Nonlinear Taylor dispersion in gravity currents in porous media
Szulczewski, Michael; Juanes, Ruben
2012-11-01
Taylor dispersion describes how a non-uniform flow can accelerate diffusive mixing between fluids by elongating the fluid-fluid interface over which diffusion acts. While Taylor dispersion has been extensively studied in simple systems such as Poiseuille and Couette flows, it is poorly understood in more complex systems such as porous-media flows. Here, we study Taylor dispersion in porous media during a gravity-driven flow using theory and simulations. We consider a simple geometry for physical insight: a horizontal, confined layer of permeable rock in which two fluids of different densities are initially separated by a vertical interface. We show that the flow exhibits a non-uniform velocity field that leads to Taylor dispersion at the aquifer scale. Unlike the classical model of Taylor dispersion, however, the diffusive mixing is coupled to the flow velocity because it reduces the lateral density gradient that drives the flow. This coupling causes the flow to continually decelerate and eventually stop completely. To model the flow, we develop a non-linear diffusion equation for the concentration of the more dense fluid, which admits an analytical similarity solution. We discuss applications of the model to CO2 sequestration.
Defocusing regimes of nonlinear waves in media with negative dispersion
DEFF Research Database (Denmark)
Bergé, L.; Kuznetsov, E.A.; Juul Rasmussen, J.
1996-01-01
Defocusing regimes of quasimonochromatic waves governed by a nonlinear Schrodinger equation with mixed-sign dispersion are investigated. For a power-law nonlinearity, we show that localized solutions to this equation defined at the so-called critical dimension cannot collapse in finite time...
Travelling Wave Solutions in Nonlinear Diffusive and Dispersive Media
Bazeia, D; Raposo, and E.P.
1998-01-01
We investigate the presence of soliton solutions in some classes of nonlinear partial differential equations, namely generalized Korteweg-de Vries-Burgers, Korteveg-de Vries-Huxley, and Korteveg-de Vries-Burgers-Huxley equations, which combine effects of diffusion, dispersion, and nonlinearity. We emphasize the chiral behavior of the travelling solutions, whose velocities are determined by the parameters that define the equation. For some appropriate choices, we show that these equations can be mapped onto equations of motion of relativistic 1+1 dimensional phi^{4} and phi^{6} field theories of real scalar fields. We also study systems of two coupled nonlinear equations of the types mentioned.
Rogue and shock waves in nonlinear dispersive media
Resitori, Stefania; Baronio, Fabio
2016-01-01
This self-contained set of lectures addresses a gap in the literature by providing a systematic link between the theoretical foundations of the subject matter and cutting-edge applications in both geophysical fluid dynamics and nonlinear optics. Rogue and shock waves are phenomena that may occur in the propagation of waves in any nonlinear dispersive medium. Accordingly, they have been observed in disparate settings – as ocean waves, in nonlinear optics, in Bose-Einstein condensates, and in plasmas. Rogue and dispersive shock waves are both characterized by the development of extremes: for the former, the wave amplitude becomes unusually large, while for the latter, gradients reach extreme values. Both aspects strongly influence the statistical properties of the wave propagation and are thus considered together here in terms of their underlying theoretical treatment. This book offers a self-contained graduate-level text intended as both an introduction and reference guide for a new generation of scientists ...
Nonlocal quintic nonlinearity by cascaded THG in dispersive media
DEFF Research Database (Denmark)
Eilenberger, F.; Bache, Morten; Minardi, S.;
2011-01-01
We discuss a perturbed nonlocal cubicquintic equation describing the propagation of light pulses in a dispersive, cubic nonlinearmedium in the presence of phase and velocity mismatched third harmonic generation....
Pulse splitting in nonlinear media with anisotropic dispersion properties
DEFF Research Database (Denmark)
Bergé, L.; Juul Rasmussen, J.; Schmidt, M.R.
1998-01-01
to a singularity in the transverse plane. Instead, the pulse spreads out along the direction of negative dispersion and splits up into small-scale cells, which may undergo further splitting events. The analytical results are supported by direct numerical solutions of the three dimensional cubic Schrodinger...
Institute of Scientific and Technical Information of China (English)
文双春; 范滇元
2002-01-01
Spatiotemporal instability in nonlinear dispersive media is investigated on the basis of the nonlinear envelope equation. A general expression for instability gain which includes the effects of space-time focusing, arbitrarily higher-order dispersions and self-steepening is obtained. It is found that, for both normal and anomalous group-velocity dispersions, space-time focusing may lead to the appearance of new instability regions and influence the original instability gain spectra mainly by shrinking their regions. The region of the original instability gain spectrum shrinks much more in normal dispersion case than in anomalous one. In the former case, space-time focusing completely suppresses the growing of higher frequency components. In addition, we find that all the oddth-order dispersions contribute none to instability, while all the eventh-order dispersions influence instability region and do not influence the maximum instability gain, therein the fourth-order dispersion plays the same role as space-time focusing in spatiotemporal instability. The main role played by self-steepening in spatiotemporal instability is that it reduces the instability gain and exerts much more significant influence on the new instability regions resulting from space-time focusing.
Kartashova, Elena
2013-01-01
In this Letter we study the form of the energy spectrum of Riemann waves in weakly nonlinear non-dispersive media. For quadratic and cubic nonlinearity we demonstrate that the deformation of an Riemann wave over time yields an exponential energy spectrum which turns into power law asymptotic with the slope being approximately -8/3 at the last stage of evolution before breaking. We argue, that this is the universal asymptotic behaviour of Riemann waves in any nonlinear non-dispersive medium at the point of breaking. The results reported in this Letter can be used in various non-dispersive media, e.g. magneto-hydro dynamics, physical oceanography, nonlinear acoustics.
Institute of Scientific and Technical Information of China (English)
Yang Hong; Tang Yi
2008-01-01
We investigate the energy exchange between (3+1)D colliding spatiotemporal solitons (STSs) in dispersive media with cubic-quintic (CQ) nonlinearity by numerical simulations. Energy exchange between two (3+l)D head on colliding STSs caused by their phase difference is observed, just as occurring in other optical media. Moreover, energy exchange between two head-on colliding STSs with different speeds is firstly shown in the CQ and saturable media.This phenomenon, we believe, may arouse some interest in the future studies of soliton collision in optical media.
Kapoyko, Yury A.; Drozdov, Arkadiy A.; Kozlov, Sergei A.; Zhang, Xi-Cheng
2016-09-01
Simple arithmetic dependencies of the velocity of the mass center motion and the root-mean-square duration of initially single-cycle, two-cycle, and Gaussian pulses with a random number of oscillations under the pulse envelope are derived depending on their center frequency, initial duration, and peak field amplitude, as well as on dispersive and nonlinear characteristics of homogeneous isotropic dielectric media. In media with normal group dispersion, it is shown that due to nonresonant dispersion the square of the few-cycle pulse duration increases with distance inversely proportional to the fourth power of the number of input pulse cycles. In media with normal group dispersion, the square of the pulse duration is inversely proportional to the number of input pulse cycles due to cubic nonlinearity. In media with anomalous group dispersion, it is shown that due to cubic nonlinearity, few-cycle pulse self-compression decreases with the reduction of the number of cycles in the initial pulse. This pulse self-compression effect has a threshold nature and terminates at a fixed number of cycles of the input pulse. Such a number of cycles is determined by the input intensity and the central frequency of the pulse, as well as by the dispersive and nonlinear characteristics of the medium.
Dispersive shock waves with nonlocal nonlinearity
Barsi, Christopher; Sun, Can; Fleischer, Jason W
2007-01-01
We consider dispersive optical shock waves in nonlocal nonlinear media. Experiments are performed using spatial beams in a thermal liquid cell, and results agree with a hydrodynamic theory of propagation.
Dispersive shock waves with nonlocal nonlinearity.
Barsi, Christopher; Wan, Wenjie; Sun, Can; Fleischer, Jason W
2007-10-15
We consider dispersive optical shock waves in nonlocal nonlinear media. Experiments are performed using spatial beams in a thermal liquid cell, and results agree with a hydrodynamic theory of propagation.
Goos-Haenchen shift and time delay in dispersive nonlinear media
Energy Technology Data Exchange (ETDEWEB)
Ilic, I. [Vinca Institute of Nuclear Sciences, University of Belgrade, P.O. Box 522, 11001 Belgrade (Serbia); Belicev, P.P., E-mail: petrab@vinca.r [Vinca Institute of Nuclear Sciences, University of Belgrade, P.O. Box 522, 11001 Belgrade (Serbia); Milanovic, V.; Radovanovic, J. [Faculty of Electrical Engineering, University of Belgrade, Bul. kralja Aleksandra 73, 11120 Belgrade (Serbia); Hadzievski, Lj. [Vinca Institute of Nuclear Sciences, University of Belgrade, P.O. Box 522, 11001 Belgrade (Serbia)
2011-03-07
We present an analysis of the influence of the Goos-Haenchen effect on tunneling times, group delay and dwell time, of electromagnetic waves propagating through an obstacle made of left-handed metamaterial embedded in a dielectric which exhibits saturable type of nonlinearity. The derived equations show that only the group delay, is affected by the Goos-Haenchen shift without any impact on the dwell time. Besides the reduction of the group delay, the most remarkable result is the possibility for total reduction of the Goos-Haenchen shift for finite incident angles. These phenomena are observable in the frequency region for which metamaterial exhibits negative index of refraction.
Acoustic Rectification in Dispersive Media
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.
Analysis of Wave Nonlinear Dispersion Relation
Institute of Scientific and Technical Information of China (English)
LI Rui-jie; TAO Jian-fu
2005-01-01
The nonlinear dispersion relations and modified relations proposed by Kirby and Hedges have the limitation of intermediate minimum value. To overcome the shortcoming, a new nonlinear dispersion relation is proposed. Based on the summarization and comparison of existing nonlinear dispersion relations, it can be found that the new nonlinear dispersion relation not only keeps the advantages of other nonlinear dispersion relations, but also significantly reduces the relative errors of the nonlinear dispersion relations for a range of the relative water depth of 1＜kh＜1.5 and has sufficient accuracy for practical purposes.
Introduction to nonlinear dispersive equations
Linares, Felipe
2015-01-01
This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research. The second edition of Introdu...
Institute of Scientific and Technical Information of China (English)
Liu Bing-Can; Yu Li; Lu Zhi-Xin
2011-01-01
The analytic surface plasmon polaritons (SPPs) dispersion relation is studied in a system consisting of a thin metallic film bounded by two sides media of nonlinear dielectric of arbitrary nonlinearity is studied by applying a generalised first integral approach. We consider both asymmetric and symmetric structures. Especially, in the symmetric system, two possible modes can exist: the odd mode and the even mode. The dispersion relations of the two modes are obtained. Due to the nonlinear dielectric, the magnitude of the electric field at the interface appears and alters the dispersion relations. The changes in SPPs dispersion relations depending on film thicknesses and nonlinearity are studied.
Model of anisotropic nonlinearity in self-defocusing photorefractive media.
Barsi, C; Fleischer, J W
2015-09-21
We develop a phenomenological model of anisotropy in self-defocusing photorefractive crystals. In addition to an independent term due to nonlinear susceptibility, we introduce a nonlinear, non-separable correction to the spectral diffraction operator. The model successfully describes the crossover between photovoltaic and photorefractive responses and the spatially dispersive shock wave behavior of a nonlinearly spreading Gaussian input beam. It should prove useful for characterizing internal charge dynamics in complex materials and for accurate image reconstruction through nonlinear media.
Stabilization of spatiotemporal solitons in Kerr media by dispersive coupling
Kartashov, Yaroslav V; Konotop, Vladimir V; Lobanov, Valery E; Torner, Lluis
2015-01-01
We introduce a mechanism to stabilize spatiotemporal solitons in Kerr nonlinear media, based on the dispersion of linear coupling between the field components forming the soliton states. Specifically, we consider solitons in a two-core guiding structure with inter-core coupling dispersion (CD). We show that CD profoundly affects properties of the solitons, causing the complete stabilization of the otherwise highly unstable spatiotemporal solitons in Kerr media with focusing nonlinearity. We also find that the presence of CD stimulates the formation of bound states, which however are unstable.
Nonlinear Dispersion Effect on Wave Transformation
Institute of Scientific and Technical Information of China (English)
LI Ruijie; Dong-Young LEE
2000-01-01
A new nonlinear dispersion relation is given in this paper, which can overcome the limitation of the intermediate minimum value in the dispersion relation proposed by Kirby and Dalrymple (1986), and which has a better approximation to Hedges＇ empirical relation than the modilied relations by Hedges (1987). Kirby and Dahymple (1987) for shallow waters. The new dispersion relation is simple in form. thus it can be used easily in practice. Meanwhile. a general explicil approximalion to the new dispersion rela tion and olher nonlinear dispersion relations is given. By use of the explicit approximation to the new dispersion relation along with the mild slope equation taking inlo account weakly nonlinear effect, a mathematical model is obtained, and it is applied to laboratory data. The results show that the model developed vith the new dispersion relation predicts wave translornation over complicated topography quite well.
Nonlinear Dispersion Relation in Wave Transformation
Institute of Scientific and Technical Information of China (English)
李瑞杰; 严以新; 曹宏生
2003-01-01
A nonlinear dispersion relation is presented to model the nonlinear dispersion of waves over the whole range of possible water depths. It reduces the phase speed over-prediction of both Hedges′ modified relation and Kirby and Dalrymple′s modified relation in the region of 1＜kh＜1.5 for small wave steepness and maintains the monotonicity in phase speed variation for large wave steepness. And it has a simple form. By use of the new nonlinear dispersion relation along with the mild slope equation taking into account weak nonlinearity, a mathematical model of wave transformation is developed and applied to laboratory data. The results show that the model with the new dispersion relation can predict wave transformation over complicated bathymetry satisfactorily.
Nonlinear dispersion effects in elastic plates: numerical modelling and validation
Kijanka, Piotr; Radecki, Rafal; Packo, Pawel; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.
2017-04-01
Nonlinear features of elastic wave propagation have attracted significant attention recently. The particular interest herein relates to complex wave-structure interactions, which provide potential new opportunities for feature discovery and identification in a variety of applications. Due to significant complexity associated with wave propagation in nonlinear media, numerical modeling and simulations are employed to facilitate design and development of new measurement, monitoring and characterization systems. However, since very high spatio- temporal accuracy of numerical models is required, it is critical to evaluate their spectral properties and tune discretization parameters for compromise between accuracy and calculation time. Moreover, nonlinearities in structures give rise to various effects that are not present in linear systems, e.g. wave-wave interactions, higher harmonics generation, synchronism and | recently reported | shifts to dispersion characteristics. This paper discusses local computational model based on a new HYBRID approach for wave propagation in nonlinear media. The proposed approach combines advantages of the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE). The methods are investigated in the context of their accuracy for predicting nonlinear wavefields, in particular shifts to dispersion characteristics for finite amplitude waves and secondary wavefields. The results are validated against Finite Element (FE) calculations for guided waves in copper plate. Critical modes i.e., modes determining accuracy of a model at given excitation frequency - are identified and guidelines for numerical model parameters are proposed.
Hawking Radiation in Dispersive Media
Robertson, Scott James
2011-01-01
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 em...
Influence of Dispersion on Transport of Tracer through Unsaturated Porous Media
Directory of Open Access Journals (Sweden)
T Bunsri
2008-01-01
Full Text Available The dispersion phenomenon has resulted from the various water flow magnitude and direction in porous media. The dissolved tracer tends to spread due to dispersion and then travel time of tracer through the porous media increases. In unsaturated porous media, dispersion coefficient varies with non-linear Darcy’s velocity and the water content. These effects observed in both of the laboratory scale sand and soil columns (20 cm. The unsaturated infiltration column and tracer tests have been used to interpret the relationships between Darcy’s velocity and the water content together with the dispersion coefficient. However, the dispersivity coefficient cannot be measured directly, it has to determine from advection-dispersion equation (ADE, which can be used to model the tracer transport in unsaturated porous media. The model was used to describe the non-linear functions of water contents and dispersivities for both porous media. The simulations have been verified that the dispersion of tracer through soil is higher than sand column and also travel time of tracer through soil is longer than sand column. Even though, soil has very low degree of pore velocity, the high dispersivity is observed in the simulations. The water content and tracer concentration profiles reveal that the increase of dispersivity induces the increase of flow path distance and the decrease of pore velocity. The maximum dispersivity was observed when the water content of porous media is relatively low; this leads the maximum of spreading of tracer.
Nonlinear Acoustics in a Dispersive Continuum: Random Waves, Radiation Pressure, and Quantum Noise.
1983-03-01
Karpman , Nonlinear Waves in Dispersive Media, Pergamon Press, New York, 1975, p. 76. 26. R. Beyers, Nonlinear Acoustics, U.S. Government Printing...20301 U. S. Army Research nffice 2 copies Box 12211 Research Triangle Park tlorth Carolina 27709 Defense Technical Information Center 12 copies Cameron
Anderson Localization in Nonlocal Nonlinear Media
Folli, Viola; 10.1364/OL.37.000332
2012-01-01
The effect of focusing and defocusing nonlinearities on Anderson localization in highly nonlocal media is theoretically and numerically investigated. A perturbative approach is developed to solve the nonlocal nonlinear Schroedinger equation in the presence of a random potential, showing that nonlocality stabilizes Anderson states.
Multipole vector solitons in nonlocal nonlinear media.
Kartashov, Yaroslav V; Torner, Lluis; Vysloukh, Victor A; Mihalache, Dumitru
2006-05-15
We show that multipole solitons can be made stable via vectorial coupling in bulk nonlocal nonlinear media. Such vector solitons are composed of mutually incoherent nodeless and multipole components jointly inducing a nonlinear refractive index profile. We found that stabilization of the otherwise highly unstable multipoles occurs below certain maximum energy flow. Such a threshold is determined by the nonlocality degree.
Dispersion managed solitons in the presence of saturated nonlinearity
Hundertmark, Dirk; Lee, Young-Ran; Ried, Tobias; Zharnitsky, Vadim
2017-10-01
The averaged dispersion managed nonlinear Schrödinger equation with saturated nonlinearity is considered. It is shown that under rather general assumptions on the saturated nonlinearity, the ground state solution corresponding to the dispersion managed soliton can be found for both zero residual dispersion and positive residual dispersion. The same applies to diffraction management solitons, which are a discrete version describing certain waveguide arrays.
Generalized dispersive wave emission in nonlinear fiber optics.
Webb, K E; Xu, Y Q; Erkintalo, M; Murdoch, S G
2013-01-15
We show that the emission of dispersive waves in nonlinear fiber optics is not limited to soliton-like pulses propagating in the anomalous dispersion regime. We demonstrate, both numerically and experimentally, that pulses propagating in the normal dispersion regime can excite resonant dispersive radiation across the zero-dispersion wavelength into the anomalous regime.
Pulse splitting of self-focusing-beams in normally dispersive media
DEFF Research Database (Denmark)
Bergé, L.; Juul Rasmussen, J.
1996-01-01
The influence of the normal group-velocity dispersion on anisotropic self-focusing beams in nonlinear Kerr media is studied analytically. It is shown that a light pulse self-focusing in the presence of normal dispersion is split up into several small-scale cells preventing a catastrophic collapse...
Viscous Fluid Conduits as a Prototypical Nonlinear Dispersive Wave Platform
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
Studies of Tracer Dispersion and Fluid Flow in Porous Media
Energy Technology Data Exchange (ETDEWEB)
Rage, T.
1996-12-31
This doctoral thesis explores the connection between the topology of a porous medium and its macroscopic transport properties and is based on computerized simulation. In porous media, both diffusion and convection contribute to the dispersion of a tracer and their combined effect is emphasized. The governing equations are solved numerically, using finite differences and Monte Carlo technique. The influence of finite Reynolds number on the outcome of echo-experiments is discussed. Comparing experiments and simulations it is found that nonlinear inertial forces lead to a visible deformation of a returned tracer at surprisingly small Reynolds numbers. In a study of tracer dispersion and fluid flow in periodic arrays of discs it is demonstrated that the mechanisms of mechanical dispersion in periodic media and in natural (non-periodic) porous media are essentially different. Measurements of the percolation probability distribution of a sandstone sample is presented. Local porosity theory predicts that this simple geometric function of a porous medium is of dominant importance for its macroscopic transport properties. It is demonstrated that many aspects of transport through fractures can be studied by using simple but realistic models and readily available computer resources. An example may be the transport of hydrocarbon fluids from the source rock to a reservoir. 165 refs., 44 figs., 1 table
Modulational instability in nonlocal nonlinear Kerr media
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole; Juul Rasmussen, Jens
2001-01-01
We study modulational instability (MI) of plane waves in nonlocal nonlinear Kerr media. For a focusing nonlinearity we show that, although the nonlocality tends to suppress MI, it can never remove it completely, irrespective of the particular profile of the nonlocal response function....... For a defocusing nonlinearity the stability properties depend sensitively on the response function profile: for a smooth profile (e.g., a Gaussian) plane waves are always stable, but MI may occur for a rectangular response. We also find that the reduced model for a weak nonlocality predicts MI in defocusing media...... for arbitrary response profiles, as long as the intensity exceeds a certain critical value. However, it appears that this regime of MI is beyond the validity of the reduced model, if it is to represent the weakly nonlocal limit of a general nonlocal nonlinearity, as in optics and the theory of Bose...
Modulation instability of broad optical beams in nonlinear media with general nonlinearity
Institute of Scientific and Technical Information of China (English)
Hongcheng Wang; Weilong She
2006-01-01
@@ The modulation instability of quasi-plane-wave optical beams is investigated in the frame of generalized Schr(o)dinger equation with the nonlinear term of a general form. General expressions are derived for the dispersion relation, the critical transverse spatial frequency, as well as the instability growth rate.The analysis generalizes the known results reported previously. A detailed discussion on the modulation instability in biased centrosymmetric photorefractive media is also given.
Nonlinear Acoustic Wave Interactions in Layered Media.
1980-03-06
Generated Components in Dispersive Media. . . . . . . . . . . . . 62 4.4 Dispersion in Medium II . . . . . . . . .. 68 V. CONCLUSIONS...give rise to leaky wave modes which are more thoroughly discussed 17 18 by Kapany and Burke, and by Marcuse . Leaky modes are C.C. Ghizoni, J.M...1977), 843-848. 1 7N.S. Kapany and J.J. Burke, Optical Waveeeuides, (New York: Academic Press, 1972), pp. 24-34. D. Marcuse , Theory of Dielectric Optical
Inflationary cosmology with nonlinear dispersion relations
Zhu, Tao; Cleaver, Gerald; Kirsten, Klaus; Sheng, Qin
2013-01-01
We present a technique, {\\em the uniform asymptotic approximation}, to construct accurate analytical solutions of the linear perturbations of inflation after quantum effects of the early universe are taken into account, for which the dispersion relations generically become nonlinear. We construct explicitly the error bounds associated with the approximations and then study them in detail. With the understanding of the errors and the proper choice of the Liouville transformations of the differential equations of the perturbations, we show that the analytical solutions describe the exact evolution of the linear perturbations extremely well even only to the first-order approximations. As a simple application of the approximate analytical solutions, we calculate the power spectra and indices of scalar and tensor perturbations in the de Sitter background, and find that the amplitudes of the power spectra get modified due to the quantum effects, while the power spectrum indices remain the same as in the linear case...
Boundary control of long waves in nonlinear dispersive systems
DEFF Research Database (Denmark)
Hasan, Agus; Foss, Bjarne; Aamo, Ole Morten
2011-01-01
Unidirectional propagation of long waves in nonlinear dispersive systems may be modeled by the Benjamin-Bona-Mahony-Burgers equation, a third order partial differential equation incorporating linear dissipative and dispersive terms, as well as a term covering nonlinear wave phenomena. For higher...... orders of the nonlinearity, the equation may have unstable solitary wave solutions. Although it is a one dimensional problem, achieving a global result for this equation is not trivial due to the nonlinearity and the mixed partial derivative. In this paper, two sets of nonlinear boundary control laws...... that achieve global exponential stability and semi-global exponential stability are derived for both linear and nonlinear cases....
Slow light pulse propagation in dispersive media
DEFF Research Database (Denmark)
Nielsen, Torben Roland; Mørk, Jesper; Lavrinenko, Andrei
2009-01-01
-difference-time-domain Maxwell-Bloch simulations and compared to analytic results. For long pulses the group index (transmission) for the combined system is significantly enhanced (reduced) relative to slow light based on purely material or waveguide dispersion. Shorter pulses are strongly distorted and depending on parameters......We present a theoretical and numerical analysis of pulse propagation in a semiconductor photonic crystal waveguide with embedded quantum dots in a regime where the pulse is subjected to both waveguide and material dispersion. The group index and the transmission are investigated by finite...... broadening or break-up of the pulse may be observed. The transition from linear to nonlinear pulse propagation is quantified in terms of the spectral width of the pulse. To cite this article: T.R. Nielsen et al., C. R. Physique 10 (2009). (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All...
Solitons in nonlocal nonlinear media: Exact solutions
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole
2001-01-01
We investigate the propagation of one-dimensional bright and dark spatial solitons in a nonlocal Kerr-like media, in which the nonlocality is of general form. We find an exact analytical solution to the nonlinear propagation equation in the case of weak nonlocality. We study the properties...
Q factors for antennas in dispersive media
Gustafsson, Mats; Cismasu, Marius
2014-01-01
Stored energy and Q-factors are used to quantify the performance of small antennas. Accurate and efficient evaluation of the stored energy is also essential for current optimization and the associated physical bounds. Here, it is shown that the frequency derivative of the input impedance and the stored energy can be determined from the frequency derivative of the electric field integral equation. The expressions for the differentiated input impedance and stored energies differ by the use of a transpose and Hermitian transpose in the quadratic forms. The quadratic forms also provide simple single frequency formulas for the corresponding Q-factors. The expressions are further generalized to antennas integrated in temporally dispersive media. Numerical examples that compare the different Q-factors are presented for dipole and loop antennas in conductive, Debye, Lorentz, and Drude media. The computed Q-factors are also verified with the Q-factor obtained from the stored energy in Brune synthesized circuit models.
Electric characterization of a nonlinear dispersive transmission line
Energy Technology Data Exchange (ETDEWEB)
Ferreira, E.S.; Ricotta, R.M. [Faculdade de Tecnologia de Sao Paulo (FATEC-SP), SP (Brazil)], Emails: ferreira@fatecsp.br, regina@fatecsp.br
2009-07-01
A preliminary study of electrical soliton propagation in a nonlinear dispersion electrical line is presented. This is probably the simplest system that allows the observation of such waves whose main characteristic is the perfect balance of nonlinear and dispersive aspects. (author)
Improved fiber nonlinearity mitigation in dispersion managed optical OFDM links
Tamilarasan, Ilavarasan; Saminathan, Brindha; Murugappan, Meenakshi
2017-02-01
Fiber nonlinearity is seen as a capacity limiting factor in OFDM based dispersion managed links since the Four Wave Mixing effects become enhanced due to the high PAPR. In this paper, the authors have compared the linear and nonlinear PAPR reduction techniques for fiber nonlinearity mitigation in OFDM based dispersion managed links. In the existing optical systems, linear transform techniques such as SLM and PTS have been implemented to reduce nonlinear effects. In the proposed study, superior performance of the L2-by-3 nonlinear transform technique is demonstrated for PAPR reduction to mitigate fiber nonlinearities. The performance evaluation is carried out by interfacing multiple simulators. The results of both linear and nonlinear transform techniques have been compared and the results show that nonlinear transform technique outperforms the linear transform in terms of nonlinearity mitigation and improved BER performance.
Nonlinear and Dispersive Optical Pulse Propagation
Dijaili, Sol Peter
In this dissertation, there are basically four novel contributions to the field of picosecond pulse propagation and measurement. The first contribution is the temporal ABCD matrix which is an analog of the traditional ABCD ray matrices used in Gaussian beam propagation. The temporal ABCD matrix allows for the easy calculation of the effects of linear chirp or group velocity dispersion in the time domain. As with Gaussian beams in space, there also exists a complete Hermite-Gaussian basis in time whose propagation can be tracked with the temporal ABCD matrices. The second contribution is the timing synchronization between a colliding pulse mode-locked dye laser and a gain-switched Fabry-Perot type AlGaAs laser diode that has achieved less than 40 femtoseconds of relative timing jitter by using a pulsed optical phase lock loop (POPLL). The relative timing jitter was measured using the error voltage of the feedback loop. This method of measurement is accurate since the frequencies of all the timing fluctuations fall within the loop bandwidth. The novel element is a broad band optical cross-correlator that can resolve femtosecond time delay errors between two pulse trains. The third contribution is a novel dispersive technique of determining the nonlinear frequency sweep of a picosecond pulse with relatively good accuracy. All the measurements are made in the time domain and hence there is no time-bandwidth limitation to the accuracy. The fourth contribution is the first demonstration of cross -phase modulation in a semiconductor laser amplifier where a variable chirp was observed. A simple expression for the chirp imparted on a weak signal pulse by the action of a strong pump pulse is derived. A maximum frequency excursion of 16 GHz due to the cross-phase modulation was measured. A value of 5 was found for alpha _{xpm} which is a factor for characterizing the cross-phase modulation in a similar manner to the conventional linewidth enhancement factor, alpha.
Dispersion and nonlinear effects in OFDM-RoF system
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.
Electromagnetic beam propagation in nonlinear media
Institute of Scientific and Technical Information of China (English)
V.V.Semak; M.N.Shneider
2015-01-01
We deduce a complete wave propagation equation that includes inhomogeneity of the dielectric constant and present this propagation equation in compact vector form. Although similar equations are known in narrow fields such as radio wave propagation in the ionosphere and electromagnetic and acoustic wave propagation in stratified media, we develop here a novel approach of using such equations in the modeling of laser beam propagation in nonlinear media. Our approach satisfies the correspondence principle since in the limit of zero-length wavelength it reduces from physical to geometrical optics.
Dispersion of Sound in Dilute Suspensions with Nonlinear Particle Relaxation
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
TESTING FOR VARYING DISPERSION IN DISCRETE EXPONENTIAL FAMILY NONLINEAR MODELS
Institute of Scientific and Technical Information of China (English)
LinJinguan; WeiBocheng; ZhangNansong
2003-01-01
It is necessary to test for varying dispersion in generalized nonlinear models. Wei ,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponential family nonlinear models. This type of problem in the framework of general discrete exponential family nonlinear models is discussed. Two types of varying dispersion, which are random coefficients model and random effects model, are proposed,and corresponding score test statistics are constructed and expressed in simple ,easy to use ,matrix formulas.
A Boussinesq model with alleviated nonlinearity and dispersion
Institute of Scientific and Technical Information of China (English)
ZHANG Dian-xin; TAO Jian-hua
2008-01-01
The classical Boussinesq equation is a weakly nonlinear and weakly dispersive equation, which has been widely applied to simulate wave propagation in off-coast shallow waters. A new form of the Boussinesq model for an uneven bottoms is derived in this paper. In the new model, nonlinearity is reduced without increasing the order of the highest derivative in the differential equations. Dispersion relationship of the model is improved to the order of Pade (2,2) by adjusting a parameter in the model based on the long wave approximation. Analysis of the linear dispersion, linear shoaling and nonlinearity of the present model shows that the performances in terms of nonlinearity, dispersion and shoaling of this model are improved. Numerical results obtained with the present model are in agreement with experimental data.
Local Influence Analysis for Semiparametric Reproductive Dispersion Nonlinear Models
Institute of Scientific and Technical Information of China (English)
Xue-dong CHEN; Nian-sheng TANG; Xue-ren WANG
2012-01-01
The present paper proposes a semiparametric reproductive dispersion nonlinear model (SRDNM)which is an extension of the nonlinear reproductive dispersion models and the semiparameter regression models.Maximum penalized likelihood estimates (MPLEs) of unknown parameters and nonparametric functions in SRDNM are presented.Assessment of local influence for various perturbation schemes are investigated.Some local influence diagnostics are given.A simulation study and a real example are used to illustrate the proposed methodologies.
Plasma metamaterials as cloaking and nonlinear media
Sakai, O.; Yamaguchi, S.; Bambina, A.; Iwai, A.; Nakamura, Y.; Tamayama, Y.; Miyagi, S.
2017-01-01
Plasma metamaterials, composites of low-temperature plasmas and periodic functional microstructures, work as cloaking and nonlinear media. Due to functions of the microstructures like negative permeability, electromagnetic waves in and around plasma metamaterials propagate in a quite different manner from the case with the conventional space in which relative permeability is positive and unity. Using plasmas and plasma metamaterials, we achieve various controls of microwave propagating paths such as unidirectionality and cloaking in the two- or 3D spaces. For instance, a concentric plasma layer makes wave propagation unidirectional, and waves propagate in different routes when they start inside or outside the concentric layer. Furthermore, due to spatial permittivity gradient and anisotropic refractive index, electromagnetic waves detour in plasma metamaterial layers. Another significant point that plasma metamaterials can realize is nonlinearity. When we study high-power electromagnetic waves propagating in them, we observe several properties describable in terms of nonlinear dynamics and nonlinear photonics. Microwaves beyond threshold energy trigger bifurcations in plasma permittivity, and the second harmonic wave detected simultaneously is generated with strong emission levels. Such electromagnetic wave propagation is achieved with advantages over other materials, since plasmas and metallic microstructures work in harmony and in synergy.
Beam Combining by Phase Transition Nonlinear Media
1990-02-01
use the Redlich Kwong equation of state for the media we consider. This equation of state can be written RT a p - -b -FT(p.-’ + b)p ; 2-I M (2-1) where...as ac 3 dg-A7 C VA/\\CIIJT (6) The Redlich - Kwong equation of state; i.e., _ RT T-1/2 v-P v(v+P) (7) can be used to compute aP/lT, where the relevant...practical the application of nonlinear phase conjugate techniques to the beam combining of multiple lasers with a coherence characteristic of a
Dispersion-induced nonlinearities in semiconductors
DEFF Research Database (Denmark)
Mørk, Jesper; Mecozzi, A.
2002-01-01
A dispersive and saturable medium is shown, under very general conditions, to possess ultrafast dynamic behaviour due to non-adiabatic polarisation dynamics. Simple analytical expressions relating the effect to the refractive index dispersion of a semiconductor ire derived and the magnitude...... of the equivalent Kerr coefficient is shown to be in qualitative agreement with measurements on active semiconductor waveguides....
Particulate dispersions for magnetic recording media
Mercer, T
2001-01-01
'plug' of constant solids concentration falls down into, and is continually subsumed by, the rising layers of the lower compression region. The plug effectively contracts about its mid-point and the initial constant rate of fall is only maintained up to the point where the plug is destroyed. It was also found that the model only gave a reasonable comparison with experiment when the effective ratio of trapped fluid was large; giving further confidence in the trapped fluid estimate. The theory of the scanning column magnetometer technique has been developed beyond that already known. This resulted in good agreement between theory and experiment in characterising the main detection coil response, or 'form factor' and means that future design work will be enhanced. The effects of magnetic interaction in the magnetic media dispersion have been investigated by varying the magnetic gamma-Fe sub 2 O sub 3 content by dilution with alpha-Fe sub 2 O sub 3 (produced from the same particles) whilst holding the total parti...
Modulational stability and dark solitons in periodic quadratic nonlinear media
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2000-01-01
We show that stable dark solitons exist in quadratic nonlinear media with periodic linear and nonlinear susceptibilities. We investigate the modulational stability of plane waves in such systems, a necessary condition for stable dark solitons....
Optical angular momentum in dispersive media
Philbin, T G
2012-01-01
The angular momentum density and flux of light in a dispersive, rotationally symmetric medium are derived from Noether's theorem. Optical angular momentum in a dispersive medium has no simple relation to optical linear momentum, even if the medium is homogeneous. A circularly polarized monochromatic beam in a homogeneous, dispersive medium carries a spin angular momentum per unit energy of $\\pm\\omega^{-1}$, as in vacuum. This result demonstrates the non-trivial interplay of dispersive contributions to optical angular momentum and energy.
Rashidian Vaziri, Mohammad Reza
2013-07-10
In this paper, the Z-scan theory for nonlocal nonlinear media has been further developed when nonlinear absorption and nonlinear refraction appear simultaneously. To this end, the nonlinear photoinduced phase shift between the impinging and outgoing Gaussian beams from a nonlocal nonlinear sample has been generalized. It is shown that this kind of phase shift will reduce correctly to its known counterpart for the case of pure refractive nonlinearity. Using this generalized form of phase shift, the basic formulas for closed- and open-aperture beam transmittances in the far field have been provided, and a simple procedure for interpreting the Z-scan results has been proposed. In this procedure, by separately performing open- and closed-aperture Z-scan experiments and using the represented relations for the far-field transmittances, one can measure the nonlinear absorption coefficient and nonlinear index of refraction as well as the order of nonlocality. Theoretically, it is shown that when the absorptive nonlinearity is present in addition to the refractive nonlinearity, the sample nonlocal response can noticeably suppress the peak and enhance the valley of the Z-scan closed-aperture transmittance curves, which is due to the nonlocal action's ability to change the beam transverse dimensions.
van Milligen, B Ph
2014-01-01
The dispersion of solute in porous media shows a non-linear increase in the transition from diffusion to advection dominated dispersion as the flow velocity is raised. In the past, the behavior in this intermediate regime has been explained with a variety of models. {We present and use a simplified numerical model which does not contain any turbulence, Taylor dispersion, or fractality. With it, we show that the non-linearity in the intermediate regime nevertheless occurs. Furthermore,} 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. Taylor dispersion, often invoked to exp...
Propagation of ultrashort pulsed beams in dispersive media
Institute of Scientific and Technical Information of China (English)
刘志军; 吕百达
2003-01-01
Starting from the Rayleigh diffraction integral, the propagation equation of ultrashort pulsed beams in dispersive media is derived without making the paraxial approximation and slowly varying envelope approximation (SVEA). The spatiotemporal properties of ultrashort pulsed beams in dispersive media, such as spectrum redshifting, narrowing and pulse distortion are illustrated with pulsed Gaussian beams. It is stressed that the "antibeam" behaviour of ultrashort pulsed beams can be avoided, if a suitable truncation function is chosen.
Nearly linear dynamics of nonlinear dispersive waves
Erdogan, M B; Zharnitsky, V
2010-01-01
Dispersive averaging e?ffects are used to show that KdV equation with periodic boundary conditions possesses high frequency solutions which behave nearly linearly. Numerical simulations are presented which indicate high accuracy of this approximation. Furthermore, this result is applied to shallow water wave dynamics in the limit of KdV approximation, which is obtained by asymptotic analysis in combination with numerical simulations of KdV.
Measurement of the Acoustic Nonlinearity Parameter for Biological Media.
Cobb, Wesley Nelson
In vitro measurements of the acoustic nonlinearity parameter are presented for several biological media. With these measurements it is possible to predict the distortion of a finite amplitude wave in biological tissues of current diagnostic and research interest. The measurement method is based on the finite amplitude distortion of a sine wave that is emmitted by a piston source. The growth of the second harmonic component of this wave is measured by a piston receiver which is coaxial with and has the same size as the source. The experimental measurements and theory are compared in order to determine the nonlinearity parameter. The density, sound speed, and attenuation for the medium are determined in order to make this comparison. The theory developed for this study accounts for the influence of both diffraction and attenuation on the experimental measurements. The effects of dispersion, tissue inhomogeneity and gas bubbles within the excised tissues are studied. To test the measurement method, experimental results are compared with established values for the nonlinearity parameter of distilled water, ethylene glycol and glycerol. The agreement between these values suggests that the measurement uncertainty is (+OR-) 5% for liquids and (+OR-) 10% for solid tissues. Measurements are presented for dog blood and bovine serum albumen as a function of concentration. The nonlinearity parameters for liver, kidney and spleen are reported for both human and canine tissues. The values for the fresh tissues displayed little variation (6.8 to 7.8). Measurements for fixed, normal and cirrhotic tissues indicated that the nonlinearity parameter does not depend strongly on pathology. However, the values for fixed tissues were somewhat higher than those of the fresh tissues.
Nonlinear Quantum Optics in Artificially Structured Media
Helt, Lukas Gordon
This thesis presents an analysis of photon pairs generated via either spontaneous parametric downconversion or spontaneous four-wave mixing in channel waveguides as well as in microring resonators side-coupled to channel waveguides. The state of photons exiting a particular device is calculated within a general Hamiltonian formalism that simplifies the link between quantum nonlinear optics experiments and classical nonlinear optics experiments. This state contains information regarding photon pair production efficiency as well as modal and spectral correlations between the two photons, characterized by a two-dimensional spectral distribution function called the biphoton wave function. In the limit of a low probability of pair production, photon pair production efficiencies are cast into forms resembling corresponding well-known classical nonlinear optical frequency conversion efficiencies, making it easy to see what plays the role of a classical "seed" field in an un-seeded (quantum) process. This also allows photon pair production efficiencies to be calculated based on the results of classical nonlinear optical experiments. It is further calculated that, unless generated photons are collected over a very narrow frequency range, their generation efficiency does not scale the same way with device length in a channel waveguide, or resonance quality factor in a microring resonator, as might be expected from the corresponding classical frequency conversion efficiency. Although calculations do not include self- or cross-phase modulation, nor two-photon absorption or free-carrier absorption, it is calculated that their neglect is justified in the low pair production probability limit. Linear (scattering) loss is also neglected, though partially addressed in the final chapter of this thesis. Biphoton wave functions are calculated explicitly, such that their shape and orientation, including approximate analytic expressions for their widths, can easily be determined. This
Carrier field shock formation of long wavelength femtosecond pulses in dispersive media
Panagiotopoulos, Paris; Kolesik, Miroslav; Moloney, Jerome V
2015-01-01
We numerically demonstrate the formation of carrier field shocks in various dispersive media for a wide variety of input conditions using two different electric field propagation models. In addition, an investigation of the impact of numerous physical effects on carrier wave shock is performed. It is shown that in many cases a field shock is essentially unavoidable and therefore extremely important in the propagation of intense long wavelength pulses in weakly dispersive nonlinear media such as noble gases, air, and single-crystal diamond. The results presented here are expected to have a significant impact in the field of ultrashort nonlinear optics, attosecond pulse generation, and wavepacket synthesis where the use of mid-IR wavelengths is becoming increasingly more important.
Fukui, M.; So, V. C.-Y.; Stegeman, G. I.
1980-07-01
The recent experiments of DeMartini, Colocci, Kohn, and Shen [Phys. Rev. Lett. 38, 1223 (1977)] on the nonlinear generation of C1- (n=1 in the series) surface exciton polaritons in spatially dispersive ZnO are analyzed. It is shown for a prism-air-sample geometry that the air-gap thickness plays an important role in determining the polariton attenuation, and to a lesser degree the polariton energy. Reasonably good agreement with the experimental dispersion relations of DeMartini and co-workers is obtained by including spatial dispersion via the additional boundary condition (ABC) ∂P→ex/∂z=0 for the excitonic polarization P→ex at the surface: The ABC P→ex=0 does not yield a good fit. The theory of the nonlinear generation of surface exciton polaritons in isotropic, spatially dispersive media is developed and applied to angle- and frequency-scanning experimental geometries. Numerical estimates of both the power radiated out via the prism (in the absence of surface roughness) and the line shape were also found to be in reasonable agreement with experiment for the ABC ∂P→ex/∂x=0, but not for P→ex=0.
Pakarzadeh, H.; Rezaei, S. M.
2016-01-01
In this article, we investigate for the first time the dispersion and the nonlinear characteristics of the tapered photonic crystal fibers (PCFs) as a function of length z, via solving the eigenvalue equation of the guided mode using the finite-difference frequency-domain method. Since the structural parameters such as the air-hole diameter and the pitch of the microstructured cladding change along the tapered PCFs, dispersion and nonlinear properties change with the length as well. Therefore, it is important to know the exact behavior of such fiber parameters along z which is necessary for nonlinear optics applications. We simulate the z dependency of the zero-dispersion wavelength, dispersion slope, effective mode area, nonlinear parameter, and the confinement loss along the tapered PCFs and propose useful relations for describing dispersion and nonlinear parameters. The results of this article, which are in a very good agreement with the available experimental data, are important for simulating pulse propagation as well as investigating nonlinear effects such as supercontinuum generation and parametric amplification in tapered PCFs.
Nonlinear surface waves in soft, weakly compressible elastic media.
Zabolotskaya, Evgenia A; Ilinskii, Yurii A; Hamilton, Mark F
2007-04-01
Nonlinear surface waves in soft, weakly compressible elastic media are investigated theoretically, with a focus on propagation in tissue-like media. The model is obtained as a limiting case of the theory developed by Zabolotskaya [J. Acoust. Soc. Am. 91, 2569-2575 (1992)] for nonlinear surface waves in arbitrary isotropic elastic media, and it is consistent with the results obtained by Fu and Devenish [Q. J. Mech. Appl. Math. 49, 65-80 (1996)] for incompressible isotropic elastic media. In particular, the quadratic nonlinearity is found to be independent of the third-order elastic constants of the medium, and it is inversely proportional to the shear modulus. The Gol'dberg number characterizing the degree of waveform distortion due to quadratic nonlinearity is proportional to the square root of the shear modulus and inversely proportional to the shear viscosity. Simulations are presented for propagation in tissue-like media.
Cosmic neutrinos: A dispersive and nonlinear fluid
Inman, Derek; Pen, Ue-Li
2017-03-01
We present a description of cosmic neutrinos as a dispersive fluid. In this approach, the neutrino phase space is reduced to density and velocity fields alongside a scale-dependent sound speed. This sound speed depends on redshift, the initial neutrino phase space density and the cold dark matter gravitational potential. The latter is a new coupling between neutrinos and large scale structure not described by previous fluid approaches. We compute the sound speed in linear theory and find that it asymptotes to constants at small and large scales regardless of the gravitational potential. By comparing with neutrino N-body simulations, we measure the small scale sound speed and find it to be lower than linear theory predictions. This allows for an explanation of the discrepancy between N-body and linear response predictions for the neutrino power spectrum: neutrinos are still driven predominantly by the cold dark matter, but the sound speed on small scales is not stable to perturbations and decreases. Finally, we present a calibrated model for the neutrino power spectrum that requires no additional integrations outside of standard Boltzmann codes.
Cosmic neutrinos: dispersive and non-linear
Inman, Derek
2016-01-01
We present a description of cosmic neutrinos as a dispersive fluid. In this approach, the neutrino phase space is reduced to density and velocity fields alongside a scale-dependent sound speed. This sound speed depends on redshift, the initial neutrino phase space density and the cold dark matter gravitational potential. The latter is a new coupling between neutrinos and large scale structure not described by previous fluid approaches. We compute the sound speed in linear theory and find that it asymptotes to constants at small and large scales regardless of the gravitational potential. By comparing with neutrino N-body simulations, we measure the small scale sound speed and find it to be lower than linear theory predictions. This allows for an explanation of the discrepency between N-body and linear response predictions for the neutrino power spectrum: neutrinos are still driven predominantly by the cold dark matter, but the sound speed on small scales is not stable to perturbations and decreases. Finally, w...
Optical dispersive shock waves in defocusing colloidal media
An, X.; Marchant, T. R.; Smyth, N. F.
2017-03-01
The propagation of an optical dispersive shock wave, generated from a jump discontinuity in light intensity, in a defocusing colloidal medium is analysed. The equations governing nonlinear light propagation in a colloidal medium consist of a nonlinear Schrödinger equation for the beam and an algebraic equation for the medium response. In the limit of low light intensity, these equations reduce to a perturbed higher order nonlinear Schrödinger equation. Solutions for the leading and trailing edges of the colloidal dispersive shock wave are found using modulation theory. This is done for both the perturbed nonlinear Schrödinger equation and the full colloid equations for arbitrary light intensity. These results are compared with numerical solutions of the colloid equations.
Spiralling solitons and multipole localized modes in nonlocal nonlinear media
DEFF Research Database (Denmark)
Buccoliero, Daniel; Lopez-Aguayo, Servando; Skupin, Stefan
2007-01-01
We analyze the propagation of rotating multi-soliton localized structures in optical media with spatially nonlocal nonlinearity. We demonstrate that nonlocality stabilizes the azimuthal breakup of rotating dipole as well as multipole localized soliton modes. We compare the results for two differe...... models of nonlocal nonlinearity and suggest that the stabilization mechanism is a generic property of a spatial nonlocal nonlinear response independent of its particular functional form.......We analyze the propagation of rotating multi-soliton localized structures in optical media with spatially nonlocal nonlinearity. We demonstrate that nonlocality stabilizes the azimuthal breakup of rotating dipole as well as multipole localized soliton modes. We compare the results for two different...
Spinning solitons in cubic-quintic nonlinear media
Indian Academy of Sciences (India)
Lucian-Cornel Crasovan; Boris A Malomed; Dumitru Mihalache
2001-11-01
We review recent theoretical results concerning the existence, stability and unique features of families of bright vortex solitons (doughnuts, or ‘spinning’ solitons) in both conservative and dissipative cubic-quintic nonlinear media.
Anomalous interaction of nonlocal solitons in media with competing nonlinearities
DEFF Research Database (Denmark)
Esbensen, B. K.; Bache, Morten; Bang, Ole
2012-01-01
We theoretically investigate properties of individual bright spatial solitons and their interaction in nonlocal media with competing focusing and defocusing nonlinearities. We consider the general case with both nonlinear responses characterized by different strengths and degrees of nonlocality. We...... and interaction of solitons using numerical simulations of the full model of beam propagation. The numerical simulations fully confirm our analytical results....
Time shift of pulses due to dispersion slope and nonlinearity
Energy Technology Data Exchange (ETDEWEB)
Marcuse, D.; Menyuk, C.R.; Holzloehner, R.
1999-12-01
The authors show that the time delay of optical pulses traveling in long fibers is influenced by the dispersion slope and the fiber nonlinearity. Consequently, one or more new pulses that are inserted by add-drop operations into a pulse train that has already traveled a long distance may shift relative to the old pulses. This time shift delays the initial pulses more than the newly inserted ones, so that the newly inserted pulses can leave their time frames, leading to errors.
Self-guiding light in layered nonlinear media
DEFF Research Database (Denmark)
Bergé, L.; Mezentsev, V. K.; Juul Rasmussen, Jens;
2000-01-01
We study the propagation of intense optical beams in layered Kerr media. With appropriate shapes, beams with a power close to the self-focusing threshold are shown to propagate over long distances as quasistationary waveguides in cubic media supporting a periodic nonlinear refractive index. (C...
A Spectral Element Method for Nonlinear and Dispersive Water Waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Bigoni, Daniele; Eskilsson, Claes
The use of flexible mesh discretisation methods are important for simulation of nonlinear wave-structure interactions in offshore and marine settings such as harbour and coastal areas. For real applications, development of efficient models for wave propagation based on unstructured discretisation...... methods is of key interest. We present a high-order general-purpose three-dimensional numerical model solving fully nonlinear and dispersive potential flow equations with a free surface.......The use of flexible mesh discretisation methods are important for simulation of nonlinear wave-structure interactions in offshore and marine settings such as harbour and coastal areas. For real applications, development of efficient models for wave propagation based on unstructured discretisation...
Dispersive optical nonlinearities in an EIT-Rydberg medium
Stanojevic, Jovica; Bimbard, Erwan; Ourjoumtsev, Alexei; Grangier, Philippe
2013-01-01
We investigate dispersive optical nonlinearities that arise from Rydberg excitation blockade in cold Rydberg gases. We consider a two-photon transition scheme and study the non-linear response to a weak optical probe in presence of a strong control beam. For very low probe fields, the dominant nonlinearities are of the third order and they can be exactly evaluated in a steady state regime. In a more general case, the change in average atomic populations and coherences due to Rydberg interactions can be characterized by properly defined scaling parameters, which are generally complex numbers but in certain situations take the usual meaning of the number of atoms in a blockade sphere. They can be used in a simple "universal scaling" formula to determine the dispersive optical nonlinearity of the medium. We also develop a novel technique to account for the Rydberg interaction effects, by simplifying the treatment of nonlocal interaction terms, the so-called collisional integrals. We find algebraic relations that...
Peculiarities of Cherenkov Radiation in Dispersive Media
Afanasiev, G N; Ruzicka, J
2001-01-01
Previously obtained space-time distributions of the radiation generated by a charge uniformly moving in medium with dispersion are applied to concrete substances with quite different physical properties (iodine and ZnSe) for which the parametrizations of dielectric permittivity are known from physical literature. For iodine, the resonance frequency lies in a far ultraviolet region, while for ZnSe it is in a far infrared. Both analytical and numerical spectral distributions corresponding to this radiation are obtained. It turns out that for iodine there is only one critical velocity below and above of which the moving charge radiates in a quite different way. There are two critical velocity for ZnSe. We discuss possible complications arising when the radiation of the point-like charge is measured below the Cherenkov threshold. Probably, these considerations are applicable to the recent experiment in which the radiation of electric dipoles below the Cherenkov threshold was observed. The alternative reasons for ...
Enhanced circular dichroism via slow light in dispersive structured media
DEFF Research Database (Denmark)
Pedersen, Jesper Goor; Mortensen, Asger
2007-01-01
Circular dichroism (CD) is in widespread use as a means of determining enantiomeric excess. We show how slow-light phenomena in dispersive structured media allow for a reduction in the required optical path length of an order of magnitude. The same ideas may be used to enhance the sensitivity of CD...
Solute transport through porous media using asymptotic dispersivity
Indian Academy of Sciences (India)
P K Sharma; Teodrose Atnafu Abgaze
2015-08-01
In this paper, multiprocess non-equilibrium transport equation has been used, which accounts for both physical and chemical non-equilibrium for reactive transport through porous media. An asymptotic distance dependent dispersivity is used to embrace the concept of scale-dependent dispersion for solute transport in heterogeneous porous media. Semi-analytical solution has been derived of the governing equations with an asymptotic distance dependent dispersivity by using Laplace transform technique and the power series method. For application of analytical model, we simulated observed experimental breakthrough curves from 1500 cm long soil column experiments conducted in the laboratory. The simulation results of break-through curves were found to deviate from the observed breakthrough curves for both mobile–immobile and multiprocess non-equilibrium transport with constant dispersion models. However, multiprocess non-equilibrium with an asymptotic dispersion model gives better fit of experimental breakthrough curves through long soil column and hence it is more useful for describing anomalous solute transport through hetero-geneous porous media. The present model is simpler than the stochastic numerical method.
Permeability of mono- and bi-dispersed porous media
Directory of Open Access Journals (Sweden)
Kim S.J.
2013-04-01
Full Text Available 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.
Gurbatov, S N; Saichev, A I
2012-01-01
"Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonlinear waves of various physical nature. It may also be useful as a handbook for engineers and researchers who encounter the necessity of taking nonlinear wave effects into account of their work. Dr. Gurbatov S.N. is the head of Department, and Vice Rector for Research of Nizhny Novgorod State University. Dr. Rudenko O.V. is...
Leblond, Hervé; Mihalache, Dumitru; 10.1103/PHYSREVA.80.053812
2011-01-01
By using a powerful reductive perturbation technique, or a multiscale analysis, a generic Kadomtsev-Petviashvili evolution equation governing the propagation of femtosecond spatiotemporal optical solitons in quadratic nonlinear media beyond the slowly varying envelope approximation is put forward. Direct numerical simulations show the formation, from adequately chosen few-cycle input pulses, of both stable line solitons (in the case of a quadratic medium with normal dispersion) and of stable lumps (for a quadratic medium with anomalous dispersion). Besides, a typical example of the decay of the perturbed unstable line soliton into stable lumps for a quadratic nonlinear medium with anomalous dispersion is also given.
Dispersion analysis for waves propagated in fractured media
Energy Technology Data Exchange (ETDEWEB)
Lesniak, A.; Niitsuma, H. [Tohoku University, Sendai (Japan). Faculty of Engineering
1996-05-01
Dispersion of velocity is defined as a variation of the phase velocity with frequency. This paper describes the dispersion analysis of compressional body waves propagated in the heterogeneous fractured media. The new method proposed and discussed here permitted the evaluation of the variation in P wave arrival with frequency. For this processing method, any information about the attenuation of the medium are not required, and only an assumption of weak heterogeneity is important. It was shown that different mechanisms of dispersion can be distinguished and its value can be quantitatively estimated. Although the frequency used in this study was lower than those in most previous experiments reported in literature, the evaluated dispersion was large. It was suggested that such a large dispersion may be caused by the velocity structure of the media studied and by frequency dependent processes in a highly fractured zone. It was demonstrated that the present method can be used in the evaluation of subsurface fracture systems or characterization of any kind of heterogeneities. 10 refs., 6 figs.
Laboratory investigation of longitudinal dispersion in anisotropic porous media
Silliman, S.E.; Konikow, L.F.; Voss, C.I.
1987-01-01
In this study, laboratory experiments were used to investigate mechanisms that may cause anisotropy in the dispersion coefficient and to investigate the relation between anisotropy in hydraulic conductivity and anisotropy in longitudinal dispersion. Measurements of sodium chloride concentration (used as a tracer) were made at 105 in situ sampling locations in a new type of sand box designed to allow flow in either of two perpendicular directions. Two types of hydraulic anisotropy were examined. The first consisted of structured zones of increased hydraulic conductivity within a lower-conductivity medium. The second type involved low-conductivity platelike inclusions within a homogeneous, isotropic medium. The plates were aligned such that the tortuosity was increased only in one principal direction of permeability. Results using two examples of the first type of media showed that the apparent longitudinal dispersivities for flow parallel to the high-conductivity direction were greater than those perpendicular to this direction. Two examples of the second type of media produced smaller apparent longitudinal dispersivities for flow parallel to the high-conductivity direction. The results suggest that the mechanisms causing dispersive anisotropy can be related, conceptually, to the factors causing hydraulic anisotropy.
Chromatic and Dispersive Effects in Nonlinear Integrable Optics
Webb, Stephen D; Valishev, Alexander; Nagaitsev, Sergei N; Danilov, Viatcheslav V
2015-01-01
Proton accumulator rings and other circular hadron accelerators are susceptible to intensity-driven parametric instabilities because the zero-current charged particle dynamics are characterized by a single tune. Landau damping can suppress these instabilities, which requires energy spread in the beam or introducing nonlinear magnets such as octupoles. However, this approach reduces dynamic aperture. Nonlinear integrable optics can suppress parametric instabilities independent of energy spread in the distribution, while preserving the dynamic aperture. This novel approach promises to reduce particle losses and enable order-of-magnitude increases in beam intensity. In this paper we present results, obtained using the Lie operator formalism, on how chromaticity and dispersion affect particle orbits in integrable optics. We conclude that chromaticity in general breaks the integrability, unless the vertical and horizontal chromaticities are equal. Because of this, the chromaticity correcting magnets can be weaker ...
Diffusive–Dispersive and Reactive Fronts in Porous Media
DEFF Research Database (Denmark)
Haberer, Christina M.; Muniruzzaman, Muhammad; Grathwohl, Peter
2015-01-01
, across the unsaturated–saturated interface, under both conservative and reactive transport conditions. As reactive system we considered the abiotic oxidation of Fe2+ in the presence of O2. We studied the reaction kinetics in batch experiments and its coupling with diffusive and dispersive transport......Diffusive–dispersive mass transfer is important for many groundwater quality problems as it drives the interaction between different reactants, thus influencing a wide variety of biogeochemical processes. In this study, we performed laboratory experiments to quantify O2 transport in porous media...
Ultratransparent Media and Transformation Optics with Shifted Spatial Dispersions
Luo, Jie; Yang, Yuting; Yao, Zhongqi; Lu, Weixin; Hou, Bo; Hang, Zhi Hong; Chan, C. T.; Lai, Yun
2016-11-01
By using pure dielectric photonic crystals, we demonstrate the realization of ultratransparent media, which allow near 100% transmission of light for all incident angles and create aberration-free virtual images. The ultratransparency effect is well explained by spatially dispersive effective medium theory for photonic crystals, and verified by both simulations and proof-of-principle microwave experiments. Designed with shifted elliptical equal frequency contours, such ultratransparent media not only provide a low-loss and feasible platform for transformation optics devices at optical frequencies, but also enable new freedom for phase manipulation beyond the local medium framework.
On a class of nonlinear dispersive-dissipative interactions
Energy Technology Data Exchange (ETDEWEB)
Rosenau, P. [Tel Aviv Univ. (Israel). School of Mathematical Sciences
1997-07-29
The authors study the prototypical, genuinely nonlinear, equation; u{sub t} + a(u{sup m}){sub x} + (u{sup n}){sub xxx} = {mu}(u{sup k}){sub xx}, a, {mu} = consts., which encompasses a wide variety of dissipative-dispersive interactions. The parametric surface k = (m + n)/2 separates diffusion dominated from dissipation dominated phenomena. On this surface dissipative and dispersive effects are in detailed balance for all amplitudes. In particular, the m = n + 2 = k + 1 subclass can be transformed into a form free of convection and dissipation making it accessible to theoretical studies. Both bounded and unbounded oscillations are found and certain exact solutions are presented. When a = (2{mu}3/){sup 2} the map yields a linear equation; rational, periodic and aperiodic solutions are constructed.
On a class of nonlinear dispersive-dissipative interactions
Energy Technology Data Exchange (ETDEWEB)
Rosenau, P. [Tel Aviv Univ. (Israel). School of Mathematical Sciences
1997-07-29
The authors study the prototypical, genuinely nonlinear, equation; u{sub t} + a(u{sup m}){sub x} + (u{sup n}){sub xxx} = {mu}(u{sup k}){sub xx}, a, {mu} = consts., which encompasses a wide variety of dissipative-dispersive interactions. The parametric surface k = (m + n)/2 separates diffusion dominated from dissipation dominated phenomena. On this surface dissipative and dispersive effects are in detailed balance for all amplitudes. In particular, the m = n + 2 = k + 1 subclass can be transformed into a form free of convection and dissipation making it accessible to theoretical studies. Both bounded and unbounded oscillations are found and certain exact solutions are presented. When a = (2{mu}3/){sup 2} the map yields a linear equation; rational, periodic and aperiodic solutions are constructed.
Optical Beams in Nonlocal Nonlinear Media
DEFF Research Database (Denmark)
Królikowski, W.; Bang, Ole; Wyller, J.
2003-01-01
We discuss propagation of optical beams in nonlocal Kerr-like media with the nonlocality of general form. We study the effect of nonlocality on modulational instability of the plane wave fronts, collapse of finite beams and formation of spatial solitons.......We discuss propagation of optical beams in nonlocal Kerr-like media with the nonlocality of general form. We study the effect of nonlocality on modulational instability of the plane wave fronts, collapse of finite beams and formation of spatial solitons....
Modeling highly-dispersive transparency in planar nonlinear metamaterials
Potravkin, N. N.; Makarov, V. A.; Perezhogin, I. A.
2017-02-01
We consider propagation of light in planar optical metamaterial, which basic element is composed of two silver stripes, and it possesses strong dispersion in optical range. Our method of numerical modeling allows us to take into consideration the nonlinearity of the material and the effects of light self-action without considerable increase of the calculation time. It is shown that plasmonic resonances originating in such a structure result in multiple enhancement of local field and high sensitivity of the transmission coefficient to the intensity of incident monochromatic wave.
TRAVELING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR DISPERSIVE EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The method of the phase plane is emploied to investigate the solitary and periodic traveling waves for a class of nonlinear dispersive partial differential equations.By using the bifurcation theory of dynamical systems to do qualitative analysis,all possible phase portraits in the parametric space for the traveling wave systems are obtained.It can be shown that the existence of a singular straight line in the traveling wave system is the reason why smooth solitary wave solutions converge to solitary cusp wave solution when parameters are varied.The different parameter conditions for the existence of solitary and periodic wave solutions of different kinds are rigorously determined.
Demi, L; van Dongen, K W A; Verweij, M D
2011-03-01
Experimental data reveals that attenuation is an important phenomenon in medical ultrasound. Attenuation is particularly important for medical applications based on nonlinear acoustics, since higher harmonics experience higher attenuation than the fundamental. Here, a method is presented to accurately solve the wave equation for nonlinear acoustic media with spatially inhomogeneous attenuation. Losses are modeled by a spatially dependent compliance relaxation function, which is included in the Westervelt equation. Introduction of absorption in the form of a causal relaxation function automatically results in the appearance of dispersion. The appearance of inhomogeneities implies the presence of a spatially inhomogeneous contrast source in the presented full-wave method leading to inclusion of forward and backward scattering. The contrast source problem is solved iteratively using a Neumann scheme, similar to the iterative nonlinear contrast source (INCS) method. The presented method is directionally independent and capable of dealing with weakly to moderately nonlinear, large scale, three-dimensional wave fields occurring in diagnostic ultrasound. Convergence of the method has been investigated and results for homogeneous, lossy, linear media show full agreement with the exact results. Moreover, the performance of the method is demonstrated through simulations involving steered and unsteered beams in nonlinear media with spatially homogeneous and inhomogeneous attenuation.
Frequency comb generation in quadratic nonlinear media
Ricciardi, Iolanda; Parisi, Maria; Maddaloni, Pasquale; Santamaria, Luigi; De Natale, Paolo; De Rosa, Maurizio
2014-01-01
Optical frequency combs are nowadays routinely used tools in a wide range of scientific and technological applications. Different techniques have been developed for generating optical frequency combs, like mode-locking in lasers and third-order interactions in microresonators, or to extend their spectral capabilities, using frequency conversion processes in nonlinear materials. Here, we experimentally demonstrate and theoretically explain the onset of optical frequency combs in a simple cavity-enhanced second-harmonic-generation system, exploiting second-order nonlinear interactions. We develop an elemental model which provides a deep physical insight into the observed dynamics. Moreover, despite the different underlying physical mechanism, the proposed model is remarkably similar to the description of third-order effects in microresonators, revealing a potential variety of new effects to be explored. Finally, exploiting a nonlinearity intrinsically stronger than the third-order one, our work lays the groundw...
FILAMENTATION INSTABILITY OF LASER BEAMS IN NONLOCAL NONLINEAR MEDIA
Institute of Scientific and Technical Information of China (English)
文双春; 范滇元
2001-01-01
The filamentation instability of laser beams propagating in nonlocal nonlinear media is investigated. It is shown that the filamentation instability can occur in weakly nonlocal self-focusing media for any degree of nonlocality, and in defocusing media for the input light intensity exceeding a threshold related to the degree of nonlocality. A linear stability analysis is used to predict the initial growth rate of the instability. It is found that the nonlocality tends to suppress filamentation instability in self-focusing media and to stimulate filamentation instability in self-defocusing media. Numerical simulations confirm the results of the linear stability analysis and disclose a recurrence phenomenon in nonlocal self-focusing media analogous to the Fermi-Pasta-Ulam problem.
Mixed Method for Compressible Miscible Displacement with Dispersion in Porous Media
Institute of Scientific and Technical Information of China (English)
Chunguang Chen
2007-01-01
Compressible miscible displacement of one fluid by another in porous media is modelled by a nonlinear parabolic system. A finite element procedure is introduced to approximate the concentration of one fluid and the pressure of the mixture. The concentration is treated by a Galerkin method while the pressure is treated by a parabolic mixed finite element method. The effect of dispersion,which is neglected in [1],is considered. Optimal order estimates in L2 are derived for the errors in the approximate solutions.
Ring vortex solitons in nonlocal nonlinear media
DEFF Research Database (Denmark)
Briedis, D.; Petersen, D.E.; Edmundson, D.;
2005-01-01
or higher charge fundamental vortices as well as higher order (multiple ring) vortex solitons. Our results pave the way for experimental observation of stable vortex rings in other nonlocal nonlinear systems including Bose-Einstein condensates with pronounced long-range interparticle interaction....
Saturation-Dependence of Dispersion in Porous Media
Ghanbarian-Alavijeh, B; Hunt, Allen G
2012-01-01
In this study, we develop a saturation-dependent treatment of dispersion in porous media using concepts from critical path analysis, cluster statistics of percolation, and fractal scaling of percolation clusters. We calculate spatial solute distributions as a function of time and calculate arrival time distributions as a function of system size. Our previous results correctly predict the range of observed dispersivity values over ten orders of magnitude in experimental length scale, but that theory contains no explicit dependence on porosity or relative saturation. This omission complicates comparisons with experimental results for dispersion, which are often conducted at saturation less than 1. We now make specific comparisons of our predictions for the arrival time distribution with experiments on a single column over a range of saturations. This comparison suggests that the most important predictor of such distributions as a function of saturation is not the value of the saturation per se, but the applicab...
Studies on dispersive stabilization of porous media flows
Energy Technology Data Exchange (ETDEWEB)
Daripa, Prabir, E-mail: prabir.daripa@math.tamu.edu; Gin, Craig [Department of Mathematics, Texas A& M University, College Station, Texas 77843 (United States)
2016-08-15
Motivated by a need to improve the performance of chemical enhanced oil recovery (EOR) processes, we investigate dispersive effects on the linear stability of three-layer porous media flow models of EOR for two different types of interfaces: permeable and impermeable interfaces. Results presented are relevant for the design of smarter interfaces in the available parameter space of capillary number, Peclet number, longitudinal and transverse dispersion, and the viscous profile of the middle layer. The stabilization capacity of each of these two interfaces is explored numerically and conditions for complete dispersive stabilization are identified for each of these two types of interfaces. Key results obtained are (i) three-layer porous media flows with permeable interfaces can be almost completely stabilized by diffusion if the optimal viscous profile is chosen, (ii) flows with impermeable interfaces can also be almost completely stabilized for short time, but become more unstable at later times because diffusion flattens out the basic viscous profile, (iii) diffusion stabilizes short waves more than long waves which leads to a “turning point” Peclet number at which short and long waves have the same growth rate, and (iv) mechanical dispersion further stabilizes flows with permeable interfaces but in some cases has a destabilizing effect for flows with impermeable interfaces, which is a surprising result. These results are then used to give a comparison of the two types of interfaces. It is found that for most values of the flow parameters, permeable interfaces suppress flow instability more than impermeable interfaces.
Othman, N.; Shah, N. S. M.; Tay, K. G.; Pakarzadeh, H.; Cholan, N. A.; Talib, R.
2017-09-01
The highly-nonlinear fiber is the ideal gain medium for many applications particularly because its dispersion can be easily engineered. However, the modification of the fiber dispersion will affect the higher-order dispersion coefficients. Hence, this paper investigates the effect of highly-nonlinear dispersion-shifted fiber dispersion profile on the higher-order dispersion coefficients which are the fourth-order and sixth-order dispersion coefficients. The dispersion profile was modified by varying the slope at zero-dispersion wavelength. The fourth-order dispersion coefficient exhibits changes from positive to negative value as the slope at zero-dispersion wavelength is getting higher. Meanwhile, sixth-order dispersion coefficient remains with the positive value even though it shows the reduction as the slope is increased, however it will eventually become negative when the dispersion is high enough. In short, the values of both fourth-order and sixth-order dispersion coefficients at zero-dispersion wavelength decrease when the slope increases.
Controlling nonlinear waves in excitable media
Energy Technology Data Exchange (ETDEWEB)
Puebla, Hector [Departamento de Energia, Universidad Autonoma Metropolitana, Av. San Pablo No. 180, Reynosa-Tamaulipas, Azcapotzalco 02200, DF, Mexico (Mexico)], E-mail: hpuebla@correo.azc.uam.mx; Martin, Roland [Laboratoire de Modelisation et d' Imagerie en Geosciences, CNRS UMR and INRIA Futurs Magique-3D, Universite de Pau (France); Alvarez-Ramirez, Jose [Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa (Mexico); Aguilar-Lopez, Ricardo [Departamento de Biotecnologia y Bioingenieria, CINVESTAV-IPN (Mexico)
2009-01-30
A new feedback control method is proposed to control the spatio-temporal dynamics in excitable media. Applying suitable external forcing to the system's slow variable, successful suppression and control of propagating pulses as well as spiral waves can be obtained. The proposed controller is composed by an observer to infer uncertain terms such as diffusive transport and kinetic rates, and an inverse-dynamics feedback function. Numerical simulations shown the effectiveness of the proposed feedback control approach.
Study On Nonlinear effect In 2D Plastic Media
Wenjie, D.; Chen, X.
2011-12-01
Unlike the perfect elastic, homogeneous and isotropic model, the properties of real earth media are heterogeneous, plastic and anisotropic to a certain extend. To accurately simulate the strong ground motion in a basin, nonlinear or plastic effect should be considered in simulation. In this study, we use DRP/opt MacCormack non-staggered finite difference method to simulate 2D seismic wave propagation in anisotropic and plastic media. Compared with the traditional staggered grid FDM, this scheme is more accurate and more efficient. We focus on the nonlinear character of the sedimentary basin model. The preliminary ground motion results indicate that the energy of seismic wave has obvious nonlinear dissipation and irreversible deformations which is danger to buildings in the sedimentary basin.
Nonlinear property of slightly compressible media permeated with air-filled bubbles
Institute of Scientific and Technical Information of China (English)
Bo QIN
2009-01-01
Based on the nonlinear oscillation of an air- filled bubble in weakly compressible media at prestressed state, the effective medium method is used to study the nonlinear property of the slightly compressible media permeated with air bubbles. It is this nonlinear oscilla- tion of air bubbles that results in the nonlinear property of the porous media. Numerical results have confirmed that the nonlinearity of the porous media is usually high, though the optimal porosity is very small. Moreover, the nonlinear property is greatly affected by the prestressed state, porosity, and shear modulus of the matrix media.
Nonlinear self-focus of pulsed-wave beams in Kerr media
Energy Technology Data Exchange (ETDEWEB)
Judkins, J.B.
1992-12-31
A modified finite-difference time-domain method for solving Maxwell`s equations in nonlinear media is presented. This method allows for a finite response time to be incorporated in the medium, physically creating dispersion and absorption mechanisms. The technique models electromagnetic fields in two space dimensions and time and encompasses both the TE{sub z} and TM{sub z} set of decoupled field equations. Aspects of an ultra-short pulsed Gaussian beam are studied in a variety of linear and nonlinear environments to demonstrate that the methods developed here can be used efficaciously in the modeling of pulses in complex problem space geometries even when nonlinearities are present.
Nonlinear waves in electromigration dispersion in a capillary
Christov, Ivan C
2016-01-01
We construct exact solutions to an unusual nonlinear advection--diffusion equation arising in the study of Taylor--Aris (also known as shear) dispersion due to electroosmotic flow during electromigration in a capillary. An exact reduction to a Darboux equation is found under a traveling-wave anzats. The equilibria of this ordinary differential equation are analyzed, showing that their stability is determined solely by the (dimensionless) wave speed without regard to any (dimensionless) physical parameters. Integral curves, connecting the appropriate equilibria of the Darboux equation that governs traveling waves, are constructed, which in turn are shown to be asymmetric kink solutions ({\\it i.e.}, non-Taylor shocks). Furthermore, it is shown that the governing Darboux equation exhibits bistability, which leads to two coexisting non-negative kink solutions for (dimensionless) wave speeds greater than unity. Finally, we give some remarks on other types of traveling-wave solutions and a discussion of some approx...
Dispersion of nonresonant third-order nonlinearities in Silicon Carbide
De Leonardis, Francesco; Soref, Richard A.; Passaro, Vittorio M. N.
2017-01-01
In this paper we present a physical discussion of the indirect two-photon absorption (TPA) occuring in silicon carbide with either cubic or wurtzite structure. Phonon-electron interaction is analyzed by finding the phonon features involved in the process as depending upon the crystal symmetry. Consistent physical assumptions about the phonon-electron scattering mechanisms are proposed in order to give a mathematical formulation to predict the wavelength dispersion of TPA and the Kerr nonlinear refractive index n2. The TPA spectrum is investigated including the effects of band nonparabolicity and the influence of the continuum exciton. Moreover, a parametric analysis is presented in order to fit the experimental measurements. Finally, we have estimated the n2 in a large wavelength range spanning the visible to the mid-IR region. PMID:28098223
Dispersion of nonresonant third-order nonlinearities in Silicon Carbide
de Leonardis, Francesco; Soref, Richard A.; Passaro, Vittorio M. N.
2017-01-01
In this paper we present a physical discussion of the indirect two-photon absorption (TPA) occuring in silicon carbide with either cubic or wurtzite structure. Phonon-electron interaction is analyzed by finding the phonon features involved in the process as depending upon the crystal symmetry. Consistent physical assumptions about the phonon-electron scattering mechanisms are proposed in order to give a mathematical formulation to predict the wavelength dispersion of TPA and the Kerr nonlinear refractive index n2. The TPA spectrum is investigated including the effects of band nonparabolicity and the influence of the continuum exciton. Moreover, a parametric analysis is presented in order to fit the experimental measurements. Finally, we have estimated the n2 in a large wavelength range spanning the visible to the mid-IR region.
Nonlinear plasmonic dispersion and coupling analysis in the symmetric graphene sheets waveguide
Jiang, Xiangqian; Yuan, Haiming; Sun, Xiudong
2016-12-01
We study the nonlinear dispersion and coupling properties of the graphene-bounded dielectric slab waveguide at near-THz/THz frequency range, and then reveal the mechanism of symmetry breaking in nonlinear graphene waveguide. We analyze the influence of field intensity and chemical potential on dispersion relation, and find that the nonlinearity of graphene affects strongly the dispersion relation. As the chemical potential decreases, the dispersion properties change significantly. Antisymmetric and asymmetric branches disappear and only symmetric one remains. A nonlinear coupled mode theory is established to describe the dispersion relations and its variation, which agrees with the numerical results well. Using the nonlinear couple model we reveal the reason of occurrence of asymmetric mode in the nonlinear waveguide.
Interface modes at step edges of media with anisotropic dispersion
Toedt, Jan-Niklas; Mansfeld, Sebastian; Mellem, Daniel; Hansen, Wolfgang; Heitmann, Detlef; Mendach, Stefan
2016-05-01
Time-resolved scanning Kerr microscopy data are presented that illustrate the refraction and total reflection of spin waves in a Ni80Fe20 film at a film-thickness step. In our experiments spin waves are excited with microwaves on coplanar wave guides. By changing the orientation of an externally applied magnetic field, we can manipulate the group velocity of the wave and hence control the angle of incidence on the step. An interface mode bound at the step is observed, when the magnetic field vector is perpendicular to the step. We point out the general conditions under which such interface modes can be expected in media with strongly anisotropic dispersion.
Magnetoviscous effect in ferrofluids with different dispersion media
Borin, D. Yu; Korolev, V. V.; Ramazanova, A. G.; Odenbach, S.; Balmasova, O. V.; Yashkova, V. I.; Korolev, D. V.
2016-10-01
Ferrofluids based on magnetite nanoparticles dispersed in different carrier media (dialkyldiphenyl and polyethylsiloxane) have been synthesized using mixed surfactants (oleic acid, stearic acid and alkenyl succinic anhydride). Magnetic properties of the samples and a change of their shear viscosities in an applied magnetic field have been studied in order to evaluate an influence of the carrier medium on a magnetoviscous effect. A significance of the interaction of the carrier medium and surfactant with a consideration of the magnetic and rheological behavior of ferrofluids was demonstrated.
Covariant Description of Transformation Optics in Linear and Nonlinear Media
Paul, Oliver
2011-01-01
The technique of transformation optics (TO) is an elegant method for the design of electromagnetic media with tailored optical properties. In this paper, we focus on the formal structure of TO theory. By using a complete covariant formalism, we present a general transformation law that holds for arbitrary materials including bianisotropic, magneto-optical, nonlinear and moving media. Due to the principle of general covariance, the formalism is applicable to arbitrary space-time coordinate transformations and automatically accounts for magneto-electric coupling terms. The formalism is demonstrated for the calculation of the second harmonic generation in a twisted TO concentrator.
Quantum and classical optics of dispersive and absorptive structured media
Bhat, Navin Andrew Rama
This thesis presents a Hamiltonian formulation of the electromagnetic fields in structured (inhomogeneous) media of arbitrary dimensionality, with arbitrary material dispersion and absorption consistent with causality. The method is based on an identification of the photonic component of the polariton modes of the system. Although the medium degrees of freedom are introduced in an oscillator model, only the macroscopic response of the medium appears in the derived eigenvalue equation for the polaritons. For both the discrete transparent-regime spectrum and the continuous absorptive-regime spectrum, standard codes for photonic modes in nonabsorptive systems can easily be leveraged to calculate polariton modes. Two applications of the theory are presented: pulse propagation and spontaneous parametric down-conversion (SPDC). In the propagation study, the dynamics of the nonfluctuating part of a classical-like pulse are expressed in terms of a Schrodinger equation for a polariton effective field. The complex propagation parameters of that equation can be obtained from the same generalized dispersion surfaces typically used while neglecting absorption, without incurring additional computational complexity. As an example I characterize optical pulse propagation in an Au/MgF 2 metallodielectric stack, using the empirical response function, and elucidate the various roles of Bragg scattering, interband absorption and field expulsion. Further, I derive the Beer coefficient in causal structured media. The SPDC calculation is rigorous, captures the full 3D physics, and properly incorporates linear dispersion. I obtain an expression for the down-converted state, quantify pair-production properties, and characterize the scaling behavior of the SPDC energy. Dispersion affects the normalization of the polariton modes, and calculations of the down-conversion efficiency that neglect this can be off by 100% or more for common media regardless of geometry if the pump is near the band
Stability Analysis of Continuous Waves in Nonlocal Random Nonlinear Media
Directory of Open Access Journals (Sweden)
Maxim A. Molchan
2007-08-01
Full Text Available On the basis of the competing cubic-quintic nonlinearity model, stability (instability of continuous waves in nonlocal random non-Kerr nonlinear media is studied analytically and numerically. Fluctuating media parameters are modeled by the Gaussian white noise. It is shown that for different response functions of a medium nonlocality suppresses, as a rule, both the growth rate peak and bandwidth of instability caused by random parameters. At the same time, for a special form of the response functions there can be an ''anomalous'' subjection of nonlocality to the instability development which leads to further increase of the growth rate. Along with the second-order moments of the modulational amplitude, higher-order moments are taken into account.
Engineering chromatic dispersion and effective nonlinearity in a dual-slot waveguide.
Liu, Yan; Yan, Jing; Han, Genquan
2014-09-20
In this paper, we propose a new dual slot based on rib-like structure, which exhibits a flat and near-zero dispersion over a 198 nm wide wavelength range. Chromatic dispersion of dual-slot silicon (Si) waveguide is mainly determined by waveguide dispersion due to the manipulating mode effective area rather than by the material dispersion. Moreover, the nonlinear coefficient and effective mode area of the waveguide are also explored in detail. A nonlinear coefficient of 1460/m/W at 1550 nm is achieved, which is 10 times larger than that of the Si rib waveguide. By changing different waveguide variables, both the dispersion and nonlinear coefficient can be tailored, thus enabling the potential for a highly nonlinear waveguide with uniform dispersion over a wide wavelength range, which could benefit the performance of broadband optical signal systems.
Institute of Scientific and Technical Information of China (English)
Xiao Li; Zhang Wei; Huang Yi-Dong; Peng Jiang-De
2008-01-01
High nonlinear microstructure fibre (HNMF) is preferred in nonlinear fibre optics, especially in the applications of optical parametric effects, due to its high optical nonlinear coefficient. However, polarization dependent dispersion will impact the nonlinear optical parametric process in HNMFs. In this paper, modulation instability (MI) method is used to measure the polarization dependent dispersion of a piece of commercial HNMF, including the group velocity dispersion, the dispersion slope, the fourth-order dispersion and group birefringence. It also experimentally demonstrates the impact of the polarization dependent dispersion on the continuous wave supercontinuum (SC) generation. On one axis MI sidebands with symmetric frequency dctunings are generated, while on the other axis with larger MI frequency detuning, SC is generated by soliton self-frequency shift.
Stabilization of vortex beams in Kerr media by nonlinear absorption
Porras, Miguel A.; Carvalho, Márcio; Leblond, Hervé; Malomed, Boris A.
2016-11-01
We elaborate a solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form robust tubular filaments in transparent dielectrics as common as air, water, and optical glasses at sufficiently high intensities. We also show that the tubular, rotating, and specklelike filamentation regimes, previously observed in experiments with axicon-generated Bessel beams, can be explained as manifestations of the stability or instability of a specific nonlinear Bessel-vortex state, which is fully identified.
Stabilization of vortex beams in Kerr media by nonlinear absorption
Porras, Miguel A; Leblond, Hervé; Malomed, Boris A
2016-01-01
We elaborate a new solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form robust tubular filaments in transparent dielectrics as common as air, water and optical glasses at sufficiently high intensities. We also show that the tubular, rotating and speckle-like filamentation regimes, previously observed in experiments with axicon-generated Bessel beams, can be explained as manifestations of the stability or instability of a specific nonlinear Bessel-vortex state, which is fully identified.
A WEAKLY NONLINEAR WATER WAVE MODEL TAKING INTO ACCOUNT DISPERSION OF WAVE PHASE VELOCITY
Institute of Scientific and Technical Information of China (English)
李瑞杰; 李东永
2002-01-01
This paper presents a weakly nonlinear water wave model using a mild slope equation and a new explicit formulation which takes into account dispersion of wave phase velocity, approximates Hedges' (1987) nonlinear dispersion relationship, and accords well with the original empirical formula. Comparison of the calculating results with those obtained from the experimental data and those obtained from linear wave theory showed that the present water wave model considering the dispersion of phase velocity is rational and in good agreement with experiment data.
Dispersion-engineered and highly-nonlinear microstructured polymer optical fibres
DEFF Research Database (Denmark)
Frosz, Michael Henoch; Nielsen, Kristian; Hlubina, Petr;
2009-01-01
We demonstrate dispersion-engineering of microstructured polymer optical fibres (mPOFs) made of poly(methyl methacrylate) (PMMA). A significant shift of the total dispersion from the material dispersion is confirmed through measurement of the mPOF dispersion using white-light spectral....... To increase the nonlinearity of the mPOFs we investigated doping of PMMA with the highly-nonlinear dye Disperse Red 1. Both doping of a PMMA cane and direct doping of a PMMA mPOF was performed....
Dawood, M.; Alejos, A. V.
2011-06-01
The electromagnetic (EM) waves propagating through causal, linear, and lossy dispersive media (soil, foliage, plasma, water, biological tissue, etc.), experience frequency-dependent attenuation and phase distortion. This has assumed significant importance for systems operating with ultrawideband (UWB) spectrum. This paper analyzes the dynamical evolution of UWB noise radar signals through dispersive media. The effects on the signal propagation due to the evolution of the Brillouin precursor through dispersive media are discussed. The evolving waveforms are then compared with the Brillouin precursor due to rectangular sine-modulated deterministic signals. The advantages of random noise waveforms through dispersive media are also discussed.
Indian Academy of Sciences (India)
R Ganapathy; V C Kuriakose
2002-04-01
We obtain conditions for the occurrence of cross-phase modulational instability in the normal dispersion regime for the coupled higher order nonlinear Schrödinger equation with higher order dispersion and nonlinear terms.
Magnetoviscous effect in ferrofluids with different dispersion media
Energy Technology Data Exchange (ETDEWEB)
Borin, D.Yu [TU Dresden, Institute of Fluid Mechanics, Dresden 01062 (Germany); Korolev, V.V. [G.A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences, Ivanovo (Russian Federation); Ramazanova, A.G., E-mail: agr@isc-ras.ru [G.A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences, Ivanovo (Russian Federation); Odenbach, S. [TU Dresden, Institute of Fluid Mechanics, Dresden 01062 (Germany); Balmasova, O.V.; Yashkova, V.I. [G.A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences, Ivanovo (Russian Federation); Korolev, D.V. [Federal Sate Unitary Enterprise all Russian Scientific Research Institute of Aviation Materials (Russian Federation)
2016-10-15
Ferrofluids based on magnetite nanoparticles dispersed in different carrier media (dialkyldiphenyl and polyethylsiloxane) have been synthesized using mixed surfactants (oleic acid, stearic acid and alkenyl succinic anhydride). Magnetic properties of the samples and a change of their shear viscosities in an applied magnetic field have been studied in order to evaluate an influence of the carrier medium on a magnetoviscous effect. A significance of the interaction of the carrier medium and surfactant with a consideration of the magnetic and rheological behavior of ferrofluids was demonstrated. - Highlights: • Ferrofluids based on mixed surfactants were synthesized. • Oleic, stearic acid and alkenylsuccinic anhydride were used. • The nature of the surfactant has a high impact on the ferrofluids' shear viscosity. • The core size distribution is not the only determining reason of the structuring. • Significance of the interaction of the carrier medium and surfactant is demonstrated.
Optical Momentum, Spin, and Angular Momentum in Dispersive Media
Bliokh, Konstantin Y.; Bekshaev, Aleksandr Y.; Nori, Franco
2017-08-01
We examine the momentum, spin, and orbital angular momentum of structured monochromatic optical fields in dispersive inhomogeneous isotropic media. There are two bifurcations in this general problem: the Abraham-Minkowski dilemma and the kinetic (Poynting-like) versus canonical (spin-orbital) pictures. We show that the kinetic Abraham momentum describes the energy flux and group velocity of the wave in the medium. At the same time, we introduce novel canonical Minkowski-type momentum, spin, and orbital angular momentum densities of the field. These quantities exhibit fairly natural forms, analogous to the Brillouin energy density, as well as multiple advantages as compared with previously considered formalisms. As an example, we apply this general theory to inhomogeneous surface plasmon-polariton (SPP) waves at a metal-vacuum interface and show that SPPs carry a "supermomentum," proportional to the wave vector kp>ω /c , and a transverse spin, which can change its sign depending on the frequency ω .
The interaction of long and short waves in dispersive media
Deconinck, Bernard; Nguyen, Nghiem V.; Segal, Benjamin L.
2016-10-01
The KdV equation models the propagation of long waves in dispersive media, while the NLS equation models the dynamics of narrow-bandwidth wave packets consisting of short dispersive waves. A system that couples the two equations to model the interaction of long and short waves is mathematically attractive and such a system has been studied over the last decades. We evaluate the validity of this system as a physical model, discussing two main problems. First, only the system coupling the linear Schrödinger equation with KdV has been derived in the literature. Second, the time variables appearing in the equations are of a different order. It appears that in the manuscripts that study the coupled NLS-KdV system, an assumption has been made that the coupled system can be derived, justifying its mathematical study. In fact, this is true even for the papers where the asymptotic derivation with the problems described above is presented. In addition to discussing these inconsistencies, we present an alternative system describing the interaction of long and short waves.
Institute of Scientific and Technical Information of China (English)
文双春; 钱列加; 范滇元
2003-01-01
A new method for generation of a train of ultrashort pulses or a sequence of ultrashort light bullets is proposed.This method is based on the fourth-order dispersion-dependent spatiotemporal instability in dispersive Kerr media. The repetition-rate of the generated bullets can be made quite large by increasing the corresponding spatial modulation frequency locating in the new instability region resulted from fourth-order dispersion.
The Whitham approach to dispersive shocks in systems with cubic–quintic nonlinearities
Crosta, M
2012-09-12
By employing a rigorous approach based on the Whitham modulation theory, we investigate dispersive shock waves arising in a high-order nonlinear Schrödinger equation with competing cubic and quintic nonlinear responses. This model finds important applications in both nonlinear optics and Bose–Einstein condensates. Our theory predicts the formation of dispersive shocks with totally controllable properties, encompassing both steering and compression effects. Numerical simulations confirm these results perfectly. Quite remarkably, shock tuning can be achieved in the regime of a very small high order, i.e. quintic, nonlinearity.
Critique of Burnett-Frind dispersion tensor for axisymmetric porous media
Energy Technology Data Exchange (ETDEWEB)
Lichtner, Peter C [Los Alamos National Laboratory; Kelkar, Sharad [Los Alamos National Laboratory; Robinson, Bruce A [Los Alamos National Laboratory
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.
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.
DEFF Research Database (Denmark)
2015-01-01
A method and a pulse compressor (1) for compressing an optical pulse, wherein the pulse compressor comprising a bulk quadratic nonlinear medium (2) adapted for generating a negative nonlinear phase variation on the optical pulse and having a negative group-velocity dispersion, and a dispersive un...... subsequently be compressed by providing normal dispersion. As KDP crystals can be glued together, large apertures of the pulse compressor are possible making this method suitable for pulse compression in Joule-class lasers....
A large-scale nonlinear eigensolver for the analysis of dispersive nanostructures
Guo, Hua; Arbenz, Peter; Oswald, Benedikt
2013-08-01
We introduce the electromagnetic eigenmodal solver code FemaxxNano for the numerical analysis of nanometer structured optical systems, a scientific field generally know as nanooptics. FemaxxNano solves the electric field vector wave equation and calculates the electromagnetic eigenmodes of nearly arbitrary 3-dimensional resonators, embedded either in free-space, vacuum or a background medium. Here, the study of the interaction between nanometer sized metallic structures and light is at the heart of the physical problem. Since metals in the optical region of the electromagnetic spectrum are highly dispersive and, thus, dissipative, dielectric media, we eventually obtain a nonlinear eigenvalue problem. We discretize the electromagnetic eigenvalue problem with the finite element method (FEM) in 3-dimensional space and on unstructured tetrahedral grids. We introduce a fully iterative scheme to solve the nonlinear problem for complex coefficient matrices that depend on wavelength. We investigate the properties of the algorithm in detail and demonstrate its performance by analyzing a nanometer sized optical dimer structure, a specific type of optical antenna, on distributed-memory parallel computers.
Nonlinear Pulse Compression and Reshaping Using Cross-Phase Modulation in a Dispersion-Shifted Fiber
Institute of Scientific and Technical Information of China (English)
S.; W.; Chan; K.; K.; Chow; C.; Shu
2003-01-01
Nonlinear pulse compression has been demonstrated by cross-phase modulation in a dispersion-shifted fiber. The output is obtained from filtering of the broadened optical spectrum and a pulse width reduction from 61 to 28 ps is achieved.
A comparison of nonlinear media for parametric all-optical signal processing
DEFF Research Database (Denmark)
Martinez Diaz, Jordi; Bohigas Nadal, Jaume; Vukovic, Dragana;
2013-01-01
We systematically compare nonlinear media for parametric signal processing by determining the minimum pump power that is required for a given conversion efficiency in a degenerate four-wave mixing process, including the effect of nonlinear loss....
Institute of Scientific and Technical Information of China (English)
赵应桥; 朱鹤元; 刘建华; 孙迭篪; 李富铭
1997-01-01
A time-resolved cross-phase modulation method combined with a modified nonlinear Schrodinger equation is used to study the effects of nonlinear response time on the propagation of ultrashort pulses in nonlinear dispersion media. Evolution of cross-phase modulation spectrum with the different time delay between the probe pulse and pump pulse is simulated using split-step Fourier method. It is shown that both normal self-frequency-shift-red-shift and abnormal self-frequency-shift-blue-shift can occur in the frequency domain for the probe pulse, and a satisfactory theoretical interpretation is given.
New Optical Solitons in High-Order Dispersive Cubic-Quintic Nonlinear Schrodinger Equation
Institute of Scientific and Technical Information of China (English)
LI Hua-Mei; XU You-Shen; LIN Ji
2004-01-01
By using the generalized tanh-function method, we find bright and dark solitary wave solutions to an extended nonlinear Schrodinger equation with the third-order and fourth-order dispersion and the cubic-quintic nonlinear terms, describing the propagation of extremely short pulses. At the same time, we also obtained other types of exact solutions.
New explicit exact solutions to a nonlinear dispersive-dissipative equation
Institute of Scientific and Technical Information of China (English)
Naranmandula; Wang Ke-Xie
2004-01-01
Using the first-integral method, we obtain a series of new explicit exact solutions such as exponential function solutions, triangular function solutions, singular solitary wave solution and kink solitary wave solution of a nonlinear dispersive-dissipative equation, which describes weak nonlinear ion-acoustic waves in plasma consisting of cold ions and warm electrons.
E Heebner, John; Boyd, Robert W; Park, Q-Han
2002-03-01
We describe an optical transmission line that consists of an array of wavelength-scale optical disk resonators coupled to an optical waveguide. Such a structure leads to exotic optical characteristics, including ultraslow group velocities of propagation, enhanced optical nonlinearities, and large dispersion with a controllable magnitude and sign. This device supports soliton propagation, which can be described by a generalized nonlinear Schrodinger equation.
Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves
DEFF Research Database (Denmark)
Eldeberky, Y.; Madsen, Per A.
1999-01-01
This paper presents a new and more accurate set of deterministic evolution equations for the propagation of fully dispersive, weakly nonlinear, irregular, multidirectional waves. The equations are derived directly from the Laplace equation with leading order nonlinearity in the surface boundary c...
Chemotaxis and flow disorder shape microbial dispersion in porous media
De Anna, Pietro; Yawata, Yutaka; Stocker, Roman; Juanes, Ruben
2017-04-01
Bacteria drive a plethora of natural processes in the subsurface, consuming organic matter and catalysing chemical reactions that are key to global elemental cycles. These macro-scale consequences result from the collective action of individual bacteria at the micro-scale, which are modulated by the highly heterogeneous subsurface environment, dominated by flow disorder and strong chemical gradients. Yet, despite the generally recognized importance of these microscale processes, microbe-host medium interaction at the pore scale remain poorly characterized and understood. Here, we introduce a microfluidic model system to directly image and quantify the role of cell motility on bacterial dispersion and residence time in confined, porous, media. Using the soil-dwelling bacterium Bacillus subtilis and the common amino acid serine as a resource, we observe that chemotaxis in highly disordered and confined physico-chemical environment affords bacteria an increase in their ability to persistently occupy the host medium. Our findings illustrate that the interplay between bacterial behaviour and pore-scale disorder in fluid velocity and nutrient concentration directly impacts the residence time, transport and bio-geo-chemical transformation rates of biota in the subsurface, and thus likely the processes they mediate.
Dispersion engineering silicon nitride waveguides for broadband nonlinear frequency conversion
Epping, J.P.
2015-01-01
In this thesis, we investigated nonlinear frequency conversion of optical wavelengths using integrated silicon nitride (Si3N4) waveguides. Two nonlinear conversion schemes were considered: seeded four-wave mixing and supercontinuum generation. The first—seeded four-wave mixing—is investigated by a n
DEFF Research Database (Denmark)
Da Ros, Francesco; Sackey, I.; Jazayerifar, M.
2015-01-01
Kerr nonlinearity compensation by optical phase conjugation is demonstrated in a WDM PDM 16-QAM system. Improved received signal quality is reported for both dispersion-compensated and dispersion-uncompensated transmission and a comparison with digital backpropagation is provided....
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Johansson, M.
1998-01-01
The dynamics of discrete two-dimensional nonlinear Schrodinger models with long-range dispersive interactions is investigated. In particular, we focus on the cases where the dispersion arises from a dipole-dipole interaction, assuming the dipole moments at each lattice site to be aligned either...
Nonlinear Interactions of Dispersion-managed Soliton in OTDM Systems
Institute of Scientific and Technical Information of China (English)
CAI Ju; MAO Yu; LU Hui; ZHANG Li-na; YANG Xiang-lin
2003-01-01
The dispersion-managed soliton (DMS) transmission model of dispersion-managed systems is established,and the intrachannel DMS interactions equation is obtained.The impact of soliton interactions on DMS systems are numerically investigated.Finally,the relationships of the collision length changing with map strength are revealed.
Fractional quantum Hall edge: Effect of nonlinear dispersion and edge roton
Jolad, Shivakumar; Sen, Diptiman; Jain, Jainendra K.
2010-01-01
According to Wen's theory, a universal behavior of the fractional quantum Hall edge is expected at sufficiently low energies, where the dispersion of the elementary edge excitation is linear. A microscopic calculation shows that the actual dispersion is indeed linear at low energies, but deviates from linearity beyond certain energy, and also exhibits an "edge roton minimum." We determine the edge exponent from a microscopic approach, and find that the nonlinearity of the dispersion makes a s...
Flow and dispersion in anisotropic porous media: a Lattice-Boltzmann study
Maggiolo, Dario; Guarnieri, Massimo
2016-01-01
Given their capability of spreading active chemical species and collecting electricity, porous media made of carbon fibers are extensively used as diffusion layers in energy storage systems, such as redox flow batteries. In spite of this, the dispersion dynamics of species inside porous media is still not well understood and often lends itself to different interpretations. Actually, the microscopic design of efficient porous media which can potentially and effectively improve the performances of flow batteries, is a still open challenge. The present study aims to investigate the effect of fibrous media micro-structure on dispersion, in particular the effect of fiber orientation on drag and dispersion dynamics. Several Lattice-Boltzmann simulations of {flows through} differently-oriented fibrous media coupled with Lagrangian simulations of particle tracers have been performed. Results show that orienting fibers preferentially along the streamwise direction minimizes the drag and maximizes the dispersion, which...
Dispersion of the nonlinear refractive index of optical crystals
Adair, Robert; Chase, L. L.; Payne, Stephen A.
1992-09-01
The nonlinear refractive indices of several important optical materials have been measured at the second and third harmonic wavelengths of the Nd laser using nearly degenerate four-wave mixing. Measurements made relative to the nonlinear index of fused silica have the highest accuracy. Absolute measurements were also made using the Raman cross-section of benzene as a nonlinear reference standard. The relative measurements are compared with a despersion model base on parameters fitted to the linear refractive indicies and also to a recently proposed model based on Kramers-Kronig transformation of the calculated, two-band, two-photon loss spectrum.
Nonlinear acoustics in a dispersive continuum: Random waves, radiation pressure, and quantum noise
Cabot, M. A.
The nonlinear interaction of sound with sound is studied using dispersive hydrodynamics which derived from a variational principle and the assumption that the internal energy density depends on gradients of the mass density. The attenuation of sound due to nonlinear interaction with a background is calculated and is shown to be sensitive to both the nature of the dispersion and decay bandwidths. The theoretical results are compared to those of low temperature helium experiments. A kinetic equation which described the nonlinear self-inter action of a background is derived. When a Deybe-type cutoff is imposed, a white noise distribution is shown to be a stationary distribution of the kinetic equation. The attenuation and spectrum of decay of a sound wave due to nonlinear interaction with zero point motion is calculated. In one dimension, the dispersive hydrodynamic equations are used to calculate the Langevin and Rayleigh radiation pressures of wave packets and solitary waves.
Could the photon dispersion relation be non-linear ?
2008-01-01
The free photon dispersion relation is a reference quantity for high precision tests of Lorentz Invariance. We first outline theoretical approaches to a conceivable Lorentz Invariance Violation (LIV). Next we address phenomenological tests based on the propagation of cosmic rays, in particular in Gamma Ray Bursts (GRBs). As a specific concept, which could imply LIV, we then focus on field theory in a non-commutative (NC) space, and we present non-perturbative results for the dispersion relati...
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.
DEFF Research Database (Denmark)
Bache, Morten; Zhou, Binbin
2014-01-01
A new high-energy pulse compressor uses self-defocusing spectral broadening in anomalously dispersive quadratic nonlinear crystals, followed by positive group-delay-dispersion compensation. Compression to sub-50 fs is possible from Joule-class 1.03 µm femtosecond amplifiers in large-aperture KDP....
A general theory of two-wave mixing in nonlinear media
DEFF Research Database (Denmark)
Chi, Mingjun; Huignard, Jean-Pierre; Petersen, Paul Michael
2009-01-01
A general theory of two-wave mixing in nonlinear media is presented. Assuming a gain (or absorption) grating and a refractive index grating are generated because of the nonlinear process in a nonlinear medium, the coupled-wave equations of two-wave mixing are derived based on the Maxwell’s wave e...
Nonlinear wave propagation studies, dispersion modeling, and signal parameters correction
Czech Academy of Sciences Publication Activity Database
Převorovský, Zdeněk
..: ..., 2004, 00. [European Workshop on FP6-AERONEWS /1./. Naples (IT), 13.09.2004-16.09.2004] EU Projects: European Commission(XE) 502927 - AERO-NEWS Institutional research plan: CEZ:AV0Z2076919 Keywords : nodestructive testing * nonlinear elastic wave spectroscopy Subject RIV: BI - Acoustics
Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Eskilsson, Claes; Bigoni, Daniele
2016-01-01
). In the present paper we use a single layer of quadratic (in 2D) and prismatic (in 3D) elements. The model has been stabilized through a combination of over-integration of the Galerkin projections and a mild modal filter. We present numerical tests of nonlinear waves serving as a proof-of-concept validation...
Adaptive control of the propagation of ultrafast light through random and nonlinear media
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
Environmental Consequences of Nanotechnologies: Nanoparticle Dispersion in Aqueous Media: SOP-T-1
2015-02-01
ER D C/ EL S R- 15 -2 Environmental Consequences of Nanotechnologies Nanoparticle Dispersion in Aqueous Media: SOP-T-1 En vi ro nm en...dispersions of nanoparticles (NPs) for use in bioassay media for exposures/characterizations are a crucial need in ecotoxicology assays. The present...protocol provides guidance and step-by-step methods for: (1) creating a working stock from nanoparticle powder and nanoparticle aqueous suspensions
Dispersion-induced non-linearities in semiconductors
DEFF Research Database (Denmark)
Mørk, Jesper; Mecozzi, A.
1999-01-01
We show that index dispersion in connection with the standard (slow) saturation of the medium due to carrier density changes, lead to ultrafast gain and index dynamics. Analytical formulas are derived, and it is shown that these new contributions may dominate experimentally observed results....
Design of broadband nearly-zero flattened dispersion highly nonlinear photonic crystal fiber
Institute of Scientific and Technical Information of China (English)
Shuqin Lou; Hong Fang; Honglei Li; Tieying Guo; Lei Yao; Liwen Wang; Weiguo Chen; Shuisheng Jian
2008-01-01
We propose a new structure of broadband nearly-zero flattened dispersion highly nonlinear photonic crystal fiber (PCF). Through optimizing the diameters of the first two inner rings of air-holes and the GeO2 doping concentration of the core, the nonlinear coefficient is up to 47 W-1.km-1 at the wavelength of 1.55 μm and nearly-zero flattened dispersion of±0.5 ps/(nm.km) is achieved in the telecommunication window (1460 - 1625 nm). Due to the use of GeO2-doped core, this innovative structure can offer not only a large nonlinear coefficient and broadband nearly-zero flattened dispersion but also low leakage losses.
Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi
2017-05-01
This paper studies the dynamics of solitons to the nonlinear Schrödinger’s equation (NLSE) with spatio-temporal dispersion (STD). The integration algorithm that is employed in this paper is the Riccati-Bernoulli sub-ODE method. This leads to dark and singular soliton solutions that are important in the field of optoelectronics and fiber optics. The soliton solutions appear with all necessary constraint conditions that are necessary for them to exist. There are four types of nonlinear media studied in this paper. They are Kerr law, power law, parabolic law and dual law. The conservation laws (Cls) for the Kerr law and parabolic law nonlinear media are constructed using the conservation theorem presented by Ibragimov.
Non-Linear Noise Contributions in Highly Dispersive Optical Transmission Systems
Matera, Francesco
2016-01-01
This article reports an analytical investigation, confirmed by numerical simulations, about the non-linear noise contribution in single-channel systems adopting generic modulation-detection formats in long links with both managed and unmanaged dispersion compensation and its impact in system performance. This noise contribution is expressed in terms of a pulse non-linear interaction length and permits a simple calculation of the Q-factor. Results point out the dependence of this non-linear noise on the number of amplifiers spans, N, according to the adopted chromatic dispersion compensation scheme, the modulation-detection format, and the signal baud rate. It is also shown how the effects of polarization multiplexing can be taken into account and how this single-channel non-linear noise contribution can be used in a wavelength-division multiplexing (WDM) environment.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Semiparametric reproductive dispersion nonlinear model (SRDNM) is an extension of nonlinear reproductive dispersion models and semiparametric nonlinear regression models, and includes semiparametric nonlinear model and semiparametric generalized linear model as its special cases. Based on the local kernel estimate of nonparametric component, profile-kernel and backfitting estimators of parameters of interest are proposed in SRDNM, and theoretical comparison of both estimators is also investigated in this paper. Under some regularity conditions, strong consistency and asymptotic normality of two estimators are proved. It is shown that the backfitting method produces a larger asymptotic variance than that for the profile-kernel method. A simulation study and a real example are used to illustrate the proposed methodologies.
Dispersion and polarization dependence of mobile carrier optical nonlinearities
Rustagi, K. C.
1984-06-01
Based on the author's earlier work, it is shown that the proper inclusion of carrier scattering should strongly modify the frequency and polarization dependence of optical nonlinearities due to mobile carriers in semiconductors. When the momentum relaxation is much faster than the energy relaxation, the intensity dependent refractive index is enhanced, the induced birefringence becomes a sharp function of the difference frequency ωa-ωb, and a collision induced stimulated Raman effect becomes important.
Exact solutions to a nonlinear dispersive model with variable coefficients
Energy Technology Data Exchange (ETDEWEB)
Yin Jun [Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074 (China); Lai Shaoyong [Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074 (China)], E-mail: laishaoy@swufe.edu.cn; Qing Yin [Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074 (China)
2009-05-15
A mathematical technique based on an auxiliary differential equation and the symbolic computation system Maple is employed to investigate a prototypical and nonlinear K(n, n) equation with variable coefficients. The exact solutions to the equation are constructed analytically under various circumstances. It is shown that the variable coefficients and the exponent appearing in the equation determine the quantitative change in the physical structures of the solutions.
Nonlinear coupling of left and right handed circularly polarized dispersive Alfvén wave
Energy Technology Data Exchange (ETDEWEB)
Sharma, R. P., E-mail: rpsharma@ces.iitd.ac.in; Sharma, Swati, E-mail: swati.sharma704@gmail.com; Gaur, Nidhi, E-mail: nidhiphysics@gmail.com [Centre for Energy Studies, Indian Institute of Technology Delhi, New Delhi 110016 (India)
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.
Collapse arrest and soliton stabilization in nonlocal nonlinear media
DEFF Research Database (Denmark)
Bang, Ole; Krolikowski, Wieslaw; Wyller, John
2002-01-01
We investigate the properties of localized waves in cubic nonlinear materials with a symmetric nonlocal nonlinear response of arbitrary shape and degree of nonlocality, described by a general nonlocal nonlinear Schrodinger type equation. We prove rigorously by bounding the Hamiltonian that nonloc......We investigate the properties of localized waves in cubic nonlinear materials with a symmetric nonlocal nonlinear response of arbitrary shape and degree of nonlocality, described by a general nonlocal nonlinear Schrodinger type equation. We prove rigorously by bounding the Hamiltonian...
Dispersion-insensitive low-coherent pulses emerging from nonlinear polarization switching
Mao, D.; Liu, X. M.; Lu, H.; Wang, L. R.; Duan, L. N.
2011-11-01
We have experimentally investigated low-repetition nanosecond pulses delivered from an erbium-doped fiber (EDF) laser operating in ultra-large anomalous dispersion regime. The output pulses with rectangular profile and Gaussian spectrum almost keep invariable when they propagate through either normal- or anomalous-dispersion fibers. After nanosecond pulses are amplified via a two-stage EDF amplifier, they are broken up and exhibited as flatly broadened supercontinuum from 1520 to 1700 nm if amplified pulses are launched into a 10-km single-mode fiber, whereas the pulses retain the same duration with a broadband supercontinuum from 1200 to 1750 nm if they are input into a 100-m highly-nonlinear low-dispersion photonic-crystal fiber (PCF). The experimental observations demonstrate that the nanosecond pulses result from nonlinear polarization switching and can be regarded as dispersion-insensitive low-coherent pulses rather than compressible pulses.
Bright Chirp-free and Chirped Nonautonomous solitons under Dispersion and Nonlinearity Management
Yang, Zhan-Ying; Zhang, Tao; Yue, Rui-Hong
2011-01-01
We present a series of chirp-free and chirped analytical nonautonomous soliton solutions to the generalized nonlinear Schrodinger equation (NLSE) with distributed coefficients by Darboux transformation from a trivial seed. For chirpfree nonautonomous soliton, the dispersion management term can change the motion of nonautonomous soliton and do not affect its shape at all. Especially,the classical optical soliton can be presented with variable dispersion term and nonlinearity when there is no gain. For chirped nonautonomous soliton, dispersion management can affect the shape and motion of nonautonomous solitons meanwhile. The periodic dispersion term can be used to control its "breathing" shape, and it does not affect the trajectory of nonautonomous soliton center with a certain condition.
Convergence rates for dispersive approximation schemes to nonlinear Schr\\"odinger equations
Ignat, Liviu I
2011-01-01
This article is devoted to the analysis of the convergence rates of several numerical approximation schemes for linear and nonlinear Schr\\"odinger equations on the real line. Recently, the authors have introduced viscous and two-grid numerical approximation schemes that mimic at the discrete level the so-called Strichartz dispersive estimates of the continuous Schr\\"odinger equation. This allows to guarantee the convergence of numerical approximations for initial data in L2(R), a fact that can not be proved in the nonlinear setting for standard conservative schemes unless more regularity of the initial data is assumed. In the present article we obtain explicit convergence rates and prove that dispersive schemes fulfilling the Strichartz estimates are better behaved for H^s(R) data if 0 < s < 1/2. Indeed, while dispersive schemes ensure a polynomial convergence rate, non-dispersive ones only yield logarithmic decay rates.
Strojan, Klemen; Leonardi, Adrijana; Bregar, Vladimir B.; Križaj, Igor; Svete, Jurij; Pavlin, Mojca
2017-01-01
Protein corona of nanoparticles (NPs), which forms when these particles come in to contact with protein-containing fluids, is considered as an overlooked factor in nanomedicine. Through numerous studies it has been becoming increasingly evident that it importantly dictates the interaction of NPs with their surroundings. Several factors that determine the compositions of NPs protein corona have been identified in recent years, but one has remained largely ignored—the composition of media used for dispersion of NPs. Here, we determined the effect of dispersion media on the composition of protein corona of polyacrylic acid-coated cobalt ferrite NPs (PAA NPs) and silica NPs. Our results confirmed some of the basic premises such as NPs type-dependent specificity of the protein corona. But more importantly, we demonstrated the effect of the dispersion media on the protein corona composition. The differences between constituents of the media used for dispersion of NPs, such as divalent ions and macromolecules were responsible for the differences in protein corona composition formed in the presence of fetal bovine serum (FBS). Our results suggest that the protein corona composition is a complex function of the constituents present in the media used for dispersion of NPs. Regardless of the dispersion media and FBS concentration, majority of proteins from either PAA NPs or silica NPs coronas were involved in the process of transport and hemostasis. Interestingly, corona of silica NPs contained three complement system related proteins: complement factor H, complement C3 and complement C4 while PAA NPs bound only one immune system related protein, α-2-glycoprotein. Importantly, relative abundance of complement C3 protein in corona of silica NPs was increased when NPs were dispersed in NaCl, which further implies the relevance of dispersion media used to prepare NPs. PMID:28052135
Strojan, Klemen; Leonardi, Adrijana; Bregar, Vladimir B; Križaj, Igor; Svete, Jurij; Pavlin, Mojca
2017-01-01
Protein corona of nanoparticles (NPs), which forms when these particles come in to contact with protein-containing fluids, is considered as an overlooked factor in nanomedicine. Through numerous studies it has been becoming increasingly evident that it importantly dictates the interaction of NPs with their surroundings. Several factors that determine the compositions of NPs protein corona have been identified in recent years, but one has remained largely ignored-the composition of media used for dispersion of NPs. Here, we determined the effect of dispersion media on the composition of protein corona of polyacrylic acid-coated cobalt ferrite NPs (PAA NPs) and silica NPs. Our results confirmed some of the basic premises such as NPs type-dependent specificity of the protein corona. But more importantly, we demonstrated the effect of the dispersion media on the protein corona composition. The differences between constituents of the media used for dispersion of NPs, such as divalent ions and macromolecules were responsible for the differences in protein corona composition formed in the presence of fetal bovine serum (FBS). Our results suggest that the protein corona composition is a complex function of the constituents present in the media used for dispersion of NPs. Regardless of the dispersion media and FBS concentration, majority of proteins from either PAA NPs or silica NPs coronas were involved in the process of transport and hemostasis. Interestingly, corona of silica NPs contained three complement system related proteins: complement factor H, complement C3 and complement C4 while PAA NPs bound only one immune system related protein, α-2-glycoprotein. Importantly, relative abundance of complement C3 protein in corona of silica NPs was increased when NPs were dispersed in NaCl, which further implies the relevance of dispersion media used to prepare NPs.
DEFF Research Database (Denmark)
Rasmussen, Kim; Christiansen, Peter Leth; Johansson, Magnus
1998-01-01
A one-dimensional discrete nonlinear Schrodinger (DNLS) model with the power dependence, r(-s) on the distance r, of dispersive interactions is proposed. The stationary states of the system are studied both analytically and numerically. Two kinds of trial functions, exp-like and sech-like are exp......A one-dimensional discrete nonlinear Schrodinger (DNLS) model with the power dependence, r(-s) on the distance r, of dispersive interactions is proposed. The stationary states of the system are studied both analytically and numerically. Two kinds of trial functions, exp-like and sech...
Kim, Kihong; Phung, D K; Rotermund, F; Lim, H
2008-01-21
We develop a generalized version of the invariant imbedding method, which allows us to solve the electromagnetic wave equations in arbitrarily inhomogeneous stratified media where both the dielectric permittivity and magnetic permeability depend on the strengths of the electric and magnetic fields, in a numerically accurate and efficient manner. We apply our method to a uniform nonlinear slab and find that in the presence of strong external radiation, an initially uniform medium of positive refractive index can spontaneously change into a highly inhomogeneous medium where regions of positive or negative refractive index as well as metallic regions appear. We also study the wave transmission properties of periodic nonlinear media and the influence of nonlinearity on the mode conversion phenomena in inhomogeneous plasmas. We argue that our theory is very useful in the study of the optical properties of a variety of nonlinear media including nonlinear negative index media fabricated using wires and split-ring resonators.
Nonlinear effect of dispersal rate on spatial synchrony of predator-prey cycles.
Fox, Jeremy W; Legault, Geoffrey; Legault, Geoff; Vasseur, David A; Einarson, Jodie A
2013-01-01
Spatially-separated populations often exhibit positively correlated fluctuations in abundance and other population variables, a phenomenon known as spatial synchrony. Generation and maintenance of synchrony requires forces that rapidly restore synchrony in the face of desynchronizing forces such as demographic and environmental stochasticity. One such force is dispersal, which couples local populations together, thereby synchronizing them. Theory predicts that average spatial synchrony can be a nonlinear function of dispersal rate, but the form of the dispersal rate-synchrony relationship has never been quantified for any system. Theory also predicts that in the presence of demographic and environmental stochasticity, realized levels of synchrony can exhibit high variability around the average, so that ecologically-identical metapopulations might exhibit very different levels of synchrony. We quantified the dispersal rate-synchrony relationship using a model system of protist predator-prey cycles in pairs of laboratory microcosms linked by different rates of dispersal. Paired predator-prey cycles initially were anti-synchronous, and were subject to demographic stochasticity and spatially-uncorrelated temperature fluctuations, challenging the ability of dispersal to rapidly synchronize them. Mean synchrony of prey cycles was a nonlinear, saturating function of dispersal rate. Even extremely low rates of dispersal (systems are sufficient to generate and maintain synchrony of cyclic population dynamics, at least when environments are not too spatially heterogeneous.
The Influence of the Balance of Dispersion and Nonlinearity on the Transmission Quality in Fiber
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
This article analyzes the effect of the balance of dispersion and nonlinearity on the quality of a transmission system with super Gauss pulse input by altering the input power and adding a section of dispersion compensation fiber (DCF). The same mechanisms are applied to a 2-channel wave divide multiplex system(WDM) as well. DCF is proved to be a good solution in both situations.
Institute of Scientific and Technical Information of China (English)
Peng Jin-Zhang; Yang Hong; Tang Yi
2009-01-01
By making use of the split-step Fourier method, this paper numerically simulates dynamical behaviors, including repulsion, fusion, scattering and spiraling of colliding (3+1)D spatiotemporal solitons in both the dispersive medium with cubic-quintic and the saturable medium. Careful comparison of the colliding behaviors in these two media is presented. Although the origin of the nonlinearities is different in these two media, the obtained results show that the dynamical behaviors are very similar. This presents additional evidence to support the supposition of universality of interactions between solitons.
Directory of Open Access Journals (Sweden)
Shi Jing
2014-01-01
Full Text Available The solving processes of the homogeneous balance method, Jacobi elliptic function expansion method, fixed point method, and modified mapping method are introduced in this paper. By using four different methods, the exact solutions of nonlinear wave equation of a finite deformation elastic circular rod, Boussinesq equations and dispersive long wave equations are studied. In the discussion, the more physical specifications of these nonlinear equations, have been identified and the results indicated that these methods (especially the fixed point method can be used to solve other similar nonlinear wave equations.
Dispersion properties of helical waves in radially inhomogeneous elastic media.
Syresin, D E; Zharnikov, T V; Tyutekin, V V
2012-06-01
In this paper, a method describing dispersion curve calculation for waves propagating in radially layered, inhomogeneous isotropic elastic waveguides is developed. Particular emphasis is placed on the helical waves with noninteger azimuthal wavenumbers, which can be potentially applied in such fields as nondestructive evaluation, acoustic tomography, etc., stipulating their practical importance. To solve the problem under consideration, the matrix Riccati equation is formulated for an impedance matrix. The use of the latter yields a simple form of the dispersion equation. Numerical computation of dispersion curves can encounter difficulties, which are due to potential singularities of the impedance matrix and the necessity to separate roots of the dispersion equation. These difficulties are overcome by employing the Cayley transform and invoking the parametric continuation method. The method developed by the authors is demonstrated by calculating dispersion diagrams in support of helical waves for several models of practical interest. Such computations for an inhomogeneous layer and its approximation by a set of homogeneous layers using a transfer matrix and Riccati equation methods revealed higher computational accuracy of the latter. Dispersion curves calculated for layers with different types of inhomogeneity demonstrated significant discrepancies at low frequencies.
Tuning the nonlinear response of (6,5)-enriched single-wall carbon nanotubes dispersions
Aréstegui, O. S.; Silva, E. C. O.; Baggio, A. L.; Gontijo, R. N.; Hickmann, J. M.; Fantini, C.; Alencar, M. A. R. C.; Fonseca, E. J. S.
2017-04-01
Ultrafast nonlinear optical properties of (6,5)-enriched single-wall carbon nanotubes (SWCNTs) dispersions are investigated using the thermally managed Z-scan technique. As the (6,5) SWCNTs presented a strong resonance in the range of 895-1048 nm, the nonlinear refractive index (n2) and the absorption coefficients (β) measurements were performed tuning the laser exactly around absorption peak of the (6,5) SWCNTs. It is observed that the nonlinear response is very sensitive to the wavelength and the spectral behavior of n2 is strongly correlated to the tubes one-photon absorption band, presenting also a peak when the laser photon energy is near the tube resonance energy. This result suggests that a suitable selection of nanotubes types may provide optimized nonlinear optical responses in distinct regions of the electromagnetic spectrum. Analysis of the figures of merit indicated that this material is promising for ultrafast nonlinear optical applications under near infrared excitation.
Optical tsunamis: shoaling of shallow water rogue waves in nonlinear fibers with normal dispersion
Wabnitz, Stefan
2013-01-01
In analogy with ocean waves running up towards the beach, shoaling of prechirped optical pulses may occur in the normal group-velocity dispersion regime of optical fibers. We present exact Riemann wave solutions of the optical shallow water equations and show that they agree remarkably well with the numerical solutions of the nonlinear Schr\\"odinger equation, at least up to the point where a vertical pulse front develops. We also reveal that extreme wave events or optical tsunamis may be generated in dispersion tapered fibers in the presence of higher-order dispersion.
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
2016-07-01
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
Relativistic regimes for dispersive shock-waves in non-paraxial nonlinear optics
Gentilini, Silvia; Conti, Claudio
2014-01-01
We investigate the effect of non-paraxiality in the dynamics of dispersive shock waves in the defocusing nonlinear Schroedinger equation. We show that the problem can be described in terms of a relativistic particle moving in a potential. Lowest order corrections enhance the wave-breaking and impose a limit to the highest achievable spectrum in an amount experimentally testable.
Switching between bistable states in a discrete nonlinear model with long-range dispersion
DEFF Research Database (Denmark)
Johansson, Magnus; Gaididei, Yuri B.; Christiansen, Peter Leth
1998-01-01
In the framework of a discrete nonlinear Schrodinger equation with long-range dispersion, we propose a general mechanism for obtaining a controlled switching between bistable localized excitations. We show that the application of a spatially symmetric kick leads to the excitation of an internal...
Controllability of nonlinear third-order dispersion inclusions with infinite delay
Directory of Open Access Journals (Sweden)
Meili Li
2013-07-01
Full Text Available This article shows the controllability of nonlinear third-order dispersion inclusions with infinite delay. Sufficient conditions are obtained by using a fixed-point theorem for multivalued maps. Particularly, the compactness of the operator semigroups is not assumed in this article.
Compact and noncompact structures of the nonlinearly dispersive GNLS(m,n,k,l equation
Directory of Open Access Journals (Sweden)
Bülent Kılıç
2015-02-01
Full Text Available In this paper, we establish exact-special solutions of the generalized nonlinear dispersion GNLS(m,n,k,l equation. We use the ansatz method for acquiring the compactons, solitary patterns, solitons and other types of solutions.
Jeong, Seongmook; Ju, Seongmin; Kim, Youngwoong; Watekar, Pramod R; Jeong, Hyejeong; Lee, Ho-Jae; Boo, Seongjae; Kim, Dug Young; Han, Won-Taek
2012-01-01
The dispersion-shifted fiber (DSF) incorporated with Si nanocrystals (Si-NCs) having highly nonlinear optical property was fabricated to investigate the effective supercontinuum generation characteristics by using the MCVD process and the drawing process. Optical nonlinearity was enhanced by incorporating Si nanocrystals in the core of the fiber and the refractive index profile of a dispersion-shifted fiber was employed to match its zero-dispersion wavelength to that of the commercially available pumping source for generating effective supercontinuum. The non-resonant nonlinear refractive index, n2, of the Si-NCs doped DSF measured by the cw-SPM method was measured to be 7.03 x 10(-20) [m2/W] and the coefficient of non-resonant nonlinearity, gamma, was 7.14 [W(-1) km(-1)]. To examine supercontinuum generation of the Si-NCs doped DSF, the femtosecond fiber laser with the pulse width of 150 fs (at 1560 nm) was launched into the fiber core. The output spectrum of the Si-NCs doped DSF was found to broaden from 1300 nm to wavelength well beyond 1700 nm, which can be attributed to the enhanced optical nonlinearity by Si-NCs embedded in the fiber core. The short wavelength of the supercontinuum spectrum in the Si-NCs doped DSF showed shift from 1352 nm to 1220 nm for the fiber length of 2.5 m and 200 m, respectively.
Yu, Changyuan
Chromatic dispersion, polarization mode dispersion (PMD) and nonlinear effects are important issues on the physical layer of high-speed reconfigurable WDM optical fiber communication systems. For beyond 10 Gbit/s optical fiber transmission system, it is essential that chromatic dispersion and PMD be well managed by dispersion monitoring and compensation. One the other hand, dispersive and nonlinear effects in optical fiber systems can also be beneficial and has applications on pulse management, all-optical signal processing and network function, which will be essential for high bite-rate optical networks and replacing the expensive optical-electrical-optical (O/E/O) conversion. In this Ph.D. dissertation, we present a detailed research on dispersive and nonlinear effects in high-speed optical communication systems. We have demonstrated: (i) A novel technique for optically compensating the PMD-induced RF power fading that occurs in single-sideband (SSB) subcarrier-multiplexed systems. By aligning the polarization states of the optical carrier and the SSB, RF power fading due to all orders of PMD can be completely compensated. (ii) Chromatic-dispersion-insensitive PMD monitoring by using a narrowband FBG notch filter to recover the RF clock power for 10Gb/s NRZ data, and apply it as a control signal for PMD compensation. (iii) Chirp-free high-speed optical pulse generation with a repetition rate of 160 GHz (which is four times of the frequency of the electrical clock) using a phase modulator and polarization maintaining (PM) fiber. (iv) Polarization-insensitive all-optical wavelength conversion based on four-wave mixing in dispersion-shifted fiber (DSF) with a fiber Bragg grating and a Faraday rotator mirror. (v) Width-tunable optical RZ pulse train generation based on four-wave mixing in highly-nonlinear fiber. By electrically tuning the delay between two pump pulse trains, the pulse-width of a generated pulse train is continuously tuned. (vi) A high-speed all
Two-dimensional dispersive shock waves in dissipative optical media
Kartashov, Yaroslav V
2013-01-01
We study generation of two-dimensional dispersive shock waves and oblique dark solitons upon interaction of tilted plane waves with negative refractive index defects embedded into defocusing material with linear gain and two-photon absorption. Different evolution regimes are encountered including the formation of well-localized disturbances for input tilts below critical one, and generation of extended shock waves containing multiple intensity oscillations in the "upstream" region and gradually vanishing oblique dark solitons in "downstream" region for input tilts exceeding critical one. The generation of stable dispersive shock waves is possible only below certain critical defect strength.
Indian Academy of Sciences (India)
K Nithyanandan; R Vasantha Jayakantha Raja; T Uthayakumar; K Porsezian
2014-02-01
A theoretical analysis of modulational instability (MI) of optical pulses propagating near the zero dispersion wavelength of a lossless fibre with the effect of delayed saturable nonlinear response is presented. We calculate the exact dispersion relation with the effect of higher dispersion for the harmonic perturbation. We analysed the impact of fourth-order dispersion effects in the MI spectrum. We examine the possibility of MI in both dispersion regimes, regardless of the sign of the group velocity dispersion.
Clack, C
2009-01-01
The nonlinear theory of driven magnetohydrodynamics (MHD) waves in strongly anisotropic and dispersive plasmas, developed for slow resonance by Clack and Ballai [Phys. Plasmas, 15, 2310 (2008)] and Alfv\\'en resonance by Clack \\emph{et al.} [A&A,494, 317 (2009)], is used to study the weakly nonlinear interaction of fast magnetoacoustic (FMA) waves in a one-dimensional planar plasma. The magnetic configuration consists of an inhomogeneous magnetic slab sandwiched between two regions of semi-infinite homogeneous magnetic plasmas. Laterally driven FMA waves penetrate the inhomogeneous slab interacting with the localized slow or Alfv\\'{e}n dissipative layer and are partly reflected, dissipated and transmitted by this region. The nonlinearity parameter defined by Clack and Ballai (2008) is assumed to be small and a regular perturbation method is used to obtain analytical solutions in the slow dissipative layer. The effect of dispersion in the slow dissipative layer is to further decrease the coefficient of ener...
Directory of Open Access Journals (Sweden)
Mostafa H. Ali, Ahmed E. Elsamahy, Maher A. Farhoud and Taymour A. Hamdalla
2012-10-01
Full Text Available Near field distribution, propagation constant and dispersion characteristics of nonlinear single-mode optical fibers have been investigated. Shooting-method technique is used and implemented into a computer code for both profiles of step-index and graded-index fibers. An error function is defined to estimate the discrepancy between the expected electric-field radial derivative at the core-cladding interface and that obtained by numerically integrating the wave equation through the use of Runge-Kutta method. All of the above calculations done under the ocean depth in which the depth will affect the refractive index that have a direct effect on all the optical fiber parameters.KeyWords: Nonlinear refractive index, Normalized propagation constant, Mode delay factor, Material dispersion, Waveguide dispersion.
Lim, C. W.; Wu, B. S.; He, L. H.
2001-12-01
A novel approach is presented for obtaining approximate analytical expressions for the dispersion relation of periodic wavetrains in the nonlinear Klein-Gordon equation with even potential function. By coupling linearization of the governing equation with the method of harmonic balance, we establish two general analytical approximate formulas for the dispersion relation, which depends on the amplitude of the periodic wavetrain. These formulas are valid for small as well as large amplitude of the wavetrain. They are also applicable to the large amplitude regime, which the conventional perturbation method fails to provide any solution, of the nonlinear system under study. Three examples are demonstrated to illustrate the excellent approximate solutions of the proposed formulas with respect to the exact solutions of the dispersion relation. (c) 2001 American Institute of Physics.
Fusion arrest and collapse phenomena due to Kerr-nonlinearity in quadratic media
DEFF Research Database (Denmark)
Johansen, Steffen Kjær; Bang, Ole; Sørensen, Mads Peter
2000-01-01
Emphasizing collapse phenomena it is investigated to what extend the always present cubic nonlinearity affects the properties of soliton interaction in quadratic bulk media. An effective particle approach is applied and verified by numerical simulations....
Zhang, Ya-Ni; Ren, Li-Yong; Gong, Yong-Kang; Li, Xiao-Hui; Wang, Lei-Ran; Sun, Chuan-Dong
2010-06-01
We have proposed a novel type of photonic crystal fiber (PCF) with low dispersion and high nonlinearity for four-wave mixing. This type of fiber is composed of a solid silica core and a cladding with a squeezed hexagonal lattice elliptical airhole along the fiber length. Its dispersion and nonlinearity coefficient are investigated simultaneously by using the full vectorial finite element method. Numerical results show that the proposed highly nonlinear low-dispersion fiber has a total dispersion as low as +/-2.5 ps nm(-1) km(-1) over an ultrabroad wavelength range from 1.43 to 1.8 microm, and the corresponding nonlinearity coefficient and birefringence are about 150 W(-1) km(-1) and 2.5x10(-3) at 1.55 microm, respectively. The proposed PCF with low ultraflattened dispersion, high nonlinearity, and high birefringence can have important application in four-wave mixing.
Scale-Dependent Solute Dispersion in Variably Saturated Porous Media
Energy Technology Data Exchange (ETDEWEB)
Rockhold, Mark L. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Zhang, Z. F. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Bott, Yi-Ju [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
2016-03-29
This work was performed to support performance assessment (PA) calculations for the Integrated Disposal Facility (IDF) at the Hanford Site. PA calculations require defensible estimates of physical, hydraulic, and transport parameters to simulate subsurface water flow and contaminant transport in both the near- and far-field environments. Dispersivity is one of the required transport parameters.
Self-focusing of optical pulses in media with normal dispersion
DEFF Research Database (Denmark)
Bergé, L.; Kuznetsov, E.A.; Juul Rasmussen, J.;
1996-01-01
propagating in a nonlinear medium with normal dispersion will not collapse to a singularity in the transverse diffraction plane. It is explicitly shown that the pulse spreads out along the ''time-direction'' and ultimately splits up. The analytical results are supported by direct numerical solutions.......The self-focusing of ultra short optical pulses in a nonlinear medium with normal (i.e., negative) group-velocity dispersion is investigated. By using a combination of various techniques like virial-type arguments and self-similar transformations, we obtain strong evidence suggesting that a pulse...
Pal, Anoop K; Aalaei, Iraj; Gadde, Suresh; Gaines, Peter; Schmidt, Daniel; Demokritou, Philip; Bello, Dhimiter
2014-09-23
In vitro toxicity assessment of engineered nanomaterials (ENM), the most common testing platform for ENM, requires prior ENM dispersion, stabilization, and characterization in cell culture media. Dispersion inefficiencies and active aggregation of particles often result in polydisperse and multimodal particle size distributions. Accurate characterization of important properties of such polydisperse distributions (size distribution, effective density, charge, mobility, aggregation kinetics, etc.) is critical for understanding differences in the effective dose delivered to cells as a function of time and dispersion conditions, as well as for nano-bio interactions. Here we have investigated the utility of tunable nanopore resistive pulse sensing (TRPS) technology for characterization of four industry relevant ENMs (oxidized single-walled carbon nanohorns, carbon black, cerium oxide and nickel nanoparticles) in cell culture media containing serum. Harvard dispersion and dosimetry platform was used for preparing ENM dispersions and estimating delivered dose to cells based on dispersion characterization input from dynamic light scattering (DLS) and TRPS. The slopes of cell death vs administered and delivered ENM dose were then derived and compared. We investigated the impact of serum protein content, ENM concentration, and cell medium on the size distributions. The TRPS technology offers higher resolution and sensitivity compared to DLS and unique insights into ENM size distribution and concentration, as well as particle behavior and morphology in complex media. The in vitro dose-response slopes changed significantly for certain nanomaterials when delivered dose to cells was taken into consideration, highlighting the importance of accurate dispersion and dosimetry in in vitro nanotoxicology.
Decay of high order optical vortices in anisotropic nonlinear optical media
DEFF Research Database (Denmark)
Mamaev, A.V.; Saffman, M.; Zozulya, A.A.
1997-01-01
We present an experimental and theoretical study of the decay of high order optical vortices in media with an anisotropic nonlocal nonlinearity. Vortices with charge n decay into an aligned array of n vortices of unit charge.......We present an experimental and theoretical study of the decay of high order optical vortices in media with an anisotropic nonlocal nonlinearity. Vortices with charge n decay into an aligned array of n vortices of unit charge....
Numerical study of propagation properties of surface plasmon polaritons in nonlinear media
Sagor, Rakibul Hasan
2016-03-29
We present a time-domain algorithm for simulating nonlinear propagation of surface plasmon polaritons (SPPs) in chalcogenide glass. Due to the high non-linearity property and strong dispersion and confinement chalcogenide glasses are widely known as ultrafast nonlinear materials. We have used the finite difference time domain (FDTD) method to develop the simulation algorithm for the current analysis. We have modeled the frequency dependent dispersion properties and third order nonlinearity property of chalcogenide glass utilizing the general polarization algorithm merged in the auxiliary differential equation (ADE) method. The propagation dynamics of the whole structure with and without third order nonlinearity property of chalcogenide glass have been simulated and the effect of nonlinearity on the propagation properties of SPP has been investigated. © 2016 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.
Nonlinear Behavior Of Saturated Porous Media Under External Impact
Perepechko, Y.
2005-12-01
This paper deals with nonlinear behavior of liquid saturated porous media in gravity filed under external impact. The continuum is assumed to be a two-velocity medium; it consists of a deformable porous matrix (with Maxwell's reology) and a Newtonian liquid that saturates this matrix. The energy dissipation in this model takes place due the interface friction between the solid matrix and saturating liquid, and also through relaxation of inelastic shear stress in the porous matrix. The elaborated nonisothermal mathematical model for this kind of medium is a thermodynamically consistent and closed model. Godunov's explicit difference scheme was used for computer simulation; the method implies numerical simulation for discontinuity decay in flux calculations. As an illustrative example, we consider the formation of dissipation structures in a plain layer of that medium after pulse or periodic impact on the background of liquid filtration through the porous matrix. At the process beginning, one can observe elastic behavior of the porous matrix. Deformation spreading through the saturated porous matrix occurs almost without distortions and produces a channel-shaped zone of stretching with a high porosity. Later on, dissipation processes and reology properties of porous medium causes the diffusion of this channel. We also observe a correlation between the liquid distribution (porosity for the solid matrix) and dilatancy fields; this allows us to restore the dilatancy field from the measured fluid saturation of the medium. This work was supported by the RFBR (Grant No. 04-05-64107), the Presidium of SB RAS (Grant 106), the President's Grants (NSh-2118.2003.5, NSh-1573.2003.5).
Microscopic Models for Electromagnetic Wave Propagation in Highly Dispersive Media
1990-06-18
rotations, the effects of pressure and temperature and to show the classes of density fluctuations in I which give spatial dispersion, ie, the k- dependance ...complex plane the response e (co, Q) lives on some Riemann surface which is determined by the k- dependance . 2. Talks and Publications Three talks were...sources of 1- dependance (k- dependance in Fourier transform variables) have been identified. One is bubbles or cavitation which scatter the propagating
Stability of two-dimensional spatial solitons in nonlocal nonlinear media
DEFF Research Database (Denmark)
Skupin, S.; Bang, Ole; Edmundson, D.;
2006-01-01
We discuss the existence and stability of two-dimensional solitons in media with spatially nonlocal nonlinear response. We show that such systems, which include thermal nonlinearity and dipolar Bose-Einstein condensates, may support a variety of stationary localized structures, including rotating...
Modulation instability, solitons and beam propagation in spatially nonlocal nonlinear media
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole; Nikolov, Nikola Ivanov
2004-01-01
We present an overview of recent advances in the understanding of optical beams in nonlinear media with a spatially nonlocal nonlinear response. We discuss the impact of nonlocality on the modulational instability of plane waves, the collapse of finite-size beams, and the formation and interaction...
Exact bright and dark spatial soliton solutions in saturable nonlinear media
Energy Technology Data Exchange (ETDEWEB)
Calvo, Gabriel F. [Departamento de Matematicas, E.T.S. de Ingenieros Industriales, Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), E.T.S.I. Industriales, Avda. Camilo Jose Cela, 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain); Belmonte-Beitia, Juan [Departamento de Matematicas, E.T.S. de Ingenieros Industriales, Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), E.T.S.I. Industriales, Avda. Camilo Jose Cela, 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)], E-mail: Juan.Belmonte@uclm.es; Perez-Garcia, Victor M. [Departamento de Matematicas, E.T.S. de Ingenieros Industriales, Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), E.T.S.I. Industriales, Avda. Camilo Jose Cela, 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)
2009-08-30
We present exact analytical bright and dark (black and grey) solitary wave solutions of a nonlinear Schroedinger-type equation describing the propagation of spatial beams in media exhibiting a saturable nonlinearity (such as centrosymmetric photorefractive materials). A qualitative study of the stationary equation is carried out together with a discussion of the stability of the solutions.
Apparatus and Methods Using Highly Optically Dispersive Media
2011-08-02
of two-beam interferometers , such as, e.g., a Michelson interferometer , a Twyman-Green interferometer , and others known in the art. An alternative...guiding fiber . 20 32. The apparatus of claim 1, wherein the apparatus is a spectroscopic interferometer . 33. The apparatus of claim 1, wherein the...Zhimin et a!. "Enhancing the spectral sensitivity of interferometers using slow-light media". Optics Letters, vol. 32, No. 8, Apr. 15, 2007, pp. 915
Institute of Scientific and Technical Information of China (English)
Lijuan Chen; Junyan Xu
2009-01-01
In this paper,a set of sufficient conditions which ensure the permanence of a nonlinear periodic predator-prey system with prey dispersal and predator density-independence are obtained,where the prey species can disperse among n patches,while the density-independent predator is confined to one of the patches and cannot disperse. Our results generalize some known results.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper,a set of suffcient conditions which ensure the permanence of a nonlinear periodic predator-prey system with prey dispersal and predator density-independence are obtained,where the prey species can disperse among n patches,while the density-independent predator is confined to one of the patches and cannot disperse. Our results generalize some known results.
Xu, Daguang; Huang, Yong; Kang, Jin U
2013-01-01
We propose a novel compressive sensing (CS) method on spectral domain optical coherence tomography (SDOCT). By replacing the widely used uniform discrete Fourier transform (UDFT) matrix with a new sensing matrix which is a modification of the non-uniform discrete Fourier transform (NUDFT) matrix, it is shown that undersampled non-linear wavenumber spectral data can be used directly in the CS reconstruction. Thus k-space grid filling and k-linear mask calibration which were proposed to obtain linear wavenumber sampling from the non-linear wavenumber interferometric spectra in previous studies of CS in SDOCT (CS-SDOCT) are no longer needed. The NUDFT matrix is modified to promote the sparsity of reconstructed A-scans by making them symmetric while preserving the value of the desired half. In addition, we show that dispersion compensation can be implemented by multiplying the frequency-dependent correcting phase directly to the real spectra, eliminating the need for constructing complex component of the real spectra. This enables the incorporation of dispersion compensation into the CS reconstruction by adding the correcting term to the modified NUDFT matrix. With this new sensing matrix, A-scan with dispersion compensation can be reconstructed from undersampled non-linear wavenumber spectral data by CS reconstruction. Experimental results show that proposed method can achieve high quality imaging with dispersion compensation.
A Fractal Model for the Transverse Thermal Dispersion Conductivity in Porous Media
Institute of Scientific and Technical Information of China (English)
郁伯铭; 李建华
2004-01-01
A quasi-analytical model, i.e. the fractal model, for the transverse thermal dispersion conductivity in porous media is presented based on the fractal characteristics of tortuous flow paths/streamlines in porous media. The fractal dimension of tortuous flow paths, the spatial deviation velocity and the transverse thermal dispersion conductivity are derived. The proposed model is expressed as functions of the fractal dimension of tortuous flow paths/streamlines, Peclet number, porosity and structural parameters. The present results are compared with those from the existing correlation, and good agreement is found between the present model predictions and those from the existing correlation.
Institute of Scientific and Technical Information of China (English)
SHU Wei-Xing; LUO Hai-Lu; LI Fei; REN Zhong-Zhou
2006-01-01
@@ We investigate the propagation of electromagnetic waves at the interface between an isotropic material and the anisotropic medium with a unique dispersion relation. We show that the refraction behaviour of E-polarized waves is opposite to that of H-polarized waves, though the dispersion relations for E- and H-polarized waves are the same. It is found that waves exhibit different propagation properties in anisotropic media with different sign combinations of the permittivity and permeability tensors. Some interesting properties of propagation are also found in the special anisotropic media, leading to potential applications.
Spectral anomalies of diffracted pulsed Hermite-Gaussian beams in dispersive media
Institute of Scientific and Technical Information of China (English)
Zhao Zhi-Guo; Pan Liu-Zhan; Lü Bai-Da
2008-01-01
This paper derives and uses the recurrence expressions for the power spectra of diffracted pulsed Hermite-Gaussian (HG) beams in dispersive media to study the spectral anomalies of pulsed HG beams in the far field. Numerical results are given to illustrate the dependence of spectral switches on the pulse parameters, truncation parameter and dispersive property of the medium. The potential application of spectral anomalies of ultrashort pulsed beams in information encoding and transmission is discussed.
Energy Technology Data Exchange (ETDEWEB)
Nguyen, Ba Phi [Central University of Construction, Tuy Hoa (Viet Nam); Kim, Ki Hong [Ajou University, Suwon (Korea, Republic of)
2014-06-15
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 Schroedinger 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.
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.
Reciprocity breaking during nonlinear propagation of adapted beams through random media
Palastro, J P; Nelson, W; DiComo, G; Johnson, L A; Helle, M H; Hafizi, B
2016-01-01
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.
RADIONUCLIDE DISPERSION RATES BY AEOLIAN, FLUVIAL, AND POROUS MEDIA TRANSPORT
Energy Technology Data Exchange (ETDEWEB)
J. Walton; P. Goodell; C. Brashears; D. French; A. Kelts
2005-07-11
Radionuclide transport was measured from high grade uranium ore boulders near the Nopal I Site, Chihuahua, Mexico. High grade uranium ore boulders were left behind after removal of a uranium ore stockpile at the Prior High Grade Stockpile (PHGS). During the 25 years when the boulder was present, radionuclides were released and transported by sheetflow during precipitation events, wind blown resuspension, and infiltration into the unsaturated zone. In this study, one of the boulders was removed, followed by grid sampling of the surrounding area. Measured gamma radiation levels in three dimensions were used to derive separate dispersion rates by the three transport mechanisms.
Is ‘Superluminal’Light Propagation Possible in Dispersive Media?
Institute of Scientific and Technical Information of China (English)
CHEN Kai; WU Ling-An; SHIH Yan-Hua
2004-01-01
@@ In a dispersive medium, different monochromatic modes of light have different phase velocities. Under special circumstances, a superposition of these modes results in an interesting effect wherein the group velocity (the velocity at which the peak of the wavepacket propagates) could be greater than c or even negative although the phase velocities of the modes are all less than c. Can this superluminal group velocity be used for information velocity of its component modes. Thus the maximum speed for information transfer, which involves the sending of a finite pulse, cannot be greater than the maximum phase velocity in the medium.
Light-induced nonlinear effects on dispersion relation of ultracold Bose gas
Institute of Scientific and Technical Information of China (English)
胡正峰; 杜春光; 李师群
2003-01-01
We have investigated the optical properties of A-configuration ultracold dense Bose gas interacting with two laser pulses, which usually result in electromagnetically induced transparency. With the nonrelativistic quantum electrodynamics and taking into account the atomic dipole-dipole interaction and local field effect, we have derived the Maxwell-Bloch equations of the system. The dispersion relation of an ultracold Bose gas has been obtained and the light-induced nonlinear effects have been analysed. The light-induced nonlinear effects are different from the effects induced by two-body collision of Bose-Einstein condensation atoms which have a frequency shift of transparent window.
Light—induced nonlinear effects of dispersion relation of ultracold Bose gas
Institute of Scientific and Technical Information of China (English)
HuZheng-Feng; DuChunGuang; LiShi-Qun
2003-01-01
We have investigated the optical properties of A-configuration ultracold dense Bose gas interacting with two laser pulses, which usually result in electromagnetically induced transparency. With the nonrelativistic quantum electrodynamics and taking into account the atomic dipole-dipole interaction and local field effect, we have derived the Maxwell-Bloch equations of the system. The dispersion relation of an ultracold Bose gas has been obtained and the light-induced nonlinear effects have been analysed. The light-induced nonlinear effects are different from the effects induced by two-body collision of Bose-Einstein condensation atoms which have a frequency shift of transparent window.
Three kinds of nonlinear dispersive waves in elastic rods with finite deformation
Institute of Scientific and Technical Information of China (English)
ZHANG Shan-yuan; LIU Zhi-fang
2008-01-01
On the basis of classical linear theory on longitudinal, torsional and flexural waves in thin elastic rods, and taking finite deformation and dispersive effects into consideration, three kinds of nonlinear evolution equations are derived. Qualitative analysis of three kinds of nonlinear equations are presented. It is shown that these equations have homoclinic or heteroclinic orbits on the phase plane, corresponding to solitary wave or shock wave solutions, respectively. Based on the principle of homogeneous balance, these equations are solved with the Jacobi elliptic function expansion method. Results show that existence of solitary wave solution and shock wave solution is possible under certain conditions. These conclusions are consistent with qualitative analysis.
Spatiotemporal coupled-mode theory in dispersive media under a dynamic modulation
Dana, Brenda; Bahabad, Alon
2014-01-01
A simple and general formalism for mode coupling by a spatial, temporal or spatiotemporal perturbation in dispersive materials is developed. This formalism can be used for studying various linear and non-linear optical interactions involving a dynamic modulation of the interaction parameters such as non-reciprocal phenomena, time reversal of signals and spatiotemporal quasi phase matching
Karpinski, Michal; Banaszek, Konrad
2012-01-01
We present experimental realization of type-II spontaneous parametric down-conversion in a periodically poled potassium titanyl phosphate (KTiOPO4) nonlinear waveguide. We demonstrate that by careful exploitation of intermodal dispersion in the waveguide it is feasible to produce photon pairs in well defined transverse modes without any additional spatial filtering at the output. Spatial characteristics is verified by measurements of the M2 beam quality factors. We also prepared a postselected polarization-entangled two-photon state shown to violate Bell's inequality. Similar techniques based on intermodal dispersion can be used to generate spatial entanglement and hyperentanglement.
Flat super-continuum generation based on normal dispersion nonlinear photonic crystal fibre
DEFF Research Database (Denmark)
Chow, K.K.; Takushima, Y.; Lin, C.
2006-01-01
Flat super-continuum generation spanning over the whole telecommunication band using a passively modelocked fibre laser source at 1550 nm together with a dispersion-flattened nonlinear photoinc crystal fibre is demonstrated. Since the pulses propagate in the normal dispersion regime of the fibre...... only, linear frequency chirp is induced by self-phase modulation which leads to a flat super-continuum. By launching the compressed 170 fs modelocked pulses with an average power of 10 mW into the fibre, super-continuum over 185 nm with less than 5 dB fluctuation is obtained from the all...
Astra, Egon; Olsson, Samuel L I; Eliasson, Henrik; Andrekson, Peter A
2017-06-12
We present an investigation of dispersion map optimization for two-span single-channel 28 GBaud QPSK transmission systems with phase-sensitive amplifiers (PSAs). In experiments, when the PSA link is operated in a highly nonlinear regime, a 1.4 dB error vector magnitude (EVM) improvement is achieved compared to a one-span optimized dispersion map link due to improved nonlinearity mitigation. The two-span optimized dispersion map of a PSA link differs from the optimized dispersion map of a dispersion managed phase-insensitive amplifier (PIA) link. Simulations show that the performance of the two-span dispersion map optimized PSA link does not improve by residual dispersion optimization. Further, by using the two-span optimized dispersion maps repeatedly in a long-haul PSA link instead of one-span optimized maps, the maximum transmission reach can be improved 1.5 times.
Solitary waves for a coupled nonlinear Schrodinger system with dispersion management
Directory of Open Access Journals (Sweden)
Panayotis Panayotaros
2010-08-01
Full Text Available We consider a system of coupled nonlinear Schrodinger equations with periodically varying dispersion coefficient that arises in the context of fiber-optics communication. We use Lions's Concentration Compactness principle to show the existence of standing waves with prescribed L^2 norm in an averaged equation that approximates the coupled system. We also use the Mountain Pass Lemma to prove the existence of standing waves with prescribed frequencies.
Nonlinear optical properties of polymer dispersed liquid crystals doped with La2CaB10019
Zegadlo, Krzysztof B.; El Ouazzani, Hasnaa; Cieslik, Iwona; Weglowski, Rafal; Zmija, Jozef; Klosowicz, Stanislaw; Majchrowski, Andrzej; Mysliwiec, Jaroslaw; Sahraoui, Bouchta; Karpierz, Miroslaw A.
2012-08-01
Second order nonlinearity in polymer dispersed liquid crystal structures containing La2CaB10O19 nanocrystals were measured with use of the Maker fringes method. The composites with different concentration of La2CaB10O19 crystallites or without them were compared. It was shown that there is a strong influence of the crystals concentration on the second harmonic generation in such structures which can be additionally modified by external electric field.
Rius, Manuel; Bolea, Mario; Mora, José; Ortega, Beatriz; Capmany, José
2015-05-18
We experimentally demonstrate, for the first time, a chirped microwave pulses generator based on the processing of an incoherent optical signal by means of a nonlinear dispersive element. Different capabilities have been demonstrated such as the control of the time-bandwidth product and the frequency tuning increasing the flexibility of the generated waveform compared to coherent techniques. Moreover, the use of differential detection improves considerably the limitation over the signal-to-noise ratio related to incoherent processing.
Modeling Solution of Nonlinear Dispersive Partial Differential Equations using the Marker Method
Energy Technology Data Exchange (ETDEWEB)
Jerome L.V. Lewandowski
2005-01-25
A new method for the solution of nonlinear dispersive partial differential equations is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details.
Institute of Scientific and Technical Information of China (English)
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 A,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.
Wear, Keith A
2015-03-01
Through-transmission measurements were performed on 30 human calcaneus samples in vitro. Nonlinear attenuation and dispersion measurements were investigated by estimating 95% confidence intervals of coefficients of polynomial expansions of log magnitude and phase of transmission coefficients. Bone mineral density (BMD) was measured with dual x-ray absorptiometry. Microarchitecture was measured with microcomputed tomography. Statistically significant nonlinear attenuation and nonzero dispersion were confirmed for a clinical bandwidth of 300-750 kHz in 40%-43% of bone samples. The mean linear coefficient for attenuation was 10.3 dB/cm MHz [95% confidence interval (CI): 9.0-11.6 dB/cm MHz]. The mean quadratic coefficient for attenuation was 1.6 dB/cm MHz(2) (95% CI: 0.4-2.8 dB/cm MHz(2)). Nonlinear attenuation provided little information regarding BMD or microarchitecture. The quadratic coefficient for phase (which is related to dispersion) showed moderate correlations with BMD (r = -0.65; 95% CI: -0.82 to -0.36), bone surface-to-volume ratio (r = 0.47; 95% CI: 0.12-0.72) and trabecular thickness (r = -0.40; 95% CI: -0.67 to -0.03). Dispersion was proportional to bone volume fraction raised to an exponent of 2.1 ± 0.2, which is similar to the value for parallel nylon-wire phantoms (2.4 ± 0.2) and supports a multiple-scattering model for dispersion.
Cauchy problem for a class of nonlinear dispersive wave equations arising in elasto-plastic flow
Zhijian, Yang
2006-01-01
The paper studies the existence, both locally and globally in time, stability, decay estimates and blowup of solutions to the Cauchy problem for a class of nonlinear dispersive wave equations arising in elasto-plastic flow. Under the assumption that the nonlinear term of the equations is of polynomial growth order, say [alpha], it proves that when [alpha]>1, the Cauchy problem admits a unique local solution, which is stable and can be continued to a global solution under rather mild conditions; when [alpha][greater-or-equal, slanted]5 and the initial data is small enough, the Cauchy problem admits a unique global solution and its norm in L1,p(R) decays at the rate for 2
nonlinear term, the local solutions of the Cauchy problem blow up in finite time.
Institute of Scientific and Technical Information of China (English)
CAO; Wenhua; LIU; Songhao
2004-01-01
A novel scheme to compress optical pulses is proposed and demonstrated numerically, which is based on a nonlinear optical loop mirror constructed from dispersion decreasing fiber (DDF). We show that, in contrast to the conventional soliton-effect pulse compression in which compressed pulses are always accompanied by pedestals and frequency chirps owning to nonlinear effects, the proposed scheme can completely suppress pulse pedestals and frequency chirps. Unlike the adiabatic compression technique in which DDF length must increase exponentially with input pulsewidth, the proposed scheme does not require adiabatic condition and therefore can be used to compress long pulses by using reasonable fiber lengths. For input pulses with peak powers higher than a threshold value, the compressed pulses can propagate like fundamental solitons. Furthermore, the scheme is fairly insensitive to small variations in the loop length and is more robust to higher-order nonlinear effects and initial frequency chirps than the adiabatic compression technique.
Tomita, Yasuo; Matsushima, Shun-suke; Yamagami, Ryu-ichi; Jinzenji, Taka-aki; Sakuma, Shohei; Liu, Xiangming; Izuishi, Takuya; Shen, Qing
2017-06-01
We describe the nonlinear optical properties of inorganic-organic nanocomposite films in which semiconductor CdSe quantum dots as high as 6.8 vol.% are dispersed. Open/closed Z-scan measurements, degenerate multi-wave mixing and femtosecond pump-probe/transient grating measurements are conducted. It is shown that the observed fifth-order optical nonlinearity has the cascaded third-order contribution that becomes prominent at high concentrations of CdSe QDs. It is also shown that there are picosecond-scale intensity-dependent and nanosecond-scale intensity-independent decay components in absorptive and refractive nonlinearities. The former is caused by the Auger process, while the latter comes from the electron-hole recombination process.
Sorokin, Vladislav S; Thomsen, Jon Juel
2016-02-01
The paper deals with analytically predicting the effects of weak nonlinearity on the dispersion relation and frequency band-gaps of a periodic Bernoulli-Euler beam performing bending oscillations. Two cases are considered: (i) large transverse deflections, where nonlinear (true) curvature, nonlinear material and nonlinear inertia owing to longitudinal motions of the beam are taken into account, and (ii) mid-plane stretching nonlinearity. A novel approach is employed, the method of varying amplitudes. As a result, the isolated as well as combined effects of the considered sources of nonlinearities are revealed. It is shown that nonlinear inertia has the most substantial impact on the dispersion relation of a non-uniform beam by removing all frequency band-gaps. Explanations of the revealed effects are suggested, and validated by experiments and numerical simulation.
Conditioning-induced elastic nonlinearity in hysteretic media
Gliozzi, A. S.; Scalerandi, M.; Antonaci, P.; Bruno, C. L. E.
2010-08-01
The definition and measurement of the nonlinear elastic properties of a sample is of great importance for a large number of applications, including characterization of material performances and damage detection. However, such measurements are often influenced by spurious effects due to a combination of nonlinearity and nonequilibrium phenomena. We will present experimental data to show how nonlinearity due to small cracks in concrete samples increases as a consequence of conditioning, i.e., after having perturbed them with a constant amplitude excitation. In addition, our experimental data highlight "memory effects," i.e., they show that when the excitation is removed, the elastic modulus does not return instantaneously to the initial value.
Institute of Scientific and Technical Information of China (English)
林金官; 韦博成
2004-01-01
In this paper, it is discussed that two tests for varying dispersion of binomial data in the framework of nonlinear logistic models with random effects, which are widely used in analyzing longitudinal binomial data. One is the individual test and power calculation for varying dispersion through testing the randomness of cluster effects, which is extensions of Dean(1992) and Commenges et al (1994). The second test is the composite test for varying dispersion through simultaneously testing the randomness of cluster effects and the equality of random-effect means. The score test statistics are constructed and expressed in simple, easy to use, matrix formulas. The authors illustrate their test methods using the insecticide data (Giltinan, Capizzi & Malani (1988)).
Cortinez, J. M.; Valocchi, A. J.; Herrera, P. A.
2013-12-01
Because of the finite size of numerical grids, it is very difficult to correctly account for processes that occur at different spatial scales to accurately simulate the migration of conservative and reactive compounds dissolved in groundwater. In one hand, transport processes in heterogeneous porous media are controlled by local-scale dispersion associated to transport processes at the pore-scale. On the other hand, variations of velocity at the continuum- or Darcy-scale produce spreading of the contaminant plume, which is referred to as macro-dispersion. Furthermore, under some conditions both effects interact, so that spreading may enhance the action of local-scale dispersion resulting in higher mixing, dilution and reaction rates. Traditionally, transport processes at different spatial scales have been included in numerical simulations by using a single dispersion coefficient. This approach implicitly assumes that the separate effects of local-dispersion and macro-dispersion can be added and represented by a unique effective dispersion coefficient. Moreover, the selection of the effective dispersion coefficient for numerical simulations usually do not consider the filtering effect of the grid size over the small-scale flow features. We have developed a multi-scale Lagragian numerical method that allows using two different dispersion coefficients to represent local- and macro-scale dispersion. This technique considers fluid particles that carry solute mass and whose locations evolve according to a deterministic component given by the grid-scale velocity and a stochastic component that corresponds to a block-effective macro-dispersion coefficient. Mass transfer between particles due to local-scale dispersion is approximated by a meshless method. We use our model to test under which transport conditions the combined effect of local- and macro-dispersion are additive and can be represented by a single effective dispersion coefficient. We also demonstrate that for
Center for Analysis of Heterogeneous and Nonlinear Media
1989-10-14
computation of singular solutions of the nonlinear Schroedinger equation) Xue Xin (nonlinear homogenization) Jing-Yi Zhu (Ph.D. 1989, adaptive vortex method...numerical analysis of the vortex method for vortex sheets were carried out by Krasny and by Caflisch and Lowengrub. 2. Exact singular solutions of the...restriction to analytic functions. - 18- Singularities - Examples and the Generic Form of Singularities Singular solutions of the Birkhoff-Rott equation (1
Transition between self-focusing and self-defocusing in nonlocally nonlinear media
Liang, Guo; Hu, Yahong; Wang, Jing; Wang, Zhuo; Li, Yingbing; Guo, Qi; Hu, Wei; Lou, Senyue; Christodoulides, Demetrios N
2015-01-01
We reveal the relevance between the nonlocality and the focusing/defocusing states in nonlocally nonlinear media, and predict a novel phenomenon that the self-focusing/self-defocusing property of the optical beam in the nonlocally nonlinear medium with a sine-oscillation response function depends on its degree of nonlocality. The transition from the focusing nonlinearity to the defocusing nonlinearity of the nonlinear refractive index will happen when the degree of nonlocality of the system goes cross a critical value, and vise verse. Bright and dark soliton solutions are obtained, respectively, in the focusing state and in the defocusing state, and their stabilities are also discussed. It is mentioned that such a phenomenon might be experimentally realized in the nematic liquid crystal with negative dielectric anisotropy or in the quadratic nonlinear medium.
Multisplitting and collapse of self-focusing anisotropic beams in normal/anomalous dispersive media
DEFF Research Database (Denmark)
Bergé, L.; Juul Rasmussen, J.
1996-01-01
Three-dimensional self-focusing light pulses in normal and anomalous dispersive media are investigated by means of a waveguide instability analysis, a Lagrangian approach, and a quasi-self-similar analysis. In the case of normal dispersion for which no localized ground state exists, it is shown...... that a high-intensity elongated beam cannot self-similarly collapse. Even when the incident beam power widely exceeds the critical power for a two-dimensional self-focusing, the beam is shown to split into multiple cells that ultimately disperse when their individual mass lies below the critical power...... also play an important role in an anomalous dispersive medium. In this case, unlike the former one, the beam self-contracts along its propagation axis and reconcentrates its shape back toward the center where it ultimately collapses in a finite time. (C) 1996 American Institute of Physics....
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.
Lai, Puxiang; Tay, Jian Wei; Wang, Lihong V
2014-01-01
Non-invasively focusing light into strongly scattering media, such as biological tissue, is highly desirable but challenging. Recently, wavefront shaping technologies guided by ultrasonic encoding or photoacoustic sensing have been developed to address this limitation. So far, these methods provide only acoustic diffraction-limited optical focusing. Here, we introduce nonlinear photoacoustic wavefront shaping (PAWS), which achieves optical diffraction-limited (i.e. single-speckle-grain) focusing in scattering media. We develop an efficient dual-pulse excitation approach to generate strong nonlinear photoacoustic (PA) signals based on the Grueneisen memory effect. These nonlinear PA signals are used as feedback to guide iterative wavefront optimization. By maximizing the amplitude of the nonlinear PA signal, light is effectively focused to a single optical speckle grain. Experimental results demonstrate a clear optical focus on the scale of 5-7 micrometers, which is ~10 times smaller than the acoustic focus in...
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
Nonlinear plasmonics with Kerr-like media for sensing
Crutcher, Sihon H.; Ruffin, Paul B.; Edwards, Eugene; Brantley, Christina L.
2014-04-01
Sensing technologies are currently needed for better maintainability, reliability, safety, and monitoring small variable changes on microscopic and nanoscale systems. Plasmonic sensor research has contributed to chemical and biological sensing needs by monitoring ultrafast temporal and spatial changes in optoelectronic systems. Nonlinear plasmonic waveguides with subwavelength confinement can further enhance the capabilities of plasmonic devices. Results in this paper highlight the derivation of the full-vector Maxwell Equations for the single metal- dielectric slot waveguide and the metal -dielectric -metal waveguide with the dielectric having a Kerr-like nonlinearity. These waveguides, typically have metallic losses that compete with nonlinearity at certain frequencies that can hinder surface plasmon wave propagation. By considering temporal and spatial beam propagation in these waveguides one expects to observe novel effects that could be used for sensing applications such as femtosecond pulse propagation with plasmon self-focusing, self-trapping, and frequency conversion with reduction in metallic losses.
1992-02-13
niobate and absolute measurements of nonlinear optical coefficients of six different commonly used nonlinear optical materials. The refractometry data for...applied radiation and is now an established technology for Nd:YAG lasers. Optical parametric oscillation and amplification provide a method of generating...continuously tunable output -3- The relative advantages of nonlinear optical frequency conversion compared to other methods for the generation of near
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 coag...
Stable one-dimensional periodic waves in Kerr-type saturable and quadratic nonlinear media
Energy Technology Data Exchange (ETDEWEB)
Kartashov, Yaroslav V [ICFO-Institut de Ciencies Fotoniques, and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, E-08034 Barcelona (Spain); Egorov, Alexey A [Physics Department, M V Lomonosov Moscow State University, 119899, Moscow (Russian Federation); Vysloukh, Victor A [Departamento de Fisica y Matematicas, Universidad de las Americas-Puebla, Santa Catarina Martir, 72820, Puebla, Cholula (Mexico); Torner, Lluis [ICFO-Institut de Ciencies Fotoniques, and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, E-08034 Barcelona (Spain)
2004-05-01
We review the latest progress and properties of the families of bright and dark one-dimensional periodic waves propagating in saturable Kerr-type and quadratic nonlinear media. We show how saturation of the nonlinear response results in the appearance of stability (instability) bands in a focusing (defocusing) medium, which is in sharp contrast with the properties of periodic waves in Kerr media. One of the key results discovered is the stabilization of multicolour periodic waves in quadratic media. In particular, dark-type waves are shown to be metastable, while bright-type waves are completely stable in a broad range of energy flows and material parameters. This yields the first known example of completely stable periodic wave patterns propagating in conservative uniform media supporting bright solitons. Such results open the way to the experimental observation of the corresponding self-sustained periodic wave patterns.
DEFF Research Database (Denmark)
Sorokin, Vladislav S.; Thomsen, Jon Juel
2016-01-01
The paper deals with analytically predicting the effects of weak nonlinearity on the dispersion relation and frequency band-gaps of a periodic Bernoulli– Euler beam performing bending oscillations. Two cases are considered: (i) large transverse deflections, where nonlinear (true) curvature...
DEFF Research Database (Denmark)
Parigi, V.; Bimbard, E.; Stanojevic, J.
2012-01-01
We observe and measure dispersive optical nonlinearities in an ensemble of cold Rydberg atoms placed inside an optical cavity. The experimental results are in agreement with a simple model where the optical nonlinearities are due to the progressive appearance of a Rydberg blockaded volume within ...
Parigi, Valentina; Bimbard, Erwan; Stanojevic, Jovica; Hilliard, Andrew J; Nogrette, Florence; Tualle-Brouri, Rosa; Ourjoumtsev, Alexei; Grangier, Philippe
2012-12-07
We observe and measure dispersive optical nonlinearities in an ensemble of cold Rydberg atoms placed inside an optical cavity. The experimental results are in agreement with a simple model where the optical nonlinearities are due to the progressive appearance of a Rydberg blockaded volume within the medium. The measurements allow a direct estimation of the "blockaded fraction" of atoms within the atomic ensemble.
Dispersion Analysis of Gravity Waves in Fluid Media Discretized by Energy-Orthogonal Finite Elements
José Brito Castro, Francisco
2014-11-01
This article studies the dispersion of gravity waves in fluid media discretized by the finite element method. The element stiffness matrix is split into basic and higher-order components which are respectively related to the mean and deviatoric components of the gradient of displacement potential. This decomposition is applied to the kinetic energy. The dispersion analysis yields a correlation between the higher-order kinetic energy and the kinetic energy error. The use of this correlation as a reference to apply the higher-order energy as an error indicator for the sloshing modes computed by the finite element method is explored.
Laser beam propagation in non-linearly absorbing media
CSIR Research Space (South Africa)
Forbes, A
2006-08-01
Full Text Available Many analytical techniques exist to explore the propagation of certain laser beams in free space, or in a linearly absorbing medium. When the medium is nonlinearly absorbing the propagation must be described by an iterative process using the well...
DEFF Research Database (Denmark)
Guo, Hairun; Zeng, Xianglong; Zhou, Binbin
2013-01-01
We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic...
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.
Analysis of Nonlinear Dispersion of a Pollutant Ejected by an External Source into a Channel Flow
Directory of Open Access Journals (Sweden)
T. Chinyoka
2010-01-01
Full Text Available This paper focuses on the transient analysis of nonlinear dispersion of a pollutant ejected by an external source into a laminar flow of an incompressible fluid in a channel. The influence of density variation with pollutant concentration is approximated according to the Boussinesq approximation, and the nonlinear governing equations of momentum and pollutant concentration are obtained. The problem is solved numerically using a semi-implicit finite difference method. Solutions are presented in graphical form and given in terms of fluid velocity, pollutant concentration, skin friction, and wall mass transfer rate for various parametric values. The model can be a useful tool for understanding the polluting situations of an improper discharge incident and evaluating the effects of decontaminating measures for the water body.
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.
Institute of Scientific and Technical Information of China (English)
Ao Sheng-Mei; Yan Jia-Ren; Yu Hui-You
2007-01-01
We solve the generalized nonlinear Schrodinger equation describing the propagation of femtosecond pulses in a nonlinear optical fibre with higher-order dispersions by using the direct approach to perturbation for bright solitons, and discuss the combined effects of the third- and fourth-order dispersions on velocity, temporal intensity distribution and peak intensity of femtosecond pulses. It is noticeable that the combined effects of the third- and fourth-order dispersions on an initial propagated soliton can partially compensate each other, which seems to be significant for the stability controlling of soliton propagation features.
A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model
Bonneton, Philippe; Lannes, David; Marche, Fabien; Tissier, Marion
2010-01-01
The fully nonlinear and weakly dispersive Green-Naghdi model for shallow water waves of large amplitude is studied. The original model is first recast under a new formulation more suitable for numerical resolution. An hybrid finite volume and finite difference splitting approach is then proposed. The hyperbolic part of the equations is handled with a high-order finite volume scheme allowing for breaking waves and dry areas. The dispersive part is treated with a classical finite difference approach. Extensive numerical validations are then performed in one horizontal dimension, relying both on analytical solutions and experimental data. The results show that our approach gives a good account of all the processes of wave transformation in coastal areas: shoaling, wave breaking and run-up.
Determination of Diffusion and Dispersion Parameters for Flow in Porous Media
Kohno, Iichiro; Nishigaki, Makoto
1982-01-01
The purposes of this research is an investigation of the intrusion of sea water into coastal aquifers. For this subject, this paper deals with proposing rational methods of getting diffusion coefficient and dispersion parameter for flow in porous media in a laboratory. These parameters of soil are indispensable in order to apply an analytical approach or a numerical approach to actual salt water intrusion problems. Experimental apparatuses were constructed and test procedures were also develo...
Effects of Higher Order Dispersion Terms in the Nonlinear Schrodinger Equation
Directory of Open Access Journals (Sweden)
Robert Beech
2005-01-01
Full Text Available This study presents a concise graphical analysis of solitonic solutions to a nonlinear Schrodinger equation (NLSE. A sequence of code using the standard NDSolve function has been developed in Mathematica to investigate the acceptable accuracy of the NLSE in relatively small ranges of the dispersive parameter space. An operator splitting approach was used in the numerical solutions to expand the boundaries and reduce the artifacts for a reliable solution. These numerical routines were implemented through the use with Mathematica and the results give a very clear view of this interesting and important practical phenomenon.
Properties of nonlinear noise in long, dispersion-uncompensated fiber links
Dar, Ronen; Mecozzi, Antonio; Shtaif, Mark
2013-01-01
We study the properties of nonlinear interference noise (NLIN) in fiber-optic communications systems with large accumulated dispersion. Our focus is on settling the discrepancy between the Gaussian noise model which follows from the frequency domain approach, and the time-domain approach according to which NLIN is not additive and its nature strongly depends on the modulation format. Upon reviewing the two approaches we attribute the discrepancy to several subtle, but critical assumptions that were made in the frequency domain analysis and that we believe to be unjustified. The predictions of the time domain approach are validated numerically in simulations.
Existence of traveling wave solutions for a nonlinear dissipative-dispersive equation
Institute of Scientific and Technical Information of China (English)
M. B. A. Mansour
2009-01-01
In this paper, we consider a dissipative-dispersive nonlinear equation appliable to many physical phenomena. Using the geometric singular perturbation method based on the theory of dynamical systems, we investigate the existence of its traveling wave solutions with the dissipative terms having sufficiently small coefficients. The results show that the traveling waves exist on a two-dimensional slow manifold in a three-dimensional system of ordinary differential equations (ODEs). Then, we use the Melnikov method to establish the existence of a homoclinic orbit in this manifold corresponding to a solitary wave solution of the equation. Furthermore, we present some numerical computations to show the approximations of such wave orbits.
Canonical structure of evolution equations with non-linear dispersive terms
Indian Academy of Sciences (India)
B Talukdar; J Shamanna; S Ghosh
2003-07-01
The inverse problem of the variational calculus for evolution equations characterized by non-linear dispersive terms is analysed with a view to clarify why such a system does not follow from Lagrangians. Conditions are derived under which one could construct similar equations which admit a Lagrangian representation. It is shown that the system of equations thus obtained can be Hamiltonized by making use of the Dirac’s theory of constraints. The speciﬁc results presented refer to the third- and ﬁfth-order equations of the so-called distinguished subclass.
Institute of Scientific and Technical Information of China (English)
Qiao Yao-Jun; Liu Xue-Jun; Ji Yue-Feng
2011-01-01
This paper introduces a joint nonlinearity and chromatic dispersion pre-compensation method for coherent optical orthogonal frequency-division multiplexing systems.The research results show that this method can reduce the walkoff effect and can therefore equalize the nonlinear impairments effectively. Compared with the only other existing nonlinearity pre-compensation method,the joint nonlinearity and chromatic dispersion pre-compensation method is not only suitable for low-dispersion optical orthogonal frequency-division multiplexing system,but also effective for highdispersion optical orthogonal frequency-division multiplexing transmission system with higher input power but without optical dispersion compensation.The suggested solution does not increase computation complexity compared with only nonlinearity pre-compensation method.For 40 Gbit/s coherent optical orthogonal frequency-division multiplexing 20 × 80 km standard single-mode fibre system,the suggested method can improve the nonlinear threshold (for Q ＞ 10 dB) about 2.7,1.2 and 1.0 dB,and the maximum Q factor about 1.2,0.4 and 0.3 dB,for 2,8 and 16 ps/(nm·km) dispersion coefficients.
Doppler effect of nonlinear waves and superspirals in oscillatory media.
Brusch, Lutz; Torcini, Alessandro; Bär, Markus
2003-09-01
Nonlinear waves emitted from a moving source are studied. A meandering spiral in a reaction-diffusion medium provides an example in which waves originate from a source exhibiting a back-and-forth movement in a radial direction. The periodic motion of the source induces a Doppler effect that causes a modulation in wavelength and amplitude of the waves ("superspiral"). Using direct simulations as well as numerical nonlinear analysis within the complex Ginzburg-Landau equation, we show that waves subject to a convective Eckhaus instability can exhibit monotonic growth or decay as well as saturation of these modulations depending on the perturbation frequency. Our findings elucidate recent experimental observations concerning superspirals and their decay to spatiotemporal chaos.
Double resonant processes in $\\chi^{(2)}$ nonlinear periodic media
Konotop, V. V.; Kuzmiak, V.
2000-01-01
In a one-dimensional periodic nonlinear $\\chi^{(2)}$ medium, by choosing a proper material and geometrical parameters of the structure, it is possible to obtain two matching conditions for simultaneous generation of second and third harmonics. This leads to new diversity of the processes of the resonant three-wave interactions, which are discussed within the framework of slowly varying envelope approach. In particular, we concentrate on the fractional conversion of the frequency $\\omega \\to (...
Controlled opacity in a class of nonlinear dielectric media
Bittencourt, Eduardo; De Lorenci, Vitorio A; Klippert, Renato
2016-01-01
Motivated by new technologies on designing and tailoring metamaterials, we seek for properties of certain classes of nonlinear optical materials that allow room for a reversibly controlled opacityto-transparency phase transition through the application of external electromagnetic fields. We examine some mathematically simple models for the dielectric parameters of the medium, and compute the relevant geometric quantities that describe the speed and polarization of light rays.
Controlled opacity in a class of nonlinear dielectric media
Bittencourt, E.; Camargo, G. H. S.; De Lorenci, V. A.; Klippert, R.
2017-03-01
Motivated by new technologies for designing and tailoring metamaterials, we seek properties for certain classes of nonlinear optical materials that allow room for a reversibly controlled opacity-to-transparency phase transition through the application of external electromagnetic fields. We examine some mathematically simple models for the dielectric parameters of the medium and compute the relevant geometric quantities that describe the speed and polarization of light rays.
Vectorial spatial solitons in bulk periodic quadratically nonlinear media
Energy Technology Data Exchange (ETDEWEB)
Panoiu, N-C [Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027 (United States); Mihalache, D [Department of Theoretical Physics, Institute of Atomic Physics, PO Box MG-6, Bucharest (Romania); Mazilu, D [Department of Theoretical Physics, Institute of Atomic Physics, PO Box MG-6, Bucharest (Romania); Lederer, F [Institute of Solid State Theory and Theoretical Optics, Friedrich Schiller University Jena, Max-Wien-Platz 1, Jena, D-07743 (Germany); Osgood, R M Jr [Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027 (United States)
2004-05-01
We present a comprehensive analysis of the generation, propagation and characteristic properties of two-dimensional spatial solitons formed in quasi-phase-matched gratings through type-II vectorial interaction. By employing an averaging approach based on asymptotic expansion theory, we show that the dynamics of soliton propagation in the grating and their stability properties are strongly influenced by induced Kerr-like nonlinearities. Finally, through extensive numerical simulations, we verify the validity of our theoretical predictions.
A Fundamental Approach to the Simulation of Flow and Dispersion in Fractured Media
Energy Technology Data Exchange (ETDEWEB)
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.
pH controlled dispersion and slip casting of Si3N4 in aqueous media
Indian Academy of Sciences (India)
R Ramachandra Rao; H N Roopa; T S Kannan
2001-02-01
The dispersion characteristics of commercial Si3N4 powder in aqueous media (deionized water) was studied as a function of pH in the range 2–11. The slip was characterized for its dispersion quality by various experimental techniques like particle size analysis, sedimentation phenomena, viscosity and flow behaviour and zeta potential analysis. The optimum dispersion was found to be in the pH region 9–11 wherein the slurry displayed minimum sedimentation height, minimum viscosity, near Newtonian flow behaviour and maximum zeta potential. The slip is highly agglomerated in the pH range 2–8 as manifested by higher sedimentation height, higher viscosity, lower zeta potential and thixotropic non-Newtonian flow behaviour. The 72 wt% (44 vol.%) Si3N4 slips made at pH = 10 resulted in green bodies having 53–59% of theoretical density after casting into plaster molds.
Plant Roots Increase Bacterivorous Nematode Dispersion through Nonuniform Glass-bead Media.
Trap, Jean; Bernard, Laetitia; Brauman, Alain; Pablo, Anne-Laure; Plassard, Claude; Ranoarisoa, Mahafaka Patricia; Blanchart, Eric
2015-12-01
Dispersion of bacterivorous nematodes in soil is a crucial ecological process that permits settlement and exploitation of new bacterial-rich patches. Although plant roots, by modifying soil structure, are likely to influence this process, they have so far been neglected. In this study, using an original three-compartment microcosm experimental design and polyvinyl chloride (PVC) bars to mimic plant roots, we tested the ability of roots to improve the dispersion of bacterivorous nematode populations through two wet, nonuniform granular (glass bead) media imitating contrasting soil textures. We showed that artificial roots increased migration time of bacterivorous nematode populations in the small-bead medium, suggesting that plant roots may play an important role in nematode dispersion in fine-textured soils or when soil compaction is high.
Finite difference methods for transient signal propagation in stratified dispersive media
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.
Nonlinear Gamow vectors, shock waves and irreversibility in optically nonlocal media
Gentilini, Silvia; Marcucci, Giulia; DelRe, Eugenio; Conti, Claudio
2015-01-01
Dispersive shock waves dominate wave-breaking phenomena in Hamiltonian systems. In the absence of loss, these highly irregular and disordered waves are potentially reversible. However, no experimental evidence has been given about the possibility of inverting the dynamics of a dispersive shock wave and turn it into a regular wave-front. Nevertheless, the opposite scenario, i.e., a smooth wave generating turbulent dynamics is well studied and observed in experiments. Here we introduce a new theoretical formulation for the dynamics in a highly nonlocal and defocusing medium described by the nonlinear Schroedinger equation. Our theory unveils a mechanism that enhances the degree of irreversibility. This mechanism explains why a dispersive shock cannot be reversed in evolution even for an arbitrarirly small amount of loss. Our theory is based on the concept of nonlinear Gamow vectors, i.e., power dependent generalizations of the counter-intuitive and hereto elusive exponentially decaying states in Hamiltonian sys...
Stable One-Dimensional Periodic Wave in Kerr-Type and Quadratic Nonlinear Media
Directory of Open Access Journals (Sweden)
Roxana Savastru
2012-01-01
Full Text Available We present the propagation of optical beams and the properties of one-dimensional (1D spatial solitons (“bright” and “dark” in saturated Kerr-type and quadratic nonlinear media. Special attention is paid to the recent advances of the theory of soliton stability. We show that the stabilization of bright periodic waves occurs above a certain threshold power level and the dark periodic waves can be destabilized by the saturation of the nonlinear response, while the dark quadratic waves turn out to be metastable in the broad range of material parameters. The propagation of (1+1 a dimension-optical field on saturated Kerr media using nonlinear Schrödinger equations is described. A model for the envelope one-dimensional evolution equation is built up using the Laplace transform.
Elegant Ince-Gaussian breathers in strongly nonlocal nonlinear media
Institute of Scientific and Technical Information of China (English)
Bai Zhi-Yong; Deng Dong-Mei; Guo Qi
2012-01-01
A novel class of optical breathers,called elegant Ince-Gaussian breathers,are presented in this paper.They are exact analytical solutions to Snyder and Mitchell's mode in an elliptic coordinate system,and their transverse structures are described by Ince-polynomials with complex arguments and a Gaussian function.We provide convincing evidence for the correctness of the solutions and the existence of the breathers via comparing the analytical solutions with numerical simulation of the nonlocal nonlinear Schr(o)dinger equation.
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 WS2 and WSe2 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 ∼103 cm GW-1, and a dispersion of nonlinear refractive index in the WS2 films that translated from positive in the monolayer to negative in bulk materials.
Propagation of a Laguerre-Gaussian correlated Schell-model beam in strongly nonlocal nonlinear media
Qiu, Yunli; Chen, Zhaoxi; He, Yingji
2017-04-01
Analytical expressions for the cross-spectral density function and the second-order moments of the Wigner distribution function of a Laguerre-Gaussian correlated Schell-model (LGCSM) beam propagating in strongly nonlocal nonlinear media are derived. The propagation properties, such as beam irradiance, beam width, the spectral degree of coherence and the propagation factor of a LGCSM beam inside the media are investigated in detail. The effect of the beam parameters and the input power on the evolution properties of a LGCSM is illustrated numerically. It is found that the beam width varies periodically or keeps invariant for a certain proper input power. And both the beam irradiance and the spectral degree of coherence of the LGCSM beam change periodically with the propagation distance for the arbitrary input power which however has no influence on the propagation factor. The coherent length and the mode order mainly affect the evolution speed of the LGCSM beam in strongly nonlocal nonlinear media.
Wright, E. S.; Aleem, T.
2003-12-01
In 1953, G.I.~Taylor published his landmark paper concerning the transport of a contaminant dissolved in a fluid flowing through a pipe of narrow diameter. He demonstrated that an interaction between the transverse variations in the fluid's velocity field and the transverse diffusion of the solute yielded an effective downstream mixing mechanism for the transverse average of the solute. This mechanism has since been dubbed ``Taylor Dispersion.'' Since his original publication, many related studies have surfaced. These include generalizations of channel geometry, generalizations of the velocity field (including turbulent field), applications to sedimentation problems, etc. However, much less attention has been given to the effects of nonlinear chemical reactions upon a system of solutes undergoing Taylor Dispersion. We present a rigorous mathematical model for the evolution of the transverse averages of reacting solutes that travel within a fluid flowing down a pipe of arbitrary cross-section. The technique for deriving this model is a generalization of a multiple scales perturbation approach described by P.C.~Fife for linear (reactionless) problems. The key outcome is that while one still finds an effective mechanism for downstream mixing, but also there is also a effective mechanism for nonlinear advection.
Nonlinear dynamics of direction-selective recurrent neural media.
Xie, Xiaohui; Giese, Martin A
2002-05-01
The direction selectivity of cortical neurons can be accounted for by asymmetric lateral connections. Such lateral connectivity leads to a network dynamics with characteristic properties that can be exploited for distinguishing in neurophysiological experiments this mechanism for direction selectivity from other possible mechanisms. We present a mathematical analysis for a class of direction-selective neural models with asymmetric lateral connections. Contrasting with earlier theoretical studies that have analyzed approximations of the network dynamics by neglecting nonlinearities using methods from linear systems theory, we study the network dynamics with nonlinearity taken into consideration. We show that asymmetrically coupled networks can stabilize stimulus-locked traveling pulse solutions that are appropriate for the modeling of the responses of direction-selective neurons. In addition, our analysis shows that outside a certain regime of stimulus speeds the stability of these solutions breaks down, giving rise to lurching activity waves with specific spatiotemporal periodicity. These solutions, and the bifurcation by which they arise, cannot be easily accounted for by classical models for direction selectivity.
DYNAMICS OF A NONLINEAR NON-AUTONOMOUS n-PATCHES PREDATOR-PREY DISPERSION-DELAY MODEL
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, a nonlinear nonautonomous predator-prey dispersion model with continuous distributed delay is studied, where all parameters are time-dependent. In this system consisting of n-patches the prey species can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. It is proved that the system is uniformly persistent under any dispersion rate effect. Furthermore, some sufficient conditions are established for the existence of a unique almost periodic solution of the system. The example shows that the criteria in the paper are new, general and easily verifiable.
Zhou, Binbin
2015-01-01
We experimentally observe long-wavelength dispersive waves generation in a BBO crystal. A soliton was formed in normal GVD regime of the crystal by a self-defocusing and negative nonlinearity through phase-mismatched quatradic interaction. Strong temporal pulse compression confirmed the formation of soliton during the pulse propagation inside the crystal. Significant dispersive wave radiation was measured in the anomalous GVD regime of the BBO crystal. With the pump wavelengths from 1.24 to 1.4 $\\mu$m, tunable dispersive waves are generated around 1.9 to 2.2 $\\mu$m. The observed dispersive wave generation is well understood by simulations.
Directory of Open Access Journals (Sweden)
Marilú Chávez-Castillo
2015-01-01
Full Text Available Two copolymers of 3-alkylthiophene (alkyl = hexyl, octyl and a thiophene functionalized with disperse red 19 (TDR19 as chromophore side chain were synthesized by oxidative polymerization. The synthetic procedure was easy to perform, cost-effective, and highly versatile. The molecular structure, molecular weight distribution, film morphology, and optical and thermal properties of these polythiophene derivatives were determined by NMR, FT-IR, UV-Vis GPC, DSC-TGA, and AFM. The third-order nonlinear optical response of these materials was performed with nanosecond and femtosecond laser pulses by using the third-harmonic generation (THG and Z-scan techniques at infrared wavelengths of 1300 and 800 nm, respectively. From these experiments it was observed that although the TRD19 incorporation into the side chain of the copolymers was lower than 5%, it was sufficient to increase their nonlinear response in solid state. For instance, the third-order nonlinear electric susceptibility (χ3 of solid thin films made of these copolymers exhibited an increment of nearly 60% when TDR19 incorporation increased from 3% to 5%. In solution, the copolymers exhibited similar two-photon absorption cross sections σ2PA with a maximum value of 8545 GM and 233 GM (1 GM = 10−50 cm4 s per repeated monomeric unit.
Benoit, Michel; Yates, Marissa L.; Raoult, Cécile
2017-04-01
Efficient and accurate numerical models simulating wave propagation are required for a variety of engineering projects including the evaluation of coastal risks, the design of protective coastal structures, and the estimation of the potential for marine renewable energy devices. Nonlinear and dispersive effects are particularly significant in the coastal zone where waves interact with the bottom, the shoreline, and coastal structures. The main challenge in developing a numerical models is finding a compromise between computational efficiency and the required accuracy of the simulated wave field. Here, a potential approach is selected and the (fully nonlinear) water wave problem is formulated using the Euler-Zakharov equations (Zakharov, 1968) describing the temporal evolution of the free surface elevation and velocity potential. The proposed model (Yates and Benoit, 2015) uses a spectral approach in the vertical (i.e. the vertical variation of the potential is approximated by a linear combination of the first NT+1 Chebyshev polynomials, following the work of Tian and Sato (2008)). The Zakharov equations are integrated in time using a fourth-order Runge-Kutta scheme with a constant time step. At each sub-timestep, the Laplace Boundary Value Problem (BVP) is solved to estimate the free surface vertical velocity using the spectral approach, with typical values of NT between 5 to 8 for practical applications. The 1DH version of the code is validated with comparisons to the experimental data set of Becq-Girard et al. (1999), which studied the propagation of irregular waves over a beach profile with a submerged bar. The nonlinear and dispersive capacities of the model are verified with the correct representation of wave-wave interactions, in particular the transfer of energy between different harmonic components during wave propagation (analysis of the transformation of the variance spectrum along the channel). Evolution of wave skewness, asymmetry and kurtosis along the
Soliton gyroscopes in media with spatially growing repulsive nonlinearity
Driben, Rodislav; Malomed, Boris A; Meier, Torsten; Torner, Lluis
2013-01-01
We find that the recently introduced model of self-trapping supported by a spatially growing strength of a repulsive nonlinearity gives rise to robust vortex-soliton tori, i.e., three-dimensional vortex solitons, with topological charges S. The family with S=1 is completely stable, while the one with S=2 has alternating regions of stability and instability. The families are nearly exactly reproduced in an analytical form by the Thomas-Fermi approximation (TFA). Unstable states with S=2 and 3 split into persistently rotating pairs or triangles of unitary vortices. Application of a moderate torque to the vortex torus initiates a persistent precession mode, with the torus' axle moving along a conical surface. A strong torque heavily deforms the vortex solitons, but, nonetheless, they restore themselves with the axle oriented according to the vectorial addition of angular momenta.
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.
de Aguiar, Hilton B; Brasselet, Sophie
2016-01-01
Despite the tremendous progresses in wavefront control through or inside complex scattering media, several limitations prevent reaching practical feasibility for nonlinear imaging in biological tissues. While the optimization of nonlinear signals might suffer from low signal to noise conditions and from possible artifacts at large penetration depths, it has nevertheless been largely used in the multiple scattering regime since it provides a guide star mechanism as well as an intrinsic compensation for spatiotemporal distortions. Here, we demonstrate the benefit of Transmission Matrix (TM) based approaches under broadband illumination conditions, to perform nonlinear imaging. Using ultrashort pulse illumination with spectral bandwidth comparable but still lower than the spectral width of the scattering medium, we show strong nonlinear enhancements of several orders of magnitude, through thicknesses of a few transport mean free paths, which corresponds to millimeters in biological tissues. Linear TM refocusing ...
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.
Inexact Picard iterative scheme for steady-state nonlinear diffusion in random heterogeneous media.
Mohan, P Surya; Nair, Prasanth B; Keane, Andy J
2009-04-01
In this paper, we present a numerical scheme for the analysis of steady-state nonlinear diffusion in random heterogeneous media. The key idea is to iteratively solve the nonlinear stochastic governing equations via an inexact Picard iteration scheme, wherein the nonlinear constitutive law is linearized using the current guess of the solution. The linearized stochastic governing equations are then spatially discretized and approximately solved using stochastic reduced basis projection schemes. The approximation to the solution process thus obtained is used as the guess for the next iteration. This iterative procedure is repeated until an appropriate convergence criterion is met. Detailed numerical studies are presented for diffusion in a square domain for varying degrees of nonlinearity. The numerical results are compared against benchmark Monte Carlo simulations, and it is shown that the proposed approach provides good approximations for the response statistics at modest computational effort.
Directory of Open Access Journals (Sweden)
Musko Monika
2014-12-01
Full Text Available 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.
Nonlinear Wave Propagation and Solitary Wave Formation in Two-Dimensional Heterogeneous Media
Luna, Manuel
2011-05-01
Solitary wave formation is a well studied nonlinear phenomenon arising in propagation of dispersive nonlinear waves under suitable conditions. In non-homogeneous materials, dispersion may happen due to effective reflections between the material interfaces. This dispersion has been used along with nonlinearities to find solitary wave formation using the one-dimensional p-system. These solitary waves are called stegotons. The main goal in this work is to find two-dimensional stegoton formation. To do so we consider the nonlinear two-dimensional p-system with variable coefficients and solve it using finite volume methods. The second goal is to obtain effective equations that describe the macroscopic behavior of the variable coefficient system by a constant coefficient one. This is done through a homogenization process based on multiple-scale asymptotic expansions. We compare the solution of the effective equations with the finite volume results and find a good agreement. Finally, we study some stability properties of the homogenized equations and find they and one-dimensional versions of them are unstable in general.
DEFF Research Database (Denmark)
Oster, Michael; Gaididei, Yuri B.; Johansson, Magnus
2004-01-01
We study the continuum limit of a nonlinear Schrodinger lattice model with both on-site and inter-site nonlinearities, describing weakly coupled optical waveguides or Bose-Einstein condensates. The resulting continuum nonlinear Schrodinger-type equation includes both nonlocal and nonlinear...
Basch, Angelika; Strnad, Simona
2011-01-20
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.
Pore-scale simulation of fluid flow and solute dispersion in three-dimensional porous media
Icardi, Matteo
2014-07-31
In the present work fluid flow and solute transport through porous media are described by solving the governing equations at the pore scale with finite-volume discretization. Instead of solving the simplified Stokes equation (very often employed in this context) the full Navier-Stokes equation is used here. The realistic three-dimensional porous medium is created in this work by packing together, with standard ballistic physics, irregular and polydisperse objects. Emphasis is placed on numerical issues related to mesh generation and spatial discretization, which play an important role in determining the final accuracy of the finite-volume scheme and are often overlooked. The simulations performed are then analyzed in terms of velocity distributions and dispersion rates in a wider range of operating conditions, when compared with other works carried out by solving the Stokes equation. Results show that dispersion within the analyzed porous medium is adequately described by classical power laws obtained by analytic homogenization. Eventually the validity of Fickian diffusion to treat dispersion in porous media is also assessed. © 2014 American Physical Society.
The permeability of poly-disperse porous media and effective particle size
Markicevic, B. I.; Preston, C.; Osterroth, S.; Iliev, O.; Hurwitz, M.
2015-11-01
The interactions between the fluid and solid phases in porous media account for the openness and length of the flow path that the fluid needs to travel within. The same reasoning applies for both mono- and poly-disperse media, and is reflected in the adoption of the same permeability models. The only difference is that an effective particle size diameter has to be used for the poly-disperse samples. A filtration experiment is used to form a particle layer, filter cake, consisting of particles of different sizes. Both inflow and outflow particle size distribution are measured by particle counting method, and from their difference, the particle size distribution in the cake is determined. In a set of experiments, the filtration history is altered by changing (i) filtration medium; (ii) suspension flow rate; and (iii) particle concentration, where in all cases investigated the cake permeability remains constant. In order to predict the permeability of poly-disperse cake from the analytical models, the particle size distribution moments are calculated, and the permeability is found for each moment. Comparing the experimental to the analytical permeability values the effective particle size is found, where the permeability calculated by using the harmonic mean of the particle size distribution reproduces the permeability experimental value best. Finally, in the parametric study, reducing the cake porosity and/or lowering the particle retention shifts effective particle size used in the permeability model toward higher moments of the particle size distribution function.
Local numerical modelling of ultrasonic guided waves in linear and nonlinear media
Packo, Pawel; Radecki, Rafal; Kijanka, Piotr; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.
2017-04-01
Nonlinear ultrasonic techniques provide improved damage sensitivity compared to linear approaches. The combination of attractive properties of guided waves, such as Lamb waves, with unique features of higher harmonic generation provides great potential for characterization of incipient damage, particularly in plate-like structures. Nonlinear ultrasonic structural health monitoring techniques use interrogation signals at frequencies other than the excitation frequency to detect changes in structural integrity. Signal processing techniques used in non-destructive evaluation are frequently supported by modeling and numerical simulations in order to facilitate problem solution. This paper discusses known and newly-developed local computational strategies for simulating elastic waves, and attempts characterization of their numerical properties in the context of linear and nonlinear media. A hybrid numerical approach combining advantages of the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE) is proposed for unique treatment of arbitrary strain-stress relations. The iteration equations of the method are derived directly from physical principles employing stress and displacement continuity, leading to an accurate description of the propagation in arbitrarily complex media. Numerical analysis of guided wave propagation, based on the newly developed hybrid approach, is presented and discussed in the paper for linear and nonlinear media. Comparisons to Finite Elements (FE) are also discussed.
Luo, Ting
As optical communications approach more data bandwidth, longer transmission distance, and more reconfigurability, dispersion, nonlinearity and polarization-dependent effects are becoming key issues for future all-optical fiber optic systems and networks. For ≥10 Gbit/s optical fiber transmission systems, it is critical that chromatic dispersion and polarization-mode-dispersion be well monitored and compensated using some type of dispersion monitoring and compensation. On the other hand, dispersive and nonlinear effects in optical fiber systems can also be beneficial and have applications on pulse management, all-optical signal processing and network function, which will be essential for high bite-rate optical networks and replacing the expensive optical-electrical-optical (O/E/O) conversion. In this Ph.D. dissertation, we present a detailed research on dispersion, nonlinearity, and polarization-dependent effects in high-speed optical communication systems. We have demonstrated: (i) A dynamic channel-spacing tunable multi-wavelength Erbium-doped fiber laser; (ii) Chromatic-dispersion-insensitive PMD monitoring by tracking the radio-frequency extracted from the vestigial-sideband; (iii) A method for simultaneous chromatic and polarization-mode dispersions monitoring by adding a frequency-shifted carrier; (iv) Polarization-insensitive optical parametric amplification by depolarizing the pump; (v) All optical chromatic dispersion monitoring potential for ultra-high speed (>40 Gbit/s) optical systems using cross-phase modulation in a highly nonlinear fiber; (vi) A novel fiber-based autocorrelator using polarimetric four-wave mixing effect and a tunable differential-group-delay element; (vii) A simple all-fiber-based autocorrelator by measuring the degree-of-polarization; and (viii) Reduction of pattern dependent data distortion in a stimulated Brillouin scattering based slow light element. These techniques will play key roles in future high-speed dynamic WDM optical
Institute of Scientific and Technical Information of China (English)
SUN Xue-ming; ZHANG Hui-jian; ZUO Meng; GU Wan-yi; XU Da-xiong
2006-01-01
Dense wavelength division multiplexing (DWDM) system is the ultimate selection as an optical communication system because of its high speeds and capacities.However,the fiber nonlinear effects and polarization mode dispersion severely limit the performance of the system when signal propagates at 40 Gbit/s in a single channel.The coupled nonlinear Schr(o)dinger equations of a single channel in DWDM,which are all considered factors of group velocity dispersion (GVD),self phase modulation (SPM),cross phase modulation (XPM),four wave mixing (FWM) and polarization mode dispersion (PMD),are derived,while their number results are obtained with extended split-step Fourier method.Finally,to analyze the impacts of the fiber nonlinear effects and PMD on the optical communication system,the simulated results of an 8x40 Gbit/s DWDM system are discussed under different conditions respectively.
Nonlinear dynamics in flow through unsaturated fractured-porous media: Status and perspectives
Energy Technology Data Exchange (ETDEWEB)
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.
Nonlinear dynamics in flow through unsaturated fractured-porous media: Status and perspectives
Energy Technology Data Exchange (ETDEWEB)
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.
Institute of Scientific and Technical Information of China (English)
HUANG; Guanhua; HUANG; Quanzhong; ZHAN; Hongbin
2005-01-01
The newly developed Fractional Advection-Dispersion Equation (FADE), which is FADE was extended and used in this paper for modelling adsorbing contaminant transport by adding an adsorbing term. A parameter estimation method and its corresponding FORTRAN based program named FADEMain were developed on the basis of Nonlinear Least Square Algorithm and the analytical solution for one-dimensional FADE under the conditions of step input and steady state flow. Data sets of adsorbing contaminants Cd and NH4+-N transport in short homogeneous soil columns and conservative solute NaCI transport in a long homogeneous soil column, respectively were used to estimate the transport parameters both by FADEMain and the advection-dispersion equation (ADE) based program CXTFIT2.1. Results indicated that the concentration simulated by FADE agreed well with the measured data. Compared to the ADE model, FADE can provide better simulation for the concentration in the initial lower concentration part and the late higher concentration part of the breakthrough curves for both adsorbing contaminants. The dispersion coefficients for ADE were from 0.13 to 7.06 cm2/min, while the dispersion coefficients for FADE ranged from 0.119 to 3.05 cm1.856/min for NaCI transport in the long homogeneous soil column. We found that the dispersion coefficient of FADE increased with the transport distance, and the relationship between them can be quantified with an exponential function. Less scale-dependent was also found for the dispersion coefficient of FADE with respect to ADE.
Nonlinear to Linear Elastic Code Coupling in 2-D Axisymmetric Media.
Energy Technology Data Exchange (ETDEWEB)
Preston, Leiph [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-08-01
Explosions within the earth nonlinearly deform the local media, but at typical seismological observation distances, the seismic waves can be considered linear. Although nonlinear algorithms can simulate explosions in the very near field well, these codes are computationally expensive and inaccurate at propagating these signals to great distances. A linearized wave propagation code, coupled to a nonlinear code, provides an efficient mechanism to both accurately simulate the explosion itself and to propagate these signals to distant receivers. To this end we have coupled Sandia's nonlinear simulation algorithm CTH to a linearized elastic wave propagation code for 2-D axisymmetric media (axiElasti) by passing information from the nonlinear to the linear code via time-varying boundary conditions. In this report, we first develop the 2-D axisymmetric elastic wave equations in cylindrical coordinates. Next we show how we design the time-varying boundary conditions passing information from CTH to axiElasti, and finally we demonstrate the coupling code via a simple study of the elastic radius.
Institute of Scientific and Technical Information of China (English)
TANG NianSheng; CHEN XueDong; WANG XueRen
2009-01-01
Semiparametric reproductive dispersion nonlinear model (SRDNM) is an extension of nonlinear reproductive dispersion models and semiparametric nonlinear regression models, and includes semiparametric nonlinear model and semiparametric generalized linear model as its special cases. Based on the local kernel estimate of nonparametric component, profile-kernel and backfitting estimators of parameters of interest are proposed in SRDNM, and theoretical comparison of both estimators is also investigated in this paper. Under some regularity conditions, strong consistency and asymptotic normality of two estimators are proved. It is shown that the backtitting method produces a larger asymptotic variance than that for the profile-kernel method. A simulation study and a real example are used to illustrate the proposed methodologies.
Institute of Scientific and Technical Information of China (English)
YAN Minhui; CHEN Jianping
2002-01-01
This paper analyzes the high bit-rate optical pulse trasmission in single mode optical fiber with chromatic dispersion, polarization mode dispersion (small random birefringence) and nonlinearity. Numerical method employed can precisely describe their interactive effect on transmission performance. Different dispersion maps and the related performance are analysed. Various simulation results and discussion are given. The results show that chromatic dispersion compensation should be carefully designed. Appropriate dispersion management can also alleviate the effect of polarization mode dispersion.
Guo, Shuqin; Le, Zichun; Quan, Bisheng
2006-01-01
By numerical simulation, we show that the fourth-order dispersion (FOD) makes sub-picosecond optical pulse broaden as second-order dispersion (SOD), makes optical pulse oscillate simultaneously as third-order dispersion (TOD). Based on above two reasons, sub-picosecond optical pulse will be widely broaden and lead to emission of continuum radiation during propagation. Here, resemble to two- and third-order dispersion compensation, fourth-order dispersion compensation is also suggested in a dispersion-managed optical fiber link, which is realized by arranging two kinds of fiber with opposite dispersion sign in each compensation cell. For sake of avoiding excessively broadening, ultra short scale dispersion compensation cell is required in ultra high speed optical communication system. In a full dispersion compensation optical fiber system which path average dispersion is zero about SOD, TOD, and FOD, even suffering from affection of high order nonlinear like self-steep effect and self-frequency shift, 200 fs gauss optical pulse can stable propagate over 1000 km with an optimal initial chirp. When space between neighboring optical pulse is only 2 picoseconds corresponding to 500 Gbit/s transmitting capacity, eye diagram is very clarity after 1000 km. The results demonstrate that ultra short scale dispersion compensation including FOD is need and effective in ultra-high speed optical communication.
Parigi, Valentina; Stanojevic, Jovica; Hilliard, Andrew J; Nogrette, Florence; Tualle-Brouri, Rosa; Ourjoumtsev, Alexei; Grangier, Philippe
2012-01-01
We observe and measure dispersive optical non-linearities in an ensemble of cold Rydberg atoms placed inside an optical cavity. The experimental results are in agreement with a simple model where the optical non-linearities are due to the progressive appearance of a Rydberg blockaded volume within the medium. The measurements allow a direct estimation of the "blockaded fraction" of atoms within the atomic ensemble.
Dispersion coefficients for the interaction of Cs atom with different material media
Kaur, Kiranpreet; Kaur, Jasmeet; Sahoo, B. K.; Arora, Bindiya
2016-10-01
Motivated by a large number of applications, the dispersion (C3) coefficients for the interaction of a Cs atom with different material media such as Au (metal), Si (semiconductor) and various dielectric surfaces like vitreous SiO2, SiNx, sapphire and YAG are determined using accurate values of the dynamic polarizabilities of the Cs atom obtained employing the relativistic coupled-cluster approach and the dynamic dielectric constants of the walls. Moreover, we also give the retardation function in the graphical representation as functions of separation distances to describe the interaction potentials between the Cs atom with the above considered material media. For the easy access to the interaction potentials at a given distance of separation, we give a simple working functional fitting form for the retardation functions in terms of four fitting parameters that are quoted for the respective medium.
Configuring Web-based Media for Communication in Dispersed Project Groups
DEFF Research Database (Denmark)
Scheepers, Rens; Nicolajsen, Hanne Westh
2006-01-01
meetings, telephone) are not always viable options. Instead, computer-based communication media such as email, project intranets and extranets become surrogate conduits for day-to-day project communication and exchange of project-related content. We examined the effect of different media configurations......We studied how project groups in a pharmaceutical organization communicate project content. The project groups are geographically dispersed, and operate in different time zones. In such project environments, synchronous or geographically bounded modes of communication channels (e.g., face to face...... on the nature of content created by the project groups. We found that configuration decisions, notably the responsibility for content provision and who had access to content, influenced medium choice and the nature of communication taking place via the medium. More substantive content resulted when content...
Full 3D dispersion curve solutions for guided waves in generally anisotropic media
Hernando Quintanilla, F.; Lowe, M. J. S.; Craster, R. V.
2016-02-01
Dispersion curves of guided waves provide valuable information about the physical and elastic properties of waves propagating within a given waveguide structure. Algorithms to accurately compute these curves are an essential tool for engineers working in non-destructive evaluation and for scientists studying wave phenomena. Dispersion curves are typically computed for low or zero attenuation and presented in two or three dimensional plots. The former do not always provide a clear and complete picture of the dispersion loci and the latter are very difficult to obtain when high values of attenuation are involved and arbitrary anisotropy is considered in single or multi-layered systems. As a consequence, drawing correct and reliable conclusions is a challenging task in the modern applications that often utilize multi-layered anisotropic viscoelastic materials. These challenges are overcome here by using a spectral collocation method (SCM) to robustly find dispersion curves in the most complicated cases of high attenuation and arbitrary anisotropy. Solutions are then plotted in three-dimensional frequency-complex wavenumber space, thus gaining much deeper insight into the nature of these problems. The cases studied range from classical examples, which validate this approach, to new ones involving materials up to the most general triclinic class for both flat and cylindrical geometry in multi-layered systems. The apparent crossing of modes within the same symmetry family in viscoelastic media is also explained and clarified by the results. Finally, the consequences of the centre of symmetry, present in every crystal class, on the solutions are discussed.
Unifying diffusion and seepage for nonlinear gas transport in multiscale porous media
Song, Hongqing; Wang, Yuhe; Wang, Jiulong; Li, Zhengyi
2016-09-01
We unify the diffusion and seepage process for nonlinear gas transport in multiscale porous media via a proposed new general transport equation. A coherent theoretical derivation indicates the wall-molecule and molecule-molecule collisions drive the Knudsen and collective diffusive fluxes, and constitute the system pressure across the porous media. A new terminology, nominal diffusion coefficient can summarize Knudsen and collective diffusion coefficients. Physical and numerical experiments show the support of the new formulation and provide approaches to obtain the diffusion coefficient and permeability simultaneously. This work has important implication for natural gas extraction and greenhouse gases sequestration in geological formations.
SPACE-TIME DISCONTINUOUS GALERKIN METHOD FOR MAXWELL EQUATIONS IN DISPERSIVE MEDIA
Institute of Scientific and Technical Information of China (English)
汪波; 谢资清; 张智民
2014-01-01
In this paper, a unified model for time-dependent Maxwell equations in dispersive media is considered. The space-time DG method developed in [29] is applied to solve the un-derlying problem. Unconditional L2-stability and error estimate of order O?τr+1+hk+1/2? are obtained when polynomials of degree at most r and k are used for the temporal dis-cretization and spatial discretization respectively. 2-D and 3-D numerical examples are given to validate the theoretical results. Moreover, numerical results show an ultra-convergence of order 2r+1 in temporal variable t.
Traversal of electromagnetic pulses through dispersive media with negative refractive index
Nanda, L.; Ramakrishna, S. A.
2017-05-01
We investigate the traversal of electromagnetic pulses through dispersive media with negative refractive index in such a way that no resonant effects come into play. It has been verified that for evanescent waves, the definitions of the group delay and the reshaping delay times get interchanged in comparison to the propagating waves. We show that for a negative refractive index medium (NRM) with ɛ(ω)=μ(ω), the reshaping delay time identically vanishes for propagating waves. The total delay time in NRM is otherwise contributed by both the group and the reshaping delay times, whereas for the case of broadband pulses in NRM the total delay time is always subluminal.
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.
Dispersion and absorption in one-dimensional nonlinear lattices: A resonance phonon approach
Xu, Lubo; Wang, Lei
2016-09-01
Based on the linear response theory, we propose a resonance phonon (r-ph) approach to study the renormalized phonons in a few one-dimensional nonlinear lattices. Compared with the existing anharmonic phonon (a-ph) approach, the dispersion relations derived from this approach agree with the expectations of the effective phonon (e-ph) theory much better. The application is also largely extended, i.e., it is applicable in many extreme situations, e.g., high frequency, high temperature, etc., where the existing one can hardly work. Furthermore, two separated phonon branches (one acoustic and one optical) with a clear gap in between can be observed by the r-ph approach in a diatomic anharmonic lattice. While only one combined branch can be detected in the same lattice with both the a-ph approach and the e-ph theory.
Fiber optical parametric oscillator based on highly nonlinear dispersion-shifted fiber
Institute of Scientific and Technical Information of China (English)
Sigang YANG; Kenneth K. Y. WONG; Minghua CHEN; Shizhong XIE
2013-01-01
The development of fiber optical parametric oscillators （FOPO） based on highly nonlinear dispersion- shifted fiber is reviewed in this paper. Firstly, the background and motivation are introduced, and it is pointed out that the FOPO is promising to act as optical source in non-conventional wavelength bands. Subsequently, the context focuses principally on the problem of inherent multiple-longitudinal-mode characteristic of FOPO and the corresponding solutions to it. The primary technique is by locking the phase of multiple longitudinal modes. The first reported actively mode locked FOPO is also presented in this article. However, it is not probable to realize passively mode locked FOPO because of the random phase dithering of the pump required for suppressing stimulated Brillouin scattering. Furthermore, a regeneratively mode locked FOPO is demonstrated, which can generate wide band tunable radiation in non- conventional wavelengths. Besides mode locked FOPO, the single-longitudinal-mode FOPO is also introduced. Finally, potential future directions are discussed.
Nonlinear effects related to circularly polarized dispersive Alfvén waves
Sharma, Swati; Gaur, Nidhi; Sharma, R. P.
2016-09-01
In situ measurements of solar wind have strongly implicated its turbulent behavior. The observed power spectra report a breakpoint around length scales of the order of ion scales. As one of the responsible mechanisms for the observed steepening in power spectrum, our approach includes a right circularly polarized dispersive Alfvén wave (DAW) with finite frequency correction which, when subjected to transverse collapse/filamentation instability, may possibly result in steepening of spectrum and progressive transfer of energy from larger scales to smaller scales. We have studied the nonlinear effects associated with coupling of DAW with kinetic Alfvén wave in solar wind at 1 A.U. The formation of localized structures provides a clue about the emergence of turbulence. Numerical simulation is performed to study localization and power spectral density of the field and density fluctuations. The results show steeper spectrum indicating transfer of large scale turbulent energy down to small scales.
Frequency-domain nonlinear optics in two-dimensionally patterned quasi-phase-matching media
Phillips, C R; Gallmann, L; Keller, U
2015-01-01
Advances in the amplification and manipulation of ultrashort laser pulses has led to revolutions in several areas. Examples include chirped pulse amplification for generating high peak-power lasers, power-scalable amplification techniques, pulse shaping via modulation of spatially-dispersed laser pulses, and efficient frequency-mixing in quasi-phase-matched nonlinear crystals to access new spectral regions. In this work, we introduce and demonstrate a new platform for nonlinear optics which has the potential to combine all of these separate functionalities (pulse amplification, frequency transfer, and pulse shaping) into a single monolithic device. Moreover, our approach simultaneously offers solutions to the performance-limiting issues in the conventionally-used techniques, and supports scaling in power and bandwidth of the laser source. The approach is based on two-dimensional patterning of quasi-phase-matching gratings combined with optical parametric interactions involving spatially dispersed laser pulses...
Zhang, Di; Capoglu, Ilker; Li, Yue; Cherkezyan, Lusik; Chandler, John; Spicer, Graham; Subramanian, Hariharan; Taflove, Allen; Backman, Vadim
2016-06-01
Combining finite-difference time-domain (FDTD) methods and modeling of optical microscopy modalities, we previously developed an open-source software package called Angora, which is essentially a "microscope in a computer." However, the samples being simulated were limited to nondispersive media. Since media dispersions are common in biological samples (such as cells with staining and metallic biomarkers), we have further developed a module in Angora to simulate samples having complicated dispersion properties, thereby allowing the synthesis of microscope images of most biological samples. We first describe a method to integrate media dispersion into FDTD, and we validate the corresponding Angora dispersion module by applying Mie theory, as well as by experimentally imaging gold microspheres. Then, we demonstrate how Angora can facilitate the development of optical imaging techniques with a case study.
Nonlinear coda wave analysis of hysteretic elastic behavior in strongly scattering media
Ouarabi, M. Ait; Boubenider, F.; Gliozzi, A. S.; Scalerandi, M.
2016-10-01
Strongly scattering elastic media, such as consolidated granular materials, respond to ultrasonic pulse excitations with a long response signal with peculiar properties. The portion of the signal at late times, termed coda, is due to multiple scattering. It contains information about the elastic properties of the material, and it has been proven to be very sensitive to small variations in the modulus. Here we propose a technique based on a nonlinear analysis of the coda of a signal, which might be applied to quantify the nonlinear elastic response in consolidated granular media exhibiting a hysteretic elastic behavior. The method proposed allows for an intrinsic definition of the reference signal which is normally needed for applying coda-based methods.
Propagation dynamics of finite-energy Airy beams in nonlocal nonlinear media
Wu, Zhen-Kun; Li, Peng; Gu, Yu-Zong
2017-10-01
We investigate periodic inversion and phase transition of normal and displaced finite-energy Airy beams propagating in nonlocal nonlinear media with the split-step Fourier method. Numerical simulation results show that parameters such as the degree of nonlocality and amplitude have profound effects on the intensity distribution of the period of an Airy beam. Nonlocal nonlinear media will reduce into a harmonic potential if the nonlocality is strong enough, which results in the beam fluctuating in an approximately cosine mode. The beam profile changes from an Airy profile to a Gaussian one at a critical point, and during propagation the process repeats to form an unusual oscillation. We also briefly discus the two-dimensional case, being equivalent to a product of two one-dimensional cases.
Dipole Solitons in Nonlinear Media with an Exponential-Decay Nonlocal Response
Institute of Scientific and Technical Information of China (English)
YANG Zhen-Jun; MA Xue-Kai; ZHENG Yi-Zhou; GAO Xing-Hui; LU Da-Quan; HU Wei
2011-01-01
By applying the variational approach,the analytical expression of dipole solitons is obtained in nonlinear media with an exponential-decay nonlocal response.The relations of the soliton power versus the propagation constant and the soliton width are given.Some numerical simulations are carried out.The results show that the analytical expression is in excellent agreement with the numerical results for the strongly nonlocal case.
DEFF Research Database (Denmark)
Mamaev, A.V.; Saffman, M.; Zozulya, A.A.
1996-01-01
We analyze the evolution of (1+1) dimensional dark stripe beams in bulk media with a photorefractive nonlinear response. These beams, including solitary wave solutions, are shown to be unstable with respect to symmetry breaking and formation of structure along the initially homogeneous coordinate....... Experimental results show the complete sequence of events starting from self-focusing of the stripe, its bending due to the snake instability, and subsequent decay into a set of optical vortices....
Field computation in non-linear magnetic media using particle swarm optimization
Energy Technology Data Exchange (ETDEWEB)
Adly, A.A. E-mail: amradlya@intouch.com; Abd-El-Hafiz, S.K
2004-05-01
This paper presents an automated particle swarm optimization approach using which field computations may be carried out in devices involving non-linear magnetic media. Among the advantages of the proposed approach are its ability to handle complex geometries and its computational efficiency. The proposed approach has been implemented and computations were carried out for an electromagnet subject to different DC excitation conditions. These computations showed good agreement with the results obtained by the finite-element approach.
Mechanical balance laws for fully nonlinear and weakly dispersive water waves
Kalisch, Henrik; Mitsotakis, Dimitrios
2015-01-01
The Serre-Green-Naghdi system is a coupled, fully nonlinear system of dispersive evolution equations which approximates the full water wave problem. The system is an extension of the well known shallow-water system to the situation where the waves are long, but not so long that dispersive effects can be neglected. In the current work, the focus is on deriving mass, momentum and energy densities and fluxes associated with the Serre-Green-Naghdi system. These quantities arise from imposing balance equations of the same asymptotic order as the evolution equations. In the case of an even bed, the conservation equations are satisfied exactly by the solutions of the Serre-Green-Naghdi system. The case of variable bathymetry is more complicated, with mass and momentum conservation satisfied exactly, and energy conservation satisfied only in a global sense. In all cases, the quantities found here reduce correctly to the corresponding counterparts in both the Boussinesq and the shallow-water scaling. One consequence o...
Global-local nonlinear model reduction for flows in heterogeneous porous media
AlOtaibi, Manal
2015-08-01
In this paper, we combine discrete empirical interpolation techniques, global mode decomposition methods, and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM), to reduce the computational complexity associated with nonlinear flows in highly-heterogeneous porous media. To solve the nonlinear governing equations, we employ the GMsFEM to represent the solution on a coarse grid with multiscale basis functions and apply proper orthogonal decomposition on a coarse grid. Computing the GMsFEM solution involves calculating the residual and the Jacobian on a fine grid. As such, we use local and global empirical interpolation concepts to circumvent performing these computations on the fine grid. The resulting reduced-order approach significantly reduces the flow problem size while accurately capturing the behavior of fully-resolved solutions. We consider several numerical examples of nonlinear multiscale partial differential equations that are numerically integrated using fully-implicit time marching schemes to demonstrate the capability of the proposed model reduction approach to speed up simulations of nonlinear flows in high-contrast porous media.
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.
Tracing Analytic Ray Curves for Light and Sound Propagation in Non-Linear Media.
Mo, Qi; Yeh, Hengchin; Manocha, Dinesh
2016-11-01
The physical world consists of spatially varying media, such as the atmosphere and the ocean, in which light and sound propagates along non-linear trajectories. This presents a challenge to existing ray-tracing based methods, which are widely adopted to simulate propagation due to their efficiency and flexibility, but assume linear rays. We present a novel algorithm that traces analytic ray curves computed from local media gradients, and utilizes the closed-form solutions of both the intersections of the ray curves with planar surfaces, and the travel distance. By constructing an adaptive unstructured mesh, our algorithm is able to model general media profiles that vary in three dimensions with complex boundaries consisting of terrains and other scene objects such as buildings. Our analytic ray curve tracer with the adaptive mesh improves the efficiency considerably over prior methods. We highlight the algorithm's application on simulation of visual and sound propagation in outdoor scenes.
Institute of Scientific and Technical Information of China (English)
李志斌; 陈天华
2002-01-01
An algorithm for constructing exact solitary wave solutions and singular solutions for a class of nonlinear dissipative-dispersive system is presented. With the aid of symbolic manipulation system Maple, some explicit solutions are obtained for the system in physically interesting but non-integrable cases.
Radiation pressure of light pulses and conservation of linear momentum in dispersive media.
Scalora, Michael; D'Aguanno, Giuseppe; Mattiucci, Nadia; Bloemer, Mark J; Centini, Marco; Sibilia, Concita; Haus, Joseph W
2006-05-01
We derive an expression for the Minkowski momentum under conditions of dispersive susceptibility and permeability, and compare it to the Abraham momentum in order to test the principle of conservation of linear momentum when matter is present. We investigate cases when an incident pulse interacts with a variety of structures, including thick substrates, resonant, free-standing, micron-sized multilayer stacks, and negative index materials. In general, we find that for media only a few wavelengths thick the Minkowski and Abraham momentum densities yield similar results. For more extended media, including substrates and Bragg mirrors embedded inside thick dielectric substrates, our calculations show dramatic differences between the Minkowski and Abraham momenta. Without exception, in all cases investigated the instantaneous Lorentz force exerted on the medium is consistent only with the rate of change of the Abraham momentum. As a practical example, we use our model to predict that electromagnetic momentum and energy buildup inside a multilayer stack can lead to widely tunable accelerations that may easily reach and exceed 10(10) m/s(2) for a mass of 10(-5) g. Our results suggest that the physics of the photonic band edge and other similar finite structures may be used as a testing ground for basic electromagnetic phenomena such as momentum transfer to macroscopic media.
Directory of Open Access Journals (Sweden)
Ashkan Ghanbari
2014-12-01
Full Text Available In the present study, we investigate the evolution of the super continuum generation (SCG through the triangular photonic crystal fiber (PCF at 1310nm by using both full-vector multi pole method (M.P.M and novel concrete algorithms: Symmetric Split-step Fourier (SSF and fourth order Runge Kutta(RK4 which is an accurate method to solve the general nonlinear Schrodinger equation (GNLSE. We propose an ideal solid-core PCF structure featuring a minimum anomalous group velocity dispersion (GVD, small higher order dispersions (HODs and enhanced nonlinearity for appropriate super continuum generation with low input pulse energies over discrete distances of the PCF. We also investigate the impact of the linear and nonlinear effects on the super continuum spectra in detail and compare the results with different status.
Mechanical balance laws for fully nonlinear and weakly dispersive water waves
Kalisch, Henrik; Khorsand, Zahra; Mitsotakis, Dimitrios
2016-10-01
The Serre-Green-Naghdi system is a coupled, fully nonlinear system of dispersive evolution equations which approximates the full water wave problem. The system is known to describe accurately the wave motion at the surface of an incompressible inviscid fluid in the case when the fluid flow is irrotational and two-dimensional. The system is an extension of the well known shallow-water system to the situation where the waves are long, but not so long that dispersive effects can be neglected. In the current work, the focus is on deriving mass, momentum and energy densities and fluxes associated with the Serre-Green-Naghdi system. These quantities arise from imposing balance equations of the same asymptotic order as the evolution equations. In the case of an even bed, the conservation equations are satisfied exactly by the solutions of the Serre-Green-Naghdi system. The case of variable bathymetry is more complicated, with mass and momentum conservation satisfied exactly, and energy conservation satisfied only in a global sense. In all cases, the quantities found here reduce correctly to the corresponding counterparts in both the Boussinesq and the shallow-water scaling. One consequence of the present analysis is that the energy loss appearing in the shallow-water theory of undular bores is fully compensated by the emergence of oscillations behind the bore front. The situation is analyzed numerically by approximating solutions of the Serre-Green-Naghdi equations using a finite-element discretization coupled with an adaptive Runge-Kutta time integration scheme, and it is found that the energy is indeed conserved nearly to machine precision. As a second application, the shoaling of solitary waves on a plane beach is analyzed. It appears that the Serre-Green-Naghdi equations are capable of predicting both the shape of the free surface and the evolution of kinetic and potential energy with good accuracy in the early stages of shoaling.
Sun, HongGuang; Zhang, Yong; Chen, Wen; Reeves, Donald M.
2014-02-01
Field and numerical experiments of solute transport through heterogeneous porous and fractured media show that the growth of contaminant plumes may not exhibit constant scaling, and may instead transition between diffusive states (i.e., superdiffusion, subdiffusion, and Fickian diffusion) at various transport scales. These transitions are likely attributed to physical properties of the medium, such as spatial variations in medium heterogeneity. We refer to this transitory dispersive behavior as "transient dispersion", and propose a variable-index fractional-derivative model (FDM) to describe the underlying transport dynamics. The new model generalizes the standard constant-index FDM which is limited to stationary heterogeneous media. Numerical methods including an implicit Eulerian method (for spatiotemporal transient dispersion) and a Lagrangian solver (for multiscaling dispersion) are utilized to produce variable-index FDM solutions. The variable-index FDM is then applied to describe transient dispersion observed at two field tracer tests and a set of numerical experiments. Results show that 1) uranine transport at the small-scale Grimsel test site transitions from strong subdispersion to Fickian dispersion, 2) transport of tritium at the regional-scale Macrodispersion Experimental (MADE) site transitions from near-Fickian dispersion to strong superdispersion, and 3) the conservative particle transport through regional-scale discrete fracture network transitions from superdispersion to Fickian dispersion. The variable-index model can efficiently quantify these transitions, with the scale index varying linearly in time or space.
Sun, Hongguang; Zhang, Yong; Chen, Wen; Reeves, Donald M
2014-02-01
Field and numerical experiments of solute transport through heterogeneous porous and fractured media show that the growth of contaminant plumes may not exhibit constant scaling, and may instead transition between diffusive states (i.e., superdiffusion, subdiffusion, and Fickian diffusion) at various transport scales. These transitions are likely attributed to physical properties of the medium, such as spatial variations in medium heterogeneity. We refer to this transitory dispersive behavior as "transient dispersion", and propose a variable-index fractional-derivative model (FDM) to describe the underlying transport dynamics. The new model generalizes the standard constant-index FDM which is limited to stationary heterogeneous media. Numerical methods including an implicit Eulerian method (for spatiotemporal transient dispersion) and a Lagrangian solver (for multiscaling dispersion) are utilized to produce variable-index FDM solutions. The variable-index FDM is then applied to describe transient dispersion observed at two field tracer tests and a set of numerical experiments. Results show that 1) uranine transport at the small-scale Grimsel test site transitions from strong subdispersion to Fickian dispersion, 2) transport of tritium at the regional-scale Macrodispersion Experimental (MADE) site transitions from near-Fickian dispersion to strong superdispersion, and 3) the conservative particle transport through regional-scale discrete fracture network transitions from superdispersion to Fickian dispersion. The variable-index model can efficiently quantify these transitions, with the scale index varying linearly in time or space.
Bright solitons in defocusing media with spatial modulation of the quintic nonlinearity
Zeng, Jianhua
2012-01-01
It has been recently demonstrated that self-defocusing (SDF) media with the cubic nonlinearity, whose local coefficient grows from the center to 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 $% g_{0}+\\sinh ^{2}(\\beta x) $. 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 $\\mathrm{sech}$", which provides for an ...
Directory of Open Access Journals (Sweden)
Monika N. Mehta
2012-04-01
Full Text Available An approximate solution of longitudinal dispersion phenomena occurring in two phase miscible fluid flow through porous media has been obtained by using the group theoretic approach. The longitudinal dispersion coefficient is assumed to be directly proportional to the concentration of the fluid for a distance x and at any time t > 0. The graphical representation for the concentration of the fluid for a distance x and at time t > 0 has been obtained using Mat lab coding.
Zayed, Elsayed M. E.; Al-Nowehy, Abdul-Ghani; Elshater, Mona E. M.
2017-06-01
The (G^'/G)-expansion method, the improved Sub-ODE method, the extended auxiliary equation method, the new mapping method and the Jacobi elliptic function method are applied in this paper for finding many new exact solutions including Jacobi elliptic solutions, solitary solutions, singular solitary solutions, trigonometric function solutions and other solutions to the nonlinear Schrödinger equation with fourth-order dispersion and dual power law nonlinearity whose balance number is not positive integer. The used methods present a wider applicability for handling the nonlinear partial differential equations. A comparison of our new results with the well-known results is made. Also, we compare our results with each other yielding from these five integration tools.
Artem'ev, V. A.; Nezvanov, A. Yu.; Nesvizhevsky, V. V.
2016-01-01
We discuss properties of the interaction of slow neutrons with nano-dispersed media and their application for neutron reflectors. In order to increase the accuracy of model simulation of the interaction of neutrons with nanopowders, we perform precise quantum mechanical calculation of potential scattering of neutrons on single nanoparticles using the method of phase functions. We compare results of precise calculations with those performed within first Born approximation for nanodiamonds with the radius of 2-5 nm and for neutron energies 3 × 10-7-10-3 eV. Born approximation overestimates the probability of scattering to large angles, while the accuracy of evaluation of integral characteristics (cross sections, albedo) is acceptable. Using Monte-Carlo method, we calculate albedo of neutrons from different layers of piled up diamond nanopowder.
Emission of correlated photon pairs from superluminal perturbations in dispersive media
Piazza, Francesco Dalla; Cacciatori, Sergio Luigi; Faccio, Daniel
2012-01-01
We develop a perturbative theory that describes a superluminal refractive perturbation propagating in a dispersive medium and the subsequent excitation of the quantum vacuum zero-point fluctuations. We find a process similar to the anomalous Doppler effect: photons are emitted in correlated pairs and mainly within a Cerenkov-like cone, one on the forward and the other in backward directions. The number of photon pairs emitted from the perturbation increases strongly with the degree of superluminality and under realizable experimental conditions, it can reach up to ~0.01 photons per pulse. Moreover, it is in principle possible to engineer the host medium so as to modify the effective group refractive index. In the presence of "fast light" media, e.g. a with group index smaller than unity, a further ~10x enhancement may be achieved and the photon emission spectrum is characterized by two sharp peaks that, in future experiments would clearly identify the correlated emission of photon pairs.
Fridjonsson, Einar O; Seymour, Joseph D; Schultz, Logan N; Gerlach, Robin; Cunningham, Alfred B; Codd, Sarah L
2011-03-01
Noninvasive measurements of hydrodynamic dispersion by nuclear magnetic resonance (NMR) are made in a model porous system before and after a biologically mediated precipitation reaction. Traditional magnetic resonance imaging (MRI) was unable to detect the small scale changes in pore structure visualized during light microscopy analysis after destructive sampling of the porous medium. However, pulse gradient spin echo nuclear magnetic resonance (PGSE NMR) measurements clearly indicated a change in hydrodynamics including increased pore scale mixing. These changes were detected through time-dependent measurement of the propagator by PGSE NMR. The dynamics indicate an increased pore scale mixing which alters the preasymptotic approach to asymptotic Gaussian dynamics governed by the advection diffusion equation. The methods described here can be used in the future to directly measure the transport of solutes in biomineral-affected porous media and contribute towards reactive transport models, which take into account the influence of pore scale changes in hydrodynamics.
Energy Technology Data Exchange (ETDEWEB)
Artem’ev, V. A., E-mail: niitm@inbox.ru [Research Institute of Materials Technology (Russian Federation); Nezvanov, A. Yu. [Moscow State Industrial University (Russian Federation); Nesvizhevsky, V. V. [Institut Max von Laue—Paul Langevin (France)
2016-01-15
We discuss properties of the interaction of slow neutrons with nano-dispersed media and their application for neutron reflectors. In order to increase the accuracy of model simulation of the interaction of neutrons with nanopowders, we perform precise quantum mechanical calculation of potential scattering of neutrons on single nanoparticles using the method of phase functions. We compare results of precise calculations with those performed within first Born approximation for nanodiamonds with the radius of 2–5 nm and for neutron energies 3 × 10{sup -7}–10{sup -3} eV. Born approximation overestimates the probability of scattering to large angles, while the accuracy of evaluation of integral characteristics (cross sections, albedo) is acceptable. Using Monte-Carlo method, we calculate albedo of neutrons from different layers of piled up diamond nanopowder.
Clobert, J.; Danchin, E.; Dhondt, A.A.; Nichols, J.D.
2001-01-01
The ability of species to migrate and disperse is a trait that has interested ecologists for many years. Now that so many species and ecosystems face major environmental threats from habitat fragmentation and global climate change, the ability of species to adapt to these changes by dispersing, migrating, or moving between patches of habitat can be crucial to ensuring their survival. This book provides a timely and wide-ranging overview of the study of dispersal and incorporates much of the latest research. The causes, mechanisms, and consequences of dispersal at the individual, population, species and community levels are considered. The potential of new techniques and models for studying dispersal, drawn from molecular biology and demography, is also explored. Perspectives and insights are offered from the fields of evolution, conservation biology and genetics. Throughout the book, theoretical approaches are combined with empirical data, and care has been taken to include examples from as wide a range of species as possible.
Larecki, Wieslaw; Banach, Zbigniew
2014-01-01
This paper analyzes the propagation of the waves of weak discontinuity in a phonon gas described by the four-moment maximum entropy phonon hydrodynamics involving a nonlinear isotropic phonon dispersion relation. For the considered hyperbolic equations of phonon gas hydrodynamics, the eigenvalue problem is analyzed and the condition of genuine nonlinearity is discussed. The speed of the wave front propagating into the region in thermal equilibrium is first determined in terms of the integral formula dependent on the phonon dispersion relation and subsequently explicitly calculated for the Dubey dispersion-relation model: |k|=ωc-1(1+bω2). The specification of the parameters c and b for sodium fluoride (NaF) and semimetallic bismuth (Bi) then makes it possible to compare the calculated dependence of the wave-front speed on the sample’s temperature with the empirical relations of Coleman and Newman (1988) describing for NaF and Bi the variation of the second-sound speed with temperature. It is demonstrated that the calculated temperature dependence of the wave-front speed resembles the empirical relation and that the parameters c and b obtained from fitting respectively the empirical relation and the original material parameters of Dubey (1973) are of the same order of magnitude, the difference being in the values of the numerical factors. It is also shown that the calculated temperature dependence is in good agreement with the predictions of Hardy and Jaswal’s theory (Hardy and Jaswal, 1971) on second-sound propagation. This suggests that the nonlinearity of a phonon dispersion relation should be taken into account in the theories aiming at the description of the wave-type phonon heat transport and that the Dubey nonlinear isotropic dispersion-relation model can be very useful for this purpose.
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.
Nonlinear localized modes in PT-symmetric optical media with competing gain and loss
Midya, Bikashkali
2014-01-01
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 expressions 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 effect 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.
Nonlinear interaction of charged particles with strong laser pulses in a gaseous media
Directory of Open Access Journals (Sweden)
H. K. Avetissian
2007-07-01
Full Text Available The charged particles nonlinear dynamics in the field of a strong electromagnetic wave pulse of finite duration and certain form of the envelope, in the refractive medium with a constant and variable refraction indexes, is investigated by means of numerical integration of the classical relativistic equations of motion. The particle energy dependence on the pulse intensity manifests the nonlinear threshold phenomenon of a particle reflection and capture by actual laser pulses in dielectric-gaseous media that takes place for a plane electromagnetic wave in the induced Cherenkov process. Laser acceleration of the particles in the result of the reflection from the pulse envelope and in the capture regime with the variable refraction index along the pulse propagation direction is investigated.
Non-Linear Stability of an Electrified Plane Interface in Porous Media
El-Dib, Yusry O.; Moatimid, Galal M.
2004-03-01
The non-linear electrohydrodynamic stability of capillary-gravity waves on the interface between two semi-infinite dielectric fluids is investigated. The system is stressed by a vertical electric field in the presence of surface charges. The work examines a few representative porous media configurations. The analysis includes Rayleigh-Taylor and Kelvin-Helmholtz instabilities. The boundary - value problem leads to a non-linear equation governing the surface evolution. Taylor theory is adopted to expand this equation, in the light of multiple scales, in order to obtain a non-linear Schr¨odinger equation describing the behavior of the perturbed interface. The latter equation, representing the amplitude of the quasi-monochromatic traveling wave, is used to describe the stability criteria. These criteria are discussed both analytically and numerically. In order to identifiy regions of stability and instability, the electric field intensity is plotted versus the wave number. Through a linear stability approach it is found that Darcy's coefficients have a destabilizing influence, while in the non-linear scope these coefficients as well as the electric field intensity play a dual role on the stability.
An experimental study of dielectric dispersion in porous media and its dependence on pore geometry
Energy Technology Data Exchange (ETDEWEB)
Haslund, E.
1996-12-31
Understanding water saturated composite media are important in the study of oil reservoirs. This doctoral thesis discusses measurements of the frequency dependent permittivity and conductivity of water saturated porous glass specimens. The experiments are designed to investigate the dispersion resulting from the geometrical properties of the pore space. Measurements are presented of the effective complex dielectric constant of water saturated porous glass specimens for frequencies below 13 MHz. The specimens are made from sintered glass spheres, and in some specimens thin plates are mixed in with the spheres. Low-conductivity water is used to saturate the pore space in order to scale the frequency range of the Maxwell-Wagner dispersion into the measurement range. The experiments are compared with two different effective medium approaches. One approach is the Mendelson and Cohen theory with randomly oriented spheroidal grains in addition to spherical grains, the other the Local porosity theory due to Hilfer. Both theories were found to be in good agreement with the experimental observations. 175 refs., 59 figs., 1 table
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.
Hybrid dispersive media with controllable wave propagation: A new take on smart materials
Energy Technology Data Exchange (ETDEWEB)
Bergamini, Andrea E., E-mail: andrea.bergamini@empa.ch [Empa, Materials Science and Technology, Laboratory for Mechanical Integrity of Energy Systems, Überlandstrasse 129, CH-8600, Dübendorf (Switzerland); Zündel, Manuel [ETH Zürich, Institute of Mechanical Systems, Leonhardstrasse 21, CH-8092 Zürich (Switzerland); Flores Parra, Edgar A.; Ermanni, Paolo [ETH Zürich, Composite Materials and Adaptive Structures Laboratory, Leonhardstrasse 21, CH-8092 Zürich (Switzerland); Delpero, Tommaso [Empa, Materials Science and Technology, Laboratory for Mechanical Integrity of Energy Systems, Überlandstrasse 129, CH-8600 Dübendorf (Switzerland); Ruzzene, Massimo [Georgia Institute of Technology, G.W. Woodruff School of Mechanical Engineering, 801 Ferst Drive, Atlanta, Georgia 30332-0405 (United States)
2015-10-21
In this paper, we report on the wave transmission characteristics of a hybrid one dimensional (1D) medium. The hybrid characteristic is the result of the coupling between a 1D mechanical waveguide in the form of an elastic beam, supporting the propagation of transverse waves and a discrete electrical transmission line, consisting of a series of inductors connected to ground through capacitors. The capacitors correspond to a periodic array of piezoelectric patches that are bonded to the beam and that couple the two waveguides. The coupling leads to a hybrid medium that is characterized by a coincidence condition for the frequency/wavenumber value corresponding to the intersection of the branches of the two waveguides. In the frequency range centered at coincidence, the hybrid medium features strong attenuation of wave motion as a result of the energy transfer towards the electrical transmission line. This energy transfer, and the ensuing attenuation of wave motion, is alike the one obtained through internal resonating units of the kind commonly used in metamaterials. However, the distinct shape of the dispersion curves suggests how this energy transfer is not the result of a resonance and is therefore fundamentally different. This paper presents the numerical investigation of the wave propagation in the considered media, it illustrates experimental evidence of wave transmission characteristics and compares the performance of the considered configuration with that of internal resonating metamaterials. In addition, the ability to conveniently tune the dispersion properties of the electrical transmission line is exploited to adapt the periodicity of the domain and to investigate diatomic periodic configurations that are characterized by a richer dispersion spectrum and broader bandwidth of wave attenuation at coincidence. The medium consisting of mechanical, piezoelectric, and analog electronic elements can be easily interfaced to digital devices to offer a novel
Hybrid dispersive media with controllable wave propagation: A new take on smart materials
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
Energy Technology Data Exchange (ETDEWEB)
Kobayashi, Yasuaki [Meme Media Laboratory, Hokkaido University, Sapporo 060-0813 (Japan); Kori, Hiroshi [Division of Advanced Sciences, Ochadai Academic Production, Ochanomizu University, Tokyo 112-8610 (Japan)], E-mail: kobayashi@nsc.es.hokudai.ac.jp, E-mail: kori.hiroshi@ocha.ac.jp
2009-03-15
A theoretical framework is developed for the precise control of spatial patterns in oscillatory media using nonlinear global feedback, where a proper form of the feedback function corresponding to a specific pattern is predicted through the analysis of a phase diffusion equation with global coupling. In particular, feedback functions that generate the following spatial patterns are analytically given: (i) 2-cluster states with an arbitrary population ratio, (ii) equally populated multi-cluster states and (iii) a desynchronized state. Our method is demonstrated numerically by using the Brusselator model in the oscillatory regime. Experimental realization is also discussed.
Large net-normal dispersion Er-doped fibre laser mode-locked with a nonlinear amplifying loop mirror
Bowen, Patrick; Broderick, Neil G R
2016-01-01
We report on an environmentally stable, all-PM-fibre, Er-doped, mode-locked laser with a central wavelength of 1550 nm. Significantly, the laser possesses large net-normal dispersion such that its dynamics are comparable to that of an all-normal dispersion fibre laser at 1 {\\mu}m with an analogous architecture. The laser is mode-locked with a nonlinear amplifying loop mirror to produce pulses that are externally compressible to 500 fs. Experimental results are in good agreement with numerical simulations.
Design of a High-Nonlinearity Single-Mode Holey Fiber with Flattened Dispersion around 800 nm
Institute of Scientific and Technical Information of China (English)
WANG Wei; SOU Lan-Tian; LIU Zhao-Lun; ZHOU Gui-Yao
2009-01-01
We numerically demonstrate a high-nonlinearity single-mode holey fiber with flattened dispersion around the Ti-Za laser band at 800 nm. The dispersion profile of the fiber has the shape of a quadratic curve, which reaches its maximun 5.96ps·km~(-1)·nm~(-1)at 800nm and its minimum -0.897 ps·km-1·nm~(-1) at both 750 and 850 nm.The nonlinear coefficient is 170 W~(-1)km~(-1) at 800nm and so higher order modes exit. A six-layer air-hole cladding ensures a loss less than 0.067 db/m in the 750 to 850nm range. Two more air-hole rings will reduce the loss to below 0.1db/km.
Biswas, Piyali; Biswas, Abhijit; Pal, Bishnu P
2016-01-01
We numerically demonstrate self-similar propagation of parabolic optical pulses through a highly nonlinear and passive specialty photonic bandgap fiber at 2.8 micron. In this context, we have proposed a scheme endowed with a rapidly varying, but of nearly-mean-zero longitudinal dispersion and modulated nonlinear profile in order to achieve self-similarity of the formed parabolic pulse propagating over longer distances. To implement the proposed scheme, we have designed a segmented bandgap fiber with suitably tapered counterparts to realize such customized dispersion with chalchogenide glass materials. A self-similar parabolic pulse with full-width-at-half-maxima of 4.12 ps and energy of ~ 39 pJ as been achieved at the output. Along with a linear chirp spanning over the entire pulse duration, 3dB spectral broadening of about 38 nm at the output has been reported.
Chow, K K; Shu, C; Lin, Chinlon; Bjarklev, A
2005-10-31
We demonstrate extinction ratio improvement by using pump-modulated four-wave mixing in a dispersion-flattened nonlinear photonic crystal fiber. A 6-dB improvement in the extinction ratio of a degraded return-to-zero signal has been achieved. A power penalty improvement of 3 dB at 10(-9) bit-error-rate level is obtained in the 10 Gb/s bit-error-rate measurements.
非线性再生散度模型的诊断%SOME DIAGNOSTICS IN NONLINEAR REPRODUCTIVE DISPERSION MODELS
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
This article discusses the problem of the detection of influential cases in nonlinear reproductive dispersion models (NRDM). A diagnostic based on case-deletion approach in estimating equations is proposed. The relationships between the generalized leverage defined by Wei et al. in 1998, statistical curvature, and the local influence of the response vector perturbations are investigated in NRDM. Two numerical examples are given to illustrate the results.
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
Using trial equation method, abundant exact envelope traveling wave solutions of high-order dispersive cubic-quintic nonlinear Schrodinger equation, which include envelope soliton solutions, triangular function envelope solutions, and Jacobian elliptic function envelope solutions, are obtained. To our knowledge, all of these results are new.In particular, our proposed method is very simple and can be applied to a lot of similar equations.
Chen Yong; Zhang Hong Qin
2003-01-01
Based on the idea of homogenous balance method and with the help of Mathematica, we obtain a new auto-Baecklund transformation for modified nonlinear dispersive equation mK(m,n). Then based on the Baecklund transformation, some solitary patterns solution for mK(m,n) equation are derived. In addition, we also obtain the general solutions for mK(n,n) in higher dimensional spatial domains, even in N dimensional space.
Energy Technology Data Exchange (ETDEWEB)
Cui, Jianbo, E-mail: jianbocui@lsec.cc.ac.cn [Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, 100190 (China); Hong, Jialin, E-mail: hjl@lsec.cc.ac.cn [Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, 100190 (China); Liu, Zhihui, E-mail: liuzhihui@lsec.cc.ac.cn [Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, 100190 (China); Zhou, Weien, E-mail: weienzhou@nudt.edu.cn [College of Science, National University of Defense Technology, Changsha 410073 (China)
2017-08-01
We indicate that the nonlinear Schrödinger equation with white noise dispersion possesses stochastic symplectic and multi-symplectic structures. Based on these structures, we propose the stochastic symplectic and multi-symplectic methods, which preserve the continuous and discrete charge conservation laws, respectively. Moreover, we show that the proposed methods are convergent with temporal order one in probability. Numerical experiments are presented to verify our theoretical results.
Directory of Open Access Journals (Sweden)
Y. W. Sun
2013-08-01
Full Text Available In this paper, we present an optimized analysis algorithm for non-dispersive infrared (NDIR to in situ monitor stack emissions. The proposed algorithm simultaneously compensates for nonlinear absorption and cross interference among different gases. We present a mathematical derivation for the measurement error caused by variations in interference coefficients when nonlinear absorption occurs. The proposed algorithm is derived from a classical one and uses interference functions to quantify cross interference. The interference functions vary proportionally with the nonlinear absorption. Thus, interference coefficients among different gases can be modeled by the interference functions whether gases are characterized by linear or nonlinear absorption. In this study, the simultaneous analysis of two components (CO2 and CO serves as an example for the validation of the proposed algorithm. The interference functions in this case can be obtained by least-squares fitting with third-order polynomials. Experiments show that the results of cross interference correction are improved significantly by utilizing the fitted interference functions when nonlinear absorptions occur. The dynamic measurement ranges of CO2 and CO are improved by about a factor of 1.8 and 3.5, respectively. A commercial analyzer with high accuracy was used to validate the CO and CO2 measurements derived from the NDIR analyzer prototype in which the new algorithm was embedded. The comparison of the two analyzers show that the prototype works well both within the linear and nonlinear ranges.
Alpatova, Alla L; Shan, Wenqian; Babica, Pavel; Upham, Brad L; Rogensues, Adam R; Masten, Susan J; Drown, Edward; Mohanty, Amar K; Alocilja, Evangelyn C; Tarabara, Volodymyr V
2010-01-01
As the range of applications for carbon nanotubes (CNTs) rapidly expands, understanding the effect of CNTs on prokaryotic and eukaryotic cell systems has become an important research priority, especially in light of recent reports of the facile dispersion of CNTs in a variety of aqueous systems including natural water. In this study, single-walled carbon nanotubes (SWCNTs) were dispersed in water using a range of natural (gum arabic, amylose, Suwannee River natural organic matter) and synthetic (polyvinyl pyrrolidone, Triton X-100) dispersing agents (dispersants) that attach to the CNT surface non-covalently via different physiosorption mechanisms. The charge and the average effective hydrodynamic diameter of suspended SWCNTs as well as the concentration of exfoliated SWCNTs in the dispersion were found to remain relatively stable over a period of 4 weeks. The cytotoxicity of suspended SWCNTs was assessed as a function of dispersant type and exposure time (up to 48 h) using general viability bioassay with Escherichia coli and using neutral red dye uptake (NDU) bioassay with WB-F344 rat liver epithelia cells. In the E. coli viability bioassays, three types of growth media with different organic loadings and salt contents were evaluated. When the dispersant itself was non-toxic, no losses of E. coli and WB-F344 viability were observed. The cell viability was affected only by SWCNTs dispersed using Triton X-100, which was cytotoxic in SWCNT-free (control) solution. The epigenetic toxicity of dispersed CNTs was evaluated using gap junction intercellular communication (GJIC) bioassay applied to WB-F344 rat liver epithelial cells. With all SWCNT suspensions except those where SWCNTs were dispersed using Triton X-100 (wherein GJIC could not be measured because the sample was cytotoxic), no inhibition of GJIC in the presence of SWCNTs was observed. These results suggest a strong dependence of the toxicity of SWCNT suspensions on the toxicity of the dispersant and point to
Two-component vector solitons in defocusing Kerr-type media with spatially modulated nonlinearity
Energy Technology Data Exchange (ETDEWEB)
Zhong, Wei-Ping, E-mail: zhongwp6@126.com [Department of Electronic and Information Engineering, Shunde Polytechnic, Guangdong Province, Shunde 528300 (China); Texas A and M University at Qatar, P.O. Box 23874 Doha (Qatar); Belić, Milivoj [Texas A and M University at Qatar, P.O. Box 23874 Doha (Qatar); Institute of Physics, University of Belgrade, P.O. Box 57, 11001 Belgrade (Serbia)
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.
Fu, Libi; Song, Weiguo; Lo, Siuming
2017-01-01
Emergencies involved in mass events are related to a variety of factors and processes. An important factor is the transmission of information on danger that has an influence on nonlinear crowd dynamics during the process of crowd dispersion. Due to much uncertainty in this process, there is an urgent need to propose a method to investigate the influence. In this paper, a novel fuzzy-theory-based method is presented to study crowd dynamics under the influence of information transmission. Fuzzy functions and rules are designed for the ambiguous description of human states. Reasonable inference is employed to decide the output values of decision making such as pedestrian movement speed and directions. Through simulation under four-way pedestrian situations, good crowd dispersion phenomena are achieved. Simulation results under different conditions demonstrate that information transmission cannot always induce successful crowd dispersion in all situations. This depends on whether decision strategies in response to information on danger are unified and effective, especially in dense crowds. Results also suggest that an increase in drift strength at low density and the percentage of pedestrians, who choose one of the furthest unoccupied Von Neumann neighbors from the dangerous source as the drift direction at high density, is helpful in crowd dispersion. Compared with previous work, our comprehensive study improves an in-depth understanding of nonlinear crowd dynamics under the effect of information on danger.
Meyer, Daniel W.; Tchelepi, Hamdi A.; Jenny, Patrick
2010-05-01
In risk analysis applications involving heterogeneous formations, the knowledge of the solute concentration probability density function (PDF) at different spatial locations and times is crucial. We propose a new joint velocity-concentration PDF method applicable for highly heterogeneous porous media that accounts for advective transport, pore-scale dispersion and molecular diffusion. Unlike in low order approximation (LOA) methods that are valid for low conductivity variances ?Y 2 and where the one-point velocity PDF is typically assumed to be a Gaussian, the proposed joint PDF method honors the increasingly non-Gaussian velocity one-point PDF and the long-term velocity correlations that were reported in different Monte Carlo (MC) studies for ?Y 2 > 0.5 [e.g., Salandin, P. and V. Fiorotto, WRR, 1998. 34(5) and Trefry, M.G., F.P. Ruan, and D. McLaughlin, WRR, 2003. 39(3)]. Furthermore, the new joint PDF method does not involve any a-priori assumption about the shape of the resulting marginal concentration PDF. LOA methods that provide information on the concentration mean and variance [Fiori, A. and G. Dagan, Journal of Contaminant Hydrology, 2000. 45(1-2)] on the other hand are typically complemented by assuming that the concentration PDF has a β-PDF shape [Bellin, A. and D. Tonina, Journal of Contaminant Hydrology, 2007. 94(1-2)]. The Eulerian joint velocity-concentration PDF transport equation in our model is numerically solved with a computationally efficient particle method. The suggested joint PDF method is validated by comparison with MC data reported by Caroni and Fiorotto for Péclet numbers ranging from 10 to 104 and ?Y 2 = 1 and 2 [Caroni, E. and V. Fiorotto, Transport in Porous Media, 2005. 59(1)].
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:
Koch, Herbert; Vişan, Monica
2014-01-01
The first part of the book provides an introduction to key tools and techniques in dispersive equations: Strichartz estimates, bilinear estimates, modulation and adapted function spaces, with an application to the generalized Korteweg-de Vries equation and the Kadomtsev-Petviashvili equation. The energy-critical nonlinear Schrödinger equation, global solutions to the defocusing problem, and scattering are the focus of the second part. Using this concrete example, it walks the reader through the induction on energy technique, which has become the essential methodology for tackling large data critical problems. This includes refined/inverse Strichartz estimates, the existence and almost periodicity of minimal blow up solutions, and the development of long-time Strichartz inequalities. The third part describes wave and Schrödinger maps. Starting by building heuristics about multilinear estimates, it provides a detailed outline of this very active area of geometric/dispersive PDE. It focuses on concepts and ide...
Xu, Zhi-Jie
2015-01-01
We first propose fundamental solutions of wave propagation in dispersive chain subject to a localized initial perturbation in the displacement. Analytical solutions are obtained for both second order nonlinear dispersive chain and homogenous harmonic chain using stationary phase approximation. Solution is also compared with numerical results from molecular dynamics (MD) simulations. Locally dominant phonon modes (k-space) are introduced based on these solutions. These locally defined spatially and temporally varying phonon modes k(x, t) are critical to the concept of the local thermodynamic equilibrium (LTE). Wave propagation accompanying with the nonequilibrium dynamics leads to the excitation of these locally defined phonon modes. It is found that the system energy is gradually redistributed among these excited phonons modes (k-space). This redistribution process is only possible with nonlinear dispersion and requires a finite amount of time to achieve a steady state distribution. This time scale is dependent on the spatial distribution (or frequency content) of the initial perturbation and the dispersion relation. Sharper and more concentrated perturbation leads to a faster energy redistribution and dissipation. This energy redistribution generates localized phonons with various frequencies that can be important for phonon-phonon interaction and energy dissipation in nonlinear systems. Depending on the initial perturbation and temperature, the time scale associated with this energy distribution can be critical for energy dissipation compared to the Umklapp scattering process. Ballistic type of heat transport along the harmonic chain reveals that at any given position, the lowest mode (k = 0) is excited first and gradually expanding to the highest mode (kmax(x,t)), where kmax(x,t) can only asymptotically approach the maximum mode kB of the first Brillouin zone (kmax(x,t) → kB). No energy distributed into modes with kmax(x,t) proportional to the sound speed
Coupling micro-CT with computer simulations to analyze dispersion in porous media
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.
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.
Extreme nonlinearities in InAs/InP nanowire gain media: the two-photon induced laser
DEFF Research Database (Denmark)
Capua, Amir; Kami, Ouri; Eisenstein, Gadi;
2012-01-01
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...
Liu, Jinjie; Brio, Moysey; Moloney, Jerome V
2012-11-15
In this Letter, we have shown that the subpixel smoothing technique that eliminates the staircasing error in the finite-difference time-domain method can be extended to material interface between dielectric and dispersive media by local coordinate rotation. First, we show our method is equivalent to the subpixel smoothing method for dielectric interface, then we extend it to a more general case where dispersive/dielectric interface is present. Finally, we provide a numerical example on a scattering problem to demonstrate that we were able to significantly improve the accuracy.
DEFF Research Database (Denmark)
Pedersen, Martin Erland Vestergaard; Cheng, Ji; Xu, Chris
2013-01-01
An improved version of the generalized nonlinear Schrödinger equation is derived, which takes into account the correct dispersion of the transverse field distribution. The new improved version of the generalized nonlinear Schrödinger equation is verified to give the same results as the standard...
Energy Technology Data Exchange (ETDEWEB)
Prakash, Deo [School of Computer Science & Engineering, Faculty of Engineering, SMVD University, Kakryal, Katra 182320, J& K (India); Shaaban, E.R., E-mail: esam_ramadan2008@yahoo.com [Physics Department, Faculty of Science, Al-Azhar University, Assiut 71542 (Egypt); Shapaan, M. [Department of Physics, Faculty of Science, Al-Azahar University, Cairo (Egypt); Mohamed, S.H. [Physics Department, Faculty of Science, Sohag University, 82524 Sohag (Egypt); Othman, A.A. [Physics Department, Faculty of Science, Assiut University, Assiut 71516 (Egypt); Verma, K.D., E-mail: kdverma1215868@gmail.com [Material Science Research Laboratory, Department of Physics, S. V. College, Aligarh 202001, U.P. (India)
2016-08-15
Highlights: • Combined experimental and theoretical researches on ZnSe Thin Films. • The film thickness and refractive index were determined using envelope method. • The absorption coefficient and the energy gap were calculated. • Dispersion parameters were determined using Wemple-DiDomenico relation. • The third order susceptibility and nonlinear refractive index were calculated. - Abstract: Zinc selenide (ZnSe) thin films with different thicknesses were evaporated onto glass substrates using the thermal evaporation technique. X-ray diffraction analysis confirmed that both the film and powder have cubic zinc-blende structure. The fundamental optical parameters like absorption coefficient, extinction coefficient and band gap were evaluated in transparent region of transmittance and reflectance spectrum. The optical transition of the films was found to be allowed, where the energy gap increased from 2.576 to 2.702 eV with increasing film thickness. Also, the refractive index value increase with increasing film thickness. The refractive indices evaluated through envelope method were extrapolated by Cauchy dispersion relationship over the whole spectra range. Additionally, the dispersion of refractive index was determined in terms of Wemple-DiDomenico single oscillator model. Third order susceptibility and nonlinear refractive index were determined for different thickness of ZnSe thin films.
Nonlinear Dynamics of Ion Concentration Polarization in Porous Media: The Leaky Membrane Model
Dydek, E Victoria
2013-01-01
The conductivity of highly charged membranes is nearly constant, due to counter-ions screening pore surfaces. Weakly charged porous media, or "leaky membranes", also contain a significant concentration of co-ions, whose depletion at high current leads to ion concentration polarization and conductivity shock waves. To describe these nonlinear phenomena the absence of electro-osmotic flow, a simple Leaky Membrane Model is formulated, based on macroscopic electroneutrality and Nernst-Planck ionic fluxes. The model is solved in cases of unsupported binary electrolytes: steady conduction from a reservoir to a cation-selective surface, transient response to a current step, steady conduction to a flow-through porous electrode, and steady conduction between cation-selective surfaces in cross flow. The last problem is motivated by separations in leaky membranes, such as shock electrodialysis. The article begins with a tribute to Neal Amundson, whose pioneering work on shock waves in chromatography involved similar mat...
A 2D spring model for the simulation of ultrasonic wave propagation in nonlinear hysteretic media.
Delsanto, P P; Gliozzi, A S; Hirsekorn, M; Nobili, M
2006-07-01
A two-dimensional (2D) approach to the simulation of ultrasonic wave propagation in nonclassical nonlinear (NCNL) media is presented. The approach represents the extension to 2D of a previously proposed one dimensional (1D) Spring Model, with the inclusion of a PM space treatment of the intersticial regions between grains. The extension to 2D is of great practical relevance for its potential applications in the field of quantitative nondestructive evaluation and material characterization, but it is also useful, from a theoretical point of view, to gain a better insight of the interaction mechanisms involved. The model is tested by means of virtual 2D experiments. The expected NCNL behaviors are qualitatively well reproduced.
Optical solitons in resonant and nonresonant nonlinear media in the presence of perturbations.
Piscureanu, M; Manaila-Maximean, D
2000-01-01
We studied the optical solitons in nonlinear resonant and nonresonant media in the presence of perturbations, assuming that the transient effects are stimulated by the light scanning beam. We treated a slight deviation from the exact necessary condition for the soliton existence (2betanu=1), as a small perturbation for the integrable system, studying its influence upon the soliton propagation conditions. The approximation is constructed by the help of an algebraic version of the soliton perturbation theory using a Riemann boundary problem in connection with the inverse scattering method. We have obtained the soliton equation and we have solved it in the presence of a small perturbation in the adiabatic approximation. In this case we have demonstrated that for a Lorentz profile line the amplitude of the soliton remains unchanged, the only effect of the perturbation results in a phase shift.
A study on biological media of ultrasonic nonlinear parameter B/A
Energy Technology Data Exchange (ETDEWEB)
Kim, Jeong Koo; Jung, Hong Ryang; Lim, Cheong Hwan [Hanseo Univ, Seosan (Korea, Republic of)
2001-06-01
This study deals with the relationship between the magnitude of ultrasonic nonlinear parameter B/A, and sound speed of amount of fat present in biological media to measure B/A system using a wide band ultrasonic transducer. To represent this case, mixtures of egg whites and egg yolk were studied. Even though the differences in density and sound speed of the two egg components were in the range of 1%, B/A increase parabolically as a function of the fat density, which is not in agreement with the Yoshizumi et al.'s suggestion. In skim, milk that dose not contain fat, both the B/A and the sound speed increase with the solubility. It is considered that protein could affect these values.
Superfast non-linear diffusion: Capillary transport in particulate porous media
Lukyanov, A V; Baines, M J; Theofanous, T G
2013-01-01
The migration of liquids in porous media, such as sand, has been commonly considered at high saturation levels with liquid pathways at pore dimensions. In this letter we reveal a low saturation regime observed in our experiments with droplets of extremely low volatility liquids deposited on sand. In this regime the liquid is mostly found within the grain surface roughness and in the capillary bridges formed at the contacts between the grains. The bridges act as variable-volume reservoirs and the flow is driven by the capillary pressure arising at the wetting front according to the roughness length scales. We propose that this migration (spreading) is the result of interplay between the bridge volume adjustment to this pressure distribution and viscous losses of a creeping flow within the roughness. The net macroscopic result is a special case of non-linear diffusion described by a superfast diffusion equation (SFDE) for saturation with distinctive mathematical character. We obtain solutions to a moving bounda...
DEFF Research Database (Denmark)
Yu, Jianjun; Jeppesen, Palle
2001-01-01
Using cross-phase modulation in a 1-km high-nonlinearity dispersion-shifted fiber with subsequent filtering by a tunable optical filter, 80-Gb/s pulsewidth maintained wavelength conversion is realized. Penalty-free transmission over 80-km conventional single-mode fiber and 12-km dispersion...
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
Nonlinear localized modes in PT-symmetric optical media with competing gain and loss
Energy Technology Data Exchange (ETDEWEB)
Midya, Bikashkali, E-mail: bikash.midya@gmail.com [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India); Roychoudhury, Rajkumar, E-mail: rroychoudhury123@gmail.com [Advanced Center for Nonlinear and Complex Phenomena, Kolkata 700075 (India)
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.
Herbert, Eric; Mordant, Nicolas; Falcon, Eric
2010-10-01
We report experiments on gravity-capillary wave turbulence on the surface of a fluid. The wave amplitudes are measured simultaneously in time and space by using an optical method. The full space-time power spectrum shows that the wave energy is localized on several branches in the wave-vector-frequency space. The number of branches depends on the power injected within the waves. The measurement of the nonlinear dispersion relation is found to be well described by a law suggesting that the energy transfer mechanisms involved in wave turbulence are restricted not only to purely resonant interaction between nonlinear waves. The power-law scaling of the spatial spectrum and the probability distribution of the wave amplitudes at a given wave number are also measured and compared to the theoretical predictions.
Weakly nonlinear dispersion and stop-band effects for periodic structures
DEFF Research Database (Denmark)
Sorokin, Vladislav; Thomsen, Jon Juel
Continua and structures composed of periodically repeated elements (cells) are used in many fields of science and technology. Examples of continua are composite materials, consisting of alternating volumes of substances with different properties, mechanical filters and wave guides. Examples of en...... suggested. The work is carried out with financial support from the Danish Council for Independent Research and COFUND: DFF – 1337-00026...... of these methods for studying nonlinear problems isimpossible or cumbersome, since Floquet theory is applicable only for linear systems. Thus the nonlinear effects for periodic structures are not yet fully uncovered, while at the same time applications may demand effects of nonlinearity on structural response...
Chouhan, Romita; Baraskar, Priyanka; Agrawal, Arpana; Gupta, Mukul; Sen, Pranay K.; Sen, Pratima
2017-07-01
We report annealing induced sign reversal of dispersive optical nonlinearity in ion beam sputtered NiO thin films deposited at 30% and 70% oxygen partial pressures. In the Ultraviolet-visible spectra of the samples, the transmission peak corresponding to d-d transitions is observed near 2 eV. A shift in this peak towards higher energy was observed when the same films were annealed at 523 K. The near resonant photoinduced transitions produced giant nonlinear optical susceptibilities of both third- and fifth- orders when the annealed film was irradiated by a continuous wave 632.8 nm He-Ne laser. The role of the thermo-optic effect has been examined critically. Experimental studies further reveal that the oxygen partial pressure influences the growth direction of the grains in the thin films. The well known Z-scan experimental procedure has been followed for measurements of optical nonlinearities in all the NiO films. The nonlinear refractive indices of both the as-deposited and annealed NiO thin films are defined in terms of the thermo-optic coefficients (d/nd T ) T =T0 and (d/2nd T2 ) T =T0 .
Zhao, Tongtong; Lou, Shuqin; Su, Wei; Wang, Xin
2016-01-01
We propose an As2Se3-based highly nonlinear photonic quasi-crystal fiber with dual zero-dispersion wavelengths (ZDWs). Using a full-vector finite element method, the proposed fiber is optimized to obtain high nonlinear coefficient, low confinement loss and two zero-dispersion points by optimizing the structure parameters. Numerical results demonstrate that the proposed photonic quasi-crystal fiber (PQF) has dual ZDWs and the nonlinear coefficient up to 2600 W-1 km-1 within the wavelength range from 2 to 5.5 μm. Due to the introduction of the large air holes in the third ring of the proposed fiber, the ability of confining the fundamental mode field can be improved effectively and thus the low confinement loss can be obtained. The proposed PQF with high nonlinearity and dual ZDWs will have a number of potential applications in four-wave mixing, super-continuum generation, and higher-order dispersion effects.
AN APPLICATION OF DOUBLE-SCALE METHOD TO THE STUDY OF NON-LINEAR DISSIPATIVE WAVES IN JEFFREYS MEDIA
Directory of Open Access Journals (Sweden)
Adelina Georgescu
2011-07-01
Full Text Available In previous papers we sketched out the general use of the doublescalemethod to nonlinear hyperbolic partial differential equations(PDEs in order to study the asymptotic waves and as an examplethe model governing the motion of a rheological medium (Maxwellmedium with one mechanical internal variable was studied. In thispaper the double scale method is applied to investigate non-linear dissipative waves in viscoanelastic media without memory of order one(Jeffreys media, that were studied by one of the authors (L. R. inmore classical way. For these media the equations of motion includesecond order derivative terms multiplied by a very small parameter. We give a physical interpretation of the new (fast variable, related to the surfaces across which the solutions or/and some of their derivatives vary steeply. The paper concludes with one-dimensional application containing original results.
Impact of third-order dispersion on nonlinear bifurcations in optical resonators
Energy Technology Data Exchange (ETDEWEB)
Leo, François [Service OPERA-photonique, Université libre de Bruxelles (ULB), 50 Avenue F.D. Roosevelt, CP 194/5, B-1050 Bruxelles (Belgium); Photonics Research Group, Department of Information Technology, Ghent University–IMEC, Ghent B-9000 (Belgium); Coen, Stéphane [Department of Physics, c, Private Bag, 92019, Auckland (New Zealand); Kockaert, Pascal; Emplit, Philippe; Haelterman, Marc [Service OPERA-photonique, Université libre de Bruxelles (ULB), 50 Avenue F.D. Roosevelt, CP 194/5, B-1050 Bruxelles (Belgium); Mussot, Arnaud [PhLAM, Université de Lille 1, Bât. P5-bis, UMR CNRS/USTL 8523, F-59655 Villeneuve d' Ascq (France); Taki, Majid, E-mail: abdelmajid.taki@univ-lille1.fr [PhLAM, Université de Lille 1, Bât. P5-bis, UMR CNRS/USTL 8523, F-59655 Villeneuve d' Ascq (France)
2015-09-18
It is analytically shown that symmetry breaking, in dissipative systems, affects the nature of the bifurcation at onset of instability resulting in transitions from super to subcritical bifurcations. In the case of a nonlinear fiber cavity, we have derived an amplitude equation to describe the nonlinear dynamics above threshold. An analytical expression of the critical transition curve is obtained and the predictions are in excellent agreement with the numerical solutions of the full dynamical model.
Institute of Scientific and Technical Information of China (English)
邓英尔; 刘慈群
2003-01-01
A mathematical model of two-phase fluid nonlinear flow in the direction ofnormal of ellipse through low-permeability porous media was established according to anonlinear flow law expressed in a continuous function with three parameters, a massconservation law and a concept of turbulent ellipses. A solution to the model was obtainedby using a finite difference method and an extrapolation method. Formulas of calculatingdevelopment index not only before but also after water breaks through an oil well in thecondition of two-phase fluid nonlinear flow in the media were derived. An example wasdiscussed. Water saturation distribution was presented. The moving law of drainage frontwas found. Laws of change of pressure difference with time were recognized. Results showthat there is much difference of water saturation distribution between nonlinear flow andlinear flow; that drainage front by water moves faster, water breaks through sooner and theindex gets worse because of the nonlinear flow ; and that dimensionless pressure differencegets larger at the same dimensionless time and difficulty of oil development becomes biggerby the nonlinear flow . Thus, it is necessary that influence of nonlinear flow on developmentindexes of the oil fields be taken into account. The results provide water-floodingdevelopment of the oil fields with scientific basis.
Yang, Haijian
2016-07-26
Fully implicit methods are drawing more attention in scientific and engineering applications due to the allowance of large time steps in extreme-scale simulations. When using a fully implicit method to solve two-phase flow problems in porous media, one major challenge is the solution of the resultant nonlinear system at each time step. To solve such nonlinear systems, traditional nonlinear iterative methods, such as the class of the Newton methods, often fail to achieve the desired convergent rate due to the high nonlinearity of the system and/or the violation of the boundedness requirement of the saturation. In the paper, we reformulate the two-phase model as a variational inequality that naturally ensures the physical feasibility of the saturation variable. The variational inequality is then solved by an active-set reduced-space method with a nonlinear elimination preconditioner to remove the high nonlinear components that often causes the failure of the nonlinear iteration for convergence. To validate the effectiveness of the proposed method, we compare it with the classical implicit pressure-explicit saturation method for two-phase flow problems with strong heterogeneity. The numerical results show that our nonlinear solver overcomes the often severe limits on the time step associated with existing methods, results in superior convergence performance, and achieves reduction in the total computing time by more than one order of magnitude.
Directory of Open Access Journals (Sweden)
M. Caputo
1998-06-01
Full Text Available Since the dispersion and attenuation properties of dielectric and anelastic media, in the frequency domain, are expressed by similar formulae, as shown experimentally by Cole and Cole (1941 and Bagley and Torvik (1983, 1986 respectively, we note that the same properties may be represented in the time domain by means of an equation of the same form; this is obtained by introducing derivatives of fractional order into the system functions of the media. The Laplace Transforms (LT of such system functions contain fractional powers of the imaginary frequency and are, therefore, multivalued functions defined in the Riemann Sheets (RS of the function. We determine the response of the medium (dielectric o anelastic to a generic signal summing the time domain representation due to the branches of the solutions in the RSs of the LT. It is found that, if the initial conditions are equal in all the RSs, the solution is a sum of two exponentials with complex exponents, if the initial conditions are different in some of the RSs, then a transient for each of those RSs is added to the exponentials. In all cases a monochromatic wave is split into a set of waves with the same frequency and slightly different wavelengths which interfere and disperse. As a consequence a monochromatic electromagnetic wave with frequency around 1 MHz in water has a relevant dispersion and beats generating a tunnel effect. In the atmosphere of the Earth the dispersion of a monochromatic wave with frequency around 1 GHz, like those used in tracking artificial satellites, has a negligible effect on the accuracy of the determination of the position of the satellites and the positioning of the bench marks on the Earth. We also find the split eigenfunctions of the free modes of infinite plates and shells made of dielectric and anelastic media.
Frictionless dispersive hydrodynamics of Stokes flows
Maiden, Michelle D; Anderson, Dalton V; Schubert, Marika E; Hoefer, Mark A
2016-01-01
Effectively frictionless, dispersive flow characterizes superfluids, nonlinear optical diffraction, and geophysical fluid interfaces. Dispersive shock waves (DSWs) and solitons are fundamental nonlinear excitations in these media, but DSW studies to date have been severely constrained by a loss of coherence. Here we report on a novel dispersive hydrodynamics testbed: the effectively frictionless flow of interfacial waves between two high contrast, low Reynolds' number Stokes fluids. This system enables high fidelity observations of large amplitude DSWs, found to agree quantitatively with a nonlinear wave averaging theory. We then report on observations of highly coherent phenomena including DSW backflow, the refraction or absorption of solitons by DSWs, and multi-phase DSW-DSW merger. The complex, coherent, nonlinear mixing of DSWs and solitons observed here are universal features of dissipationless, dispersive hydrodynamic flows.
Francés, Jorge; Bleda, Sergio; Bej, Subhajit; Tervo, Jani; Navarro-Fuster, Víctor; Fenoll, Sandra; Martínez-Gaurdiola, Francisco J.; Neipp, Cristian
2016-04-01
In this work the split-field finite-difference time-domain method (SF-FDTD) has been extended for the analysis of two-dimensionally periodic structures with third-order nonlinear media. The accuracy of the method is verified by comparisons with the nonlinear Fourier Modal Method (FMM). Once the formalism has been validated, examples of one- and two-dimensional nonlinear gratings are analysed. Regarding the 2D case, the shifting in resonant waveguides is corroborated. Here, not only the scalar Kerr effect is considered, the tensorial nature of the third-order nonlinear susceptibility is also included. The consideration of nonlinear materials in this kind of devices permits to design tunable devices such as variable band filters. However, the third-order nonlinear susceptibility is usually small and high intensities are needed in order to trigger the nonlinear effect. Here, a one-dimensional CBG is analysed in both linear and nonlinear regime and the shifting of the resonance peaks in both TE and TM are achieved numerically. The application of a numerical method based on the finite- difference time-domain method permits to analyse this issue from the time domain, thus bistability curves are also computed by means of the numerical method. These curves show how the nonlinear effect modifies the properties of the structure as a function of variable input pump field. When taking the nonlinear behaviour into account, the estimation of the electric field components becomes more challenging. In this paper, we present a set of acceleration strategies based on parallel software and hardware solutions.
Grimsmo, Arne L.; Parkins, Scott
2014-03-01
We consider a generalized version of the Rabi model that includes a nonlinear, dispersive-type atom-field interaction in addition to the usual linear dipole coupling, as well as cavity dissipation. An effective system of this sort arises, for example, in a quantum simulation of the Rabi model based upon Raman transitions in an optical cavity QED setting [A. L. Grimsmo and S. Parkins, Phys. Rev. A 87, 033814 (2013), 10.1103/PhysRevA.87.033814]. For a range of the nonlinear interaction strength about a special value, degeneracies or near degeneracies of the states in the cavity-mode vacuum and single-photon subspaces, in combination with cavity loss, gives rise to an essentially closed cycle of excitations and photon emissions within these subspaces. Consequently, the cavity output field is strongly antibunched, while over this range of nonlinear strengths the atomic population undergoes an abrupt inversion. We develop a quantum-trajectory-based description of the system that models its key properties very well, and use a simple dressed-state picture to explain the novel structure of the cavity fluorescence spectrum. We also present numerical results for a potential realization of the system using a rubidium atom coupled strongly to a high-finesse optical cavity mode.
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).
Dispersion and nonlinearity tolerance of modulation formats for 160 Gb/s systems
DEFF Research Database (Denmark)
Zhenbo, Xu; Peucheret, Christophe; Siahlo, Andrei
2004-01-01
We compare the RZ-DQPSK modulation format in 160 Gb/s single channel systems with RZ, CSRZ, RZ-DPSK and CSRZ-DPSK for the first time. We find that RZ-DQPSK offers nearly three time better dispersion tolerance than CSRZ-DPSK.......We compare the RZ-DQPSK modulation format in 160 Gb/s single channel systems with RZ, CSRZ, RZ-DPSK and CSRZ-DPSK for the first time. We find that RZ-DQPSK offers nearly three time better dispersion tolerance than CSRZ-DPSK....
Nonlinear wavelength conversion in photonic crystal fibers with three zero dispersion points
Stark, S P; Podlipensky, A; Russell, P St J
2010-01-01
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
DEFF Research Database (Denmark)
Zibar, Darko; Winther, Ole; Franceschi, Niccolo
2012-01-01
In this paper, we show numerically and experimentally that expectation maximization (EM) algorithm is a powerful tool in combating system impairments such as fibre nonlinearities, inphase and quadrature (I/Q) modulator imperfections and laser linewidth. The EM algorithm is an iterative algorithm...
Dispersion of nonresonant third-order nonlinearities in GeSiSn ternary alloys
de Leonardis, Francesco; Troia, Benedetto; Soref, Richard A.; Passaro, Vittorio M. N.
2016-09-01
Silicon (Si), tin (Sn), and germanium (Ge) alloys have attracted research attention as direct band gap semiconductors with applications in electronics and optoelectronics. In particular, GeSn field effect transistors can exhibit very high performance in terms of power reduction and operating speed because of the high electron drift mobility, while the SiGeSn system can be constructed using CMOS-compatible techniques to realize lasers, LED, and photodetectors. The wide Si, Ge and Sn transparencies allow the use of binary and ternary alloys extended to mid-IR wavelengths, where nonlinearities can also be employed. However, neither theoretical or experimental predictions of nonlinear features in SiGeSn alloys are reported in the literature. For the first time, a rigorous and detailed physical investigation is presented to estimate the two photon absorption (TPA) coefficient and the Kerr refractive index for the SiGeSn alloy up to 12 μm. The TPA spectrum, the effective TPA wavelength cut-off, and the Kerr nonlinear refractive index have been determined as a function of alloy compositions. The promising results achieved can pave the way to the demonstration of on-chip nonlinear-based applications, including mid-IR spectrometer-on-a-chip, all-optical wavelength down/up-conversion, frequency comb generation, quantum-correlated photon-pair source generation and supercontinuum source creation, as well as Raman lasing.
DEFF Research Database (Denmark)
Lillieholm, Mads; Galili, Michael; Oxenløwe, Leif Katsuo
2016-01-01
We present a segmented composite HNLF optimised for mitigation of dispersion-fluctuation impairments for broadband pulsed four-wave mixing. The HNLF-segmentation allows for pulsed FWMprocessing of a 13-nm wide input WDM-signal with -4.6-dB conversion efficiency...
Robust Multiscale Iterative Solvers for Nonlinear Flows in Highly Heterogeneous Media
Efendiev, Y.
2012-08-01
In this paper, we study robust iterative solvers for finite element systems resulting in approximation of steady-state Richards\\' equation in porous media with highly heterogeneous conductivity fields. It is known that in such cases the contrast, ratio between the highest and lowest values of the conductivity, can adversely affect the performance of the preconditioners and, consequently, a design of robust preconditioners is important for many practical applications. The proposed iterative solvers consist of two kinds of iterations, outer and inner iterations. Outer iterations are designed to handle nonlinearities by linearizing the equation around the previous solution state. As a result of the linearization, a large-scale linear system needs to be solved. This linear system is solved iteratively (called inner iterations), and since it can have large variations in the coefficients, a robust preconditioner is needed. First, we show that under some assumptions the number of outer iterations is independent of the contrast. Second, based on the recently developed iterative methods, we construct a class of preconditioners that yields convergence rate that is independent of the contrast. Thus, the proposed iterative solvers are optimal with respect to the large variation in the physical parameters. Since the same preconditioner can be reused in every outer iteration, this provides an additional computational savings in the overall solution process. Numerical tests are presented to confirm the theoretical results. © 2012 Global-Science Press.
Ye, S.; Sleep, B. E.
2012-12-01
The effects of biofilm growth on the flow and transport in porous media were investigated in an anaerobic two-dimensional coarse sand-filled cell. The cell was inoculated with a mixed microbial culture fed methanol. Biomass concentrations attached to the sand and suspended in the water in the cell were determined by protein analysis. The biofilm thickness on individual sand grains was investigated with confocal laser scanning microscopy (CLSM). The biofilm thickness for individual sand grains had a range of mean values from 59 to 316 microns in this study. To investigate the implications of the variability of biofilm thicknesses, four models were used to calculate reductions in porous media permeability as a function of biofilm thickness. Taylor's model (Taylor et al., 1990) predicted a reduction by a factor ranging from 14 to 5000 from minimum to maximum mean biofilm thickness. Vandevivere's Model (Vandevivere et al.,1995) predicted a reduction in permeability by a factor ranging from 769 to 3846 from minimum to maximum mean biofilm thickness. Seki's model (Seki and Miyazaki, 2001) could not be applied in this study. Clement's model (Clement et al., 1996) predicted a reduction ranging from 1 to 1.14 over the range of biomass levels observed in the cell. To investigate the implications of the variability of biofilm thicknesses for dispersivity, Taylor and Jaffe's models (1990) were used to calculate increase in porous media dispersivity as a function of biofilm thickness. The model predicted an increase in dispersivity by a factor ranging from 20 to 1883 by a simplified dispersivity model and a factor ranging from 4 to 85 by a dispersivity model based on a cut-and-random-rejoin type model of pore geometry from minimum to maximum mean biofilm thickness. Acknowledgements Funding for this research from US Dupont Company, and also from NSFC40872155, 40725010 and 41030746 is gratefully acknowledged. References: Clement, T.P., Hooker, B.S. and Skeen, R.S., 1996
Surface Modification of Alumina Nanoparticles: A Dispersion Study in Organic Media.
Soleimani, Esmaiel; Zamani, Narges
2017-09-01
The alumina nanoparticles (NPs) have been synthesized from reaction between alum with ammonia and then calcined the precipitate at 1200 °C for 4 h. Its surface was modified by oleic acid (OA) and trimethoxyvinylsilane (TMVS) in o-xylene at 50 °C. The alumina NPs and its modified were characterized by XRD, FT-IR, SEM, EDX and TGA. The TGA analysis indicated that the grafting amount of OA and TMVS were 10.5 and 8.0% respectively. The dispersion of modified NPs was determined in monomers such as methyl methacrylate (MMA), butyl acrylate (BuA) and styrene (St) and in solvents such as ethanol, hexane and acetone. The experimental results showed that the highest dispersion was happened NPs modified by oleic acid in n-hexane, while the highest dispersion was observed NPs modified by TMVS in acetone. The results indicate that NPs modified by oleic acid formed a stable dispersion in MMA and BuA. The highest amount of dispersion happened NPs modified by oleic acid in MMA and BuA in initial weight of 5 and 2.5% respectively, while stable dispersion is formed in styrene when TMVS is used as modifier. The highest amount of dispersion was happened NPs modified by TMVS in styrene in initial weight of 2.5%.
Westergaard, Philip G; Tieri, David; Matin, Rastin; Cooper, John; Holland, Murray; Ye, Jun; Thomsen, Jan W
2014-01-01
As an alternative to state-of-the-art laser frequency stabilisation using ultra-stable cavities, it has been proposed to exploit the non-linear effects from coupling of atoms with a narrow atomic transition to an optical cavity. Here we have constructed such a system and observed non-linear phase shifts of a narrow optical line by 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 multi-photon scattering events (Dopplerons) that affect the cavity transmission significantly while leaving the phase signature relatively unaffected. By varying the number of atoms and the intra-cavity power we systematically study this non-linear phase signature which displays roughly the same features as for much lower temperature samples. This demonstration in a relatively simple sys...
Dispersing multi-component and unstable powders in aqueous media using comb-type anionic polymers
DEFF Research Database (Denmark)
Laarz, E.; Kauppi, A.; Andersson, K.M.
2006-01-01
of the grafted ethylene oxide side chains showed that the dispersants adsorb onto a MgO surface and infer a repulsion where the range scales with the length of the poly ethylene oxide side chains. The compressibility and the consolidation behavior of MgO particle networks in response to a centrifugal force field...... dispersants also in multi-component powder mixtures with a complex solution and surface chemistry and result in more robust suspensions at significantly higher solids loading compared with e.g., a traditional cationic polyelectrolyte. Direct force measurements on comb-type dispersants with different lengths...
Robertson, Scott; Leonhardt, Ulf
2014-11-01
Hawking radiation has become experimentally testable thanks to the many analog systems which mimic the effects of the event horizon on wave propagation. These systems are typically dominated by dispersion and give rise to a numerically soluble and stable ordinary differential equation only if the rest-frame dispersion relation Ω^{2}(k) is a polynomial of relatively low degree. Here we present a new method for the calculation of wave scattering in a one-dimensional medium of arbitrary dispersion. It views the wave equation as an integral equation in Fourier space, which can be solved using standard and efficient numerical techniques.
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.
Energy Technology Data Exchange (ETDEWEB)
Horst, Allison M., E-mail: ahorst@umail.ucsb.edu [University of California at Santa Barbara, Bren School of Environmental Science and Management (United States); Ji, Zhaoxia [UC Center for the Environmental Implications of Nanotechnology (UC CEIN) (United States); Holden, Patricia A. [University of California at Santa Barbara, Bren School of Environmental Science and Management (United States)
2012-08-15
Nanoparticle exposure in toxicity studies requires that nanoparticles are bioavailable by remaining highly dispersed in culture media. However, reported dispersion approaches are variable, mostly study-specific, and not transferable owing to their empirical basis. Furthermore, many published approaches employ proteinaceous dispersants in rich laboratory media, both of which represent end members in environmental scenarios. Here, a systematic approach was developed to disperse initially agglomerated TiO{sub 2} nanoparticles (Aeroxide Registered-Sign TiO{sub 2} P25, Evonik, NJ; primary particle size range 6.4-73.8 nm) in oligotrophic culture medium for environmentally relevant bacterial toxicity studies. Based on understanding particle-particle interactions in aqueous media and maintaining environmental relevance, the approach involves (1) quantifying the relationship between pH and zeta potential to determine the point of zero charge of select nanoparticles in water; (2) nominating, then testing and selecting, environmentally relevant stabilizing agents; and (3) dispersing via 'condition and capture' whereby stock dry powder nanoparticles are sonicated in pre-conditioned (with base, or acid, plus stabilizing agent) water, then diluted into culture media. The 'condition and capture' principle is transferable to other nanoparticle and media chemistries: simultaneously, mechanically and electrostatically, nanoparticles can be dispersed with surrounding stabilizers that coat and sterically hinder reagglomeration in the culture medium.
Magnetic resonance imaging measurements evidence weak dispersion in homogeneous porous media
Lehoux, A. P.; Rodts, S.; Faure, P.; Michel, E.; Courtier-Murias, D.; Coussot, P.
2016-11-01
We measure the dispersion coefficient through homogeneous bead or sand packings at different flow rates from direct magnetic resonance imaging (MRI) visualizations of the transport characteristics of a pulse of paramagnetic nanoparticles. Through two-dimensional imaging we observe homogeneous dispersion inside the sample, but we show that entrance effects may induce significant radial heterogeneities, which would affect the interpretation of the breakthrough curve. Another MRI approach then provides quantitative measurements of the evolution in time of the longitudinal particle distribution in the sample. These data can be analyzed to deduce the coefficient of dispersion independently of entrance effects. The values obtained for this "effective" dispersion coefficient are almost ten times lower than the commonly accepted values.
Directory of Open Access Journals (Sweden)
Hidehiro Kamiya and Motoyuki Iijima
2010-01-01
Full Text Available 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.
Energy Technology Data Exchange (ETDEWEB)
Kamiya, Hidehiro; Iijima, Motoyuki, E-mail: kamiya@cc.tuat.ac.j [Institute of Engineering, Tokyo University of Agriculture and Technology, Koganei, Tokyo 184-8588 (Japan)
2010-08-15
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. (topical review)
Kamiya, Hidehiro; Iijima, Motoyuki
2010-01-01
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...
Configuring Web-based Media for Communication in Dispersed Project Groups
DEFF Research Database (Denmark)
Scheepers, Rens; Nicolajsen, Hanne Westh
2006-01-01
the communicated. We explain these findings by proposing a “triad” of three interrelated concepts arising from both media richness theory and genre theory: content, medium and genre. We argue that substantive use (and acceptance of the medium and content) occurs when there is a “fit” between genre, medium...... meetings, telephone) are not always viable options. Instead, computer-based communication media such as email, project intranets and extranets become surrogate conduits for day-to-day project communication and exchange of project-related content. We examined the effect of different media configurations...... provision was decentralized and access to content restricted to specific sub-groups. Content providers resorted to superficial use of “openly configured” Web-based media or used email if unsure who could access content, or if they suspected that recipients might lack the background to understand...
Zlenko, A. S.; Akhmetshin, U. G.; Bogatyrjov, V. A.; Bulatov, L. I.; Dvoyrin, V. V.; Firstov, S. V.; Dianov, E. M.
2009-10-01
A germanium-doped silica-core fiber with an active region in the form of a thin ring of silica doped with bismuth ions was fabricated. Bismuth doping in the ring surrounding the core allows to stabilize bismuth in silica glass, and it does not impose any restrictions on the composition of the core. The bismuth concentration in the ring is less than 0.2 wt.%. The GeO2 concentration in the core is more than 15 mol.%. A high germanium concentration in the core allows to shift the zero dispersion wavelength to 1860 nm and to obtain a high nonlinear refractive index (n2 more than 3,2*10-20 m2/W). Spectroscopic investigations were carried out in the visible and near infrared (800-1700 nm) spectral range. Despite the small concentration of bismuth, we observed the absorption and luminescence characteristic bands, confirming the presence of bismuth active centers in silica glass. Upon pumping at 1350 nm the on/off gain spectrum was measured on a 20-m fiber. The gain was observed throughout investigated range of 1430-1530 nm. The maximal gain of ~9.5 dB was obtained near 1430 nm. The results of the spectroscopic investigations of the fiber with a thin active Bi-doped ring showed prospects of the creation and application of such fiber type for laser and nonlinear optics.
Institute of Scientific and Technical Information of China (English)
Zhong Xian-Qiong; Cheng Ke; Xiang An-Ping
2013-01-01
On the basis of the standard linear stability analysis and Drude electromagnetic model,the impacts of higher-order dispersions and three kinds of typical saturable nonlinearities on modulation instability (MI) have been analyzed and calculated for negative-refractive metamaterials (MMs).Our results show that the MI gain spectra consist of only one spectral region instead of one or two regions in ordinary materials,which may be close to or far from the zero point.Particularly,the spectrum far from the zero point has a high cut-off frequency but a narrow spectral width,which is obviously beneficial to the generation of high-repetition-rate pulse trains.Moreover,MI characteristics here will vary with the normalized angular frequency which can be modified by adjusting the structures of negative-refractive MMs,signifying the controllability of bistable solitons and MI based applications.The effects of saturable nonlinearities are similar to those in ordinary materials.
Directory of Open Access Journals (Sweden)
2008-11-01
Full Text Available A novel poly(urethane-imide (PUI containing dispersed red chromophore was synthesized. The PUI was characterized by FT-IR, UV-Vis, DSC and TGA. The results of DSC and TGA indicated that the PUI exhibited high thermal stability up to its glass-transition temperature (Tg of 196°C and 5% heat weight loss temperature of 229°C. According to UV-Vis spectrum and working curve, the maximum molar absorption coefficient and absorption wavelength were measured. They were used to calculate the third-order nonlinear optical coefficient χ(3. At the same time, the chromophore density of PUI, nonlinear refractive index coefficient and molecular hyperpolarizability of PUI were obtained. The fluorescence spectra of PUI and model compound DR-19 were determined at excitation wavelength 300 nm. The electron donor and acceptor in polymer formed the exciplex through the transfer of the electric charges. The results show that the poly(urethane-imide is a promising candidate for application in optical devices.
Effective Block-Scale Dispersion and Its Self-Averaging Behavior in Heterogeneous Porous Media
de Barros, Felipe; Dentz, Marco
2015-04-01
Upscaled (effective) dispersion coefficients in spatially heterogeneous flow fields must (1) account for the sub-scale variability that is filtered out by homogenization and (2) be modeled as a random function to incorporate the uncertainty associated with non-ergodic solute bodies. In this study, we use the framework developed in de Barros and Rubin (2011) [de Barros F.P.J. and Rubin Y., Modelling of block-scale macrodispersion as a random function. Journal of Fluid Mechanics 676 (2011): 514-545] to develop novel semi-analytical expressions for the first two statistical moments of the block-effective dispersion coefficients in three-dimensional spatially random flow fields as a function of the key characteristic length scales defining the transport problem. The derived expressions are based on perturbation theory and limited to weak-to-mild heterogeneity and uniform-in-the-mean steady state flow fields. The semi-analytical solutions provide physical insights of the main controlling factors influencing the temporal scaling of the dispersion coefficient of the solute body and its self-averaging dispersion behavior. Our results illustrate the relevance of the joint influence of the block-scale and local-scale dispersion in diminishing the macrodispersion variance under non-ergodic conditions. The impact of the statistical anisotropy ratio in the block-effective macrodispersion self-averaging behavior is also investigated. The analysis performed in this work has implications in numerical modeling and grid design.
Characterizing dispersivity and stagnation in porous media using NMR flow propagators
Singer, P. M.; Mitchell, J.; Fordham, E. J.
2016-09-01
Low-field nuclear magnetic resonance (NMR) displacement probability distributions (flow propagators) are presented for water flowing through heterogeneous porous materials. Four sedimentary rocks have been chosen as example systems: Dolostone, Bentheimer sandstone, Berea sandstone, and Indiana limestone (in order of decreasing permeability). The fluid displacement is characterized by pre-asymptotic Stokes' flow and so the probability distributions are bimodal, with peaks corresponding to stagnant fluid in dead-end pores and flowing fluid in the connected porosity. Cut-off Gaussian functions are used to fit the flowing and stagnant peaks independently. An effective dispersivity length scale Lv (also known as the mixing length scale) is estimated by fitting the portion of the probability distribution corresponding to the flowing fluid. For the relatively homogeneous Bentheimer sandstone, the ratio of effective dispersivity length scale to effective transport diameter dt is Lv /dt ≈ 16 , which is an order of magnitude larger than for randomly packed glass beads where Lv /dt ≈ 1.8 . We compare these dispersivity parameters to similar values extracted from a cumulant analysis of the entire propagator. Fitting a cut-off Gaussian avoids the usual complications of analyzing dispersion in the presence of the ubiquitous stagnant fluid, and results in a clear demonstration of the influence of long-range heterogeneities on the dispersivity for flow in real sedimentary rocks.
Characterizing dispersivity and stagnation in porous media using NMR flow propagators.
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.
Soliton clusters in three-dimensional media with competing cubic and quintic nonlinearities
Energy Technology Data Exchange (ETDEWEB)
Mihalache, D [Department of Theoretical Physics, Institute of Atomic Physics, PO Box MG-6, Bucharest (Romania); Mazilu, D [Department of Theoretical Physics, Institute of Atomic Physics, PO Box MG-6, Bucharest (Romania); Crasovan, L-C [ICFO-Institut de Ciencies Fotoniques and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, ES 8034 Barcelona (Spain); Malomed, B A [Department of Interdisciplinary Studies, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel); Lederer, F [Institute of Solid State Theory and Theoretical Optics, Friedrich-Schiller-Universitaet Jena, Max-Wien-Platz 1, D-07743, Jena (Germany); Torner, L [ICFO-Institut de Ciencies Fotoniques and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, ES 8034 Barcelona (Spain)
2004-05-01
We introduce a class of robust soliton clusters composed of N fundamental solitons in three-dimensional media combining the self-focusing cubic and self-defocusing quintic nonlinearities. The angular momentum is lent to the initial cluster through staircase or continuous ramp-like phase distribution. Formation of these clusters is predicted analytically, by calculating an effective interaction Hamiltonian H{sub int}. If a minimum of H{sub int} is found, direct three-dimensional simulations demonstrate that, when the initial pattern is close to the predicted equilibrium size, a very robust rotating cluster does indeed exist, featuring persistent oscillations around the equilibrium configuration (clusters composed of N = 4,5, and 6 fundamental solitons are investigated in detail). If a strong random noise is added to the initial configuration, the cluster eventually develops instability, either splitting into several fundamental solitons or fusing into a nearly axisymmetric vortex torus. These outcomes match the stability or instability of the three-dimensional vortex solitons with the same energy and spin; in particular, the number of the fragments in the case of the break-up is different from the number of solitons in the original cluster, being instead determined by the dominant mode of the azimuthal instability of the corresponding vortex soliton. The initial form of the phase distribution is important too: under the action of the noise, the cluster with the built-in staircase-like phase profile features azimuthal instability, while the one with the continuous distribution fuses into a vortex torus.
Configuring Web-based Media for Communication in Dispersed Project Groups
DEFF Research Database (Denmark)
Scheepers, Rens; Nicolajsen, Hanne Westh
2006-01-01
meetings, telephone) are not always viable options. Instead, computer-based communication media such as email, project intranets and extranets become surrogate conduits for day-to-day project communication and exchange of project-related content. We examined the effect of different media configurations...... on the nature of content created by the project groups. We found that configuration decisions, notably the responsibility for content provision and who had access to content, influenced medium choice and the nature of communication taking place via the medium. More substantive content resulted when content...... provision was decentralized and access to content restricted to specific sub-groups. Content providers resorted to superficial use of "openly configured" Web-based media or used email if unsure who could access content, or if they suspected that recipients might lack the background to understand...
Dispersing multi-component and unstable powders in aqueous media using comb-type anionic polymers
DEFF Research Database (Denmark)
Laarz, E.; Kauppi, A.; Andersson, K.M.
2006-01-01
of the grafted ethylene oxide side chains showed that the dispersants adsorb onto a MgO surface and infer a repulsion where the range scales with the length of the poly ethylene oxide side chains. The compressibility and the consolidation behavior of MgO particle networks in response to a centrifugal force field......We have investigated the effect of polymeric dispersants on the rheological properties and consolidation behavior of concentrated cemented carbide (WC-Co) and magnesia (MgO) suspensions. The relatively novel types of comb-type anionic polymers with grafted non-ionic side chains are effective...
Gorokhovskii, A. V.; Gorshkov, N. V.; Burmistrov, I. N.; Goffman, V. G.; Tret'yachenko, E. V.; Sevryugin, A. V.; Fedorov, F. S.; Kovyneva, N. N.
2016-06-01
The electrical properties of dispersions of a powdered ferroelectric nanocomposite based on ilmenite (FeTiO3) and hollandite (K1.46Ti7.2Fe0.8O16) in dioctyl phthalate have been studied by impedance spectroscopy techniques in a frequency range of 10-1-106 Hz. The influence of stabilizing additives of cationic and anionic surfactants and iron acetylacetonate on the permittivity, conductivity, and dielectric losses was determined for dispersions containing 40 mass % of the solid composite. The influence of composition on the mechanisms of relaxation processes in the system is discussed.
Robertson, Scott
2014-11-01
Analog gravity experiments make feasible the realization of black hole space-times in a laboratory setting and the observational verification of Hawking radiation. Since such analog systems are typically dominated by dispersion, efficient techniques for calculating the predicted Hawking spectrum in the presence of strong dispersion are required. In the preceding paper, an integral method in Fourier space is proposed for stationary 1+1-dimensional backgrounds which are asymptotically symmetric. Here, this method is generalized to backgrounds which are different in the asymptotic regions to the left and right of the scattering region.
DEFF Research Database (Denmark)
Muniruzzaman, Muhammad; Rolle, Massimo
Electrochemical cross-coupling plays a significant role for transport of charged species in porous media [1, 2]. In this study we performed flow-through experiments in a quasi two-dimensional setup using dilute solutions of strong electrolytes to study the influence of charge interactions on mass...... transfer of ionic species in saturated porous media. The experiments were carried out under advection-dominated conditions (seepage velocity: 1 and 1.5 m/day) in two well-defined heterogeneous domains where flow diverging around a low-permeability inclusion and flow focusing in high-permeability zones...
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) Geophysical Journal International ?? 2011 RAS.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
By making use of the generalized sine-Gordon equation expansion method, we find cnoidal periodic wave solutions and fundamental bright and dark optical solitarywave solutions for the fourth-order dispersive and the quintic nonlinear Schrodinger equation with self-steepening, and self-frequency shift. Moreover, we discuss the formation conditions of the bright and dark solitary waves.
High-concentration-gradient dispersion in porous media : experiments, analysis and approximations
R.J. Schotting; H. Moser; S.M. Hassanizadeh
1997-01-01
textabstractVarious experimental and theoretical studies have shown that Fick's law, based on the assumption of a linear relation between solute dispersive mass flux and concentration gradient, is not valid when high concentration gradients are encountered in a porous medium. The value of the macrod
Arshad, M.; Seadawy, Aly R.; Lu, Dianchen
2017-08-01
The higher-order nonlinear Schrödinger equation (NLSE) with fourth-order dispersion, cubic-quintic terms, self-steepening and nonlinear dispersive terms describes the propagation of extremely short pulses in optical fibers. In this paper, the elliptic function, bright and dark solitons and solitary wave solutions of higher-order NLSE are constructed by employing a modified extended direct algebraic method, which has important applications in applied mathematics and physics. Furthermore, we also present the formation conditions of the bright and dark solitons for this equation. The modulation instability is utilized to discuss the stability of these solutions, which shows that all solutions are exact and stable. Many other higher-order nonlinear evolution equations arising in applied sciences can also be solved by this powerful, effective and reliable method.
On the Role of Osmosis for Non-Linear Shock Waves f Pressure and Solute in Porous Media
Kanivesky, Roman; Salusti, Ettore; Caserta, Arrigo
2013-04-01
A novel non-Osanger model focusing on non-linear mechanic and chemo-poroelastic coupling of fluids and solute in porous rocks is developed based on the modern wave theory. Analyzing in 1-D a system of two adjacent rocks with different conditions we obtain two coupled non-linear equations for fluid pressure and solute (salt or pollutants) concentration, evolving under the action of strong stress from one "source" rock towards the other rock. Their solutions allow to identify quick non-linear solitary (Burgers) waves of coupled fluid pressure and solute density, that are different from diffusive or perturbative solutions found in other analyses. The strong transient waves for low permeability porous media, such as clay and shale, are analyzed in detail. For medium and high-permeability porous media (sandstones) this model is also tentatively applied. Indeed in recent works of Alexander (1990) and Hart(2009) is supported the presence of small osmotic phenomena in other rocks where osmosis was previously ignored. An attempt to apply our model to soils in Calabria (Italy), such as clastic marine and fluvial deposits as well as discontinuous remnants of Miocene and Pliocene carbonate and terrigeneous deposits, is also discussed.
Long wave-short wave resonance in nonlinear negative refractive index media.
Chowdhury, Aref; Tataronis, John A
2008-04-18
We show that long wave-short wave resonance can be achieved in a second-order nonlinear negative refractive index medium when the short wave lies on the negative index branch. With the medium exhibiting a second-order nonlinear susceptibility, a number of nonlinear phenomena such as solitary waves, paired solitons, and periodic wave trains are possible or enhanced through the cascaded second-order effect. Potential applications include the generation of terahertz waves from optical pulses.
Neutrino dispersion through hot and dense media in minimally extended standard model
Mughal, M A
1998-01-01
Corrections to neutrino transitions. Some of the implications of these results to the solar neutrino problem supernovae and early universe are discussed and compared with earlier works. We also study the issue of lepton flavour violating Z sup 0 decays in minimal supersymmetric standard model. This result in the vacuum serves as an input in the framework of the FTD theory yielding further results of interest to astrophysics and cosmology. We have explicitly demonstrated that in this model, present limits from low energy processes can in principle accommodate these decays to values near the experimental bounds. The phenomenon of neutrino dispersion traversing and interacting with fields (matter and electromagnetic) in a medium has been under intense study for several years as neutrino dispersion in the framework of minimal standard model. Such a study is known to yield matter and magnetic field induced neutrino oscillations. For its applicability to and interest in solar neutrino problem, cosmology and other i...
Directory of Open Access Journals (Sweden)
Kim C.K.
2015-06-01
Full Text Available In this study, nickel nanoparticles were synthesized in ethanol using portable pulsed wire evaporation, which is a one-step physical method. From transmission electron microscopy images, it was found that the Ni nanoparticles exhibited a spherical shape with an average diameter of 7.3 nm. To prevent aggregation of the nickel nanoparticles, a polymer surfactant was added into the ethanol before the synthesis of nickel nanoparticles, and adsorbed on the freshly synthesized nickel nanoparticles during the wire explosion. The dispersion stability of the prepared nickel nanofluids was investigated by zeta-potential analyzer and Turbiscan optical analyzer. As a result, the optimum concentration of polymer surfactant to be added was suggested for the maximized dispersion stability of the nickel nanofluids.
Institute of Scientific and Technical Information of China (English)
Xia Ji; Wei Cai; Pingwen Zhang
2008-01-01
In this paper, we analyze the transmission and reflection properties of a high order discontinuous Galerkin method for dispersive Maxwell's equations, originally proposed by Lu et al. [J. Comput. Phys. 200 (2004), pp. 549-580]. We study the reflection and transmission properties of the numerical method for up to second-order polynomial elements for one-and two-dimensional Maxwell's equations with rectangular meshes. High order accuracy has been shown for reflection and transmission coefficients near material interfaces.
Scheven, U. M.
2013-12-01
This paper describes a new variant of established stimulated echo pulse sequences, and an analytical method for determining diffusion or dispersion coefficients for Gaussian or non-Gaussian displacement distributions. The unipolar displacement encoding PFGSTE sequence uses trapezoidal gradient pulses of equal amplitude g and equal ramp rates throughout while sampling positive and negative halves of q-space. Usefully, the equal gradient amplitudes and gradient ramp rates help to reduce the impact of experimental artefacts caused by residual amplifier transients, eddy currents, or ferromagnetic hysteresis in components of the NMR magnet. The pulse sequence was validated with measurements of diffusion in water and of dispersion in flow through a packing of spheres. The analytical method introduced here permits the robust determination of the variance of non-Gaussian, dispersive displacement distributions. The noise sensitivity of the analytical method is shown to be negligible, using a demonstration experiment with a non-Gaussian longitudinal displacement distribution, measured on flow through a packing of mono-sized spheres.
Simos, Theodore E.; Kovalnogov, Vladislav N.; Shevchuk, Igor V.
2017-07-01
The perspective of mathematical modeling and research of formation of disperse phase clusters of working media for next-generation technologies of production and transformation of energy on organic and synthetic hydrocarbon fuel is presented. Approach to creation of a problem-oriented complex of the theory, the models, knowledge bases as well as software-and-informational tools providing in total an opportunity for high-precision simulation, working off and prototyping in a computing experiment of the perspective technologies based on optimization and targeted formation of disperse phase clusters of a working media is considered.
Analytical expressions for Z-scan with arbitrary phase change in thin nonlocal nonlinear media.
Ortega, A Balbuena; Carrasco, M L Arroyo; Otero, M M Méndez; Lara, E Reynoso; Ramírez, E V García; Castillo, M D Iturbe
2014-11-17
Analytical expressions for the normalized transmittance of a thin material with simultaneous nonlocal nonlinear change in refraction and absorption are reported. Gaussian decomposition method was used to obtain the formulas that are adequate for any magnitude of the nonlinear changes. Particular cases of no locality are compared with the local case. Experimental results are reproduced (fitted) with the founded expressions.
Loures, Cristian Redondo; Biancalana, Fabio
2014-01-01
We study the influence of third-harmonic generation (THG) and negative frequency polarization terms in the self-phase modulation (SPM) of short and intense pulses in Kerr media. We find that THG induces additional symmetric lobes in the SPM process. The amplitude of these new sidebands are greatly enhanced by the contributions of the negative frequency Kerr (NFK) term and the shock operator. We compare our theoretical predictions based on the analytical nonlinear phase with simulations carried out by using the full unidirectional pulse propagation equation (UPPE).
Institute of Scientific and Technical Information of China (English)
Yirang YUAN
2006-01-01
For nonlinear coupled system of multilayer dynamics of fluids in porous media, the second order and first order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward, and two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates, are adopted. Optimal order estimates in L2 norm are derived to determine the error in the second order approximate solution.This method has already been applied to the numerical simulation of migration-accumulation of oil resources.
Propagation of time-truncated Airy-type pulses in media with quadratic and cubic dispersion
Hernández, José Angel Borda; Shaarawi, Amr; Besieris, Ioannis M
2015-01-01
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, based on the superposition of exponentially truncated Airy pulses, is very effective, allowing 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.
Directory of Open Access Journals (Sweden)
Paul C. Rivera
2006-01-01
Full Text Available A common approach in modeling the generation and propagation of tsunami is based on the assumption of a kinematic vertical displacement of ocean water that is analogous to the ocean bottom displacement during a submarine earthquake and the use of a non-dispersive long-wave model to simulate its physical transformation as it radiates outward from the source region. In this study, a new generation mechanism and the use of a highly-dispersive wave model to simulate tsunami inception, propagation and transformation are proposed. The new generation model assumes that transient ground motion during the earthquake can accelerate horizontal currents with opposing directions near the fault line whose successive convergence and divergence generate a series of potentially destructive oceanic waves. The new dynamic model incorporates the effects of earthquake moment magnitude, ocean compressibility through the buoyancy frequency, the effects of focal and water depths, and the orientation of ruptured fault line in the tsunami magnitude and directivity.For tsunami wave simulation, the nonlinear momentum-based wave model includes important wave propagation and transformation mechanisms such as refraction, diffraction, shoaling, partial reflection and transmission, back-scattering, frequency dispersion, and resonant wave-wave interaction. Using this model and a coarse-resolution bathymetry, the new mechanism is tested for the Indian Ocean tsunami of December 26, 2004. A new flooding and drying algorithm that consider waves coming from every direction is also proposed for simulation of inundation of low-lying coastal regions.It is shown in the present study that with the proposed generation model, the observed features of the Asian tsunami such as the initial drying of areas east of the source region and the initial flooding of western coasts are correctly simulated. The formation of a series of tsunami waves with periods and lengths comparable to observations
Hui, Zhan-Qiang; Zhang, Jian-Guo
2012-05-01
We propose the use of cross-phase modulation (XPM) and four-wave mixing (FWM) in dispersion-flattened highly nonlinear photonic crystal fibers (HNL-PCFs) to implement the functionalities of wavelength conversion, simultaneous time demultiplexing and wavelength multicasting in optical time-division multiplexing (OTDM) systems. The experiments on wavelength conversion at 80 Gbit s-1and OTDM demultiplexing from 80 to 10 Gbit s-1 with wavelength multicasting of two channels are successfully demonstrated to validate the proposed scheme, which are carried out by using two segments of dispersion-flattened HNL-PCFs with lengths of 100 and 50 m, respectively. Moreover, the bit error rate (BER) performance is also measured. The results show that our designed system can achieve a power penalty of less than 4.6 dB for two multicasting channels with a 24 nm wavelength span at the BER of 10-9 when compared with the 10 Gbit/s back-to-back measurement. The proposed system is transparent to bit rate since only an ultrafast third-order nonlinear effect is used. The resulting configuration is compact, robust and reliable, benefiting from the use of dispersion-flattened HNL-PCFs with short lengths. This also makes the proposed system more flexible in the operational wavelengths than those based on dispersion-shifted fibers and traditional highly nonlinear fibers. The work was supported in part by the CAS/SAFEA International Partnership Program for Creative Research Teams.
Cao, Yuan-Cheng
2012-02-15
In this work, a method to prepare a thermally stable QDs/clay powder is reported. First, several water soluble CdTe QDs characterised by different size-dependent emission wavelengths were synthesised through wet chemistry. Montmorillonite-Na(+) clay in water was dispersed into a muddy suspension by sonication. Then, the clay-water suspension was used as the host media for CdTe QDs to prepare the QDs/clay powder by freeze drying. The experiments showed that QDs/clay powder could be re-dispersed in water without changing the luminescent property of the QDs; this process was reversible. EDX showed that Cd and Te elements existed in the QDs/clay powder and the XRD tests showed that the clay [001] reflection peaks for raw clay, QDs (λ(em)=514 nm)/clay and QDs (λ(em)=560 nm)/clay were the same, namely 2θ=7.4°. Finally, QDs/clay powder was applied to the HDPE polymer extrusion process at 200 °C to produce thin films; the resultant QDs-polymer nanocomposite film exhibited strong fluorescence.
Directory of Open Access Journals (Sweden)
Jing Yin
2015-07-01
Full Text Available A total variation diminishing-weighted average flux (TVD-WAF-based hybrid numerical scheme for the enhanced version of nonlinearly dispersive Boussinesq-type equations was developed. The one-dimensional governing equations were rewritten in the conservative form and then discretized on a uniform grid. The finite volume method was used to discretize the flux term while the remaining terms were approximated with the finite difference method. The second-order TVD-WAF method was employed in conjunction with the Harten-Lax-van Leer (HLL Riemann solver to calculate the numerical flux, and the variables at the cell interface for the local Riemann problem were reconstructed via the fourth-order monotone upstream-centered scheme for conservation laws (MUSCL. The time marching scheme based on the third-order TVD Runge-Kutta method was used to obtain numerical solutions. The model was validated through a series of numerical tests, in which wave breaking and a moving shoreline were treated. The good agreement between the computed results, documented analytical solutions, and experimental data demonstrates the correct discretization of the governing equations and high accuracy of the proposed scheme, and also conforms the advantages of the proposed shock-capturing scheme for the enhanced version of the Boussinesq model, including the convenience in the treatment of wave breaking and moving shorelines and without the need for a numerical filter.
Nonlinearization and waves in bounded media: old wine in a new bottle
Mortell, Michael P.; Seymour, Brian R.
2017-02-01
We consider problems such as a standing wave in a closed straight tube, a self-sustained oscillation, damped resonance, evolution of resonance and resonance between concentric spheres. These nonlinear problems, and other similar ones, have been solved by a variety of techniques when it is seen that linear theory fails. The unifying approach given here is to initially set up the appropriate linear difference equation, where the difference is the linear travel time. When the linear travel time is replaced by a corrected nonlinear travel time, the nonlinear difference equation yields the required solution.
Existence of solutions of a nonlinear system modelling fluid flow in porous media
Directory of Open Access Journals (Sweden)
dam Besenyei
2006-12-01
Full Text Available We investigate the existence of weak solutions for nonlinear differential equations that describe fluid flow through a porous medium. Existence is proved using the theory of monotone operators, and some examples are given.
Nonlinear Optical Wave Equation for Micro- and Nano-Structured Media and Its Application
2013-03-01
distribution is unlimited. 3 Summary Major trends recently occurred in the modern physics and applications of nonlinear optics are closely linked with...interaction in an optically transparent nonmagnetic continuous medium is the subject area of the macroscopic electrodynamics [1,2]. For the majority of...activity worldwide in the area of linear and nonlinear nanophotonics. References. [1]. L. D. Landau and E. M. Lifshitz, Electrodynamics of
Analysis of Synchronization Phenomena in Broadband Signals with Nonlinear Excitable Media
Directory of Open Access Journals (Sweden)
Klaus Lehnertz
2009-01-01
Full Text Available We apply the method of frequency-selective excitation waves in excitable media to characterize synchronization phenomena in interacting complex dynamical systems by measuring coincidence rates of induced excitations. We relax the frequency-selectivity of excitable media and demonstrate two applications of the method to signals with broadband spectra. Findings obtained from analyzing time series of coupled chaotic oscillators as well as electroencephalographic (EEG recordings from an epilepsy patient indicate that this method can provide an alternative and complementary way to estimate the degree of phase synchronization in noisy signals.
Energy Technology Data Exchange (ETDEWEB)
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.
Energy Technology Data Exchange (ETDEWEB)
Murata, Mikio [Nuclear Engineering Co., Ltd., Hitachi, Ibaraki (Japan); Noguchi, Hiroshi; Yokoyama, Sumi [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment
2000-11-01
A computer code (TRIDOSE) was developed to assess the environmental impact of atmospheric released tritium gas (T{sub 2}) from nuclear fusion related facilities. The TRIDOSE simulates dispersion of T{sub 2} and resultant HTO in the atmosphere, land, plant, water and foods in the environment, and evaluates contamination concentrations in the media and exposure doses. A part of the mathematical models in TRIDOSE were verified by comparison of the calculation with the results of the short range (400 m) dispersion experiment of HT gas performed in Canada postulating a short-time (30 minutes) accidental release. (author)
Exact solutions of optical pulse propagation in nonlinear meta-materials
Nanda, Lipsa
2017-01-01
An analytical and simulation based method has been used to exactly solve the nonlinear wave propagation in bulk media exhibiting frequency dependent dielectric susceptibility and magnetic permeability. The method has been further extended to investigate the intensity distribution in a nonlinear meta-material with negative refractive index where both ɛ and μ are dispersive and negative in nature.
Andreasen, J; Kolesik, M
2012-09-01
Unidirectional pulse propagation equations [UPPE, Phys. Rev. E 70, 036604 (2004)] have provided a theoretical underpinning for computer-aided investigations into dynamics of high-power ultrashort laser pulses and have been successfully utilized for almost a decade. Unfortunately, they are restricted to applications in bulk media or, with additional approximations, to simple waveguide geometries in which only a few guided modes can approximate the propagating waveform. The purpose of this work is to generalize the directional pulse propagation equations to structures characterized by strong refractive index differences and material interfaces. We also outline a numerical solution framework that draws on the combination of the bulk-media UPPE method with single-frequency beam-propagation techniques.
Yang, Haijian
2016-12-10
Most existing methods for solving two-phase flow problems in porous media do not take the physically feasible saturation fractions between 0 and 1 into account, which often destroys the numerical accuracy and physical interpretability of the simulation. To calculate the solution without the loss of this basic requirement, we introduce a variational inequality formulation of the saturation equilibrium with a box inequality constraint, and use a conservative finite element method for the spatial discretization and a backward differentiation formula with adaptive time stepping for the temporal integration. The resulting variational inequality system at each time step is solved by using a semismooth Newton algorithm. To accelerate the Newton convergence and improve the robustness, we employ a family of adaptive nonlinear elimination methods as a nonlinear preconditioner. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm. A comparison is also included to show the superiority of the proposed fully implicit approach over the classical IMplicit Pressure-Explicit Saturation (IMPES) method in terms of the time step size and the total execution time measured on a parallel computer.
Yang, Haijian; Sun, Shuyu; Yang, Chao
2017-03-01
Most existing methods for solving two-phase flow problems in porous media do not take the physically feasible saturation fractions between 0 and 1 into account, which often destroys the numerical accuracy and physical interpretability of the simulation. To calculate the solution without the loss of this basic requirement, we introduce a variational inequality formulation of the saturation equilibrium with a box inequality constraint, and use a conservative finite element method for the spatial discretization and a backward differentiation formula with adaptive time stepping for the temporal integration. The resulting variational inequality system at each time step is solved by using a semismooth Newton algorithm. To accelerate the Newton convergence and improve the robustness, we employ a family of adaptive nonlinear elimination methods as a nonlinear preconditioner. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm. A comparison is also included to show the superiority of the proposed fully implicit approach over the classical IMplicit Pressure-Explicit Saturation (IMPES) method in terms of the time step size and the total execution time measured on a parallel computer.
Institute of Scientific and Technical Information of China (English)
WANG Jun-Min
2011-01-01
With the aid of Mathematica, three auxiliary equations, i.e.the Riccati equation, the Lenard equation and the Hyperbolic equation, are employed to investigate traveling wave solutions of a cosh-Gaussian laser beam in both Kerr and cubic quintic nonlinear media. As a result, many traveling wave solutions are obtained, including soliton-like solutions, hyperbolic function solutions and trigonometric function solutions.
Balzer, Jan C; Döpke, Benjamin; Brenner, Carsten; Klehr, Andreas; Erbert, Götz; Tränkle, Günther; Hofmann, Martin R
2014-07-28
We analyze the influence of second and third order intracavity dispersion on a passively mode-locked diode laser by introducing a spatial light modulator (SLM) into the external cavity. The dispersion is optimized for chirped pulses with highest possible spectral bandwidth that can be externally compressed to the sub picosecond range. We demonstrate that the highest spectral bandwidth is achieved for a combination of second and third order dispersion. With subsequent external compression pulses with a duration of 437 fs are generated.
Canonical and Singular Propagation of Ultrashort Pulses in a Nonlinear Medium
Karl Glasner; Miroslav Kolesik; Moloney, Jerome V.; Newell, Alan C.
2012-01-01
We examine the two types of singular behaviors of ultrashort pulses in a nonlinear medium, pulse steepening if the weak longitudinal dispersion is normal and collapse if it is anomalous. Connections with analogous behaviors of wave packets of almost monochromatic waves in strongly dispersive media are discussed.
Scaling Laws for the Response of Nonlinear Elastic Media with Implications for Cell Mechanics
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.
Coexistence of synchrony and incoherence in oscillatory media under nonlinear global coupling
Energy Technology Data Exchange (ETDEWEB)
Schmidt, Lennart; García-Morales, Vladimir [Physik-Department, Nonequilibrium Chemical Physics, Technische Universität München, James-Franck-Str. 1, D-85748 Garching (Germany); Institute for Advanced Study, Technische Universität München, Lichtenbergstr. 2a, D-85748 Garching (Germany); Schönleber, Konrad; Krischer, Katharina, E-mail: krischer@tum.de [Physik-Department, Nonequilibrium Chemical Physics, Technische Universität München, James-Franck-Str. 1, D-85748 Garching (Germany)
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.
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.
Nonlinear propagation and control of acoustic waves in phononic superlattices
Jiménez, Noé; Picó, Rubén; García-Raffi, Lluís M; Sánchez-Morcillo, Víctor J
2015-01-01
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 cancelled). The presented ideas open a way towards the control of acoustic wave propagation in nonlinear regime.
Paolo Delsanto, Pier; Hirsekorn, Sigrun
2004-04-01
Recent experiments on rocks and other materials, such as soil, cement, concrete and damaged elastic materials, have led to the discovery of nonlinear (NL) hysteretic effects in their elastic behaviour. These observations suggest the existence of a NL mesoscopic elasticity universality class, to which all the aforementioned materials belong. The purpose of the present contribution is to search for the basic mathematical roots for nonclassical nonlinearity, in order to explain its universality, classify it and correlate it with the underlying meso- or microscopic interaction mechanisms. In our discussions we explicitly consider two quite different kinds of specimens: a two-bonded-elements structure and a thin multigrained bar. It is remarkable that, although the former includes only one interface and the latter very many interstices, the same "interaction box" formalism can be applied to both. Another important result of the proposed formalism is that the spectral contents of an arbitrary system for any input amplitude may be predicted, under certain assumptions, from the result of a single experiment at a higher amplitude.
Directory of Open Access Journals (Sweden)
M.J. Uddin
2016-06-01
Full Text Available A numerical investigation of two dimensional steady state laminar boundary layer flow of a viscous electrically-conducting nanofluid in the vicinity of a stretching/shrinking porous flat plate located in a Darcian porous medium is performed. The nonlinear Rosseland radiation effect is taken into account. Velocity slip and thermal slip at the boundary as well as the newly developed zero mass flux boundary conditions are also implemented to achieve physically applicable results. The governing transport equations are reduced to a system of nonlinear ordinary differential equations using appropriate similarity transformations and these are then solved numerically using a variational finite element method (FEM. The influence of the governing parameters (Darcy number, magnetic field, velocity and thermal slip, temperature ratio, transpiration, Brownian motion, thermophoresis, Lewis number and Reynolds number on the dimensionless velocity, temperature, nanoparticle volume fraction as well as the skin friction, the heat transfer rates and the mass transfer rates are examined and illustrated in detail. The FEM code is validated with earlier studies for non-magnetic non-slip flow demonstrating close correlation. The present study is relevant to high-temperature nano-materials processing operations.
Theory of backward second-harmonic localization in nonlinear left-handed media
Centeno, Emmanuel; Ciracì, Cristian
2008-12-01
Recent research on photonic crystals possessing a quadratic nonlinear response has revealed a second-harmonic light localization phenomenon that originates from an all-angle phase matching between counterpropagating Bloch modes at the fundamental and double frequencies [E. Centeno , Phys. Rev. Lett. 98, 263903 (2007)]. In this paper, we develop an electromagnetic theory describing the nature of this parametric light localization, which appears in properly design metamaterials or photonic crystals exhibiting nonlinear left-handed behaviors. We demonstrate that interferences between converging phase-matched and diverging anti-phase-matched waves create a localized second-harmonic wave focused on the pump emitter on the scale of half the wavelength. This light trapping is accompanied by the enhancement of the second-harmonic intensity, which linearly increases with the size of the two-dimensional domain. We finally show that the second-harmonic localization effect previously proposed for GaN photonic crystals can also be obtained with LiNbO3 material.
Spatiotemporal focusing in opaque scattering media by wave front shaping with nonlinear feedback.
Aulbach, Jochen; Gjonaj, Bergin; Johnson, Patrick; Lagendijk, Ad
2012-12-31
We experimentally demonstrate spatiotemporal focusing of light on single nanocrystals embedded inside a strongly scattering medium. Our approach is based on spatial wave front shaping of short pulses, using second harmonic generation inside the target nanocrystals as the feedback signal. We successfully develop a model both for the achieved pulse duration as well as the observed enhancement of the feedback signal. The approach enables exciting opportunities for studies of light propagation in the presence of strong scattering as well as for applications in imaging, micro- and nanomanipulation, coherent control and spectroscopy in complex media.
Riaz, Amir; Tchelepi, Hamdi A.
2004-12-01
Linear stability analysis of immiscible displacements is carried out for both viscously and gravitationally unstable two-phase flows in porous media with very large adverse viscosity ratios. Capillary dispersion is the proper dissipative mechanism in this case which sets both the preferred length scale and the band width of the spectrum of unstable length scales. The growth rate, the most dangerous and the cutoff wavenumbers, all scale linearly with the capillary number. We show that the instability is governed by fluid properties across the shock rather than those across the full Buckley-Leverett profile. The shock total mobility ratio provides a sufficient condition for the onset of instability; however, it is not an appropriate criterion for predicting the magnitude of the growth rate, particularly for large viscosity ratios. The details of the relative permeability functions are observed to have a significant influence on the stability characteristics. For neutrally buoyant flows the maximum growth rate scales linearly with the viscosity ratio while the most dangerous and the cutoff wavenumbers scale with the square root of the viscosity ratio. In the case of displacements with density contrast, the maximum growth rate scales with the square of the unstable gravity number while the most dangerous and the cutoff wavenumbers scale with an exponent of 1.2, for all viscosity ratios. A marginal stability curve is computed for stable and unstable regions in the parameter space of the viscosity ratio and the gravity number. It is found that flows with unstable viscosity contrasts are more readily stabilized with buoyancy as compared to the viscous stabilization of gravitationally unstable flows.
DEFF Research Database (Denmark)
Zhou, Binbin; Guo, Hairun; Bache, Morten
2015-01-01
and without critical phase-matching requirements. Pumping a bulk quadratic nonlinear crystal (unpoled LiNbO3 cut for noncritical phase-mismatched interaction) with sub-mJ near-IR 50-fs pulses, tunable and broadband (∼ 1,000 cm−1) mid-IR pulses around 3.0 μm are generated with excellent spatio-temporal pulse...... quality, having up to 10.5 μJ energy (6.3% conversion). The mid-IR pulses are dispersive waves phase-matched to near-IR self-defocusing solitons created by the induced self-defocusing cascaded nonlinearity. This process is filament-free and the input pulse energy can therefore be scaled arbitrarily...
Richoux, Olivier; Hardy, Jean
2009-01-01
This paper presents an application of time-frequency methods to characterize the dispersion of acoustic waves travelling in a one-dimensional periodic or disordered lattice made up of Helmholtz resonators connected to a cylindrical tube. These methods allow (1) to evaluate the velocity of the wave energy when the input signal is an acoustic pulse ; (2) to display the evolution of the spectral content of the transient signal ; (3) to show the role of the localized nonlinearities on the propagation .i.e the emergence of higher harmonics. The main result of this paper is that the time-frequency methods point out how the nonlinearities break the localization of the waves and/or the filter effects of the lattice.
Chandra, S.; Vardhanan, A. Vishnu; Gangopadhyay, R.
2007-11-01
Optical phase conjugation (OPC) and distributed Raman amplifier (DRA) combination (OPC-DRA) is demonstrated as a potential enabling solution for simultaneous reduction of fiber non-linearities and dispersion compensation of a sub-carrier multiplexed (SCM) optical transmission link. The present work is focused on the use of OPC-DRA combination for system performance improvement in terms of composite second order distortion (CSO) and carrier to noise ratio (CNR) of the SCM link. The analysis further shows that, introduction of DRA with proper pumping scheme significantly reduce fiber non-linearity resulting in improvement of the system performance in terms of CNR, compared to the situation where only mid-way optical phase conjugation is used.
DEFF Research Database (Denmark)
Zhou, Binbin; Guo, Hairun; Bache, Morten
2015-01-01
and without critical phase-matching requirements. Pumping a bulk quadratic nonlinear crystal (unpoled LiNbO3 cut for noncritical phase-mismatched interaction) with sub-mJ near-IR 50-fs pulses, tunable and broadband (∼ 1,000 cm−1) mid-IR pulses around 3.0 μm are generated with excellent spatio-temporal pulse...... quality, having up to 10.5 μJ energy (6.3% conversion). The mid-IR pulses are dispersive waves phase-matched to near-IR self-defocusing solitons created by the induced self-defocusing cascaded nonlinearity. This process is filament-free and the input pulse energy can therefore be scaled arbitrarily...... by using large-aperture crystals. The technique can readily be implemented with other crystals and laser wavelengths, and can therefore potentially replace current ultrafast frequency-conversion processes to the mid-IR....
DEFF Research Database (Denmark)
Andersen, Peter Andreas; Tokle, Torger; Geng, Yan
2005-01-01
by the gain bandwidth of erbium-doped fiber amplifiers, are obtained in only 50-m dispersion-flattened HNL-PCF with nonlinear coefficient equal to 11 W-1·km-1. This experiment demonstrates the potential of four-wave mixing in HNL-PCF as a modulation format and bit rate transparent wavelength conversion......Wavelength conversion of a 40-Gb/s return-to-zero differential phase-shift keying signal is demonstrated in a highly nonlinear photonic crystal fiber (HNL-PCF) for the first time. A conversion efficiency of -20 dB for a pump power of 23 dBm and a conversion bandwidth of 31 nm, essentially limited...
Yarmoghaddam, Elahe; Rakheja, Shaloo
2017-08-01
We theoretically model the dispersion characteristics of surface plasmons in a graphene-based parallel-plate waveguide geometry using nonlinear Kerr-type core (inter-plate) dielectric. The optical nonlinearity of graphene in the terahertz band under high light intensity is specifically included in the analysis. By solving Maxwell's equations and applying appropriate boundary conditions, we show that the waveguide supports four guided plasmon modes, each of which can be categorized as either symmetric or anti-symmetric based on the electric field distribution in the structure. Of the four guided modes, two modes are similar in characteristics to the modes obtained in the structure with linear graphene coating, while the two new modes have distinct characteristics as a result of the nonlinearity of graphene. We note that the group velocity of one of the plasmon modes acquires a negative value under high light intensity. Additionally, the optical nonlinearity of the core dielectric leads to a significant enhancement in the localization length of various plasmon modes. The description of the intra-band optical conductivity of graphene incorporates effects of carrier scatterings due to charged impurities, resonant scatterers, and acoustic phonons at 300 K. The proposed structure offers flexibility to tune the waveguide characteristics and the mode index by changing light intensity and electrochemical potential in graphene for reconfigurable plasmonic devices.
Institute of Scientific and Technical Information of China (English)
Yan Wang; Qing Wang; Wei Zhang; Xiaoming Liu; Jiangde Peng
2005-01-01
@@ A broadband multiwavelength Raman fiber ring laser (RFRL) covering the whole C-band at room temperature are presented. The effect of the intracavity highly nonlinear dispersion-shifted fiber on broadening and flattening the output spectrum envelope is discussed and experimentally demonstrated. More than 45-dB extinction-ratio multiwavelength output from 1527.76 to 1566.86 nm with 100-GHz channel spacing and 2.1-dB power ripple has been achieved by carefully controlling the individual powers of three pump lasers.
Johansson, Magnus; Derevyanko, Stanislav A
2013-01-01
We investigate the mobility of nonlinear localized modes in a one-dimensional waveguide array in an active Kerr medium with intrinsic, saturable gain and damping, described by a generalized discrete Ginzburg-Landau type model. 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 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...
Nonlinear propagation and decay of intense regular and random waves in relaxing media
Gurbatov, S. N.; Rudenko, O. V.; Demin, I. Yu.
2015-10-01
An integro-differential equation is written down that contains terms responsible for nonlinear absorption, visco-heat-conducting dissipation, and relaxation processes in a medium. A general integral expression is obtained for calculating energy losses of the wave with arbitrary characteristics—intensity, profile (frequency spectrum), and kernel describing the internal dynamics of the medium. Profiles of stationary solutions are constructed both for an exponential relaxation kernel and for other types of kernels. Energy losses at the front of week shock waves are calculated. General integral formulas are obtained for energy losses of intense noise, which are determined by the form of the kernel, the structure of the noise correlation function, and the mean square of the derivative of realization of a random process.
Dave, Utsav D; Kuyken, Bart; Leo, François; Gorza, Simon-Pierre; Combrie, Sylvain; De Rossi, Alfredo; Raineri, Fabrice; Roelkens, Gunther
2015-02-23
We propose high index contrast InGaP photonic wires as a platform for the integration of nonlinear optical functions in the telecom wavelength window. We characterize the linear and nonlinear properties of these waveguide structures. Waveguides with a linear loss of 12 dB/cm and which are coupled to a single mode fiber through gratings with a -7.5 dB coupling loss are realized. From four wave mixing experiments, we extract the real part of the nonlinear parameter γ to be 475 ± 50 W(-1)m(-1) and from nonlinear transmission measurements we infer the absence of two-photon absorption and measure a three-photon absorption coefficient of (2.5 ± 0.5) x 10(-2) cm(3)GW(-2).
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.
Twisted toroidal vortex-solitons in inhomogeneous media with repulsive nonlinearity
Kartashov, Y V; Shnir, Y; Torner, L
2014-01-01
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 the field theory, ferromagnetics, and semi- and superconductors. Such topological states are normally generated in multi-component systems, or as trapped quasi-linear 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 m1. 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...
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.
Gasbarri, Carla; Croce, Fausto; Meschini, Ida; Bowen, Christopher H; Marinelli, Lisa; Di Stefano, Antonio; Angelini, Guido
2016-01-11
Dispersions of single-walled carbon nanotubes (SWNTs) have been prepared by using the room-temperature ionic liquid [BMIM][BF4 ] (1-butyl-3-methylimidazolium tetrafluoroborate), the triblock copolymer Pluronic L121 [poly(ethylene oxide)5 -poly(propylene oxide)68 -poly(ethylene oxide)5 ] and the non-ionic surfactant Triton X-100 (TX100) in the pure state. The size of the SWNTs aggregates and the dispersion degree in the three viscous systems depend on the sonication time, as highlighted by UV/Vis/NIR spectroscopy and optical microscopy analysis. A nonlinear increase in conductivity can be observed as a function of the SWNTs loading, as suggested by electrochemical impedance spectroscopy. The generation of a three-dimensional network of SWNTs showing a viscoelastic gel-like behavior above a critical percolation concentration has been found at 25 °C in all the investigated systems by oscillatory rheology measurements.
Navarrete, Alvaro; Paredes, Angel; Salgueiro, José R.; Michinel, Humberto
2017-01-01
We analyze theoretically the Schrödinger-Poisson equation in two transverse dimensions in the presence of a Kerr term. The model describes the nonlinear propagation of optical beams in thermo-optical media and can be regarded as an analog system for a self-gravitating self-interacting wave. We compute numerically the family of radially symmetric ground-state bright stationary solutions for focusing and defocusing local nonlinearity, keeping in both cases a focusing nonlocal nonlinearity. We also analyze excited states and oscillations induced by fixing the temperature at the borders of the material. We provide simulations of soliton interactions, drawing analogies with the dynamics of galactic cores in the scalar field dark-matter scenario.
DEFF Research Database (Denmark)
Pugliese, Lorenzo; Poulsen, Tjalfe; Straface, Salvatore
2013-01-01
data. This paper evaluates the possibility for estimating solute dispersion based on gas dispersion measurements. Breakthrough measurements were carried out at different fluid velocities (covering the same range in Reynolds number), using O2 and NaCl as gas and solute tracers, respectively. Three...... different, granular porous materials were used: (1) crushed granite (very angular particles), (2) gravel (particles of intermediate roundness) and (3) Leca® (almost spherical particles). For each material, 21 different particle size fractions were used. Gas and solute dispersion coefficients were determined...
2010-03-01
indeed studied the dynamics of our systems at impulses approaching speeds 750 m /s and preliminary analyses using state of the art hydrocodes17...These systems, now referred to as deco - rated TCs DTCs, represent a significant improvement and turn out to be strongly nonlinear in their...presented. Hard sphere approximations for both systems follow in Sec. III. Section IV outlines the numerical approach and results for the deco - rated chain
Sahimi, Muhammad
1998-12-01
We review and discuss recent progress in modelling non-linear and non-local transport processes in heterogeneous media. The non-locality that we consider is caused by long-range correlations that either exist in the morphology of the media, or are caused by the transport processes themselves. The interplay between the non-linearity and non-locality is discussed in depth with the aim of establishing that, often non-linearity and non-locality are “two sides of the same coin”, such that one may have no meaning without the presence of the other one. First, we discuss linear and scalar, but non-local transport processes and, in particular, consider those in percolation systems with long-range correlations. It appears that there are significant differences between percolative transport processes in which the long-range correlations (or the covariance function) decrease with the distance r between two points, and those in which they increase as r does. Application of this problem to flow and transport in geological formations is discussed. We then consider linear vector percolation, one type of which, the rigidity percolation, provides an example of a non-local vector transport in heterogeneous media. Applications of vector percolation to modelling elastic properties of glasses, composite solids and rock, mechanical and viscoelastic properties of polymers, and vibrations and dynamical properties of heterogeneous materials are discussed. Non-linear and non-local scalar transport processes are discussed next, including various breakdown phenomena in disordered composites, power-law transport, piecewise linear transport characterized by a threshold, and non-linear processes that arise as a result of imposing a large external potential gradient on a heterogeneous medium. Their relevance to flow of non-Newtonian fluids in porous media, to electrical currents and dielectric breakdown in composite solids and doped polycrystalline semiconductors, and several other problems is
Xia, Ya-Rong; Xin, Xiang-Peng; Zhang, Shun-Li
2017-01-01
This paper mainly discusses the (2+1)-dimensional modified dispersive water-wave (MDWW) system which will be proved nonlinear self-adjointness. This property is applied to construct conservation laws corresponding to the symmetries of the system. Moreover, via the truncated Painlevé analysis and consistent tanh-function expansion (CTE) method, the soliton-cnoidal periodic wave interaction solutions and corresponding images will be eventually achieved. Supported by National Natural Science Foundation of China under Grant Nos. 11371293, 11505090, the Natural Science Foundation of Shaanxi Province under Grant No. 2014JM2-1009, Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No. BS2015SF009 and the Science and Technology Innovation Foundation of Xi’an under Grant No. CYX1531WL41
Directory of Open Access Journals (Sweden)
Zhan-Qiang Hui
2014-01-01
Full Text Available 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.
Directory of Open Access Journals (Sweden)
Xiangming Liu
2012-01-01
Full Text Available We present a theory of open- and closed-aperture Gaussian beam Z-scan for nonlinear optical materials with saturable absorption and high-order nonlinear refraction. We show that an approximate expression for a transmitted intensity through the nonlinear optical material is possible by means of the Adomian’s decomposition method and the thin film approximation. The theory is applied to semiconductor CdSe quantum dot-polymer nanocomposite films. It is shown that the theory well explains measured results of open- and closed-aperture transmittances in the Z-scan setup. It is also shown that the nanocomposite film possesses simultaneous third- and fifth-order nonlinear refraction as well as saturable absorption of a homogeneously broadened type.
Hruška, Vlastimil; Svobodová, Jana; Beneš, Martin; Gaš, Bohuslav
2012-12-07
We introduce a new nonlinear electrophoretic model for complex-forming systems with a fully charged analyte and a neutral ligand. The background electrolyte is supposed to be composed of two constituents, which do not interact with the ligand. In order to characterize the electromigration dispersion (EMD) of the analyte zone we define a new parameter, the nonlinear electromigration mobility slope, S(EMD,A). The parameter can be easily utilized for quantitative prediction of the EMD and for comparisons of the model with the simulated and experimental profiles. We implemented the model to the new version of PeakMaster 5.3 Complex that can calculate some characteristic parameters of the electrophoretic system and can plot the dependence of S(EMD,A) on the concentration of the ligand. Besides S(EMD,A), also the relative velocity slope, S(X), can be calculated. It is commonly used as a measure of EMD in electrophoretic systems. PeakMaster 5.3 Complex software can be advantageously used for optimization of the separation conditions to avoid high EMD in complexing systems. Based on the theoretical model we analyze the S(EMD,A) and reveal that this parameter is composed of six terms. We show that the major factor responsible for the electromigration dispersion in complex-forming electrophoretic systems is the complexation equilibrium and particularly its impact on the effective mobility of the analyte. To prove the appropriateness of the model we showed that there is a very good agreement between peak shapes calculated by PeakMaster 5.3 Complex (plotted using the HVLR function) and the profiles simulated by means of Simul 5 Complex. The detailed experimental verification of the new mode of PeakMaster 5.3 Complex is in the next part IV of the series.
Chitgarha, Mohammad Reza; Khaleghi, Salman; Ziyadi, Morteza; Mohajerin-Ariaei, Amirhossein; Almaiman, Ahmed; Daab, Wajih; Rogawski, Devora; Tur, Moshe; Touch, Joseph D; Langrock, Carsten; Fejer, Martin M; Willner, Alan E
2014-05-15
We propose and demonstrate an all-optical phase noise reduction scheme that uses optical nonlinear mixing and tunable optical delays to suppress the low-speed phase noise induced by laser linewidth. By utilizing the phase conjugate copy of the original signal and two narrow-linewidth optical pumps, the phase noise induced by laser linewidth can be reduced by a factor of ∼5 for a laser with 500-MHz phase noise bandwidth. The error-vector-magnitude can be improved from ∼30% to ∼14% for the same laser linewidth for 40-Gbit/s quadrature phase shift keying signal.
DEFF Research Database (Denmark)
Germaschewski, K.; Grauer, R.; Bergé, L.
2001-01-01
are detailed and compared with those characterizing collapsing objects with no anisotropic dispersion. Their ability to mutually coalesce is also analyzed and modeled from the interaction of Gaussian components. Next, bunch-type and snake-type instabilities, which result from periodic modulations driven...... by even and odd localized modes, are studied. The influence of the initial wave amplitude, the amplitude and wavenumber of the perturbations on the interplay of snake and bunch patterns are finally discussed. (C) 2001 Elsevier Science B.V. All rights reserved....
Xiao, Xiaosheng; Hua, Yi
2016-10-01
All-normal-dispersion (ANDi) mode-locked Yb-doped fiber laser is a promising seed source for supercontinuum (SC) generation, due to its compact structure and broadband output. The influences of output ports of the ANDi laser mode-locked by nonlinear polarization rotation (NPR), on the generated SC are investigated. Two output ports of ANDi laser are considered, one of which is the conventional nonlinear polarization rotation (NPR) port and the other is extracted from a coupler after the NPR port. It is found that, the SC originated from the coupler port is much broader than that from the NPR port, which is validated by lots of experiments with different output parameters. Furthermore, the conclusion is verified and generalized to general ANDi lasers by numerical simulations, because the output pulse from coupler port could be cleaner than that from NPR port. Besides, there are no significant differences in the phase coherence and temporal stability between the SCs generated from both ports. Hence for the SC generation based on ANDi laser, it is preferred to use the pulse of coupler port (i.e. pulse after NPR port) serving as the seed source.
Zhou, B B; Bache, M
2014-01-01
Generating energetic femtosecond mid-IR pulses is crucial for ultrafast spectroscopy, and currently relies on parametric processes that, while efficient, are also complex. Here we experimentally show a simple alternative that uses a single pump wavelength without any pump synchronization and without critical phase-matching requirements. Pumping a bulk quadratic nonlinear crystal (unpoled LiNbO$_3$ cut for noncritical phase-mismatched interaction) with sub-mJ near-IR 50-fs pulses, tunable and broadband ($\\sim 1,000$ cm$^{-1}$) mid-IR pulses around $3.0~\\mu\\rm m$ are generated with excellent spatio-temporal pulse quality, having up to 10.5 $\\mu$J energy (6.3% conversion). The mid-IR pulses are dispersive waves phase-matched to near-IR self-defocusing solitons created by the induced self-defocusing cascaded nonlinearity. This process is filament-free and the input pulse energy can therefore be scaled arbitrarily by using large-aperture crystals. The technique can readily be implemented with other crystals and la...
Nonlinear waves in waveguides with stratification
Leble, Sergei B
1991-01-01
S.B. Leble's book deals with nonlinear waves and their propagation in metallic and dielectric waveguides and media with stratification. The underlying nonlinear evolution equations (NEEs) are derived giving also their solutions for specific situations. The reader will find new elements to the traditional approach. Various dispersion and relaxation laws for different guides are considered as well as the explicit form of projection operators, NEEs, quasi-solitons and of Darboux transforms. Special points relate to: 1. the development of a universal asymptotic method of deriving NEEs for guide propagation; 2. applications to the cases of stratified liquids, gases, solids and plasmas with various nonlinearities and dispersion laws; 3. connections between the basic problem and soliton- like solutions of the corresponding NEEs; 4. discussion of details of simple solutions in higher- order nonsingular perturbation theory.
Energy Technology Data Exchange (ETDEWEB)
Reshak, A. H., E-mail: maalidph@yahoo.com [New Technologies - Research Centre, University of West Bohemia, Univerzitni 8, 306 14 Pilsen (Czech Republic); Center of Excellence Geopolymer and Green Technology, School of Material Engineering, University Malaysia Perlis, 01007 Kangar, Perlis (Malaysia); Brik, M. G. [College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065 (China); Institute of Physics, University of Tartu, Ravila 14C, Tartu 50411 (Estonia); Auluck, S. [Council of Scientific and Industrial Research—National Physical Laboratory Dr. K S Krishnan Marg, New Delhi 110012 (India)
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.
Dispersive shock waves and modulation theory
El, G. A.; Hoefer, M. A.
2016-10-01
There is growing physical and mathematical interest in the hydrodynamics of dissipationless/dispersive media. Since G.B. Whitham's seminal publication fifty years ago that ushered in the mathematical study of dispersive hydrodynamics, there has been a significant body of work in this area. However, there has been no comprehensive survey of the field of dispersive hydrodynamics. Utilizing Whitham's averaging theory as the primary mathematical tool, we review the rich mathematical developments over the past fifty years with an emphasis on physical applications. The fundamental, large scale, coherent excitation in dispersive hydrodynamic systems is an expanding, oscillatory dispersive shock wave or DSW. Both the macroscopic and microscopic properties of DSWs are analyzed in detail within the context of the universal, integrable, and foundational models for uni-directional (Korteweg-de Vries equation) and bi-directional (Nonlinear Schrödinger equation) dispersive hydrodynamics. A DSW fitting procedure that does not rely upon integrable structure yet reveals important macroscopic DSW properties is described. DSW theory is then applied to a number of physical applications: superfluids, nonlinear optics, geophysics, and fluid dynamics. Finally, we survey some of the more recent developments including non-classical DSWs, DSW interactions, DSWs in perturbed and inhomogeneous environments, and two-dimensional, oblique DSWs.
DEFF Research Database (Denmark)
Kwok, C.H.; Chow, C.W.; Tsang, H.K.;
2006-01-01
We study the conversion bandwidth of the cross-polarization-modulation (YPoIM)-based wavelength conversion scheme with a dispersion-flattened highly nonlinear photonic-crystal fiber for signals with a nonreturn-to-zero (NRZ) modulation format. Both theoretical and experimental results show...... using the YPoIM approach compared with the four-wave mixing approach previously reported is demonstrated....
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.
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.
Desmet, Gert
2013-11-01
The finite length parallel zone (FPZ)-model is proposed as an alternative model for the axial- or eddy-dispersion caused by the occurrence of local velocity biases or flow heterogeneities in porous media such as those used in liquid chromatography columns. The mathematical plate height expression evolving from the model shows that the A- and C-term band broadening effects that can originate from a given velocity bias should be coupled in an exponentially decaying way instead of harmonically as proposed in Giddings' coupling theory. In the low and high velocity limit both models converge, while a 12% difference can be observed in the (practically most relevant) intermediate range of reduced velocities. Explicit expressions for the A- and C-constants appearing in the exponential decay-based plate height expression have been derived for each of the different possible velocity bias levels (single through-pore and particle level, multi-particle level and trans-column level). These expressions allow to directly relate the band broadening originating from these different levels to the local fundamental transport parameters, hence offering the possibility to include a velocity-dependent and, if, needed retention factor-dependent transversal dispersion coefficient. Having developed the mathematics for the general case wherein a difference in retention equilibrium establishes between the two parallel zones, the effect of any possible local variations in packing density and/or retention capacity on the eddy-dispersion can be explicitly accounted for as well. It is furthermore also shown that, whereas the lumped transport parameter model used in the basic variant of the FPZ-model only provides a first approximation of the true decay constant, the model can be extended by introducing a constant correction factor to correctly account for the continuous transversal dispersion transport in the velocity bias zones.
Directory of Open Access Journals (Sweden)
Wright R. J.
2006-11-01
Full Text Available Dispersion within layered porous media is examined under conditions for which no analytical solutions are available. The findings are restricted to miscible displacement in which no fluid density or viscosity differences are present. The region of interest is that of intermediate values of a dimensionless time which quantifies transverse dispersion. Long times, which have been treated by previous authors, allow reduction of the system to a single effective layer in which an increased longitudional dispersion coefficient operates. Shorter times however, correspond to a complex interaction between the convection profile and transverse dispersion and cannot be treated in a one-dimensional manner. An approximate analytical solution for the composition within a given cross-section of an individual layer in a dual-layer model is compared with the result of numerical simulation. The analytical model is then applied to the deconvolution of tracer effluent profiles produced by a multilayered system. It is shown that the fundamental layer characteristics, fluid conductivity and mass-transfer rate, can be obtained from pairs of tracer tests which span a certain range of dimensionless time. Example data from laboratory tests on heterogeneous core samples are used to illustrate application of the method, which should also be applicable to field interwell tracer tests. On examine la dispersion dans un milieu poreux stratifié dans des conditions pour lesquelles il n'y a pas de solution analytique disponible. Les résultats sont limités au déplacement miscible de fluides ayant même viscosité et masse volumique. Le domaine concerné dans cet article est celui des valeurs intermédiaires d'un temps sans dimension qui quantifie la dispersion transversale. Les longues durées de temps, qui ont été traitées par d'autres auteurs, permettent de réduire le système à une simple couche effective dans laquelle intervient un coefficient de dispersion
Nonlinear electrostatic drift Kelvin-Helmholtz instability
Sharma, Avadhesh C.; Srivastava, Krishna M.
1993-01-01
Nonlinear analysis of electrostatic drift Kelvin-Helmholtz instability is performed. It is shown that the analysis leads to the propagation of the weakly nonlinear dispersive waves, and the nonlinear behavior is governed by the nonlinear Burger's equation.
Dispersed Gradient Method of High Order Nonlinear Schr(o)dinger Equation%高阶非线性薛定谔方程的离散梯度法
Institute of Scientific and Technical Information of China (English)
骆思宇; 蒋朝龙; 孙建强
2013-01-01
In the report,a new dispersed gradient method was proposed for solving the high order nonlinear Schr(o)dinger Equation.Firstly,the dispersed gradient method was used to discrete the high order nonlinear Schrodinger Equation and the dispersed gradient scheme of the high order nonlinear Schrodinger Equation was obtained.Secondly,the discrete gradient scheme and the corresponding symplectic scheme of the high order nonlinear Schrodinger Equation with the different saturated nonlinear effects and the different amplitudes were used to simulate the soliton behaviors.The results indicated that the dispersed gradient scheme can simulate the solitons behaviors of the high order nonlinear Schrodinger equation very well and preserve the energy conservation of the Hamiltonian system better than the symplectic scheme.%提出了一种新的离散梯度法求解高阶非线性薛定谔方程.首先利用离散梯度法离散高阶非线性薛定谔方程,得到高阶非线性薛定谔方程的离散梯度格式,然后利用高阶非线性薛定谔方程的离散梯度格式和相应的辛格式,在不同饱和非线性效应和不同振辐下对孤立子进行数值模拟.数值结果表明,离散梯度格式能很好地模拟高阶非线性薛定谔方程中孤立子行为,比辛格式更好地保持Hamilton系统的能量.
采用DSP技术适用于任意色散媒质的FDTD方法研究%Frequency-Dependent FDTD Method Using DSP for Arbitrary Dispersive Media
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A new frequency dependent finite difference time domain (FD-FDTD) method using digital signal processing (DSP) is proposed.The dispersive media is characterized as an infinite-impulse response (IIR) filter, directly leading to FDTD equations. The representation of a dispersive medium is therefore converted to a problem of digital fIR design. It is shown that the numerical results are consistent with analytic solution.
Zheng, Jie-Ning; Li, Shan-Shan; Ma, Xiaohong; Chen, Fang-Yi; Wang, Ai-Jun; Chen, Jian-Rong; Feng, Jiu-Ju
2014-09-01
Well-defined core-shell gold-palladium@palladium nanocrystals (AuPd@Pd) are facilely prepared by a simple and green wet-chemical method at 25 °C. A Good's buffer, 2-[4-(2-hydroxyethyl)-1-piperazinyl] ethanesulfonic acid (HEPES), is used as a reducing agent and a shape-directing agent, while there is no template, seed, organic solvent, or surfactant involved. The AuPd@Pd nanocrystals are uniformly dispersed on graphene nanosheets by ultrasonication, resulting in the formation of graphene supported AuPd@Pd (G-AuPd@Pd). The as-prepared nanocomposites exhibit the improved catalytic activity, good tolerance, and better stability for oxygen reduction reaction (ORR) and methanol oxidation reaction (MOR) in alkaline media, compared with the G-Pd and commercial Pd black catalysts. The as-developed method may provide a promising pathway for large-scale fabrication of AuPd-based catalysts.
Itoh, Tomomichi; Fukutani, Kaori; Hino, Masato; Ihara, Eiji; Inoue, Kenzo
2009-02-15
The effects of polystyrene-b-poly(aminomethyl styrene) (PS(n)-b-PAMS(m)) stabilizers on the particle size (D(n)) and size distribution (PSD) in dispersion polymerization of styrene were investigated. The block copolymers, PS(n)-b-PAMS(m), were prepared as follows: (i) atom transfer radical polymerization (ATRP) of styrene (PS-Br), (ii) ATRP of vinylbenzylphthalimide with the PS-Br (PS-b-PVBP), and (iii) treatment of the PS-b-PVBP with hydrazine. When the dispersion polymerization of styrene proceeded at 60 degrees C in ethanol with PS(19)-b-PAMS(130) stabilizer, spherical polystyrene particles with D(n)=0.91 microm (PSD=1.01) were obtained. The particle size was strongly affected by the copolymer composition. With an increase in PAMS block length from m=54 to 100 in PS(17)-b-PAMS(m), particle diameter became smaller from 1.55 to 0.91 microm. On the other hand, an increase in the length from m=20 to 82 in PS(34)-b-PAMS(m)s caused an increase in particle size from 0.35 to 0.70 microm. Titration of the particles suggests that 14-81% of stabilizers used in the polymerization system were attached on the polystyrene particle surfaces, depending on the composition of the block copolymers. Thus, for the dispersion polymerization of styrene, PS(n)-b-PAMS(m) block copolymers have both functions as a stabilizer during polymerization and surface-modification sites of polystyrene particles.