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)
Yakura, S. Joe
2001-06-01
The Perfectly Matched Layer (PML) method is used to absorb outgoing electromanetic waves in finite difference time domain (FDTD) numerical simulations to create the notion of infinity within the finite numerical simulation volume. Starting with unsplit-field uniaxial PML formulation, a FDTD/PML algorithm, that is accurate to second order in time, is obtained for the first time using the piecewise-linear approximation for linear and nonlinear dispersive media. Use of the FDTD/PML algorithm results in the proper long time limit behavior where the electric field value decrease exponentially to zero inside a PML medium long after an electromagnetic pulse is incident on the PML medium. The behavior is consistent with the other PML algorithm, such as Gedney's two-step approach in the case of the linear dispersive medium. Also, in the case of the nonlinear dispersive medium, FDTD/PML algorithm reduces to the usual nonlinear dispersive FDTD algorithm [1] in the absence of the PML interface. Ref. [1]: S. J. Yakura, J. MacGillivray and David Dietz, "Finite-Difference Time-Domain Calculations Based on Recursive Convolution Approach for Propagation of Electromagnetic Waves in Nonlinear Dispersive Media," Accepted for publication in the Applied Computational Electromagnetics Society (ACES) Journal in 2001.
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. PMID:26723152
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.
Tomography of dispersive media
Ernst; Herman
2000-07-01
When waves propagate through layered structures, the phase velocity is frequency dependent (dispersive). If one wants to reconstruct the velocity variations in this medium, conventional traveltime-based tomographic methods cannot be used, since each frequency component has a different traveltime. A tomographic method is presented for reconstructing the phase velocity of guided waves in laterally varying media. The dispersive character of guided waves is explicitly accounted for by using a phase-based error criterium instead of "picked" traveltimes. Phase velocity and source waveform can be reconstructed to within a few percent, and the algorithm is shown to be robust in the presence of interference noise. When applied to seismic field data, the reconstructed phase velocity field correlates well with the topography of the area. PMID:10923876
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.
Spatiotemporal coupling in dispersive nonlinear planar waveguides
NASA Astrophysics Data System (ADS)
Ryan, Andrew T.; Agrawal, Govind P.
1995-12-01
The multidimensional nonlinear Schrodinger equation governs the spatial and temporal evolution of an optical field inside a nonlinear dispersive medium. Although spatial (diffractive) and temporal (dispersive) effects can be studied independently in a linear medium, they become mutually coupled in a nonlinear medium. We present the results of numerical simulations showing this spatiotemporal coupling for ultrashort pulses propagating in dispersive Kerr media. We investigate how spatiotemporal coupling affects the behavior of the optical field in each of the four regimes defined by the type of group-velocity dispersion (normal or anomalous) and the type of nonlinearity (focusing or defocusing). We show that dispersion, through spatiotemporal coupling, can either enhance or suppress self-focusing and self-defocusing. Similarly, we demonstrate that diffraction can either enhance or suppress pulse compression or broadening. We also discuss how these effects can be controlled with optical phase modulation, such as that provided by a lens (spatial phase modulation) or frequency chirping (temporal phase modulation). Copyright (c) 1995 Optical Society of America
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.
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.
Kalocsai, A.G.
1992-12-31
An asymptotic analysis is presented for two distinct and independent problems: (I) Wave propagation in dispersive optical media with quadratic nonlinearity (II) Hypersonic flows with three dimensional self-similarity. In the optics problem, we at first study single and multiple input propagating waves at frequencies away from dielectric resonances. Here we compare the Slowly Varying Envelope Approximation to the Method of Multiple Scales and show that the Method of Multiple Scales is a superior technique that can be applied self consistently to any perturbation order which in turn predicts new physical effects. For the single slowly modulated input wave problem, under appropriate conditions, we shown that at the O({epsilon}{sup 2}) perturbation, we obtain the cubic nonlinear Schrodinger equation. This means that for the single input wave propagating in a quadratic nonlinear medium, self-modulation effects and soliton behavior may be observed depending on the boundary conditions. For the single input wave near a classical dielectric resonance, we find that the wave number becomes amplitude dependent. The method of multiple scales is replaced by Whitham`s averaged Lagrangian. We derive the associated modulated envelope equations. We investigate an effective medium regime and the full nonlinear problem. The hypersonic flow problem requires the use of asymptotic matching that arises from the geometry from the problem. Here the pressure field and lift to drag C{sup 3/2}{sub L}/C{sub D} is evaluated for a wide delta wing with small power law curvature. Use is made of Hypersonic Small Disturbance Theory and three dimensional power law similarity. It is shown that an improvement for C{sup 3/2}{sub L}/C{sub D} occurs for wings with power law curvatures greater than one, when compared to flat delta wings. This improvement in performance agrees qualitatively with other types of concave wings.
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)
Avesani, Diego; Herrera, Paulo; Chiogna, Gabriele; Bellin, Alberto; Dumbser, Michael
2015-06-01
Most numerical schemes applied to solve the advection-diffusion equation are affected by numerical diffusion. Moreover, unphysical results, such as oscillations and negative concentrations, may emerge when an anisotropic dispersion tensor is used, which induces even more severe errors in the solution of multispecies reactive transport. To cope with this long standing problem we propose a modified version of the standard Smoothed Particle Hydrodynamics (SPH) method based on a Moving-Least-Squares-Weighted-Essentially-Non-Oscillatory (MLS-WENO) reconstruction of concentrations. This scheme formulation (called MWSPH) approximates the diffusive fluxes with a Rusanov-type Riemann solver based on high order WENO scheme. We compare the standard SPH with the MWSPH for different a few test cases, considering both homogeneous and heterogeneous flow fields and different anisotropic ratios of the dispersion tensor. We show that, MWSPH is stable and accurate and that it reduces the occurrence of negative concentrations compared to standard SPH. When negative concentrations are observed, their absolute values are several orders of magnitude smaller compared to standard SPH. In addition, MWSPH limits spurious oscillations in the numerical solution more effectively than classical SPH. Convergence analysis shows that MWSPH is computationally more demanding than SPH, but with the payoff a more accurate solution, which in addition is less sensitive to particles position. The latter property simplifies the time consuming and often user dependent procedure to define the initial dislocation of the particles.
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.
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.
Perturbation approach to dispersion curves calculation for nonlinear Lamb waves
NASA Astrophysics Data System (ADS)
Packo, Pawel; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.
2015-05-01
Analysis of elastic wave propagation in nonlinear media has gained recent research attention due to the recognition of their amplitude-dependent behavior. This creates opportunities for increased accuracy of damage detection and localization, development of new structural monitoring strategies, and design of new structures with desirable acoustic behavior (e.g., amplitude-dependent frequency bandgaps, wave beaming, and filtering). This differs from more traditional nonlinear analysis approaches which target the prediction of higher harmonic growth. Of particular interest in this work is the analysis of amplitude-dependent shifts in Lamb wave dispersion curves. Typically, dispersion curves are calculated for nominally linear material parameters and geometrical features of a waveguide, even when the constitutive law is nonlinear. Instead, this work employs a Lindstedt - Poincare perturbation approach to calculate amplitude-dependent dispersion curves, and shifts thereof, for nonlinearly-elastic plates. As a result, a set of first order corrections to frequency (or equivalently wavenumber) are calculated. These corrections yield significant amplitude dependence in the spectral characteristics of the calculated waves, especially for high frequency waves, which differs fundamentally from linear analyses. Numerical simulations confirm the analytical shifts predicted. Recognition of this amplitude-dependence in Lamb wave dispersion may suggest, among other things, that the analysis of guided wave propagation phenomena within a fully nonlinear framework needs to revisit mode-mode energy flux and higher harmonics generation conditions.
Acoustic nonlinearity in dispersive solids
NASA Technical Reports Server (NTRS)
Cantrell, John H.; Yost, William T.
1991-01-01
An investigation to consider the effects of dispersion on the generation of the static acoustic wave component is presented. It is considered that an acoustic toneburst may be modeled as a modulated continuous waveform and that the generated initial static displacement pulse may be viewed as a modulation-confined disturbance. A theoretical model for the generation of the acoustic modulation solitons evolved is developed and experimental evidence in samples of vitreous silica demonstrating the essential validity of the model is provided.
Nonlinear rheology of colloidal dispersions.
Brader, J M
2010-09-15
Colloidal dispersions are commonly encountered in everyday life and represent an important class of complex fluid. Of particular significance for many commercial products and industrial processes is the ability to control and manipulate the macroscopic flow response of a dispersion by tuning the microscopic interactions between the constituents. An important step towards attaining this goal is the development of robust theoretical methods for predicting from first-principles the rheology and nonequilibrium microstructure of well defined model systems subject to external flow. In this review we give an overview of some promising theoretical approaches and the phenomena they seek to describe, focusing, for simplicity, on systems for which the colloidal particles interact via strongly repulsive, spherically symmetric interactions. In presenting the various theories, we will consider first low volume fraction systems, for which a number of exact results may be derived, before moving on to consider the intermediate and high volume fraction states which present both the most interesting physics and the most demanding technical challenges. In the high volume fraction regime particular emphasis will be given to the rheology of dynamically arrested states. PMID:21386516
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.
Effective higher-order nonlinear coefficients of composites with weakly nonlinear media
NASA Astrophysics Data System (ADS)
Natenapit, Mayuree; Thongboonrithi, Chaivej
2010-05-01
The field equations, based on the third-order perturbation expansion of electrostatic potential, are derived, and our general formulae for higher-order effective nonlinear coefficients based on the energy definition, are presented and applied to dielectric composites consisting of dilute linear cylindrical inclusions randomly dispersed in a weakly nonlinear host media. The effective nonlinear coefficients are determined up to the ninth order. In addition, the results are also compared to those obtained using the average field method and likely to provide more accurate predictions of effective higher-order nonlinear responses.
Hawking Radiation in Dispersive Media
NASA Astrophysics Data System (ADS)
Robertson, Scott James
2011-06-01
Hawking radiation, despite its presence in theoretical physics for over thirty years, remains elusive and undetected. It also suffers, in its original context of gravitational black holes, from conceptual difficulties. Of particular note is the trans-Planckian problem, which is concerned with the apparent origin of the radiation in absurdly high frequencies. In order to gain better theoretical understanding and, it is hoped, experimental verification of Hawking radiation, much study is being devoted to systems which model the spacetime geometry of black holes, and which, by analogy, are also thought to emit Hawking radiation. These analogue systems typically exhibit dispersion, which regularizes the wave behaviour at the horizon but does not lend itself well to analytic treatment, thus rendering Hawking's prediction less secure. A general analytic method for dealing with Hawking radiation in dispersive systems has proved difficult to find. This thesis presents new numerical and analytic results for Hawking emission spectra in dispersive systems. It examines two black-hole analogue systems: it begins by introducing the well-known acoustic model, presenting some original results in that context; then, through analogy with the acoustic model, goes on to develop the lesser-known fibre-optical model.
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.
Dispersion of nonlinearity and modulation instability in subwavelength semiconductor waveguides.
Gorbach, A V; Zhao, X; Skryabin, D V
2011-05-01
Tight confinement of light in subwavelength waveguides induces substantial dispersion of their nonlinear response. We demonstrate that this dispersion of nonlinearity can lead to the modulational instability in the regime of normal group velocity dispersion through the mechanism independent from higher order dispersions of linear waves. A simple phenomenological model describing this effect is the nonlinear Schrödinger equation with the intensity dependent group velocity dispersion. PMID:21643190
Nonlinear Biot waves in granular media
NASA Astrophysics Data System (ADS)
Dazel, Olivier; Tournat, V.
2010-01-01
The nonlinear propagation through unconsolidated model granular media is investigated in the frame of the Biot-Allard theory extended to the case of a nonlinear quadratic behavior of the solid frame (the elastic beads and their contacts). We evaluate the importance of mode coupling between solid and fluid waves, depending on the actual fluid and the bead diameter. The application of these results to other media supporting Biot's waves (trabecular bones, porous ceramics, polymer foams...) is straightforward, provided the parameters of the Biot-Allard model are available for these media.
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.
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
Ultrashort Pulse Propagation in Nonlinear Dispersive Fibers
NASA Astrophysics Data System (ADS)
Agrawal, Govind P.
Ultrashort optical pulses are often propagated through optical waveguides for a variety of applications including telecommunications and supercontinuum generation [1]. Typically the waveguide is in the form of an optical fiber but it can also be a planar waveguide. The material used to make the waveguide is often silica glass, but other materials such as silicon or chalcogenides have also been used in recent years. What is common to all such materials is they exhibit chromatic dispersion as well as the Kerr nonlinearity. The former makes the refractive index frequency dependent, whereas the latter makes it to depend on the intensity of light propagating through the medium [2]. Both of these effects become more important as optical pulses become shorter and more intense. For pulses not too short (pulse widths > 1 ns) and not too intense (peak powers < 10 mW), the waveguide plays a passive role (except for small optical losses) and acts as a transporter of optical pulses from one place to another, without significantly affecting their shape or spectrum. However, as pulses become shorter and more intense, both the dispersion and the Kerr nonlinearity start to affect the shape and spectrum of an optical pulse during its propagation inside the waveguide. This chapter focuses on silica fibers but similar results are expected for other waveguides made of different materials
Interface solitons in thermal nonlinear media
Ma Xuekai; Yang Zhenjun; Lu Daquan; Hu Wei
2011-05-15
We demonstrate the existence of fundamental and dipole interface solitons in one-dimensional thermal nonlinear media with a step in linear refractive index. Fundamental interface solitons are found to be always stable and the stability of dipole interface solitons depends on the difference in linear refractive index. The mass center of interface solitons always locates in the side with higher refractive index. The two intensity peaks of dipole interface solitons are unequal except under some specific conditions, which is different from their counterparts in uniform thermal nonlinear media.
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.
Nonlinear acoustics of micro-inhomogeneous media
NASA Astrophysics Data System (ADS)
Nazarov, Veniamin E.; Ostrovsky, Lev A.; Soustova, Irina A.; Sutin, Aleksandr M.
1988-01-01
Acoustic waves can interact in micro-inhomogeneous media much more intensively than in homogeneous media. This has been repeatedly observed in experiments with ground species, marine sediments, porous materials and metals. This paper considers two models of such media which seem to be applicable to the description of these results. One of them is based on the consideration of nonlinear sound scattering by separate spherical cavities in liquids and solids. The second model is based on the phenomenological stress-deformation relation in solids with microplasticity which often has hysteresis (heritage) properties associated with the micro-inhomogeneities. In metals, for example, it is caused by the movement of dislocations. Different nonlinear effects in such media (harmonic and combination frequency generation, nonlinear, variations of resonance frequency amplitude-dependent losses) are considered. Some results of experiments with metallic resonators supporting the theory developed here are also presented. These mechanisms may determine the nonlinear properties of real soils and rocks summarized in a table given in the paper.
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. PMID:18197238
Electric field in media with power-law spatial dispersion
NASA Astrophysics Data System (ADS)
Tarasov, Vasily E.
2016-04-01
In this paper, we consider electric fields in media with power-law spatial dispersion (PLSD). Spatial dispersion means that the absolute permittivity of the media depends on the wave vector. Power-law type of this dispersion is described by derivatives and integrals of non-integer orders. We consider electric fields of point charge and dipole in media with PLSD, infinite charged wire, uniformly charged disk, capacitance of spherical capacitor and multipole expansion for PLSD-media.
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
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. PMID:27586758
Lajunen, Hanna; Torres-Company, Víctor; Lancis, Jesús; Silvestre, Enrique; Andrès, Pedro
2010-07-01
We propose a numerical method for analyzing extensively the evolution of the coherence functions of nonstationary optical pulses in dispersive, instantaneous nonlinear Kerr media. Our approach deals with the individual propagation of samples from a properly selected ensemble that reproduces the coherence properties of the input pulsed light. In contrast to the usual strategy assuming Gaussian statistics, our numerical algorithm allows us to model the propagation of arbitrary partially coherent pulses in media with strong and instantaneous nonlinearities. PMID:20639984
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.
Dispersion of solutes in porous media
NASA Astrophysics Data System (ADS)
Hunt, A. G.; Skinner, T. E.; Ewing, R. P.; Ghanbarian-Alavijeh, B.
2011-04-01
A recently introduced theory of solute transport in porous media is tested by comparison with experiment. The solute transport is predicted using an adaptation of the cluster statistics of percolation theory to critical path analysis together with knowledge of how the structure of such percolation clusters affects the time of transport across them. Only the effects of a single scale of medium heterogeneity are incorporated, and a minimal amount of information regarding the structure of the medium is required. This framework is used to find effectively the distributions of solute velocities and travel distances and thus generate arrival time distributions. The comparison with experiment focuses on the dispersivity (the ratio of the second to the first moment of the spatial solute distribution). The predictions of the theory in the absence of diffusion are verified by comparing with over 2200 experiments over length scales from a few microns to 100 km. At larger length scales (centimeters on up) about 95% of the data lie within our predicted bounds. At smaller length scales approximately 99.8% of the data lie where we predict. These comparisons are not trivial as the typical values of the dispersivity increase by ten orders of magnitude over ten orders of magnitude of length scale. Noteworthy is that the classical advection-dispersion (ADE) equation predicts that the dispersivity should be independent of length scale! This agreement with experiment requires rethinking of the relevance of diffusion and multi-scale heterogeneity and would also appear to signal the complete inappropriateness of using the classical ADE or any of its derivatives to model solute transport.
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.
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
Discrete spectral incoherent solitons in nonlinear media with noninstantaneous response
Michel, Claire; Kibler, Bertrand; Picozzi, Antonio
2011-02-15
We show theoretically that nonlinear optical media characterized by a finite response time may support the existence of discrete spectral incoherent solitons. The structure of the soliton consists of three incoherent spectral bands that propagate in frequency space toward the low-frequency components in a discrete fashion and with a constant velocity. Discrete spectral incoherent solitons do not exhibit a confinement in the space-time domain, but exclusively in the frequency domain. The kinetic theory describes in detail all the essential properties of discrete spectral incoherent solitons: A quantitative agreement has been obtained between simulations of the kinetic equation and the nonlinear Schroedinger equation. Discrete spectral incoherent solitons may be supported in both the normal dispersion regime or the anomalous dispersion regime. These incoherent structures find their origin in the causality condition inherent to the nonlinear response function of the material. Considering the concrete example of the Raman effect, we show that discrete incoherent solitons may be spontaneously generated through the process of supercontinuum generation in photonic crystal fibers.
Soliton dispersion management in nonlinear optical fibers
NASA Astrophysics Data System (ADS)
Ganapathy, R.
2012-12-01
We consider the concept of quasisoliton propagation in a dispersion management fiber and study the soliton dynamics for soliton dispersion management case, soliton energy control case and guiding center soliton case. We also study the interaction scenario in detail for all the cases.
Chromatic dispersions in highly nonlinear glass nanofibers
NASA Astrophysics Data System (ADS)
Chaudhari, Chitrarekha; Suzuki, Takenobu; Ohishi, Yasutake
2008-08-01
We design air cladding tellurite (TeO2), bismuth oxide (Bi2O3) based, and chalcogenide (As2S3) nanofibers, and calculate the chromatic dispersions. For each material, wavelength dependent propagation constants of the nanofiber are obtained from the exact solutions of the Maxwell's equations, and from the propagation constants the chromatic dispersion is calculated. We tailor the dispersion to zero at the communication wavelength, 1.5 μm, by proper selection of the core diameter of the nanofiber for all the above materials. We further explain the technique for flattening the zero dispersion in telecommunication window, using glass instead of air, as the cladding of the nanofiber structure. Using the glass cladding has the advantage of easy handling, specially, for the communication purposes. Further, the glass cladding causes larger effective index difference between various modes of the nanofiber, thus reducing the mode coupling. We present the numerical results of the dispersion flattening technique by assuming the borosilicate glass cladding to the chalcogenide As2S3 glass core nanofiber. With the borosilicate cladding the dispersion characteristics of the nanofiber change drastically and flattening of the zero dispersion is achieved at 1.408 μm wavelength, when the core diameter is 724 nm.
A single expression for solute and heat dispersion in homogeneous porous media
NASA Astrophysics Data System (ADS)
van Milligen, Boudewijn Ph.; Bons, Paul D.
2014-05-01
A variety of expressions have been proposed for dispersion in homogeneous porous media. These expressions are either for heat (thermal) or solute dispersion, and often only valid for a limited range of flow rates, typically expressed in terms of the Péclet number. We present a single, universal expression for both the heat and solute dispersion coefficient (both transverse and longitudinal) in homogeneous porous media, valid over a wide range of Péclet numbers as long as flow is laminar. The expression covers the complex intermediate regime between diffusion and advection controlled dispersion, where dispersion increases non-linearly with flow velocity. Using numerical simulations of pore channel networks, we show that that the intermediate regime can be regarded as a phase transition between random, diffusive transport at low flow velocity and ordered transport controlled by the geometry of the pore space at high flow velocities. This phase transition explains the first-order behavior in the intermediate regime. A new quantifier, the ratio of the amount of solute in dominantly advective versus dominantly diffusive pore channels, plays the role of "order parameter" of this phase transition. Bons, P.D., van Milligen, B.P., Blum, P. 2013. A general unified expression for solute and heat dispersion in homegeneous porous media. Water Resources Research 49, 1-13. van Milligen, B.Ph., Bons, P.D. 2012. Analytical model for tracer dispersion in porous media. Physical Review E 85.
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.
An integrable shallow water equation with linear and nonlinear dispersion.
Dullin, H R; Gottwald, G A; Holm, D D
2001-11-01
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. PMID:11690414
Nonlinear, dispersive, elliptically polarized Alfven wavaes
NASA Technical Reports Server (NTRS)
Kennel, C. F.; Buti, B.; Hada, T.; Pellat, R.
1988-01-01
The derivative nonlinear Schroedinger (DNLS) equation is derived by an efficient means that employs Lagrangian variables. An expression for the stationary wave solutions of the DNLS that contains vanishing and nonvanishing and modulated and nonmodulated boundary conditions as subcases is then obtained. The solitary wave solutions for elliptically polarized quasiparallel Alfven waves in the magnetohydrodynamic limit (nonvanishing, unmodulated boundary conditions) are obtained. These converge to the Korteweg-de Vries and the modified Korteweg-de Vries solitons obtained previously for oblique propagation, but are more general. It is shown that there are no envelope solitary waves if the point at infinity is unstable to the modulational instability. The periodic solutions of the DNLS are characterized.
Statistical theory for incoherent light propagation in nonlinear media.
Hall, B; Lisak, M; Anderson, D; Fedele, R; Semenov, V E
2002-03-01
A statistical approach based on the Wigner transform is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. An evolution equation for the Wigner transform is derived from a nonlinear Schrödinger equation with arbitrary nonlinearity. It is shown that random phase fluctuations of an incoherent plane wave lead to a Landau-like damping effect, which can stabilize the modulational instability. In the limit of the geometrical optics approximation, incoherent, localized, and stationary wave fields are shown to exist for a wide class of nonlinear media. PMID:11909156
Adiabatic nonlinear waves with trapped particles. II. Wave dispersion
Dodin, I. Y.; Fisch, N. J.
2012-01-15
A general nonlinear dispersion relation is derived in a nondifferential form for an adiabatic sinusoidal Langmuir wave in collisionless plasma, allowing for an arbitrary distribution of trapped electrons. The linear dielectric function is generalized, and the nonlinear kinetic frequency shift {omega}{sub NL} is found analytically as a function of the wave amplitude a. Smooth distributions yield {omega}{sub NL}{proportional_to}{radical}(a), as usual. However, beam-like distributions of trapped electrons result in different power laws, or even a logarithmic nonlinearity, which are derived as asymptotic limits of the same dispersion relation. Such beams are formed whenever the phase velocity changes, because the trapped distribution is in autoresonance and thus evolves differently from the passing distribution. Hence, even adiabatic {omega}{sub NL}(a) is generally nonlocal.
Microscopic models for electromagnetic wave propagation in highly dispersive media
NASA Astrophysics Data System (ADS)
Defacio, Brian
1990-06-01
The purpose of this project was to advance the understanding of the propagation of ultrafast picosecond electromagnetic pulses in biological solutions and ultimately, in human tissue. Present day standards of the allowed electromagnetic doses do not include dispersion, modulation or envelope effects, memory or nonlinearity. It is well-known experimentally that biological solutions are highly dispersive. It is plausible, but not established, that modulation, memory, and nonlinearity may be important in biological solutions. Hence, this project represents a first step toward better standards.
Gaussian beam diffraction in inhomogeneous and logarithmically saturable nonlinear media
NASA Astrophysics Data System (ADS)
Berczynski, Pawel
2012-08-01
The method of paraxial complex geometrical optics (PCGO) is presented, which describes Gaussian beam (GB) diffraction and self-focusing in smoothly inhomogeneous and nonlinear saturable media of cylindrical symmetry. PCGO reduces the problem of Gaussian beam diffraction in nonlinear and inhomogeneous media to the system of the first order ordinary differential equations for the complex curvature of the wave front and for GB amplitude, which can be readily solved both analytically and numerically. As a result, PCGO radically simplifies the description of Gaussian beam diffraction in inhomogeneous and nonlinear media as compared to the numerical and analytical methods of nonlinear optics. The power of PCGO method is presented on the example of Gaussian beam evolution in logarithmically saturable medium with either focusing and defocusing refractive profile. Besides, the influence of initial curvature of the wave front on GB evolution in nonlinear saturable medium is discussed in this paper.
Nonlinearity correction and dispersion analysis in FMCW laser radar
NASA Astrophysics Data System (ADS)
Zhao, Hao; Liu, Bingguo; Liu, Guodong; Chen, Fengdong; Zhuang, Zhitao; Yu, Yahui; Gan, Yu
2014-12-01
Frequency Modulated Continuous Wave laser radar is one of the most important ways to measure the large-size targets , combining the advantages of laser with conventional FMCW radar. Dispersion compensation and non-linear calibration are two key aspects in FMCW laser radar measurement. The paper studies the method of frequency-sampling to correct the Nonlinearity and analyzes the importance of dispersion compensation. We set up experimental verification platform, choose 1550nm band continuously tunable external cavity infrared laser as the light source, use all-fiber optical device structures, choose balanced detectors as photoelectric conversion, and finally acquire data with high speed PCI-E data acquisition card, write a measurement software with Labview. We measured the gage block 1 meter away. The experiment results show that the frequency sampling method correct the Nonlinearity well and there is a significant impact on the accuracy because of the fiber dispersion, dispersion must be compensated to obtain high accuracy. The experiment lays the foundation for further research on FMCW Laser radar.
Highly concentrated active nonlinear media based on oxides
Bakin, D.V.; Dorozhkin, L.M.; Krasilov, Yu.I.; Kuznetsov, N.T.; Potemkin, A.V.; Tadzhi-Aglaev, K.S.; Shestakov, A.V.
1987-07-01
Important characteristics of highly concentrated active nonlinear media were studied which were based on oxide compounds of phosphates, niobates, tantalates, and titanates of neodymium with alkaline earth metals. Compounds of the indicated classes were synthesized and their spectral luminescent and nonlinear optical properties were studied. Single crystals were grown from the selected compounds (5-8mm) and preliminary measurements of the laser and nonlinear optical parameters were taken. Formulas are given for materials that demonstrated high nonlinear and luminescent properties simultaneously. Spectroscopic and nonlinear optical properties of some oxygen compounds of rare earth elements are shown.
Modulational instability and solitons in nonlocal media with competing nonlinearities
Esbensen, B. K.; Bache, M.; Bang, O.; Wlotzka, A.; Krolikowski, W.
2011-11-15
We investigate analytically and numerically propagation and spatial localization of light in nonlocal media with competing nonlinearities. In particular, we discuss conditions for the modulational instability of plane waves and formation of spatial solitons. We show that the competing focusing and defocusing nonlinearities enable coexistence of dark or bright spatial solitons in the same medium by varying the intensity of the beam.
NASA Astrophysics Data System (ADS)
Ganapathy, R.; Kuriakose, V. C.
2002-04-01
We obtain conditions for the occurrence of cross-phase modulational instability in the normal dispersion regime for the coupled higher order nonlinear Schrödinger equation with higher order dispersion and nonlinear terms.
NASA Astrophysics Data System (ADS)
Ranjbar, Monireh; Bahari, Ali
2016-09-01
Four-wave mixing in propagation of cylindrical waves in a homogeneous nonlinear optical media has been investigated theoretically. An explicit analytical expression which contains all the main nonlinear optical effects, including third harmonic generation, sum and difference frequency generation has been obtained. A comparison between sum frequency efficiency for exact and approximation expression in a homogeneous nonlinear medium has been done. The effect of increasing the nonlinear optical coefficient (χeff(3)) and increasing the frequency difference between two adjacent waves (Δ ω) , on the efficiency of sum frequency generation in homogeneous media has been investigated.
Permeability of mono- and bi-dispersed porous media
NASA Astrophysics Data System (ADS)
Byon, C.; Kim, S. J.
2013-04-01
In this study, the permeability of mono- and bi-dispersed porous media is considered. The effects of the particle size distribution and the packing structure of particles on the permeability are investigated experimentally and analytically. Both experimental and analytic results suggest that the particlesize distribution is close to the log-normal distribution, and the permeability of the mono-dispersed porous media quasi-linearly decreases as the range of the particle size distribution increases. On the other hand, the effect of packing structure of particles on the permeability is shown to be negligible.The permeability of the bidispersed porous media quasi-linearly decreases as the range of cluster size increases, and nearly independent of the particle size distribution. The present model is valid over the range of parameters typically found in heat transfer applications.
Dispersion of solute in spatially-periodic chromatography media
NASA Astrophysics Data System (ADS)
Kirchner, J. J.; Griffiths, S. K.; Hasselbrink, E. F.; Kanouff, M. P.
2002-11-01
The purpose of this study is to investigate the effects of spatially periodic chromatography media on the dispersion of solute in microfluidic systems. Two numerical methods are used to model this process. The first is a a method for calculating dispersion in porous media developed by Brenner (1980) and based on an analysis of asymptotic long-time moments. The second is a direct numerical solution of convection and diffusion based on Monte Carlo methods. Validity of both methods was tested on the well-known case of two-dimensional pressure-driven (Poiseuille) flow (Aris (1956), Wooding (1960)). Modelled geometries include square, triangle, and semi-circle constrictions. Raw numerical results are reduced to obtain a correlation between the periodic geometries modelled and dispersivity coefficients. This presentation will include background for the research, a description of the methods used, and a summary of current results.
Necklace beam generation in nonlinear colloidal engineered media.
Silahli, Salih Z; Walasik, Wiktor; Litchinitser, Natalia M
2015-12-15
Modulational instability is a phenomenon that reveals itself as the exponential growth of weak perturbations in the presence of an intense pump beam propagating in a nonlinear medium. It plays a key role in such nonlinear optical processes as supercontinuum generation, light filamentation, rogue waves, and ring (or necklace) beam formation. To date, a majority of studies of these phenomena have focused on light-matter interactions in self-focusing Kerr media existing in nature. However, a large and tunable nonlinear response of a colloidal suspension can be tailored at will by judiciously engineering the optical polarizability. Here, we analytically and numerically show the possibility of necklace beam generation originating from spatial modulational instability of vortex beams in engineered soft-matter nonlinear media with different types of exponential nonlinearity. PMID:26670494
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.
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.
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.
Complex geometrical optics of inhomogeneous and nonlinear saturable media
NASA Astrophysics Data System (ADS)
Berczynski, Pawel
2013-05-01
The method of complex geometrical optics (CGO) is presented, which describes Gaussian beam (GB) diffraction and self-focusing along curvilinear trajectory in smoothly inhomogeneous and nonlinear saturable media. CGO method reduces the problem of Gaussian beam propagation in inhomogeneous and nonlinear media to the system of the first order ordinary differential equations for the complex curvature of the wave front and for GB amplitude, which can be readily solved both analytically and numerically. As a result, CGO radically simplifies the description of Gaussian beam diffraction and self-focusing effects as compared to the other methods of nonlinear optics such as: variational method approach, method of moments and beam propagation method. The power of CGO method is presented on the example of the evolution of beam intensity and wave front cross-section along curvilinear central ray with torsion in weakly absorptive and nonlinear saturable graded-index fiber, where the effect of initial beam ellipticity is included into our description.
Combined optical solitons with parabolic law nonlinearity and spatio-temporal dispersion
NASA Astrophysics Data System (ADS)
Zhou, Qin; Zhu, Qiuping
2015-03-01
In this work, combined optical solitons are constructed in a weakly nonlocal nonlinear medium. The spatio-temporal dispersion (STD), parabolic law nonlinearity, detuning, nonlinear dispersion as well as inter-modal dispersion are taken into account. The integration tool that is applied is the complex envelope function ansatz. The influences of different parameters on dynamical behavior of combined optical solitons are discussed. The results are useful in describing the propagation of combined optical solitons with STD and parabolic law nonlinearity.
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.
Nonlinear dispersion of a pollutant ejected into a channel flow
NASA Astrophysics Data System (ADS)
Van Gorder, Robert A.; Vajravelu, Kuppalapalle
2011-10-01
In this paper, we study the nonlinear coupled boundary value problem arising from the nonlinear dispersion of a pollutant ejected by an external source into a channel flow. We obtain exact solutions for the steady flow for some special cases and an implicit exact solution for the unsteady flow. Additionally, we obtain analytical solutions for the transient flow. From the obtained solutions, we are able to deduce the qualitative influence of the model parameters on the solutions. Furthermore, we are able to give both exact and analytical expressions for the skin friction and wall mass transfer rate as functions of the model parameters. The model considered can be useful for understanding the polluting situations of an improper discharge incident and evaluating the effects of decontaminating measures for the water bodies.
NASA Astrophysics Data System (ADS)
Berczynski, Pawel
2013-12-01
In this paper complex geometrical optics (CGO) is applied to spatiotemporal evolution of 2D Gaussian wavepackets in nonlinear media of Kerr type. Instead of solving the commonly accepted nonlinear Schrödinger equation (NLS), we propose equations of geometrical optics: a complex eikonal equation and a complex transport equation. The eikonal equation lets us derive immediately the ordinary differential equations for spatial and temporal widths, omitting in this way the complicated variational process used in nonlinear optics. Moreover, the obtained CGO equations for actual spatial and temporal widths happen to be identical to those obtained by the variational method approach. From the transport equation we obtain the first order ordinary differential equation for complex amplitude evolution and the conservation principle for energy flux in the packet cross-section. For the combined effect of diffraction, anomalous dispersion and nonlinear refraction, we observe three types of solution for temporal and spatial widths of the packet propagating in a nonlinear medium of Kerr type: the diffraction/dispersion widening, the stationary solution and the solution under the effect of the spatiotemporal collapse. Moreover, we discuss the evolution of the 2D Gaussian wavepacket in a nonlinear inhomogeneous waveguide and we present conditions for stable propagation without the collapse effect. Under these conditions the wavepacket asymptotically approaches stationary solutions when the parameters of the waveguide change over the propagation distance. The paper also discusses the influence of initial spatial and temporal chirps on Gaussian wavepacket evolution in nonlinear media of Kerr type and in nonlinear inhomogeneous waveguides. Moreover, we notice that the equations for temporal and spatial widths of the 2D wavepacket have the same structure as the equations for the evolution of the elliptical Gaussian beam. Thus, the description of the 2D spatiotemporal wavepacket can be
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.
Nonlinear interaction between pulse and noise signals in nondispersive media
NASA Astrophysics Data System (ADS)
Gurbatov, S. N.; Demin, I. Iu.; Pronchatov-Rubtsov, N. V.
1986-10-01
The evolution of a perturbation which initially represents the sum of a regular pulsed signal and stationary noise is investigated by using the nonlinear Burgers equation. The effect of a decrease in the pulse front velocity and its broadening due to turbulent viscosity is identified. An abrupt increase in noise dispersion in the discontinuity region and a decrease in noise dispersion at the trailing edge of a pulse are also noted. Results of a numerical simulation are presented.
Upscaling and dispersion for transport in heterogeneous media
NASA Astrophysics Data System (ADS)
Eberhard, Jens
2004-10-01
This paper focuses on upscaling of the transport equation for heterogeneous porous media with random flow. We consider the local flow field being a stationary random field and develop an upscaling by the recently developed coarse graining method which is based on filtering procedures in Fourier space. The coarse graining method is used to obtain an upscaled dispersion tensor which depends on the given length scale of the upscaling. We give explicit results for the scale-dependent dispersion coefficient in lowest-order perturbation theory. For finite length scales the upscaled dispersion models the effect of the unresolved subscale flow fluctuations, and for a global upscaling the upscaled value agrees with the well-known macrodispersion coefficient, which is, however, nearly approached for length scales larger than tenfold of the correlation length.
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. PMID:24093262
Kummer solitons in strongly nonlocal nonlinear media
NASA Astrophysics Data System (ADS)
Zhong, Wei-Ping; Belić, Milivoj
2009-01-01
We solve the three-dimensional (3D) time-dependent strongly nonlocal nonlinear Schrödinger equation (NNSE) in spherical coordinates, with the help of Kummer's functions. We obtain analytical solitary solutions, which we term the Kummer solitons. We compare analytical solutions with the numerical solutions of NNSE. We discuss higher-order Kummer spatial solitons, which can exist in various forms, such as the 3D vortex solitons and the multipole solitons.
NASA Astrophysics Data System (ADS)
Kanka, Jiri
2009-05-01
For most telecom nonlinear applications a high effective nonlinearity, low group velocity dispersion with a low dispersion slope and a short fibre length are the key parameters. Combining photonic crystal fibre (PCF) technology with highly nonlinear glasses could meet these requirements very well. We have performed dispersion optimization of PCFs made from selected nonlinear glasses with a solid core and small number of hexagonally arrayed air holes. The optimization procedure employs the Nelder-Mead downhill simplex algorithm. For the modal analysis of the photonic crystal fibre structure a fully-vectorial mode solver based on the finite element method is used. We have obtained two types of dispersion optimized nonlinear PCF designs: PCFs of the first type are single-mode and highly nonlinear with a small and flattened dispersion in the 1500-1600 nm range. These PCF structures have air holes hexagonally arrayed in from 3 to 5 rings, however, their dispersion characteristics are very sensitive to variations in structural parameters. PCFs of the second type are two-ring PCFs with larger multi-mode cores. They have fundamental mode's zero dispersion wavelength around 1550 nm with non-zero moderate dispersion slopes which are less sensitive to structural variation. It is supposed that this alternative PCF design will be easier to fabricate. The effects of fabrication imprecision on the dispersion characteristics for both PCF designs are demonstrated numerically and discussed in the context of nonlinear telecom applications.
Two-dimensional multipole solitons in nonlocal nonlinear media.
Rotschild, Carmel; Segev, Mordechai; Xu, Zhiyong; Kartashov, Yaroslav V; Torner, Lluis; Cohen, Oren
2006-11-15
We present the experimental observation of scalar multipole solitons in highly nonlocal nonlinear media, including dipole, tripole, quadrupole, and necklace-type solitons, organized as arrays of out-of-phase bright spots. These complex solitons are metastable, but with a large parameters range where the instability is weak, permitting their experimental observation. PMID:17072407
Bright vector solitons in cross-defocusing nonlinear media
Yakimenko, A. I.; Prikhodko, O. O.; Vilchynskyi, S. I.
2010-07-15
We study two-dimensional soliton-soliton vector pairs in media with self-focusing nonlinearities and defocusing cross interactions. The general properties of the stationary states and their stability are investigated. The different scenarios of instability are observed using numerical simulations. The quasistable propagation regime of the high-power vector solitons is revealed.
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.
Superfluid light in bulk nonlinear media.
Carusotto, Iacopo
2014-09-01
We review how the paraxial approximation naturally leads to a hydrodynamic description of light propagation in a bulk Kerr nonlinear medium in terms of a wave equation analogous to the Gross-Pitaevskii equation for the order parameter of a superfluid. The main features of the many-body collective dynamics of the fluid of light in this propagating geometry are discussed: generation and observation of Bogoliubov sound waves in the fluid of light is first described. Experimentally accessible manifestations of superfluidity are then highlighted. Perspectives in view of realizing analogue models of gravity are finally given. PMID:25197252
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
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.
Numerical simulations for parabolic pulse shaping in non-linear media
NASA Astrophysics Data System (ADS)
Nora, R. C.; Durfee, C. G.; Carr, L. D.
2007-03-01
Pulses with parabolic temporal profiles have the property that they can propagate through non-linear media in a self similar manner. Parabolic pulses have been generated experimentally in fiber amplifiers. Input pulses develop into parabolic pulses by the combined action of group velocity dispersion, non-linear refractive index, and gain. In this work, we are exploring the feasibility of generating ultrafast parabolic pulses in laser resonators. We have successfully numerically simulated the generation of parabolic pulses in fiber amplifiers using two different algorithms, the Cayley method, and fourth order Runge-Kutta, to solve the Nonlinear Schrodinger equation with gain and periodic boundary conditions. In contrast to fiber amplifiers, pulses in laser resonators must maintain a stable pulse shape on each round trip through the optical cavity. We are exploring the prediction that a time dependent saturable gain will stabilize the pulse in the oscillator and yield parabolic pulses.
Microwaves in dispersive magnetic composite media (Review Article)
NASA Astrophysics Data System (ADS)
Tarapov, S. I.; Belozorov, D. P.
2012-07-01
Review discusses some special questions of physics of composite media (metamaterials), which are formed by elements made from natural materials of two kinds. The first ones are "carriers of permittivity" and are presented by plasma-like media and semiconductors. The second ones are "carriers of permeability"—they are presented by ferromagnets. Among such ferromagnets are ferrodielectrics (ferrites) and manganite-perovskite compounds. In the first chapter of the review some principal aspects of the electrodynamics of periodical structures—magnetophotonic crystals are considered. The questions of zone structure and possible violations of periodicity (Tamm states, defect mode) as well as the influence of external magnetic field on the spectral characteristics of magnetophotonic crystals are considered. The second chapter of the review is devoted to the electrodynamics of left-handed media (left-handed metamaterials). Different versions of composite left-handed media are considered. Particular attention is paid to features of electrodynamics of artificially synthesized left-handed media, the doped lanthanum manganites-perovskites, which in a certain concentrations of doping element and temperature range can serve as an example of natural left-handed media. The Appendix describes the details of experimental techniques radiophysical research. Note that the research and design of the metamaterials listed above in a range of low temperatures are particularly important. This is due to the fact that at low temperatures a main disadvantage of artificial materials mentioned above (quite large losses) becomes less noticeable. At the same time the main their advantage (namely the possibility to control their frequency dispersion) remains. Thus it seems that the most prospective areas of application and further study of the magnetic metamaterials lie at low temperatures.
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.
Nonlinearities in energy-harvesting media
NASA Astrophysics Data System (ADS)
Andrews, David L.; Jenkins, Robert D.
2001-07-01
Both in natural photosynthetic systems and also their molecularly engineered mimics, energy is generally transferred to the sites of its chemical storage from other sites of primary optical excitation. This migration process generally entails a number of steps, frequently involving intermediary chromophore units, with each step characterised by high efficiency and rapidity. Energy thereby accrues at reaction centres where its chemical storage occurs. At high levels of irradiation, energy harvesting material can exhibit novel forms of optical nonlinearity. Such behaviour is associated with the direct pooling of excitation energy, enabling secondary acceptors to undergo transitions to states whose energy equals that of two or more input photons, subject to decay losses. Observations of this kind have now been made on a variety of materials, ranging from photoactive dyes, through fullerene derivatives, to lanthanide doped crystals. Recently developed theory has established the underlying principles and links between the modes of operation of these systems. Key factors include the chromophore layout and geometry, electronic structure and optical selection rules. Mesoscopic symmetry, especially in photosynthetic pigment arrays and also in their dendrimeric mimics, is here linked to the transient establishment of excitons. The involvement of excitons in energy harvesting is nonetheless substantially compromised by local disorder. The interplay of these factors in photoactive materials design is discussed in the context of new materials for operation with intense laser light.
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.
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)
Ganikhanov, Feruz; Yang, Shan; Adhikari, Sanjay
2013-03-01
Precise information on dispersion of the nonlinear optical susceptibility of Raman active media is essential in order to get an insight into physics and chemistry of intra- and inter-molecular interactions. 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 0.1 cm-1 thus making our approach an essential tool in quantitative microscopic characterization of complex biological media. Time-domain CARS transients traced with femtosecond pulses within orders of magnitude in the signal decay can lead to resolution of fine spectral features in χ(3) dispersion that can not be reliably detected by frequency-domain Raman based spectroscopy/microscopy techniques, including coherent methods. We will present results of the method's application in biological cells and tissue. Namely, we accessed a protein line at 1245 cm-1 in E-coli cell, major DNA and protein lines in red blood cells and triglyceride Raman active peaks in fat tissue.
Colloidal Dispersions in Polymeric Media: Interparticle Forces, Microstructure and Rheology
NASA Astrophysics Data System (ADS)
Ndong, Rose Seynabou
the range and origin of the rheology possible with particles dispersed in polymeric media.
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.
Marhic, M E; Kagi, N; Chiang, T K; Kazovsky, L G
1995-04-15
We show that in principle it is possible to cancel third-order nonlinear effects in optical fiber links. The necessary conditions exist in two-segment links, with dispersion compensation, phase conjugation, and amplification between the two, as well as opposite chromatic dispersion coefficients in the segments. The cancellation is independent of loss, modulation format, and modulation frequency. PMID:19859355
Complex geometrical optics of Kerr type nonlinear media
NASA Astrophysics Data System (ADS)
Berczynski, P.; Kravtsov, Yu. A.; Sukhorukov, A. P.
2010-03-01
The paper generalizes paraxial complex geometrical optics (PCGO) for Gaussian beam (GB) propagation in nonlinear media of Kerr type. Ordinary differential equations for the beam amplitude and for complex curvature of the wave front are derived, which describe the evolution of axially symmetric GB in a Kerr type nonlinear medium. It is shown that PCGO readily provides the solutions of NLS equation obtained earlier from diffraction theory on the basis of the aberration-free approach. Besides reproducing classical results of self-focusing PCGO readily describes an influence of the initial curvature of the wave front on the beam evolution in a medium of Kerr type including a nonlinear graded-index fiber. The range of applicability of the PCGO theory is discussed as well which is helpful for avoiding nonphysical solutions.
Modulational instability in nonlinearity-managed optical media
NASA Astrophysics Data System (ADS)
Centurion, Martin; Porter, Mason A.; Pu, Ye; Kevrekidis, P. G.; Frantzeskakis, D. J.; Psaltis, Demetri
2007-06-01
We investigate analytically, numerically, and experimentally the modulational instability in a layered, cubically nonlinear (Kerr) optical medium that consists of alternating layers of glass and air. We model this setting using a nonlinear Schrödinger (NLS) equation with a piecewise constant nonlinearity coefficient and conduct a theoretical analysis of its linear stability, obtaining a Kronig-Penney equation whose forbidden bands correspond to the modulationally unstable regimes. We find very good quantitative agreement between the theoretical analysis of the Kronig-Penney equation, numerical simulations of the NLS equation, and the experimental results for the modulational instability. Because of the periodicity in the evolution variable arising from the layered medium, we find multiple instability regions rather than just the one that would occur in uniform media.
Modulational instability in nonlinearity-managed optical media
Centurion, Martin; Porter, Mason A.; Pu Ye; Psaltis, Demetri; Kevrekidis, P. G.; Frantzeskakis, D. J.
2007-06-15
We investigate analytically, numerically, and experimentally the modulational instability in a layered, cubically nonlinear (Kerr) optical medium that consists of alternating layers of glass and air. We model this setting using a nonlinear Schroedinger (NLS) equation with a piecewise constant nonlinearity coefficient and conduct a theoretical analysis of its linear stability, obtaining a Kronig-Penney equation whose forbidden bands correspond to the modulationally unstable regimes. We find very good quantitative agreement between the theoretical analysis of the Kronig-Penney equation, numerical simulations of the NLS equation, and the experimental results for the modulational instability. Because of the periodicity in the evolution variable arising from the layered medium, we find multiple instability regions rather than just the one that would occur in uniform media.
Compensating for dispersion and the nonlinear Kerr effect without phase conjugation.
Paré, C; Villeneuve, A; Bélanger, P A; Doran, N J
1996-04-01
We propose the use of a dispersive medium with a negative nonlinear refractive-index coefficient as a way to compensate for the dispersion and the nonlinear effects resulting from pulse propagation in an optical fiber. The undoing of pulse interaction might allow for increased bit rates. PMID:19865438
Impact of saturation on dispersion and mixing in porous media
NASA Astrophysics Data System (ADS)
Jimenez-Martinez, J.; De Anna, P.; Turuban, R.; Tabuteau, H.; Le Borgne, T.; Meheust, Y.
2014-12-01
In partially saturated porous media, the spatial distribution of wetting (e.g., water) and non-wetting (e.g., air) phases causes the liquid flow to be focused onto narrow and complex flow paths, leaving large volumes of wetting fluid trapped in between non-wetting phase clusters. The impact of the resulting highly heterogeneous wetting fluid velocity distributions on the dispersion and mixing of a solute in this wetting phase is critical for predicting reactive transport processes that take place in partially saturated porous media. We study the dependence of dispersion and mixing on the saturation degree using a 2D experimental setup consisting of cylindrical grains built using soft lithography. The joint injection of the two phases (wetting and non-wetting) provides a controlled homogeneous saturation in the medium. The simultaneous measurement of the flow velocity field, the spatial distribution of the wetting and non-wetting phases, and the tracer concentration field are used to investigate the relationship between the flow field complexity induced by desaturation and dispersion/mixing properties. We analyze the temporal behavior of the mean concentration gradient and the scalar dissipation rate, which quantify the temporal variation of the concentration variability and the potential for mixing-controlled chemical reactivity. The formation of preferential flowpaths in unsaturated flows is found to have an important impact on the mixing behavior. While the mean concentration gradient decays in time for saturated flow following the classical diffusive smoothing of concentration gradients, the creation of highly channelized finger structures in unsaturated flows induces persistently large concentration gradients which decay slowly in time. The highly resolved concentration field images show that this effect is due to i) a drastic increase of the surface available for creating concentration gradients across the finger boundaries, ii) the existence of dead-ends with
Surface lattice solitons in diffusive nonlinear media with spatially modulated nonlinearity.
Zhan, Kaiyun; Jiao, Zhiyong; Li, Xi; Jia, Yulei; Zhang, Hui
2015-09-01
Two families of gap and twisted surface lattice solitons in diffusive nonlinear periodic media with spatially modulated nonlinearity are reported. It is shown that the existence and stability of such solitons are extremely spatially modulated nonlinearity sensitive. For self-focusing nonlinearity, gap surface solitons belonging to the semi-infinite gap are stable in whole existence domain, twisted surface solitons are also linearly stable in low modulated strength region and a very narrow unstable region near the upper cutoff appears in high modulated strength region. In the self-defocusing case, surface gap solitons belonging to the first gap can propagate stably in whole existence domain except for an extremely narrow region close to the Bloch band, twisted solitons belonging to this gap are unstable in the entire existence domain. PMID:26368497
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.
Wei, Haiqing; Plant, David V
2005-09-15
A method of packaging dispersion-compensating fibers (DCFs) is discussed that achieves optimal nonlinearity compensation and a good signal-to-noise ratio simultaneously. An optimally packaged dispersion-compensating module (DCM) may consist of portions of DCFs with higher and lower loss coefficients. Such optimized DCMs may be paired with transmission fibers to form scaled translation-symmetric lines that could effectively compensate for signal distortions due to dispersion and nonlinearity, with or without optical phase conjugation. PMID:16196322
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
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.
NONLINEAR SIMULATION OF TURBULENT FIELD LINES: DISPERSAL STATISTICS
Ragot, B. R.
2010-11-10
A new method for the full nonlinear computation of sets of turbulent field lines is introduced that extends the sums of random numbers distribution method previously applied to the computation of individual field lines. With a multiscale variation of the phases consistent with in situ observations of intermittent solar wind (SW) turbulence, the new method allows inclusion of the equivalent of more than four decades of turbulent scales with a fully three-dimensional distribution of wavevectors. As a first application, pairs of magnetic field lines are computed in independent realizations of the turbulence, for spectra typical of the quiet slow SW near 1 AU. The statistics of field-line dispersal are then studied from the simulated pairs of magnetic field lines and compared to earlier theoretical predictions. It appears that while the earlier theoretical picture remains relatively accurate as long as the mean variation of separation logarithm {Lambda} is less than one, the qualitative picture is quickly altered as {Lambda} grows past one.
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
Critique of Burnett-Frind dispersion tensor for axisymmetric porous media
Lichtner, Peter C; Kelkar, Sharad; Robinson, Bruce A
2008-01-01
This technical note provides a critique of the Burnett and Frind (1987) dispersion tensor for porous media with axial symmetry based on a previous publication by the authors (Lichtner et aI., 2002). In this work a new approach is used based on unit eigenvectors which simplifies the analysis. It is demonstrated that the Burnett-Frind dispersion tensor, although acceptable for small values of the vertical velocity, produces the incorrect behavior for both longitudinal and transverse dispersivity as the flow velocity varies from parallel to perpendicular to the axis of symmetry. A new form of the dispersion tensor is derived for axially symmetric porous media involving four dispersivity coefficients corresponding to longitudinal and transverse dispersion in horizontal and vertical directions, defined as perpendicular and parallel to the axis of symmetry, respectively. This new dispersion tensor corrects two fundamental problems with the dispersion tensor proposed by Burnett and Frind (1987) for axial symmetric media.
Vorticity and upscaled dispersion in 3D heterogeneous porous media
NASA Astrophysics Data System (ADS)
Di Dato, Mariaines; Chiogna, Gabriele; de Barros, Felipe; Bellin, Alberto; Fiori, Aldo
2015-04-01
-structure (inclusion's type and shape). The purpose of this work is to study how different micro-structures impact the vorticity. The analysis is carried on for a binary medium, as a function of conductivity contrast κ, and for heterogeneous ensemble of inclusions with a lognomal distribution of κ, as a function of heterogeneity degree σln κ2. Inclusion's type and shape have a great influence on the vorticity field: in media defined by the same volume fraction and anisotropy degree, thinner inclusions yield more vorticity, therefore the smaller is e the greater is the vorticity. This effect is more evident if inclusions are more conductive, due to flow focusing effects. We demonstrate that the statistical anisotropy of the medium plays an important role: the smaller is the statistical anisotropy ratio, the higher is the vorticity produced by the mixture of inclusions. Furthermore, considering heterogeneous mixture of inclusions, it is showed that vorticity growths with increasing the variance of the conductivity contrast distribution. In addition to analyzing the rotational properties of the spatially variable flow field, we illustrate how the global vorticity of the medium affects solute transport. This is achieved by evaluating the upscaled dispersion coefficients.
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.
Surface-wave solitons between linear media and nonlocal nonlinear media
Shi Zhiwei; Li Huagang; Guo Qi
2011-02-15
We address surface solitons at the interface between linear media and nonlocal nonlinear media in the presence of a discontinuity in refractive index at the surface of these two materials. We investigated the influence of the degree of nonlocality on the stability, energy flow, and full width at half-maximum of the surface wave solitons. It is shown that surface solitons will be stable only if the degree of nonlocality exceeds a critical value. We find that the refractive index difference can affect the power distribution of the surface solitons in the two media. Also, different boundary values at the interface can lead to different relative peak positions of the surface solitons. However, neither the refractive index nor the boundary conditions can affect the stability of the solitons, for a given degree of nonlocality.
Dispersion and nonlinear effects in the 2011 Tohoku-Oki earthquake tsunami
NASA Astrophysics Data System (ADS)
Saito, Tatsuhiko; Inazu, Daisuke; Miyoshi, Takayuki; Hino, Ryota
2014-08-01
This study reveals the roles of the wave dispersion and nonlinear effects for the 2011 Tohoku-Oki earthquake tsunami. We conducted tsunami simulations based on the nonlinear dispersive equations with a high-resolution source model. The simulations successfully reproduced the waveforms recorded in the offshore, deep sea, and focal areas. The calculated inundation area coincided well with the actual inundation for the Sendai Plain, which was the widest inundation area during this event. By conducting sets of simulations with different tsunami equations, we obtained the followings insights into the wave dispersion, nonlinear effects, and energy dissipation for this event. Although the wave dispersion was neglected in most studies, the maximum amplitude was significantly overestimated in the deep sea if the dispersion was not included. The waveform observed at the station with the largest tsunami height (˜2 m) among the deep-ocean stations also verified the necessity of the dispersion. It is well known that the nonlinear effects play an important role for the propagation of a tsunami into bays and harbors. Additionally, nonlinear effects need to be considered to accurately model later waves, even for offshore stations. In particular, including nonlinear terms rather than the inundation was more important when precisely modeling the waves reflected from the coast.
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. PMID:19721553
Dispersion and nonlinear management for femtosecond optical solitons
NASA Astrophysics Data System (ADS)
Porsezian, K.; Hasegawa, A.; Serkin, V. N.; Belyaeva, T. L.; Ganapathy, R.
2007-02-01
We consider the concept of femtosecond propagation for optical solitons in a dispersion management fiber and study the optimal amplification of optical solitons through dispersion wells and barriers and also for the dispersion tailored profile case. For the former, we observed periodic soliton trapping for the in-phase injection case when their respective velocities were equal and opposite with their amplitudes being unequal and no soliton trapping for the off-phase injection case when the two pulses are having a phase difference of π. For the latter, we observed an enormous amplification of the soliton pulses which is one of our main results in this Letter.
Saitoh, Kunimasa; Koshiba, Masanori
2004-05-17
We propose a new structure of highly nonlinear dispersion-flattened (HNDF) photonic crystal fiber (PCF) with nonlinear coefficient as large as 30 W(-1)km(-1) at 1.55 microm designed by varying the diameters of the air-hole rings along the fiber radius. This innovative HNDF-PCF has a unique effective-index profile that can offer not only a large nonlinear coefficient but also flat dispersion slope and low leakage losses. It is shown through numerical results that the novel microstructured optical fiber with small normal group-velocity dispersion and nearly zero dispersion slope offers the possibility of efficient supercontinuum generation in the telecommunication window using a few ps pulses. PMID:19475038
NASA Astrophysics Data System (ADS)
Saitoh, Kunimasa; Koshiba, Masanori
2004-05-01
We propose a new structure of highly nonlinear dispersion-flattened (HNDF) photonic crystal fiber (PCF) with nonlinear coefficient as large as 30 W-1km-1 at 1.55 Âµm designed by varying the diameters of the air-hole rings along the fiber radius. This innovative HNDF-PCF has a unique effective-index profile that can offer not only a large nonlinear coefficient but also flat dispersion slope and low leakage losses. It is shown through numerical results that the novel microstructured optical fiber with small normal group-velocity dispersion and nearly zero dispersion slope offers the possibility of efficient supercontinuum generation in the telecommunication window using a few ps pulses.
Computational aspects of dispersive computational continua for elastic heterogeneous media
NASA Astrophysics Data System (ADS)
Fafalis, Dimitrios; Fish, Jacob
2015-12-01
The present manuscript focusses on computational aspects of dispersive computational continua (C^2) formulation previously introduced by the authors. The dispersive C^2 formulation is a multiscale approach that showed strikingly accurate dispersion curves. However, the seemingly theoretical advantage may be inconsequential due to tremendous computational cost involved. Unlike classical dispersive methods pioneered more than a half a century ago where the unit cell is quasi-static and provides effective mechanical and dispersive properties to the coarse-scale problem, the dispersive C^2 gives rise to transient problems at all scales and for all microphases involved. An efficient block time-integration scheme is proposed that takes advantage of the fact that the transient unit cell problems are not coupled to each other, but rather to a single coarse-scale finite element they are positioned in. We show that the computational cost of the method is comparable to the classical dispersive methods for short load durations.
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
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. PMID:25322369
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.
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.
NASA Astrophysics Data System (ADS)
Sharifimehr, Mohammad Reza; Ayoubi, Kazem; Mohajerani, Ezeddin
2015-11-01
Measuring nonlinear optical response of a specific material in a mixture, not only leads to investigate the behavior of a particular component in various circumstances, but also can be a way to select suitable combination and optimum concentration of additives and therefore obtaining the maximum nonlinear optical signals. In this work, by using dual-arm Z-scan technique, the nonlinear refractive index of Disperse Red1 (DR1) organic dye molecules inside the core of prepared polymeric nanocapsules was measured among various materials which prepared nanocapsules were made of them. Then the measured value was compared with nonlinear refractive index of DR1 solved in dichloromethane.
Adaptive control of the propagation of ultrafast light through random and nonlinear media
NASA Astrophysics Data System (ADS)
Moores, Mark David
2001-12-01
Ultrafast light sources generate coherent pulses with durations of less than one picosecond, and represent the next generation of illuminators for medical imaging and optical communications applications. Such sources are already widely used experimentally. Correction of temporal widths or pulse envelopes after traversal of optically non-ideal materials is critical for the delivery of optimal ultrashort pulses. It is important to investigate the physical mechanisms that distort pulses and to develop and implement methods for minimizing these effects. In this work, we investigate methods for characterizing and manipulating pulse propagation dynamics in random (scattering) and nonlinear optical media. In particular, we use pulse shaping to manipulate the light field of ultrashort infrared pulses. Application of spectral phase by a liquid crystal spatial light modulator is used to control the temporal pulse shape. The applied phase is controlled by a genetic algorithm that adaptively responds to the feedback from previous phase profiles. Experiments are detailed that address related aspects of the character of ultrafast pulses-the short timescales and necessarily wide frequency bandwidths. Material dispersion is by definition frequency dependent. Passage through an inhomogeneous system of randomly situated boundaries (scatterers) causes additional distortion of ballistic pulses due to multiple reflections. The reflected rays accumulate phase shifts that depend on the separation of the reflecting boundaries and the photon frequency. Ultrafast bandwidths present a wide range of frequencies for dispersion and interaction with macroscopic dielectric structure. The shaper and adaptive learning algorithm are used to reduce these effects, lessening the impact of the scattering medium on propagating pulses. The timescale of ultrashort pulses results in peak intensities that interact with the electronic structure of optical materials to induce polarization that is no longer
Symmetry analysis for a class of nonlinear dispersive equations
NASA Astrophysics Data System (ADS)
Charalambous, K.; Sophocleous, C.
2015-05-01
A class of dispersive equations is studied within the framework of group analysis of differential equations. The enhanced Lie group classification is achieved. The complete list of equivalence transformations is presented. It is shown that certain equations from the class admit nonclassical reductions. Potential and potential nonclassical symmetries are also considered.
NASA Astrophysics Data System (ADS)
Fakhri, P.; Rashidian Vaziri, M. R.; Jaleh, B.; Partovi Shabestari, N.
2016-01-01
In this paper, we report on the preparation of graphene oxide and graphene oxide-Au nanodispersions in various solvents, such as water, DMF (N,N-dimethylformamide) and NMP (N-methyl-2-pyrrolidone). Optical, structural and nonlinear optical properties of all the samples have been studied. The nonlinear optical properties have been measured using the z-scan technique. It is shown that the incorporation of Au nanoparticles can greatly improve the nonlinear optical properties of graphene oxide. More importantly, the fact is recognized that the media that surround the nonlinear sample can influence its nonlinear optical properties by their nonlocal action. The nonlocal z-scan theory has been used to estimate the role of the surrounding medium in changing the samples’ nonlinear responses.
Iterative Time Reversal Simulation for Selective Focusing in Multi-target Nonlinear Media
NASA Astrophysics Data System (ADS)
Su, Chang; Peng, Zhefan; Lin, Weijun
In High Intensity Focused Ultrasound (HIFU), when multiple targets are present in a linear medium, ultrasound can focus on the strongest target by using an iterative time-reversal(TR) method. However, the validation of iterative TR in nonlinear human tissue still needs to be investigated. In the study, the TR and iterative TR processes are numerically simulated with a finite difference method in two dimension, considering the nonlinear effects. Results show that TR is valid in nonlinear human tissues with some difference in focus accuracy and intensity gain comparing to that in linear media. The nonlinearity of the media increases the intensity gain at the focal point, while the absorption decreases the focal gain and changes the position of the focal spot. Iterative TR works well in nonlinear media and the lobe on the weaker target attenuates more rapidly than in linear media.
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.
Flow Intermittency, Dispersion, and Correlated Continuous Time Random Walks in Porous Media
de Anna, Pietro; Le Borgne, Tanguy; Dentz, Marco; Tartakovsky, Alexandre M.; Bolster, Diogo; Davy, Philippe
2013-05-01
We study the intermittency of fluid velocities in porous media and its relation to anomalous dispersion. Lagrangian velocities measured at equidistant points along streamlines are shown to form a spatial Markov process. As a consequence of this remarkable property, the dispersion of fluid particles can be described by a continuous time random walk with correlated temporal increments. This new dynamical picture of intermittency provides a direct link between the microscale flow, its intermittent properties, and non-Fickian dispersion.
NASA Astrophysics Data System (ADS)
Cao, Wenhua
2016-05-01
Predispersion for reduction of intrachannel nonlinear impairments in quasi-linear strongly dispersion-managed transmission system is analyzed in detail by numerical simulations. We show that for moderate amount of predispersion there is an optimal value at which reduction of the nonlinear impairments can be obtained, which is consistent with previous well-known predictions. However, we found that much better transmission performance than that of the previous predictions can be obtained if predispersion is increased to some extent. For large predispersion, the nonlinear impairments reduce monotonically with increasing predispersion and then they tend to be stabilized when predispersion is further increased. Thus, transmission performance can be efficiently improved by inserting a high-dispersive element, such as a chirped fiber bragg grating (CFBG), at the input end of the transmission link to broaden the signal pulses while, at the output end, using another CFBG with the opposite dispersion to recompress the signal.
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.
Xie, Chen; Liu, Bowen; Niu, Hailiang; Song, Youjian; Li, Yi; Hu, Minglie; Zhang, Yueguang; Shen, Weidong; Liu, Xu; Wang, Chingyue
2011-11-01
We report on a femtosecond nonlinear amplification fiber laser system using a vector-dispersion compressor, which consists of a transmission grating pair and multipass cell based Gires-Tournois interferometer mirrors. The mirror is designed with nearly zero group-delay dispersion and large negative third-order dispersion. As a result, the third-order dispersion of the compressor can be adjusted independently to compensate the nonlinear phase shift of amplified pulses to reduce the pulse pedestal. With this scheme, the system outputs 44 fs laser pulses with little wing at 26.6 W output average power and 531 nJ pulse energy, corresponding to 10.8 MW peak power. PMID:22048347
Nonlinear dynamics, granular media and dynamic earthquake triggering.
Johnson, Paul A; Jia, Xiaoping
2005-10-01
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. PMID:16208368
NASA Astrophysics Data System (ADS)
Ntsime, Basetsana P.; Moitsheki, Raseelo J.
2016-06-01
In this paper we consider a nonlinear convection-dispersion equation arising in contaminant transport. The water flow velocity is considered to be spatially-dependent and dispersion coefficient depends on concentration. A direct group classification resulted in a number of cases for which the governing equation admits Lie point symmetries. In each case the one dimensional optimal system of subalgebras is constructed. Reductions are performed. The reduced ordinary differential equations (ODEs) are nonlinear and difficult to solve exactly. On the other hand we consider the steady state problem and applied the method of canonical coordinates to determine exact solutions.
Controllable broadband nonlinear optical response of graphene dispersions by tuning vacuum pressure.
Cheng, Xin; Dong, Ningning; Li, Bin; Zhang, Xiaoyan; Zhang, Saifeng; Jiao, Jia; Blau, Werner J; Zhang, Long; Wang, Jun
2013-07-15
Nonlinear scattering, originating from laser induced solvent micro-bubbles and/or micro-plasmas, is regarded as the principal mechanism for nonlinear optical (NLO) response of graphene dispersions at ns timescale. In this work, we report the significant enhancement of NLO response of graphene dispersions by decreasing the atmospheric pressure, which has strong influence on the formation and growth of micro-bubbles and/or micro-plasmas. A modified open-aperture Z-scan apparatus in combination with a vacuum system was used to study the effect of vacuum pressure on the NLO property of graphene dispersions prepared by liquid-phase exfoliation technique. We show that the atmospheric pressure can be utilized to control and tune the nonlinear responses of the graphene dispersions for ns laser pulses at both 532 nm and 1064 nm. The lower the vacuum pressure was, the larger the NLO response was. In contrast, the NLO property of fullerene was found to be independent of the pressure change, due to its nature of nonlinear absorption. This work affords a simple method to distinguish the nonlinear scattering and absorption mechanisms for NLO nanomaterials. PMID:23938499
Experiments on nonlinear wave propagation in disordered media
NASA Astrophysics Data System (ADS)
McKenna, M. J.; Keat, Justin; Wang, Jun; Maynard, J. D.
1994-02-01
A fundamental question concerning systems which are both disordered and nonlinear is whether or not Anderson localization is weakened by the nonlinearity. Theory predicts that localized eigenstates will survive nonlinearity, whereas nonlinear pulses may or may not experience the effects of localization depending on the relative magnitude of the Anderson localization length and the characteristic width of the pulse. We have used nonlinear surface waves on a superfluid helium film to obtain results in agreement with the theoretical predictions.
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.
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
Abe, H.; Okuda, H.
1993-08-01
In this Letter, we first present 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. The model was then used for studying linear and nonlinear wave propagation in the dielectric medium such as an optical fiber. It is shown that the model may be useful for studying nonlinear wave propagation and harmonics generation in the nonlinear dielectric media.
The dispersion and aggregation of graphene oxide in aqueous media.
Wang, Meng; Niu, Yang; Zhou, Jihan; Wen, Hao; Zhang, Zhenyu; Luo, Da; Gao, Dongliang; Yang, Juan; Liang, Dehai; Li, Yan
2016-08-14
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. PMID:27432559
Accurate FDTD modelling for dispersive media using rational function and particle swarm optimisation
NASA Astrophysics Data System (ADS)
Chung, Haejun; Ha, Sang-Gyu; Choi, Jaehoon; Jung, Kyung-Young
2015-07-01
This article presents an accurate finite-difference time domain (FDTD) dispersive modelling suitable for complex dispersive media. A quadratic complex rational function (QCRF) is used to characterise their dispersive relations. To obtain accurate coefficients of QCRF, in this work, we use an analytical approach and a particle swarm optimisation (PSO) simultaneously. In specific, an analytical approach is used to obtain the QCRF matrix-solving equation and PSO is applied to adjust a weighting function of this equation. Numerical examples are used to illustrate the validity of the proposed FDTD dispersion model.
Correlated few-photon transport in one-dimensional waveguides: Linear and nonlinear dispersions
Roy, Dibyendu
2011-04-15
We address correlated few-photon transport in one-dimensional waveguides coupled to a two-level system (TLS), such as an atom or a quantum dot. We derive exactly the single-photon and two-photon current (transmission) for linear and nonlinear (tight-binding sinusoidal) energy-momentum dispersion relations of photons in the waveguides and compare the results for the different dispersions. A large enhancement of the two-photon current for the sinusoidal dispersion has been seen at a certain transition energy of the TLS away from the single-photon resonances.
NASA Astrophysics Data System (ADS)
Yan, Zhenya; Bluman, George
2002-11-01
The special exact solutions of nonlinearly dispersive Boussinesq equations (called B( m, n) equations), utt- uxx- a( un) xx+ b( um) xxxx=0, is investigated by using four direct ansatze. As a result, abundant new compactons: solitons with the absence of infinite wings, solitary patterns solutions having infinite slopes or cups, solitary waves and singular periodic wave solutions of these two equations are obtained. The variant is extended to include linear dispersion to support compactons and solitary patterns in the linearly dispersive Boussinesq equations with m=1. Moreover, another new compacton solution of the special case, B(2,2) equation, is also found.
NASA Astrophysics Data System (ADS)
Matsuno, Yoshimasa
2014-03-01
We develop a direct method for solving a modified Camassa-Holm equation with cubic nonlinearity and linear dispersion under the rapidly decreasing boundary condition. We obtain a compact parametric representation for the multisoliton solutions and investigate their properties. We show that the introduction of a linear dispersive term exhibits various new features in the structure of solutions. In particular, we find the smooth solitons whose characteristics are different from those of the Camassa-Holm equation, as well as the novel types of singular solitons. A remarkable feature of the soliton solutions is that the underlying structure of the associated tau-functions is the same as that of a model equation for shallow-water waves introduced by Ablowitz et al (1974 Stud. Appl. Math. 53 249-315). Finally, we demonstrate that the short-wave limit of the soliton solutions recovers the soliton solutions of the short pulse equation which describes the propagation of ultra-short optical pulses in nonlinear media.
NASA Astrophysics Data System (ADS)
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.
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.
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
On shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients
Abdel-Gawad, Hamdy I.; Osman, Mohamed
2014-01-01
In this paper, we studied the progression of shallow water waves relevant to the variable coefficient Korteweg–de Vries (vcKdV) equation. We investigated two kinds of cases: when the dispersion and nonlinearity coefficients are proportional, and when they are not linearly dependent. In the first case, it was shown that the progressive waves have some geometric structures as in the case of KdV equation with constant coefficients but the waves travel with time dependent speed. In the second case, the wave structure is maintained when the nonlinearity balances the dispersion. Otherwise, water waves collapse. The objectives of the study are to find a wide class of exact solutions by using the extended unified method and to present a new algorithm for treating the coupled nonlinear PDE’s. PMID:26199750
On shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients.
Abdel-Gawad, Hamdy I; Osman, Mohamed
2015-07-01
In this paper, we studied the progression of shallow water waves relevant to the variable coefficient Korteweg-de Vries (vcKdV) equation. We investigated two kinds of cases: when the dispersion and nonlinearity coefficients are proportional, and when they are not linearly dependent. In the first case, it was shown that the progressive waves have some geometric structures as in the case of KdV equation with constant coefficients but the waves travel with time dependent speed. In the second case, the wave structure is maintained when the nonlinearity balances the dispersion. Otherwise, water waves collapse. The objectives of the study are to find a wide class of exact solutions by using the extended unified method and to present a new algorithm for treating the coupled nonlinear PDE's. PMID:26199750
Nanoparticle dispersion in disordered porous media with and without polymer additives.
Babayekhorasani, Firoozeh; Dunstan, Dave E; Krishnamoorti, Ramanan; Conrad, Jacinta C
2016-06-29
In purely viscous Newtonian fluids, mechanical mixing of the fluid stream as it moves through an unstructured porous medium controls the long-time dispersion of molecular tracers. In applications ranging from environmental remediation to materials processing, however, particles are transported through porous media in polymer solutions and melts, for which the fluid properties depend on the shear rate and extent of deformation. How the flow characteristics of polymer solutions affect the spreading of finite-sized particles remains poorly understood - both on the microscopic scale as local velocity profiles, and on the macroscale as dispersion. Here, we show across a range of flow rates and disordered porous media configurations that the long-time transport coefficients of particles flowed in water, in a viscous Newtonian fluid, and in a non-Newtonian shear-thinning polymer solution collapse onto scaling curves, independent of the fluid rheology. Thus the addition of polymer does not impact nanoparticle dispersion through disordered porous media. PMID:27328208
Fluid dispersion effects on density-driven thermohaline flow and transport in porous media
NASA Astrophysics Data System (ADS)
Jamshidzadeh, Zahra; Tsai, Frank T.-C.; Mirbagheri, Seyed Ahmad; Ghasemzadeh, Hasan
2013-11-01
This study introduces the dispersive fluid flux of total fluid mass to the density-driven flow equation to improve thermohaline modeling of salt and heat transports in porous media. The dispersive fluid flux in the flow equation is derived to account for an additional fluid flux driven by the density gradient and mechanical dispersion. The coupled flow, salt transport and heat transport governing equations are numerically solved by a fully implicit finite difference method to investigate solution changes due to the dispersive fluid flux. The numerical solutions are verified by the Henry problem and the thermal Elder problem under a moderate density effect and by the brine Elder problem under a strong density effect. It is found that increment of the maximum ratio of the dispersive fluid flux to the advective fluid flux results in increasing dispersivity for the Henry problem and the brine Elder problem. The effects of the dispersive fluid flux on salt and heat transports under high density differences and high dispersivities are more noticeable than under low density differences and low dispersivities. Values of quantitative indicators such as the Nusselt number, mass flux, salt mass stored and maximum penetration depth in the brine Elder problem show noticeable changes by the dispersive fluid flux. In the thermohaline Elder problem, the dispersive fluid flux shows a considerable effect on the shape and the number of developed fingers and makes either an upwelling or a downwelling flow in the center of the domain. In conclusion, for the general case that involves strong density-driven flow and transport modeling in porous media, the dispersive fluid flux should be considered in the flow equation.
Derivation of Hawking radiation in dispersive dielectric media
NASA Astrophysics Data System (ADS)
Linder, Malte F.; Schützhold, Ralf; Unruh, William G.
2016-05-01
Motivated by recent experimental efforts, we study a black hole analog induced by the propagation of a strong laser pulse in a nonlinear dielectric medium. Based on the Hopfield model (one pair of Sellmeier coefficients), we perform an analytic and fully relativistic microscopic derivation of the analog of Hawking radiation in this setup. The Hawking temperature is determined by the analog of the surface gravity (as expected), but we also find a frequency-dependent gray-body factor (i.e., a nonthermal spectrum at infinity) due to the breaking of conformal invariance in this setup.
NASA Astrophysics Data System (ADS)
Nguyen, Ba Phi; Kim, Kihong
2014-06-01
We study theoretically the influence of nonlinear gain effects on the transmission and the Anderson localization of waves in both uniform and random one-dimensional amplifying media by using the discrete nonlinear Schrödinger equation. In uniform amplifying media with nonlinear gain, we find that the strong oscillatory behavior of the transmittance and the reflectance for odd and even values of the sample length disappears for large nonlinearities. The exponential decay rate of the transmittance in the asymptotic limit is found to be independent of nonlinear gain. In random amplifying media, we find that the maximum values of the disorder-averaged logarithmic transmittance and reflectance depend nonmonotonically on the strength of nonlinear gain. We also find that the localization length is independent of nonlinear gain. In other words, the Anderson localization is neither enhanced nor weakened due to nonlinear gain. In both the uniform and the random cases, the crossover length, which is the critical length for the amplification to be efficient, is strongly reduced by the nonlinear nature of the gain.
Focused optical and acoustic beams in media with nonlinear absorption
NASA Astrophysics Data System (ADS)
Rudenko, O. V.; Sukhorukov, A. A.
1996-11-01
Optical and acoustic beams are known to be useful for medical and biological applications, such as diagnostics, surgery, etc. At high intensities both nonlinear lens effects and nonlinear absorption can be significant for the beams. The nonlinear absorption arises due to two-photon optical processes or acoustic shock wave formation. The present work is devoted to the theoretical description of nonlinear beam propagation and focal spot formation taking into account the competition between focusing, diffraction and absorption. We derived a new nonlinear integro- differential equation describing the spatial evolution of the beam width. The general analytical solution of this equation is obtained for arbitrary boundary conditions. The simple formulas are derived for the angle divergence in the far field, as well as for beam width at nonlinear waist. The results of the analysis of these key parameters in different situations are presented.
Reciprocity breaking during nonlinear propagation of adapted beams through random media
NASA Astrophysics Data System (ADS)
Palastro, J. P.; Peñano, J.; Nelson, W.; DiComo, G.; Helle, M.; Johnson, L. A.; Hafizi, B.
2016-08-01
Adaptive optics (AO) systems rely on the principle of reciprocity, or symmetry with respect to the interchange of point sources and receivers. These systems use the light received from a low power emitter on or near a target to compensate profile aberrations acquired by a laser beam during linear propagation through random media. If, however, the laser beam propagates nonlinearly, reciprocity is broken, potentially undermining AO correction. Here we examine the consequences of this breakdown. While discussed for general random and nonlinear media, we consider specific examples of Kerr-nonlinear, turbulent atmosphere.
Reciprocity breaking during nonlinear propagation of adapted beams through random media.
Palastro, J P; Peñano, J; Nelson, W; DiComo, G; Helle, M; Johnson, L A; Hafizi, B
2016-08-22
Adaptive optics (AO) systems rely on the principle of reciprocity, or symmetry with respect to the interchange of point sources and receivers. These systems use the light received from a low power emitter on or near a target to compensate phase aberrations acquired by a laser beam during linear propagation through random media. If, however, the laser beam propagates nonlinearly, reciprocity is broken, potentially undermining AO correction. Here we examine the consequences of this breakdown, providing the first analysis of AO applied to high peak power laser beams. While discussed for general random and nonlinear media, we consider specific examples of Kerr-nonlinear, turbulent atmosphere. PMID:27557166
Sharp nonlinear stability for centrifugal filtration convection in magnetizable media.
Saravanan, S; Brindha, D
2011-11-01
A nonlinear stability theory is adopted to study centrifugal thermal convection in a magnetic-fluid-saturated and differentially heated porous layer placed in a zero-gravity environment. The axis of rotation of the layer is placed within its boundaries that leads to an alternating direction of the centrifugal body force. An analysis through the variational principles is made to find the unconditional and sharp nonlinear limits. The compound matrix method is employed to solve the eigenvalue problems of the nonlinear and corresponding linear theories. The importance of nonlinear theory is established by demonstrating the failure of the linear theory in capturing the physics of the onset of convection. PMID:22181509
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.
Compensation of nonlinear phase shifts with third-order dispersion in short-pulse fiber amplifiers.
Zhou, Shian; Kuznetsova, Lyuba; Chong, Andy; Wise, Frank
2005-06-27
We show that nonlinear phase shifts and third-order dispersion can compensate each other in short-pulse fiber amplifiers. This compen-sation can be exploited in any implementation of chirped-pulse amplification, with stretching and compression accomplished with diffraction gratings, single-mode fiber, microstructure fiber, fiber Bragg gratings, etc. In particular, we consider chirped-pulse fiber amplifiers at wavelengths for which the fiber dispersion is normal. The nonlinear phase shift accumulated in the amplifier can be compensated by the third-order dispersion of the combination of a fiber stretcher and grating compressor. A numerical model is used to predict the compensation, and experimental results that exhibit the main features of the calculations are presented. In the presence of third-order dispersion, an optimal nonlinear phase shift reduces the pulse duration, and enhances the peak power and pulse contrast compared to the pulse produced in linear propagation. Contrary to common belief, fiber stretchers can perform as well or better than grating stretchers in fiber amplifiers, while offering the major practical advantages of a waveguide medium. PMID:19498473
Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model
NASA Astrophysics Data System (ADS)
Cousins, Will; Sapsis, Themistoklis P.
2014-07-01
The aim of this work is the quantification and prediction of rare events characterized by extreme intensity in nonlinear waves with broad spectra. We consider a one-dimensional nonlinear model with deep-water waves dispersion relation, the Majda-McLaughlin-Tabak (MMT) model, in a dynamical regime that is characterized by a broadband spectrum and strong nonlinear energy transfers during the development of intermittent events with finite-lifetime. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A statistical analysis of the Gabor coefficients reveals (i) the low-dimensionality of the intermittent structures, (ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as (iii) the critical scales (or critical Gabor coefficients) where a critical amount of energy can trigger the formation of an extreme event. We analyze the unstable character of these special localized modes directly through the system equation and show that these intermittent events are due to the interplay of the system nonlinearity, the wave dispersion, and the wave dissipation which mimics wave breaking. These localized instabilities are triggered by random localizations of energy in space, created by the dispersive propagation of low-amplitude waves with random phase. Based on these properties, we design low-dimensional functionals of these Gabor coefficients that allow for the prediction of the extreme event well before the nonlinear interactions begin to occur.
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
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.
NASA Astrophysics Data System (ADS)
Glückstad, J.; Saffman, M.
1995-03-01
We have observed the spontaneous formation of transverse spatial patterns in a thin film of bacteriorhodopsin with a feedback mirror. Bacteriorhodopsin has a mixed absorptive-dispersive nonlinearity at the wavelength used in the experiments (633 nm). Threshold values of the incident intensity for observation of pattern formation are found from a linear stability analysis of a model that describes bacteriorhodopsin as a sluggish saturable nonlinear medium with a complex Kerr coefficient. The calculated threshold intensity is in good agreement with the experimental observations, and the patterns are predicted to be frequency offset from the pump radiation.
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.
Fractional Advective-Dispersive Equation as a Model of Solute Transport in Porous Media
Technology Transfer Automated Retrieval System (TEKTRAN)
Understanding and modeling transport of solutes in porous media is a critical issue in the environmental protection. The common model is the advective-dispersive equation (ADE) describing the superposition of the advective transport and the Brownian motion in water-filled pore space. Deviations from...
Analytical solution for the advection-dispersion transport equation in layered media
Technology Transfer Automated Retrieval System (TEKTRAN)
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...
NASA Astrophysics Data System (ADS)
Jiménez, Noé; Camarena, Francisco; Redondo, Javier; Sánchez-Morcillo, Víctor; Konofagou, Elisa E.
2015-10-01
We report a numerical method for solving the constitutive relations of nonlinear acoustics, where multiple relaxation processes are included in a generalized formulation that allows the time-domain numerical solution by an explicit finite differences scheme. Thus, the proposed physical model overcomes the limitations of the one-way Khokhlov-Zabolotskaya-Kuznetsov (KZK) type models and, due to the Lagrangian density is implicitly included in the calculation, the proposed method also overcomes the limitations of Westervelt equation in complex configurations for medical ultrasound. In order to model frequency power law attenuation and dispersion, such as observed in biological media, the relaxation parameters are fitted to both exact frequency power law attenuation/dispersion media and also empirically measured attenuation of a variety of tissues that does not fit an exact power law. Finally, a computational technique based on artificial relaxation is included to correct the non-negligible numerical dispersion of the finite difference scheme, and, on the other hand, improve stability trough artificial attenuation when shock waves are present. This technique avoids the use of high-order finite-differences schemes leading to fast calculations. The present algorithm is especially suited for practical configuration where spatial discontinuities are present in the domain (e.g. axisymmetric domains or zero normal velocity boundary conditions in general). The accuracy of the method is discussed by comparing the proposed simulation solutions to one dimensional analytical and k-space numerical solutions.
A Stochastic Non-Gaussian Velocity Model for Tracer Dispersion in Heterogeneous Porous Media
NASA Astrophysics Data System (ADS)
Meyer, D. W.; Tchelepi, H. A.
2009-12-01
To model tracer transport in porous media, computationally expensive Monte Carlo (MC) techniques or low-order approximation methods (LOAM) are applicable [1]. The latter are inexpensive but limited to relatively homogeneous media with low conductivity or transmissivity variations, and approximately Gaussian one-point velocity statistics. MC studies have shown that heterogeneous media lead to distinctly skewed non-Gaussian velocity distributions [2]. In addition to MC and LOAM, continuous time random walk (CTRW) or Lévy motion (LM) approaches were proposed for the modeling of dispersion in highly heterogeneous media, e.g, fractured rock [3,4]. Both models involve discontinuous stochastic processes for the displacement of tracer particles. The parameters that determine these processes, however, are not always easy to identify. In this work, a new particle-based model for the simulation of tracer dispersion in homogeneous and heterogeneous porous media is presented. Other than in CTRW or LM models, a continuous stochastic process for the Lagrangian velocity of a tracer particle is formulated. The suggested formulation encompasses Gaussian and skewed velocity statistics, and the model parameters can be related more easily to medium characteristics. Numerical simulations of the tracer plume evolution in the Borden tracer experiment and of breakthrough curves in homogeneous and uniformly heterogeneous sand packs are successfully validated with experimental data [5,6]. Non-Fickian dispersion behavior resulting from the scale effect (plume-size dependent dispersivities) and skewed velocity statistics is demonstrated and analyzed. [1] Zhang, Y. K. and D. Zhang (2004). "Forum: The state of stochastic hydrology." Stochastic Environmental Research and Risk Assessment 18(4): 265-265. [2] Salandin, P. and V. Fiorotto (1998). "Solute transport in highly heterogeneous aquifers." Water Resources Research 34(5): 949-961. [3] Benson, D. A., R. Schumer, et al. (2001). "Fractional
Electromagnetic fields in dispersive chiral media generated by modulated nonuniformly moving sources
NASA Astrophysics Data System (ADS)
Kravchenko, V. V.; Oviedo-Galdeano, H.; Rabinovich, V. S.
2013-03-01
A representation for the fields generated by moving sources in chiral media in the form of double time-frequency oscillating integrals is obtained by using quaternionic analysis methods. Some additional assumptions concerning the source allow us to introduce a large dimensionless parameter λ > 0 which characterizes simultaneously the slowness of variations of the amplitude and of the velocity of the source. Application of the two-dimensional stationary phase method to the integral representation of the field leads to asymptotic formulas for the electromagnetic field for large λ > 0, and efficient formulas for the frequency and the time Doppler effects in dispersive chiral media. As an application of the proposed method, we consider the Vavilov-Cherenkov radiation in chiral dispersive media.
Record setting during dispersive transport in porous media
NASA Astrophysics Data System (ADS)
Edery, Yaniv; Kostinski, Alex; Berkowitz, Brian
2011-08-01
How often does a contaminant ‘particle’ migrating in a porous medium set a distance record, i.e., advance farther from the origin than at all previous time steps? This question is of fundamental importance in characterizing the nature of the leading edge of a contaminant plume as it is transported through an aquifer. It was proven theoretically by Majumdar and Ziff (2008) that, in the 1d case for pure diffusion, record setting of a random walker scales with n1/2, where n is the number of steps, regardless of the length and time distribution of steps. Here, we use numerical simulations, benchmarked against the 1d analytical solution, to extend this result also for pure diffusion in 2d and 3d domains. We then consider transport in the presence of a drift (i.e., advective-dispersive transport), and show that the record-setting pace of random walkers changes abruptly from $\\propto$ n1/2 to $\\propto$ n1. We explore the dependence of the prefactor on the distribution of step length and number of spatial dimensions. The key implication is that when, after a brief transitional period, the scaling regime commences, the maximum distance reached by the leading edge of a migrating contaminant plume scales linearly with n, regardless of the drift magnitude.
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. PMID:24663923
The modulational instability for 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 study the modulational instability 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. We employ Whitham's averaged Lagrangian method to study the modulational instability. This complements studies of the modulational instability by Hada (1993) and Hollweg (1994), who did not use the averaged Lagrangian approach.
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.
NASA Astrophysics Data System (ADS)
Zhang, Ya-Ni
2013-01-01
A simple type of photonic crystal fiber (PCF) for supercontinuum generation is proposed for the first time. The proposed PCF is composed of a solid silica core and a cladding with square lattice uniform elliptical air holes, which offers not only a large nonlinear coefficient but also a high birefringence and low leakage losses. The PCF with nonlinear coefficient as large as 46 W-1 · km-1 at the wavelength of 1.55 μm and a total dispersion as low as ±2.5 ps · nm-1 · km-1 over an ultra-broad waveband range of the S—C—L band (wavelength from 1.46 μm to 1.625 μm) is optimized by adjusting its structure parameter, such as the lattice constant Λ, the air-filling fraction f, and the air-hole ellipticity η. The novel PCF with ultra-flattened dispersion, highly nonlinear coefficient, and nearly zero negative dispersion slope will offer a possibility of efficient super-continuum generation in telecommunication windows using a few ps pulses.
Nonlinear optical and optical limiting properties of graphene oxide dispersion in femtosecond regime
NASA Astrophysics Data System (ADS)
Zheng, Zebo; Zhu, Liang; Zhao, Fuli
2014-08-01
The third-order nonlinear optical properties of graphene oxide (GO) dispersion in distilled water were investigated in femtosecond regime, using a single beam z-scan technique. Induced by a focused Gaussian beam (λ~800 nm) with 150 fs pulse duration, the graphene oxide shows strong nonlinear absorption, which was dominated by reverse saturable absorption (RSA), originates from two-photon absorption (TPA) in GO. In addition, the optical limiting performance of GO was experimentally derived, indicating that the occurrence of RSA make GO a candidate for optical limiting. In addition, the further increasing of input intensity would enhance the nonlinear scattering effects in the sample so that the optical limiting threshold was reached.
Exact kink solitons in the presence of diffusion, dispersion, and polynomial nonlinearity
NASA Astrophysics Data System (ADS)
Raposo, E. P.; Bazeia, D.
1999-03-01
We describe exact travelling-wave kink soliton solutions in some classes of nonlinear partial differential equations, such as generalized Korteweg-de Vries-Burgers, Korteweg-de Vries-Huxley, and Korteweg-de Vries-Burgers-Huxley equations, as well as equations in the generic form ut + P( u) ux + vuxx - δuxxx = A( u), with polynomial functions P( u) and A( u) of u = u( x, t), whose generality allows the identification with a number of relevant equations in physics. We focus on the analysis of the role of diffusion, dispersion, nonlinear effects, and parity of the polynomials to the properties of the solutions, particularly their velocity of propagation. In addition, we show that, for some appropriate choices, these equations can be mapped onto equations of motion of relativistic (1 + 1)-dimensional φ4 and φ6 field theories of real scalar fields. Systems of two coupled nonlinear equations are also considered.
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
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.
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
Self-focusing suppression in a system of two nonlinear media and a spatial filter
Garanin, S G; L'vov, L V; Sukharev, S A; Epatko, I V; Serov, R V
2007-12-31
It is shown that the rate of development of spatial instability caused by small-scale self-focusing strongly depends on the mutual arrangement of nonlinear media and spatial filters in a setup. The expressions are obtained for the arrangement of elements providing the minimal growth rate of intensity fluctuations. The results of two-dimensional calculations confirm the efficiency of this method of suppressing small-scale self-focusing. (nonlinear optical phenomena)
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.
Drop Impingement Induced Dispersal of Microorganisms and Contaminants Within Porous Media
NASA Astrophysics Data System (ADS)
Joung, Young Soo; Ge, Zhifei; Buie, Cullen
2014-11-01
We investigate migration of chemicals and microbes with aerosol generated by drop impingement on porous media. In our previous work we found that aerosol generation from droplets hitting porous media within a specific range of the Weber number (We) and a modified Pelect number (Pe). We and Pe reflect the impact condition of droplets and the wetting properties of porous media, respectively. The relationship between We and Pe can be expressed by a third dimensionless group, the Washburn Reynolds number (ReW = We/Pe). In a specific range of ReW, hundreds of aerosol particles can be generated within milliseconds of drop impingement. In this work we investigate if microbes such as Corynebacterium glutamicum, a soil bacterium, and chemicals such as Rhodamine B can be dispersed by aerosols generated from droplet impact. Experimentally, C. glutamicum and Rhodamine B are permeated into porous media. Then drop impingements are conducted on the porous media with different We and Pe in an airflow tunnel. We quantitatively investigate the volume and speed of aerosol migration as a function of ReW of the drop impingement and Re of the airflow. Results of this study will shed light upon the dispersal of elemental compounds and microbes within soils due to aerosol generated by rainfall.
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.
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. PMID:27410356
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.
NASA Astrophysics Data System (ADS)
Namihira, Yoshinori; Hossain, Md. Anwar; Koga, Taito; Islam, Md. Ashraful; Razzak, S. M. Abdur; Kaijage, Shubi F.; Hirako, Yuki; Higa, Hiroki
2012-03-01
In this paper, we propose a highly nonlinear dispersion flattened hexagonal photonic crystal fiber (HNDF-HPCF) with nonlinear coefficients as large as 57.5W-1 km-1 at 1.31 μm wavelength for dental optical coherence tomography (OCT) applications. This HNDF-HPCF offers not only large nonlinear coefficient but also very flat dispersion slope and very low confinement losses. Using these characteristics of our proposed PCF, it is shown through simulations by using finite difference method with an anisotropic perfectly matched boundary layer that this PCF offers the efficient supercontinuum (SC) generation for dental OCT applications at 1.31 μm wavelength using a picosecond pulse easily produced by commercially available less expensive laser sources. Coherent length of light source using SC is found 10 μm and the spatial resolutions in the depth direction for dental applications of OCT are found about 6.1 μm for enamel and 6.5 μm for dentin.
Wave-induced fluid flow in random porous media: attenuation and dispersion of elastic waves.
Müller, Tobias M; Gurevich, Boris
2005-05-01
A detailed analysis of the relationship between elastic waves in inhomogeneous, porous media and the effect of wave-induced fluid flow is presented. Based on the results of the poroelastic first-order statistical smoothing approximation applied to Biot's equations of poroelasticity, a model for elastic wave attenuation and dispersion due to wave-induced fluid flow in 3-D randomly inhomogeneous poroelastic media is developed. Attenuation and dispersion depend on linear combinations of the spatial correlations of the fluctuating poroelastic parameters. The observed frequency dependence is typical for a relaxation phenomenon. Further, the analytic properties of attenuation and dispersion are analyzed. It is shown that the low-frequency asymptote of the attenuation coefficient of a plane compressional wave is proportional to the square of frequency. At high frequencies the attenuation coefficient becomes proportional to the square root of frequency. A comparison with the 1-D theory shows that attenuation is of the same order but slightly larger in 3-D random media. Several modeling choices of the approach including the effect of cross correlations between fluid and solid phase properties are demonstrated. The potential application of the results to real porous materials is discussed. PMID:15957744
Solution for (1+1)-dimensional surface solitons in thermal nonlinear media
Ma Xuekai; Yang Zhenjun; Lu Daquan; Guo Qi; Hu Wei
2011-03-15
Analytical solutions for (1+1)-dimensional surface fundamental solitons in thermal nonlinear media are obtained. The stationary position and the critical power of surface solitons are obtained using these analytical solutions. The analytical solutions are verified by numerical simulations. The solutions for surface breathers and their breathing period, along with solutions for surface dipole and tripole solitons, are also given.
Solution for (1+1)-dimensional surface solitons in thermal nonlinear media
NASA Astrophysics Data System (ADS)
Ma, Xuekai; Yang, Zhenjun; Lu, Daquan; Guo, Qi; Hu, Wei
2011-03-01
Analytical solutions for (1+1)-dimensional surface fundamental solitons in thermal nonlinear media are obtained. The stationary position and the critical power of surface solitons are obtained using these analytical solutions. The analytical solutions are verified by numerical simulations. The solutions for surface breathers and their breathing period, along with solutions for surface dipole and tripole solitons, are also given.
Three-dimensional optical vortex and necklace solitons in highly nonlocal nonlinear media
NASA Astrophysics Data System (ADS)
Zhong, Wei-Ping; Belić, Milivoj
2009-02-01
We demonstrate the existence of localized optical vortex and necklace solitons in three-dimensional (3D) highly nonlocal nonlinear media, both analytically and numerically. The 3D solitons are constructed with the help of Kummer’s functions in spherical coordinates and their unique properties are discussed. The procedure we follow offers ways for generation, control, and manipulation of spatial solitons.
Effects of focusing on third-order nonlinear processes in isotropic media. [laser beam interactions
NASA Technical Reports Server (NTRS)
Bjorklund, G. C.
1975-01-01
Third-order nonlinear processes in isotropic media have been successfully used for tripling the efficiency of high-power laser radiation for the production of tunable and fixed-frequency coherent vacuum UV radiation and for up-conversion of IR radiation. The effects of focusing on two processes of this type are studied theoretically and experimentally.
A Fundamental Approach to the Simulation of Flow and Dispersion in Fractured Media
Miller, J.D.
1983-12-15
Fracture systems may be generalized in terms of number and orientation of sets of parallel fractures and the distribution of length, width, thickness and separation. Borehole measurements may be used to particularize these parameters for a specific site. Global flow and dispersion in an aquifer occur in the interconnected fractures and may be related to specific fracture elements. A fluid dynamics code named SALE has been used to solve the Navier-Stokes equations for laminar flow in these elemental geometries. A marker particle calculation has been added to characterize longitudinal dispersion due to the velocity profile across the fracture and lateral dispersion due to flow disturbances at junctions. Local flow and dispersion in the matrix occur in the finer fracture structure and are evaluated using porous media approaches. These results or models are integrated in a 2D isothermal reservoir simulator named FRACSL. Discrete fractures are superimposed on the edges or diagnoals of rectangular grid elements. Water may flow from node to node through the matrix or through the fracture. The heads are found by iterating for the distribution which conserves the appropriate local mass. Marker particles are used to monitor the tracer dispersion due to motion in the fractures, in the matrix and between the two. Results are given showing flow and dispersion in an orthogonal junction and in a sample fractured reservoir.
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.
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.
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.
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. 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
2015-01-01
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
NASA Astrophysics Data System (ADS)
Zhang, Lijun; Chen, Li-Qun; Zhang, Jianming
2013-10-01
Bifurcation and exact solutions of the modified nonlinearly dispersive mK (m,n,k) equation with nonlinear dispersion um-1ut+a(un)x+b(uk)xxx = 0,nk≠0 are investigated in this paper. As a result, under different parameter conditions, abundant compactons, peakons and solitary solutions including not only some known results but also some new ones are obtained. We also point out the original reason of the existence of the non-smooth traveling wave solutions. The approach we used here is also suitable for the study of traveling wave solutions of some other nonlinear equations.
All-fiber smooth supercontinuum generation in highly nonlinear dispersion-shifted fiber
NASA Astrophysics Data System (ADS)
Zhang, Xianming; Gu, Chun; Xu, Lixin; Wang, Anting; Chen, Guoliang; Zheng, Huan; Zheng, Rui; Fu, Huaiduo; Ming, Hai
2009-11-01
Supercontinuum(SC) source has found numerous applications, such as DWDM, frequency metrology, optical coherence tomography, and optical measurement. We demonstrate an all-fiber supercontimuun source generated in highly nonlinear fiber (HNLF). The HNLF is pumped by our mode-locked fiber laser with pulse width and peak power, 21.1ps and kW, respectively. An ultra-broadband supercontinuum extends from 1000 nm to 1750 nm is obtained, and the spectrum is flat with the amplitude variation less than 4dB except around the fiber zero dispersion wavelength. The spectrum of our supercontinuum source can extend beyond 1750 nm, but due to the limitation of the measured range of optical spectrum analyzer (AQ6317B), the spectrum of the supercontinuum source beyond 1750 nm is not yet obtained in our lab now. The spectral broadening mechanism of smoothed supercontinnum is considered by the higher-order soliton fission and their blue-shifted dispersive wave.
Dispersion engineering in nonlinear soft glass photonic crystal fibers infiltrated with liquids.
Pniewski, Jacek; Stefaniuk, Tomasz; Van, Hieu Le; Long, Van Cao; Van, Lanh Chu; Kasztelanic, Rafał; Stępniewski, Grzegorz; Ramaniuk, Aleksandr; Trippenbach, Marek; Buczyński, Ryszard
2016-07-01
We present a numerical study of the dispersion characteristic modification of nonlinear photonic crystal fibers infiltrated with liquids. A photonic crystal fiber based on the soft glass PBG-08, infiltrated with 17 different organic solvents, is proposed. The glass has a light transmission window in the visible-mid-IR range of 0.4-5 μm and has a higher refractive index than fused silica, which provides high contrast between the fiber structure and the liquids. A fiber with air holes is designed and then developed in the stack-and-draw process. Analyzing SEM images of the real fiber, we calculate numerically the refractive index, effective mode area, and dispersion of the fundamental mode for the case when the air holes are filled with liquids. The influence of the liquids on the fiber properties is discussed. Numerical simulations of supercontinuum generation for the fiber with air holes only and infiltrated with toluene are presented. PMID:27409187
NASA Astrophysics Data System (ADS)
Song, Xianhai; Li, Lei; Zhang, Xueqiang; Huang, Jianquan; Shi, Xinchun; Jin, Si; Bai, Yiming
2014-10-01
In recent years, Rayleigh waves are gaining popularity to obtain near-surface shear (S)-wave velocity profiles. However, inversion of Rayleigh wave dispersion curves is challenging for most local-search methods due to its high nonlinearity and to its multimodality. In this study, we proposed and tested a new Rayleigh wave dispersion curve inversion scheme based on differential evolution (DE) algorithm. DE is a novel stochastic search approach that possesses several attractive advantages: (1) Capable of handling non-differentiable, non-linear and multimodal objective functions because of its stochastic search strategy; (2) Parallelizability to cope with computation intensive objective functions without being time consuming by using a vector population where the stochastic perturbation of the population vectors can be done independently; (3) Ease of use, i.e. few control variables to steer the minimization/maximization by DE's self-organizing scheme; and (4) Good convergence properties. The proposed inverse procedure was applied to nonlinear inversion of fundamental-mode Rayleigh wave dispersion curves for near-surface S-wave velocity profiles. To evaluate calculation efficiency and stability of DE, we firstly inverted four noise-free and four noisy synthetic data sets. Secondly, we investigated effects of the number of layers on DE algorithm and made an uncertainty appraisal analysis by DE algorithm. Thirdly, we made a comparative analysis with genetic algorithms (GA) by a synthetic data set to further investigate the performance of the proposed inverse procedure. Finally, we inverted a real-world example from a waste disposal site in NE Italy to examine the applicability of DE on Rayleigh wave dispersion curves. Furthermore, we compared the performance of the proposed approach to that of GA to further evaluate scores of the inverse procedure described here. Results from both synthetic and actual field data demonstrate that differential evolution algorithm applied
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.
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.
Barothropic relaxing media under pressure perturbations: Nonlinear dynamics
NASA Astrophysics Data System (ADS)
Kuetche, Victor K.
2015-12-01
In this paper, we delve into the dynamics of a barothropic relaxing medium under pressure perturbations originating from blast wave explosions in the milieu. Analyzing the problem within the viewpoint of the Lyakhov formalism of geodynamic systems, we derive a complex-valued nonlinear evolution equation which models the wave propagation of the pressure perturbations within the barothropic medium. As a result, we find that the previous system can be circularly polarized and hence support traveling rotating pressure excitations which profiles strongly depend upon their angular momenta. In the wake of these results, we address some physical implications of the findings alongside their potential applications.
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
Modelling Gaussian beam propagation through thick nonlinear refractive and absorptive media
NASA Astrophysics Data System (ADS)
Namarathne, D.; Walden, S.; Shortell, M.; Jaatinen, E.
2016-04-01
A novel numerical finite difference beam propagation method developed for quadratic refractive index media is presented and applied to TEM00 Gaussian beams propagating through nonlinear optical media. The beam's diffraction through the medium was calculated by using the nonlinear Schrodinger equation on small slices which proved to be effective for thick samples. The performance of the model was compared to experimental z-scan observations of colloidal ZnO particles at low cw and high pulsed peak powers at a wavelength of 532 nm. Different optical behaviours were observed in these two power regimes. Negligible nonlinear absorption and refraction were observed at low cw powers, with strong defocusing arising through thermal lensing in the colloidal solution. For the pulsed experiments with peak powers up to 43-kW and 7-ns pulses, values for the intensity-dependent absorption were determined to be β = 1.0 × 10^{ - 10} {text{m/W}} and n_{{2{text{R}}}} = 2.0 × 10^{ - 18} {text{m}}2 /{text{W}}. Despite the very different nonlinear and thermal-optical behaviours in two power regimes, there was good agreement between the model and observations. This demonstrates the effectiveness of the approach in extracting the nonlinear properties of a medium even if it is not optically thin and in the case when a sample displays both strong nonlinear refraction and absorption.
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)
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)
Sharifi Haddad, Amin
Fractured porous media are important structures in petroleum engineering and geohydrology. The accelerating global demand for energy has turned the focus to fractured formations. The fractured porous media are also found in conventional naturally fractured reservoirs and the water supply from karst (carbonate) aquifers. Studying mass transfer processes allows us to explore the complexities and uncertainties encountered with fractured rocks. This dissertation is developing an analytical methodology for the study of mass transfer in fractured reservoirs. The dissertation begins with two cases that demonstrate the importance of the rock matrix block size distribution and dispersivity through a transient mass exchange mechanism between rock matrix blocks and fractures. The first case assumes a medium with no surface adsorption, and the second case includes the surface adsorption variable. One of the main focuses of this work is the characterization of the rock matrix block size distribution in fractured porous media. Seismic surveying, well test analysis, well logging, and geomechanical tools are currently used to characterize this property, based on measurements of different variables. This study explores an innovative method of using solute transport to determine the fracture intensity. This methodology is applied to slab-shaped rock matrix blocks and can easily be extended to other geometries. Another focus of this dissertation is the characterization of dispersivity in field scale studies. Improving our knowledge of dispersivity will enable more accurate mass transfer predictions and advance the study of transport processes. Field tracer tests demonstrated that dispersivity is scale-dependent. Proposed functions for the increasing trend of dispersivity include linear and asymptotic scale-dependence. This study investigated the linear dispersivity trend around the injection wellbore. An analysis of the tracer concentration in a monitoring well was used to
Interaction of highly nonlinear solitary waves with linear elastic media
NASA Astrophysics Data System (ADS)
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.
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. PMID:21599325
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. PMID:27036279
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. PMID:27152806
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. PMID:25531786
Lee, Wonmok; Kim, Seulgi; Kim, Seulki; Kim, Jin-Ho; Lee, Hyunjung
2015-02-15
There are active researches on well ordered opal films due to their possible applications to various photonic devices. A recently developed slide coating method is capable of rapid fabrication of large area opal films from aqueous colloidal dispersion. In the current study, the slide coating of polystyrene colloidal dispersions in water/i-propanol (IPA) binary media is investigated. Under high IPA content in a dispersing medium, resulting opal film showed a deterioration of long range order, as well as a decreased film thickness due to dilution effect. From the binary liquid, the dried opal films exhibited the unprecedented topological groove patterns with varying periodic distances as a function of alcohol contents in the media. The groove patterns were consisted of the hierarchical structures of the terraced opal layers with periodic thickness variations. The origin of the groove patterns was attributed to a shear-induced periodic instability of colloidal concentration within a thin channel during the coating process which was directly converted to a groove patterns in a resulting opal film due to rapid evaporation of liquid. The groove periods of opal films were in the range of 50-500 μm, and the thickness differences between peak and valley of the groove were significantly large enough to be optically distinguishable, such that the coated films can be utilized as the optical grating film to disperse infra-red light. Utilizing a lowered hydrophilicity of water/IPA dispersant, an opal film could be successfully coated on a flexible Mylar film without significant dewetting problem. PMID:25460710
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.
NASA Astrophysics Data System (ADS)
Zhong, Xian-qiong; Xiang, Wen-li; Cheng, Ke
2013-11-01
After taking the higher-order dispersion and three kinds of saturable nonlinearities into account, we investigate the characteristics of modulation instability (MI) in real units in the positive refractive region of metamaterials (MMs). The results show that the gain spectra of MI consist of two spectral regions, one of which is close to and the other is far from the zero point. In particular, the spectral region far from the zero point also has high cut-off frequency but narrow spectral width just as those revealed in the negative refractive region. Moreover, the gain spectra can change with the normalized angular frequency, the normalized optical power and the form of the saturable nonlinearity. Concretely, the spectral width increases with increase of the normalized angular frequency. But both of the spectral width and the peak gain increase and then decrease with increase of the normalized optical power. In other words, the MI characteristics and MI related applications can be controlled by adjusting the structure of the MMs, the form of the saturable nonlinearity and the normalized optical power.
Chromatic dispersion and nonlinear phase noise compensation based on KLMS method
NASA Astrophysics Data System (ADS)
Nouri, Mahdi; Shayesteh, Mahrokh G.; Farhangian, Nooshin
2015-09-01
In this study, kernel least mean square (KLMS) algorithm with fractionally spaced equalizing structure is proposed for electrical compensation of chromatic dispersion (CD) and nonlinear phase noise (NLPN) in a dual polarization optical communications system with coherent detection. We consider single mode fiber channel. At the receiver, the additive optical noise is represented as additive white Gaussian noise. Phase modification is utilized at high signal powers to maintain the validity of Gaussian model of noise. We consider QAM and PSK modulations and evaluate the performance of the proposed method in terms of error rate, phase error, and error vector magnitude (EVM). The results are obtained in both linear and nonlinear regimes. In the linear region, the KLMS algorithm can compensate CD and NLPN effectively and outperforms the existing compensation methods such as LMS, minimum mean square error (MMSE), and time domain FIR filter. In nonlinear regime, where the input power is higher, NLPN is stronger which results in compensation performance degradation. However, KLMS still achieves better results than the above algorithms.
Twisted toroidal vortex solitons in inhomogeneous media with repulsive nonlinearity.
Kartashov, Yaroslav V; Malomed, Boris A; Shnir, Yasha; Torner, Lluis
2014-12-31
Toroidal modes in the form of so-called Hopfions, with two independent winding numbers, a hidden one (twist s), which characterizes a circular vortex thread embedded into a three-dimensional soliton, and the vorticity around the vertical axis (m), appear in many fields, including field theory, ferromagnetics, and semi- and superconductors. Such topological states are normally generated in multicomponent systems, or as trapped quasilinear modes in toroidal potentials. We uncover that stable solitons with this structure can be created, without any linear potential, in the single-component setting with the strength of repulsive nonlinearity growing fast enough from the center to the periphery, for both steep and smooth modulation profiles. Toroidal modes with s=1 and vorticity m=0, 1, 2 are produced. They are stable for m≤1, and do not exist for s>1. An approximate analytical solution is obtained for the twisted ring with s=1, m=0. Under the application of an external torque, it rotates like a solid ring. The setting can be implemented in a Bose-Einstein condensate (BEC) by means of the Feshbach resonance controlled by inhomogeneous magnetic fields. PMID:25615341
Basch, Angelika; Strnad, Simona
2011-01-01
This work investigated colloidal properties such as the zeta-potential, the electrophoretic mobilities and the wetting behaviour of alumina dispersed in non-aqueous media. Non-aqueous dispersions of alumina were prepared in the solvent N-methyl-2-pyrrolidinone (NMP). The wetting behaviour of alumina in NMP was characterized by the powder contact angle method and the Wilhemy plate method. The behaviour of the dispersion should provide information for the development of a substrate-induced coagulation (SIC) coating process of nano-sized alumina in non-aqeous media. SIC is a dip-coating process that coats pretreated but chemically different surfaces with nano-sized particles. It was found that the anionic surfactant dioctyl sulfosuccinate (AOT) had no stabilizing effect on alumina dispersed in NMP. PMID:21317977
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.
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
Mokhtarpour, Laleh; Ponomarenko, Sergey A
2015-11-16
We numerically investigate partially coherent short pulse propagation in nonlinear media near optical resonance. We examine how the pulse state of coherence at the source affects the evolution of the ensemble averaged intensity, mutual coherence function, and temporal degree of coherence of the pulse ensemble. We report evidence of self-induced transparency random phase soliton formation for the relatively coherent incident pulses with sufficiently large average areas. We also show that random pulses lose their coherence on propagation in resonant media and we explain this phenomenon in qualitative terms. PMID:26698507
NASA Astrophysics Data System (ADS)
Song, Shiyu; Wang, Suxin; Wang, Yongjin
2016-08-01
Motivated by the close connection between the skew Brownian motion and the random particle motion in heterogeneous media, we investigate the reflected skew Brownian motion and try to find out its relationship with the corresponding dispersion problem when there exists a reflecting boundary. Through the use of the knowledge of stochastic analysis, we provide some basic properties of reflected skew Brownian motions, including the transition density, the Laplace transform of the first passage time, and some related results. A simple method to generate the sample path is also proposed. At the end of this paper, we reveal the strong relationship between the reflected skew Brownian motion and the solute dispersion in the presence of a sharp interface and a reflecting boundary.
Disentangling the Complex Pore-Scale Dispersion Process in Natural Porous Media by Means of DNS
NASA Astrophysics Data System (ADS)
Medellin-Azuara, J.; Howitt, R. E.; MacEwan, D.; Lund, J. R.
2014-12-01
Over the recent past, important advances have been made in the area of micro-CT scanning of natural porous media. The acquired pore-space geometries enable detailed investigations of flow and transport via pore-scale direct numerical simulation (DNS). In this work, we utilize pore-scale DNS to investigate single-phase pore-scale dispersion. We focus on data stemming from beadpacks, Bentheimer sandstone, and Ketton and Estaillades carbonates. Our DNS results clearly show the transition from ballistic dispersion to the asymptotic Fickian regime (see figure a) at decimeter or meter scale depending on the medium type. We outline a universal Lagrangian model for tracer dispersion that is based on a low-dimensional parametrization of the complex three-dimensional motion of tracer particles (see figure b). We relate the process parameters to certain pore-geometry characteristics such as the tortuosity. Our model accurately captures the wide range of flow and transport dynamics observed in the samples considered. We establish the accuracy of the model by validating its limiting dispersion behavior, the resulting velocity statistics, and also, most challenging, snapshots of tracer plumes at travel times encompassing both ballistic and Fickian behavior.
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.
Kerr nonlinearity and dispersion characterization of core-pumped thulium-doped fiber at 2 μm.
Kharitonov, Svyatoslav; Billat, Adrien; Brès, Camille-Sophie
2016-07-15
A nonlinear coefficient of 3.6-4.1 W^{-1} km^{-1} and group velocity dispersion of -20 ps^{2}/km of a commercial core-pumped thulium-doped fiber have been evaluated using degenerate four-wave mixing at 2 μm. The anomalous dispersion behavior of the fiber has been confirmed by linear measurements with an all-fiber Mach-Zehnder interferometer (MZI). Additionally, no pump-induced dispersion changes due to excitation of Tm^{3+} cations have been detected. These characteristics make these fibers attractive for pulsed fiber laser applications. A nonlinear-polarization rotation mode-locked laser involving nonlinear polarization evolution directly in the doped fiber is demonstrated. PMID:27420488
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.
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.
Beam width evolution of astigmatic hollow Gaussian beams in highly nonlocal nonlinear media
NASA Astrophysics Data System (ADS)
Yang, Zhen-Feng; Jiang, Xue-Song; Yang, Zhen-Jun; Li, Jian-Xing; Zhang, Shu-Min
We investigate the beam width evolution of astigmatic hollow Gaussian beams propagating in highly nonlocal nonlinear media. The input-power-induced different evolutions of the beam width are illustrated: (i) the beam widths in two transverse directions are compressed or broadened at the same time; (ii) the beam width in one transverse direction keeps invariant, and the other is compressed or broadened; (iii) furthermore, the beam width in one transverse direction is compressed, whereas it in the other transverse direction is broadened.
Wang, Gaozhong; Zhang, Saifeng E-mail: jwang@siom.ac.cn; Cheng, Xin; Dong, Ningning; Zhang, Long; Wang, Jun E-mail: jwang@siom.ac.cn; Umran, Fadhil A.; Coghlan, Darragh; Blau, Werner J.; Cheng, Ya
2014-04-07
Spatial self-phase modulation (SSPM) was observed directly when a focused He-Ne laser beam at 633 nm went through liquid-phase-exfoliated graphene dispersions. The diffraction pattern of SSPM was found to be distorted rapidly right after the incident beam horizontally passing through the dispersions, while no distortion for the vertically incident geometry. We show that the distortion is originated mainly from the non-axis-symmetrical thermal convections of the graphene nanosheets induced by laser heating, and the relative change of nonlinear refractive index can be determined by the ratio of the distortion angle to the half-cone angle. Therefore, the effective nonlinear refractive index of graphene dispersions can be tuned by changing the incident intensity and the temperature of the dispersions.
NASA Astrophysics Data System (ADS)
Li, Wan-Tong; Wang, Jia-Bing; Zhang, Li
2016-08-01
This paper is concerned with the new types of entire solutions other than traveling wave solutions of nonlocal dispersal equations with monostable nonlinearity in space periodic habitats. We first establish the existence and properties of spatially periodic solutions connecting two steady states. Then new types of entire solutions are constructed by combining the rightward and leftward pulsating traveling fronts with different speeds and a spatially periodic solution. Finally, for a class of special heterogeneous reaction, we further establish the uniqueness of entire solutions and the continuous dependence of such an entire solution on parameters, such as wave speeds and the shifted variables. In other words, we build a five-dimensional manifold of solutions and the traveling wave solutions are on the boundary of the manifold.
Nonlinear photoacoustic response of opaque media in gas microphone signal detection
NASA Astrophysics Data System (ADS)
Madvaliev, U.; Salikhov, T. Kh.; Sharifov, D. M.; Khan, N. A.
2006-03-01
We have theoretically studied the effect of thermal nonlinearity, due to the temperature dependence of the thermophysical and optical parameters for thermally thick opaque media, on the characteristics of the fundamental photoacoustic signal when the signal is detected by a gas microphone. We have shown that the dependence of the amplitude of the nonlinear component of the signal on the intensity of the incident radiation I0 is expressed by means of the dependence of the temperature rise for the irradiated sample surface Θ0 on I0, and the thermal nonlinearity does not affect the phase of the photoacoustic signal. We propose a theory for generation of the second harmonic of the photoacoustic signal. We have established that the phase shift of the photoacoustic signal is equal to 3π/4, while its amplitude depends on the frequency (˜ω-3/2) and the intensity (˜ I{0/2}).
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
Seifzadeh, A; Wang, J; Oguamanam, D C D; Papini, M
2011-08-01
A nonlinear biphasic fiber-reinforced porohyperviscoelastic (BFPHVE) model of articular cartilage incorporating fiber reorientation effects during applied load was used to predict the response of ovine articular cartilage at relatively high strains (20%). The constitutive material parameters were determined using a coupled finite element-optimization algorithm that utilized stress relaxation indentation tests at relatively high strains. The proposed model incorporates the strain-hardening, tension-compression, permeability, and finite deformation nonlinearities that inherently exist in cartilage, and accounts for effects associated with fiber dispersion and reorientation and intrinsic viscoelasticity at relatively high strains. A new optimization cost function was used to overcome problems associated with large peak-to-peak differences between the predicted finite element and experimental loads that were due to the large strain levels utilized in the experiments. The optimized material parameters were found to be insensitive to the initial guesses. Using experimental data from the literature, the model was also able to predict both the lateral displacement and reaction force in unconfined compression, and the reaction force in an indentation test with a single set of material parameters. Finally, it was demonstrated that neglecting the effects of fiber reorientation and dispersion resulted in poorer agreement with experiments than when they were considered. There was an indication that the proposed BFPHVE model, which includes the intrinsic viscoelasticity of the nonfibrillar matrix (proteoglycan), might be used to model the behavior of cartilage up to relatively high strains (20%). The maximum percentage error between the indentation force predicted by the FE model using the optimized material parameters and that measured experimentally was 3%. PMID:21950897
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. PMID:26517371
Frequency dispersion of the first hyperpolarizabilities of reference molecules for nonlinear optics
NASA Astrophysics Data System (ADS)
de Wergifosse, Marc; Castet, Frédéric; Champagne, Benoît
2015-05-01
The frequency dispersion of the hyper-Rayleigh scattering first hyperpolarizabilities (βHRS) 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 βHRS 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 βxyz 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.
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.
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
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
On the self-averaging of dispersion for transport in quasi-periodic random media
NASA Astrophysics Data System (ADS)
Eberhard, J. P.; Suciu, N.; Vamos, C.
2007-01-01
In this study we present a numerical analysis for the self-averaging of the longitudinal dispersion coefficient for transport in heterogeneous media. This is done by investigating the mean-square sample-to-sample fluctuations of the dispersion for finite times and finite numbers of modes for a random field using analytical arguments as well as numerical simulations. We consider transport of point-like injections in a quasi-periodic random field with a Gaussian correlation function. In particular, we focus on the asymptotic and pre-asymptotic behaviour of the fluctuations with the aid of a probability density function for the dispersion, and we verify the logarithmic growth of the sample-to-sample fluctuations as earlier reported in Eberhard (2004 J. Phys. A: Math. Gen. 37 2549-71). We also comment on the choice of the relevant parameters to generate quasi-periodic realizations with respect to the self-averaging of transport in statistically homogeneous Gaussian velocity fields.
Dispersion properties in porous media: application to Redox Flow Battery electrodes
NASA Astrophysics Data System (ADS)
Picano, Francesco; Maggiolo, Dario; Marion, Andrea; Guarnieri, Massimo
2015-11-01
Redox Flow Batteries (RFBs) represent a promising technology as a way to store energy. However, in order to improve RFBs performance, some conceptual and technological issues are still open. In particular, a properly designed geometry of flow channels and porous medium is still under investigation in order to uniformly distribute the reacting species all along the electrode. The ideal configuration aims to minimize the drag maximizing the mixing so to increase the overall performance and efficiency. In the present work a Lattice Boltzmann 3D model (LBM) has been used to better understand the dependence of mass and momentum transports on the porosity and carbon fiber preferential orientation. The LBM has been coupled with a Lagrangian particle tracking algorithm in order to investigate the dispersion mechanisms induced by the porous medium on the species flowing in a typical RFB. Results show that the drag is considerably reduced when the medium fibers are preferentially oriented along the streamwise direction. Surprisingly, this configuration shows also the highest transversal dispersion rate characterized by a super-diffusive behavior. Actually, the dispersion features are found to strongly depend on the porous media microstructure showing either anomalous or regular diffusion.
NASA Technical Reports Server (NTRS)
Lobashov, A. A.; Mostepanenko, V. M.
1993-01-01
The theory of quantum effects in nonlinear dielectric media is developed. The nonlinear dielectric media is influenced by an external pumping field. The diagonalization of the Hamiltonian of a quantized field is obtained by the canonical Bogoliubov transformations. The transformations allow us to obtain the general expressions for the number of created photons and for the degree of squeezing. In the case of a plane pumping wave, for example, the results are calculated by using the zero order of the secular perturbation theory, with small parameters characterizing the medium nonlinearity. The Heisenberg equations of motion are obtained for non-stationary case and a commonly used Hamiltonian is derived from the first principles of quantum electrodynamics.
NASA Astrophysics Data System (ADS)
Berczyński, Paweł; Kravtsov, Yury A.; Żeglinski, Grzegorz
2008-09-01
The method of paraxial complex geometrical optics (CGO) is presented, which describes Gaussian beam diffraction in arbitrary smoothly inhomogeneous media, including lens-like waveguides. By way of an example, the known analytical solution for Gaussian beam diffraction in free space is presented. Paraxial CGO reduces the problem of Gaussian beam diffraction in inhomogeneous media to the system of the first order ordinary differential equations, which can be readily solved numerically. As a result, CGO radically simplifies the description of Gaussian beam diffraction in inhomogeneous media as compared to the numerical methods of wave optics. For the paraxial on-axis Gaussian beam propagation in lens-like waveguide, we compare CGO solutions with numerical results for finite differences beam propagation method (FD-BPM). The CGO method is shown to provide 50-times higher rate of calculation then FD-BPM at comparable accuracy. Besides, paraxial eikonal-based complex geometrical optics is generalized for nonlinear Kerr type medium. This paper presents CGO analytical solutions for cylindrically symmetric Gaussian beam in Kerr type nonlinear medium and effective numerical solutions for the self-focusing effect of Gaussian beam with elliptic cross section. Both analytical and numerical solutions are shown to be in a good agreement with previous results, obtained by other methods.
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
Self-organization of frozen light in near-zero-index media with cubic nonlinearity.
Marini, A; de Abajo, F J García
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
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.
Parallel numerical integration of Maxwell's full-vector equations in nonlinear focusing media
NASA Astrophysics Data System (ADS)
Bennett, Paul Murray
Maxwell's equations governing the evolution of ultrashort intense coherent pulses of light in a nonlinear focusing dielectric are presented. A discretization of this model using Kane Yee's grid is presented. Initial and boundary conditions are derived, and a serial finite difference algorithm using Yee's grid with the initial and boundary conditions is given. A parallelization of the serial algorithm to more aptly handle the large computational size is performed, and speedup and efficiency results of the parallel program are presented. The parallel code is first used to study the effect of the focusing nonlinearity upon dispersionless pulse propagation. Indications are given of the development of shocks on the optical carrier wave and upon the pulse envelope. The parallel code is then used to study the effect of varying the focusing of the light by varying the intensity as a way to compensate linear dispersion. Blow-up of the pulse in finite propagation distance is demonstrated, and the dependence of the blow-up position upon the intensity of the light is presented. Optical saturation is considered to counter blow-up of intense pulses. Finally, the parallel code is used to study the evolution of intense ultrashort optical pulses in a model featuring nonlinear dispersion, focusing, and optical saturation.
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.
Zhong, Zhi-Jian; Xu, Yi; Lan, Sheng; Dai, Qiao-Feng; Wu, Li-Jun
2010-01-01
Based on the excitation of surface plasmon polaritons (SPPs), we analytically and numerically investigate the transmission response in metal-dielectric-metal (MDM) plasmonic waveguides with a side coupled nanocavity (SCNC). By filling the nanocavity with a Kerr nonlinear medium, the position of the resonant dip in the transmission spectrum can be tuned by the incident light intensity. The oscillation of a Fabry-Perot nanocavity formed by incorporating a finite length of the same Kerr nonlinear media into the MDM waveguide acts as a background for the transmission response of the system and induces a sharp and asymmetric response line shape. As a result, the wavelength shift required for the plasmonic device to be switched from the maximum to the minimum transmission can be reduced by half in a structure less than 400 nm long. Such an effect may be potentially applied to constructing SPP-based all-optical switching with low power threshold at nanoscale. PMID:20173825
Dispersion and attenuation of acoustic guided waves in layered fluid-filled porous media
Parra, J.O.; Xu, P. )
1994-01-01
The analysis of acoustic wave propagation in fluid-filled porous media based on Biot and homogenization theories has been adapted to calculate dispersion and attenuation of guided waves trapped in low-velocity layered media. Constitutive relations, the balance equation, and the generalized Darcy law of the modified Biot theory yield a coupled system of differential equations which governs the wave motion in each layer. The displacement and stress fields satisfy the boundary conditions of continuity of displacements and tractions across each interface, and the radiation condition at infinity. To avoid precision problems caused by the growing exponential in individual matrices for large wave numbers, the global matrix method was implemented as an alternative to the traditional propagation approach to determine the periodic equations. The complex wave numbers of the guided wave modes were determined using a combination of two-dimensional bracketing and minimization techniques. The results of this work indicate that the acoustic guided wave attenuation is sensitive to the [ital in] [ital situ] permeability. In particular, the attenuation changes significantly as the [ital in] [ital situ] permeability of the low-velocity layer is varied at the frequency corresponding to the minimum group velocity (Airy phase). Alternatively, the attenuation of the wave modes are practically unaffected by those permeability variations in the layer at the frequency corresponding to the maximum group velocity.
Lagrangian Statistics and Modeling of Pore-Scale Dispersion in Heterogeneous Natural Porous Media
NASA Astrophysics Data System (ADS)
Meyer, D. W.; Bijeljic, B.; Blunt, M. J.
2014-12-01
Recent advances made in the area of micro-CT scanning of natural pore-space geometries enable detailed investigations of flow and transport processes at the pore-scale, e.g., [Bijeljic et al., Phys. Rev. E, 87, 2013]. A study is reported of Lagrangian statistics of fluid-particle velocity and acceleration in natural porous media of different rock type. The underlying 3d pore-space geometries were obtained by means of micro-CT scans of a beadpack, Bentheimer sandstone, and Ketton and Estaillades carbonates. Based on these statistics, we introduce a new Lagrangian model for transport that reproduces the aforementioned statistics. Our model is based on a spatio-temporal Markov process of the Lagrangian velocity of fluid particles, where the model parametrization is related to the medium characteristics. Transport predictions are validated against flow and transport results from pore-scale direct numerical simulation. The new model enables the detailed investigation of the transition between non-Fickian and Fickian dispersion in real porous media. Moreover, the model sheds light on the connection between geometrical pore-space characteristics and transport behavior.
Multiple-type solutions for multipole interface solitons in thermal nonlinear media
Ma Xuekai; Yang Zhenjun; Lu Daquan; Hu Wei
2011-09-15
We address the existence of multipole interface solitons in one-dimensional thermal nonlinear media with a step in the linear refractive index at the sample center. It is found that there exist two types of solutions for tripole and quadrupole interface solitons. The two types of interface solitons have different profiles, beam widths, mass centers, and stability regions. For a given propagation constant, only one type of interface soliton is proved to be stable, while the other type can also survive over a long distance. In addition, three types of solutions for fifth-order interface solitons are found.
Time domain adjoint sensitivity analysis of electromagnetic problems with nonlinear media.
Bakr, Mohamed H; Ahmed, Osman S; El Sherif, Mohamed H; Nomura, Tsuyoshi
2014-05-01
In this paper, we propose a theory for wideband adjoint sensitivity analysis of problems with nonlinear media. We show that the sensitivities of the desired response with respect to all shape and material parameters are obtained through one extra adjoint simulation. Unlike linear problems, the system matrices of this adjoint simulation are time varying. Their values are determined during the original simulation. The proposed theory exploits the time-domain transmission line modeling (TLM) and provides an efficient AVM approach for sensitivity analysis of general time domain objective functions. The theory has been illustrated through a number of examples. PMID:24921783
Multiple-type solutions for multipole interface solitons in thermal nonlinear media
NASA Astrophysics Data System (ADS)
Ma, Xuekai; Yang, Zhenjun; Lu, Daquan; Hu, Wei
2011-09-01
We address the existence of multipole interface solitons in one-dimensional thermal nonlinear media with a step in the linear refractive index at the sample center. It is found that there exist two types of solutions for tripole and quadrupole interface solitons. The two types of interface solitons have different profiles, beam widths, mass centers, and stability regions. For a given propagation constant, only one type of interface soliton is proved to be stable, while the other type can also survive over a long distance. In addition, three types of solutions for fifth-order interface solitons are found.
NASA Astrophysics Data System (ADS)
Dai, Zhiping; Yang, Zhenjun; Ling, Xiaohui; Zhang, Shumin; Pang, Zhaoguang; Li, Jianxing
2016-05-01
The motion of two interactional solitons is investigated in nonlinear media with an exponential nonlocal response. A differential equation describing the motion trajectories of soliton center is proposed. Some numerical simulations are performed to illustrate the characteristics of the motion trajectories. The results show that the trajectories always oscillate periodically. However, if the two solitons are launched with a relative inclined angle which is larger than a critical value, they do not collide any more but diverge from each other. The critical angle is also given.
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.
Effect of gas accumulation and biofilm growth on the dispersivity of porous media
NASA Astrophysics Data System (ADS)
Ye, S.; Sleep, B. E.; Chien, C.
2009-12-01
The effects of biofilm growth and methane gas accumulation on the transport in porous media were investigated in an anaerobic two-dimensional sand-filled cell. Inoculation of the lower portion of the cell with a methanogenic culture and addition of methanol to the bottom of the cell led to biomass growth and formation of a gas phase. Gas generated at the bottom of the cell in the biologically active zone moved upwards in discrete fingers, so that gas saturations in the biologically active zone at the bottom of the cell did not exceed 40-50%, while gas accumulation at the top of the cell produced gas saturations as high as 80%. In the most biologically active zone at the bottom of the cell, porosity reductions due to biofilm growth were estimated to be 80-95%. The effects of biofilm and gas generation on the dispersivity were separated by performing one tracer test in the presence of both biofilm and a gas phase and a second tracer test after removal of the gas phase through water flushing. The dispersivity increased by 20 times in the presence of both biofilm and a gas phase, and increased by 4.8 times in the presence of only biofilm. The results of tracer tests demonstrated that transport in the two-dimensional cell were significantly affected by gas accumulation and biofilm growth, and especially by gas accumulation.
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.
Akhmediev, Nail; Soto-Crespo, J M; Grelu, Philippe
2007-09-01
Nonlinear dissipative systems display the full (3+1)D spatiotemporal dynamics of stable optical solitons. We review recent results that were obtained within the complex cubic-quintic Ginzburg-Landau equation model. Numerical simulations reveal the existence of stationary bell-shaped (3+1)D solitons for both anomalous and normal chromatic dispersion regimes, as well as the formation of double soliton complexes. We provide additional insight concerning the possible dynamics of these soliton complexes, consider collision cases between two solitons, and discuss the ways nonstationary evolution can lead to optical pattern formation. PMID:17903019
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
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
NASA Astrophysics Data System (ADS)
Tarazkar, M.; Romanov, D. A.; Levis, R. J.
2016-07-01
Dynamic second-order hyperpolarizabilities of atomic noble gases and their multiply ionized ions are computed using ab initio multiconfigurational self-consistent field cubic response theory. For each species, the calculations are performed at wavelengths ranging from the static regime to those about 100 nm above the first multiphoton resonance. The second-order hyperpolarizability coefficients progressively decrease as the electrons are removed from the system, in qualitative agreement with phenomenological calculations. In higher ionization states, the resulting nonlinear refractive index becomes less dispersive as a function of wavelength. At each ionization stage, the sign of the optical response depends on the number of electrons in the system and, if multiple state symmetries are possible, on the spin of the particular quantum state. Thus, for N e3 + and N e4 + , the hyperpolarizability coefficients in the low-spin states (P2u, and S1g, respectively) are positive, while in the high-spin states (S4u, and P3g) they are negative. However, for doubly, triply, and quadruply charged Ar and Kr these coefficients do not undergo a sign change.
Tian, Yuan; Gao, Bin; Ziegler, Kirk J
2011-02-28
Knowledge of the mobility of carbon nanotubes (CNTs) in porous media is very important to assess their impacts on the environment. In this study, a series of laboratory experiments were conducted to explore the transport mechanisms of sonication shortened, sodium dodecylbenzene sulfonate (SDBS) dispersed single-walled nanotubes (SWNTs) in both saturated and unsaturated sand columns. Laboratory columns packed with quartz sand with different combinations of moisture content and grain-size distribution were used to examine the breakthrough behavior of the SDBS-dispersed SWNTs. Bubble column experiments were also conducted to study the interactions between the SDBS-dispersed SWNTs and the air-water interface. Packed-column experimental results showed that the SDBS-dispersed SWNTs were highly mobile for most of the experimental conditions tested. The surface deposition of the SWNTs in the sand columns was low because all the interactive surfaces were negatively charged. Physical trapping was not observed for the SWNTs in the saturated porous media of different grain-size distributions because the SWNTs might orient parallel to the streamlines in flow to reduce their retention. Retention of the SWNTs in unsaturated porous media occurred only at a very low moisture content (<0.10). Otherwise, reduction in moisture content showed little impact on the retention and transport of the SWNTs in unsaturated porous media. Findings from the bubble-column experiments confirmed that the SDBS-dispersed SWNTs did not attach to the air-water interface. A mathematical model based on the advection-dispersion equation coupled with reaction-rate laws successfully described the retention and transport of the SDBS-dispersed SWNTs in both water-saturated and unsaturated columns. PMID:21236566
Scalora, Michael; Syrchin, Maxim S; Akozbek, Neset; Poliakov, Evgeni Y; D'Aguanno, Giuseppe; Mattiucci, Nadia; Bloemer, Mark J; Zheltikov, Aleksei M
2005-07-01
A new generalized nonlinear Schrödinger equation describing the propagation of ultrashort pulses in bulk media exhibiting frequency dependent dielectric susceptibility and magnetic permeability is derived and used to characterize wave propagation in a negative index material. The equation has new features that are distinct from ordinary materials (mu=1): the linear and nonlinear coefficients can be tailored through the linear properties of the medium to attain any combination of signs unachievable in ordinary matter, with significant potential to realize a wide class of solitary waves. PMID:16090616
NASA Astrophysics Data System (ADS)
Siwicki, Bartłomiej; Kasztelanic, Rafał; Klimczak, Mariusz; Cimek, Jarosław; Pysz, Dariusz; Stępień, Ryszard; Buczyński, Ryszard
2016-06-01
The bandwidth of coherent supercontinuum generated in optical fibres is strongly determined by the all-normal dispersion characteristic of the fibre. We investigate all-normal dispersion limitations in all-solid oxide-based soft glass photonic crystal fibres with various relative inclusion sizes and lattice constants. The influence of material dispersion on fibre dispersion characteristics for a selected pair of glasses is also examined. A relation between the material dispersion of the glasses and the fibre dispersion has been described. We determined the parameters which limit the maximum range of flattened all-normal dispersion profile achievable for the considered pair of heavy-metal-oxide soft glasses.
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.
Smith, P.A.
1993-12-31
In the safety assessment of nuclear waste repositories, sorption of radionuclides on the surfaces of colloids may significantly modify transport behavior where colloid concentration is sufficiently high. In the case of fractured geological media, colloids may be excluded from matrix pores, in which case radionuclides bound to them are not subject to the retarding effects of matrix diffusion and sorption onto matrix pore surfaces. A model is presented describing colloid facilitated transport through fractured media with non-linear sorption. A simple criterion is developed to predict when the presence of colloids will have a significant influence on transport and effects resulting from non-linearity of sorption are described. However, lack of comprehensive sorption data, as well as computational efficiency, mean that the use of a simplified transport model, with linear sorption both on pore surfaces and colloids, is desirable if it can be demonstrated to be conservative. A further criterion is developed to predict where such a model, with linear sorption calculated for the highest concentration encountered along the flow path, would be expected to yield conservative results.
Frequency-domain nonlinear optics in two-dimensionally patterned quasi-phase-matching media.
Phillips, C R; Mayer, B W; Gallmann, L; Keller, U
2016-07-11
Advances in the amplification and manipulation of ultrashort laser pulses have led to revolutions in several areas. Examples include chirped pulse amplification for generating high peak-power lasers, power-scalable amplification techniques, pulse shaping via modulation of spatially-dispersed laser pulses, and efficient frequency-mixing in quasi-phase-matched nonlinear crystals to access new spectral regions. In this work, we introduce and demonstrate a new platform for nonlinear optics which has the potential to combine these separate functionalities (pulse amplification, frequency transfer, and pulse shaping) into a single monolithic device that is bandwidth- and power-scalable. The approach is based on two-dimensional (2D) patterning of quasi-phase-matching (QPM) gratings combined with optical parametric interactions involving spatially dispersed laser pulses. Our proof of principle experiment demonstrates this technique via mid-infrared optical parametric chirped pulse amplification of few-cycle pulses. Additionally, we present a detailed theoretical and numerical analysis of such 2D-QPM devices and how they can be designed. PMID:27410862
Two-dimensional solitons in media with stripe-shaped nonlinearity modulation
Hung, Nguyen Viet; Zin, Pawel; Trippenbach, Marek; Malomed, Boris A.
2010-10-15
We introduce a model of media with the cubic attractive nonlinearity concentrated along a single or double stripe in the two-dimensional (2D) plane. The model can be realized in terms of nonlinear optics (in the spatial and temporal domains alike) and BEC. It is known from recent works that search for stable 2D solitons in models with a spatially localized self-attractive nonlinearity is a challenging problem. We make use of the variational approximation (VA) and numerical methods to investigate conditions for the existence and stability of solitons in the present setting. The result crucially depends on the transverse shape of the stripe: while the rectangular profile supports stable 2D solitons, its smooth Gaussian-shaped counterpart makes all the solitons unstable. This difference is explained, in particular, by the VA. The double stripe with the rectangular profile admits stable solitons of three distinct types: symmetric and asymmetric ones with a single-peak, and double-peak symmetric solitons. The shape and stability of the single-peak solitons of either type are accurately predicted by the VA. Collisions between identical stable solitons are briefly considered too, by means of direct simulations. Depending on the collision velocity, we observe excitation of intrinsic oscillations of the solitons, or their decay, or the collapse (catastrophic self-focusing).
NASA Astrophysics Data System (ADS)
Kharin, Nikolay A.
2001-05-01
The novel solution of the KZK equation for acoustic pressure of the second harmonic in slightly focused beam of a circular transducer was obtained in a closed form for moderately nonlinear absorbing media (Gol'dberg numbers ~ 1). The solution is based on the method of slowly changing wave profile in combination with the method of successive approximations. Two pairs of transducers (Valpey-Fisher Corp.) Were compared to investigate the influence of focusing on the applicability of the moderate nonlinearity approach. The first pair was of 0.25' diameter and the second was of 0.5' diameter. Both pairs has one transducer with flat surface and the other geometrically focused at 4'. The central frequency for all transducers was 5 MHz. Measurements were undertaken in the blood-mimicking solution of water and glycerine. The results demonstrated that for slightly focused transducers with circular apertures, the moderate nonlinearity approach is still valid, as it was proved for flat sources with the same source level, despite the higher pressures in the focal region. The peak pressure for the weakly focused system occurs at a shorter range than focal length.
Effects of nonlinearity on the propagation of acoustic pulses in random media
NASA Astrophysics Data System (ADS)
Cleveland, Robin; Dallois, Laurent; Blanc-Benon, Philippe
2002-11-01
We conducted a numerical investigation into the propagation of finite-amplitude pulses in media with inhomogeneous random sound speed. An N wave (idealized sonic boom) was used as the pulse shape. Initial simulations considered a medium with a single spherical scattering object with a slow sound speed. This object acted as a focusing lens. As the amplitude of the N wave was increased nonlinear effects initially led to enhancement of focusing, reduction in shock risetime, and a shift of the peak away from the object. However, for high amplitude, energy loss at the shock led to a dramatic reduction in the amplitude of the focus and a shift towards the object. Simulations were then carried out in a two-dimensional random media. The sound speed in the random media was constructed using a Fourier mode decomposition with parameters appropriate for turbulence in the atmospheric boundary layer. For low amplitude waves the N wave was focused and defocused by regions of low and high sound speed, respectively. However, the presence of multiple paths means that the wave form no longer resembled an N-wave after propagating about 10 wavelengths. As the amplitude was increased the focusing was enhanced and more localized.
Non-Fickian dispersion in porous media explained by heterogeneous microscale matrix diffusion
NASA Astrophysics Data System (ADS)
Gouze, Philippe; Melean, Yasmin; Le Borgne, Tanguy; Dentz, Marco; Carrera, Jesus
2008-11-01
Mobile-immobile mass transfer is widely used to model non-Fickian dispersion in porous media. Nevertheless, the memory function, implemented in the sink/source term of the transport equation to characterize diffusion in the matrix (i.e., the immobile domain), is rarely measured directly. Therefore, the question can be posed as to whether the memory function is just a practical way of increasing the degrees of freedom for fitting tracer test breakthrough curves or whether it actually models the physics of tracer transport. In this paper we first present a technique to measure the memory function of aquifer samples and then compare the results with the memory function fitted from a set of field-scale tracer tests performed in the same aquifer. The memory function is computed by solving the matrix diffusion equation using a random walk approach. The properties that control diffusion (i.e., mobile-immobile interface and immobile domain cluster shapes, porosity, and tortuosity) are investigated by X-ray microtomography. Once the geometry of the matrix clusters is measured, the shape of the memory function is controlled by the value of the porosity at the percolation threshold and of the tortuosity of the diffusion path. These parameters can be evaluated from microtomographic images. The computed memory function compares well with the memory function deduced from the field-scale tracer tests. We conclude that for the reservoir rock studied here, the atypical non-Fickian dispersion measured from the tracer test is well explained by microscale diffusion processes in the immobile domain. A diffusion-controlled mobile-immobile mass transfer model therefore appears to be valid for this specific case.
2D experiments for characterizing solute dispersion in unsaturated heterogeneous porous media
NASA Astrophysics Data System (ADS)
Jimenez-Martinez, J.; De Anna, P.; Turuban, R.; Tabuteau, H.; Le Borgne, T.; Meheust, Y.
2012-12-01
The unsaturated zone plays a key role in the transfer of chemical elements from the surface to the subsurface. Yet, predicting the transport of chemical species through unsaturated porous media is still an open issue. The distribution of water and air clusters creates flow paths that are controlled by the water saturation, with the feature of a large velocity distribution. As saturation decreases, very low velocity zones in regions of trapped fluid coexist with connected fluid clusters with relatively high velocities. As a consequence the dispersion of solute elements strongly depends on the saturation degree. Numerical simulations of unsaturated flows at the pore scale are feasible, but to our knowledge no simulation of solute transport in the water phase during two-phase flow has been achieved yet. Due to technical difficulties, there also exists relatively few laboratory experiments that allow for visualization and quantification of unsaturated flow and transport at the pore scale. We have developed a two-dimensional (2D) horizontal set up, built by lithographic technique and in which a joint injection of the two phases (wetting and non-wetting) provides a controlled homogeneous saturation in the medium. The simultaneous precise measurement of the flow field, the spatial distribution of water and air, and the 2D tracer concentration field, as well as breakthrough curves at different locations, are used to investigate the relationship between the flow field complexity (velocity distribution and its correlation properties) and dispersion properties. Experimental results show non-Fickian transport behaviors, characterized by heavy tailed breakthrough curves, whose characteristics depend on the average saturation.
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:
Nonlinear optical materials as coherence filters for noninvasive imaging through turbid media
NASA Astrophysics Data System (ADS)
Anderson, Denise Brown
Noninvasive optical imaging of the internal structure of objects that are obscured by diffusive media has recently attracted interest for characterizing the internal porous structure of certain types of composite materials and for diagnostic imaging of medical or biological tissue. However, strong scattering of the optical radiation by these inhomogeneous materials can severely degrade image resolution by randomizing the optical image information in the object's transmitted or reflected optical signals. Thus, to improve image resolution, some form of gating technique is necessary to separate the minimally scattered light from the severely scattered light. A coherence gating technique based on degenerate four- wave mixing (DFWM) in thin nonlinear optical materials is described. Two-dimensional (2-D) depth-resolved imaging through a 4 mean free path (mfp) scattering media was obtained for a BaTiO3 photorefractive crystal, with an achievable depth resolution of 20 μm. In addition, a dyedoped K15 nematic liquid crystal film was used to provide for the first time single shot image acquisition through a 2 mfp scattering media, with an achievable transverse resolution of 70 μm. The direct current (DC) electric field-assisted nonlinear optical (NLO) properties of K15 were used to increase the sensitivity of the DFWM technique (i.e., increase the phase conjugate reflectivity) by one order of magnitude. The NLO characteristics of K15 liquid crystal samples under applied DC electric fields were also investigated. A birefringence experiment was used to qualitatively investigate the in-plane alignment of several liquid crystal films before and after the application of DC fields. Finally, Raman spectroscopy measurements provided evidence of the destruction of the molecular ordering of these films for increases in Rhodamine dye concentrations (from 0.15% to 0.5%). The DFWM imaging technique can be used to provide instantaneous, depth-resolved, 2-D images of the internal
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)
Bouchelaghem, F.; Vulliet, L.
2001-10-01
The development of a predictive model of behaviour of porous media during injection of miscible grout, taking into account convection, dilution and filtration of grout solution with interstitial water, as well as consolidation aspects, is presented. Model assumptions are reviewed and discussed first. During the establishment of the model, we insist on surface terms and their physical relevance in expressing adsorption effects. Constitutive laws such as Fick's law for diffusive mass transport, hydrodynamic dispersion tensor dealing with miscibility, are modified by taking into account filtration effects. A new surface term appears in mass balance equations as a consequence of filtration. According to the filtration laws used, an initial filtration rate is estimated on the basis of a one-dimensional experimental campaign. The field equations are discretized by using Galerkin finite element and -scheme standard method. For transport equation, Streamline Upwind Petrov Galerkin method is employed to prevent numerical oscillations. Lastly, confrontation of numerical results with laboratory experiments constitutes a first step to validate the model on a realistic basis.
Nonlinear diffusion in two-dimensional ordered porous media based on a free volume theory
NASA Astrophysics Data System (ADS)
Godec, A.; Gaberscek, M.; Jamnik, J.; Merzel, F.
2009-12-01
A continuum nonlinear diffusion model is developed to describe molecular transport in ordered porous media. An existing generic van der Waals equation of state based free volume theory of binary diffusion coefficients is modified and introduced into the two-dimensional diffusion equation. The resulting diffusion equation is solved numerically with the alternating-direction fully implicit method under Neumann boundary conditions. Two types of pore structure symmetries are considered, hexagonal and cubic. The former is modeled as parallel channels while in case of the latter equal-sized channels are placed perpendicularly thus creating an interconnected network. First, general features of transport in both systems are explored, followed by the analysis of the impact of molecular properties on diffusion inside and out of the porous matrix. The influence of pore size on the diffusion-controlled release kinetics is assessed and the findings used to comment recent experimental studies of drug release profiles from ordered mesoporous silicates.
Nonlinear acoustics: Reflection and refraction, scattering of sound by sound, and periodic media
NASA Astrophysics Data System (ADS)
Blackstock, David T.
1988-07-01
Research on three topics in nonlinear acoustics is described: (1) reflection and refraction at a plane interface between two fluids. Previously a modified form of Snell's law was derived; theoretical work is underway to investigate assumptions on which the derivation was based, (2) scattering of sound by sound. Work on a single beam experiment and a crossed-beams experiment is in progress, and (3) propagation in periodic media. An experiment is being designed to measure finite-amplitude distortion in a plane wave tube loaded periodically with reactive branch elements. Other work, on noncollinear interaction and on biomedical ultrasonics, is described briefly. Two journal articles, five oral papers, and one technical report are listed.
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.
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)
Leong, J. Y. Y.; Petropoulos, P.; Price, J. H. V.; Ebendorff-Heidepriem, Heike; Asimakis, S.; Moore, R. C.; Frampton, K. E.; Finazzi, V.; Feng, X.; Monro, T. M.; Richardson, D. J.
2006-01-01
This paper reports on the recent progress in the design and fabrication of high-nonlinearity lead-silicate holey fibers (HFs). First, the fabrication of a fiber designed to offer close to the maximum possible nonlinearity per unit length in this glass type is described. A value of gamma = 1860 W-1 · km-1 at a wavelength of 1.55 µm is achieved, which is believed to be a record for any fiber at this wavelength. Second, the design and fabrication of a fiber with a slightly reduced nonlinearity but with dispersion-shifted characteristics tailored to enhance broadband supercontinuum (SC) generation when pumped at a wavelength of 1.06 µm-a wavelength readily generated using Yb-doped fiber lasers-are described. SC generation spanning more than 1000 nm is observed for modest pulse energies of sim 100 pJ using a short length of this fiber. Finally, the results of numerical simulations of the SC process in the proposed fibers are presented, which are in good agreement with the experimental observations and highlight the importance of accurate control of the zero-dispersion wavelength (ZDW) when optimizing such fibers for SC performance.
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
On the dispersion relation of nonlinear wave current interaction by means of the HAM
NASA Astrophysics Data System (ADS)
Liu, Zeng; Lin, Zhiliang; Liao, Shijun
2012-09-01
The influence of exponentially sheared currents on unidirectional bichromatic waves in deep water is investigated by the HAM. The governing equations contain four coupled PDEs, including a nonlinear vorticity transport equation and two nonlinear free-surface conditions on the unknown wave elevation. No constrain is made for the primary wave amplitudes, and the current owns a exponential type profile along the vertical line. Convergent solutions are obtained with the help of convergence-control parameter. It is found that a critical characteristic current profile slope exists for each parts of phase velocity caused by nonlinear interaction, under/above which the mean flow vorticity increases/decreases the corresponding part of phase velocity. This work indicates that the HAM is a powerful tool for complicated coupled nonlinear PDEs, which deserves more attention for further development.
Observation of the Predicted Behavior of Nonlinear Pulse Propagation in Disordered Media
NASA Astrophysics Data System (ADS)
Hopkins, Vernon A.; Keat, Justin; Meegan, G. Douglas; Zhang, Tianming; Maynard, J. D.
1996-02-01
A fundamental question concerning systems which are both disordered and nonlinear is whether or not Anderson localization is weakened by the nonlinearity. Theory predicts that localized eigenstates will survive nonlinearity, whereas nonlinear pulses may or may not experience the effects of localization depending on the relative magnitude of the Anderson localization length and a characteristic ``nonlinearity'' length for the pulse. We have used nonlinear surface waves on a superfluid helium film to obtain results in agreement with theoretical predictions.
Traveling waves for conservation laws with cubic nonlinearity and BBM type dispersion
NASA Astrophysics Data System (ADS)
Shearer, Michael; Spayd, Kimberly R.; Swanson, Ellen R.
2015-10-01
Scalar conservation laws with non-convex fluxes have shock wave solutions that violate the Lax entropy condition. In this paper, such solutions are selected by showing that some of them have corresponding traveling waves for the equation supplemented with dissipative and dispersive higher-order terms. For a cubic flux, traveling waves can be calculated explicitly for linear dissipative and dispersive terms. Information about their existence can be used to solve the Riemann problem, in which we find solutions for some data that are different from the classical Lax-Oleinik construction. We consider dispersive terms of a BBM type and show that the calculation of traveling waves is somewhat more intricate than for a KdV-type dispersion. The explicit calculation is based upon the calculation of parabolic invariant manifolds for the associated ODE describing traveling waves. The results extend to the p-system of one-dimensional elasticity with a cubic stress-strain law.
Bolea, Mario; Mora, José; Ortega, Beatriz; Capmany, José
2012-03-12
A novel all-optical technique based on the incoherent processing of optical signals using high-order dispersive elements is analyzed for microwave arbitrary pulse generation. We show an approach which allows a full reconfigurability of a pulse in terms of chirp, envelope and central frequency by the proper control of the second-order dispersion and the incoherent optical source power distribution, achieving large values of time-bandwidth product. PMID:22418557
Dong, Ningning; Li, Yuanxin; Zhang, Saifeng; McEvoy, Niall; Zhang, Xiaoyan; Cui, Yun; Zhang, Long; Duesberg, Georg S; Wang, Jun
2016-09-01
Both the nonlinear absorption and nonlinear refraction properties of WS_{2} and WSe_{2} semiconductor films have been characterized by using Z-scan technique with femtosecond pulses at the wavelength of 1040 nm. It is found that these films have two-photon absorption response with the nonlinear absorption coefficient of ∼10^{3} cm GW^{-1}, and a dispersion of nonlinear refractive index in the WS_{2} films that translated from positive in the monolayer to negative in bulk materials. PMID:27607941
NASA Astrophysics Data System (ADS)
Osorio, A. G.; Silveira, I. C. L.; Bueno, V. L.; Bergmann, C. P.
2008-12-01
Chemical functionalization is a procedure used in materials science to oxidize the surface of materials. Several researchers use this technique to improve carbon nanotubes (CNTs) interaction and dispersion. The present article evaluates the effect of different functionalization methodologies on dispersion of CNTs in aqueous media. Sulfuric, nitric and chloridric acids were used on the first functionalization. For the second procedure tested the addition of chloridric acid was eliminated; and the third functionalization was done using only nitric acid. Experimental results obtained by Raman spectroscopy indicated the maintenance of the structure of CNTs after all oxidations. The presence of other structures was proved by thermogravimetry decomposition and the addition of functional groups was confirmed by transform Fourier infrared spectroscopy. From these experimental results, we conclude that all methodologies used showed a percentage of adsorption of functional groups on the CNTs. However, based on dispersion analysis in aqueous media, it is observed that this adsorption showed more efficiency on the first functionalization method, followed by the second method.
Jorge, Kelly C; García, Hans A; Amaral, Anderson M; Reyna, Albert S; Menezes, Leonardo de S; de Araújo, Cid B
2015-07-27
The Scattered Light Imaging Method (SLIM) was applied to measure the nonlinear refractive index of scattering media. The measurements are based on the analysis of the side-view images of the laser beam propagating inside highly scattering liquid suspensions. Proof-of-principle experiments were performed with colloids containing silica nanoparticles that behave as light scatterers. The technique allows measurements with lasers operating with arbitrary repetition rate as well as in the single-shot regime. The new method shows advantages and complementarity with respect to the Z-scan technique which is not appropriate to characterize scattering media. PMID:26367609
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). PMID:18825217
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.
Taming the non-linearity problem in GPR full-waveform inversion for high contrast media
NASA Astrophysics Data System (ADS)
Meles, Giovanni; Greenhalgh, Stewart; van der Kruk, Jan; Green, Alan; Maurer, Hansruedi
2012-03-01
We present a new algorithm for the inversion of full-waveform ground-penetrating radar (GPR) data. It is designed to tame the non-linearity issue that afflicts inverse scattering problems, especially in high contrast media. We first investigate the limitations of current full-waveform time-domain inversion schemes for GPR data and then introduce a much-improved approach based on a combined frequency-time-domain analysis. We show by means of several synthetic tests and theoretical considerations that local minima trapping (common in full bandwidth time-domain inversion) can be avoided by starting the inversion with only the low frequency content of the data. Resolution associated with the high frequencies can then be achieved by progressively expanding to wider bandwidths as the iterations proceed. Although based on a frequency analysis of the data, the new method is entirely implemented by means of a time-domain forward solver, thus combining the benefits of both frequency-domain (low frequency inversion conveys stability and avoids convergence to a local minimum; whereas high frequency inversion conveys resolution) and time-domain methods (simplicity of interpretation and recognition of events; ready availability of FDTD simulation tools).
Taming the non-linearity problem in GPR full-waveform inversion for high contrast media
NASA Astrophysics Data System (ADS)
Meles, Giovanni; Greenhalgh, Stewart; van der Kruk, Jan; Green, Alan; Maurer, Hansruedi
2011-02-01
We present a new algorithm for the inversion of full-waveform ground-penetrating radar (GPR) data. It is designed to tame the non-linearity issue that afflicts inverse scattering problems, especially in high contrast media. We first investigate the limitations of current full-waveform time-domain inversion schemes for GPR data and then introduce a much-improved approach based on a combined frequency-time-domain analysis. We show by means of several synthetic tests and theoretical considerations that local minima trapping (common in full bandwidth time-domain inversion) can be avoided by starting the inversion with only the low frequency content of the data. Resolution associated with the high frequencies can then be achieved by progressively expanding to wider bandwidths as the iterations proceed. Although based on a frequency analysis of the data, the new method is entirely implemented by means of a time-domain forward solver, thus combining the benefits of both frequency-domain (low frequency inversion conveys stability and avoids convergence to a local minimum; whereas high frequency inversion conveys resolution) and time-domain methods (simplicity of interpretation and recognition of events; ready availability of FDTD simulation tools).
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 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
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.
Modeling of Ultra-Short Soliton Propagation in Deterministic and Stochastic Nonlinear Cubic Media
NASA Astrophysics Data System (ADS)
Kurt, Levent
We study the short pulse dynamics in the deterministic and stochastic environment in this thesis. The integrable short pulse equation is a modelling equation for ultra-short pulse propagation in the infrared range in the optical fibers. We investigate the numerical proof for the exact solitary solution of the short pulse equation. Moreover, we demonstrate that the short pulse solitons approximate the solution of the Maxwell equation numerically. Our numerical experiments prove the particle-like behaviour of the short pulse solitons. Furthermore, we derive a short pulse equation in the higher order. A stochastic counterpart of the short pulse equation is also derived through the use of the multiple scale expansion method for more realistic situations where stochastic perturbations in the dispersion are present. We numerically show that the short pulse solitary waves persist even in the presence of the randomness. The numerical schemes developed demonstrate that the statistics of the coarse-graining noise of the short pulse equation over the slow scale, and the microscopic noise of the nonlinear wave equation over the fast scale, agree to fairly good accuracy.
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. PMID:26627574
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
Westergaard, Philip G; Christensen, Bjarke T R; Tieri, David; Matin, Rastin; Cooper, John; Holland, Murray; Ye, Jun; Thomsen, Jan W
2015-03-01
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. PMID:25793810
NASA Astrophysics Data System (ADS)
Westergaard, Philip G.; Christensen, Bjarke T. R.; Tieri, David; Matin, Rastin; Cooper, John; Holland, Murray; Ye, Jun; Thomsen, Jan W.
2015-03-01
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.
Extreme nonlinearities in InAs/InP nanowire gain media: the two-photon induced laser.
Capua, Amir; Karni, Ouri; Eisenstein, Gadi; Reithmaier, Johann Peter; Yvind, Kresten
2012-03-12
We demonstrate a novel laser oscillation scheme in an InAs / InP wire-like quantum dash gain medium. A short optical pulse excites carriers by two photon absorption which relax to the energy levels providing gain thereby enabling laser oscillations. The nonlinear dynamic interaction is analyzed and quantified using multi-color pump-probe measurements and shows a highly efficient nonlinear two photon excitation process which is larger by more than an order of magnitude compared to common quantum well and bulk gain media. The dynamic response of the nonlinearly induced laser line is characterized by spectrally resolved temporal response measurements, while changes incurring upon propagation in the stimulating short pulse itself are characterized by frequency resolved optical gating (FROG). PMID:22418475
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. PMID:12714311
NASA Astrophysics Data System (ADS)
Arqub, Omar Abu; El-Ajou, Ahmad; Momani, Shaher
2015-07-01
Building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics, physics, and engineering. In this work, a new analytical technique for constructing and predicting solitary pattern solutions of time-fractional dispersive partial differential equations is proposed based on the generalized Taylor series formula and residual error function. The new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software. For method evaluation and validation, the proposed technique was applied to three different models and compared with some of the well-known methods. The resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct, as well as the prediction of solitary pattern solutions for time-fractional dispersive partial differential equations.
NASA Astrophysics Data System (ADS)
Duan, Zhongchao; Liao, Meisong; Yan, Xin; Kito, Chihiro; Suzuki, Takenobu; Ohishi, Yasutake
2011-07-01
We report the fabrication of tellurite composite microstructured optical fibers (CMOFs) which consist of a TeO2-Li2O-WO3-MoO3-Nb2O5 (TLWMN) tellurite glass core and TeO2-ZnO-Na2O-La2O3 (TZNL) tellurite glass cladding. Flattened chromatic dispersion and tunable zero dispersion wavelength (ZDW) were realized in the small core diameter (˜1.5 µm) fiber with six surrounding air holes. The optical loss was measured to be about 4.0 dB/m in the spectral range of 1510-1640 nm. Supercontinuum (SC) generation was demonstrated by a femtosecond laser pumping at 1.55 µm. The threshold pump power for this novel tellurite CMOF was the lowest among tellurite microstructured optical fibers (MOFs).
NASA Astrophysics Data System (ADS)
Ramadan, Omar
2015-09-01
In this paper, systematic wave-equation finite difference time domain (WE-FDTD) formulations are presented for modeling electromagnetic wave-propagation in linear and nonlinear dispersive materials. In the proposed formulations, the complex conjugate pole residue (CCPR) pairs model is adopted in deriving a unified dispersive WE-FDTD algorithm that allows modeling different dispersive materials, such as Debye, Drude and Lorentz, in the same manner with the minimal additional auxiliary variables. Moreover, the proposed formulations are incorporated with the wave-equation perfectly matched layer (WE-PML) to construct a material independent mesh truncating technique that can be used for modeling general frequency-dependent open region problems. Several numerical examples involving linear and nonlinear dispersive materials are included to show the validity of the proposed formulations.
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
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.
NASA Astrophysics Data System (ADS)
Amooshahi, M.
2016-08-01
Modeling a nonlinear anisotropic magnetodielectric medium with spatial-temporal dispersion by two continuum collections of three dimensional harmonic oscillators, a fully canonical quantization of the electromagnetic field is demonstrated in the presence of such a medium. Some coupling tensors of various ranks are introduced that couple the magnetodielectric medium with the electromagnetic field. The polarization and magnetization fields of the medium are defined in terms of the coupling tensors and the oscillators modeling the medium. The electric and magnetic susceptibility tensors of the medium are obtained in terms of the coupling tensors. It is shown that the electric field satisfy an integral equation in frequency domain. The integral equation is solved by an iteration method and the electric field is found up to an arbitrary accuracy.
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. PMID:27434778
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)
Mohanty, Ritesh P.; Zia, Roseanna N.
2015-03-01
In active microrheology, a probe is driven through a complex medium. Most work thus far has focused on steady behavior and established the relationship between the microstructure, probe speed, and rheology. But important information about structural development and relaxation are captured by startup and cessation of flows in the non-linear regime, where the structure is driven far from equilibrium. Here we study theoretically the rate of stress formation and relaxation under non-linear microrheological forcing of hydrodynamically interacting colloids. We study the behavior analytically in the dual limits of weak and strong probe forcing and weak and strong hydrodynamic interactions and numerically in between. To elucidate the detailed role of hydrodynamic, Brownian, and interparticle forces in stress formation and relaxation, we employ an excluded annulus model to introduce each systematically, and study the rheological and structural response for arbitrary forcing and strength of hydrodynamic interactions. Hydrodynamics introduce an additional mode of dissipation, which manifests as a reduction in the rate of stress formation during startup. While this non-equilibrium contribution vanishes instantly upon flow shutoff, a delicate interplay between Brownian and interparticle forces influences relaxation, revealing multiple relaxation modes. The recovery of entropically stored energy is studied.
A new formulation of the dispersion tensor in homogeneous porous media
NASA Astrophysics Data System (ADS)
Valdés-Parada, Francisco J.; Lasseux, Didier; Bellet, Fabien
2016-04-01
Dispersion is the result of two mass transport processes, namely molecular diffusion, which is a pure mixing effect and hydrodynamic dispersion, which combines mixing and spreading. The identification of each contribution is crucial and is often misinterpreted. Traditionally, under a volume averaging framework, a single closure problem is solved and the resulting fields are substituted into diffusive and dispersive filters. However the diffusive filter (that leads to the effective diffusivity) allows passing information from convection, which leads to an incorrect definition of the effective medium coefficients composing the total dispersion tensor. In this work, we revisit the definitions of the effective diffusivity and hydrodynamic dispersion tensors using the method of volume averaging. Our analysis shows that, in the context of laminar flow with or without inertial effects, two closure problems need to be computed in order to correctly define the corresponding effective medium coefficients. The first closure problem is associated to momentum transport and needs to be solved for a prescribed Reynolds number and flow orientation. The second closure problem is related to mass transport and it is solved first with a zero Péclet number and second with the required Péclet number and flow orientation. All the closure problems are written using closure variables only as required by the upscaling method. The total dispersion tensor is shown to depend on the microstructure, macroscopic flow angles, the cell (or pore) Péclet number and the cell (or pore) Reynolds number. It is non-symmetric in the general case. The condition for quasi-symmetry is highlighted. The functionality of the longitudinal and transverse components of this tensor with the flow angle is investigated for a 2D model porous structure obtaining consistent results with previous studies.
NASA Astrophysics Data System (ADS)
Beech, Robert; Osman, Frederick
2005-10-01
This paper will present the nonlinearity and dispersion effects involved in propagation of optical solitons, which can be understood by using a numerical routine to solve the nonlinear Schrödinger equation (NLSE). Here, Mathematica v5© (Wolfram, 2003) is used to explore in depth several features of optical solitons formation and propagation. These numerical routines were implemented through the use of Mathematica v5© and the results give a very clear idea of this interesting and important practical phenomenon. It is hoped that this work will open up an important new approach to the cause, effect, and correction of interference from secondary radiation found in the uses of soliton waves in lasers and in optical fiber telecommunication. It is believed that these results will be of considerable use in any work or research in this field and in self-focusing properties of the soliton (Osman et al., 2004a, 2004b; Hora, 1991). In a previous paper on this topic (Beech & Osman, 2004), it was shown that solitons of NLSE radiate. This paper goes on from there to show that these radiations only occur in solitons derived from cubic, or odd-numbered higher orders of NLSE, and that there are no such radiations from solitons of quadratic, or even-numbered higher order of NLSE. It is anticipated that this will stimulate research into practical means to control or eliminate such radiations.
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.
Xue, Yuying; Zhang, Ting; Zhang, Bangyong; Gong, Fan; Huang, Yanmei; Tang, Meng
2016-03-01
Silver nanoparticles (Ag NPs) have been widely used in medical and healthcare products owing to their unique antibacterial activities. However, their safety for humans and the environment has not yet been established. This study evaluated the cellular proliferation and apoptosis of Ag NPs suspended in different solvents using human liver HepG2 cells. The ionization of Ag NPs in different dispersion media [deionized water, phosphate-buffered saline (PBS), saline and cell culture] was measured using an Ag ion selective electrode. The MTT assay was used to examine the cell proliferation activities. The effects of Ag NPs on cell cycle, induction of apoptosis, production of reactive oxygen species (ROS) and mitochondrial membrane potential (MMP) were analyzed using flow cytometry. The degree of Ag NPs ionization differed with dispersion media, with the concentrations of silver ions in deionized water being the highest in all suspensions. Ag NPs could inhibit the viability of HepG2 cells in a time- and concentration-dependent manner. Ag NPs (40, 80 and 160 µg ml(-1)) exposure could cause cell-cycle arrest in the G2/M phase, significantly increasing the apoptosis rate and ROS generation, and decreasing the MMP in HepG2 cells more sensitive to deionized water than in cell culture. These results suggested that the cellular toxicological mechanism of Ag NPs might be related to the oxidative stress of cells by the generation of ROS, leading to mitochondria injury and induction of apoptosis. It also implies that it is important to assess the physicochemical properties of NPs in the media where the biological toxicity tests are performed. PMID:26198703
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; Vitkalov, Sergey; Sergeev, A.; Bollinger, Anthony T.; Božović, Ivan
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)
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.
Nonlinear modulation of periodic waves in the small dispersion limit of the Benjamin-Ono equation
NASA Astrophysics Data System (ADS)
Matsuno, Y.
1998-12-01
The Whitham modulation theory is used to construct large time asymptotic solutions of the Benjamin-Ono (BO) equation in the small dispersion limit. For a wide class of initial data, asymptotic solutions are represented by a single-phase periodic solution of the BO equation with slowly varying amplitude and wave number. The Whitham system of modulation equations for these wave parameters has a very simple structure, and it can be solved exactly under appropriate boundary conditions. It is found that the oscillating zone expands with time, and eventually evolves into a train of solitary waves. In the case of localized initial data, the number density function of solitary waves is derived in a closed form. The resulting expression coincides with the corresponding formula obtained from the asymptotic theory based on the conservation laws of the BO equation. For steplike initial data, the total number of created solitary waves increases without limit in proportion to time.
Wave-dispersed third-order nonlinear optical properties of C 60 thin films
NASA Astrophysics Data System (ADS)
Kajzar, F.; Taliani, C.; Danieli, R.; Rossini, S.; Zamboni, R.
1994-01-01
Results of wave-dispersed third harmonic generation measurements in sublimed C 60 thin films are reported and discussed within a three-level model. Two strong resonant enhancements in cubic susceptibility χ (3)(-3ω; ω, ω, ω) are observed. The first one, occurring at a fundamental wavelength of 1.3 μm with a χ (3)(-3ω; ω, ω, ω) maximum value of 6.1×10 -11 esu, is interpreted in terms of a two-photon resonance with the one-photon forbidden electronic T 1g level. The second resonance at 1.064 μm, with a maximum value of χ (3)(-3ω; ω, ω, ω)=8.2×10 -11 esu is interpreted as a three-photon resonance with the lowest one-photon allowed T 1u electronic level.
Garnier, Josselin; Picozzi, Antonio
2010-03-15
This article presents a unified kinetic formulation of partially coherent nonlinear optical waves propagating in a noninstantaneous response Kerr medium. We derive a kinetic equation that combines the weak Langmuir turbulence kinetic equation and a Vlasov-like equation within a general framework: It describes the evolution of the spectrum of a random field that exhibits a quasistationary statistics in the presence of a noninstantaneous nonlinear response. The kinetic equation sheds new light on the dynamics of partially coherent nonlinear waves and allows for a qualitative interpretation of the interplay between the noninstantaneous nonlinearity and the nonstationary statistics of the incoherent field. It is shown that the incoherent modulational instability of a random nonlinear wave can be suppressed by the noninstantaneous nonlinear response. Moreover, incoherent modulational instability can prevent the generation of spectral incoherent solitons.
NASA Astrophysics Data System (ADS)
Levitz, P.; Korb, J.-P.; Bryant, R. G.
1999-10-01
We address the question of probing the fluid dynamics in disordered interfacial media by Pulsed field gradient (PFG) and Magnetic relaxation dispersion (MRD) techniques. We show that the PFG method is useful to separate the effects of morphology from the connectivity in disordered macroporous media. We propose simulations of molecular dynamics and spectral density functions, J(ω), in a reconstructed mesoporous medium for different limiting conditions at the pore surface. An algebraic form is found for J(ω) in presence of a surface diffusion and a local exploration of the pore network. A logarithmic form of J(ω) is found in presence of a pure surface diffusion. We present magnetic relaxation dispersion experiments (MRD) for water and acetone in calibrated mesoporous media to support the main results of our simulations and theories. Nous présentons les avantages respectifs des méthodes de gradients de champs pulsés (PFG) et de relaxation magnétique nucléaire en champs cyclés (MRD) pour sonder la dynamique moléculaire dans les milieux interfaciaux désordonnés. La méthode PFG est utile pour séparer la morphologie et la connectivité dans des milieux macroporeux. Des simulations de diffusion moléculaire et de densité spectrale J(ω) en milieux mésoporeux sont présentées dans différentes conditions limites aux interfaces des pores. Nous trouvons une forme de dispersion algébrique de J(ω) pour une diffusion de surface assistée d'une exploration locale du réseau de pores et une forme logarithmique dans le cas d'une simple diffusion de surface. Les résultats expérimentaux de la méthode MRD pour de l'eau et de l'acétone dans des milieux mésoporeux calibrés supportent les résultats principaux de nos simulations et théories.
Spatial backward planar projection in absorbing media possessing an arbitrary dispersion relation
Clement, Gregory T.
2011-01-01
Planar projection methods have been shown to rapidly relate fields between two planes. Such an approach is particularly useful for characterizing transducers, since only a single plane needs to be measured in order to characterize an entire field. The present work considers the same approach in the presence of an arbitrary dispersion relation. Unlike traditional methods that use Fourier solutions of the time-domain wave equation, the approach starts from a frequency-domain Helmholtz equation for waves in a dispersive medium. It is shown that a transfer function similar to that derived from time domain equations can be utilized. Both the forward- and backward-projection behaviors are examined and it is demonstrated that the approach is invariant to propagation direction. PMID:21611135
Tardajos, Myriam G; Aranaz, Inmaculada; Sayar, Filiz; Elvira, Carlos; Reinecke, Helmut; Piskin, Erhan; Gallardo, Alberto
2012-04-01
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. PMID:22400912
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)
Chen, Yong; Yan, Zhenya
2016-03-01
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.
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
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
ERIC Educational Resources Information Center
Allen, Lee E., Ed.
1974-01-01
Intended for secondary English teachers, the materials and ideas presented here suggest ways to use media in the classroom in teaching visual and auditory discrimination while enlivening classes and motivating students. Contents include "Media Specialists Need Not Apply," which discusses the need for preparation of media educators with…
Propagation of time-truncated Airy-type pulses in media with quadratic and cubic dispersion.
Borda-Hernández, José A; Zamboni-Rached, Michel; Shaarawi, Amr; Besieris, Ioannis M
2015-10-01
In this paper, we describe analytically the propagation of Airy-type pulses truncated by a finite-time aperture when second- and third-order dispersion effects are considered. The mathematical method presented here, which is based on the superposition of exponentially truncated Airy pulses, is very effective and allows us to avoid the use of time-consuming numerical simulations. We analyze the behavior of the time-truncated ideal Airy pulse and also the interesting case of a time-truncated Airy pulse with a "defect" in its initial profile, which reveals the self-healing property of this kind of pulse solution. PMID:26479932
NASA Astrophysics Data System (ADS)
Yuval; Bekhor, Shlomo; Broday, David M.
2013-11-01
Spatially detailed estimation of exposure to air pollutants in the urban environment is needed for many air pollution epidemiological studies. To benefit studies of acute effects of air pollution such exposure maps are required at high temporal resolution. This study introduces nonlinear optimisation framework that produces high resolution spatiotemporal exposure maps. An extensive traffic model output, serving as proxy for traffic emissions, is fitted via a nonlinear model embodying basic dispersion properties, to high temporal resolution routine observations of traffic-related air pollutant. An optimisation problem is formulated and solved at each time point to recover the unknown model parameters. These parameters are then used to produce a detailed concentration map of the pollutant for the whole area covered by the traffic model. Repeating the process for multiple time points results in the spatiotemporal concentration field. The exposure at any location and for any span of time can then be computed by temporal integration of the concentration time series at selected receptor locations for the durations of desired periods. The methodology is demonstrated for NO2 exposure using the output of a traffic model for the greater Tel Aviv area, Israel, and the half-hourly monitoring and meteorological data from the local air quality network. A leave-one-out cross-validation resulted in simulated half-hourly concentrations that are almost unbiased compared to the observations, with a mean error (ME) of 5.2 ppb, normalised mean error (NME) of 32%, 78% of the simulated values are within a factor of two (FAC2) of the observations, and the coefficient of determination (R2) is 0.6. The whole study period integrated exposure estimations are also unbiased compared with their corresponding observations, with ME of 2.5 ppb, NME of 18%, FAC2 of 100% and R2 that equals 0.62.
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.
Wu, Yu-Shu; Forsyth, Peter A.
2006-04-13
Numerical issues with modeling transport of chemicals or solute in realistic large-scale subsurface systems have been a serious concern, even with the continual progress made in both simulation algorithms and computer hardware in the past few decades. The problem remains and becomes even more difficult when dealing with chemical transport in a multiphase flow system using coarse, multidimensional regular or irregular grids, because of the known effects of numerical dispersion associated with moving plume fronts. We have investigated several total-variation-diminishing (TVD) or flux-limiter schemes by implementing and testing them in the T2R3D code, one of the TOUGH2 family of codes. The objectives of this paper are (1) to investigate the possibility of applying these TVD schemes, using multi-dimensional irregular unstructured grids, and (2) to help select more accurate spatial averaging methods for simulating chemical transport given a numerical grid or spatial discretization. We present an application example to show that such TVD schemes are able to effectively reduce numerical dispersion.
Wang, Xiang-Hua; Yin, Wen-Yan; Chen, Zhi Zhang David
2013-09-01
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. PMID:24103929
Near-field dynamics of ultrashort pulsed Bessel beams in media with Kerr nonlinearity.
Polesana, P; Dubietis, A; Porras, M A; Kucinskas, E; Faccio, D; Couairon, A; Di Trapani, P
2006-05-01
The near-field dynamics of a femtosecond Bessel beam propagating in a Kerr nonlinear medium (fused silica) is investigated both numerically and experimentally. We demonstrate that the input Bessel beam experiences strong nonlinear reshaping. Due to the combined action of self-focusing and nonlinear losses the reshaped beam exhibits a radial compression and reduced visibility of the Bessel oscillations. Moreover, we show that the reshaping process starts from the intense central core and gradually replaces the Bessel beam profile during propagation, highlighting the conical geometry of the energy flow. PMID:16803062
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.
Size dispersion and colloid mediated radionuclide transport in a synthetic porous media.
Delos, A; Walther, C; Schäfer, T; Büchner, S
2008-08-01
Size dispersion effects during the migration of natural submicron bentonite colloids (<200 nm) through a ceramic column are observed for the first time by laser-induced breakdown detection (LIBD) at ppm (parts per million) mass concentration. Larger size fractions ( approximately 200 nm) arrive prior to smaller size fractions (<100 nm) at the column outlet in agreement with model predictions and earlier findings with carboxylated polystyrene spheres. By addition of trace amounts of americium(III) and plutonium(IV), colloid mediated transport of these radionuclides is studied. The peak arrival times of Pu-244 and Am-241, as measured by ICP-MS, match the bentonite colloid breakthrough and occur significantly prior to the conservative tracer (HTO) indicating the colloid-borne migration of tri- and tetravalent radionuclides. PMID:18514680
Numerical calculation of nonlinear ultrashort laser pulse propagation in transparent Kerr media
NASA Astrophysics Data System (ADS)
Arnold, Cord L.; Heisterkamp, Alexander; Ertmer, Wolfgang; Lubatschowski, Holger
2005-03-01
In the focal region of tightly focused ultrashort laser pulses, sufficient high intensities to initialize nonlinear ionization processes are easily achieved. Due to these nonlinear ionization processes, mainly multiphoton ionization and cascade ionization, free electrons are generated in the focus resulting in optical breakdown. A model including both nonlinear pulse propagation and plasma generation is used to calculate numerically the interaction of ultrashort pulses with their self-induced plasma in the vicinity of the focus. The model is based on a (3+1)-dimensional nonlinear Schroedinger equation describing the pulse propagation coupled to a system of rate equations covering the generation of free electrons. It is applicable to any transparent Kerr medium, whose linear and nonlinear optical parameters are known. Numerical calculations based on this model are used to understand nonlinear side effects, such as streak formation, occurring in addition to optical breakdown during short pulse refractive eye surgeries like fs-LASIK. Since the optical parameters of water are a good first-order approximation to those of corneal tissue, water is used as model substance. The free electron density distribution induced by focused ultrashort pulses as well as the pulses spatio-temporal behavior are studied in the low-power regime around the critical power for self-focusing.
NASA Astrophysics Data System (ADS)
Reshak, A. H.; Auluck, S.
2014-12-01
The dispersion of the linear and nonlinear optical susceptibilities of bismuth subcarbonate Bi2O2CO3 are calculated using density functional theory (DFT). We have employed the state-of-art all-electron full potential linearized augmented plane wave (FP-LAPW) method. Calculations are performed within the recently modified Becke-Johnson potential (mBJ) to obtain the self consistency conditions. The calculated linear optical susceptibilities exhibit a considerable anisotropy which is useful for second harmonic generation (SHG) and optical parametric oscillation (OPO). The calculated absorption coefficient show good agreement with the available experimental data. The values of calculated uniaxial anisotropy δɛ = -0.168 and the birefringence Δn(0) = 0.166 indicate considerable anisotropy. The calculated SHG of the dominant component |χ322(2) (ω) | is about d32 = 5.3 pm/V at λ = 1064 nm (1.165 eV) which is in excellent agreement with the available experimental data (d32 = 5.49 pm/V) obtained using pulsed Nd:YAG laser at wavelength λ = 1064 nm (10 ns, 3 mj 10 kHz). To analyze the origin of the high SHG of bismuth subcarbonate Bi2O2CO3 we have correlated the features of |χ322(2) (ω) | spectra with the features of ɛ2(ω) spectra as a function of ω/2 and ω.
Benisti, Didier; Gremillet, Laurent
2008-03-15
The kinetic nonlinear dispersion relation, and frequency shift {delta}{omega}{sub srs}, of a plasma wave driven by stimulated Raman scattering are presented. Our theoretical calculations are fully electromagnetic, and use an adiabatic expression for the electron susceptibility which accounts for the change in phase velocity as the wave grows. When k{lambda}{sub D} > or approx. 0.35 (k being the plasma wave number and {lambda}{sub D} the Debye length), {delta}{omega}{sub srs} is significantly larger than could be inferred by assuming that the wave is freely propagating. Our theory is in excellent agreement with 1D Eulerian Vlasov-Maxwell simulations when 0.3{<=}k{lambda}{sub D}{<=}0.58, and allows discussion of previously proposed mechanisms for Raman saturation. In particular, we find that no ''loss of resonance'' of the plasma wave would limit the Raman growth rate, and that saturation through a phase detuning between the plasma wave and the laser drive is mitigated by wave number shifts.
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)
Mohammed, K. Elboree
2015-10-01
In this paper, we investigate the traveling wave solutions for the nonlinear dispersive equation, Korteweg-de Vries Zakharov-Kuznetsov (KdV-ZK) equation and complex coupled KdV system by using extended simplest equation method, and then derive the hyperbolic function solutions include soliton solutions, trigonometric function solutions include periodic solutions with special values for double parameters and rational solutions. The properties of such solutions are shown by figures. The results show that this method is an effective and a powerful tool for handling the solutions of nonlinear partial differential equations (NLEEs) in mathematical physics.
Reply to ``Comment on `Frequency-dependent dispersion in porous media' ''
NASA Astrophysics Data System (ADS)
Valdés-Parada, Francisco J.; Alvarez-Ramirez, Jose
2012-07-01
In a recent paper [Valdés-Parada and Alvarez-Ramirez, Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.84.031201 84, 031201 (2011)], we studied the passive transport of a solute in a rigid and homogeneous porous medium in the domain of frequency and obtained good agreement between upscaled and pore-scale results for several values of the frequency. This work was commented on by Davit and Quintard, who wrote about the closure problem in the Laplace domain and provided the correct definition of the dispersion coefficient. However, the obtention of the inverse Laplace transform is not always an easy (or even possible) task to perform. For this reason, in this Reply we show that the same result reached by Davit and Quintard can be obtained using integral equation formulations based on Green's functions without the need of the Laplace transform. In addition, we identify three time stages for the transport process and we point out that the derivations provided by Davit and Quintard are only valid once a pre-asymptotic stage has been reached in which there is a separation of characteristic length scales that allows treating volume averaged quantities as constants in space but not in time.
NASA Astrophysics Data System (ADS)
Yang, Lei; Yang, DingHui; Nie, JianXin
2014-06-01
In this paper, we introduce the complex modulus to express the viscoelasticity of a medium. According to the correspondence principle, the Biot-Squirt (BISQ) equations in the steady-state case are presented for the space-frequency domain described by solid displacements and fluid pressure in a homogeneous viscoelastic medium. The effective bulk modulus of a multiphase flow is computed by the Voigt formula, and the characteristic squirt-flow length is revised for the gas-included case. We then build a viscoelastic BISQ model containing a multiphase flow. Through using this model, wave dispersion and attenuation are studied in a medium with low porosity and low permeability. Furthermore, this model is applied to observed interwell seismic data. Analysis of these data reveals that the viscoelastic parameter tan δ is not a constant. Thus, we present a linear frequency-dependent function in the interwell seismic frequency range to express tan δ. This improves the fit between the observed data and theoretical results.
NASA Astrophysics Data System (ADS)
Zou, Qihui; Hu, Qianhuan; Guo, Jie; Duan, Xi; Tong, Shihong
2015-10-01
Based on the Fresnel-Kirchhoff diffraction integral and Fourier transform, the propagation equation and its Fourier spectrum for ultra-short chirped pulsed Gaussian beams diffracted by Gaussian aperture are derived in dispersive medium, and the frequency-domain analytical electric field are presented. The effects of relative aperture, transmission distance and chirp parameter on the axial spectral properties are illustrated with numerical calculation results, and the variations of off-axis power spectrum with relative aperture, transmission distance and off-axis radius are given. It is found that the axial power spectrum of ultra-short chirped pulsed Gaussian increases with increasing relative aperture, the axial spectral blue-shift increases and approaches an asymptotic value associated with chirp parameter and propagation distance. The axial spectra of ultra-short chirped pulsed Gaussian become broadened with increasing the absolute value of the chirp parameter. With increasing off-axis radius, the off-axis power spectrum reduce rapidly, and the distribution of spectra shifts to the left. The off-axis spectral redshift increases with increasing off-axis radius.
Temporal dynamics of incoherent waves in noninstantaneous response nonlinear Kerr media.
Kibler, B; Michel, C; Garnier, J; Picozzi, A
2012-07-01
We consider the temporal evolution of an incoherent optical wave that propagates in a noninstantaneous response nonlinear medium, such as single mode optical fibers. In contrast with the expected Raman-like spectral redshift due to a delayed nonlinear response, we show that a highly noninstantaneous response leads to a genuine modulational instability of the incoherent optical wave. We derive a Vlasov-like kinetic equation that provides a detailed description of this process of incoherent modulational instability in the temporal domain. PMID:22743425
Emergence of linear wave segments and predictable traits in saturated nonlinear media
NASA Astrophysics Data System (ADS)
Delre, Eugenio; D'Ercole, Angelo; Agranat, Aharon J.
2003-02-01
We find the key behind the existence traits of asymptotic saturated nonlinear optical solitons in the emergence of linear wave segments. These traits, produced by the progressive relegation of nonlinear dynamics to wave tails, allow a direct and versatile analytical prediction of self-trapping existence conditions and simple soliton scaling laws, which we confirm experimentally in saturated-Kerr self-trapping observed in photorefractives. This approach provides the means to correctly evaluate beam tails in the saturated regime, which is instrumental in the prediction of soliton interaction forces.
Emergence of linear wave segments and predictable traits in saturated nonlinear media.
DelRe, Eugenio; D'Ercole, Angelo; Agranat, Aharon J
2003-02-15
We find the key behind the existence traits of asymptotic saturated nonlinear optical solitons in the emergence of linear wave segments. These traits, produced by the progressive relegation of nonlinear dynamics to wave tails, allow a direct and versatile analytical prediction of self-trapping existence conditions and simple soliton scaling laws, which we confirm experimentally in saturated-Kerr self-trapping observed in photorefractives. This approach provides the means to correctly evaluate beam tails in the saturated regime, which is instrumental in the prediction of soliton interaction forces. PMID:12653365
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.
Propagation of an Airy-Gaussian vortex beam in linear and nonlinear media
NASA Astrophysics Data System (ADS)
Chen, Chidao; Peng, Xi; Chen, Bo; Peng, Yulian; Zhou, Meiling; Yang, Xiangbo; Deng, Dongmei
2016-05-01
We investigate the propagation of an Airy-Gaussian vortex (AiGV) beam in free space and Kerr media. It is interesting to see that the beam will perform self-healing and main lobe focusing both in free space and Kerr media when the vortex locates at the center of the plane. By controlling the number of the topological charge, the beam distribution factor χ 0 and the position of the vortex, we can control the intensity distribution of the AiGV beam in the out plane both in free space and Kerr media. It is found that when the vortex is close to the center of the plane, it has a strong effect on the intensity distribution of the beam. When the beam propagates in the number of the topological charge, the partial collapse will take place even with low initial input power. We find that the main lobe focusing contributes to this partial collapse.
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.
Cinar, Mehmet; Coruh, Ali; Karabacak, Mehmet
2014-03-25
In the present work, a combined experimental and quantum chemical study on ground state equilibrium structure, spectroscopic and nonlinear optical properties of selected disperse azo dye molecules are reported. The vibrational transitions were identified based on the recorded FT-IR spectra in the range of 4000-400 cm(-1) for solid state, simulated IR spectra and total energy distribution (TED) of vibrational modes. The chemical shifts were determined from the results of observed (1)H and (13)C NMR spectra in chloroform and dimethylsulfoxide solution. The DFT/gauge-invariant atomic orbital (GIAO) methodology was applied to predict the magnetic properties. Electronic properties were carried out by UV-Vis spectroscopy and TD-DFT/CIS approach. The nonlinear optical (NLO) features were addressed theoretically. A detailed description of spectroscopic and NLO behaviors of studied disperse azo dyes was reported with the help of comparison of experimental measurements and theoretical calculations. PMID:24345608
NASA Astrophysics Data System (ADS)
Cinar, Mehmet; Coruh, Ali; Karabacak, Mehmet
2014-03-01
In the present work, a combined experimental and quantum chemical study on ground state equilibrium structure, spectroscopic and nonlinear optical properties of selected disperse azo dye molecules are reported. The vibrational transitions were identified based on the recorded FT-IR spectra in the range of 4000-400 cm-1 for solid state, simulated IR spectra and total energy distribution (TED) of vibrational modes. The chemical shifts were determined from the results of observed 1H and 13C NMR spectra in chloroform and dimethylsulfoxide solution. The DFT/gauge-invariant atomic orbital (GIAO) methodology was applied to predict the magnetic properties. Electronic properties were carried out by UV-Vis spectroscopy and TD-DFT/CIS approach. The nonlinear optical (NLO) features were addressed theoretically. A detailed description of spectroscopic and NLO behaviors of studied disperse azo dyes was reported with the help of comparison of experimental measurements and theoretical calculations.
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.
Smirnov, Sergey; Kobtsev, Sergey; Kukarin, Sergey; Ivanenko, Aleksey
2012-11-19
We show experimentally and numerically new transient lasing regime between stable single-pulse generation and noise-like generation. We characterize qualitatively all three regimes of single pulse generation per round-trip of all-normal-dispersion fiber lasers mode-locked due to effect of nonlinear polarization evolution. We study spectral and temporal features of pulses produced in all three regimes as well as compressibility of such pulses. Simple criteria are proposed to identify lasing regime in experiment. PMID:23187603
Laser beam propagation through bulk nonlinear media: Numerical simulation and experiment
NASA Astrophysics Data System (ADS)
Kovsh, Dmitriy I.
This dissertation describes our efforts in modeling the propagation of high intensity laser pulses through optical systems consisting of one or multiple nonlinear elements. These nonlinear elements can be up to 103 times thicker than the depth of focus of the laser beam, so that the beam size changes drastically within the medium. The set of computer codes developed are organized in a software package (NLO_BPM). The ultrafast nonlinearities of the bound-electronic n2 and two-photon absorption as well as time dependent excited-state, free-carrier and thermal nonlinearities are included in the codes for modeling propagation of picosecond to nanosecond pulses and pulse trains. Various cylindrically symmetric spatial distributions of the input beam are modeled. We use the cylindrical symmetry typical of laser outputs to reduce the CPU and memory requirements making modeling a real- time task on PC's. The hydrodynamic equations describing the rarefaction of the medium due to heating and electrostriction are solved in the transient regime to determine refractive index changes on a nanosecond time scale. This effect can be simplified in some cases by an approximation that assumes an instantaneous expansion. We also find that the index change obtained from the photo-acoustic equation overshoots its steady-state value once the ratio between the pulse width and the acoustic transit time is greater than unity. We numerically study the sensitivity of the closed- aperture Z-scan experiment to nonlinear refraction for various input beam profiles. If the beam has a ring structure with a minimum (or zero) on axis in the far field, the sensitivity of Z-scan measurements can be increased by up to one order of magnitude. The linear propagation module integrated with the nonlinear beam propagation codes allows the simulation of typical experiments such as Z-scan and optical limiting experiments. We have used these codes to model the performance of optical limiters. We study two of the
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
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.
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.
NASA Astrophysics Data System (ADS)
Hong, Woo-Pyo; Jung, Young-Dae
2013-10-01
We find the existence conditions for stationary dipole and tripole surface solitons formed at the interface of a nonlocal nonlinear medium and a lattice with linearly modulated frequency. We investigate how the degree of nonlocality, the depth, and the modulation frequency of the optical lattice field affect on the existence of the surface solitons and their dynamics. The relationship between the power and the model parameters is identified. The stability of the surface dipole and tripole solitons is numerically investigated.
Mahmood, Mohammed Shuker
2007-12-26
Numerical scheme based on the modified method of characteristics with adjusted advection combined with a relaxation scheme for solving strongly nonlinear degenerate convection diffusion problem which arises in the contaminant transport in porous media with dual porosity. A series of computational experiments and comparisons with other solutions are carried out to illustrate the rate of convergence, the behavior and the capability of the scheme.
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.
Kwon, Dongwook; Park, Jonghoon; Park, Jaehong; Choi, Seo Yeon; Yoon, Tae Hyun
2014-01-01
The extrinsic physicochemical properties of nanoparticles (NPs), such as hydrodynamic size, surface charge, surface functional group, and colloidal stabilities, in toxicity testing media are known to have a significant influence on in vitro toxicity assessments. Therefore, interpretation of nanotoxicity test results should be based on reliable characterization of the NPs' extrinsic properties in actual toxicity testing media. Here, we present a set of physicochemical characterization results for commercially available ZnO NPs, including core diameter, hydrodynamic diameter, surface charges, and colloidal stabilities, in two in vitro toxicity testing media (Roswell Park Memorial Institute [RPMI] and Dulbecco's Modified Eagle's Medium [DMEM]), as well as simple cell viability assay results for selected ZnO NPs. Four commercially available and manufactured ZnO NPs, with different core sizes, were used in this study, and their surface charge was modified with five different surface coating materials (sodium citrate, tris(2-aminoethyl)amine, poly(acrylic acid), poly(allylamine hydrochloride), and poly-L-lysine hydrochloride). The results showed that ZnO NPs were better dispersed in cell culture media via surface modification with positively or negatively charged molecules. Moreover, in the presence of fetal bovine serum (FBS) in RPMI and DMEM media, ZnO NPs were found even better dispersed for a longer period (at least 48 hours). For the HeLa cells exposed to ZnO NPs in DMEM media without FBS, surface charge-dependent cytotoxicity trends were observed, while these trends were not observed for those cells cultured in FBS-containing media. This confirmed the important roles of surface-modifying compounds and of surface charge on the resultant cytotoxicities of NPs. PMID:25565826
Coexistence of synchrony and incoherence in oscillatory media under nonlinear global coupling
NASA Astrophysics Data System (ADS)
Schmidt, Lennart; Schönleber, Konrad; Krischer, Katharina; García-Morales, Vladimir
2014-03-01
We report a novel mechanism for the formation of chimera states, a peculiar spatiotemporal pattern with coexisting synchronized and incoherent domains found in ensembles of identical oscillators. Considering Stuart-Landau oscillators, we demonstrate that a nonlinear global coupling can induce this symmetry breaking. We find chimera states also in a spatially extended system, a modified complex Ginzburg-Landau equation. This theoretical prediction is validated with an oscillatory electrochemical system, the electro-oxidation of silicon, where the spontaneous formation of chimeras is observed without any external feedback control.
Coexistence of synchrony and incoherence in oscillatory media under nonlinear global coupling
Schmidt, Lennart; García-Morales, Vladimir; Schönleber, Konrad; Krischer, Katharina
2014-03-15
We report a novel mechanism for the formation of chimera states, a peculiar spatiotemporal pattern with coexisting synchronized and incoherent domains found in ensembles of identical oscillators. Considering Stuart-Landau oscillators, we demonstrate that a nonlinear global coupling can induce this symmetry breaking. We find chimera states also in a spatially extended system, a modified complex Ginzburg-Landau equation. This theoretical prediction is validated with an oscillatory electrochemical system, the electro-oxidation of silicon, where the spontaneous formation of chimeras is observed without any external feedback control.
NASA Technical Reports Server (NTRS)
Smith, David D.
2002-01-01
This talk will review the linear and nonlinear optical properties of metal nanoparticles and dielectric microparticles, with an emphasis on local field effects, and whispering gallery modes (WGMs), as well as the conjunction of these two effects for enhanced Raman. In particular, enhanced optical properties that result from electromagnetic coupling effects will be discussed in the context of Mie scattering from concentric spheres and bispheres. Predictions of mode splitting and photonic bandgaps in micro-spheres will be presented and will be shown to be analogous to effects that occur in coupled resonator optical waveguides (CROW). Slow and fast light in SCISSOR / CROW configurations will also be discussed.
Scaling Laws for the Response of Nonlinear Elastic Media with Implications for Cell Mechanics
NASA Astrophysics Data System (ADS)
Shokef, Yair; Safran, Samuel A.
2012-04-01
We show how strain stiffening affects the elastic response to internal forces, caused either by material defects and inhomogeneities or by active forces that molecular motors generate in living cells. For a spherical force dipole in a material with a strongly nonlinear strain energy density, strains change sign with distance, indicating that, even around a contractile inclusion or molecular motor, there is radial compression; it is only at a long distance that one recovers the linear response in which the medium is radially stretched. Scaling laws with irrational exponents relate the far-field renormalized strain to the near-field strain applied by the inclusion or active force.
NASA Astrophysics Data System (ADS)
Canabarro, Askery; Santos, B.; de Lima Bernardo, B.; Moura, André L.; Soares, W. C.; de Lima, E.; Gléria, Iram; Lyra, M. L.
2016-02-01
Taking into account relaxing Kerr nonlinearity and walk-off effects, the conditions and gain spectra of cross-phase modulation-induced modulational instability (XPM-MI) of two incoherently copropagating optical waves of different frequencies and same polarization are investigated. We devote particular attention to the mixed case in which one pulse propagates under the normal group-velocity dispersion (GVD) regime, while the second one is under an anomalous GVD regime. We unveil that in the limit of an instantaneuous nonlinear response, the typical frequency with maximum gain converges to a finite value in the mixed GDV regime, while it continuously grows with the group-velocity mismatch in the normal GVD regime. As a result, the maximum gain typically decreases with the group-velocity mismatch in the mixed regime, contrasting with the opposite trend in the normal GVD regime. Further, we show that besides the mode having maximum gain at a frequency decaying with 1 /τ1 /3 in the slow response limit, there is a second mode having maximum gain with a distinct scaling behavior Ωmax∝1 /τ in the absence of group-velocity mismatch. The associated maximum gains scale, respectively, as 1 /τ2 /3 and 1 /τ , thus signaling the corresponding quadratic and linear dispersion relation of these modes in the low-frequency limit. A detailed analysis of the influence of the nonlinear response time and group-velocity dispersion on the MI gain spectrum is also provided.
Creation of vortices by torque in multidimensional media with inhomogeneous defocusing nonlinearity
Driben, Rodislav; Meier, Torsten; Malomed, Boris A.
2015-01-01
Recently, a new class of nonlinear systems was introduced, in which the self-trapping of fundamental and vortical localized modes in space of dimension D is supported by cubic self-repulsion with a strength growing as a function of the distance from the center, r, at any rate faster that rD. These systems support robust 2D and 3D modes which either do not exist or are unstable in other nonlinear systems. Here we demonstrate a possibility to create solitary vortices in this setting by applying a phase-imprinting torque to the ground state. Initially, a strong torque completely destroys the ground state. However, contrary to usual systems, where the destruction is irreversible, the present ones demonstrate a rapid restabilization and the creation of one or several shifted vortices orbiting the center. For the sake of comparison, we show analytically that, in the linear system with a 3D trapping potential, the action of a torque on the ground state is inefficient and creates only even-vorticity states with a small probability. PMID:25800140
NASA Astrophysics Data System (ADS)
Johansson, Magnus; Prilepsky, Jaroslaw E.; Derevyanko, Stanislav A.
2014-04-01
We investigate the mobility of nonlinear localized modes in a generalized discrete Ginzburg-Landau-type model, describing a one-dimensional waveguide array in an active Kerr medium with intrinsic, saturable gain and damping. It is shown that exponentially localized, traveling discrete dissipative breather-solitons may exist as stable attractors supported only by intrinsic properties of the medium, i.e., in the absence of any external field or symmetry-breaking perturbations. Through an interplay by the gain and damping effects, the moving soliton may overcome the Peierls-Nabarro barrier, present in the corresponding conservative system, by self-induced time-periodic oscillations of its power (norm) and energy (Hamiltonian), yielding exponential decays to zero with different rates in the forward and backward directions. In certain parameter windows, bistability appears between fast modes with small oscillations and slower, large-oscillation modes. The velocities and the oscillation periods are typically related by lattice commensurability and exhibit period-doubling bifurcations to chaotically "walking" modes under parameter variations. If the model is augmented by intersite Kerr nonlinearity, thereby reducing the Peierls-Nabarro barrier of the conservative system, the existence regime for moving solitons increases considerably, and a richer scenario appears including Hopf bifurcations to incommensurately moving solutions and phase-locking intervals. Stable moving breathers also survive in the presence of weak disorder.
Modeling the injection of non-Newtonian shear-thinning dispersions of iron particles in porous media
NASA Astrophysics Data System (ADS)
sethi, R.; Tosco, T.; Gastone, F.
2013-12-01
In the context of groundwater remediation, an increasing interest has been devoted to the use of nanoscale and microscale zero-valent iron particles (NZVI and MZVI, respectively). MZVI and NZVI are not stable when dispersed in water, due to the occurrence of fast aggregation and sedimentation. Consequently, the use of shear thinning solutions of green biopolymers has been recently studied as kinetic stabilizers and viscous carrier for the delivery of MZVI and NZVI in the subsurface. Shear thinning fluids exhibit high viscosity in static conditions, improving the colloidal stability, and lower viscosity at high flow rates enabling the injection at limited pressures. In this work, co-funded by European Union project AQUAREHAB (FP7 - Grant Agreement Nr. 226565), a modeling approach is described, and implemented in E-MNM1D software (www.polito.it/groundwater/software), to simulate the transport in porous media of nanoscale iron slurries. Colloid transport mechanisms are controlled by particle-collector and particle-particle interactions, usually modeled using a non equilibrium kinetic model accounting for deposition and release processes. The key aspects included in the E-MNM1D are clogging phenomena (i.e. reduction of porosity and permeability due to particles deposition), and the rheological properties of the carrier fluid (in this project, guar gum solution). The influence of colloid transport on porosity, permeability, and fluid viscosity is explicitly lumped into the model and the shear-thinning nature of the iron slurries is described by a modified Darcy law generalized for non Newtonian fluids. Since during the injection in wells the velocity field is not constant over the distance, E-MNM1D was modified in order to account for variable colloidal transport coefficients, thus allowing the estimation of the radius of influence during a full scale intervention.
Linear and nonlinear optical precursors in inhomogeneously broadened two-level media
NASA Astrophysics Data System (ADS)
Marskar, Robert; Österberg, Ulf L.
2012-12-01
By solving the two-level Maxwell-Bloch equations for resonant pulses numerically, we observe precursors in a regime where the area theorem is fulfilled. The precursors are 0π pulses traveling at a velocity close to the speed of light, and the main signal is a self-induced transparency (SIT) 2π soliton traveling at a much lower velocity. The manifestation of the precursors is strongest when the input pulse duration is on the same order as the inhomogeneous lifetime and the input area is close to π. Depending on the relationship between the input pulse duration and the inhomogeneous lifetime, the precursors can interact linearly or nonlinearly with the material. Experimental confirmation of these results should offer a direct and reasonably straightforward way of measuring optical precursors.
Nonlinear optical spectroscopy and microscopy of model random and biological media
NASA Astrophysics Data System (ADS)
Guo, Yici
Nonlinear optical (NLO) spectroscopy and microscopy applied to biomedical science are emerging as new and rapidly growing areas which offer important insight into basic phenomena. Ultrafast NLO processes provide temporal, spectral and spatial sensitivities complementary or superior to those achieved through conventional linear optical approaches. The goal of this thesis is to explore the potential of two fundamental NLO processes to produce noninvasive histological maps of biological tissues. Within the goal of the thesis, steady state intensity, polarization and angular measurements of second- and third-harmonic generations (SHG, THG) have been performed on model random scattering and animal tissue samples. The nonlinear optical effects have been evaluated using models. Conversion efficiencies of SHG and THG from animal tissue interfaces have been determined, ranging from 10-7 to 10-10. The changes in the multiharmonic signals were found to depend on both local and overall histological structures of biological samples. The spectral signatures of two photon excitation induced fluorescence from intrinsic fluorophores have been acquired and used to characterize the physical state and types of tissues. Two dimensional scanning SHG and TPF tomographic images have been obtained from in vitro animal tissues, normal and diseased human breast tissues, and resolved subsurface layers and histo-chemical distributions. By combining consecutive 2D maps, a 3D image can be produced. The structure and morphology dependence of the SH signal has been utilized to image and evaluate subsurface tumor progression depth. Second harmonic microscopy in model random and biological cells has been studied using a CCD camera to obtain direct images from subcellular structures. Finally, near infrared (NIR) NLO spectroscopy and microscopy based on SHG and TPF have demonstrated high spatial resolution, deeper penetration depth, low level photo-damaging and enhanced morphological sensitivity for
Nonlinear propagation and control of acoustic waves in phononic superlattices
NASA Astrophysics Data System (ADS)
Jiménez, Noé; Mehrem, Ahmed; Picó, Rubén; García-Raffi, Lluís M.; Sánchez-Morcillo, Víctor J.
2016-05-01
The propagation of intense acoustic waves in a one-dimensional phononic crystal is studied. The medium consists in a structured fluid, formed by a periodic array of fluid layers with alternating linear acoustic properties and quadratic nonlinearity coefficient. The spacing between layers is of the order of the wavelength, therefore Bragg effects such as band gaps appear. We show that the interplay between strong dispersion and nonlinearity leads to new scenarios of wave propagation. The classical waveform distortion process typical of intense acoustic waves in homogeneous media can be strongly altered when nonlinearly generated harmonics lie inside or close to band gaps. This allows the possibility of engineer a medium in order to get a particular waveform. Examples of this include the design of media with effective (e.g., cubic) nonlinearities, or extremely linear media (where distortion can be canceled). The presented ideas open a way towards the control of acoustic wave propagation in nonlinear regime. xml:lang="fr"
Nonlinear spatial focusing in random layered media by spectral pulse shaping
NASA Astrophysics Data System (ADS)
Han, Alex C.; Milner, Valery
2016-02-01
We demonstrate numerically a method of focusing two-photon fields inside one-dimensional random media. The approach is based on coherent control of backscattering achieved by adaptive spectral pulse shaping. The spectral phases of a femtosecond laser pulse are adjusted for the constructive interference of its backward-traveling components, resulting in an enhanced reflection from within the random system. A delayed forward-propagating second pulse overlaps with the controlled reflection, increasing the interpulse multiphoton field at a location determined by the delay between the two pulses. The technique is shown to be robust against the variations of the disorder and to work with realistic pulse-shaping parameters, hence enabling applications in controlling random lasing and multiphoton imaging in scattering materials.
Tu, Haohua; Liu, Yuan; Lægsgaard, Jesper; Sharma, Utkarsh; Siegel, Martin; Kopf, Daniel; Boppart, Stephen A
2010-12-20
We quantitatively predict the observed continuum-like spectral broadening in a 90-mm weakly birefringent all-normal dispersion-flattened photonic crystal fiber pumped by 1041-nm 229-fs 76-MHz pulses from a solid-state Yb:KYW laser. The well-characterized continuum pulses span a bandwidth of up to 300 nm around the laser wavelength, allowing high spectral power density pulse shaping useful for various coherent control applications. We also identify the nonlinear polarization effect that limits the bandwidth of these continuum pulses, and therefore report the path toward a series of attractive alternative broadband coherent optical sources. PMID:21197060
Tu, Haohua; Liu, Yuan; Lægsgaard, Jesper; Sharma, Utkarsh; Siegel, Martin; Kopf, Daniel; Boppart, Stephen A.
2010-01-01
We quantitatively predict the observed continuum-like spectral broadening in a 90-mm weakly birefringent all-normal dispersion-flattened photonic crystal fiber pumped by 1041-nm 229-fs 76-MHz pulses from a solid-state Yb:KYW laser. The well-characterized continuum pulses span a bandwidth of up to 300 nm around the laser wavelength, allowing high spectral power density pulse shaping useful for various coherent control applications. We also identify the nonlinear polarization effect that limits the bandwidth of these continuum pulses, and therefore report the path toward a series of attractive alternative broadband coherent optical sources. PMID:21197060
Numerical Modeling of the Nonlinear Evolution of Permeability in Naturally Fractured Porous Media
NASA Astrophysics Data System (ADS)
Castelletto, N.; Garipov, T.; Tchelepi, H.
2014-12-01
The hydromechanical coupling between fluid flow and geomechanical response plays a key role whenever significant volumes of fluid are injected into the subsurface. An emerging engineering application of this class of problem is represented by CO2 sequestration in deep geological formations. We present a modeling approach to tackle coupled fluid flow and geomechanics in naturally fractured reservoir. The system of partial differential equations is solved using a combination of finite-volume and finite-element discretization schemes, respectively, for the flow and mechanics problems. The model accounts for flow along fractures and can predict fracture reactivation by accurately simulating normal and shear stresses acting on the fracture surfaces. The focus is on the effects induced by changes in the stress field in fracture permeability. The fracture permeability evolution is described by a constitutive model that depends on the tangential displacement that develops between the two contact surfaces defining a fracture, and the effective normal traction, giving rise to a highly non-linear problem. The proposed model is verified against both simple single-fracture test cases and more complex fracture network configurations.
Antiplane wave scattering from a cylindrical cavity in pre-stressed nonlinear elastic media
Shearer, Tom; Parnell, William J.; Abrahams, I. David
2015-01-01
The effect of a longitudinal stretch and a pressure-induced inhomogeneous radial deformation on the scattering of antiplane elastic waves from a cylindrical cavity is determined. Three popular nonlinear strain energy functions are considered: the neo-Hookean, the Mooney–Rivlin and a two-term Arruda–Boyce model. A new method is developed to analyse and solve the governing wave equations. It exploits their properties to determine an asymptotic solution in the far-field, which is then used to derive a boundary condition to numerically evaluate the equations local to the cavity. This method could be applied to any linear ordinary differential equation whose inhomogeneous coefficients tend to a constant as its independent variable tends to infinity. The effect of the pre-stress is evaluated by considering the scattering cross section. A longitudinal stretch is found to decrease the scattered power emanating from the cavity, whereas a compression increases it. The effect of the pressure difference depends on the strain energy function employed. For a Mooney–Rivlin material, a cavity inflation increases the scattered power and a deflation decreases it; for a neo-Hookean material, the scattering cross section is unaffected by the radial deformation; and for a two-term Arruda–Boyce material, both inflation and deflation are found to decrease the scattered power. PMID:26543398
NASA Astrophysics Data System (ADS)
Zhang, Y.; Tournat, V.; Abraham, O.; Durand, O.; Letourneur, S.; Le Duff, A.; Lascoup, B.
2013-02-01
An ultrasonic method providing for an efficient global detection of defects in complex media (multiple scattering or reverberating media) is reported herein; this method is based on the nonlinear acoustic mixing of coda waves (stemming from multiple scattering) with lower frequency-swept pump waves. Such a nonlinear mixing step is made possible by the presence of nonlinear scatterers, such as cracks and delamination, yet remains absent when the waves are scattered only by linear scatterers, as is the case in a complex but defect-free medium. A global inspection is achieved thanks to the use of wide-band coda and pump signals, which ensure the excitation of many resonances along with a homogeneous acoustic energy distribution in the medium. We introduce the existing sensitivity tools developed for Coda Wave Interferometry in extracting the pump amplitude-dependent parameters of the coda waves associated with effective nonlinear parameters of the medium. By comparing results at two damage levels, these effective nonlinear parameters are shown to be correlated with crack presence in glass samples. The mechanisms potentially responsible for the observed amplitude dependence on the tested elastic parameters and waveform modification are discussed.
NASA Technical Reports Server (NTRS)
Huang, N. E.; Tung, C.-C.
1977-01-01
The influence of the directional distribution of wave energy on the dispersion relation is calculated numerically using various directional wave spectrum models. The results indicate that the dispersion relation varies both as a function of the directional energy distribution and the direction of propagation of the wave component under consideration. Furthermore, both the mean deviation and the random scatter from the linear approximation increase as the energy spreading decreases. Limited observational data are compared with the theoretical results. The agreement is favorable.
NASA Astrophysics Data System (ADS)
Vikhansky, Alexander; Ginzburg, Irina
2014-02-01
This article describes a generalization of the method of moments, called extended method of moments (EMM), for dispersion in periodic structures composed of impermeable or permeable porous inclusions. Prescribing pre-computed steady state velocity field in a single periodic cell, the EMM sequentially solves specific linear stationary advection-diffusion equations and restores any-order moments of the resident time distribution or the averaged concentration distribution. Like the pioneering Brenner's method, the EMM recovers mean seepage velocity and Taylor dispersion coefficient as the first two terms of the perturbative expansion. We consider two types of dispersion: spatial dispersion, i.e., spread of initially narrow pulse of concentration, and temporal dispersion, where different portions of the solute have different residence times inside the system. While the first (mean velocity) and the second (Taylor dispersion coefficient) moments coincide for both problems, the higher moments are different. Our perturbative approach allows to link them through simple analytical expressions. Although the relative importance of the higher moments decays downstream, they manifest the non-Gaussian behaviour of the breakthrough curves, especially if the solute can diffuse into less porous phase. The EMM quantifies two principal effects of bi-modality, as the appearance of sharp peaks and elongated tails of the distributions. In addition, the moments can be used for the numerical reconstruction of the corresponding distribution, avoiding time-consuming computations of solute transition through heterogeneous media. As illustration, solutions for Taylor dispersion, skewness, and kurtosis in Poiseuille flow and open/impermeable stratified systems, both in rectangular and cylindrical channels, power-law duct flows, shallow channels, and Darcy flow in parallel porous layers are obtained in closed analytical form for the entire range of Péclet numbers. The high-order moments and
Hartmann, Nanna B; Jensen, Keld Alstrup; Baun, Anders; Rasmussen, Kirsten; Rauscher, Hubert; Tantra, Ratna; Cupi, Denisa; Gilliland, Douglas; Pianella, Francesca; Riego Sintes, Juan M
2015-01-01
Selecting appropriate ways of bringing engineered nanoparticles (ENP) into aqueous dispersion is a main obstacle for testing, and thus for understanding and evaluating, their potential adverse effects to the environment and human health. Using different methods to prepare (stock) dispersions of the same ENP may be a source of variation in the toxicity measured. Harmonization and standardization of dispersion methods applied in mammalian and ecotoxicity testing are needed to ensure a comparable data quality and to minimize test artifacts produced by modifications of ENP during the dispersion preparation process. Such harmonization and standardization will also enhance comparability among tests, labs, and studies on different types of ENP. The scope of this review was to critically discuss the essential parameters in dispersion protocols for ENP. The parameters are identified from individual scientific studies and from consensus reached in larger scale research projects and international organizations. A step-wise approach is proposed to develop tailored dispersion protocols for ecotoxicological and mammalian toxicological testing of ENP. The recommendations of this analysis may serve as a guide to researchers, companies, and regulators when selecting, developing, and evaluating the appropriateness of dispersion methods applied in mammalian and ecotoxicity testing. However, additional experimentation is needed to further document the protocol parameters and investigate to what extent different stock dispersion methods affect ecotoxicological and mammalian toxicological responses of ENP. PMID:26397955
NASA Astrophysics Data System (ADS)
Murai, Yoshio
2007-01-01
We compute the synthetic seismograms of multiply scattered SH waves in 2-D elastic media with densely distributed parallel cracks. We assume randomly distributed cracks in a rectangular-bounded region, which simulate a cracked zone. The crack surfaces are assumed to be stress-free. When the incident wavelength is longer than the crack size, the delay in the arrival of the primary wave is observed at stations beyond the cracked zone and the amplitude of the primary wave is amplified in the cracked zone in the synthetic seismograms. This is because the cracked zone behaves as a low velocity and soft material to the incident long-wavelength wave due to the crack distribution. When the half-wavelength of the incident wave is shorter than the crack length, the scattered waves are clearly observed in the synthetic seismograms and the amplitude of the primary wave is largely attenuated beyond the cracked zone. The calculated attenuation coefficient Q-1 of the primary wave is directly proportional to the crack density in the range of νa2 <= 0.1, where ν and a are the number density and half the length of cracks, respectively. This is consistent with that obtained by a stochastic analysis based on Foldy's approximation. A periodic distribution of cracks in a zone is considered as an utterly different model in order to investigate the effect of spatial distributions on the attenuation and dispersion of seismic waves. When cracks are distributed densely, the values of Q-1 for the periodic crack distribution appear to differ from those for the random distribution of cracks in the low wavenumber range. This suggests that the effect of multiple interactions among densely distributed cracks depends on not only the density but also the spatial distribution of cracks at low wavenumbers. The calculated phase velocity of the primary wave is consistent with that from the stochastic analysis in the range of νa2 <= 0.1 and does not depend on the spatial distribution of cracks. This
Observation of Dispersive Shock Waves, Solitons, and Their Interactions in Viscous Fluid Conduits
NASA Astrophysics Data System (ADS)
Maiden, Michelle D.; Lowman, Nicholas K.; Anderson, Dalton V.; Schubert, Marika E.; Hoefer, Mark A.
2016-04-01
Dispersive shock waves and solitons are fundamental nonlinear excitations in dispersive media, but dispersive shock wave studies to date have been severely constrained. Here, we report on a novel dispersive hydrodynamic test bed: the effectively frictionless dynamics of interfacial waves between two high viscosity contrast, miscible, low Reynolds number Stokes fluids. This scenario is realized by injecting from below a lighter, viscous fluid into a column filled with high viscosity fluid. The injected fluid forms a deformable pipe whose diameter is proportional to the injection rate, enabling precise control over the generation of symmetric interfacial waves. Buoyancy drives nonlinear interfacial self-steepening, while normal stresses give rise to the dispersion of interfacial waves. Extremely slow mass diffusion and mass conservation imply that the interfacial waves are effectively dissipationless. This enables high fidelity observations of large amplitude dispersive shock waves in this spatially extended system, found to agree quantitatively with a nonlinear wave averaging theory. Furthermore, several highly coherent phenomena are investigated including dispersive shock wave backflow, the refraction or absorption of solitons by dispersive shock waves, and the multiphase merging of two dispersive shock waves. The complex, coherent, nonlinear mixing of dispersive shock waves and solitons observed here are universal features of dissipationless, dispersive hydrodynamic flows.
Observation of Dispersive Shock Waves, Solitons, and Their Interactions in Viscous Fluid Conduits.
Maiden, Michelle D; Lowman, Nicholas K; Anderson, Dalton V; Schubert, Marika E; Hoefer, Mark A
2016-04-29
Dispersive shock waves and solitons are fundamental nonlinear excitations in dispersive media, but dispersive shock wave studies to date have been severely constrained. Here, we report on a novel dispersive hydrodynamic test bed: the effectively frictionless dynamics of interfacial waves between two high viscosity contrast, miscible, low Reynolds number Stokes fluids. This scenario is realized by injecting from below a lighter, viscous fluid into a column filled with high viscosity fluid. The injected fluid forms a deformable pipe whose diameter is proportional to the injection rate, enabling precise control over the generation of symmetric interfacial waves. Buoyancy drives nonlinear interfacial self-steepening, while normal stresses give rise to the dispersion of interfacial waves. Extremely slow mass diffusion and mass conservation imply that the interfacial waves are effectively dissipationless. This enables high fidelity observations of large amplitude dispersive shock waves in this spatially extended system, found to agree quantitatively with a nonlinear wave averaging theory. Furthermore, several highly coherent phenomena are investigated including dispersive shock wave backflow, the refraction or absorption of solitons by dispersive shock waves, and the multiphase merging of two dispersive shock waves. The complex, coherent, nonlinear mixing of dispersive shock waves and solitons observed here are universal features of dissipationless, dispersive hydrodynamic flows. PMID:27176524
NASA Astrophysics Data System (ADS)
Kamiya, Hidehiro; Iijima, Motoyuki
2010-08-01
Inorganic nanoparticles are indispensable for science and technology as materials, pigments and cosmetics products. Improving the dispersion stability of nanoparticles in various liquids is essential for those applications. In this review, we discuss why it is difficult to control the stability of nanoparticles in liquids. We also overview the role of surface interaction between nanoparticles in their dispersion and characterization, e.g. by colloid probe atomic force microscopy (CP-AFM). Two types of surface modification concepts, post-synthesis and in situ modification, were investigated in many previous studies. Here, we focus on post-synthesis modification using adsorption of various kinds of polymer dispersants and surfactants on the particle surface, as well as surface chemical reactions of silane coupling agents. We discuss CP-AFM as a technique to analyze the surface interaction between nanoparticles and the effect of surface modification on the nanoparticle dispersion in liquids.
NASA Astrophysics Data System (ADS)
Chernov, A.; Korytko, A.; Kostenko, I.; Pelinovsky, E.; Yalciner, A.; Zaytsev, A.
2009-04-01
1960 Chilean centered Pacific Ocean tsunami and 2004 North West Sumatra centered Indian Ocean Tsunami are two important tsunamis of long distance propagation and impacts of tsunamis. Recent international studies on the propagation and dispersion effects of Indian Ocean tsunami showed that dispersion is one of the important parameters of numerical solutions of tsunami propagation. May 23, 1960 earthquake with the approximate magnitude 9.0 caused approximately 750km rupture and generated tsunami at offshore Chilean Coast. Tsunami has reached 15-20m height at Chilean coast. The effects of this tsunami were observed not only near Chilean Coast but also in Japan after 22 hours propagation. Chilean tsunami was also felt in Kuril Islands and tsunami height reached to 4.7m near Severo-Kurilsk (Paramushir Island). Houses near the coast, warehouses and mooring facilities have been flooded. In Malokurilsk (Shikotan Island), the height of tsunami reached 4m, flooded the moorings facilities and some buildings, and damaged the bridge on a land. Many vessels became stranded because of broken anchors. Tsunami was also observed on all islands of the Kuril Ridge. The maximal height of rising of water was 4m at Shikotan Islands and 2.2m at on Kunashir Island, 2.5m at Iturup Island, and 1.3-1.5m at Matua Island. Tsunami entered the Sea of Okhotsk. In Magadan the height of rising of water was 2.2 m. the weak tsunami also was observed near Sakhalin Island. The dispersion effect of 1960 Chilean tsunami and its long distance effects on Kuril Ridge have not been studied yet. In this study we developed the numerical model solving the long distance propagation of 1960 Chilean tsunami in Pacific Ocean and the assessment of its far field effects at Kuril Ridge. According to the modeling efforts, we made comparisons between the results of the numerical solutions using dispersive and non-dispersive long wave equations. The dispersion effects of long distance propagation of 1960 Chilean tsunami
Hui, Zhan-Qiang
2014-01-01
All-optical multicasting of performing data routing from single node to multiple destinations in the optical domain is promising for next generation ultrahigh-peed photonic networks. Based on the self-phase modulation in dispersion flattened highly nonlinear photonic crystal fiber and followed spectral filtering, simultaneous 1-to-8 all-optical wavelength multicasting return-to-zero (RZ) signal at 20 Gbit/s with 100 GHz channel spaced is achieved. Wavelength tunable range and dynamic characteristic of proposed wavelength multicasting scheme is further investigated. The results show our designed scheme achieve operation wavelength range of 25 nm, OSNR of 32.01 dB and Q factor of 12.8. Moreover, the scheme has simple structure as well as high tolerance to signal power fluctuation. PMID:24711738
Seth J. Putterman
2006-01-10
FINAL REPORT ON : NON-LINEAR WAVES IN CONTINUOUS MEDIA Doe DE FG03-87ER13686 (001312-001) Submitted January 10, 2006 by Seth J. Putterman 310-8252269 Physics Department University of California Los Angeles, CA 90095 puherman@ritva.physics.ucla.edu NON-LINEAR WAVES IN CONTINUOUS MEDIA I am happy to report that this project has been a big success. For over 10 years the DOE [Division of Materials Sciences and Engineering] has funded our research program on the overarching theme of spontaneous energy focusing phenomena. These effects occur when a nonlinear macroscopic system is excited so as to drive it far from equilibrium. The subsequent relaxation to equilibrium does not occur smoothly but instead is accompanied by the formation of structured domains where the energy density is highly concentrated. A signature example is picosecond sonoluminescence [1] wherein a smooth sound wave has its energy density focused by 12 orders of magnitude to generate a clock-like string of picosecond flashes of ultraviolet light. Our earlier work on solitons [2] demonstrated how uniform surface waves break up into stable localized structures. Our experimental work on turbulence produced photos of localized structures lying many standard deviations outside the range of gaussian statistics[3]. This effect is referred to as intermittency. Our recent work on friction finds its motivation in those theories of sonoluminescence which invoke frictional electricity. In its most common form this is the generation of a spark when we touch a doorknob after walking over a carpet. Our reading of the literature on this subject indicated that frictional electricity like sonoluminescence is not understood. So to probe triboelectrification we set up a modern version of an experiment performed by Bernoulli in 1700. Here sparking is caused by the rubbing of glass against mercury. We indeed observed flashes of light which were accompanied by events of stick-slip friction at the interface between the
NASA Astrophysics Data System (ADS)
Hammer, Daniel X.; Noojin, Gary D.; Thomas, Robert J.; Stolarski, David J.; Rockwell, Benjamin A.; Welch, Ashley J.
1999-06-01
Spectrally resolved white-light interferometry (SRWLI) was used to measure the wavelength dependence of refractive index (i.e., dispersion) for various ocular components. The accuracy of the technique was assessed by measurement of fused silica and water, the refractive indices of which have been measured at several different wavelengths. The dispersion of bovine and rabbit aqueous and vitreous humor was measured from 400 to 1100 nm. Also, the dispersion was measured from 400 to 700 nm for aqueous and vitreous humor extracted from goat and rhesus monkey eyes. For the humors, the dispersion did not deviate significantly from water. In an additional experiment, the dispersion of aqueous and vitreous humor that had aged up to a month was compared to freshly harvested material. No difference was found between the fresh and aged media. An unsuccessful attempt was also made to use the technique for dispersion measurement of bovine cornea and lens. Future refinement may allow measurement of the dispersion of cornea and lens across the entire visible and near-infrared wavelength band. The principles of white- light interferometry including image analysis, measurement accuracy, and limitations of the technique, are discussed. In addition, alternate techniques and previous measurements of ocular dispersion are reviewed.
NASA Astrophysics Data System (ADS)
Cenedese, Antonio; Viotti, Paolo
1996-08-01
An experimental technique based on image analysis was used to perform a Lagrangian description of passive pollutant particle motion in a three-dimensional saturated porous medium. To allow for optical access, the experiment was carried out with Pyrex grains as the solid matrix and glycerol as the liquid phase in order to have two phases with the same refractive index. Statistical analysis of the experimental data allowed for estimation of velocity and displacement probability density functions (pdf), velocity component correlation functions, Lagrangian integral scales, and mechanical dispersion coefficient tensor components. The results obtained suggest that the longitudinal velocity component has a log normal pdf while the transversal component has a symmetrical pdf, which is nevertheless not Gaussian for high values of the kurtosis. Furthermore, the velocity components' autocorrelation functions are well represented by exponential laws, and the integral scale is dependent on filtration velocity and grain size. As foreseen in the theory the total displacement pdf shows the tendency to reach normal distribution after many integral scales. The evaluated dispersion coefficient tensor components are dependent on travel time; the components start from zero and reach an asymptotic value after several integral scales. Furthermore, the tensor is anisotropic, with the longitudinal component greater than the transversal one by about 1 order of magnitude. Comparison with other experimental data shows agreement at least for the longitudinal dispersion component. Dagan's linear theory has been used for comparing the analytical longitudinal component of the dispersion tensor with that obtained by means of the experiments.
Varshney, Shailendra; Fujisawa, Takeshi; Saitoh, Kunimasa; Koshiba, Masanori
2005-11-14
In this paper, we report, for the first time, an inherently gain-flattened discrete highly nonlinear photonic crystal fiber (HNPCF) Raman amplifier (HNPCF-RA) design which shows 13.7 dB of net gain (with +/-0.85-dB gain ripple) over 28-nm bandwidth. The wavelength dependent leakage loss property of HNPCF is used to flatten the Raman gain of the amplifier module. The PCF structural design is based on W-shaped refractive index profile where the fiber parameters are well optimized by homely developed genetic algorithm optimization tool integrated with an efficient vectorial finite element method (V-FEM). The proposed fiber design has a high Raman gain efficiency of 4.88 W(-1) . km(-1) at a frequency shift of 13.1 THz, which is precisely evaluated through V-FEM. Additionally, the designed module, which shows ultra-wide single mode operation, has a slowly varying negative dispersion coefficient (-107.5 ps/nm/km at 1550 nm) over the operating range of wavelengths. Therefore, our proposed HNPCF-RA module acts as a composite amplifier with dispersion compensator functionality in a single component using a single pump. PMID:19503154
Reshak, A. H.; Brik, M. G.; Auluck, S.
2014-09-14
Based on the electronic band structure, we have calculated the dispersion of the linear and nonlinear optical susceptibilities for the mixed CuAl(S{sub 1–x}Se{sub x})₂ chaclcopyrite compounds with x=0.0, 0.25, 0.5, 0.75, and 1.0. Calculations are performed within the Perdew-Becke-Ernzerhof general gradient approximation. The investigated compounds possess a direct band gap of about 2.2 eV (CuAlS₂), 1.9 eV (CuAl(S₀.₇₅Se₀.₂₅)₂), 1.7 eV (CuAl(S₀.₅Se₀.₅)₂), 1.5 eV (CuAl(S₀.₂₅Se₀.₇₅)₂), and 1.4 eV (CuAlSe₂) which tuned to make them optically active for the optoelectronics and photovoltaic applications. These results confirm that substituting S by Se causes significant band gaps' reduction. The optical function's dispersion ε₂{sup xx}(ω) and ε₂{sup zz}(ω)/ε₂{sup xx}(ω), ε₂{sup yy}(ω), and ε₂{sup zz}(ω) was calculated and discussed in detail. To demonstrate the effect of substituting S by Se on the complex second-order nonlinear optical susceptibility tensors, we performed detailed calculations for the complex second-order nonlinear optical susceptibility tensors, which show that the neat parents compounds CuAlS₂ and CuAlSe₂ exhibit | χ₁₂₂²}(-2ω;ω;ω) | as the dominant component, while the mixed alloys exhibit | χ₁₁₁²(-2ω;ω;ω) | as the dominant component. The features of | χ₁₂₃²}(-2ω;ω;ω) | and | χ{sub 111}²}(-2ω;ω;ω) | spectra were analyzed on the basis of the absorptive part of the corresponding dielectric function ε₂(ω) as a function of both ω/2 and ω.
Sanz-Prat, Alicia; Lu, Chuanhe; Amos, Richard T; Finkel, Michael; Blowes, David W; Cirpka, Olaf A
2016-09-01
the two types of biomass at late times. Results obtained by mapping the exposure-time based results to the two-dimensional domain are compared with simulations based on the two-dimensional, spatially explicit advection-dispersion-reaction equation. Once quasi-steady state has been reached, we find a good agreement in terms of the chemical-compound concentrations between the two approaches inside the reactive zones, whereas the exposure-time based model is not able to capture reactions occurring in the zones with zero electron-donor release. We conclude that exposure-time models provide good approximations of nonlinear bio-reactive transport when transverse mixing is not the overall controlling process and all reactions are essentially restricted to distinct reactive zones. PMID:27343827
NASA Astrophysics Data System (ADS)
Sanz-Prat, Alicia; Lu, Chuanhe; Amos, Richard T.; Finkel, Michael; Blowes, David W.; Cirpka, Olaf A.
2016-09-01
the two types of biomass at late times. Results obtained by mapping the exposure-time based results to the two-dimensional domain are compared with simulations based on the two-dimensional, spatially explicit advection-dispersion-reaction equation. Once quasi-steady state has been reached, we find a good agreement in terms of the chemical-compound concentrations between the two approaches inside the reactive zones, whereas the exposure-time based model is not able to capture reactions occurring in the zones with zero electron-donor release. We conclude that exposure-time models provide good approximations of nonlinear bio-reactive transport when transverse mixing is not the overall controlling process and all reactions are essentially restricted to distinct reactive zones.
Kono, Shunsuke; Watanabe, Hideki; Koda, Rintaro; Fuutagawa, Noriyuki; Narui, Hironobu
2015-12-14
Blue-violet optical pulses of 140-fs duration and 60-W peak power were obtained from a dispersion-compensated GaInN mode-locked semiconductor laser diode using a nonlinear pulse compression technique. Wavelength-dependent group velocity dispersion expressed by third-order phase dispersion was applied to the optical pulses using a pulse compressor with a spatial light modulator. The obtained optical pulses had the shortest duration ever obtained for a mode-locked semiconductor laser diode using edge-emitting type devices. PMID:26698968
NASA Astrophysics Data System (ADS)
Ramirez-Garcia, Sonia; Chen, Lan; Morris, Michael A.; Dawson, Kenneth A.
2011-11-01
We report here a highly successful and original protocol for the dispersion of nanoparticles in biocompatible fluids for in vitro and in vivo studies of the nanoparticle-biology interaction. Titania is chosen as a suitable model as it is one of the priority materials listed by the OECD and small particles of the anatase structure are extensively used as e.g. photocatalysts in solar cells. Consequently, its delivery into the environment and its interaction with biological organisms is unavoidable. Therefore, its biological effect needs to be understood. In this work, we prepared stable nanoparticle dispersions of anatase aggregates using citrate stabilisations between 45 and 55 nm at concentrations of up to 10 mg mL-1. The optimum pH for this type of suspension was 7, resulting in ζ-potentials of approximately -50 mV. The stabilised aggregates were the subject of dialysis to produce stable dispersions without the chemical stabiliser, thus allowing studies in the absence of potentially toxic chemicals. Different sizing techniques such as Dynamic Light Scattering (DLS), Nanoparticle Tracking Analysis (NTA) and Differential Centrifuge Sedimentation (DCS) were used to characterise the different suspensions. The results obtained with each of these techniques are compared and a critical analysis of the suitability of each technique is given.We report here a highly successful and original protocol for the dispersion of nanoparticles in biocompatible fluids for in vitro and in vivo studies of the nanoparticle-biology interaction. Titania is chosen as a suitable model as it is one of the priority materials listed by the OECD and small particles of the anatase structure are extensively used as e.g. photocatalysts in solar cells. Consequently, its delivery into the environment and its interaction with biological organisms is unavoidable. Therefore, its biological effect needs to be understood. In this work, we prepared stable nanoparticle dispersions of anatase aggregates
NASA Astrophysics Data System (ADS)
Tagwo, H.; Tiofack, C. G. L.; Dafounansou, O.; Mohamadou, A.; Kofane, T. C.
2016-03-01
We investigate analytically and numerically the modulational instability (MI) of plane waves under competing nonlocal cubic-local quintic nonlinearities. The generic properties of the MI gain spectra are then demonstrated for the Gaussian response function, exponential response function, and rectangular response function. Special attention is paid to competing nonlocal cubic-local quintic nonlinearities on the MI. We observe that the focusing local quintic nonlinearity increases the growth rate and bandwidth of instability contrary to the small values of defocusing local quintic nonlinearity which decrease the growth rate and bandwidth of instability. Numerical simulations of the full model equation describing the dynamics of the waves are been carried out and leads to the development of pulse trains, depending upon the sign the quintic nonlinearity.
NASA Astrophysics Data System (ADS)
Ostrosablina, A. A.; Sidorov, A. I.
2005-07-01
This paper presents the experimental and theoretical results of a study of the interaction of pulsed laser radiation with thick composite media containing nanoparticles of vanadium dioxide (VO2). It establishes that the reversible semiconductor-metal phase transition that occurs in VO2 nanoparticles under the action of radiation can produce self-defocusing of radiation in the visible and near-IR regions because of the formation of a photoinduced dynamic lens. An analysis is carried out of how the radiation intensity affects the dynamics of these processes. It is shown that photoinduced absorption and scattering play a role in forming the nonlinear optical response.
NASA Astrophysics Data System (ADS)
Liu, Wen-Chao; Yao, Jun; Chen, Zhang-Xin
2014-02-01
Based on Huang's accurate tri-sectional nonlinear kinematic equation (1997), a dimensionless simplified mathematical model for nonlinear flow in one-dimensional semi-infinite long porous media with low permeability is presented for the case of a constant flow rate on the inner boundary. This model contains double moving boundaries, including an internal moving boundary and an external moving boundary, which are different from the classical Stefan problem in heat conduction: The velocity of the external moving boundary is proportional to the second derivative of the unknown pressure function with respect to the distance parameter on this boundary. Through a similarity transformation, the nonlinear partial differential equation (PDE) system is transformed into a linear PDE system. Then an analytical solution is obtained for the dimensionless simplified mathematical model. This solution can be used for strictly checking the validity of numerical methods in solving such nonlinear mathematical models for flows in low-permeable porous media for petroleum engineering applications. Finally, through plotted comparison curves from the exact analytical solution, the sensitive effects of three characteristic parameters are discussed. It is concluded that with a decrease in the dimensionless critical pressure gradient, the sensitive effects of the dimensionless variable on the dimensionless pressure distribution and dimensionless pressure gradient distribution becomemore serious; with an increase in the dimensionless pseudo threshold pressure gradient, the sensitive effects of the dimensionless variable become more serious; the dimensionless threshold pressure gradient (TPG) has a great effect on the external moving boundary but has little effect on the internal moving boundary. [Figure not available: see fulltext.
NASA Astrophysics Data System (ADS)
Liu, Wen-Chao; Yao, Jun; Chen, Zhang-Xin
2014-01-01
Based on Huang's accurate tri-sectional nonlinear kinematic equation (1997), a dimensionless simplified mathematical model for nonlinear flow in one-dimensional semi-infinite long porous media with low permeability is presented for the case of a constant flow rate on the inner boundary. This model contains double moving boundaries, including an internal moving boundary and an external moving boundary, which are different from the classical Stefan problem in heat conduction: The velocity of the external moving boundary is proportional to the second derivative of the unknown pressure function with respect to the distance parameter on this boundary. Through a similarity transformation, the nonlinear partial differential equation (PDE) system is transformed into a linear PDE system. Then an analytical solution is obtained for the dimensionless simplified mathematical model. This solution can be used for strictly checking the validity of numerical methods in solving such nonlinear mathematical models for flows in low-permeable porous media for petroleum engineering applications. Finally, through plotted comparison curves from the exact analytical solution, the sensitive effects of three characteristic parameters are discussed. It is concluded that with a decrease in the dimensionless critical pressure gradient, the sensitive effects of the dimensionless variable on the dimensionless pressure distribution and dimensionless pressure gradient distribution become more serious; with an increase in the dimensionless pseudo threshold pressure gradient, the sensitive effects of the dimensionless variable become more serious; the dimensionless threshold pressure gradient (TPG) has a great effect on the external moving boundary but has little effect on the internal moving boundary.
NASA Astrophysics Data System (ADS)
Sivan, Y.; Rozenberg, S.; Halstuch, A.
2016-04-01
We present an extension of the canonical coupled-mode theory of electromagnetic waves to the case of pulses and spatiotemporal perturbations in complex media. Unlike previous attempts to derive such a model, our approach involves no approximation, and it does not impose any restriction on the spatiotemporal profile. Moreover, the effect of modal dispersion on mode evolution and on the coupling to other modes is fully taken into account. Thus, our approach can yield any required accuracy by retaining as many terms in the expansion as needed. It also avoids various artifacts of previous derivations by introducing the correct form of the solution. We then validate the coupled-mode equations with exact numerical simulations, and we demonstrate the wide range of possibilities enabled by spatiotemporal perturbations of pulses, including pulse shortening or broadening or more complex shaping. Our formulation is valid across the electromagnetic spectrum, and it can be applied directly also to other wave systems.
Villalobos-Hernández, J R; Müller-Goymann, C C
2005-05-01
The purpose of this study was to characterize carrier systems for inorganic sunscreens based on a matrix composed of carnauba wax and decyl oleate. Ultraviolet radiation attenuators like barium sulfate, strontium carbonate and titanium dioxide were tested. The lipid matrices were used either as capsules or as accompanying vehicles for the pigments in aqueous dispersions. Manufacturing was performed using high pressure homogenization at 300bar and a temperature of 75 degrees C. To evaluate the effect of the pigments on the crystalline structure of the wax-oil mixture, X-ray diffraction and differential scanning calorimetry were used. Further parameters determined were particle size, polydispersity index, z-potential, viscosity and sun protection factor (SPF). Transmission electron microscopy was also applied for visualization of nanoparticles. The X-ray diffraction patterns and the melting points of the lipid mixtures remained unchanged after the pigments were added. The particle sizes of the encapsulated species ranged from 239 to 749.9nm showing polydispersity values between 0.100 and 0.425. Surface charge measurements comprising values up to -40.8mV denoted the presence of stable dispersions. The formulations could be described as ideal viscous presenting viscosities in a range of 1.40-20.5mPas. Significant increases in SPF up to about 50 were reported after the encapsulation of titanium dioxide. Freeze fracture micrographs confirmed the presence of encapsulated inorganic crystals. PMID:15848063
Niu, Xiangheng; Lan, Minbo; Zhao, Hongli; Chen, Chen
2013-07-15
The investigation of highly efficient catalysts for the electrochemical oxidation of glucose is the most critical challenge to commercialize nonenzymatic glucose sensors, which display a few attractive superiorities including the sufficient stability of their properties and the desired reproducibility of results over enzyme electrodes. Herein we propose a new and very promising catalyst: Pt cubes well-dispersed on the porous Cu foam, for the the electrochemical oxidation reaction of glucose in neutral media. The catalyst is fabricated in situ on a homemade screen-printed carbon electrode (SPCE) substrate through initially synthesizing the three-dimensional (3D) porous Cu foam using a hydrogen evolution assisted electrodeposition strategy, followed by electrochemically reducing the platinic precursor simply and conveniently. Field emission scanning electron microscopy (FESEM) and transmission electron microscopy (TEM) proofs demonstrate that Pt cubes, with an average size (the distance of opposite faces) of 185.1 nm, highly dispersed on the macro/nanopore integrated Cu foam support can be reproducibly obtained. The results of electrochemical tests indicate that the cubic Pt-based catalyst exhibits significant enhancement on the catalytic activity towards the electrooxidation of glucose in the presence of chloride ions, providing a specific activity 6.7 times and a mass activity 5.3 times those of commercial Pt/C catalysts at -0.4 V (vs. Ag/AgCl). In addition, the proposed catalyst shows excellent stability of performance, with only a 2.8% loss of electrocatalytic activity after 100 repetitive measurements. PMID:23744705
Webb, S.W.
1996-05-01
Two models for gas-phase diffusion and advection in porous media, the Advective-Dispersive Model (ADM) and the Dusty-Gas Model (DGM), are reviewed. The ADM, which is more widely used, is based on a linear addition of advection calculated by Darcy`s Law and ordinary diffusion using Fick`s Law. Knudsen diffusion is often included through the use of a Klinkenberg factor for advection, while the effect of a porous medium on the diffusion process is through a porosity-tortuosity-gas saturation multiplier. Another, more comprehensive approach for gas-phase transport in porous media has been formulated by Evans and Mason, and is referred to as the Dusty- Gas Model (DGM). This model applies the kinetic theory of gases to the gaseous components and the porous media (or ``dust``) to develop an approach for combined transport due to ordinary and Knudsen diffusion and advection including porous medium effects. While these two models both consider advection and diffusion, the formulations are considerably different, especially for ordinary diffusion. The various components of flow (advection and diffusion) are compared for both models. Results from these two models are compared to isothermal experimental data for He-Ar gas diffusion in a low-permeability graphite. Air-water vapor comparisons have also been performed, although data are not available, for the low-permeability graphite system used for the helium-argon data. Radial and linear air-water heat pipes involving heat, advection, capillary transport, and diffusion under nonisothermal conditions have also been considered.
REVIEW ARTICLE: Fast light in atomic media
NASA Astrophysics Data System (ADS)
Akulshin, Alexander M.; McLean, Russell J.
2010-10-01
Atomic media have played a major role in studies of fast light. One of their attractive features is the ability to manipulate experimental parameters to control the dispersive properties that determine the group velocity of a propagating light pulse. We give an overview of the experimental methods, based on both linear and nonlinear atom-light interaction, that have produced superluminal propagation in atomic media, and discuss some of the significant theoretical contributions to the issues of pulse preservation and reconciling faster-than-light propagation and the principle of causality. The comparison of storage of light, enhanced Kerr nonlinearity and efficient wave mixing processes in slow and fast light atomic media illustrates their common and distinct features.
NASA Astrophysics Data System (ADS)
Ateto, M. S.
2015-08-01
Entanglement dynamics of two identical non-interacting atoms (qubits) coupled individually with simultaneous classical and quantum fields are studied. The cavity field is filled with a nonlinear Kerr medium and initially prepared in a coherent state. The atoms are initially set up as a Bell-like pure state (BS). We present an approach for diagonalization of time-dependent nonlinear Hamiltonian of the system exactly. Connection between the change in the degree of entanglement and tomography of field state in phase space are also illustrated and interpreted. We demonstrate the possibility of atom-atom (qubit-qubit) entanglement optimization by suitably choosing initial interaction settings. Overall, we show that both classical driving amplitude and detuning as well as Kerr media and initial atomic states acts as the control parameters for the qubit-qubit entanglement. By adjusting of these parameters, accurately, entanglement can be enhanced noticeably and high degree of steady periodical entanglement can be generated. Moreover, starting with initial atomic BSs in presence of classical driving suppresses coherences randomness and considerably accompanied with (for specific values of detuning) slight decrease in their amplitudes. Furthermore, the addition of cross Kerr term suppresses degree of entanglement noticeably, where entanglement creation and enhancement could just be possible if cross Kerr effect is moved out from interaction. Our present approach promises the great advantage of being suitable for large quantum systems of various kinds of nonlinearities.
Stratification effects on nonlinear elastic surface waves
NASA Astrophysics Data System (ADS)
Parker, D. F.
1988-01-01
On a homogeneous elastic half-space, linear surface waves are nondispersive. In each direction, waves having any profile travel without distortion. Nonlinearity causes intermodulation between the various wavelengths so that the signal distorts. Even when nonlinearity is small, sinusoidal profiles do not remain approximately sinusoidal. The absence of dispersion means that profiles suffer cumulative distortion, until the surface slope and strain become locally unbounded. Although this behaviour is typical of many signals, there are some signals for which intermodulation is constructive. These signals can travel coherently over large distances. For seismological applications, it is important to study the effects due to stratification. Dependence of the material constants on depth modifies the nonlinear evolution equations previously derived for homogeneous media. It has a smaller effect on higher frequencies than on lower frequencies. An approximate theory for short wavelength (high frequency) signals is introduced. Calculations show that when nonlinearity is no more important than dispersion, initially sinusoidal profiles propagate with surface slope remaining finite. When dispersion is small compared to nonlinearity, certain sharp peaked profiles can travel large distances while suffering little distortion.
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. PMID:27475076
NASA Astrophysics Data System (ADS)
Parker, Jack C.; Kim, Ungtae
2015-11-01
The mono-continuum advection-dispersion equation (mADE) is commonly regarded as unsuitable for application to media that exhibit rapid breakthrough and extended tailing associated with diffusion between high and low permeability regions. This paper demonstrates that the mADE can be successfully used to model such conditions if certain issues are addressed. First, since hydrodynamic dispersion, unlike molecular diffusion, cannot occur upstream of the contaminant source, models must be formulated to prevent "back-dispersion." Second, large variations in aquifer permeability will result in differences between volume-weighted average concentration (resident concentration) and flow-weighted average concentration (flux concentration). Water samples taken from wells may be regarded as flux concentrations, while soil samples may be analyzed to determine resident concentrations. While the mADE is usually derived in terms of resident concentration, it is known that a mADE of the same mathematical form may be written in terms of flux concentration. However, when solving the latter, the mathematical transformation of a flux boundary condition applied to the resident mADE becomes a concentration type boundary condition for the flux mADE. Initial conditions must also be consistent with the form of the mADE that is to be solved. Thus, careful attention must be given to the type of concentration data that is available, whether resident or flux concentrations are to be simulated, and to boundary and initial conditions. We present 3-D analytical solutions for resident and flux concentrations, discuss methods of solving numerical models to obtain resident and flux concentrations, and compare results for hypothetical problems. We also present an upscaling method for computing "effective" dispersivities and other mADE model parameters in terms of physically meaningful parameters in a diffusion-limited mobile-immobile model. Application of the latter to previously published studies of
Parker, Jack C; Kim, Ungtae
2015-11-01
The mono-continuum advection-dispersion equation (mADE) is commonly regarded as unsuitable for application to media that exhibit rapid breakthrough and extended tailing associated with diffusion between high and low permeability regions. This paper demonstrates that the mADE can be successfully used to model such conditions if certain issues are addressed. First, since hydrodynamic dispersion, unlike molecular diffusion, cannot occur upstream of the contaminant source, models must be formulated to prevent "back-dispersion." Second, large variations in aquifer permeability will result in differences between volume-weighted average concentration (resident concentration) and flow-weighted average concentration (flux concentration). Water samples taken from wells may be regarded as flux concentrations, while soil samples may be analyzed to determine resident concentrations. While the mADE is usually derived in terms of resident concentration, it is known that a mADE of the same mathematical form may be written in terms of flux concentration. However, when solving the latter, the mathematical transformation of a flux boundary condition applied to the resident mADE becomes a concentration type boundary condition for the flux mADE. Initial conditions must also be consistent with the form of the mADE that is to be solved. Thus, careful attention must be given to the type of concentration data that is available, whether resident or flux concentrations are to be simulated, and to boundary and initial conditions. We present 3-D analytical solutions for resident and flux concentrations, discuss methods of solving numerical models to obtain resident and flux concentrations, and compare results for hypothetical problems. We also present an upscaling method for computing "effective" dispersivities and other mADE model parameters in terms of physically meaningful parameters in a diffusion-limited mobile-immobile model. Application of the latter to previously published studies of
Prisutova, Jevgenija; Horoshenkov, Kirill; Groby, Jean-Philippe; Brouard, Bruno
2014-12-01
The measurement of acoustic material characteristics using a standard impedance tube method is generally limited to the plane wave regime below the tube cut-on frequency. This implies that the size of the tube and, consequently, the size of the material specimen must remain smaller than a half of the wavelength. This paper presents a method that enables the extension of the frequency range beyond the plane wave regime by at least a factor of 3, so that the size of the material specimen can be much larger than the wavelength. The proposed method is based on measuring of the sound pressure at different axial locations and applying the spatial Fourier transform. A normal mode decomposition approach is used together with an optimization algorithm to minimize the discrepancy between the measured and predicted sound pressure spectra. This allows the frequency and angle dependent reflection and absorption coefficients of the material specimen to be calculated in an extended frequency range. The method has been tested successfully on samples of melamine foam and wood fiber. The measured data are in close agreement with the predictions by the equivalent fluid model for the acoustical properties of porous media. PMID:25480044
NASA Astrophysics Data System (ADS)
Gouze, P.; Le Borgne, T.; Leprovost, R.; Lods, G.; Poidras, T.; Pezard, P.
2008-06-01
We present a set of single-well injection withdrawal tracer tests in a paleoreef porous reservoir displaying important small-scale heterogeneity. An improved dual-packer probe was designed to perform dirac-like tracer injection and accurate downhole automatic measurements of the tracer concentration during the recovery phase. By flushing the tracer, at constant flow rate, for increasing time duration, we can probe distinctly different reservoir volumes and test the multiscale predictability of the (non-Fickian) dispersion models. First we describe the characteristics, from microscale to meter scale, of the reservoir rock. Second, the specificity of the tracer test setup and the results obtained using two different tracers and measurement methods (salinity-conductivity and fluorescent dye-optical measurement, respectively) are presented. All the tracer tests display strongly tailed breakthrough curves (BTC) consistent with diffusion in immobile regions. Conductivity results, measured over 3 orders of magnitude only, could have been easily interpreted by the conventional mobile-immobile (MIM) diffusive mass transfer model of asymptotic log-log slope of -2. However, the fluorescent dye sensor, which allows exploring much lower concentration values, shows that a change in the log-log slope occurs at larger time with an asymptotic value of -1.5, corresponding to the double-porosity model. These results suggest that the conventional, one-slope MIM transfer rate model is too simplistic to account for the real multiscale heterogeneity of the diffusion-dominant fraction of the reservoir.
Spatiotemporal soliton supported by parity-time symmetric potential with competing nonlinearities
NASA Astrophysics Data System (ADS)
Xu, Si-Liu; Zhao, Yuan; Petrović, Nikola Z.; Belić, Milivoj R.
2016-07-01
We construct explicit spatiotemporal or light bullet (LB) solutions to the (3 + 1)-dimensional nonlinear Schrödinger equation (NLSE) with inhomogeneous diffraction/dispersion and nonlinearity in the presence of parity-time (PT) symmetric potential with competing nonlinearities. The solution is based on the similarity transformation, by which the initial inhomogeneous problem is reduced to the standard NLSE with constant coefficients but with redefined variables and potential. Transmission characteristics of LB solutions, such as the phase change, half width and chirp, are studied in the media with exponentially decreasing diffraction/dispersion and with periodic modulation. Our outcomes demonstrate that diffraction/dispersion and nonlinearity management can prolong the stability of LBs in a PT potential.
Transparency in nonlinear frequency conversion
NASA Astrophysics Data System (ADS)
Longhi, Stefano
2016-04-01
Suppression of wave scattering and the realization of transparency effects in engineered optical media and surfaces have attracted great attention in the past recent years. In this work the problem of transparency is considered for optical wave propagation in a nonlinear dielectric medium with second-order χ(2 ) susceptibility. Because of nonlinear interaction, a reference signal wave at carrier frequency ω1 can exchange power, thus being amplified or attenuated, when phase-matching conditions are satisfied and frequency conversion takes place. Therefore, rather generally the medium is not transparent to the signal wave because of "scattering" in the frequency domain. Here we show that broadband transparency, corresponding to the full absence of frequency conversion in spite of phase matching, can be observed for the signal wave in the process of sum frequency generation whenever the effective susceptibility χ(2 ) along the nonlinear medium is tailored following a suitable spatial apodization profile and the power level of the pump wave is properly tuned. While broadband transparency is observed under such conditions, the nonlinear medium is not invisible owing to an additional effective dispersion for the signal wave introduced by the nonlinear interaction.
NASA Astrophysics Data System (ADS)
Kong, Youchao
2016-07-01
A class of new spatiotemporal solitary solution to nonlinear Schrödinger equation with a parabolic potential is investigated analytically and numerically using the F-expansion method and homogeneous balance principle. The propagation characteristics of soliton wave solutions are analyzed with/without spatial-temporal chirp. It is noteworthy that, by calculating spatial and temporal second-order intensity moment, several novel features of optical beam propagations are obtained, such as stable, oscillating, decaying and blowing up. Additionally, controllability of these solutions with the modulation depth of the parabolic potential is demonstrated.
A Column Dispersion Experiment.
ERIC Educational Resources Information Center
Corapcioglu, M. Y.; Koroglu, F.
1982-01-01
Crushed glass and a Rhodamine B solution are used in a one-dimensional optically scanned column experiment to study the dispersion phenomenon in porous media. Results indicate that the described model gave satisfactory results and that the dispersion process in this experiment is basically convective. (DC)
NASA Astrophysics Data System (ADS)
Martin, Elly; Treeby, Bradley E.
2015-10-01
To increase the effectiveness of high intensity focused ultrasound (HIFU) treatments, prediction of ultrasound propagation in biological tissues is essential, particularly where bones are present in the field. This requires complex full-wave computational models which account for nonlinearity, absorption, and heterogeneity. These models must be properly validated but there is a lack of analytical solutions which apply in these conditions. Experimental validation of the models is therefore essential. However, accurate measurement of HIFU fields is not trivial. Our aim is to establish rigorous methods for obtaining reference data sets with which to validate tissue realistic simulations of ultrasound propagation. Here, we present preliminary measurements which form an initial validation of simulations performed using the k-Wave MATLAB toolbox. Acoustic pressure was measured on a plane in the field of a focused ultrasound transducer in free field conditions to be used as a Dirichlet boundary condition for simulations. Rectangular and wedge shaped olive oil scatterers were placed in the field and further pressure measurements were made in the far field for comparison with simulations. Good qualitative agreement was observed between the measured and simulated nonlinear pressure fields.
Envelope Solitons in Acoustically Dispersive Vitreous Silica
NASA Technical Reports Server (NTRS)
Cantrell, John H.; Yost, William T.
2012-01-01
Acoustic radiation-induced static strains, displacements, and stresses are manifested as rectified or dc waveforms linked to the energy density of an acoustic wave or vibrational mode via the mode nonlinearity parameter of the material. An analytical model is developed for acoustically dispersive media that predicts the evolution of the energy density of an initial waveform into a series of energy solitons that generates a corresponding series of radiation-induced static strains (envelope solitons). The evolutionary characteristics of the envelope solitons are confirmed experimentally in Suprasil W1 vitreous silica. The value (-11.9 plus or minus 1.43) for the nonlinearity parameter, determined from displacement measurements of the envelope solitons via a capacitive transducer, is in good agreement with the value (-11.6 plus or minus 1.16) obtained independently from acoustic harmonic generation measurements. The agreement provides strong, quantitative evidence for the validity of the model.
Nonlocal homogenization for nonlinear metamaterials
NASA Astrophysics Data System (ADS)
Gorlach, Maxim A.; Voytova, Tatiana A.; Lapine, Mikhail; Kivshar, Yuri S.; Belov, Pavel A.
2016-04-01
We present a consistent theoretical approach for calculating effective nonlinear susceptibilities of metamaterials taking into account both frequency and spatial dispersion. Employing the discrete dipole model, we demonstrate that effects of spatial dispersion become especially pronounced in the vicinity of effective permittivity resonance where nonlinear susceptibilities reach their maxima. In that case spatial dispersion may enable simultaneous generation of two harmonic signals with the same frequency and polarization but different wave vectors. We also prove that the derived expressions for nonlinear susceptibilities transform into the known form when spatial dispersion effects are negligible. In addition to revealing new physical phenomena, our results provide useful theoretical tools for analyzing resonant nonlinear metamaterials.
Airy-type solitary wave in highly noninstantaneous Kerr media.
Deng, Fu; Hong, Weiyi; Deng, Dongmei
2016-07-11
We investigate the dynamics of a decelerating Airy pulse in the highly noninstantaneous Kerr media. It is found that the deceleration of the Airy pulse can be counteracted by the highly noninstantaneous nonlinearity. When the power of the pulse is specifically chosen, the deceleration of the Airy pulse can be totally restrained, and an Airy-type solitary wave is observed within several dispersion lengths. PMID:27410868
Chabchoub, A.; Kibler, B.; Finot, C.; Millot, G.; Onorato, M.; Dudley, J.M.; Babanin, A.V.
2015-10-15
The dynamics of waves in weakly nonlinear dispersive media can be described by the nonlinear Schrödinger equation (NLSE). An important feature of the equation is that it can be derived in a number of different physical contexts; therefore, analogies between different fields, such as for example fiber optics, water waves, plasma waves and Bose–Einstein condensates, can be established. Here, we investigate the similarities between wave propagation in optical Kerr media and water waves. In particular, we discuss the modulation instability (MI) in both media. In analogy to the water wave problem, we derive for Kerr-media the Benjamin–Feir index, i.e. a nondimensional parameter related to the probability of formation of rogue waves in incoherent wave trains.
Simple model for the nonlinear optical response of gases in the transparency region.
Schuh, K; Kolesik, M; Wright, E M; Moloney, J V
2014-09-01
We present a simple model for the nonlinear optical response of atomic gases for pulses with center wavelengths in the transparency region and peak fields for which ionization is not prevalent. By comparing with simulations based on the Schrödinger equation for a hydrogen atom we demonstrate that the model accurately captures the dispersion of the nonlinear polarization as well as noninstantaneous effects for a variety of photon energies and also a two-color pulse. Our approach should be of utility in simulating near- and mid-infrared pulse propagation in dielectric media for which extreme nonlinear effects can arise. PMID:25166080
An exact approach to intensity analysis of optical pulses in nonlinear meta-materials
NASA Astrophysics Data System (ADS)
Nanda, Lipsa
2016-05-01
The nonlinear pulse propagation has been analytically studied by solving the nonlinear Schrödinger's equation (NLSE) in bulk media exhibiting frequency dependent dielectric permittivity(ɛ) and magnetic permeability(μ). The exact solutions obtained are shown to be of trigonometric & localized types. The analytical and simulation based method has been further extended to investigate the intensity distribution in a nonlinear meta-material which behaves as a negative refractive medium (NRM), where both ɛ and μ are shown to be dispersive and negative in nature.
NASA Astrophysics Data System (ADS)
Shukla, P. K.; Bingham, R.; Stenflo, L.; Dawson, J. M.
1996-01-01
Starting in 1989 we have created a forum at the International Centre for Theoretical Physics, Trieste, where scientists from different parts of the world can meet and exchange information in the frontier areas of physics. In the three previous meetings, we focused on large amplitude waves and fields in plasmas, the physics of dusty plasmas, and wave-particle interactions and energization in plasmas. In 1995, we came up with a fresh idea of organizing somewhat enlarged but still well focused research topics that are cross-disciplinary. Thus, the usual 'fourth-week activity' of the Plasma Physics College at the ICTP was replaced by an International Topical Workshop on Plasma Physics: Coherent Processes in Nonlinear Media, which was held at the ICTP during the period 16-20 October, 1995. This provided us an opportunity to draw eminent speakers from many closely related fields such as plasma physics, fluid dynamics, nonlinear optics, and astrophysics. The Workshop was attended by 82 delegates from 34 countries, and the participation from the industrial and the developing countries was about half each. The programme included 4 review and 29 topical invited lectures. In addition, about 30 contributed papers were presented as posters in two sessions. The latter were created in order to give opportunities to younger physicists for displaying the results of their recent work and to obtain constructive comments from the other participants. During the five days at the ICTP, we focused on almost all the various aspects of nonlinear phenomena that are common in different branches of science. The review and topical lectures as well as the posters dealt with the most recent advances in coherent nonlinear processes in space and astrophysical plasmas, in fluids and optics, in low temperature dusty plasmas, as well as in laser produced and magnetically confined laboratory plasmas. The focus was on the physics of various types of waves and their generation mechanisms, the development
NASA Astrophysics Data System (ADS)
Splinter, Robert; Svenson, Robert H.; Sosa, Eduardo; Buchele d'Avila, Andre Luiz; Scanavacca, Mauricio; Pruitt, Ernest; Kasell, Jackie H.
2003-02-01
When irradiating particular biological media in general there will be a range of optical properties to deal with, with respect to the irradiating wavelength, and the respective tissues that make up the organ under treatment or being imaged. In addition to this we saw changing optical properties under influence of denaturization, dehydration and carbonization. We also observed optical nonlinearities that are irradiance dependent, in addition to the birefringence which affects the light distribution throughout the tissue differently than the polarization birefringence used in optical polarization microscopy. In the treatment of ventricular tachycardia with laser photocoagulation the success of the procedure depends on whether sufficient energy has been directed to the relevant region of the myocardium to ablate the entire arrhythmogenic focus. A new high power diode laser operating in the near infrared was used in an animal infarct model and in human arrhythmia ablation. The light distribution measured for Chagasic heart tissues at the diode laser wavelength demonstrated the key potential to create controlled deep photocoagulation lesions. From our observations we may conclude that the diode laser - catheter combination offers significant potential for the elimination of arrhythmia's resulting from Chagas disease.
Physical explanations of non-Darcy effects for fluid flow in porous media
Ma, H.; Ruth, D.
1997-03-01
The nature of nonlinear flow in porous media is analyzed by means of the volumetric averaging approach for a medium modeled by diverging/converging capillaries. To clarify the mechanism responsible for the nonlinearity, a physical explanation is deduced for the dispersion term in the averaged momentum equation. With the present periodical model, the numerically obtained microscopic flow fields, in association with the macroscopic coefficients calculated by the average momentum balance, indicated quantitatively that the microscopic inertial phenomena, which lead to distorted pore velocity and pressure fields, is the fundamental reason for the onset of nonlinear effects as filtration velocity increases.
Adams, J
2002-08-09
New crystalline materials were investigated for applications in frequency conversion of near-infrared wavelengths and as gain media for tunable mid-infrared solid-state lasers. GaCa{sub 4}O(BO{sub 3}){sub 3} (GdCOB), YCa{sub 4}O(BO{sub 3}){sub 3} (YCOB), LaCa{sub 4}O(BO{sub 3}){sub 3} (LaCOB), and Gd{sub 0.275}Y{sub 0.725}Ca{sub 4}O(BO{sub 3}){sub 3} were characterized for frequency conversion of 1 {micro}m lasers. For type I doubling at 1064 nm, LaCOB, GdCOB, and YCOB were found to have effective coupling coefficients (d{sub eff}) of 0.52 {+-} 0.05, 0.78 {+-} 0.06, and 1.12 {+-} 0.07 pm/V, respectively. LaCOB was measured to have angular and thermal sensitivities of 1224 {+-} 184 (cm-rad){sup -1} and < 0.10 (cm-{sup o}C){sup -1}, respectively. The effective coupling coefficient for type II noncritically phasematched (NCPM) doubling at 1064 nm in Gd{sub 0.275}Y{sub 0.725}Ca{sub 4}O(BO{sub 3}){sub 3} was measured to be 0.37 {+-} 0.04 pm/V. We predict LaCOB to have a type I NCPM fundamental wavelength of 1042 {+-} 1.5 nm. Due to its low angular and thermal sensitivities for doubling near 1047 nm, LaCOB has potential for frequency doubling of high-average power Nd:LiYF{sub 4} and Yb:Sr{sub 5}(P0{sub 4}){sub 3}F lasers. LaCOB, GdCOB, and YCOB were also investigated for optical parametric oscillator applications and we determined that they may have potential in a Ti:sapphire pumped oscillator. The effective linear electro-optic coefficients (r{sub eff}) were measured along dielectric directions in YCOB and a maximum r{sub eff} of 10.8 pm/V was found. For a crystal with a 5:1 aspect ratio, the corresponding half-wave voltage at 1064 nm would be 19.6 kV. Therefore a Pockels cell composed of two YCOB crystals with 5:1 aspect ratios would have a required half-wave voltage <10 kV. Moderate coupling coefficients (3 x KH{sub 2}PO{sub 4}), low thermal sensitivities, ease of growth to large sizes, non-hygroscopicity, and favorable polishing and coating characteristics make La
Liu Jiansheng; Li Ruxin; Xu Zhizhan
2006-10-15
The nonlinear dynamics of 1.6-{mu}m fs laser pulses propagating in fused silica is investigated by employing a full-order dispersion model. Different from the x-wave generation in normally dispersive media, a few-cycle spatiotemporally compressed soliton wave is generated with the contrary contributions of anomalous group velocity dispersion (GVD) and self-phase-modulation. However, at the tailing edge of the pulse forms a shock wave which generates separate and strong supercontinuum peaked at 670 nm. It is also the origin of conical emission formed both in time and frequency domain with the contribution of normal GVD at visible light.
Self-action of few-cycle pulses in a dispersive medium
Balakin, A. A.; Litvak, A. G.; Mironov, V. A.; Skobelev, S. A.
2009-12-15
Basing on the nonlinear wave equation as the reflection-free approximation, we study the self-focusing dynamics of laser pulses under rather general assumptions about media dispersion. The methods for qualitative investigation of the self-action dynamics of ultrashort pulses are developed. It is shown that a new effect here is steepening of the longitudinal pulse profile, which is determined by the dependence of group velocity on the amplitude. Results of numerical simulation in media without dispersion and with anomalous dispersion confirm the conclusion about outrunning formation of a shock wave during pulse self-focusing. The formation of a power spectrum of the field, which is characteristic for a shock wave, is retained also when medium ionization is taken into account. In the case of a normal-dispersion medium, nonlinear dispersion leads to a violation of the symmetry in the longitudinal splitting of the pulse in the process of self-focusing. The possibility of tuning of the optical-pulse frequency into the short-wave area is shown for the pulse self-action near the zero-dispersion point.
Nonlinear Hysteretic Torsional Waves.
Cabaret, J; Béquin, P; Theocharis, G; Andreev, V; Gusev, V E; Tournat, V
2015-07-31
We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters. PMID:26274421
Nonlinear Hysteretic Torsional Waves
NASA Astrophysics Data System (ADS)
Cabaret, J.; Béquin, P.; Theocharis, G.; Andreev, V.; Gusev, V. E.; Tournat, V.
2015-07-01
We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters.
Kenmogne, Fabien; Yemélé, David
2013-10-01
The modulational instability (MI) phenomenon in the nonlinear Schrödinger equation (NLSE) extended by two different nonlinear dispersion terms and the gradient term is investigated. We find that the possibility of instability of plane waves depends on the sign of the nonlinear dispersion parameters with regard to the linear dispersion coefficient. In contrast to the basic NLSE, the system may exhibit instability in the defocusing media for amplitude exceeding a critical value depending on the magnitude of the nonlinear dispersion. An additional feature, namely the higher order or the infinite gain band, absent in the NLSE case, may appear and in which MI induces the birth of the nonlinear localized wave (NLW) of different carrier wave numbers. The result of the qualitative investigations of the system's dynamics indicates the existence of the NLW, such as peak, bright, dark, and compact dark solitary waves which can be well predicted by the MI criteria. In addition the nonlinear dispersion induces the existence of a pair of bright-dark solitary waves which is usually exhibited by the coupled NLSEs only, and the pairs of peak-dark and compact dark-bright solitary waves. PMID:24229297
Dark three-sister rogue waves in normally dispersive optical fibers with random birefringence.
Chen, Shihua; Soto-Crespo, Jose M; Grelu, Philippe
2014-11-01
We investigate dark rogue wave dynamics in normally dispersive birefringent optical fibers, based on the exact rational solutions of the coupled nonlinear Schrödinger equations. Analytical solutions are derived up to the second order via a nonrecursive Darboux transformation method. Vector dark "three-sister" rogue waves as well as their existence conditions are demonstrated. The robustness against small perturbations is numerically confirmed in spite of the onset of modulational instability, offering the possibility to observe such extreme events in normal optical fibers with random birefringence, or in other Manakov-type vector nonlinear media. PMID:25401907
Blackbody Emission from Light Interacting with an Effective Moving Dispersive Medium
NASA Astrophysics Data System (ADS)
Petev, M.; Westerberg, N.; Moss, D.; Rubino, E.; Rimoldi, C.; Cacciatori, S. L.; Belgiorno, F.; Faccio, D.
2013-07-01
Intense laser pulses excite a nonlinear polarization response that may create an effective flowing medium and, under appropriate conditions, a blocking horizon for light. Here, we analyze in detail the interaction of light with such laser-induced flowing media, fully accounting for the medium dispersion properties. An analytical model based on a first Born approximation is found to be in excellent agreement with numerical simulations based on Maxwell’s equations and shows that when a blocking horizon is formed, the stimulated medium scatters light with a blackbody emission spectrum. Based on these results, diamond is proposed as a promising candidate medium for future studies of Hawking emission from artificial, dispersive horizons.
Solitonization of a dispersive wave.
Braud, F; Conforti, M; Cassez, A; Mussot, A; Kudlinski, A
2016-04-01
We report the observation of a nonlinear propagation scenario in which a dispersive wave is transformed into a fundamental soliton in an axially varying optical fiber. The dispersive wave is initially emitted in the normal dispersion region and the fiber properties change longitudinally so that the dispersion becomes anomalous at the dispersive wave wavelength, which allows it to be transformed into a soliton. The solitonic nature of the field is demonstrated by solving the direct Zakharov-Shabat scattering problem. Experimental characterization performed in spectral and temporal domains show evidence of the solitonization process in an axially varying photonic crystal fiber. PMID:27192249
Numerical solutions of Maxwell's equations for nonlinear-optical pulse propagation
NASA Astrophysics Data System (ADS)
Hile, Cheryl V.; Kath, William L.
1996-06-01
A model and numerical solutions of Maxwell's equations describing the propagation of short, solitonlike pulses in nonlinear dispersive optical media are presented. The model includes linear dispersion expressed in the time domain, a Kerr nonlinearity, and a coordinate system moving with the group velocity of the pulse. Numerical solutions of Maxwell's equations are presented for circularly polarized and linearly polarized electromagnetic fields. When the electromagnetic fields are assumed to be circularly polarized, numerical solutions are compared directly with solutions of the nonlinear Schrodinger (NLS) equation. These comparisons show good agreement and indicate that the NLS equation provides an excellent model for short-pulse propagation. When the electromagnetic fields are assumed to be linearly polarized, the propagation of daughter pulses, small-amplitude pulses at three times the frequency of the solitonlike pulse, are observed in the numerical solution. These daughter pulses are shown to be the direct result of third harmonics generated by the main, solitonlike, pulse.
Sackey, Isaac; Da Ros, Francesco; Jazayerifar, Mahmoud; Richter, Thomas; Meuer, Christian; Nölle, Markus; Molle, Lutz; Peucheret, Christophe; Petermann, Klaus; Schubert, Colja
2014-11-01
We present experimental and numerical investigations of Kerr nonlinearity compensation in a 400-km standard single-mode fiber link with distributed Raman amplification with backward pumping. A dual-pump polarization-independent fiber-based optical parametric amplifier is used for mid-link spectral inversion of 5 × 28-GBd polarization-multiplexed 16-QAM signals. Signal quality factor (Q-factor) improvements of 1.1 dB and 0.8 dB were obtained in the cases of a single-channel and a five-channel wavelength-division multiplexing (WDM) system, respectively. The experimental results are compared to numerical simulations with good agreement. It is also shown with simulations that a maximum transmission reach of 2400 km enabled by the optical phase conjugator is possible for the WDM signal. PMID:25401887
Flaherty, L.M.
1989-01-01
This book contains papers presented at a symposium of the American Society for Testing and Materials. The topics covered include: The effect of elastomers on the efficiency of oil spill dispersants; planning for dispersant use; field experience with dispersants for oil spills on land; and measurements on natural dispersion.
NASA Astrophysics Data System (ADS)
Jasinski, Jerzy
2015-05-01
In the paper propagation of axially-symmetric (1+2)D beam in nonlinear medium with dual-power nonlinearity is analyzed. The ordinary differential equation for transverse stationary profile of the propagating field is derived and solved using a perturbation technique. The simple analytical formulas for the three lowest order solutions are obtained. They describe fields of algebraic profiles. The zero order solution satisfies exactly the nonlinear Schrödinger equation in (1+2)D case. Higher order solutions are determined by propagation constant and describe fields of different initial amplitude. The accuracy of approximation and stability of the obtained solutions are discussed.
Matsuo, K.; Klabunde, K.J.
1982-02-26
Highly dispersed Ni/support catalysts were prepared from toluene-solvated nickel atoms (solvated metal atom dispersed or SMAD). Catalysts were prepared on MgO, Al/sub 2/O/sub 3/, SiO/sub 2/, and carbon, and their activities were tested for hydrogenolysis of methylcyclopentane, hydrogenation of toluene, dehydrogenation of isopropyl alcohol, and methanation of carbon monoxide. Conventional catalysts were also studied and compared with the SMAD systems. The effect of the support on SMAD catalyst activities was minimal for hydrogenolysis of methylcyclopentane, hydrogenation of toluene, and dehydration of isopropyl alcohol. However, conventional catalysts showed a significant effect of support when these reactions were studied. This difference between SMAD and conventional catalysts is attributed to the presence of an insulating layer of carbonaceous species between Ni and the support in the SMAD systems. Conversely, catalyst activity for methanation of carbon monoxide was significantly affected by support, especially MgO. This phenomenon reflects a synergistic effect of MgO when Ni is present, where CO can be adsorbed readily on MgO which apparently aids in the initial CO reduction step. The SMAD method in combination with high surface area supports yields highly dispersed catalysts with very small particle sizes. Carbon, a support with a particularly high surface area, allows formation of the smallest particle sizes, and this phenomenon is believed to indicate a direct dependency ofmetal particle size on the surface area of the support. The implications of this finding on the mechanism of particle formation are discussed, as well as the observation of optimum nickel particle size effects for the reactions studied. 5 figures, 4 tables.
Benedé, Juan L; Chisvert, Alberto; Giokas, Dimosthenis L; Salvador, Amparo
2014-10-01
A novel microextraction technique combining the principles of stir bar sorptive extraction (SBSE) and dispersive micro-solid phase extraction (DμSPE) is presented. The main feature of the method is the use of a neodymium-core stirring bar physically coated with a hydrophobic magnetic nanosorbent. Depending on stirring speed, the magnetic sorbent either acts as a coating material to the stir bar, thus affording extraction alike SBSE, or as a dispersed nanosorbent medium for the collection and extraction of the target analytes, in close analogy to DμSPE. Once the stirring process is finished, the strong magnetic field of the stir bar prevails again and rapidly retrieves the dispersed MNPs. Alike SBSE, the stir bar is collected and the analytes are back-extracted by liquid desorption into an appropriate organic solvent, which is used for analysis. This enrichment technique is easy to prepare since it does not require special surface modification procedures, uses low volumes of non-toxic organic solvents and most importantly imbues SBSE with additional functionalities against a wide range of analytes (since nanosorbents with various coatings can be employed) while it affords additional merits to DμSPE in terms of extraction and post-extraction treatment. As proof-of-concept this new approach was applied to the determination of organic UV filters in seawater samples using oleic acid-coated cobalt ferrite (CoFe2O4@oleic acid) magnetic nanoparticles as sorbent material. The method showed good analytical features in terms of linearity, enrichment factors (11-148), limits of detection (low ngmL(-1)), intra- and inter-day repeatability (RSD<11%) and relative recoveries (87-120%). PMID:25173996
Dispersion-tailored active-fiber solitons
NASA Astrophysics Data System (ADS)
van Tartwijk, Guido H. M.; Essiambre, René-Jean; Agrawal, Govind P.
1996-12-01
We show analytically that tailoring the fiber dispersion appropriately can cause optical solitons to propagate unperturbed, without emission of dispersive waves, in a distributed-gain fiber amplifier with a nonuniform gain profile. We apply our scheme to a bidirectionally pumped fiber amplifier and discuss the importance of higher-order nonlinear and dispersive effects for short solitons.
Dark- and bright-rogue-wave solutions for media with long-wave-short-wave resonance.
Chen, Shihua; Grelu, Philippe; Soto-Crespo, J M
2014-01-01
Exact explicit rogue-wave solutions of intricate structures are presented for the long-wave-short-wave resonance equation. These vector parametric solutions feature coupled dark- and bright-field counterparts of the Peregrine soliton. Numerical simulations show the robustness of dark and bright rogue waves in spite of the onset of modulational instability. Dark fields originate from the complex interplay between anomalous dispersion and the nonlinearity driven by the coupled long wave. This unusual mechanism, not available in scalar nonlinear wave equation models, can provide a route to the experimental realization of dark rogue waves in, for instance, negative index media or with capillary-gravity waves. PMID:24580164
Novotny, Laura A.; Jurcisek, Joseph A.; Ward, Michael O.; Jordan, Zachary B.; Goodman, Steven D.; Bakaletz, Lauren O.
2015-01-01
Summary Despite resulting in a similar overall outcome, unlike antibodies directed against the DNABII protein, integration host factor (IHF), which induce catastrophic structural collapse of biofilms formed by nontypeable Haemophilus influenzae (NTHI), those directed against a recombinant soluble form of PilA [the majority subunit of Type IV pili (Tfp) produced by NTHI], mediated gradual ‘top-down’ dispersal of NTHI from biofilms. This dispersal occurred via a mechanism that was dependent upon expression of both PilA (and by inference, Tfp) and production of AI-2 quorum signaling molecules by LuxS. The addition of rsPilA to a biofilm-targeted therapeutic vaccine formulation comprised of IHF plus the powerful adjuvant dmLT, and delivered via a non-invasive transcutaneous immunization route, induced an immune response that targeted two important determinants essential for biofilm formation by NTHI. This resulted in significantly earlier eradication of NTHI from both planktonic and adherent populations in the middle ear, disruption of mucosal biofilms already resident within middle ears prior to immunization, and rapid resolution of signs of disease in an animal model of experimental otitis media. These data support continued development of this novel combinatorial immunization approach for resolution and/or prevention of multiple diseases of the respiratory tract caused by NTHI. PMID:25597921
Novotny, Laura A; Jurcisek, Joseph A; Ward, Michael O; Jordan, Zachary B; Goodman, Steven D; Bakaletz, Lauren O
2015-04-01
Despite resulting in a similar overall outcome, unlike antibodies directed against the DNABII protein, integration host factor (IHF), which induce catastrophic structural collapse of biofilms formed by nontypeable Haemophilus influenzae (NTHI), those directed against a recombinant soluble form of PilA [the majority subunit of Type IV pili (Tfp) produced by NTHI], mediated gradual 'top-down' dispersal of NTHI from biofilms. This dispersal occurred via a mechanism that was dependent upon expression of both PilA (and by inference, Tfp) and production of AI-2 quorum signaling molecules by LuxS. The addition of rsPilA to a biofilm-targeted therapeutic vaccine formulation comprised of IHF plus the powerful adjuvant dmLT and delivered via a noninvasive transcutaneous immunization route induced an immune response that targeted two important determinants essential for biofilm formation by NTHI. This resulted in significantly earlier eradication of NTHI from both planktonic and adherent populations in the middle ear, disruption of mucosal biofilms already resident within middle ears prior to immunization and rapid resolution of signs of disease in an animal model of experimental otitis media. These data support continued development of this novel combinatorial immunization approach for resolution and/or prevention of multiple diseases of the respiratory tract caused by NTHI. PMID:25597921
Self-channeling of ultrashort laser pulses in materials with anomalous dispersion
NASA Astrophysics Data System (ADS)
Bergé, L.; Skupin, S.
2005-06-01
The nonlinear dynamics of femtosecond optical pulses propagating in solid media with anomalous group-velocity dispersion (GVD) is investigated. A map fixing the boundaries of collapse or noncollapse regimes for high-power beams versus the relative strength of GVD is first established. Next, from a nonlinear Schrödinger model accounting for higher-order dispersion, self-steepening, and plasma generation, the possibility of producing extended collapse events that promote a long self-guiding is confirmed, in agreement with recent experiments [K.D. Moll and A.L. Gaeta, Opt. Lett. 29, 995 (2004)]. Three-dimensional collapsing pulses are shown to propagate by emitting quasiperiodically bursts of temporally compressed light bullets, with durations close to the single cycle limit.
Benedé, Juan L; Chisvert, Alberto; Giokas, Dimosthenis L; Salvador, Amparo
2016-07-01
A new and sensitive analytical method based on the recently developed approach termed stir bar-sorptive dispersive microextraction (SBSDME) using a magnetic CoFe2O4@SiO2-nylon 6 composite as sorbent material is presented for the extraction of hydrophilic organic compounds. The simultaneous determination of four hydrophilic UV filters in environmental water samples has been chosen as a model analytical application due to the increasing awareness regarding the occurrence of sunscreen residuals in natural waters. The developed SBSDME approach combines the principles and benefits of stir bar sorptive extraction (SBSE) and dispersive solid phase extraction (DSPE) but allows for lower extraction time and easier post-extraction treatment. Moreover, most importantly, it enables the use of new magnetic materials that affords higher versatility and can be tailored to the needs of the analysis. The main experimental parameters involved in the SBSDME process (i.e. composite amount, extraction time, pH, ionic strength, desorption solvent and desorption time) were evaluated to provide the best enrichment factors. Under the optimized conditions, the method was successfully validated showing good linearity, enrichment factors between 105 and 145 depending on the analyte, limits of detection and quantification in the low ng mL(-1) range (1.6-2.9 ng mL(-1) and 5.4-9.6 ng mL(-1), respectively) and good intra- and inter-day repeatability (RSD < 13%). The developed method was applied to the analysis of water samples of different origin (sea, river and swimming pool). Relative recovery values ranged between 90 and 115%, thus showing that the matrices under consideration do not affect the extraction process. PMID:27216394
NASA Astrophysics Data System (ADS)
Yang, Bin; Zhong, Wei-Ping; Belić, Milivoj R.
2010-05-01
We study analytically and numerically the propagation of spatial solitons in a two-dimensional strongly nonlocal nonlinear medium. Exact analytical solutions in the form of self-similar spatial solitons are obtained involving higher-order Hermite-Gaussian functions. Our theoretical predictions provide new insights into the low-energy spatial soliton transmission with high fidelity.
NASA Astrophysics Data System (ADS)
Jacobs, Verne
2016-05-01
Semi-classical and quantum-field descriptions for the interaction of light with matter are systematically discussed. Applications of interest include resonant pump-probe optical phenomena, such as electromagnetically induced transparency. In the quantum-mechanical description of matter systems, we introduce a general reduced-density-matrix framework. Time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations are developed in a unified and self-consistent manner, using a Liouville-space operator representation. In the semi-classical description, the electromagnetic field is described as a classical field satisfying the Maxwell equations. Compact Liouville-space operator expressions are derived for the linear and the general (n'th order) non-linear electromagnetic-response tensors describing moving many-electron systems. The tetradic matrix elements of the Liouville-space self-energy operators are evaluated for environmental collisional and radiative interactions. The quantized-field approach is essential for a fully self-consistent quantum-mechanical description. Work supported by the Office of Naval Research through the Basic Research Program at The Naval Research Laboratory.
Nonlinear heat conduction with combustion
Galaktionov, V.A.; Kurclyumov, S.P.; Samarskiv, A.A. )
1991-01-01
This paper deals with a study of the properties of high-intensity combustion of a solid nonlinear heat conducting medium which is described by the quasilinear parabolic-type equation for nonlinear heat conduction with a source. The paper summarizes a significant range of investigations dealing with the study of high-intensity thermal processes in solid nonlinear media carried out by the authors in the past decade.
NASA Astrophysics Data System (ADS)
Chen, Yi-Xiang; Xu, Zhou-Xiang; Jiang, Yun-Feng; Shi, Jin; Xu, Fang-Qian
2015-07-01
We obtain exact spatial localized mode solutions of a (2+1)-dimensional nonlinear Schrödinger equation with constant diffraction and cubic-quintic nonlinearity in Script PScript T-symmetric potential, and study the linear stability of these solutions. Based on these results, we further derive exact spatial localized mode solutions in a cubic-quintic medium with harmonic and Script PScript T-symmetric potentials. Moreover, the dynamical behaviors of spatial localized modes in the exponential diffraction decreasing waveguide and the periodic distributed amplification system are investigated. Supported by the Project of Technology Office in Zhejiang Province under Grant No. 2014C32006, the Special Foundation for theoretical physics Research Program of China under Grant No. 11447124, National Natural Science Foundation of China under Grant No. 11374254 and the Higher School Visiting Scholar Development under Grant No. FX2013103
NASA Astrophysics Data System (ADS)
Cherkasskii, M. A.; Nikitin, A. A.; Kalinikos, B. A.
2016-04-01
A theory is developed to describe the wave processes that occur in waveguide media having several types of nonlinearity, specifically, multinonlinear media. It is shown that the nonlinear Schrödinger equation can be used to describe the general wave process that occurs in such media. The competition between the electric wave nonlinearity and the magnetic wave nonlinearity in a layered multinonlinear ferrite-ferroelectric structure is found to change a total repulsive nonlinearity into a total attractive nonlinearity.
NASA Astrophysics Data System (ADS)
Vinogradova, O. P.; Ostrosablina, A. A.; Sidorov, A. I.
2006-02-01
This paper presents the experimental and theoretical results of a study of the interaction of pulsed laser radiation with thick composite media containing nanoparticles of vanadium dioxide (VO2). It is established that the reversible semiconductor-metal phase transition that occurs in the VO2 nanoparticles under the action of radiation can produce self-focusing of the mid-IR radiation by the formation of a photoinduced dynamic lens. An analysis is carried out of how the radiation intensity affects the dynamics of the given process.
New avenues for phase matching in nonlinear hyperbolic metamaterials.
Duncan, C; Perret, L; Palomba, S; Lapine, M; Kuhlmey, B T; de Sterke, C Martijn
2015-01-01
Nonlinear optical processes, which are of paramount importance in science and technology, involve the generation of new frequencies. This requires phase matching to avoid that light generated at different positions interferes destructively. Of the two original approaches to achieve this, one relies on birefringence in optical crystals, and is therefore limited by the dispersion of naturally occurring materials, whereas the other, quasi-phase-matching, requires direct modulation of material properties, which is not universally possible. To overcome these limitations, we propose to exploit the unique dispersion afforded by hyperbolic metamaterials, where the refractive index can be arbitrarily large. We systematically analyse the ensuing opportunities and demonstrate that hyperbolic phase matching can be achieved with a wide range of material parameters, offering access to the use of nonlinear media for which phase matching cannot be achieved by other means. With the rapid development in the fabrication of hyperbolic metamaterials, our approach is destined to bring significant advantages over conventional techniques for the phase matching of a variety of nonlinear processes. PMID:25757863
Migration of dispersive GPR data
Powers, M.H.; Oden, C.P.
2004-01-01
Electrical conductivity and dielectric and magnetic relaxation phenomena cause electromagnetic propagation to be dispersive in earth materials. Both velocity and attenuation may vary with frequency, depending on the frequency content of the propagating energy and the nature of the relaxation phenomena. A minor amount of velocity dispersion is associated with high attenuation. For this reason, measuring effects of velocity dispersion in ground penetrating radar (GPR) data is difficult. With a dispersive forward model, GPR responses to propagation through materials with known frequency-dependent properties have been created. These responses are used as test data for migration algorithms that have been modified to handle specific aspects of dispersive media. When either Stolt or Gazdag migration methods are modified to correct for just velocity dispersion, the results are little changed from standard migration. For nondispersive propagating wavefield data, like deep seismic, ensuring correct phase summation in a migration algorithm is more important than correctly handling amplitude. However, the results of migrating model responses to dispersive media with modified algorithms indicate that, in this case, correcting for frequency-dependent amplitude loss has a much greater effect on the result than correcting for proper phase summation. A modified migration is only effective when it includes attenuation recovery, performing deconvolution and migration simultaneously.
Fractal scattering of Gaussian solitons in directional couplers with logarithmic nonlinearities
NASA Astrophysics Data System (ADS)
Teixeira, Rafael M. P.; Cardoso, Wesley B.
2016-08-01
In this paper we study the interaction of Gaussian solitons in a dispersive and nonlinear media with log-law nonlinearity. The model is described by the coupled logarithmic nonlinear Schrödinger equations, which is a nonintegrable system that allows the observation of a very rich scenario in the collision patterns. By employing a variational approach and direct numerical simulations, we observe a fractal-scattering phenomenon from the exit velocities of each soliton as a function of the input velocities. Furthermore, we introduce a linearization model to identify the position of the reflection/transmission window that emerges within the chaotic region. This enables us the possibility of controlling the scattering of solitons as well as the lifetime of bound states.
Calculations of precursor propagation in dispersive dielectrics.
Bacon, Larry Donald
2003-08-01
The present study is a numerical investigation of the propagation of electromagnetic transients in dispersive media. It considers propagation in water using Debye and composite Rocard-Powles-Lorentz models for the complex permittivity. The study addresses this question: For practical transmitted spectra, does precursor propagation provide any features that can be used to advantage over conventional signal propagation in models of dispersive media of interest? A companion experimental study is currently in progress that will attempt to measure the effects studied here.
On the Nonlinear Effects in Focused Ultrasound Beams with Frequency Power Law Attenuation
NASA Astrophysics Data System (ADS)
Jiménez, N.; Redondo, J.; Sánchez-Morcillo, V.; Iglesias, P. C.; Camarena, F.
When finite amplitude ultrasound propagation is considered, changes in spatial features of focused ultrasound beams can be observed. These nonlinear effects typically appear in thermoviscous fluids as focal displacements, beam-width variations or gain changes. However, in soft-tissue media, the frequency dependence of the attenuation doesn't obey a squared law. In this way, these complex media response leads to weak dispersion that prevents the cumulative processes of energy transfer to higher harmonics. In this work we explore the influence of different frequency power law attenuation responses and its influence on the self-defocusing effects in focused ultrasound beams. Thus, we numerically explore the spatial field distributions produced by low-Fresnel number devices and High Intensity Focused Ultrasound (HIFU) radiating trough different soft-tissue media.
NASA Technical Reports Server (NTRS)
Lee, M. A.; Lerche, I.
1974-01-01
Study illustrating how the presence of a high-intensity pulse of radiation can distort its own passage through a plane differentially shearing medium. It is demonstrated that the distortion is a sensitive function of the precise, and detailed, variation of the medium's refractive index by considering a couple of simple examples which are worked out numerically. In view of the high-intensity pulses observed from pulsars (approximately 10 to the 30th ergs per pulse), it is believed that the present calculations are of more than academic interest in helping unravel the fundamental properties of pulse production in, and propagating through, differentially sheared media - such as pulsars' magnetospheres within the so-called speed-of-light circle.
``Once Nonlinear, Always Nonlinear''
NASA Astrophysics Data System (ADS)
Blackstock, David T.
2006-05-01
The phrase "Once nonlinear, always nonlinear" is attributed to David F. Pernet. In the 1970s he noticed that nonlinearly generated higher harmonic components (both tones and noise) don't decay as small signals, no matter how far the wave propagates. Despite being out of step with the then widespread notion that small-signal behavior is restored in "old age," Pernet's view is supported by the Burgers-equation solutions of the early 1960s. For a plane wave from a sinusoidally vibrating source in a thermoviscous fluid, the old-age decay of the nth harmonic is e-nαx, not e-n2αx (small-signal expectation), where α is the absorption coefficient at the fundamental frequency f and x is propagation distance. Moreover, for spherical waves (r the distance) the harmonic diminishes as e-nαx/rn, not e-n2αx/r. While not new, these results have special application to aircraft noise propagation, since the large propagation distances of interest imply old age. The virtual source model may be used to explain the "anomalous" decay rates. In old age most of the nth harmonic sound comes from virtual sources close to the receiver. Their strength is proportional to the nth power of the local fundamental amplitude, and that sets the decay law for the nth harmonic.
Dissipative effects in nonlinear Klein-Gordon dynamics
NASA Astrophysics Data System (ADS)
Plastino, A. R.; Tsallis, C.
2016-03-01
We consider dissipation in a recently proposed nonlinear Klein-Gordon dynamics that admits exact time-dependent solutions of the power-law form e_qi(kx-wt) , involving the q-exponential function naturally arising within the nonextensive thermostatistics (e_qz \\equiv [1+(1-q)z]1/(1-q) , with e_1^z=ez ). These basic solutions behave like free particles, complying, for all values of q, with the de Broglie-Einstein relations p=\\hbar k , E=\\hbar ω and satisfying a dispersion law corresponding to the relativistic energy-momentum relation E2 = c^2p2 + m^2c4 . The dissipative effects explored here are described by an evolution equation that can be regarded as a nonlinear generalization of the celebrated telegraph equation, unifying within one single theoretical framework the nonlinear Klein-Gordon equation, a nonlinear Schrödinger equation, and the power-law diffusion (porous-media) equation. The associated dynamics exhibits physically appealing traveling solutions of the q-plane wave form with a complex frequency ω and a q-Gaussian square modulus profile.
Fractional power-law spatial dispersion in electrodynamics
Tarasov, Vasily E.; Trujillo, Juan J.
2013-07-15
Electric fields in non-local media with power-law spatial dispersion are discussed. Equations involving a fractional Laplacian in the Riesz form that describe the electric fields in such non-local media are studied. The generalizations of Coulomb’s law and Debye’s screening for power-law non-local media are characterized. We consider simple models with anomalous behavior of plasma-like media with power-law spatial dispersions. The suggested fractional differential models for these plasma-like media are discussed to describe non-local properties of power-law type. -- Highlights: •Plasma-like non-local media with power-law spatial dispersion. •Fractional differential equations for electric fields in the media. •The generalizations of Coulomb’s law and Debye’s screening for the media.
Coherent quantum effects through dispersive bosonic media
Ye Saiyun; Yang Zhenbiao; Zheng Shibiao; Serafini, Alessio
2010-07-15
The coherent evolution of two qubits mediated by a set of bosonic field modes is investigated. By assuming a specific asymmetric encoding of the quantum states in the internal levels of the qubits, we show that entangling quantum gates can be realized, with high fidelity, even when a large number of mediating modes is involved. The effect of losses and imperfections on the gates' operation is also considered in detail.
Shen, Y.R.; Chen, C.K.; de Castro, A.R.B.
1980-01-01
Surface electromagnetic waves are waves propagating along the interface of two media. Their existence was predicted by Sommerfield in 1909. In recent years, interesting applications have been found in the study of overlayers and molecular adsorption on surfaces, in probing of phase transitions, and in measurements of refractive indices. In the laboratory, the nonlinear interaction of surface electromagnetic waves were studied. The preliminary results of this recent venture in this area are presented.
ERIC Educational Resources Information Center
Budiansky, Stephen
1980-01-01
This article discusses the need for more accurate and complete input data and field verification of the various models of air pollutant dispension. Consideration should be given to changing the form of air quality standards based on enhanced dispersion modeling techniques. (Author/RE)
Asphaltene dispersants as demulsification aids
Manek, M.B.
1995-11-01
Destabilization of petroleum asphaltenes may cause a multitude of problems in crude oil recovery and production. One major problem is their agglomeration at the water-oil interface of crude oil emulsions. Once agglomeration occurs, destabilized asphaltenes can form a thick pad in the dehydration equipment, which significantly reduces the demulsification rate. Certain polymeric dispersants increase asphaltene solubilization in hydrocarbon media, and when used in conjunction with emulsion breakers, facilitate the demulsification process. Two case studies are presented that demonstrate how asphaltene dispersants can efficiently inhibit pad formation and help reduce demulsifier dosage. Criteria for dispersant application and selection are discussed, which include the application of a novel laboratory technique to assess asphaltene stabilization in the crude oil. The technique monitors asphaltene agglomeration while undergoing titration with an incompatible solvent (precipitant). The method was used to evaluate stabilization of asphaltenes in the crude oil and to screen asphaltene dispersants.
NASA Astrophysics Data System (ADS)
Eringen, A. Cemal; Maugin, Gerard A.
A unified approach is presented to the nonlinear continuum theory of deformable and fluent media subject to electromagnetic and thermal loads. Basic laws are used to establish the macroscopic electromagnetic theory are treated from first principles and nonlinear constitutive equations for large fields are developed. Many solutions of linear and nonlinear problems in the field of rigid media, elastic dielectrics, piezoelecticity, magnetoelasticity, ferromagnets, and magnetohydrodynamics are discussed. Applications are extended to ferrofluids, electrodynamics, memory-dependent materials, nonlocal theories, and relativistic continua.
Eringen, A.C.; Maugin, G.A.
1990-01-01
A unified approach is presented to the nonlinear continuum theory of deformable and fluent media subject to electromagnetic and thermal loads. Basic laws are used to establish the macroscopic electromagnetic theory are treated from first principles and nonlinear constitutive equations for large fields are developed. Many solutions of linear and nonlinear problems in the field of rigid media, elastic dielectrics, piezoelectricity, magnetoelasticity, ferromagnets, and magnetohydrodynamics are discussed. Applications are extended to ferrofluids, electrodynamics, memory-dependent materials, nonlocal theories, and relativistic continua.
Hata, Shigefumi; Nakao, Hiroya; Mikhailov, Alexander S.
2014-01-01
As shown by Alan Turing in 1952, differential diffusion may destabilize uniform distributions of reacting species and lead to emergence of patterns. While stationary Turing patterns are broadly known, the oscillatory instability, leading to traveling waves in continuous media and sometimes called the wave bifurcation, remains less investigated. Here, we extend the original analysis by Turing to networks and apply it to ecological metapopulations with dispersal connections between habitats. Remarkably, the oscillatory Turing instability does not lead to wave patterns in networks, but to spontaneous development of heterogeneous oscillations and possible extinction of species. We find such oscillatory instabilities for all possible food webs with three predator or prey species, under various assumptions about the mobility of individual species and nonlinear interactions between them. Hence, the oscillatory Turing instability should be generic and must play a fundamental role in metapopulation dynamics, providing a common mechanism for dispersal-induced destabilization of ecosystems. PMID:24394959
Hata, Shigefumi; Nakao, Hiroya; Mikhailov, Alexander S
2014-01-01
As shown by Alan Turing in 1952, differential diffusion may destabilize uniform distributions of reacting species and lead to emergence of patterns. While stationary Turing patterns are broadly known, the oscillatory instability, leading to traveling waves in continuous media and sometimes called the wave bifurcation, remains less investigated. Here, we extend the original analysis by Turing to networks and apply it to ecological metapopulations with dispersal connections between habitats. Remarkably, the oscillatory Turing instability does not lead to wave patterns in networks, but to spontaneous development of heterogeneous oscillations and possible extinction of species. We find such oscillatory instabilities for all possible food webs with three predator or prey species, under various assumptions about the mobility of individual species and nonlinear interactions between them. Hence, the oscillatory Turing instability should be generic and must play a fundamental role in metapopulation dynamics, providing a common mechanism for dispersal-induced destabilization of ecosystems. PMID:24394959
NASA Astrophysics Data System (ADS)
Hata, Shigefumi; Nakao, Hiroya; Mikhailov, Alexander S.
2014-01-01
As shown by Alan Turing in 1952, differential diffusion may destabilize uniform distributions of reacting species and lead to emergence of patterns. While stationary Turing patterns are broadly known, the oscillatory instability, leading to traveling waves in continuous media and sometimes called the wave bifurcation, remains less investigated. Here, we extend the original analysis by Turing to networks and apply it to ecological metapopulations with dispersal connections between habitats. Remarkably, the oscillatory Turing instability does not lead to wave patterns in networks, but to spontaneous development of heterogeneous oscillations and possible extinction of species. We find such oscillatory instabilities for all possible food webs with three predator or prey species, under various assumptions about the mobility of individual species and nonlinear interactions between them. Hence, the oscillatory Turing instability should be generic and must play a fundamental role in metapopulation dynamics, providing a common mechanism for dispersal-induced destabilization of ecosystems.
ERIC Educational Resources Information Center
Vennebush, G. Patrick
2004-01-01
Media Clips aims to offer readers contemporary, authentic applications of quantitative reasoning based on print or electronic media. Clips may be in text or graphic format, and clip sources may be either print or electronic media.
NASA Technical Reports Server (NTRS)
Frost, W.; Christensen, L. S.; Collins, F. G.; Camp, D. W.
1980-01-01
A study of economically viable techniques for dispersing warm fog at commercial airports is presented. Five fog dispersion techniques are examined: evaporation suppression, downwash, mixing, seeding with hygroscopic material, thermal techniques, and charged particle techniques. Thermal techniques, although effective, were found to be too expensive for routine airport operations, and detrimental to the environment. Seeding or helicopter downwash are practical for small-scale or temporary fog clearing, but are probably not useful for airport operations on a routine basis. Considerable disagreement exists on the capability of charged particle techniques, which stems from the fact that different assumptions and parameter values are used in the analytical models. Recommendations resulting from the review of this technique are listed, and include: experimental measurements of the parameters in question; a study to ascertain possible safety hazards, such as increased electrical activity or fuel ignition during refueling operations which could render charged particle techniques impractical; and a study of a single charged particle generator.
NASA Astrophysics Data System (ADS)
Yang, Desen; Zhang, Haoyang; Shi, Shengguo; Li, Di; Shi, Jie; Hu, Bo
2015-10-01
The propagation of plane acoustic waves can be investigated by taking advantage of the electro-acoustical analogy between the one-dimensional acoustic waveguide and the electrical transmission line, because they share the same type of equation. This paper follow the previous studies and expand the analogy into the cases of quadratic nonlinearity and dispersion produced by relaxation process. From the basic equations relating acoustic pressure, density fluctuation and velocity, which are valid for the nonlinear and relaxing media, the equivalent travelling-wave circuits of one-dimensional acoustic waveguide with the consideration of nonlinearity and relaxation processes are obtained. Furthermore, we also discuss the analogy relationship of parameters which exist in the acoustical and electrical systems.
Dispersive tristability in microring resonators.
Dumeige, Yannick; Féron, Patrice
2005-12-01
Combining a transfer matrix analysis and slowly varying envelope approximation, we propose a simple method to describe steady states associated with dispersive multistability in coupled microring resonators. This approach allows us to consider nonlinear interactions between independent forward and backward propagative fields. We applied this simple formalism first to decrease the tristability intensity threshold in linearly coupled resonators and second to optically control the tristable behavior in a single microring resonator. PMID:16486080
NASA Astrophysics Data System (ADS)
Colin, M.; Di Menza, L.; Saut, J. C.
2016-03-01
In this paper, we investigate the properties of solitonic structures arising in quadratic media. First, we recall the derivation of systems governing the interaction process for waves propagating in such media and we check the local and global well-posedness of the corresponding Cauchy problem. Then, we look for stationary states in the context of normal or anomalous dispersion regimes, that lead us to either elliptic or non-elliptic systems and we address the problem of orbital stability. Finally, some numerical experiments are carried out in order to compute localized states for several regimes and to study dynamic stability as well as long-time asymptotics.
Strasburger, Victor C
2010-11-01
The American Academy of Pediatrics recognizes that exposure to mass media (eg, television, movies, video and computer games, the Internet, music lyrics and videos, newspapers, magazines, books, advertising) presents health risks for children and adolescents but can provide benefits as well. Media education has the potential to reduce the harmful effects of media and accentuate the positive effects. By understanding and supporting media education, pediatricians can play an important role in reducing harmful effects of media on children and adolescents. PMID:20876180
Anomalous dispersions of `hedgehog' particles
NASA Astrophysics Data System (ADS)
Bahng, Joong Hwan; Yeom, Bongjun; Wang, Yichun; Tung, Siu On; Hoff, J. Damon; Kotov, Nicholas
2015-01-01
Hydrophobic particles in water and hydrophilic particles in oil aggregate, but can form colloidal dispersions if their surfaces are chemically camouflaged with surfactants, organic tethers, adsorbed polymers or other particles that impart affinity for the solvent and increase interparticle repulsion. A different strategy for modulating the interaction between a solid and a liquid uses surface corrugation, which gives rise to unique wetting behaviour. Here we show that this topographical effect can also be used to disperse particles in a wide range of solvents without recourse to chemicals to camouflage the particles' surfaces: we produce micrometre-sized particles that are coated with stiff, nanoscale spikes and exhibit long-term colloidal stability in both hydrophilic and hydrophobic media. We find that these `hedgehog' particles do not interpenetrate each other with their spikes, which markedly decreases the contact area between the particles and, therefore, the attractive forces between them. The trapping of air in aqueous dispersions, solvent autoionization at highly developed interfaces, and long-range electrostatic repulsion in organic media also contribute to the colloidal stability of our particles. The unusual dispersion behaviour of our hedgehog particles, overturning the notion that like dissolves like, might help to mitigate adverse environmental effects of the use of surfactants and volatile organic solvents, and deepens our understanding of interparticle interactions and nanoscale colloidal chemistry.
Spectral Hole Burning via Kerr Nonlinearity
NASA Astrophysics Data System (ADS)
Khan, Anwar Ali; Abdul Jabar, M. S.; Jalaluddin, M.; Bacha, Bakht Amin; Iftikhar, Ahmad
2015-10-01
Spectral hole burning is investigated in an optical medium in the presence of Doppler broadening and Kerr nonlinearity. The Kerr nonlinearity generates coherent hole burning in the absorption spectrum. The higher order Kerr nonlinearity enhances the typical lamb dip of the hole. Normal dispersion in the hole burning region while Steep anomalous dispersion between the two hole burning regions also enhances with higher order Kerr effect. A large phase shift creates large delay or advancement in the pulse propagation while no distortion is observed in the pulse. These results provide significant steps to improve optical memory, telecom devices, preservation of information and image quality. Supported by Higher Education Commission (HEC) of Pakistan
Anderson localization in metamaterials and other complex media (Review Article)
NASA Astrophysics Data System (ADS)
Gredeskul, Sergey A.; Kivshar, Yuri S.; Asatryan, Ara A.; Bliokh, Konstantin Y.; Bliokh, Yuri P.; Freilikher, Valentin D.; Shadrivov, Ilya V.
2012-07-01
This is a review of some recent (mostly ours) results on Anderson localization of light and electron waves in complex disordered systems, including: (i) left-handed metamaterials, (ii) magnetoactive optical structures, (iii) graphene superlattices, and (iv) nonlinear dielectric media. First, we demonstrate that left-handed metamaterials can significantly suppress localization of light and lead to an anomalously enhanced transmission. This suppression is essential at the long-wavelength limit in the case of normal incidence, at specific angles of oblique incidence (Brewster anomaly), and in vicinity of zero-ɛ or zero-μ frequencies for dispersive metamaterials. Remarkably, in disordered samples comprised of alternating normal and left-handed metamaterials, the reciprocal Lyapunov exponent and reciprocal transmittance increment can differ from each other. Second, we study magnetoactive multilayered structures, which exhibit nonreciprocal localization of light depending on the direction of propagation and on polarization. At resonant frequencies or realizations such nonreciprocity results in effectively unidirectional transport of light. Third, we discuss the analogy between wave propagation through multilayered samples with metamaterials and charge transport in graphene, which provides a simple physical explanation of unusual conductive properties of disordered graphene superlatices. We predict disorder-induced resonance of the transmission coefficient at oblique incidence of Dirac quasiparticles. Finally, we demonstrate that an interplay of nonlinearity and disorder in dielectric media can lead to bistability of individual localized states excited inside the medium at resonant frequencies. This results in nonreciprocity of wave transmission and unidirectional transport of light.
Magnetic particle dispersion in polymer solution
NASA Astrophysics Data System (ADS)
Jeon, Kwang Seoung
Magnetic particle dispersions were prepared in order to observe the effect of particle surface properties, concentration and functional group of binder, milling time, and solvent on dispersion properties. Rheology and transverse susceptibility measurements were used to characterize the dispersion quality of the magnetic paints macroscopically and microscopically, respectively. In this study, by applying the acid-base concept, methods to optimize magnetic dispersions were established. Initially, interaction between acid-base sites on particles and binder was investigated by poisoning the sites with chemicals, then quantifying each type of adsorption (hydrogen and chemical adsorption) using thermogravimetric analysis. With this fundamental information, effects of typical dispersion parameters were investigated. The acid base interaction between binder solution and particles was related to the magnetic and rheological properties of magnetic inks. The results have significant implications for high density particulate media where dispersion will become increasingly important.
Zinc Oxide Nanocrystals for Non-resonant Nonlinear Optical Microscopy in Biology and Medicine.
Kachynski, Aliaksandr V; Kuzmin, Andrey N; Nyk, Marcin; Roy, Indrajit; Prasad, Paras N
2008-07-24
In this paper we show that biocompatible zinc oxide (ZnO) nanocrystals (NCs) having non-centrosymmetric structure can be used as non-resonant nonlinear optical probes for targeting in bioimaging applications in vitro by use of the second order processes of second harmonic and sum frequency generation, as well as the third order process of four wave mixing. These non-resonant processes provide advantages above and beyond traditional two-photon bioimaging: (i) the probes do not photo-bleach; (ii) the input wavelength can be judiciously selected; and (iii) no heat is dissipated into the cells, ensuring longer cell viability and ultimately longer imaging times. ZnO NCs have been synthesized in organic media by using a non-hydrolytic sol-gel process, and subsequently dispersed in aqueous media using phospholipid micelles, and incorporated with the biotargeting molecule folic acid (FA). Sum Frequency, Second Harmonic and non-resonant four wave mixing non-linear signals from this stable dispersion of ZnO NCs, targeted to the live tumor (KB) cells were used for imaging. Robust intracellular accumulation of the targeted (FA incorporated) ZnO nanocrystals could be observed, without any indication of cytotoxicity. PMID:19633706
Continuous control of the nonlinearity phase for harmonic generations.
Li, Guixin; Chen, Shumei; Pholchai, Nitipat; Reineke, Bernhard; Wong, Polis Wing Han; Pun, Edwin Yue Bun; Cheah, Kok Wai; Zentgraf, Thomas; Zhang, Shuang
2015-06-01
The capability of locally engineering the nonlinear optical properties of media is crucial in nonlinear optics. Although poling is the most widely employed technique for achieving locally controlled nonlinearity, it leads only to a binary nonlinear state, which is equivalent to a discrete phase change of π in the nonlinear polarizability. Here, inspired by the concept of spin-rotation coupling, we experimentally demonstrate nonlinear metasurfaces with homogeneous linear optical properties but spatially varying effective nonlinear polarizability with continuously controllable phase. The continuous phase control over the local nonlinearity is demonstrated for second and third harmonic generation by using nonlinear metasurfaces consisting of nanoantennas of C3 and C4 rotational symmetries, respectively. The continuous phase engineering of the effective nonlinear polarizability enables complete control over the propagation of harmonic generation signals. Therefore, this method seamlessly combines the generation and manipulation of harmonic waves, paving the way for highly compact nonlinear nanophotonic devices. PMID:25849530
Dispersion in tidally averaged transport equation
Cheng, R.T.; Casulli, V.
1992-01-01
A general governing inter-tidal transport equation for conservative solutes has been derived without invoking the weakly nonlinear approximation. The governing inter-tidal transport equation is a convection-dispersion equation in which the convective velocity is a mean Lagrangian residual current, and the inter-tidal dispersion coefficient is defined by a dispersion patch. When the weakly nonlinear condition is violated, the physical significance of the Stokes' drift, as used in tidal dynamics, becomes questionable. For nonlinear problems, analytical solutions for the mean Lagrangian residual current and for the inter-tidal dispersion coefficient do not exist, they must be determined numerically. A rectangular tidal inlet with a constriction is used in the first example. The solutions of the residual currents and the computed properties of the inter-tidal dispersion coefficient are used to illuminate the mechanisms of the inter-tidal transport processes. Then, the present formulation is tested in a geometrically complex tidal estuary – San Francisco Bay, California. The computed inter-tidal dispersion coefficients are in the range between 5×104 and 5×106 cm2/sec., which are consistent with the values reported in the literature
URANIUM BISMUTHIDE DISPERSION IN MOLTEN METAL
Teitel, R.J.
1959-10-27
The formation of intermetallic bismuth compounds of thorium or uranium dispersed in a liquid media containing bismuth and lead is described. A bismuthide of uranium dispersed in a liquid metal medium is formed by dissolving uranium in composition of lead and bismuth containing less than 80% lead and lowering the temperature of the composition to a temperature below the point at which the solubility of uranium is exceeded and above the melting point of the composition.
NASA Astrophysics Data System (ADS)
Russel, W. B.; Saville, D. A.; Schowalter, W. R.
1992-03-01
The book covers the physical side of colloid science from the individual forces acting between submicron particles suspended in a liquid through the resulting equilibrium and dynamic properties. The relevant forces include Brownian motion, electrostatic repulsion, dispersion attraction, both attraction and repulsion due to soluble polymer, and viscous forces due to relative motion between the particles and the liquid. The balance among Brownian motion and the interparticle forces decides the questions of stability and phase behavior. Imposition of external fields produces complex effects, i.e. electrokinetic phenomena (electric field), sedimentation (gravitational field), diffusion (concentration/chemical potential gradient), and non-Newtonian rheology (shear field). The treatment aims to impart a sound, quantitative understanding based on fundamental theory and experiments with well-characterized model systems. This broad grasp of the fundamentals lends insight and helps to develop the intuitive sense needed to isolate essential features of technological problems and design critical experiments. Some exposure to fluid mechanics, statistical mechanics, and electricity and magnetism is assumed, but each subject is reintroduced in a self-contained manner.
ERIC Educational Resources Information Center
Downtown Business Quarterly, 1998
1998-01-01
This theme issue explores lower Manhattan's burgeoning "New Media" industry, a growing source of jobs in lower Manhattan. The first article, "New Media Manpower Issues" (Rodney Alexander), addresses manpower, training, and workforce demands faced by new media companies in New York City. The second article, "Case Study: Hiring @ Dynamid" (John…
ERIC Educational Resources Information Center
Marklund, Inger, Ed.; Hanse, Mona-Britt, Ed.
1984-01-01
The Swedish Media Panel is a research program about children and young persons and their use of mass media. The aim of the ten-year (1975-1985) project is to explain how media habits originate, how they change as children grow older, what factors on the part of children themselves and in their surroundings may be connected with a certain use of…
Engineering integrable nonautonomous nonlinear Schroedinger equations
He Xugang; Zhao Dun; Li Lin; Luo Honggang
2009-05-15
We investigate Painleve integrability of a generalized nonautonomous one-dimensional nonlinear Schroedinger (NLS) equation with time- and space-dependent dispersion, nonlinearity, and external potentials. Through the Painleve analysis some explicit requirements on the dispersion, nonlinearity, dissipation/gain, and the external potential as well as the constraint conditions are identified. It provides an explicit way to engineer integrable nonautonomous NLS equations at least in the sense of Painleve integrability. Furthermore analytical solutions of this class of integrable nonautonomous NLS equations can be obtained explicitly from the solutions of the standard NLS equation by a general transformation. The result provides a significant way to control coherently the soliton dynamics in the corresponding nonlinear systems, as that in Bose-Einstein condensate experiments. We analyze explicitly the soliton dynamics under the nonlinearity management and the external potentials and discuss its application in the matter-wave dynamics. Some comparisons with the previous works have also been discussed.
Highly dispersive photonic band-gap prism.
Lin, S Y; Hietala, V M; Wang, L; Jones, E D
1996-11-01
We propose the concept of a photonic band-gap (PBG) prism based on two-dimensional PBG structures and realize it in the millimeter-wave spectral regime. We recognize the highly nonlinear dispersion of PBG materials near Brillouin zone edges and utilize the dispersion to achieve strong prism action. Such a PBG prism is very compact if operated in the optical regime, ~20 mm in size for lambda ~ 700 nm, and can serve as a dispersive element for building ultracompact miniature spectrometers. PMID:19881796
Physical models of polarization mode dispersion
Menyuk, C.R.; Wai, P.K.A.
1995-12-31
The effect of randomly varying birefringence on light propagation in optical fibers is studied theoretically in the parameter regime that will be used for long-distance communications. In this regime, the birefringence is large and varies very rapidly in comparison to the nonlinear and dispersive scale lengths. We determine the polarization mode dispersion, and we show that physically realistic models yield the same result for polarization mode dispersion as earlier heuristic models that were introduced by Poole. We also prove an ergodic theorem.
Polariton spectrum in nonlinear dielectric medium.
Dzedolik, Igor V; Karakchieva, Olga
2013-05-01
We obtain theoretically the phonon-polariton spectrum in nonlinear dielectric medium with the third-order Kerr-type nonlinearity. We investigate the dependence of number of the polariton spectrum branches on the intensity of electromagnetic field and demonstrate that the appearance of new branches located in the polariton spectrum gap is caused by the influence of dispersion of the third-order dielectric susceptibility at the intensive electromagnetic field in the medium. The modulation instability of new spectrum branch waves leads to the appearance of the cnoidal waves or solitons. These new nonlinear waves one can use for designing optical devices such as the nonlinear optical filter converter. PMID:23669776
Vortex stabilization by means of spatial solitons in nonlocal media
NASA Astrophysics Data System (ADS)
Izdebskaya, Yana; Krolikowski, Wieslaw; Smyth, Noel F.; Assanto, Gaetano
2016-05-01
We investigate how optical vortices, which tend to be azimuthally unstable in local nonlinear materials, can be stabilized by a copropagating coaxial spatial solitary wave in nonlocal, nonlinear media. We focus on the formation of nonlinear vortex-soliton vector beams in reorientational soft matter, namely nematic liquid crystals, and report on experimental results, as well as numerical simulations.
Guided Waves with and Without Dispersion
NASA Astrophysics Data System (ADS)
Joshi, Narayan R.
2008-02-01
In the application of elastic waves of ultrasonic frequencies for nondestructive evaluations of industrial components and welded structures various types of waves like Rayleigh waves, Surface waves, Longitudinal body waves, Shear body waves, and Lamb waves are used to detect defects in the objects under investigation. In many cases these waves travel in bounded media and are affected by boundaries. Because they are guided by boundaries of objects under investigation, they are called sometimes guided waves or waveguides at other times. Some of these guided waves are dispersive in character while others are nondispersive. Efforts are made here to distinguish between guided waves with dispersion and those without dispersion.
Dispersion Method Using Focused Ultrasonic Field
NASA Astrophysics Data System (ADS)
Kim, Jungsoon; Kim, Moojoon; Ha, Kanglyel; Chu, Minchul
2010-07-01
The dispersion of powders into liquids has become one of the most important techniques in high-tech industries and it is a common process in the formulation of various products, such as paint, ink, shampoo, beverages, and polishing media. In this study, an ultrasonic system with a cylindrical transducer is newly introduced for pure nanoparticle dispersion. The acoustics pressure field and the characteristics of the shock pulse caused by cavitation are investigated. The frequency spectrum of the pulse from the collapse of air bubbles in the cavitation is analyzed theoretically. It was confirmed that a TiO2 water suspension can be dispersed effectively using the suggested system.
Power-law spatial dispersion from fractional Liouville equation
Tarasov, Vasily E.
2013-10-15
A microscopic model in the framework of fractional kinetics to describe spatial dispersion of power-law type is suggested. The Liouville equation with the Caputo fractional derivatives is used to obtain the power-law dependence of the absolute permittivity on the wave vector. The fractional differential equations for electrostatic potential in the media with power-law spatial dispersion are derived. The particular solutions of these equations for the electric potential of point charge in this media are considered.
Forward model nonlinearity versus inverse model nonlinearity
Mehl, S.
2007-01-01
The issue of concern is the impact of forward model nonlinearity on the nonlinearity of the inverse model. The question posed is, "Does increased nonlinearity in the head solution (forward model) always result in increased nonlinearity in the inverse solution (estimation of hydraulic conductivity)?" It is shown that the two nonlinearities are separate, and it is not universally true that increased forward model nonlinearity increases inverse model nonlinearity. ?? 2007 National Ground Water Association.
NASA Astrophysics Data System (ADS)
Naveed, M.; Kawamoto, K.; Hamamoto, S.; Sakaki, T.; Moldrup, P.; Komatsu, T.
2010-12-01
The transport and fate of gases in the soil are governed by gas advection, diffusion and dispersion phenomena. Among three gas transport phenomena, gas dispersion is least understood. Main objective of this study is to investigate the gas dispersion phenomena, emphasising on the effect of moisture content, sand particle shape, particle size, particle size distribution, and scale dependency on gas dispersion. One dimensional laboratory column experiments, in an apparatus consisting of an acrylic column attached to inlet and outlet chambers (Hamamoto et al., SSAJ, 2009), were conducted for the measurements of gas dispersion coefficient (DH). Various types of sands (Narita and Toyoura sands from Japan, and Granusils and Accusands from United States) and glass beads with variable moisture contents were used as porous media. Shape of the sand particles were characterized in terms of sphericity and roundness. The changes in the oxygen concentration within the soil column and in the inlet and outlet chambers were monitored. In addition the air pressure at inlet and middle of the soil column was also monitored to ensure the uniform density of porous media along the column. The measured breakthrough curves were fitted with the analytical solution of the advection dispersion equation to determine dispersion coefficients. The measured dispersion coefficient (DH) showed linear increase with pore velocity (u0). Measured dispersivity (λ= DH/u0) increases with decrease in air filled porosity induced by adding moisture contents in sands. Its values varies from 0 to 3 cm on decreasing air filled porosity from 0.50 (air dry) to 0.25 (field capacity). Shape of the sand particles has no significant effect on gas dispersion. When gas dispersion phenomena was studied on different shape of the sand particles at various air filled porosities, it was found that for angular sand particles initially gas dispersivity increases more rapidly as compared to rounded sand particles and finally
Single-cycle coherent terahertz-pulse propagation in rigid-rotor molecular media
NASA Astrophysics Data System (ADS)
Marskar, Robert; Ã-sterberg, Ulf L.
2015-08-01
We theoretically analyze linear and nonlinear coherent propagation of linearly polarized, plane-wave, resonant single-cycle terahertz pulses through spatially extended rigid-rotor molecular media. Our model incorporates mixed state medium preparation, nonperturbative nonlinearities, saturation, coherence, memory effects, and propagation, but ignores the effects of damping. Explicit solutions are reported in the linear propagation regime. These solutions are the multilevel superposition of linear, single-cycle 0 π pulses, and appear as temporal beats in the time domain. For media initially in thermal equilibrium, the pulse and molecular beats are dispersive and broaden temporally with increased propagation distance. In the simplified limit of equal rotational line strength (an idealized situation), the emitted impulses are exact temporal copies of the input pulse. An efficient, scalable computational method for solving the reduced multilevel Maxwell-Bloch equations for molecular media is reported. This method is based on a standard differential method for the propagation equation together with an operator splitting method for the Bloch equations. It invokes neither the slowly varying envelope (SVEA) or rotating wave approximations (RWA), and incorporates a large number of possible energy eigenstates (we solve for 7744 levels). Case studies of nonlinear single-cycle pulse propagation are then provided by means of computer solutions. In the nonlinear regime, we observe strong molecular orientations and suppression of the pulse and orientational revivals predicted by linear theory. For sufficiently strong pulses, coherent bleaching effects lead to increased transmission of the driving pulse, which also bears signs of self-modulation and carrier-shock formation.