports a notion of a (purely) "nonlinear spectrum" in a system which allows no sound wave propagation (due to zero sound speed: the so-called sonic vacuum). We rationalize this behavior in terms of purely nonlinear building blocks: apparent traveling and standing nonlinear waves. PMID:26764846
Simultaneous elastic parameter inversion in 2-D/3-D TTI medium combined later arrival times
NASA Astrophysics Data System (ADS)
Bai, Chao-ying; Wang, Tao; Yang, Shang-bei; Li, Xing-wang; Huang, Guo-jiao
2016-04-01
Traditional traveltime inversion for anisotropic medium is, in general, based on a "weak" assumption in the anisotropic property, which simplifies both the forward part (ray tracing is performed once only) and the inversion part (a linear inversion solver is possible). But for some real applications, a general (both "weak" and "strong") anisotropic medium should be considered. In such cases, one has to develop a ray tracing algorithm to handle with the general (including "strong") anisotropic medium and also to design a non-linear inversion solver for later tomography. Meanwhile, it is constructive to investigate how much the tomographic resolution can be improved by introducing the later arrivals. For this motivation, we incorporated our newly developed ray tracing algorithm (multistage irregular shortest-path method) for general anisotropic media with a non-linear inversion solver (a damped minimum norm, constrained least squares problem with a conjugate gradient approach) to formulate a non-linear inversion solver for anisotropic medium. This anisotropic traveltime inversion procedure is able to combine the later (reflected) arrival times. Both 2-D/3-D synthetic inversion experiments and comparison tests show that (1) the proposed anisotropic traveltime inversion scheme is able to recover the high contrast anomalies and (2) it is possible to improve the tomographic resolution by introducing the later (reflected) arrivals, but not as expected in the isotropic medium, because the different velocity (qP, qSV and qSH) sensitivities (or derivatives) respective to the different elastic parameters are not the same but are also dependent on the inclination angle.
Geometrically nonlinear analysis of layered composite plates and shells
NASA Technical Reports Server (NTRS)
Chao, W. C.; Reddy, J. N.
1983-01-01
A degenerated three dimensional finite element, based on the incremental total Lagrangian formulation of a three dimensional layered anisotropic medium was developed. Its use in the geometrically nonlinear, static and dynamic, analysis of layered composite plates and shells is demonstrated. A two dimenisonal finite element based on the Sanders shell theory with the von Karman (nonlinear) strains was developed. It is shown that the deflections obtained by the 2D shell element deviate from those obtained by the more accurate 3D element for deep shells. The 3D degenerated element can be used to model general shells that are not necessarily doubly curved. The 3D degenerated element is computationally more demanding than the 2D shell theory element for a given problem. It is found that the 3D element is an efficient element for the analysis of layered composite plates and shells undergoing large displacements and transient motion.
Nonlinear waves and shocks in relativistic two-fluid hydrodynamics
NASA Astrophysics Data System (ADS)
Haim, L.; Gedalin, M.; Spitkovsky, A.; Krasnoselskikh, V.; Balikhin, M.
2012-06-01
Relativistic shocks are present in a number of objects where violent processes are accompanied by relativistic outflows of plasma. The magnetization parameter σ = B2/4πnmc2 of the ambient medium varies in wide range. Shocks with low σ are expected to substantially enhance the magnetic fields in the shock front. In non-relativistic shocks the magnetic compression is limited by nonlinear effects related to the deceleration of flow. Two-fluid analysis of perpendicular relativistic shocks shows that the nonlinearities are suppressed for σ<<1 and the magnetic field reaches nearly equipartition values when the magnetic energy density is of the order of the ion energy density, Beq2 ~ 4πnmic2γ. A large cross-shock potential eφ/mic2γ0 ~ B2/Beq2 develops across the electron-ion shock front. This potential is responsible for electron energization.
Doppler effect of nonlinear waves and superspirals in oscillatory media.
Brusch, Lutz; Torcini, Alessandro; Bär, Markus
2003-09-01
Nonlinear waves emitted from a moving source are studied. A meandering spiral in a reaction-diffusion medium provides an example in which waves originate from a source exhibiting a back-and-forth movement in a radial direction. The periodic motion of the source induces a Doppler effect that causes a modulation in wavelength and amplitude of the waves ("superspiral"). Using direct simulations as well as numerical nonlinear analysis within the complex Ginzburg-Landau equation, we show that waves subject to a convective Eckhaus instability can exhibit monotonic growth or decay as well as saturation of these modulations depending on the perturbation frequency. Our findings elucidate recent experimental observations concerning superspirals and their decay to spatiotemporal chaos.
Nonlinear stability of solar type III radio bursts. I - Theory
NASA Technical Reports Server (NTRS)
Smith, R. A.; Goldstein, M. L.; Papadopoulos, K.
1979-01-01
A theory of the excitation of solar type III bursts is presented. Electrons initially unstable to the linear bump-in-tail instability are shown to rapidly amplify Langmuir waves to energy densities characteristic of strong turbulence. The three-dimensional equations which describe the strong coupling (wave-wave) interactions are derived. For parameters characteristic of the interplanetary medium the equations reduce to one-dimension. In that case the oscillating two-stream instability (OTSI) is the dominant nonlinear instability. OTSI is stabilized through the production of nonlinear ion density fluctuations that efficiently scatter Langmuir waves out of resonance with the electron beam. An analytical model of the electron distribution function is also developed which is used to estimate the total energy losses suffered by the electron beam as it propagates from the solar corona to 1 AU and beyond.
Marangoni mixed convection flow with Joule heating and nonlinear radiation
Hayat, Tasawar; Shaheen, Uzma; Shafiq, Anum; Alsaedi, Ahmed; Asghar, Saleem
2015-07-15
Marangoni mixed convective flow of Casson fluid in a thermally stratified medium is addressed. Flow analysis has been carried out in presence of inclined magnetic field. Heat transfer analysis is discussed in the presence of viscous dissipation, Joule heating and nonlinear thermal radiation. The governing nonlinear partial differential equations are first converted into ordinary differential systems and then developed the convergent series solutions. Flow pattern with the influence of pertinent parameters namely the magnetic parameter, Casson fluid parameter, temperature ratio parameter, stratification parameter, Prandtl number, Eckert number and radiation parameter is investigated. Expression of local Nusselt number is computed and analyzed. It is found that the Nusselt number decreases by increasing magnetic parameter, temperature ratio parameter, angle of inclination and stratification parameter. Moreover the effect of buoyancy parameter on the velocity distribution is opposite in both the opposing and assisting flow phenomena. Thermal field and associated layer thickness are enhanced for larger radiation parameter.
Nonlinear algebra and Bogoliubov's recursion
NASA Astrophysics Data System (ADS)
Morozov, A. Yu.; Serbyn, M. N.
2008-02-01
We give many examples of applying Bogoliubov’s forest formula to iterative solutions of various nonlinear equations. The same formula describes an extremely wide class of objects, from an ordinary quadratic equation to renormalization in quantum field theory.
Reconstruction of nonlinear wave propagation
Fleischer, Jason W; Barsi, Christopher; Wan, Wenjie
2013-04-23
Disclosed are systems and methods for characterizing a nonlinear propagation environment by numerically propagating a measured output waveform resulting from a known input waveform. The numerical propagation reconstructs the input waveform, and in the process, the nonlinear environment is characterized. In certain embodiments, knowledge of the characterized nonlinear environment facilitates determination of an unknown input based on a measured output. Similarly, knowledge of the characterized nonlinear environment also facilitates formation of a desired output based on a configurable input. In both situations, the input thus characterized and the output thus obtained include features that would normally be lost in linear propagations. Such features can include evanescent waves and peripheral waves, such that an image thus obtained are inherently wide-angle, farfield form of microscopy.
Nonlinear viscoelastic characterization of polycarbonate
NASA Technical Reports Server (NTRS)
Caplan, E. S.; Brinson, H. F.
1982-01-01
Uniaxial tensile creep and recovery data from polycarbonate at six temperatures and six stress levels are analyzed for nonlinear viscoelastic constitutive modeling. A theory to account for combined effects of two or more accelerating factors is presented.
Nonlinear interaction between single photons.
Guerreiro, T; Martin, A; Sanguinetti, B; Pelc, J S; Langrock, C; Fejer, M M; Gisin, N; Zbinden, H; Sangouard, N; Thew, R T
2014-10-24
Harnessing nonlinearities strong enough to allow single photons to interact with one another is not only a fascinating challenge but also central to numerous advanced applications in quantum information science. Here we report the nonlinear interaction between two single photons. Each photon is generated in independent parametric down-conversion sources. They are subsequently combined in a nonlinear waveguide where they are converted into a single photon of higher energy by the process of sum-frequency generation. Our approach results in the direct generation of photon triplets. More generally, it highlights the potential for quantum nonlinear optics with integrated devices and, as the photons are at telecom wavelengths, it opens the way towards novel applications in quantum communication such as device-independent quantum key distribution.
Interaction Terms in Nonlinear Models
Karaca-Mandic, Pinar; Norton, Edward C; Dowd, Bryan
2012-01-01
Objectives To explain the use of interaction terms in nonlinear models. Study Design We discuss the motivation for including interaction terms in multivariate analyses. We then explain how the straightforward interpretation of interaction terms in linear models changes in nonlinear models, using graphs and equations. We extend the basic results from logit and probit to difference-in-differences models, models with higher powers of explanatory variables, other nonlinear models (including log transformation and ordered models), and panel data models. Empirical Application We show how to calculate and interpret interaction effects using a publicly available Stata data set with a binary outcome. Stata 11 has added several features which make those calculations easier. LIMDEP code also is provided. Conclusions It is important to understand why interaction terms are included in nonlinear models in order to be clear about their substantive interpretation. PMID:22091735
Detecting mineral content in turbid medium using nonlinear Raman imaging: feasibility study
Arora, Rajan; Petrov, Georgi I.; Noojin, Gary D.; Thomas, Patrick A.; Denton, Michael L.; Rockwell, Benjamin A.; Thomas, Robert J.; Yakovlev, Vladislav V.
2012-01-01
Osteoporosis is a bone disease characterized by reduced mineral content with resulting changes in bone architecture, which in turn increases the risk of bone fracture. Raman spectroscopy has an intrinsic sensitivity to the chemical content of the bone, but its application to study bones in vivo is limited due to strong optical scattering in tissue. It has been proposed that Raman excitation with photoacoustic detection can successfully address the problem of chemically specific imaging in deep tissue. In this report, the principal possibility of photoacoustic imaging for detecting mineral content is evaluated. PMID:22337734
Nonlinear acoustics in biomedical ultrasound
NASA Astrophysics Data System (ADS)
Cleveland, Robin O.
2015-10-01
Ultrasound is widely used to image inside the body; it is also used therapeutically to treat certain medical conditions. In both imaging and therapy applications the amplitudes employed in biomedical ultrasound are often high enough that nonlinear acoustic effects are present in the propagation: the effects have the potential to be advantageous in some scenarios but a hindrance in others. In the case of ultrasound imaging the nonlinearity produces higher harmonics that result in images of greater quality. However, nonlinear effects interfere with the imaging of ultrasound contrast agents (typically micron sized bubbles with a strong nonlinear response of their own) and nonlinear effects also result in complications when derating of pressure measurements in water to in situ values in tissue. High intensity focused ultrasound (HIFU) is emerging as a non-invasive therapeutic modality which can result in thermal ablation of tissue. For thermal ablation, the extra effective attenuation resulting from nonlinear effects can result in enhanced heating of tissue if shock formation occurs in the target region for ablation - a highly desirable effect. However, if nonlinearity is too strong it can also result in undesired near-field heating and reduced ablation in the target region. The disruption of tissue (histotripsy) and fragmentation of kidney stones (lithotripsy) exploits shock waves to produce mechanically based effects, with minimal heating present. In these scenarios it is necessary for the waves to be of sufficient amplitude that a shock exists when the waveform reaches the target region. This talk will discuss how underlying nonlinear phenomenon act in all the diagnostic and therapeutic applications described above.
Studies of Nonlinear Problems. I
DOE R&D Accomplishments Database
Fermi, E.; Pasta, J.; Ulam, S.
1955-05-01
A one-dimensional dynamical system of 64 particles with forces between neighbors containing nonlinear terms has been studied on the Los Alamos computer MANIAC I. The nonlinear terms considered are quadratic, cubic, and broken linear types. The results are analyzed into Fourier components and plotted as a function of time. The results show very little, if any, tendency toward equipartition of energy among the degrees of freedom.
Nonlinear scattering in gold nanospheres
NASA Astrophysics Data System (ADS)
Shen, Po-Ting; Lin, Cheng-Wei; Liu, Hsiang-Lin; Chu, Shi-Wei
2016-03-01
Nonlinearity enhanced by noble metallic nanoparticles provide novel light manipulation capabilities and innovative applications. Recently, we discovered a new nonlinear phenomenon on the scattering of metallic nanoparticles by continuous-wave (CW) lasers at the intensity around MW/cm2 and applied to super-resolution microscopy that allowed spatial resolution of plasmonic nanostructures down to λ/8. However, its mechanism is still unknown. In this work, we elaborate the mechanism behind the nonlinear scattering of gold nanospheres. There are four possible candidates: intraband transition, interband transition, hot electron, and hot lattice. Each of them has a corresponding nonlinear refractive index (n2), which is related to temporal dependence of its light-matter interaction. We first measure the intensity dependence of nonlinear scattering to extract the effective n2 value. We find out it has the closest n2 value to hot lattice, which causes either the shift or weakening of the surface plasmon resonance (SPR). To further verify the mechanism, the nanospheres are heated up with both a hot plate and a CW laser, and the variation of single-particle SPR scattering spectra are measured. In both cases, more than 50% reduction of scattering is observed, when temperature rises a few tens of degrees or when illumination intensity reaches the order of 1MW/cm2. Thus, we conclude the spectra variation by the two different heating source, as well as the nonlinear scattering are all due to hot lattice, and subsequent permittivity change with temperature. The innovative concept of hot lattice plasmonics not only opens up a new dimension for nonlinear plasmonics, but also predicts the potential of similar nonlinearity in other materials as long as their permittivity changes with temperature.
Mobius Strip underlying Nonlinear Oscillators
NASA Astrophysics Data System (ADS)
Lopaz, Edaurdo; Satija, Indubala
2004-03-01
Geometrical and topolgocial aspects of phase space orbits of driven nonlinear oscillators are shown to share many features with the circuits on the mobius strips. Most important characteristic shared by nonlinear oscillators and the mobius strip is the first order geometrical phase transition characterized in terms of local variable torsion and the global variable the geometrical phase . These geometrical transitions are geometrical resonances and lead to geometrical localization that underlie not only limit cycles but also the strange attractors.
Dynamics of Cochlear Nonlinearity.
Cooper, Nigel P; van der Heijden, Marcel
2016-01-01
Dynamic aspects of cochlear mechanical compression were studied by recording basilar membrane (BM) vibrations evoked by tone pairs ("beat stimuli") in the 11-19 kHz region of the gerbil cochlea. The frequencies of the stimulus components were varied to produce a range of "beat rates" at or near the characteristic frequency (CF) of the BM site under study, and the amplitudes of the components were balanced to produce near perfect periodic cancellations, visible as sharp notches in the envelope of the BM response. We found a compressive relation between instantaneous stimulus intensity and BM response magnitude that was strongest at low beat rates (e.g., 10-100 Hz). At higher beat rates, the amount of compression reduced progressively (i.e. the responses became linearized), and the rising and falling flanks of the response envelope showed increasing amounts of hysteresis; the rising flank becoming steeper than the falling flank. This hysteresis indicates that cochlear mechanical compression is not instantaneous, and is suggestive of a gain control mechanism having finite attack and release times. In gain control terms, the linearization that occurs at higher beat rates occurs because the instantaneous gain becomes smoothened, or low-pass filtered, with respect to the magnitude fluctuations in the stimulus. In terms of peripheral processing, the linearization corresponds to an enhanced coding, or decompression, of rapid amplitude modulations. These findings are relevant both to those who wish to understand the underlying mechanisms and those who need a realistic model of nonlinear processing by the auditory periphery. PMID:27080667
NASA Technical Reports Server (NTRS)
Leslie, Thomas M.
1993-01-01
A focused approach to development and evaluation of organic polymer films for use in optoelectronics is presented. The issues and challenges that are addressed include: (1) material synthesis, purification, and the tailoring of the material properties; (2) deposition of uniform thin films by a variety of methods; (3) characterization of material physical properties (thermal, electrical, optical, and electro-optical); and (4) device fabrication and testing. Photonic materials, devices, and systems were identified as critical technology areas by the Department of Commerce and the Department of Defense. This approach offers strong integration of basic material issues through engineering applications by the development of materials that can be exploited as the active unit in a variety of polymeric thin film devices. Improved materials were developed with unprecedented purity and stability. The absorptive properties can be tailored and controlled to provide significant improvement in propagation losses and nonlinear performance. Furthermore, the materials were incorporated into polymers that are highly compatible with fabrication and patterning processes for integrated optical devices and circuits. By simultaneously addressing the issues of materials development and characterization, keeping device design and fabrication in mind, many obstacles were overcome for implementation of these polymeric materials and devices into systems. We intend to considerably improve the upper use temperature, poling stability, and compatibility with silicon based devices. The principal device application that was targeted is a linear electro-optic modulation etalon. Organic polymers need to be properly designed and coupled with existing integrated circuit technology to create new photonic devices for optical communication, image processing, other laser applications such as harmonic generation, and eventually optical computing. The progression from microscopic sample to a suitable film
The Circumgalactic Medium of Quasars
NASA Astrophysics Data System (ADS)
Hennawi, Joe
2014-07-01
I will argue that observations of the diffuse gas in the outskirts of quasar host galaxies, or the so called circumgalactic medium, are essential for understanding how luminous quasars evolve in a cosmological context. Such observations also provide a fruitful comparison to theory, because hydrodynamics at moderate overdensities is much easier to simulate than the complicated processes which trigger quasar activity. A novel technique will be introduced, whereby a foreground quasar can be studied in absorption against a background quasar, resolving scales as small as 30 kpc. This experiment reveals a rich absorption spectrum which contains a wealth of information about the physical conditions of diffuse gas around quasars. Hydrodynamical simulations of the massive dark matter halos which host luminous quasars under predict the amount of cool gas observed in quasar environs by a large factor, challenging our understanding of how massive galaxies form. I will also discuss a very sensitive search for Ly-alpha emission from the same gas which we study in absorption.
Studies in medium energy physics
Green, A.; Hoffmann, G.W.; McDonough, J.; Purcell, M.J.; Ray, R.L.; Read, D.E.; Worn, S.D.
1991-12-01
This document constitutes the (1991--1992) technical progress report and continuation proposal for the ongoing medium energy nuclear physics research program supported by the US Department of Energy through special Research Grant DE-FG05-88ER40444. The experiments discussed are conducted at the Los Alamos National Laboratory's (LANL) Clinton P. Anderson Meson Physics Facility (LAMPF) and the Alternating Gradient Synchrotron (AGS) facility of the Brookhaven National Laboratory (BNL). The overall motivation for the work discussed in this document is driven by three main objectives: (1) provide hadron-nucleon and hadron-nucleus scattering data which serve to facilitate the study of effective two-body interactions, test (and possibly determine) nuclear structure, and help study reaction mechanisms and dynamics; (2) provide unique, first-of-a-kind exploratory'' hadron-nucleus scattering data in the hope that such data will lead to discovery of new phenomena and new physics; and (3) perform precision tests of fundamental interactions, such as rare decay searches, whose observation would imply fundamental new physics.
BOOK REVIEW: Nonlinear Magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Shafranov, V.
1998-08-01
Nonlinear magnetohydrodynamics by Dieter Biskamp is a thorough introduction to the physics of the most impressive non-linear phenomena that occur in conducting magnetoplasmas. The basic systems, in which non-trivial dynamic processes are observed, accompanied by changes of geometry of the magnetic field and the effects of energy transformation (magnetic energy into kinetic energy or the opposite effect in magnetic dynamos), are the plasma magnetic confinement systems for nuclear fusion and space plasmas, mainly the solar plasma. A significant number of the examples of the dynamic processes considered are taken from laboratory plasmas, for which an experimental check of the theory is possible. Therefore, though the book is intended for researchers and students interested in both laboratory, including nuclear fusion, and astrophysical plasmas, it is most probably closer to the first category of reader. In the Introduction the author notes that unlike the hydrodynamics of non-conducting fluids, where the phenomena caused by rapid fluid motions are the most interesting, for plasmas in a strong magnetic field the quasi-static configurations inside which the local dynamic processes occur are often the most important. Therefore, the reader will also find in this book rather traditional material on the theory of plasma equilibrium and stability in magnetic fields. In addition, it is notable that, as opposed to a linear theory, the non-linear theory, as a rule, cannot give quite definite explanations or predictions of phenomena, and consequently there are in the book many results obtained by consideration of numerical models with the use of supercomputers. The treatment of non-linear dynamics is preceded by Chapters 2 to 4, in which the basics of MHD theory are presented with an emphasis on the role of integral invariants of the magnetic helicity type, a derivation of the reduced MHD equations is given, together with examples of the exact solutions of the equilibrium
Numerical model of heat transfer in three phases of the poroelastic medium
NASA Astrophysics Data System (ADS)
Uciechowska-Grakowicz, Anna; Strzelecki, Tomasz
2016-06-01
In this paper, the results of numerical analysis of the thermal consolidation of a two phase medium, under the assumption of independent heat transfer in fluid and the solid phase of the medium, are presented. Three cases of pore fluid were considered: liquid, represented by water, and gas, represented by air and carbon dioxide. The mathematical model was derived from irreversible thermodynamics, with the assumption of a constant heat transfer between the phases. In the case of the accepted geometry of the classical dimensions of the soil sample and boundary conditions, the process leads to equalization of temperatures of the skeleton on the pore fluid. Heat transfer is associated with the fluid flow in the pores of the medium. In the case of gas as the pore fluid, a non-linear mathematical model of gas filtration through the pores of the medium was accepted. For the computing process, relationships between viscosity or density and temperature proposed by other authors were taken into account. Despite accepting mechanical constants of the solid phase that do not depend on temperature, the obtained model is nonlinear and develops the classical Biot-Darcy model.
Additional waves in the graphene layered medium.
Chern, Ruey-Lin; Han, Dezhuan; Zhang, Z Q; Chan, C T
2014-12-29
We investigate the features of additional waves that arise in the graphene layered medium, within the framework of nonlocal effective medium model. The additional wave is manifest on the biquadratic dispersion relation of the medium and represents as a distinctive nonlocal character at long wavelength. In particular, the reflection and transmission coefficients for the nonlocal medium are underdetermined by Maxwell's boundary conditions. An additional boundary condition based on modal expansions is proposed to derive the generalized Fresnel equations, based on which the additional wave in the graphene layered medium is determined. The additional wave tends to be significant near the effective plasma frequency, near which the graphene plasmons are excited inside the medium. PMID:25607138
Nonlinear ion-acoustic structures in dusty plasma with superthermal electrons and positrons
El-Tantawy, S. A.; El-Bedwehy, N. A.; Moslem, W. M.
2011-05-15
Nonlinear ion-acoustic structures are investigated in an unmagnetized, four-component plasma consisting of warm ions, superthermal electrons and positrons, as well as stationary charged dust impurities. The basic set of fluid equations is reduced to modified Korteweg-de Vries equation. The latter admits both solitary waves and double layers solutions. Numerical calculations indicate that these nonlinear structures cannot exist for all physical parameters. Therefore, the existence regions for both solitary and double layers excitations have been defined precisely. Furthermore, the effects of temperature ratios of ions-to-electrons and electrons-to-positrons, positrons and dust concentrations, as well as superthermal parameters on the profiles of the nonlinear structures are investigated. Also, the acceleration and deceleration of plasma species have been highlight. It is emphasized that the present investigation may be helpful in better understanding of nonlinear structures which propagate in astrophysical environments, such as in interstellar medium.
Theoretical analysis on nonlinear vibration of fluid flow in single-walled carbon nanotube
NASA Astrophysics Data System (ADS)
Valipour, P.; Ghasemi, S. E.; Khosravani, Mohammad Reza; Ganji, D. D.
2016-09-01
In this study, the concept of nonlocal continuum theory is used to characterize the nonlinear vibration of an embedded single-walled carbon nanotube. The Pasternak-type model is employed to simulate the interaction of the SWNTs. The parameterized perturbation method is used to solve the corresponding nonlinear differential equation. The effects of the vibration amplitude, flow velocity, nonlocal parameter, and stiffness of the medium on the nonlinear frequency variation are presented. The result shows that by increasing the Winkler constant, the nonlinear frequency decreases, especially for low vibration amplitudes. In addition, it is resulted that influence of the nonlocal parameter is greater at higher flow velocities in comparison with lower flow velocities.
The syncytial Drosophila embryo as a mechanically excitable medium.
Idema, Timon; Dubuis, Julien O; Kang, Louis; Manning, M Lisa; Nelson, Philip C; Lubensky, Tom C; Liu, Andrea J
2013-01-01
Mitosis in the early syncytial Drosophila embryo is highly correlated in space and time, as manifested in mitotic wavefronts that propagate across the embryo. In this paper we investigate the idea that the embryo can be considered a mechanically-excitable medium, and that mitotic wavefronts can be understood as nonlinear wavefronts that propagate through this medium. We study the wavefronts via both image analysis of confocal microscopy videos and theoretical models. We find that the mitotic waves travel across the embryo at a well-defined speed that decreases with replication cycle. We find two markers of the wavefront in each cycle, corresponding to the onsets of metaphase and anaphase. Each of these onsets is followed by displacements of the nuclei that obey the same wavefront pattern. To understand the mitotic wavefronts theoretically we analyze wavefront propagation in excitable media. We study two classes of models, one with biochemical signaling and one with mechanical signaling. We find that the dependence of wavefront speed on cycle number is most naturally explained by mechanical signaling, and that the entire process suggests a scenario in which biochemical and mechanical signaling are coupled.
COMPARISON OF MONTE CARLO METHODS FOR NONLINEAR RADIATION TRANSPORT
W. R. MARTIN; F. B. BROWN
2001-03-01
Five Monte Carlo methods for solving the nonlinear thermal radiation transport equations are compared. The methods include the well-known Implicit Monte Carlo method (IMC) developed by Fleck and Cummings, an alternative to IMC developed by Carter and Forest, an ''exact'' method recently developed by Ahrens and Larsen, and two methods recently proposed by Martin and Brown. The five Monte Carlo methods are developed and applied to the radiation transport equation in a medium assuming local thermodynamic equilibrium. Conservation of energy is derived and used to define appropriate material energy update equations for each of the methods. Details of the Monte Carlo implementation are presented, both for the random walk simulation and the material energy update. Simulation results for all five methods are obtained for two infinite medium test problems and a 1-D test problem, all of which have analytical solutions. Conclusions regarding the relative merits of the various schemes are presented.
The performance of dense medium processes
Horsfall, D.W.
1993-12-31
Dense medium washing in baths and cyclones is widely carried out in South Africa. The paper shows the reason for the preferred use of dense medium processes rather than gravity concentrators such as jigs. The factors leading to efficient separation in baths are listed and an indication given of the extent to which these factors may be controlled and embodied in the deployment of baths and dense medium cyclones in the planning stages of a plant.
[Nonlinear magnetohydrodynamics]. Final report
Montgomery, D.C.
1998-11-01
This is a final report on the research activities carried out under the above grant at Dartmouth. During the period considered, the grant was identified as being for nonlinear magnetohydrodynamics, considered as the most tractable theoretical framework in which the plasma problems associated with magnetic confinement of fusion plasmas could be studied. During the first part of the grant`s lifetime, the author was associated with Los Alamos National Laboratory as a consultant and the work was motivated by the reversed-field pinch. Later, when that program was killed at Los Alamos, the problems became ones that could be motivated by their relation to tokamaks. Throughout the work, the interest was always on questions that were as fundamental as possible, compatible with those motivations. The intent was always to contribute to plasma physics as a science, as well as to the understanding of mission-oriented confined fusion plasmas. Twelve Ph.D. theses were supervised during this period and a comparable number of postdoctoral research associates were temporarily supported. Many of these have gone on to distinguished careers, though few have done so in the context of the controlled fusion program. Their work was a combination of theory and numerical computation, in gradually less and less idealized settings, moving from rectangular periodic boundary conditions in two dimensions, through periodic straight cylinders and eventually, before the grant was withdrawn, to toroids, with a gradually more prominent role for electrical and mechanical boundary conditions. The author never had access to a situation where he could initiate experiments and relate directly to the laboratory data he wanted. Computers were the laboratory. Most of the work was reported in referred publications in the open literature, copies of which were transmitted one by one to DOE at the time they appeared. The Appendix to this report is a bibliography of published work which was carried out under the
Chemically defined medium and Caenorhabditis elegans
NASA Technical Reports Server (NTRS)
Szewczyk, Nathaniel J.; Kozak, Elena; Conley, Catharine A.
2003-01-01
BACKGROUND: C. elegans has been established as a powerful genetic system. Use of a chemically defined medium (C. elegans Maintenance Medium (CeMM)) now allows standardization and systematic manipulation of the nutrients that animals receive. Liquid cultivation allows automated culturing and experimentation and should be of use in large-scale growth and screening of animals. RESULTS: We find that CeMM is versatile and culturing is simple. CeMM can be used in a solid or liquid state, it can be stored unused for at least a year, unattended actively growing cultures may be maintained longer than with standard techniques, and standard C. elegans protocols work well with animals grown in defined medium. We also find that there are caveats to using defined medium. Animals in defined medium grow more slowly than on standard medium, appear to display adaptation to the defined medium, and display altered growth rates as they change the composition of the defined medium. CONCLUSIONS: As was suggested with the introduction of C. elegans as a potential genetic system, use of defined medium with C. elegans should prove a powerful tool.
Tian, Si-Cong Tong, Cun-Zhu Zhang, Jin-Long; Shan, Xiao-Nan; Fu, Xi-Hong; Zeng, Yu-Gang; Qin, Li; Ning, Yong-Qiang; Wan, Ren-Gang
2015-06-15
The optical bistability of a triangular quantum dot molecules embedded inside a unidirectional ring cavity is studied. The type, the threshold and the hysteresis loop of the optical bistability curves can be modified by the tunneling parameters, as well as the probe laser field. The linear and nonlinear susceptibilities of the medium are also studied to interpret the corresponding results. The physical interpretation is that the tunneling can induce the quantum interference, which modifies the linear and the nonlinear response of the medium. As a consequence, the characteristics of the optical bistability are changed. The scheme proposed here can be utilized for optimizing and controlling the optical switching process.
Spheroidizing of medium carbon steels
NASA Astrophysics Data System (ADS)
O'Brien, James Michael
2000-11-01
An investigation has been made of spheroidization of medium carbon steels used in the bolt industry. Two process cycles were considered. One was the intercritical cycle, widely used in industry, in which the steel was heated above the A1 temperature for approximately 2 hours and then cooled to 688°C (1270°F) and held for various periods. The other was a subcritical cycle that involved heating to 704°C (1300°F) for various times. Wire samples were 0.4-in. diameter AISI 1541, considered high in manganese and difficult to spheroidize. Although AISI 4037 is considered easier to spheroidize, this alloy was also tested due to its extensive industrial use. It was found that the intercritical cycle produced a somewhat faster drop in hardness. However, one hour of the subcritical cycle yielded greater ductility than 32 hours of the intercritical process, as measured by tensile tests. Similar ductility results were achieved using a new flare test. The level of spheroidization was defined in this study to be the percentage of carbide particles with aspect ratios less than 3. The subcritical cycle produced the same level of spheroidization in 1/2 hour as that reached by the intercritical cycle in 32 hours. Faster spheroidization of cementite plates in the subcritical process appears to be due to the fine pearlite generated by the current practice of rapid cooling off the hot mill. This advantage is lost in the intercritical process because the original pearlite is dissolved above the A1 temperature.
Dagrau, Franck; Rénier, Mathieu; Marchiano, Régis; Coulouvrat, François
2011-07-01
Numerical simulation of nonlinear acoustics and shock waves in a weakly heterogeneous and lossless medium is considered. The wave equation is formulated so as to separate homogeneous diffraction, heterogeneous effects, and nonlinearities. A numerical method called heterogeneous one-way approximation for resolution of diffraction (HOWARD) is developed, that solves the homogeneous part of the equation in the spectral domain (both in time and space) through a one-way approximation neglecting backscattering. A second-order parabolic approximation is performed but only on the small, heterogeneous part. So the resulting equation is more precise than the usual standard or wide-angle parabolic approximation. It has the same dispersion equation as the exact wave equation for all forward propagating waves, including evanescent waves. Finally, nonlinear terms are treated through an analytical, shock-fitting method. Several validation tests are performed through comparisons with analytical solutions in the linear case and outputs of the standard or wide-angle parabolic approximation in the nonlinear case. Numerical convergence tests and physical analysis are finally performed in the fully heterogeneous and nonlinear case of shock wave focusing through an acoustical lens.
Synthetic Ground Motions for Engineering Applications and the Role of Nonlinear Site Response
NASA Astrophysics Data System (ADS)
Assimaki, D.; Li, W.
2008-12-01
Quantitative criteria are being developed for the efficient integration of site response models in broadband ground motion simulations. For this purpose, downhole array observations and broadband synthetics are combined, and the sensitivity of ground motion and nonlinear structural performance attributed to bias and uncertainty in nonlinear site response models is investigated. Results from medium-to-soft soil sites in Southern California are here presented, subjected to synthetic ground motions estimated for finite-source dynamic rupture scenarios of weak, medium and large magnitude events (M = 3.5~7.5), on a surface station grid of epicentral distances 2km~75km. For each site, elastic and nonlinear site response analyses are evaluated using multiple soil models, and the modeling ground motion variability is estimated by means of the COV (coefficient of variation) of site amplification. For each soil model, the parametric uncertainty of ground motion predictions is next estimated by systematically randomizing selected model parameters. Quantitative measures are developed that may describe the site properties and ground motion characteristics where the nonlinear models show large prediction COV, namely where incremental nonlinear analyses significantly deviate from empirical methodologies. Finally, the role of nonlinear soil response in physics-based seismic hazard predictions is illustrated by subjecting a series of inelastic SDOF (single-degree-of-freedom) oscillators to the ensemble of ground motion predictions, and evaluating the bias and uncertainty introduced as a result, in the structural response predictions. It is shown that the bias and uncertainty introduced in structural performance analyses when nonlinear site effects are not accounted for, strongly correlates with the deviation observed when the assessment of structural response is evaluated using synthetic seismograms from existing methodologies as opposed to real motions. It is concluded that soil
Axisymmetric flows from fluid injection into a confined porous medium
NASA Astrophysics Data System (ADS)
Guo, Bo; Zheng, Zhong; Celia, Michael A.; Stone, Howard A.
2016-02-01
We study the axisymmetric flows generated from fluid injection into a horizontal confined porous medium that is originally saturated with another fluid of different density and viscosity. Neglecting the effects of surface tension and fluid mixing, we use the lubrication approximation to obtain a nonlinear advection-diffusion equation that describes the time evolution of the sharp fluid-fluid interface. The flow behaviors are controlled by two dimensionless groups: M, the viscosity ratio of displaced fluid relative to injected fluid, and Γ, which measures the relative importance of buoyancy and fluid injection. For this axisymmetric geometry, the similarity solution involving R2/T (where R is the dimensionless radial coordinate and T is the dimensionless time) is an exact solution to the nonlinear governing equation for all times. Four analytical expressions are identified as asymptotic approximations (two of which are new solutions): (i) injection-driven flow with the injected fluid being more viscous than the displaced fluid (Γ ≪ 1 and M < 1) where we identify a self-similar solution that indicates a parabolic interface shape; (ii) injection-driven flow with injected and displaced fluids of equal viscosity (Γ ≪ 1 and M = 1), where we find a self-similar solution that predicts a distinct parabolic interface shape; (iii) injection-driven flow with a less viscous injected fluid (Γ ≪ 1 and M > 1) for which there is a rarefaction wave solution, assuming that the Saffman-Taylor instability does not occur at the reservoir scale; and (iv) buoyancy-driven flow (Γ ≫ 1) for which there is a well-known self-similar solution corresponding to gravity currents in an unconfined porous medium [S. Lyle et al. "Axisymmetric gravity currents in a porous medium," J. Fluid Mech. 543, 293-302 (2005)]. The various axisymmetric flows are summarized in a Γ-M regime diagram with five distinct dynamic behaviors including the four asymptotic regimes and an intermediate regime
Vu, Cung Khac; Nihei, Kurt Toshimi; Johnson, Paul A.; Guyer, Robert A.; Ten Cate, James A.; Le Bas, Pierre-Yves; Larmat, Carene S.
2016-06-07
A system and method of characterizing properties of a medium from a non-linear interaction are include generating, by first and second acoustic sources disposed on a surface of the medium on a first line, first and second acoustic waves. The first and second acoustic sources are controllable such that trajectories of the first and second acoustic waves intersect in a mixing zone within the medium. The method further includes receiving, by a receiver positioned in a plane containing the first and second acoustic sources, a third acoustic wave generated by a non-linear mixing process from the first and second acoustic waves in the mixing zone; and creating a first two-dimensional image of non-linear properties or a first ratio of compressional velocity and shear velocity, or both, of the medium in a first plane generally perpendicular to the surface and containing the first line, based on the received third acoustic wave.
Nonlinear analysis of pupillary dynamics.
Onorati, Francesco; Mainardi, Luca Tommaso; Sirca, Fabiola; Russo, Vincenzo; Barbieri, Riccardo
2016-02-01
Pupil size reflects autonomic response to different environmental and behavioral stimuli, and its dynamics have been linked to other autonomic correlates such as cardiac and respiratory rhythms. The aim of this study is to assess the nonlinear characteristics of pupil size of 25 normal subjects who participated in a psychophysiological experimental protocol with four experimental conditions, namely “baseline”, “anger”, “joy”, and “sadness”. Nonlinear measures, such as sample entropy, correlation dimension, and largest Lyapunov exponent, were computed on reconstructed signals of spontaneous fluctuations of pupil dilation. Nonparametric statistical tests were performed on surrogate data to verify that the nonlinear measures are an intrinsic characteristic of the signals. We then developed and applied a piecewise linear regression model to detrended fluctuation analysis (DFA). Two joinpoints and three scaling intervals were identified: slope α0, at slow time scales, represents a persistent nonstationary long-range correlation, whereas α1 and α2, at middle and fast time scales, respectively, represent long-range power-law correlations, similarly to DFA applied to heart rate variability signals. Of the computed complexity measures, α0 showed statistically significant differences among experimental conditions (p<0.001). Our results suggest that (a) pupil size at constant light condition is characterized by nonlinear dynamics, (b) three well-defined and distinct long-memory processes exist at different time scales, and (c) autonomic stimulation is partially reflected in nonlinear dynamics. PMID:26351899
Nonlinear problems in flight dynamics
NASA Technical Reports Server (NTRS)
Chapman, G. T.; Tobak, M.
1984-01-01
A comprehensive framework is proposed for the description and analysis of nonlinear problems in flight dynamics. Emphasis is placed on the aerodynamic component as the major source of nonlinearities in the flight dynamic system. Four aerodynamic flows are examined to illustrate the richness and regularity of the flow structures and the nature of the flow structures and the nature of the resulting nonlinear aerodynamic forces and moments. A framework to facilitate the study of the aerodynamic system is proposed having parallel observational and mathematical components. The observational component, structure is described in the language of topology. Changes in flow structure are described via bifurcation theory. Chaos or turbulence is related to the analogous chaotic behavior of nonlinear dynamical systems characterized by the existence of strange attractors having fractal dimensionality. Scales of the flow are considered in the light of ideas from group theory. Several one and two degree of freedom dynamical systems with various mathematical models of the nonlinear aerodynamic forces and moments are examined to illustrate the resulting types of dynamical behavior. The mathematical ideas that proved useful in the description of fluid flows are shown to be similarly useful in the description of flight dynamic behavior.
Nonlinear variations in axisymmetric accretion
NASA Astrophysics Data System (ADS)
Bose, Soumyajit; Sengupta, Anindya; Ray, Arnab K.
2014-05-01
We subject the stationary solutions of inviscid and axially symmetric rotational accretion to a time-dependent radial perturbation, which includes nonlinearity to any arbitrary order. Regardless of the order of nonlinearity, the equation of the perturbation bears a form that is similar to the metric equation of an analogue acoustic black hole. We bring out the time dependence of the perturbation in the form of a Liénard system by requiring the perturbation to be a standing wave under the second order of nonlinearity. We perform a dynamical systems analysis of the Liénard system to reveal a saddle point in real time, whose implication is that instabilities will develop in the accreting system when the perturbation is extended into the nonlinear regime. We also model the perturbation as a high-frequency traveling wave and carry out a Wentzel-Kramers-Brillouin analysis, treating nonlinearity iteratively as a very feeble effect. Under this approach, both the amplitude and the energy flux of the perturbation exhibit growth, with the acoustic horizon segregating the regions of stability and instability.
Measurement of the Acoustic Nonlinearity Parameter for Biological Media.
NASA Astrophysics Data System (ADS)
Cobb, Wesley Nelson
In vitro measurements of the acoustic nonlinearity parameter are presented for several biological media. With these measurements it is possible to predict the distortion of a finite amplitude wave in biological tissues of current diagnostic and research interest. The measurement method is based on the finite amplitude distortion of a sine wave that is emmitted by a piston source. The growth of the second harmonic component of this wave is measured by a piston receiver which is coaxial with and has the same size as the source. The experimental measurements and theory are compared in order to determine the nonlinearity parameter. The density, sound speed, and attenuation for the medium are determined in order to make this comparison. The theory developed for this study accounts for the influence of both diffraction and attenuation on the experimental measurements. The effects of dispersion, tissue inhomogeneity and gas bubbles within the excised tissues are studied. To test the measurement method, experimental results are compared with established values for the nonlinearity parameter of distilled water, ethylene glycol and glycerol. The agreement between these values suggests that the measurement uncertainty is (+OR-) 5% for liquids and (+OR-) 10% for solid tissues. Measurements are presented for dog blood and bovine serum albumen as a function of concentration. The nonlinearity parameters for liver, kidney and spleen are reported for both human and canine tissues. The values for the fresh tissues displayed little variation (6.8 to 7.8). Measurements for fixed, normal and cirrhotic tissues indicated that the nonlinearity parameter does not depend strongly on pathology. However, the values for fixed tissues were somewhat higher than those of the fresh tissues.
Nonlinear dynamics of drift structures in a magnetized dissipative plasma
NASA Astrophysics Data System (ADS)
Aburjania, G. D.; Rogava, D. L.; Kharshiladze, O. A.
2011-06-01
A study is made of the nonlinear dynamics of solitary vortex structures in an inhomogeneous magnetized dissipative plasma. A nonlinear transport equation for long-wavelength drift wave structures is derived with allowance for the nonuniformity of the plasma density and temperature equilibria, as well as the magnetic and collisional viscosity of the medium and its friction. The dynamic equation describes two types of nonlinearity: scalar (due to the temperature inhomogeneity) and vector (due to the convectively polarized motion of the particles of the medium). The equation is fourth order in the spatial derivatives, in contrast to the second-order Hasegawa-Mima equations. An analytic steady solution to the nonlinear equation is obtained that describes a new type of solitary dipole vortex. The nonlinear dynamic equation is integrated numerically. A new algorithm and a new finite difference scheme for solving the equation are proposed, and it is proved that the solution so obtained is unique. The equation is used to investigate how the initially steady dipole vortex constructed here behaves unsteadily under the action of the factors just mentioned. Numerical simulations revealed that the role of the vector nonlinearity is twofold: it helps the dispersion or the scalar nonlinearity (depending on their magnitude) to ensure the mutual equilibrium and, thereby, promote self-organization of the vortical structures. It is shown that dispersion breaks the initial dipole vortex into a set of tightly packed, smaller scale, less intense monopole vortices-alternating cyclones and anticyclones. When the dispersion of the evolving initial dipole vortex is weak, the scalar nonlinearity symmetrically breaks a cyclone-anticyclone pair into a cyclone and an anticyclone, which are independent of one another and have essentially the same intensity, shape, and size. The stronger the dispersion, the more anisotropic the process whereby the structures break: the anticyclone is more intense
Nonlinear dynamics of drift structures in a magnetized dissipative plasma
Aburjania, G. D.; Rogava, D. L.; Kharshiladze, O. A.
2011-06-15
A study is made of the nonlinear dynamics of solitary vortex structures in an inhomogeneous magnetized dissipative plasma. A nonlinear transport equation for long-wavelength drift wave structures is derived with allowance for the nonuniformity of the plasma density and temperature equilibria, as well as the magnetic and collisional viscosity of the medium and its friction. The dynamic equation describes two types of nonlinearity: scalar (due to the temperature inhomogeneity) and vector (due to the convectively polarized motion of the particles of the medium). The equation is fourth order in the spatial derivatives, in contrast to the second-order Hasegawa-Mima equations. An analytic steady solution to the nonlinear equation is obtained that describes a new type of solitary dipole vortex. The nonlinear dynamic equation is integrated numerically. A new algorithm and a new finite difference scheme for solving the equation are proposed, and it is proved that the solution so obtained is unique. The equation is used to investigate how the initially steady dipole vortex constructed here behaves unsteadily under the action of the factors just mentioned. Numerical simulations revealed that the role of the vector nonlinearity is twofold: it helps the dispersion or the scalar nonlinearity (depending on their magnitude) to ensure the mutual equilibrium and, thereby, promote self-organization of the vortical structures. It is shown that dispersion breaks the initial dipole vortex into a set of tightly packed, smaller scale, less intense monopole vortices-alternating cyclones and anticyclones. When the dispersion of the evolving initial dipole vortex is weak, the scalar nonlinearity symmetrically breaks a cyclone-anticyclone pair into a cyclone and an anticyclone, which are independent of one another and have essentially the same intensity, shape, and size. The stronger the dispersion, the more anisotropic the process whereby the structures break: the anticyclone is more intense
A high-order numerical method for the nonlinear Helmholtz equation in multidimensional layered media
NASA Astrophysics Data System (ADS)
Baruch, G.; Fibich, G.; Tsynkov, S.
2009-06-01
We present a novel computational methodology for solving the scalar nonlinear Helmholtz equation (NLH) that governs the propagation of laser light in Kerr dielectrics. The methodology addresses two well-known challenges in nonlinear optics: Singular behavior of solutions when the scattering in the medium is assumed predominantly forward (paraxial regime), and the presence of discontinuities in the optical properties of the medium. Specifically, we consider a slab of nonlinear material which may be grated in the direction of propagation and which is immersed in a linear medium as a whole. The key components of the methodology are a semi-compact high-order finite-difference scheme that maintains accuracy across the discontinuities and enables sub-wavelength resolution on large domains at a tolerable cost, a nonlocal two-way artificial boundary condition (ABC) that simultaneously facilitates the reflectionless propagation of the outgoing waves and forward propagation of the given incoming waves, and a nonlinear solver based on Newton's method. The proposed methodology combines and substantially extends the capabilities of our previous techniques built for 1D and for multi-D. It facilitates a direct numerical study of nonparaxial propagation and goes well beyond the approaches in the literature based on the "augmented" paraxial models. In particular, it provides the first ever evidence that the singularity of the solution indeed disappears in the scalar NLH model that includes the nonparaxial effects. It also enables simulation of the wavelength-width spatial solitons, as well as of the counter-propagating solitons.
Dai, Chao-Qing; Wang, Yan
2014-01-01
The spatiotemporal nonlinear Schrödinger equation with power-law nonlinearity in -symmetric potentials is investigated, and two families of analytical three-dimensional spatiotemporal structure solutions are obtained. The stability of these solutions is tested by the linear stability analysis and the direct numerical simulation. Results indicate that solutions are stable below some thresholds for the imaginary part of -symmetric potentials in the self-focusing medium, while they are always unstable for all parameters in the self-defocusing medium. Moreover, some dynamical properties of these solutions are discussed, such as the phase switch, power and transverse power-flow density. The span of phase switch gradually enlarges with the decrease of the competing parameter k in -symmetric potentials. The power and power-flow density are all positive, which implies that the power flow and exchange from the gain toward the loss domains in the cell. PMID:24983624
Temperature Distribution in a Uniformly Moving Medium
ERIC Educational Resources Information Center
Mitchell, Joseph D.; Petrov, Nikola P.
2009-01-01
We apply several physical ideas to determine the steady temperature distribution in a medium moving with uniform velocity between two infinite parallel plates. We compute it in the coordinate frame moving with the medium by integration over the "past" to account for the influence of an infinite set of instantaneous point sources of heat in past…
49 CFR 236.811 - Speed, medium.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 49 Transportation 4 2012-10-01 2012-10-01 false Speed, medium. 236.811 Section 236.811 Transportation Other Regulations Relating to Transportation (Continued) FEDERAL RAILROAD ADMINISTRATION... Speed, medium. A speed not exceeding 40 miles per hour....
49 CFR 236.811 - Speed, medium.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 49 Transportation 4 2010-10-01 2010-10-01 false Speed, medium. 236.811 Section 236.811 Transportation Other Regulations Relating to Transportation (Continued) FEDERAL RAILROAD ADMINISTRATION... Speed, medium. A speed not exceeding 40 miles per hour....
49 CFR 236.811 - Speed, medium.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 49 Transportation 4 2013-10-01 2013-10-01 false Speed, medium. 236.811 Section 236.811 Transportation Other Regulations Relating to Transportation (Continued) FEDERAL RAILROAD ADMINISTRATION... Speed, medium. A speed not exceeding 40 miles per hour....
49 CFR 236.811 - Speed, medium.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 49 Transportation 4 2011-10-01 2011-10-01 false Speed, medium. 236.811 Section 236.811 Transportation Other Regulations Relating to Transportation (Continued) FEDERAL RAILROAD ADMINISTRATION... Speed, medium. A speed not exceeding 40 miles per hour....
49 CFR 236.811 - Speed, medium.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 49 Transportation 4 2014-10-01 2014-10-01 false Speed, medium. 236.811 Section 236.811 Transportation Other Regulations Relating to Transportation (Continued) FEDERAL RAILROAD ADMINISTRATION... Speed, medium. A speed not exceeding 40 miles per hour....
Generalized electromagnetic fields in a chiral medium
NASA Astrophysics Data System (ADS)
Bisht, P. S.; Singh, Jivan; Negi, O. P. S.
2007-09-01
The time-dependent Dirac-Maxwell's equations in the presence of electric and magnetic sources are reformulated in a chiral medium, and the solutions for the classical problem are obtained in a unique, simple and consistent manner. The quaternion reformulation of generalized electromagnetic fields in the chiral medium has also been discussed in a compact, simple and consistent manner.
NASA Astrophysics Data System (ADS)
Smirnov, Yu. G.; Valovik, D. V.
2016-10-01
The paper focuses on a transmission eigenvalue problem for Maxwell's equations with cubic nonlinearity that describes the propagation of transverse magnetic waves along the boundaries of a dielectric layer filled with nonlinear (Kerr) medium. Using an original approach, it is proved that even for small values of the nonlinearity coefficient, the nonlinear problem has infinitely many nonperturbative solutions (eigenvalues and eigenwaves), whereas the corresponding linear problem always has a finite number of solutions. This fact implies the theoretical existence of a novel type of eigenwaves that do not reduce to the linear ones in the limit in which the nonlinear coefficient reduces to zero. Asymptotic distribution of the eigenvalues is found, periodicity of the eigenfunctions is proved, the exact formula for the period is found, and the zeros of the eigenfunctions are determined.
Nonlinear acoustics - History and outlook
NASA Astrophysics Data System (ADS)
Rott, N.
1980-08-01
A historical review of the development of nonlinear acoustics before the epoch beginning with Riemann is presented followed by a review of the more recent developments of the last 20 years, including a cinematical view of nonlinear acoustic waves. The review emphasizes the works of Poisson and his equations and solutions of particle and wave velocity as well as Stoke's theory of sound. Attention is given to the developments of the last two decades through an examination of Lagrange and Chester problems, such as the transition of Euler coordinates into Lagrange coordinates and equations. The nonlinear theory of resonance is discussed by describing a closed tube resonance problem where periodic excitation through a piston characterizes wave movements.
Nonlinear Single Spin Spectrum Analyzer
NASA Astrophysics Data System (ADS)
Kotler, Shlomi; Akerman, Nitzan; Glickman, Yinnon; Ozeri, Roee
2014-03-01
Qubits have been used as linear spectrum analyzers of their environments, through the use of decoherence spectroscopy. Here we solve the problem of nonlinear spectral analysis, required for discrete noise induced by a strongly coupled environment. Our nonperturbative analytical model shows a nonlinear signal dependence on noise power, resulting in a spectral resolution beyond the Fourier limit as well as frequency mixing. We develop a noise characterization scheme adapted to this nonlinearity. We then apply it using a single trapped ion as a sensitive probe of strong, non-Gaussian, discrete magnetic field noise. Finally, we experimentally compared the performance of equidistant vs Uhrig modulation schemes for spectral analysis. Phys. Rev. Lett. 110, 110503 (2013). Synopsis at http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.110.110503 Current position: NIST, Boulder, CO.
Nonlinear photoacoustic spectroscopy of hemoglobin
Danielli, Amos; Maslov, Konstantin; Favazza, Christopher P.; Xia, Jun; Wang, Lihong V.
2015-05-18
As light intensity increases in photoacoustic imaging, the saturation of optical absorption and the temperature dependence of the thermal expansion coefficient result in a measurable nonlinear dependence of the photoacoustic (PA) signal on the excitation pulse fluence. Here, under controlled conditions, we investigate the intensity-dependent photoacoustic signals from oxygenated and deoxygenated hemoglobin at varied optical wavelengths and molecular concentrations. The wavelength and concentration dependencies of the nonlinear PA spectrum are found to be significantly greater in oxygenated hemoglobin than in deoxygenated hemoglobin. These effects are further influenced by the hemoglobin concentration. These nonlinear phenomena provide insights into applications of photoacoustics, such as measurements of average inter-molecular distances on a nm scale or with a tuned selection of wavelengths, a more accurate quantitative PA tomography.
Neoclassical Transport Including Collisional Nonlinearity
Candy, J.; Belli, E. A.
2011-06-10
In the standard {delta}f theory of neoclassical transport, the zeroth-order (Maxwellian) solution is obtained analytically via the solution of a nonlinear equation. The first-order correction {delta}f is subsequently computed as the solution of a linear, inhomogeneous equation that includes the linearized Fokker-Planck collision operator. This equation admits analytic solutions only in extreme asymptotic limits (banana, plateau, Pfirsch-Schlueter), and so must be solved numerically for realistic plasma parameters. Recently, numerical codes have appeared which attempt to compute the total distribution f more accurately than in the standard ordering by retaining some nonlinear terms related to finite-orbit width, while simultaneously reusing some form of the linearized collision operator. In this work we show that higher-order corrections to the distribution function may be unphysical if collisional nonlinearities are ignored.
Influence of loading pulse duration on dynamic load transfer in a simulated granular medium
NASA Astrophysics Data System (ADS)
Shukla, A.; Sadd, M. H.; Xu, Y.; Tai, Q. M.
1993-11-01
AN EXPERIMENTAL and numerical investigation was conducted to study the dynamic response of granular media when subjected to impact loadings with different periods or wavelengths. The granular medium was simulated by a one-dimensional assembly of circular disks arranged in a straight single chain. In the experimental study, the dynamic loading was produced using projectile impact from a gas gun onto one end of the granular assembly, and the measured wave signal was collected using strain gages. The numerical simulations were conducted using the distinct element method. It was found from the experiments and numerical simulations that input waves with a short period (τ ≈ 90 μs) will propagate in this granular medium with little waveform change under steady amplitude attenuation ; whereas longer waves (τ $̆200 μs) will propagate with significant waveform dispersion. For these longer wavelength signals, the smooth waveform will undergo separation into a series of short oscillatory signals, and this rearrangement of energy allows a portion of the transmitted signal to increase in amplitude during the initial phases of propagation. Thus the granular medium acts as a nonlinear wave guide, and local microstructure and contact nonlinearity will allow input signals of sufficiently long wavelength to excite resonant sub-units of the medium to produce this observed ringing separation. Following a modeling scheme originally proposed by NESTERENKO[J. Appl. Mech. Tech. Phys. 5,733 (1983)], a nonlinear wave equation model was developed which is related to soliton dynamics and leads to travelling wave solutions of specific wavelength found in our experimental and numerical studies.
Chirped solitary pulses for a nonic nonlinear Schrödinger equation on a continuous-wave background
NASA Astrophysics Data System (ADS)
Triki, Houria; Porsezian, K.; Choudhuri, Amitava; Dinda, P. Tchofo
2016-06-01
A class of derivative nonlinear Schrödinger equation with cubic-quintic-septic-nonic nonlinear terms describing the propagation of ultrashort optical pulses through a nonlinear medium with higher-order Kerr responses is investigated. An intensity-dependent chirp ansatz is adopted for solving the two coupled amplitude-phase nonlinear equations of the propagating wave. We find that the dynamics of field amplitude in this system is governed by a first-order nonlinear ordinary differential equation with a tenth-degree nonlinear term. We demonstrate that this system allows the propagation of a very rich variety of solitary waves (kink, dark, bright, and gray solitary pulses) which do not coexist in the conventional nonlinear systems that have appeared so far in the literature. The stability of the solitary wave solution under some violation on the parametric conditions is investigated. Moreover, we show that, unlike conventional systems, the nonlinear Schrödinger equation considered here meets the special requirements for the propagation of a chirped solitary wave on a continuous-wave background, involving a balance among group velocity dispersion, self-steepening, and higher-order nonlinearities of different nature.
Chaotic behavior in nonlinear polarization dynamics
David, D.; Holm, D.D.; Tratnik, M.V. )
1989-01-01
We analyze the problem of two counterpropagating optical laser beams in a slightly nonlinear medium from the point of view of Hamiltonian systems; the one-beam subproblem is also investigated as a special case. We are interested in these systems as integrable dynamical systems which undergo chaotic behavior under various types of perturbations. The phase space for the two-beam problem is C{sup 2} {times} C{sup 2} when we restricted the the regime of travelling-wave solutions. We use the method of reduction for Hamiltonian systems invariant under one-parameter symmetry groups to demonstrate that the phase space reduces to the two-sphere S{sup 2} and is therefore completely integrable. The phase portraits of the system are classified and we also determine the bifurcations that modify these portraits; some new degenerate bifurcations are presented in this context. Finally, we introduce various physically relevant perturbations and use the Melnikov method to prove that horseshoe chaos and Arnold diffusion occur as consequences of these perturbations. 10 refs., 7 figs., 1 tab.
Evaluation of a wave-vector-frequency-domain method for nonlinear wave propagation
Jing, Yun; Tao, Molei; Clement, Greg T.
2011-01-01
A wave-vector-frequency-domain method is presented to describe one-directional forward or backward acoustic wave propagation in a nonlinear homogeneous medium. Starting from a frequency-domain representation of the second-order nonlinear acoustic wave equation, an implicit solution for the nonlinear term is proposed by employing the Green’s function. Its approximation, which is more suitable for numerical implementation, is used. An error study is carried out to test the efficiency of the model by comparing the results with the Fubini solution. It is shown that the error grows as the propagation distance and step-size increase. However, for the specific case tested, even at a step size as large as one wavelength, sufficient accuracy for plane-wave propagation is observed. A two-dimensional steered transducer problem is explored to verify the nonlinear acoustic field directional independence of the model. A three-dimensional single-element transducer problem is solved to verify the forward model by comparing it with an existing nonlinear wave propagation code. Finally, backward-projection behavior is examined. The sound field over a plane in an absorptive medium is backward projected to the source and compared with the initial field, where good agreement is observed. PMID:21302985
Generation of Nonlinear Vortex Precursors.
Chen, Yue-Yue; Feng, Xun-Li; Liu, Chengpu
2016-07-01
We numerically study the propagation of a few-cycle pulse carrying orbital angular momentum (OAM) through a dense atomic system. Nonlinear precursors consisting of high-order vortex harmonics are generated in the transmitted field due to carrier effects associated with ultrafast Bloch oscillation. The nonlinear precursors survive to propagation effects and are well separated with the main pulse, which provides a straightforward way to measure precursors. By virtue of carrying high-order OAM, the obtained vortex precursors as information carriers have potential applications in optical information and communication fields where controllable loss, large information-carrying capacity, and high speed communication are required.
Higher dimensional nonlinear massive gravity
NASA Astrophysics Data System (ADS)
Do, Tuan Q.
2016-05-01
Inspired by a recent ghost-free nonlinear massive gravity in four-dimensional spacetime, we study its higher dimensional scenarios. As a result, we are able to show the constantlike behavior of massive graviton terms for some well-known metrics such as the Friedmann-Lemaitre-Robertson-Walker, Bianchi type I, and Schwarzschild-Tangherlini (anti-) de Sitter metrics in a specific five-dimensional nonlinear massive gravity under an assumption that its fiducial metrics are compatible with physical ones. In addition, some simple cosmological solutions of the five-dimensional massive gravity are figured out consistently.
Prediction of nonlinear soil effects
Hartzell, S.; Bonilla, L.F.; Williams, R.A.
2004-01-01
Mathematical models of soil nonlinearity in common use and recently developed nonlinear codes compared to investigate the range of their predictions. We consider equivalent linear formulations with and without frequency-dependent moduli and damping ratios and nonlinear formulations for total and effective stress. Average velocity profiles to 150 m depth with midrange National Earthquake Hazards Reduction Program site classifications (B, BC, C, D, and E) in the top 30 m are used to compare the response of a wide range of site conditions from rock to soft soil. Nonlinear soil models are compared using the amplification spectrum, calculated as the ratio of surface ground motion to the input motion at the base of the velocity profile. Peak input motions from 0.1g to 0.9g are considered. For site class B, no significant differences exist between the models considered in this article. For site classes BC and C, differences are small at low input motions (0.1g to 0.2g), but become significant at higher input levels. For site classes D and E the overdamping of frequencies above about 4 Hz by the equivalent linear solution with frequency-independent parameters is apparent for the entire range of input motions considered. The equivalent linear formulation with frequency-dependent moduli and damping ratios under damps relative to the nonlinear models considered for site class C with larger input motions and most input levels for site classes D and E. At larger input motions the underdamping for site classes D and E is not as severe as the overdamping with the frequency-independent formulation, but there are still significant differences in the time domain. A nonlinear formulation is recommended for site classes D and E and for site classes BC and C with input motions greater than a few tenths of the acceleration of gravity. The type of nonlinear formulation to use is driven by considerations of the importance of water content and the availability of laboratory soils data. Our
Generation of Nonlinear Vortex Precursors.
Chen, Yue-Yue; Feng, Xun-Li; Liu, Chengpu
2016-07-01
We numerically study the propagation of a few-cycle pulse carrying orbital angular momentum (OAM) through a dense atomic system. Nonlinear precursors consisting of high-order vortex harmonics are generated in the transmitted field due to carrier effects associated with ultrafast Bloch oscillation. The nonlinear precursors survive to propagation effects and are well separated with the main pulse, which provides a straightforward way to measure precursors. By virtue of carrying high-order OAM, the obtained vortex precursors as information carriers have potential applications in optical information and communication fields where controllable loss, large information-carrying capacity, and high speed communication are required. PMID:27447507
Time series with tailored nonlinearities
NASA Astrophysics Data System (ADS)
Räth, C.; Laut, I.
2015-10-01
It is demonstrated how to generate time series with tailored nonlinearities by inducing well-defined constraints on the Fourier phases. Correlations between the phase information of adjacent phases and (static and dynamic) measures of nonlinearities are established and their origin is explained. By applying a set of simple constraints on the phases of an originally linear and uncorrelated Gaussian time series, the observed scaling behavior of the intensity distribution of empirical time series can be reproduced. The power law character of the intensity distributions being typical for, e.g., turbulence and financial data can thus be explained in terms of phase correlations.
Stability Analysis of Nonlinear Systems with Slope Restricted Nonlinearities
Du, Jiajia
2014-01-01
The problem of absolute stability of Lur'e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP) lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results. PMID:24592160
The King of All Mediums: A Field Study of College Students Use of Mediums for News
ERIC Educational Resources Information Center
Obaidi, Jabbar Al-A.; Lamb-Williams, Christopher; Mordas, Victoria
2004-01-01
As the media progresses and grows it creates more information and new mediums for users to access information. With this growth it becomes increasingly more difficult for users to decipher which medium should be used to access information. Each medium offers both positive and negative aspects; some are more accurate when reporting news, while…
PREFACE Integrability and nonlinear phenomena Integrability and nonlinear phenomena
NASA Astrophysics Data System (ADS)
Gómez-Ullate, David; Lombardo, Sara; Mañas, Manuel; Mazzocco, Marta; Nijhoff, Frank; Sommacal, Matteo
2010-10-01
Back in 1967, Clifford Gardner, John Greene, Martin Kruskal and Robert Miura published a seminal paper in Physical Review Letters which was to become a cornerstone in the theory of integrable systems. In 2006, the authors of this paper received the AMS Steele Prize. In this award the AMS pointed out that `In applications of mathematics, solitons and their descendants (kinks, anti-kinks, instantons, and breathers) have entered and changed such diverse fields as nonlinear optics, plasma physics, and ocean, atmospheric, and planetary sciences. Nonlinearity has undergone a revolution: from a nuisance to be eliminated, to a new tool to be exploited.' From this discovery the modern theory of integrability bloomed, leading scientists to a deep understanding of many nonlinear phenomena which is by no means reachable by perturbation methods or other previous tools from linear theories. Nonlinear phenomena appear everywhere in nature, their description and understanding is therefore of great interest both from the theoretical and applicative point of view. If a nonlinear phenomenon can be represented by an integrable system then we have at our disposal a variety of tools to achieve a better mathematical description of the phenomenon. This special issue is largely dedicated to investigations of nonlinear phenomena which are related to the concept of integrability, either involving integrable systems themselves or because they use techniques from the theory of integrability. The idea of this special issue originated during the 18th edition of the Nonlinear Evolution Equations and Dynamical Systems (NEEDS) workshop, held at Isola Rossa, Sardinia, Italy, 16-23 May 2009 (http://needs-conferences.net/2009/). The issue benefits from the occasion offered by the meeting, in particular by its mini-workshops programme, and contains invited review papers and contributed papers. It is worth pointing out that there was an open call for papers and all contributions were peer reviewed
Nonlinear Raman-Type Acoustic Scattering in Three-Phase Marine Sediments
NASA Astrophysics Data System (ADS)
Pushkina, N. I.
2001-03-01
Stimulated Raman-type acoustic scattering by bubble oscillations in three-phase marine sediments, which consist of a solid frame, the pore water, and air bubbles, is considered. A model is developed for the case of the bubbles surrounded by water. The acoustic properties of the sediments are described on the basis of the Biot theory of sound propagation in a fluid-saturated porous medium. Nonlinear wave equations are obtained for marine sediments containing air bubbles. Expressions for the nonlinear scattering coefficient and the threshold intensity of the exciting sound wave are derived. A possibility of an experimental observation of the scattering process is discussed.
Kuzmina, M S; Khazanov, E A
2013-10-31
The problem on laser radiation propagation in a birefringent medium is solved with the allowance made for thermally induced linear birefringence under the conditions of cubic nonlinearity. It is shown that at high average and peak radiation powers the degree of isolation in a Faraday isolator noticeably reduces due to the cubic nonlinearity: by more than an order of magnitude when the B-integral is equal to unity. This effect is substantial for pulses with the energy of 0.2 – 3 J, duration of 10 ps to 4 ns and pulse repetition rate of 0.2 – 40 kHz. (components of laser devices)
The nature of enhanced linear and nonlinear optical effects in fullerene solutions
Sheka, E. F. Razbirin, B. S. Starukhin, A. N.; Nelson, D. K.; Degunov, M. Yu.; Lyubovskaya, R. N.; Troshin, P. A.
2009-05-15
The 'blue' emission from fullerene C{sub 60} and its derivatives in frozen toluene solution is discovered and analyzed in the framework of the electromagnetic theory of enhanced optical effects. It is shown that the emission, combining enhanced spectra of Raman scattering and one-photon luminescence, is due to clustering of fullerene molecules in solution. Photoexcitation of charge-transfer excitons in clusters provides the polarization required for the enhancement. A direct relationship is established between the observed phenomenon and nonlinear optical properties of the medium. Empirical and computational tests are proposed to select matrices with various nonlinear optical properties.
In vitro exposure: Linear and non-linear thermodynamic events in Petri dishes.
Paffi, Alessandra; Liberti, Micaela; Apollonio, Francesca; Sheppard, Asher; Balzano, Quirino
2015-10-01
We conducted an electromagnetic-thermal analysis of Petri dishes filled with different medium volumes under different radio frequency exposure conditions with the aim of identifying linear and non-linear parameters that might explain contradictory results of many in vitro bioelectromagnetic experiments. We found that power loss density and temperature depend on shape, size, and orientation of the exposed sample with respect to direction of incident energy, showing that the liquid medium acts as a receiving antenna. In addition, we investigated the possibility of convection from thermodynamic principles within the liquid medium. For a 35 mm diameter Petri dish, a 2 or 4 ml medium volume is too small to support vertical convection. Conversely, horizontal convective motion is possible for H-polarization exposures at 1.8 GHz. PMID:25995097
In vitro exposure: Linear and non-linear thermodynamic events in Petri dishes.
Paffi, Alessandra; Liberti, Micaela; Apollonio, Francesca; Sheppard, Asher; Balzano, Quirino
2015-10-01
We conducted an electromagnetic-thermal analysis of Petri dishes filled with different medium volumes under different radio frequency exposure conditions with the aim of identifying linear and non-linear parameters that might explain contradictory results of many in vitro bioelectromagnetic experiments. We found that power loss density and temperature depend on shape, size, and orientation of the exposed sample with respect to direction of incident energy, showing that the liquid medium acts as a receiving antenna. In addition, we investigated the possibility of convection from thermodynamic principles within the liquid medium. For a 35 mm diameter Petri dish, a 2 or 4 ml medium volume is too small to support vertical convection. Conversely, horizontal convective motion is possible for H-polarization exposures at 1.8 GHz.
Instability of fluid flow over saturated porous medium
NASA Astrophysics Data System (ADS)
Lyubimova, Tatyana; Kolchanova, Ekaterina; Lyubimov, Dmitry
2013-04-01
growth. The numerical calculations were also conducted for nonlinear regimes of the flow applying the finite-element method. Flow characteristics are determined at supercritical values of parameters. The work was made under the financial support of Russian Foundation for Basic Research (Grant 12-01-00795). 1. Ochoa-Tapia J. A. and Whitaker S. Momentum transfer at the boundary between a porous medium and a homogeneous fluid-I. Theoretical development. Int. J. Heat Mass Transfer. 1995. N 38. P. 2635-2646. 2. Ochoa-Tapia J. A. and Whitaker S. Momentum transfer at the boundary between a porous medium and a homogeneous fluid-II. Comparison with experiment. Int. J. Heat Mass Transfer. 1995. N 38. P. 2647-2655.
Hayat, Tasawar; Awais, Muhammad; Imtiaz, Amna
2016-01-01
This communication deals with the properties of heat source/sink in a magneto-hydrodynamic flow of a non-Newtonian fluid immersed in a porous medium. Shrinking phenomenon along with the permeability of the wall is considered. Mathematical modelling is performed to convert the considered physical process into set of coupled nonlinear mathematical equations. Suitable transformations are invoked to convert the set of partial differential equations into nonlinear ordinary differential equations which are tackled numerically for the solution computations. It is noted that dual solutions for various physical parameters exist which are analyzed in detail. PMID:27598314
Hayat, Tasawar; Awais, Muhammad; Imtiaz, Amna
2016-01-01
This communication deals with the properties of heat source/sink in a magneto-hydrodynamic flow of a non-Newtonian fluid immersed in a porous medium. Shrinking phenomenon along with the permeability of the wall is considered. Mathematical modelling is performed to convert the considered physical process into set of coupled nonlinear mathematical equations. Suitable transformations are invoked to convert the set of partial differential equations into nonlinear ordinary differential equations which are tackled numerically for the solution computations. It is noted that dual solutions for various physical parameters exist which are analyzed in detail. PMID:27598314
Collaborative Manufacturing for Small-Medium Enterprises
NASA Astrophysics Data System (ADS)
Irianto, D.
2016-02-01
Manufacturing systems involve decisions concerning production processes, capacity, planning, and control. In a MTO manufacturing systems, strategic decisions concerning fulfilment of customer requirement, manufacturing cost, and due date of delivery are the most important. In order to accelerate the decision making process, research on decision making structure when receiving order and sequencing activities under limited capacity is required. An effective decision making process is typically required by small-medium components and tools maker as supporting industries to large industries. On one side, metal small-medium enterprises are expected to produce parts, components or tools (i.e. jigs, fixture, mold, and dies) with high precision, low cost, and exact delivery time. On the other side, a metal small- medium enterprise may have weak bargaining position due to aspects such as low production capacity, limited budget for material procurement, and limited high precision machine and equipment. Instead of receiving order exclusively, a small-medium enterprise can collaborate with other small-medium enterprise in order to fulfill requirements high quality, low manufacturing cost, and just in time delivery. Small-medium enterprises can share their best capabilities to form effective supporting industries. Independent body such as community service at university can take a role as a collaboration manager. The Laboratory of Production Systems at Bandung Institute of Technology has implemented shared manufacturing systems for small-medium enterprise collaboration.
Gulyaev, A V; Tikhonova, O V
2013-07-31
The propagation of femtosecond laser pulses in a molecular gaseous medium is studied with the rotational dynamics of molecules under the action of these pulses taken into account. Based on the simultaneous numerical solution of the wave equation describing the laser pulse evolution and the Schroedinger equation that determines the quantum state evolution of the medium molecules, the rotational dynamics of molecules in the laser field and the laser pulse evolution are analysed with their mutual influence taken into account. Efficient dynamic alignment of molecules along the direction of laser radiation polarisation is observed, which causes variation in the spatiotemporal pulse profile, as well as significant broadening and deformation of its spectrum in the course of propagation through the medium. The physical mechanisms of the observed phenomena are analysed by using the approximate analytical solution of the problem, derived for the case of preliminary excitation of the medium by a pump pulse (the pump-probe scheme). (nonlinear optical phenomena)
Nonlinear Shock Acceleration and Photon Emission in Supernova Remnants
NASA Technical Reports Server (NTRS)
Ellison, Donald C.; Berezhko, Evgeny G.; Baring, Matthew G.
2000-01-01
We have extended a simple model of nonlinear diffusive shock acceleration (Berezhko & Ellison 1999: Ellison &, Berezhko 1999a) to include the injection and acceleration of electrons and the production of photons from bremsstrahlung, synchrotron, inverse Compton, and pion-decay processes. We argue that, the results of this model, which is simpler to use than more elaborate ones, offer a significant improvement, over test-particle, power-law spectra which are often used in astrophysical applications of diffusive shock acceleration. With an evolutionary supernova remnant (SNR) model to obtain shock parameters as functions of ambient interstellar medium parameters and time, we predict broad-band continuum photon emission from supernova remnants in general, and SN1006 in particular, showing that our results compare well with the more complete time-dependent and spherically symmetric nonlinear model of Berezhko, Ksenofontov, & Petukhov (1999a). We discuss the implications nonlinear shock acceleration has for X-ray line emission, and use our model to describe how ambient conditions determine the TeV/radio flux ratio, an important parameter for gamma-ray observations of radio SNRs.
Duffing's Equation and Nonlinear Resonance
ERIC Educational Resources Information Center
Fay, Temple H.
2003-01-01
The phenomenon of nonlinear resonance (sometimes called the "jump phenomenon") is examined and second-order van der Pol plane analysis is employed to indicate that this phenomenon is not a feature of the equation, but rather the result of accumulated round-off error, truncation error and algorithm error that distorts the true bounded solution onto…
Nonlinear analysis of drought dynamics
NASA Astrophysics Data System (ADS)
Ma, M.
2015-12-01
Drought is an extreme natural hazard and becomes a severe problem in the world. It arises as a result of interactions between climate input and human activity, displaying the nonlinearity and complexity. Nonlinear time series analyses open a way to study the underlying dynamic characteristics of drought, and then provide the forward knowledge to understanding the physical mechanism of drought event. The rationale behind this idea is that information about the representation of nonlinear properties could be used as an additional quality indicator. To that end, the correlation dimension method, a powerful nonlinear time series analysis method based on the chaos theory, has been suggested to assess the intrinsic dimensionality or degree of freedom of time series according to Takens (1981). It can provide an assessment of the dominant processes that is required to map the observed dynamics. In this study, daily discharge and hourly groundwater level data of 63 catchments in Germany and China were investigated with correlation dimension method. The results indicated that the correlation dimension values of studied discharge exhibited none clear spatial patterns, but showed significant correlations with the spatial heterogeneity within the catchments. In contrast, the correlation dimension values of groundwater level displayed spatial patterns due to the different aquifer conditions (confined or unconfined). High correlation dimension values indicate partly confined conditions. In addition, Hurst analysis was involved to qualify the persistence of drought. It seems that drought mechanisms can be learnt from the data themselves in an inverse manner.
Nonlinear bubble dynamics of cavitation.
An, Yu
2012-01-01
For cavitation clouds generated in a standing sound wave driven by an ultrasonic horn, the nonlinear acoustic wave equation governing cavitation dynamics is numerically solved together with the bubble motion equation under an approximation. This conceptual calculation can qualitatively reproduce the observed characteristics of cavitation.
Gauge fields, nonlinear realizations, supersymmetry
NASA Astrophysics Data System (ADS)
Ivanov, E. A.
2016-07-01
This is a brief survey of the all-years research activity in the Sector "Supersymmetry" (the former Markov Group) at the Bogoliubov Laboratory of Theoretical Physics. The focus is on the issues related to gauge fields, spontaneously broken symmetries in the nonlinear realizations approach, and diverse aspects of supersymmetry.
Nonlinear connectivity by Granger causality.
Marinazzo, Daniele; Liao, Wei; Chen, Huafu; Stramaglia, Sebastiano
2011-09-15
The communication among neuronal populations, reflected by transient synchronous activity, is the mechanism underlying the information processing in the brain. Although it is widely assumed that the interactions among those populations (i.e. functional connectivity) are highly nonlinear, the amount of nonlinear information transmission and its functional roles are not clear. The state of the art to understand the communication between brain systems are dynamic causal modeling (DCM) and Granger causality. While DCM models nonlinear couplings, Granger causality, which constitutes a major tool to reveal effective connectivity, and is widely used to analyze EEG/MEG data as well as fMRI signals, is usually applied in its linear version. In order to capture nonlinear interactions between even short and noisy time series, a few approaches have been proposed. We review them and focus on a recently proposed flexible approach has been recently proposed, consisting in the kernel version of Granger causality. We show the application of the proposed approach on EEG signals and fMRI data.
Nonlinear eigenvalue problems in smectics
Marchenko, V. I. Podolyak, E. R.
2010-01-15
The asymptotic forms of strains in a smectic around the linear distributions of multipole force are determined. The law of a decrease in strains is specified by the indices, which are eigenvalues of nonlinear equations describing the angular dependence of the strains.
Multilevel algorithms for nonlinear optimization
NASA Technical Reports Server (NTRS)
Alexandrov, Natalia; Dennis, J. E., Jr.
1994-01-01
Multidisciplinary design optimization (MDO) gives rise to nonlinear optimization problems characterized by a large number of constraints that naturally occur in blocks. We propose a class of multilevel optimization methods motivated by the structure and number of constraints and by the expense of the derivative computations for MDO. The algorithms are an extension to the nonlinear programming problem of the successful class of local Brown-Brent algorithms for nonlinear equations. Our extensions allow the user to partition constraints into arbitrary blocks to fit the application, and they separately process each block and the objective function, restricted to certain subspaces. The methods use trust regions as a globalization strategy, and they have been shown to be globally convergent under reasonable assumptions. The multilevel algorithms can be applied to all classes of MDO formulations. Multilevel algorithms for solving nonlinear systems of equations are a special case of the multilevel optimization methods. In this case, they can be viewed as a trust-region globalization of the Brown-Brent class.
Photonic-resonant left-handed medium
NASA Astrophysics Data System (ADS)
Shen, Jian Qi
2006-08-01
A new scheme to realize simultaneously negative permittivity and permeability in a coherent atomic vapor medium (photonic-resonant material) via a coherent driving mechanism is suggested. It is verified that the atomic system coherently driven by a strong optical field will give rise to a negative refractive index in certain probe frequency ranges. One of the most remarkable features of the present scheme is such that a slab fabricated by the left-handed vapor medium is an ideal candidate for designing perfect lenses since the photonic-resonant atomic vapor cannot only exhibit an isotropic negative refractive index, but also provide a good impedance match at the air-medium interfaces.
Meson's correlation functions in a nuclear medium
NASA Astrophysics Data System (ADS)
Park, Chanyong
2016-09-01
We investigate meson's spectrum, decay constant and form factor in a nuclear medium through holographic two- and three-point correlation functions. To describe a nuclear medium composed of protons and neutrons, we consider a hard wall model on the thermal charged AdS geometry and show that due to the isospin interaction with a nuclear medium, there exist splittings of the meson's spectrum, decay constant and form factor relying on the isospin charge. In addition, we show that the ρ-meson's form factor describing an interaction with pseudoscalar fluctuation decreases when the nuclear density increases, while the interaction with a longitudinal part of an axial vector meson increases.
Method to prepare nanoparticles on porous mediums
Vieth, Gabriel M [Knoxville, TN; Dudney, Nancy J [Oak Ridge, TN; Dai, Sheng [Knoxville, TN
2010-08-10
A method to prepare porous medium decorated with nanoparticles involves contacting a suspension of nanoparticles in an ionic liquid with a porous medium such that the particles diffuse into the pores of the medium followed by heating the resulting composition to a temperature equal to or greater than the thermal decomposition temperature of the ionic liquid resulting in the removal of the liquid portion of the suspension. The nanoparticles can be a metal, an alloy, or a metal compound. The resulting compositions can be used as catalysts, sensors, or separators.
Fatigue damage localization using time-domain features extracted from nonlinear Lamb waves
NASA Astrophysics Data System (ADS)
Hong, Ming; Su, Zhongqing; Lu, Ye; Cheng, Li
2014-03-01
Nonlinear guided waves are sensitive to small-scale fatigue damage that may hardly be identified by traditional techniques. A characterization method for fatigue damage is established based on nonlinear Lamb waves in conjunction with the use of a piezoelectric sensor network. Theories on nonlinear Lamb waves for damage detection are first introduced briefly. Then, the ineffectiveness of using pure frequency-domain information of nonlinear wave signals for locating damage is discussed. With a revisit to traditional gross-damage localization techniques based on the time of flight, the idea of using temporal signal features of nonlinear Lamb waves to locate fatigue damage is introduced. This process involves a time-frequency analysis that enables the damage-induced nonlinear signal features, which are either undiscernible in the original time history or uninformative in the frequency spectrum, to be revealed. Subsequently, a finite element modeling technique is employed, accounting for various sources of nonlinearities in a fatigued medium. A piezoelectric sensor network is configured to actively generate and acquire probing Lamb waves that involve damageinduced nonlinear features. A probability-based diagnostic imaging algorithm is further proposed, presenting results in diagnostic images intuitively. The approach is experimentally verified on a fatigue-damaged aluminum plate, showing reasonably good accuracy. Compared to existing nonlinear ultrasonics-based inspection techniques, this approach uses a permanently attached sensor network that well accommodates automated online health monitoring; more significantly, it utilizes time-domain information of higher-order harmonics from time-frequency analysis, and demonstrates a great potential for quantitative characterization of small-scale damage with improved localization accuracy.
BUOYANCY INSTABILITIES IN A WEAKLY COLLISIONAL INTRACLUSTER MEDIUM
Kunz, Matthew W.; Stone, James M.; Bogdanovic, Tamara; Reynolds, Christopher S. E-mail: jstone@astro.princeton.edu E-mail: chris@astro.umd.edu
2012-08-01
The intracluster medium (ICM) of galaxy clusters is a weakly collisional plasma in which the transport of heat and momentum occurs primarily along magnetic-field lines. Anisotropic heat conduction allows convective instabilities to be driven by temperature gradients of either sign: the magnetothermal instability (MTI) in the outskirts of clusters and the heat-flux buoyancy-driven instability (HBI) in their cooling cores. We employ the Athena magnetohydrodynamic code to investigate the nonlinear evolution of these instabilities, self-consistently including the effects of anisotropic viscosity (i.e., Braginskii pressure anisotropy), anisotropic conduction, and radiative cooling. We find that, in all but the innermost regions of cool-core clusters, anisotropic viscosity significantly impairs the ability of the HBI to reorient magnetic-field lines orthogonal to the temperature gradient. Thus, while radio-mode feedback appears necessary in the central few Multiplication-Sign 10 kpc, heat conduction may be capable of offsetting radiative losses throughout most of a cool core over a significant fraction of the Hubble time. Magnetically aligned cold filaments are then able to form by local thermal instability. Viscous dissipation during cold filament formation produces accompanying hot filaments, which can be searched for in deep Chandra observations of cool-core clusters. In the case of MTI, anisotropic viscosity leads to a nonlinear state with a folded magnetic field structure in which field-line curvature and field strength are anti-correlated. These results demonstrate that, if the HBI and MTI are relevant for shaping the properties of the ICM, one must self-consistently include anisotropic viscosity in order to obtain even qualitatively correct results.
Acoustics of a Nonhomogeneous Moving Medium.
NASA Technical Reports Server (NTRS)
Blokhintsev, D I
1956-01-01
Theoretical basis of the acoustics of a moving nonhomogeneous medium is considered in this report. Experiments that illustrate or confirm some of the theoretical explanation or derivation of these acoustics are also included.
Propagation of light in a Dense Medium
NASA Astrophysics Data System (ADS)
Masood, Samina; Saleem, Iram
Propagation of light is studied in a very dense system. Renormalization scheme of QED is used to understand the propagation of light in a hot and dense medium. We consider a medium of a very large chemical potential with relatively small temperature. The generalized results of vacuum polarization of photon in a hot and dense medium is used to study the behavior of light in such a system. Our hypothetical system corresponds to a heat bath of electrons at an equilibrium temperature and the density of electrons is larger as compared to the temperature of the medium. Such type of systems have previously been identified as classical systems because the chemical potential is large enough to dominate temperature.
Solitary waves in the nonlinear Dirac equation with arbitrary nonlinearity.
Cooper, Fred; Khare, Avinash; Mihaila, Bogdan; Saxena, Avadh
2010-09-01
We consider the nonlinear Dirac equations (NLDE's) in 1+1 dimension with scalar-scalar self interaction g{2}/k+1(ΨΨ){k+1} , as well as a vector-vector self interaction g{2}/k+1(Ψγ{μ}ΨΨγ{μ}Ψ){1/2(k+1)} . We find the exact analytic form for solitary waves for arbitrary k and find that they are a generalization of the exact solutions for the nonlinear Schrödinger equation (NLSE) and reduce to these solutions in a well defined nonrelativistic limit. We perform the nonrelativistic reduction and find the 1/2m correction to the NLSE, valid when |ω-m|<2m , where ω is the frequency of the solitary wave in the rest frame. We discuss the stability and blowup of solitary waves assuming the modified NLSE is valid and find that they should be stable for k<2 . PMID:21230200
Nonlinear vortex-phonon interactions in a Bose-Einstein condensate
NASA Astrophysics Data System (ADS)
Mendonça, J. T.; Haas, F.; Gammal, A.
2016-07-01
We consider the nonlinear coupling between an exact vortex solution in a Bose-Einstein condensate and a spectrum of elementary excitations in the medium. These excitations, or Bogoliubov-de Gennes modes, are indeed a special kind of phonons. We treat the spectrum of elementary excitations in the medium as a gas of quantum particles, sometimes also called bogolons. An exact kinetic equation for the bogolon gas is derived, and an approximate form of this equation, valid in the quasi-classical limit, is also obtained. We study the energy transfer between the vortex and the bogolon gas, and establish conditions for vortex instability and damping.
Nonlinear electron oscillations in a warm plasma
Sarkar, Anwesa; Maity, Chandan; Chakrabarti, Nikhil
2013-12-15
A class of nonstationary solutions for the nonlinear electron oscillations of a warm plasma are presented using a Lagrangian fluid description. The solution illustrates the nonlinear steepening of an initial Gaussian electron density disturbance and also shows collapse behavior in time. The obtained solution may indicate a class of nonlinear transient structures in an unmagnetized warm plasma.
Unsymmetrical squaraines for nonlinear optical materials
NASA Technical Reports Server (NTRS)
Marder, Seth R. (Inventor); Chen, Chin-Ti (Inventor); Cheng, Lap-Tak (Inventor)
1996-01-01
Compositions for use in non-linear optical devices. The compositions have first molecular electronic hyperpolarizability (.beta.) either positive or negative in sign and therefore display second order non-linear optical properties when incorporated into non-linear optical devices.
From linear mechanics to nonlinear mechanics
NASA Technical Reports Server (NTRS)
Loeb, Julian
1955-01-01
Consideration is given to the techniques used in telecommunication where a nonlinear system (the modulator) results in a linear transposition of a signal. It is then shown that a similar method permits linearization of electromechanical devices or nonlinear mechanical devices. A sweep function plays the same role as the carrier wave in radio-electricity. The linearizations of certain nonlinear functionals are presented.
Nonlinear Principal Components Analysis: Introduction and Application
ERIC Educational Resources Information Center
Linting, Marielle; Meulman, Jacqueline J.; Groenen, Patrick J. F.; van der Koojj, Anita J.
2007-01-01
The authors provide a didactic treatment of nonlinear (categorical) principal components analysis (PCA). This method is the nonlinear equivalent of standard PCA and reduces the observed variables to a number of uncorrelated principal components. The most important advantages of nonlinear over linear PCA are that it incorporates nominal and ordinal…
NASA Astrophysics Data System (ADS)
Timoumi, M.; Chérif, B.; Sifaoui, M. S.
2005-12-01
In this paper, heat transfer problem through a semi-transparent porous medium in a cylindrical enclosure is investigated. The governing equations for this problem and the boundary conditions are non-linear differential equations depending on the dimensionless radial coordinate, Planck number N, scattering albedo ω, walls emissivity and thermal conductivity ratio kr. The set of differential equations are solved by a numerical technique taken from the IMSL MATH/LIBRARY. Various results are obtained for the dimensionless temperature profiles in the solid and fluid phases and the radiative heat flux. The effects of some radiative properties of the medium on the heat transfer rate are examined.
New Medium for Pharmaceutical Grade Arthrospira
Amara, Amro A.; Steinbüchel, Alexander
2013-01-01
The aim of this study is to produce a pharmaceutical grade single cell product of Arthrospira from a mixed culture. We have designed a medium derived from a combination between George's and Zarrouk's media. Our new medium has the ability to inhibit different forms of cyanobacterium and microalgae except the Chlorella. The medium and the cultivation conditions have been investigated to map the points where only Arthrospira could survive. For that, a mixed culture of pure Chlorella and Arthrospira (~90 : 10) has been used to develop the best medium composition that can lead to the enrichment of the Arthrospira growth and the inhibition of the Chlorella growth. To enable better control and to study its growth, an 80 l photobioreactor has been used. We have used high saline (2xA-St) medium which has been followed by in fermentor reducing its concentration to 1.5x. The investigation proves that Chlorella has completely disappeared. A method and a new saline medium have been established using a photobioreactor for in fermentor production of single cell Arthrospira. Such method enables the production of pure pharmaceutical grade Arthrospira for medicinal and pharmaceutical applications or as a single cell protein. PMID:26904724
NASA Technical Reports Server (NTRS)
Young, G.
1982-01-01
A design methodology capable of dealing with nonlinear systems, such as a controlled ecological life support system (CELSS), containing parameter uncertainty is discussed. The methodology was applied to the design of discrete time nonlinear controllers. The nonlinear controllers can be used to control either linear or nonlinear systems. Several controller strategies are presented to illustrate the design procedure.
Low-Dispersion Scheme for Nonlinear Acoustic Waves in Nonuniform Flow
NASA Technical Reports Server (NTRS)
Baysal, Oktay; Kaushik, Dinesh K.; Idres, Moumen
1997-01-01
The linear dispersion-relation-preserving scheme and its boundary conditions have been extended to the nonlinear Euler equations. This allowed computing, a nonuniform flowfield and a nonlinear acoustic wave propagation in such a medium, by the same scheme. By casting all the equations, boundary conditions, and the solution scheme in generalized curvilinear coordinates, the solutions were made possible for non-Cartesian domains and, for the better deployment of the grid points, nonuniform grid step sizes could be used. It has been tested for a number of simple initial-value and periodic-source problems. A simple demonstration of the difference between a linear and nonlinear propagation was conducted. The wall boundary condition, derived from the momentum equations and implemented through a pressure at a ghost point, and the radiation boundary condition, derived from the asymptotic solution to the Euler equations, have proven to be effective for the nonlinear equations and nonuniform flows. The nonreflective characteristic boundary conditions also have shown success but limited to the nonlinear waves in no mean flow, and failed for nonlinear waves in nonuniform flow.
Topics in complex nonlinear systems
NASA Astrophysics Data System (ADS)
Ying, Linghang
In the dissertation, I include two topics of my research in nonlinear dynamic systems. In the first topic, we use numerical optimization techniques to investigate the behavior of the success rates for two- and three-qubit entangling gates, first for perfect fidelity, and then extended to imperfect gates. We find that as the perfect fidelity condition is relaxed, the maximum attainable success rates increase in a predictable fashion depending on the size of the system, and we compare that rate of increase for several gates. Finally, we propose an experiment to test our imperfect LOQC gates using number-resolving photon detectors. We suggest a relatively simple physical apparatus capable of producing CZ gates with controllable fidelity less than 1 and success rates higher than the current theoretical maximum (S=2/27) for perfect fidelity. These experimental setups are within the reach of many experimental groups and would provide an interesting experiment in photonic quantum computing. In the second topic, we quantitatively study nonlinear effects on the evolution of surface gravity waves on the ocean, to explore systematically the effects of various input parameters on the probability of rogue wave formation. The fourth-order current-modified nonlinear Schrodinger equation (CNLS4) is employed to describe the wave evolution. First, we show that when the average wave steepness is small and nonlinear wave effects are subleading, the wave height distribution is well explained by a single "freak index" parameter, which describes the strength of (linear) wave scattering by random currents relative to the angular spread of the incoming random sea. When the average steepness is large, the wave height distribution takes a very similar functional form, but the key variables determining the probability distribution are the steepness, and the angular and frequency spread of the incoming waves. Then, we obtain quantitative predictions for the wave height distribution as a
Nonlinear dynamic behavior of microscopic bubbles near a rigid wall
NASA Astrophysics Data System (ADS)
Suslov, Sergey A.; Ooi, Andrew; Manasseh, Richard
2012-06-01
The nonlinear dynamic behavior of microscopic bubbles near a rigid wall is investigated. Oscillations are driven by the ultrasonic pressure field that arises in various biomedical applications such as ultrasound imaging or targeted drug delivery. It is known that, when bubbles approach a blood-vessel wall, their linear dynamic response is modified. This modification may be very useful for real-time detection of bubbles that have found targets; in future therapeutic technologies, it may be useful for controlled release of medical agents encapsulating microbubbles. In this paper, the nonlinear response of microbubbles near a wall is studied. The Keller-Miksis-Parlitz equation is adopted, but modified to account for the presence of a rigid wall. This base model describes the time evolution of the bubble surface, which is assumed to remain spherical, and accounts for the effect of acoustic radiation losses owing to liquid compressibility in the momentum conservation. Two situations are considered: the base case of an isolated bubble in an unbounded medium, and a bubble near a rigid wall. In the latter case, the wall influence is modeled by including a symmetrically oscillating image bubble. The bubble dynamics is traced using a numerical solution of the model equation. Subsequently, Floquet theory is used to accurately detect the bifurcation point where bubble oscillations stop following the driving ultrasound frequency and undergo period-changing bifurcations. Of particular interest is the detection of the subcritical period-tripling and -quadrupling transition. The parametric bifurcation maps are obtained as functions of nondimensional parameters representing the bubble radius, the frequency and pressure amplitude of the driving ultrasound field, and the distance from the wall. It is shown that the presence of the wall generally stabilises the bubble dynamics, so that much larger values of the pressure amplitude are needed to generate nonlinear responses. Thus, a
Nonlinear force-free magnetic fields. [quasi-steady state evolution of astrophysical fields
NASA Technical Reports Server (NTRS)
Low, B. C.
1982-01-01
The nonlinear properties of force-free magnetic fields are reviewed with particular reference to the mechanisms for the sudden release of stored energy in flares during the quasi-steady evolution of solar fields. It is shown that in the solar atmosphere, force-free fields with a nonconstant scalar function in the field equations are more likely to occur than those with a constant scalar function, and the nonlinear properties of these fields may give rise to many interesting physical effects. Consideration is then given to two possible mechanisms of field evolution: a model in which a force-free field in a medium of infinite electrical conductivity evolves in response to slowly changing boundary conditions brought about by photospheric motions in the solar active region, and a model in which a field in a medium of small finite electrical conductivity evolves in response to the slow Ohmic dissipation of the electric current.
Hidden possibilities in controlling optical soliton in fiber guided doped resonant medium
NASA Astrophysics Data System (ADS)
Kundu, Anjan
2011-06-01
Fiber guided optical signal propagating in a Erbium doped nonlinear resonant medium is known to produce cleaner solitonic pulse, described by the self induced transparency (SIT) coupled to nonlinear Schrödinger equation. We discover two new possibilities hidden in its integrable structure, for amplification and control of the optical pulse. Using the variable soliton width permitted by the integrability of this model, the broadening pulse can be regulated by adjusting the initial population inversion of the dopant atoms. The effect can be enhanced by another innovative application of its constrained integrable hierarchy, proposing a system of multiple SIT media. These theoretical predictions are workable analytically in details, correcting a well known result.
Breaking of non-Newtonian character in flows through a porous medium.
Chevalier, T; Rodts, S; Chateau, X; Chevalier, C; Coussot, P
2014-02-01
From NMR measurements we show that the velocity field of a yield stress fluid flowing through a disordered well-connected porous medium is very close to that for a Newtonian fluid. In particular, it is shown that no arrested regions exist even at very low velocities, for which the solid regime is expected to be dominant. This suggests that these results obtained for strongly nonlinear fluid can be extrapolated to any nonlinear fluid. We deduce a generalized form of Darcy's law for such materials and provide insight into the physical origin of the coefficients involved in this expression, which are shown to be moments of the second invariant of the strain rate tensor.
NASA Astrophysics Data System (ADS)
Slavchev, V.; Kovachev, L.; Ivanov, L. M.
2015-03-01
In the present work it is demonstrated two efficient methods of self-compression of femtosecond pulses based on suitable selection of optical elements, parameters of the medium and laser radiation. The basic idea is that the phase modulated pulses more efficiently can be compressed trough nonlinear mechanisms. The first method can be applied for mediums with significant dispersion like fused silica, where the sign of the dispersion of the group velocity is important. We show that the combination of focusing by optical lens and a balance between anomalous dispersion and nonlinearity lead to significant compression from 100fs to~20-30fs of optical pulse. The second method for self-compression is by using only one optical diffraction grating to obtain broadband pulses and the following self-compression in nonlinear regime. In the second case in addition is observed generation of X wave.
Noise in Nonlinear Dynamical Systems
NASA Astrophysics Data System (ADS)
Moss, Frank; McClintock, P. V. E.
2009-08-01
List of contributors; Preface; Introduction to volume three; 1. The effects of coloured quadratic noise on a turbulent transition in liquid He II J. T. Tough; 2. Electrohydrodynamic instability of nematic liquid crystals: growth process and influence of noise S. Kai; 3. Suppression of electrohydrodynamic instabilities by external noise Helmut R. Brand; 4. Coloured noise in dye laser fluctuations R. Roy, A. W. Yu and S. Zhu; 5. Noisy dynamics in optically bistable systems E. Arimondo, D. Hennequin and P. Glorieux; 6. Use of an electronic model as a guideline in experiments on transient optical bistability W. Lange; 7. Computer experiments in nonlinear stochastic physics Riccardo Mannella; 8. Analogue simulations of stochastic processes by means of minimum component electronic devices Leone Fronzoni; 9. Analogue techniques for the study of problems in stochastic nonlinear dynamics P. V. E. McClintock and Frank Moss; Index.
Condition assessment of nonlinear processes
Hively, Lee M.; Gailey, Paul C.; Protopopescu, Vladimir A.
2002-01-01
There is presented a reliable technique for measuring condition change in nonlinear data such as brain waves. The nonlinear data is filtered and discretized into windowed data sets. The system dynamics within each data set is represented by a sequence of connected phase-space points, and for each data set a distribution function is derived. New metrics are introduced that evaluate the distance between distribution functions. The metrics are properly renormalized to provide robust and sensitive relative measures of condition change. As an example, these measures can be used on EEG data, to provide timely discrimination between normal, preseizure, seizure, and post-seizure states in epileptic patients. Apparatus utilizing hardware or software to perform the method and provide an indicative output is also disclosed.
Max-Planck-Institut fur Quantenoptik; Goulielmakis, E.; Schultze, M.; Hofstetter, M.; Yakovlev, V. S.; Gagnon, J.; Uiberacker, M.; Aquila, A. L.; gullikson, E. M.; attwood, D. T.; Kienberger, R.; Krausz, F.; Kleineberg, U.
2008-11-05
Nonlinear optics plays a central role in the advancement of optical science and laser-based technologies. We report on the confinement of the nonlinear interaction of light with matter to a single wave cycle and demonstrate its utility for time-resolved and strong-field science. The electric field of 3.3-femtosecond, 0.72-micron laser pulses with a controlled and measured waveform ionizes atoms near the crests of the central wave cycle, with ionization being virtually switched off outside this interval. Isolated sub-100-attosecond pulses of extreme ultraviolet light (photon energy {approx} 80 electron volts), containing {approx} 0.5 nanojoule of energy, emerge from the interaction with a conversion efficiency of {approx} 10{sup -6}. These tools enable the study of the precision control of electron motion with light fields and electron-electron interactions with a resolution approaching the atomic unit of time ({approx} 24 attoseconds).
Some nonlinear space decomposition algorithms
Tai, Xue-Cheng; Espedal, M.
1996-12-31
Convergence of a space decomposition method is proved for a general convex programming problem. The space decomposition refers to methods that decompose a space into sums of subspaces, which could be a domain decomposition or a multigrid method for partial differential equations. Two algorithms are proposed. Both can be used for linear as well as nonlinear elliptic problems and they reduce to the standard additive and multiplicative Schwarz methods for linear elliptic problems. Two {open_quotes}hybrid{close_quotes} algorithms are also presented. They converge faster than the additive one and have better parallelism than the multiplicative method. Numerical tests with a two level domain decomposition for linear, nonlinear and interface elliptic problems are presented for the proposed algorithms.
Solitons and nonlinear wave equations
Dodd, Roger K.; Eilbeck, J. Chris; Gibbon, John D.; Morris, Hedley C.
1982-01-01
A discussion of the theory and applications of classical solitons is presented with a brief treatment of quantum mechanical effects which occur in particle physics and quantum field theory. The subjects addressed include: solitary waves and solitons, scattering transforms, the Schroedinger equation and the Korteweg-de Vries equation, and the inverse method for the isospectral Schroedinger equation and the general solution of the solvable nonlinear equations. Also considered are: isolation of the Korteweg-de Vries equation in some physical examples, the Zakharov-Shabat/AKNS inverse method, kinks and the sine-Gordon equation, the nonlinear Schroedinger equation and wave resonance interactions, amplitude equations in unstable systems, and numerical studies of solitons. 45 references.
Advances in nonlinear optical materials and devices
NASA Technical Reports Server (NTRS)
Byer, Robert L.
1991-01-01
The recent progress in the application of nonlinear techniques to extend the frequency of laser sources has come from the joint progress in laser sources and in nonlinear materials. A brief summary of the progress in diode pumped solid state lasers is followed by an overview of progress in nonlinear frequency extension by harmonic generation and parametric processes. Improved nonlinear materials including bulk crystals, quasiphasematched interactions, guided wave devices, and quantum well intersubband studies are discussed with the idea of identifying areas of future progress in nonlinear materials and devices.
Nonlinear dynamics in cardiac conduction
NASA Technical Reports Server (NTRS)
Kaplan, D. T.; Smith, J. M.; Saxberg, B. E.; Cohen, R. J.
1988-01-01
Electrical conduction in the heart shows many phenomena familiar from nonlinear dynamics. Among these phenomena are multiple basins of attraction, phase locking, and perhaps period-doubling bifurcations and chaos. We describe a simple cellular-automation model of electrical conduction which simulates normal conduction patterns in the heart as well as a wide range of disturbances of heart rhythm. In addition, we review the application of percolation theory to the analysis of the development of complex, self-sustaining conduction patterns.
A nonlinear SIR with stability
NASA Astrophysics Data System (ADS)
Trisilowati, Darti, I.; Fitri, S.
2014-02-01
The aim of this work is to develop a mathematical model of a nonlinear susceptible-infectious-removed (SIR) epidemic model with vaccination. We analyze the stability of the model by linearizing the model around the equilibrium point. Then, diphtheria data from East Java province is fitted to the model. From these estimated parameters, we investigate which parameters that play important role in the epidemic model. Some numerical simulations are given to illustrate the analytical results and the behavior of the model.
Townes' contribution to nonlinear optics
NASA Astrophysics Data System (ADS)
Garmire, Elsa
2015-03-01
In honour of the Fiftieth Anniversary of the Nobel Prize in Physics, this talk introduced the contributions of Nicholas Basov and Alexei Prokhorov, who shared the prize with Charles Townes. The talk then detailed the quantum electronics research of Townes, particularly at MIT, which was related to nonlinear optics. The years from 1961 to 1968 were particularly exciting, as the ruby laser enabled a wide variety of new physics to be discovered and explored.
Linear superposition in nonlinear equations.
Khare, Avinash; Sukhatme, Uday
2002-06-17
Several nonlinear systems such as the Korteweg-de Vries (KdV) and modified KdV equations and lambda phi(4) theory possess periodic traveling wave solutions involving Jacobi elliptic functions. We show that suitable linear combinations of these known periodic solutions yield many additional solutions with different periods and velocities. This linear superposition procedure works by virtue of some remarkable new identities involving elliptic functions. PMID:12059300
Nonlinear transient simulation of transformers
Pierrat, L.; Tran-Quoc, T. |; Montmeat, A.
1995-12-31
In this paper, a nonlinear model of transformer which takes into account both the saturation and the hysteresis is proposed. In order to simulate transient phenomena in transformers, a system of equations is presented. The digital simulation of the energization and de-energization of a three-phase distribution transformer is studied. Ferroresonant phenomena in iron core transformers supplied through capacitive links are presented. Finally, the influence of MOV arresters on overvoltage reduction is investigated.
Nonlinear positron acoustic solitary waves
Tribeche, Mouloud; Aoutou, Kamel; Younsi, Smain; Amour, Rabia
2009-07-15
The problem of nonlinear positron acoustic solitary waves involving the dynamics of mobile cold positrons is addressed. A theoretical work is presented to show their existence and possible realization in a simple four-component plasma model. The results should be useful for the understanding of the localized structures that may occur in space and laboratory plasmas as new sources of cold positrons are now well developed.
Nonlinear input-output systems
NASA Technical Reports Server (NTRS)
Hunt, L. R.; Luksic, Mladen; Su, Renjeng
1987-01-01
Necessary and sufficient conditions that the nonlinear system dot-x = f(x) + ug(x) and y = h(x) be locally feedback equivalent to the controllable linear system dot-xi = A xi + bv and y = C xi having linear output are found. Only the single input and single output case is considered, however, the results generalize to multi-input and multi-output systems.
Ethanol production using a soy hydrolysate-based medium or a yeast autolysate-based medium
Ingram, Lonnie O.
2000-01-01
This invention presents a method for the production of ethanol that utilizes a soy hydrolysate-based nutrient medium or a yeast autolysate-based medium nutrient medium in conjunction with ethanologenic bacteria and a fermentable sugar for the cost-effective production of ethanol from lignocellulosic biomass. The invention offers several advantages over presently available media for use in ethanol production, including consistent quality, lack of toxins and wide availability.
Gachet, David; Brustlein, Sophie; Rigneault, Hervé
2010-05-28
In the Young's double slit experiment, the spatial shift of the interference pattern projected onto a screen is directly related to the phase difference between the fields diffracted by the two slits. We apply this property to fields emitted by nonlinear processes and thus demonstrate background-free coherent anti-Stokes Raman scattering microscopy near an axial interface between a resonant and a nonresonant medium. This method is relevant to remove the nonresonant background in other coherent resonant processes.
Geomedium as a nonlinear dynamic system. An evolutionary concept of earthquake development
Makarov, Pavel V.
2014-11-14
An evolutionary approach to earthquake development is proposed. A medium under loading is treated as a multiscale nonlinear dynamic system. Its failure involves a number of stages typical of any dynamic system: dynamic chaos, self-organized criticality, and global stability loss in the final stage of its evolution. In the latter stage, the system evolves in a blow-up mode accompanied by catastrophic superfast movements of the elements of this geomedium.
Nonlinear microscopy of collagen fibers
NASA Astrophysics Data System (ADS)
Strupler, M.; Pena, A.-M.; Hernest, M.; Tharaux, P.-L.; Fabre, A.; Marchal-Somme, J.; Crestani, B.; Débarre, D.; Martin, J.-L.; Beaurepaire, E.; Schanne-Klein, M.-C.
2007-02-01
We used intrinsic Second Harmonic Generation (SHG) by fibrillar collagen to visualize the three-dimensional architecture of collagen fibrosis at the micrometer scale using laser scanning nonlinear microscopy. We showed that SHG signals are highly specific to fibrillar collagen and provide a sensitive probe of the micrometer-scale structural organization of collagen in tissues. Moreover, recording simultaneously other nonlinear optical signals in a multimodal setup, we visualized the tissue morphology using Two-Photon Excited Fluorescence (2PEF) signals from endogenous chromophores such as NADH or elastin. We then compared different methods to determine accurate indexes of collagen fibrosis using nonlinear microscopy, given that most collagen fibrils are smaller than the microscope resolution and that second harmonic generation is a coherent process. In order to define a robust method to process our three-dimensional images, we either calculated the fraction of the images occupied by a significant SHG signal, or averaged SHG signal intensities. We showed that these scores provide an estimation of the extension of renal and pulmonary fibrosis in murine models, and that they clearly sort out the fibrotic mice.
Nonlinear Single Spin Spectrum Analayzer
NASA Astrophysics Data System (ADS)
Kotler, Shlomi; Akerman, Nitzan; Glickman, Yinnon; Ozeri, Roee
2014-05-01
Qubits are excellent probes of their environment. When operating in the linear regime, they can be used as linear spectrum analyzers of the noise processes surrounding them. These methods fail for strong non-Gaussian noise where the qubit response is no longer linear. Here we solve the problem of nonlinear spectral analysis, required for strongly coupled environments. Our non-perturbative analytic model shows a nonlinear signal dependence on noise power, resulting in a spectral resolution beyond the Fourier limit as well as frequency mixing. We developed a noise characterization scheme adapted to this non-linearity. We then applied it using a single trapped 88Sr+ ion as the a sensitive probe of strong, non-Gaussian, discrete magnetic field noise. With this method, we attained a ten fold improvement over the standard Fourier limit. Finally, we experimentally compared the performance of equidistant vs. Uhrig modulation schemes for spectral analysis. Phys. Rev. Lett. 110, 110503 (2013), Synopsis at http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.110.110503 Current position: National Institute of Standards and Tehcnology, Boulder, CO.
Focus issue introduction: nonlinear photonics.
Akhmediev, Nail; Rottwitt, Karsten
2012-11-19
It is now 23 years since the first Topical Meeting "Nonlinear Guided Wave Phenomena" (Houston, TX, February 2-4, 1989) has been organised by George Stegeman and Allan Boardman with support of the Optical Society of America. These series of the OSA conferences known as NLGW, continued under the name "Nonlinear Photonics" starting from 2007. The latest one, in Colorado Springs in June 17-21, 2012 has been a great success despite the fierce fires advancing around the city at the time of the conference. This Focus issue is a collection of several papers presented at the conference with extended content submitted to Optics Express. Although this collection is small in comparison to the total number of papers presented at the conference, it gives a flavor of the topics considered at the meeting. It is also worthy to mention here that the next meeting "Nonlinear Photonics" is planned to be held in Barcelona - one of the main European centers on this subject.
NASA Astrophysics Data System (ADS)
Rincon, F.; Schekochihin, A. A.; Cowley, S. C.
2015-02-01
Slow dynamical changes in magnetic-field strength and invariance of the particles' magnetic moments generate ubiquitous pressure anisotropies in weakly collisional, magnetized astrophysical plasmas. This renders them unstable to fast, small-scale mirror and firehose instabilities, which are capable of exerting feedback on the macroscale dynamics of the system. By way of a new asymptotic theory of the early non-linear evolution of the mirror instability in a plasma subject to slow shearing or compression, we show that the instability does not saturate quasi-linearly at a steady, low-amplitude level. Instead, the trapping of particles in small-scale mirrors leads to non-linear secular growth of magnetic perturbations, δB/B ∝ t2/3. Our theory explains recent collisionless simulation results, provides a prediction of the mirror evolution in weakly collisional plasmas and establishes a foundation for a theory of non-linear mirror dynamics with trapping, valid up to δB/B = O(1).
Challenges in nonlinear gravitational clustering
NASA Astrophysics Data System (ADS)
Padmanabhan, Thanu
2006-04-01
This article addresses some issues related to the statistical description of gravitating systems in an expanding backgrounds. In particular, I describe (a) how the nonlinear mode-mode coupling transfers power from one scale to another in the Fourier space if the initial power spectrum is sharply peaked at a given scale and (b) what are the asymptotic characteristics of gravitational clustering that are independent of the initial conditions. The analysis uses a new approach based on an integro-differential equation for the evolution of the gravitational potential in the Fourier space. I show how this equation allows one to understand several aspects of nonlinear gravitational clustering and provides insight in to the transfer of power from one scale to another through nonlinear mode coupling. Numerical simulations as well as analytic work shows that power transfer leads to a universal power spectrum at late times, somewhat reminiscent of the existence of Kolmogorov spectrum in fluid turbulence. To cite this article: T. Padmanabhan, C. R. Physique 7 (2006).
spin pumping occurred under nonlinear spin precession
NASA Astrophysics Data System (ADS)
Zhou, Hengan; Fan, Xiaolong; Ma, Li; Zhou, Shiming; Xue, Desheng
Spin pumping occurs when a pure-spin current is injected into a normal metal thin layer by an adjacent ferromagnetic metal layer undergoing ferromagnetic resonance, which can be understood as the inverse effect of spin torque, and gives access to the physics of magnetization dynamics and damping. An interesting question is that whether spin pumping occurring under nonlinear spin dynamics would differ from linear case. It is known that nonlinear spin dynamics differ distinctly from linear response, a variety of amplitude dependent nonlinear effect would present. It has been found that for spin precession angle above a few degrees, nonlinear damping term would present and dominated the dynamic energy/spin-moment dissipation. Since spin pumping are closely related to the damping process, it is interesting to ask whether the nonlinear damping term could be involved in spin pumping process. We studied the spin pumping effect occurring under nonlinear spin precession. A device which is a Pt/YIG microstrip coupled with coplanar waveguide was used. High power excitation resulted in spin precession entering in a nonlinear regime. Foldover resonance lineshape and nonlinear damping have been observed. Based on those nonlinear effects, we determined the values of the precession cone angles, and the maximum cone angle can reach a values as high as 21.5 degrees. We found that even in nonlinear regime, spin pumping is still linear, which means the nonlinear damping and foldover would not affect spin pumping process.
Global methods for nonlinear complementarity problems
More, J.J.
1994-04-01
Global methods for nonlinear complementarity problems formulate the problem as a system of nonsmooth nonlinear equations approach, or use continuation to trace a path defined by a smooth system of nonlinear equations. We formulate the nonlinear complementarity problem as a bound-constrained nonlinear least squares problem. Algorithms based on this formulation are applicable to general nonlinear complementarity problems, can be started from any nonnegative starting point, and each iteration only requires the solution of systems of linear equations. Convergence to a solution of the nonlinear complementarity problem is guaranteed under reasonable regularity assumptions. The converge rate is Q-linear, Q-superlinear, or Q-quadratic, depending on the tolerances used to solve the subproblems.
Earth solids and dynamic nonlinear elasticity
Johnson, P.A. |; Abeele, K.E.A. Van Den
1997-05-01
The authors` intention is to describe several manifestations of nonlinear behavior in rock. Nonlinear response may manifest itself in a variety of manners, including a nonlinear stress-strain relation, nonlinear attenuation, harmonic generation, resonant peak shift and slow dynamics, all of which are related. The authors have ample evidence that the responsible mechanism for nonlinear response [to first order] is the presence of compliant features and the influence of fluid. They define compliant features as those features that are the weakest in the rock, e.g., grain-to-grain contacts, low aspect ratio cracks, joints, etc. In addition, there may be other mechanisms responsible as yet unidentified. In the following, the authors emphasize the robust nature of observations by illustrating several experimental examples. They do not review the related theoretical framework. Finally, they do not present nonlinear parameters derived from these experiments as the purpose in this paper is to illustrate rather than quantify nonlinear response.
Chirped Peregrine solitons in a class of cubic-quintic nonlinear Schrödinger equations
NASA Astrophysics Data System (ADS)
Chen, Shihua; Baronio, Fabio; Soto-Crespo, Jose M.; Liu, Yi; Grelu, Philippe
2016-06-01
We shed light on the fundamental form of the Peregrine soliton as well as on its frequency chirping property by virtue of a pertinent cubic-quintic nonlinear Schrödinger equation. An exact generic Peregrine soliton solution is obtained via a simple gauge transformation, which unifies the recently-most-studied fundamental rogue-wave species. We discover that this type of Peregrine soliton, viable for both the focusing and defocusing Kerr nonlinearities, could exhibit an extra doubly localized chirp while keeping the characteristic intensity features of the original Peregrine soliton, hence the term chirped Peregrine soliton. The existence of chirped Peregrine solitons in a self-defocusing nonlinear medium may be attributed to the presence of self-steepening effect when the latter is not balanced out by the third-order dispersion. We numerically confirm the robustness of such chirped Peregrine solitons in spite of the onset of modulation instability.
Nonlinear Dielectric Properties of Yeast Cells Cultured in Different Environmental Conditions
NASA Astrophysics Data System (ADS)
Kawanishi, Gomon; Fukuda, Naoki; Muraji, Masafumi
The harmonics of the electric current through yeast suspensions, the nonlinear dielectric properties of yeast cells, have particular patterns according to the biological activity of the cells and the measurement of these patterns is a technique for determining the activity of living cells. The concentration of glucose and oxygen in yeast culture medium influences the manifestation of fermentation or respiration of yeast cells. Measurements were made with yeast cells (Saccharomyces cerevisiae) cultured aerobically and anaerobically in sufficient glucose concentration, aerobic fermentation and anaerobic fermentation, and aerobically in limited glucose concentration, respiration. The results showed that the harmonics were barely apparent for yeast cells in aerobic fermentation and respiratory; however, cells in the anaerobic fermentation displayed substantial third and fifth harmonics. We can say that environmental condition affects the yeast cells' nonlinear properties, from another viewpoint, the measurements of the nonlinear properties are available to determine the activity of yeast cells adjusted to the conditions of their cultivation.
Non-linear shipboard shock analysis of the Tomahawk missile shock isolation system
NASA Technical Reports Server (NTRS)
Leifer, Joel; Gross, Michael
1987-01-01
The identification, quantification, computer modeling and verification of the Tomahawk nonlinear liquid spring shock isolation system in a surface ship Vertical Launch System (VLS) are discussed. The isolation system hardware and mode of operation is detailed in an effort to understand the nonlinearities. These nonlinearities are then quantified and modeled using the MSC/NASTRAN finite element code. The model was verified using experimental data from the Navel Ordnance Systems Center MIL-S-901 medium weight shock tests of August 1986. The model was then used to predict the Tomahawk response to the CG-53 USS Mobile Bay shock trials of May-June 1987. Results indicate that the model is an accurate mathematical representation of the physical system either functioning as designed or in an impaired condition due to spring failure.
Nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating embedded in water
NASA Astrophysics Data System (ADS)
Jiménez, N.; Romero-García, V.; Picó, R.; Garcia-Raffi, L. M.; Staliunas, K.
2015-11-01
We report the nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating immersed in water. In the linear regime, the system presents high focal gain (32 dB), with a narrow beam-width and intense side lobes as it is common in focusing by Fresnel-like lenses. Activating the nonlinearity of the host medium by using high amplitude incident waves, the focusing properties of the lens dramatically change. Theoretical predictions show that the focal gain of the system extraordinary increases in the strongly nonlinear regime (Mach number of 6.1 × 10-4). Particularly, the harmonic generation is locally activated at the focal spot, and the second harmonic beam is characterized by strongly reduced side-lobes and an excellent beam profile as experiments show in agreement with theory. The results can motivate applications in medical therapy or second harmonic imaging.
Stimulated Raman scattering and nonlinear focusing of high-power laser beams propagating in water.
Hafizi, B; Palastro, J P; Peñano, J R; Gordon, D F; Jones, T G; Helle, M H; Kaganovich, D
2015-04-01
The physical processes associated with propagation of a high-power (power > critical power for self-focusing) laser beam in water include nonlinear focusing, stimulated Raman scattering (SRS), optical breakdown, and plasma formation. The interplay between nonlinear focusing and SRS is analyzed for cases where a significant portion of the pump power is channeled into the Stokes wave. Propagation simulations and an analytical model demonstrate that the Stokes wave can re-focus the pump wave after the power in the latter falls below the critical power. It is shown that this novel focusing mechanism is distinct from cross-phase focusing. The phenomenon of gain-focusing discussed here for propagation in water is expected to be of general occurrence applicable to any medium supporting nonlinear focusing and stimulated Raman scattering.
Stimulated Raman scattering and nonlinear focusing of high-power laser beams propagating in water
NASA Astrophysics Data System (ADS)
Hafizi, B.; Palastro, J. P.; Peñano, J. R.; Gordon, D. F.; Jones, T. G.; Helle, M. H.; Kaganovich, D.
2015-04-01
The physical processes associated with propagation of a high-power (power > critical power for self-focusing) laser beam in water include nonlinear focusing, stimulated Raman scattering (SRS), optical breakdown and plasma formation. The interplay between nonlinear focusing and SRS is analyzed for cases where a significant portion of the pump power is channeled into the Stokes wave. Propagation simulations and an analytical model demonstrate that the Stokes wave can re-focus the pump wave after the power in the latter falls below the critical power. It is shown that this novel focusing mechanism is distinct from cross-phase focusing. While discussed here in the context of propagation in water, the gain-focusing phenomenon is general to any medium supporting nonlinear focusing and stimulated forward Raman scattering.
Nonlinear self-focus of pulsed-wave beams in Kerr media
Judkins, J.B.
1992-12-31
A modified finite-difference time-domain method for solving Maxwell`s equations in nonlinear media is presented. This method allows for a finite response time to be incorporated in the medium, physically creating dispersion and absorption mechanisms. The technique models electromagnetic fields in two space dimensions and time and encompasses both the TE{sub z} and TM{sub z} set of decoupled field equations. Aspects of an ultra-short pulsed Gaussian beam are studied in a variety of linear and nonlinear environments to demonstrate that the methods developed here can be used efficaciously in the modeling of pulses in complex problem space geometries even when nonlinearities are present.
Nonlinear terahertz response of HgTe/CdTe quantum wells
Chen, Qinjun; Sanderson, Matthew; Zhang, Chao
2015-08-24
Without breaking the topological order, HgTe/CdTe quantum wells can have two types of bulk band structure: direct gap type (type I) and indirect gap type (type II). We report that the strong nonlinear optical responses exist in both types of bulk states under a moderate electric field in the terahertz regime. Interestingly, for the type II band structure, the third order conductivity changes sign when chemical potentials lies below 10 meV due to the significant response of the hole excitation close to the bottom of conduction band. Negative nonlinear conductivities suggest that HgTe/CdTe quantum wells can find application in the gain medium of a laser for terahertz radiation. The thermal influences on nonlinear optical responses of HgTe/CdTe quantum wells are also studied.
Nonlinear Jaynes–Cummings model for two interacting two-level atoms
NASA Astrophysics Data System (ADS)
de los Santos-Sánchez, O.; González-Gutiérrez, C.; Récamier, J.
2016-08-01
In this work we examine a nonlinear version of the Jaynes–Cummings model for two identical two-level atoms allowing for Ising-like and dipole–dipole interplays between them. The model is said to be nonlinear in the sense that it can incorporate both a general intensity-dependent interaction between the atomic system and the cavity field and/or the presence of a nonlinear medium inside the cavity. As an example, we consider a particular type of atom-field coupling based upon the so-called Buck–Sukumar model and a lossless Kerr-like cavity. We describe the possible effects of such features on the evolution of some quantities of current interest, such as atomic excitation, purity, concurrence, the entropy of the field and the evolution of the latter in phase space.
Universal nonlinear scattering in ultra-high Q whispering gallery-mode resonators.
Lin, Guoping; Diallo, Souleymane; Dudley, John M; Chembo, Yanne K
2016-06-27
Universal nonlinear scattering processes such as Brillouin, Raman, and Kerr effects are fundamental light-matter interactions of particular theoretical and experimental importance. They originate from the interaction of a laser field with an optical medium at the lattice, molecular, and electronic scale, respectively. These nonlinear effects are generally observed and analyzed separately, because they do not often occur concomitantly. In this article, we report the simultaneous excitation of these three fundamental interactions in mm-size ultra-high Q whispering gallery mode resonators under continuous wave pumping. Universal nonlinear scattering is demonstrated in barium fluoride and strontium fluoride, separately. We further propose a unified theory based on a spatiotemporal formalism for the understanding of this phenomenology. PMID:27410640
Stimulated Raman scattering and nonlinear focusing of high-power laser beams propagating in water.
Hafizi, B; Palastro, J P; Peñano, J R; Gordon, D F; Jones, T G; Helle, M H; Kaganovich, D
2015-04-01
The physical processes associated with propagation of a high-power (power > critical power for self-focusing) laser beam in water include nonlinear focusing, stimulated Raman scattering (SRS), optical breakdown, and plasma formation. The interplay between nonlinear focusing and SRS is analyzed for cases where a significant portion of the pump power is channeled into the Stokes wave. Propagation simulations and an analytical model demonstrate that the Stokes wave can re-focus the pump wave after the power in the latter falls below the critical power. It is shown that this novel focusing mechanism is distinct from cross-phase focusing. The phenomenon of gain-focusing discussed here for propagation in water is expected to be of general occurrence applicable to any medium supporting nonlinear focusing and stimulated Raman scattering. PMID:25831383
Nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating embedded in water
Jiménez, N.; Picó, R.; Romero-García, V.; Garcia-Raffi, L. M.
2015-11-16
We report the nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating immersed in water. In the linear regime, the system presents high focal gain (32 dB), with a narrow beam-width and intense side lobes as it is common in focusing by Fresnel-like lenses. Activating the nonlinearity of the host medium by using high amplitude incident waves, the focusing properties of the lens dramatically change. Theoretical predictions show that the focal gain of the system extraordinary increases in the strongly nonlinear regime (Mach number of 6.1 × 10{sup −4}). Particularly, the harmonic generation is locally activated at the focal spot, and the second harmonic beam is characterized by strongly reduced side-lobes and an excellent beam profile as experiments show in agreement with theory. The results can motivate applications in medical therapy or second harmonic imaging.
NASA Astrophysics Data System (ADS)
Hummel, N.; Shapiro, S. A.
2012-12-01
Borehole fluid injections into geothermal and hydrocarbon reservoirs are used to hydraulically stimulate the rock. Usually, hydraulic stimulation operations are accompanied by microseismic activity. In particular, hydraulic fracturing has become a standard industry technique aimed to enhance the permeability of tight reservoir rocks. During such treatments the structure of the rock is actively altered. As a result, the formation permeability can significantly increase and the corresponding interaction between fluid and reservoir rock becomes nonlinear. We show how the fluid-rock interaction can be characterized from the spatio-temporal behavior of induced seismicity. Furthermore, we reveal how the fluid-rock interaction can be used to estimate the permeability evolution inside of the fracture stimulated rock. For this purpose we consider microseismic data recorded during a hydraulic fracturing treatment in the Barnett Shale. We present a scaling approach to transform clouds of hypocenters of events obtained in a hydraulically anisotropic medium into those obtained in an effective isotropic medium. In this approach we assume that the pressure-dependence of permeability is independent of a specific direction although the anisotropic permeability depends on the geological structure and strength of the rock. Hence, we approximate the real medium by a model with a factorized anisotropy and nonlinearity. We analyze the spatio-temporal behavior of Barnett Shale seismicity and find that the fluid-rock interaction is significantly nonlinear. To understand the nonlinear nature of the fluid-rock interaction and to explain corresponding spatio-temporal characteristics of induced seismicity we consider a nonlinear diffusional relaxation of the pore-fluid pressure perturbation. Nonlinearity is introduced by a power-law pressure-dependence of hydraulic permeability. For such a nonlinear fluid-rock interaction we present a numerical modeling approach to generate synthetic