Ultrafast spatiotemporal coupling in nonlinear dispersive media
NASA Astrophysics Data System (ADS)
Ryan, Andrew Thomas
1997-10-01
In this thesis the results of a systematic investigation into the behavior of ultrashort optical pulses propagating in dispersive media with a Kerr nonlinearity (and intensity-dependent refractive index) are presented. The effect of the nonlinear index is to couple the spatial and temporal behaviors of the optical field together in a process known as spatiotemporal coupling. In the first chapter, a review of the previous work done in describing spatiotemporal coupling is presented as well as a discussion of its relevance to the remaining chapters. Optical wave propagation in general is described by Maxwell's equations. In the second chapter Maxwell's equations are used to derive the various forms of the nonlinear Schrodinger equation (NSE) which describe optical wave propagation in the presence of a Kerr nonlinearity. The different forms of the NSE account for different propagation geometries and conditions. The numerical model based on the NSE which is used to derive many of the results in the remainder of the thesis is also described. In chapter three, the numerical model is employed to give a thorough description of the dynamics of the pulse behavior in the presence of spatiotemporal coupling. An explanation of enhanced beam-broadening in self-defocusing media and localized pulse compression in normally dispersive self-focusing media are presented. The remaining two chapters describe experimental conditions under which spatiotemporal coupling may become important. In chapter four, the model is used to describe a means to exploit the ultrafast Kerr nonlinearity to achieve pulse compression with spatial phase modulation. The process relies on the nonlinear coupling among the overlapping subbeams produced by the modulation resulting in an intensity-dependence of the steering angles of the several peaks of the modulated pulse. In the fifth and final chapter, the influence of spatiotemporal coupling on Z-scan measurements of the nonlinear refractive index is
NASA Astrophysics Data System (ADS)
Bona, J. L.; Chen, M.; Saut, J.-C.
2004-05-01
In part I of this work (Bona J L, Chen M and Saut J-C 2002 Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media I: Derivation and the linear theory J. Nonlinear Sci. 12 283-318), a four-parameter family of Boussinesq systems was derived to describe the propagation of surface water waves. Similar systems are expected to arise in other physical settings where the dominant aspects of propagation are a balance between the nonlinear effects of convection and the linear effects of frequency dispersion. In addition to deriving these systems, we determined in part I exactly which of them are linearly well posed in various natural function classes. It was argued that linear well-posedness is a natural necessary requirement for the possible physical relevance of the model in question. In this paper, it is shown that the first-order correct models that are linearly well posed are in fact locally nonlinearly well posed. Moreover, in certain specific cases, global well-posedness is established for physically relevant initial data. In part I, higher-order correct models were also derived. A preliminary analysis of a promising subclass of these models shows them to be well posed.
NASA Astrophysics Data System (ADS)
Dakova, D.; Dakova, A.; Slavchev, V.; Staykov, P.; Kovachev, L.
2016-01-01
In last two decades the phenomena resulting from the evolution of ultra-short laser pulses in nonlinear dispersive medium actively are being studied. The most commonly used equation for describing the dynamics of optical pulses in one-dimensional and planar waveguides is the standard nonlinear Schrodinger equation (NSE). It works very well for nanosecond and picosecond laser pulses, but in the frames of femtosecond optics, it is necessary two additional terms to be included. They are responsible for higher order of linear dispersion and dispersion of nonlinearity. These effects are significant in the range of ultra-short light pulses. In the present paper, it is presented a theoretical model of the propagation of optical solitons. We found an exact analytical soliton solution of the modified NSE, including third order of linear dispersion and dispersion of nonlinearity. It is possible to observe a soliton as a result of the dynamic balance between effects of higher order of dispersion and nonlinearity.
NASA Astrophysics Data System (ADS)
Li, Ping-Wah
1994-12-01
In his paper [J. Acoust. Soc. Am. 77, 2050 (1985)] Blackstock presented a generalized Burgers equation for the propagation of one-dimensional weakly nonlinear waves in various media. His results, and the approach he employed there, however, are limited to harmonic waves. In this paper, we present a general approach to model nonlinear waves of more general wave forms that propagate in media with arbitrary absorption and dispersion relations. The resulting equation is again called the generalized Burgers equation (to follow the terminology of the literature). It is found that steady shock solutions for various media can be described by the corresponding simplified version of the equation. An efficient numerical method by means of spectral analysis is developed for solving the generalized Burgers equation. Typical results exemplified by the case of a sinusoidal wave source are also reported in this paper.
NASA Astrophysics Data System (ADS)
Nikitenkova, S.; Singh, N.; Stepanyants, Y.
2015-12-01
In this paper, we revisit the problem of modulation stability of quasi-monochromatic wave-trains propagating in a media with the double dispersion occurring both at small and large wavenumbers. We start with the shallow-water equations derived by Shrira [Izv., Acad. Sci., USSR, Atmos. Ocean. Phys. (Engl. Transl.) 17, 55-59 (1981)] which describes both surface and internal long waves in a rotating fluid. The small-scale (Boussinesq-type) dispersion is assumed to be weak, whereas the large-scale (Coriolis-type) dispersion is considered as without any restriction. For unidirectional waves propagating in one direction, only the considered set of equations reduces to the Gardner-Ostrovsky equation which is applicable only within a finite range of wavenumbers. We derive the nonlinear Schrödinger equation (NLSE) which describes the evolution of narrow-band wave-trains and show that within a more general bi-directional equation the wave-trains, similar to that derived from the Ostrovsky equation, are also modulationally stable at relatively small wavenumbers k < kc and unstable at k > kc, where kc is some critical wavenumber. The NLSE derived here has a wider range of applicability: it is valid for arbitrarily small wavenumbers. We present the analysis of coefficients of the NLSE for different signs of coefficients of the governing equation and compare them with those derived from the Ostrovsky equation. The analysis shows that for weakly dispersive waves in the range of parameters where the Gardner-Ostrovsky equation is valid, the cubic nonlinearity does not contribute to the nonlinear coefficient of NLSE; therefore, the NLSE can be correctly derived from the Ostrovsky equation.
Nikitenkova, S; Singh, N; Stepanyants, Y
2015-12-01
In this paper, we revisit the problem of modulation stability of quasi-monochromatic wave-trains propagating in a media with the double dispersion occurring both at small and large wavenumbers. We start with the shallow-water equations derived by Shrira [Izv., Acad. Sci., USSR, Atmos. Ocean. Phys. (Engl. Transl.) 17, 55-59 (1981)] which describes both surface and internal long waves in a rotating fluid. The small-scale (Boussinesq-type) dispersion is assumed to be weak, whereas the large-scale (Coriolis-type) dispersion is considered as without any restriction. For unidirectional waves propagating in one direction, only the considered set of equations reduces to the Gardner-Ostrovsky equation which is applicable only within a finite range of wavenumbers. We derive the nonlinear Schrödinger equation (NLSE) which describes the evolution of narrow-band wave-trains and show that within a more general bi-directional equation the wave-trains, similar to that derived from the Ostrovsky equation, are also modulationally stable at relatively small wavenumbers k < kc and unstable at k > kc, where kc is some critical wavenumber. The NLSE derived here has a wider range of applicability: it is valid for arbitrarily small wavenumbers. We present the analysis of coefficients of the NLSE for different signs of coefficients of the governing equation and compare them with those derived from the Ostrovsky equation. The analysis shows that for weakly dispersive waves in the range of parameters where the Gardner-Ostrovsky equation is valid, the cubic nonlinearity does not contribute to the nonlinear coefficient of NLSE; therefore, the NLSE can be correctly derived from the Ostrovsky equation.
NASA Astrophysics Data System (ADS)
Kapoyko, Yury A.; Drozdov, Arkadiy A.; Kozlov, Sergei A.; Zhang, Xi-Cheng
2016-09-01
Simple arithmetic dependencies of the velocity of the mass center motion and the root-mean-square duration of initially single-cycle, two-cycle, and Gaussian pulses with a random number of oscillations under the pulse envelope are derived depending on their center frequency, initial duration, and peak field amplitude, as well as on dispersive and nonlinear characteristics of homogeneous isotropic dielectric media. In media with normal group dispersion, it is shown that due to nonresonant dispersion the square of the few-cycle pulse duration increases with distance inversely proportional to the fourth power of the number of input pulse cycles. In media with normal group dispersion, the square of the pulse duration is inversely proportional to the number of input pulse cycles due to cubic nonlinearity. In media with anomalous group dispersion, it is shown that due to cubic nonlinearity, few-cycle pulse self-compression decreases with the reduction of the number of cycles in the initial pulse. This pulse self-compression effect has a threshold nature and terminates at a fixed number of cycles of the input pulse. Such a number of cycles is determined by the input intensity and the central frequency of the pulse, as well as by the dispersive and nonlinear characteristics of the medium.
Aseeva, N. V. Gromov, E. M.; Tyutin, V. V.
2015-12-15
The dynamics of high-frequency field solitons is considered using the extended nonhomogeneous nonlinear Schrödinger equation with induced scattering from damped low-frequency waves (pseudoinduced scattering). This scattering is a 3D analog of the stimulated Raman scattering from temporal spatially homogeneous damped low-frequency modes, which is well known in optics. Spatial inhomogeneities of secondorder linear dispersion and cubic nonlinearity are also taken into account. It is shown that the shift in the 3D spectrum of soliton wavenumbers toward the short-wavelength region is due to nonlinearity increasing in coordinate and to decreasing dispersion. Analytic results are confirmed by numerical calculations.
NASA Astrophysics Data System (ADS)
Milgrom, Mordehai
2002-02-01
I investigate the properties of forces on bodies in theories governed by the generalized Poisson equation μ(|ϕ| /a0)ϕ] ∝ Gρ, for the potential ϕ produced by a distribution of sources ρ. This equation describes, inter alia, media with a response coefficient, μ, that depends on the field strength, such as in nonlinear, dielectric or diamagnetic, media; nonlinear transport problems with field-strength-dependent conductivity or diffusion coefficient; nonlinear electrostatics, as in the Born-Infeld theory; certain stationary potential flows in compressible fluids, in which case the forces act on sources or obstacles in the flow. The expressions for the force on a point charge are derived exactly for the limits of very low and very high charge. The force on an arbitrary body in an external field of asymptotically constant gradient, -g0, is shown to be F = Qg0, where Q is the total effective charge of the body. The corollary Q = 0 → F = 0 is a generalization of d'Alembert's paradox. I show that for G > 0 (as in Newtonian gravity) two point charges of the same (opposite) sign still attract (repel). The opposite is true for G < 0. I discuss its generalization to extended bodies and derive virial relations.
Acoustic Rectification in Dispersive Media
NASA Technical Reports Server (NTRS)
Cantrell, John H.
2008-01-01
It is shown that the shapes of acoustic radiation-induced static strain and displacement pulses (rectified acoustic pulses) are defined locally by the energy density of the generating waveform. Dispersive properties are introduced analytically by assuming that the rectified pulses are functionally dependent on a phase factor that includes both dispersive and nonlinear terms. The dispersion causes an evolutionary change in the shape of the energy density profile that leads to the generation of solitons experimentally observed in fused silica.
ACOUSTIC RECTIFICATION IN DISPERSIVE MEDIA
Cantrell, John H.
2009-03-03
It is shown that the shapes of acoustic radiation-induced static strain and displacement pulses (rectified acoustic pulses) are defined locally by the energy density of the generating waveform. Dispersive properties are introduced analytically by assuming that the rectified pulses are functionally dependent on a phase factor that includes both dispersive and nonlinear terms. The dispersion causes an evolutionary change in the shape of the energy density profile that leads to the generation of solitons experimentally observed in fused silica.
NASA Technical Reports Server (NTRS)
Goorjian, Peter M.; Taflove, Allen
1992-01-01
The initial results for femtosecond electromagnetic soliton propagation and collision obtained from first principles, i.e., by a direct time integration of Maxwell's equations are reported. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit the modeling of 2D and 3D optical soliton propagation, scattering, and switching from the full-vector Maxwell's equations.
NASA Astrophysics Data System (ADS)
Bona, G.; Chen, J. A.; Saut, Jing Ping
2002-08-01
Considered herein are a number of variants of the classical Boussinesq system and their higher-order generalizations. Such equations were first derived by Boussinesq to describe the two-way propagation of small-amplitude, long wavelength, gravity waves on the surface of water in a canal. These systems arise also when modeling the propagation of long-crested waves on large lakes or the ocean and in other contexts. Depending on the modeling of dispersion, the resulting system may or may not have a linearization about the rest state which is well posed. Even when well posed, the linearized system may exhibit a lack of conservation of energy that is at odds with its status as an approximation to the Euler equations. In the present script, we derive a four-parameter family of Boussinesq systems from the two-dimensional Euler equations for free-surface flow and formulate criteria to help decide which of these equations one might choose in a given modeling situation. The analysis of the systems according to these criteria is initiated.
Nonlinear dispersive similariton: spectral interferometric study
Zeytunyan, A S; Khachikyan, T J; Palandjan, K A; Esayan, G L; Muradyan, L Kh
2010-06-23
A similariton formed in a passive optical fibre is experimentally found and investigated by spectral interferometry completely characterising the complex radiation field. A nonlinear dispersive character of similariton formation leads to chirp linearisation and spectrotemporal similarity of this similariton. (nonlinear optical phenomena)
Diffractive wave transmission in dispersive media
NASA Astrophysics Data System (ADS)
Lescarret, Vincent
The aim of this paper is to study the reflection-transmission of diffractive geometrical optic rays described by semi-linear symmetric hyperbolic systems such as the Maxwell-Lorentz equations with the anharmonic model of polarization. The framework is that of P. Donnat's thesis [P. Donnat, Quelques contributions mathématiques en optique non linéaire, chapters 1 and 2, thèse, 1996] and V. Lescarret [V. Lescarret, Wave transmission in dispersive media, M3AS 17 (4) (2007) 485-535]: we consider an infinite WKB expansion of the wave over long times/distances O(1/ɛ) and because of the boundary, we decompose each profile into a hyperbolic (purely oscillating) part and elliptic (evanescent) part as in M. William [M. William, Boundary layers and glancing blow-up in nonlinear geometric optics, Ann. Sci. École Norm. Sup. 33 (2000) 132-209]. Then to get the usual sublinear growth on the hyperbolic part of the profiles, for every corrector, we consider E, the space of bounded functions decomposing into a sum of pure transports and a "quasi compactly" supported part. We make a detailed analysis on the nonlinear interactions on E which leads us to make a restriction on the set of resonant phases. We finally give a convergence result which justifies the use of "quasi compactly" supported profiles.
Wave modulation in a nonlinear dispersive medium
Kim, Y.C.; Khadra, L.; Powers, E.J.
1980-11-01
A model describing the simultaneous amplitude and phase modulation of a carrier wave propagating in a nonlinear dispersive medium is developed in terms of nonlinear wave-wave interactions between the sidebands and a low frequency wave. It is also shown that the asymmetric distribution of sidebands is determined by the wavenumber dependence of the coupling coefficient. Digital complex demodulation techniques are used to study modulated waves in a weakly ionized plasma and the experimental results support the analytical model.
Nonlinear dispersion effects in elastic plates: numerical modelling and validation
NASA Astrophysics Data System (ADS)
Kijanka, Piotr; Radecki, Rafal; Packo, Pawel; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.
2017-04-01
Nonlinear features of elastic wave propagation have attracted significant attention recently. The particular interest herein relates to complex wave-structure interactions, which provide potential new opportunities for feature discovery and identification in a variety of applications. Due to significant complexity associated with wave propagation in nonlinear media, numerical modeling and simulations are employed to facilitate design and development of new measurement, monitoring and characterization systems. However, since very high spatio- temporal accuracy of numerical models is required, it is critical to evaluate their spectral properties and tune discretization parameters for compromise between accuracy and calculation time. Moreover, nonlinearities in structures give rise to various effects that are not present in linear systems, e.g. wave-wave interactions, higher harmonics generation, synchronism and | recently reported | shifts to dispersion characteristics. This paper discusses local computational model based on a new HYBRID approach for wave propagation in nonlinear media. The proposed approach combines advantages of the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE). The methods are investigated in the context of their accuracy for predicting nonlinear wavefields, in particular shifts to dispersion characteristics for finite amplitude waves and secondary wavefields. The results are validated against Finite Element (FE) calculations for guided waves in copper plate. Critical modes i.e., modes determining accuracy of a model at given excitation frequency - are identified and guidelines for numerical model parameters are proposed.
Electromagnetic energy momentum in dispersive media
Philbin, T. G.
2011-01-15
The standard derivations of electromagnetic energy and momentum in media take Maxwell's equations as the starting point. It is well known that for dispersive media this approach does not directly yield exact expressions for the energy and momentum densities. Although Maxwell's equations fully describe electromagnetic fields, the general approach to conserved quantities in field theory is not based on the field equations, but rather on the action. Here an action principle for macroscopic electromagnetism in dispersive, lossless media is used to derive the exact conserved energy-momentum tensor. The time-averaged energy density reduces to Brillouin's simple formula when the fields are monochromatic. The time-averaged momentum density for monochromatic fields corresponds to the familiar Minkowski expression DxB, but for general fields in dispersive media the momentum density does not have the Minkowski value. The results are unaffected by the debate over momentum balance in light-matter interactions.
Nonlinear optical characterization of Disperse Orange 3
NASA Astrophysics Data System (ADS)
Derkowska-Zielinska, Beata; Fedus, Kamil; Wang, Hongzhen; Cassagne, Christophe; Boudebs, Georges
2017-10-01
The nonlinear optical responses of Disperse Orange 3 (DO3) dissolved in tetrahydrofuran (THF) with different concentrations were investigated by Z-scan D4σ technique employing 12 ps and 17 ps pulses of Nd:YAG laser at 532 nm and 1064 nm, respectively. The comparison of the experimental results at both wavelengths demonstrates the strong influence of the resonant phenomena related to the linear absorption on the nonlinear response at 532 nm. In particular, DO3 solution was found to exhibit negative resonant nonlinear refraction with negligible saturable and multi-photon absorption. Moreover, the competition between negative and positive nonlinear refractive indices (n2) of the solute and the solvent was observed at low concentrations. The linear dependence of n2 on the latter quantity allowed to estimate an effective second-order hyperpolarizability of DO3 molecule at 532 nm.
Dispersivity in heterogeneous permeable media
Chesnut, D.A.
1994-01-01
When one fluid displaces another through a one-dimensional porous medium, the composition changes from pure displacing fluid at the inlet to pure displaced fluid some distance downstream. The distance over which an arbitrary percentage of this change occurs is defined as the mixing zone length, which increases with increasing average distance traveled by the displacement front. For continuous injection, the mixing zone size can be determined from a breakthrough curve as the time required for the effluent displacing fluid concentration to change from, say, 10% to 90%. In classical dispersion theory, the mixing zone grows in proportion to the square root of the mean distance traveled, or, equivalently, to the square root of the mean breakthrough time. In a multi-dimensional heterogeneous medium, especially at field scales, the size of the mixing zone grows almost linearly with mean distance or travel time. If an observed breakthrough curve is forced to fit the, clinical theory, the resulting effective dispersivity, instead of being constant, also increases almost linearly with the spatial or temporal scale of the problem. This occurs because the heterogeneity in flow properties creates a corresponding velocity distribution along the different flow pathways from the inlet to the outlet of the system. Mixing occurs mostly at the outlet, or wherever the fluid is sampled, rather than within the medium. In this paper, we consider the effects. of this behavior on radionuclide or other contaminant migration.
Nonlinear Acoustics in a Dispersive Continuum: Random Waves, Radiation Pressure, and Quantum Noise.
1983-03-01
Karpman , Nonlinear Waves in Dispersive Media, Pergamon Press, New York, 1975, p. 76. 26. R. Beyers, Nonlinear Acoustics, U.S. Government Printing...20301 U. S. Army Research nffice 2 copies Box 12211 Research Triangle Park tlorth Carolina 27709 Defense Technical Information Center 12 copies Cameron
Phase space distributions tailored for dispersive media.
Petruccelli, Jonathan C; Alonso, Miguel A
2010-05-01
New phase space distributions are proposed for describing pulse propagation in dispersive media for one spatial dimension. These distributions depend on time, position, and velocity, so that the pulse's spatial propagation or temporal evolution is described by a free-particle-like transformation followed by integration over velocity. Examples are considered for approximate Lorentz-model dielectrics and metallic waveguides.
Multipole vector solitons in nonlocal nonlinear media.
Kartashov, Yaroslav V; Torner, Lluis; Vysloukh, Victor A; Mihalache, Dumitru
2006-05-15
We show that multipole solitons can be made stable via vectorial coupling in bulk nonlocal nonlinear media. Such vector solitons are composed of mutually incoherent nodeless and multipole components jointly inducing a nonlinear refractive index profile. We found that stabilization of the otherwise highly unstable multipoles occurs below certain maximum energy flow. Such a threshold is determined by the nonlocality degree.
Dispersion managed solitons in the presence of saturated nonlinearity
NASA Astrophysics Data System (ADS)
Hundertmark, Dirk; Lee, Young-Ran; Ried, Tobias; Zharnitsky, Vadim
2017-10-01
The averaged dispersion managed nonlinear Schrödinger equation with saturated nonlinearity is considered. It is shown that under rather general assumptions on the saturated nonlinearity, the ground state solution corresponding to the dispersion managed soliton can be found for both zero residual dispersion and positive residual dispersion. The same applies to diffraction management solitons, which are a discrete version describing certain waveguide arrays.
Generalized dispersive wave emission in nonlinear fiber optics.
Webb, K E; Xu, Y Q; Erkintalo, M; Murdoch, S G
2013-01-15
We show that the emission of dispersive waves in nonlinear fiber optics is not limited to soliton-like pulses propagating in the anomalous dispersion regime. We demonstrate, both numerically and experimentally, that pulses propagating in the normal dispersion regime can excite resonant dispersive radiation across the zero-dispersion wavelength into the anomalous regime.
Effect of chromatic dispersion on nonlinear phase noise.
Green, A G; Mitra, P P; Wegener, L G L
2003-12-15
We consider the combined effects of amplified spontaneous emission noise, optical Kerr nonlinearity, and chromatic dispersion on phase noise in an optical communication system. The effect of amplified spontaneous emission noise and Kerr nonlinearity were considered previously by Gordon and Mollenauer [Opt. Lett. 15, 1351 (1990)], and the effect of nonlinearity was found to be severe. We investigate the effect of chromatic dispersion on phase noise and show that it can either enhance or suppress the nonlinear noise amplification. For large absolute values of dispersion the nonlinear effect is suppressed, and the phase noise is reduced to its linear value. For a range of negative values of dispersion, however, nonlinear phase noise is enhanced and exhibits a maximum related to the modulation instability found in amplitude fluctuations. Nonlinear phase noise is quenched by these effects even in dispersion-compensated systems; the degree of suppression is sensitively dependent on the dispersion map. We demonstrate these results analytically with a simple linearized model.
Dark periodic lattices in nonlinear liquid media
NASA Astrophysics Data System (ADS)
Alvarado-Méndez, Edgar; Trejo-Durán, Mónica; Cano-Lara, Miroslava; Huerta-Mascotte, Eduardo; Castaňo, Víctor M.
2007-11-01
Experimental evidence of the formation of one- and two-dimensional dark periodic lattices in a negative Kerr-type nonlinear liquid media is presented. Bright periodic lattices propagate throughout two nonlinear liquids [alcohol with rhodamine (R6G), and acetone with R6G] as the negative nonlinear refractive index forms a dark periodic lattice. Our experiments demonstrate that the nonlinearity increases with the optical power and that a proper selection of the period leads to self-phase modulation of the lattice.
Viscous Fluid Conduits as a Prototypical Nonlinear Dispersive Wave Platform
NASA Astrophysics Data System (ADS)
Lowman, Nicholas K.
This thesis is devoted to the comprehensive characterization of slowly modulated, nonlinear waves in dispersive media for physically-relevant systems using a threefold approach: analytical, long-time asymptotics, careful numerical simulations, and quantitative laboratory experiments. In particular, we use this interdisciplinary approach to establish a two-fluid, interfacial fluid flow setting known as viscous fluid conduits as an ideal platform for the experimental study of truly one dimensional, unidirectional solitary waves and dispersively regularized shock waves (DSWs). Starting from the full set of fluid equations for mass and linear momentum conservation, we use a multiple-scales, perturbation approach to derive a scalar, nonlinear, dispersive wave equation for the leading order interfacial dynamics of the system. Using a generalized form of the approximate model equation, we use numerical simulations and an analytical, nonlinear wave averaging technique, Whitham-El modulation theory, to derive the key physical features of interacting large amplitude solitary waves and DSWs. We then present the results of quantitative, experimental investigations into large amplitude solitary wave interactions and DSWs. Overtaking interactions of large amplitude solitary waves are shown to exhibit nearly elastic collisions and universal interaction geometries according to the Lax categories for KdV solitons, and to be in excellent agreement with the dynamics described by the approximate asymptotic model. The dispersive shock wave experiments presented here represent the most extensive comparison to date between theory and data of the key wavetrain parameters predicted by modulation theory. We observe strong agreement. Based on the work in this thesis, viscous fluid conduits provide a well-understood, controlled, table-top environment in which to study universal properties of dispersive hydrodynamics. Motivated by the study of wave propagation in the conduit system, we
Relativistic radiation transport in dispersive media
Kichenassamy, S.; Krikorian, R.A.
1985-10-15
A general-relativistic radiative transfer equation in an isotropic, weakly absorbing, nonmagnetized dispersive medium is derived using the kinetic-theoretical approach and the relativistic Hamiltonian theory of geometrical optics in those media. It yields the generally accepted classical equation in the special-relativistic approximation and in stationary conditions. The influence of the gravitational field and of space-time variations of the refractive index n on the radiation distribution is made explicit in the case of spherical symmetry.
Generation of dispersion in nondispersive nonlinear waves in thermal equilibrium.
Lee, Wonjung; Kovačič, Gregor; Cai, David
2013-02-26
In this work, we examine the important theoretical question of whether dispersion relations can arise from purely nonlinear interactions among waves that possess no linear dispersive characteristics. Using two prototypical examples of nondispersive waves, we demonstrate how nonlinear interactions can indeed give rise to effective dispersive-wave-like characteristics in thermal equilibrium. Physically, these example systems correspond to the strong nonlinear coupling limit in the theory of wave turbulence. We derive the form of the corresponding dispersion relation, which describes the effective dispersive structures, using the generalized Langevin equations obtained in the Zwanzig-Mori projection framework. We confirm the validity of this effective dispersion relation in our numerical study using the wavenumber-frequency spectral analysis. Our work may provide insight into an important connection between highly nonlinear turbulent wave systems, possibly with no discernible dispersive properties, and the dispersive nature of the corresponding renormalized waves.
Nonlinear lattice waves in heterogeneous media
NASA Astrophysics Data System (ADS)
Laptyeva, T. V.; Ivanchenko, M. V.; Flach, S.
2014-12-01
We discuss recent advances in the understanding of the dynamics of nonlinear lattice waves in heterogeneous media, which enforce complete wave localization in the linear wave equation limit, especially Anderson localization for random potentials, and Aubry-André localization for quasiperiodic potentials. Additional nonlinear terms in the wave equations can either preserve the phase-coherent localization of waves, or destroy it through nonintegrability and deterministic chaos. Spreading wave packets are observed to show universal features in their dynamics which are related to properties of nonlinear diffusion equations.
Amplitude-dependent Lamb wave dispersion in nonlinear plates.
Packo, Pawel; Uhl, Tadeusz; Staszewski, Wieslaw J; Leamy, Michael J
2016-08-01
The paper presents a perturbation approach for calculating amplitude-dependent Lamb wave dispersion in nonlinear plates. Nonlinear dispersion relationships are derived in closed form using a hyperelastic stress-strain constitutive relationship, the Green-Lagrange strain measure, and the partial wave technique integrated with a Lindstedt-Poincaré perturbation approach. Solvability conditions are derived using an operator formalism with inner product projections applied against solutions to the adjoint problem. When applied to the first- and second-order problems, these solvability conditions lead to amplitude-dependent, nonlinear dispersion corrections for frequency as a function of wavenumber. Numerical simulations verify the predicted dispersion shifts for an example nonlinear plate. The analysis and identification of amplitude-dependent, nonlinear Lamb wave dispersion complements recent research focusing on higher harmonic generation and internally resonant waves, which require precise dispersion relationships for frequency-wavenumber matching.
Computational studies of nonlinear dispersive plasma systems
NASA Astrophysics Data System (ADS)
Qian, Xin
Plasma systems with dispersive waves are ubiquitous. Dispersive waves have the property that their wave velocity depends on the wave number of the wave. These waves show up in weakly as well as strongly coupled plasmas, and play a significant role in the underlying plasma dynamics. Dispersive waves bring new challenges to the computer simulation of nonlinear phenomena. The goal of this thesis is to discuss two computational studies of plasma phenomena, one drawn from strongly coupled complex or dusty plasmas, and the other from weakly coupled hydrogen plasmas. In the realm of dusty plasmas, we focus on the problem of three-dimensional (3D) Mach cones which we study by means of Molecular Dynamics (MD) simulations, assuming that the dust particles interact via a Yukawa potential. While laboratory and MD simulations have explored thoroughly the properties of Mach cones in 2D, elucidating the important role of dispersive waves in the formation of multiple cones, the simulations presented in this thesis represent the first 3D MD studies of Mach cones in strongly coupled dusty plasmas. These results have qualitative similarities with experimental observations on 3D Mach cones from the PK-3 plus project, which studies complex plasmas under microgravity conditions aboard the International Space station. In the realm of weakly coupled plasmas, we present results on the application of non-oscillatory central schemes to Hall MHD reconnection problems, in which the presence of dispersive whistler waves presents a formidable challenge for numerical algorithms that rely on explicit time-stepping schemes. In particular, we focus on the semi-discrete central formulation of Kurganov and Tadmor (2000), which has the advantage that it allow for larger time steps, and with significantly smaller numerical viscosity, than fully discrete schemes. We implement the Hall MHD equations through the CentPACK software package that implements the Kurganov-Tadmor formulation for a wide range of
Nonlinear flow in porous media
NASA Astrophysics Data System (ADS)
Rojas, Sergio Jesus
1998-07-01
Numerical solutions of the Navier-Stokes equations in two-dimensional quasi-periodic and quasi-isotropic random media were obtained to analyze the local and large scale aspects of finite Reynolds number flow. For Reynolds number less than one, the results show a first correction to Darcy's law which is cubic in the Darcy (averaged) velocity, while for Reynolds number greater than one, the results are in agreement with Forchheimer equation. That is, the correction to Darcy's law is quadratic in the average (Darcy) velocity. The cubic correction to Darcy's law support Mei and Auriault's (1991) theoretical study, based on homogenization theory. In addition, the results show support to a unifying empirical equation describing fluid flow in porous media of similar structure, first proposed by Beavers and Sparrow (1969). Also, the results show agreement, except by a multiplicative constant, with Sangani and Acrivos (1982) equation for the drag on dilute array of cylinders.
Spiraling multivortex solitons in nonlocal nonlinear media.
Buccoliero, Daniel; Desyatnikov, Anton S; Krolikowski, Wieslaw; Kivshar, Yuri S
2008-01-15
We demonstrate the existence of a broad class of higher-order rotating spatial solitons in nonlocal nonlinear media. We employ the generalized Hermite-Laguerre-Gaussian ansatz for constructing multivortex soliton solutions and study numerically their dynamics and stability. We discuss in detail the tripole soliton carrying two spiraling phase dislocations, or self-trapped optical vortices.
Nonlinear Poisson Equation for Heterogeneous Media
Hu, Langhua; Wei, Guo-Wei
2012-01-01
The Poisson equation is a widely accepted model for electrostatic analysis. However, the Poisson equation is derived based on electric polarizations in a linear, isotropic, and homogeneous dielectric medium. This article introduces a nonlinear Poisson equation to take into consideration of hyperpolarization effects due to intensive charges and possible nonlinear, anisotropic, and heterogeneous media. Variational principle is utilized to derive the nonlinear Poisson model from an electrostatic energy functional. To apply the proposed nonlinear Poisson equation for the solvation analysis, we also construct a nonpolar solvation energy functional based on the nonlinear Poisson equation by using the geometric measure theory. At a fixed temperature, the proposed nonlinear Poisson theory is extensively validated by the electrostatic analysis of the Kirkwood model and a set of 20 proteins, and the solvation analysis of a set of 17 small molecules whose experimental measurements are also available for a comparison. Moreover, the nonlinear Poisson equation is further applied to the solvation analysis of 21 compounds at different temperatures. Numerical results are compared to theoretical prediction, experimental measurements, and those obtained from other theoretical methods in the literature. A good agreement between our results and experimental data as well as theoretical results suggests that the proposed nonlinear Poisson model is a potentially useful model for electrostatic analysis involving hyperpolarization effects. PMID:22947937
Nonlinear Poisson equation for heterogeneous media.
Hu, Langhua; Wei, Guo-Wei
2012-08-22
The Poisson equation is a widely accepted model for electrostatic analysis. However, the Poisson equation is derived based on electric polarizations in a linear, isotropic, and homogeneous dielectric medium. This article introduces a nonlinear Poisson equation to take into consideration of hyperpolarization effects due to intensive charges and possible nonlinear, anisotropic, and heterogeneous media. Variational principle is utilized to derive the nonlinear Poisson model from an electrostatic energy functional. To apply the proposed nonlinear Poisson equation for the solvation analysis, we also construct a nonpolar solvation energy functional based on the nonlinear Poisson equation by using the geometric measure theory. At a fixed temperature, the proposed nonlinear Poisson theory is extensively validated by the electrostatic analysis of the Kirkwood model and a set of 20 proteins, and the solvation analysis of a set of 17 small molecules whose experimental measurements are also available for a comparison. Moreover, the nonlinear Poisson equation is further applied to the solvation analysis of 21 compounds at different temperatures. Numerical results are compared to theoretical prediction, experimental measurements, and those obtained from other theoretical methods in the literature. A good agreement between our results and experimental data as well as theoretical results suggests that the proposed nonlinear Poisson model is a potentially useful model for electrostatic analysis involving hyperpolarization effects.
Improved fiber nonlinearity mitigation in dispersion managed optical OFDM links
NASA Astrophysics Data System (ADS)
Tamilarasan, Ilavarasan; Saminathan, Brindha; Murugappan, Meenakshi
2017-02-01
Fiber nonlinearity is seen as a capacity limiting factor in OFDM based dispersion managed links since the Four Wave Mixing effects become enhanced due to the high PAPR. In this paper, the authors have compared the linear and nonlinear PAPR reduction techniques for fiber nonlinearity mitigation in OFDM based dispersion managed links. In the existing optical systems, linear transform techniques such as SLM and PTS have been implemented to reduce nonlinear effects. In the proposed study, superior performance of the L2-by-3 nonlinear transform technique is demonstrated for PAPR reduction to mitigate fiber nonlinearities. The performance evaluation is carried out by interfacing multiple simulators. The results of both linear and nonlinear transform techniques have been compared and the results show that nonlinear transform technique outperforms the linear transform in terms of nonlinearity mitigation and improved BER performance.
Absorbing Boundary Conditions For Optical Pulses In Dispersive, Nonlinear Materials
NASA Technical Reports Server (NTRS)
Goorjian, Peter M.; Kwak, Dochan (Technical Monitor)
1995-01-01
This paper will present results in computational nonlinear optics. An algorithm will be described that provides absorbing boundary conditions for optical pulses in dispersive, nonlinear materials. A new numerical absorber at the boundaries has been developed that is responsive to the spectral content of the pulse. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of "light bullet" like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. Comparisons will be shown of calculations that use the standard boundary conditions and the new ones.
Nonlinear and Dispersive Optical Pulse Propagation
NASA Astrophysics Data System (ADS)
Dijaili, Sol Peter
In this dissertation, there are basically four novel contributions to the field of picosecond pulse propagation and measurement. The first contribution is the temporal ABCD matrix which is an analog of the traditional ABCD ray matrices used in Gaussian beam propagation. The temporal ABCD matrix allows for the easy calculation of the effects of linear chirp or group velocity dispersion in the time domain. As with Gaussian beams in space, there also exists a complete Hermite-Gaussian basis in time whose propagation can be tracked with the temporal ABCD matrices. The second contribution is the timing synchronization between a colliding pulse mode-locked dye laser and a gain-switched Fabry-Perot type AlGaAs laser diode that has achieved less than 40 femtoseconds of relative timing jitter by using a pulsed optical phase lock loop (POPLL). The relative timing jitter was measured using the error voltage of the feedback loop. This method of measurement is accurate since the frequencies of all the timing fluctuations fall within the loop bandwidth. The novel element is a broad band optical cross-correlator that can resolve femtosecond time delay errors between two pulse trains. The third contribution is a novel dispersive technique of determining the nonlinear frequency sweep of a picosecond pulse with relatively good accuracy. All the measurements are made in the time domain and hence there is no time-bandwidth limitation to the accuracy. The fourth contribution is the first demonstration of cross -phase modulation in a semiconductor laser amplifier where a variable chirp was observed. A simple expression for the chirp imparted on a weak signal pulse by the action of a strong pump pulse is derived. A maximum frequency excursion of 16 GHz due to the cross-phase modulation was measured. A value of 5 was found for alpha _{xpm} which is a factor for characterizing the cross-phase modulation in a similar manner to the conventional linewidth enhancement factor, alpha.
Dispersion and nonlinear effects in OFDM-RoF system
NASA Astrophysics Data System (ADS)
Alhasson, Bader H.; Bloul, Albe M.; Matin, M.
2010-08-01
The radio-over-fiber (RoF) network has been a proven technology to be the best candidate for the wireless-access technology, and the orthogonal frequency division multiplexing (OFDM) technique has been established as the core technology in the physical layer of next generation wireless communication system, as a result OFDM-RoF has drawn attentions worldwide and raised many new research topics recently. At the present time, the trend of information industry is towards mobile, wireless, digital and broadband. The next generation network (NGN) has motivated researchers to study higher-speed wider-band multimedia communication to transmit (voice, data, and all sorts of media such as video) at a higher speed. The NGN would offer services that would necessitate broadband networks with bandwidth higher than 2Mbit/s per radio channel. Many new services emerged, such as Internet Protocol TV (IPTV), High Definition TV (HDTV), mobile multimedia and video stream media. Both speed and capacity have been the key objectives in transmission. In the meantime, the demand for transmission bandwidth increased at a very quick pace. The coming of 4G and 5G era will provide faster data transmission and higher bit rate and bandwidth. Taking advantages of both optical communication and wireless communication, OFDM Radio over Fiber (OFDM-RoF) system is characterized by its high speed, large capacity and high spectral efficiency. However, up to the present there are some problems to be solved, such as dispersion and nonlinearity effects. In this paper we will study the dispersion and nonlinearity effects and their elimination in OFDM-radio-over-fiber system.
Special discontinuities in nonlinearly elastic media
NASA Astrophysics Data System (ADS)
Chugainova, A. P.
2017-06-01
Solutions of a nonlinear hyperbolic system of equations describing weakly nonlinear quasitransverse waves in a weakly anisotropic elastic medium are studied. The influence of small-scale processes of dissipation and dispersion is investigated. The small-scale processes determine the structure of discontinuities (shocks) and a set of discontinuities with a stationary structure. Among the discontinuities with a stationary structure, there are special ones that, in addition to relations following from conservation laws, satisfy additional relations required for the existence of their structure. In the phase plane, the structure of such discontinuities is represented by an integral curve joining two saddles. Special discontinuities lead to nonunique self-similar solutions of the Riemann problem. Asymptotics of non-self-similar problems for equations with dissipation and dispersion are found numerically. These asymptotics correspond to self-similar solutions of the problems.
Dispersion-engineered and highly nonlinear microstructured polymer optical fibres
NASA Astrophysics Data System (ADS)
Frosz, Michael H.; Nielsen, Kristian; Hlubina, Petr; Stefani, Alessio; Bang, Ole
2009-05-01
We demonstrate dispersion-engineering of microstructured polymer optical fibres (mPOFs) made of poly(methyl methacrylate) (PMMA). A significant shift of the total dispersion from the material dispersion is confirmed through measurement of the mPOF dispersion using white-light spectral interferometry. The influence of strong loss peaks on the dispersion (through the Kramers-Kronig relations) is investigated theoretically. It is found that the strong loss peaks of PMMA above 1100 nm can significantly modify the dispersion, while the losses below 1100 nm only modify the dispersion slightly. To increase the nonlinearity of the mPOFs we investigated doping of PMMA with the highly-nonlinear dye Disperse Red 1. Both doping of a PMMA cane and direct doping of a PMMA mPOF was performed.
Dispersion of sound in dilute suspensions with nonlinear particle relaxation.
Kandula, Max
2010-03-01
The theory accounting for nonlinear particle relaxation (viscous and thermal) has been applied to the prediction of dispersion of sound in dilute suspensions. The results suggest that significant deviations exist for sound dispersion between the linear and nonlinear theories at large values of omegatau(d), where omega is the circular frequency and tau(d) is the Stokesian particle relaxation time. It is revealed that the nonlinear effect on the dispersion coefficient due to viscous contribution is larger relative to that of thermal conduction.
Dispersion of Sound in Dilute Suspensions with Nonlinear Particle Relaxation
NASA Technical Reports Server (NTRS)
Kandula, Max
2010-01-01
The theory accounting for nonlinear particle relaxation (viscous and thermal) has been applied to the prediction of dispersion of sound in dilute suspensions. The results suggest that significant deviations exist for sound dispersion between the linear and nonlinear theories at large values of Omega(Tau)(sub d), where Omega is the circular frequency, and Tau(sub d) is the Stokesian particle relaxation time. It is revealed that the nonlinear effect on the dispersion coefficient due to viscous contribution is larger relative to that of thermal conduction
Nonlinearity compensation using dispersion-folded digital backward propagation.
Zhu, Likai; Li, Guifang
2012-06-18
A computationally efficient dispersion-folded (D-folded) digital backward propagation (DBP) method for nonlinearity compensation of dispersion-managed fiber links is proposed. At the optimum power level of long-haul fiber transmission, the optical waveform evolution along the fiber is dominated by the chromatic dispersion. The optical waveform and, consequently, the nonlinear behavior of the optical signal repeat at locations of identical accumulated dispersion. Hence the DBP steps can be folded according to the accumulated dispersion. Experimental results show that for 6,084 km single channel transmission, the D-folded DBP method reduces the computation by a factor of 43 with negligible penalty in performance. Simulation of inter-channel nonlinearity compensation for 13,000 km wavelength-division multiplexing (WDM) transmission shows that the D-folded DBP method can reduce the computation by a factor of 37.
Nonlinear Dispersion of Magnetostatic Surface Waves on Ferromagnetic Films
NASA Astrophysics Data System (ADS)
A, D. Boardman; Bao, Jiashan; Wang, Qi; Cai, Yingshi; S, A. Nikitov
1991-11-01
The wave equation of nonlinear magnetostatic surface waves (MSSW) on ferromagnetic films is derived and its solution is found. The nonlinear dispersion relation of MSSW is discussed. Our result shows that the wave power has a little effect to the frequency shift of MSSW with lower frequency, but has a considerably larger effect to that with higher frequency within the band.
Imaging Through Random Discrete-Scatterer Dispersive Media
2015-08-27
AFRL-AFOSR-VA-TR-2015-0255 Imaging through random discrete-scatterer dispersive media Elizabeth Bleszynski MONOPOLE RESEARCH THOUSAND OAKS CA Final...DATES COVERED Final report 15 April 2012 – 14 April 2015 4. TITLE AND SUBTITLE Imaging Through Random Discrete-Scatterer Dispersive Media 5. FUNDING...and/or target detection through optically obscuring, dilute, discrete-scatterer media such as clouds, fog, dust and other aerosols. (A) Properties of
Plasma metamaterials as cloaking and nonlinear media
NASA Astrophysics Data System (ADS)
Sakai, O.; Yamaguchi, S.; Bambina, A.; Iwai, A.; Nakamura, Y.; Tamayama, Y.; Miyagi, S.
2017-01-01
Plasma metamaterials, composites of low-temperature plasmas and periodic functional microstructures, work as cloaking and nonlinear media. Due to functions of the microstructures like negative permeability, electromagnetic waves in and around plasma metamaterials propagate in a quite different manner from the case with the conventional space in which relative permeability is positive and unity. Using plasmas and plasma metamaterials, we achieve various controls of microwave propagating paths such as unidirectionality and cloaking in the two- or 3D spaces. For instance, a concentric plasma layer makes wave propagation unidirectional, and waves propagate in different routes when they start inside or outside the concentric layer. Furthermore, due to spatial permittivity gradient and anisotropic refractive index, electromagnetic waves detour in plasma metamaterial layers. Another significant point that plasma metamaterials can realize is nonlinearity. When we study high-power electromagnetic waves propagating in them, we observe several properties describable in terms of nonlinear dynamics and nonlinear photonics. Microwaves beyond threshold energy trigger bifurcations in plasma permittivity, and the second harmonic wave detected simultaneously is generated with strong emission levels. Such electromagnetic wave propagation is achieved with advantages over other materials, since plasmas and metallic microstructures work in harmony and in synergy.
Deciphering Nonlinear Waves in Excitable Media
NASA Astrophysics Data System (ADS)
Jung, Peter; Zhou, Yin; Gailey, Paul
2000-03-01
The analysis of dynamics in spatially extended systems is often hampered by only partially accessible information. Prominent examples are the electric excitation waves in cardiac tissue. In many cases, however, projected data streams, presenting integrated measures of the entire system, are available. In the case of cardiac tissue such an integrated measure can be the heart-dipole vector. EEG's are examples of integrated measures of organized spatiotemporal activity in brain tissue. As an example we consider nonlinear waves in noisy excitable media. We discuss the fingerprints of their spatiotemporal properties burried in data streams of integrated measures.
Optical wavemixing in nonlinear absorptive Kerr media
NASA Astrophysics Data System (ADS)
Skirtach, Andrei G.
1997-12-01
This dissertation presents both detailed experimental and extensive theoretical studies of optical wavemixing in nonlinear absorptive Kerr media. Non-degenerate two wave mixing (NDTWM) is a simple and powerful technique widely used to study the nonlinear refractive index and the grating decay time. It is unique due to its ability to separate the phase and the absorptive grating contributions. The work included in this thesis has evolved from trying to explain the unexplained results on the symmetric component of the NDTWM gain reported as 'anomalous' behavior in ruby. We note that all previous theories for NDTWM have taken the approximation that the strong pump beam intensity was constant. In this approximation, the origin of unsymmetry in energy exchange between the two interacting beams was due only to the absorption grating of the weak probe beam. We have shown both experimentally and theoretically that the contribution of the absorption grating can be neglected but not the nonlinear bias absorption-just opposite to what had been common practice. Our approach also accounts for a range of inconsistencies related to intensity dependence of both the NDTWM gain and ratio of the imaginary to the real part of the nonlinear refractive index. Weakening the probe beam, earlier believed to improve accuracy of the approximation of the constant pump beam, actually destroys the symmetry of the energy exchange between the beams, enhancing the weak probe beam at the expense of the pump beam due to nonlinear absorption. This same two-beam coupling analysis has also been applied to interpret non-degenerate four wave mixing. Amplification of the phase conjugate signal is thus obtained. The spectral response in the frequency domain results in a tunable notch filter which can be controlled by the incident intensities of the pump beams.
Compact bright pulse and ultrashort-pulse in the nonlinear Kerr-like media
NASA Astrophysics Data System (ADS)
Pokam Nguewawe, Chancelor; Yemele, David; Donkeng, Hatou-Yvelin; Kofane, Timoléon Crépin
2017-02-01
The extended nonlinear Schrödinger equation describing the propagation of light beam in the weak nonlocal nonlinear media in general, and in the optical fibers with nearly instantaneous nonlinear response of the medium in particular, is investigated. In the zero-dispersion limit, we show that the system exhibits stable stationary compact bright pulse with an arbitrary nonlinear phase-shift both for the focusing and the defocusing media. However, in the presence of the large linear dispersion, this compact pulse become unstable and may be either disintegrate or transform into the ultrashort bright pulse according to whether the system operates in the normal or in the anomalous region. The exact analytical expressions of these two pulses are derived and the results checked through numerical simulations.
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.
Zhang, Xiao-Liang; Liu, Zhi-Bo; Li, Xiao-Chun; Ma, Qiang; Chen, Xu-Dong; Tian, Jian-Guo; Xu, Yan-Fei; Chen, Yong-Sheng
2013-03-25
The nonlinear refraction (NLR) properties of graphene oxide (GO) in N, N-Dimethylformamide (DMF) was studied in nanosecond, picosecond and femtosecond time regimes by Z-scan technique. Results show that the dispersion of GO in DMF exhibits negative NLR properties in nanosecond time regime, which is mainly attributed to transient thermal effect in the dispersion. The dispersion also exhibits negative NLR in picosecond and femtosecond time regimes, which are arising from sp(2)- hybridized carbon domains and sp(3)- hybridized matrix in GO sheets. To illustrate the relations between NLR and nonlinear absorption (NLA), NLA properties of the dispersion were also studied in nanosecond, picosecond and femtosecond time regimes.
Spiraling elliptic beam in nonlocal nonlinear media.
Liang, Guo; Guo, Qi; Cheng, Wenjing; Yin, Naiqiang; Wu, Ping; Cao, Hongmin
2015-09-21
Analytically discussed is the dynamical properties of the spiraling elliptic beams in nonlocal nonlinear media. This class of spiraling elliptic beams carry the orbital angular momentum (OAM), and can rotate on the cross section perpendicular to the propagation direction during the propagations. The optical intensity, the beam width, and specially the angular velocity are both analytically and numerically discussed in details. We shown that both the deviations from the critical power and the deviations from the critical OAM can make the spiraling elliptic beams breathe. The decrease (increase) of the OAM or the increase (decrease) of the power can both make the spiraling elliptic breathers contract (diffract), however, there still exist differences between them. The rotating speed can be changed by the input optical power or the input OAM, which may have potential applications in the controlling of the optical beams.
Finite element characterization of chromatic dispersion in nonlinear holey fibers.
Fujisawa, Takeshi; Koshiba, Masanori
2003-06-30
Chromatic dispersion characteristics of nonlinear photonic crystal fibers are, for the first time to our knowledge, theoretically investigated. A self-consistent numerical approach based on the full-vector finite-element method in terms of all the components of electric fields is described for the steady-state analysis of axially-nonsymmetrical nonlinear optical fibers. Electric fields obtained with this approach can be directly utilized for evaluating nonlinear refractive index distributions. To eliminate nonphysical, spurious solutions and to accurately model curved boundaries of circular air holes, curvilinear hybrid edge/nodal elements are introduced. It is found from the numerical results that under high optical intensity, chromatic dispersion characteristics become different from those of the linear state due to optical Kerr-effect nonlinearity, especially in short wavelength region.
An integrable shallow water equation with linear and nonlinear dispersion.
Dullin, H R; Gottwald, G A; Holm, D D
2001-11-05
We use asymptotic analysis and a near-identity normal form transformation from water wave theory to derive a 1+1 unidirectional nonlinear wave equation that combines the linear dispersion of the Korteweg-deVries (KdV) equation with the nonlinear/nonlocal dispersion of the Camassa-Holm (CH) equation. This equation is one order more accurate in asymptotic approximation beyond KdV, yet it still preserves complete integrability via the inverse scattering transform method. Its traveling wave solutions contain both the KdV solitons and the CH peakons as limiting cases.
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.
FDTD scattered field formulation for scatterers in stratified dispersive media.
Olkkonen, Juuso
2010-03-01
We introduce a simple scattered field (SF) technique that enables finite difference time domain (FDTD) modeling of light scattering from dispersive objects residing in stratified dispersive media. The introduced SF technique is verified against the total field scattered field (TFSF) technique. As an application example, we study surface plasmon polariton enhanced light transmission through a 100 nm wide slit in a silver film.
Nonlinear Quantum Optics in Artificially Structured Media
NASA Astrophysics Data System (ADS)
Helt, Lukas Gordon
This thesis presents an analysis of photon pairs generated via either spontaneous parametric downconversion or spontaneous four-wave mixing in channel waveguides as well as in microring resonators side-coupled to channel waveguides. The state of photons exiting a particular device is calculated within a general Hamiltonian formalism that simplifies the link between quantum nonlinear optics experiments and classical nonlinear optics experiments. This state contains information regarding photon pair production efficiency as well as modal and spectral correlations between the two photons, characterized by a two-dimensional spectral distribution function called the biphoton wave function. In the limit of a low probability of pair production, photon pair production efficiencies are cast into forms resembling corresponding well-known classical nonlinear optical frequency conversion efficiencies, making it easy to see what plays the role of a classical "seed" field in an un-seeded (quantum) process. This also allows photon pair production efficiencies to be calculated based on the results of classical nonlinear optical experiments. It is further calculated that, unless generated photons are collected over a very narrow frequency range, their generation efficiency does not scale the same way with device length in a channel waveguide, or resonance quality factor in a microring resonator, as might be expected from the corresponding classical frequency conversion efficiency. Although calculations do not include self- or cross-phase modulation, nor two-photon absorption or free-carrier absorption, it is calculated that their neglect is justified in the low pair production probability limit. Linear (scattering) loss is also neglected, though partially addressed in the final chapter of this thesis. Biphoton wave functions are calculated explicitly, such that their shape and orientation, including approximate analytic expressions for their widths, can easily be determined. This
NASA Astrophysics Data System (ADS)
Pakarzadeh, H.; Rezaei, S. M.
2016-01-01
In this article, we investigate for the first time the dispersion and the nonlinear characteristics of the tapered photonic crystal fibers (PCFs) as a function of length z, via solving the eigenvalue equation of the guided mode using the finite-difference frequency-domain method. Since the structural parameters such as the air-hole diameter and the pitch of the microstructured cladding change along the tapered PCFs, dispersion and nonlinear properties change with the length as well. Therefore, it is important to know the exact behavior of such fiber parameters along z which is necessary for nonlinear optics applications. We simulate the z dependency of the zero-dispersion wavelength, dispersion slope, effective mode area, nonlinear parameter, and the confinement loss along the tapered PCFs and propose useful relations for describing dispersion and nonlinear parameters. The results of this article, which are in a very good agreement with the available experimental data, are important for simulating pulse propagation as well as investigating nonlinear effects such as supercontinuum generation and parametric amplification in tapered PCFs.
Nonlinear surface waves in soft, weakly compressible elastic media.
Zabolotskaya, Evgenia A; Ilinskii, Yurii A; Hamilton, Mark F
2007-04-01
Nonlinear surface waves in soft, weakly compressible elastic media are investigated theoretically, with a focus on propagation in tissue-like media. The model is obtained as a limiting case of the theory developed by Zabolotskaya [J. Acoust. Soc. Am. 91, 2569-2575 (1992)] for nonlinear surface waves in arbitrary isotropic elastic media, and it is consistent with the results obtained by Fu and Devenish [Q. J. Mech. Appl. Math. 49, 65-80 (1996)] for incompressible isotropic elastic media. In particular, the quadratic nonlinearity is found to be independent of the third-order elastic constants of the medium, and it is inversely proportional to the shear modulus. The Gol'dberg number characterizing the degree of waveform distortion due to quadratic nonlinearity is proportional to the square root of the shear modulus and inversely proportional to the shear viscosity. Simulations are presented for propagation in tissue-like media.
Cosmic neutrinos: A dispersive and nonlinear fluid
NASA Astrophysics Data System (ADS)
Inman, Derek; Pen, Ue-Li
2017-03-01
We present a description of cosmic neutrinos as a dispersive fluid. In this approach, the neutrino phase space is reduced to density and velocity fields alongside a scale-dependent sound speed. This sound speed depends on redshift, the initial neutrino phase space density and the cold dark matter gravitational potential. The latter is a new coupling between neutrinos and large scale structure not described by previous fluid approaches. We compute the sound speed in linear theory and find that it asymptotes to constants at small and large scales regardless of the gravitational potential. By comparing with neutrino N-body simulations, we measure the small scale sound speed and find it to be lower than linear theory predictions. This allows for an explanation of the discrepancy between N-body and linear response predictions for the neutrino power spectrum: neutrinos are still driven predominantly by the cold dark matter, but the sound speed on small scales is not stable to perturbations and decreases. Finally, we present a calibrated model for the neutrino power spectrum that requires no additional integrations outside of standard Boltzmann codes.
Soliton solutions with power-law nonlinearity in inhomogeneous media
NASA Astrophysics Data System (ADS)
Dai, Chao-Qing; Yu, Fang-Bo
2013-04-01
We construct the relation between the variable coefficient nonlinear Schrödinger equations with power-law nonlinearity and the constant coefficient one via a transformation. Based on this transformation, we analytically obtain the closed-form bright and dark soliton solutions for variable coefficient nonlinear Schrödinger equations with power-law nonlinearity, third-order dispersion and self-steepening effect. The dynamic behaviors of bright and dark solitons in dispersion-decreasing fibers with hyperbolic, exponential, linear, logarithmic and Gaussian profiles are analyzed.
Optical dispersive shock waves in defocusing colloidal media
NASA Astrophysics Data System (ADS)
An, X.; Marchant, T. R.; Smyth, N. F.
2017-03-01
The propagation of an optical dispersive shock wave, generated from a jump discontinuity in light intensity, in a defocusing colloidal medium is analysed. The equations governing nonlinear light propagation in a colloidal medium consist of a nonlinear Schrödinger equation for the beam and an algebraic equation for the medium response. In the limit of low light intensity, these equations reduce to a perturbed higher order nonlinear Schrödinger equation. Solutions for the leading and trailing edges of the colloidal dispersive shock wave are found using modulation theory. This is done for both the perturbed nonlinear Schrödinger equation and the full colloid equations for arbitrary light intensity. These results are compared with numerical solutions of the colloid equations.
Angular radiation transfer in inhomogeneous dispersive media
NASA Astrophysics Data System (ADS)
Saad, E. A.; El Ghazaly, A. A.; Krim, M. S. Abdel
1988-10-01
The equation of radiative transfer for an inhomogeneous dispersive finite medium subject to general boundary conditions is solved. The Padé approximation technique is used to calculate the angular distribution of radiation. Numerical results for the [0/1] Padé approximant lead to numerical results that compare with the exact results.
Nonlinear Dispersive ALFVÉN Waves in Magnetoplasmas
NASA Astrophysics Data System (ADS)
Shukla, P. K.; Eliasson, B.; Stenflo, L.; Bingham, R.
2008-03-01
Large amplitude Alfvén waves are frequently found in magnetized space and laboratory plasmas. Our objective here is to discuss the linear and nonlinear properties of dispersive Alfvén waves (DAWs) in a uniform magnetoplasma. We first consider the effects of finite frequency (ω/ωci) and ion gyroradius on inertial and kinetic Alfvén waves, where ωci is the ion gyrofrequency. Next, we focus on nonlinear effects caused by the dispersive Alfvén waves. Such effects include the plasma density enhancement and depression by the Alfvén wave ponderomotive force, nonlinear interactions among the DAWs, the generation of zonal flows by the DAWs, as well as the electron and ion heating due to wave-particle interactions. The relevance of our investigation to the appearance of nonlinear dispersive Alfvén waves in the Earth's auroral acceleration region, in the solar corona, and in the Large Plasma Device (LAPD) at UCLA is discussed.
Dispersion of the nonlinear susceptibility in gold nanoantennas
NASA Astrophysics Data System (ADS)
Knittel, V.; Fischer, M. P.; Vennekel, M.; Rybka, T.; Leitenstorfer, A.; Brida, D.
2017-09-01
Femtosecond optical pulses tunable in the near infrared are exploited to drive third harmonic generation (THG) and incoherent multiphoton photoluminescence (MPPL) in gold plasmonic nanoantennas. By comparing the yield of the two processes concurrently occurring on the same nanostructure, we extract the coherent third-order response of the antenna. Its contribution is enhanced at shorter excitation wavelengths allowing the observation of dispersion in the nonlinear susceptibility of gold.
Nonlinear Cherenkov radiation at the interface of two different nonlinear media.
Zhao, Xiaohui; Zheng, Yuanlin; Ren, Huaijin; An, Ning; Deng, Xuewei; Chen, Xianfeng
2016-06-13
We discuss the nonlinear response due to the spatial modulation of the second-order susceptibility at the interface between two nonlinear media, and experimentally demonstrate that the nonlinear Cherenkov radiation is enhanced by the interface of two nonlinear crystals with a large disparity in χ^{(2)}. In our experiment, the intensity of the nonlinear Cherenkov radiation generated at the nonlinear interface was approximately 4 to 10 times that at the crystal boundary. This result suggests potential applications to efficient frequency conversion.
Electrokinetic induced solute dispersion in porous media; pore network modeling
NASA Astrophysics Data System (ADS)
Li, Shuai; Schotting, Ruud; Raoof, Amir
2013-04-01
Electrokinetic flow plays an important role in remediation process, separation technique, and chromatography. The solute dispersion is a key parameter to determine transport efficiency. In this study, we present the electrokinetic effects on solute dispersion in porous media at the pore scale, using a pore network model. The analytical solution of the electrokinetic coupling coefficient was obtained to quantity the fluid flow velocity in a cylinder capillary. The effect of electrical double layer on the electrokinetic coupling coefficient was investigated by applying different ionic concentration. By averaging the velocity over cross section within a single pore, the average flux was obtained. Applying such single pore relationships, in the thin electrical double layer limit, to each and every pore within the pore network, potential distribution and the induced fluid flow was calculated for the whole domain. The resulting pore velocities were used to simulate solute transport within the pore network. By averaging the results, we obtained the breakthrough curve (BTC) of the average concentration at the outlet of the pore network. Optimizing the solution of continuum scale advection-dispersion equation to such a BTC, solute dispersion coefficient was estimated. We have compared the dispersion caused by electrokinetic flow and pure pressure driven flow under different Peclet number values. In addition, the effect of microstructure and topological properties of porous media on fluid flow and solute dispersion is presented, mainly based on different pore coordination numbers.
Variance of Dispersion Coefficients in Heterogeneous Porous Media
NASA Astrophysics Data System (ADS)
Dentz, Marco; De Barros, Felipe P. J.
2013-04-01
We study the dispersion of a passive solute in heterogeneous porous media using a stochastic modeling approach. Heterogeneity on one hand leads to an increase of solute spreading, which is described by the well-known macrodispersion phenomenon. On the other hand, it induces uncertainty about the dispersion behavior, which is quantified by ensemble averages over suitably defined dispersion coefficients in single medium realizations. We focus here on the sample to sample fluctuations of dispersion coefficients about their ensemble mean values for solutes evolving from point-like and extended source distributions in d = 2 and d = 3 spatial dimensions. The definition of dispersion coefficients in single medium realizations for finite source sizes is not unique, unlike for point-like sources. Thus, we first discuss a series of dispersion measures, which describe the extension of the solute plume, as well as dispersion measures that quantify the solute dispersion relative to the injection point. The sample to sample fluctuations of these observables are quantified in terms of the variance with respect to their ensemble averages. We find that the ensemble averages of these dispersion measures may be identical, their fluctuation behavior, however, may be very different. This is quantified using perturbation expansions in the fluctuations of the random flow field. We derive explicit expressions for the time evolution of the variance of the dispersion coefficients. The characteristic time scale for the variance evolution is given by the typical dispersion time over the characteristic heterogeneity scale and the dimensions of the source. We find that the dispersion variances asymptotically decrease to zero in d = 3 dimensions, which means, the dispersion coefficients are self-averaging observables, at least for moderate heterogeneity. In d = 2 dimensions, the variance converges towards a finite asymptotic value that is independent of the source distribution. Dispersion is not
Dispersion Resulting from Flow through Spatially Periodic Porous Media
NASA Astrophysics Data System (ADS)
Brenner, H.
1980-07-01
A rigorous theory of dispersion in both granular and sintered spatially-periodic porous media is presented, utilizing concepts originating from Brownian motion theory. A precise prescription is derived for calculating both the Darcy-scale interstitial velocity vector {v}* and dispersivity dyadic {D}* of a tracer particle. These are expressed in terms of the local fluid velocity vector field v at each point within the interstices of a unit cell of the spatially periodic array and, for the dispersivity, the molecular diffusivity D of the tracer particle through the fluid. Though the theory is complete, numerical results are not yet available owing to the complex structure of the local interstitial velocity field v. However, as an illustrative exercise, the theory is shown to correctly reduce in an appropriate limiting case to the well-known Taylor-Aris results for dispersion in circular capillaries.
Fidelity and fidelity susceptibility of pulses in dispersive media
Wang Ligang; Gu Shijian
2009-07-15
Motivated by the growing importance of the fidelity and fidelity susceptibility (FS) in quantum critical phenomena, we use these concepts to describe the pulse propagation inside the dispersive media. It is found that there is a dramatic change in the fidelity and the FS of the pulse at a critical propagation distance inside a dispersive medium, and whether such a dramatic change for a light pulse occurs or not strongly depends on both the dispersive strength of the media and the pulse property. We study in detail about the changes in the fidelity and the FS for both a smooth and a truncated Gaussian pulse through the abnormal and normal dispersive media, where the group velocities are well defined. Our results show that both the fidelity and the FS could be very useful to determine whether the pulse is completely distorted or not at the critical distance; therefore it would be very helpful to find the maximal effective propagation region of the pulse's group velocity, in terms of the changes in the pulse's fidelity and FS.
Influence of Chemotaxis on Bacterial Dispersion in Porous Media
NASA Astrophysics Data System (ADS)
Ford, R. M.; Narayanaswamy, K.; Wood, B. D.
2007-12-01
Bioremediation of groundwater is limited by the degree to which microorganisms and pollutants are mixed together in the subsurface environment. Good mixing is difficult to achieve because of the structure of geological media and the unavailability of external mixing devices. Chemotaxis, which is the ability of motile bacteria to sense chemical concentration gradients in their local surroundings and swim toward higher concentrations of attractants, could potentially enhance the mixing and expedite the biodegradation process. The chemotactic migration on the pore-scale could eventually result in greater dispersion at the field-scale. In this study, the volume averaging method was used to derive an expression that accounts for chemotactic responses to local chemical gradients in the dispersion coefficient at larger scales. We will present results where the upscaling scheme was applied to problems with well defined hydraulic conditions such as a series of inline cylinders, and well-defined chemical gradients. In general, increasing the attractant gradients resulted in greater bacterial dispersion coefficients. Engineering correlations were developed to relate the enhanced dispersion to dimensionless groups such as the Peclet number and a dimensionless chemotactic driving force defined in this work. It was found that under certain constraints, the effect of chemotaxis was to increase the dispersion coefficient by an additional term that was a linear function of the chemotactic driving force, i.e. E=Dbulk+α v+ β σ, where Dbulk is the bulk diffusion coefficient, v is the fluid velocity, σ is the dimensionless chemotactic driving force we defined, and α and β are appropriate dispersivities. This study will improve our physical understanding of how chemotaxis impacts dispersion and allow us to quantify dispersion in terms of bacterial properties and structure of the geologic media. The engineering correlations that result are critical for improving our assessment and
Laboratory investigation of longitudinal dispersion in anisotropic porous media
Silliman, S.E.; Konikow, L.F.; Voss, C.I.
1987-01-01
In this study, laboratory experiments were used to investigate mechanisms that may cause anisotropy in the dispersion coefficient and to investigate the relation between anisotropy in hydraulic conductivity and anisotropy in longitudinal dispersion. Measurements of sodium chloride concentration (used as a tracer) were made at 105 in situ sampling locations in a new type of sand box designed to allow flow in either of two perpendicular directions. Two types of hydraulic anisotropy were examined. The first consisted of structured zones of increased hydraulic conductivity within a lower-conductivity medium. The second type involved low-conductivity platelike inclusions within a homogeneous, isotropic medium. The plates were aligned such that the tortuosity was increased only in one principal direction of permeability. Results using two examples of the first type of media showed that the apparent longitudinal dispersivities for flow parallel to the high-conductivity direction were greater than those perpendicular to this direction. Two examples of the second type of media produced smaller apparent longitudinal dispersivities for flow parallel to the high-conductivity direction. The results suggest that the mechanisms causing dispersive anisotropy can be related, conceptually, to the factors causing hydraulic anisotropy.
Electret processes in disordered systems based on liquid dispersion media
NASA Astrophysics Data System (ADS)
Shcherbachenko, L. A.; Maksimova, N. T.; Komarov, E. S.; Ruzhnikov, L. I.; Karnakov, V. A.; Baryshnikov, E. S.; Krasnov, D. A.; Troshev, A. A.; Baryshnikov, D. S.; Ezhova, L. I.
2012-10-01
Electret-thermal analysis (ETA) of disordered systems based on dispersed media is carried out. It is shown that the method of thermally stimulated currents makes it possible to estimate the structural changes occurring in a liquid dispersion medium. It is found that liquid water in a free state exhibits the electret properties. The observed multiple peaks on the thermally stimulated current curve are the evidence of the multicomponent nature of the "free water" system. The mechanisms of processes leading to the formation of the electret state in such systems are considered.
Ultratransparent Media and Transformation Optics with Shifted Spatial Dispersions
NASA Astrophysics Data System (ADS)
Luo, Jie; Yang, Yuting; Yao, Zhongqi; Lu, Weixin; Hou, Bo; Hang, Zhi Hong; Chan, C. T.; Lai, Yun
2016-11-01
By using pure dielectric photonic crystals, we demonstrate the realization of ultratransparent media, which allow near 100% transmission of light for all incident angles and create aberration-free virtual images. The ultratransparency effect is well explained by spatially dispersive effective medium theory for photonic crystals, and verified by both simulations and proof-of-principle microwave experiments. Designed with shifted elliptical equal frequency contours, such ultratransparent media not only provide a low-loss and feasible platform for transformation optics devices at optical frequencies, but also enable new freedom for phase manipulation beyond the local medium framework.
Ultratransparent Media and Transformation Optics with Shifted Spatial Dispersions.
Luo, Jie; Yang, Yuting; Yao, Zhongqi; Lu, Weixin; Hou, Bo; Hang, Zhi Hong; Chan, C T; Lai, Yun
2016-11-25
By using pure dielectric photonic crystals, we demonstrate the realization of ultratransparent media, which allow near 100% transmission of light for all incident angles and create aberration-free virtual images. The ultratransparency effect is well explained by spatially dispersive effective medium theory for photonic crystals, and verified by both simulations and proof-of-principle microwave experiments. Designed with shifted elliptical equal frequency contours, such ultratransparent media not only provide a low-loss and feasible platform for transformation optics devices at optical frequencies, but also enable new freedom for phase manipulation beyond the local medium framework.
On a class of nonlinear dispersive-dissipative interactions
Rosenau, P.
1997-07-29
The authors study the prototypical, genuinely nonlinear, equation; u{sub t} + a(u{sup m}){sub x} + (u{sup n}){sub xxx} = {mu}(u{sup k}){sub xx}, a, {mu} = consts., which encompasses a wide variety of dissipative-dispersive interactions. The parametric surface k = (m + n)/2 separates diffusion dominated from dissipation dominated phenomena. On this surface dissipative and dispersive effects are in detailed balance for all amplitudes. In particular, the m = n + 2 = k + 1 subclass can be transformed into a form free of convection and dissipation making it accessible to theoretical studies. Both bounded and unbounded oscillations are found and certain exact solutions are presented. When a = (2{mu}3/){sup 2} the map yields a linear equation; rational, periodic and aperiodic solutions are constructed.
Modeling highly-dispersive transparency in planar nonlinear metamaterials
NASA Astrophysics Data System (ADS)
Potravkin, N. N.; Makarov, V. A.; Perezhogin, I. A.
2017-02-01
We consider propagation of light in planar optical metamaterial, which basic element is composed of two silver stripes, and it possesses strong dispersion in optical range. Our method of numerical modeling allows us to take into consideration the nonlinearity of the material and the effects of light self-action without considerable increase of the calculation time. It is shown that plasmonic resonances originating in such a structure result in multiple enhancement of local field and high sensitivity of the transmission coefficient to the intensity of incident monochromatic wave.
Dark spatial solitons splitting in logarithmically saturable nonlinear media
NASA Astrophysics Data System (ADS)
Zhang, Yuhong; Liu, Baoyuan; Lu, Keqing; Liu, Wangyun; Han, Jun
2014-12-01
We numerically simulate the evolution of the dark-notch-bearing optical beam in the logarithmically saturable nonlinear media based on beam propagation method (BPM). The simulation results indicate that the multiple dark spatial solitons are deep, possible in this type of nonlinear media. The number of multiple dark spatial solitons depends on the width of the dark notch, the initial conditions and the peak intensity of the initial input beam. Under the odd and even initial conditions, the odd and even number sequence of multiple dark spatial solitons can be obtained, respectively. For an input beam with fixed optical intensity, the number of dark solitons increases with the width of the initial input dark notch. The behavior of the multiple dark solitons in this type of media is similar to that in a photorefractive nonlinear crystal.
Demi, L; van Dongen, K W A; Verweij, M D
2011-03-01
Experimental data reveals that attenuation is an important phenomenon in medical ultrasound. Attenuation is particularly important for medical applications based on nonlinear acoustics, since higher harmonics experience higher attenuation than the fundamental. Here, a method is presented to accurately solve the wave equation for nonlinear acoustic media with spatially inhomogeneous attenuation. Losses are modeled by a spatially dependent compliance relaxation function, which is included in the Westervelt equation. Introduction of absorption in the form of a causal relaxation function automatically results in the appearance of dispersion. The appearance of inhomogeneities implies the presence of a spatially inhomogeneous contrast source in the presented full-wave method leading to inclusion of forward and backward scattering. The contrast source problem is solved iteratively using a Neumann scheme, similar to the iterative nonlinear contrast source (INCS) method. The presented method is directionally independent and capable of dealing with weakly to moderately nonlinear, large scale, three-dimensional wave fields occurring in diagnostic ultrasound. Convergence of the method has been investigated and results for homogeneous, lossy, linear media show full agreement with the exact results. Moreover, the performance of the method is demonstrated through simulations involving steered and unsteered beams in nonlinear media with spatially homogeneous and inhomogeneous attenuation. © 2011 Acoustical Society of America
Averaged model for momentum and dispersion in hierarchical porous media.
Chabanon, Morgan; David, Bertrand; Goyeau, Benoît
2015-08-01
Hierarchical porous media are multiscale systems, where different characteristic pore sizes and structures are encountered at each scale. Focusing the analysis to three pore scales, an upscaling procedure based on the volume-averaging method is applied twice, in order to obtain a macroscopic model for momentum and diffusion-dispersion. The effective transport properties at the macroscopic scale (permeability and dispersion tensors) are found to be explicitly dependent on the mesoscopic ones. Closure problems associated to these averaged properties are numerically solved at the different scales for two types of bidisperse porous media. Results show a strong influence of the lower-scale porous structures and flow intensity on the macroscopic effective transport properties.
Stabilization of vortex solitons in nonlocal nonlinear media
Minzoni, Antonmaria A.; Smyth, Noel F.; Worthy, Annette L.; Kivshar, Yuri S.
2007-12-15
We study the evolution of vortex solitons in optical media with a nonlocal nonlinear response. We employ a modulation theory for the vortex parameters based on an averaged Lagrangian, and analyze the azimuthal evolution of both the vortex width and diffractive radiation. We describe analytically the physical mechanism for vortex stabilization due to the long-range nonlocal nonlinear response, the effect observed earlier in numerical simulations only.
Asymmetric partially coherent solitons in saturable nonlinear media.
Litchinitser, N M; Królikowski, W; Akhmediev, N N; Agrawal, G P
1999-08-01
We investigate theoretically properties of partially coherent solitons in optical nonlinear media with slow saturable nonlinearity. We have found numerically that such a medium can support spatial solitons which are asymmetric in shape and are composed of only a finite number of modes associated with the self-induced waveguide. It is shown that these asymmetric spatial solitons can propagate many diffraction lengths without changes, but that collisions change their shape and may split them apart.
Mechanisms of anomalous dispersion in flow through heterogeneous porous media
NASA Astrophysics Data System (ADS)
Tyukhova, Alina; Dentz, Marco; Kinzelbach, Wolfgang; Willmann, Matthias
2016-11-01
We study the origins of anomalous dispersion in heterogeneous porous media in terms of the medium and flow properties. To identify and quantify the heterogeneity controls, we focus on porous media which are organized in assemblies of equally sized conductive inclusions embedded in a constant conductivity matrix. We study the behavior of particle arrival times for different conductivity distributions and link the statistical medium characteristics to large-scale transport using a continuous time random walk (CTRW) approach. The CTRW models particle motion as a sequence of transitions in space and time. We derive an explicit map of the conductivity onto the transition time distribution. The derived CTRW model predicts solute transport based on the conductivity distribution and the characteristic heterogeneity length. In this way, heavy tails in solute arrival times and anomalous particle dispersion as measured by the centered mean square displacement are directly related to the medium properties. These findings shed light on the mechanisms of anomalous dispersion in heterogeneous porous media, and provide a basis for the predictive modeling of large-scale transport.
Studies on dispersive stabilization of porous media flows
NASA Astrophysics Data System (ADS)
Daripa, Prabir; Gin, Craig
2016-08-01
Motivated by a need to improve the performance of chemical enhanced oil recovery (EOR) processes, we investigate dispersive effects on the linear stability of three-layer porous media flow models of EOR for two different types of interfaces: permeable and impermeable interfaces. Results presented are relevant for the design of smarter interfaces in the available parameter space of capillary number, Peclet number, longitudinal and transverse dispersion, and the viscous profile of the middle layer. The stabilization capacity of each of these two interfaces is explored numerically and conditions for complete dispersive stabilization are identified for each of these two types of interfaces. Key results obtained are (i) three-layer porous media flows with permeable interfaces can be almost completely stabilized by diffusion if the optimal viscous profile is chosen, (ii) flows with impermeable interfaces can also be almost completely stabilized for short time, but become more unstable at later times because diffusion flattens out the basic viscous profile, (iii) diffusion stabilizes short waves more than long waves which leads to a "turning point" Peclet number at which short and long waves have the same growth rate, and (iv) mechanical dispersion further stabilizes flows with permeable interfaces but in some cases has a destabilizing effect for flows with impermeable interfaces, which is a surprising result. These results are then used to give a comparison of the two types of interfaces. It is found that for most values of the flow parameters, permeable interfaces suppress flow instability more than impermeable interfaces.
Studies on dispersive stabilization of porous media flows
Daripa, Prabir Gin, Craig
2016-08-15
Motivated by a need to improve the performance of chemical enhanced oil recovery (EOR) processes, we investigate dispersive effects on the linear stability of three-layer porous media flow models of EOR for two different types of interfaces: permeable and impermeable interfaces. Results presented are relevant for the design of smarter interfaces in the available parameter space of capillary number, Peclet number, longitudinal and transverse dispersion, and the viscous profile of the middle layer. The stabilization capacity of each of these two interfaces is explored numerically and conditions for complete dispersive stabilization are identified for each of these two types of interfaces. Key results obtained are (i) three-layer porous media flows with permeable interfaces can be almost completely stabilized by diffusion if the optimal viscous profile is chosen, (ii) flows with impermeable interfaces can also be almost completely stabilized for short time, but become more unstable at later times because diffusion flattens out the basic viscous profile, (iii) diffusion stabilizes short waves more than long waves which leads to a “turning point” Peclet number at which short and long waves have the same growth rate, and (iv) mechanical dispersion further stabilizes flows with permeable interfaces but in some cases has a destabilizing effect for flows with impermeable interfaces, which is a surprising result. These results are then used to give a comparison of the two types of interfaces. It is found that for most values of the flow parameters, permeable interfaces suppress flow instability more than impermeable interfaces.
Modulation instability of optical nonlinear media: a route to chaos
NASA Astrophysics Data System (ADS)
Sharif, Morteza A.
2011-12-01
Modulation Instability is known as intrinsic property of a nonlinear medium like Kerr medium or photorefractive medium; through the such media, the system behavior is possible to transit form stationary regime to chaotic regime; this paper deals with Modulation Instability (MI) in a nonlinear medium and investigates the analogy of MI of optical nonlinear medium and the consequent chaotic regime based on extracting Lyapunov exponent through the power spectrum and equivalently intensity-time diagram of MI; the experimental observation truly confirms the results of MI as the route to the chaotic regime.
Self-induced mode transformation in nonlocal nonlinear media.
Izdebskaya, Yana V; Desyatnikov, Anton S; Kivshar, Yuri S
2013-09-20
We report on the first experimental observation of self-induced optical mode transformations in nonlocal nonlinear media. We show that the quadrupole Hermite-Gaussian mode experiences complex nonlinear dynamics in a nematic liquid crystal, including power-dependent conversion into a radially symmetric Laguerre-Gaussian mode. The physical mechanism responsible for self-induced transformation is the excitation of internal modes of a metastable quadrupole nonlocal soliton and its subsequent transmutation into a robust soliton with a bright peak surrounded by a bright ring. We also observe the onset of transformations of higher-order modes, proving the generic character of this nonlinear phenomenon.
Saturation-dependent solute dispersivity in porous media: Pore-scale processes
NASA Astrophysics Data System (ADS)
Raoof, A.; Hassanizadeh, S. M.
2013-04-01
It is known that in variably saturated porous media, dispersion coefficient depends on Darcy velocity and water saturation. In one-dimensional flow, it is commonly assumed that the dispersion coefficient is a linear function of velocity. The coefficient of proportionality, called the dispersivity, is considered to depend on saturation. However, there is not much known about its dependence on saturation. In this study, we investigate, using a pore network model, how the longitudinal dispersivity varies nonlinearly with saturation. We schematize the porous medium as a network of pore bodies and pore throats with finite volumes. The pore space is modeled using the multidirectional pore-network concept, which allows for a distribution of pore coordination numbers. This topological property together with the distribution of pore sizes are used to mimic the microstructure of real porous media. The dispersivity is calculated by solving the mass balance equations for solute concentration in all network elements and averaging the concentrations over a large number of pores. We have introduced a new formulation of solute transport within pore space, where we account for different compartments of residual water within drained pores. This formulation makes it possible to capture the effect of limited mixing due to partial filling of the pores under variably saturated conditions. We found that dispersivity increases with the decrease in saturation, it reaches a maximum value, and then decreases with further decrease in saturation. To show the capability of our formulation to properly capture the effect of saturation on solute dispersion, we applied it to model the results of a reported experimental study.
NASA Astrophysics Data System (ADS)
Othman, N.; Shah, N. S. M.; Tay, K. G.; Pakarzadeh, H.; Cholan, N. A.; Talib, R.
2017-09-01
The highly-nonlinear fiber is the ideal gain medium for many applications particularly because its dispersion can be easily engineered. However, the modification of the fiber dispersion will affect the higher-order dispersion coefficients. Hence, this paper investigates the effect of highly-nonlinear dispersion-shifted fiber dispersion profile on the higher-order dispersion coefficients which are the fourth-order and sixth-order dispersion coefficients. The dispersion profile was modified by varying the slope at zero-dispersion wavelength. The fourth-order dispersion coefficient exhibits changes from positive to negative value as the slope at zero-dispersion wavelength is getting higher. Meanwhile, sixth-order dispersion coefficient remains with the positive value even though it shows the reduction as the slope is increased, however it will eventually become negative when the dispersion is high enough. In short, the values of both fourth-order and sixth-order dispersion coefficients at zero-dispersion wavelength decrease when the slope increases.
Dispersive Evolution of Nonlinear Fast Magnetoacoustic Wave Trains
NASA Astrophysics Data System (ADS)
Pascoe, D. J.; Goddard, C. R.; Nakariakov, V. M.
2017-10-01
Quasi-periodic rapidly propagating wave trains are frequently observed in extreme ultraviolet observations of the solar corona, or are inferred by the quasi-periodic modulation of radio emission. The dispersive nature of fast magnetohydrodynamic waves in coronal structures provides a robust mechanism to explain the detected quasi-periodic patterns. We perform 2D numerical simulations of impulsively generated wave trains in coronal plasma slabs and investigate how the behavior of the trapped and leaky components depend on the properties of the initial perturbation. For large amplitude compressive perturbations, the geometrical dispersion associated with the waveguide suppresses the nonlinear steepening for the trapped wave train. The wave train formed by the leaky components does not experience dispersion once it leaves the waveguide and so can steepen and form shocks. The mechanism we consider can lead to the formation of multiple shock fronts by a single, large amplitude, impulsive event and so can account for quasi-periodic features observed in radio spectra.
Diffusion, Dispersion, and Uncertainty in Anisotropic Fractal Porous Media
NASA Astrophysics Data System (ADS)
Monnig, N. D.; Benson, D. A.
2007-12-01
Motivated by field measurements of aquifer hydraulic conductivity (K), recent techniques were developed to construct anisotropic fractal random fields, in which the scaling, or self-similarity parameter, varies with direction and is defined by a matrix. Ensemble numerical results are analyzed for solute transport through these 2-D "operator-scaling" fractional Brownian motion (fBm) ln(K) fields. Contrary to some analytic stochastic theories for monofractal K fields, the plume growth rates never exceed Mercado's (1967) purely stratified aquifer growth rate of plume apparent dispersivity proportional to mean distance. Apparent super-stratified growth must be the result of other demonstrable factors, such as initial plume size. The addition of large local dispersion and diffusion does not significantly change the effective longitudinal dispersivity of the plumes. In the presence of significant local dispersion or diffusion, the concentration coefficient of variation CV={σc}/{\\langle c \\rangle} remains large at the leading edge of the plumes. This indicates that even with considerable mixing due to dispersion or diffusion, there is still substantial uncertainty in the leading edge of a plume moving in fractal porous media.
Beam steering and routing in quadratic nonlinear media
Aceves, A.B.; Santos, M.C.; Torner, L.
1997-04-01
We show how the spatial phase modulation of weak second-harmonic signals controls the overall direction of propagation of spatial solitons in quadratic nonlinear media. We investigate numerically such a process and discuss its applications to all-optical beam routing. 5 refs., 3 figs.
Peiponen, Kai-Erik; Saarinen, Jarkko J.; Svirko, Yuri
2004-04-01
Dispersion relations and sum rules for nonlinear susceptibilities are derived using complex analysis and especially the concept of a meromorphic function. The dispersion relations and sum rules provide frames to investigate the consistency between the theory and experiments.
Liu, Jianguo; Xue, Lifang; Wang, Yingjian; Kai, Guiyun; Dong, Xiaoyi
2007-11-01
We numerically investigated the impacts of the imperfect geometry structure on the nonlinear and chromatic dispersion properties of a microstructure fiber (MF). The statistical results show that the imperfect geometry structure degrades the high nonlinearity and fluctuates the chromatic dispersion in a MF. Moreover, the smaller air holes and the larger pitch are more likely to maintain the properties of nonlinearity and chromatic dispersion. Finally, the nonlinearity and chromatic dispersion are more insensitive to air-hole nonuniformity than to air-hole disorder. All of these will provide references for designing and fabricating MF.
Study On Nonlinear effect In 2D Plastic Media
NASA Astrophysics Data System (ADS)
Wenjie, D.; Chen, X.
2011-12-01
Unlike the perfect elastic, homogeneous and isotropic model, the properties of real earth media are heterogeneous, plastic and anisotropic to a certain extend. To accurately simulate the strong ground motion in a basin, nonlinear or plastic effect should be considered in simulation. In this study, we use DRP/opt MacCormack non-staggered finite difference method to simulate 2D seismic wave propagation in anisotropic and plastic media. Compared with the traditional staggered grid FDM, this scheme is more accurate and more efficient. We focus on the nonlinear character of the sedimentary basin model. The preliminary ground motion results indicate that the energy of seismic wave has obvious nonlinear dissipation and irreversible deformations which is danger to buildings in the sedimentary basin.
Superfluid light in bulk nonlinear media
Carusotto, Iacopo
2014-01-01
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 ultrasonic propagation in biological media.
Dunn, F.; Law, W. K.; Frizzell, L. A.
1982-01-01
The nonlinearity parameter B/A for several biological materials was determined by measuring the amplitude of the second harmonic pressure as a function of distance from the source and the amplitude of the fundamental at the source. The B/A values for bovine serum albumin and haemoglobin solutions were found to increase approximately linearly with solution concentration. Blood and homogenized liver exhibit a B/A value similar to a haemoglobin solution of the same dry weight, but whole liver has a greater B/A value. PMID:6950775
Spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity
Golubkov, A A; Makarov, Vladimir A
2011-11-30
We present a brief review of the results of fifty years of development efforts in spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity. The recent original results obtained by the authors show the fundamental possibility of determining, from experimental data, the coordinate dependences of complex quadratic susceptibility tensor components of a onedimensionally inhomogeneous (along the z axis) medium with an arbitrary frequency dispersion, if the linear dielectric properties of the medium also vary along the z axis and are described by a diagonal tensor of the linear dielectric constant. It is assumed that the medium in question has the form of a plane-parallel plate, whose surfaces are perpendicular to the direction of the inhomogeneity. Using the example of several components of the tensors X{sup (2)}(z, {omega}{sub 1} {+-} {omega}{sub 2}; {omega}{sub 1}, {+-} {omega}{sub 2}), we describe two methods for finding their spatial profiles, which differ in the interaction geometry of plane monochromatic fundamental waves with frequencies {omega}{sub 1} and {omega}{sub 2}. The both methods are based on assessing the intensity of the waves propagating from the plate at the sum or difference frequency and require measurements over a range of angles of incidence of the fundamental waves. Such measurements include two series of additional estimates of the intensities of the waves generated under special conditions by using the test and additional reference plates, which eliminates the need for complicated phase measurements of the complex amplitudes of the waves at the sum (difference) frequency.
NASA Astrophysics Data System (ADS)
Hidayat, A.; Listanti, A.; Latifah, E.; Wisodo, H.; P, Nugroho A.; Taufiq, A.
2017-05-01
Influence of coupling and intermodal dispersion coefficient on pulse splitting in double core optical fibre was investigated by using solutions of normalized coupled nonlinear Schrödinger equations. It was found that if coupling coefficient and intermodal dispersion coefficient was small, and then nonlinearity cannot balance intermodal dispersion effect. Consequently, pulse was distorted. Furthermore, if intermodal dispersion coefficient was large enough, then pulse splitting occurred. Increasing coupling coefficient avoids pulse splitting and the pulse was stable.
Nonlinear self-focus of pulsed-wave beams in Kerr media
Judkins, Justin Boyd
1992-01-01
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_{z} and TM_{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.
Attenuation, dispersion and nonlinearity effects in graphene-based waveguides
Mota, João Cesar Moura; Sombra, Antonio Sergio Bezerra
2015-01-01
Summary We simulated and analyzed in detail the behavior of ultrashort optical pulses, which are typically used in telecommunications, propagating through graphene-based nanoribbon waveguides. In this work, we showed the changes that occur in the Gaussian and hyperbolic secant input pulses due to the attenuation, high-order dispersive effects and nonlinear effects. We concluded that it is possible to control the shape of the output pulses with the value of the input signal power and the chemical potential of the graphene nanoribbon. We believe that the obtained results will be highly relevant since they can be applied to other nanophotonic devices, for example, filters, modulators, antennas, switches and other devices. PMID:26171299
Dispersion of nonresonant third-order nonlinearities in Silicon Carbide.
De Leonardis, Francesco; Soref, Richard A; Passaro, Vittorio M N
2017-01-18
In this paper we present a physical discussion of the indirect two-photon absorption (TPA) occuring in silicon carbide with either cubic or wurtzite structure. Phonon-electron interaction is analyzed by finding the phonon features involved in the process as depending upon the crystal symmetry. Consistent physical assumptions about the phonon-electron scattering mechanisms are proposed in order to give a mathematical formulation to predict the wavelength dispersion of TPA and the Kerr nonlinear refractive index n2. The TPA spectrum is investigated including the effects of band nonparabolicity and the influence of the continuum exciton. Moreover, a parametric analysis is presented in order to fit the experimental measurements. Finally, we have estimated the n2 in a large wavelength range spanning the visible to the mid-IR region.
Dispersion of nonresonant third-order nonlinearities in Silicon Carbide
NASA Astrophysics Data System (ADS)
de Leonardis, Francesco; Soref, Richard A.; Passaro, Vittorio M. N.
2017-01-01
In this paper we present a physical discussion of the indirect two-photon absorption (TPA) occuring in silicon carbide with either cubic or wurtzite structure. Phonon-electron interaction is analyzed by finding the phonon features involved in the process as depending upon the crystal symmetry. Consistent physical assumptions about the phonon-electron scattering mechanisms are proposed in order to give a mathematical formulation to predict the wavelength dispersion of TPA and the Kerr nonlinear refractive index n2. The TPA spectrum is investigated including the effects of band nonparabolicity and the influence of the continuum exciton. Moreover, a parametric analysis is presented in order to fit the experimental measurements. Finally, we have estimated the n2 in a large wavelength range spanning the visible to the mid-IR region.
Dispersion of nonresonant third-order nonlinearities in Silicon Carbide
De Leonardis, Francesco; Soref, Richard A.; Passaro, Vittorio M. N.
2017-01-01
In this paper we present a physical discussion of the indirect two-photon absorption (TPA) occuring in silicon carbide with either cubic or wurtzite structure. Phonon-electron interaction is analyzed by finding the phonon features involved in the process as depending upon the crystal symmetry. Consistent physical assumptions about the phonon-electron scattering mechanisms are proposed in order to give a mathematical formulation to predict the wavelength dispersion of TPA and the Kerr nonlinear refractive index n2. The TPA spectrum is investigated including the effects of band nonparabolicity and the influence of the continuum exciton. Moreover, a parametric analysis is presented in order to fit the experimental measurements. Finally, we have estimated the n2 in a large wavelength range spanning the visible to the mid-IR region. PMID:28098223
Nonlinear plasmonic dispersion and coupling analysis in the symmetric graphene sheets waveguide.
Jiang, Xiangqian; Yuan, Haiming; Sun, Xiudong
2016-12-15
We study the nonlinear dispersion and coupling properties of the graphene-bounded dielectric slab waveguide at near-THz/THz frequency range, and then reveal the mechanism of symmetry breaking in nonlinear graphene waveguide. We analyze the influence of field intensity and chemical potential on dispersion relation, and find that the nonlinearity of graphene affects strongly the dispersion relation. As the chemical potential decreases, the dispersion properties change significantly. Antisymmetric and asymmetric branches disappear and only symmetric one remains. A nonlinear coupled mode theory is established to describe the dispersion relations and its variation, which agrees with the numerical results well. Using the nonlinear couple model we reveal the reason of occurrence of asymmetric mode in the nonlinear waveguide.
Nonlinear plasmonic dispersion and coupling analysis in the symmetric graphene sheets waveguide
NASA Astrophysics Data System (ADS)
Jiang, Xiangqian; Yuan, Haiming; Sun, Xiudong
2016-12-01
We study the nonlinear dispersion and coupling properties of the graphene-bounded dielectric slab waveguide at near-THz/THz frequency range, and then reveal the mechanism of symmetry breaking in nonlinear graphene waveguide. We analyze the influence of field intensity and chemical potential on dispersion relation, and find that the nonlinearity of graphene affects strongly the dispersion relation. As the chemical potential decreases, the dispersion properties change significantly. Antisymmetric and asymmetric branches disappear and only symmetric one remains. A nonlinear coupled mode theory is established to describe the dispersion relations and its variation, which agrees with the numerical results well. Using the nonlinear couple model we reveal the reason of occurrence of asymmetric mode in the nonlinear waveguide.
Nonlinear plasmonic dispersion and coupling analysis in the symmetric graphene sheets waveguide
Jiang, Xiangqian; Yuan, Haiming; Sun, Xiudong
2016-01-01
We study the nonlinear dispersion and coupling properties of the graphene-bounded dielectric slab waveguide at near-THz/THz frequency range, and then reveal the mechanism of symmetry breaking in nonlinear graphene waveguide. We analyze the influence of field intensity and chemical potential on dispersion relation, and find that the nonlinearity of graphene affects strongly the dispersion relation. As the chemical potential decreases, the dispersion properties change significantly. Antisymmetric and asymmetric branches disappear and only symmetric one remains. A nonlinear coupled mode theory is established to describe the dispersion relations and its variation, which agrees with the numerical results well. Using the nonlinear couple model we reveal the reason of occurrence of asymmetric mode in the nonlinear waveguide. PMID:27976749
Electromagnetic sinc Schell-model pulses in dispersive media
NASA Astrophysics Data System (ADS)
Tang, Miaomiao; Zhao, Daomu; Zhu, Yingbin; Ang, Lay-Kee
2016-02-01
A class of random electromagnetic pulsed sources with sinc Schell-model correlations is introduced. Analytical formulas for the electromagnetic pulses generated by such pulsed sources propagating in dispersive media are derived. It is shown that the temporal intensity distribution of this new type of pulse exhibits unique propagation features, such as reshaping its average intensity from the initial Gaussian profile to a double-layer flat-top distribution at far field. The effects, arising from the source temporal coherent length and the dispersion coefficient, on the profiles of the temporal intensity distribution and the temporal degree of polarization are analyzed in detail. The results presented here demonstrate the potential of coherence modulation for pulse shaping applications.
Ultrasonic wave velocity in the restructuring of disperse media
NASA Astrophysics Data System (ADS)
Koltsova, I. S.; Khomutova, A. S.; Deinega, M. A.
2016-03-01
The ultrasonic wave velocities in the restructuring of disperse media were measured using interference and pulsed techniques and the coefficient of reflection in suspensions of starch, Al2O3, and SiO2 particles, glass bulbs, their porous sediments, and composites of Fe3O4 particles in 10% gelatin aqueous solution at a frequency of 3 MHz. The experiments showed alternating variation in the concentration velocity coefficient during the transition of the dispersed phase concentration from the subpercolation to percolation region. The minimum ultrasonic wave velocity in the region of discrete clusters correlates with the ratio between the particle and matrix densities. The results obtained are explained using the Isakovich, Chaban, Rytov, Biot, Hausdorff, and other theories.
Nonlinear Optical Wave Equation for Micro- and Nano-Structured Media and Its Application
2013-03-01
AFRL-AFOSR-UK-TR-2013-0012 Nonlinear Optical Wave Equation for Micro - and Nano - Structured Media and Its Application Dr...September 2012 4. TITLE AND SUBTITLE Nonlinear Optical Wave Equation for Micro - and Nano - Structured Media and Its...Equation, Nano -structed Media, Nonlinear Fiber Lasers 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT SAR 18, NUMBER OF PAGES 12
Interface modes at step edges of media with anisotropic dispersion
NASA Astrophysics Data System (ADS)
Toedt, Jan-Niklas; Mansfeld, Sebastian; Mellem, Daniel; Hansen, Wolfgang; Heitmann, Detlef; Mendach, Stefan
2016-05-01
Time-resolved scanning Kerr microscopy data are presented that illustrate the refraction and total reflection of spin waves in a Ni80Fe20 film at a film-thickness step. In our experiments spin waves are excited with microwaves on coplanar wave guides. By changing the orientation of an externally applied magnetic field, we can manipulate the group velocity of the wave and hence control the angle of incidence on the step. An interface mode bound at the step is observed, when the magnetic field vector is perpendicular to the step. We point out the general conditions under which such interface modes can be expected in media with strongly anisotropic dispersion.
The Numerical Solution of Acoustic Propagation through Dispersive Moving Media
2010-06-01
domain version [3] of the Kramer- Kronig relationships (K-K), [6] he arrived at a general form for the operator. Szabo’s operator was originally...for longitudinal and shear wave propagation in viscoelastic media,” J. Acoust. Soc. Am. 107, 2437-2446, 2000. [6] R. D. L. Kronig , “On the theory...domain representation of the Kramers- Kronig dispersion relations,” J. Acoust. Soc. Am. 108, 2114-2119, 2000. [8] G. V. Norton and J. C. Novarini
Magnetoviscous effect in ferrofluids with different dispersion media
NASA Astrophysics Data System (ADS)
Borin, D. Yu; Korolev, V. V.; Ramazanova, A. G.; Odenbach, S.; Balmasova, O. V.; Yashkova, V. I.; Korolev, D. V.
2016-10-01
Ferrofluids based on magnetite nanoparticles dispersed in different carrier media (dialkyldiphenyl and polyethylsiloxane) have been synthesized using mixed surfactants (oleic acid, stearic acid and alkenyl succinic anhydride). Magnetic properties of the samples and a change of their shear viscosities in an applied magnetic field have been studied in order to evaluate an influence of the carrier medium on a magnetoviscous effect. A significance of the interaction of the carrier medium and surfactant with a consideration of the magnetic and rheological behavior of ferrofluids was demonstrated.
Radiating dispersive shock waves in non-local optical media
El, Gennady A.
2016-01-01
We consider the step Riemann problem for the system of equations describing the propagation of a coherent light beam in nematic liquid crystals, which is a general system describing nonlinear wave propagation in a number of different physical applications. While the equation governing the light beam is of defocusing nonlinear Schrödinger (NLS) equation type, the dispersive shock wave (DSW) generated from this initial condition has major differences from the standard DSW solution of the defocusing NLS equation. In particular, it is found that the DSW has positive polarity and generates resonant radiation which propagates ahead of it. Remarkably, the velocity of the lead soliton of the DSW is determined by the classical shock velocity. The solution for the radiative wavetrain is obtained using the Wentzel–Kramers–Brillouin approximation. It is shown that for sufficiently small initial jumps the nematic DSW is asymptotically governed by a Korteweg–de Vries equation with the fifth-order dispersion, which explicitly shows the resonance generating the radiation ahead of the DSW. The constructed asymptotic theory is shown to be in good agreement with the results of direct numerical simulations. PMID:27118911
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.
Probing the permeability of porous media by NMR measurement of stochastic dispersion dynamics
NASA Astrophysics Data System (ADS)
Brosten, Tyler; Maier, Robert; Codd, Sarah; Vogt, Sarah; Seymour, Joseph
2011-11-01
A generalized short-time expansion of hydrodynamic dispersion is derived using non-linear response theory. The result is in accordance with the well-known reduced cases of shear flow in ducts and pipes. In terms of viscous dominated (low Reynolds number) flow in porous media the generalized expansion facilitates the measurement of permeability by PGSE-NMR measurement of time dependent molecular displacement dynamics. To be more precise, for porous media characterized by a homogeneous permeability coefficient along the direction of flow K, and fluid volume fraction ɛ, the effective dispersion coefficient D (t) = < | R-
NASA Astrophysics Data System (ADS)
Muniruzzaman, Muhammad; Haberer, Christina; Grathwohl, Peter; Rolle, Massimo
2014-05-01
We study the influence of Coulombic effects on transport of charged species in saturated porous media in advection-dominated flow regimes. We focus on transverse hydrodynamic dispersion and we performed quasi two-dimensional flow-through experiments in homogeneous and spatially variable flow fields to investigate transport of dilute electrolyte solutions. The experiments were conducted at flow velocities (1.0, 1.5 and 6 m/day) where advection is the dominant mass transfer process. High-resolution measurements at the outlet were performed to determine the concentration of different cations and anions. In order to interpret the laboratory experiments we develop a two-dimensional numerical model. The adopted modeling approach is based on a multicomponent formulation, charge conservation, and the accurate description of local transverse dispersion. The latter entails a non-linear dependence of the transverse dispersion coefficient on the flow velocity as well as a compound-specific dependence on the molecular diffusion of the transported solutes. The model was benchmarked by comparing the results of the 2D steady-state multicomponent simulations with 1D transient results of PHREEQC in homogeneous scenarios, and it was successively used to quantitatively evaluate the experimental results in both homogeneous and heterogeneous porous media. Our experimental and modeling results show that Coulombic cross-coupling of dispersive fluxes of charged species in porous media significantly affects the lateral displacement of charged ions in both homogeneous and heterogeneous flow-through systems. Such effects are remarkable not only in diffusion-dominated but also in advection-dominated flow regimes.
Self-similarity and optical kinks in resonant nonlinear media
Ponomarenko, Sergey A.; Haghgoo, Soodeh
2010-11-15
We show that self-similar optical waves with a kink structure exist in a wide class of resonant nonlinear media, adequately treated in the two-level approximation. The self-similar structure of the present kinks is reflected in the time evolution of the field profile, atomic dipole moment, and one-atom inversion. We develop an analytical theory of such kinks. We show that the discovered kinks are accelerating nonlinear waves, asymptotically attaining their shape and the speed of light. We also numerically explore the formation and eventual disintegration of our kinks due to energy relaxation processes. Thus, the present kinks can be viewed as intermediate asymptotics of the system.
1986-04-30
TenCate , who is supported by ONR Contract NOOO I 4-84-K-0574, in the completion of work on pure tones that interact in higher order modes of a...rectangular duct.26 Through collaboration with TenCate , Lind has acquired experience with the same experimental apparatus that he will use beginning I June...34 J. Acoust. Soc. " .. Am. 65.1127-1133(1979). 36. J. A TenCate and K F. Hamilton, "Dispersive nonlinear wave interactions in a rectangular duct," In
Elliptically polarised cnoidal waves in a medium with spatial dispersion of cubic nonlinearity
Makarov, Vladimir A; Perezhogin, I A; Petnikova, V M; Potravkin, N N; Shuvalov, Vladimir V
2012-02-28
We present new specific analytic solutions of a system of nonlinear Schroedinger equations, corresponding to elliptically polarised cnoidal waves in an isotropic gyrotropic medium with spatial dispersion of cubic nonlinearity and second-order frequency dispersion under the conditions of formation of the waveguides of the same type for each of the circularly polarised components of the light field.
Quantum and classical optics of dispersive and absorptive structured media
NASA Astrophysics Data System (ADS)
Bhat, Navin Andrew Rama
This thesis presents a Hamiltonian formulation of the electromagnetic fields in structured (inhomogeneous) media of arbitrary dimensionality, with arbitrary material dispersion and absorption consistent with causality. The method is based on an identification of the photonic component of the polariton modes of the system. Although the medium degrees of freedom are introduced in an oscillator model, only the macroscopic response of the medium appears in the derived eigenvalue equation for the polaritons. For both the discrete transparent-regime spectrum and the continuous absorptive-regime spectrum, standard codes for photonic modes in nonabsorptive systems can easily be leveraged to calculate polariton modes. Two applications of the theory are presented: pulse propagation and spontaneous parametric down-conversion (SPDC). In the propagation study, the dynamics of the nonfluctuating part of a classical-like pulse are expressed in terms of a Schrodinger equation for a polariton effective field. The complex propagation parameters of that equation can be obtained from the same generalized dispersion surfaces typically used while neglecting absorption, without incurring additional computational complexity. As an example I characterize optical pulse propagation in an Au/MgF 2 metallodielectric stack, using the empirical response function, and elucidate the various roles of Bragg scattering, interband absorption and field expulsion. Further, I derive the Beer coefficient in causal structured media. The SPDC calculation is rigorous, captures the full 3D physics, and properly incorporates linear dispersion. I obtain an expression for the down-converted state, quantify pair-production properties, and characterize the scaling behavior of the SPDC energy. Dispersion affects the normalization of the polariton modes, and calculations of the down-conversion efficiency that neglect this can be off by 100% or more for common media regardless of geometry if the pump is near the band
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.
Engineering chromatic dispersion and effective nonlinearity in a dual-slot waveguide.
Liu, Yan; Yan, Jing; Han, Genquan
2014-09-20
In this paper, we propose a new dual slot based on rib-like structure, which exhibits a flat and near-zero dispersion over a 198 nm wide wavelength range. Chromatic dispersion of dual-slot silicon (Si) waveguide is mainly determined by waveguide dispersion due to the manipulating mode effective area rather than by the material dispersion. Moreover, the nonlinear coefficient and effective mode area of the waveguide are also explored in detail. A nonlinear coefficient of 1460/m/W at 1550 nm is achieved, which is 10 times larger than that of the Si rib waveguide. By changing different waveguide variables, both the dispersion and nonlinear coefficient can be tailored, thus enabling the potential for a highly nonlinear waveguide with uniform dispersion over a wide wavelength range, which could benefit the performance of broadband optical signal systems.
Particle dispersion and deposition in porous media: a computational perspective
NASA Astrophysics Data System (ADS)
Boccardo, Gianluca; Crevacore, Eleonora; Sethi, Rajandrea; Marchisio, Daniele
2015-11-01
This work investigates particle dispersion in porous media, which is of central relevance in a number of applications ranging from groundwater remediation tochemical engineering. The challenge lies in studying the complex fluid dynamics behavior arising at the microscale (very difficult to observe experimentally) and obtaining transport models to be employed at the macroscopic scale of interest. While a wealth of studies have approached this problem, the case of particle transport with a concurrent heterogeneous chemical reaction (e.g.: particle deposition) still lacks a satisfactory description, especially when considering a polydisperse population of solid particles. Moreover, the oft-used simplified descriptions of the porous medium (via array of spheres or similar strategies) fail to fully take into account the effect of the packing structure. Our novel approach relies on an ``in-silico'' procedure where many 3-D realistic porous media models are constructed via rigid-body simulations and fluid flowand particle transport are then investigated through computational fluid dynamics. The results evidence the need for a deeper look, afforded by these methodology, into the influence of the features of realistic porous media on particle transport and deposition.
Stabilization of vortex beams in Kerr media by nonlinear absorption
NASA Astrophysics Data System (ADS)
Porras, Miguel A.; Carvalho, Márcio; Leblond, Hervé; Malomed, Boris A.
2016-11-01
We elaborate a solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form robust tubular filaments in transparent dielectrics as common as air, water, and optical glasses at sufficiently high intensities. We also show that the tubular, rotating, and specklelike filamentation regimes, previously observed in experiments with axicon-generated Bessel beams, can be explained as manifestations of the stability or instability of a specific nonlinear Bessel-vortex state, which is fully identified.
All-fiber nonlinearity- and dispersion-managed dissipative soliton nanotube mode-locked laser
NASA Astrophysics Data System (ADS)
Zhang, Z.; Popa, D.; Wittwer, V. J.; Milana, S.; Hasan, T.; Jiang, Z.; Ferrari, A. C.; Ilday, F. Ö.
2015-12-01
We report dissipative soliton generation from an Yb-doped all-fiber nonlinearity- and dispersion-managed nanotube mode-locked laser. A simple all-fiber ring cavity exploits a photonic crystal fiber for both nonlinearity enhancement and dispersion compensation. The laser generates stable dissipative solitons with large linear chirp in the net normal dispersion regime. Pulses that are 8.7 ps long are externally compressed to 118 fs, outperforming current nanotube-based Yb-doped fiber laser designs.
All-fiber nonlinearity- and dispersion-managed dissipative soliton nanotube mode-locked laser
Zhang, Z.; Popa, D. Wittwer, V. J.; Milana, S.; Hasan, T.; Jiang, Z.; Ferrari, A. C.; Ilday, F. Ö.
2015-12-14
We report dissipative soliton generation from an Yb-doped all-fiber nonlinearity- and dispersion-managed nanotube mode-locked laser. A simple all-fiber ring cavity exploits a photonic crystal fiber for both nonlinearity enhancement and dispersion compensation. The laser generates stable dissipative solitons with large linear chirp in the net normal dispersion regime. Pulses that are 8.7 ps long are externally compressed to 118 fs, outperforming current nanotube-based Yb-doped fiber laser designs.
Controlling Spatiotemporal Chaos in Active Dissipative-Dispersive Nonlinear Systems
NASA Astrophysics Data System (ADS)
Gomes, Susana; Pradas, Marc; Kalliadasis, Serafim; Papageorgiou, Demetrios; Pavliotis, Grigorios
2015-11-01
We present a novel generic methodology for the stabilization and control of infinite-dimensional dynamical systems exhibiting low-dimensional spatiotemporal chaos. The methodology is exemplified with the generalized Kuramoto-Sivashinsky equation, the simplest possible prototype that retains that fundamental elements of any nonlinear process involving wave evolution. The equation is applicable on a wide variety of systems including falling liquid films and plasma waves with dispersion due to finite banana width. We show that applying the appropriate choice of time-dependent feedback controls via blowing and suction, we are able to stabilize and/or control all stable or unstable solutions, including steady solutions, travelling waves and spatiotemporal chaos, but also use the controls obtained to stabilize the solutions to more general long wave models. We acknowledge financial support from Imperial College through a Roth PhD studentship, Engineering and Physical Sciences Research Council of the UK through Grants No. EP/H034587, EP/J009636, EP/K041134, EP/L020564 and EP/L024926 and European Research Council via Advanced Grant No. 247031.
Optical Momentum, Spin, and Angular Momentum in Dispersive Media
NASA Astrophysics Data System (ADS)
Bliokh, Konstantin Y.; Bekshaev, Aleksandr Y.; Nori, Franco
2017-08-01
We examine the momentum, spin, and orbital angular momentum of structured monochromatic optical fields in dispersive inhomogeneous isotropic media. There are two bifurcations in this general problem: the Abraham-Minkowski dilemma and the kinetic (Poynting-like) versus canonical (spin-orbital) pictures. We show that the kinetic Abraham momentum describes the energy flux and group velocity of the wave in the medium. At the same time, we introduce novel canonical Minkowski-type momentum, spin, and orbital angular momentum densities of the field. These quantities exhibit fairly natural forms, analogous to the Brillouin energy density, as well as multiple advantages as compared with previously considered formalisms. As an example, we apply this general theory to inhomogeneous surface plasmon-polariton (SPP) waves at a metal-vacuum interface and show that SPPs carry a "supermomentum," proportional to the wave vector kp>ω /c , and a transverse spin, which can change its sign depending on the frequency ω .
Optical Momentum, Spin, and Angular Momentum in Dispersive Media.
Bliokh, Konstantin Y; Bekshaev, Aleksandr Y; Nori, Franco
2017-08-18
We examine the momentum, spin, and orbital angular momentum of structured monochromatic optical fields in dispersive inhomogeneous isotropic media. There are two bifurcations in this general problem: the Abraham-Minkowski dilemma and the kinetic (Poynting-like) versus canonical (spin-orbital) pictures. We show that the kinetic Abraham momentum describes the energy flux and group velocity of the wave in the medium. At the same time, we introduce novel canonical Minkowski-type momentum, spin, and orbital angular momentum densities of the field. These quantities exhibit fairly natural forms, analogous to the Brillouin energy density, as well as multiple advantages as compared with previously considered formalisms. As an example, we apply this general theory to inhomogeneous surface plasmon-polariton (SPP) waves at a metal-vacuum interface and show that SPPs carry a "supermomentum," proportional to the wave vector k_{p}>ω/c, and a transverse spin, which can change its sign depending on the frequency ω.
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
Wave velocity dispersion and attenuation in media exhibiting internal oscillations
NASA Astrophysics Data System (ADS)
Frehner, Marcel; Steeb, Holger; Schmalholz, Stefan M.
2010-05-01
Understanding the dynamical and acoustical behavior of porous and heterogeneous rocks is of great importance in geophysics, e.g. earthquakes, and for various seismic engineering applications, e.g. hydrocarbon exploration. Within a heterogeneous medium oscillations with a characteristic resonance frequency, depending on the mass and internal length of the heterogeneity, can occur. When excited, heterogeneities can self-oscillate with their natural frequency. Another example of internal oscillations is the dynamical behavior of non-wetting fluid blobs or fluid patches in residually saturated pore spaces. Surface tension forces or capillary forces act as the restoring force that drives the oscillation. Whatever mechanism is involved, an oscillatory phenomena within a heterogeneous medium will have an effect on acoustic or seismic waves propagating through such a medium, i.e. wave velocity dispersion and frequency-dependent attenuation. We present two models for media exhibiting internal oscillations and discuss the frequency-dependent wave propagation mechanism. Both models give similar results: (1) The low-frequency (i.e. quasi-static) limit for the phase velocity is identical with the Gassmann-Wood limit and the high-frequency limit is larger than this value and (2) Around the resonance frequency a very strong phase velocity change and the largest attenuation occurs. (1) Model for a homogeneous medium exhibiting internal oscillations We present a continuum model for an acoustic medium exhibiting internal damped oscillations. The obvious application of this model is water containing oscillating gas bubbles, providing the material and model parameters for this study. Two physically based momentum interaction terms between the two inherent constituents are used: (1) A purely elastic term of oscillatory nature that scales with the volume of the bubbles and (2) A viscous term that scales with the specific surface of the bubble. The model is capable of taking into account
The Whitham approach to dispersive shocks in systems with cubic-quintic nonlinearities
NASA Astrophysics Data System (ADS)
Crosta, M.; Trillo, S.; Fratalocchi, A.
2012-09-01
By employing a rigorous approach based on the Whitham modulation theory, we investigate dispersive shock waves arising in a high-order nonlinear Schrödinger equation with competing cubic and quintic nonlinear responses. This model finds important applications in both nonlinear optics and Bose-Einstein condensates. Our theory predicts the formation of dispersive shocks with totally controllable properties, encompassing both steering and compression effects. Numerical simulations confirm these results perfectly. Quite remarkably, shock tuning can be achieved in the regime of a very small high order, i.e. quintic, nonlinearity.
NASA Astrophysics Data System (ADS)
Hopkins, James; Gaudette, Jamie; Mehta, Priyanth
2013-10-01
With the advent of digital signal processing (DSP) in optical transmitters and receivers, the ability to finely tune the ratio of pre and post dispersion compensation can be exploited to best mitigate the nonlinear penalties caused by the Kerr effect. A portion of the nonlinear penalty in optical communication channels has been explained by an increase in peak to average power ratio (PAPR) inherent in highly dispersed signals. The standard approach for minimizing these impairments applies 50% pre dispersion compensation and 50% post dispersion compensation, thereby decreasing average PAPR along the length of the cable, as compared with either 100% pre or post dispersion compensation. In this paper we demonstrate that simply considering the net accumulated dispersion, and applying 50/50 pre/post dispersion is not necessarily the best way to minimize PAPR and subsequent Kerr nonlinearities. Instead, we consider the cumulative dispersion along the entire length of the cable, and, taking into account this additional information, derive an analytic formula for the minimization of PAPR. Alignment with simulation and experimental measurements is presented using a commercially available 100Gb/s dual-polarization binary phase-shift-keying (DP-BPSK) coherent modem, with transmitter and receiver DSP. Measurements are provided from two different 5000km dispersion managed Submarine test-beds, as well as a 3800km terrestrial test-bed with a mixture of SMF-28 and TWRS optical fiber. This method is shown to deviate significantly from the conventional 50/50 method described above, in dispersion managed communications systems, and more closely aligns with results obtained from simulation and data collected from laboratory test-beds.
Stochastic theory of an optical vortex in nonlinear media.
Kuratsuji, Hiroshi
2013-07-01
A stochastic theory is given of an optical vortex occurring in nonlinear Kerr media. This is carried out by starting from the nonlinear Schrödinger type equation which accommodates vortex solution. By using the action functional method, the evolution equation of vortex center is derived. Then the Langevin equation is introduced in the presence of random fluctuations, which leads to the Fokker-Planck equation for the distribution function of the vortex center coordinate by using a functional integral. The Fokker-Planck equation is analyzed for a specific form of pinning potential by taking into account an interplay between the strength of the pinning potential and the random parameters, diffusion and dissipation constants. This procedure is performed by several approximate schemes.
Stochastic theory of an optical vortex in nonlinear media
NASA Astrophysics Data System (ADS)
Kuratsuji, Hiroshi
2013-07-01
A stochastic theory is given of an optical vortex occurring in nonlinear Kerr media. This is carried out by starting from the nonlinear Schrödinger type equation which accommodates vortex solution. By using the action functional method, the evolution equation of vortex center is derived. Then the Langevin equation is introduced in the presence of random fluctuations, which leads to the Fokker-Planck equation for the distribution function of the vortex center coordinate by using a functional integral. The Fokker-Planck equation is analyzed for a specific form of pinning potential by taking into account an interplay between the strength of the pinning potential and the random parameters, diffusion and dissipation constants. This procedure is performed by several approximate schemes.
Cai, Yangjian; Lin, Qiang; Ge, Di
2002-10-01
By adopting a new tensor method, we derived an analytical propagation formula for the cross-spectral density of partially coherent twisted anisotropic Gaussian Schell-model (GSM) beams through dispersive and absorbing media. Using the derived formula, we studied the evolution properties and spectrum properties of twisted anisotropic GSM beams in dispersive and absorbing media. The results show that the dispersive and absorbing media have strong influences on the propagation properties of twisted anisotropic GSM beams and their spectrum evolution. Our method provides a simple and convenient way to study the propagation of twisted anisotropic GSM beams in media with complex refractive index.
Christodoulides, D N; Joseph, R L
1984-06-01
The propagation of nonlinear optical pulses in fibers is discussed, taking into account physical effects arising from nonlinearity, dispersion, and transverse confinement. The wave equation is solved by treating the radial dependence of the field in an exact way. The conditions supporting bright solitary waves are presented and compared with previous results.
Chemotaxis and flow disorder shape microbial dispersion in porous media
NASA Astrophysics Data System (ADS)
De Anna, Pietro; Yawata, Yutaka; Stocker, Roman; Juanes, Ruben
2017-04-01
Bacteria drive a plethora of natural processes in the subsurface, consuming organic matter and catalysing chemical reactions that are key to global elemental cycles. These macro-scale consequences result from the collective action of individual bacteria at the micro-scale, which are modulated by the highly heterogeneous subsurface environment, dominated by flow disorder and strong chemical gradients. Yet, despite the generally recognized importance of these microscale processes, microbe-host medium interaction at the pore scale remain poorly characterized and understood. Here, we introduce a microfluidic model system to directly image and quantify the role of cell motility on bacterial dispersion and residence time in confined, porous, media. Using the soil-dwelling bacterium Bacillus subtilis and the common amino acid serine as a resource, we observe that chemotaxis in highly disordered and confined physico-chemical environment affords bacteria an increase in their ability to persistently occupy the host medium. Our findings illustrate that the interplay between bacterial behaviour and pore-scale disorder in fluid velocity and nutrient concentration directly impacts the residence time, transport and bio-geo-chemical transformation rates of biota in the subsurface, and thus likely the processes they mediate.
NONLINEAR OPTICAL PHENOMENA: Dispersive regime of spectral compression
NASA Astrophysics Data System (ADS)
Kutuzyan, A. A.; Mansuryan, T. G.; Esayan, G. L.; Akopyan, R. S.; Muradyan, Kh
2008-04-01
The role of the group velocity dispersion in the spectral compression of subpicosecond laser pulses is analysed based on numerical and experimental studies. It is shown that the group velocity dispersion in an optical fibre can substantially change the physical pattern of the spectral compression process.
Flow and dispersion in anisotropic porous media: A lattice-Boltzmann study
NASA Astrophysics Data System (ADS)
Maggiolo, D.; Picano, F.; Guarnieri, M.
2016-10-01
Given their capability of spreading active chemical species and collecting electricity, porous media made of carbon fibers are extensively used as diffusion layers in energy storage systems, such as redox flow batteries. In spite of this, the dispersion dynamics of species inside porous media is still not well understood and often lends itself to different interpretations. Actually, the microscopic design of efficient porous media, which can potentially and effectively improve the performances of flow batteries, is still an open challenge. The present study aims to investigate the effect of fibrous media micro-structure on dispersion, in particular the effect of fiber orientation on drag and dispersion dynamics. Several lattice-Boltzmann simulations of flows through differently oriented fibrous media coupled with Lagrangian simulations of particle tracers have been performed. Results show that orienting fibers preferentially along the streamwise direction minimizes the drag and maximizes the dispersion, which is the most desirable condition for diffusion layers in flow batteries' applications.
Nonlinear acoustics in a dispersive continuum: Random waves, radiation pressure, and quantum noise
NASA Astrophysics Data System (ADS)
Cabot, M. A.
The nonlinear interaction of sound with sound is studied using dispersive hydrodynamics which derived from a variational principle and the assumption that the internal energy density depends on gradients of the mass density. The attenuation of sound due to nonlinear interaction with a background is calculated and is shown to be sensitive to both the nature of the dispersion and decay bandwidths. The theoretical results are compared to those of low temperature helium experiments. A kinetic equation which described the nonlinear self-inter action of a background is derived. When a Deybe-type cutoff is imposed, a white noise distribution is shown to be a stationary distribution of the kinetic equation. The attenuation and spectrum of decay of a sound wave due to nonlinear interaction with zero point motion is calculated. In one dimension, the dispersive hydrodynamic equations are used to calculate the Langevin and Rayleigh radiation pressures of wave packets and solitary waves.
Design of highly nonlinear photonic crystal fibers with flattened chromatic dispersion.
Li, Xuyou; Xu, Zhenlong; Ling, Weiwei; Liu, Pan
2014-10-10
A novel (to our knowledge) type of photonic crystal fiber (PCF) with high nonlinearity and flattened dispersion is proposed. The propagation characteristics of chromatic dispersion, effective area, and nonlinearity are studied numerically by using the full-vector finite element method. Several PCF designs with high nonlinearity and nearly zero flattened dispersion or broadband flattened, and even ultraflattened, dispersion over different wavelength bands are obtained by optimizing the structural parameters. One optimized PCF has a nearly zero ultraflattened dispersion of 2.3 ps/(nm·km) with a dispersion variation of 0.2 ps/(nm·km) over the C+L+U wavelength bands. In addition, the dispersion slope and nonlinear coefficient at 1.55 μm can be up to 2.2×10(-3) ps/nm(2)·km and 33.2 W(-1)·km(-1), respectively. The designs proposed in this paper have bright prospects for applications in all-optical format conversion, supercontinuum generation, optical wavelength conversion, and many other fields.
High-order FDTD methods for transverse electromagnetic systems in dispersive inhomogeneous media.
Zhao, Shan
2011-08-15
This Letter introduces a novel finite-difference time-domain (FDTD) formulation for solving transverse electromagnetic systems in dispersive media. Based on the auxiliary differential equation approach, the Debye dispersion model is coupled with Maxwell's equations to derive a supplementary ordinary differential equation for describing the regularity changes in electromagnetic fields at the dispersive interface. The resulting time-dependent jump conditions are rigorously enforced in the FDTD discretization by means of the matched interface and boundary scheme. High-order convergences are numerically achieved for the first time in the literature in the FDTD simulations of dispersive inhomogeneous media.
Spiraling elliptic solitons in lossy nonlocal nonlinear media.
Liang, Guo; Cheng, Wenjing; Dai, Zhiping; Jia, Tingjian; Wang, Meng; Li, Huangxin
2017-05-15
We address the propagation dynamics of the spiraling elliptic beams in nonlocal nonlinear media with losses based on the variational approach. It is found that the spiraling elliptic beams exhibit complicated behaviors, which result from the combined effects of the losses and orbital angular momentum (OAM). The OAM brings in an effective anisotropic diffraction and rotation for the spiraling elliptic beams. However, due to the losses, the rotation of the spiraling beams slows down. Besides, the ellipticity of the spiraling elliptic beams is greatly affected by the lossesand the OAM. When the OAM is not equal to its critical value, a periodic oscillation of the ellipticity is found in the presence of losses. However, when the OAM is equal to the critical one, the ellipticity of the spiraling elliptic beam remains unchanged during propagation regardless of the loss factor. The comparisons between our approximate analytic solutions and numerical simulations confirm our results.
Local computational strategies for predicting wave propagation in nonlinear media
NASA Astrophysics Data System (ADS)
Leamy, Michael J.; Autrusson, Thibaut B.; Staszewski, Wieslaw J.; Uhl, Tadeusz; Packo, Pawel
2014-03-01
Two local computational strategies for modeling elastic wave propagation, namely the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE), are compared and contrasted in analyzing bulk waves in two-dimensional nonlinear media. Each strategy formulates the problem from the perspective of a cell and its local interactions with other cells, leading to robust treatments of anisotropy, heterogeneity, and nonlinearity. The local approach also enables straight-forward parallelization on high performance computing clusters. While the two share a common local perspective, they differ in two major respects. The first is that CAFE employs both rectangular and triangular cells, while LISA considers only rectangular. The second is that LISA appeared much earlier than CAFE (early 1990's versus late 2000's), and as such has been developed to a much greater degree with a multitude of material models, cell-to-cell interactions, loading possibilities, and boundary treatments. A hybrid approach which combines the two is of great interest since the non-uniform mesh capability of the CAFE triangular cell can be readily coupled to LISA's rectangular grids, taking advantage of the built-in LISA features on the uniform portion of the domain. For linear material domains, the hybrid implementation appears straight-forward since both methods have been shown to recover the same equations in the rectangular case. For nonlinear material domains, the formulations cannot be put into a one-to-one correspondence, and hybrid implementation may be more problematic. This paper addresses these differences by first presenting the underlying formulations, and then computing results for growth of a second harmonic in an introduced bulk pressure wave. Rectangular cells are used in both LISA and CAFE. Results from both approaches are compared to an approximate, analytical solution based on a two-scale field representation. Differences in the LISA and CAFE computed
Nonlinear dispersive evolution of coherent trapped particle structures in collisionless plasmas
NASA Astrophysics Data System (ADS)
Mandal, Debraj; Sharma, Devendra
2016-10-01
The nonlinear limit of the collective perturbations in plasma is characterized by the onset of amplitude dependence in the wave dispersion. In a special class of nonlinear effects having origin in plasma kinetic theory, this amplitude dependence is removed only by collisions such that perturbations have no linear counterpart in collisionless limit and must follow a nonlinear dispersion relation (NDR). Exploring whether these fundamentally nonlinear perturbations can be driven unstable without entropy production might transform the character of the linear threshold based operating mechanism of the plasma turbulence that relies on well defined discrete spectrum prescribed by the linear plasma dispersion. In our multiscale, exact mass ratio, kinetic simulations the evolution of fundamentally nonlinear trapped particle structures is explored on both fast and slow ion and electron acoustic branches of the associated Nonlinear dispersion relation, respectively. The propagating structures that mutually interact exhibit a near continuum of the phase velocities and show microscopic evolution of the separatrix between streaming and trapped particle regions in the phase space, describing the subtle continuity between discrete and continuum bases of the plasma turbulence.
NASA Astrophysics Data System (ADS)
Rajan, M. S. Mani
2016-08-01
In this manuscript, the ultrashort soliton pulse propagation through nonlinear tunneling in cubic quintic media is investigated. The effect of chirping on propagation characteristics of the soliton pulse is analytically investigated using similarity transformation. In particular, we investigate the propagation dynamics of ultrashort soliton pulse through dispersion barrier for both chirp and chirp-free soliton. By investigating the obtained soliton solution, we found that chirping has strong influence on soliton dynamics such as pulse compression with amplification. These two important dynamics of chirped soliton in cubic quintic media open new possibilities to improve the solitonic communication system. Moreover, we surprisingly observe that a dispersion well is formed for the chirped case whereas a barrier is formed for the chirp-free case, which has certain applications in the construction of logic gate devices to achieve ultrafast switching.
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.
Zhang, Yiqi; Belić, Milivoj R; Zheng, Huaibin; Chen, Haixia; Li, Changbiao; Li, Yuanyuan; Zhang, Yanpeng
2014-03-24
We investigate numerically interactions between two in-phase or out-of-phase Airy beams and nonlinear accelerating beams in Kerr and saturable nonlinear media in one transverse dimension. We discuss different cases in which the beams with different intensities are launched into the medium, but accelerate in opposite directions. Since both the Airy beams and nonlinear accelerating beams possess infinite oscillating tails, we discuss interactions between truncated beams, with finite energies. During interactions we see solitons and soliton pairs generated that are not accelerating. In general, the higher the intensities of interacting beams, the easier to form solitons; when the intensities are small enough, no solitons are generated. Upon adjusting the interval between the launched beams, their interaction exhibits different properties. If the interval is large relative to the width of the first lobes, the generated soliton pairs just propagate individually and do not interact much. However, if the interval is comparable to the widths of the maximum lobes, the pairs strongly interact and display varied behavior.
NASA Astrophysics Data System (ADS)
Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi
2017-05-01
This paper studies the dynamics of solitons to the nonlinear Schrödinger’s equation (NLSE) with spatio-temporal dispersion (STD). The integration algorithm that is employed in this paper is the Riccati-Bernoulli sub-ODE method. This leads to dark and singular soliton solutions that are important in the field of optoelectronics and fiber optics. The soliton solutions appear with all necessary constraint conditions that are necessary for them to exist. There are four types of nonlinear media studied in this paper. They are Kerr law, power law, parabolic law and dual law. The conservation laws (Cls) for the Kerr law and parabolic law nonlinear media are constructed using the conservation theorem presented by Ibragimov.
Solitary-wave interaction. [model equation solutions for long waves in dispersive media
NASA Technical Reports Server (NTRS)
Bona, J. L.; Pritchard, W. G.; Scott, L. R.
1980-01-01
The interaction of solitary-wave solutions of a model equation for long waves in dispersive media is examined numerically. It is found that the waves do not emerge from the interaction unscathed. Instead, two new solitary waves, having slightly different amplitudes from the original waves, together with a small dispersive tail are generated as a result of the interaction.
Non-Linear Noise Contributions in Highly Dispersive Optical Transmission Systems
NASA Astrophysics Data System (ADS)
Matera, Francesco
2016-01-01
This article reports an analytical investigation, confirmed by numerical simulations, about the non-linear noise contribution in single-channel systems adopting generic modulation-detection formats in long links with both managed and unmanaged dispersion compensation and its impact in system performance. This noise contribution is expressed in terms of a pulse non-linear interaction length and permits a simple calculation of the Q-factor. Results point out the dependence of this non-linear noise on the number of amplifiers spans, N, according to the adopted chromatic dispersion compensation scheme, the modulation-detection format, and the signal baud rate. It is also shown how the effects of polarization multiplexing can be taken into account and how this single-channel non-linear noise contribution can be used in a wavelength-division multiplexing (WDM) environment.
Nonlinear coupling of left and right handed circularly polarized dispersive Alfvén wave
Sharma, R. P. Sharma, Swati Gaur, Nidhi
2014-07-15
The nonlinear phenomena are of prominent interests in understanding the particle acceleration and transportation in the interplanetary space. The ponderomotive nonlinearity causing the filamentation of the parallel propagating circularly polarized dispersive Alfvén wave having a finite frequency may be one of the mechanisms that contribute to the heating of the plasmas. The contribution will be different of the left (L) handed mode, the right (R) handed mode, and the mix mode. The contribution also depends upon the finite frequency of the circularly polarized waves. In the present paper, we have investigated the effect of the nonlinear coupling of the L and R circularly polarized dispersive Alfvén wave on the localized structures formation and the respective power spectra. The dynamical equations are derived in the presence of the ponderomotive nonlinearity of the L and R pumps and then studied semi-analytically as well as numerically. The ponderomotive nonlinearity accounts for the nonlinear coupling between both the modes. In the presence of the adiabatic response of the density fluctuations, the nonlinear dynamical equations satisfy the modified nonlinear Schrödinger equation. The equations thus obtained are solved in solar wind regime to study the coupling effect on localization and the power spectra. The effect of coupling is also studied on Faraday rotation and ellipticity of the wave caused due to the difference in the localization of the left and the right modes with the distance of propagation.
Laine, T A; Friberg, A T
2000-06-01
We investigate electromagnetic wave reflection and propagation in layered Kerr structures by introducing a method based on the application of canonical perturbation theory to fields in nonlinear media. Via the Hamilton-Jacobi formalism of classical mechanics, the waves in linear layers are expressed with constant canonical variables. The nonlinearity is treated as a small perturbation that modifies the constant invariants. We explicitly evaluate the nonlinear fields correct to first order by perturbation and compare the results to a rigorous nonlinear thin-layer model. Both polarizations, TE and TM, are considered separately. An exact quadrature solution of the nonlinear field in TM polarization is derived. We show that with weak nonlinearities the perturbative technique yields simple and accurate analytical expressions for the nonlinear fields. The results give physical insight into the use of nonlinear media for controlling the scattered fields in layered structures.
Are There Optical Solitary Wave Solutions in Linear Media with Group Velocity Dispersion?
NASA Technical Reports Server (NTRS)
Li, Zhonghao; Zhou, Guosheng
1996-01-01
A generalized exact optical bright solitary wave solution in a three dimensional dispersive linear medium is presented. The most interesting property of the solution is that it can exist in the normal group-velocity-dispersion (GVD) region. In addition, another peculiar feature is that it may achieve a condition of 'zero-dispersion' to the media so that a solitary wave of arbitrarily small amplitude may be propagated with no dependence on is pulse width.
Strojan, Klemen; Leonardi, Adrijana; Bregar, Vladimir B.; Križaj, Igor; Svete, Jurij; Pavlin, Mojca
2017-01-01
Protein corona of nanoparticles (NPs), which forms when these particles come in to contact with protein-containing fluids, is considered as an overlooked factor in nanomedicine. Through numerous studies it has been becoming increasingly evident that it importantly dictates the interaction of NPs with their surroundings. Several factors that determine the compositions of NPs protein corona have been identified in recent years, but one has remained largely ignored—the composition of media used for dispersion of NPs. Here, we determined the effect of dispersion media on the composition of protein corona of polyacrylic acid-coated cobalt ferrite NPs (PAA NPs) and silica NPs. Our results confirmed some of the basic premises such as NPs type-dependent specificity of the protein corona. But more importantly, we demonstrated the effect of the dispersion media on the protein corona composition. The differences between constituents of the media used for dispersion of NPs, such as divalent ions and macromolecules were responsible for the differences in protein corona composition formed in the presence of fetal bovine serum (FBS). Our results suggest that the protein corona composition is a complex function of the constituents present in the media used for dispersion of NPs. Regardless of the dispersion media and FBS concentration, majority of proteins from either PAA NPs or silica NPs coronas were involved in the process of transport and hemostasis. Interestingly, corona of silica NPs contained three complement system related proteins: complement factor H, complement C3 and complement C4 while PAA NPs bound only one immune system related protein, α-2-glycoprotein. Importantly, relative abundance of complement C3 protein in corona of silica NPs was increased when NPs were dispersed in NaCl, which further implies the relevance of dispersion media used to prepare NPs. PMID:28052135
Strojan, Klemen; Leonardi, Adrijana; Bregar, Vladimir B; Križaj, Igor; Svete, Jurij; Pavlin, Mojca
2017-01-01
Protein corona of nanoparticles (NPs), which forms when these particles come in to contact with protein-containing fluids, is considered as an overlooked factor in nanomedicine. Through numerous studies it has been becoming increasingly evident that it importantly dictates the interaction of NPs with their surroundings. Several factors that determine the compositions of NPs protein corona have been identified in recent years, but one has remained largely ignored-the composition of media used for dispersion of NPs. Here, we determined the effect of dispersion media on the composition of protein corona of polyacrylic acid-coated cobalt ferrite NPs (PAA NPs) and silica NPs. Our results confirmed some of the basic premises such as NPs type-dependent specificity of the protein corona. But more importantly, we demonstrated the effect of the dispersion media on the protein corona composition. The differences between constituents of the media used for dispersion of NPs, such as divalent ions and macromolecules were responsible for the differences in protein corona composition formed in the presence of fetal bovine serum (FBS). Our results suggest that the protein corona composition is a complex function of the constituents present in the media used for dispersion of NPs. Regardless of the dispersion media and FBS concentration, majority of proteins from either PAA NPs or silica NPs coronas were involved in the process of transport and hemostasis. Interestingly, corona of silica NPs contained three complement system related proteins: complement factor H, complement C3 and complement C4 while PAA NPs bound only one immune system related protein, α-2-glycoprotein. Importantly, relative abundance of complement C3 protein in corona of silica NPs was increased when NPs were dispersed in NaCl, which further implies the relevance of dispersion media used to prepare NPs.
PFG NMR study of hydrodynamic dispersion in porous media
NASA Astrophysics Data System (ADS)
Ding, Aimin
We have studied hydrodynamic dispersion in plastic bead packs using the pulsed field gradient (PFG) NMR technique. The bead diameter was varied from 15 to 138 mum and the Peclet number Pe varied from 0 to 10sp3 (the Peclet number is a dimensionless measure of the flow velocity). We studied the time dependence of both the longitudinal dispersion coefficient Dsb{||} and the transverse dispersion coefficient Dsb{⊥}. We observed transitions from decreasing with time at low Pe to increasing with time at high Pe for both Dsb{||} and Dsb{⊥}. We used our data to find the transition time tsb0 the time required for dispersion coefficient to reach its long time value. For both Dsb{||} and Dsb{⊥}, we found a power-law dependence of tsb0 on Pe, as has been predicted by Koch and Brady. The Pe dependence of tsb0 provides information on the operative dispersion mechanisms. Our results show that both convection dispersion and boundary layer dispersion contribute to longitudinal dispersion in our experiments. However, the Pe dependence of tsb0 for transverse dispersion does not agree with the theoretical prediction of Koch and Brady. We measured Dsb{||} and Dsb{⊥} as a function of Pe. Our experimental results are consistent with previous results measured using conventional methods. We found that the results for longitudinal dispersion agree with Saffman's capillary tube model in our observation range. The results for transverse dispersion agree with Koch and Brady's fixed bed model to some extent, but at low Pe, the disagreement is significant. We obtained the wave-number and frequency dependent nonlocal dispersion coefficient {buildrel{≈}/{D}}sb{| |,⊥}(q,omega) from our PFG NMR data. In the local (long time and distance) limit, our results agree with previous results obtained with conventional methods and for no flow they agree with a simple model of restricted diffusion. Our results for nonlocal dispersion with flow are in reasonable agreement with Koch and Brady
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.
Dispersive and dissipative nonlinear structures in degenerate Fermi-Dirac Pauli quantum plasma
NASA Astrophysics Data System (ADS)
Sahu, Biswajit; Sinha, Anjana; Roychoudhury, Rajkumar
2016-09-01
We study the interplay between dispersion due to the electron degeneracy parameter and dissipation caused by plasma resistivity, in degenerate Fermi-Dirac Pauli quantum plasma. Considering relativistic degeneracy pressure for electrons, we investigate both arbitrary and small amplitude nonlinear structures. The corresponding trajectories are also plotted in the phase plane. The linear analysis for the dispersion relation yields interesting features. The present work is anticipated to be of physical relevance in the study of compact magnetized astrophysical objects like white dwarfs.
Ultrashort Pulse Effects in Semiconductor Amplifiers & in Dispersive Media
1994-03-31
they lead to the two dimensional nonlinear Schr ~ dinger equation with a focusing nonlinear- ity. This equation has singularities, corresponding to a...behavior of a device we would like to have model equations , derived from the underlying physics, which do not require that the full range of time scale:s...solver to integrate full vector Maxwell in one two or three dimensions. At this time that equation is being integrated coupled to a simple two oscillator
Probing nonlocal tracer dispersion in flows through random porous media
NASA Astrophysics Data System (ADS)
Ding, A.; Candela, D.
1996-07-01
Pulsed-field-gradient NMR is used to measure tracer dispersion in flow through a porous medium. Data are presented for water flowing through packs of plastic beads at Péclet numbers 0<=Pe<=150, using strong, fast gradient pulses to measure pore-scale molecular displacements. The transition at Pe~1 from tortuosity-reduced diffusion to dispersion is observed. The data are Fourier transformed to provide a measurement of the wave-number- and frequency-dependent nonlocal dispersion coefficient. The experimental results compare favorably with an approximate calculation of Koch and Brady [J. Fluid Mech. 180, 387 (1987); Chem. Eng. Sci. 42, 1377 (1987)].
Simulations and Theory of Density-Dependent Dispersion in Weakly Heterogeneous Porous Media
NASA Astrophysics Data System (ADS)
Landman, A.; Schotting, R. J.
2004-12-01
The effect of density gradients on dispersive mixing of miscible fluids is studied. Density gradients not only affect dispersive transport for unstable flow, but also can significantly affect dispersion under stable conditions. For vertical displacements, laboratory experiments show a reduction of the longitudinal dispersivity under the influence of stabilizing density gradients. Linear Fick's law for the dispersive flux is inadequate to model these experiments. Therefore, alternative theories have been developed that incorporate the effect of density gradients. In this study, accurate numerical simulations of vertical displacements in weakly heterogeneous porous columns are performed. The numerical results confirm experimental observations. Furthermore, the computed concentration profiles are used to validate nonlinear dispersion theories applicable for high density gradients. A comparison is made with the stochastic theory of Welty and Gelhar, with homogenization theory, and with the nonlinear dispersion theory of Hassanizadeh and Leijnse. For small variances in log k, the stochastic and homogenization theory lead to reasonably good predictions of the computed concentration profiles and variances, without any fitting. In the theory of Hassanizadeh and Leijnse a fitting parameter is involved. This nonlinear dispersion parameter is not a true medium parameter, as it is found to be dependent on the flow rate and on the travel distance.
Asymptotic solutions of weakly nonlinear, dispersive wave-propagation problems by Fourier analysis
Srinivasan, R.
1989-01-01
A perturbation method based on Fourier analysis and multiple scales is introduced for solving weakly nonlinear, dispersive wave propagation problems with Fourier transformable initial conditions. Asymptotic solutions are derived for the weakly nonlinear cubic Schroedinger (NLS) equation with variable coefficients and the weakly nonlinear Kortewegde-Vries (KdV) equation; the results for the NLS equation are verified by comparison with numerical solutions. In the special case of constant coefficients, the asymptotic solution for the weakly nonlinear NLS equation agrees to leading order with previously derived results in the literature; in general, this is not true to higher orders. Therefore previous asymptotic results for the strongly nonlinear Schroedinger equation can be valid only for restricted initial conditions. Similar conclusions apply to the KdV equation.
Tuning the nonlinear response of (6,5)-enriched single-wall carbon nanotubes dispersions
NASA Astrophysics Data System (ADS)
Aréstegui, O. S.; Silva, E. C. O.; Baggio, A. L.; Gontijo, R. N.; Hickmann, J. M.; Fantini, C.; Alencar, M. A. R. C.; Fonseca, E. J. S.
2017-04-01
Ultrafast nonlinear optical properties of (6,5)-enriched single-wall carbon nanotubes (SWCNTs) dispersions are investigated using the thermally managed Z-scan technique. As the (6,5) SWCNTs presented a strong resonance in the range of 895-1048 nm, the nonlinear refractive index (n2) and the absorption coefficients (β) measurements were performed tuning the laser exactly around absorption peak of the (6,5) SWCNTs. It is observed that the nonlinear response is very sensitive to the wavelength and the spectral behavior of n2 is strongly correlated to the tubes one-photon absorption band, presenting also a peak when the laser photon energy is near the tube resonance energy. This result suggests that a suitable selection of nanotubes types may provide optimized nonlinear optical responses in distinct regions of the electromagnetic spectrum. Analysis of the figures of merit indicated that this material is promising for ultrafast nonlinear optical applications under near infrared excitation.
Chakrabarti, Nikhil; Maity, Chandan; Schamel, Hans
2011-04-08
Compressional waves in a magnetized plasma of arbitrary resistivity are treated with the lagrangian fluid approach. An exact nonlinear solution with a nontrivial space and time dependence is obtained with boundary conditions as in Harris' current sheet. The solution shows competition among hydrodynamic convection, magnetic field diffusion, and dispersion. This results in a collapse of density and the magnetic field in the absence of dispersion. The dispersion effects arrest the collapse of density but not of the magnetic field. A possible application is in the early stage of magnetic star formation.
The dispersion and aggregation of graphene oxide in aqueous media
NASA Astrophysics Data System (ADS)
Wang, Meng; Niu, Yang; Zhou, Jihan; Wen, Hao; Zhang, Zhenyu; Luo, Da; Gao, Dongliang; Yang, Juan; Liang, Dehai; Li, Yan
2016-07-01
Graphene oxide (GO), as a typical two-dimensional material, possesses a range of oxygen-containing groups and shows surfactant and/or polyelectrolyte-like characteristics. Herein, GO sheets with narrow size distribution were prepared by an ultracentrifugation-based process and the aggregation behaviour of GO in pure water and an electrolyte aqueous solution were studied using laser light scattering (LLS). When adding common electrolytes, such as NaCl and MgCl2, into the GO dispersions, aggregation occurs and irreversible coagulation eventually occurs too. However, the GO dispersion can still remain stable when adding excess AlCl3. The zeta potential of the GO dispersion changes from negative to positive after the addition of access AlCl3, indicating that electrostatic repulsion is still responsible for the dispersion of GO, which is in good agreement with the LLS results. This finding on the dispersion of GO may be applied in the solution processing of GO. It also expands the scope of the design and preparation of new GO-based hybrid materials with different functions.Graphene oxide (GO), as a typical two-dimensional material, possesses a range of oxygen-containing groups and shows surfactant and/or polyelectrolyte-like characteristics. Herein, GO sheets with narrow size distribution were prepared by an ultracentrifugation-based process and the aggregation behaviour of GO in pure water and an electrolyte aqueous solution were studied using laser light scattering (LLS). When adding common electrolytes, such as NaCl and MgCl2, into the GO dispersions, aggregation occurs and irreversible coagulation eventually occurs too. However, the GO dispersion can still remain stable when adding excess AlCl3. The zeta potential of the GO dispersion changes from negative to positive after the addition of access AlCl3, indicating that electrostatic repulsion is still responsible for the dispersion of GO, which is in good agreement with the LLS results. This finding on the
Nonlinear dynamics, granular media and dynamic earthquake triggering.
Johnson, Paul A; Jia, Xiaoping
2005-10-06
The 1992 magnitude 7.3 Landers earthquake triggered an exceptional number of additional earthquakes within California and as far north as Yellowstone and Montana. Since this observation, other large earthquakes have been shown to induce dynamic triggering at remote distances--for example, after the 1999 magnitude 7.1 Hector Mine and the 2002 magnitude 7.9 Denali earthquakes--and in the near-field as aftershocks. The physical origin of dynamic triggering, however, remains one of the least understood aspects of earthquake nucleation. The dynamic strain amplitudes from a large earthquake are exceedingly small once the waves have propagated more than several fault radii. For example, a strain wave amplitude of 10(-6) and wavelength 1 m corresponds to a displacement amplitude of about 10(-7) m. Here we show that the dynamic, elastic-nonlinear behaviour of fault gouge perturbed by a seismic wave may trigger earthquakes, even with such small strains. We base our hypothesis on recent laboratory dynamic experiments conducted in granular media, a fault gouge surrogate. From these we infer that, if the fault is weak, seismic waves cause the fault core modulus to decrease abruptly and weaken further. If the fault is already near failure, this process could therefore induce fault slip.
Gaussian-type light bullets in power-law nonlinear media with PT-symmetric potentials
NASA Astrophysics Data System (ADS)
Chen, Yi-Xiang; Dai, Chao-Qing
2015-03-01
The (3+1)-dimensional nonlinear Schrödinger equation with power-law nonlinearities in two kinds of PT-symmetric potentials is investigated, and two kinds of Gaussian-type light bullet (LB) solutions are analytically derived. Based on these analytical solutions, the powers, power-flow densities and the phase switches are discussed. The linear stability analysis and the direct numerical simulation show that LB solutions are stable only when the imaginary parts of PT-symmetric potentials are below some thresholds in the focusing power-law nonlinear media, while they are always unstable in the defocusing power-law nonlinear media.
Charalampidis, E G; Kevrekidis, P G; Frantzeskakis, D J; Malomed, B A
2016-08-01
We consider a two-component, two-dimensional nonlinear Schrödinger system with unequal dispersion coefficients and self-defocusing nonlinearities, chiefly with equal strengths of the self- and cross-interactions. In this setting, a natural waveform with a nonvanishing background in one component is a vortex, which induces an effective potential well in the second component, via the nonlinear coupling of the two components. We show that the potential well may support not only the fundamental bound state, but also multiring excited radial state complexes for suitable ranges of values of the dispersion coefficient of the second component. We systematically explore the existence, stability, and nonlinear dynamics of these states. The complexes involving the excited radial states are weakly unstable, with a growth rate depending on the dispersion of the second component. Their evolution leads to transformation of the multiring complexes into stable vortex-bright solitons ones with the fundamental state in the second component. The excited states may be stabilized by a harmonic-oscillator trapping potential, as well as by unequal strengths of the self- and cross-repulsive nonlinearities.
One-dimensional dispersion phenomena in terms of fractional media
NASA Astrophysics Data System (ADS)
Sumelka, W.; Zaera, R.; Fernández-Sáez, J.
2016-09-01
It is well know that structured solids present dispersive behaviour which cannot be captured by the classical continuum mechanics theories. A canonical problem in which this can be seen is the wave propagation in the Born-Von Karman lattice. In this paper the dispersive effects in a 1D structured solid is analysed using the Fractional Continuum Mechanics (FCM) approach previously proposed by Sumelka (2013). The formulation uses the Riesz-Caputo (RC) fractional derivative and introduces two phenomenological/material parameters: 1) the size of non-local surrounding lf, which plays the role of the lattice spacing; and 2) the order of fractional continua α, which can be devised as a fitting parameter. The results obtained with this approach have been compared with the reference dispersion curve of Born-Von Karman lattice, and the capability of the fractional model to capture the size effects present in the dynamic behaviour of discrete systems has been proved.
Nonlinear effect of dispersal rate on spatial synchrony of predator-prey cycles.
Fox, Jeremy W; Legault, Geoffrey; Legault, Geoff; Vasseur, David A; Einarson, Jodie A
2013-01-01
Spatially-separated populations often exhibit positively correlated fluctuations in abundance and other population variables, a phenomenon known as spatial synchrony. Generation and maintenance of synchrony requires forces that rapidly restore synchrony in the face of desynchronizing forces such as demographic and environmental stochasticity. One such force is dispersal, which couples local populations together, thereby synchronizing them. Theory predicts that average spatial synchrony can be a nonlinear function of dispersal rate, but the form of the dispersal rate-synchrony relationship has never been quantified for any system. Theory also predicts that in the presence of demographic and environmental stochasticity, realized levels of synchrony can exhibit high variability around the average, so that ecologically-identical metapopulations might exhibit very different levels of synchrony. We quantified the dispersal rate-synchrony relationship using a model system of protist predator-prey cycles in pairs of laboratory microcosms linked by different rates of dispersal. Paired predator-prey cycles initially were anti-synchronous, and were subject to demographic stochasticity and spatially-uncorrelated temperature fluctuations, challenging the ability of dispersal to rapidly synchronize them. Mean synchrony of prey cycles was a nonlinear, saturating function of dispersal rate. Even extremely low rates of dispersal (<0.4% per prey generation) were capable of rapidly bringing initially anti-synchronous cycles into synchrony. Consistent with theory, ecologically-identical replicates exhibited very different levels of prey synchrony, especially at low to intermediate dispersal rates. Our results suggest that even the very low rates of dispersal observed in many natural systems are sufficient to generate and maintain synchrony of cyclic population dynamics, at least when environments are not too spatially heterogeneous.
NASA Astrophysics Data System (ADS)
Yu, Changyuan
Chromatic dispersion, polarization mode dispersion (PMD) and nonlinear effects are important issues on the physical layer of high-speed reconfigurable WDM optical fiber communication systems. For beyond 10 Gbit/s optical fiber transmission system, it is essential that chromatic dispersion and PMD be well managed by dispersion monitoring and compensation. One the other hand, dispersive and nonlinear effects in optical fiber systems can also be beneficial and has applications on pulse management, all-optical signal processing and network function, which will be essential for high bite-rate optical networks and replacing the expensive optical-electrical-optical (O/E/O) conversion. In this Ph.D. dissertation, we present a detailed research on dispersive and nonlinear effects in high-speed optical communication systems. We have demonstrated: (i) A novel technique for optically compensating the PMD-induced RF power fading that occurs in single-sideband (SSB) subcarrier-multiplexed systems. By aligning the polarization states of the optical carrier and the SSB, RF power fading due to all orders of PMD can be completely compensated. (ii) Chromatic-dispersion-insensitive PMD monitoring by using a narrowband FBG notch filter to recover the RF clock power for 10Gb/s NRZ data, and apply it as a control signal for PMD compensation. (iii) Chirp-free high-speed optical pulse generation with a repetition rate of 160 GHz (which is four times of the frequency of the electrical clock) using a phase modulator and polarization maintaining (PM) fiber. (iv) Polarization-insensitive all-optical wavelength conversion based on four-wave mixing in dispersion-shifted fiber (DSF) with a fiber Bragg grating and a Faraday rotator mirror. (v) Width-tunable optical RZ pulse train generation based on four-wave mixing in highly-nonlinear fiber. By electrically tuning the delay between two pump pulse trains, the pulse-width of a generated pulse train is continuously tuned. (vi) A high-speed all
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
The zero dispersion limits of nonlinear wave equations
Tso, T.
1992-01-01
In chapter 2 the author uses functional analytic methods and conservation laws to solve the initial-value problem for the Korteweg-de Vries equation, the Benjamin-Bona-Mahony equation, and the nonlinear Schroedinger equation for initial data that satisfy some suitable conditions. In chapter 3 the energy estimates are used to show that the strong convergence of the family of the solutions of the KdV equation obtained in chapter 2 in H[sup 3](R) as [epsilon] [yields] 0; also, it is shown that the strong L[sup 2](R)-limit of the solutions of the BBM equation as [epsilon] [yields] 0 before a critical time. In chapter 4 the author uses the Whitham modulation theory and averaging method to find the 2[pi]-periodic solutions and the modulation equations of the KdV equation, the BBM equation, the Klein-Gordon equation, the NLS equation, the mKdV equation, and the P-system. It is shown that the modulation equations of the KdV equation, the K-G equation, the NLS equation, and the mKdV equation are hyperbolic but those of the BBM equation and the P-system are not hyperbolic. Also, the relations are studied of the KdV equation and the mKdV equation. Finally, the author studies the complex mKdV equation to compare with the NLS equation, and then study the complex gKdV equation.
Zhang, Ya-Ni; Ren, Li-Yong; Gong, Yong-Kang; Li, Xiao-Hui; Wang, Lei-Ran; Sun, Chuan-Dong
2010-06-01
We have proposed a novel type of photonic crystal fiber (PCF) with low dispersion and high nonlinearity for four-wave mixing. This type of fiber is composed of a solid silica core and a cladding with a squeezed hexagonal lattice elliptical airhole along the fiber length. Its dispersion and nonlinearity coefficient are investigated simultaneously by using the full vectorial finite element method. Numerical results show that the proposed highly nonlinear low-dispersion fiber has a total dispersion as low as +/-2.5 ps nm(-1) km(-1) over an ultrabroad wavelength range from 1.43 to 1.8 microm, and the corresponding nonlinearity coefficient and birefringence are about 150 W(-1) km(-1) and 2.5x10(-3) at 1.55 microm, respectively. The proposed PCF with low ultraflattened dispersion, high nonlinearity, and high birefringence can have important application in four-wave mixing.
Scale-Dependent Solute Dispersion in Variably Saturated Porous Media
Rockhold, Mark L.; Zhang, Z. F.; Bott, Yi-Ju
2016-03-29
This work was performed to support performance assessment (PA) calculations for the Integrated Disposal Facility (IDF) at the Hanford Site. PA calculations require defensible estimates of physical, hydraulic, and transport parameters to simulate subsurface water flow and contaminant transport in both the near- and far-field environments. Dispersivity is one of the required transport parameters.
Dispersion-driven instability of mixed convective flow in porous media
NASA Astrophysics Data System (ADS)
Emami-Meybodi, Hamid
2017-09-01
This paper investigates the impact of hydrodynamic dispersion on the stability of free convection in a saturated horizontal porous layer subject to a transient vertical concentration gradient and a steady horizontal background flow. A linear stability analysis (LSA) was conducted using the quasi-steady-state approximation to obtain neutral stability curves, critical times, and the corresponding wavenumbers as a function of dispersivity ratio (α) and longitudinal dispersion strength (β). The LSA results showed that the dispersive boundary layer becomes less unstable as longitudinal and transverse dispersivity increase. In addition, for the isotropic dispersive system with α = 1, the critical time and its corresponding wavenumber follow τc = 167.6/(1 - β) and κc = 0.0696 (1 - β), respectively. The nonlinear dynamics of the system were studied by examining the interaction of convective fingers, dissolution flux, and the time-dependent Sherwood number. Finally, the results were applied to 24 deep saline aquifers in the Alberta Basin.
2015-01-01
In vitro toxicity assessment of engineered nanomaterials (ENM), the most common testing platform for ENM, requires prior ENM dispersion, stabilization, and characterization in cell culture media. Dispersion inefficiencies and active aggregation of particles often result in polydisperse and multimodal particle size distributions. Accurate characterization of important properties of such polydisperse distributions (size distribution, effective density, charge, mobility, aggregation kinetics, etc.) is critical for understanding differences in the effective dose delivered to cells as a function of time and dispersion conditions, as well as for nano–bio interactions. Here we have investigated the utility of tunable nanopore resistive pulse sensing (TRPS) technology for characterization of four industry relevant ENMs (oxidized single-walled carbon nanohorns, carbon black, cerium oxide and nickel nanoparticles) in cell culture media containing serum. Harvard dispersion and dosimetry platform was used for preparing ENM dispersions and estimating delivered dose to cells based on dispersion characterization input from dynamic light scattering (DLS) and TRPS. The slopes of cell death vs administered and delivered ENM dose were then derived and compared. We investigated the impact of serum protein content, ENM concentration, and cell medium on the size distributions. The TRPS technology offers higher resolution and sensitivity compared to DLS and unique insights into ENM size distribution and concentration, as well as particle behavior and morphology in complex media. The in vitro dose–response slopes changed significantly for certain nanomaterials when delivered dose to cells was taken into consideration, highlighting the importance of accurate dispersion and dosimetry in in vitro nanotoxicology. PMID:25093451
Pal, Anoop K; Aalaei, Iraj; Gadde, Suresh; Gaines, Peter; Schmidt, Daniel; Demokritou, Philip; Bello, Dhimiter
2014-09-23
In vitro toxicity assessment of engineered nanomaterials (ENM), the most common testing platform for ENM, requires prior ENM dispersion, stabilization, and characterization in cell culture media. Dispersion inefficiencies and active aggregation of particles often result in polydisperse and multimodal particle size distributions. Accurate characterization of important properties of such polydisperse distributions (size distribution, effective density, charge, mobility, aggregation kinetics, etc.) is critical for understanding differences in the effective dose delivered to cells as a function of time and dispersion conditions, as well as for nano-bio interactions. Here we have investigated the utility of tunable nanopore resistive pulse sensing (TRPS) technology for characterization of four industry relevant ENMs (oxidized single-walled carbon nanohorns, carbon black, cerium oxide and nickel nanoparticles) in cell culture media containing serum. Harvard dispersion and dosimetry platform was used for preparing ENM dispersions and estimating delivered dose to cells based on dispersion characterization input from dynamic light scattering (DLS) and TRPS. The slopes of cell death vs administered and delivered ENM dose were then derived and compared. We investigated the impact of serum protein content, ENM concentration, and cell medium on the size distributions. The TRPS technology offers higher resolution and sensitivity compared to DLS and unique insights into ENM size distribution and concentration, as well as particle behavior and morphology in complex media. The in vitro dose-response slopes changed significantly for certain nanomaterials when delivered dose to cells was taken into consideration, highlighting the importance of accurate dispersion and dosimetry in in vitro nanotoxicology.
All-solid highly nonlinear singlemode fibers with a tailored dispersion profile.
Poletti, Francesco; Feng, Xian; Ponzo, Giorgio M; Petrovich, Marco N; Loh, Wei H; Richardson, David J
2011-01-03
We investigate a novel approach to obtain highly nonlinear fibers with a tailored group velocity dispersion around a desired wavelength region of interest. Rather than exploiting longitudinal holes to control the average refractive index of the cladding and hence the fiber's waveguide dispersion, as in holey fibers, we propose using an all-solid cladding with a suitably chosen refractive index difference relative to the core. We demonstrate numerically that this solution allows a large freedom in the manipulation of the overall fiber dispersive properties, while enabling, in practice, a much more accurate control of the fiber's structural properties during fabrication. Effectively single mode guidance over a broad wavelength range can be achieved through the use of a second outer cladding forming a W-type index profile. We derive simple design rules for dispersion controlled fibers, based on which an algorithm for the automatic dispersion optimization is proposed, implemented and used to design various nonlinear fibers for all-optical processing and supercontinuum generation. Fabrication of a lead silicate fiber with flattened dispersion at telecoms wavelengths confirms the potential of these new fibers.
Long time behavior of some nonlinear dispersive equations
NASA Astrophysics Data System (ADS)
Deng, Yu
This thesis is divided into two parts. The first part consists of Chapters 2 and 3, in which we study the random data theory for the Benjamin-Ono equation on the periodic domain. In Chapter 2 we shall prove the invariance of the Gibbs measure associated to the Hamiltonian E1 of the equation, which was constructed in [49]. Despite the fact that the support of the Gibbs measure contains very rough functions that are not even in L2, we have successfully established the global dynamics by combining probabilistic arguments, Xs,b type estimates and the hidden structure of the equation. In Chapter 3, which is joint work with N. Tzvetkov and N. Visciglia, we extend this invariance result to the weighted Gaussian measures associated with the higher order conservation laws E2 and E3, thus completing the collection of invariant measures (except for the white noise), given the result of [51]. The second part concerns the global behavior of solutions to quasilinear dispersive systems in Rd with suitably small data. In Chapter 4 we shall prove global existence and scattering for small data solutions to systems of quasilinear Klein-Gordon equations with arbitrary speed and mass in 3 D, which extends the results in [20] and [32]. Moreover, the methods introduced here are quite general, and can be applied in a number of different situations. In Chapter 5, we briefly discuss how these methods, together with other techniques, are used in recent joint work with A. Ionescu and B. Pausader to study the 2D Euler-Maxwell system.
Nonlinear Behavior Of Saturated Porous Media Under External Impact
NASA Astrophysics Data System (ADS)
Perepechko, Y.
2005-12-01
This paper deals with nonlinear behavior of liquid saturated porous media in gravity filed under external impact. The continuum is assumed to be a two-velocity medium; it consists of a deformable porous matrix (with Maxwell's reology) and a Newtonian liquid that saturates this matrix. The energy dissipation in this model takes place due the interface friction between the solid matrix and saturating liquid, and also through relaxation of inelastic shear stress in the porous matrix. The elaborated nonisothermal mathematical model for this kind of medium is a thermodynamically consistent and closed model. Godunov's explicit difference scheme was used for computer simulation; the method implies numerical simulation for discontinuity decay in flux calculations. As an illustrative example, we consider the formation of dissipation structures in a plain layer of that medium after pulse or periodic impact on the background of liquid filtration through the porous matrix. At the process beginning, one can observe elastic behavior of the porous matrix. Deformation spreading through the saturated porous matrix occurs almost without distortions and produces a channel-shaped zone of stretching with a high porosity. Later on, dissipation processes and reology properties of porous medium causes the diffusion of this channel. We also observe a correlation between the liquid distribution (porosity for the solid matrix) and dilatancy fields; this allows us to restore the dilatancy field from the measured fluid saturation of the medium. This work was supported by the RFBR (Grant No. 04-05-64107), the Presidium of SB RAS (Grant 106), the President's Grants (NSh-2118.2003.5, NSh-1573.2003.5).
Coherent propagation of waves in dilute random media with weak nonlinearity
Wellens, Thomas; Gremaud, Benoit
2009-12-15
We develop a diagrammatic theory for transport of waves in dilute disordered media with weak nonlinearity. We first represent the solution of the nonlinear wave equation as a nonlinear Born series. From this, we construct nonlinear ladder and crossed diagrams for the average wave intensity. Then, we sum up the diagrammatic series completely, i.e., nonperturbatively in the strength of the nonlinearity, and thereby obtain integral equations describing both nonlinear diffusive transport and coherent backscattering of the average intensity. As main result, we find that the nonlinearity significantly influences the magnitude of the coherent backscattering effect. Depending on the type of nonlinearity, coherent backscattering is either enhanced or suppressed, as compared to the linear case.
Microscopic Models for Electromagnetic Wave Propagation in Highly Dispersive Media
1990-06-18
rotations, the effects of pressure and temperature and to show the classes of density fluctuations in I which give spatial dispersion, ie, the k- dependance ...complex plane the response e (co, Q) lives on some Riemann surface which is determined by the k- dependance . 2. Talks and Publications Three talks were...sources of 1- dependance (k- dependance in Fourier transform variables) have been identified. One is bubbles or cavitation which scatter the propagating
Construction of the wave operator for non-linear dispersive equations
NASA Astrophysics Data System (ADS)
Tsuruta, Kai Erik
In this thesis, we will study non-linear dispersive equations. The primary focus will be on the construction of the positive-time wave operator for such equations. The positive-time wave operator problem arises in the study of the asymptotics of a partial differential equation. It is a map from a space of initial data X into itself, and is loosely defined as follows: Suppose that for a solution ψlin to the dispersive equation with no non-linearity and initial data ψ +, there exists a unique solution ψ to the non-linear equation with initial data ψ0 such that ψ behaves as ψ lin as t → infinity. Then the wave operator is the map W+ that takes ψ + to ψ0. By its definition, W+ is injective. An important additional question is whether or not the map is also surjective. If so, then every non-linear solution emanating from X behaves, in some sense, linearly as it evolves (this is known as asymptotic completeness). Thus, there is some justification for treating these solutions as their much simpler linear counterparts. The main results presented in this thesis revolve around the construction of the wave operator(s) at critical non-linearities. We will study the "semi-relativistic" Schrodinger equation as well as the Klein-Gordon-Schrodinger system on R2 . In both cases, we will impose fairly general quadratic non-linearities for which conservation laws cannot be relied upon. These non-linearities fall below the scaling required to employ such tools as the Strichartz estimates. We instead adapt the "first iteration method" of Jang, Li, and Zhang to our setting which depends crucially on the critical decay of the non-linear interaction of the linear evolution. To see the critical decay in our problem, careful analysis is needed to treat the regime where one has spatial and/or time resonance.
RADIONUCLIDE DISPERSION RATES BY AEOLIAN, FLUVIAL, AND POROUS MEDIA TRANSPORT
J. Walton; P. Goodell; C. Brashears; D. French; A. Kelts
2005-07-11
Radionuclide transport was measured from high grade uranium ore boulders near the Nopal I Site, Chihuahua, Mexico. High grade uranium ore boulders were left behind after removal of a uranium ore stockpile at the Prior High Grade Stockpile (PHGS). During the 25 years when the boulder was present, radionuclides were released and transported by sheetflow during precipitation events, wind blown resuspension, and infiltration into the unsaturated zone. In this study, one of the boulders was removed, followed by grid sampling of the surrounding area. Measured gamma radiation levels in three dimensions were used to derive separate dispersion rates by the three transport mechanisms.
Strongly nonlinear evolution of low-frequency wave packets in a dispersive plasma
NASA Technical Reports Server (NTRS)
Vasquez, Bernard J.
1993-01-01
The evolution of strongly nonlinear, strongly modulated wave packets is investigated in a dispersive plasma using a hybrid numerical code. These wave packets have amplitudes exceeding the strength of the external magnetic field, along which they propagate. Alfven (left helicity) wave packets show strong steepening for p < 1, while fast (fight heIicity) wave packets hardly steepen for any beta. Substantial regions of opposite helicity form on the leading side of steepened Alfven wave packets. This behavior differs qualitatively from that exhibited by the solutions to the derivative nonlinear Schrodinger (DNLS) equation.
Dispersion controlled highly nonlinear fibers for all-optical processing at telecoms wavelengths
NASA Astrophysics Data System (ADS)
Feng, Xian; Poletti, Francesco; Camerlingo, Angela; Parmigiani, Francesca; Petropoulos, Periklis; Horak, Peter; Ponzo, Giorgio M.; Petrovich, Marco; Shi, Jindan; Loh, Wei H.; Richardson, David J.
2010-12-01
We review our recent progress in the development of lead silicate glass fibers with high nonlinearity and tailored near-zero dispersion at telecommunication wavelengths, encompassing holey, all-solid microstructured and W-type fiber designs. The fabrication techniques and relative merits of each fiber design are described in detail. The optical properties of the fabricated fibers are assessed both experimentally and through accurate numerical simulations. The significant potential of lead silicate highly nonlinear fibers for all-optical signal processing at telecommunication wavelengths is shown via a number of key experimental demonstrators.
Dispersion relation of the nonlinear Klein-Gordon equation through a variational method.
Amore, Paolo; Raya, Alfredo
2006-03-01
We derive approximate expressions for the dispersion relation of the nonlinear Klein-Gordon equation in the case of strong nonlinearities using a method based on the linear delta expansion. All the results obtained in this article are fully analytical, never involve the use of special functions, and can be used to obtain systematic approximations to the exact results to any desired degree of accuracy. We compare our findings with similar results in the literature and show that our approach leads to better and simpler results.
On a hierarchy of nonlinearly dispersive generalized Korteweg - de Vries evolution equations
Christov, Ivan C.
2015-08-20
We propose a hierarchy of nonlinearly dispersive generalized Korteweg–de Vries (KdV) evolution equations based on a modification of the Lagrangian density whose induced action functional the KdV equation extremizes. Two recent nonlinear evolution equations describing wave propagation in certain generalized continua with an inherent material length scale are members of the proposed hierarchy. Like KdV, the equations from the proposed hierarchy possess Hamiltonian structure. Unlike KdV, the solutions to these equations can be compact (i.e., they vanish outside of some open interval) and, in addition, peaked. Implicit solutions for these peaked, compact traveling waves (“peakompactons”) are presented.
Noncontact thermoacoustic detection of targets embedded in dispersive media
NASA Astrophysics Data System (ADS)
Boyle, Kevin C.; Nan, Hao; Khuri-Yakub, Butrus T.; Arbabian, Amin
2016-10-01
A microwave-induced thermoacoustic detection system for embedded targets in lossy media is presented. The system achieves reliable detection of 5 cm × 5 cm × 2 cm targets embedded in a large Agarose sample at a 20 cm acoustic standoff. Repeated measurements across different target and sample configurations confirm the system's ability to distinguish between a target signal and a baseline control signal generated by the package without embedded targets. Post-processing techniques including filtering and baseline signal characterization further improve detection performance.
Astra, Egon; Olsson, Samuel L I; Eliasson, Henrik; Andrekson, Peter A
2017-06-12
We present an investigation of dispersion map optimization for two-span single-channel 28 GBaud QPSK transmission systems with phase-sensitive amplifiers (PSAs). In experiments, when the PSA link is operated in a highly nonlinear regime, a 1.4 dB error vector magnitude (EVM) improvement is achieved compared to a one-span optimized dispersion map link due to improved nonlinearity mitigation. The two-span optimized dispersion map of a PSA link differs from the optimized dispersion map of a dispersion managed phase-insensitive amplifier (PIA) link. Simulations show that the performance of the two-span dispersion map optimized PSA link does not improve by residual dispersion optimization. Further, by using the two-span optimized dispersion maps repeatedly in a long-haul PSA link instead of one-span optimized maps, the maximum transmission reach can be improved 1.5 times.
Real-space Hopfield diagonalization of inhomogeneous dispersive media
NASA Astrophysics Data System (ADS)
Gubbin, Christopher R.; Maier, Stefan A.; De Liberato, Simone
2016-11-01
We introduce a real-space technique able to extend the standard Hopfield approach commonly used in quantum polaritonics to the case of inhomogeneous lossless materials interacting with the electromagnetic field. We derive the creation and annihilation polaritonic operators for the system normal modes as linear, space-dependent superpositions of the microscopic light and matter fields. We prove their completeness and invert the Hopfield transformation expressing the microscopic fields as functions of the polaritonic operators. As an example, we apply our approach to the case of a planar interface between vacuum and a polar dielectric, showing how we can consistently treat both propagative and surface modes, and express their nonlinear interactions, arising from phonon anharmonicity, as polaritonic scattering terms. We also show that our theory, including the proof of completeness, can be naturally extended to the case of dissipative materials.
Xia, Cen; Liu, Xiang; Chandrasekhar, S; Fontaine, N K; Zhu, Likai; Li, G
2014-03-10
We demonstrate nonlinearity compensation of 37.5-GHz-spaced 128-Gb/s PDM-QPSK signals using dispersion-folded digital-backward-propagation and a spectrally-sliced receiver that simultaneously receives three WDM signals, showing mitigation of intra-channel and inter-channel nonlinear effects in a 2560-km dispersion-managed TWRS-fiber link. Intra-channel and adjacent inter-channel nonlinear compensation gains when WDM channels are fully populated in the C-band are estimated based on the GN-model.
NASA Astrophysics Data System (ADS)
Purvinis, Georgeanne M.
Organic crystals and certain polymer films, such as ionically self-assembled monolayer (ISAM) films, are lossy and anisotropic. These materials may have a large chi(2) nonlinear response, and thus are conceivably capable of efficient second order processes. Anomalous dispersion phase-matched second harmonic generation (ADPM-SHG) in organic media is a second order wavelength conversion process that phase matches like-order modes in a waveguide (ex: TM0o → TM02o ), thus maximizing the overlap integral. Demonstration of ADPM-SHG in economical and easily fabricated polymer ISAM film is the ultimate experimental goal of this research. In order to achieve demonstration of ADPM-SHG in an ISAM film, both theoretical and material research contributions are accomplished. The predominant analysis approaches in literature are based on the finite element method, which is approximate and computationally intensive, thus prohibiting arbitrary crystallographic media orientations in devices. This restricted treatment in the literature may be insufficient with ISAM films, as SHG occurs in a spectral region of residual absorption, the film is uniaxial, and the optic axis may not be aligned the waveguide coordinate system. Thus, the theory objectives of the dissertation research are: (1) develop an exact solution for finding the polarization states in lossy anisotropic media using a new complex orthogonal similarity transformation with the complex symmetric impermeability tensor, (2) develop a rigorous transverse resonance analysis to find the eigenmodes of general lossy anisotropic planar waveguides with arbitrary principal axes orientations, and (3) integrate the results of steps 1--2 to determine the conversion efficiency of an ISAM planar waveguide using ADPM-SHG, thus illustrating the importance of the dissertation research by highlighting the errors resulting in algorithms published in other works. Experimentally, the dissertation focuses on designing anionic and cationic
Dispersive transport and symmetry of the dispersion tensor in porous media
NASA Astrophysics Data System (ADS)
Pride, Steven R.; Vasco, Donald W.; Flekkoy, Eirik G.; Holtzman, Ran
2017-04-01
The macroscopic laws controlling the advection and diffusion of solute at the scale of the porous continuum are derived in a general manner that does not place limitations on the geometry and time evolution of the pore space. Special focus is given to the definition and symmetry of the dispersion tensor that is controlling how a solute plume spreads out. We show that the dispersion tensor is not symmetric and that the asymmetry derives from the advective derivative in the pore-scale advection-diffusion equation. When flow is spatially variable across a voxel, such as in the presence of a permeability gradient, the amount of asymmetry can be large. As first shown by Auriault [J.-L. Auriault et al. Transp. Porous Med. 85, 771 (2010), 10.1007/s11242-010-9591-y] in the limit of low Péclet number, we show that at any Péclet number, the dispersion tensor Di j satisfies the flow-reversal symmetry Di j(+q ) =Dj i(-q ) where q is the mean flow in the voxel under analysis; however, Reynold's number must be sufficiently small that the flow is reversible when the force driving the flow changes sign. We also demonstrate these symmetries using lattice-Boltzmann simulations and discuss some subtle aspects of how to measure the dispersion tensor numerically. In particular, the numerical experiments demonstrate that the off-diagonal components of the dispersion tensor are antisymmetric which is consistent with the analytical dependence on the average flow gradients that we propose for these off-diagonal components.
Light propagation in media with a highly nonlinear response: An analytical study
NASA Astrophysics Data System (ADS)
Tatarinova, Larisa L.; Garcia, Martin E.
2011-04-01
The problem of light propagation in highly nonlinear media is studied with the help of a recently introduced systematic approach to the analytical solution of equations of nonlinear optics [L.L. Tatarinova, M.E. Garcia, Exact solutions of the eikonal equations describing self-focusing in highly nonlinear geometrical optics, Phys. Rev. A 78 (2008) 021806(R)(1-4)]. Numerous particular cases of media exhibiting high-order nonlinear refractive indices are considered. We obtain analytical expressions for determining the self-focusing position and a new exact expression for calculating the filament intensity. The constructed solutions allowed us to revise a so-called self-focusing scaling law, i.e., the functional dependence of the self-focusing position on the initial light peak intensity. It was demonstrated that this dependence is governed by the form of the nonlinear refractive index and not by the laser beam shape at the boundary.
Methods of obtaining meaningful information from disperse media holograms
NASA Astrophysics Data System (ADS)
Dyomin, Victor V.
1997-05-01
The problem of nondestructive testing of microstructure parameters, both aerosols and water suspension, is actual for biology, medicine, and environmental control. Among the methods of optical investigations and diagnostics of light scattering media the holographic method plays a special role. A hologram of scattering volume allows us to reproduce the optical wave field to obtain information on the parameters of microparticles: size, shape, and spatial position. Usually this is done by analysis of the particle images reconstructed from the hologram. On the basis of calculated and experimental results, characteristics of holographic methods are analyzed in this paper. These estimations demonstrate a possibility to use the above methods for investigation of media in biomedical science and clinical practice. A lot of micro-organisms and other living particles are transparent or semitransparent ones. In this case the reconstructed image of the particle will show a spot formed due to light focusing by the particle in addition to its cross section. This circumstance allowed us to propose a method of determining of refractive index of transparent and semitransparent microparticles, that, in turn, can provide identification of the particles type. The development of this method is presented. To make measurement of the size-distribution of particles one can do this simultaneously with the reconstruction of scattering optical field from the hologram. In this case a small angle optical meter (for example, focusing lens) can be placed just behind the illuminated hologram. The reconstructed field is composed of the initial one and its conjugate. Each of these components as well as interference between them can bear an additional information on the medium. The possibility of extraction of this information is also discussed.
Rius, Manuel; Bolea, Mario; Mora, José; Ortega, Beatriz; Capmany, José
2015-05-18
We experimentally demonstrate, for the first time, a chirped microwave pulses generator based on the processing of an incoherent optical signal by means of a nonlinear dispersive element. Different capabilities have been demonstrated such as the control of the time-bandwidth product and the frequency tuning increasing the flexibility of the generated waveform compared to coherent techniques. Moreover, the use of differential detection improves considerably the limitation over the signal-to-noise ratio related to incoherent processing.
Modeling Solution of Nonlinear Dispersive Partial Differential Equations using the Marker Method
Jerome L.V. Lewandowski
2005-01-25
A new method for the solution of nonlinear dispersive partial differential equations is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details.
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.
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.
Analytical solution for the advection-dispersion transport equation in layered media
USDA-ARS?s Scientific Manuscript database
The advection-dispersion transport equation with first-order decay was solved analytically for multi-layered media using the classic integral transform technique (CITT). The solution procedure used an associated non-self-adjoint advection-diffusion eigenvalue problem that had the same form and coef...
Environmental Consequences of Nanotechnologies: Nanoparticle Dispersion in Aqueous Media: SOP-T-1
2015-02-01
environmental, health and safety assessment – issues and recommendations. Nanotoxicology 1-19. Taurozzi, J. S., V. A. Hackley, and M. R. Wiesner. 2011...2013. A standardised approach for the dispersion of titanium dioxide nanoparticles in biological media. Nanotoxicology 7(4), 389-401. Tejamaya, M., I
NASA Astrophysics Data System (ADS)
Wu, Yan; Xie, Qiongtao; Zhong, Honghua; Wen, Linghua; Hai, Wenhua
2013-05-01
We investigate algebraic bright and vortex solitons in self-defocusing (SDF) media with a type of spatially inhomogeneous nonlinearity. For a specific choice of the nonlinearity parameters, certain exact analytical solutions for algebraic bright and vortex solitons have been constructed. By applying the linear stability analysis, the stability regions of these algebraic solitons are obtained numerically. In addition, we show analytically that a homogeneous SDF nonlinearity superposed by a localized self-focusing nonlinearity can support exact algebraic bright solitons under certain conditions.
Wear, Keith A
2015-03-01
Through-transmission measurements were performed on 30 human calcaneus samples in vitro. Nonlinear attenuation and dispersion measurements were investigated by estimating 95% confidence intervals of coefficients of polynomial expansions of log magnitude and phase of transmission coefficients. Bone mineral density (BMD) was measured with dual x-ray absorptiometry. Microarchitecture was measured with microcomputed tomography. Statistically significant nonlinear attenuation and nonzero dispersion were confirmed for a clinical bandwidth of 300-750 kHz in 40%-43% of bone samples. The mean linear coefficient for attenuation was 10.3 dB/cm MHz [95% confidence interval (CI): 9.0-11.6 dB/cm MHz]. The mean quadratic coefficient for attenuation was 1.6 dB/cm MHz(2) (95% CI: 0.4-2.8 dB/cm MHz(2)). Nonlinear attenuation provided little information regarding BMD or microarchitecture. The quadratic coefficient for phase (which is related to dispersion) showed moderate correlations with BMD (r = -0.65; 95% CI: -0.82 to -0.36), bone surface-to-volume ratio (r = 0.47; 95% CI: 0.12-0.72) and trabecular thickness (r = -0.40; 95% CI: -0.67 to -0.03). Dispersion was proportional to bone volume fraction raised to an exponent of 2.1 ± 0.2, which is similar to the value for parallel nylon-wire phantoms (2.4 ± 0.2) and supports a multiple-scattering model for dispersion.
Dispersion and Stability Optimization of TiO2 Nanoparticles in Cell Culture Media
Ji, Zhaoxia; Jin, Xue; George, Saji; Xia, Tian; Meng, Huan; Wang, Xiang; Suarez, Elizabeth; Zhang, Haiyuan; Hoek, Eric M.V.; Godwin, Hilary; Nel, André E.; Zink, Jeffrey I.
2014-01-01
Accurate evaluation of engineered nanomaterial toxicity requires not only comprehensive physical-chemical characterization of nanomaterials as produced, but also thorough understanding of nanomaterial properties and behavior under conditions similar to those used for in vitro and in vivo toxicity studies. In this investigation, TiO2 nanoparticles were selected as a model nanoparticle and bovine serum albumin (BSA) was selected as a model protein for studying the effect of protein-nanoparticle interaction on TiO2 nanoparticle dispersion in six different mammalian, bacteria, and yeast cell culture media. Great improvement in TiO2 dispersion was observed upon the addition of BSA, even though the degree of dispersion varied from medium to medium and phosphate concentration in the cell culture media was one of the key factors governing nanoparticle dispersion. Fetal bovine serum (FBS) was an effective dispersing agent for TiO2 nanoparticles in all six media due to synergistic effects of its multiple protein components, successfully reproduced using a simple “FBS mimic” protein cocktail containing similar concentrations of BSA, γ-globulin, and apo-transferrin. PMID:20536146
Cauchy problem for a class of nonlinear dispersive wave equations arising in elasto-plastic flow
NASA Astrophysics Data System (ADS)
Zhijian, Yang
2006-01-01
The paper studies the existence, both locally and globally in time, stability, decay estimates and blowup of solutions to the Cauchy problem for a class of nonlinear dispersive wave equations arising in elasto-plastic flow. Under the assumption that the nonlinear term of the equations is of polynomial growth order, say [alpha], it proves that when [alpha]>1, the Cauchy problem admits a unique local solution, which is stable and can be continued to a global solution under rather mild conditions; when [alpha][greater-or-equal, slanted]5 and the initial data is small enough, the Cauchy problem admits a unique global solution and its norm in L1,p(R) decays at the rate for 2
nonlinear term, the local solutions of the Cauchy problem blow up in finite time.
NASA Astrophysics Data System (ADS)
Tomita, Yasuo; Matsushima, Shun-suke; Yamagami, Ryu-ichi; Jinzenji, Taka-aki; Sakuma, Shohei; Liu, Xiangming; Izuishi, Takuya; Shen, Qing
2017-06-01
We describe the nonlinear optical properties of inorganic-organic nanocomposite films in which semiconductor CdSe quantum dots as high as 6.8 vol.% are dispersed. Open/closed Z-scan measurements, degenerate multi-wave mixing and femtosecond pump-probe/transient grating measurements are conducted. It is shown that the observed fifth-order optical nonlinearity has the cascaded third-order contribution that becomes prominent at high concentrations of CdSe QDs. It is also shown that there are picosecond-scale intensity-dependent and nanosecond-scale intensity-independent decay components in absorptive and refractive nonlinearities. The former is caused by the Auger process, while the latter comes from the electron-hole recombination process.
Zibar, Darko; Winther, Ole; Franceschi, Niccolo; Borkowski, Robert; Caballero, Antonio; Arlunno, Valeria; Schmidt, Mikkel N; Gonzales, Neil Guerrero; Mao, Bangning; Ye, Yabin; Larsen, Knud J; Monroy, Idelfonso Tafur
2012-12-10
In this paper, we show numerically and experimentally that expectation maximization (EM) algorithm is a powerful tool in combating system impairments such as fibre nonlinearities, inphase and quadrature (I/Q) modulator imperfections and laser linewidth. The EM algorithm is an iterative algorithm that can be used to compensate for the impairments which have an imprint on a signal constellation, i.e. rotation and distortion of the constellation points. The EM is especially effective for combating non-linear phase noise (NLPN). It is because NLPN severely distorts the signal constellation and this can be tracked by the EM. The gain in the nonlinear system tolerance for the system under consideration is shown to be dependent on the transmission scenario. We show experimentally that for a dispersion managed polarization multiplexed 16-QAM system at 14 Gbaud a gain in the nonlinear system tolerance of up to 3 dB can be obtained. For, a dispersion unmanaged system this gain reduces to 0.5 dB.
Clack, Christopher T. M.; Ballai, Istvan
2009-04-15
The nonlinear theory of driven magnetohydrodynamics (MHD) waves in strongly anisotropic and dispersive plasmas, developed for slow resonance by Clack and Ballai [Phys. Plasmas 15, 2310 (2008)] and Alfven resonance by Clack et al. [Astron. Astrophys. 494, 317 (2009)], is used to study the weakly nonlinear interaction of fast magnetoacoustic (FMA) waves in a one-dimensional planar plasma. The magnetic configuration consists of an inhomogeneous magnetic slab sandwiched between two regions of semi-infinite homogeneous magnetic plasmas. Laterally driven FMA waves penetrate the inhomogeneous slab interacting with the localized slow or Alfven dissipative layer and are partly reflected, dissipated, and transmitted by this region. The nonlinearity parameter defined by Clack and Ballai (2008) is assumed to be small and a regular perturbation method is used to obtain analytical solutions in the slow dissipative layer. The effect of dispersion in the slow dissipative layer is to further decrease the coefficient of energy absorption, compared to its standard weakly nonlinear counterpart, and the generation of higher harmonics in the outgoing wave in addition to the fundamental one. The absorption of external drivers at the Alfven resonance is described within the linear MHD with great accuracy.
Nonlinear interaction of long dispersive Kelvin waves in deep natural basins
NASA Astrophysics Data System (ADS)
Budnev, Nikolay M.; Lovtsov, Sergey V.; Portyanskaya, Inna A.; Rastegin, Alexey E.; Rubtsov, Valeriy Yu.
2010-05-01
Nonlinear phenomena are of great importance for complete understanding of dynamical processes in fluids. However, direct studies of hydrodynamic equations seem to be very hard just due to nonlinear terms. Many approaches to nonlinear dispersive waves are related to the technique of multiple scales. It is one of most seminal ways to obtain those models that combine possibility of analytic investigation with actual effects of nonlinearity. Consideration of long Kelvin waves within the linear theory is well known issue of geophysical hydrodynamics. An influence of boundary effects leads to dispersion of Kelvin waves. At the same time, mutual balance between dispersive and nonlinear terms in motion equations can provide a formation of stable localized structures so-called solitary waves. When stratification is essential, different vertical modes of oscillation are typically excited. Corresponding analysis of vertical structure for solitary Rossby waves has been developed in many works, mainly due to Redekopp. But proper treatment of large-scale Kelvin waves seems to be not indicated in the literature. The principal aim of our work is to fill this lacuna. The present work has been partially inspired by temperature monitoring data obtained in south area of Lake Baikal. Under conditions of winter stratification, specific displacements of fragments of temperature profile from up to down were observed within upper layer. It is valuable that a shape of moving fragment remains almost undistorted. After ending this temperature decreasing, the temperature profile was rectified to initial shape. In all the years of observations, vertical displacements reach several tens of meters with duration of several days. These phenomena were interpreted as manifestation of long dispersive Kelvin waves, especially due to direction of propagation along the coastline. Regularly observed displacements from up to down may be evidences for nonlinear character of wave dynamics. Indeed, internal
Thomsen, Jon Juel
2016-01-01
The paper deals with analytically predicting the effects of weak nonlinearity on the dispersion relation and frequency band-gaps of a periodic Bernoulli–Euler beam performing bending oscillations. Two cases are considered: (i) large transverse deflections, where nonlinear (true) curvature, nonlinear material and nonlinear inertia owing to longitudinal motions of the beam are taken into account, and (ii) mid-plane stretching nonlinearity. A novel approach is employed, the method of varying amplitudes. As a result, the isolated as well as combined effects of the considered sources of nonlinearities are revealed. It is shown that nonlinear inertia has the most substantial impact on the dispersion relation of a non-uniform beam by removing all frequency band-gaps. Explanations of the revealed effects are suggested, and validated by experiments and numerical simulation. PMID:27118899
Sorokin, Vladislav S; Thomsen, Jon Juel
2016-02-01
The paper deals with analytically predicting the effects of weak nonlinearity on the dispersion relation and frequency band-gaps of a periodic Bernoulli-Euler beam performing bending oscillations. Two cases are considered: (i) large transverse deflections, where nonlinear (true) curvature, nonlinear material and nonlinear inertia owing to longitudinal motions of the beam are taken into account, and (ii) mid-plane stretching nonlinearity. A novel approach is employed, the method of varying amplitudes. As a result, the isolated as well as combined effects of the considered sources of nonlinearities are revealed. It is shown that nonlinear inertia has the most substantial impact on the dispersion relation of a non-uniform beam by removing all frequency band-gaps. Explanations of the revealed effects are suggested, and validated by experiments and numerical simulation.
Conditioning-induced elastic nonlinearity in hysteretic media
NASA Astrophysics Data System (ADS)
Gliozzi, A. S.; Scalerandi, M.; Antonaci, P.; Bruno, C. L. E.
2010-08-01
The definition and measurement of the nonlinear elastic properties of a sample is of great importance for a large number of applications, including characterization of material performances and damage detection. However, such measurements are often influenced by spurious effects due to a combination of nonlinearity and nonequilibrium phenomena. We will present experimental data to show how nonlinearity due to small cracks in concrete samples increases as a consequence of conditioning, i.e., after having perturbed them with a constant amplitude excitation. In addition, our experimental data highlight "memory effects," i.e., they show that when the excitation is removed, the elastic modulus does not return instantaneously to the initial value.
Measurements of nonlinear refractive index in scattering media
Samineni, Prathyush; Perret, Zachary; Warren, Warren S.; Fischer, Martin C.
2012-01-01
We have recently developed a spectral re-shaping technique to simultaneously measure nonlinear refractive index and nonlinear absorption. In this technique, the information about the nonlinearities is encoded in the frequency domain, rather than in the spatial domain as in the conventional Z-scan method. Here we show that frequency encoding is much more robust with respect to scattering. We compare spectral re-shaping and Z-scan measurements in a highly scattering environment and show that reliable spectral re-shaping measurements can be performed even in a regime that precludes standard Z-scans. PMID:20588401
NASA Astrophysics Data System (ADS)
Cortinez, J. M.; Valocchi, A. J.; Herrera, P. A.
2013-12-01
Because of the finite size of numerical grids, it is very difficult to correctly account for processes that occur at different spatial scales to accurately simulate the migration of conservative and reactive compounds dissolved in groundwater. In one hand, transport processes in heterogeneous porous media are controlled by local-scale dispersion associated to transport processes at the pore-scale. On the other hand, variations of velocity at the continuum- or Darcy-scale produce spreading of the contaminant plume, which is referred to as macro-dispersion. Furthermore, under some conditions both effects interact, so that spreading may enhance the action of local-scale dispersion resulting in higher mixing, dilution and reaction rates. Traditionally, transport processes at different spatial scales have been included in numerical simulations by using a single dispersion coefficient. This approach implicitly assumes that the separate effects of local-dispersion and macro-dispersion can be added and represented by a unique effective dispersion coefficient. Moreover, the selection of the effective dispersion coefficient for numerical simulations usually do not consider the filtering effect of the grid size over the small-scale flow features. We have developed a multi-scale Lagragian numerical method that allows using two different dispersion coefficients to represent local- and macro-scale dispersion. This technique considers fluid particles that carry solute mass and whose locations evolve according to a deterministic component given by the grid-scale velocity and a stochastic component that corresponds to a block-effective macro-dispersion coefficient. Mass transfer between particles due to local-scale dispersion is approximated by a meshless method. We use our model to test under which transport conditions the combined effect of local- and macro-dispersion are additive and can be represented by a single effective dispersion coefficient. We also demonstrate that for
Gorkovenko, A. I.; Plekhanov, A. I.; Simanchuk, A. E.; Yakimanskiy, A. V.; Nosova, G. I.; Solovskaya, N. A.; Smirnov, N. N.
2014-12-14
Detailed investigations of the quadratic nonlinear response of a series of new polyimides with covalently attached chromophore DR13 are performed by the Maker fringes method in the range of fundamental wavelength from 850 to 1450 nm. Polymer films with thickness of 100–400 nm were spin-coated on glass substrates and corona poled. For these materials, the maximum values of the second harmonic generation coefficients d{sub 33} are 80–120 pm/V. A red shift of the nonlinear response dispersion with respect to the linear absorption spectrum was observed for the DR13 chromophore. The temperature dependences of linear absorption and nonlinear coefficients d{sub 33} for studied structures are observed. It was found that the temperature changes of the absorption spectra lead to appreciable contribution to the value of the nonlinear coefficient d{sub 33}. The demonstrated high temperature stability (up to 120 °C) of chromophore-containing polyimide thin films makes it possible to eliminate the degradation of their nonlinear optical properties in the future applications of such structures.
Solitons supported by localized nonlinearities in periodic media
Dror, Nir; Malomed, Boris A.
2011-03-15
Nonlinear periodic systems, such as photonic crystals and Bose-Einstein condensates (BEC's) loaded into optical lattices, are often described by the nonlinear Schroedinger or Gross-Pitaevskii equation with a sinusoidal potential. Here, we consider a model based on such a periodic potential, with the nonlinearity (attractive or repulsive) concentrated either at a single point or at a symmetric set of two points, which are represented, respectively, by a single {delta} function or a combination of two {delta} functions. With the attractive or repulsive sign of the nonlinearity, this model gives rise to ordinary solitons or gap solitons (GS's), which reside, respectively, in the semi-infinite or finite gaps of the system's linear spectrum, being pinned to the {delta} functions. Physical realizations of these systems are possible in optics and BEC's, using diverse variants of the nonlinearity management. First, we demonstrate that the single {delta} function multiplying the nonlinear term supports families of stableregular solitons in the self-attractive case, while a family of solitons supported by the attractive {delta} function in the absence of the periodic potential is completely unstable. In addition, we show that the {delta} function can support stable GS's in the first finite band gap in both the self-attractive and repulsive models. The stability analysis for the GS's in the second finite band gap is reported too, for both signs of the nonlinearity. Alongside the numerical analysis, analytical approximations are developed for the solitons in the semi-infinite and first two finite gaps, with the single {delta} function positioned at a minimum or maximum of the periodic potential. In the model with the symmetric set of two {delta} functions, we study the effect of the spontaneous symmetry breaking of the pinned solitons. Two configurations are considered, with the {delta} functions set symmetrically with respect to the minimum or maximum of the underlying
On the interaction between gravity forces and hydrodynamic dispersion in heterogeneous porous media
NASA Astrophysics Data System (ADS)
Schotting, R.; Landman, A.; Egorov, A.; Demidov, D.
2005-12-01
In a series of independently conducted vertical displacement experiments in porous columns (The Netherlands, Germany and Australia), a peculiar phenomenon has been observed. If the resident fluid, i.e. fresh water is displaced by a saltwater solution with a higher density, the effective dispersion coefficient deacreases significantly as compared to the tracer case, where both the resident and invading fluids have (almost) identical densities. The higher the density contrast between the two fluids, the more the dispersion coefficient decreases as compared to the classical Fickian xase. This phenomenon cannot be theoretically described and modelled using classical linear Fick's Law for the dispersive mass flux. Several attempts were made to formulate adequate new theories to incorporate these density effects. Hassanizadeh extended Fick's Law with a second-order nonlinear term, including a new dispersion parameter. Although very good agreement with the aforemnetioned experiments could be achieved, this theory is not able to explain and include the underlying physics of this phenomenon. The decrease of the dispersion coefficient is the result of the interaction between gravity forces and density variations at the displacement front, due to local small-scale heterogeneities. With this phenomenon in mind, several alternative nonlinear theories have been proposed. We mention Welty and Gelhar (stochastic approach), Egorov and Demidov (homogenisation at the Darcy- scale), Demidov (homogenisation at the pore-scale). All theories have in common that the resulting nonlinear dispersion coefficient is a function of the density gradient and not of the absolute density. All of the aforementioned theories have been tested against carefully conducted massive numerical experiments, and if possible, against laboratory experiments. The results of the comparisons will be presented, and future research directions will be indicated.
NASA Astrophysics Data System (ADS)
Alejos, Ana Vazques; Dawood, Muhammad
2012-06-01
In this contribution we examine the propagation of an ultrawideband (UWB) random noise signal through dispersive media such as soil, vegetation, and water, using Fourier-based analysis. For such media, the propagated signal undergoes medium-specific impairments which degrade the received signal in a different way than the non-dispersive propagation media. Theoretically, larger penetration depths into a dispersive medium can be achieved by identifying and detecting the precursors, thereby offering significantly better signal-to-noise ratio and enhanced imaging. For a random noise signal, well defined precursors in term of peak-amplitude don't occur. The phenomenon must therefore be studied in terms of energy evolution. Additionally, the distortion undergone by the UWB random noise signal through a dispersive medium can introduce frequency-dependent uncertainty or noise in the received signal. This leads to larger degradation of the cross-correlation function (CCF), mainly in terms of sidelobe levels and main peak deformation, and consequently making the information retrieval difficult. We would further analyze one method to restore the shape and carrier frequency of the input UWB random noise signal, thereby, improving the CCF estimation.
Impact of diffusion on transverse dispersion in two-dimensional ordered and random porous media
NASA Astrophysics Data System (ADS)
Hlushkou, Dzmitry; Piatrusha, Stanislau; Tallarek, Ulrich
2017-06-01
Solute dispersion in fluid flow results from the interaction between advection and diffusion. The relative contributions of these two mechanisms to mass transport are characterized by the reduced velocity ν , also referred to as the Péclet number. In the absence of diffusion (i.e., when the solute diffusion coefficient Dm=0 and ν →∞ ), divergence-free laminar flow of an incompressible fluid results in a zero-transverse dispersion coefficient (DT=0 ) , both in ordered and random two-dimensional porous media. We demonstrate by numerical simulations that a more realistic realization of the condition ν →∞ using Dm≠0 and letting the fluid flow velocity approach infinity leads to completely different results for ordered and random two-dimensional porous media. With increasing reduced velocity, DT approaches an asymptotic value in ordered two-dimensional porous media but grows linearly in disordered (random) structures depending on the geometrical disorder of a structure: a higher degree of heterogeneity results in a stronger growth of DT with ν . The obtained results reveal that disorder in the geometrical structure of a two-dimensional porous medium leads to a growth of DT with ν even in a uniform pore-scale advection field; however, lateral diffusion is a prerequisite for this growth. By contrast, in ordered two-dimensional porous media the presence of lateral diffusion leads to a plateau for the transverse dispersion coefficient with increasing ν .
Pseudospectral modeling and dispersion analysis of Rayleigh waves in viscoelastic media
Zhang, K.; Luo, Y.; Xia, J.; Chen, C.
2011-01-01
Multichannel Analysis of Surface Waves (MASW) is one of the most widely used techniques in environmental and engineering geophysics to determine shear-wave velocities and dynamic properties, which is based on the elastic layered system theory. Wave propagation in the Earth, however, has been recognized as viscoelastic and the propagation of Rayleigh waves presents substantial differences in viscoelastic media as compared with elastic media. Therefore, it is necessary to carry out numerical simulation and dispersion analysis of Rayleigh waves in viscoelastic media to better understand Rayleigh-wave behaviors in the real world. We apply a pseudospectral method to the calculation of the spatial derivatives using a Chebyshev difference operator in the vertical direction and a Fourier difference operator in the horizontal direction based on the velocity-stress elastodynamic equations and relations of linear viscoelastic solids. This approach stretches the spatial discrete grid to have a minimum grid size near the free surface so that high accuracy and resolution are achieved at the free surface, which allows an effective incorporation of the free surface boundary conditions since the Chebyshev method is nonperiodic. We first use an elastic homogeneous half-space model to demonstrate the accuracy of the pseudospectral method comparing with the analytical solution, and verify the correctness of the numerical modeling results for a viscoelastic half-space comparing the phase velocities of Rayleigh wave between the theoretical values and the dispersive image generated by high-resolution linear Radon transform. We then simulate three types of two-layer models to analyze dispersive-energy characteristics for near-surface applications. Results demonstrate that the phase velocity of Rayleigh waves in viscoelastic media is relatively higher than in elastic media and the fundamental mode increases by 10-16% when the frequency is above 10. Hz due to the velocity dispersion of P
Localization of light in a parabolically bending waveguide array in thermal nonlinear media.
Ye, Fangwei; Dong, Liangwei; Hu, Bambi
2009-03-01
A parabolically longitudinally bending waveguide array imprinted into thermal nonlinear media is found to support the localized stationary solitons. The localization results from the suppression of a curvature effect by the nonlinearity with an infinite-range nonlocality. The localization criterion is given analytically. Solitons propagate stably along a curved trajectory without bending loss, and their locations are significantly influenced by the waveguide curvature. These solitons represent the first example of stationary localized solitons encountered in curved waveguides.
Quan, Li; Liu, Xiaozhou; Gong, Xiufen
2012-10-01
High efficiency of the second-harmonic and sum-frequency generation can be obtained in optical superlattice by using the conventional quasi-phase-matched (QPM) method. Although this trick can be played on the acoustic wave, the media with negative nonlinear parameters are not common in acoustics. Furthermore, the QPM method used in acoustic metamaterials has been less studied. In this work, a protocol is provided to realize the QPM method by using nonlinear complementary media in acoustic metamaterials in order to obtain large backward second-harmonic generation. Compared with the conventional method, the method gains a broader bandwidth and can be used in both acoustic and electromagnetic waves.
Neural Network Associative Memory Using Non-Linear Holographic Storage Media
1989-12-01
T’,?T Cýy’ ( AFIT/GEO/ENG/89D-3 AD-A214 340 L NEURAL NETWORK ASSOCIATIVE MEMORY USING NON-LINEAR HOLOGRAPHIC STORAGE MEDIA I THESIS I Presented to...order approximations of the required gain were provided. - - -In= unazn A FIT/GEO/ENG/89D-3 NEURAL NETWORK ASSOCIATIVE MEMORY USING NON-LINEAR...approxi- mations of the required gain were provided. vi NEURAL NETWORK ASSOCIATIVE MEMORY USING NON-LINEAR HOLOGRAPHIC STORAGE MEDIA I. Introduction The
Parigi, Valentina; Bimbard, Erwan; Stanojevic, Jovica; Hilliard, Andrew J; Nogrette, Florence; Tualle-Brouri, Rosa; Ourjoumtsev, Alexei; Grangier, Philippe
2012-12-07
We observe and measure dispersive optical nonlinearities in an ensemble of cold Rydberg atoms placed inside an optical cavity. The experimental results are in agreement with a simple model where the optical nonlinearities are due to the progressive appearance of a Rydberg blockaded volume within the medium. The measurements allow a direct estimation of the "blockaded fraction" of atoms within the atomic ensemble.
Integration of nonlinearity-management and dispersion-management for pulses in fiber-optic links
NASA Astrophysics Data System (ADS)
Driben, Rodislav; Malomed, Boris A.; Mahlab, Uri
2004-03-01
We introduce a model of a long-haul fiber-optic link that uses a combination of the nonlinearity- and dispersion-compensation (management) to stabilize nonsoliton pulses. The compensation of the accumulated fiber nonlinearity, and simultaneously pulse reshaping, which helps to suppress the inter-symbol interference (ISI, i.e., blurring of blank spaces between adjacent pulses), are performed by second-harmonic-generating modules, which are periodically inserted together with amplifiers. We demonstrate that the dispersion-management (DM), which was not included in an earlier considered model, drastically improves stability of the pulses. The stable-transmission length for an isolated pulse, which was less than 10 fiber spans with the use of the nonlinearity-management only, becomes indefinitely long. It is demonstrated too that the pulse is quite robust against fluctuations of its initial parameters, and the scheme operates efficiently in a very broad parameter range. The interaction between pulses can be safely suppressed for the transmission distance exceeding 16 spans (≃1000 km). The smallest temporal separation between adjacent pulses, which is necessary to prevent the ISI, attains a minimum in the case of moderate DM, similar to known results for the DM solitons. The mutually-induced distortion of co-propagating pulses being accounted for by the emission of radiation, a plausible way to further increase the stable-transmission limit is to introduce bandpass filters.
Proposal and design of Airy-based rocket pulses for invariant propagation in lossy dispersive media.
Preciado, Miguel A; Sugden, Kate
2012-12-01
A novel (to our knowledge) kind of Airy-based pulse with an invariant propagation in lossy dispersive media is proposed. The basic principle is based on an optical energy trade-off between different parts of the pulse caused by the chromatic dispersion, which is used to compensate the attenuation losses of the propagation medium. Although the ideal concept of the proposed pulses implies infinite pulse energy, the numerical simulations show that practical finite energy pulses can be designed to obtain a partially invariant propagation over a finite distance of propagation.
Comparison of equations for the EDTD solution in anisotropic and dispersive media
Burke, G.J.; Steich, D.J.
1997-01-01
The recursive-convolution solution for anisotropic and dispersive media was seen to yield accurate results for reflection from ferrite slabs up to a frequency limit set by the sampling interval. Depending on the application, the results shown might be considered usable up to about 300 GHz, which corresponds to about 13 cells per wavelength. Results at still higher frequencies might be usable when a time delay or frequency shift due to dispersion can be tolerated. Several different forms of the update equations were considered which can result from different approximations in reducing the continuous equations to discrete form.
Dispersion Analysis of Gravity Waves in Fluid Media Discretized by Energy-Orthogonal Finite Elements
NASA Astrophysics Data System (ADS)
José Brito Castro, Francisco
2014-11-01
This article studies the dispersion of gravity waves in fluid media discretized by the finite element method. The element stiffness matrix is split into basic and higher-order components which are respectively related to the mean and deviatoric components of the gradient of displacement potential. This decomposition is applied to the kinetic energy. The dispersion analysis yields a correlation between the higher-order kinetic energy and the kinetic energy error. The use of this correlation as a reference to apply the higher-order energy as an error indicator for the sloshing modes computed by the finite element method is explored.
Modulational instability in nonlocal media with competing non-Kerr nonlinearities
NASA Astrophysics Data System (ADS)
Tiofack, C. G. Latchio; Tagwo, H.; Dafounansou, O.; Mohamadou, A.; Kofane, T. C.
2015-12-01
We investigate analytically and numerically the modulational instability (MI) and propagation properties of light in nonlocal media with competing cubic-quintic nonlinearities where the response functions are assumed to be equal. By using the linear stability analysis, the generic properties of the MI gain spectra are demonstrated for the exponential and rectangular response functions. Special attention is paid to investigate the competition between the spatial scale of the cubic and quintic nonlinearities. For media with exponential response function, we have obtained the range of the wave numbers where instability occurs. It is found that the increase in the absolute value of the quintic nonlinearity suppresses the instability in the regime where the cubic nonlinearity prevails over the quintic one and promotes its development in the opposite case. For media with negative response function, additional MI bands are excited at higher wave numbers when the width of the nonlocal response function exceeds a certain threshold. In the regime where the quintic nonlinearity is dominant, the increase in the absolute value of the quintic coefficient leads to the enhancement of the gain value and the movement of the maximum gain to higher wave numbers. On the other hand, in the case of the predominance of the cubic nonlinearity, the position of the maximum gain bands move to lower wave numbers and MI domain becomes increasingly narrows when the quintic term increases. The numerical simulations fully confirm our analytical results.
Dispersion of nonlinear refraction and two-photon absorption using a white-light continuum Z-scan.
Balu, Mihaela; Hales, Joel; Hagan, David; Van Stryland, Eric
2005-05-16
We use a white-light continuum (WLC) Z-scan technique to measure the degenerate two-photon absorption spectrum and associated dispersion of the nonlinear refraction in ZnSe. The spectral components of the WLC source are separated by using a narrow band variable filter to minimize nondegenerate nonlinearities. We observe a change in sign of the ultrafast nonlinear refractive index around 0.7 of the bandgap energy as predicted by theory.
NASA Astrophysics Data System (ADS)
Li, Jin Hua; Chan, Hiu Ning; Chiang, Kin Seng; Chow, Kwok Wing
2015-11-01
Breathers and rogue waves of special coupled nonlinear Schrödinger systems (the Manakov equations) are studied analytically. These systems model the orthogonal polarization modes in an optical fiber with randomly varying birefringence. Studies earlier in the literature had shown that rogue waves can occur in these Manakov systems with dispersion and nonlinearity of opposite signs, and that the criterion for the existence of rogue waves correlates closely with the onset of modulation instability. In the present work the Hirota bilinear transform is employed to calculate the breathers (pulsating modes), and rogue waves are obtained as a long wave limit of such breathers. In terms of wave profiles, a 'black' rogue wave (intensity dropping to zero) and the transition to a four-petal configuration are elucidated analytically. Sufficiently strong modulation instabilities of the background may overwhelm or mask the development of the rogue waves, and such thresholds are correlated to actual physical properties of optical fibers. Numerical simulations on the evolution of breathers are performed to verify the prediction of the analytical formulations.
Z-scan for thin media with more than one nonlocal nonlinear response.
Irivas, B A Martinez; Carrasco, M L Arroyo; Otero, M M Mendez; García, R Ramos; Castillo, M D Iturbe
2016-06-13
A model to characterize the response of a thin media that can exhibit more than one nonlocal nonlinear response when it is illuminated with a Gaussian beam in a z-scan experiment is proposed. The model considers that these nonlocal contributions can be treated as independent contributions in the refractive or absorptive nonlinear response. Numerical results for two nonlocal nonlinear contributions with different magnitudes between them are presented. Experimental results obtained from a hydrogenated amorphous silicon sample are used to corroborate this model.
Active Resonator Reset in the Nonlinear Dispersive Regime of Circuit QED
NASA Astrophysics Data System (ADS)
Bultink, C. C.; Rol, M. A.; O'Brien, T. E.; Fu, X.; Dikken, B. C. S.; Dickel, C.; Vermeulen, R. F. L.; de Sterke, J. C.; Bruno, A.; Schouten, R. N.; DiCarlo, L.
2016-09-01
We present two pulse schemes to actively deplete measurement photons from a readout resonator in the nonlinear dispersive regime of circuit QED. One method uses digital feedback conditioned on the measurement outcome, while the other is unconditional. In the absence of analytic forms and symmetries to exploit in this nonlinear regime, the depletion pulses are numerically optimized using the Powell method. We speed up photon depletion by more than six inverse resonator linewidths, saving approximately 1650 ns compared to depletion by waiting. We quantify the benefit by emulating an ancilla qubit performing repeated quantum-parity checks in a repetition code. Fast depletion increases the mean number of cycles to a spurious error detection event from order 1 to 75 at a 1 -μ s cycle time.
NASA Astrophysics Data System (ADS)
Hasan, Md. Rabiul; Anower, Md. Shamim; Hasan, Md. Imran
2016-05-01
A simple hexagonal photonic crystal fiber is proposed to simultaneously achieve ultrahigh birefringence, large nonlinear coefficient, and two zero dispersion wavelengths (ZDWs). The finite element method with circular perfectly matched layer boundary condition is used to simulate the designed structure. Simulation results show that it is possible to achieve two closely lying ZDWs of 1.08 and 1.29 μm for x-polarization with 0.88 and 1.20 μm for y-polarization modes, respectively. In addition, an ultrahigh birefringence of 3.15×10-2 and a high nonlinear coefficient of 58 W-1 km-1 are also obtained at the excitation wavelength of 1.55 μm. The proposed fiber can have important applications in supercontinuum generation, parametric amplification, four-wave mixing, and optical sensors design.
NASA Astrophysics Data System (ADS)
Sen, Pranay K.; Kumar, Abhay; Sen, Pratima
1999-06-01
Using semiclassical time dependent perturbation treatment, the coherence radiation-semiconductor interaction under ultrashort pulsed near band-gap resonant excitation regime has been analytically investigated in a narrow direct-gap semiconductor waveguide structure. The role of excitonic effect is incorporated to study transient pulse propagation effects in GAs/AlGaAs waveguide duly irradiated by a 100 fs Ti:Sapphire laser. Nonlinear Schroedinger equation is employed to examine the role of group velocity dispersion and nonlinear optical effect on the transmission characteristics of the pulse at various excitation intensities and waveguide lengths. The results suggest the occurrence of pulse break-up and pulse narrowing during propagation of the pulse through the GaAs/AlGaAs waveguide.
Rhén, Christin; Isacsson, Andreas
2017-01-01
The harmonic oscillator is one of the most widely used model systems in physics: an indispensable theoretical tool in a variety of fields. It is well known that an otherwise linear oscillator can attain novel and nonlinear features through interaction with another dynamical system. We investigate such an interacting system: a superconducting LC-circuit dispersively coupled to a superconducting quantum interference device (SQUID). We find that the SQUID phase behaves as a classical two-level system, whose two states correspond to one linear and one nonlinear regime for the LC-resonator. As a result, the circuit’s response to forcing can become multistable. The strength of the nonlinearity is tuned by the level of noise in the system, and increases with decreasing noise. This tunable nonlinearity could potentially find application in the field of sensitive detection, whereas increased understanding of the classical harmonic oscillator is relevant for studies of the quantum-to-classical crossover of Jaynes-Cummings systems. PMID:28120946
NASA Astrophysics Data System (ADS)
Rhén, Christin; Isacsson, Andreas
2017-01-01
The harmonic oscillator is one of the most widely used model systems in physics: an indispensable theoretical tool in a variety of fields. It is well known that an otherwise linear oscillator can attain novel and nonlinear features through interaction with another dynamical system. We investigate such an interacting system: a superconducting LC-circuit dispersively coupled to a superconducting quantum interference device (SQUID). We find that the SQUID phase behaves as a classical two-level system, whose two states correspond to one linear and one nonlinear regime for the LC-resonator. As a result, the circuit’s response to forcing can become multistable. The strength of the nonlinearity is tuned by the level of noise in the system, and increases with decreasing noise. This tunable nonlinearity could potentially find application in the field of sensitive detection, whereas increased understanding of the classical harmonic oscillator is relevant for studies of the quantum-to-classical crossover of Jaynes-Cummings systems.
NASA Astrophysics Data System (ADS)
Tang, Guangxin
Ultrasonic techniques have been widely used for nondestructively inspecting and monitoring various engineering structures. Most of the existing ultrasonic nondestructive evaluation (NDE) techniques utilize the linear behavior of the wave field to detect macrostructure discontinuities such as cracks, voids, interfaces, etc. However, such linear ultrasonic techniques are unable to assess the damage before crack initiation. In order to assess microstructure changes prior to crack formation, this thesis studies nonlinear wave motion, and develops techniques to characterize and quantify the microstructure changes. These newly developed nonlinear ultrasonic techniques offer the potential to detect early stages of damage in structural materials. The dissertation consists of two major parts: theoretical analyses of wave propagation in elastic solids with quadratic nonlinearity and experimental demonstrations of using nonlinear ultrasonic for assessing damage in metallic materials. First, this study investigates the mechanics of the propagation of ultrasonic waves in nonlinear media with heterogeneous quadratic nonlinearities. A variety of methods such as transfer matrix method, perturbation method, green's function method (both transient and steady state green's function are used), finite difference method and Monte Carlo simulation are used. Typical procedures of using these methods to model and solve different problems in nonlinear wave propagation are given, and the advantages and limitations of each method are discussed. Emphasis is placed on determining the scattered second harmonic wave field generated by the interaction between incident waves and a nonlinear system with heterogeneous nonlinearity distribution. Several potential applications of nonlinear ultrasonic waves based on the theoretical results are discussed. Second, examples of using nonlinear ultrasonic waves for assessing damage in metallic materials are described. Two experiments have been done with a
Finite-difference and finite-volume methods for nonlinear standing ultrasonic waves in fluid media.
Vanhille, C; Conde, C; Campos-Pozuelo, C
2004-04-01
In the framework of the application of high-power ultrasonics in industrial processing in fluid media, the mathematical prediction of the acoustical parameters inside resonators should improve the development of practical systems. This can be achieved by the use of numerical tools able to treat the nonlinear acoustics involved in these phenomena. In particular, effects like nonlinear distortion and nonlinear attenuation are fundamental in applications. In this paper, three one-dimensional numerical models in the time domain for calculating the nonlinear acoustic field inside a one-dimensional resonant cavity are presented and compared. They are based on the finite-difference and the finite-volume methods. These different algorithms solve the differential equations, from the linear up to the strongly nonlinear case (including weak shock). Some physical results obtained from the modelling of ultrasonic waves and a comparison of the efficiency of the different algorithms are presented.
NASA Astrophysics Data System (ADS)
Vijayalekshmi, S.; Mani Rajan, M. S.; Mahalingam, A.; Uthayakumar, A.
2015-09-01
We investigate the controllable behavior of nonautonomous soliton in external potentials with variable dispersion and nonlinearity management functions, which describes the propagation of optical pulses in an inhomogeneous fiber system. We derive the Lax pair with a variable spectral parameter and the exact multi-soliton solution is generated via Darboux transformation. Based on these solutions, several novel optical solitons are constructed by selecting appropriate functions and the main evolution features of these waves are shown by some interesting figures with computer simulation. As few examples, breathers in periodic potential, soliton compression in an exponentially dispersion decreasing fiber and interaction of boomerang solitons are discussed. The presented results have applications in the study of nonautonomous soliton birefringence-managed switching architecture. These results are potentially useful in the management of nonautonomous soliton with external potentials in the optical soliton communications and long-haul telecommunication networks.
NASA Astrophysics Data System (ADS)
Qiao, Yaojun; Li, Ming; Yang, Qiuhong; Xu, Yanfei; Ji, Yuefeng
2015-01-01
Closed-form expressions of nonlinear interference of dense wavelength-division-multiplexed (WDM) systems with dispersion managed transmission (DMT) are derived. We carry out a simulative validation by addressing an ample and significant set of the Nyquist-WDM systems based on polarization multiplexed quadrature phase-shift keying (PM-QPSK) subcarriers at a baud rate of 32 Gbaud per channel. Simulation results show the simple closed-form analytical expressions can provide an effective tool for the quick and accurate prediction of system performance in DMT coherent optical systems.
Dispersion characteristics of step index single mode optical fiber with Kerr nonlinearity
NASA Astrophysics Data System (ADS)
Burdin, Vladimir A.; Bourdine, Anton V.
2017-04-01
In this paper is presented an approximate solution for the fundamental mode of the step-index optical fiber with taking into account the Kerr nonlinearity. The solution is obtained by a known method of Gauss approximation. The derivation of the characteristic equation for the equivalent mode spot radius and analytical expressions for the propagation constant and its first, second and third derivatives are described. The analytical formulas for time delay and chromatic dispersion are given too. Based on the obtained analytical solution there were calculated the dependencies from the optical power the parameters of fundamental mode for the sample of the step-index optical fiber.
Symmetries of the TDNLS equations for weakly nonlinear dispersive MHD waves
NASA Technical Reports Server (NTRS)
Webb, G. M.; Brio, M.; Zank, G. P.
1995-01-01
In this paper we consider the symmetries and conservation laws for the TDNLS equations derived by Hada (1993) and Brio, Hunter and Johnson, to describe the propagation of weakly nonlinear dispersive MHD waves in beta approximately 1 plasmas. The equations describe the interaction of the Alfven and magnetoacoustic modes near the triple umbilic, where the fast magnetosonic, slow magnetosonic and Alfven speeds coincide and a(g)(exp 2) = V(A)(exp 2) where a(g) is the gas sound speed and V(A) is the Alfven speed. We discuss Lagrangian and Hamiltonian formulations, and similarity solutions for the equations.
Influence of wavelength-dependent-loss on dispersive wave in nonlinear optical fibers.
Herrera, Rodrigo Acuna
2012-11-01
In this work, we study numerically the influence of wavelength-dependent loss on the generation of dispersive waves (DWs) in nonlinear fiber. This kind of loss can be obtained, for instance, by the acousto-optic effect in fiber optics. We show that this loss lowers DW frequency in an opposite way that the Raman effect does. Also, we see that the Raman effect does not change the DW frequency too much when wavelength-dependent loss is included. Finally, we show that the DW frequency is not practically affected by fiber length.
NASA Astrophysics Data System (ADS)
Al-Akhaly, Galal A.; Dey, Bishwajyoti
2011-09-01
We show the existence of a type of excitation, which we term as “gap compactonlike,” within the gap of the linear spectrum of a system of coupled Kortweg-de Vries equations with linear and nonlinear dispersions. Since the solutions lie in the gap region of the spectra, they avoid resonance with the linear oscillatory wave and, therefore, do not decay into radiations. These types of solutions are important in energy localization and transport in polymers and biopolymers, optical systems, etc.
Effects Of Relative Strength Of Dispersion On The Formation Of Nonlinear Waves In Dusty Plasmas
Asgari, H.; Muniandy, S. V.; Wong, C. S.; Yap, S. L.
2009-07-07
In this paper, we studied the effect of strength of dispersion on the formation of solitons and shock waves in un-magnetized dusty plasma using the reductive perturbative technique. Different relational forms of strength parameter epsilon were chosen such a way that it altered the stretching of space, x and time, t variables, thereby leading to different nonlinearities. First, we considered the form zeta = sq root(epsilon(x-v{sub 0}t)) and tau = sq root(epsilont), where v{sub 0} is the phase velocity, with 0
NASA Astrophysics Data System (ADS)
Kaur, Jasmeet; Schoonen, Martin A.
2017-06-01
The formation of hydroxyl radicals was studied in mixed pyrite-chalcopyrite dispersions in water using the conversion rate of adenine as a proxy for hydroxyl radical formation rate. Experiments were conducted as a function of pH, presence of phosphate buffer, surface loading, and pyrite-to-chalcopyrite ratio. The results indicate that hydroxyl radical formation rate in mixed systems is non-linear with respect to the rates in the pure endmember dispersions. The only exception is a set of experiments in which phosphate buffer is used. In the presence of phosphate buffer, the hydroxyl radical formation is suppressed in mixtures and the rate is close to that predicted based on the reaction kinetics of the pure endmembers. The non-linear hydroxyl radical formation in dispersions containing mixtures of pyrite and chalcopyrite is likely the result of two complementary processes. One is the fact that pyrite and chalcopyrite form a galvanic couple. In this arrangement, chalcopyrite oxidation is accelerated, while pyrite passes electrons withdrawn from chalcopyrite to molecular oxygen, the oxidant. The incomplete reduction of molecular oxygen leads to the formation of hydrogen peroxide and hydroxyl radical. The galvanic coupling appears to be augmented by the fact that chalcopyrite generates a significant amount of hydrogen peroxide upon dispersal in water. This hydrogen peroxide is then available for conversion to hydroxyl radical, which appears to be facilitated by pyrite as chalcopyrite itself produces only minor amounts of hydroxyl radical. In essence, pyrite is a ;co-factor; that facilitates the conversion of hydrogen peroxide to hydroxyl radical. This conversion reaction is a surface-mediated reaction. Given that hydroxyl radical is one of the most reactive species in nature, the formation of hydroxyl radicals in aqueous systems containing chalcopyrite and pyrite has implications for the stability of organic molecules, biomolecules, the viability of microbes, and
Moving Bragg grating solitons in a cubic-quintic nonlinear medium with dispersive reflectivity
NASA Astrophysics Data System (ADS)
Dasanayaka, Sahan; Atai, Javid
2013-08-01
The stability and collision dynamics of moving solitons in Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity are investigated. Two disjoint families of solitons are found on the plane of the coefficient of quintic nonlinearity versus the normalized frequency (η,Ωnorm). Through numerical stability analysis, we have identified stability regions on the (η,Ωnorm) plane for various values of dispersive reflectivity parameter (m) and velocity (v). The size of stability regions is found to be dependent on m and v. Collisions of counterpropgating Type 1 and Type 2 solitons have been systematically investigated. It is found that for low to moderate values of dispersive reflectivity, the collisions of Type 1 solitons can result in various outcomes such as separation of solitons with reduced, increased, unchanged, or asymmetric velocities and generation of a quiescent soliton by merger or formation of three solitons. For strong dispersive reflectivity (e.g., m=0.5), the collisions of low-velocity in-phase Type 1 solitons may lead to repulsion of solitons, asymmetric separation, merger into a single soliton, or formation of three solitons (one quiescent and two moving solitons). At higher velocities collisions predominantly lead to the formation of three solitons. For m=0.5, in-phase Type 2 solitons may repel or form a temporary bound state of quiescent Type 1 solitons that subsequently splits into two asymmetrically separating Type 1 solitons. π-out-of-phase Type 2 solitons may also merge to form a quiescent Type 1 soliton.
Observation of surface dark solitons in nonlocal nonlinear media.
Gao, XingHui; Wang, Jing; Zhou, Luohong; Yang, ZhenJun; Ma, Xuekai; Lu, Daquan; Guo, Qi; Hu, Wei
2014-07-01
We investigated surface dark solitons (SDSs) at the interface between a self-defocusing nonlocal nonlinear medium and a linear medium, both theoretically and experimentally. We demonstrate that fundamental and higher-order SDSs can exist when the linear refractive index of the self-defocusing medium is much greater than that of the linear medium. The fundamental and second-order solitons are observed at the interface between air and a weakly absorbing liquid.
Controlled opacity in a class of nonlinear dielectric media
NASA Astrophysics Data System (ADS)
Bittencourt, E.; Camargo, G. H. S.; De Lorenci, V. A.; Klippert, R.
2017-03-01
Motivated by new technologies for designing and tailoring metamaterials, we seek properties for certain classes of nonlinear optical materials that allow room for a reversibly controlled opacity-to-transparency phase transition through the application of external electromagnetic fields. We examine some mathematically simple models for the dielectric parameters of the medium and compute the relevant geometric quantities that describe the speed and polarization of light rays.
Upscaling of Solute Transport in Heterogeneous Media with Non-uniform Flow and Dispersion Fields
Xu, Zhijie; Meakin, Paul
2013-10-01
An analytical and computational model for non-reactive solute transport in periodic heterogeneous media with arbitrary non-uniform flow and dispersion fields within the unit cell of length ε is described. The model lumps the effect of non-uniform flow and dispersion into an effective advection velocity Ve and an effective dispersion coefficient De. It is shown that both Ve and De are scale-dependent (dependent on the length scale of the microscopic heterogeneity, ε), dependent on the Péclet number Pe, and on a dimensionless parameter α that represents the effects of microscopic heterogeneity. The parameter α, confined to the range of [-0.5, 0.5] for the numerical example presented, depends on the flow direction and non-uniform flow and dispersion fields. Effective advection velocity Ve and dispersion coefficient De can be derived for any given flow and dispersion fields, and . Homogenized solutions describing the macroscopic variations can be obtained from the effective model. Solutions with sub-unit-cell accuracy can be constructed by homogenized solutions and its spatial derivatives. A numerical implementation of the model compared with direct numerical solutions using a fine grid, demonstrated that the new method was in good agreement with direct solutions, but with significant computational savings.
Bright solitons in nonlinear media with a self-defocusing double-well nonlinearity
NASA Astrophysics Data System (ADS)
Xie, Qiongtao; Wang, Linmao; Wang, Yizhen; Shen, Zhenjiang; Fu, Jun
2014-12-01
We show that stable bright solitons can appear in a medium with spatially inhomogeneous self-defocusing (SDF) nonlinearity of a double-well structure. For a specific choice of the nonlinearity parameters, we obtain exact analytical solutions for the fundamental bright solitons. By making use of the linear stability analysis, the stability region in the parameter space for the exact fundamental bright soliton is obtained numerically. We also show the bifurcation from an antisymmetric to an asymmetric bright soliton for the SDF double-well nonlinearity.
Nonlinear Gamow vectors, shock waves, and irreversibility in optically nonlocal media
NASA Astrophysics Data System (ADS)
Gentilini, Silvia; Braidotti, Maria Chiara; Marcucci, Giulia; DelRe, Eugenio; Conti, Claudio
2015-08-01
Dispersive shock waves dominate wave-breaking phenomena in Hamiltonian systems. In the absence of loss, these highly irregular and disordered waves are potentially reversible. However, no experimental evidence has been given about the possibility of inverting the dynamics of a dispersive shock wave and turn it into a regular wavefront. Nevertheless, the opposite scenario, i.e., a smooth wave generating turbulent dynamics, is well studied and observed in experiments. Here we introduce a theoretical formulation for the dynamics in a highly nonlocal and defocusing medium described by the nonlinear Schroedinger equation. Our theory unveils a mechanism that enhances the degree of irreversibility. This mechanism explains why a dispersive shock cannot be reversed in evolution even for an arbitrarily small amount of loss. Our theory is based on the concept of nonlinear Gamow vectors, i.e., power-dependent generalizations of the counterintuitive and hereto-elusive exponentially decaying states in Hamiltonian systems. We theoretically show that nonlinear Gamow vectors play a fundamental role in nonlinear Schroedinger models: They may be used as a generalized basis for describing the dynamics of the shock waves and affect the degree of irreversibility of wave-breaking phenomena. Gamow vectors allow analytical calculation of the amount of breaking of time reversal with a quantitative agreement with numerical solutions. We also show that a nonlocal, nonlinear optical medium may act as a simulator for the experimental investigation of quantum irreversible models, as the reversed harmonic oscillator.
Dispersive effects on the multi-layer porous media flows with permeable and impermeable interfaces
NASA Astrophysics Data System (ADS)
Daripa, Prabir; Gin, Craig
2016-11-01
We investigate dispersive effects on the linear stability of multi-layer porous media flow models of enhanced oil recovery for two different types of interfaces: permeable and impermeable interfaces. Results presented are relevant for the design of smarter interfaces in the available parameter space of Capillary number, Peclet number, longitudinal and transverse dispersion and the viscous profile of the middle layer. The stabilization capacity of each of these two interfaces is explored numerically and conditions for complete dispersive stabilization are identified for each of these two types of interfaces. Several key results will be presented including our finding that for most values of the flow parameters, permeable interfaces suppress flow instability more than impermeable interfaces. Time permitting, full simulation results will also be presented. NSF Grant # DMS-1522782 and QNRF NPRP Grant 08-777-1-141.
Plant Roots Increase Bacterivorous Nematode Dispersion through Nonuniform Glass-bead Media
Trap, Jean; Bernard, Laetitia; Brauman, Alain; Pablo, Anne-Laure; Plassard, Claude; Ranoarisoa, Mahafaka Patricia; Blanchart, Eric
2015-01-01
Dispersion of bacterivorous nematodes in soil is a crucial ecological process that permits settlement and exploitation of new bacterial-rich patches. Although plant roots, by modifying soil structure, are likely to influence this process, they have so far been neglected. In this study, using an original three-compartment microcosm experimental design and polyvinyl chloride (PVC) bars to mimic plant roots, we tested the ability of roots to improve the dispersion of bacterivorous nematode populations through two wet, nonuniform granular (glass bead) media imitating contrasting soil textures. We showed that artificial roots increased migration time of bacterivorous nematode populations in the small-bead medium, suggesting that plant roots may play an important role in nematode dispersion in fine-textured soils or when soil compaction is high. PMID:26941457
Plant Roots Increase Bacterivorous Nematode Dispersion through Nonuniform Glass-bead Media.
Trap, Jean; Bernard, Laetitia; Brauman, Alain; Pablo, Anne-Laure; Plassard, Claude; Ranoarisoa, Mahafaka Patricia; Blanchart, Eric
2015-12-01
Dispersion of bacterivorous nematodes in soil is a crucial ecological process that permits settlement and exploitation of new bacterial-rich patches. Although plant roots, by modifying soil structure, are likely to influence this process, they have so far been neglected. In this study, using an original three-compartment microcosm experimental design and polyvinyl chloride (PVC) bars to mimic plant roots, we tested the ability of roots to improve the dispersion of bacterivorous nematode populations through two wet, nonuniform granular (glass bead) media imitating contrasting soil textures. We showed that artificial roots increased migration time of bacterivorous nematode populations in the small-bead medium, suggesting that plant roots may play an important role in nematode dispersion in fine-textured soils or when soil compaction is high.
Finite difference methods for transient signal propagation in stratified dispersive media
NASA Technical Reports Server (NTRS)
Lam, D. H.
1975-01-01
Explicit difference equations are presented for the solution of a signal of arbitrary waveform propagating in an ohmic dielectric, a cold plasma, a Debye model dielectric, and a Lorentz model dielectric. These difference equations are derived from the governing time-dependent integro-differential equations for the electric fields by a finite difference method. A special difference equation is derived for the grid point at the boundary of two different media. Employing this difference equation, transient signal propagation in an inhomogeneous media can be solved provided that the medium is approximated in a step-wise fashion. The solutions are generated simply by marching on in time. It is concluded that while the classical transform methods will remain useful in certain cases, with the development of the finite difference methods described, an extensive class of problems of transient signal propagating in stratified dispersive media can be effectively solved by numerical methods.
Oskooi, Ardavan; Johnson, Steven G.
2011-04-01
We show that some previous proposals for perfectly matched layer (PML) absorbers in anisotropic media or for waveguides at oblique incidence are not, in fact true PMLs; in previous work we similarly showed a failure of several PML proposals for periodic media (photonic crystals). We therefore argue that a more careful validation scheme is required for PML proposals, in contrast to past authors who have typically checked only that reflections are small for a fixed resolution, and suggest a simple validation scheme that can be readily applied to any PML proposal regardless of derivation or implementation. We demonstrate this test for a corrected, unsplit-field PML valid for anisotropic, dispersive media, implemented in both planewave-expansion and finite-difference time-domain (FDTD) methods.
Zolotovskii, I O; Korobko, D A; Lapin, V A
2014-01-31
The modulation instability in waveguides with high Kerr nonlinearity, characterised by a delayed nonlinear response, has been investigated with allowance for the self-steepening parameter and third-order dispersion. General expressions for the modulation gain are obtained. The influence of the waveguide parameters on the gain is analysed. It is shown that the joint effect of the delayed nonlinear response and negative nonlinearity dispersion leads to an increase in the modulation gain. The relations obtained are confirmed by numerical simulation. The results of this study can be used to design compact generators of high-frequency pulse trains. (nonlinear optical phenomena)
Propagation of a Laguerre-Gaussian correlated Schell-model beam in strongly nonlocal nonlinear media
NASA Astrophysics Data System (ADS)
Qiu, Yunli; Chen, Zhaoxi; He, Yingji
2017-04-01
Analytical expressions for the cross-spectral density function and the second-order moments of the Wigner distribution function of a Laguerre-Gaussian correlated Schell-model (LGCSM) beam propagating in strongly nonlocal nonlinear media are derived. The propagation properties, such as beam irradiance, beam width, the spectral degree of coherence and the propagation factor of a LGCSM beam inside the media are investigated in detail. The effect of the beam parameters and the input power on the evolution properties of a LGCSM is illustrated numerically. It is found that the beam width varies periodically or keeps invariant for a certain proper input power. And both the beam irradiance and the spectral degree of coherence of the LGCSM beam change periodically with the propagation distance for the arbitrary input power which however has no influence on the propagation factor. The coherent length and the mode order mainly affect the evolution speed of the LGCSM beam in strongly nonlocal nonlinear media.
Sputtered stoichiometric TeO2 glass films: Dispersion of linear and nonlinear optical properties
NASA Astrophysics Data System (ADS)
D'Amore, Franco; Di Giulio, Massimo; Pietralunga, Silvia M.; Zappettini, Andrea; Nasi, Lucia; Rigato, Valentino; Martinelli, Mario
2003-08-01
We report on the optical characterization of TeO2 amorphous films deposited by radio-frequency (rf) reactive sputtering. X-ray diffraction, electronic microscopy, and Rutherford backscattering analysis have been performed in order to assess the structural and compositional properties of the samples. The linear optical characterization has been performed by variable angle spectroscopic ellipsometry at wavelengths between 260 and 1700 nm, leading to determination of the dispersion of the complex refractive index for sputtered tellurium dioxide. In the spectral range of transparency, between 1700 and 500 nm, refractive index values ranging from 2.05 to 2.16 have been obtained. The dispersion of the complex third-order nonlinear optical coefficient of the sample has been evaluated in the near-infrared spectral range by third harmonic generation measurements. The out-of-resonance value of the χ(3) coefficient for TeO2 is in the range between 1.2×10-12 and 1.4×10-12 esu. The conjugation of optical transparency, high nonlinear refractive index and the possibility of growing films of good optical quality, make rf sputtered TeO2 a promising material for the implementation of devices for the processing of optical communication signals.
Nonlinear acoustic pulse propagation in dispersive sediments using fractional loss operators.
Maestas, Joseph T; Collis, Jon M
2016-03-01
The nonlinear progressive wave equation (NPE) is a time-domain formulation of the Euler fluid equations designed to model low-angle wave propagation using a wave-following computational domain. The wave-following frame of reference permits the simulation of long-range propagation and is useful in modeling blast wave effects in the ocean waveguide. Existing models do not take into account frequency-dependent sediment attenuation, a feature necessary for accurately describing sound propagation over, into, and out of the ocean sediment. Sediment attenuation is addressed in this work by applying lossy operators to the governing equation that are based on a fractional Laplacian. These operators accurately describe frequency-dependent attenuation and dispersion in typical ocean sediments. However, dispersion within the sediment is found to be a secondary process to absorption and effectively negligible for ranges of interest. The resulting fractional NPE is benchmarked against a Fourier-transformed parabolic equation solution for a linear case, and against the analytical Mendousse solution to Burgers' equation for the nonlinear case. The fractional NPE is then used to investigate the effects of attenuation on shock wave propagation.
NASA Astrophysics Data System (ADS)
Wright, E. S.; Aleem, T.
2003-12-01
In 1953, G.I.~Taylor published his landmark paper concerning the transport of a contaminant dissolved in a fluid flowing through a pipe of narrow diameter. He demonstrated that an interaction between the transverse variations in the fluid's velocity field and the transverse diffusion of the solute yielded an effective downstream mixing mechanism for the transverse average of the solute. This mechanism has since been dubbed ``Taylor Dispersion.'' Since his original publication, many related studies have surfaced. These include generalizations of channel geometry, generalizations of the velocity field (including turbulent field), applications to sedimentation problems, etc. However, much less attention has been given to the effects of nonlinear chemical reactions upon a system of solutes undergoing Taylor Dispersion. We present a rigorous mathematical model for the evolution of the transverse averages of reacting solutes that travel within a fluid flowing down a pipe of arbitrary cross-section. The technique for deriving this model is a generalization of a multiple scales perturbation approach described by P.C.~Fife for linear (reactionless) problems. The key outcome is that while one still finds an effective mechanism for downstream mixing, but also there is also a effective mechanism for nonlinear advection.
Nonlinear dynamics of direction-selective recurrent neural media.
Xie, Xiaohui; Giese, Martin A
2002-05-01
The direction selectivity of cortical neurons can be accounted for by asymmetric lateral connections. Such lateral connectivity leads to a network dynamics with characteristic properties that can be exploited for distinguishing in neurophysiological experiments this mechanism for direction selectivity from other possible mechanisms. We present a mathematical analysis for a class of direction-selective neural models with asymmetric lateral connections. Contrasting with earlier theoretical studies that have analyzed approximations of the network dynamics by neglecting nonlinearities using methods from linear systems theory, we study the network dynamics with nonlinearity taken into consideration. We show that asymmetrically coupled networks can stabilize stimulus-locked traveling pulse solutions that are appropriate for the modeling of the responses of direction-selective neurons. In addition, our analysis shows that outside a certain regime of stimulus speeds the stability of these solutions breaks down, giving rise to lurching activity waves with specific spatiotemporal periodicity. These solutions, and the bifurcation by which they arise, cannot be easily accounted for by classical models for direction selectivity.
Shock formation and non-linear dispersion in a microvascular capillary network.
Pop, S R; Richardson, G; Waters, S L; Jensen, O E
2007-12-01
Temporal and spatial fluctuations are a common feature of blood flow in microvascular networks. Among many possible causes, previous authors have suggested that the non-linear rheological properties of capillary blood flow (notably the Fåhraeus effect, the Fåhraeus-Lindqvist effect and the phase-separation effect at bifurcations) may be sufficient to generate temporal fluctuations even in very simple networks. We have simulated blood flow driven by a fixed pressure drop through a simple arcade network using coupled hyperbolic partial differential equations (PDEs) that incorporate well-established empirical descriptions of these rheological effects, accounting in particular for spatially varying haematocrit distributions; we solved the PDE system using a characteristic-based method. Our computations indicate that, under physiologically realistic conditions, there is a unique steady flow in an arcade network which is linearly stable and that plasma skimming suppresses the oscillatory decay of perturbations. In addition, we find that non-linear perturbations to haematocrit distributions can develop shocks via the Fåhraeus effect, providing a novel mechanism for non-linear dispersion in microvascular networks.
Nonlinear effects associated with dispersive Alfvén waves in plasmas
NASA Astrophysics Data System (ADS)
Shukla, P. K.; Stenflo, L.; Bingham, R.; Eliasson, B.
2004-12-01
Large amplitude Alfvén waves are frequently found in magnetized space and laboratory plasmas. Our objective here is to discuss the linear and nonlinear properties of dispersive Alfvén waves (DAWs) in a uniform magnetoplasma. We first consider finite frequency (ω/ωci) and ion gyroradius effects on inertial and kinetic Alfvén waves, where ωci is the ion gyrofrequency. Next, we focus on nonlinear effects caused by DAWs. Such effects include plasma density enhancement and depression by the Alfvén wave ponderomotive force, electron Joule heating by the thermal Alfvén wave force, the generation of zonal flows due to the shear Alfvén wave mode couplings as well as the formation of localized Alfvénic structures and Alfvénic vortices. The relevance of our investigation to the appearance of nonlinear Alfvén waves in the Earth's auroral acceleration region, in the solar corona and in the large plasma device at UCLA is discussed.
On the closure of circular holes in nonlinear viscous media.
NASA Astrophysics Data System (ADS)
Cornet, Jan; Dabrowski, Marcin; Schmid, Daniel
2016-04-01
Many rocks exhibit viscous behaviors which have to be taken into account in applications ranging from wellbores creeping during drilling to salt caves or hard rock mine tunnels shrinking with time. We address all these different cases using a unified configuration. We consider a 2D plane strain problem where a circular hole, representing the wellbore, the cave or the mine tunnel depending on the application, is embedded in an infinite incompressible non-linear viscous material. The problem is purely mechanical. Not only the rheological model used here is well suited for real formations but it can also represent many different sorts of rocks like salts, shales, quartzite and even ice. The major difference between the applications concerns the relevant time scales and they must therefore be separated according to that. For short timescale applications like wellbore creep during drilling it is first necessary to determine whether an elastic component must or must not be taken into account. This analysis is carried out using a non-linear viscoelastic Maxwell model. If it is acknowledged that a purely viscous rheology is enough, as can be the case for salts, then we can proceed with our unified configuration. We start by considering the case where the medium is isotropic and where pressure boundary conditions are prescribed both at the hole rim and at infinity. This problem is 1D due to axial symmetry. Analytical solutions to very similar problems have already been provided and we compare the solution we have derived to the existing ones. We show that our solution is consistent and that we recover similar results to the ones derived for comparable rheologies. Using MILAMIN, a fast finite element code, we investigate further two cases which lead to angular dependency and stress concentrations around the hole. In the first case we add a deviatoric stress at infinity and we study the impact of this extra stress on the solution. It is important to understand this parameter
NASA Astrophysics Data System (ADS)
Benoit, Michel; Yates, Marissa L.; Raoult, Cécile
2017-04-01
Efficient and accurate numerical models simulating wave propagation are required for a variety of engineering projects including the evaluation of coastal risks, the design of protective coastal structures, and the estimation of the potential for marine renewable energy devices. Nonlinear and dispersive effects are particularly significant in the coastal zone where waves interact with the bottom, the shoreline, and coastal structures. The main challenge in developing a numerical models is finding a compromise between computational efficiency and the required accuracy of the simulated wave field. Here, a potential approach is selected and the (fully nonlinear) water wave problem is formulated using the Euler-Zakharov equations (Zakharov, 1968) describing the temporal evolution of the free surface elevation and velocity potential. The proposed model (Yates and Benoit, 2015) uses a spectral approach in the vertical (i.e. the vertical variation of the potential is approximated by a linear combination of the first NT+1 Chebyshev polynomials, following the work of Tian and Sato (2008)). The Zakharov equations are integrated in time using a fourth-order Runge-Kutta scheme with a constant time step. At each sub-timestep, the Laplace Boundary Value Problem (BVP) is solved to estimate the free surface vertical velocity using the spectral approach, with typical values of NT between 5 to 8 for practical applications. The 1DH version of the code is validated with comparisons to the experimental data set of Becq-Girard et al. (1999), which studied the propagation of irregular waves over a beach profile with a submerged bar. The nonlinear and dispersive capacities of the model are verified with the correct representation of wave-wave interactions, in particular the transfer of energy between different harmonic components during wave propagation (analysis of the transformation of the variance spectrum along the channel). Evolution of wave skewness, asymmetry and kurtosis along the
Interaction of highly nonlinear solitary waves with linear elastic media.
Yang, Jinkyu; Silvestro, Claudio; Khatri, Devvrath; De Nardo, Luigi; Daraio, Chiara
2011-04-01
We study the interaction of highly nonlinear solitary waves propagating in granular crystals with an adjacent linear elastic medium. We investigate the effects of interface dynamics on the reflection of incident waves and on the formation of primary and secondary reflected waves. Experimental tests are performed to correlate the linear medium geometry, materials, and mass with the formation and propagation of reflected waves. We compare the experimental results with theoretical analysis based on the long-wavelength approximation and with numerical predictions obtained from discrete particle models. Experimental results are found to be in agreement with theoretical analysis and numerical simulations. This preliminary study establishes the foundation for utilizing reflected solitary waves as novel information carriers in nondestructive evaluation of elastic material systems.
Inexact Picard iterative scheme for steady-state nonlinear diffusion in random heterogeneous media.
Mohan, P Surya; Nair, Prasanth B; Keane, Andy J
2009-04-01
In this paper, we present a numerical scheme for the analysis of steady-state nonlinear diffusion in random heterogeneous media. The key idea is to iteratively solve the nonlinear stochastic governing equations via an inexact Picard iteration scheme, wherein the nonlinear constitutive law is linearized using the current guess of the solution. The linearized stochastic governing equations are then spatially discretized and approximately solved using stochastic reduced basis projection schemes. The approximation to the solution process thus obtained is used as the guess for the next iteration. This iterative procedure is repeated until an appropriate convergence criterion is met. Detailed numerical studies are presented for diffusion in a square domain for varying degrees of nonlinearity. The numerical results are compared against benchmark Monte Carlo simulations, and it is shown that the proposed approach provides good approximations for the response statistics at modest computational effort.
Self-Organization of Light in Optical Media with Competing Nonlinearities.
Maucher, F; Pohl, T; Skupin, S; Krolikowski, W
2016-04-22
We study the propagation of light beams through optical media with competing nonlocal nonlinearities. We demonstrate that the nonlocality of competing focusing and defocusing nonlinearities gives rise to self-organization and stationary states with stable hexagonal intensity patterns, akin to transverse crystals of light filaments. Signatures of this long-range ordering are shown to be observable in the propagation of light in optical waveguides and even in free space. We consider a specific form of the nonlinear response that arises in atomic vapor upon proper light coupling. Yet, the general phenomenon of self-organization is a generic consequence of competing nonlocal nonlinearities, and may, hence, also be observed in other settings.
Self-Organization of Light in Optical Media with Competing Nonlinearities
NASA Astrophysics Data System (ADS)
Maucher, F.; Pohl, T.; Skupin, S.; Krolikowski, W.
2016-04-01
We study the propagation of light beams through optical media with competing nonlocal nonlinearities. We demonstrate that the nonlocality of competing focusing and defocusing nonlinearities gives rise to self-organization and stationary states with stable hexagonal intensity patterns, akin to transverse crystals of light filaments. Signatures of this long-range ordering are shown to be observable in the propagation of light in optical waveguides and even in free space. We consider a specific form of the nonlinear response that arises in atomic vapor upon proper light coupling. Yet, the general phenomenon of self-organization is a generic consequence of competing nonlocal nonlinearities, and may, hence, also be observed in other settings.
Musko, Monika; Sznitowska, Malgorzata
2014-12-01
Available tablets or capsules for adults are often used to prepare extemporaneously formulated medicines appropriate for children. The most acceptable drug forms in pediatric population are oral liquids and pharmacists use commercial dispersing media to compound syrups from an active substance or from tablets available on the market. In many countries ready-to-use dispersing media are not available or refunded, but pharmacists can use other compounded media, providing their compatibility and stability are proven. The aim of this study was to formulate and evaluate the stability of syrups with candesartan cilexetil (1 mg mL-1) and valsartan (4 mg mL-1) extemporaneously prepared using commercial tablets (Diovan® and Atacand®). The following three different suspending media, which could be easily made in a pharmacy, were investigated: V1 - with xanthan gum (0.5 %), V2 - the USP/NF vehicle for oral solution and V3 - the medium based on a simple sucrose syrup. The stability of preparations was studied during 35 days of storage in a dark place at controlled temperature of 25 and 4 °C. During the study, microscopic observation was carried out and pH, viscosity, and concentration of candesartan cilexetil and valsartan were analyzed. Syrups with valsartan prepared with V2 and V3 media were stable for 3 or 4 weeks when stored at 25 °C, while syrups with candesartan were stable for as long as 35 days. For syrups prepared using V1 medium, the 14-day expiry date was not achieved because of microbial deterioration.
Shape-dependent effects of dielectrically nonlinear inclusions in heterogeneous media
NASA Astrophysics Data System (ADS)
Giordano, Stefano; Rocchia, Walter
2005-11-01
In this work the electrical response of a mixture composed of dielectrically nonlinear ellipsoids dispersed in a linear matrix is modeled. The inclusions may be randomly oriented. The aim is both to set up a methodology apt to deal with this kind of system and to use it to study the effect of marked nonsphericity of inclusions on the global behavior of a mixture. The results are quite interesting from both these points of view. The method here developed extends the Maxwell-Garnett theory [A Treatise on Electricity and Magnetism (Clarendon, Oxford, 1881)], which deals with dielectrically linear inclusions, and it allows, inter alia, to obtain a closed-form expression for the hypersusceptibility ratio of the mixture to the dispersed inclusions. These latter can range from cylinders to spheres, already present in the literature, to "penny-shaped" particles. The theoretical framework is based on the assumption that the dispersion is very dilute. We were able to show that in a specific case, when oblate particles such as elliptic lamellae are dispersed in a matrix having dielectric constant lower than the linear term of inclusion permittivity, a remarkable nonlinear effect occurs. This theory finds application in fields such as nonlinear optics and, more broadly, in many branches of material science.
The permeability of poly-disperse porous media and effective particle size
NASA Astrophysics Data System (ADS)
Markicevic, B. I.; Preston, C.; Osterroth, S.; Iliev, O.; Hurwitz, M.
2015-11-01
The interactions between the fluid and solid phases in porous media account for the openness and length of the flow path that the fluid needs to travel within. The same reasoning applies for both mono- and poly-disperse media, and is reflected in the adoption of the same permeability models. The only difference is that an effective particle size diameter has to be used for the poly-disperse samples. A filtration experiment is used to form a particle layer, filter cake, consisting of particles of different sizes. Both inflow and outflow particle size distribution are measured by particle counting method, and from their difference, the particle size distribution in the cake is determined. In a set of experiments, the filtration history is altered by changing (i) filtration medium; (ii) suspension flow rate; and (iii) particle concentration, where in all cases investigated the cake permeability remains constant. In order to predict the permeability of poly-disperse cake from the analytical models, the particle size distribution moments are calculated, and the permeability is found for each moment. Comparing the experimental to the analytical permeability values the effective particle size is found, where the permeability calculated by using the harmonic mean of the particle size distribution reproduces the permeability experimental value best. Finally, in the parametric study, reducing the cake porosity and/or lowering the particle retention shifts effective particle size used in the permeability model toward higher moments of the particle size distribution function.
Local numerical modelling of ultrasonic guided waves in linear and nonlinear media
NASA Astrophysics Data System (ADS)
Packo, Pawel; Radecki, Rafal; Kijanka, Piotr; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.
2017-04-01
Nonlinear ultrasonic techniques provide improved damage sensitivity compared to linear approaches. The combination of attractive properties of guided waves, such as Lamb waves, with unique features of higher harmonic generation provides great potential for characterization of incipient damage, particularly in plate-like structures. Nonlinear ultrasonic structural health monitoring techniques use interrogation signals at frequencies other than the excitation frequency to detect changes in structural integrity. Signal processing techniques used in non-destructive evaluation are frequently supported by modeling and numerical simulations in order to facilitate problem solution. This paper discusses known and newly-developed local computational strategies for simulating elastic waves, and attempts characterization of their numerical properties in the context of linear and nonlinear media. A hybrid numerical approach combining advantages of the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE) is proposed for unique treatment of arbitrary strain-stress relations. The iteration equations of the method are derived directly from physical principles employing stress and displacement continuity, leading to an accurate description of the propagation in arbitrarily complex media. Numerical analysis of guided wave propagation, based on the newly developed hybrid approach, is presented and discussed in the paper for linear and nonlinear media. Comparisons to Finite Elements (FE) are also discussed.
NASA Astrophysics Data System (ADS)
Luo, Ting
As optical communications approach more data bandwidth, longer transmission distance, and more reconfigurability, dispersion, nonlinearity and polarization-dependent effects are becoming key issues for future all-optical fiber optic systems and networks. For ≥10 Gbit/s optical fiber transmission systems, it is critical that chromatic dispersion and polarization-mode-dispersion be well monitored and compensated using some type of dispersion monitoring and compensation. On the other hand, dispersive and nonlinear effects in optical fiber systems can also be beneficial and have applications on pulse management, all-optical signal processing and network function, which will be essential for high bite-rate optical networks and replacing the expensive optical-electrical-optical (O/E/O) conversion. In this Ph.D. dissertation, we present a detailed research on dispersion, nonlinearity, and polarization-dependent effects in high-speed optical communication systems. We have demonstrated: (i) A dynamic channel-spacing tunable multi-wavelength Erbium-doped fiber laser; (ii) Chromatic-dispersion-insensitive PMD monitoring by tracking the radio-frequency extracted from the vestigial-sideband; (iii) A method for simultaneous chromatic and polarization-mode dispersions monitoring by adding a frequency-shifted carrier; (iv) Polarization-insensitive optical parametric amplification by depolarizing the pump; (v) All optical chromatic dispersion monitoring potential for ultra-high speed (>40 Gbit/s) optical systems using cross-phase modulation in a highly nonlinear fiber; (vi) A novel fiber-based autocorrelator using polarimetric four-wave mixing effect and a tunable differential-group-delay element; (vii) A simple all-fiber-based autocorrelator by measuring the degree-of-polarization; and (viii) Reduction of pattern dependent data distortion in a stimulated Brillouin scattering based slow light element. These techniques will play key roles in future high-speed dynamic WDM optical
Spatiotemporal solitons in birefringent media near the zero-dispersion point
NASA Astrophysics Data System (ADS)
Fitrakis, E. P.; Nistazakis, H. E.; Malomed, B. A.; Frantzeskakis, D. J.; Kevrekidis, P. G.
2006-09-01
We present a new species of spatiotemporal solitons (STSs, alias light bullets) that may be formed through the interaction of two waves with different polarizations in a birefringent Kerr medium near the point at which the second-order group-velocity dispersion (GVD) vanishes in the presence of a uniform cw background in one component. The analysis is based on an asymptotic reduction of the two cross-phase, modulation-coupled (2+1)-dimensional nonlinear Schrödinger equations, incorporating the third-order GVD to the Davey-Stewartson (DS) systems of type I or II for the self-defocusing and focusing Kerr nonlinearity, respectively. The STSs are then predicted following the pattern of the dromion solutions of the DS-I system and lump solitons of the DS-II system. Strictly speaking, the solitons are unstable, but they are shown to be stable objects on experimentally relevant scales of the propagation distance.
Nonlinear dynamics in flow through unsaturated fractured-porous media: Status and perspectives
Faybishenko, Boris
2002-11-27
The need has long been recognized to improve predictions of flow and transport in partially saturated heterogeneous soils and fractured rock of the vadose zone for many practical applications, such as remediation of contaminated sites, nuclear waste disposal in geological formations, and climate predictions. Until recently, flow and transport processes in heterogeneous subsurface media with oscillating irregularities were assumed to be random and were not analyzed using methods of nonlinear dynamics. The goals of this paper are to review the theoretical concepts, present the results, and provide perspectives on investigations of flow and transport in unsaturated heterogeneous soils and fractured rock, using the methods of nonlinear dynamics and deterministic chaos. The results of laboratory and field investigations indicate that the nonlinear dynamics of flow and transport processes in unsaturated soils and fractured rocks arise from the dynamic feedback and competition between various nonlinear physical processes along with complex geometry of flow paths. Although direct measurements of variables characterizing the individual flow processes are not technically feasible, their cumulative effect can be characterized by analyzing time series data using the models and methods of nonlinear dynamics and chaos. Identifying flow through soil or rock as a nonlinear dynamical system is important for developing appropriate short- and long-time predictive models, evaluating prediction uncertainty, assessing the spatial distribution of flow characteristics from time series data, and improving chemical transport simulations. Inferring the nature of flow processes through the methods of nonlinear dynamics could become widely used in different areas of the earth sciences.
Javan, N. Sepehri Homami, S. H. H.
2015-02-15
Self-guided nonlinear propagation of intense circularly-polarized electromagnetic waves in a hot electron-positron-ion magnetoplasma is studied. Using a relativistic fluid model, a nonlinear equation is derived, which describes the interaction of the electromagnetic wave with the plasma in the quasi-neutral approximation. Transverse Eigen modes, the nonlinear dispersion relation and the group velocity are obtained. Results show that the transverse profile in the case of magnetized plasma with cylindrical symmetry has a radially damping oscillatory form. Effect of applying external magnetic fields, existence of the electron-positron pairs, changing the amplitude of the electromagnetic wave, and its polarization on the nonlinear dispersion relation and Eigen modes are studied.
Double resonant processes in 1D nonlinear periodic media
NASA Astrophysics Data System (ADS)
Kuzmiak, Vladimir; Konotop, Vladimir
2001-03-01
We consider one-dimensional periodic structure consisting of alternating layers fabricated from the materials possessing \\chi^(2) nonlinearity and assume that the filling fraction and the dielectric permittivities of the slabs are chosen in such a way that resonant contions for the generation for the second and third harmonic are satisfied simultaneously. The possibility of such process is demonstrated in the structure consisting of the alternating slabs of AlGaAs and InSb. The wave evolution is described in terms of envelope function approach. By taking account three resonant waves one obtains a system of coupled-mode differential equations. One of the solutions which is of special importance is that of having a constant amplitude and the first and third harmonic having zero amplitude. We analyze the stability of the solutions and show that the use of the double resonance allows one to obtain difference generation. A particular example of such a process is fractional conversion ω arrow (2/3)ω which takes place with the participation of the mode with the frequency ω/3.
NASA Astrophysics Data System (ADS)
Guo, Shuqin; Le, Zichun; Quan, Bisheng
2006-01-01
By numerical simulation, we show that the fourth-order dispersion (FOD) makes sub-picosecond optical pulse broaden as second-order dispersion (SOD), makes optical pulse oscillate simultaneously as third-order dispersion (TOD). Based on above two reasons, sub-picosecond optical pulse will be widely broaden and lead to emission of continuum radiation during propagation. Here, resemble to two- and third-order dispersion compensation, fourth-order dispersion compensation is also suggested in a dispersion-managed optical fiber link, which is realized by arranging two kinds of fiber with opposite dispersion sign in each compensation cell. For sake of avoiding excessively broadening, ultra short scale dispersion compensation cell is required in ultra high speed optical communication system. In a full dispersion compensation optical fiber system which path average dispersion is zero about SOD, TOD, and FOD, even suffering from affection of high order nonlinear like self-steep effect and self-frequency shift, 200 fs gauss optical pulse can stable propagate over 1000 km with an optimal initial chirp. When space between neighboring optical pulse is only 2 picoseconds corresponding to 500 Gbit/s transmitting capacity, eye diagram is very clarity after 1000 km. The results demonstrate that ultra short scale dispersion compensation including FOD is need and effective in ultra-high speed optical communication.
Discrete multipole dark solitons in saturable nonlinearity media with parity-time symmetric lattices
NASA Astrophysics Data System (ADS)
Shi, Zhiwei; Xue, Jing; Xing, Zhu; Li, Yang; Li, Huagang
2017-02-01
We investigate numerically the existence and stability of discrete multipole dark solitons in saturable nonlinearity media with parity-time (PT) symmetric lattices. The dipole and triple solitons share the same existence domain associated with the propagation constant, gain-loss coefficient and the degree of saturable nonlinearity. However, the solitons stably propagate in a different area of the aforementioned three parameters. The beam power monotonously increases with the increase of propagation constant and the saturable degree, but gently decreases with the gain-loss coefficient. Moreover, the power of the triple solitons is higher than that of dipole solitons under the same conditions.
NASA Astrophysics Data System (ADS)
Burdin, Vladimir A.; Bourdine, Anton V.; Volkov, Kirill A.
2012-01-01
We represent results of numerical simulations for upgrade of optical link with SMF by using the DDMS technique based on application of compensating optical cable coiled around of optical closure. We propose this technique for minimization land cost. Nonlinearity management for decreasing of quasi-solitons interaction is considered. Based on NLSE the model of optical link regeneration section with dispersion and nonlinearity management is described. The NLSE was solved numerically. Estimated values for optical system performance were derived by taking into account the amplified spontaneous emission noise, parameters of dispersion map deviations, and the interaction of quasi-solitons.
1988-09-01
decomposed into a series of associated aperiodic solitary waves, as can be achieved for solutions of the KdV equation [11], is still under investigation. 3...The organization of the paper is as follows: In Section 2, we discuss aperiodic and periodic solitary wave solutions of a model equation with...Periodic Solitary Wave Solutions of the Nonlinear Klein Gordon Equation without Dispersion We shall take, as our model equation , the nonlinear Klein
Caleap, Mihai; Aristégui, Christophe; Poncelet, Olivier
2013-01-01
Attention is focused on the propagation of antiplane coherent wave obliquely incident on mutually parallel and randomly distributed cracks. A fundamental question in this study concerns the ability of describing the coherent wave propagation in all directions from the knowledge of the effective material properties along the effective principal directions, only. Its relevance is illustrated by considering two cases of coherent wave propagation: homogeneous and inhomogeneous waves. For both cases, the effective phase slownesses approximated from the dispersion equation specific for orthotropic homogeneous media are compared to reference results obtained from a direct calculation considering waves obliquely incident on cracks. This work reveals that the effective stiffnesses of this dispersion equation have to be dependent on the propagation direction of the incident wave in order to make this equation consistent.
Dispersion coefficients for the interaction of Cs atom with different material media
NASA Astrophysics Data System (ADS)
Kaur, Kiranpreet; Kaur, Jasmeet; Sahoo, B. K.; Arora, Bindiya
2016-10-01
Motivated by a large number of applications, the dispersion (C3) coefficients for the interaction of a Cs atom with different material media such as Au (metal), Si (semiconductor) and various dielectric surfaces like vitreous SiO2, SiNx, sapphire and YAG are determined using accurate values of the dynamic polarizabilities of the Cs atom obtained employing the relativistic coupled-cluster approach and the dynamic dielectric constants of the walls. Moreover, we also give the retardation function in the graphical representation as functions of separation distances to describe the interaction potentials between the Cs atom with the above considered material media. For the easy access to the interaction potentials at a given distance of separation, we give a simple working functional fitting form for the retardation functions in terms of four fitting parameters that are quoted for the respective medium.
Full 3D dispersion curve solutions for guided waves in generally anisotropic media
NASA Astrophysics Data System (ADS)
Hernando Quintanilla, F.; Lowe, M. J. S.; Craster, R. V.
2016-02-01
Dispersion curves of guided waves provide valuable information about the physical and elastic properties of waves propagating within a given waveguide structure. Algorithms to accurately compute these curves are an essential tool for engineers working in non-destructive evaluation and for scientists studying wave phenomena. Dispersion curves are typically computed for low or zero attenuation and presented in two or three dimensional plots. The former do not always provide a clear and complete picture of the dispersion loci and the latter are very difficult to obtain when high values of attenuation are involved and arbitrary anisotropy is considered in single or multi-layered systems. As a consequence, drawing correct and reliable conclusions is a challenging task in the modern applications that often utilize multi-layered anisotropic viscoelastic materials. These challenges are overcome here by using a spectral collocation method (SCM) to robustly find dispersion curves in the most complicated cases of high attenuation and arbitrary anisotropy. Solutions are then plotted in three-dimensional frequency-complex wavenumber space, thus gaining much deeper insight into the nature of these problems. The cases studied range from classical examples, which validate this approach, to new ones involving materials up to the most general triclinic class for both flat and cylindrical geometry in multi-layered systems. The apparent crossing of modes within the same symmetry family in viscoelastic media is also explained and clarified by the results. Finally, the consequences of the centre of symmetry, present in every crystal class, on the solutions are discussed.
Unifying diffusion and seepage for nonlinear gas transport in multiscale porous media
NASA Astrophysics Data System (ADS)
Song, Hongqing; Wang, Yuhe; Wang, Jiulong; Li, Zhengyi
2016-09-01
We unify the diffusion and seepage process for nonlinear gas transport in multiscale porous media via a proposed new general transport equation. A coherent theoretical derivation indicates the wall-molecule and molecule-molecule collisions drive the Knudsen and collective diffusive fluxes, and constitute the system pressure across the porous media. A new terminology, nominal diffusion coefficient can summarize Knudsen and collective diffusion coefficients. Physical and numerical experiments show the support of the new formulation and provide approaches to obtain the diffusion coefficient and permeability simultaneously. This work has important implication for natural gas extraction and greenhouse gases sequestration in geological formations.
Shen, Ming; Gao, Jinsong; Ge, Lijuan
2015-01-01
We investigate the spatially optical solitons shedding from Airy beams and anomalous interactions of Airy beams in nonlocal nonlinear media by means of direct numerical simulations. Numerical results show that nonlocality has profound effects on the propagation dynamics of the solitons shedding from the Airy beam. It is also shown that the strong nonlocality can support periodic intensity distribution of Airy beams with opposite bending directions. Nonlocality also provides a long-range attractive force between Airy beams, leading to the formation of stable bound states of both in-phase and out-of-phase breathing Airy solitons which always repel in local media. PMID:25900878
Traversal of electromagnetic pulses through dispersive media with negative refractive index
NASA Astrophysics Data System (ADS)
Nanda, L.; Ramakrishna, S. A.
2017-05-01
We investigate the traversal of electromagnetic pulses through dispersive media with negative refractive index in such a way that no resonant effects come into play. It has been verified that for evanescent waves, the definitions of the group delay and the reshaping delay times get interchanged in comparison to the propagating waves. We show that for a negative refractive index medium (NRM) with ɛ(ω)=μ(ω), the reshaping delay time identically vanishes for propagating waves. The total delay time in NRM is otherwise contributed by both the group and the reshaping delay times, whereas for the case of broadband pulses in NRM the total delay time is always subluminal.
Energy-momentum tensor of the electromagnetic field in dispersive media
NASA Astrophysics Data System (ADS)
Toptygin, I. N.; Levina, K.
2016-02-01
We study the relation between the energy-momentum tensor of the electromagnetic field and the group velocity of quasi-monochromatic waves in a nonabsorptive, isotropic, spatially and temporally dispersive dielectric. It is shown that the Abraham force acting on a dielectric is not needed for the momentum conservation law to hold if the dielectric is free of external charges and currents and if the Abraham momentum density is used. The energy-momentum tensor turns out to be symmetric, and the Maxwell stress tensor is expressed either in terms of the momentum density vector and the group velocity or in terms of the energy density and the group velocity. The stress tensor and the energy density are essentially dependent on the frequency and wave vector derivatives of the functions that describe the electromagnetic properties of the medium (i.e., the dielectric permittivity and the magnetic permeability). The obtained results are applicable to both ordinary and left-handed media. The results are compared with those of other authors. The pressure a wave exerts on the interface between two media is calculated. For both ordinary and left-handed media, either 'radiation pressure' or 'radiation attraction' can occur at the interface, depending on the material parameters of the two media. For liquid dielectrics, the striction effect is considered.
NASA Astrophysics Data System (ADS)
Kuis, Robinson
The early use of the induced grating autocorrelation (IGA) method to measure the nonlinear refractive index of single mode fibers utilized 50-70 ps pulses at 1064-nm and required only 15-20 m lengths of fiber. Exotic fibers, such as photonic crystal fibers (PCFs), are extremely expensive and limit many applications to a few meters. Therefore, a practical measurement of the nonlinear coefficient for such exotic fibers requires a technique sensitive to shorter fiber lengths (< 5 m). To reduce the fiber length requirements, the IGA technique must use shorter pulses. In this work, a new mathematical description was developed for the IGA technique that is applicable to pulses as short as 100 fs. This model includes effects such as dispersion, self-phase modulation, stimulated Raman scattering, intra-pulse Raman scattering and self-steepening. The model was used to investigate pulse propagation at three pulsewidths: 50 ps, 2 ps, and 120 fs. The model predicted the sensitivity of IGA measurements to dispersive and nonlinear effects at these pulsewidths. The numerical model led to the successful experimental determination of both the dispersion and nonlinear coefficients of a 15m long single-mode fiber using a 2 ps Ti: sapphire laser at 800 nm. The nonlinear coefficient for several PCFs (a 30 cm long highly nonlinear PCF and two large mode area PCFs of 4.5 m and 4.9 m long) were also successfully measured with excellent numerical fits using this new IGA model.
NASA Astrophysics Data System (ADS)
Horst, Allison M.; Ji, Zhaoxia; Holden, Patricia A.
2012-08-01
Nanoparticle exposure in toxicity studies requires that nanoparticles are bioavailable by remaining highly dispersed in culture media. However, reported dispersion approaches are variable, mostly study-specific, and not transferable owing to their empirical basis. Furthermore, many published approaches employ proteinaceous dispersants in rich laboratory media, both of which represent end members in environmental scenarios. Here, a systematic approach was developed to disperse initially agglomerated TiO2 nanoparticles (Aeroxide® TiO2 P25, Evonik, NJ; primary particle size range 6.4-73.8 nm) in oligotrophic culture medium for environmentally relevant bacterial toxicity studies. Based on understanding particle-particle interactions in aqueous media and maintaining environmental relevance, the approach involves (1) quantifying the relationship between pH and zeta potential to determine the point of zero charge of select nanoparticles in water; (2) nominating, then testing and selecting, environmentally relevant stabilizing agents; and (3) dispersing via "condition and capture" whereby stock dry powder nanoparticles are sonicated in pre-conditioned (with base, or acid, plus stabilizing agent) water, then diluted into culture media. The "condition and capture" principle is transferable to other nanoparticle and media chemistries: simultaneously, mechanically and electrostatically, nanoparticles can be dispersed with surrounding stabilizers that coat and sterically hinder reagglomeration in the culture medium.
Nonlinear effects related to circularly polarized dispersive Alfvén waves
NASA Astrophysics Data System (ADS)
Sharma, Swati; Gaur, Nidhi; Sharma, R. P.
2016-09-01
In situ measurements of solar wind have strongly implicated its turbulent behavior. The observed power spectra report a breakpoint around length scales of the order of ion scales. As one of the responsible mechanisms for the observed steepening in power spectrum, our approach includes a right circularly polarized dispersive Alfvén wave (DAW) with finite frequency correction which, when subjected to transverse collapse/filamentation instability, may possibly result in steepening of spectrum and progressive transfer of energy from larger scales to smaller scales. We have studied the nonlinear effects associated with coupling of DAW with kinetic Alfvén wave in solar wind at 1 A.U. The formation of localized structures provides a clue about the emergence of turbulence. Numerical simulation is performed to study localization and power spectral density of the field and density fluctuations. The results show steeper spectrum indicating transfer of large scale turbulent energy down to small scales.
Dispersion and absorption in one-dimensional nonlinear lattices: A resonance phonon approach
NASA Astrophysics Data System (ADS)
Xu, Lubo; Wang, Lei
2016-09-01
Based on the linear response theory, we propose a resonance phonon (r-ph) approach to study the renormalized phonons in a few one-dimensional nonlinear lattices. Compared with the existing anharmonic phonon (a-ph) approach, the dispersion relations derived from this approach agree with the expectations of the effective phonon (e-ph) theory much better. The application is also largely extended, i.e., it is applicable in many extreme situations, e.g., high frequency, high temperature, etc., where the existing one can hardly work. Furthermore, two separated phonon branches (one acoustic and one optical) with a clear gap in between can be observed by the r-ph approach in a diatomic anharmonic lattice. While only one combined branch can be detected in the same lattice with both the a-ph approach and the e-ph theory.
NASA Astrophysics Data System (ADS)
Zhang, Di; Capoglu, Ilker; Li, Yue; Cherkezyan, Lusik; Chandler, John; Spicer, Graham; Subramanian, Hariharan; Taflove, Allen; Backman, Vadim
2016-06-01
Combining finite-difference time-domain (FDTD) methods and modeling of optical microscopy modalities, we previously developed an open-source software package called Angora, which is essentially a "microscope in a computer." However, the samples being simulated were limited to nondispersive media. Since media dispersions are common in biological samples (such as cells with staining and metallic biomarkers), we have further developed a module in Angora to simulate samples having complicated dispersion properties, thereby allowing the synthesis of microscope images of most biological samples. We first describe a method to integrate media dispersion into FDTD, and we validate the corresponding Angora dispersion module by applying Mie theory, as well as by experimentally imaging gold microspheres. Then, we demonstrate how Angora can facilitate the development of optical imaging techniques with a case study.
Nonlinear coda wave analysis of hysteretic elastic behavior in strongly scattering media
NASA Astrophysics Data System (ADS)
Ouarabi, M. Ait; Boubenider, F.; Gliozzi, A. S.; Scalerandi, M.
2016-10-01
Strongly scattering elastic media, such as consolidated granular materials, respond to ultrasonic pulse excitations with a long response signal with peculiar properties. The portion of the signal at late times, termed coda, is due to multiple scattering. It contains information about the elastic properties of the material, and it has been proven to be very sensitive to small variations in the modulus. Here we propose a technique based on a nonlinear analysis of the coda of a signal, which might be applied to quantify the nonlinear elastic response in consolidated granular media exhibiting a hysteretic elastic behavior. The method proposed allows for an intrinsic definition of the reference signal which is normally needed for applying coda-based methods.
Propagation dynamics of finite-energy Airy beams in nonlocal nonlinear media
NASA Astrophysics Data System (ADS)
Wu, Zhen-Kun; Li, Peng; Gu, Yu-Zong
2017-10-01
We investigate periodic inversion and phase transition of normal and displaced finite-energy Airy beams propagating in nonlocal nonlinear media with the split-step Fourier method. Numerical simulation results show that parameters such as the degree of nonlocality and amplitude have profound effects on the intensity distribution of the period of an Airy beam. Nonlocal nonlinear media will reduce into a harmonic potential if the nonlocality is strong enough, which results in the beam fluctuating in an approximately cosine mode. The beam profile changes from an Airy profile to a Gaussian one at a critical point, and during propagation the process repeats to form an unusual oscillation. We also briefly discus the two-dimensional case, being equivalent to a product of two one-dimensional cases.
Transmission of pulses in a dispersion-managed fiber link with extra nonlinear segments
NASA Astrophysics Data System (ADS)
Driben, Rodislav; Malomed, Boris A.; Chu, P. L.
2005-01-01
We introduce an extended version of the dispersion-management (DM) model, which includes an extra nonlinear element, and consider transmission of return-to-zero pulses in this system (they are not solitons). The pulses feature self-compression, accompanied by generation of side peaks (in the temporal domain). An optimal transmission distance, zopt, is identified, up to which the pulse continues to compress itself (the eventual width-compression factor is ≃2), while the amplitude of the side peaks remains small enough. The distance zopt virtually does not depend on the strength S of the DM part of the system in the interval 1.5 < S < 11, but it is sensitive to the nonlinearity strength in the extra segment. The system provides essentially stronger suppression of the noise-induced jitter of the pulses than the ordinary DM model. The most important issue is interaction between adjacent pulses, which is a basic difficulty in the case of DM solitons. In a broad parameter region, the system provides effective isolation between pulses. The minimum initial temporal distance between them, necessary for the isolation, is quite small, slightly larger than 1.5 the pulse's width. The transmission actually improves the quality of multi-pulse arrays, as it leads to deepening of hiatuses between originally overlapping pulses.
Suppression of two-photon resonantly enhanced nonlinear processes in extended media
Garrett, W.R.; Moore, M.A.; Payne, M.G.; Wunderlich, R.K.
1988-11-01
On the basis of combined experimental and theoretical studies of nonlinear processes associated with two-photon excitations near 3d and 4d states in Na, we show how resonantly enhanced stimulated hyper-Raman emission, parametric four-wave mixing processes and total resonant two-photon absorption can become severely suppressed through the actions of internally generated fields on the total atomic response in extended media. 7 refs., 3 figs.
Frequency dispersion of the first hyperpolarizabilities of reference molecules for nonlinear optics
Wergifosse, Marc de; Champagne, Benoît; Castet, Frédéric
2015-05-21
The frequency dispersion of the hyper-Rayleigh scattering first hyperpolarizabilities (β{sub HRS}) of five reference molecules for nonlinear optics, namely, carbon tetrachloride, chloroform, dichloromethane, acetonitrile, and trichloroacetonitrile, is described using the coupled-cluster singles and doubles quadratic response function (CCSD-QRF) as well as approximate schemes. Comparisons to approximate schemes in which the frequency dispersion is evaluated as either a multiplicative or an additive correction to the static hyperpolarizability yield the following observations: (i) errors of the order of 10% or less are usually encountered when using the multiplicative scheme for photon energies far from the lowest dipole-allowed excitation energies, (ii) spurious cases cannot be excluded as evidenced by carbon tetrachloride where the multiplicative scheme predicts a decrease of β{sub HRS} in contradiction to the increase obtained using the CCSD-QRF method, and (iii) the additive scheme is at best as reliable as the multiplicative approximation. The two-state approximation presents the advantage of correcting the wrong behavior of the additive and multiplicative schemes for carbon tetrachloride, but it is not an improved solution for the other compounds, while the question of selecting the appropriate dominant excited state remains unanswered. Finally, a new β{sub xyz} value of 18.9 a.u. is proposed for carbon tetrachloride in gas phase at λ = 1064 nm, to be compared with the measured 16.9 ± 1.4 a.u. value due to Shelton.
1992-02-13
Self-diffusion studies of Se in CdSe and chemical interdiffusion studies of Se in CdTe, on the other hand, revealed diffusivities on the order of 107...pp. 922-933 (1990). - 23 - 10. R. S. Fiegelson and R. S. Route, "Improved yield of Bridgman grown AgGaSe 2 crystals using shaped crucibles," J. Cryst...and F. G. Storz, "Linear and nonlinear optical properties of ZnGeP2 and CdSe ," Appl. Phys. Lett. 18, pp. 301-303 (1971). 50. K. L. Vodopyanov, L. A
On incremental non-linearity in granular media: phenomenological and multi-scale views
NASA Astrophysics Data System (ADS)
Darve, Félix; Nicot, François
2005-12-01
On the basis of fundamental constitutive laws such as elasticity, perfect plasticity, and pure viscosity, many elasto-viscoplastic constitutive relations have been developed since the 1970s through phenomenological approaches. In addition, a few more recent micro-mechanical models based on multi-scale approaches are now able to describe the main macroscopic features of the mechanical behaviour of granular media. The purpose of this paper is to compare a phenomenological constitutive relation and a micro-mechanical model with respect to a basic issue regularly raised about granular assemblies: the incrementally non-linear character of their behaviour. It is shown that both phenomenological and micro-mechanical models exhibit an incremental non-linearity. In addition, the multi-scale approach reveals that the macroscopic incremental non-linearity could stem from the change in the regime of local contacts between particles (from plastic regime to elastic regime) in terms of the incremental macroscopic loading direction. Copyright
Halamoda-Kenzaoui, Blanka; Ceridono, Mara; Colpo, Pascal; Valsesia, Andrea; Urbán, Patricia; Ojea-Jiménez, Isaac; Gioria, Sabrina; Gilliland, Douglas; Rossi, François; Kinsner-Ovaskainen, Agnieszka
2015-01-01
Given the increasing variety of manufactured nanomaterials, suitable, robust, standardized in vitro screening methods are needed to study the mechanisms by which they can interact with biological systems. The in vitro evaluation of interactions of nanoparticles (NPs) with living cells is challenging due to the complex behaviour of NPs, which may involve dissolution, aggregation, sedimentation and formation of a protein corona. These variable parameters have an influence on the surface properties and the stability of NPs in the biological environment and therefore also on the interaction of NPs with cells. We present here a study using 30 nm and 80 nm fluorescently-labelled silicon dioxide NPs (Rubipy-SiO2 NPs) to evaluate the NPs dispersion behaviour up to 48 hours in two different cellular media either supplemented with 10% of serum or in serum-free conditions. Size-dependent differences in dispersion behaviour were observed and the influence of the living cells on NPs stability and deposition was determined. Using flow cytometry and fluorescence microscopy techniques we studied the kinetics of the cellular uptake of Rubipy-SiO2 NPs by A549 and CaCo-2 cells and we found a correlation between the NPs characteristics in cell media and the amount of cellular uptake. Our results emphasize how relevant and important it is to evaluate and to monitor the size and agglomeration state of nanoparticles in the biological medium, in order to interpret correctly the results of the in vitro toxicological assays. PMID:26517371
Halamoda-Kenzaoui, Blanka; Ceridono, Mara; Colpo, Pascal; Valsesia, Andrea; Urbán, Patricia; Ojea-Jiménez, Isaac; Gioria, Sabrina; Gilliland, Douglas; Rossi, François; Kinsner-Ovaskainen, Agnieszka
2015-01-01
Given the increasing variety of manufactured nanomaterials, suitable, robust, standardized in vitro screening methods are needed to study the mechanisms by which they can interact with biological systems. The in vitro evaluation of interactions of nanoparticles (NPs) with living cells is challenging due to the complex behaviour of NPs, which may involve dissolution, aggregation, sedimentation and formation of a protein corona. These variable parameters have an influence on the surface properties and the stability of NPs in the biological environment and therefore also on the interaction of NPs with cells. We present here a study using 30 nm and 80 nm fluorescently-labelled silicon dioxide NPs (Rubipy-SiO2 NPs) to evaluate the NPs dispersion behaviour up to 48 hours in two different cellular media either supplemented with 10% of serum or in serum-free conditions. Size-dependent differences in dispersion behaviour were observed and the influence of the living cells on NPs stability and deposition was determined. Using flow cytometry and fluorescence microscopy techniques we studied the kinetics of the cellular uptake of Rubipy-SiO2 NPs by A549 and CaCo-2 cells and we found a correlation between the NPs characteristics in cell media and the amount of cellular uptake. Our results emphasize how relevant and important it is to evaluate and to monitor the size and agglomeration state of nanoparticles in the biological medium, in order to interpret correctly the results of the in vitro toxicological assays.
Ramirez, E V Garcia; Carrasco, M L Arroyo; Otero, M M Mendez; Cerda, S Chavez; Castillo, M D Iturbe
2010-10-11
In this work we present a simple model that can be used to calculate the far field intensity distributions when a Gaussian beam cross a thin sample of nonlinear media but the response can be nonlocal.
Tracing Analytic Ray Curves for Light and Sound Propagation in Non-Linear Media.
Mo, Qi; Yeh, Hengchin; Manocha, Dinesh
2016-11-01
The physical world consists of spatially varying media, such as the atmosphere and the ocean, in which light and sound propagates along non-linear trajectories. This presents a challenge to existing ray-tracing based methods, which are widely adopted to simulate propagation due to their efficiency and flexibility, but assume linear rays. We present a novel algorithm that traces analytic ray curves computed from local media gradients, and utilizes the closed-form solutions of both the intersections of the ray curves with planar surfaces, and the travel distance. By constructing an adaptive unstructured mesh, our algorithm is able to model general media profiles that vary in three dimensions with complex boundaries consisting of terrains and other scene objects such as buildings. Our analytic ray curve tracer with the adaptive mesh improves the efficiency considerably over prior methods. We highlight the algorithm's application on simulation of visual and sound propagation in outdoor scenes.
Patrick C. Tobin; Ottar N. Bjornstad
2005-01-01
Natural enemy-victim systems may exhibit a range of dynamic space-time patterns. We used a theoretical framework to study spatiotemporal structuring in a transient natural enemy-victim system subject to differential rates of dispersal, stochastic forcing, and nonlinear dynamics. Highly mobile natural enemies that attacked less mobile victims were locally spatially...
Yang, Shan; Ganikhanov, Feruz
2013-11-15
We propose and experimentally demonstrate a method that is capable of resolving both real and imaginary parts of third-order nonlinearity (χ(3)) in the vicinity of Raman resonances. Dispersion of χ(3) can be obtained from a medium probed within microscopic volumes with a spectral resolution of better than 0.10 cm(-1).
NASA Astrophysics Data System (ADS)
Grathwohl, P.; Piepenbrink, M.; Eberhardt, C.; Kasper, M.; Gauglitz, G.
2005-12-01
Natural attenuation (mainly biodegradation) of organic pollutants in groundwater often depends on mixing of electron donors and acceptors in the plume fringes, the spatial distribution of these highly reactive zones, compared to the volume of the whole plume, is quite small and characterized by steep concentration gradients. Mixing in the field is the result of transverse dispersion, which is a function of groundwater flow velocity, the typical length scale in the aquifer (e.g. grain size) as well as the aquifer heterogeneities, and the dynamics of the natural flow system. The objectives of this work are to investigate dispersion-limited reactions in well-controlled bench-scale experiments i.e. to elaborate how heterogeneities and transient conditions at the field scale (in time and space) influence the overall natural attenuation rates of organic pollutants in groundwater. Experiments in which (a) the spreading of a conservative tracer cloud or (b) the reaction of two reaction partners at the plume fringe is limited by transverse dispersion are currently investigated in the lab. As the quantification of transverse dispersivities in heterogeneous media under transient flow conditions requires monitoring with high resolution in space and time new optical tools (CCD camera) are employed for the quantitative mapping of the plumes.The first experiments were conducted at bench scale using a continuous injection of a conservative colour tracers (fluorescine), which show absorption only at a specific range of wavelengths in the visible spectrum, a quantification of this tracers is thus possible by its colour depth. Quality control of the quantification obtained by the CCD set-up is done via conventional sampling and analysis at the outlet ports during steady state flow conditions. Currently, well controlled acid-base reactions, are monitored by the colour changes of pH-indicators.This efficient spatially and time-resolved monitoring of concentration gradient changes by
Pantsyrnaya, T; Blanchard, F; Delaunay, S; Goergen, J L; Guédon, E; Guseva, E; Boudrant, J
2011-03-01
In the present study surfactant addition with the help of either a mechanical dispersion or a thermal treatment was applied in order to increase the solubility and the bioavailability of phenanthrene in aqueous media, and therefore to promote its biodegradation. Among four tested surfactants (Tween 80, Brij 30, sodium dodecyl sulphate and rhamnolipids), Brij 30 (0.5 gL(-1)) showed the best results allowing us to attain about 20 mgL(-1) of soluble phenanthrene. An additional thermal treatment at 60°C for 24h, 200 rpm permitted to increase the solubility of phenanthrene in the presence of Brij 30 (0.5 gL(-1)) to about 30 mgL(-1). Higher dispersions of phenanthrene particles as well as the reduction of their size were obtained using Ultra-Turrax and French press. The biodegradation of phenanthrene by Pseudomonas putida was then investigated. The reduction of size of phenanthrene particles by mechanical dispersion did not influence its biodegradation, suggesting that P. putida consumed only soluble phenanthrene. The addition of Brij 30 (0.5 gL(-1)) permitted to obtain more phenanthrene metabolized. The use of Brij 30 coupled with a transitory heating of phenanthrene-containing medium at 60°C led to an even more complete biodegradation. This might be a promising way to enhance biodegradation of PAHs.
Particle dispersion in porous media: Differentiating effects of geometry and fluid rheology
NASA Astrophysics Data System (ADS)
Jacob, Jack D. C.; Krishnamoorti, Ramanan; Conrad, Jacinta C.
2017-08-01
We investigate the effects of geometric order and fluid rheology on the dispersion of micron-sized particles in two-dimensional microfluidic porous media. Particles suspended in a mixture of glycerol and water or in solutions of partially hydrolyzed polyacrylamide (HPAM) polymers were imaged as they flowed through arrays of microscale posts. From the trajectories of the particles, we calculated the velocity distributions and thereafter obtained the longitudinal and transverse dispersion coefficients. Particles flowed in the shear-thinning HPAM solution through periodic arrays of microposts were more likely to switch between streamlines, due to elastic instabilities. As a result, the distributions of particle velocity were broader in HPAM solutions than in glycerol-water mixtures for ordered geometries. In a disordered array of microposts, however, there was little difference between the velocity distributions obtained in glycerol-water and in HPAM solutions. Correspondingly, particles flowed through ordered post arrays in HPAM solutions exhibited enhanced transverse dispersion. This result suggests that periodic geometric order amplifies the effects of the elasticity-induced velocity fluctuations, whereas geometric disorder of barriers effectively averages out the fluctuations.
Radiation pressure of light pulses and conservation of linear momentum in dispersive media.
Scalora, Michael; D'Aguanno, Giuseppe; Mattiucci, Nadia; Bloemer, Mark J; Centini, Marco; Sibilia, Concita; Haus, Joseph W
2006-05-01
We derive an expression for the Minkowski momentum under conditions of dispersive susceptibility and permeability, and compare it to the Abraham momentum in order to test the principle of conservation of linear momentum when matter is present. We investigate cases when an incident pulse interacts with a variety of structures, including thick substrates, resonant, free-standing, micron-sized multilayer stacks, and negative index materials. In general, we find that for media only a few wavelengths thick the Minkowski and Abraham momentum densities yield similar results. For more extended media, including substrates and Bragg mirrors embedded inside thick dielectric substrates, our calculations show dramatic differences between the Minkowski and Abraham momenta. Without exception, in all cases investigated the instantaneous Lorentz force exerted on the medium is consistent only with the rate of change of the Abraham momentum. As a practical example, we use our model to predict that electromagnetic momentum and energy buildup inside a multilayer stack can lead to widely tunable accelerations that may easily reach and exceed 10(10) m/s(2) for a mass of 10(-5) g. Our results suggest that the physics of the photonic band edge and other similar finite structures may be used as a testing ground for basic electromagnetic phenomena such as momentum transfer to macroscopic media.
Synthesis of Silver Nanoparticles Dispersed in Various Aqueous Media Using Laser Ablation
Tajdidzadeh, M.; Azmi, B. Z.; Yunus, W. Mahmood M.; Talib, Z. Abidin; Sadrolhosseini, A. R.; Karimzadeh, K.; Gene, S. A.; Dorraj, M.
2014-01-01
The particle size, morphology, and stability of Ag-NPs were investigated in the present study. A Q-Switched Nd: YAG pulsed laser (λ = 532 nm, 360 mJ/pulse) was used for ablation of a pure Ag plate for 30 min to prepare Ag-NPs in the organic compound such as ethylene glycol (EG) and biopolymer such as chitosan. The media (EG, chitosan) permitted the making of NPs with well dispersed and average size of Ag-NPs in EG is about 22 nm and in chitosan is about 10 nm in spherical form. Particle size, morphology, and stability of NPs were compared with distilled water as a reference. The stability of the samples was studied by measuring UV-visible absorption spectra of samples after one month. The result indicated that the formation efficiency of NPs in chitosan was higher than other media and NPs in chitosan solution were more stable than other media during one month storage. This method for synthesis of silver NPs could be as a green method due to its environmentally friendly nature. PMID:25295298
Makarov, V A; Petnikova, V M; Shuvalov, V V
2015-09-30
Three unusual classes of particular analytical solutions to a system of four nonlinear equations are found for slowly varying complex amplitudes of circularly polarised components of the electric field. The system describes the self-action and interaction of two elliptically polarised plane waves collinearly propagating in an isotropic medium with second-order frequency dispersion and spatial dispersion of cubic nonlinearity. The solutions correspond to self-consistent combinations of two elliptically polarised cnoidal waves whose mutually orthogonal polarisation components vary in accordance with pairwise identical laws during propagation. At the same time, the amplitudes of the component with the same circular polarisation are proportional to two different elliptic Jacobi functions with the same periods. (nonlinear optical phenomena)
Yi, Xiaogang; Wu, Jian; Li, Yan; Li, Wei; Hong, Xiaobin; Guo, Hongxiang; Zuo, Yong; Lin, Jintong
2012-12-03
Considering the polarization mode dispersion(PMD), the transmission penalty induced by nonlinear signal-noise interactions (NSNI) between the amplified spontaneous emission noise (ASE) and the information signal is investigated numerically for 40(100)G dispersion-managed(DM) polarization-multiplexed quadrature phase-shift keying (PM-QPSK) systems. We show that for single-channel PM-QPSK systems, PMD is helpful to reduce the NSNI-induced penalty. For multi-channel PM-QPSK system, however, the NSNI-induced nonlinear penalty is significantly enhanced by PMD, especially at low bit-rate. Our results show that due to the NSNI, the reduction of allowed input power that gives 1-dB Q penalty after 1600-km nonlinear transmission will increase from 1dB without PMD to 3.7dB with PMD for 42.8-Gbit/s coherent return-to-zero (RZ)-PM-QPSK systems.
NASA Astrophysics Data System (ADS)
Liao, Jianfei; Xie, Yingmao; Wang, Xinghua; Li, Dongbo; Huang, Tianye
2017-07-01
A slot silicon photonic crystal fiber (PCF) is proposed to simultaneously achieve ultrahigh birefringence, large nonlinearity and ultra-flattened nearly-zero dispersion over a wide wavelength range. By taking advantage on the slot effect, ultrahigh birefringence up to 0.0736 and ultrahigh nonlinear coefficient up to 211.48 W-1 m-1 for quasi-TE mode can be obtained at the wavelength of 1.55 μm. Moreover, ultra-flattened dispersion of 0.49 ps/(nm km) for quasi-TE mode can be achieved over a 180 nm wavelength range with low dispersion slope of 1.85 × 10-3 ps/(nm2 km) at 1.55 μm. Leveraging on these advantages, the proposed slot PCF has great potential for efficient all-optical signal processing applications.
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.
ERIC Educational Resources Information Center
Gutenko, Gregory
For a new course in media editing at the University of Missouri at Kansas City, a nonlinear, affordable AVID Media Suite Pro system was selected for the student video laboratory, a textbook was chosen, and an instructor was trained. However, there were difficulties concerning the acquisition, delivery, setup, and debugging of the editing…
NASA Astrophysics Data System (ADS)
Kim, Bong-Sik
Three dimensional (3D) Navier-Stokes-alpha equations are considered for uniformly rotating geophysical fluid flows (large Coriolis parameter f = 2O). The Navier-Stokes-alpha equations are a nonlinear dispersive regularization of usual Navier-Stokes equations obtained by Lagrangian averaging. The focus is on the existence and global regularity of solutions of the 3D rotating Navier-Stokes-alpha equations and the uniform convergence of these solutions to those of the original 3D rotating Navier-Stokes equations for large Coriolis parameters f as alpha → 0. Methods are based on fast singular oscillating limits and results are obtained for periodic boundary conditions for all domain aspect ratios, including the case of three wave resonances which yields nonlinear "2½-dimensional" limit resonant equations for f → 0. The existence and global regularity of solutions of limit resonant equations is established, uniformly in alpha. Bootstrapping from global regularity of the limit equations, the existence of a regular solution of the full 3D rotating Navier-Stokes-alpha equations for large f for an infinite time is established. Then, the uniform convergence of a regular solution of the 3D rotating Navier-Stokes-alpha equations (alpha ≠ 0) to the one of the original 3D rotating NavierStokes equations (alpha = 0) for f large but fixed as alpha → 0 follows; this implies "shadowing" of trajectories of the limit dynamical systems by those of the perturbed alpha-dynamical systems. All the estimates are uniform in alpha, in contrast with previous estimates in the literature which blow up as alpha → 0. Finally, the existence of global attractors as well as exponential attractors is established for large f and the estimates are uniform in alpha.
Mechanical balance laws for fully nonlinear and weakly dispersive water waves
NASA Astrophysics Data System (ADS)
Kalisch, Henrik; Khorsand, Zahra; Mitsotakis, Dimitrios
2016-10-01
The Serre-Green-Naghdi system is a coupled, fully nonlinear system of dispersive evolution equations which approximates the full water wave problem. The system is known to describe accurately the wave motion at the surface of an incompressible inviscid fluid in the case when the fluid flow is irrotational and two-dimensional. The system is an extension of the well known shallow-water system to the situation where the waves are long, but not so long that dispersive effects can be neglected. In the current work, the focus is on deriving mass, momentum and energy densities and fluxes associated with the Serre-Green-Naghdi system. These quantities arise from imposing balance equations of the same asymptotic order as the evolution equations. In the case of an even bed, the conservation equations are satisfied exactly by the solutions of the Serre-Green-Naghdi system. The case of variable bathymetry is more complicated, with mass and momentum conservation satisfied exactly, and energy conservation satisfied only in a global sense. In all cases, the quantities found here reduce correctly to the corresponding counterparts in both the Boussinesq and the shallow-water scaling. One consequence of the present analysis is that the energy loss appearing in the shallow-water theory of undular bores is fully compensated by the emergence of oscillations behind the bore front. The situation is analyzed numerically by approximating solutions of the Serre-Green-Naghdi equations using a finite-element discretization coupled with an adaptive Runge-Kutta time integration scheme, and it is found that the energy is indeed conserved nearly to machine precision. As a second application, the shoaling of solitary waves on a plane beach is analyzed. It appears that the Serre-Green-Naghdi equations are capable of predicting both the shape of the free surface and the evolution of kinetic and potential energy with good accuracy in the early stages of shoaling.
Tho, Ingunn; Liepold, Bernd; Rosenberg, Joerg; Maegerlein, Markus; Brandl, Martin; Fricker, Gert
2010-04-16
The objective of the study was to characterise the aqueous dispersions of ritonavir melt extrudates. More specifically to look into the particular system formed when melt extrudate of a poorly soluble drug dissolved in a hydrophilic polymer matrix containing a surfactant is dispersed in an aqueous medium. Melt extrudates with and without ritonavir were studied. The drug containing extrudate was confirmed to be molecular dispersions of drug in a polymer/surfactant matrix. Particulate dispersions were formed in water from both drug and placebo extrudates. The dispersions were investigated with respect to mean particle size and particle size distribution (photon correlation spectroscopy and optical particle counting), surface charge (zeta potential), particle composition (ultracentrifugation), tendency to form aggregates and precipitate (turbidity), in vitro dissolution rate and drug release. It was concluded that dispersion of melt extrudates in aqueous medium give rise to nano/micro-dispersions. The stability of the nano/micro-dispersion is sensitive to anions and may be subjected to association/aggregation/flocculation as time proceeds after preparation of dispersion. Melt extrudate showed improved dissolution rate and drug release properties compared to crystalline raw material. From studies of single components and physical mixtures of the formulation composition it can be concluded that the drug delivery system itself, namely solid dispersion prepared by melt extrusion technology, plays a key role for the formation of the observed particles.
NASA Astrophysics Data System (ADS)
Sun, HongGuang; Zhang, Yong; Chen, Wen; Reeves, Donald M.
2014-02-01
Field and numerical experiments of solute transport through heterogeneous porous and fractured media show that the growth of contaminant plumes may not exhibit constant scaling, and may instead transition between diffusive states (i.e., superdiffusion, subdiffusion, and Fickian diffusion) at various transport scales. These transitions are likely attributed to physical properties of the medium, such as spatial variations in medium heterogeneity. We refer to this transitory dispersive behavior as "transient dispersion", and propose a variable-index fractional-derivative model (FDM) to describe the underlying transport dynamics. The new model generalizes the standard constant-index FDM which is limited to stationary heterogeneous media. Numerical methods including an implicit Eulerian method (for spatiotemporal transient dispersion) and a Lagrangian solver (for multiscaling dispersion) are utilized to produce variable-index FDM solutions. The variable-index FDM is then applied to describe transient dispersion observed at two field tracer tests and a set of numerical experiments. Results show that 1) uranine transport at the small-scale Grimsel test site transitions from strong subdispersion to Fickian dispersion, 2) transport of tritium at the regional-scale Macrodispersion Experimental (MADE) site transitions from near-Fickian dispersion to strong superdispersion, and 3) the conservative particle transport through regional-scale discrete fracture network transitions from superdispersion to Fickian dispersion. The variable-index model can efficiently quantify these transitions, with the scale index varying linearly in time or space.
Sun, Hongguang; Zhang, Yong; Chen, Wen; Reeves, Donald M
2014-02-01
Field and numerical experiments of solute transport through heterogeneous porous and fractured media show that the growth of contaminant plumes may not exhibit constant scaling, and may instead transition between diffusive states (i.e., superdiffusion, subdiffusion, and Fickian diffusion) at various transport scales. These transitions are likely attributed to physical properties of the medium, such as spatial variations in medium heterogeneity. We refer to this transitory dispersive behavior as "transient dispersion", and propose a variable-index fractional-derivative model (FDM) to describe the underlying transport dynamics. The new model generalizes the standard constant-index FDM which is limited to stationary heterogeneous media. Numerical methods including an implicit Eulerian method (for spatiotemporal transient dispersion) and a Lagrangian solver (for multiscaling dispersion) are utilized to produce variable-index FDM solutions. The variable-index FDM is then applied to describe transient dispersion observed at two field tracer tests and a set of numerical experiments. Results show that 1) uranine transport at the small-scale Grimsel test site transitions from strong subdispersion to Fickian dispersion, 2) transport of tritium at the regional-scale Macrodispersion Experimental (MADE) site transitions from near-Fickian dispersion to strong superdispersion, and 3) the conservative particle transport through regional-scale discrete fracture network transitions from superdispersion to Fickian dispersion. The variable-index model can efficiently quantify these transitions, with the scale index varying linearly in time or space. Copyright © 2013 Elsevier B.V. All rights reserved.
NASA Astrophysics Data System (ADS)
Ouyang, Wei; Mao, Weijian; Li, Wuqun; Zhang, Pan
2016-11-01
An approach for approximate direct quadratic nonlinear inversion in two-parameter (density and bulk modulus) heterogeneous acoustic media is being presented and discussed in this paper. The approach consists of two parts: the first is a linear generalized Radon transform (GRT) migration procedure based on the weighted true-amplitude summation of pre-stack seismic scattered data that is adapted to a virtually arbitrary observing system, and the second is a non-iterative quadratic inversion operation, produced from the explicit expression of amplitude radiation pattern that is acting on the migrated data. This ensures the asymptotic inversion can continue to simultaneously locate the discontinuities and reconstruct the size of the discontinuities in the perturbation parameters describing the acoustic media. We identify that the amplitude radiation pattern is the binary quadratic combination of the parameters in the process of formulating nonlinear inverse scattering problems based on second-order Born approximation. The coefficients of the quadratic terms are computed by appropriately handling the double scattering effects. These added quadratic terms provide a better amplitude correction for the parameters inversion. Through numerical tests, we show that for strong perturbations, the errors of the linear inversion are significant and unacceptable. In contrast, the quadratic nonlinear inversion can give fairly accurate inversion results and keep almost the same computational complexity as conventional GRT liner inversion.
Forty-five degree backscattering-mode nonlinear absorption imaging in turbid media
NASA Astrophysics Data System (ADS)
Cui, Liping; Knox, Wayne H.
2010-03-01
Two-color nonlinear absorption imaging has been previously demonstrated with endogenous contrast of hemoglobin and melanin in turbid media using transmission-mode detection and a dual-laser technology approach. For clinical applications, it would be generally preferable to use backscattering mode detection and a simpler single-laser technology. We demonstrate that imaging in backscattering mode in turbid media using nonlinear absorption can be obtained with as little as 1-mW average power per beam with a single laser source. Images have been achieved with a detector receiving backscattered light at a 45-deg angle relative to the incoming beams' direction. We obtain images of capillary tube phantoms with resolution as high as 20 μm and penetration depth up to 0.9 mm for a 300-μm tube at SNR ~1 in calibrated scattering solutions. Simulation results of the backscattering and detection process using nonimaging optics are demonstrated. A Monte Carlo-based method shows that the nonlinear signal drops exponentially as the depth increases, which agrees well with our experimental results. Simulation also shows that with our current detection method, only 2% of the signal is typically collected with a 5-mm-radius detector.
NASA Astrophysics Data System (ADS)
Ouyang, Wei; Mao, Weijian; Li, Wuqun; Zhang, Pan
2017-02-01
An approach for approximate direct quadratic non-linear inversion in two-parameter (density and bulk modulus) heterogeneous acoustic media is being presented and discussed in this paper. The approach consists of two parts: the first is a linear generalized Radon transform (GRT) migration procedure based on the weighted true-amplitude summation of pre-stack seismic scattered data that is adapted to a virtually arbitrary observing system, and the second is a non-iterative quadratic inversion operation, produced from the explicit expression of amplitude radiation pattern that is acting on the migrated data. This ensures the asymptotic inversion can continue to simultaneously locate the discontinuities and reconstruct the size of the discontinuities in the perturbation parameters describing the acoustic media. We identify that the amplitude radiation pattern is the binary quadratic combination of the parameters in the process of formulating non-linear inverse scattering problems based on second-order Born approximation. The coefficients of the quadratic terms are computed by appropriately handling the double scattering effects. These added quadratic terms provide a better amplitude correction for the parameters inversion. Through numerical tests, we show that for strong perturbations, the errors of the linear inversion are significant and unacceptable. In contrast, the quadratic non-linear inversion can give fairly accurate inversion results and keep almost the same computational complexity as conventional GRT liner inversion.
Self-organization of frozen light in near-zero-index media with cubic nonlinearity
NASA Astrophysics Data System (ADS)
Marini, A.; García de Abajo, F. J.
2016-02-01
Optical beams are generally unbound in bulk media, and propagate with a velocity approximately amounting to the speed of light in free-space. Guidance and full spatial confinement of light are usually achieved by means of waveguides, mirrors, resonators, and photonic crystals. Here we theoretically demonstrate that nonlinear self-organization can be exploited to freeze optical beams in bulk near-zero-index media, thus enabling three-dimensional self-trapping of still light without the need of optical resonators. Light is stopped to a standstill owing to the divergent wavelength and the vanishing group velocity, effectively rendering, through nonlinearity, a positive-epsilon trapping cavity carved in an otherwise slightly-negative-epsilon medium. By numerically solving Maxwell’s equations, we find a soliton-like family of still azimuthal doughnuts, which we further study through an adiabatic perturbative theory that describes soliton evaporation in lossy media or condensation in actively pumped materials. Our results suggest applications in optical data processing and storage, quantum optical memories, and soliton-based lasers without cavities. Additionally, near-zero-index conditions can also be found in the interplanetary medium and in the atmosphere, where we provide a complementary explanation to the rare phenomenon of ball-lightning.
Self-organization of frozen light in near-zero-index media with cubic nonlinearity
Marini, A.; García de Abajo, F. J.
2016-01-01
Optical beams are generally unbound in bulk media, and propagate with a velocity approximately amounting to the speed of light in free-space. Guidance and full spatial confinement of light are usually achieved by means of waveguides, mirrors, resonators, and photonic crystals. Here we theoretically demonstrate that nonlinear self-organization can be exploited to freeze optical beams in bulk near-zero-index media, thus enabling three-dimensional self-trapping of still light without the need of optical resonators. Light is stopped to a standstill owing to the divergent wavelength and the vanishing group velocity, effectively rendering, through nonlinearity, a positive-epsilon trapping cavity carved in an otherwise slightly-negative-epsilon medium. By numerically solving Maxwell’s equations, we find a soliton-like family of still azimuthal doughnuts, which we further study through an adiabatic perturbative theory that describes soliton evaporation in lossy media or condensation in actively pumped materials. Our results suggest applications in optical data processing and storage, quantum optical memories, and soliton-based lasers without cavities. Additionally, near-zero-index conditions can also be found in the interplanetary medium and in the atmosphere, where we provide a complementary explanation to the rare phenomenon of ball-lightning. PMID:26847877
NASA Astrophysics Data System (ADS)
Zayed, Elsayed M. E.; Al-Nowehy, Abdul-Ghani; Elshater, Mona E. M.
2017-06-01
The (G^'/G)-expansion method, the improved Sub-ODE method, the extended auxiliary equation method, the new mapping method and the Jacobi elliptic function method are applied in this paper for finding many new exact solutions including Jacobi elliptic solutions, solitary solutions, singular solitary solutions, trigonometric function solutions and other solutions to the nonlinear Schrödinger equation with fourth-order dispersion and dual power law nonlinearity whose balance number is not positive integer. The used methods present a wider applicability for handling the nonlinear partial differential equations. A comparison of our new results with the well-known results is made. Also, we compare our results with each other yielding from these five integration tools.
NASA Astrophysics Data System (ADS)
Artem'ev, V. A.; Nezvanov, A. Yu.; Nesvizhevsky, V. V.
2016-01-01
We discuss properties of the interaction of slow neutrons with nano-dispersed media and their application for neutron reflectors. In order to increase the accuracy of model simulation of the interaction of neutrons with nanopowders, we perform precise quantum mechanical calculation of potential scattering of neutrons on single nanoparticles using the method of phase functions. We compare results of precise calculations with those performed within first Born approximation for nanodiamonds with the radius of 2-5 nm and for neutron energies 3 × 10-7-10-3 eV. Born approximation overestimates the probability of scattering to large angles, while the accuracy of evaluation of integral characteristics (cross sections, albedo) is acceptable. Using Monte-Carlo method, we calculate albedo of neutrons from different layers of piled up diamond nanopowder.
Artem’ev, V. A.; Nezvanov, A. Yu.; Nesvizhevsky, V. V.
2016-01-15
We discuss properties of the interaction of slow neutrons with nano-dispersed media and their application for neutron reflectors. In order to increase the accuracy of model simulation of the interaction of neutrons with nanopowders, we perform precise quantum mechanical calculation of potential scattering of neutrons on single nanoparticles using the method of phase functions. We compare results of precise calculations with those performed within first Born approximation for nanodiamonds with the radius of 2–5 nm and for neutron energies 3 × 10{sup -7}–10{sup -3} eV. Born approximation overestimates the probability of scattering to large angles, while the accuracy of evaluation of integral characteristics (cross sections, albedo) is acceptable. Using Monte-Carlo method, we calculate albedo of neutrons from different layers of piled up diamond nanopowder.
Talukder, Muhammad Anisuzzaman; Menyuk, Curtis R
2010-03-15
We consider the impact of saturable nonlinearity and group velocity dispersion on self-induced transparency (SIT) modelocking of quantum cascade lasers (QCLs). We find that self-induced transparency modelocking in QCLs can be obtained in the presence of saturable nonlinearity if the saturable loss or gain is below a critical limit. The limit for the saturable loss is significantly more stringent than the limit for the saturable gain. Stable modelocked pulses are also obtained in the presence of both normal and anomalous group velocity dispersion when its magnitude is below a critical value. The stability limit for the saturable loss becomes less stringent when group velocity dispersion is simultaneously present. However, the stability limit for the saturable gain is not significantly affected. All these limits depend on the ratio of the SIT-induced gain and absorpt n to the linear loss. Realistic values for both the saturable nonlinearity and chromatic dispersion are within the range in which SIT modelocking is predicted to be stable.
Clobert, J.; Danchin, E.; Dhondt, A.A.; Nichols, J.D.
2001-01-01
The ability of species to migrate and disperse is a trait that has interested ecologists for many years. Now that so many species and ecosystems face major environmental threats from habitat fragmentation and global climate change, the ability of species to adapt to these changes by dispersing, migrating, or moving between patches of habitat can be crucial to ensuring their survival. This book provides a timely and wide-ranging overview of the study of dispersal and incorporates much of the latest research. The causes, mechanisms, and consequences of dispersal at the individual, population, species and community levels are considered. The potential of new techniques and models for studying dispersal, drawn from molecular biology and demography, is also explored. Perspectives and insights are offered from the fields of evolution, conservation biology and genetics. Throughout the book, theoretical approaches are combined with empirical data, and care has been taken to include examples from as wide a range of species as possible.
NASA Astrophysics Data System (ADS)
Larecki, Wieslaw; Banach, Zbigniew
2014-01-01
This paper analyzes the propagation of the waves of weak discontinuity in a phonon gas described by the four-moment maximum entropy phonon hydrodynamics involving a nonlinear isotropic phonon dispersion relation. For the considered hyperbolic equations of phonon gas hydrodynamics, the eigenvalue problem is analyzed and the condition of genuine nonlinearity is discussed. The speed of the wave front propagating into the region in thermal equilibrium is first determined in terms of the integral formula dependent on the phonon dispersion relation and subsequently explicitly calculated for the Dubey dispersion-relation model: |k|=ωc-1(1+bω2). The specification of the parameters c and b for sodium fluoride (NaF) and semimetallic bismuth (Bi) then makes it possible to compare the calculated dependence of the wave-front speed on the sample’s temperature with the empirical relations of Coleman and Newman (1988) describing for NaF and Bi the variation of the second-sound speed with temperature. It is demonstrated that the calculated temperature dependence of the wave-front speed resembles the empirical relation and that the parameters c and b obtained from fitting respectively the empirical relation and the original material parameters of Dubey (1973) are of the same order of magnitude, the difference being in the values of the numerical factors. It is also shown that the calculated temperature dependence is in good agreement with the predictions of Hardy and Jaswal’s theory (Hardy and Jaswal, 1971) on second-sound propagation. This suggests that the nonlinearity of a phonon dispersion relation should be taken into account in the theories aiming at the description of the wave-type phonon heat transport and that the Dubey nonlinear isotropic dispersion-relation model can be very useful for this purpose.
Trust-region based solver for nonlinear transport in heterogeneous porous media
NASA Astrophysics Data System (ADS)
Wang, Xiaochen; Tchelepi, Hamdi A.
2013-11-01
We describe a new nonlinear solver for immiscible two-phase transport in porous media, where viscous, buoyancy, and capillary forces are significant. The flux (fractional flow) function, F, is a nonlinear function of saturation and typically has inflection points and can be non-monotonic. The non-convexity and non-monotonicity of F are major sources of difficulty for nonlinear solvers of coupled multiphase flow and transport in natural porous media. We describe a modified Newton algorithm that employs trust regions of the flux function to guide the Newton iterations. The flux function is divided into saturation trust regions delineated by the inflection, unit-flux, and end points. The updates are performed such that two successive iterations cannot cross any trust-region boundary. If a crossing is detected, the saturation value is chopped back to the appropriate trust-region boundary. The proposed trust-region Newton solver, which is demonstrated across the parameter space of viscous, buoyancy and capillary effects, is a significant extension of the inflection-point strategy of Jenny et al. (JCP, 2009) [5] for viscous dominated flows. We analyze the discrete nonlinear transport equation obtained using finite-volume discretization with phase-based upstream weighting. Then, we prove convergence of the trust-region Newton method irrespective of the timestep size for single-cell problems. Numerical results across the full range of the parameter space of viscous, gravity and capillary forces indicate that our trust-region scheme is unconditionally convergent for 1D transport. That is, for a given choice of timestep size, the unique discrete solution is found independently of the initial guess. For problems dominated by buoyancy and capillarity, the trust-region Newton solver overcomes the often severe limits on timestep size associated with existing methods. To validate the effectiveness of the new nonlinear solver for large reservoir models with strong heterogeneity
On the existence of optical vortex solitons propagating in saturable nonlinear media
NASA Astrophysics Data System (ADS)
Medina, Luciano
2017-01-01
In this paper, an existence theory is established for ring-profiled optical vortex solitons. We consider such solitons in the context of an electromagnetic light wave propagating in a self-focusing nonlinear media and governed by a nonlinear Schrödinger type equation. A variational principle and constrained minimization approach is used to prove the existence of positive solutions for an undetermined wave propagation constant. We provide a series of explicit estimates related to the wave propagation constant, a prescribed energy flux, and vortex winding number. Further, on a Nehari manifold, the existence of positive solutions for a wide range of parameter values is proved. We also provide numerical analysis to illustrate the behavior of the soliton's amplitude and wave propagation constant with respect to a prescribed energy flux and vortex winding number.
Non-Linear Stability of an Electrified Plane Interface in Porous Media
NASA Astrophysics Data System (ADS)
El-Dib, Yusry O.; Moatimid, Galal M.
2004-03-01
The non-linear electrohydrodynamic stability of capillary-gravity waves on the interface between two semi-infinite dielectric fluids is investigated. The system is stressed by a vertical electric field in the presence of surface charges. The work examines a few representative porous media configurations. The analysis includes Rayleigh-Taylor and Kelvin-Helmholtz instabilities. The boundary - value problem leads to a non-linear equation governing the surface evolution. Taylor theory is adopted to expand this equation, in the light of multiple scales, in order to obtain a non-linear Schr¨odinger equation describing the behavior of the perturbed interface. The latter equation, representing the amplitude of the quasi-monochromatic traveling wave, is used to describe the stability criteria. These criteria are discussed both analytically and numerically. In order to identifiy regions of stability and instability, the electric field intensity is plotted versus the wave number. Through a linear stability approach it is found that Darcy's coefficients have a destabilizing influence, while in the non-linear scope these coefficients as well as the electric field intensity play a dual role on the stability.
Dispersion in porous media, continuous-time random walks, and percolation.
Sahimi, Muhammad
2012-01-01
A promising approach to the modeling of anomalous (non-Gaussian) dispersion in flow through heterogeneous porous media is the continuous-time random walk (CTRW) method. In such a formula on the waiting time distribution ψ(t) is usually assumed to be given by ψ(t)∼t-1-α, with α fitted to the experimental data. The exponent α is also related to the power-law growth of the mean-square displacement of the solute with the time t
Li, Ming; Zhang, Fan; Chen, Zhangyuan; Xu, Anshi
2008-12-22
We propose a diverse vestigial-sideband-filtering feed forward equalizer and decision feedback equalizer (DVSB-FFE-DFE), which is capable of compensating residual chromatic dispersion (CD) as well as mitigating fiber nonlinearity in on-off keying (OOK) systems. In DVSBFFE-DFE, the upper and the lower VSB filtered signals are jointly equalized with FFE followed by DFE. Simulation results show that in a 42.7 Gbit/s nonreturn-to-zero OOK system, DVSB-FFE-DFE can effectively mitigate the required optical signal-to-noise ratio penalty induced by residual CD and fiber nonlinearity.
NASA Astrophysics Data System (ADS)
Islam, Md. Ibadul; Khatun, Maksuda; Ahmed, Kawsar
2017-04-01
This paper presents dispersion tailoring of photonic crystal fibers creating artificial defect along one of the regular square axes. A finite element method (FEM) has been enforced for numerical investigation of several guiding properties of the PCF covering a broad wavelength range about 1340-1640 nm over the telecommunication windows. According to simulation, the proposed PCF has obtained a strictly single-mode fiber, which has an ultra-high negative dispersion of about -584.60 to -2337.60 ps/(nm-km) and also possible to cover the highest nonlinearity order of 131.91 W-1 km-1 under the operating wavelength. Moreover, the proposed PCF structure experimentally focuses on higher nonlinear coefficient, which successfully compensates the chromatic dispersion of standard single mode in entire band of interest and greatly applicable to the optical transmission system. Additionally, the single mode behavior of S-PCF is explicated by employing V parameter. In our dispersion sensitive analysis, this fiber is significantly more robust due to successfully achieve ultra-high negative dispersion, which gains more promiscuous compared to the prior best results.
NASA Astrophysics Data System (ADS)
Islam, Md. Ibadul; Khatun, Maksuda; Ahmed, Kawsar
2017-02-01
This paper presents dispersion tailoring of photonic crystal fibers creating artificial defect along one of the regular square axes. A finite element method (FEM) has been enforced for numerical investigation of several guiding properties of the PCF covering a broad wavelength range about 1340-1640 nm over the telecommunication windows. According to simulation, the proposed PCF has obtained a strictly single-mode fiber, which has an ultra-high negative dispersion of about -584.60 to -2337.60 ps/(nm-km) and also possible to cover the highest nonlinearity order of 131.91 W-1 km-1 under the operating wavelength. Moreover, the proposed PCF structure experimentally focuses on higher nonlinear coefficient, which successfully compensates the chromatic dispersion of standard single mode in entire band of interest and greatly applicable to the optical transmission system. Additionally, the single mode behavior of S-PCF is explicated by employing V parameter. In our dispersion sensitive analysis, this fiber is significantly more robust due to successfully achieve ultra-high negative dispersion, which gains more promiscuous compared to the prior best results.
Hybrid dispersive media with controllable wave propagation: A new take on smart materials
Bergamini, Andrea E.; Zündel, Manuel; Flores Parra, Edgar A.; Ermanni, Paolo; Delpero, Tommaso; Ruzzene, Massimo
2015-10-21
In this paper, we report on the wave transmission characteristics of a hybrid one dimensional (1D) medium. The hybrid characteristic is the result of the coupling between a 1D mechanical waveguide in the form of an elastic beam, supporting the propagation of transverse waves and a discrete electrical transmission line, consisting of a series of inductors connected to ground through capacitors. The capacitors correspond to a periodic array of piezoelectric patches that are bonded to the beam and that couple the two waveguides. The coupling leads to a hybrid medium that is characterized by a coincidence condition for the frequency/wavenumber value corresponding to the intersection of the branches of the two waveguides. In the frequency range centered at coincidence, the hybrid medium features strong attenuation of wave motion as a result of the energy transfer towards the electrical transmission line. This energy transfer, and the ensuing attenuation of wave motion, is alike the one obtained through internal resonating units of the kind commonly used in metamaterials. However, the distinct shape of the dispersion curves suggests how this energy transfer is not the result of a resonance and is therefore fundamentally different. This paper presents the numerical investigation of the wave propagation in the considered media, it illustrates experimental evidence of wave transmission characteristics and compares the performance of the considered configuration with that of internal resonating metamaterials. In addition, the ability to conveniently tune the dispersion properties of the electrical transmission line is exploited to adapt the periodicity of the domain and to investigate diatomic periodic configurations that are characterized by a richer dispersion spectrum and broader bandwidth of wave attenuation at coincidence. The medium consisting of mechanical, piezoelectric, and analog electronic elements can be easily interfaced to digital devices to offer a novel
Hybrid dispersive media with controllable wave propagation: A new take on smart materials
NASA Astrophysics Data System (ADS)
Bergamini, Andrea E.; Zündel, Manuel; Flores Parra, Edgar A.; Delpero, Tommaso; Ruzzene, Massimo; Ermanni, Paolo
2015-10-01
In this paper, we report on the wave transmission characteristics of a hybrid one dimensional (1D) medium. The hybrid characteristic is the result of the coupling between a 1D mechanical waveguide in the form of an elastic beam, supporting the propagation of transverse waves and a discrete electrical transmission line, consisting of a series of inductors connected to ground through capacitors. The capacitors correspond to a periodic array of piezoelectric patches that are bonded to the beam and that couple the two waveguides. The coupling leads to a hybrid medium that is characterized by a coincidence condition for the frequency/wavenumber value corresponding to the intersection of the branches of the two waveguides. In the frequency range centered at coincidence, the hybrid medium features strong attenuation of wave motion as a result of the energy transfer towards the electrical transmission line. This energy transfer, and the ensuing attenuation of wave motion, is alike the one obtained through internal resonating units of the kind commonly used in metamaterials. However, the distinct shape of the dispersion curves suggests how this energy transfer is not the result of a resonance and is therefore fundamentally different. This paper presents the numerical investigation of the wave propagation in the considered media, it illustrates experimental evidence of wave transmission characteristics and compares the performance of the considered configuration with that of internal resonating metamaterials. In addition, the ability to conveniently tune the dispersion properties of the electrical transmission line is exploited to adapt the periodicity of the domain and to investigate diatomic periodic configurations that are characterized by a richer dispersion spectrum and broader bandwidth of wave attenuation at coincidence. The medium consisting of mechanical, piezoelectric, and analog electronic elements can be easily interfaced to digital devices to offer a novel
Bright solitons in defocusing media with spatial modulation of the quintic nonlinearity
NASA Astrophysics Data System (ADS)
Zeng, Jianhua; Malomed, Boris A.
2012-09-01
It has been recently demonstrated that self-defocusing (SDF) media with cubic nonlinearity, whose local coefficient grows from the center to the periphery fast enough, support stable bright solitons without the use of any linear potential. Our objective is to test the genericity of this mechanism for other nonlinearities, by applying it to one- and two-dimensional (1D and 2D) quintic SDF media. The models may be implemented in optics (in particular, in colloidal suspensions of nanoparticles), and the 1D model may be applied to the description of the Tonks-Girardeau gas of ultracold bosons. In 1D, the nonlinearity-modulation function is taken as g0+sinh2βx. This model admits a subfamily of exact solutions for fundamental solitons. Generic soliton solutions are constructed in a numerical form and also by means of the Thomas-Fermi and variational approximations (TFA and VA). In particular, a new ansatz for the VA is proposed, in the form of “raised sech,” which provides for an essentially better accuracy than the usual Gaussian ansatz. The stability of all the fundamental (nodeless) 1D solitons is established through the computation of the corresponding eigenvalues for small perturbations and also verified by direct simulations. Higher-order 1D solitons with two nodes have a limited stability region, all the modes with more than two nodes being unstable. It is concluded that the recently proposed inverted Vakhitov-Kolokolov stability criterion for fundamental bright solitons in systems with SDF nonlinearities holds here too. Particular exact solutions for 2D solitons are produced as well.
MeDiA: Mean Distance Association and Its Applications in Nonlinear Gene Set Analysis.
Peng, Hesen; Ma, Junjie; Bai, Yun; Lu, Jianwei; Yu, Tianwei
2015-01-01
Probabilistic association discovery aims at identifying the association between random vectors, regardless of number of variables involved or linear/nonlinear functional forms. Recently, applications in high-dimensional data have generated rising interest in probabilistic association discovery. We developed a framework based on functions on the observation graph, named MeDiA (Mean Distance Association). We generalize its property to a group of functions on the observation graph. The group of functions encapsulates major existing methods in association discovery, e.g. mutual information and Brownian Covariance, and can be expanded to more complicated forms. We conducted numerical comparison of the statistical power of related methods under multiple scenarios. We further demonstrated the application of MeDiA as a method of gene set analysis that captures a broader range of responses than traditional gene set analysis methods.
Ziółkowski, Andrzej
2014-12-15
Nonlinear light propagation in photorefractive media can be analyzed by numerical methods. The presented numerical approach has regard to the effects of time nonlocality. Two algorithms are presented, and compared in terms of physical results and computing times. The possibility to address the issue of time nonlocality in two ways is attributed to the fact that, it is possible to completely separate carrier dynamics evaluation and wave equation calculation. This in turn, allows to choose a short integration time for carrier dynamics and a longer one to solve the wave equation. The tests of the methods were carried out for a one-carrier model that describes most of photorefractive media, and for a model with bipolar transport and hot electron effect, used in descriptions of semiconductor materials.
Nonlinearity-mediated soliton ejection from trapping potentials in nonlocal media
Ye Fangwei; Kartashov, Yaroslav V.; Torner, Lluis; Hu Bambi
2010-08-15
We address the properties of optical solitons in thermal nonlinear media with a local refractive index defect that is capable of trapping solitons launched close to the sample boundary despite the boundary-mediated forces that tend to deflect all beams toward the center of the sample. We show that while such forces become more pronounced with an increasing of the input beam power the defect can trap only light below a critical power above which solitons are ejected. The dynamics of soliton ejection and the subsequent propagation may be controlled.
Spiraling elliptic Hermite-Gaussian solitons in nonlocal nonlinear media without anisotropy.
Liang, Guo; Dai, Zhiping
2017-06-12
We introduce a kind of the spiraling elliptic Hermite-Gaussian solitons in nonlocal nonlinear media without anisotropy, which carries the orbital angular momentum and can rotate in the transverse. The n-th mode of the spiraling elliptic Hermite-Gaussian solitons has n holes nested in the elliptic profile. The analytical spiraling elliptic Hermite-Gaussian solitons solutions are obtained based on the variational approach, which agree well with the numerical simulations. It is found that the critical power and the critical angular velocity for the spiraling elliptic Hermite-Gaussian solitons are the same as the counterpart of the ground mode.
2007-09-01
dispersive media, electromagnetic Debye model [23] of orientational polarization phenomena [24] transient propagation , ultrawideband radar . and the Rocard...airframes), the remote detection of buried structures (such as landmines and lED’s), ionospheric pulse propagation (for remote sensing from an orbiting... ionospheric pulse propagation (for remote sensing from an orbiting satellite), as well as the problem of ultrawideband electromagnetic pulse exposure
NASA Astrophysics Data System (ADS)
Lee, C. T.; Lee, C. C.
2015-04-01
This paper introduces a systematic approach to investigate a higher order nonlinear dispersive wave equation for modeling different wave modes. We present both the conventional KdV-type soliton and anomaly type solitons for the equation. We also show the conservation laws and Hamiltonian structures for the equation. Our results suggest that the underlying equation has more interacting soliton phenomena than one would have known for the classical KdV and Boussinesq equation.
NASA Astrophysics Data System (ADS)
Baskonus, Haci Mehmet; Bulut, Hasan
2015-10-01
In this study, we have studied to obtain some new analytical solutions to the (1 + 1)-dimensional nonlinear Dispersive Modified Benjamin-Bona-Mahony equation by using modified exp-function method. We have submitted the general structure of modified exp-function method. We have founded some new analytical solutions such as hyperbolic and rational function solutions. Afterward, we have plotted 2D and 3D surfaces of analytical solutions obtained in this study by using computer programming wolfram Mathematica 9.
Chow, K K; Shu, C; Lin, Chinlon; Bjarklev, A
2005-10-31
We demonstrate extinction ratio improvement by using pump-modulated four-wave mixing in a dispersion-flattened nonlinear photonic crystal fiber. A 6-dB improvement in the extinction ratio of a degraded return-to-zero signal has been achieved. A power penalty improvement of 3 dB at 10(-9) bit-error-rate level is obtained in the 10 Gb/s bit-error-rate measurements.
NASA Astrophysics Data System (ADS)
Sun, Y. W.; Liu, C.; Chan, K. L.; Xie, P. H.; Liu, W. Q.; Zeng, Y.; Wang, S. M.; Huang, S. H.; Chen, J.; Wang, Y. P.; Si, F. Q.
2013-08-01
In this paper, we present an optimized analysis algorithm for non-dispersive infrared (NDIR) to in situ monitor stack emissions. The proposed algorithm simultaneously compensates for nonlinear absorption and cross interference among different gases. We present a mathematical derivation for the measurement error caused by variations in interference coefficients when nonlinear absorption occurs. The proposed algorithm is derived from a classical one and uses interference functions to quantify cross interference. The interference functions vary proportionally with the nonlinear absorption. Thus, interference coefficients among different gases can be modeled by the interference functions whether gases are characterized by linear or nonlinear absorption. In this study, the simultaneous analysis of two components (CO2 and CO) serves as an example for the validation of the proposed algorithm. The interference functions in this case can be obtained by least-squares fitting with third-order polynomials. Experiments show that the results of cross interference correction are improved significantly by utilizing the fitted interference functions when nonlinear absorptions occur. The dynamic measurement ranges of CO2 and CO are improved by about a factor of 1.8 and 3.5, respectively. A commercial analyzer with high accuracy was used to validate the CO and CO2 measurements derived from the NDIR analyzer prototype in which the new algorithm was embedded. The comparison of the two analyzers show that the prototype works well both within the linear and nonlinear ranges.
Alpatova, Alla L; Shan, Wenqian; Babica, Pavel; Upham, Brad L; Rogensues, Adam R; Masten, Susan J; Drown, Edward; Mohanty, Amar K; Alocilja, Evangelyn C; Tarabara, Volodymyr V
2010-01-01
As the range of applications for carbon nanotubes (CNTs) rapidly expands, understanding the effect of CNTs on prokaryotic and eukaryotic cell systems has become an important research priority, especially in light of recent reports of the facile dispersion of CNTs in a variety of aqueous systems including natural water. In this study, single-walled carbon nanotubes (SWCNTs) were dispersed in water using a range of natural (gum arabic, amylose, Suwannee River natural organic matter) and synthetic (polyvinyl pyrrolidone, Triton X-100) dispersing agents (dispersants) that attach to the CNT surface non-covalently via different physiosorption mechanisms. The charge and the average effective hydrodynamic diameter of suspended SWCNTs as well as the concentration of exfoliated SWCNTs in the dispersion were found to remain relatively stable over a period of 4 weeks. The cytotoxicity of suspended SWCNTs was assessed as a function of dispersant type and exposure time (up to 48 h) using general viability bioassay with Escherichia coli and using neutral red dye uptake (NDU) bioassay with WB-F344 rat liver epithelia cells. In the E. coli viability bioassays, three types of growth media with different organic loadings and salt contents were evaluated. When the dispersant itself was non-toxic, no losses of E. coli and WB-F344 viability were observed. The cell viability was affected only by SWCNTs dispersed using Triton X-100, which was cytotoxic in SWCNT-free (control) solution. The epigenetic toxicity of dispersed CNTs was evaluated using gap junction intercellular communication (GJIC) bioassay applied to WB-F344 rat liver epithelial cells. With all SWCNT suspensions except those where SWCNTs were dispersed using Triton X-100 (wherein GJIC could not be measured because the sample was cytotoxic), no inhibition of GJIC in the presence of SWCNTs was observed. These results suggest a strong dependence of the toxicity of SWCNT suspensions on the toxicity of the dispersant and point to
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.
Makarov, Vladimir A; Petnikova, V M; Potravkin, N N; Shuvalov, Vladimir V
2012-12-31
It is found that chirped elliptically polarised cnoidal waves can propagate and aperiodic regimes, resembling polarisation chaos, can emerge in an isotropic medium with local and nonlocal components of cubic nonlinearity and second-order frequency dispersion. In the particular case of the formation of the waveguides of the same profile for two circularly polarised components of the light field relevant analytical solutions are derived and the frequencies of chirped components are shown to vary in concord with periodic changes of their intensities. In this case, the nature of the changes in the polarisation state during the light wave propagation depends on the values of nonlinear phase shifts of circularly polarised components of the field during the period and is sensitive to changes in the initial conditions. (nonlinear optical phenomena)
Bi, Chong-hao; Li, Dong; Wang, Li-jun; Wang, Yong; Adhikari, Benu
2013-02-15
The effect of flaxseed gum (FG) on the rheological and nonlinear stress response behaviors of mixed soy protein isolate (SPI)-flaxseed gum (FG) dispersions were studied. Results showed that the viscosity of the SPI-FG mixed dispersions increased significantly with increase in the FG concentration. Both the shear stress and the apparent viscosity values as a function of shear rate were fitted well using Power law model as expected. The frequency dependence of G', G'' and tanδ of soy protein isolate decreased as the FG concentration increased. The large amplitude oscillatory shear (LAOS) test and Fourier transform (FT) rheology analysis showed that the addition of flaxseed gum strongly affected the structure of the SPI-FG mixed dispersion system as shown by deformation of the nonlinear stress response curve and significantly altered magnitude of higher harmonic curve. The addition of FG increased the instantaneous strain softening effect of the SPI-FG mixed dispersion system. Copyright © 2012 Elsevier Ltd. All rights reserved.
NASA Astrophysics Data System (ADS)
Fu, Libi; Song, Weiguo; Lo, Siuming
2017-01-01
Emergencies involved in mass events are related to a variety of factors and processes. An important factor is the transmission of information on danger that has an influence on nonlinear crowd dynamics during the process of crowd dispersion. Due to much uncertainty in this process, there is an urgent need to propose a method to investigate the influence. In this paper, a novel fuzzy-theory-based method is presented to study crowd dynamics under the influence of information transmission. Fuzzy functions and rules are designed for the ambiguous description of human states. Reasonable inference is employed to decide the output values of decision making such as pedestrian movement speed and directions. Through simulation under four-way pedestrian situations, good crowd dispersion phenomena are achieved. Simulation results under different conditions demonstrate that information transmission cannot always induce successful crowd dispersion in all situations. This depends on whether decision strategies in response to information on danger are unified and effective, especially in dense crowds. Results also suggest that an increase in drift strength at low density and the percentage of pedestrians, who choose one of the furthest unoccupied Von Neumann neighbors from the dangerous source as the drift direction at high density, is helpful in crowd dispersion. Compared with previous work, our comprehensive study improves an in-depth understanding of nonlinear crowd dynamics under the effect of information on danger.
Simulating dispersion in porous media and the influence of segmentation on stagnancy in carbonates
NASA Astrophysics Data System (ADS)
Gray, F.; Cen, J.; Shah, S. M.; Crawshaw, J. P.; Boek, E. S.
2016-11-01
Understanding the transport of chemical components in porous media is fundamentally important to many reservoir processes such as contaminant transport and reactive flows involved in CO2 sequestration. Carbonate rocks in particular present difficulties for pore-scale simulations because they contain large amounts of sub-micron porosity. In this work, we introduce a new hybrid simulation model to calculate hydrodynamic dispersion in pore-scale images of real porous media and use this to elucidate the origins and behaviour of stagnant zones arising in transport simulations using micro-CT images of carbonates. For this purpose a stochastic particle model for simulating the transport of a solute is coupled to a Lattice-Boltzmann algorithm to calculate the flow field. The particle method incorporates second order spatial and temporal resolution to resolve finer features of the domain. We demonstrate how dispersion coefficients can be accurately obtained in capillaries, where corresponding analytical solutions are available, even when these are resolved to just a few lattice units. Then we compute molecular displacement distributions for pore-spaces of varying complexity: a pack of beads; a Bentheimer sandstone; and a Portland carbonate. Our calculated propagator distributions are compared directly with recent experimental PFG-NMR propagator distributions (Scheven et al., 2005; Mitchell et al., 2008), the latter excluding spin relaxation mechanisms. We observe that the calculated transport propagators can be quantitatively compared with the experimental distribution, provided that spin relaxations in the experiment are excluded, and good agreement is found for both the sandstone and the carbonate. However, due to the absence of explicit micro-porosity from the carbonate pore space image used for flow field simulations we note that there are fundamental differences in the physical origins of the stagnant zones for micro-porous rocks between simulation and experiment. We
NASA Astrophysics Data System (ADS)
Chrysikopoulos, Constantinos V.; Manariotis, Ioannis D.; Syngouna, Vasiliki I.
2014-05-01
Accurate prediction of colloid and biocolloid transport in porous media relies heavily on usage of suitable dispersion coefficients. The widespread procedure for dispersion coefficient determination consists of conducting conservative tracer experiments and subsequently fitting the collected breakthrough data with a selected advection-dispersion transport model. The fitted dispersion coefficient is assumed to characterize the porous medium and is often used thereafter to analyze experimental results obtained from the same porous medium with other solutes, colloids, and biocolloids. The classical advection-dispersion equation implies that Fick's first law of diffusion adequately describes the dispersion process, or that the dispersive flux is proportional to the concentration gradient. Therefore, the above-described procedure inherently assumes that the dispersive flux of all solutes, colloids and biocolloids under the same flow field conditions is exactly the same. Furthermore, the available mathematical models for colloid and biocoloid transport in porous media do not adequately account for gravity effects. Here an extensive laboratory study was undertaken in order to assess whether the dispersivity, which traditionally has been considered to be a property of the porous medium, is dependent on colloid particle size, interstitial velocity and length scale. The breakthrough curves were successfully simulated with a mathematical model describing colloid and biocolloid transport in homogeneous, water saturated porous media. The results demonstrated that the dispersivity increases very slowly with increasing interstitial velocity, and increases with column length. Furthermore, contrary to earlier results, which were based either on just a few experimental observations or experimental conditions leading to low mass recoveries, dispersivity was positively correlated with colloid particle size. Also, transport experiments were performed with biocolloids (bacteriophages:
NASA Astrophysics Data System (ADS)
Yankovskii, A. P.
2015-03-01
On the basis of an algorithm of time steps, a method to simulate the creep is developed for rib-reinforced composite media made of nonlinear hereditary phase materials whose behavior is described by the Rabotnov theory. The technique proposed allows one, at discrete moments of time, to consider such a composition as nonlinear elastic with the initial stress state. The use of an iterative process of the type of the method of variable elasticity parameters allowed us to linearize the governing relationships and to reduce the problem of calculation of creep of the composite media at discrete points in time to a series of linear elastic problems of the mechanics of composites.
NASA Astrophysics Data System (ADS)
Porras, Miguel A.; Ruiz-Jiménez, Carlos; Carvalho, Márcio
2017-04-01
We report on the stationary and robust propagation of light beams with rather arbitrary and controllable intensity and dissipation transverse patterns in self-focusing Kerr media with nonlinear absorption. When nonlinear absorption is due to multiphoton ionization at high beam powers in transparent media such as glasses and air, these beams can generate multiple plasma channels with tailored geometries. Their nature and spatial characteristics are discussed in detail, as well as the laws determining their spontaneous formation from coherent superpositions of Bessel beams of different amplitudes and topological charges.
NASA Astrophysics Data System (ADS)
Sun, Y.-W.; Liu, C.; Chan, K.-L.; Xie, P.-H.; Liu, W.-Q.; Zeng, Y.; Wang, S.-M.; Huang, S.-H.; Chen, J.; Wang, Y.-P.; Si, F.-Q.
2013-02-01
In this paper, we present an optimized analysis algorithm for non-dispersive infrared (NDIR) to monitor stack emissions. The newly developed analysis algorithm simultaneously compensates for nonlinear absorption and cross-interference between different gases. We present a mathematical derivation for the measurement error caused by variations in interference coefficients when nonlinear absorption occurs. The optimized algorithm is derived from a classical one and uses interference functions to quantify cross-interference. The interference functions vary proportionally with the nonlinear absorption. Thus, interference coefficients among different gases can be modeled by the interference functions whether gases are characterized by linear or nonlinear absorption. In this study, the simultaneous analysis of two components (CO2 and CO) serves as an example for the validation of the optimized algorithm. The interference functions in this case can be obtained by least-squares fitting with three-order polynomials. Experiments show that the results of cross-interference correction are improved significantly by utilizing fitted interference functions when nonlinear absorptions occur. The dynamic measurement ranges of CO2 and CO are improved by about a factor of 1.8 and 3.5, respectively. A commercial NDIR multi-gas analyzer with high accuracy was used to validate the CO and CO2 measurements derived from the NDIR analyzer prototype in which the new cross-interference correction algorithm was embedded. Both measurements well agreed.
Coupling micro-CT with computer simulations to analyze dispersion in porous media
NASA Astrophysics Data System (ADS)
Sobhani, Sadaf; Dunnmon, Jared; Werer, Michael
2015-11-01
In recent years, table-top X-ray Computed Tomography (XCT) systems have been utilized to analyze various samples with a resolution on the order of 1 μm -100 μm . In this study, we explore the use of these systems both in extracting high-resolution topologies of porous structures for use as inputs into computational simulations and in directly characterizing gas dispersion within such structures using fluoroscopic imaging of dense gaseous tracers. The opaque-solid environment and small pore-scale effects in porous media restrict the use of conventional imaging techniques, thereby making XCT a potentially useful diagnostic technique for understanding internal flows in porous and optically inaccessible structures. In the present work, we extract the topology of various reticulated porous foams from 3D XCT data and perform numerical simulations of the flow inside these structures. Permeability and tortuosity, which are key parameters in volume-averaged models are evaluated from the resulting flow fields and knowledge of the solid structure.
NASA Astrophysics Data System (ADS)
Zimmerling, Jörn; Wei, Lei; Urbach, Paul; Remis, Rob
2016-06-01
In this paper we present a Krylov subspace model-order reduction technique for time- and frequency-domain electromagnetic wave fields in linear dispersive media. Starting point is a self-consistent first-order form of Maxwell's equations and the constitutive relation. This form is discretized on a standard staggered Yee grid, while the extension to infinity is modeled via a recently developed global complex scaling method. By applying this scaling method, the time- or frequency-domain electromagnetic wave field can be computed via a so-called stability-corrected wave function. Since this function cannot be computed directly due to the large order of the discretized Maxwell system matrix, Krylov subspace reduced-order models are constructed that approximate this wave function. We show that the system matrix exhibits a particular physics-based symmetry relation that allows us to efficiently construct the time- and frequency-domain reduced-order models via a Lanczos-type reduction algorithm. The frequency-domain models allow for frequency sweeps meaning that a single model provides field approximations for all frequencies of interest and dominant field modes can easily be determined as well. Numerical experiments for two- and three-dimensional configurations illustrate the performance of the proposed reduction method.
NASA Astrophysics Data System (ADS)
Jiménez-Martínez, Joaquín.; Le Borgne, Tanguy; Tabuteau, Hervé; Méheust, Yves
2017-02-01
The dynamics of solute dispersion and mixing in unsaturated flows is analyzed from photobleaching experiments in two-dimensional porous micromodels. This technique allows producing pulse line (delta-Dirac) injections of a conservative tracer by bleaching a finite volume of fluorescent without disturbing the flow field. The temporal evolution of the concentration field and the spatial distribution of the air and water phases can be monitored at pore scale. We study the dispersion and mixing of a line of tracer under different water saturations. While dispersion in saturated porous media follows an approximately Fickian scaling, a shift to ballistic scaling is observed as soon as saturation is lowered. Hence, at the time scale of observation, dispersion in our unsaturated flows is dominated by the ballistic separation of tracer blobs within the water phase, between trapped clusters and preferential flow paths. While diffusion plays a minor role in the longitudinal dispersion during the time scale of the experiments, its interplay with fluid deformation is apparent in the dynamics of mixing. The scalar dissipation rates show an initial stretching regime, during which mixing is enhanced by fluid deformation, followed by a dissipation regime, during which diffusion overcomes compression induced by stretching. The transition between these two regimes occurs at the mixing time, when concentration gradients are maximum. We propose a predictive analytical model, based on shear-enhanced diffusion, that captures the dynamics of mixing from basic unsaturated porous media parameters, suggesting that this type of model may be a useful framework at larger scales.
Coupled periodic waves with opposite dispersions in a nonlinear optical fiber
NASA Astrophysics Data System (ADS)
Tsang, S. C.; Nakkeeran, K.; Malomed, Boris A.; Chow, K. W.
2005-05-01
Using the Hirota's method and elliptic θ-functions, we obtain three families of exact periodic (cnoidal) wave solutions for two nonlinear Schrödinger (NLS) equations coupled by XPM (cross-phase-modulation) terms, with a ratio σ of the XPM and SPM (self-phase-modulation) coefficients. Unlike the previous works, we obtain the solutions for the case when the coefficients of the group-velocity-dispersion (GVD) in the coupled equations have opposite signs. In the limit of the infinite period, the solutions with σ > 1 carry over into inverted bound states of bright and dark solitons in the normal- and anomalous-GVD modes (known as "symbiotic solitons"), while the infinite-period solution with σ < 1 is an uninverted bound state (also an unstable one). The case of σ = 2 is of direct interest to fiber-optic telecommunications, as it corresponds to a scheme with a pulse stream in an anomalous-GVD payload channel stabilized by a concomitant strong periodic signal in a mate normal-GVD channel. The case of arbitrary σ may be implemented in a dual-core waveguide. To understand the stability of the coupled waves, we first analytically explore the modulational stability of CW (constant-amplitude) solutions, concluding that they may be completely stable for σ ⩾ 1, provided that the absolute value of the GVD coefficient is smaller in the anomalous-GVD mode than in the normal-GVD one, and certain auxiliary conditions on the amplitudes are met. The stability of the exact cnoidal-wave solutions is tested in direct simulations. We infer that, while, strictly speaking, in the practically significant case of σ = 2 all the solutions are unstable, in many cases the instability may be strongly attenuated, rendering the above-mentioned paired channels scheme usable. In particular, the instability is milder for a smaller period of the wave pattern, and/or if the anomalous GVD is weaker than the normal GVD in the mate channel. When the instability sets in, it first initiates quasi
Essama, Bedel Giscard Onana; Atangana, Jacques; Frederick, Biya Motto; Mokhtari, Bouchra; Eddeqaqi, Noureddine Cherkaoui; Kofane, Timoleon Crepin
2014-09-01
We investigate the behavior of the electromagnetic wave that propagates in a metamaterial for negative index regime. Second-order dispersion and cubic-quintic nonlinearities are taken into account. The behavior obtained for negative index regime is compared to that observed for absorption regime. The collective coordinates technique is used to characterize the light pulse intensity profile at some frequency ranges. Five frequency ranges have been pointed out. The perfect combination of second-order dispersion and cubic nonlinearity leads to a robust soliton at each frequency range for negative index regime. The soliton peak power progressively decreases for absorption regime. Further, this peak power also decreases with frequency. We show that absorption regime can induce rogue wave trains generation at a specific frequency range. However, this rogue wave trains generation is maintained when the quintic nonlinearity comes into play for negative index regime and amplified for absorption regime at a specific frequency range. It clearly appears that rogue wave behavior strongly depends on the frequency and the regime considered. Furthermore, the stability conditions of the electromagnetic wave have also been discussed at frequency ranges considered for both negative index and absorption regimes.
NASA Astrophysics Data System (ADS)
Rasmussen, K. Ø.; Christiansen, P. L.; Johansson, M.; Gaididei, Yu. B.; Mingaleev, S. F.
1998-03-01
A one-dimensional discrete nonlinear Schrödinger (DNLS) model with the power dependence, r- s on the distance r, of dispersive interactions is proposed. The stationary states of the system are studied both analytically and numerically. Two kinds of trial functions, exp-like and sech-like are exploited and the results of both approaches are compared. Both on-site and inter-site stationary states are investigated. It is shown that for s sufficiently large all features of the model are qualitatively the same as in the DNLS model with nearest-neighbor interaction. For s less than some critical value, scr, there is an interval of bistability where two stable stationary states exist at each excitation number. The bistability of on-site solitons may occur for dipole-dipole dispersive interaction ( s = 3), while scr for inter-site solitions is close to 2.1. In the framework of the DNLS equation with nearest-neighbor coupling we discuss the stability of highly localized, “breather-like”, excitations under the influence of thermal fluctuations. Numerical analysis shows that the lifetime of the breather is always finite and in a large parameter region inversely proportional to the noise variance for fixed damping and nonlinearity. We also find that the decay rate of the breather decreases with increasing nonlinearity and with increasing damping.
Prakash, Deo; Shaaban, E.R.; Shapaan, M.; Mohamed, S.H.; Othman, A.A.; Verma, K.D.
2016-08-15
Highlights: • Combined experimental and theoretical researches on ZnSe Thin Films. • The film thickness and refractive index were determined using envelope method. • The absorption coefficient and the energy gap were calculated. • Dispersion parameters were determined using Wemple-DiDomenico relation. • The third order susceptibility and nonlinear refractive index were calculated. - Abstract: Zinc selenide (ZnSe) thin films with different thicknesses were evaporated onto glass substrates using the thermal evaporation technique. X-ray diffraction analysis confirmed that both the film and powder have cubic zinc-blende structure. The fundamental optical parameters like absorption coefficient, extinction coefficient and band gap were evaluated in transparent region of transmittance and reflectance spectrum. The optical transition of the films was found to be allowed, where the energy gap increased from 2.576 to 2.702 eV with increasing film thickness. Also, the refractive index value increase with increasing film thickness. The refractive indices evaluated through envelope method were extrapolated by Cauchy dispersion relationship over the whole spectra range. Additionally, the dispersion of refractive index was determined in terms of Wemple-DiDomenico single oscillator model. Third order susceptibility and nonlinear refractive index were determined for different thickness of ZnSe thin films.
NASA Astrophysics Data System (ADS)
Wang, Wei; Hou, Lan-Tian; Lu, Ming; Zhou, Gui-Yao
2009-11-01
We present a design of double cladding nearly zero dispersion flattened nonlinear photonic crystal fiber (PCF) with the core consisting of seven missing holes. The dispersion of the designed PCF fluctuates from -0.28 to 0.29 ps·km-1·nm-1 in the range of 1.35-1.795μm and the dispersion slope is -0.0038 ps·km-1·nm-2 at 1.55 μm. Due to its small air-hole to air-hole pitch in the inner cladding, the effective mode area is 6.48μm2 and the effective nonlinearity γ is as high as 13.78 W-1 km-1 at 1.55 μm. Two layers of air-hole rings in the outer cladding ensures the loss of the fundamental mode to be 2.9dB/km at 1.55 μm and two more air-hole rings can further reduce the fundamental mode's loss to the level of 4.2 × 10-3 dB/km.
Popov, A.K.; Myslivets, S.A.; George, Thomas F.
2005-04-01
Specific features of nonlinear interference processes at quantum transitions in near- and fully resonant Doppler-broadened optically dense media are studied. The possibility of all-optical switching of the medium to opaque or, alternatively, to absolutely transparent, or even to strongly amplifying states is explored, which is controlled by a small variation of two driving or probe radiations and does not require any change of the level populations. Optimum conditions for inversionless amplification of short-wavelength radiation above the oscillation threshold at the expense of the longer-wavelength control fields are investigated. The feasibility of overcoming the fundamental limitation on a velocity-interval of resonantly coupled molecules imposed by the Doppler effect is shown, based on quantum coherence.
A 2D spring model for the simulation of ultrasonic wave propagation in nonlinear hysteretic media.
Delsanto, P P; Gliozzi, A S; Hirsekorn, M; Nobili, M
2006-07-01
A two-dimensional (2D) approach to the simulation of ultrasonic wave propagation in nonclassical nonlinear (NCNL) media is presented. The approach represents the extension to 2D of a previously proposed one dimensional (1D) Spring Model, with the inclusion of a PM space treatment of the intersticial regions between grains. The extension to 2D is of great practical relevance for its potential applications in the field of quantitative nondestructive evaluation and material characterization, but it is also useful, from a theoretical point of view, to gain a better insight of the interaction mechanisms involved. The model is tested by means of virtual 2D experiments. The expected NCNL behaviors are qualitatively well reproduced.
Hermite-Gaussian stationary solutions in strongly nonlocal nonlinear optical media
NASA Astrophysics Data System (ADS)
Zhong, Lanhua; Yang, Jing; Ren, Zhanmei; Guo, Qi
2017-01-01
Approximate analytical stationary solutions (SSs) of a cluster of Hermite-Gaussian (HG) shape is obtained in strongly nonlocal nonlinear media by the variational approach. The evolution of the HG SSs shows that when the order n ⩽ 3, they propagate stably and form solitons; otherwise, when n ⩾ 4, they always propagate unstably and evolve into self-trapped speckle-like beams. However, all these SSs maintain nearly invariant statistic beam-width during their propagation. Furthermore, when the input power deviates from the so-called critical power, the unstable HG beam will adjust its beam-width to form a new self-trapped beam, unlike the soliton which will turn to be a breather. But the average beam-widths are independent of the stability of the propagation of the HG SSs.
Optical solitons in resonant and nonresonant nonlinear media in the presence of perturbations.
Piscureanu, M; Manaila-Maximean, D
2000-01-01
We studied the optical solitons in nonlinear resonant and nonresonant media in the presence of perturbations, assuming that the transient effects are stimulated by the light scanning beam. We treated a slight deviation from the exact necessary condition for the soliton existence (2betanu=1), as a small perturbation for the integrable system, studying its influence upon the soliton propagation conditions. The approximation is constructed by the help of an algebraic version of the soliton perturbation theory using a Riemann boundary problem in connection with the inverse scattering method. We have obtained the soliton equation and we have solved it in the presence of a small perturbation in the adiabatic approximation. In this case we have demonstrated that for a Lorentz profile line the amplitude of the soliton remains unchanged, the only effect of the perturbation results in a phase shift.
NASA Astrophysics Data System (ADS)
Kujawska, T.; Wójcik, J.; Nowicki, A.
Knowledge of the acoustic nonlinearity parameter, B/A, of biological fluids or soft tissues is necessary whenever high intensity pressure fields are induced. A numerical model recently developed in our lab is capable of fast predicting the nonlinear distortion of pulsed finite-amplitude acoustic waves generated from axisymmetric sources propagating through multilayer attenuating media. Quantitative analysis of the obtained results enabled developing the alternative method for determination of the B/A of biological media. First, the method involves measuring the nonlinear waveform distortion of the tone burst propagating through water. Then, it involves numerical modeling (in frequency domain) using the Time-Averaged Wave Envelope (TAWE) approach. The numerical simulation results are fitted to the experimental data by adjusting the source boundary conditions to determine accurately the source pressure, effective radius and apodization function being the input parameters to the numerical solver. Next, the method involves measuring the nonlinear distortion of idem tone burst passing through the two-layer system of parallel media. Then, we numerically model nonlinear distortion in two-layer system of media in frequency domain under experimental boundary conditions. The numerical simulation results are fitted to the experimental data by adjusting the B/A value of the tested material. Values of the B/A for 1.3-butanediol at both the ambient (25°C) and physiological (36.6°C) temperatures were determined. The obtained result (B/A = 10.5 ± 5% at 25°C) is in a good agreement with that available in literature. The B/A = 11.5 ± 5% at 36.6°C was determined.
Liang, Heng
2007-09-01
The matrix forms of local Lagrangian approach (LLA) are developed based on Lagrangian description for single-component in nonlinear, non-ideal chromatography. A local thermodynamic path (LTP) is designed based on essential physical principles, such as the Lagrangian description, the local equilibrium assumption and the thermodynamic state functions. With the LTP, the iteration equations of fully thermodynamic states on time sequence in the matrix forms are obtained with the Markov character. And the convergence, compatibility and stability of the LLA based on the LTP are discussed with some theoretical analysis and numerical experiments, and the stability condition of the LLA is given. The algorithm of the LLA in the vector form is shown as the computer program to simulate the elution profiles affected by a few of factors, space-distribution, axial diffusions, injection samples, etc. According to the LLA, the corresponding relationships are established between the trajectories of discrete time state and discrete time control vectors in the ergodic space. And a compendium algorithm of multistage decision problems concerning the optimal control of nonlinear, non-idea chromatography is given with Bellman's dynamic programming to find the optimal trajectories of state vector and control vector. The matrix forms of the LLA remove the gap between preparative chromatography theories and Markov decision processes or optimal control approaches based on discrete time states.
NASA Astrophysics Data System (ADS)
Hoefer, Mark A.
This thesis examines nonlinear wave phenomena, in two physical systems: a Bose-Einstein condensate (BEC) and thin film ferromagnets where the magnetization dynamics are excited by the spin momentum transfer (SMT) effect. In the first system, shock waves generated by steep gradients in the BEC wavefunction are shown to be of the disperse type. Asymptotic and averaging methods are used to determine shock speeds and structure in one spatial dimension. These results are compared with multidimensional numerical simulations and experiment showing good, qualitative agreement. In the second system, a model of magnetization dynamics due to SMT is presented. Using this model, nonlinear oscillating modes---nano-oscillators---are found numerically and analytically using perturbative methods. These results compare well with experiment. A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, e.g. traveling fronts with steep gradients. However, the governing Gross-Pitaevskii (GP) equation that describes the mean field of a BEC admits no dissipation hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave (DSW). Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical 1D dissipative and dispersive shock problem shows significant differences in shock structure and shock front speed. Numerical results associated with laboratory experiments show that three and two-dimensional approximations are in excellent agreement and one dimensional approximations are in qualitative agreement. The interaction of two DSWs is investigated analytically and numerically. Using one dimensional DSW theory it is argued
Bull, Larry; Budd, Adam; Stone, Christopher; Uroukov, Ivan; de Lacy Costello, Ben; Adamatzky, Andrew
2008-01-01
We propose that the behavior of nonlinear media can be controlled automatically through evolutionary learning. By extension, forms of unconventional computing (viz., massively parallel nonlinear computers) can be realized by such an approach. In this initial study a light-sensitive subexcitable Belousov-Zhabotinsky reaction in which a checkerboard image, composed of cells of varying light intensity projected onto the surface of a thin silica gel impregnated with a catalyst and indicator, is controlled using a learning classifier system. Pulses of wave fragments are injected into the checkerboard grid, resulting in rich spatiotemporal behavior, and a learning classifier system is shown to be able to direct the fragments to an arbitrary position through dynamic control of the light intensity within each cell in both simulated and real chemical systems. Similarly, a learning classifier system is shown to be able to control the electrical stimulation of cultured neuronal networks so that they display elementary learning. Results indicate that the learned stimulation protocols identify seemingly fundamental properties of in vitro neuronal networks. Use of another learning scheme presented in the literature confirms that such fundamental behavioral characteristics of a given network must be considered in training experiments.
Nonlinear localized modes in PT-symmetric optical media with competing gain and loss
Midya, Bikashkali; Roychoudhury, Rajkumar
2014-02-15
The existence and stability of the nonlinear spatial localized modes are investigated in parity-time symmetric optical media characterized by a generic complex hyperbolic refractive index distribution with competing gain and loss profile. The exact analytical expression of the localized modes are found for all values of the competing parameter and in the presence of both the self-focusing and self-defocusing Kerr nonlinearity. The effects of competing gain/loss profile on the stability structure of these localized modes are discussed with the help of linear stability analysis followed by the direct numerical simulation of the governing equation. The spatial localized modes in two-dimensional geometry as well as the transverse power-flow density associated with these localized modes are also examined. -- Highlights: • Existence of localized modes is investigated in PT-symmetric complex potentials. • Exact analytical expression of the localized modes is obtained. • Effect of gain/loss profile on the stability of these localized modes is discussed. • Localized modes in 2D and associated transverse power-flow density are also examined.
Li, Xiaolin; Zhang, Fan; Chen, Zhangyuan; Xu, Anshi
2007-12-24
We numerically investigate XPM effect and XPM-induced nonlinear phase noise in both RZ-DPSK and multi-format (RZ-DPSK and RZ-OOK) WDM systems operating at 40 Gbit/s with different dispersion maps. The relative strength of XPM effect and XPM-induced nonlinear phase noise is discussed for both RZ-DPSK and multi-format WDM transmission. With optimum dispersion mapping, XPM and XPM-induced nonlinear phase noise from neighboring channels carrying either OOK or DPSK signals can both be effectively suppressed.
NASA Astrophysics Data System (ADS)
Seadawy, Aly R.
2017-01-01
The propagation of three-dimensional nonlinear irrotational flow of an inviscid and incompressible fluid of the long waves in dispersive shallow-water approximation is analyzed. The problem formulation of the long waves in dispersive shallow-water approximation lead to fifth-order Kadomtsev-Petviashvili (KP) dynamical equation by applying the reductive perturbation theory. By using an extended auxiliary equation method, the solitary travelling-wave solutions of the two-dimensional nonlinear fifth-order KP dynamical equation are derived. An analytical as well as a numerical solution of the two-dimensional nonlinear KP equation are obtained and analyzed with the effects of external pressure flow.
Multiphase continuum model to describe dynamic loading effects in nonlinear porous media
Swift, R.P.; Burton, D.E.; Bryan, J.B.; Glenn, H.D.
1985-03-01
A multiphase constitutive model that couples nonlinear deformation to porous flow has been developed for numerical analyses of dynamic behavior of geological media. The model has been incorporated into the explicit finite-difference code TENSOR and applied to examine the phenomenology associated with contained explosions and nuclear surface cratering in a coral geology. For contained explosions in nearly saturated media, the model predicts a region of liquefaction to exist adjacent to the cavity. This region is markedly enhanced for the case of total saturation and the associated pore pressure buildup indicate that the stability of the residual stress field may be threatened. Based on plausible assumptions about the geology and the constitutive relations of coral, we have shown that the multiphase constitutive model can relate subsidence to calculational parameters such as peak effective stress. Most of the observed volume of the Koa crater at the Pacific Proving Grounds can be accounted for by late time consolidation of the damaged coral. 21 refs., 10 figs.
NASA Astrophysics Data System (ADS)
Chouhan, Romita; Baraskar, Priyanka; Agrawal, Arpana; Gupta, Mukul; Sen, Pranay K.; Sen, Pratima
2017-07-01
We report annealing induced sign reversal of dispersive optical nonlinearity in ion beam sputtered NiO thin films deposited at 30% and 70% oxygen partial pressures. In the Ultraviolet-visible spectra of the samples, the transmission peak corresponding to d-d transitions is observed near 2 eV. A shift in this peak towards higher energy was observed when the same films were annealed at 523 K. The near resonant photoinduced transitions produced giant nonlinear optical susceptibilities of both third- and fifth- orders when the annealed film was irradiated by a continuous wave 632.8 nm He-Ne laser. The role of the thermo-optic effect has been examined critically. Experimental studies further reveal that the oxygen partial pressure influences the growth direction of the grains in the thin films. The well known Z-scan experimental procedure has been followed for measurements of optical nonlinearities in all the NiO films. The nonlinear refractive indices of both the as-deposited and annealed NiO thin films are defined in terms of the thermo-optic coefficients (d/nd T ) T =T0 and (d/2nd T2 ) T =T0 .
NASA Astrophysics Data System (ADS)
Selima, Ehab S.; Seadawy, Aly R.; Yao, Xiaohua
2016-12-01
The three-dimensional (3-D) nonlinear and dispersive PDEs system for surface waves propagating at undisturbed water surface under the gravity force and surface tension effects are studied. By applying the reductive perturbation method, we derive the (2 + 1) -dimensions form of the Davey-Stewartson (DS) system for the modulation of 2-D harmonic waves. By using the simplest equation method, we find exact traveling wave solutions and a general form of the multiple-soliton solution of the DS model. The dispersion analysis as well as the conservation law of the DS system are discussed. It is revealed that the consistency of the results with the conservation of the potential energy increases with increasing Ursell parameter. Also, the stability of the ODEs form of the DS system is presented by using the phase portrait method.
Experimental investigation of wave dispersion in hardened concrete and reference liquid media
NASA Astrophysics Data System (ADS)
Iliopoulos, Sokratis N.; Malm, Fabian; Grosse, Christian U.; Aggelis, Dimitrios G.
2017-04-01
Nowadays, more and more, the monitoring of concrete's setting and hardening as well as concrete's condition assessment and mechanical characterization is realized with the Ultrasonic Pulse Velocity technique. However, despite its increasing use, the high potential and the vast applicability over a wide range of materials and structures, the aforementioned nondestructive testing technique is only partially exploited since a) a default pulse usually not selected by the user is transmitted, b) a single frequency band dependent on the testing equipment (pulse generator and sensors) is excited and c) usually the first part of the signal is only considered. Moreover, the technique, as defined by its name, is based on pulse velocity measurements which strongly rely on a predefined threshold value for the calculation of the travel time between the transmitting and receiving sensor. To overcome all these issues, in the current experimental campaign, user-defined signals are generated, a broad range of ultrasonic frequencies is excited, while the full length of the signal is also taken into account. In addition, the pulse velocity measurements are replaced by the more advanced phase velocity calculations determined by reference phase points of the time domain signals or by phase differences of the signals transformed in the frequency domain. The experiments are mainly conducted in hardened concrete specimens but the aggregates are substituted by spherical glass beads of well-defined sizes and contents in order to better control the microstructure. Reference liquid media are also examined for comparison purposes. The results in both cases show strong dispersive trends indicated by significant changes in the phase velocity.
NASA Astrophysics Data System (ADS)
Ebrahimi, Ali N.; Or, Dani
2014-09-01
The dispersal rates of self-propelled microorganisms affect their spatial interactions and the ecological functioning of microbial communities. Microbial dispersal rates affect risk of contamination of water resources by soil-borne pathogens, the inoculation of plant roots, or the rates of spoilage of food products. In contrast with the wealth of information on microbial dispersal in water replete systems, very little is known about their dispersal rates in unsaturated porous media. The fragmented aqueous phase occupying complex soil pore spaces suppress motility and limits dispersal ranges in unsaturated soil. The primary objective of this study was to systematically evaluate key factors that shape microbial dispersal in model unsaturated porous media to quantify effects of saturation, pore space geometry, and chemotaxis on characteristics of principles that govern motile microbial dispersion in unsaturated soil. We constructed a novel 3-D angular pore network model (PNM) to mimic aqueous pathways in soil for different hydration conditions; within the PNM, we employed an individual-based model that considers physiological and biophysical properties of motile and chemotactic bacteria. The effects of hydration conditions on first passage times in different pore networks were studied showing that fragmentation of aquatic habitats under dry conditions sharply suppresses nutrient transport and microbial dispersal rates in good agreement with limited experimental data. Chemotactically biased mean travel speed of microbial cells across 9 mm saturated PNM was ˜3 mm/h decreasing exponentially to 0.45 mm/h for the PNM at matric potential of -15 kPa (for -35 kPa, dispersal practically ceases and the mean travel time to traverse the 9 mm PNM exceeds 1 year). Results indicate that chemotaxis enhances dispersal rates by orders of magnitude relative to random (diffusive) motions. Model predictions considering microbial cell sizes relative to available liquid pathways sizes were
NASA Astrophysics Data System (ADS)
Alakus, Bayram
Mathematical modeling involving porous heterogeneous media is important in a number of composite manufacturing processes, such as resin transfer molding (RTM), injection molding and the like. Of interest here are process modeling issues as related to composites manufacturing by RTM, because of the ability of the method to manufacture consolidated net shapes of complex geometric parts. In this research, we propose a mathematical model by utilizing the local volume averaging technique to establish the governing equations and therein provide finite element computational developments to predict the flow behavior of a viscous and viscoelastic fluid through a porous fiber network. The developments predict the velocity, pressure, and polymeric stress by modeling the conservation laws (e.g. mass and momentum) of the flow field coupled with constitutive equations for polymeric stress field. The governing equations of the flow are averaged for the fluid phase. Furthermore, the simulations target a variety of viscoelastic models (e.g. Newtonian model, Upper-Convected-Maxwell Model, Oldroyd-B model and Giesekus model) to provide a fundamental understanding of the elastic effects on the flow field. To solve the complex coupled nonlinear equations of the mathematical model described above, a combination of Newton linearization and the Galerkin and Streamline-Upwinding-Petrov-Galerkin (SUPG) finite element procedures are employed to accurately capture the representative physics. The formulations are first validated with available test cases of viscoelastic flows without porous media. Therein, the simulations are described for viscoelastic flow through porous media and the comparative results of different constitutive models are presented and discussed at length.
NASA Astrophysics Data System (ADS)
Zhao, Tongtong; Lou, Shuqin; Su, Wei; Wang, Xin
2016-01-01
We propose an As2Se3-based highly nonlinear photonic quasi-crystal fiber with dual zero-dispersion wavelengths (ZDWs). Using a full-vector finite element method, the proposed fiber is optimized to obtain high nonlinear coefficient, low confinement loss and two zero-dispersion points by optimizing the structure parameters. Numerical results demonstrate that the proposed photonic quasi-crystal fiber (PQF) has dual ZDWs and the nonlinear coefficient up to 2600 W-1 km-1 within the wavelength range from 2 to 5.5 μm. Due to the introduction of the large air holes in the third ring of the proposed fiber, the ability of confining the fundamental mode field can be improved effectively and thus the low confinement loss can be obtained. The proposed PQF with high nonlinearity and dual ZDWs will have a number of potential applications in four-wave mixing, super-continuum generation, and higher-order dispersion effects.
Enhancement of a nano cavity lifetime by induced slow light and nonlinear dispersions.
Grinberg, P; Bencheikh, K; Brunstein, M; Yacomotti, A M; Dumeige, Y; Sagnes, I; Raineri, F; Bigot, L; Levenson, J A
2012-11-19
We start from a 2D photonic crystal nanocavity with moderate Q-factor and dynamically increase it by two order of magnitude by the joint action of coherent population oscillations and nonlinear refractive index.
Williams, Ross; Cherin, Emmanuel; Lam, Toby Y J; Tavakkoli, Jahangir; Zemp, Roger J; Foster, F Stuart
2006-11-21
Nonlinear propagation has been demonstrated to have a significant impact on ultrasound imaging. An efficient computational algorithm is presented to simulate nonlinear ultrasound propagation through layered liquid and tissue-equivalent media. Results are compared with hydrophone measurements. This study was undertaken to investigate the role of nonlinear propagation in high frequency ultrasound micro-imaging. The acoustic field of a focused transducer (20 MHz centre frequency, f-number 2.5) was simulated for layered media consisting of water and tissue-mimicking phantom, for several wide-bandwidth source pulses. The simulation model accounted for the effects of diffraction, attenuation and nonlinearity, with transmission and refraction at layer boundaries. The parameter of nonlinearity, B/A, of the water and tissue-mimicking phantom were assumed to be 5.2 and 7.4, respectively. The experimentally measured phantom B/A value found using a finite-amplitude insert-substitution method was shown to be 7.4 +/- 0.6. Relative amounts of measured second and third harmonic pressures as a function of the fundamental pressures at the focus were in good agreement with simulations. Agreement within 3% was found between measurements and simulations of the beam widths of the fundamental and second harmonic signals following propagation through the tissue phantom. The results demonstrate significant nonlinear propagation effects for high frequency imaging beams.
NASA Astrophysics Data System (ADS)
Kandidov, V. P.; Militsin, V. O.; Bykov, A. V.; Priezzhev, A. V.
2006-11-01
Two ways of simulating statistically the propagation of laser radiation in dispersive media by the Monte-Carlo method are compared. The first approach can be called corpuscular because it is based on the calculation of random photon trajectories, while the second one can be referred to as the wave approach because it is based on the calculation of characteristics of random wave fields. It is shown that, although these approaches are based on different physical concepts of radiation scattering by particles, they yield almost equivalent results for the intensity of a restricted beam in a dispersive medium. However, there exist some differences. The corpuscular Monte-Carlo method does not reproduce the diffraction divergence of the beam, which can be taken into account by introducing the diffraction factor. The wave method does not consider backscattering, which corresponds to the quasi-optical approximation.
NASA Astrophysics Data System (ADS)
Gaudot, I.; Beucler, E.; Mocquet, A.; Drilleau, M.; Le Feuvre, M.
2015-12-01
Cross-correlations of ambient seismic noise are widely used to retrieve the information of the medium between pairs of stations. For periods between 1 and 50 s, the diffuse wavefield is dominated by microseismic energy which travels mostly as surface waves. Therefore, such waves are mainly reconstructed in the cross-correlations, and information about the structure are obtained using dispersion analysis, i.e computing phase or group velocities. Classical group velocity determination relies on tracking the maximum energy in the dispersion diagrams in order to get a unique dispersion curve. This procedure may often present problems due to the presence of several maxima. Moreover, the estimation of associated measurement errors usually depends on ad hoc user's criteria. We handle the non-unicity of the problem by inverting the whole dispersion diagram using a non-linear inversion scheme. For each frequency, the seismic energy is mapped into a time-dependent probability density function. The resulting map is inverted for the S-wave velocity structure using a Markov-chain Monte Carlo algorithm. Each time a new model is randomly sampled, the misfit value is computed according to the position of the corresponding group velocity curve in the probability density functions map. This method is applied for the analysis of vertical component noise cross-correlations computed from seismic data recorded in western Europe by the temporary PYROPE and IBERARRAY networks. The inversion of the fundamental mode Rayleigh wave dispersion diagrams between 5 and 50 s period gives a set of 1D S-wave velocity models, which are regionalized to infer a 3D S-wave velocity model of western France.
Density Waves in Saturn's Rings: Non-linear Dispersion and Moon Libration Effects
NASA Astrophysics Data System (ADS)
Sremcevic, Miodrag; Stewart, G. R.; Albers, N.; Colwell, J. E.; Esposito, L. W.
2008-05-01
We analyze strong spiral density waves in stellar occultations by Saturn's A ring observed with the Cassini Ultraviolet Imaging Spectrograph (UVIS) and find that waves dispersion relation exhibits a clear deviation from the linear trend. All waves examined here reveal an intrinsic quadratic radial dependence on the wavenumber. We provide evidence that the deviation from the linear trend is caused by the ring's pressure term acting against the self-gravity of the ring particles. From the observed dispersion relation and using the theory of Goldreich and Tremaine (1978, 1979, ApJ) where the pressure is parameterized as p=σ c2, we measure the velocity dispersion c=2-5 mm/s in the A ring. Additionally, in all first order Pandora waves the dispersion relation exhibits a wiggly structure. Comparing 60 stellar UVIS occultations between 2004 and 2008 we infer that this wavenumber oscillation propagates away from the resonance location with a period of about 600 days. This inferred period is consistent with the 3:2 near corotation resonance between Pandora and Mimas (French et al., 2003, Icarus). The observed libration in wavenumber allows us to accurately measure the group velocity in the rings and obtain independent estimates of both surface density and velocity dispersion of the rings.
NASA Astrophysics Data System (ADS)
Golubkov, A. A.; Makarov, Vladimir A.
2010-12-01
The possibility of unique reconstruction of the spatial profile of the cubic nonlinear susceptibility tensor component \\hat\\chi_{yyyy}^{(3)}(z,\\omega,-\\omega,\\omega,\\omega) of a one-dimensionally inhomogeneous plate whose medium has a symmetry plane m_y perpendicular to its surface is proved for the first time and the unique reconstruction algorithm is proposed. The amplitude complex coefficients of reflection and transmission (measured in some range of angles of incidence) as well as of conversion of an s-polarised plane signal monochromatic wave into two waves propagating on both sides of the plate make it possible to reconstruct the profile. These two waves result from nonlinear interaction of a signal wave with an intense plane wave incident normally on the plate. All the waves under consideration have the same frequency \\omega, and so its variation helps study the frequency dispersion of the cubic nonlinear susceptibility tensor component \\hat\\chi_{yyyy}^{(3)}(z,\\omega,-\\omega,\\omega,\\omega). For media with additional symmetry axes 2_z, 4_z, 6_z, or \\infty_z that are perpendicular to the plate surface, the proposed method can be used to reconstruct the profile and to examine the frequency dispersion of about one third of all independent complex components of the tensor \\hat\\chi^{(3)}.
NASA Astrophysics Data System (ADS)
Zambo Abou'ou, M. N.; Tchofo Dinda, P.; Ngabireng, C. M.; Pitois, S.; Kibler, B.
2013-03-01
We examine processes of polarization-modulational instability (PMI) in two categories of weakly birefringent optical fibers, namely, fibers whose nonlinearity is comparable to that of a standard telecom fiber, and high-index glass fibers whose nonlinearity is enhanced by several orders of magnitude as compared to that of a standard fiber. We show that the fourth-order dispersion (FOD) has a strong impact on PMI processes in both types of fibers, both at the qualitative and quantitative levels. At the qualitative level, the FOD enriches the phase diagram with nonconventional processes that generate two pairs of sidebands in certain parameter regions, while in other regions we obtain a single pair of sidebands whose frequency is independent of the pump power. The highly nonlinear birefringent fibers cause a pump depletion of a magnitude such that the frequency of the PMI sidebands becomes unstable and undergoes a continual drift. We demonstrate the existence of conditions in which the PMI process takes place in a manner similar to that of a process coupled with a photon reservoir, which feeds in situ the PMI process by continuously providing photons in compensation for those absorbed by the fiber.
Phased-array cancellation of nonlinear FWM in coherent OFDM dispersive multi-span links.
Nazarathy, Moshe; Khurgin, Jacob; Weidenfeld, Rakefet; Meiman, Yehuda; Cho, Pak; Noe, Reinhold; Shpantzer, Isaac; Karagodsky, Vadim
2008-09-29
We develop an analytic model of Coherent Optical Orthogonal Frequency Division Multiplexing (OFDM) propagation and detection over multi-span long-haul fiber links, comprehensively and rigorously analyzing the impairments due the combined effects of FWM, Dispersion and ASE noise. Consistent with prior work of Innoe and Schadt in the WDM context, our new closed-form expressions for the total FWM received power fluctuations in the wake of dispersive phase mismatch in OFDM transmission, indicate that the FWM contributions of the multitude of spans build-up on a phased-array basis. For particular ultra-long haul link designs, the effectiveness of dispersion in reducing FWM is far greater than previously assumed in OFDM system analysis. The key is having the dominant FWM intermodulation products due to the multiple spans, destructively interfere, mutually cancelling their FWM intermodulation products, analogous to operating at the null of a phased-array antenna system. By applying the new analysis tools, this mode of effectively mitigating the FWM impairment, is shown under specific dispersion and spectral management conditions, to substantially suppress the FWM power fluctuations. Accounting for the phased-array concept and applying the compact OFDM design formulas developed here, we analyzed system performance of a 40 Gbps coherent OFDM system, over standard G.652 fiber, with cyclic prefix based electronic dispersion compensation but no optical compensation along the link. The transmission range for 10-3 target BER is almost tripled from 2560 km to 6960 km, relative to a reference system performing optical dispersion compensation in every span (ideally accounting for FWM and ASE noise and the cyclic prefix overhead, but excluding additional impairments).
Fujioka, J; Espinosa, A
2015-11-01
In this article, we show that if the nonlinear Schrödinger (NLS) equation is generalized by simultaneously taking into account higher-order dispersion, a quintic nonlinearity, and self-steepening terms, the resulting equation is interesting as it has exact soliton solutions which may be (depending on the values of the coefficients) stable or unstable, standard or "embedded," fixed or "moving" (i.e., solitons which advance along the retarded-time axis). We investigate the stability of these solitons by means of a modified version of the Vakhitov-Kolokolov criterion, and numerical tests are carried out to corroborate that these solitons respond differently to perturbations. It is shown that this generalized NLS equation can be derived from a Lagrangian density which contains an auxiliary variable, and Noether's theorem is then used to show that the invariance of the action integral under infinitesimal gauge transformations generates a whole family of conserved quantities. Finally, we study if this equation has the Painlevé property.
NASA Astrophysics Data System (ADS)
Fujioka, J.; Espinosa, A.
2015-11-01
In this article, we show that if the nonlinear Schrödinger (NLS) equation is generalized by simultaneously taking into account higher-order dispersion, a quintic nonlinearity, and self-steepening terms, the resulting equation is interesting as it has exact soliton solutions which may be (depending on the values of the coefficients) stable or unstable, standard or "embedded," fixed or "moving" (i.e., solitons which advance along the retarded-time axis). We investigate the stability of these solitons by means of a modified version of the Vakhitov-Kolokolov criterion, and numerical tests are carried out to corroborate that these solitons respond differently to perturbations. It is shown that this generalized NLS equation can be derived from a Lagrangian density which contains an auxiliary variable, and Noether's theorem is then used to show that the invariance of the action integral under infinitesimal gauge transformations generates a whole family of conserved quantities. Finally, we study if this equation has the Painlevé property.
Lee, Seoung Hun; Kim, Seung Hwan; Kim, Kyong Hon; Lee, Min Hee; Lee, El-Hang
2009-06-08
We report, for the first time to our knowledge, a novel and simple method for measuring continuous dispersion spectrum of unclamped linear electro-optic (EO) coefficient using a white-light interferometry. This method detects phase changes of the interference patterns with and without an applied electric voltage, and allows a simultaneous measurement of wavelength and polarization dependent EO coefficients of birefringent materials. Both of the unclamped EO coefficients, r(13) (T) and r(33) (T), of a congruent LiNbO(3) (LN) crystal have been measured simultaneously with the method, and their continuous dispersion curves have been also obtained.
Nonlinear wavelength conversion in photonic crystal fibers with three zero-dispersion points
Stark, S. P.; Biancalana, F.; Podlipensky, A.; St. J. Russell, P.
2011-02-15
In this theoretical study, we show that a simple endlessly single-mode photonic crystal fiber can be designed to yield, not just two, but three zero-dispersion wavelengths. The presence of a third dispersion zero creates a rich phase-matching topology, enabling enhanced control over the spectral locations of the four-wave-mixing and resonant-radiation bands emitted by solitons and short pulses. The greatly enhanced flexibility in the positioning of these bands has applications in wavelength conversion, supercontinuum generation, and pair-photon sources for quantum optics.
Dispersion Effects in Nonlinear Light Propagation in 1-D Fiber Gratings
2007-11-02
Fundamentos Matemáticos E.T.S.I. Aeronáuticos Universidad Politécnica de Madrid 28040 Madrid, SPAIN Contents 1 Introduction...is based on the analysis and numerical simulations of the so-called nonlinear coupled mode equations (NLCME). This system of equations accounts for the
Dispersion of nonresonant third-order nonlinearities in GeSiSn ternary alloys
De Leonardis, Francesco; Troia, Benedetto; Soref, Richard A.; Passaro, Vittorio M. N.
2016-01-01
Silicon (Si), tin (Sn), and germanium (Ge) alloys have attracted research attention as direct band gap semiconductors with applications in electronics and optoelectronics. In particular, GeSn field effect transistors can exhibit very high performance in terms of power reduction and operating speed because of the high electron drift mobility, while the SiGeSn system can be constructed using CMOS-compatible techniques to realize lasers, LED, and photodetectors. The wide Si, Ge and Sn transparencies allow the use of binary and ternary alloys extended to mid-IR wavelengths, where nonlinearities can also be employed. However, neither theoretical or experimental predictions of nonlinear features in SiGeSn alloys are reported in the literature. For the first time, a rigorous and detailed physical investigation is presented to estimate the two photon absorption (TPA) coefficient and the Kerr refractive index for the SiGeSn alloy up to 12 μm. The TPA spectrum, the effective TPA wavelength cut-off, and the Kerr nonlinear refractive index have been determined as a function of alloy compositions. The promising results achieved can pave the way to the demonstration of on-chip nonlinear-based applications, including mid-IR spectrometer-on-a-chip, all-optical wavelength down/up-conversion, frequency comb generation, quantum-correlated photon-pair source generation and supercontinuum source creation, as well as Raman lasing. PMID:27622979
Dispersion of nonresonant third-order nonlinearities in GeSiSn ternary alloys
NASA Astrophysics Data System (ADS)
de Leonardis, Francesco; Troia, Benedetto; Soref, Richard A.; Passaro, Vittorio M. N.
2016-09-01
Silicon (Si), tin (Sn), and germanium (Ge) alloys have attracted research attention as direct band gap semiconductors with applications in electronics and optoelectronics. In particular, GeSn field effect transistors can exhibit very high performance in terms of power reduction and operating speed because of the high electron drift mobility, while the SiGeSn system can be constructed using CMOS-compatible techniques to realize lasers, LED, and photodetectors. The wide Si, Ge and Sn transparencies allow the use of binary and ternary alloys extended to mid-IR wavelengths, where nonlinearities can also be employed. However, neither theoretical or experimental predictions of nonlinear features in SiGeSn alloys are reported in the literature. For the first time, a rigorous and detailed physical investigation is presented to estimate the two photon absorption (TPA) coefficient and the Kerr refractive index for the SiGeSn alloy up to 12 μm. The TPA spectrum, the effective TPA wavelength cut-off, and the Kerr nonlinear refractive index have been determined as a function of alloy compositions. The promising results achieved can pave the way to the demonstration of on-chip nonlinear-based applications, including mid-IR spectrometer-on-a-chip, all-optical wavelength down/up-conversion, frequency comb generation, quantum-correlated photon-pair source generation and supercontinuum source creation, as well as Raman lasing.
NASA Astrophysics Data System (ADS)
Germaschewski, K.; Grauer, R.; Bergé, L.; Mezentsev, V. K.; Juul Rasmussen, J.
2001-05-01
The self-focusing and splitting mechanisms of waves governed by the cubic nonlinear Schrödinger equation with anisotropic dispersion are investigated numerically by means of an adaptive mesh refinement code. Wave-packets having a power far above the self-focusing threshold undergo a transversal compression and are shown to split into two symmetric peaks. These peaks can sequentially decay into smaller-scale structures developing near the front edge of a shock, as long as their individual power remains above threshold, until the final dispersion of the wave. Their phase and amplitude dynamics are detailed and compared with those characterizing collapsing objects with no anisotropic dispersion. Their ability to mutually coalesce is also analyzed and modeled from the interaction of Gaussian components. Next, bunch-type and snake-type instabilities, which result from periodic modulations driven by even and odd localized modes, are studied. The influence of the initial wave amplitude, the amplitude and wavenumber of the perturbations on the interplay of snake and bunch patterns are finally discussed.
Non-linear Inversion of Probability Density Functions of Surface Wave Dispersion
NASA Astrophysics Data System (ADS)
Beucler, E.; Drilleau, M.; Gaudot, I.; Mocquet, A.; Bodin, T.; Lognonne, P. H.
2016-12-01
A commonly used approach for inferring 3D shear wave velocity structure from surface wave measurements relies on regionalization of group (or phase) velocity curves at different frequencies as an intermediate step before inversion at depth for each grid point. This choice relies on tracking the maximum energy in the dispersion diagram in order to get a unique dispersion curve and the estimate of associated measurement uncertainties usually depends on ad hoc user's criteria. We present an alternative by directly inverting the waveform, once it is converted into probability density functions of dispersion, in order to obtain a posterior probability of 1D shear wave structure integrated along the ray path. For each 1D S-wave velocity trial model, the corresponding group velocity curve is compared to the dispersion diagram. The goodness of fit is then directly measured by the likelihood. Different type of parameterizations for the S-wave velocity structure can be chosen, we use here Bézier curves in order to ensure smooth variations and a fast forward problem. For each depth of the 1D shear wave posterior probabilities, path averaged velocities can be regionalized using classical least-squares criterion. We show inversion results of cross-correlations of ambient seismic noise in a regional context and at global scale of multiple orbit surface wave trains. This latter approach can be used for planetary purposes in the event of deployment of one seismic station on another planet such as the InSight mission.
Rotation induced nonlinear dispersive dust drift waves can be the progenitors of spokes
NASA Astrophysics Data System (ADS)
Masood, W.; Rizvi, H.; Hasnain, H.; Haque, Q.
2012-03-01
Rotation induced dispersive dust drift waves are suggested as the possible cause of the formation of spokes in the Saturn's B ring. Using the plasma parameters found in the Saturn's B ring, it has been shown that the theoretically predicted spatio-temporal scalelengths agree well with the satellites and Hubble Space telescope observations of the spokes.
NASA Astrophysics Data System (ADS)
Herrmann, Joachim
1992-08-01
An analytical dark soliton solution of the generalized nonlinear Schrödinger equation has been found for a dispersive medium with a linear and quadratic intensity depending refraction index change of the form n= n2| A| 2+ n4| A| 4. It i s shown that for the parameter range n2n4<0, and k″ 1n2>0, two-valued (bistable) soliton states exist, which describe undistorted hol es with the same width but two different amplitudes. Under certain conditions such two-valued soliton states show an unexpected behaviour at collisions, as soliton fusion and other effects.
An efficient distribution method for nonlinear transport problems in stochastic porous media
NASA Astrophysics Data System (ADS)
Ibrahima, F.; Tchelepi, H.; Meyer, D. W.
2015-12-01
Because geophysical data are inexorably sparse and incomplete, stochastic treatments of simulated responses are convenient to explore possible scenarios and assess risks in subsurface problems. In particular, understanding how uncertainties propagate in porous media with nonlinear two-phase flow is essential, yet challenging, in reservoir simulation and hydrology. We give a computationally efficient and numerically accurate method to estimate the one-point probability density (PDF) and cumulative distribution functions (CDF) of the water saturation for the stochastic Buckley-Leverett problem when the probability distributions of the permeability and porosity fields are available. The method draws inspiration from the streamline approach and expresses the distributions of interest essentially in terms of an analytically derived mapping and the distribution of the time of flight. In a large class of applications the latter can be estimated at low computational costs (even via conventional Monte Carlo). Once the water saturation distribution is determined, any one-point statistics thereof can be obtained, especially its average and standard deviation. Moreover, rarely available in other approaches, yet crucial information such as the probability of rare events and saturation quantiles (e.g. P10, P50 and P90) can be derived from the method. We provide various examples and comparisons with Monte Carlo simulations to illustrate the performance of the method.
Interaction trajectory of solitons in nonlinear media with an arbitrary degree of nonlocality
Dai, Zhiping; Yang, Zhenjun; Ling, Xiaohui; Zhang, Shumin; Pang, Zhaoguang
2016-03-15
The interaction trajectory of solitons in nonlocal nonlinear media is investigated. A simple differential equation describing the interaction trajectories is derived based on the light ray equation. Numerical calculations are carried out to illustrate the interaction trajectories with different parameters. The results show that the degree of nonlocality greatly affects the interaction of solitons. For a strongly nonlocal case, the interaction trajectory can be described by a cosine function. Analytical expressions describing the trajectory and the oscillation period are obtained. For generally and weakly nonlocal cases, the interaction trajectories still oscillate periodically, however it is no longer sinusoidal and the oscillation period increases with the nonlocal degree decreasing. In addition, the trajectory of two solitons launched with a relative angle at the entrance plane is investigated. It is found that there exists a critical angle. When the initial relative angle is larger than the critical angle, the two solitons do not collide on propagation. The influence of the degree of nonlocality on the critical angle is also discussed.
NASA Astrophysics Data System (ADS)
Ye, S.; Sleep, B. E.
2012-12-01
The effects of biofilm growth on the flow and transport in porous media were investigated in an anaerobic two-dimensional coarse sand-filled cell. The cell was inoculated with a mixed microbial culture fed methanol. Biomass concentrations attached to the sand and suspended in the water in the cell were determined by protein analysis. The biofilm thickness on individual sand grains was investigated with confocal laser scanning microscopy (CLSM). The biofilm thickness for individual sand grains had a range of mean values from 59 to 316 microns in this study. To investigate the implications of the variability of biofilm thicknesses, four models were used to calculate reductions in porous media permeability as a function of biofilm thickness. Taylor's model (Taylor et al., 1990) predicted a reduction by a factor ranging from 14 to 5000 from minimum to maximum mean biofilm thickness. Vandevivere's Model (Vandevivere et al.,1995) predicted a reduction in permeability by a factor ranging from 769 to 3846 from minimum to maximum mean biofilm thickness. Seki's model (Seki and Miyazaki, 2001) could not be applied in this study. Clement's model (Clement et al., 1996) predicted a reduction ranging from 1 to 1.14 over the range of biomass levels observed in the cell. To investigate the implications of the variability of biofilm thicknesses for dispersivity, Taylor and Jaffe's models (1990) were used to calculate increase in porous media dispersivity as a function of biofilm thickness. The model predicted an increase in dispersivity by a factor ranging from 20 to 1883 by a simplified dispersivity model and a factor ranging from 4 to 85 by a dispersivity model based on a cut-and-random-rejoin type model of pore geometry from minimum to maximum mean biofilm thickness. Acknowledgements Funding for this research from US Dupont Company, and also from NSFC40872155, 40725010 and 41030746 is gratefully acknowledged. References: Clement, T.P., Hooker, B.S. and Skeen, R.S., 1996
Surface Modification of Alumina Nanoparticles: A Dispersion Study in Organic Media.
Soleimani, Esmaiel; Zamani, Narges
2017-09-01
The alumina nanoparticles (NPs) have been synthesized from reaction between alum with ammonia and then calcined the precipitate at 1200 °C for 4 h. Its surface was modified by oleic acid (OA) and trimethoxyvinylsilane (TMVS) in o-xylene at 50 °C. The alumina NPs and its modified were characterized by XRD, FT-IR, SEM, EDX and TGA. The TGA analysis indicated that the grafting amount of OA and TMVS were 10.5 and 8.0% respectively. The dispersion of modified NPs was determined in monomers such as methyl methacrylate (MMA), butyl acrylate (BuA) and styrene (St) and in solvents such as ethanol, hexane and acetone. The experimental results showed that the highest dispersion was happened NPs modified by oleic acid in n-hexane, while the highest dispersion was observed NPs modified by TMVS in acetone. The results indicate that NPs modified by oleic acid formed a stable dispersion in MMA and BuA. The highest amount of dispersion happened NPs modified by oleic acid in MMA and BuA in initial weight of 5 and 2.5% respectively, while stable dispersion is formed in styrene when TMVS is used as modifier. The highest amount of dispersion was happened NPs modified by TMVS in styrene in initial weight of 2.5%.
Westergaard, Philip G; Christensen, Bjarke T R; Tieri, David; Matin, Rastin; Cooper, John; Holland, Murray; Ye, Jun; Thomsen, Jan W
2015-03-06
As an alternative to state-of-the-art laser frequency stabilization using ultrastable cavities, it has been proposed to exploit the nonlinear effects from coupling of atoms with a narrow transition to an optical cavity. Here, we have constructed such a system and observed nonlinear phase shifts of a narrow optical line by a strong coupling of a sample of strontium-88 atoms to an optical cavity. The sample temperature of a few mK provides a domain where the Doppler energy scale is several orders of magnitude larger than the narrow linewidth of the optical transition. This makes the system sensitive to velocity dependent multiphoton scattering events (Dopplerons) that affect the cavity field transmission and phase. By varying the number of atoms and the intracavity power, we systematically study this nonlinear phase signature which displays roughly the same features as for much lower temperature samples. This demonstration in a relatively simple system opens new possibilities for alternative routes to laser stabilization at the sub-100 mHz level and superradiant laser sources involving narrow-line atoms. The understanding of relevant motional effects obtained here has direct implications for other atomic clocks when used in relation to ultranarrow clock transitions.
Robertson, Scott; Leonhardt, Ulf
2014-11-01
Hawking radiation has become experimentally testable thanks to the many analog systems which mimic the effects of the event horizon on wave propagation. These systems are typically dominated by dispersion and give rise to a numerically soluble and stable ordinary differential equation only if the rest-frame dispersion relation Ω^{2}(k) is a polynomial of relatively low degree. Here we present a new method for the calculation of wave scattering in a one-dimensional medium of arbitrary dispersion. It views the wave equation as an integral equation in Fourier space, which can be solved using standard and efficient numerical techniques.
Coupling of mass transfer and reactive transport for nonlinear reactions in heterogeneous media
NASA Astrophysics Data System (ADS)
Willmann, M.; Carrera, J.; Sanchez-Vila, X.; Silva, O.; Dentz, M.
2010-07-01
Fast chemical reactions are driven by mixing-induced chemical disequilibrium. Mixing is poorly represented by the advection-dispersion equation. Instead, effective dynamics models, such as multirate mass transfer (MRMT), have been successful in reproducing observed field-scale transport, notably, breakthrough curves (BTCs) of conservative solutes. The objective of this work is to test whether such effective models, derived from conservative transport observations, can be used to describe effective multicomponent reactive transport in heterogeneous media. We use a localized formulation of the MRMT model that allows us to solve general reactive transport problems. We test this formulation on a simple three-species mineral precipitation problem at equilibrium. We first simulate the spatial and temporal distribution of mineral precipitation rates in synthetic hydraulically heterogeneous aquifers. We then compare these reaction rates to those corresponding to an equivalent (i.e., same conservative BTC) homogenized medium with transport characterized by a nonlocal in time equation involving a memory function. We find an excellent agreement between the two models in terms of cumulative precipitated mass for a broad range of generally stationary heterogeneity structures. These results indicate that mass transfer models can be considered to represent quite accurately the large-scale effective dynamics of mixing controlled reactive transport at least for the cases tested here, where individual transport paths sample the full range of heterogeneities represented by the BTC.
Coupling of Mass Transfer and Reactive Transport for Non-Linear Reactions in Heterogeneous Media
NASA Astrophysics Data System (ADS)
Willmann, M.; Carrera Ramirez, J.; Sanchez-Vila, X.; Silva, O.; Dentz, M.
2009-12-01
Fast chemical reactions are driven by mixing-induced chemical disequilibrium. Mixing is poorly represented by the Advection Dispersion Equation (ADE). Instead, effective dynamics models, such as Multi-Rate Mass Transfer (MRMT) amongst others, have been successful in reproducing observed field scale transport, notably breakthrough curves (BTCs) of conservative solutes. The objective of this work is to test whether such effective models, derived from conservative transport observations, can be used to describe effective multicomponent reactive transport in heterogeneous media. We use a localized formulation of the MRMT model that allows us to solve general reactive transport problems. We test this formulation on a simple three species mineral precipitation problem at equilibrium. We first simulate the spatial and temporal distribution of mineral precipitation rates in synthetic hydraulically heterogeneous aquifers. We then compare these reaction rates to those corresponding to an equivalent (i.e. same conservative BTC) homogenized medium with transport characterized by a non-local in time equation involving a memory function. We find an excellent agreement between the two models in terms of cumulative precipitated mass for a broad range of generally stationary heterogeneity structures. These results indicate that mass transfer models can be considered to represent quite accurately the large scale effective dynamics of mixing controlled reactive transport.
Magnetic resonance imaging measurements evidence weak dispersion in homogeneous porous media
NASA Astrophysics Data System (ADS)
Lehoux, A. P.; Rodts, S.; Faure, P.; Michel, E.; Courtier-Murias, D.; Coussot, P.
2016-11-01
We measure the dispersion coefficient through homogeneous bead or sand packings at different flow rates from direct magnetic resonance imaging (MRI) visualizations of the transport characteristics of a pulse of paramagnetic nanoparticles. Through two-dimensional imaging we observe homogeneous dispersion inside the sample, but we show that entrance effects may induce significant radial heterogeneities, which would affect the interpretation of the breakthrough curve. Another MRI approach then provides quantitative measurements of the evolution in time of the longitudinal particle distribution in the sample. These data can be analyzed to deduce the coefficient of dispersion independently of entrance effects. The values obtained for this "effective" dispersion coefficient are almost ten times lower than the commonly accepted values.
Modeling dispersion in three-dimensional heterogeneous fractured media at Yucca Mountain.
McKenna, Sean A; Walker, Douglas D; Arnold, Bill
2003-01-01
Highly resolved numerical simulations are conducted to evaluate the longitudinal and transverse dispersivities proposed for use in the larger-scale Yucca Mountain saturated zone (SZ) site-scale model. Two different stochastic continuum models (SCM) that define the spatial variability of permeability are inferred from the observed fracture characteristics and the measured permeabilities. These models are created with a combination of indicator geostatistics and boolean simulation that allow for modeling different correlation lengths and anisotropy ratios at different permeability thresholds as well as the inclusion of large, high-permeability features. Longitudinal and transverse (horizontal and vertical) dispersion through the permeability realizations is evaluated for both distributed and focused source geometries using groundwater flow and streamline particle tracking. These numerical results are compared to behavior predicted by an analytical solution and to dispersivities estimated by an expert panel. Early time transport results are significantly non-Gaussian due to the strong heterogeneity of the fractured medium. At late times, travel distances of 23 correlation lengths, the longitudinal and transverse horizontal dispersivity results are well approximated by the analytical solution and the expert elicitation estimates. The calculated transverse vertical dispersivity values are smaller than those estimated from the analytical solution. Inclusion of high-permeability features of the same size as the model domain with a distributed planar source creates extreme values of the longitudinal and transverse horizontal dispersivity.
Santamaria-Echart, Arantzazu; Fernandes, Isabel; Saralegi, Ainara; Costa, Mário Rui P F N; Barreiro, Filomena; Corcuera, Maria Angeles; Eceiza, Arantxa
2016-08-15
The possibility of tailoring the final properties of environmentally friendly waterborne polyurethane and polyurethane-urea dispersions and the films they produce makes them attractive for a wide range of applications. Both the reagents content and the synthesis route contribute to the observed final properties. A series of polyurethane-urea and polyurethane aqueous dispersions were synthesized using 1,2-ethanediamine and/or 1,4-butanediol as chain extenders. The diamine content was varied from 0 to 4.5wt%. Its addition was carried out either by the classical heterogeneous reaction medium (after phase inversion step), or else by the alternative homogeneous medium (prior to dispersion formation). Dispersions as well as films prepared from dispersions have been later extensively characterized. 1,2-Ethanediamine addition in heterogeneous medium leads to dispersions with high particle sizes and broad distributions whereas in homogeneous medium, lower particle sizes and narrow distributions were observed, thus leading to higher uniformity and cohesiveness among particles during film formation. Thereby, stress transfer is favored adding the diamine in a homogeneous medium; and thus the obtained films presented quite higher stress and modulus values. Furthermore, the higher uniformity of films tends to hinder water molecules transport through the film, resulting, in general, in a lower water absorption capacity. Copyright © 2016 Elsevier Inc. All rights reserved.
Three-dimensional light bullets in anisotropic microdispersive media
NASA Astrophysics Data System (ADS)
Sazonov, Sergey V.; Bugay, Aleksandr N.; Kalinovich, Alexey A.; Komissarova, Maria V.; Zakharova, Irina G.
2017-05-01
Three-dimensional light bullets in Kerr media are known to be unstable. Different schemes were proposed to overcome this obstacle. One of them is to use a nonlinear parametric interaction. Such a type of interaction can be achieved in anisotropic micro-dispersive media where space dispersion is of importance. These media allow us to reach a simultaneous approximate fulfillment of group and phase matching. To study the general (3+1)D case we apply both an approximate analytical approach and numerical simulations. We suggest that nonlinear refraction manifests itself earlier than diffraction and dispersion. Both the general (3+1)D case and axial-symmetry case are studied. With the help of averaged Lagrangian method analytical solutions are derived provided that the fixed relation between the negative coefficients of the group velocity dispersion on both harmonics holds. We demonstrate that a spatiotemporal light bullet propagates for at least 300 nonlinear lengths in anisotropic media at second harmonic generation.
NASA Astrophysics Data System (ADS)
Zhang, Guo-Bao; Ma, Ruyun
2014-10-01
This paper is concerned with the traveling wave solutions and the spreading speeds for a nonlocal dispersal equation with convolution-type crossing-monostable nonlinearity, which is motivated by an age-structured population model with time delay. We first prove the existence of traveling wave solution with critical wave speed c = c*. By introducing two auxiliary monotone birth functions and using a fluctuation method, we further show that the number c = c* is also the spreading speed of the corresponding initial value problem with compact support. Then, the nonexistence of traveling wave solutions for c < c* is established. Finally, by means of the (technical) weighted energy method, we prove that the traveling wave with large speed is exponentially stable, when the initial perturbation around the wave is relatively small in a weighted norm.
Treeby, Bradley E; Jaros, Jiri; Rendell, Alistair P; Cox, B T
2012-06-01
The simulation of nonlinear ultrasound propagation through tissue realistic media has a wide range of practical applications. However, this is a computationally difficult problem due to the large size of the computational domain compared to the acoustic wavelength. Here, the k-space pseudospectral method is used to reduce the number of grid points required per wavelength for accurate simulations. The model is based on coupled first-order acoustic equations valid for nonlinear wave propagation in heterogeneous media with power law absorption. These are derived from the equations of fluid mechanics and include a pressure-density relation that incorporates the effects of nonlinearity, power law absorption, and medium heterogeneities. The additional terms accounting for convective nonlinearity and power law absorption are expressed as spatial gradients making them efficient to numerically encode. The governing equations are then discretized using a k-space pseudospectral technique in which the spatial gradients are computed using the Fourier-collocation method. This increases the accuracy of the gradient calculation and thus relaxes the requirement for dense computational grids compared to conventional finite difference methods. The accuracy and utility of the developed model is demonstrated via several numerical experiments, including the 3D simulation of the beam pattern from a clinical ultrasound probe.
Nonlinear dispersion of resonance extraordinary wave in a plasma with strong magnetic field
Krasovitskiy, V. B.; Turikov, V. A.; Sotnikov, V. I.
2007-09-15
In this paper, the efficiency of electron acceleration by a short, powerful laser pulse propagating across an external magnetic field is investigated. Conditions for the decay of a laser pulse with frequency close to the upper hybrid resonance frequency are analyzed. It is also shown that a laser pulse propagating as an extraordinary wave in cold, magnetized, low-density plasma takes the form of a nonlinear wave with the modulated amplitude (envelope soliton). Finally, simulation results on the interaction of an electromagnetic pulse with a semi-infinite plasma, obtained with the help of an electromagnetic relativistic PIC code, are discussed and a comparison with the obtained theoretical results is presented.
NASA Astrophysics Data System (ADS)
Rudenko, O. V.; Hedberg, C. M.
2015-01-01
The stationary profile in the focal region of a focused nonlinear acoustic wave is described. Three models following from the Khokhlov-Zabolotskaya (KZ) equation with three independent variables are used: (i) the simplified one-dimensional Ostrovsky-Vakhnenko equation, (ii) the system of equations for paraxial series expansion of the acoustic field in powers of transverse coordinates, and (iii) the KZ equation reduced to two independent variables. The structure of the last equation is analogous to the Westervelt equation. Linearization through the Legendre transformation and reduction to the well-studied Euler-Tricomi equation is shown. At high intensities the stationary profiles are periodic sequences of arc sections having singularities of derivative in their matching points. The occurrence of arc profiles was pointed out by Makov. These appear in different nonlinear systems with low-frequency dispersion. Profiles containing discontinuities (shock fronts) change their form while passing through the focal region and are non-stationary waves. The numerical estimations of maximum pressure and intensity in the focus agree with computer calculations and experimental measurements.
NASA Astrophysics Data System (ADS)
Hossain, M. A.; Namihira, Y.; Razzak, S. M. A.; Islam, M. A.; Liu, J.; Kaijage, S. F.; Hirako, Y.
2012-06-01
In this paper, we investigate the generation of supercontinuum (SC) light source based on a highly nonlinear Germanium (Ge) doped photonic crystal fiber (HNL-GePCF) with all normal group velocity dispersion (GVD). By doping 3% higher refractive index Ge inside silica, nonlinear coefficient γ is increased as large as 110.6 W -1 km -1 at 1.31 μm. Using finite element method (FEM) with a circular perfectly matched boundary layer (PML), it is shown through simulations that the proposed HNL-GePCF offers an efficient SC generation for dental optical coherence tomography (OCT) applications at 1.31 μm. By propagating sech 2 picosecond optical pulses having 2.5 ps and 1.0 ps pulsewidth at a full width at half maximum (FWHM) through the proposed HNL-GePCF, output optical pulses are analyzed by the split-step Fourier method to obtain the spectral contents. Simulation results show that 105 m of the proposed HNL-GePCF can produce 100 nm spectrum (10 dB bandwidth) at 1.31 μm for 2.5 ps input optical pulse and 110 m of such HNL-GePCF can produce 140 nm spectrum (10 dB bandwidth) for 1.0 ps input optical pulse. Therefore, the highest longitudinal resolutions in the depth direction for dental OCT are found about 3.28 μm for enamel and 3.51 μm for dentin.
Effective Block-Scale Dispersion and Its Self-Averaging Behavior in Heterogeneous Porous Media
NASA Astrophysics Data System (ADS)
de Barros, Felipe; Dentz, Marco
2015-04-01
Upscaled (effective) dispersion coefficients in spatially heterogeneous flow fields must (1) account for the sub-scale variability that is filtered out by homogenization and (2) be modeled as a random function to incorporate the uncertainty associated with non-ergodic solute bodies. In this study, we use the framework developed in de Barros and Rubin (2011) [de Barros F.P.J. and Rubin Y., Modelling of block-scale macrodispersion as a random function. Journal of Fluid Mechanics 676 (2011): 514-545] to develop novel semi-analytical expressions for the first two statistical moments of the block-effective dispersion coefficients in three-dimensional spatially random flow fields as a function of the key characteristic length scales defining the transport problem. The derived expressions are based on perturbation theory and limited to weak-to-mild heterogeneity and uniform-in-the-mean steady state flow fields. The semi-analytical solutions provide physical insights of the main controlling factors influencing the temporal scaling of the dispersion coefficient of the solute body and its self-averaging dispersion behavior. Our results illustrate the relevance of the joint influence of the block-scale and local-scale dispersion in diminishing the macrodispersion variance under non-ergodic conditions. The impact of the statistical anisotropy ratio in the block-effective macrodispersion self-averaging behavior is also investigated. The analysis performed in this work has implications in numerical modeling and grid design.
Characterizing dispersivity and stagnation in porous media using NMR flow propagators.
Singer, P M; Mitchell, J; Fordham, E J
2016-09-01
Low-field nuclear magnetic resonance (NMR) displacement probability distributions (flow propagators) are presented for water flowing through heterogeneous porous materials. Four sedimentary rocks have been chosen as example systems: Dolostone, Bentheimer sandstone, Berea sandstone, and Indiana limestone (in order of decreasing permeability). The fluid displacement is characterized by pre-asymptotic Stokes' flow and so the probability distributions are bimodal, with peaks corresponding to stagnant fluid in dead-end pores and flowing fluid in the connected porosity. Cut-off Gaussian functions are used to fit the flowing and stagnant peaks independently. An effective dispersivity length scale Lv (also known as the mixing length scale) is estimated by fitting the portion of the probability distribution corresponding to the flowing fluid. For the relatively homogeneous Bentheimer sandstone, the ratio of effective dispersivity length scale to effective transport diameter dt is Lv/dt≈16, which is an order of magnitude larger than for randomly packed glass beads where Lv/dt≈1.8. We compare these dispersivity parameters to similar values extracted from a cumulant analysis of the entire propagator. Fitting a cut-off Gaussian avoids the usual complications of analyzing dispersion in the presence of the ubiquitous stagnant fluid, and results in a clear demonstration of the influence of long-range heterogeneities on the dispersivity for flow in real sedimentary rocks.
Characterizing dispersivity and stagnation in porous media using NMR flow propagators
NASA Astrophysics Data System (ADS)
Singer, P. M.; Mitchell, J.; Fordham, E. J.
2016-09-01
Low-field nuclear magnetic resonance (NMR) displacement probability distributions (flow propagators) are presented for water flowing through heterogeneous porous materials. Four sedimentary rocks have been chosen as example systems: Dolostone, Bentheimer sandstone, Berea sandstone, and Indiana limestone (in order of decreasing permeability). The fluid displacement is characterized by pre-asymptotic Stokes' flow and so the probability distributions are bimodal, with peaks corresponding to stagnant fluid in dead-end pores and flowing fluid in the connected porosity. Cut-off Gaussian functions are used to fit the flowing and stagnant peaks independently. An effective dispersivity length scale Lv (also known as the mixing length scale) is estimated by fitting the portion of the probability distribution corresponding to the flowing fluid. For the relatively homogeneous Bentheimer sandstone, the ratio of effective dispersivity length scale to effective transport diameter dt is Lv /dt ≈ 16 , which is an order of magnitude larger than for randomly packed glass beads where Lv /dt ≈ 1.8 . We compare these dispersivity parameters to similar values extracted from a cumulant analysis of the entire propagator. Fitting a cut-off Gaussian avoids the usual complications of analyzing dispersion in the presence of the ubiquitous stagnant fluid, and results in a clear demonstration of the influence of long-range heterogeneities on the dispersivity for flow in real sedimentary rocks.
NASA Astrophysics Data System (ADS)
Choudhury, Raja Roy; Choudhury, Arundhati Roy; Ghose, Mrinal Kanti
2013-09-01
To characterize nonlinear optical fiber, a semi-analytical formulation using variational principle and the Nelder-Mead Simplex method for nonlinear unconstrained minimization is proposed. The number of optimizing parameters in order to optimize core parameter U has been increased to incorporate more flexibility in the formulation of an innovative form of fundamental modal field. This formulation provides accurate analytical expressions for modal dispersion parameter (g) of optical fiber with Kerr nonlinearity. The minimization of core parameter (U), which involves Kerr nonlinearity through the nonstationary expression of propagation constant, is carried out by the Nelder-Mead Simplex method of nonlinear unconstrained minimization, suitable for problems with nonsmooth functions as the method does not require any derivative information. This formulation has less computational burden for calculation of modal parameters than full numerical methods.
NASA Astrophysics Data System (ADS)
Ibrahima, Fayadhoi; Meyer, Daniel; Tchelepi, Hamdi
2016-04-01
Because geophysical data are inexorably sparse and incomplete, stochastic treatments of simulated responses are crucial to explore possible scenarios and assess risks in subsurface problems. In particular, nonlinear two-phase flows in porous media are essential, yet challenging, in reservoir simulation and hydrology. Adding highly heterogeneous and uncertain input, such as the permeability and porosity fields, transforms the estimation of the flow response into a tough stochastic problem for which computationally expensive Monte Carlo (MC) simulations remain the preferred option.We propose an alternative approach to evaluate the probability distribution of the (water) saturation for the stochastic Buckley-Leverett problem when the probability distributions of the permeability and porosity fields are available. We give a computationally efficient and numerically accurate method to estimate the one-point probability density (PDF) and cumulative distribution functions (CDF) of the (water) saturation. The distribution method draws inspiration from a Lagrangian approach of the stochastic transport problem and expresses the saturation PDF and CDF essentially in terms of a deterministic mapping and the distribution and statistics of scalar random fields. In a large class of applications these random fields can be estimated at low computational costs (few MC runs), thus making the distribution method attractive. Even though the method relies on a key assumption of fixed streamlines, we show that it performs well for high input variances, which is the case of interest. Once the saturation distribution is determined, any one-point statistics thereof can be obtained, especially the saturation average and standard deviation. Moreover, the probability of rare events and saturation quantiles (e.g. P10, P50 and P90) can be efficiently derived from the distribution method. These statistics can then be used for risk assessment, as well as data assimilation and uncertainty reduction
Robertson, Scott
2014-11-01
Analog gravity experiments make feasible the realization of black hole space-times in a laboratory setting and the observational verification of Hawking radiation. Since such analog systems are typically dominated by dispersion, efficient techniques for calculating the predicted Hawking spectrum in the presence of strong dispersion are required. In the preceding paper, an integral method in Fourier space is proposed for stationary 1+1-dimensional backgrounds which are asymptotically symmetric. Here, this method is generalized to backgrounds which are different in the asymptotic regions to the left and right of the scattering region.
NASA Astrophysics Data System (ADS)
Gorokhovskii, A. V.; Gorshkov, N. V.; Burmistrov, I. N.; Goffman, V. G.; Tret'yachenko, E. V.; Sevryugin, A. V.; Fedorov, F. S.; Kovyneva, N. N.
2016-06-01
The electrical properties of dispersions of a powdered ferroelectric nanocomposite based on ilmenite (FeTiO3) and hollandite (K1.46Ti7.2Fe0.8O16) in dioctyl phthalate have been studied by impedance spectroscopy techniques in a frequency range of 10-1-106 Hz. The influence of stabilizing additives of cationic and anionic surfactants and iron acetylacetonate on the permittivity, conductivity, and dielectric losses was determined for dispersions containing 40 mass % of the solid composite. The influence of composition on the mechanisms of relaxation processes in the system is discussed.
Dietrich, Scott; Mayer, William; Byrnes, Sean; Vitkalov, Sergey; Sergeev, A.; Bollinger, Anthony T.; Božović, Ivan
2015-02-20
The effects of microwave radiation on transport properties of atomically thin La_{2-x}Sr_{x}CuO₄ films were studied in the 0.1-20 GHz frequency range. Resistance changes induced by microwaves were investigated at different temperatures (8–15 K) near the superconducting transition. A strong decrease of the nonlinear response is observed within a few GHz of a cutoff frequency ν_{cut} ≈ 2GHz. The expected frequency dependence vastly underestimates the sharpness of this drop. Numerical simulations that assume ac response to follow dc V-I characteristics of the films reproduce well the low frequency behavior, but fail above ν_{cut}. Thus, high-frequency radiation is much less effective in inducing vortex-antivortex dissociation in the oscillating superconducting condensate.
Dietrich, Scott; Mayer, William; Byrnes, Sean; ...
2015-02-20
The effects of microwave radiation on transport properties of atomically thin La2-xSrxCuO₄ films were studied in the 0.1-20 GHz frequency range. Resistance changes induced by microwaves were investigated at different temperatures (8–15 K) near the superconducting transition. A strong decrease of the nonlinear response is observed within a few GHz of a cutoff frequency νcut ≈ 2GHz. The expected frequency dependence vastly underestimates the sharpness of this drop. Numerical simulations that assume ac response to follow dc V-I characteristics of the films reproduce well the low frequency behavior, but fail above νcut. Thus, high-frequency radiation is much less effective inmore » inducing vortex-antivortex dissociation in the oscillating superconducting condensate.« less
NASA Astrophysics Data System (ADS)
Tao, Wei; Bao, Hongchun; Gu, Min
2011-05-01
Real-time monitoring the variation of chlorophyll distributions and cellular structures in leaves during plant growth provides important information for understanding the physiological statuses of plants. Two-photon-excited autofluorescence imaging and second harmonic generation imaging of leaves can be used for monitoring the nature intrinsic fluorophores distribution and cellular structures of leaves by the use of the near-infrared region of light which has minimal light absorption by endogenous molecules and thus increases tissue penetration. However, the two-photon absorption peak of intrinsic fluorophores of a ficus benjamina leaf is 50 nm away from the second harmonic generation excitation wavelength, which cannot be effectively excited by a femtosecond laser beam with one central wavelength. This paper shows that a highly polarized supercontinuum light generated from a birefringent nonlinear photonic crystal fiber with two zero-dispersion wavelengths can effectively excite two-photon autofluorescence as well as second harmonic generation signals for simultaneously monitoring intrinsic fluorophore distributions and non-centrosymmetric structures of leaves.
Tao, Wei; Bao, Hongchun; Gu, Min
2011-05-01
Real-time monitoring the variation of chlorophyll distributions and cellular structures in leaves during plant growth provides important information for understanding the physiological statuses of plants. Two-photon-excited autofluorescence imaging and second harmonic generation imaging of leaves can be used for monitoring the nature intrinsic fluorophores distribution and cellular structures of leaves by the use of the near-infrared region of light which has minimal light absorption by endogenous molecules and thus increases tissue penetration. However, the two-photon absorption peak of intrinsic fluorophores of a ficus benjamina leaf is 50 nm away from the second harmonic generation excitation wavelength, which cannot be effectively excited by a femtosecond laser beam with one central wavelength. This paper shows that a highly polarized supercontinuum light generated from a birefringent nonlinear photonic crystal fiber with two zero-dispersion wavelengths can effectively excite two-photon autofluorescence as well as second harmonic generation signals for simultaneously monitoring intrinsic fluorophore distributions and non-centrosymmetric structures of leaves.
NASA Astrophysics Data System (ADS)
Leble, Sergei B.
S.B. Leble's book deals with nonlinear waves and their propagation in metallic and dielectric waveguides and media with stratification. The underlying nonlinear evolution equations (NEEs) are derived giving also their solutions for specific situations. The reader will find new elements to the traditional approach. Various dispersion and relaxation laws for different guides are considered as well as the explicit form of projection operators, NEEs, quasi-solitons and of Darboux transforms. Special points relate to: 1. the development of a universal asymptotic method of deriving NEEs for guide propagation; 2. applications to the cases of stratified liquids, gases, solids and plasmas with various nonlinearities and dispersion laws; 3. connections between the basic problem and soliton- like solutions of the corresponding NEEs; 4. discussion of details of simple solutions in higher- order nonsingular perturbation theory.
Sonya Sachdeva; Sarah M. McCaffrey; Dexter Locke
2016-01-01
Wildfires have significant effects on human populations, economically, environmentally, and in terms of their general wellbeing. Smoke pollution, in particular, from either prescribed burns or uncontrolled wildfires, can have significant health impacts. Some estimates suggest that smoke dispersion from fire events may affect the health of one in three residents in the...
NASA Astrophysics Data System (ADS)
Sandulyak, A. S.; Sandulyak, D. A.; Polismakova, M. N.; Sandulyak, A. V.; Kiselev, D. O.; Ershova, V. A.
2017-07-01
Analysis has been made of the dependences of magnetic susceptibilities of powders and colloids with a dispersed phase of magnetite particles depending on their concentration for volume fractions of ferroparticles of 0.1-0.85 at a magnetic field strength from 25 to 520 kA/m.
Acelas, Nancy Y; Martin, Benjamin D; López, Diana; Jefferson, Bruce
2015-01-01
Hydrated ferric oxide (HFeO), hydrated zirconium oxide (HZrO) and hydrated copper oxide (HCuO) were immobilized within a microporous anion exchange resin (IRA-400), forming hybrid media for enhanced phosphate removal from aqueous systems. Empirical data from batch kinetic trials fitted the pseudo second order mechanism for chemical adsorption and each media was rate limited by intraparticle diffusion overall. These models were also used to predict the adsorption rate constants and the equilibrium adsorption capacities, which ranged from 26.51 to 30.44 mgP g(-1), and from 24.15 to 27.90 mgP g(-1) of media for the calculated and experimental capacities, respectively. The phosphate adsorption behavior by the hybrid materials fit both the Langmuir and Freundlich adsorption isotherms (R(2)>0.94), and the maximum adsorption capacities were 111.1 mgP g(-1) for HFeO, 91.74 mgP g(-1) for HZrO and 74.07 mgP g(-1) for HCuO. The effect of competing ions such as sulfate reduced these capacities to 18.52 mgP g(-1) for HFeO and 18.97 mgP g(-1) for HZrO. Despite this decrease, HFeO was capable of reducing the phosphate in a real wastewater matrix by 83%, and the HZrO media was able to reduce it by 86%, suggesting that such hybrid media have the potential for application at full scale.
NASA Astrophysics Data System (ADS)
Arshad, M.; Seadawy, Aly R.; Lu, Dianchen
2017-08-01
The higher-order nonlinear Schrödinger equation (NLSE) with fourth-order dispersion, cubic-quintic terms, self-steepening and nonlinear dispersive terms describes the propagation of extremely short pulses in optical fibers. In this paper, the elliptic function, bright and dark solitons and solitary wave solutions of higher-order NLSE are constructed by employing a modified extended direct algebraic method, which has important applications in applied mathematics and physics. Furthermore, we also present the formation conditions of the bright and dark solitons for this equation. The modulation instability is utilized to discuss the stability of these solutions, which shows that all solutions are exact and stable. Many other higher-order nonlinear evolution equations arising in applied sciences can also be solved by this powerful, effective and reliable method.
On the Role of Osmosis for Non-Linear Shock Waves f Pressure and Solute in Porous Media
NASA Astrophysics Data System (ADS)
Kanivesky, Roman; Salusti, Ettore; Caserta, Arrigo
2013-04-01
A novel non-Osanger model focusing on non-linear mechanic and chemo-poroelastic coupling of fluids and solute in porous rocks is developed based on the modern wave theory. Analyzing in 1-D a system of two adjacent rocks with different conditions we obtain two coupled non-linear equations for fluid pressure and solute (salt or pollutants) concentration, evolving under the action of strong stress from one "source" rock towards the other rock. Their solutions allow to identify quick non-linear solitary (Burgers) waves of coupled fluid pressure and solute density, that are different from diffusive or perturbative solutions found in other analyses. The strong transient waves for low permeability porous media, such as clay and shale, are analyzed in detail. For medium and high-permeability porous media (sandstones) this model is also tentatively applied. Indeed in recent works of Alexander (1990) and Hart(2009) is supported the presence of small osmotic phenomena in other rocks where osmosis was previously ignored. An attempt to apply our model to soils in Calabria (Italy), such as clastic marine and fluvial deposits as well as discontinuous remnants of Miocene and Pliocene carbonate and terrigeneous deposits, is also discussed.
Light generation at the anomalous dispersion high energy range of a nonlinear opal film.
Botey, Muriel; Maymó, Marc; Molinos-Gómez, Alberto; Dorado, Luis; Depine, Ricardo A; Lozano, Gabriel; Mihi, Agustín; Míguez, Hernán; Martorell, Jordi
2009-07-20
We study experimentally and theoretically light propagation and generation at the high energy range of a close-packed fcc photonic crystal of polystyrene spheres coated with a nonlinear material. We observe an enhancement of the second harmonic generation of light that may be explained on the basis of amplification effects arising from propagation at anomalous group velocities. Theoretical calculations are performed to support this assumption. The vector KKR method we use allows us to determine, from the linear response of the crystal, the behavior of the group velocity in our finite photonic structures when losses introduced by absorption or scattering by defects are taken into account assuming a nonzero imaginary part for the dielectric constant. In such structures, we predict large variations of the group velocity for wavelengths on the order or smaller than the lattice constant of the structure, where an anomalous group velocity behavior is associated with the flat bands of the photonic band structure. We find that a direct relation may be established between the group velocity reduction and the enhancement of a light generation processes such as the second harmonic generation we consider. However, frequencies for which the enhancement is found, in the finite photonic crystals we use, do not necessarily coincide with the frequencies of flat high energy bands.
Chen, Yong; Yan, Zhenya
2016-03-22
Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields.
Chen, Yong; Yan, Zhenya
2016-01-01
Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields. PMID:27002543
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.
Tardajos, Myriam G; Aranaz, Inmaculada; Sayar, Filiz; Elvira, Carlos; Reinecke, Helmut; Piskin, Erhan; Gallardo, Alberto
2012-04-03
The differential reactivity of methylmethacrylate (MMA) and vinylpyrrolidone (VP) in free radical copolymerization, with stirring in methanol, renders an emulsified two phase system. The dispersed and continuous liquid phases contain copolymers rich in MMA and VP, respectively. When Fe(3)O(4) magnetic nanoparticles (mNPs) stabilized with tetramethylammonium hydroxide are added to this emulsion, the mNPs are located in the continuous phase. Very small chemical changes in the methacrylic or vinylic chains are able to guide the mNP toward the interface or to the inside of the dispersed phase since quite a selective functionalization of each phase may be achieved separately. Thus, a small addition of methacrylic acid as comonomer (0.5% molar) guides all of the mNPs to the interface while a 0.5% molar of sulfopropyl methacrylate induces the migration of all mNPs to the dispersed phase. When 0.5% molar of a VP derivative bearing sulfonate functionality is added, the mNPs are found both in the interface and in the continuous phase. The addition of water allows solid MMA-based microspheres to be obtained incorporating the mNPs selectively either at the surface or in the core.
NASA Astrophysics Data System (ADS)
Simos, Theodore E.; Kovalnogov, Vladislav N.; Shevchuk, Igor V.
2017-07-01
The perspective of mathematical modeling and research of formation of disperse phase clusters of working media for next-generation technologies of production and transformation of energy on organic and synthetic hydrocarbon fuel is presented. Approach to creation of a problem-oriented complex of the theory, the models, knowledge bases as well as software-and-informational tools providing in total an opportunity for high-precision simulation, working off and prototyping in a computing experiment of the perspective technologies based on optimization and targeted formation of disperse phase clusters of a working media is considered.
NASA Astrophysics Data System (ADS)
Faccio, Daniele; Clerici, Matteo; Averchi, Alessandro; Lotti, Antonio; Jedrkiewicz, Ottavia; Dubietis, Audrius; Tamosauskas, Gintaras; Couairon, Arnaud; Bragheri, Francesca; Papazoglou, Dimitris; Tzortzakis, Stelios; di Trapani, Paolo
2008-09-01
We study ultrashort laser-pulse propagation and filamentation dynamics in dispersive Kerr media. We identify the regime for which the filamentation threshold (Pth) is considerably higher than the critical power (Pcr) for monochromatic beam collapse in pure Kerr media. In particular, we compare the threshold for the formation of filaments with that for the formation of X -waves. At powers Pcr
dispersion, and no filaments or X -waves are formed. At P⩾Pth , we observe X -wave formation and a weak filamentation regime. At P≫Pth , we observe both X -waves and fully formed filaments.
NASA Astrophysics Data System (ADS)
Doney, Robert L.; Agui, Juan H.; Sen, Surajit
2009-09-01
Rapid absorption of impulses using light-weight, small, reusable systems is a challenging problem. An axially aligned set of progressively shrinking elastic spheres, a "tapered chain," has been shown to be a versatile and scalable shock absorber in earlier simulational, theoretical, and experimental works by several authors. We have recently shown (see R. L. Doney and S. Sen, Phys. Rev. Lett. 97, 155502 (2006)) that the shock absorption ability of a tapered chain can be dramatically enhanced by placing small interstitial grains between the regular grains in the tapered chain systems. Here we focus on a detailed study of the problem introduced in the above mentioned letter, present extensive dynamical simulations using parameters for a titanium-aluminum-vanadium alloy Ti6Al4V, derive attendant hard-sphere analyses based formulae to describe energy dispersion, and finally discuss some preliminary experimental results using systems with chrome spheres and small Nitinol interstitial grains to present the underlying nonlinear dynamics of this so-called decorated tapered granular alignment. We are specifically interested in small systems, comprised of several grains. This is because in real applications, mass and volume occupied must inevitably be minimized. Our conclusion is that the decorated tapered chain offers enhanced energy dispersion by locking in much of the input energy in the grains of the tapered chain rather than in the small interstitial grains. Thus, the present study offers insights into how the shock absorption capabilities of these systems can be pushed even further by improving energy absorption capabilities of the larger grains in the tapered chains. We envision that these scalable, decorated tapered chains may be used as shock absorbing components in body armor, armored vehicles, building applications and in perhaps even in applications in rehabilitation science.
Analytical expressions for Z-scan with arbitrary phase change in thin nonlocal nonlinear media.
Ortega, A Balbuena; Carrasco, M L Arroyo; Otero, M M Méndez; Lara, E Reynoso; Ramírez, E V García; Castillo, M D Iturbe
2014-11-17
Analytical expressions for the normalized transmittance of a thin material with simultaneous nonlocal nonlinear change in refraction and absorption are reported. Gaussian decomposition method was used to obtain the formulas that are adequate for any magnitude of the nonlinear changes. Particular cases of no locality are compared with the local case. Experimental results are reproduced (fitted) with the founded expressions.
On the propagation of second-sound in linear and nonlinear media: Results from Green-Naghdi theory
NASA Astrophysics Data System (ADS)
Bargmann, S.; Steinmann, P.; Jordan, P. M.
2008-06-01
We investigate thermal wave propagation in one-dimensional media according to Green-Naghdi's heat conduction theory. Under the linearized theory, the dynamic propagation of a Heaviside input signal in a half-space is examined. Exact analytical solutions are derived for the three cases (i.e., types I-III) of this theory. We then numerically compare the evolution of the linear and nonlinear type-II temperature profiles, and track the finite-time blow-up of the latter's temperature rate wave, in the setting of an initial-boundary value problem involving a sudden sinusoidal input signal. Lastly, an exact traveling wave solution of a lossless, nonlinear equation, which arises under type-II theory, is determined and analyzed.
NASA Astrophysics Data System (ADS)
Rauter, N.; Lammering, R.
2015-04-01
In order to detect micro-structural damages accurately new methods are currently developed. A promising tool is the generation of higher harmonic wave modes caused by the nonlinear Lamb wave propagation in plate like structures. Due to the very small amplitudes a cumulative effect is used. To get a better overview of this inspection method numerical simulations are essential. Previous studies have developed the analytical description of this phenomenon which is based on the five-constant nonlinear elastic theory. The analytical solution has been approved by numerical simulations. In this work first the nonlinear cumulative wave propagation is simulated and analyzed considering micro-structural cracks in thin linear elastic isotropic plates. It is shown that there is a cumulative effect considering the S1-S2 mode pair. Furthermore the sensitivity of the relative acoustical nonlinearity parameter regarding those damages is validated. Furthermore, an influence of the crack size and orientation on the nonlinear wave propagation behavior is observed. In a second step the micro-structural cracks are replaced by a nonlinear material model. Instead of the five-constant nonlinear elastic theory hyperelastic material models that are implemented in commonly used FEM software are used to simulate the cumulative effect of the higher harmonic Lamb wave generation. The cumulative effect as well as the different nonlinear behavior of the S1-S2 and S2-S4 mode pairs are found by using these hyperelastic material models. It is shown that, both numerical simulations, which take into account micro-structural cracks on the one hand and nonlinear material on the other hand, lead to comparable results. Furthermore, in comparison to the five-constant nonlinear elastic theory the use of the well established hyperelastic material models like Neo-Hooke and Mooney-Rivlin are a suitable alternative to simulate the cumulative higher harmonic generation.
NASA Astrophysics Data System (ADS)
Li, Xiaobo; Dong, Liangguo; Zhao, Qun
2014-12-01
Seismic wave propagation in patchy-saturated porous media is studied by numerical simulation in time domain at the seismic frequency band (1-1000 Hz). The models consist of hundreds of representative elementary volumes (REVs), where the REV is partially saturated with water and gas pockets. Seismic modelling experiments are implemented in a traditional way, with ‘periodic’ boundary conditions applied to get rid of undrained boundary conditions at the outer edges of the REVs. The characteristics of confining pressure, induced pore pressure, solid particle velocities and Darcy filtration velocities are analysed. The snapshots show that strong pore pressure gradients are generated across the interface between gas and water phases, and significant fluid flow occurs. The conversion of a fast P-wave into a dissipating slow P-wave takes place at seismic frequencies, and the converted slow P-wave diffuses strongly in both gas- and water-saturated phases. These numerical results can help us to understand the loss mechanism at seismic frequencies. Then, P-wave attenuation and velocity dispersion of a heterogeneous REV are calculated during traditional seismic modelling at seismic frequencies. The numerical results show good agreement with theoretical predictions obtained from patchy saturation theory. Furthermore, the effects of different fluid distributions on P-wave attenuation and velocity dispersion are analysed numerically. A series of experiments are implemented by considering large, small and random gas-patchy inclusions. The decrease of gas pocket size makes the peak frequency move towards high frequencies. Random distribution of gas patches may affect both the peak attenuation and peak frequencies. Seismic attenuation caused by Biot global flow, elastic scattering and wave-induced fluid flow (WIFF) associated with patchy saturation are computed numerically. The results show that the contribution of Biot’s global flow and scattering to the overall attenuation
Kumar, Shiva; Shao, Jing; Liang, Xiaojun
2014-12-29
In the presence of pre-dispersion, an exact solution of nonlinear Schrödinger equation (NLSE) is derived for impulse input. The phase factor of the exact solution is obtained in a closed form using the exponential integral. The nonlinear interaction among periodically placed impulses launched at the input is investigated, and the condition under which these pulses do not exchange energy is examined. It is found that if the complex weights of the impulses at the input have a secant-hyperbolic envelope and a proper chirp factor, they will propagate over long distances without exchanging energy. To describe their interaction, a discrete version of NLSE is derived. The derived equation is a form of discrete self-trapping (DST) equation, which is found to admit fundamental and higher order soliton solutions in the presence of high pre-dispersion. Nonlinear eigenmodes derived here may be useful for description of signal propagation and nonlinear interaction in highly pre-dispersion fiber-optic systems.
NASA Astrophysics Data System (ADS)
Manikandan, K.; Senthilvelan, M.
2016-07-01
We construct spatiotemporal localized envelope solutions of a (3 + 1)-dimensional nonlinear Schrödinger equation with varying coefficients such as dispersion, nonlinearity and gain parameters through similarity transformation technique. The obtained localized rational solutions can serve as prototypes of rogue waves in different branches of science. We investigate the characteristics of constructed localized solutions in detail when it propagates through six different dispersion profiles, namely, constant, linear, Gaussian, hyperbolic, logarithm, and exponential. We also obtain expressions for the hump and valleys of rogue wave intensity profiles for these six dispersion profiles and study the trajectory of it in each case. Further, we analyze how the intensity of another localized solution, namely, breather, changes when it propagates through the aforementioned six dispersion profiles. Our studies reveal that these localized solutions co-exist with the collapsing solutions which are already found in the (3 + 1)-dimensional nonlinear Schrödinger equation. The obtained results will help to understand the corresponding localized wave phenomena in related fields.
NASA Astrophysics Data System (ADS)
Hui, Zhan-Qiang; Zhang, Jian-Guo
2012-05-01
We propose the use of cross-phase modulation (XPM) and four-wave mixing (FWM) in dispersion-flattened highly nonlinear photonic crystal fibers (HNL-PCFs) to implement the functionalities of wavelength conversion, simultaneous time demultiplexing and wavelength multicasting in optical time-division multiplexing (OTDM) systems. The experiments on wavelength conversion at 80 Gbit s-1and OTDM demultiplexing from 80 to 10 Gbit s-1 with wavelength multicasting of two channels are successfully demonstrated to validate the proposed scheme, which are carried out by using two segments of dispersion-flattened HNL-PCFs with lengths of 100 and 50 m, respectively. Moreover, the bit error rate (BER) performance is also measured. The results show that our designed system can achieve a power penalty of less than 4.6 dB for two multicasting channels with a 24 nm wavelength span at the BER of 10-9 when compared with the 10 Gbit/s back-to-back measurement. The proposed system is transparent to bit rate since only an ultrafast third-order nonlinear effect is used. The resulting configuration is compact, robust and reliable, benefiting from the use of dispersion-flattened HNL-PCFs with short lengths. This also makes the proposed system more flexible in the operational wavelengths than those based on dispersion-shifted fibers and traditional highly nonlinear fibers. The work was supported in part by the CAS/SAFEA International Partnership Program for Creative Research Teams.
Dual-Lagrangian description adapted to quantum optics in dispersive and dissipative dielectric media
NASA Astrophysics Data System (ADS)
Drezet, Aurélien
2016-11-01
We develop a dual description of quantum optics adapted to dielectric systems without magnetic property. Our formalism, which is shown to be equivalent to the standard one within some dipolar approximations discussed in the article, is applied to the description of polaritons in dielectric media. We show that the dual formalism leads to the Huttner-Barnett equations [B. Huttner and S. M. Barnett, Phys. Rev. A 46, 4306 (1992), 10.1103/PhysRevA.46.4306] for QED in dielectric systems. More generally, we discuss the role of electromagnetic duality in the quantization procedure for optical systems and derive the structure of the dynamical laws in the various representations.
NASA Astrophysics Data System (ADS)
Wang, L. Y.; Xu, W. C.; Luo, Z. C.; Cao, W. J.; Luo, A. P.; Dong, J. L.; Wang, H. Y.
2011-10-01
We experimentally demonstrate a passively Q-switched mode-locking (QML) operation in an Erbium-doped fiber ring laser with net normal dispersion by using nonlinear polarization rotation technique. A 2 m long section of dispersion compensating fiber (DCF) with extra large positive dispersion was inserted into the cavity to ensure the fiber laser working in the region of net positive dispersion. By carefully adjusting the polarization controller, both uniform dissipative mode-locking pulses with fundamental repetition rate and QML pulse trains with tunable repetition rate from 71.58 to 98.83 kHz are achieved. It is found that the QML operation is caused by the interaction between the polarization state of the pulse and the intracavity polarizer.
Wang, Xiang-Hua; Yin, Wen-Yan; Chen, Zhi Zhang David
2013-09-09
The one-step leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method is reformulated for simulating general electrically dispersive media. It models material dispersive properties with equivalent polarization currents. These currents are then solved with the auxiliary differential equation (ADE) and then incorporated into the one-step leapfrog ADI-FDTD method. The final equations are presented in the form similar to that of the conventional FDTD method but with second-order perturbation. The adapted method is then applied to characterize (a) electromagnetic wave propagation in a rectangular waveguide loaded with a magnetized plasma slab, (b) transmission coefficient of a plane wave normally incident on a monolayer graphene sheet biased by a magnetostatic field, and (c) surface plasmon polaritons (SPPs) propagation along a monolayer graphene sheet biased by an electrostatic field. The numerical results verify the stability, accuracy and computational efficiency of the proposed one-step leapfrog ADI-FDTD algorithm in comparison with analytical results and the results obtained with the other methods.
Tu, Yaoquan; Zhang, Qiong; Agren, Hans
2007-04-12
We demonstrate a complete procedure for simulations of electric field poled polymeric nonlinear optical systems with the purpose to evaluate the macroscopic electro-optic coefficients. The simulations cover the electric field poling effects on the chromophore order at the liquid state, the cooling procedure from the liquid to the solid state in the presence of the poling field, and the back-relaxation of the system after the removal of the field. We use Disperse Red chromophore molecules doped in a poly(methyl methacrylate) matrix for a numerical demonstration of the total procedure. On the basis of the simulation results, the polymer mobility and the static properties of the dopant chromophores are derived. In the liquid state, the chromophore molecules are closer to the side chains than to the backbones of the polymer matrix, and after the simulated annealing, the polymer matrix tends to be closely packed, leading to a significant change in the polymer structure around the chromophore molecules. Besides predicting the absolute macroscopic electro-optic coefficient values, the results are used to derive the microscopic origin of these values in terms of geometric and electronic structure, loading, poling, and back-relaxation effects, thereby aiding to establish design principles for optimum guest-host configurations.
Gagnon, Yakir L; Kröger, Ronald H H; Söderberg, Bo
2010-04-21
Color dispersion, i.e., the dependency of refractive index of any transparent material on the wavelength of light, has important consequences for the function of optical instruments and animal eyes. Using a multi-objective goal attainment optimization algorithm, a dispersion model was successfully fitted to measured refractive indices of various ocular media and the longitudinal chromatic aberration determined by laser-scanning in the crystalline lens of the African cichlid fish, Astatotilapia burtoni. The model describes the effects of color dispersion in fish lenses and may be applicable to the eyes of other vertebrates as well.
Casanova, Axelle; Carriere, Marie; Herlin-Boime, Nathalie
2011-02-01
In this paper, results concerning the dispersion by different ways of a very common industrial titania NP (Degussa P25 produced in ton quantities). When dispersed in water, the suspensions of NP appear stable for weeks. When transferred in the cell culture medium (DMEM) or if directly dispersed in DMEM, strong evolution of size is seen as well as sedimentation. To address this problem and avoid direct aggregation, when going to DMEM, a "surfactant" relevant with biological studies (FBS) prior to transfer in DMEM (or other cell media) can be used. The main results are presented here.
NASA Astrophysics Data System (ADS)
Glasgow, Scott Alan; Corson, John; Verhaaren, Chris
2010-07-01
Free energies of dissipative media are reviewed. Then we use free-energy-optimal excitation and de-excitation fields to generate a dielectric’s time-reversal spectrum, with several properties: a) The spectrum generalizes the time-reversal parity from “even” and “odd” of conservative systems to an interval [-1,+1] of “time-reversal eigenvalues” λ in dissipative media. b) It yields eigenmodes that are complete: any state of the medium is optimally excitable or de-excitable by them. c) These excitations are orthogonal with respect to the work function of the medium and, so, d) characterize field excitations for the given medium that, when superimposed, only do work on the medium, not on each other via the medium-field interaction mechanism. Notions of en masse potential and kinetic energy in the dissipative medium arise through even (λ=+1) and odd (λ=-1) parity, but also other energy notions via alternative parity (|λ|<1) under time reversal.
Zhang, Y.; Xu, Y.; Xia, J.
2011-01-01
We analyse dispersion and attenuation of surface waves at free surfaces of possible vacuum/poroelastic media: permeable-'open pore', impermeable-'closed pore' and partially permeable boundaries, which have not been previously reported in detail by researchers, under different surface-permeable, viscous-damping, elastic and fluid-flowing conditions. Our discussion is focused on their characteristics in the exploration-seismic frequency band (a few through 200 Hz) for near-surface applications. We find two surface-wave modes exist, R1 waves for all conditions, and R2 waves for closed-pore and partially permeable conditions. For R1 waves, velocities disperse most under partially permeable conditions and least under the open-pore condition. High-coupling damping coefficients move the main dispersion frequency range to high frequencies. There is an f1 frequency dependence as a constant-Q model for attenuation at high frequencies. R1 waves for the open pore are most sensitive to elastic modulus variation, but least sensitive to tortuosities variation. R1 waves for partially permeable surface radiate as non-physical waves (Im(k) < 0) at low frequencies. For R2 waves, velocities are slightly lower than the bulk slow P2 waves. At low frequencies, both velocity and attenuation are diffusive of f1/2 frequency dependence, as P2 waves. It is found that for partially permeable surfaces, the attenuation displays -f1 frequency dependence as frequency increasing. High surface permeability, low-coupling damping coefficients, low Poisson's ratios, and low tortuosities increase the slope of the -f1 dependence. When the attenuation coefficients reach 0, R2 waves for partially permeable surface begin to radiate as non-physical waves. ?? 2011 The Authors Geophysical Journal International ?? 2011 RAS.
Nonlinearization and waves in bounded media: old wine in a new bottle
NASA Astrophysics Data System (ADS)
Mortell, Michael P.; Seymour, Brian R.
2017-02-01
We consider problems such as a standing wave in a closed straight tube, a self-sustained oscillation, damped resonance, evolution of resonance and resonance between concentric spheres. These nonlinear problems, and other similar ones, have been solved by a variety of techniques when it is seen that linear theory fails. The unifying approach given here is to initially set up the appropriate linear difference equation, where the difference is the linear travel time. When the linear travel time is replaced by a corrected nonlinear travel time, the nonlinear difference equation yields the required solution.
Pikal, M J; Lukes, A L
1976-09-01
The gravimetric Knudsen method for vapor pressure measurement may be subject to serious systematic errors when the sample: (a) consists of the volatile component dispersed in an inert porous matrix and/or (b) contains a dissolved polymeric solute. Vaporization of water present as an impurity in the matrix may result in an appreciable "background" mass loss, and "nonequilibrium effects" may be present; i.e., The vapor of interest may be unable to escape from the sample rapidly enough to maintain the equilibrium vapor pressure in the Knudsen cell. Methods for eliminating the interference due to background effects are described, and a theoretical analysis of nonequilibrium effects is presented. The essential validity of the theories for nonequilibrium effects and the effectiveness of the methods for circumventing background effects were verified by experimental studies with molded nitroglycerin tablets. With nitroglycerin tablets, accurate Knudsen vapor pressure data may be obtained using the modified procedures and data analysis presented in this report.
NASA Astrophysics Data System (ADS)
Schoofs, Stan; Trompert, Ron A.; Hansen, Ulrich
2000-03-01
Horizontally layered structures can develop in porous or partially molten environments, such as hydrothermal systems, magmatic intrusions and the early Earth's mantle. The porosity φ of these natural environments is typically small. Since dissolved chemical elements unlike heat cannot diffuse through the solid rocks, heat and solute influence the interstitial fluid density in a different manner: heat advects slower than solute through the liquid by the factor φ, while diffusion of heat through the bulk porous medium is larger by the factor φ-1 times the ratio between the thermal and chemical diffusivities. By performing numerical experiments in which a rigid low-porosity medium is heated from below, we have studied the formation and evolution of layers in an initially stably stratified liquid. Growth of a convective layer through convective entrainment, the formation of a stable density interface on top of the layer and destabilization of the next layer are intimately linked. By monitoring the heat (solute) fluxes, it is observed that the transport of heat (solute) across the interface changes from convective entrainment towards a regime in which transfer is purely diffusive (dispersive). Because this transition occurs before the stage at which the lower layer arrives at the thermal equilibrium, we conclude that the layer growth stops when the density interface on top has grown sufficiently strong to keep the ascending plumes in the lower layer from convectively entraining more fluid from above. A simple balance between the most important forces, exerted on a fluid parcel in the lower layer, is proposed to determine this transition. This force balance also indicates whether a density interface keeps intact, migrates upwards or breaks down during the further evolution of the layered sequence. Finally, mechanical dispersion tends to increase transport of chemically dissolved elements across the density interface. Since this reduces the density difference between
NASA Astrophysics Data System (ADS)
Scaife, B. K. P.
2017-01-01
The response of a material to an electromagnetic field is governed by the frequency-dependent dielectric and magnetic parameters ɛ and μ . An analysis is presented of the storage and transport of energy in an electromagnetic wave passing through an isotropic non-dissipative dispersive medium. This is achieved by the use of electric circuits as analogues of the actual mechanisms within the medium that account for the dispersive behaviour. These analogue circuits are treated in a general way with the aid of Foster's Reactance Theorem. The energy within a polarized material consists of two parts: the strain energy, made up of the field and elastic energies, and the kinetic energy of the constituent particles. For an electric field e =E cos ω t it is shown that the mean, total, stored energy density is 1/4 ɛ0E2d (ω ɛ ) /d ω , an exact relation involving no approximations. Furthermore, the difference between the mean strain energy and the mean kinetic energy densities is 1/4 ɛ0E2ɛ . Similar results hold in the magnetic case. The early results obtained by Abraham, and by Brillouin, are confirmed and extended. The models proposed for ɛ and μ admit of the possibility that either, or both, of these parameters may become negative at some frequencies. It is shown that the Poynting vector and the propagation vector are always parallel to one another provided that ɛ and μ have the same sign. The speed of energy transmission is calculated and is shown to differ from the group velocity. No support is found for the possibility of negative refraction by materials with negative ɛ and μ , however it is found that such materials would display unusual refractive properties.
A self-consistent theory of localization in nonlinear random media
NASA Astrophysics Data System (ADS)
Cherroret, Nicolas
2017-01-01
The self-consistent theory of localization is generalized to account for a weak quadratic nonlinear potential in the wave equation. For spreading wave packets, the theory predicts the destruction of Anderson localization by the nonlinearity and its replacement by algebraic subdiffusion, while classical diffusion remains unaffected. In 3D, this leads to the emergence of a subdiffusion-diffusion transition in place of the Anderson transition. The accuracy and the limitations of the theory are discussed.
Bright spatial solitons in defocusing Kerr media supported by cascaded nonlinearities.
Bang, O; Kivshar, Y S; Buryak, A V
1997-11-15
We show that resonant wave mixing that is due to quadratic nonlinearity can support stable bright spatial solitons, even in the most counterintuitive case of a bulk medium with defocusing Kerr nonlinearity. We analyze the structure and stability of such self-guided beams and demonstrate that they can be generated from a Gaussian input beam, provided that its power is above a certain threshold.
Modeling of Nonlinear Optical Response in Gaseous Media and Its Comparison with Experiment
NASA Astrophysics Data System (ADS)
Xia, Yi
This thesis demonstrates the model and application of nonlinear optical response with Metastable Electronic State Approach (MESA) in ultrashort laser propagation and verifies accuracy of MESA through extensive comparison with experimental data. The MESA is developed from quantum mechanics to describe the nonlinear off-resonant optical response together with strong-field ionization in gaseous medium. The conventional light-matter interaction models are based on a piece-wise approach where Kerr effect and multi-photon ionization are treated as independent nonlinear responses. In contrast, MESA is self-consistent as the response from freed electrons and bound electrons are microscopically linked. It also can be easily coupled to the Unidirectional Pulse Propagation Equations (UPPE) for large scale simulation of experiments. This work tests the implementation of MESA model in simulation of nonlinear phase transients of ultrashort pulse propagation in a gaseous medium. The phase transient has been measured through Single-Shot Supercontinuum Spectral Interferometry. This technique can achieve high temporal resolution (10 fs) and spatial resolution (5 mum). Our comparison between simulation and experiment gives a quantitive test of MESA model including post-adiabatic corrections. This is the first time such a comparison was achieved for a theory suitable for large scale numerical simulation of modern nonlinear-optics experiments. In more than one respect, ours is a first-of-a-kind achievement. In particular, • Large amount of data are compared. We compare the data of nonlinear response induced by different pump intensity in Ar and Nitrogen. The data sets are three dimensions including two transverse spacial dimensions and one axial temporal dimension which reflect the whole structure of nonlinear response including the interplay between Kerr and plasma-induced effects. The resolutions of spatial and temporal dimension are about a few micrometer and several femtosecond
Zhang, Guiying; Block, David E
2009-01-01
Optimization of fermentation media and processes is a difficult task due to the potential for high dimensionality and nonlinearity. Here we develop and evaluate variations on two novel and highly efficient methods for experimental fermentation optimization. The first approach is based on using a truncated genetic algorithm with a developing neural network model to choose the best experiments to run. The second approach uses information theory, along with Bayesian regularized neural network models, for experiment selection. To evaluate these methods experimentally, we used them to develop a new chemically defined medium for Lactococcus lactis IL1403, along with an optimal temperature and initial pH, to achieve maximum cell growth. The media consisted of 19 defined components or groups of components. The optimization results show that the maximum cell growth from the optimal process of each novel method is generally comparable to or higher than that achieved using a traditional statistical experimental design method, but these optima are reached in about half of the experiments (73-94 vs. 161, depending on the variants of methods). The optimal chemically defined media developed in this work are rich media that can support high cell density growth 3.5-4 times higher than the best reported synthetic medium and 72% higher than a commonly used complex medium (M17) at optimization scale. The best chemically defined medium found using the method was evaluated and compared with other defined or complex media at flask- and fermentor-scales. (c) 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009.
Computational modeling of nonlinear electromagnetic phenomena
NASA Technical Reports Server (NTRS)
Goorjian, Peter M.; Taflove, Allen
1992-01-01
A new algorithm has been developed that permits, for the first time, the direct time integration of the full-vector nonlinear Maxwell's equations. This new capability permits the modeling of linear and nonlinear, instantaneous and dispersive effects in the electric polarization material media. Results are presented of first-time calculations in 1D of the propagation and collision of femtosecond electromagnetic solitons that retain the optical carrier.
NASA Astrophysics Data System (ADS)
Szczepanek, Jan; Kardaś, Tomasz; Nejbauer, Michał; Radzewicz, Czesław; Stepanenko, Yuriy
2016-03-01
In this paper we report an all-PM-fiber laser amplifier system seeded by an all-normal-dispersion oscillator mode-locked with a Nonlinear Optical Loop Mirror (NOLM). The presented all-normal-dispersion cavity works in a dissipative soliton regime and delivers highly-chirped, high energy pulses above 2.5 nJ with full width at half maximum below 200 fs. The ultrafast oscillator followed by the all-PM-fiber amplifying stage delivered pulses with the energy of 42.5 nJ and time duration below 190 fs. The electrical field of optical pulses from the system was reconstructed using the SPIDER technique. The influence of nonlinear processes on the pulse temporal envelope was investigated.
NASA Astrophysics Data System (ADS)
Wang, Wei; Hou, Lan-Tian; Liu, Zhao-Lun; Zhou, Gui-Yao
2009-11-01
We numerically demonstrate a high-nonlinearity single-mode holey fiber with flattened dispersion around the Ti-Za laser band at 800 nm. The dispersion profile of the fiber has the shape of a quadratic curve, which reaches its maximum 5.96 ps.km-1 .nm-1 at 800 nm and its minimum -0.897 ps.km-1 .nm-1 at both 750 and 850 nm. The nonlinear coefficient is 170 W-1 km-1 at 800 nm and no higher order modes exit. A six-layer air-hole cladding ensures a loss less than 0.067 db/m in the 750 to 850 nm range. Two more air-hole rings will reduce the loss to below 0.1 db/km.
NASA Astrophysics Data System (ADS)
Li, Boxiao; Tchelepi, Hamdi A.
2015-09-01
Nonlinear convergence problems in numerical reservoir simulation can lead to unacceptably large computational time and are often the main impediment to performing simulation studies of large-scale problems. We analyze the nonlinearity of the discrete transport (mass conservation) equation for immiscible, incompressible, two-phase flow in porous media in the presence of viscous, buoyancy, and capillary forces. Although simulation problems are multi-dimensional with large numbers of cells and variables, we find that the essence of the nonlinear behavior can be understood by studying the discretized (numerical) flux function for the interface between two cells. The numerical flux is expressed in terms of the saturations of the two cells. Discontinuities in the first-order derivative of the flux function (referred to as kinks) and inflection lines are identified as the cause of convergence difficulty. These critical features (kinks and inflections) change the curvature of the numerical flux function abruptly, and can lead to overshoots, oscillations, or divergence in Newton iterations. Based on our understanding of the nonlinearity, a nonlinear solver is developed, referred to as the Numerical Trust Region (NTR) solver. The solver is able to guide the Newton iterations safely and efficiently through the different saturation 'trust-regions' delineated by the kinks and inflections. Specifically, overshoots and oscillations that often lead to convergence failure are avoided. Numerical examples demonstrate that our NTR solver has superior convergence performance compared with existing methods. In particular, convergence is achieved for a wide range of timestep sizes and Courant-Friedrichs-Lewy (CFL) numbers spanning several orders of magnitude. In addition, a discretization scheme is proposed for handling heterogeneities in capillary-pressure-saturation relationship. The scheme has less degree of nonlinearity compared with the standard Single-point Phase-based Upstream
NASA Astrophysics Data System (ADS)
Zyablovsky, A. A.; Andrianov, E. S.; Nechepurenko, I. A.; Dorofeenko, A. V.; Pukhov, A. A.; Vinogradov, A. P.
2017-05-01
Solving the challenging problem of the amplification and generation of an electromagnetic field in nanostructures enables us to implement many properties of the electromagnetic field at the nanoscale in practical applications. A first-principles quantum-mechanical consideration of such a problem is sufficiently restricted by the exponentially large number of degrees of freedom and does not allow the electromagnetic-field dynamics to be described if it involves a high number of interacting atoms and modes of the electromagnetic field. Conversely, the classical description of electromagnetic fields is incorrect at the nanoscale due to the high level of quantum fluctuations connected to high dissipation and noise levels. In this paper, we develop a framework with a significantly reduced number of degrees of freedom, which describes the quantum spatial dynamics of electromagnetic fields interacting with atoms. As an example, we consider the interaction between atoms placed in a metallic subwavelength groove and demonstrate that a spontaneously excited electromagnetic pulse propagates with the group velocity. The developed approach may be exploited to describe nonuniform amplification and propagation of electromagnetic fields in arbitrary dispersive dissipative systems.
Tu, Haohua; Liu, Yuan; Liu, Xiaomin; Turchinovich, Dmitry; Lægsgaard, Jesper; Boppart, Stephen A.
2012-01-01
Dispersion-flattened dispersion-decreased all-normal dispersion (DFDD-ANDi) photonic crystal fibers have been identified as promising candidates for high-spectral-power coherent supercontinuum (SC) generation. However, the effects of the unintentional birefringence of the fibers on the SC generation have been ignored. This birefringence is widely present in nonlinear non-polarization maintaining fibers with a typical core size of 2 µm, presumably due to the structural symmetry breaks introduced in the fiber drawing process. We find that an intrinsic form-birefringence on the order of 10−5 profoundly affects the SC generation in a DFDD-ANDi photonic crystal fiber. Conventional simulations based on the scalar generalized nonlinear Schrödinger equation (GNLSE) fail to reproduce the prominent observed features of the SC generation in a short piece (9-cm) of this fiber. However, these features can be qualitatively or semi-quantitatively understood by the coupled GNLSE that takes into account the form-birefringence. The nonlinear polarization effects induced by the birefringence significantly distort the otherwise simple spectrotemporal field of the SC pulses. We therefore propose the fabrication of polarization-maintaining DFDD-ANDi fibers to avoid these adverse effects in pursuing a practical coherent fiber SC laser. PMID:22274457
Domingue, Scott R.; Bartels, Randy A.
2013-01-01
The intrinsic weak birefringence in all-normal dispersion highly nonlinear fiber, particularly ultra-high-numerical-aperture fiber, generates supercontinuum with long term polarization instabilities, even for seed pulses launched along the perceived slow axis of the fiber. Highly co/anti-correlated fluctuations in energy between regions of power spectral density mask the extent of the spectral noise in total integrated power measurements. The instability exhibits a seed pulse power threshold above which the output polarization state of the supercontinuum seeds from noise. Eliminating this instability through the utilization of nonlinear fiber with a large designed birefringence, encourages the exploration of compression schemes and seed sources. Here, we include an analysis of the difficulties for seeding supercontinuum with the highly attractive ANDi-type lasers. Lastly, we introduce an intuitive approach for understanding supercontinuum development and evolution. By modifying the traditional characteristic dispersion and nonlinear lengths to track pulse properties within the nonlinear fiber, we find simple, descriptive handles for supercontinuum evolution. PMID:23736583
Self-similar optical pulses in competing cubic-quintic nonlinear media with distributed coefficients
Zhang Jiefang; Tian Qing; Wang Yueyue; Dai Chaoqing; Wu Lei
2010-02-15
We present a systematic analysis of the self-similar propagation of optical pulses within the framework of the generalized cubic-quintic nonlinear Schroedinger equation with distributed coefficients. By appropriately choosing the relations between the distributed coefficients, we not only retrieve the exact self-similar solitonic solutions, but also find both the approximate self-similar Gaussian-Hermite solutions and compact solutions. Our analytical and numerical considerations reveal that proper choices of the distributed coefficients could make the unstable solitons stable and could restrict the nonlinear interaction between the neighboring solitons.
Feng, Xian; Poletti, Francesco; Camerlingo, Angela; Parmigiani, Francesca; Horak, Peter; Petropoulos, Periklis; Loh, Wei H; Richardson, David J
2009-10-26
We report the fabrication of an all-solid highly nonlinear microstructured optical fiber. The structured preform was made by glass extrusion using two types of commercial lead silicate glasses that provide high index-contrast. Effectively single-moded guidance was observed in the fiber at 1.55 microm. The effective nonlinearity and the propagation loss at this wavelength were measured to be 120 W(-1)km(-1) and 0.8 dB/m, respectively. Numerical simulations indicate that the fiber is dispersion-shifted with a zero-dispersion-wavelength of 1475 nm and a dispersion slope of 0.16 ps/nm(2)/km respectively at 1.55 microm. These predictions are consistent with the experimentally determined dispersion of + 12.5 ps/nm/km at 1.55 microm. Tunable and efficient four-wave-mixing based wavelength conversion was demonstrated at wavelengths around 1.55 microm using a 1.5m-length of the fiber.
NASA Astrophysics Data System (ADS)
Larré, Pierre-Élie; Biasi, Stefano; Ramiro-Manzano, Fernando; Pavesi, Lorenzo; Carusotto, Iacopo
2017-06-01
We theoretically investigate the dispersion relation of small-amplitude optical waves superimposing upon a beam of polarized monochromatic light propagating along a single-mode channel waveguide characterized by an instantaneous and spatially local Kerr nonlinearity. These small luminous fluctuations propagate along the waveguide as Bogoliubov elementary excitations on top of a one-dimensional dilute Bose quantum fluid evolve in time. They consequently display a strongly renormalized dispersion law, of Bogoliubov type. Analytical and numerical results are found in both the absence and the presence of one- and two-photon losses. Silicon and silicon-nitride waveguides are used as examples. We finally propose an experiment to measure this Bogoliubov dispersion relation, based on a stimulated four-wave mixing and interference spectroscopy techniques.
Incoherent vector vortex-mode solitons in self-focusing nonlinear media.
Motzek, Kristian; Kaiser, Friedemann; Salgueiro, José R; Kivshar, Yuri; Denz, Cornelia
2004-10-01
We suggest a novel type of composite spatial optical soliton created by a coherent vortex beam guiding a partially incoherent light beam in a self-focusing nonlinear medium. We show that the incoherence of the guided mode may enhance, rather than suppress, the vortex azimuthal instability, and we also demonstrate strong destabilization of dipole-mode solitons by partially incoherent light.
Siegrist, R.L.; Smuin, D.R.; Korte, N.E.; Greene, D.W.; Pickering, D.A.; Lowe, K.S.; Strong-Gunderson, J.
2000-08-01
Chlorocarbons like trichloroethylene (TCE) are common contaminants of concern at US Department of Energy (DOE) facilities and industrial sites across the US and abroad. These contaminants of concern are present in source areas and in soil and ground water plumes as dissolved or sorbed phase constituents as well as dense nonaqueous-phase liquids (DNAPLs). These DNAPL compounds can be released to the environment through a variety of means including leaks in storage tanks and transfer lines, spills during transportation, and land treatment of wastes. When DNAPL compounds are present in low permeability media (LPM) like silt and clay layers or deposits, there are major challenges with assessment of their behavior and implementation of effective in situ remediation technologies. This report describes a field demonstration that was conducted at the Portsmouth Gaseous Diffusion Plant (PORTS) Clean Test Site (CTS) to evaluate the feasibility of permeation and dispersal of reagents into LPM. Various reagents and tracers were injected at seven test cells primarily to evaluate the feasibility of delivery, but also to evaluate the effects of the injected reagents on LPM. The various reagents and tracers were injected at the PORTS CTS using a multi-port injection system (MPIS) developed and provided by Hayward Baker Environmental, Inc.
NASA Astrophysics Data System (ADS)
de la Garza-Rubí, R. M. A.; Güizado-Rodríguez, M.; Mayorga-Cruz, D.; Basurto-Pensado, M. A.; Guerrero-Álvarez, J. A.; Ramos-Ortiz, G.; Rodríguez, M.; Maldonado, J. L.
2015-08-01
A copolymer of 3-hexylthiophene and thiophene functionalized with disperse red 1, poly(3-HT-co-TDR1), was synthesized. Chemical structure, molecular weight distribution, optical and thermal properties of this copolymer were characterized by NMR, FT-IR, UV-vis, GPC and DSC-TGA. An optical nonlinear analysis by Z-scan method was also performed for both continuous wave (CW) and pulsed laser pumping. In the CW regime the nonlinearities were evaluated in solid films, and a negative nonlinear refractive index in the range 2.7-4.1 × 10-4 cm2/W was obtained. These values are notoriously high and allowed to observe self-defocusing effects at very low laser intensities: below 1 mW. Further, nonlinear self-phase modulation patterns, during laser irradiation, were also observed. In the pulsed excitation the nonlinear response was evaluated in solution resulting in large two-photon absorption cross section of 5725 GM for the whole copolymer chain and with a value of 232 GM per repeated monomeric unit.
Thermalization and Bose-Einstein condensation of quantum light in bulk nonlinear media
NASA Astrophysics Data System (ADS)
Chiocchetta, A.; Larré, P.-É.; Carusotto, I.
2016-07-01
We study the thermalization and the Bose-Einstein condensation of a paraxial, spectrally narrow beam of quantum light propagating in a lossless bulk Kerr medium. The spatiotemporal evolution of the quantum optical field is ruled by a Heisenberg equation analogous to the quantum nonlinear Schrödinger equation of dilute atomic Bose gases. Correspondingly, in the weak-nonlinearity regime, the phase-space density evolves according to the Boltzmann equation. Expressions for the thermalization time and for the temperature and the chemical potential of the eventual Bose-Einstein distribution are found. After discussing experimental issues, we introduce an optical setup allowing the evaporative cooling of a guided beam of light towards Bose-Einstein condensation. This might serve as a novel source of coherent light.
Nonlinear optical processing with Fabry-Perot interferometers containing phase recording media
NASA Technical Reports Server (NTRS)
Bartholomew, B. J.; Lee, S. H.
1980-01-01
New techniques in nonlinear optical processing are explored, based on the operation of intensity level selection as performed by a Fabry-Perot interferometer containing a phase object. The image being processed is recorded on a medium between the mirrors as a spatially varying phase shift less than pi. The interferometer only transmits light through those portions of the object that corresponds to a single value of the phase and hence to a single intensity level in the input. More complicated operations such as thresholding and analog-to-digital conversion are performed by modulating the light source as the different levels are selected. Photoresist and lithium niobate have been used as phase objects, and experimental data for both are presented. Three kinds of Fabry-Perot interferometers have been used to demonstrate nonlinear processing using coherent and incoherent light. Color images have been produced with black and white inputs and white light illumination.
Analytical theory for the propagation of laser beams in nonlinear media
Tatarinova, Larisa L.; Garcia, Martin E.
2007-10-15
The propagation of a laser beam of intensity I in a nonlinear medium with a refractive index n(I) of arbitrary form is studied. In particular, the influence of the functional form n=n(I) on self-focusing and self-trapping is investigated. Starting from the propagation equations and using symmetry considerations and the Bogoliubov renormalization group approach, we derive a general equation relating the self-focusing distance, the intensity, and n(I). For different polynomial dependences of n(I) on I, we construct analytical solutions for the spatial intensity profile I(r) for an initially collimated Gaussian beam inside the medium. We also explicitly analyze the case of nonlinear self-focusing accompanied by multiphoton ionization. For particular (already studied) cases, we considerably improve the accuracy of the results with respect to previous semianalytical studies and obtain very good agreement with recent numerical simulations.