Transient thermal effect, nonlinear refraction and nonlinear absorption properties of graphene oxide sheets in dispersion.

Science.gov (United States)

Zhang, Xiao-Liang; Liu, Zhi-Bo; Li, Xiao-Chun; Ma, Qiang; Chen, Xu-Dong; Tian, Jian-Guo; Xu, Yan-Fei; Chen, Yong-Sheng

2013-03-25

The nonlinear refraction (NLR) properties of graphene oxide (GO) in N, N-Dimethylformamide (DMF) was studied in nanosecond, picosecond and femtosecond time regimes by Z-scan technique. Results show that the dispersion of GO in DMF exhibits negative NLR properties in nanosecond time regime, which is mainly attributed to transient thermal effect in the dispersion. The dispersion also exhibits negative NLR in picosecond and femtosecond time regimes, which are arising from sp(2)- hybridized carbon domains and sp(3)- hybridized matrix in GO sheets. To illustrate the relations between NLR and nonlinear absorption (NLA), NLA properties of the dispersion were also studied in nanosecond, picosecond and femtosecond time regimes.

Solitonic Dispersive Hydrodynamics: Theory and Observation

Science.gov (United States)

Maiden, Michelle D.; Anderson, Dalton V.; Franco, Nevil A.; El, Gennady A.; Hoefer, Mark A.

2018-04-01

Ubiquitous nonlinear waves in dispersive media include localized solitons and extended hydrodynamic states such as dispersive shock waves. Despite their physical prominence and the development of thorough theoretical and experimental investigations of each separately, experiments and a unified theory of solitons and dispersive hydrodynamics are lacking. Here, a general soliton-mean field theory is introduced and used to describe the propagation of solitons in macroscopic hydrodynamic flows. Two universal adiabatic invariants of motion are identified that predict trapping or transmission of solitons by hydrodynamic states. The result of solitons incident upon smooth expansion waves or compressive, rapidly oscillating dispersive shock waves is the same, an effect termed hydrodynamic reciprocity. Experiments on viscous fluid conduits quantitatively confirm the soliton-mean field theory with broader implications for nonlinear optics, superfluids, geophysical fluids, and other dispersive hydrodynamic media.

Variational Boussinesq model for strongly nonlinear dispersive waves

NARCIS (Netherlands)

Lawrence, C.; Adytia, D.; van Groesen, E.

2018-01-01

For wave tank, coastal and oceanic applications, a fully nonlinear Variational Boussinesq model with optimized dispersion is derived and a simple Finite Element implementation is described. Improving a previous weakly nonlinear version, high waves over flat and varying bottom are shown to be

High-energy pulse compressor using self-defocusing spectral broadening in anomalously dispersive media

DEFF Research Database (Denmark)

2015-01-01

(3) with a net positive dispersion. Furthermore, the net positive dispersion in the dispersive unit at least partially compensates for the negative nonlinear phase variation and the negative group-velocity dispersion produced by the bulk quadratic nonlinear medium when the optical pulse passes......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 unit...

On the properties of two pulses propagating simultaneously in different dispersion regimes in a nonlinear planar waveguide

International Nuclear Information System (INIS)

Pietrzyk, M.E.

1999-02-01

Properties of two pulses propagating simultaneously in different dispersion regimes, anomalous and normal, in a Kerr-type planar waveguide are studied. It is found that the presence of the pulse propagating in normal dispersion regime can cause termination of catastrophic self-focusing of the pulse propagating in anomalous regime. It is also shown that the coupling between pulses can lead to spatio-temporal splitting of the pulse propagating in anomalous dispersion regime, but it does not lead to catastrophic self-focusing of the pulse propagating in normal dispersion regime. For the limiting case when the dispersive term of the pulse propagating in normal dispersion regime can be neglected an indication (based on the variational estimation) to a possibility of a stable self-trapped propagation of both pulses is obtained. This stabilization is similar to the one which was found earlier in media with saturation-type nonlinearity. (author)

Nonlinear evolution equations for waves in random media

International Nuclear Information System (INIS)

Pelinovsky, E.; Talipova, T.

1994-01-01

The scope of this paper is to highlight the main ideas of asymptotical methods applying in modern approaches of description of nonlinear wave propagation in random media. We start with the discussion of the classical conception of ''mean field''. Then an exactly solvable model describing nonlinear wave propagation in the medium with fluctuating parameters is considered in order to demonstrate that the ''mean field'' method is not correct. We develop new asymptotic procedures of obtaining the nonlinear evolution equations for the wave fields in random media. (author). 16 refs

Optimizing optical pre-dispersion using transmit DSP for mitigation of Kerr nonlinearities in dispersion managed cables

Science.gov (United States)

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.

Collisions of Two Spatial Solitons in Inhomogeneous Nonlinear Media

International Nuclear Information System (INIS)

Zhong Weiping; Yi Lin; Yang Zhengping; Xie Ruihua; Milivoj, Belic; Chen Goong

2008-01-01

Collisions of spatial solitons occurring in the nonlinear Schroeinger equation with harmonic potential are studied, using conservation laws and the split-step Fourier method. We find an analytical solution for the separation distance between the spatial solitons in an inhomogeneous nonlinear medium when the light beam is self-trapped in the transverse dimension. In the self-focusing nonlinear media the spatial solitons can be transmitted stably, and the interaction between spatial solitons is enhanced due to the linear focusing effect (and also diminished for the linear defocusing effect). In the self-defocusing nonlinear media, in the absence of self-trapping or in the presence of linear self-defocusing, no transmission of stable spatial solitons is possible. However, in such media the linear focusing effect can be exactly compensated, and the spatial solitons can propagate through

Wave modulation in a nonlinear dispersive medium

International Nuclear Information System (INIS)

Kim, Y.C.; Khadra, L.; Powers, E.J.

1980-01-01

A model describing the simultaneous amplitude and phase modulation of a carrier wave propagating in a nonlinear dispersive medium is developed in terms of nonlinear wave-wave interactions between the sidebands and a low frequency wave. It is also shown that the asymmetric distribution of sidebands is determined by the wavenumber dependence of the coupling coefficient. Digital complex demodulation techniques are used to study modulated waves in a weakly ionized plasma and the experimental results support the analytical model

The Whitham approach to dispersive shocks in systems with cubic–quintic nonlinearities

KAUST Repository

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.

The Whitham approach to dispersive shocks in systems with cubic–quintic nonlinearities

KAUST Repository

Crosta, M; Trillo, S; Fratalocchi, Andrea

2012-01-01

By employing a rigorous approach based on the Whitham modulation theory, we investigate dispersive shock waves arising in a high-order nonlinear Schrödinger equation with competing cubic and quintic nonlinear responses. This model finds important applications in both nonlinear optics and Bose–Einstein condensates. Our theory predicts the formation of dispersive shocks with totally controllable properties, encompassing both steering and compression effects. Numerical simulations confirm these results perfectly. Quite remarkably, shock tuning can be achieved in the regime of a very small high order, i.e. quintic, nonlinearity.

Polarization dependent dispersion and its impact on optical parametric process in high nonlinear microstructure fibre

International Nuclear Information System (INIS)

Xiao Li; Zhang Wei; Huang Yidong; Peng Jiangde

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 detunings are generated, while on the other axis with larger MI frequency detuning, SC is generated by soliton self-frequency shift

All-fiber nonlinearity- and dispersion-managed dissipative soliton nanotube mode-locked laser

Energy Technology Data Exchange (ETDEWEB)

Zhang, Z. [Department of Physics, Bilkent University, 06800 Ankara (Turkey); Nanjing University of Posts and Communications, Nanjing 210003 (China); Popa, D., E-mail: dp387@cam.ac.uk; Wittwer, V. J.; Milana, S.; Hasan, T.; Jiang, Z.; Ferrari, A. C. [Cambridge Graphene Centre, University of Cambridge, Cambridge CB3 0FA (United Kingdom); Ilday, F. Ö. [Department of Physics, Bilkent University, 06800 Ankara (Turkey); Department of Electrical and Electronics Engineering, Bilkent University, 06800 Ankara (Turkey)

2015-12-14

We report dissipative soliton generation from an Yb-doped all-fiber nonlinearity- and dispersion-managed nanotube mode-locked laser. A simple all-fiber ring cavity exploits a photonic crystal fiber for both nonlinearity enhancement and dispersion compensation. The laser generates stable dissipative solitons with large linear chirp in the net normal dispersion regime. Pulses that are 8.7 ps long are externally compressed to 118 fs, outperforming current nanotube-based Yb-doped fiber laser designs.

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 defoc...

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...

Nonlinear lattice waves in heterogeneous media

International Nuclear Information System (INIS)

Laptyeva, T V; Ivanchenko, M V; Flach, S

2014-01-01

We discuss recent advances in the understanding of the dynamics of nonlinear lattice waves in heterogeneous media, which enforce complete wave localization in the linear wave equation limit, especially Anderson localization for random potentials, and Aubry–André localization for quasiperiodic potentials. Additional nonlinear terms in the wave equations can either preserve the phase-coherent localization of waves, or destroy it through nonintegrability and deterministic chaos. Spreading wave packets are observed to show universal features in their dynamics which are related to properties of nonlinear diffusion equations. (topical review)

Dynamics of elliptic breathers in saturable nonlinear media with linear anisotropy

International Nuclear Information System (INIS)

Liang, Guo; Guo, Qi; Shou, Qian; Ren, Zhanmei

2014-01-01

We have introduced a class of dynamic elliptic breathers in saturable nonlinear media with linear anisotropy. Two kinds of evolution behavior for the dynamic breathers, rotations and molecule-like librations, are both predicted by the variational approach, and confirmed in numerical simulations. The dynamic elliptic breathers can rotate even though they have no initial orbital angular momentum (OAM). As the media are linear anisotropic, OAM is no longer conserved, and hence the angular velocity is not constant but a periodic function of the propagation distance. When the linear anisotropy is large enough, the dynamic elliptic breathers librate like molecules. The dynamic elliptic breathers are present in media with not only saturable nonlinearity but also nonlocal nonlinearity; indeed, they are universal in nonlinear media with linear anisotropy. (paper)

Model Equation for Acoustic Nonlinear Measurement of Dispersive Specimens at High Frequency

Science.gov (United States)

Zhang, Dong; Kushibiki, Junichi; Zou, Wei

2006-10-01

We present a theoretical model for acoustic nonlinearity measurement of dispersive specimens at high frequency. The nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation governs the nonlinear propagation in the SiO2/specimen/SiO2 multi-layer medium. The dispersion effect is considered in a special manner by introducing the frequency-dependant sound velocity in the KZK equation. Simple analytic solutions are derived by applying the superposition technique of Gaussian beams. The solutions are used to correct the diffraction and dispersion effects in the measurement of acoustic nonlinearity of cottonseed oil in the frequency range of 33-96 MHz. Regarding two different ultrasonic devices, the accuracies of the measurements are improved to ±2.0% and ±1.3% in comparison with ±9.8% and ±2.9% obtained from the previous plane wave model.

Special discontinuities in nonlinearly elastic media

Science.gov (United States)

Chugainova, A. P.

2017-06-01

Solutions of a nonlinear hyperbolic system of equations describing weakly nonlinear quasitransverse waves in a weakly anisotropic elastic medium are studied. The influence of small-scale processes of dissipation and dispersion is investigated. The small-scale processes determine the structure of discontinuities (shocks) and a set of discontinuities with a stationary structure. Among the discontinuities with a stationary structure, there are special ones that, in addition to relations following from conservation laws, satisfy additional relations required for the existence of their structure. In the phase plane, the structure of such discontinuities is represented by an integral curve joining two saddles. Special discontinuities lead to nonunique self-similar solutions of the Riemann problem. Asymptotics of non-self-similar problems for equations with dissipation and dispersion are found numerically. These asymptotics correspond to self-similar solutions of the problems.

Measurement of the Acoustic Nonlinearity Parameter for Biological Media.

Science.gov (United States)

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.

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.

Green function formalism for nonlinear acoustic waves in layered media

International Nuclear Information System (INIS)

Lobo, A.; Tsoy, E.; De Sterke, C.M.

2000-01-01

Full text: The applications of acoustic waves in identifying defects in adhesive bonds between metallic plates have received little attention at high intensities where the media respond nonlinearly. However, the effects of reduced bond strength are more distinct in the nonlinear response of the structure. Here we assume a weak nonlinearity acting as a small perturbation, thereby reducing the problem to a linear one. This enables us to develop a specialized Green function formalism for calculating acoustic fields in layered media

Computer modelling of contaminant migration in natural disperse media

International Nuclear Information System (INIS)

Kundas, S.P.; Gishkelyuk, I.A.; Khil'ko, O.S.

2012-01-01

The theoretical foundations for modeling of the contaminants migration in natural disperses media taking into account interconnected heat and moisture transport are developed. The calculation of mass transfer parameters based on adsorption isotherms of water and thermodynamic equations in the developed mathematical models. The artificial neural networks use to predict migration of contaminants in natural disperse media is proposed. The developed software package is presented and results of practical application of models and software are discussed. (authors)

Modulation stability and optical soliton solutions of nonlinear Schrödinger equation with higher order dispersion and nonlinear terms and its applications

Science.gov (United States)

Arshad, Muhammad; Seadawy, Aly R.; Lu, Dianchen

2017-12-01

In optical fibers, the higher order non-linear Schrödinger equation (NLSE) with cubic quintic nonlinearity describes the propagation of extremely short pulses. We constructed bright and dark solitons, solitary wave and periodic solitary wave solutions of generalized higher order NLSE in cubic quintic non Kerr medium by applying proposed modified extended mapping method. These obtained solutions have key applications in physics and mathematics. Moreover, we have also presented the formation conditions on solitary wave parameters in which dark and bright solitons can exist for this media. We also gave graphically the movement of constructed solitary wave and soliton solutions, that helps to realize the physical phenomena's of this model. The stability of the model in normal dispersion and anomalous regime is discussed by using the modulation instability analysis, which confirms that all constructed solutions are exact and stable. Many other such types of models arising in applied sciences can also be solved by this reliable, powerful and effective method.

Nonlinear Dispersive Elastic Waves in Solids: Exact, Approximate, and Numerical Solutions

Science.gov (United States)

Khajehtourian, Romik

Wave motion lies at the heart of many disciplines in the physical sciences and engineering. For example, problems and applications involving light, sound, heat, or fluid flow are all likely to involve wave dynamics at some level. A particular class of problems is concerned with the propagation of elastic waves in a solid medium, such as a fiber-reinforced composite material responding to vibratory excitations, or soil and rock admitting seismic waves moments after the onset of an earthquake, or phonon transport in a semiconducting crystal like silicon. Regardless of the type of wave, the dispersion relation provides a fundamental characterization of the elastodynamic properties of the medium. The first part of the dissertation examines the propagation of a large-amplitude elastic wave in a one-dimensional homogeneous medium with a focus on the effects of inherent nonlinearities on the dispersion relation. Considering a thin rod, where the thickness is small compared to the wavelength, an exact, closed-form formulation is presented for the treatment of two types of nonlinearity in the strain-displacement gradient relation: Green-Lagrange and Hencky. The derived relation is then verified by direct time-domain simulations, examining both instantaneous dispersion (by direct observation) and short-term, pre-breaking dispersion (by Fourier transformation). A high-order perturbation analysis is also conducted yielding an explicit analytical space-time solution, which is shown to be spectrally accurate. The results establish a perfect match between theory and simulation and reveal that regardless of the strength of the nonlinearity, the dispersion relation fully embodies all information pertaining to the nonlinear harmonic generation mechanism that unfolds as an arbitrary-profiled wave evolves in the medium. In the second part of the dissertation, the analysis is extended to a continuous periodic thin rod exhibiting multiple phases or embedded local resonators. The

Exact solution to the problem of nonlinear pulse propagation through random layered media and its connection with number triangles

International Nuclear Information System (INIS)

Sokolow, Adam; Sen, Surajit

2007-01-01

An energy pulse refers to a spatially compact energy bundle. In nonlinear pulse propagation, the nonlinearity of the relevant dynamical equations could lead to pulse propagation that is nondispersive or weakly dispersive in space and time. Nonlinear pulse propagation through layered media with widely varying pulse transmission properties is not wave-like and a problem of broad interest in many areas such as optics, geophysics, atmospheric physics and ocean sciences. We study nonlinear pulse propagation through a semi-infinite sequence of layers where the layers can have arbitrary energy transmission properties. By assuming that the layers are rigid, we are able to develop exact expressions for the backscattered energy received at the surface layer. The present study is likely to be relevant in the context of energy transport through soil and similar complex media. Our study reveals a surprising connection between the problem of pulse propagation and the number patterns in the well known Pascal's and Catalan's triangles and hence provides an analytic benchmark in a challenging problem of broad interest. We close with comments on the relationship between this study and the vast body of literature on the problem of wave localization in disordered systems

Controllable behaviours of rogue wave triplets in the nonautonomous nonlinear and dispersive system

International Nuclear Information System (INIS)

Dai Chaoqing; Tian Qing; Zhu Shiqun

2012-01-01

A similarity transformation connecting the variable coefficient nonlinear Schrödinger equation with the standard nonlinear Schrödinger equation is constructed. The self-similar rogue wave triplet solutions (rational solutions) are analytically obtained for the nonautonomous nonlinear and dispersive system. The controllable behaviours of rogue wave triplets in two typical soliton management systems are discussed. In the exponential dispersion decreasing fibre, three kinds of rogue wave triplets with controllable behaviours are analysed. In the periodic distributed system, the rogue wave triplets recur periodically in the form of a cluster. (paper)

Dispersive shock waves in nonlinear and atomic optics

Directory of Open Access Journals (Sweden)

Kamchatnov Anatoly

2017-01-01

Full Text Available A brief review is given of dispersive shock waves observed in nonlinear optics and dynamics of Bose-Einstein condensates. The theory of dispersive shock waves is developed on the basis of Whitham modulation theory for various situations taking place in these two fields. In particular, the full classification is established for types of wave structures evolving from initial discontinuities for propagation of long light pulses in fibers with account of steepening effect and for dynamics of the polarization mode in two-component Bose-Einstein condensates.

Landau fluid model for weakly nonlinear dispersive magnetohydrodynamics

International Nuclear Information System (INIS)

Passot, T.; Sulem, P. L.

2005-01-01

In may astrophysical plasmas such as the solar wind, the terrestrial magnetosphere, or in the interstellar medium at small enough scales, collisions are negligible. When interested in the large-scale dynamics, a hydrodynamic approach is advantageous not only because its numerical simulations is easier than of the full Vlasov-Maxwell equations, but also because it provides a deep understanding of cross-scale nonlinear couplings. It is thus of great interest to construct fluid models that extended the classical magnetohydrodynamic (MHD) equations to collisionless situations. Two ingredients need to be included in such a model to capture the main kinetic effects: finite Larmor radius (FLR) corrections and Landau damping, the only fluid-particle resonance that can affect large scales and can be modeled in a relatively simple way. The Modelization of Landau damping in a fluid formalism is hardly possible in the framework of a systematic asymptotic expansion and was addressed mainly by means of parameter fitting in a linearized setting. We introduced a similar Landau fluid model but, that has the advantage of taking dispersive effects into account. This model properly describes dispersive MHD waves in quasi-parallel propagation. Since, by construction, the system correctly reproduces their linear dynamics, appropriate tests should address the nonlinear regime. In a first case, we show analytically that the weakly nonlinear modulational dynamics of quasi-parallel propagating Alfven waves is well captured. As a second test we consider the parametric decay instability of parallel Alfven waves and show that numerical simulations of the dispersive Landau fluid model lead to results that closely match the outcome of hybrid simulations. (Author)

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...

Numerical study of propagation properties of surface plasmon polaritons in nonlinear media

KAUST Repository

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.

Solitons in plasma and other dispersive media

International Nuclear Information System (INIS)

Ichikawa, Y.H.; Wadati, Miki.

1977-03-01

A review is given to recent development of extensive studies of nonlinear waves with purpose of showing methods of systematic analysis of nonlinear phenomena has been now established on the basis of new concept ''soliton''. Firstly, characteristic properties of various kinds of solitons are discussed with illustration of typical nonlinear evolution equations. Brief discussions are also given to basic mechanisms which ensure the remarkable stability and individuality of solitons. The reductive perturbation theory is a key method to reduce a given nonlinear system to a soliton system. Introductory survey is presented for an example of ionic mode in plasmas, although the method can be applied to any dispersive medium. Central subject of the present review is the analytical methods of solving nonlinear evolution equations. The inverse method, the Beacklund transformation and the conservation laws are discussed to emphasize that very firm analytical basis is now available to disentangle the nonlinear problems. Finally, a notion of ''dressed'' solitons is introduced on basis of the higher order analysis of the reductive perturbation theory. In spite of the fact that success is restricted so far only for the one dimensional system, the achievement of soliton physics encourages us to face dawn of nonlinear physics with a confident expectation for forthcoming break through in the field. (auth.)

Nonlinear Poisson equation for heterogeneous media.

Science.gov (United States)

Hu, Langhua; Wei, Guo-Wei

2012-08-22

The Poisson equation is a widely accepted model for electrostatic analysis. However, the Poisson equation is derived based on electric polarizations in a linear, isotropic, and homogeneous dielectric medium. This article introduces a nonlinear Poisson equation to take into consideration of hyperpolarization effects due to intensive charges and possible nonlinear, anisotropic, and heterogeneous media. Variational principle is utilized to derive the nonlinear Poisson model from an electrostatic energy functional. To apply the proposed nonlinear Poisson equation for the solvation analysis, we also construct a nonpolar solvation energy functional based on the nonlinear Poisson equation by using the geometric measure theory. At a fixed temperature, the proposed nonlinear Poisson theory is extensively validated by the electrostatic analysis of the Kirkwood model and a set of 20 proteins, and the solvation analysis of a set of 17 small molecules whose experimental measurements are also available for a comparison. Moreover, the nonlinear Poisson equation is further applied to the solvation analysis of 21 compounds at different temperatures. Numerical results are compared to theoretical prediction, experimental measurements, and those obtained from other theoretical methods in the literature. A good agreement between our results and experimental data as well as theoretical results suggests that the proposed nonlinear Poisson model is a potentially useful model for electrostatic analysis involving hyperpolarization effects. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Collapse arrest and soliton stabilization in nonlocal nonlinear media

DEFF Research Database (Denmark)

Bang, Ole; Krolikowski, Wieslaw; Wyller, John

2002-01-01

that nonlocality of the nonlinearity prevents collapse in, e.g., Bose-Einstein condensates and optical Kerr media in all physical dimensions. The nonlocal nonlinear response must be symmetric and have a positive definite Fourier spectrum, but can otherwise be of completely arbitrary shape and degree of nonlocality...

The effect of quintic nonlinearity on the propagation characteristics of dispersion managed optical solitons

International Nuclear Information System (INIS)

Konar, S.; Mishra, Manoj; Jana, S.

2006-01-01

The role of quintic nonlinearity on the propagation characteristics of optical solitons in dispersion managed optical communication systems has been presented in this paper. It has been shown that quintic nonlinearity has only marginal influence on single pulse propagation. However, numerical simulation has been undertaken to reveal that quintic nonlinearity reduces collision distance between neighbouring pulses of the same channel. It is found that for lower map strength the collapse distance between intra channel pulses is very much sensitive to the dispersion map strength

The effect of inertially viscous interphase interaction on the acoustic characteristics of disperse media

International Nuclear Information System (INIS)

Vladimir S Fedotovsky; Tatiana N Vereshchagina; Alexey V Derbenev

2005-01-01

Full text of publication follows: The vibratory-wave dynamics of disperse media with uniformly distributed spherical and ellipsoidal inclusions is considered on the basis of the concept of effective dynamic properties. The notions of effective dynamic density and translation viscosity taking account of the effects of the inertial and viscous interaction of liquid and disperse inclusions are introduced. The effective dynamic properties governing the process of wave propagation in disperse media depend both on the density, viscosity and concentration of components and on the form and orientation of inclusions. It is shown that for disperse media with inclusions as oblate ellipsoids of rotation the effective dynamic density takes the maximum value, whereas for the medium with inclusions as extended ellipsoids - the minimum one. The dynamic density of the medium with spherical inclusions takes the intermediate value. Based on the offered concept, the relations for sound velocity and attenuation in disperse media are derived. It is shown that the acoustic characteristics of disperse media essentially depend on the form of the ellipsoidal inclusions and their orientation relative to the direction of wave propagation. (authors)

An assessment of first-order stochastic dispersion theories in porous media

Science.gov (United States)

Chin, David A.

1997-12-01

Random realizations of three-dimensional exponentially correlated hydraulic conductivity fields are used in a finite-difference numerical flow model to calculate the mean and covariance of the corresponding Lagrangian-velocity fields. The dispersivity of the porous medium is then determined from the Lagrangian-velocity statistics using the Taylor definition. This estimation procedure is exact, except for numerical errors, and the results are used to assess the accuracy of various first-order dispersion theories in both isotropic and anisotropic porous media. The results show that the Dagan theory is by far the most robust in both isotropic and anisotropic media, producing accurate values of the principal dispersivity components for σy as high as 1.0, In the case of anisotropic media where the flow is at an angle to the principal axis of hydraulic conductivity, it is shown that the dispersivity tensor is rotated away from the flow direction in the non-Fickian phase, but eventually coincides with the flow direction in the Fickian phase.

Waves and Structures in Nonlinear Nondispersive Media General Theory and Applications to Nonlinear Acoustics

CERN Document Server

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...

Self-action of few-cycle pulses in a dispersive medium

International Nuclear Information System (INIS)

Balakin, A. A.; Litvak, A. G.; Mironov, V. A.; Skobelev, S. A.

2009-01-01

Basing on the nonlinear wave equation as the reflection-free approximation, we study the self-focusing dynamics of laser pulses under rather general assumptions about media dispersion. The methods for qualitative investigation of the self-action dynamics of ultrashort pulses are developed. It is shown that a new effect here is steepening of the longitudinal pulse profile, which is determined by the dependence of group velocity on the amplitude. Results of numerical simulation in media without dispersion and with anomalous dispersion confirm the conclusion about outrunning formation of a shock wave during pulse self-focusing. The formation of a power spectrum of the field, which is characteristic for a shock wave, is retained also when medium ionization is taken into account. In the case of a normal-dispersion medium, nonlinear dispersion leads to a violation of the symmetry in the longitudinal splitting of the pulse in the process of self-focusing. The possibility of tuning of the optical-pulse frequency into the short-wave area is shown for the pulse self-action near the zero-dispersion point.

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...

Propagation of dispersion-nonlinearity-managed solitons in an inhomogeneous erbium-doped fiber system

International Nuclear Information System (INIS)

Mahalingam, A; Porsezian, K; Mani Rajan, M S; Uthayakumar, A

2009-01-01

In this paper, a generalized nonlinear Schroedinger-Maxwell-Bloch model with variable dispersion and nonlinearity management functions, which describes the propagation of optical pulses in an inhomogeneous erbium-doped fiber system under certain restrictive conditions, is under investigation. We derive the Lax pair with a variable spectral parameter and the exact soliton solution is generated from the Baecklund transformation. It is observed that stable solitons are possible only under a very restrictive condition for the spectral parameter and other inhomogeneous functions. For various forms of the inhomogeneous dispersion, nonlinearity and gain/loss functions, construction of different types of solitary waves like classical solitons, breathers, etc is discussed

Stability of Bragg grating solitons in a cubic-quintic nonlinear medium with dispersive reflectivity

International Nuclear Information System (INIS)

Dasanayaka, Sahan; Atai, Javid

2010-01-01

We investigate the existence and stability of Bragg grating solitons in a cubic-quintic medium with dispersive reflectivity. It is found that the model supports two disjoint families of solitons. One family can be viewed as the generalization of the Bragg grating solitons in Kerr nonlinearity with dispersive reflectivity. On the other hand, the quintic nonlinearity is dominant in the other family. Stability regions are identified by means of systematic numerical stability analysis. In the case of the first family, the size of the stability region increases up to moderate values of dispersive reflectivity. However for the second family (i.e. region where quintic nonlinearity dominates), the size of the stability region increases even for strong dispersive reflectivity. For all values of m, there exists a subset of the unstable solitons belonging to the first family for which the instability development leads to deformation and subsequent splitting of the soliton into two moving solitons with different amplitudes and velocities.

Surface-wave solitons between linear media and nonlocal nonlinear media

International Nuclear Information System (INIS)

Shi Zhiwei; Li Huagang; Guo Qi

2011-01-01

We address surface solitons at the interface between linear media and nonlocal nonlinear media in the presence of a discontinuity in refractive index at the surface of these two materials. We investigated the influence of the degree of nonlocality on the stability, energy flow, and full width at half-maximum of the surface wave solitons. It is shown that surface solitons will be stable only if the degree of nonlocality exceeds a critical value. We find that the refractive index difference can affect the power distribution of the surface solitons in the two media. Also, different boundary values at the interface can lead to different relative peak positions of the surface solitons. However, neither the refractive index nor the boundary conditions can affect the stability of the solitons, for a given degree of nonlocality.

High-order FDTD methods for transverse electromagnetic systems in dispersive inhomogeneous media.

Science.gov (United States)

Zhao, Shan

2011-08-15

This Letter introduces a novel finite-difference time-domain (FDTD) formulation for solving transverse electromagnetic systems in dispersive media. Based on the auxiliary differential equation approach, the Debye dispersion model is coupled with Maxwell's equations to derive a supplementary ordinary differential equation for describing the regularity changes in electromagnetic fields at the dispersive interface. The resulting time-dependent jump conditions are rigorously enforced in the FDTD discretization by means of the matched interface and boundary scheme. High-order convergences are numerically achieved for the first time in the literature in the FDTD simulations of dispersive inhomogeneous media. © 2011 Optical Society of America

The nonlinear effects on the characteristics of gravity wave packets: dispersion and polarization relations

Directory of Open Access Journals (Sweden)

S.-D. Zhang

2000-10-01

Full Text Available By analyzing the results of the numerical simulations of nonlinear propagation of three Gaussian gravity-wave packets in isothermal atmosphere individually, the nonlinear effects on the characteristics of gravity waves are studied quantitatively. The analyses show that during the nonlinear propagation of gravity wave packets the mean flows are accelerated and the vertical wavelengths show clear reduction due to nonlinearity. On the other hand, though nonlinear effects exist, the time variations of the frequencies of gravity wave packets are close to those derived from the dispersion relation and the amplitude and phase relations of wave-associated disturbance components are consistent with the predictions of the polarization relation of gravity waves. This indicates that the dispersion and polarization relations based on the linear gravity wave theory can be applied extensively in the nonlinear region.Key words: Meteorology and atmospheric dynamics (middle atmosphere dynamics; waves and tides

Laser beam propagation in nonlinear optical media

CERN Document Server

Guha, Shekhar

2013-01-01

""This is very unique and promises to be an extremely useful guide to a host of workers in the field. They have given a generalized presentation likely to cover most if not all situations to be encountered in the laboratory, yet also highlight several specific examples that clearly illustrate the methods. They have provided an admirable contribution to the community. If someone makes their living by designing lasers, optical parametric oscillators or other devices employing nonlinear crystals, or designing experiments incorporating laser beam propagation through linear or nonlinear media, then

Nonlinear Wave Propagation and Solitary Wave Formation in Two-Dimensional Heterogeneous Media

KAUST Repository

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.

Theory of Nonlinear Dispersive Waves and Selection of the Ground State

International Nuclear Information System (INIS)

Soffer, A.; Weinstein, M.I.

2005-01-01

A theory of time-dependent nonlinear dispersive equations of the Schroedinger or Gross-Pitaevskii and Hartree type is developed. The short, intermediate and large time behavior is found, by deriving nonlinear master equations (NLME), governing the evolution of the mode powers, and by a novel multitime scale analysis of these equations. The scattering theory is developed and coherent resonance phenomena and associated lifetimes are derived. Applications include Bose-Einstein condensate large time dynamics and nonlinear optical systems. The theory reveals a nonlinear transition phenomenon, 'selection of the ground state', and NLME predicts the decay of excited state, with half its energy transferred to the ground state and half to radiation modes. Our results predict the recent experimental observations of Mandelik et al. in nonlinear optical waveguides

Gas Dispersion in Granular Porous Media under Air-Dry and Wet Conditions

DEFF Research Database (Denmark)

Naveed, Muhammad; Hamamoto, S; Kawamoto, K

2012-01-01

Subsurface gaseous-phase transport is governed by three gas transport parameters: the air permeability coefficient (ka), gas diffusion coefficient (DP), and gas dispersion coefficient (DH). Among these, DH is the least understood due to hitherto limited research into the relationship between gas...... dispersion and soil physical characteristics. In this study, a series of advection–dispersion experiments was performed on granular porous media to identify the effects of soil column dimensions (length and diameter), particle size and shape, dry bulk density, and moisture content on the magnitude of gas...... dispersion. Glass beads and various sands of different shapes (angular and rounded) with mean particle diameters (d50) ranging from 0.19 to 1.51 mm at both air-dry and variable moisture contents were used as granular porous media. Gas dispersion coefficients and gas dispersivities (a = DH/v, where v...

Spiraling solitons and multipole localized modes in nonlocal nonlinear media

International Nuclear Information System (INIS)

Buccoliero, Daniel; Lopez-Aguayo, Servando; Skupin, Stefan; Desyatnikov, Anton S.; Bang, Ole; Krolikowski, Wieslaw; Kivshar, Yuri S.

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 different 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

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....

Numerical study of propagation properties of surface plasmon polaritons in nonlinear media

KAUST Repository

Sagor, Rakibul Hasan; Ghulam Saber, Md.; Alsunaidi, Mohammad

2016-01-01

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

Analysis and classification of nonlinear dispersive evolution equations in the potential representation

International Nuclear Information System (INIS)

Eichmann, U.A.; Draayer, J.P.; Ludu, A.

2002-01-01

A potential representation for the subset of travelling solutions of nonlinear dispersive evolution equations is introduced. The procedure involves reduction of a third-order partial differential equation to a first-order ordinary differential equation. The potential representation allows us to deduce certain properties of the solutions without the actual need to solve the underlying evolution equation. In particular, the paper deals with the so-called K(n, m) equations. Starting from their respective potential representations it is shown that these equations can be classified according to a simple point transformation. As a result, e.g., all equations with linear dispersion join the same equivalence class with the Korteweg-deVries equation being its representative, and all soliton solutions of higher order nonlinear equations are thus equivalent to the KdV soliton. Certain equations with both linear and quadratic dispersions can also be treated within this equivalence class. (author)

Dispersive Evolution of Nonlinear Fast Magnetoacoustic Wave Trains

Energy Technology Data Exchange (ETDEWEB)

Pascoe, D. J.; Goddard, C. R.; Nakariakov, V. M., E-mail: D.J.Pascoe@warwick.ac.uk [Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick, Coventry CV4 7AL (United Kingdom)

2017-10-01

Quasi-periodic rapidly propagating wave trains are frequently observed in extreme ultraviolet observations of the solar corona, or are inferred by the quasi-periodic modulation of radio emission. The dispersive nature of fast magnetohydrodynamic waves in coronal structures provides a robust mechanism to explain the detected quasi-periodic patterns. We perform 2D numerical simulations of impulsively generated wave trains in coronal plasma slabs and investigate how the behavior of the trapped and leaky components depend on the properties of the initial perturbation. For large amplitude compressive perturbations, the geometrical dispersion associated with the waveguide suppresses the nonlinear steepening for the trapped wave train. The wave train formed by the leaky components does not experience dispersion once it leaves the waveguide and so can steepen and form shocks. The mechanism we consider can lead to the formation of multiple shock fronts by a single, large amplitude, impulsive event and so can account for quasi-periodic features observed in radio spectra.

Propagation of hypergeometric Gaussian beams in strongly nonlocal nonlinear media

Science.gov (United States)

Tang, Bin; Bian, Lirong; Zhou, Xin; Chen, Kai

2018-01-01

Optical vortex beams have attracted lots of interest due to its potential application in image processing, optical trapping and optical communications, etc. In this work, we theoretically and numerically investigated the propagation properties of hypergeometric Gaussian (HyGG) beams in strongly nonlocal nonlinear media. Based on the Snyder-Mitchell model, analytical expressions for propagation of the HyGG beams in strongly nonlocal nonlinear media were obtained. The influence of input power and optical parameters on the evolutions of the beam width and radius of curvature is illustrated, respectively. The results show that the beam width and radius of curvature of the HyGG beams remain invariant, like a soliton when the input power is equal to the critical power. Otherwise, it varies periodically like a breather, which is the result of competition between the beam diffraction and nonlinearity of the medium.

Fast light in atomic media

International Nuclear Information System (INIS)

Akulshin, Alexander M; McLean, Russell J

2010-01-01

Atomic media have played a major role in studies of fast light. One of their attractive features is the ability to manipulate experimental parameters to control the dispersive properties that determine the group velocity of a propagating light pulse. We give an overview of the experimental methods, based on both linear and nonlinear atom–light interaction, that have produced superluminal propagation in atomic media, and discuss some of the significant theoretical contributions to the issues of pulse preservation and reconciling faster-than-light propagation and the principle of causality. The comparison of storage of light, enhanced Kerr nonlinearity and efficient wave mixing processes in slow and fast light atomic media illustrates their common and distinct features. (review article)

Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses.

Science.gov (United States)

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.

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

We introduce a new stabilized high-order and unstructured numerical model for modeling fully nonlinear and dispersive water waves. The model is based on a nodal spectral element method of arbitrary order in space and a -transformed formulation due to Cai, Langtangen, Nielsen and Tveito (1998). In...

Nanospikes functionalization as a universal strategy to disperse hydrophilic particles in non-polar media

Science.gov (United States)

Hang, Tian; Chen, Hui-Jiuan; Wang, Ji; Lin, Di-an; Wu, Jiangming; Liu, Di; Cao, Yuhong; Yang, Chengduan; Liu, Chenglin; Xiao, Shuai; Gu, Meilin; Pan, Shuolin; Wu, Mei X.; Xie, Xi

2018-05-01

Dispersion of hydrophilic particles in non-polar media has many important applications yet remains difficult. Surfactant or amphiphilic functionalization was conventionally applied to disperse particles but is highly dependent on the particle/solvent system and may induce unfavorable effects and impact particle hydrophilic nature. Recently 2 μm size polystyrene microbeads coated with ZnO nanospikes have been reported to display anomalous dispersity in phobic media without using surfactant or amphiphilic functionalization. However, due to the lack of understanding whether this phenomenon was applicable to a wider range of conditions, little application has been derived from it. Here the anomalous dispersity phenomenons of hydrophilic microparticles covered with nanospikes were systematically assessed at various conditions including different particle sizes, material compositions, particle morphologies, solvent hydrophobicities, and surface polar groups. Microparticles were functionalized with nanospikes through hydrothermal route, followed by dispersity test in hydrophobic media. The results suggest nanospikes consistently prevent particle aggregation in various particle or solvent conditions, indicating the universal applicability of the anomalous dispersion phenomenons. This work provides insight on the anomalous dispersity of hydrophilic particles in various systems and offers potential application to use this method for surfactant-free dispersions.

Impact of local diffusion on macroscopic dispersion in three-dimensional porous media

Science.gov (United States)

Dartois, Arthur; Beaudoin, Anthony; Huberson, Serge

2018-02-01

While macroscopic longitudinal and transverse dispersion in three-dimensional porous media has been simulated previously mostly under purely advective conditions, the impact of diffusion on macroscopic dispersion in 3D remains an open question. Furthermore, both in 2D and 3D, recurring difficulties have been encountered due to computer limitation or analytical approximation. In this work, we use the Lagrangian velocity covariance function and the temporal derivative of second-order moments to study the influence of diffusion on dispersion in highly heterogeneous 2D and 3D porous media. The first approach characterizes the correlation between the values of Eulerian velocity components sampled by particles undergoing diffusion at two times. The second approach allows the estimation of dispersion coefficients and the analysis of their behaviours as functions of diffusion. These two approaches allowed us to reach new results. The influence of diffusion on dispersion seems to be globally similar between highly heterogeneous 2D and 3D porous media. Diffusion induces a decrease in the dispersion in the direction parallel to the flow direction and an increase in the dispersion in the direction perpendicular to the flow direction. However, the amplification of these two effects with the permeability variance is clearly different between 2D and 3D. For the direction parallel to the flow direction, the amplification is more important in 3D than in 2D. It is reversed in the direction perpendicular to the flow direction.

Nonlinear waves in waveguides with stratification

CERN Document Server

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.

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.

The nonlinear Schrödinger equation and the propagation of weakly nonlinear waves in optical fibers and on the water surface

Energy Technology Data Exchange (ETDEWEB)

Chabchoub, A., E-mail: achabchoub@swin.edu.au [Centre for Ocean Engineering Science and Technology, Swinburne University of Technology, Hawthorn, Victoria 3122 (Australia); Kibler, B.; Finot, C.; Millot, G. [Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB), UMR 6303 CNRS, Université de Bourgogne, 21078 Dijon (France); Onorato, M. [Dipartimento di Fisica, Università degli Studi di Torino, Torino 10125 (Italy); Istituto Nazionale di Fisica Nucleare, INFN, Sezione di Torino, Torino 10125 (Italy); Dudley, J.M. [Institut FEMTO-ST, UMR 6174 CNRS- Université de Franche-Comté, 25030 Besançon (France); Babanin, A.V. [Centre for Ocean Engineering Science and Technology, Swinburne University of Technology, Hawthorn, Victoria 3122 (Australia)

2015-10-15

The dynamics of waves in weakly nonlinear dispersive media can be described by the nonlinear Schrödinger equation (NLSE). An important feature of the equation is that it can be derived in a number of different physical contexts; therefore, analogies between different fields, such as for example fiber optics, water waves, plasma waves and Bose–Einstein condensates, can be established. Here, we investigate the similarities between wave propagation in optical Kerr media and water waves. In particular, we discuss the modulation instability (MI) in both media. In analogy to the water wave problem, we derive for Kerr-media the Benjamin–Feir index, i.e. a nondimensional parameter related to the probability of formation of rogue waves in incoherent wave trains.

Walking solitons in quadratic nonlinear media

OpenAIRE

Torner Sabata, Lluís; Mazilu, D; Mihalache, Dumitru

1996-01-01

We study self-action of light in parametric wave interactions in nonlinear quadratic media. We show the existence of stationary solitons in the presence of Poynting vector beam walk-off or different group velocities between the waves. We discover that the new solitons constitute a two-parameter family, and they exist for different wave intensities and transverse velocities. We discuss the properties of the walking solitons and their experimental implications. Peer Reviewed

Effect of water content on dispersion of transferred solute in unsaturated porous media

Energy Technology Data Exchange (ETDEWEB)

Latrille, C. [CEA Saclay, DEN/DANS/DPC/SECR/L3MR, 91191 Gif sur Yvette (France)

2013-07-01

Estimating contaminant migration in the context of waste disposal and/or environmental remediation of polluted soils requires a complete understanding of the underlying transport processes. In unsaturated porous media, water content impacts directly on porous solute transfer. Depending on the spatial distribution of water content, the flow pathway is more complex than in water saturated media. Dispersivity is consequently dependent on water content. Non-reactive tracer experiments performed using unsaturated sand columns confirm the dependence of dispersivity with pore velocity; moreover, a power law relationship between dispersivity and water content is evidenced. (authors)

Pseudospectral modeling and dispersion analysis of Rayleigh waves in viscoelastic media

Science.gov (United States)

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

FDTD scattered field formulation for scatterers in stratified dispersive media.

Science.gov (United States)

Olkkonen, Juuso

2010-03-01

We introduce a simple scattered field (SF) technique that enables finite difference time domain (FDTD) modeling of light scattering from dispersive objects residing in stratified dispersive media. The introduced SF technique is verified against the total field scattered field (TFSF) technique. As an application example, we study surface plasmon polariton enhanced light transmission through a 100 nm wide slit in a silver film.

Solitary excitations in discrete two-dimensional nonlinear Schrodinger models with dispersive dipole-dipole interactions

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...

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.

Three-dimensional solutions in media with spatial dependence of nonlinear refractive index

International Nuclear Information System (INIS)

Kovachev, L.M.; Kaymakanova, N.I.; Dakova, D.Y.; Pavlov, L.I.; Donev, S.G.; Pavlov, R.L.

2004-01-01

We investigate a nonparaxial vector generalization of the scalar 3D+1 Nonlinear Schrodinger Equation (NSE). Exact analytical 3D+1 soliton solutions are obtained for the first time in media of spatial dependence of the nonlinear refractive index

Dispersion of the resonant second order nonlinearity in 2D semiconductors probed by femtosecond continuum pulses

Directory of Open Access Journals (Sweden)

Mohammad Mokim

2017-10-01

Full Text Available We demonstrate an effective microspectroscopy technique by tracing the dispersion of second order nonlinear susceptibility (χ(2 in a monolayer tungsten diselenide (WSe2. The χ(2 dispersion obtained with better than 3 meV photon energy resolution showed peak value being within 6.3-8.4×10-19 m2/V range. We estimate the fundamental bandgap to be at 2.2 eV. Sub-structure in the χ(2 dispersion reveals a contribution to the nonlinearity due to exciton transitions with exciton binding energy estimated to be at 0.7 eV.

An explicit MOT scheme for solving the TD-EFVIE on nonlinear and dispersive scatterers

KAUST Repository

Sayed, Sadeed Bin; Ulku, H. Arda; Bagci, Hakan

2017-01-01

An explicit marching-on-in-time (MOT) scheme for solving the time domain electric field volume integral equation (TD-EFVIE) on nonlinear and dispersive scatterers is described. The unknown electric field intensity, electric flux density, and polarization densities representing Kerr nonlinearity along with Lorentz dispersion relation, all of which are induced inside the scatterer upon excitation, are expanded using half and full Schaubert-Wilton-Glisson functions in space. The TD-EFVIE and the constitutive relations between polarization, field, and flux terms are cast in the form of a first-order ordinary differential equation. The resulting matrix system is integrated in time using a predictor-corrector scheme to obtain the time dependent unknown expansion coefficients. The resulting MOT scheme is explicit and accounts for nonlinearity by simple function evaluations.

An explicit MOT scheme for solving the TD-EFVIE on nonlinear and dispersive scatterers

KAUST Repository

Sayed, Sadeed Bin

2017-10-25

An explicit marching-on-in-time (MOT) scheme for solving the time domain electric field volume integral equation (TD-EFVIE) on nonlinear and dispersive scatterers is described. The unknown electric field intensity, electric flux density, and polarization densities representing Kerr nonlinearity along with Lorentz dispersion relation, all of which are induced inside the scatterer upon excitation, are expanded using half and full Schaubert-Wilton-Glisson functions in space. The TD-EFVIE and the constitutive relations between polarization, field, and flux terms are cast in the form of a first-order ordinary differential equation. The resulting matrix system is integrated in time using a predictor-corrector scheme to obtain the time dependent unknown expansion coefficients. The resulting MOT scheme is explicit and accounts for nonlinearity by simple function evaluations.

Nonlinear left-handed transmission line metamaterials

International Nuclear Information System (INIS)

Kozyrev, A B; Weide, D W van der

2008-01-01

Metamaterials, exhibiting simultaneously negative permittivity ε and permeability μ, more commonly referred to as left-handed metamaterials (LHMs) and also known as negative-index materials, have received substantial attention in the scientific and engineering communities [1]. Most studies of LHMs (and electromagnetic metamaterials in general) have been in the linear regime of wave propagation and have already inspired new types of microwave circuits and devices. The results of these studies have already been the subject of numerous reviews and books. This review covers a less explored but rapidly developing area of investigation involving media that combine nonlinearity (dependence of the permittivity and permeability on the magnitude of the propagating field) with the anomalous dispersion exhibited by LHM. The nonlinear phenomena in such media will be considered on the example of a model system: the nonlinear left-handed transmission line. These nonlinear phenomena include parametric generation and amplification, harmonic and subharmonic generation as well as modulational instabilities and envelope solitons. (topical review)

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

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...

Global-local nonlinear model reduction for flows in heterogeneous porous media

KAUST Repository

AlOtaibi, Manal; Calo, Victor M.; Efendiev, Yalchin R.; Galvis, Juan; Ghommem, Mehdi

2015-01-01

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.

Global-local nonlinear model reduction for flows in heterogeneous porous media

KAUST Repository

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.

Exact bright and dark spatial soliton solutions in saturable nonlinear media

International Nuclear Information System (INIS)

Calvo, Gabriel F.; Belmonte-Beitia, Juan; Perez-Garcia, Victor M.

2009-01-01

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.

Cross-phase modulation instability in optical fibres with exponential saturable nonlinearity and high-order dispersion

International Nuclear Information System (INIS)

Xian-Qiong, Zhong; An-Ping, Xiang

2010-01-01

Utilizing the linear-stability analysis, this paper analytically investigates and calculates the condition and gain spectra of cross-phase modulation instability in optical fibres in the case of exponential saturable nonlinearity and high-order dispersion. The results show that, the modulation instability characteristics here are similar to those of conventional saturable nonlinearity and Kerr nonlinearity. That is to say, when the fourth-order dispersion has the same sign as that of the second-order one, a new gain spectral region called the second one which is far away from the zero point may appear. The existence of the exponential saturable nonlinearity will make the spectral width as well as the peak gain of every spectral region increase with the input powers before decrease. Namely, for every spectral regime, this may lead to a unique value of peak gain and spectral width for two different input powers. In comparison with the case of conventional saturable nonlinearity, however, when the other parameters are the same, the variations of the spectral width and the peak gain with the input powers will be faster in case of exponential saturable nonlinearity. (classical areas of phenomenology)

Nonlinear waves and weak turbulence

CERN Document Server

Zakharov, V E

1997-01-01

This book is a collection of papers on dynamical and statistical theory of nonlinear wave propagation in dispersive conservative media. Emphasis is on waves on the surface of an ideal fluid and on Rossby waves in the atmosphere. Although the book deals mainly with weakly nonlinear waves, it is more than simply a description of standard perturbation techniques. The goal is to show that the theory of weakly interacting waves is naturally related to such areas of mathematics as Diophantine equations, differential geometry of waves, Poincaré normal forms, and the inverse scattering method.

Traveling waves in a delayed SIR model with nonlocal dispersal and nonlinear incidence

Science.gov (United States)

Zhang, Shou-Peng; Yang, Yun-Rui; Zhou, Yong-Hui

2018-01-01

This paper is concerned with traveling waves of a delayed SIR model with nonlocal dispersal and a general nonlinear incidence. The existence and nonexistence of traveling waves of the system are established respectively by Schauder's fixed point theorem and two-sided Laplace transform. It is also shown that the spread speed c is influenced by the dispersal rate of the infected individuals and the delay τ.

Dispersion of Nanomaterials in Aqueous Media: Towards Protocol Optimization.

Science.gov (United States)

Kaur, Inder; Ellis, Laura-Jayne; Romer, Isabella; Tantra, Ratna; Carriere, Marie; Allard, Soline; Mayne-L'Hermite, Martine; Minelli, Caterina; Unger, Wolfgang; Potthoff, Annegret; Rades, Steffi; Valsami-Jones, Eugenia

2017-12-25

The sonication process is commonly used for de-agglomerating and dispersing nanomaterials in aqueous based media, necessary to improve homogeneity and stability of the suspension. In this study, a systematic step-wise approach is carried out to identify optimal sonication conditions in order to achieve a stable dispersion. This approach has been adopted and shown to be suitable for several nanomaterials (cerium oxide, zinc oxide, and carbon nanotubes) dispersed in deionized (DI) water. However, with any change in either the nanomaterial type or dispersing medium, there needs to be optimization of the basic protocol by adjusting various factors such as sonication time, power, and sonicator type as well as temperature rise during the process. The approach records the dispersion process in detail. This is necessary to identify the time points as well as other above-mentioned conditions during the sonication process in which there may be undesirable changes, such as damage to the particle surface thus affecting surface properties. Our goal is to offer a harmonized approach that can control the quality of the final, produced dispersion. Such a guideline is instrumental in ensuring dispersion quality repeatability in the nanoscience community, particularly in the field of nanotoxicology.

Explicit solutions of two nonlinear dispersive equations with variable coefficients

International Nuclear Information System (INIS)

Lai Shaoyong; Lv Xiumei; Wu Yonghong

2008-01-01

A mathematical technique based on an auxiliary equation and the symbolic computation system Matlab is developed to construct the exact solutions for a generalized Camassa-Holm equation and a nonlinear dispersive equation with variable coefficients. It is shown that the variable coefficients of the derivative terms in the equations cause the qualitative change in the physical structures of the solutions

Time-domain simulation of constitutive relations for nonlinear acoustics including relaxation for frequency power law attenuation media modeling

Science.gov (United States)

Jiménez, Noé; Camarena, Francisco; Redondo, Javier; Sánchez-Morcillo, Víctor; Konofagou, Elisa E.

2015-10-01

We report a numerical method for solving the constitutive relations of nonlinear acoustics, where multiple relaxation processes are included in a generalized formulation that allows the time-domain numerical solution by an explicit finite differences scheme. Thus, the proposed physical model overcomes the limitations of the one-way Khokhlov-Zabolotskaya-Kuznetsov (KZK) type models and, due to the Lagrangian density is implicitly included in the calculation, the proposed method also overcomes the limitations of Westervelt equation in complex configurations for medical ultrasound. In order to model frequency power law attenuation and dispersion, such as observed in biological media, the relaxation parameters are fitted to both exact frequency power law attenuation/dispersion media and also empirically measured attenuation of a variety of tissues that does not fit an exact power law. Finally, a computational technique based on artificial relaxation is included to correct the non-negligible numerical dispersion of the finite difference scheme, and, on the other hand, improve stability trough artificial attenuation when shock waves are present. This technique avoids the use of high-order finite-differences schemes leading to fast calculations. The present algorithm is especially suited for practical configuration where spatial discontinuities are present in the domain (e.g. axisymmetric domains or zero normal velocity boundary conditions in general). The accuracy of the method is discussed by comparing the proposed simulation solutions to one dimensional analytical and k-space numerical solutions.

A discontinuous Galerkin approach for conservative modeling of fully nonlinear and weakly dispersive wave transformations

Science.gov (United States)

Sharifian, Mohammad Kazem; Kesserwani, Georges; Hassanzadeh, Yousef

2018-05-01

This work extends a robust second-order Runge-Kutta Discontinuous Galerkin (RKDG2) method to solve the fully nonlinear and weakly dispersive flows, within a scope to simultaneously address accuracy, conservativeness, cost-efficiency and practical needs. The mathematical model governing such flows is based on a variant form of the Green-Naghdi (GN) equations decomposed as a hyperbolic shallow water system with an elliptic source term. Practical features of relevance (i.e. conservative modeling over irregular terrain with wetting and drying and local slope limiting) have been restored from an RKDG2 solver to the Nonlinear Shallow Water (NSW) equations, alongside new considerations to integrate elliptic source terms (i.e. via a fourth-order local discretization of the topography) and to enable local capturing of breaking waves (i.e. via adding a detector for switching off the dispersive terms). Numerical results are presented, demonstrating the overall capability of the proposed approach in achieving realistic prediction of nearshore wave processes involving both nonlinearity and dispersion effects within a single model.

Dispersive effects on multicomponent transport through porous media

Science.gov (United States)

Dutta, Sourav; Daripa, Prabir

2017-11-01

We use a hybrid numerical method to solve a global pressure based porous media flow model of chemical enhanced oil recovery. This is an extension of our recent work. The numerical method is based on the use of a discontinuous finite element method and the modified method of characteristics. The impact of molecular diffusion and mechanical dispersion on the evolution of scalar concentration distributions are studied through numerical simulations of various flooding schemes. The relative importance of the advective, capillary diffusive and dispersive fluxes are compared over different flow regimes defined in the parameter space of Capillary number, Peclet number, longitudinal and transverse dispersion coefficients. Such studies are relevant for the design of effective injection policies and determining optimal combinations of chemical components for improving recovery. This work has been possible due to financial support from the U.S. National Science Foundation Grant DMS-1522782.

Optical fibers with low nonlinearity and low polarization-mode dispersion for terabit communications

Science.gov (United States)

Baghdadi, J. A.; Safaai-Jazi, A.; Hattori, H. T.

2001-07-01

Refractive-index nonlinearities have negligible effect on the performance of short-haul fiber-optic communication links utilizing electronic repeaters. However, in long links, nonlinearities can cause severe signal degradations. To mitigate nonlinear effects, a new generation of fibers, referred to as large effective-area fibers, have been introduced in recent years. This paper reviews the latest research and development work on these fibers conducted by several research groups around the world. Attention is focused on a class of large effective-area fibers that are based on a depressed-core multiple-cladding design. Another important issue in long-haul and high capacity fiber optic systems is the polarization-mode dispersion (PMD) which has been recognized as a serious limiting factor. In this paper, an improved fiber design is proposed which, in addition to providing large effective-area and low bending loss, eliminates PMD due to elliptical deformation in the single-mode wavelength region. Furthermore, this design is allowed to provide a small chromatic dispersion about few ps/ nm km , in order to overcome four-wave mixing effects.

Stable one-dimensional periodic waves in Kerr-type saturable and quadratic nonlinear media

International Nuclear Information System (INIS)

Kartashov, Yaroslav V; Egorov, Alexey A; Vysloukh, Victor A; Torner, Lluis

2004-01-01

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

Numerical studies on the electromagnetic properties of the nonlinear Lorentz Computational model for the dielectric media

International Nuclear Information System (INIS)

Abe, H.; Okuda, H.

1994-06-01

We study linear and nonlinear properties of a new computer simulation model developed to study the propagation of electromagnetic waves in a dielectric medium in the linear and nonlinear regimes. The model is constructed by combining a microscopic model used in the semi-classical approximation for the dielectric media and the particle model developed for the plasma simulations. It is shown that the model may be useful for studying linear and nonlinear wave propagation in the dielectric media

Modelling solute dispersion in periodic heterogeneous porous media: Model benchmarking against intermediate scale experiments

Science.gov (United States)

Majdalani, Samer; Guinot, Vincent; Delenne, Carole; Gebran, Hicham

2018-06-01

This paper is devoted to theoretical and experimental investigations of solute dispersion in heterogeneous porous media. Dispersion in heterogenous porous media has been reported to be scale-dependent, a likely indication that the proposed dispersion models are incompletely formulated. A high quality experimental data set of breakthrough curves in periodic model heterogeneous porous media is presented. In contrast with most previously published experiments, the present experiments involve numerous replicates. This allows the statistical variability of experimental data to be accounted for. Several models are benchmarked against the data set: the Fickian-based advection-dispersion, mobile-immobile, multirate, multiple region advection dispersion models, and a newly proposed transport model based on pure advection. A salient property of the latter model is that its solutions exhibit a ballistic behaviour for small times, while tending to the Fickian behaviour for large time scales. Model performance is assessed using a novel objective function accounting for the statistical variability of the experimental data set, while putting equal emphasis on both small and large time scale behaviours. Besides being as accurate as the other models, the new purely advective model has the advantages that (i) it does not exhibit the undesirable effects associated with the usual Fickian operator (namely the infinite solute front propagation speed), and (ii) it allows dispersive transport to be simulated on every heterogeneity scale using scale-independent parameters.

Multipole surface solitons supported by the interface between linear media and nonlocal nonlinear media

International Nuclear Information System (INIS)

Shi, Zhiwei; Li, Huagang; Guo, Qi

2012-01-01

We address multipole surface solitons occurring at the interface between a linear medium and a nonlocal nonlinear medium. We show the impact of nonlocality, the propagation constant, and the linear index difference of two media on the properties of the surface solitons. We find that there exist a threshold value of the degree of the nonlocality at the same linear index difference of two media, only when the degree of the nonlocality goes beyond the value, the multipole surface solitons can be stable. -- Highlights: ► We show the impact of nonlocality and the linear index difference of two media on the properties of the surface solitons. ► For the surface solitons, only when the degree of the nonlocality goes beyond a threshold value, they can be stable. ► The number of poles and the index difference of two media can all influence the threshold value.

Nonlinear hydromagnetic Rayleigh-Taylor instability for strong viscous fluids in porous media

CERN Document Server

El-Dib, Y O

2003-01-01

In the present work a weakly nonlinear stability for magnetic fluid is discussed. The research of an interface between two strong viscous homogeneous incompressible fluids through porous medium is investigated theoretically and graphically. The effect of the vertical magnetic field has been demonstrated in this study. The linear form of equation of motion is solved in the light of the nonlinear boundary conditions. The boundary value problem leads to construct nonlinear characteristic equation having complex coefficients in elevation function. The nonlinearity is kept to third-order expansion. The nonlinear characteristic equation leads to derive the well-known nonlinear Schroedinger equation. This equation having complex coefficients of the disturbance amplitude varies in both space and time. Stability criteria have been performed for nonlinear Chanderasekhar dispersion relation including the porous effects. Stability conditions are discussed through the assumption of equal kinematic viscosity. The calculati...

Ultra-flattened nearly-zero dispersion and ultrahigh nonlinear slot silicon photonic crystal fibers with ultrahigh birefringence

Science.gov (United States)

Liao, Jianfei; Xie, Yingmao; Wang, Xinghua; Li, Dongbo; Huang, Tianye

2017-07-01

A slot silicon photonic crystal fiber (PCF) is proposed to simultaneously achieve ultrahigh birefringence, large nonlinearity and ultra-flattened nearly-zero dispersion over a wide wavelength range. By taking advantage on the slot effect, ultrahigh birefringence up to 0.0736 and ultrahigh nonlinear coefficient up to 211.48 W-1 m-1 for quasi-TE mode can be obtained at the wavelength of 1.55 μm. Moreover, ultra-flattened dispersion of 0.49 ps/(nm km) for quasi-TE mode can be achieved over a 180 nm wavelength range with low dispersion slope of 1.85 × 10-3 ps/(nm2 km) at 1.55 μm. Leveraging on these advantages, the proposed slot PCF has great potential for efficient all-optical signal processing applications.

Observation and measurement of interaction-induced dispersive optical nonlinearities in an ensemble of cold rydberg atoms

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...

Model-based dispersive wave processing: A recursive Bayesian solution

International Nuclear Information System (INIS)

Candy, J.V.; Chambers, D.H.

1999-01-01

Wave propagation through dispersive media represents a significant problem in many acoustic applications, especially in ocean acoustics, seismology, and nondestructive evaluation. In this paper we propose a propagation model that can easily represent many classes of dispersive waves and proceed to develop the model-based solution to the wave processing problem. It is shown that the underlying wave system is nonlinear and time-variable requiring a recursive processor. Thus the general solution to the model-based dispersive wave enhancement problem is developed using a Bayesian maximum a posteriori (MAP) approach and shown to lead to the recursive, nonlinear extended Kalman filter (EKF) processor. The problem of internal wave estimation is cast within this framework. The specific processor is developed and applied to data synthesized by a sophisticated simulator demonstrating the feasibility of this approach. copyright 1999 Acoustical Society of America.

Dielectric dispersion of porous media as a fractal phenomenon

Science.gov (United States)

Thevanayagam, S.

1997-09-01

It is postulated that porous media is made up of fractal solid skeleton structure and fractal pore surface. The model thus developed satisfies measured anomalous dielectric behavior of three distinctly different porous media: kaolin, montmorillonite, and shaly sand rock. It is shown that the underlying mechanism behind dielectric dispersion in the kHz range to high MHz range is indeed Maxwell-Wagner mechanism but modified to take into account the multiphase nature of the porous media as opposed to the traditional two-phase Maxwell-Wagner charge accumulation effect. The conductivity of the surface water associated with the solid surface and charge accumulation across the surface irregularities, asperity, and bridging between particles at the micro-scale-level pores are shown to contribute to this modified Maxwell-Wagner mechanism. The latter is dominant at low frequencies. The surface water thickness is calculated to be about 2-6 nm for a variety of porous media.

Stochastic theory of polarized light in nonlinear birefringent media: An application to optical rotation

Science.gov (United States)

Tsuchida, Satoshi; Kuratsuji, Hiroshi

2018-05-01

A stochastic theory is developed for the light transmitting the optical media exhibiting linear and nonlinear birefringence. The starting point is the two-component nonlinear Schrödinger equation (NLSE). On the basis of the ansatz of “soliton” solution for the NLSE, the evolution equation for the Stokes parameters is derived, which turns out to be the Langevin equation by taking account of randomness and dissipation inherent in the birefringent media. The Langevin equation is converted to the Fokker-Planck (FP) equation for the probability distribution by employing the technique of functional integral on the assumption of the Gaussian white noise for the random fluctuation. The specific application is considered for the optical rotation, which is described by the ellipticity (third component of the Stokes parameters) alone: (i) The asymptotic analysis is given for the functional integral, which leads to the transition rate on the Poincaré sphere. (ii) The FP equation is analyzed in the strong coupling approximation, by which the diffusive behavior is obtained for the linear and nonlinear birefringence. These would provide with a basis of statistical analysis for the polarization phenomena in nonlinear birefringent media.

Optical tsunamis: shoaling of shallow water rogue waves in nonlinear fibers with normal dispersion

International Nuclear Information System (INIS)

Wabnitz, Stefan

2013-01-01

In analogy with ocean waves running up towards the beach, shoaling of pre-chirped 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 Schrödinger 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. (paper)

Self-transparency effects in heterogeneous nonlinear scattering media and their possible use in lasers

International Nuclear Information System (INIS)

Al'tshuler, G.B.; Ermolaev, V.S.; Krylov, K.I.; Manenkov, A.A.; Prokhorov, A.M.

1986-01-01

Transmission of intense laser beams through heterogeneous scattering media is considered. Effects of intensity limitation, self-recovery of the wave front of a transmitted beam, and bistable reflection associated with the laser-induced self-transparency (suppression of scattering) of such media are predicted because of the compensation of the linear refractive-index difference Δn/sub L/ of the heterocomponents of a medium by nonlinear change Δn/sub N//sub L/ for different mechanisms of nonlinearity. Applications of these effects in lasers for Q switching and mode locking are discussed. The observation of self-transparency effects in several heterogeneous media (glass particles in toluene and nitrobenzene, and lead molybdenite powder) for cw Ar- and pulsed Nd- and CO 2 -laser radiation is reported. Q switching and mode locking have also been demonstrated with a YAG:Nd laser using nonlinear scattering in a heterogeneous cell as a control element in a laser resonator

Strongly nonlinear evolution of low-frequency wave packets in a dispersive plasma

Science.gov (United States)

Vasquez, Bernard J.

1993-01-01

The evolution of strongly nonlinear, strongly modulated wave packets is investigated in a dispersive plasma using a hybrid numerical code. These wave packets have amplitudes exceeding the strength of the external magnetic field, along which they propagate. Alfven (left helicity) wave packets show strong steepening for p Schrodinger (DNLS) equation.

Dispersive shock waves in Bose-Einstein condensates and nonlinear nano-oscillators in ferromagnetic thin films

Science.gov (United States)

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

A conservative numerical scheme for modeling nonlinear acoustic propagation in thermoviscous homogeneous media

Science.gov (United States)

Diaz, Manuel A.; Solovchuk, Maxim A.; Sheu, Tony W. H.

2018-06-01

A nonlinear system of partial differential equations capable of describing the nonlinear propagation and attenuation of finite amplitude perturbations in thermoviscous media is presented. This system constitutes a full nonlinear wave model that has been formulated in the conservation form. Initially, this model is investigated analytically in the inviscid limit where it has been found that the resulting flux function fulfills the Lax-Wendroff theorem, and the scheme can match the solutions of the Westervelt and Burgers equations numerically. Here, high-order numerical descriptions of strongly nonlinear wave propagations become of great interest. For that matter we consider finite difference formulations of the weighted essentially non-oscillatory (WENO) schemes associated with explicit strong stability preserving Runge-Kutta (SSP-RK) time integration methods. Although this strategy is known to be computationally demanding, it is found to be effective when implemented to be solved in graphical processing units (GPUs). As we consider wave propagations in unbounded domains, perfectly matching layers (PML) have been also considered in this work. The proposed system model is validated and illustrated by using one- and two-dimensional benchmark test cases proposed in the literature for nonlinear acoustic propagation in homogeneous thermoviscous media.

Elastic Nonlinear Response in Granular Media Under Resonance Conditions

Science.gov (United States)

Jia, X.; Johnson, P. A.

2004-12-01

We are studying the elastic linear and nonlinear behavior of granular media using dynamic wave methods. In the work presented here, our goal is to quantify the elastic nonlinear response by applying wave resonance. Resonance studies are desirable because they provide the means to easily study amplitude dependencies of elastic nonlinear behavior and thus to characterize the physical nature of the elastic nonlinearity. This work has implications for a variety of topics, in particular, the in situ nonlinear response of surface sediments. For this work we constructed an experimental cell in which high sensitivity dynamic resonance studies were conducted using granular media under controlled effective pressure. We limit our studies here to bulk modes but have the capability to employ shear waves as well. The granular media are composed of glass beads held under pressure by a piston, while applying resonance waves from transducers as both the excitation and the material probe. The container is closed with two fitted pistons and a normal load is applied to the granular sample across the top piston. Force and displacement are measured directly. Resonant frequency sweeps with frequencies corresponding to the fundamental bulk mode are applied to the longitudinal source transducer. The pore pressure in the system is 1 atm. The glass beads used in our experiments are of diameter 0.5 mm, randomly deposited in a duralumin cylinder of diameter 30 mm and height of 15 mm. This corresponds to a granular skeleton acoustic wave velocity of v ª 750m/s under 50 N of force [0.07 Mpa]. The loaded system gives fundamental mode resonances in the audio frequency band at half a wavelength where resonance frequency is effective-pressure dependent. The volume fraction of glass beads thus obtained is found to be 0.63 ± 0.01. Plane-wave generating and detecting transducers of diameter 30 mm are placed on axis at the top and bottom of the cylindrical container in direct contact with the glass

Hypersonic flow past slender bodies in dispersive hydrodynamics

International Nuclear Information System (INIS)

El, G.A.; Khodorovskii, V.V.; Tyurina, A.V.

2004-01-01

The problem of two-dimensional steady hypersonic flow past a slender body is formulated for dispersive media. It is shown that for the hypersonic flow, the original 2+0 boundary-value problem is asymptotically equivalent to the 1+1 piston problem for the fully nonlinear flow in the same physical system, which allows one to take advantage of the analytic methods developed for one-dimensional systems. This type of equivalence, well known in ideal Euler gas dynamics, has not been established for dispersive hydrodynamics so far. Two examples pertaining to collisionless plasma dynamics are considered

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...

Numerical studies on soliton propagation in the dielectric media by the nonlinear Lorentz computational model

International Nuclear Information System (INIS)

Abe, H.; Okuda, H.

1994-06-01

Soliton propagation in the dielectric media has been simulated by using the nonlinear Lorentz computational model, which was recently developed to study the propagation of electromagnetic waves in a linear and a nonlinear dielectric. The model is constructed by combining a microscopic model used in the semi-classical approximation for dielectric media and the particle model developed for the plasma simulations. The carrier wave frequency is retained in the simulation so that not only the envelope of the soliton but also its phase can be followed in time. It is shown that the model may be useful for studying pulse propagation in the dielectric media

Mass-polariton theory of light in dispersive media

Science.gov (United States)

Partanen, Mikko; Tulkki, Jukka

2017-12-01

We have recently shown that the electromagnetic pulse in a medium is made of mass-polariton (MP) quasiparticles, which are quantized coupled states of the field and an atomic mass density wave (MDW) [M. Partanen et al., Phys. Rev. A 95, 063850 (2017), 10.1103/PhysRevA.95.063850]. In this work, we generalize the MP theory of light for dispersive media assuming that absorption and scattering losses are very small. Following our previous work, we present two different approaches to the coupled state of light: (1) the MP quasiparticle theory, which is derived by only using the fundamental conservation laws and the Lorentz transformation; (2) the classical optoelastic continuum dynamics (OCD), which is a generalization of the electrodynamics of continuous media to include the dynamics of the medium under the influence of optical forces. We show that the total momentum and the transferred mass of the light pulse can be determined in a straightforward way if we know the field energy of the pulse and the dispersion relation of the medium. In analogy to the nondispersive case, we also find unambiguous correspondence between the MP and OCD theories. For the coupled MP state of a single photon and the medium, we obtain the total MP momentum pMP=npℏ ω /c , where np is the phase refractive index. The field's share of the MP momentum is equal to pfield=ℏ ω /(ngc ) , where ng is the group refractive index and the share of the MDW is equal to pMDW=pMP-pfield . Thus, as in a nondispersive medium, the total momentum of the MP is equal to the Minkowski momentum and the field's share of the momentum is equal to the Abraham momentum. We also show that the correspondence between the MP and OCD models and the conservation of momentum at interfaces gives an unambiguous formula for the optical force. The dynamics of the light pulse and the related MDW lead to nonequilibrium of the medium and to relaxation of the atomic density by sound waves in the same way as for nondispersive media

The instability of nonlinear surface waves in an electrified liquid jet

International Nuclear Information System (INIS)

Moatimid, Galal M

2009-01-01

We investigate the weakly nonlinear stability of surface waves of a liquid jet. In this work, the liquids are uniformly streaming through two porous media and the gravitational effects are neglected. The system is acted upon by a uniform tangential electric field, that is parallel to the jet axis. The equations of motion are linearly treated and solved in the light of nonlinear boundary conditions. Therefore, the boundary-value problem leads to a nonlinear characteristic second-order differential equation. This characterized equation has a complex nature. The nonlinearity is kept up to the third degree. It is used to judge the behavior of the surface evolution. According to the linear stability theory, we derive the dispersion relation that accounts for the growth waves. The stability criterion is discussed analytically and a stability picture is identified for a chosen sample system. Several special cases are recovered upon appropriate data choices. In order to derive the Ginsburg-Landau equation for the general case, in the nonlinear approach, we used the method of multiple timescales with the aid of the Taylor expansion. This equation describes the competition between nonlinearity and the linear dispersion relation. As a special case for non-porous media where there is no streaming, we obtained the well-known nonlinear Schroedinger equation as it has been derived by others. The stability criteria are expressed theoretically in terms of various parameters of the problem. Stability diagrams are obtained for a set of physical parameters. We found new instability regions in the parameter space. These regions are due to the nonlinear effects.

Nanoparticle dispersion in environmentally relevant culture media: a TiO2 case study and considerations for a general approach

International Nuclear Information System (INIS)

Horst, Allison M.; Ji, Zhaoxia; Holden, Patricia A.

2012-01-01

Nanoparticle exposure in toxicity studies requires that nanoparticles are bioavailable by remaining highly dispersed in culture media. However, reported dispersion approaches are variable, mostly study-specific, and not transferable owing to their empirical basis. Furthermore, many published approaches employ proteinaceous dispersants in rich laboratory media, both of which represent end members in environmental scenarios. Here, a systematic approach was developed to disperse initially agglomerated TiO 2 nanoparticles (Aeroxide® TiO 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.

Stabilization of the Peregrine soliton and Kuznetsov-Ma breathers by means of nonlinearity and dispersion management

Science.gov (United States)

Cuevas-Maraver, J.; Malomed, Boris A.; Kevrekidis, P. G.; Frantzeskakis, D. J.

2018-04-01

We demonstrate a possibility to make rogue waves (RWs) in the form of the Peregrine soliton (PS) and Kuznetsov-Ma breathers (KMBs) effectively stable objects, with the help of properly defined dispersion or nonlinearity management applied to the continuous-wave (CW) background supporting the RWs. In particular, it is found that either management scheme, if applied along the longitudinal coordinate, making the underlying nonlinear Schrödinger equation (NLSE) self-defocusing in the course of disappearance of the PS, indeed stabilizes the global solution with respect to the modulational instability of the background. In the process, additional excitations are generated, namely, dispersive shock waves and, in some cases, also a pair of slowly separating dark solitons. Further, the nonlinearity-management format, which makes the NLSE defocusing outside of a finite domain in the transverse direction, enables the stabilization of the KMBs, in the form of confined oscillating states. On the other hand, a nonlinearity-management format applied periodically along the propagation direction, creates expanding patterns featuring multiplication of KMBs through their cascading fission.

Effects of weak nonlinearity on dispersion relations and frequency band-gaps of periodic structures

DEFF Research Database (Denmark)

Sorokin, Vladislav; Thomsen, Jon Juel

2015-01-01

of these for nonlinear problems is impossible or cumbersome, since Floquet theory is applicable for linear systems only. Thus the nonlinear effects for periodic structures are not yet fully uncovered, while at the same time applica-tions may demand effects of nonlinearity on structural response to be accounted for....... The present work deals with analytically predicting dynamic responses for nonlinear continuous elastic periodic structures. Specifically, the effects of weak nonlinearity on the dispersion re-lation and frequency band-gaps of a periodic Bernoulli-Euler beam performing bending os-cillations are analyzed......The analysis of the behaviour of linear periodic structures can be traced back over 300 years, to Sir Isaac Newton, and still attracts much attention. An essential feature of periodic struc-tures is the presence of frequency band-gaps, i.e. frequency ranges in which waves cannot propagate...

Forty-five degree backscattering-mode nonlinear absorption imaging in turbid media.

Science.gov (United States)

Cui, Liping; Knox, Wayne H

2010-01-01

Two-color nonlinear absorption imaging has been previously demonstrated with endogenous contrast of hemoglobin and melanin in turbid media using transmission-mode detection and a dual-laser technology approach. For clinical applications, it would be generally preferable to use backscattering mode detection and a simpler single-laser technology. We demonstrate that imaging in backscattering mode in turbid media using nonlinear absorption can be obtained with as little as 1-mW average power per beam with a single laser source. Images have been achieved with a detector receiving backscattered light at a 45-deg angle relative to the incoming beams' direction. We obtain images of capillary tube phantoms with resolution as high as 20 microm and penetration depth up to 0.9 mm for a 300-microm tube at SNR approximately 1 in calibrated scattering solutions. Simulation results of the backscattering and detection process using nonimaging optics are demonstrated. A Monte Carlo-based method shows that the nonlinear signal drops exponentially as the depth increases, which agrees well with our experimental results. Simulation also shows that with our current detection method, only 2% of the signal is typically collected with a 5-mm-radius detector.

Nonlinear light-matter interactions in engineered optical media

Science.gov (United States)

Litchinitser, Natalia

In this talk, we consider fundamental optical phenomena at the interface of nonlinear and singular optics in artificial media, including theoretical and experimental studies of linear and nonlinear light-matter interactions of vector and singular optical beams in metamaterials. We show that unique optical properties of metamaterials open unlimited prospects to ``engineer'' light itself. Thanks to their ability to manipulate both electric and magnetic field components, metamaterials open new degrees of freedom for tailoring complex polarization states and orbital angular momentum (OAM) of light. We will discuss several approaches to structured light manipulation on the nanoscale using metal-dielectric, all-dielectric and hyperbolic metamaterials. These new functionalities, including polarization and OAM conversion, beam magnification and de-magnification, and sub-wavelength imaging using novel non-resonant hyperlens are likely to enable a new generation of on-chip or all-fiber structured light applications. The emergence of metamaterials also has a strong potential to enable a plethora of novel nonlinear light-matter interactions and even new nonlinear materials. In particular, nonlinear focusing and defocusing effects are of paramount importance for manipulation of the minimum focusing spot size of structured light beams necessary for nanoscale trapping, manipulation, and fundamental spectroscopic studies. Colloidal suspensions offer as a promising platform for engineering polarizibilities and realization of large and tunable nonlinearities. We will present our recent studies of the phenomenon of spatial modulational instability leading to laser beam filamentation in an engineered soft-matter nonlinear medium. Finally, we introduce so-called virtual hyperbolic metamaterials formed by an array of plasma channels in air as a result of self-focusing of an intense laser pulse, and show that such structure can be used to manipulate microwave beams in a free space. This

Stationary walking solitons in bulk quadratic nonlinear media

OpenAIRE

Mihalache, Dumitru; Mazilu, D; Crasonavn, L C; Torner Sabata, Lluís

1997-01-01

We study the mutual trapping of fundamental and second-harmonic light beams propagating in bulk quadratic nonlinear media in the presence of Poynting vector beam walk-off. We show numerically the existence of a two-parameter family of (2 + 1)-dimensional stationary, spatial walking solitons. We have found that the solitons exist at various values of material parameters with different wave intensities and soliton velocities. We discuss the differences between (2 + 1) and (1 + 1)-dimensional wa...

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.

Effect of pore size distribution and flow segregation on dispersion in porous media

International Nuclear Information System (INIS)

Carbonell, R.G.

1978-11-01

In order to study the effect of the pore size distribution and flow segregation on dispersion in a porous media, the dispersion of solute in an array of parallel pores is considered. Equations are obtained for the dispersion coefficient in laminar and turbulent flow, as a function of the particle Peclet number. The theory fits quite well cumulative experimental data from various researchers in the Peclet number range from 10 -3 to 10 6 . The model also predicts some trends, backed by experimental data, regarding the effect of particle size, particle size distribution and fluid velocity on dispersion

Large time behaviour of oscillatory nonlinear solute transport in porous media

NARCIS (Netherlands)

Duijn, van C.J.; Zee, van der S.E.A.T.M.

2018-01-01

Oscillations in flow occur under many different situations in natural porous media, due to tidal, daily or seasonal patterns. In this paper, we investigate how such oscillations in flow affect the transport of an initially sharp solute front, if the solute undergoes nonlinear sorption and,

An analysis of superluminal propagation becoming subluminal in highly dispersive media

Science.gov (United States)

Nanda, L.

2018-05-01

In this article the time-moments of the Poynting vector associated with an electromagnetic pulse are used to characterize the traversal time and the pulse width as the pulse propagates through highly dispersive media. The behaviour of these quantities with propagation distance is analyzed in two physical cases: Lorentz absorptive medium, and Raman gain doublet amplifying medium. It is found that the superluminal pulse propagation in these two cases with anomalous dispersion is always accompanied by pulse compression and eventually the pulse becomes subluminal with increasing distance of propagation.

Defect solitons in saturable nonlinearity media with parity-time symmetric optical lattices

Energy Technology Data Exchange (ETDEWEB)

Hu, Sumei [Department of Physics, Guangdong University of Petrochemical Technology, Maoming 525000 (China); Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, Guangzhou 510631 (China); Hu, Wei, E-mail: huwei@scnu.edu.cn [Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, Guangzhou 510631 (China)

2013-11-15

We reported the existence and stability of defect solitons in saturable nonlinearity media with parity-time (PT) symmetric optical lattices. Families of fundamental and dipole solitons are found in the semi-infinite gap and the first gap. The power of solitons increases with the increasing of the propagation constant and saturation parameter. The existence areas of fundamental and dipole solitons shrink with the growth of saturation parameter. The instability of dipole solitons for positive and no defect induced by the imaginary part of PT symmetric potentials can be suppressed by the saturation nonlinearity, but for negative defect it cannot be suppressed by the saturation nonlinearity.

Investigation of Factors Influencing Dispersion of Liquid Hydrocarbons in Porous Media

Directory of Open Access Journals (Sweden)

Hussain Ali Baker

2016-08-01

Full Text Available An experimental work has been done to study the major factors that affect the axial dispersion of some hydrocarbons during liquid-liquid miscible displacement. Kerosene and gas oil are used as displacing phase while seven liquid hydrocarbons of high purity represent the displaced phase, three of the liquids are aromatics and the rest are of paraffinic base. In conducting the experiments, two packed beds of different porosity and permeability are used as porous media. The results showed that the displacement process is not a piston flow, breakthrough of displacing fluids are shown before one pore volume has been injected. The processes are stable with no evidence of viscous fingering. Dispersion model as adapted by Brigham et.al (1961 is used to determine the axial dispersion coefficient of displacing fluid. The results show an increasing in dispersion coefficient as the interstitial velocity and viscosity ratio increases.

Nonlinear processes in laser heating of chemically active media

Energy Technology Data Exchange (ETDEWEB)

Bunkin, F V; Kirichenko, N A; Luk' yanchuk, B S

1984-08-01

After it had been discovered and in due measure physically comprehended that numerous nontrivial phenomena observed during laser heating of chemically active media are caused primarily by self-stress of laser radiation due to the chemical intertial nonlinearity of the medium, an approach was found for solving problems of laser thermochemistry that is most adequate from the mathematical (and physical) standpoint: the approach of the theory of nonlinear oscillations in point systems and distributed systems. This approach has provided a uniform viewpoint for examination of a variety of phenomena of spatiotemporal self-organization of chemically active media under the effect of laser radiation, qualitative, and in some cases quantitative description of such phenomena as the onset of thermochemical instability, self-oscillations, various spatial structures and the like. Evidently it can be rightly considered that at this juncture a definite stage has been completed in the development of laser thermochemistry marked by the creation of an ideology, method and overall approach to interpretation of the most diverse phenomena under conditions of actual physical experiments. References to the numerous studies that make up the content of this stage of development of laser thermochemistry are to be found in survey papers. 48 references, 10 figures.

Monte Carlo simulation of nonlinear reactive contaminant transport in unsaturated porous media

International Nuclear Information System (INIS)

Giacobbo, F.; Patelli, E.

2007-01-01

In the current proposed solutions of radioactive waste repositories, the protective function against the radionuclide water-driven transport back to the biosphere is to be provided by an integrated system of engineered and natural geologic barriers. The occurrence of several nonlinear interactions during the radionuclide migration process may render burdensome the classical analytical-numerical approaches. Moreover, the heterogeneity of the barriers' media forces approximations to the classical analytical-numerical models, thus reducing their fidelity to reality. In an attempt to overcome these difficulties, in the present paper we adopt a Monte Carlo simulation approach, previously developed on the basis of the Kolmogorov-Dmitriev theory of branching stochastic processes. The approach is here extended for describing transport through unsaturated porous media under transient flow conditions and in presence of nonlinear interchange phenomena between the liquid and solid phases. This generalization entails the determination of the functional dependence of the parameters of the proposed transport model from the water content and from the contaminant concentration, which change in space and time during the water infiltration process. The corresponding Monte Carlo simulation approach is verified with respect to a case of nonreactive transport under transient unsaturated flow and to a case of nonlinear reactive transport under stationary saturated flow. Numerical applications regarding linear and nonlinear reactive transport under transient unsaturated flow are reported

Localized excitations in discrete nonlinear Schrodinger systems: Effects of nonlocal dispersive interactions and noise

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...

Dissipative Vortex Solitons in Defocusing Media with Spatially Inhomogeneous Nonlinear Absorption

Science.gov (United States)

Lai, Xian-Jing; Cai, Xiao-Ou; Zhang, Jie-Fang

2018-02-01

In this paper, by solving a complex nonlinear Schrödinger equation, radially symmetric dissipative vortex solitons are obtained analytically and are tested numerically. We find that spatially inhomogeneous nonlinear absorption gives rise to the stability of dissipative vortex solitons in self-defocusing nonlinear medium in the presence of constant linear gain. Numerical simulation reveals the interaction effect among linear gain and nonlinear loss in the azimuthal modulation instabilities of these vortices suppression. Apart from the uniform linear gain indeed affects the stability of vortex in this media, another noticeable feature of current setup is that the steep spatial modulation of the nonlinear absorption can suppress sidelobes effectively and support stable vortex solitons in situations with uniform linear gain. Under appropriate conditions, the vortex solitons can propagate stably and feature no symmetry breaking, although the beams exhibit radical compression and amplification as they propagate. Supported by the National Natural Science Foundation of China under Grant No. 11705164 and the Zhejiang Provincial Natural Science Foundation of China under Grant No. LQ16A040003

Variable-coefficient higher-order nonlinear Schroedinger model in optical fibers: Variable-coefficient bilinear form, Baecklund transformation, brightons and symbolic computation

International Nuclear Information System (INIS)

Tian Bo; Gao Yitian; Zhu Hongwu

2007-01-01

Symbolically investigated in this Letter is a variable-coefficient higher-order nonlinear Schroedinger (vcHNLS) model for ultrafast signal-routing, fiber laser systems and optical communication systems with distributed dispersion and nonlinearity management. Of physical and optical interests, with bilinear method extend, the vcHNLS model is transformed into a variable-coefficient bilinear form, and then an auto-Baecklund transformation is constructed. Constraints on coefficient functions are analyzed. Potentially observable with future optical-fiber experiments, variable-coefficient brightons are illustrated. Relevant properties and features are discussed as well. Baecklund transformation and other results of this Letter will be of certain value to the studies on inhomogeneous fiber media, core of dispersion-managed brightons, fiber amplifiers, laser systems and optical communication links with distributed dispersion and nonlinearity management

Macroscopic QED in linearly responding media and a Lorentz-Force approach to dispersion forces

Energy Technology Data Exchange (ETDEWEB)

Raabe, Christian

2008-07-08

In this thesis, a very general quantization scheme for the macroscopic electromagnetic field in arbitrary linearly responding media is presented. It offers a unified approach to QED in such media. Applying the quantization scheme, a theory of the dispersion forces on the basis of the Lorentz force is developed. By regarding the dispersion force as the (ground-state or thermal-state) expectation value of the Lorentz force that acts on appropriately defined charge and current densities, Casimir, Casimir-Polder, and van der Waals forces are united in a very natural way that makes transparent their common physical basis. Application of the theory to planar structures yields generalizations of well-known Lifschitz and Casimir-type formulas. (orig.)

Macroscopic QED in linearly responding media and a Lorentz-Force approach to dispersion forces

International Nuclear Information System (INIS)

Raabe, Christian

2008-01-01

In this thesis, a very general quantization scheme for the macroscopic electromagnetic field in arbitrary linearly responding media is presented. It offers a unified approach to QED in such media. Applying the quantization scheme, a theory of the dispersion forces on the basis of the Lorentz force is developed. By regarding the dispersion force as the (ground-state or thermal-state) expectation value of the Lorentz force that acts on appropriately defined charge and current densities, Casimir, Casimir-Polder, and van der Waals forces are united in a very natural way that makes transparent their common physical basis. Application of the theory to planar structures yields generalizations of well-known Lifschitz and Casimir-type formulas. (orig.)

1-Soliton solution of the generalized Zakharov-Kuznetsov equation with nonlinear dispersion and time-dependent coefficients

International Nuclear Information System (INIS)

Biswas, Anjan

2009-01-01

In this Letter, the 1-soliton solution of the Zakharov-Kuznetsov equation with power law nonlinearity and nonlinear dispersion along with time-dependent coefficients is obtained. There are two models for this kind of an equation that are studied. The constraint relation between these time-dependent coefficients is established for the solitons to exist. Subsequently, this equation is again analysed with generalized evolution. The solitary wave ansatz is used to carry out this investigation.

A comparison of dispersing media for various engineered carbon nanoparticles

Directory of Open Access Journals (Sweden)

Holian Andrij

2007-07-01

Full Text Available Abstract Background With the increased manufacture and use of carbon nanoparticles (CNP there has been increasing concern about the potential toxicity of fugitive CNP in the workplace and ambient environment. To address this matter a number of investigators have conducted in vitro and in vivo toxicity assessments. However, a variety of different approaches for suspension of these particles (culture media, Tween 80, dimethyl sulfoxide, phosphate-buffered saline, fetal calf serum, and others, and different sources of materials have generated potentially conflicting outcomes. The quality of the dispersion of nanoparticles is very dependent on the medium used to suspend them, and this then will most likely affect the biological outcomes. Results In this work, the distributions of different CNP (sources and types have been characterized in various media. Furthermore, the outcome of instilling the different agglomerates, or size distributions, was examined in mouse lungs after one and seven days. Our results demonstrated that CNP suspended in serum produced particle suspensions with the fewest large agglomerates, and the most uniform distribution in mouse lungs. In addition, no apparent clearance of instilled CNP took place from lungs even after seven days. Conclusion This work demonstrates that CNP agglomerates are present in all dispersing vehicles to some degree. The vehicle that contains some protein, lipid or protein/lipid component disperses the CNP best, producing fewer large CNP agglomerates. In contrast, vehicles absent of lipid and protein produce the largest CNP agglomerates. The source of the CNP is also a factor in the degree of particle agglomeration within the same vehicle.

Attenuation, dispersion and nonlinearity effects in graphene-based waveguides

Directory of Open Access Journals (Sweden)

Almir Wirth Lima Jr.

2015-05-01

Full Text Available We simulated and analyzed in detail the behavior of ultrashort optical pulses, which are typically used in telecommunications, propagating through graphene-based nanoribbon waveguides. In this work, we showed the changes that occur in the Gaussian and hyperbolic secant input pulses due to the attenuation, high-order dispersive effects and nonlinear effects. We concluded that it is possible to control the shape of the output pulses with the value of the input signal power and the chemical potential of the graphene nanoribbon. We believe that the obtained results will be highly relevant since they can be applied to other nanophotonic devices, for example, filters, modulators, antennas, switches and other devices.

Wave power balance in resonant dissipative media with spatial and temporal dispersion

International Nuclear Information System (INIS)

Tokman, M.D.; Gavrilova, M.A.; Westerhof, E. . www.rijnh.nl

2003-01-01

A power balance for waves in resonant dissipative media is formulated, which generalizes well-known expressions for dielectric wave energy density, wave energy flux, and dissipated power density. The identification of the different terms with wave energy density and flux remains only phenomenological. The result is better viewed as an equation for the evolution of wave intensity. In that form, its consequences are discussed in particular in relation to anomalous dispersion. A discrimination is made between boundary and initial value problems. For boundary value problems, anomalous dispersion is shown not to lead to unphysical results. In contrast, for initial value problems the solution for the evolution of wave intensity is shown to be at fault in the case of anomalous dispersion. Further illustration is provided by consideration of wave dispersion in a medium of charged harmonic oscillators and of ordinary-mode dispersion in plasma. Both are characterized by anomalous dispersion and show marked differences in the solutions of the dispersion relation solved either for complex wave vector at real frequency, k(ω) (applicable to boundary value problems), or for complex frequency at real wave vector ω(k) (applicable to initial value problems). (author)

High-order optical nonlinearities in nanocomposite films dispersed with semiconductor quantum dots at high concentrations

International Nuclear Information System (INIS)

Tomita, Yasuo; Matsushima, Shun-suke; Yamagami, Ryu-ichi; Jinzenji, Taka-aki; Sakuma, Shohei; Liu, Xiangming; Izuishi, Takuya; Shen, Qing

2017-01-01

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. (paper)

Dispersing and stabilizing effect of nonaqueous media with different acid-base functions when preparing process suspensions

International Nuclear Information System (INIS)

Koshevar, V.D.; Rat'ko, A.I.; Mironenko, I.N.

1999-01-01

Dispersing and stabilizing effect of organic liquids related to the Lewis acids and baser is studied when preparing the suspensions of certain minerals and metal oxides, beryllium oxide, in particular. Practical recommendations are provided for the choice of dispersing media to produce stable suspensions

Modeling Solution of Nonlinear Dispersive Partial Differential Equations using the Marker Method

International Nuclear Information System (INIS)

Lewandowski, Jerome L.V.

2005-01-01

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

A theoretical and experimental investigation of nonlinear propagation of ultrasound through tissue mimicking media

Science.gov (United States)

Rielly, Matthew Robert

An existing numerical model (known as the Bergen code) is used to investigate finite amplitude ultrasound propagation through multiple layers of tissue-like media. This model uses a finite difference method to solve the nonlinear parabolic KZK wave equation. The code is modified to include an arbitrary frequency dependence of absorption and transmission effects for wave propagation across a plane interface at normal incidence. In addition the code is adapted to calculate the total intensity loss associated with the absorption of the fundamental and nonlinearly generated harmonics. Measurements are also taken of the axial nonlinear pressure field generated from a circular focused, 2.25 MHz source, through single and multiple layered tissue mimicking fluids, for source pressures in the range from 13 kPa to 310 kPa. Two tissue mimicking fluids are developed to provide acoustic properties similar to amniotic fluid and a typical soft tissue. The values of the nonlinearity parameter, sound velocity and frequency dependence of attenuation for both fluids are presented, and the measurement procedures employed to obtain these characteristics are described in detail. These acoustic parameters, together with the measured source conditions are used as input to the numerical model, allowing the experimental conditions to be simulated. Extensive comparisons are made between the model's predictions and the axial pressure field measurements. Results are presented in the frequency domain showing the fundamental and three subsequent harmonic amplitudes on axis, as a function of axial distance. These show that significant nonlinear distortion can occur through media with characteristics typical of tissue. Time domain waveform comparisons are also made. An excellent agreement is found between theory and experiment indicating that the model can be used to predict nonlinear ultrasound propagation through multiple layers of tissue-like media. The numerical code is also used to model the

Double-resonant processes in x.sup.20.sup. nonlinear periodic media

Czech Academy of Sciences Publication Activity Database

Konotop, V. V.; Kuzmiak, Vladimír

2000-01-01

Roč. 17, č. 11 (2000), s. 1874-1883 ISSN 0740-3224 Grant - others:Fundo European de Desenvolvimento Regional and Program PRAXIS XXI(PT) PRAXIS/2/2.1/FIS/176/94 Institutional research plan: CEZ:AV0Z2067918 Keywords : nonlinear media * electromagnetic wave propagation Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.943, year: 2000

Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves

DEFF Research Database (Denmark)

Eldeberky, Y.; Madsen, Per A.

1999-01-01

and stochastic formulations are solved numerically for the case of cross shore motion of unidirectional waves and the results are verified against laboratory data for wave propagation over submerged bars and over a plane slope. Outside the surf zone the two model predictions are generally in good agreement......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...... is significantly underestimated for larger wave numbers. In the present work we correct this inconsistency. In addition to the improved deterministic formulation, we present improved stochastic evolution equations in terms of the energy spectrum and the bispectrum for multidirectional waves. The deterministic...

Study of phenomena of tracer transport and dispersion in fractured media

International Nuclear Information System (INIS)

Ippolito, Irene

1993-01-01

The objective of this research thesis is to present some transport phenomena according to two different approaches: firstly, the study of flows and tracing in a natural crack within a granitic site, and secondly, the study of flows of different geometries in model cracks, mainly by using techniques of tracer dispersion. The author first presents some properties of fractured media and elements of the theory of the phenomenon of dispersion. She notably discusses the reversibility of the Taylor dispersion which is the prevailing mechanism for simply connected geometries such as in the case of a flow between two continuous solid surfaces limiting a fracture. In the next chapters, the author reports the analysis of characteristics of local structures (mouths, roughnesses) of a single fracture by using echo dispersion. She reports experiments as well as Monte Carlo simulations performed on well defined geometries. In a parallel way, some characteristics measurements (rate-pressure, distribution of flows and tracing in transmission) and mechanical measurements of fracture deformation have been performed on a natural fracture in a granitic site [fr

Experimental photonic generation of chirped pulses using nonlinear dispersion-based incoherent processing.

Science.gov (United States)

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.

Thickness-dependent dispersion parameters, energy gap and nonlinear refractive index of ZnSe thin films

International Nuclear Information System (INIS)

Prakash, Deo; Shaaban, E.R.; Shapaan, M.; Mohamed, S.H.; Othman, A.A.; Verma, K.D.

2016-01-01

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.

Thickness-dependent dispersion parameters, energy gap and nonlinear refractive index of ZnSe thin films

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.

Rogue wave train generation in a metamaterial induced by cubic-quintic nonlinearities and second-order dispersion

Science.gov (United States)

Essama, Bedel Giscard Onana; Atangana, Jacques; Frederick, Biya Motto; Mokhtari, Bouchra; Eddeqaqi, Noureddine Cherkaoui; Kofane, Timoleon Crepin

2014-09-01

We investigate the behavior of the electromagnetic wave that propagates in a metamaterial for negative index regime. Second-order dispersion and cubic-quintic nonlinearities are taken into account. The behavior obtained for negative index regime is compared to that observed for absorption regime. The collective coordinates technique is used to characterize the light pulse intensity profile at some frequency ranges. Five frequency ranges have been pointed out. The perfect combination of second-order dispersion and cubic nonlinearity leads to a robust soliton at each frequency range for negative index regime. The soliton peak power progressively decreases for absorption regime. Further, this peak power also decreases with frequency. We show that absorption regime can induce rogue wave trains generation at a specific frequency range. However, this rogue wave trains generation is maintained when the quintic nonlinearity comes into play for negative index regime and amplified for absorption regime at a specific frequency range. It clearly appears that rogue wave behavior strongly depends on the frequency and the regime considered. Furthermore, the stability conditions of the electromagnetic wave have also been discussed at frequency ranges considered for both negative index and absorption regimes.

Transverse Field Dispersion in the Generalized Nonlinear Schrödinger Equation: Four Wave Mixing in a Higher Order Mode Fiber

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...

Pore-scale simulation of fluid flow and solute dispersion in three-dimensional porous media

KAUST Repository

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.

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...

Study of dispersive and nonlinear effects of coastal wave dynamics with a fully nonlinear potential flow model

Science.gov (United States)

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

Light-pressure-induced nonlinear dispersion of a laser field interacting with an atomic gas

International Nuclear Information System (INIS)

Grimm, R.; Mlynek, J.

1990-01-01

We report on detailed studies of the effect of resonant light pressure on the optical response of an atomic gas to a single monochromatic laser field. In this very elementary situation of laser spectroscopy, the redistribution of atomic velocities that is induced by spontaneous light pressure leads to a novel contribution to the optical dispersion curve of the medium. This light-pressure-induced dispersion phenomenon displays a pronounced nonlinear dependence on the laser intensity. Moreover, for a given intensity, its strength is closely related to the laser beam diameter. As most important feature, this light-pressure-induced dispersion displays an even symmetry with respect to the optical detuning from line center. As a result, the total Doppler-broadened dispersion curve of the gas can become asymmetric, and a significant shift of the dispersion line center can occur. In addition to a detailed theoretical description of the phenomenon, we report on its experimental investigation on the λ=555.6 nm 1 S 0 - 3 P 1 transition in atomic ytterbium vapor with the use of frequency-modulation spectroscopy. The experimental findings are in good quantitative agreement with theoretical predictions

Statistical study of the non-linear propagation of a partially coherent laser beam

International Nuclear Information System (INIS)

Ayanides, J.P.

2001-01-01

This research thesis is related to the LMJ project (Laser MegaJoule) and thus to the study and development of thermonuclear fusion. It reports the study of the propagation of a partially-coherent laser beam by using a statistical modelling in order to obtain mean values for the field, and thus bypassing a complex and costly calculation of deterministic quantities. Random fluctuations of the propagated field are supposed to comply with a Gaussian statistics; the laser central wavelength is supposed to be small with respect with fluctuation magnitude; a scale factor is introduced to clearly distinguish the scale of the random and fast variations of the field fluctuations, and the scale of the slow deterministic variations of the field envelopes. The author reports the study of propagation through a purely linear media and through a non-dispersive media, and then through slow non-dispersive and non-linear media (in which the reaction time is large with respect to grain correlation duration, but small with respect to the variation scale of the field macroscopic envelope), and thirdly through an instantaneous dispersive and non linear media (which instantaneously reacts to the field) [fr

The influence of transverse diffusion/dispersion on the migration of radionuclides in porous media

International Nuclear Information System (INIS)

Schmocker, U.

1980-07-01

Repositories in geological formations are planned for the final disposal of radioactive wastes produced by nuclear power. Generally, water entry leading to leaching of the waste matrix is considered as the critical process which can result in release of radionuclides from a waste repository. Consequently, radionuclide transport through the geosphere is of crucial importance, because the geological medium acts as the last barrier to the biosphere. The influence of the transverse diffusion/dispersion effect on the migration of radionuclides through the geosphere is dealt with. Migration in porous media only is considered which is the standard approach of most existing transport models. The present study shows that it is only for homogeneous-isotropic media that the three-dimensional time-dependent transport equation can be solved analytically - provided that only simple source geometries and leach processes are taken into account. For heterogeneous layered media only the two-dimensional quasi-stationary transport equation can be solved; the only time dependent process which can be handled is simple radioactive decay excluding extended decay chains. The study shows moreover that only for an idealized three-layer geology can analytical solutions be found. In particular the solutions for multi-layered media cannot be derived from single-layer solutions; each problem with special source and boundary conditions has to be solved directly. The numerical results from the present study show a relatively strong influence of the transverse dispersion effect in the case of homogeneous-isotropic media. (Auth.)

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....... The mechanism underlying this fragmentation process is described in terms of a stretching of the self-focusing beam along its propagation axis. The focal point, where the splitting process develops, is identified. Finally, it is shown that the longitudinal dynamical motions of self-focusing elongated pulses...

Solitonic dynamics and excitations of the nonlinear Schrödinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials.

Science.gov (United States)

Chen, Yong; Yan, Zhenya

2016-03-22

Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields.

Moessbauer investigation of static-disorder crystalline media. V. Hyperfine fields' dispersion in static-disordered crystalline media of tetragonal and trigonal iron germanates

International Nuclear Information System (INIS)

Constantinescu, S.

2007-01-01

The refined 57 Fe Moessbauer spectra of some static-disordered crystalline media (with melilite and Ca-gallate structure) evidenced observable electric and magnetic crystal field dispersions. It is the fifth in a series of papers published previously in the same journal on this subject. The data of crystalline hyperfine fields and their dispersion parameters have calculated using the modeling procedure given in a paper by Kaminskii, et al. published in 1986. The obtained values of the magnetic and quadrupole splitting parameters compared with to experimental data showed the possibility to predict the crystal fields' dispersion. (author)

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.

Time moments of the energy flow of optical pulses in highly dispersive media

International Nuclear Information System (INIS)

Nanda, Lipsa; Wanare, Harshawardhan; Ramakrishna, S Anantha

2010-01-01

We use the time moments of the Poynting vector associated with an electromagnetic pulse to characterize the traversal times and temporal pulse widths as the pulse propagates in highly dispersive media. The behaviour of these quantities with the propagation distance is analysed in three canonical cases: Lorentz absorptive medium, a Raman gain doublet amplifying medium and a medium exhibiting electromagnetically induced transparency. We find that superluminal pulse propagation in the first two cases with anomalous dispersion is usually accompanied by pulse compression and eventually the pulse becomes subluminal with increasing distance of propagation. In a medium with electromagnetically induced transparency with large normal dispersion, we identify a range of frequencies for which the pulse undergoes minimal temporal expansion while propagating with ultra-slow speed.

The cubic-quintic-septic complex Ginzburg-Landau equation formulation of optical pulse propagation in 3D doped Kerr media with higher-order dispersions

Science.gov (United States)

Djoko, Martin; Kofane, T. C.

2018-06-01

We investigate the propagation characteristics and stabilization of generalized-Gaussian pulse in highly nonlinear homogeneous media with higher-order dispersion terms. The optical pulse propagation has been modeled by the higher-order (3+1)-dimensional cubic-quintic-septic complex Ginzburg-Landau [(3+1)D CQS-CGL] equation. We have used the variational method to find a set of differential equations characterizing the variation of the pulse parameters in fiber optic-links. The variational equations we obtained have been integrated numerically by the means of the fourth-order Runge-Kutta (RK4) method, which also allows us to investigate the evolution of the generalized-Gaussian beam and the pulse evolution along an optical doped fiber. Then, we have solved the original nonlinear (3+1)D CQS-CGL equation with the split-step Fourier method (SSFM), and compare the results with those obtained, using the variational approach. A good agreement between analytical and numerical methods is observed. The evolution of the generalized-Gaussian beam has shown oscillatory propagation, and bell-shaped dissipative optical bullets have been obtained under certain parameter values in both anomalous and normal chromatic dispersion regimes. Using the natural control parameter of the solution as it evolves, named the total energy Q, our numerical simulations reveal the existence of 3D stable vortex dissipative light bullets, 3D stable spatiotemporal optical soliton, stationary and pulsating optical bullets, depending on the used initial input condition (symmetric or elliptic).

Exact solutions with solitary patterns for the Zakharov-Kuznetsov equations with fully nonlinear dispersion

International Nuclear Information System (INIS)

Inc, Mustafa

2007-01-01

In this paper, the nonlinear dispersive Zakharov-Kuznetsov ZK(m, n, k) equations are solved exactly by using the Adomian decomposition method. The two special cases, ZK(2, 2, 2) and ZK(3, 3, 3), are chosen to illustrate the concrete scheme of the decomposition method in ZK(m, n, k) equations. General formulas for the solutions of ZK(m, n, k) equations are established

Suppression of two-photon resonantly enhanced nonlinear processes in extended media

International Nuclear Information System (INIS)

Garrett, W.R.; Moore, M.A.; Payne, M.G.; Wunderlich, R.K.

1988-11-01

On the basis of combined experimental and theoretical studies of nonlinear processes associated with two-photon excitations near 3d and 4d states in Na, we show how resonantly enhanced stimulated hyper-Raman emission, parametric four-wave mixing processes and total resonant two-photon absorption can become severely suppressed through the actions of internally generated fields on the total atomic response in extended media. 7 refs., 3 figs

Layer contributions to the nonlinear acoustic radiation from stratified media.

Science.gov (United States)

Vander Meulen, François; Haumesser, Lionel

2016-12-01

This study presents the thorough investigation of the second harmonic generation scenario in a three fluid layer system. An emphasis is on the evaluation of the nonlinear parameter B/A in each layer from remote measurements. A theoretical approach of the propagation of a finite amplitude acoustic wave in a multilayered medium is developed. In the frame of the KZK equation, the weak nonlinearity of the media, attenuation and diffraction effects are computed for the fundamental and second harmonic waves propagating back and forth in each of the layers of the system. The model uses a gaussian expansion to describe the beam propagation in order to quantitatively evaluate the contribution of each part of the system (layers and interfaces) to its nonlinearity. The model is validated through measurements on a water/aluminum/water system. Transmission as well as reflection configurations are studied. Good agreement is found between the theoretical results and the experimental data. The analysis of the second harmonic field sources measured by the transducers from outside the stratified medium highlights the factors that favor the cumulative effects. Copyright © 2016 Elsevier B.V. All rights reserved.

Influence of wavelength-dependent-loss on dispersive wave in nonlinear optical fibers.

Science.gov (United States)

Herrera, Rodrigo Acuna

2012-11-01

In this work, we study numerically the influence of wavelength-dependent loss on the generation of dispersive waves (DWs) in nonlinear fiber. This kind of loss can be obtained, for instance, by the acousto-optic effect in fiber optics. We show that this loss lowers DW frequency in an opposite way that the Raman effect does. Also, we see that the Raman effect does not change the DW frequency too much when wavelength-dependent loss is included. Finally, we show that the DW frequency is not practically affected by fiber length.

Use of compounded dispersing media for extemporaneous pediatric syrups with candesartan cilexetil and valsartan

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.

Use of compounded dispersing media for extemporaneous pediatric syrups with candesartan cilexetil and valsartan.

Science.gov (United States)

Musko, Monika; Sznitowska, Malgorzata

2014-12-01

Available tablets or capsules for adults are often used to prepare extemporaneously formulated medicines appropriate for children. The most acceptable drug forms in pediatric population are oral liquids and pharmacists use commercial dispersing media to compound syrups from an active substance or from tablets available on the market. In many countries ready-to-use dispersing media are not available or refunded, but pharmacists can use other compounded media, providing their compatibility and stability are proven. The aim of this study was to formulate and evaluate the stability of syrups with candesartan cilexetil (1 mg mL-1) and valsartan (4 mg mL-1) extemporaneously prepared using commercial tablets (Diovan® and Atacand®). The following three different suspending media, which could be easily made in a pharmacy, were investigated: V1 - with xanthan gum (0.5 %), V2 - the USP/NF vehicle for oral solution and V3 - the medium based on a simple sucrose syrup. The stability of preparations was studied during 35 days of storage in a dark place at controlled temperature of 25 and 4 °C. During the study, microscopic observation was carried out and pH, viscosity, and concentration of candesartan cilexetil and valsartan were analyzed. Syrups with valsartan prepared with V2 and V3 media were stable for 3 or 4 weeks when stored at 25 °C, while syrups with candesartan were stable for as long as 35 days. For syrups prepared using V1 medium, the 14-day expiry date was not achieved because of microbial deterioration.

Gas-solute dispersivity ratio in granular porous media as related to particle size distribution and particle shape

DEFF Research Database (Denmark)

Pugliese, Lorenzo; Poulsen, Tjalfe; Straface, Salvatore

2013-01-01

Measurements of solute dispersion in porous media is generally much more time consuming than gas dispersion measurements performed under equivalent conditions. Significant time savings may therefore, be achieved if solute dispersion coefficients can be estimated based on measured gas dispersion...... 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...

Nonlinear ultrasound propagation through layered liquid and tissue-equivalent media: computational and experimental results at high frequency

International Nuclear Information System (INIS)

Williams, Ross; Cherin, Emmanuel; Lam, Toby Y J; Tavakkoli, Jahangir; Zemp, Roger J; Foster, F Stuart

2006-01-01

Nonlinear propagation has been demonstrated to have a significant impact on ultrasound imaging. An efficient computational algorithm is presented to simulate nonlinear ultrasound propagation through layered liquid and tissue-equivalent media. Results are compared with hydrophone measurements. This study was undertaken to investigate the role of nonlinear propagation in high frequency ultrasound micro-imaging. The acoustic field of a focused transducer (20 MHz centre frequency, f-number 2.5) was simulated for layered media consisting of water and tissue-mimicking phantom, for several wide-bandwidth source pulses. The simulation model accounted for the effects of diffraction, attenuation and nonlinearity, with transmission and refraction at layer boundaries. The parameter of nonlinearity, B/A, of the water and tissue-mimicking phantom were assumed to be 5.2 and 7.4, respectively. The experimentally measured phantom B/A value found using a finite-amplitude insert-substitution method was shown to be 7.4 ± 0.6. Relative amounts of measured second and third harmonic pressures as a function of the fundamental pressures at the focus were in good agreement with simulations. Agreement within 3% was found between measurements and simulations of the beam widths of the fundamental and second harmonic signals following propagation through the tissue phantom. The results demonstrate significant nonlinear propagation effects for high frequency imaging beams

Dissolution and precipitation behavior of ternary solid dispersions of ezetimibe in biorelevant media.

Science.gov (United States)

Alhayali, Amani; Tavellin, Staffan; Velaga, Sitaram

2017-01-01

The effects of different formulations and processes on inducing and maintaining the supersaturation of ternary solid dispersions of ezetimibe (EZ) in two biorelevant media fasted-state simulated intestinal fluid (FaSSIF) and fasted-state simulated gastric fluid (FaSSGF) at different temperatures (25 °C and 37 °C) were investigated in this work. Ternary solid dispersions of EZ were prepared by adding polymer PVP-K30 and surfactant poloxamer 188 using melt-quenching and spray-drying methods. The resulting solid dispersions were characterized using scanning electron microscopy, differential scanning calorimetry (DSC), modulated DSC, powder X-ray diffraction and Fourier transformation infrared spectroscopy. The dissolution of all the ternary solid dispersions was tested in vitro under non-sink conditions. All the prepared solid dispersions were amorphous in nature. In FaSSIF at 25 °C, the melt-quenched (MQ) solid dispersions of EZ were more soluble than the spray-dried (SD) solid dispersions and supersaturation was maintained. However, at 37 °C, rapid and variable precipitation behavior was observed for all the MQ and SD formulations. In FaSSGF, the melting method resulted in better solubility than the spray-drying method at both temperatures. Ternary solid dispersions show potential for improving solubility and supersaturation. However, powder dissolution experiments of these solid dispersions of EZ at 25 °C may not predict the supersaturation behavior at physiologically relevant temperatures.

Blackbody emission from light interacting with an effective moving dispersive medium.

Science.gov (United States)

Petev, M; Westerberg, N; Moss, D; Rubino, E; Rimoldi, C; Cacciatori, S L; Belgiorno, F; Faccio, D

2013-07-26

Intense laser pulses excite a nonlinear polarization response that may create an effective flowing medium and, under appropriate conditions, a blocking horizon for light. Here, we analyze in detail the interaction of light with such laser-induced flowing media, fully accounting for the medium dispersion properties. An analytical model based on a first Born approximation is found to be in excellent agreement with numerical simulations based on Maxwell's equations and shows that when a blocking horizon is formed, the stimulated medium scatters light with a blackbody emission spectrum. Based on these results, diamond is proposed as a promising candidate medium for future studies of Hawking emission from artificial, dispersive horizons.

Blackbody Emission from Light Interacting with an Effective Moving Dispersive Medium

OpenAIRE

Petev, M.; Westerberg, N.; Moss, D.; Rubino, E.; Rimoldi, C.; Cacciatori, S. L.; Belgiorno, F.; Faccio, D.

2013-01-01

Intense laser pulses excite a nonlinear polarisation response that may create an effective flowing medium and, under appropriate conditions, a blocking horizon for light. Here we analyse in detail the interaction of light with such laser-induced flowing media, fully accounting for the medium dispersion properties. An analytical model based on a first Born-approximation is found to be in excellent agreement with numerical simulations based on Maxwell's equations and shows that when a blocking ...

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....

Nonlinear dynamics in flow through unsaturated fractured porous media: Status and perspectives

International Nuclear Information System (INIS)

Faybishenko, Boris

2002-01-01

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.

Toward a unified description of nonlinearity and frequency dispersion of piezoelectric and dielectric responses in Pb(Zr,Ti)O3

International Nuclear Information System (INIS)

Damjanovic, D.; Bharadwaja, S.S.N.; Setter, N.

2005-01-01

A phenomenological approach is proposed describing both nonlinearity and frequency dispersion in dielectric and piezoelectric properties of lead zirconate titanate, Pb(Zr,Ti)O 3 (PZT), thin films and ceramics. The approach couples the frequency dependent response in form of the power law, 1/ω β , with the rate-independent nonlinear response described by the Rayleigh law. The main experimental trends are well described by the model

Hierarchical opal grating films prepared by slide coating of colloidal dispersions in binary liquid media.

Science.gov (United States)

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. Copyright © 2014 Elsevier Inc. All rights reserved.

Modal analysis of wave propagation in dispersive media

Science.gov (United States)

Abdelrahman, M. Ismail; Gralak, B.

2018-01-01

Surveys on wave propagation in dispersive media have been limited since the pioneering work of Sommerfeld [Ann. Phys. 349, 177 (1914), 10.1002/andp.19143491002] by the presence of branches in the integral expression of the wave function. In this article a method is proposed to eliminate these critical branches and hence to establish a modal expansion of the time-dependent wave function. The different components of the transient waves are physically interpreted as the contributions of distinct sets of modes and characterized accordingly. Then, the modal expansion is used to derive a modified analytical expression of the Sommerfeld precursor improving significantly the description of the amplitude and the oscillating period up to the arrival of the Brillouin precursor. The proposed method and results apply to all waves governed by the Helmholtz equations.

Filamentation and light bullet formation dynamics in solid-state dielectric media with weak, moderate and strong anomalous group velocity dispersion

International Nuclear Information System (INIS)

Gražulevičiūtė, I; Garejev, N; Majus, D; Tamošauskas, G; A Dubietis; Jukna, V

2016-01-01

We present a series of measurements, which characterize filamentation dynamics of intense ultrashort laser pulses in the space–time domain, as captured by means of three-dimensional imaging technique in sapphire and fused silica, in the wavelength range of 1.45–2.25 μm, accessing the regimes of weak, moderate and strong anomalous group velocity dispersion (GVD). In the regime of weak anomalous GVD (at 1.45 μm), pulse splitting into two sub-pulses producing a pair of light bullets with spectrally shifted carrier frequencies in both nonlinear media is observed. In contrast, in the regimes of moderate (at 1.8 μm) and strong (at 2.25 μm) anomalous GVD we observe notably different transient dynamics, which however lead to the formation of a single self-compressed quasistationary light bullet with an universal spatiotemporal shape comprised of an extended ring-shaped periphery and a localized intense core that carries the self-compressed pulse. (paper)

Filamentation and light bullet formation dynamics in solid-state dielectric media with weak, moderate and strong anomalous group velocity dispersion

Science.gov (United States)

Gražulevičiūtė, I.; Garejev, N.; Majus, D.; Jukna, V.; Tamošauskas, G.; Dubietis, A.

2016-02-01

We present a series of measurements, which characterize filamentation dynamics of intense ultrashort laser pulses in the space-time domain, as captured by means of three-dimensional imaging technique in sapphire and fused silica, in the wavelength range of 1.45-2.25 μm, accessing the regimes of weak, moderate and strong anomalous group velocity dispersion (GVD). In the regime of weak anomalous GVD (at 1.45 μm), pulse splitting into two sub-pulses producing a pair of light bullets with spectrally shifted carrier frequencies in both nonlinear media is observed. In contrast, in the regimes of moderate (at 1.8 μm) and strong (at 2.25 μm) anomalous GVD we observe notably different transient dynamics, which however lead to the formation of a single self-compressed quasistationary light bullet with an universal spatiotemporal shape comprised of an extended ring-shaped periphery and a localized intense core that carries the self-compressed pulse.

Design of compact dispersion interferometer with a high efficiency nonlinear crystal and a low power CO2 laser

Science.gov (United States)

Akiyama, T.; Yoshimura, S.; Tomita, K.; Shirai, N.; Murakami, T.; Urabe, K.

2017-12-01

When the electron density of a plasma generated in high pressure environment is measured by a conventional interferometer, the phase shifts due to changes of the neutral gas density cause significant measurement errors. A dispersion interferometer, which measures the phase shift that arises from dispersion of medium between the fundamental and the second harmonic wavelengths of laser light, can suppress the measured phase shift due to the variations of neutral gas density. In recent years, the CO2 laser dispersion interferometer has been applied to the atmospheric pressure plasmas and its feasibility has been demonstrated. By combining a low power laser and a high efficiency nonlinear crystal for the second harmonic component generation, a compact dispersion interferometer can be designed. The optical design and preliminary experiments are conducted.

A nonlinear model for frequency dispersion and DC intrinsic parameter extraction for GaN-based HEMT

Science.gov (United States)

Nguyen, Tung The-Lam; Kim, Sam-Dong

2017-11-01

We propose in this study a practical nonlinear model for the AlGaN/GaN high electron mobility transistors (HEMTs) to extract DC intrinsic transconductance (gmDC), output conductance (gdsDC), and electron mobility from the intrinsic parameter set measured at high frequencies. An excellent agreement in I-V characteristics of the model with a fitting error of 0.11% enables us successfully extract the gmDC, gdsDC, and the total transconductance dispersion. For this model, we also present a reliable analysis scheme wherein the frequency dispersion effect due regional surface states in AlGaN/GaN HEMTs is taken into account under various bias conditions.

Fractal scattering of Gaussian solitons in directional couplers with logarithmic nonlinearities

Energy Technology Data Exchange (ETDEWEB)

Teixeira, Rafael M.P.; Cardoso, Wesley B., E-mail: wesleybcardoso@gmail.com

2016-08-12

In this paper we study the interaction of Gaussian solitons in a dispersive and nonlinear media with log-law nonlinearity. The model is described by the coupled logarithmic nonlinear Schrödinger equations, which is a nonintegrable system that allows the observation of a very rich scenario in the collision patterns. By employing a variational approach and direct numerical simulations, we observe a fractal-scattering phenomenon from the exit velocities of each soliton as a function of the input velocities. Furthermore, we introduce a linearization model to identify the position of the reflection/transmission window that emerges within the chaotic region. This enables us the possibility of controlling the scattering of solitons as well as the lifetime of bound states. - Highlights: • We study the interaction of Gaussian solitons in a system with log-law nonlinearity. • The model is described by the coupled logarithmic nonlinear Schrödinger equations. • We observe a fractal-scattering phenomenon of the solitons.

Asymptotic profile of global solutions to the generalized double dispersion equation via the nonlinear term

Science.gov (United States)

Wang, Yu-Zhu; Wei, Changhua

2018-04-01

In this paper, we investigate the initial value problem for the generalized double dispersion equation in R^n. Weighted decay estimate and asymptotic profile of global solutions are established for n≥3 . The global existence result was already proved by Kawashima and the first author in Kawashima and Wang (Anal Appl 13:233-254, 2015). Here, we show that the nonlinear term plays an important role in this asymptotic profile.

Analysis of Nonlinear Periodic and Aperiodic Media: Application to Optical Logic Gates

Science.gov (United States)

Yu, Yisheng

This dissertation is about the analysis of nonlinear periodic and aperiodic media and their application to the design of intensity controlled all optical logic gates: AND, OR, and NOT. A coupled nonlinear differential equation that characterizes the electromagnetic wave propagation in a nonlinear periodic (and aperiodic) medium has been derived from the first principle. The equations are general enough that it reflects the effect of transverse modal fields and can be used to analyze both co-propagating and counter propagating waves. A numerical technique based on the finite differences method and absorbing boundary condition has been developed to solve the coupled differential equations here. The numerical method is simple and accurate. Unlike the method based on characteristics that has been reported in the literature, this method does not involve integration and step sizes of time and space coordinates are decoupled. The decoupling provides independent choice for time and space step sizes. The concept of "gap soliton" has also been re-examined. The dissertation consists of four manuscripts. Manuscript I reports on the design of all optical logic gates: AND, OR, and NOT based on the bistability property of nonlinear periodic and aperiodic waveguiding structures. The functioning of the logic gates has been shown by analysis. The numerical technique that has been developed to solve the nonlinear differential equations are addressed in manuscript II. The effect of transverse modal fields on the bistable property of nonlinear periodic medium is reported in manuscript III. The concept of "gap soliton" that are generated in a nonlinear periodic medium has been re-examined. The details on the finding of the re-examination are discussed in manuscript IV.

Roles of dispersal, stochasticity, and nonlinear dynamics in the spatial structuring of seasonal natural enemy-victim populations

Science.gov (United States)

Patrick C. Tobin; Ottar N. Bjornstad

2005-01-01

Natural enemy-victim systems may exhibit a range of dynamic space-time patterns. We used a theoretical framework to study spatiotemporal structuring in a transient natural enemy-victim system subject to differential rates of dispersal, stochastic forcing, and nonlinear dynamics. Highly mobile natural enemies that attacked less mobile victims were locally spatially...

A Research Program on the Asymptotic Description of Electromagnetic Pulse Propagation in Spatially Inhomogeneous, Temporally Dispersive, Attenuative Media

National Research Council Canada - National Science Library

Oughstun, Kurt E; Cartwright, Natalie A

2007-01-01

.... Indeed, previous studies of ultrawideband electromagnetic pulse propagation through dispersive, nonconducting media has shown the existence of a so-called Brillouin precursor whose peak amplitude...

Distributed nonlinear optical response

DEFF Research Database (Denmark)

Nikolov, Nikola Ivanov

2005-01-01

of bound states of out of phase bright solitons and dark solitons. Also, the newly introduced analogy between the nonlocal cubic nonlinear and the quadratic nonlinear media, presented in paper B and Chapter 3 is discussed. In particular it supplies intuitive physical meaning of the formation of solitons...... in quadratic nonlinear media. In the second part of the report (Chapter 4), the possibility to obtain light with ultrabroad spectrum due to the interplay of many nonlinear effects based on cubic nonlinearity is investigated thoroughly. The contribution of stimulated Raman scattering, a delayed nonlinear...... a modified nonlinear Schroedinger model equation. Chapter 4 and papers D and E are dedicated to this part of the research....

Designing quadratic nonlinear photonic crystal fibers for soliton compression to few-cycle pulses

DEFF Research Database (Denmark)

Bache, Morten; Moses, Jeffrey; Lægsgaard, Jesper

2007-01-01

phase shifts accessible. This self-defocusing nonlinearity can be used to compress a pulse when combined with normal dispersion, and problems normally encountered due to self-focusing in cubic media are avoided. Thus, having no power limit, in bulk media a self-defocusing soliton compressor can create...... high-energy near single-cycle fs pulses (Liu et al., 2006). However, the group-velocity mismatch (GVM) between the FW and second harmonic (SH), given by the inverse group velocity difference d12=1/Vg,1 - 1/Vg,2, limits the pulse quality and compression ratio. Especially very short input pulses (...

Wavelength conversion, time demultiplexing and multicasting based on cross-phase modulation and four-wave mixing in dispersion-flattened highly nonlinear photonic crystal fiber

International Nuclear Information System (INIS)

Hui, Zhan-Qiang; Zhang, Jian-Guo

2012-01-01

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 −1 and 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. (paper)

Symbolic computation and solitons of the nonlinear Schroedinger equation in inhomogeneous optical fiber media

International Nuclear Information System (INIS)

Li Biao; Chen Yong

2007-01-01

In this paper, the inhomogeneous nonlinear Schroedinger equation with the loss/gain and the frequency chirping is investigated. With the help of symbolic computation, three families of exact analytical solutions are presented by employing the extended projective Riccati equation method. From our results, many previous known results of nonlinear Schroedinger equation obtained by some authors can be recovered by means of some suitable selections of the arbitrary functions and arbitrary constants. Of optical and physical interests, soliton propagation and soliton interaction are discussed and simulated by computer, which include snake-soliton propagation and snake-solitons interaction, boomerang-like soliton propagation and boomerang-like solitons interaction, dispersion managed (DM) bright (dark) soliton propagation and DM solitons interaction

Stochastic symplectic and multi-symplectic methods for nonlinear Schrödinger equation with white noise dispersion

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.

Stochastic symplectic and multi-symplectic methods for nonlinear Schrödinger equation with white noise dispersion

International Nuclear Information System (INIS)

Cui, Jianbo; Hong, Jialin; Liu, Zhihui; Zhou, Weien

2017-01-01

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.

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.

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.

Nonlinear polarization dynamics in a weakly birefringent all-normal dispersion photonic crystal fiber : toward a practical coherent fiber supercontinuum laser

DEFF Research Database (Denmark)

Tu, Haohua; Liu, Yuan; Liu, Xiaomin

2012-01-01

Dispersion-flattened dispersion-decreased all-normal dispersion (DFDD-ANDi) photonic crystal fibers have been identified as promising candidates for high-spectral-power coherent supercontinuum (SC) generation. However, the effects of the unintentional birefringence of the fibers on the SC generat...... of polarization-maintaining DFDD-ANDi fibers to avoid these adverse effects in pursuing a practical coherent fiber SC laser.......Dispersion-flattened dispersion-decreased all-normal dispersion (DFDD-ANDi) photonic crystal fibers have been identified as promising candidates for high-spectral-power coherent supercontinuum (SC) generation. However, the effects of the unintentional birefringence of the fibers on the SC...... generation have been ignored. This birefringence is widely present in nonlinear non-polarization maintaining fibers with a typical core size of 2 µm, presumably due to the structural symmetry breaks introduced in the fiber drawing process. We find that an intrinsic form-birefringence on the order of 10...

Nonlinear surface Alfven waves

International Nuclear Information System (INIS)

Cramer, N.F.

1991-01-01

The problem of nonlinear surface Alfven waves propagating on an interface between a plasma and a vacuum is discussed, with dispersion provided by the finite-frequency effect, i.e. the finite ratio of the frequency to the ion-cyclotron frequency. A set of simplified nonlinear wave equations is derived using the method of stretched co-ordinates, and another approach uses the generation of a second-harmonic wave and its interaction with the first harmonic to obtain a nonlinear dispersion relation. A nonlinear Schroedinger equation is then derived, and soliton solutions found that propagate as solitary pulses in directions close to parallel and antiparallel to the background magnetic field. (author)

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.

ARDISC (Argonne Dispersion Code): computer programs to calculate the distribution of trace element migration in partially equilibrating media

International Nuclear Information System (INIS)

Strickert, R.; Friedman, A.M.; Fried, S.

1979-04-01

A computer program (ARDISC, the Argonne Dispersion Code) is described which simulates the migration of nuclides in porous media and includes first order kinetic effects on the retention constants. The code allows for different absorption and desorption rates and solves the coupled migration equations by arithmetic reiterations. Input data needed are the absorption and desorption rates, equilibrium surface absorption coefficients, flow rates and volumes, and media porosities

Transient compressible flows in porous media

International Nuclear Information System (INIS)

Morrison, F.A. Jr.

1975-09-01

Transient compressible flow in porous media was investigated analytically. The major portion of the investigation was directed toward improving and understanding of dispersion in these flows and developing rapid accurate numerical techniques for predicting the extent of dispersion. The results are of interest in the containment of underground nuclear experiments. The transient one-dimensional transport of a trace component in a gas flow is analyzed. A conservation equation accounting for the effects of convective transport, dispersive transport, and decay, is developed. This relation, as well as a relation governing the fluid flow, is used to predict trace component concentration as a function of position and time. A detailed analysis of transport associated with the isothermal flow of an ideal gas is done. Because the governing equations are nonlinear, numerical calculations are performed. The ideal gas flow is calculated using a highly stable implicit iterative procedure with an Eulerian mesh. In order to avoid problems of anomolous dispersion associated with finite difference calculation, trace component convection and dispersion are calculated using a Lagrangian mesh. Details of the Eulerian-Lagrangian numerical technique are presented. Computer codes have been developed and implemented on the Lawrence Livermore Laboratory computer system

Fractional power-law spatial dispersion in electrodynamics

International Nuclear Information System (INIS)

Tarasov, Vasily E.; Trujillo, Juan J.

2013-01-01

Electric fields in non-local media with power-law spatial dispersion are discussed. Equations involving a fractional Laplacian in the Riesz form that describe the electric fields in such non-local media are studied. The generalizations of Coulomb’s law and Debye’s screening for power-law non-local media are characterized. We consider simple models with anomalous behavior of plasma-like media with power-law spatial dispersions. The suggested fractional differential models for these plasma-like media are discussed to describe non-local properties of power-law type. -- Highlights: •Plasma-like non-local media with power-law spatial dispersion. •Fractional differential equations for electric fields in the media. •The generalizations of Coulomb’s law and Debye’s screening for the media

The set valued unified model of dispersion and attenuation for wave propagation in dielectric (and anelastic media

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.

Unidirectional reflection and invisibility in nonlinear media with an incoherent nonlinearity

Science.gov (United States)

Mostafazadeh, Ali; Oflaz, Neslihan

2017-11-01

We give explicit criteria for the reflectionlessness, transparency, and invisibility of a finite-range potential in the presence of an incoherent (intensity-dependent) nonlinearity that is confined to the range of the potential. This allows us to conduct a systematic study of the effects of such a nonlinearity on a locally periodic class of finite-range potentials that display perturbative unidirectional invisibility. We use our general results to examine the effects of a weak Kerr nonlinearity on the behavior of these potentials and show that the presence of nonlinearity destroys the unidirectional invisibility of these potentials. If the strength of the Kerr nonlinearity is so weak that the first-order perturbation theory is reliable, the presence of nonlinearity does not affect the unidirectional reflectionlessness and transmission reciprocity of the potential. We show that the expected violation of the latter is a second order perturbative effect.

Effect of Surface Morphology and Dispersion Media on the Properties of PEDOT:PSS/n-Si Hybrid Solar Cell Containing Functionalized Graphene

Directory of Open Access Journals (Sweden)

Pham Van Trinh

2017-01-01

Full Text Available We present the results on the effect of surface morphology and dispersion media on the properties of PEDOT:PSS/n-Si hybrid solar cell containing functionalized graphene (Gr. The hybrid solar cells based on SiNWs showed higher power conversion efficiency (PCE compared to the planar based cells due to suppressing the carrier recombination and improving carrier transport efficiency. The PCE of hybrid solar cells could be improved by adding Gr into PEDOT:PSS. Different solvents including deionized (DI water, ethylene glycol (EG, and isopropyl alcohol (IPA were used as media for Gr dispersion. The best performance was obtained for the cell containing Gr dispersed in EG with a measured PCE of 7.33% and nearly 13% and 16% enhancement in comparison with the cells using Gr dispersed in IPA and DI water, respectively. The increase in PCE is attributed to improving the carrier-mobility, electrical conductivity, PEDOT crystallinity, and ordering.

Simulation of heating by optical absorption in nanoparticle dispersions (Conference Presentation)

Science.gov (United States)

Olbricht, Benjamin C.

2017-02-01

With the proliferation of highly confined, nanophotonic waveguides and laser sources with increasing intensity, the effects of laser heating will begin to greatly impact the materials used in optical applications. In order to better understand the mechanism of laser heating, its timescales, and the dispersion of heat into the material, simulations of nanoparticles in various media are presented. A generic model to describe a variety of nanoparticle shapes and sizes is desirable to describe complex phenomenon. These particles are dispersed into various solids, liquids, or gases depending on the application. To simulate nanoparticles and their interaction with their host material, the Finite Element Method (FEM) is used. Heat transfer following an absorption event is also described by a parabolic partial differential equation, and transient solutions are generated in response to continuous, pulsed, or modulated laser radiation. The simplest physical system described by FEM is that of a broadly-absorbing round-shaped nanoparticle dispersed in viscous host fluid or solid. Many experimental and theoretical studies conveniently describe a very similar system: a carbon "black" nanoparticle suspended in water. This material is well-known to exhibit nonlinear behavior when a laser pulse carrying 0.7 J/cm2 is incident on the material. For this process the FEM simulations agree with experimental results to show that a pulse of this fluence is capable of heating the solvent elements adjacent to the nanoparticle to their boiling point. This creates nonlinear scattering which is empirically observed as a nonlinear decrease in the transmitted power at this input fluence.

Smooth and non-smooth travelling waves in a nonlinearly dispersive Boussinesq equation

International Nuclear Information System (INIS)

Shen Jianwei; Xu Wei; Lei Youming

2005-01-01

The dynamical behavior and special exact solutions of nonlinear dispersive Boussinesq equation (B(m,n) equation), u tt -u xx -a(u n ) xx +b(u m ) xxxx =0, is studied by using bifurcation theory of dynamical system. As a result, all possible phase portraits in the parametric space for the travelling wave system, solitary wave, kink and anti-kink wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions are obtained. It can be shown that the existence of singular straight line in the travelling wave system is the reason why smooth waves converge to cusp waves, finally. When parameter are varied, under different parametric conditions, various sufficient conditions guarantee the existence of the above solutions are given

Some models of propagation of extremely short electromagnetic pulses in a nonlinear medium

International Nuclear Information System (INIS)

Maimistov, Andrei I

2000-01-01

Some cases of model media considered in this paper allow analytical solutions to nonlinear wave equations to be found and the time dependence of the electric field strength to be determined in the explicit form for arbitrarily short electromagnetic pulses. Our analysis does not employ any assumptions concerning a harmonic carrier wave or the variation rate of the field in such pulses. The class of models considered includes two-level resonance and quasi-resonance systems. Nonresonance media are analysed in terms of models of anharmonic oscillators - the Duffing and Lorentz models. In most cases, only particular solutions describing the stationary propagation of a video pulse (a unipolar transient of the electric field or a pulse including a small number of oscillations of the electric field around zero) can be found. These solutions correspond to sufficiently strong electromagnetic fields when the dispersion inherent in the medium is suppressed by nonlinear processes. (invited paper)

Active-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous Media

KAUST Repository

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.

Active-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous Media

KAUST Repository

Yang, Haijian; Yang, Chao; Sun, Shuyu

2016-01-01

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.

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 interferome......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...

Stack emission monitoring using non-dispersive infrared spectroscopy with an optimized nonlinear absorption cross interference correction algorithm

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.

Numerical Simulation of Cylindrical Solitary Waves in Periodic Media

KAUST Repository

Quezada de Luna, Manuel; Ketcheson, David I.

2013-01-01

We study the behavior of nonlinear waves in a two-dimensional medium with density and stress relation that vary periodically in space. Efficient approximate Riemann solvers are developed for the corresponding variable-coefficient first-order hyperbolic system. We present direct numerical simulations of this multiscale problem, focused on the propagation of a single localized perturbation in media with strongly varying impedance. For the conditions studied, we find little evidence of shock formation. Instead, solutions consist primarily of solitary waves. These solitary waves are observed to be stable over long times and to interact in a manner approximately like solitons. The system considered has no dispersive terms; these solitary waves arise due to the material heterogeneity, which leads to strong reflections and effective dispersion.

Numerical Simulation of Cylindrical Solitary Waves in Periodic Media

KAUST Repository

Quezada de Luna, Manuel

2013-07-14

We study the behavior of nonlinear waves in a two-dimensional medium with density and stress relation that vary periodically in space. Efficient approximate Riemann solvers are developed for the corresponding variable-coefficient first-order hyperbolic system. We present direct numerical simulations of this multiscale problem, focused on the propagation of a single localized perturbation in media with strongly varying impedance. For the conditions studied, we find little evidence of shock formation. Instead, solutions consist primarily of solitary waves. These solitary waves are observed to be stable over long times and to interact in a manner approximately like solitons. The system considered has no dispersive terms; these solitary waves arise due to the material heterogeneity, which leads to strong reflections and effective dispersion.

Investigation of focused and unfocused transducer beam patterns in moderately nonlinear absorbing media

Science.gov (United States)

Kharin, Nikolay A.

2001-05-01

The novel solution of the KZK equation for acoustic pressure of the second harmonic in slightly focused beam of a circular transducer was obtained in a closed form for moderately nonlinear absorbing media (Gol'dberg numbers ~ 1). The solution is based on the method of slowly changing wave profile in combination with the method of successive approximations. Two pairs of transducers (Valpey-Fisher Corp.) Were compared to investigate the influence of focusing on the applicability of the moderate nonlinearity approach. The first pair was of 0.25' diameter and the second was of 0.5' diameter. Both pairs has one transducer with flat surface and the other geometrically focused at 4'. The central frequency for all transducers was 5 MHz. Measurements were undertaken in the blood-mimicking solution of water and glycerine. The results demonstrated that for slightly focused transducers with circular apertures, the moderate nonlinearity approach is still valid, as it was proved for flat sources with the same source level, despite the higher pressures in the focal region. The peak pressure for the weakly focused system occurs at a shorter range than focal length.

Preparation and third-order nonlinear optical property of poly(urethane-imide containing dispersed red chromophore

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.

Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials

International Nuclear Information System (INIS)

Wen, Shuangchun; Xiang, Yuanjiang; Dai, Xiaoyu; Tang, Zhixiang; Su, Wenhua; Fan, Dianyuan

2007-01-01

A metamaterial (MM) differs from an ordinary optical material mainly in that it has a dispersive magnetic permeability and offers greatly enhanced design freedom to alter the linear and nonlinear properties. This makes it possible for us to control the propagation of ultrashort electromagnetic pulses at will. Here we report on generic features of ultrashort electromagnetic pulse propagation and demonstrate the controllability of both the linear and nonlinear parameters of models for pulse propagation in MMs. First, we derive a generalized system of coupled three-dimensional nonlinear Schroedinger equations (NLSEs) suitable for few-cycle pulse propagation in a MM with both nonlinear electric polarization and nonlinear magnetization. The coupled equations recover previous models for pulse propagation in both ordinary material and a MM under the same conditions. Second, by using the coupled NLSEs in the Drude dispersive model as an example, we identify the respective roles of the dispersive electric permittivity and magnetic permeability in ultrashort pulse propagation and disclose some additional features of pulse propagation in MMs. It is shown that, for linear propagation, the sign and magnitude of space-time focusing can be controlled through adjusting the linear dispersive permittivity and permeability. For nonlinear propagation, the linear dispersive permittivity and permeability are incorporated into the nonlinear magnetization and nonlinear polarization, respectively, resulting in controllable magnetic and electric self-steepening effects and higher-order dispersively nonlinear terms in the propagation models

Dispersive shock waves in systems with nonlocal dispersion of Benjamin-Ono type

Science.gov (United States)

El, G. A.; Nguyen, L. T. K.; Smyth, N. F.

2018-04-01

We develop a general approach to the description of dispersive shock waves (DSWs) for a class of nonlinear wave equations with a nonlocal Benjamin-Ono type dispersion term involving the Hilbert transform. Integrability of the governing equation is not a pre-requisite for the application of this method which represents a modification of the DSW fitting method previously developed for dispersive-hydrodynamic systems of Korteweg-de Vries (KdV) type (i.e. reducible to the KdV equation in the weakly nonlinear, long wave, unidirectional approximation). The developed method is applied to the Calogero-Sutherland dispersive hydrodynamics for which the classification of all solution types arising from the Riemann step problem is constructed and the key physical parameters (DSW edge speeds, lead soliton amplitude, intermediate shelf level) of all but one solution type are obtained in terms of the initial step data. The analytical results are shown to be in excellent agreement with results of direct numerical simulations.

Local-in-space blow-up criteria for a class of nonlinear dispersive wave equations

Science.gov (United States)

Novruzov, Emil

2017-11-01

This paper is concerned with blow-up phenomena for the nonlinear dispersive wave equation on the real line, ut -uxxt +[ f (u) ] x -[ f (u) ] xxx +[ g (u) + f″/(u) 2 ux2 ] x = 0 that includes the Camassa-Holm equation as well as the hyperelastic-rod wave equation (f (u) = ku2 / 2 and g (u) = (3 - k) u2 / 2) as special cases. We establish some a local-in-space blow-up criterion (i.e., a criterion involving only the properties of the data u0 in a neighborhood of a single point) simplifying and precising earlier blow-up criteria for this equation.

Smooth and non-smooth traveling wave solutions of a class of nonlinear dispersive equation

International Nuclear Information System (INIS)

Zhao Xiaoshan; Wu Aidi; He Wenzhang

2009-01-01

There is the widespread existence of wave phenomena in physics, mechanics. This clearly necessitates a study of traveling waves in depth and of the modeling and analysis involved. In this paper, we study a nonlinear dispersive K(n,-n,2n) equation, which can be regarded as a generalized K(n,n) equation. Applying the bifurcation theory and the method of phase portraits analysis, we obtain the dynamical behavior and special exact solutions of the K(n,-n,2n) equation. As a result, the conditions under which peakon and compacton solutions appear are also given and the analytic expressions of peakon solutions, compacton and periodic cusp wave solutions are obtained.

Hindered bacterial mobility in porous media flow enhances dispersion

Science.gov (United States)

Dehkharghani, Amin; Waisbord, Nicolas; Dunkel, Jörn; Guasto, Jeffrey

2017-11-01

Swimming bacteria live in porous environments characterized by dynamic fluid flows, where they play a crucial role in processes ranging from the bioremediation to the spread of infections. We study bacterial transport in a quasi-two-dimensional porous microfluidic device, which is complemented by Langevin simulations. The cell trajectories reveal filamentous patterns of high cell concentration, which result from the accumulation of bacteria in the high-shear regions of the flow and their subsequent advection. Moreover, the effective diffusion coefficient of the motile bacteria is severely hindered in the transverse direction to the flow due to decorrelation of the cells' persistent random walk by shear-induced rotation. The hindered lateral diffusion has the surprising consequence of strongly enhancing the longitudinal bacterial transport through a dispersion effect. These results demonstrate the significant role of the flow and geometry in bacterial transport through porous media with potential implications for understanding ecosystem dynamics and engineering bioreactors. NSF CBET-1511340, NSF CAREER-1554095.

Solitary waves, steepening and initial collapse in the Maxwell-Lorentz system

DEFF Research Database (Denmark)

Sørensen, Mads Peter; Brio, Moysey; Webb, Garry

2002-01-01

We present a numerical study of Maxwell's equations in nonlinear dispersive optical media describing propagation of pulses in one Cartesian space dimension. Dispersion and nonlinearity are accounted for by a linear Lorentz model and an instantaneous Kerr nonlinearity, respectively. The dispersion......–Rosales weakly dispersive system. The weak dispersion in general cannot prevent the wave breaking with instantaneous or delayed nonlinearities....

Dispersive traveling wave solutions of the Equal-Width and Modified Equal-Width equations via mathematical methods and its applications

Science.gov (United States)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

The Equal-Width and Modified Equal-Width equations are used as a model in partial differential equations for the simulation of one-dimensional wave transmission in nonlinear media with dispersion processes. In this article we have employed extend simple equation method and the exp(-varphi(ξ)) expansion method to construct the exact traveling wave solutions of equal width and modified equal width equations. The obtained results are novel and have numerous applications in current areas of research in mathematical physics. It is exposed that our method, with the help of symbolic computation, provides a effective and powerful mathematical tool for solving different kind nonlinear wave problems.

Propagation of dark stripe beams in nonlinear media: Snake instability and creation of optical vortices

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....

Nonlocal and nonlinear dispersion in a nonlinear Schrodinger-type equation: exotic solitons and short-wavelength instabilities

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...

Design of Rose Bengal/FTO optical thin film system as a novel nonlinear media for infrared blocking windows

Directory of Open Access Journals (Sweden)

S.M. El-Bashir

Full Text Available Rose Bengal (RB is a new organic semiconductor with the highly stable layer, was deposited on highly cleaned conductive glass substrate known as (FTO glass with different thickness in the range from 80 to 292 nm. XRD showed an entirely amorphous structure of the studied film thicknesses. The observed peaks are the indexed peaks for FTO layer. Spectrophotometric data as transmittance, reflectance, and absorbance were used for the analysis the optical constant of RB/FTO optical thin film system. Refractive index was calculated using Fresnel’s equation with the aid of reflectance and absorption index. The dielectric constant, dielectric loss and dissipation factor were discussed and analyzed according to the applied optical theories. Nonlinear parameters such as third order nonlinear optical susceptibility and the nonlinear refractive index were calculated based on the linear refractive index of the applications of this material in nonlinear media. The results showed that Rose Bengal is a proving material for wide scale optoelectronic applications such as infrared blocking windows. Keywords: Rose Bengal, Dielectric parameters, Linear/nonlinear optics, Dye/FTO, IR blocking windows

Dispersive optical soliton solutions for the hyperbolic and cubic-quintic nonlinear Schrödinger equations via the extended sinh-Gordon equation expansion method

Science.gov (United States)

Seadawy, Aly R.; Kumar, Dipankar; Chakrabarty, Anuz Kumar

2018-05-01

The (2+1)-dimensional hyperbolic and cubic-quintic nonlinear Schrödinger equations describe the propagation of ultra-short pulses in optical fibers of nonlinear media. By using an extended sinh-Gordon equation expansion method, some new complex hyperbolic and trigonometric functions prototype solutions for two nonlinear Schrödinger equations were derived. The acquired new complex hyperbolic and trigonometric solutions are expressed by dark, bright, combined dark-bright, singular and combined singular solitons. The obtained results are more compatible than those of other applied methods. The extended sinh-Gordon equation expansion method is a more powerful and robust mathematical tool for generating new optical solitary wave solutions for many other nonlinear evolution equations arising in the propagation of optical pulses.

On the dynamics of Airy beams in nonlinear media with nonlinear losses.

Science.gov (United States)

Ruiz-Jiménez, Carlos; Nóbrega, K Z; Porras, Miguel A

2015-04-06

We investigate on the nonlinear dynamics of Airy beams in a regime where nonlinear losses due to multi-photon absorption are significant. We identify the nonlinear Airy beam (NAB) that preserves the amplitude of the inward Hänkel component as an attractor of the dynamics. This attractor governs also the dynamics of finite-power (apodized) Airy beams, irrespective of the location of the entrance plane in the medium with respect to the Airy waist plane. A soft (linear) input long before the waist, however, strongly speeds up NAB formation and its persistence as a quasi-stationary beam in comparison to an abrupt input at the Airy waist plane, and promotes the formation of a new type of highly dissipative, fully nonlinear Airy beam not described so far.

Dispersion Behaviour of Silica Nanoparticles in Biological Media and Its Influence on Cellular Uptake.

Science.gov (United States)

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.

Polythiophene derivative functionalized with disperse red 1 chromophore: Its third-order nonlinear optical properties through Z-scan technique under continuous and femtosecond irradiation

Science.gov (United States)

de la Garza-Rubí, R. M. A.; Güizado-Rodríguez, M.; Mayorga-Cruz, D.; Basurto-Pensado, M. A.; Guerrero-Álvarez, J. A.; Ramos-Ortiz, G.; Rodríguez, M.; Maldonado, J. L.

2015-08-01

A copolymer of 3-hexylthiophene and thiophene functionalized with disperse red 1, poly(3-HT-co-TDR1), was synthesized. Chemical structure, molecular weight distribution, optical and thermal properties of this copolymer were characterized by NMR, FT-IR, UV-vis, GPC and DSC-TGA. An optical nonlinear analysis by Z-scan method was also performed for both continuous wave (CW) and pulsed laser pumping. In the CW regime the nonlinearities were evaluated in solid films, and a negative nonlinear refractive index in the range 2.7-4.1 × 10-4 cm2/W was obtained. These values are notoriously high and allowed to observe self-defocusing effects at very low laser intensities: below 1 mW. Further, nonlinear self-phase modulation patterns, during laser irradiation, were also observed. In the pulsed excitation the nonlinear response was evaluated in solution resulting in large two-photon absorption cross section of 5725 GM for the whole copolymer chain and with a value of 232 GM per repeated monomeric unit.

Boundary control of fluid flow through porous media

DEFF Research Database (Denmark)

Hasan, Agus; Foss, Bjarne; Sagatun, Svein Ivar

2010-01-01

The flow of fluids through porous media can be described by the Boussinesq’s equation with mixed boundary conditions; a Neumann’s boundary condition and a nonlinear boundary condition. The nonlinear boundary condition provides a means to control the fluid flow through porous media. In this paper,......, some stabilizing controllers are constructed for various cases using Lyapunov design.......The flow of fluids through porous media can be described by the Boussinesq’s equation with mixed boundary conditions; a Neumann’s boundary condition and a nonlinear boundary condition. The nonlinear boundary condition provides a means to control the fluid flow through porous media. In this paper...

Nonlocal Symmetries, Conservation Laws and Interaction Solutions of the Generalised Dispersive Modified Benjamin-Bona-Mahony Equation

Science.gov (United States)

Yan, Xue-Wei; Tian, Shou-Fu; Dong, Min-Jie; Wang, Xiu-Bin; Zhang, Tian-Tian

2018-05-01

We consider the generalised dispersive modified Benjamin-Bona-Mahony equation, which describes an approximation status for long surface wave existed in the non-linear dispersive media. By employing the truncated Painlevé expansion method, we derive its non-local symmetry and Bäcklund transformation. The non-local symmetry is localised by a new variable, which provides the corresponding non-local symmetry group and similarity reductions. Moreover, a direct method can be provided to construct a kind of finite symmetry transformation via the classic Lie point symmetry of the normal prolonged system. Finally, we find that the equation is a consistent Riccati expansion solvable system. With the help of the Jacobi elliptic function, we get its interaction solutions between solitary waves and cnoidal periodic waves.

Symmetries of the triple degenerate DNLS equations for weakly nonlinear dispersive MHD waves

International Nuclear Information System (INIS)

Webb, G. M.; Brio, M.; Zank, G. P.

1996-01-01

A formulation of Hamiltonian and Lagrangian variational principles, Lie point symmetries and conservation laws for the triple degenerate DNLS equations describing the propagation of weakly nonlinear dispersive MHD waves along the ambient magnetic field, in β∼1 plasmas is given. The equations describe the interaction of the Alfven and magnetoacoustic modes near the triple umbilic point, where the fast magnetosonic, slow magnetosonic and Alfven speeds coincide and a g 2 =V A 2 where a g is the gas sound speed and V A is the Alfven speed. A discussion is given of the travelling wave similarity solutions of the equations, which include solitary wave and periodic traveling waves. Strongly compressible solutions indicate the necessity for the insertion of shocks in the flow, whereas weakly compressible, near Alfvenic solutions resemble similar, shock free travelling wave solutions of the DNLS equation

Chirped self-similar solutions of a generalized nonlinear Schroedinger equation

Energy Technology Data Exchange (ETDEWEB)

Fei Jin-Xi [Lishui Univ., Zhejiang (China). College of Mathematics and Physics; Zheng Chun-Long [Shaoguan Univ., Guangdong (China). School of Physics and Electromechanical Engineering; Shanghai Univ. (China). Shanghai Inst. of Applied Mathematics and Mechanics

2011-01-15

An improved homogeneous balance principle and an F-expansion technique are used to construct exact chirped self-similar solutions to the generalized nonlinear Schroedinger equation with distributed dispersion, nonlinearity, and gain coefficients. Such solutions exist under certain conditions and impose constraints on the functions describing dispersion, nonlinearity, and distributed gain function. The results show that the chirp function is related only to the dispersion coefficient, however, it affects all of the system parameters, which influence the form of the wave amplitude. As few characteristic examples and some simple chirped self-similar waves are presented. (orig.)

Lagrangian analysis of nonlinear wave-wave interactions in bounded plasmas

International Nuclear Information System (INIS)

Carr, A.R.

1979-01-01

In a weakly turbulent nonlinear wave-supporting medium, one of the important nonlinear processes which may occur is resonant three-wave interaction. Whitham's averaged Lagrangian method provides a general formulation of wave evolution laws which is easily adapted to nonlinear dispersive media. In this thesis, the strength of nonlinear interactions between three coherent, axisymmetric, low frequency, magnetohydrodynamic (Alfven) waves propagating in resonance along a cold cylindrical magnetized plasma column is calculated. Both a uniform and a parabolic density distribution have been considered. To account for a non-zero plasma temperature, pressure effects have been included. Distinctive features of the work are the use of cylindrical geometry, the presence of a finite rather than an infinite axial magnetic field, the treatment of a parabolic density distribution, and the inclusion of both ion and electron contributions in all expressions. Two astrophysical applications of the presented theory have been considered. In the first, the possibility of resonant three-wave coupling between geomagnetic micropulsations, which propagate as Alfven or magnetosonic waves along the Earth's magnetic field lines, has been investigated. The second case is the theory of energy transport through the solar chromosphere by upward propagating magnetohydrodynamic waves, which may then couple to heavily damped waves in the corona, causing the observed excess heating in that region

Comparison of numerical dispersion for finite-difference algorithms in transversely isotropic media with a vertical symmetry axis

International Nuclear Information System (INIS)

Liang, Wen-Quan; Wang, Yan-Fei; Yang, Chang-Chun

2015-01-01

Numerical simulation of the wave equation is widely used to synthesize seismograms theoretically and is also the basis of the reverse time migration and full waveform inversion. For the finite difference methods, grid dispersion often exists because of the discretization of the time and the spatial derivatives in the wave equation. How to suppress the grid dispersion is therefore a key problem for finite difference (FD) approaches. The FD operators for the space derivatives are usually obtained in the space domain. However, the wave equations are discretized in the time and space directions simultaneously. So it would be better to design the FD operators in the time–space domain. We improved the time–space domain method for obtaining the FD operators in an acoustic vertically transversely isotropic (VTI) media so as to cover a much wider range of frequencies. Dispersion analysis and seismic numerical simulation demonstrate the effectiveness of the proposed method. (paper)

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....

Stable rotating dipole solitons in nonlocal media

DEFF Research Database (Denmark)

Lopez-Aguayo, Servando; Skupin, Stefan; Desyatnikov, Anton S.

2006-01-01

We present the first example of stable rotating two-soliton bound states in nonlinear optical media with nonlocal response. We show that, in contrast to media with local response, nonlocality opens possibilities to generate stable azimuthons.......We present the first example of stable rotating two-soliton bound states in nonlinear optical media with nonlocal response. We show that, in contrast to media with local response, nonlocality opens possibilities to generate stable azimuthons....

Nonlinear optics an analytical approach

CERN Document Server

Mandel, Paul

2010-01-01

Based on the author's extensive teaching experience and lecture notes, this textbook provides a substantially analytical rather than descriptive presentation of nonlinear optics. Divided into five parts, with most chapters corresponding to a two-hour lecture, the book begins with a unique account of the historical development from Kirchhoff's law for the black-body radiation to Planck's quantum hypothesis and Einstein's discovery of spontaneous emission - providing all the explicit proofs. The subsequent sections deal with matter quantization, ultrashort pulse propagation in 2-level media, cavity nonlinear optics, chi(2) and chi(3) media. For graduate and PhD students in nonlinear optics or photonics, while also representing a valuable reference for researchers in these fields.

Supra-transmission and bistability in nonlinear media with a photonic and electronic forbidden band gap; Supratransmission et bistabilite nonlineaire dans les milieux a bandes interdites photoniques et electroniques

Energy Technology Data Exchange (ETDEWEB)

Chevriaux, D

2007-06-15

We study wave scattering in different nonlinear media possessing a natural forbidden band gap. In particular, we show the existence of a bistable behavior in media governed by the sine-Gordon equation (short pendular chain, Josephson junction array, quantum Hall bilayer), or the nonlinear Schroedinger equation (Kerr and Bragg media), in discrete and continuous models. These different media are submitted to periodic boundary conditions with a frequency in the forbidden band gap and an amplitude that determines their stability states. Indeed, for a sufficient amplitude (supra-transmission), the medium switches from reflector to transmitter, hence allowing the output signal to jump from evanescent to large values. We give a complete analytical description of the bistability that allows to understand the different stationary states observed and to predict the switch of one state to the other. (author)

A new approach to obtaining the roots of the dispersion equation for slab geometry multiplying media

International Nuclear Information System (INIS)

Silva, Davi J.M.; Barros, Ricardo C.; Alves Filho, Hermes

2013-01-01

In this work we describe an alternative approach for obtaining the roots of the dispersion equation. For the mathematical model, we used the slab-geometry neutron transport equation in the discrete ordinates (S N ), formulation, considering isotropic scattering and monoenergetic model. The basic idea is to find a basis for the kernel of the S N differential operator, whose elements are exponential eigenfunctions corresponding to distinct eigenvalues which are the roots of the dispersion equation. That strategy yields a gain in programming computational codes, including the strategy used to obtain the purely imaginary eigenvalues and their associated complex eigenfunctions, that appear in the spectral analysis of the S N equations in multiplying media. These eigenvalues and corresponding eigenfunctions are used to obtain the parameters of the auxiliary equations of the spectral nodal methods, e.g., the spectral diamond (SD) auxiliary equation. (author)

Nonlinear Wave Propagation

Science.gov (United States)

2015-05-07

associated with the lattice background; the nonlinearity is derived from the inclusion of cubic nonlinearity. Often the background potential is periodic...dispersion branch we can find discrete evolution equations for the envelope associated with the lattice NLS equation (1) by looking for solutions of...spatial operator in the above NLS equation can be elliptic, hyperbolic or parabolic . We remark that further reduction is possible by going into a moving

Treatment of Cerenkov radiation from electric and magnetic charges in dispersive and dissipative media

International Nuclear Information System (INIS)

Saffouri, M.H.

1982-07-01

A rigorous treatment of the problem of Cerenkov radiation from fast moving electric and magnetic charges is presented. This is based on the rigorous solution of Maxwell's equations in a general dispersive medium possessing dielectric and magnetic properties and with, and without, dissipation. It is shown that the fields are completely determined by one scalar function. Expressions for the exact fields are obtained. From the asymptotic fields all the relevant properties of Cerenkov radiation are reproduced. In particular, it is shown that in the absence of dissipation the energy in each mode travels with the phase velocity of that mode. For a dissipative medium the electric field develops a longitudinal component and the energy propagates at an angle to the phase velocity. Application to the case of a Tachyon shows that it must emit Cerenkov radiation in vacuum. An estimate is given for the resulting linear density of emitted radiation. Finally, two suggestions are made for the experimental detection of magnetic charges and electric dipole moments of elementary particles based upon the Cerenkov radiation which they would emit in dispersive media. (author)

One-step leapfrog ADI-FDTD method for simulating electromagnetic wave propagation in general dispersive media.

Science.gov (United States)

Wang, Xiang-Hua; Yin, Wen-Yan; Chen, Zhi Zhang David

2013-09-09

The one-step leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method is reformulated for simulating general electrically dispersive media. It models material dispersive properties with equivalent polarization currents. These currents are then solved with the auxiliary differential equation (ADE) and then incorporated into the one-step leapfrog ADI-FDTD method. The final equations are presented in the form similar to that of the conventional FDTD method but with second-order perturbation. The adapted method is then applied to characterize (a) electromagnetic wave propagation in a rectangular waveguide loaded with a magnetized plasma slab, (b) transmission coefficient of a plane wave normally incident on a monolayer graphene sheet biased by a magnetostatic field, and (c) surface plasmon polaritons (SPPs) propagation along a monolayer graphene sheet biased by an electrostatic field. The numerical results verify the stability, accuracy and computational efficiency of the proposed one-step leapfrog ADI-FDTD algorithm in comparison with analytical results and the results obtained with the other methods.

Enhanced dispersion of boron nitride nanosheets in aqueous media by using bile acid-based surfactants

Science.gov (United States)

Chae, Ari; Park, Soo-Jin; Min, Byunggak; In, Insik

2018-01-01

Facile noncovalent surface functionalization of hydroxylated boron nitride nanosheet (BNNS-OH) was attempted through the sonication-assisted exfoliation of h-BN in aqueous media in the presence of bile acid-based surfactants such as sodium cholic acid (SC) or sodium deoxycholic acid (SDC), resulting in SC- or SDC-BNNS-OH dispersion with high up to 2 mg ml-1 and enhanced dispersion stability due to the increased negative zeta potential. While prepared SC-BNNS-OH revealed multi-layered BNNS structures, the large lateral sizes of hundreds nanometers and clear h-BN lattice structures are very promising for the preparation and application of water-processable BNNS-based nanomaterials. It is regarded that noncovalent functionalization of BNNS-OH based on σ-π interaction between with σ-rich bile acid-based amphiphiles and π-rich BNNS is very effective to formulate multi-functional BNNS-based nanomaterials or hybrids that can be utilized in various applications where both the pristine properties of BNNS and the extra functions are simultaneously required.

Diffractons: Solitary Waves Created by Diffraction in Periodic Media

KAUST Repository

Ketcheson, David I.; Quezada de Luna, Manuel

2015-01-01

A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. These solitary waves depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation

Estimation of time delay and wavelength shift for highly nonlinear multilayer waveguide by using time transformation approach

Science.gov (United States)

Chatterjee, Roshmi; Basu, Mousumi

2018-02-01

The well known time transformation method is used here to derive the temporal and spectral electric field distribution at the output end of a multilayer waveguide which consists of different layers of Kerr nonlinear media. A highly nonlinear CS 3-68 glass is considered as one of the materials of the waveguide which mainly comprises of different chalcogenide glass layers. The results indicate that there is sufficient time delay as well as frequency shift between the input and output pulses which is associated with the phenomenon of adiabatic wavelength conversion (AWC). Depending on different arrangements of materials, the time delay and frequency shift can be changed. As a result an input pulse in visible green region can be blue-shifted or red-shifted according to the choices of refractive index of the non-dispersive Kerr nonlinear media. The results show that under certain conditions the input pulse is broadened or compressed for different combinations of materials. This process of AWC also includes the variation of temporal and spectral phase, time delay, temporal peak power etc. For different input pulse shapes the change in time delay is also presented. The study may be useful to find applications of AWC in optical resonators or optical signal processing to be applicable to different photonic devices.

The nonlocal elastomagnetoelectrostatics of disordered micropolar media

International Nuclear Information System (INIS)

Kabychenkov, A. F.; Lisiovskii, F. V.

2016-01-01

The interactions of electric, magnetic, and elastic subsystems in nonlinear disordered micropolar media that possess a bending–torsion tensor and an nonsymmetric strain tensor have been studied in the framework of phenomenological elastomagnetoelectrostatics. A system of nonlinear equations for determining the ground state of these media has been obtained by the variational method. It is shown that nonuniform external and internal rotations not only create elastic stresses, but also generate additional electric and magnetic fields, while nonuniform elastic stresses and external fields induce internal rotations. The nonlocal character of the micropolar media significantly influences elementary excitations and nonlinear dynamic processes.

Dispersion compensation of fiber optic communication system with direct detection using artificial neural networks (ANNs)

Science.gov (United States)

Maghrabi, Mahmoud M. T.; Kumar, Shiva; Bakr, Mohamed H.

2018-02-01

This work introduces a powerful digital nonlinear feed-forward equalizer (NFFE), exploiting multilayer artificial neural network (ANN). It mitigates impairments of optical communication systems arising due to the nonlinearity introduced by direct photo-detection. In a direct detection system, the detection process is nonlinear due to the fact that the photo-current is proportional to the absolute square of the electric field intensity. The proposed equalizer provides the most efficient computational cost with high equalization performance. Its performance is comparable to the benchmark compensation performance achieved by maximum-likelihood sequence estimator. The equalizer trains an ANN to act as a nonlinear filter whose impulse response removes the intersymbol interference (ISI) distortions of the optical channel. Owing to the proposed extensive training of the equalizer, it achieves the ultimate performance limit of any feed-forward equalizer (FFE). The performance and efficiency of the equalizer is investigated by applying it to various practical short-reach fiber optic communication system scenarios. These scenarios are extracted from practical metro/media access networks and data center applications. The obtained results show that the ANN-NFFE compensates for the received BER degradation and significantly increases the tolerance to the chromatic dispersion distortion.

Synthetic-aperture radar imaging through dispersive media

International Nuclear Information System (INIS)

Varslot, Trond; Morales, J Héctor; Cheney, Margaret

2010-01-01

In this paper we develop a method for synthetic-aperture radar (SAR) imaging through a dispersive medium. We consider the case when the sensor and scatterers are embedded in a known homogeneous dispersive material, the scene to be imaged lies on a known surface and the radar antenna flight path is an arbitrary but known smooth curve. The scattering is modeled using a linearized (Born) scalar model. We assume that the measurements are polluted with additive noise. Furthermore, we assume that we have prior knowledge about the power-spectral densities of the scene and the noise. This leads us to formulate the problem in a statistical framework. We develop a filtered-back-projection imaging algorithm in which we choose the filter according to the statistical properties of the scene and noise. We present numerical simulations for a case where the scene consists of point-like scatterers located on the ground, and demonstrate how the ability to resolve the targets depends on a quantity which we call the noise-to-target ratio. In our simulations, the dispersive material is modeled with the Fung–Ulaby equations for leafy vegetation. However, the method is also applicable to other dielectric materials where the dispersion is considered relevant in the frequency range of the transmitted signals

New solitary solutions with compact support for Boussinesq-like B(2n, 2n) equations with fully nonlinear dispersion

International Nuclear Information System (INIS)

Zhu Yonggui; Lu Chao

2007-01-01

In this paper, the Boussinesq-like equations with fully nonlinear dispersion, B(2n, 2n) equations: u tt + (u 2n ) xx + (u 2n ) xxxx 0 which exhibit compactons: solitons with compact support, are studied. New exact solitary solutions with compact support are found. The special case B(2, 2) is chosen to illustrate the concrete scheme of the decomposition method in B(2n, 2n) equations. General formulas for the solutions of B(2n, 2n) equations are established

Development of a code to simulate dispersion of atmospheric released tritium gas in the environmental media and to evaluate doses. TRIDOSE

International Nuclear Information System (INIS)

Murata, Mikio; Noguchi, Hiroshi; Yokoyama, Sumi

2000-11-01

A computer code (TRIDOSE) was developed to assess the environmental impact of atmospheric released tritium gas (T 2 ) from nuclear fusion related facilities. The TRIDOSE simulates dispersion of T 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)

A linearized dispersion relation for orthorhombic pseudo-acoustic modeling

KAUST Repository

Song, Xiaolei; Alkhalifah, Tariq Ali

2012-01-01

Wavefield extrapolation in acoustic orthorhombic anisotropic media suffers from wave-mode coupling and stability limitations in the parameter range. We introduce a linearized form of the dispersion relation for acoustic orthorhombic media to model acoustic wavefields. We apply the lowrank approximation approach to handle the corresponding space-wavenumber mixed-domain operator. Numerical experiments show that the proposed wavefield extrapolator is accurate and practically free of dispersions. Further, there is no coupling of qSv and qP waves, because we use the analytical dispersion relation. No constraints on Thomsen's parameters are required for stability. The linearized expression may provide useful application for parameter estimation in orthorhombic media.

A linearized dispersion relation for orthorhombic pseudo-acoustic modeling

KAUST Repository

Song, Xiaolei

2012-11-04

Wavefield extrapolation in acoustic orthorhombic anisotropic media suffers from wave-mode coupling and stability limitations in the parameter range. We introduce a linearized form of the dispersion relation for acoustic orthorhombic media to model acoustic wavefields. We apply the lowrank approximation approach to handle the corresponding space-wavenumber mixed-domain operator. Numerical experiments show that the proposed wavefield extrapolator is accurate and practically free of dispersions. Further, there is no coupling of qSv and qP waves, because we use the analytical dispersion relation. No constraints on Thomsen\\'s parameters are required for stability. The linearized expression may provide useful application for parameter estimation in orthorhombic media.

Optimized nonlinear inversion of surface-wave dispersion data

International Nuclear Information System (INIS)

Raykova, Reneta B.

2014-01-01

A new code for inversion of surface wave dispersion data is developed to obtain Earth’s crustal and upper mantle velocity structure. The author developed Optimized Non–Linear Inversion ( ONLI ) software, based on Monte-Carlo search. The values of S–wave velocity VS and thickness h for a number of horizontal homogeneous layers are parameterized. Velocity of P–wave VP and density ρ of relevant layers are calculated by empirical or theoretical relations. ONLI explores parameters space in two modes, selective and full search, and the main innovation of software is evaluation of tested models. Theoretical dispersion curves are calculated if tested model satisfied specific conditions only, reducing considerably the computation time. A number of tests explored impact of parameterization and proved the ability of ONLI approach to deal successfully with non–uniqueness of inversion problem. Key words: Earth’s structure, surface–wave dispersion, non–linear inversion, software

Solitons supported by localized nonlinearities in periodic media

International Nuclear Information System (INIS)

Dror, Nir; Malomed, Boris A.

2011-01-01

Nonlinear periodic systems, such as photonic crystals and Bose-Einstein condensates (BEC's) loaded into optical lattices, are often described by the nonlinear Schroedinger or Gross-Pitaevskii equation with a sinusoidal potential. Here, we consider a model based on such a periodic potential, with the nonlinearity (attractive or repulsive) concentrated either at a single point or at a symmetric set of two points, which are represented, respectively, by a single δ function or a combination of two δ functions. With the attractive or repulsive sign of the nonlinearity, this model gives rise to ordinary solitons or gap solitons (GS's), which reside, respectively, in the semi-infinite or finite gaps of the system's linear spectrum, being pinned to the δ functions. Physical realizations of these systems are possible in optics and BEC's, using diverse variants of the nonlinearity management. First, we demonstrate that the single δ function multiplying the nonlinear term supports families of stableregular solitons in the self-attractive case, while a family of solitons supported by the attractive δ function in the absence of the periodic potential is completely unstable. In addition, we show that the δ function can support stable GS's in the first finite band gap in both the self-attractive and repulsive models. The stability analysis for the GS's in the second finite band gap is reported too, for both signs of the nonlinearity. Alongside the numerical analysis, analytical approximations are developed for the solitons in the semi-infinite and first two finite gaps, with the single δ function positioned at a minimum or maximum of the periodic potential. In the model with the symmetric set of two δ functions, we study the effect of the spontaneous symmetry breaking of the pinned solitons. Two configurations are considered, with the δ functions set symmetrically with respect to the minimum or maximum of the underlying potential.

Multi-soliton management by the integrable nonautonomous nonlinear integro-differential Schrödinger equation

International Nuclear Information System (INIS)

Zhang, Yu-Juan; Zhao, Dun; Luo, Hong-Gang

2014-01-01

We consider a wide class of integrable nonautonomous nonlinear integro-differential Schrödinger equation which contains the models for the soliton management in Bose–Einstein condensates, nonlinear optics, and inhomogeneous Heisenberg spin chain. With the help of the nonisospectral AKNS hierarchy, we obtain the N-fold Darboux transformation and the N-fold soliton-like solutions for the equation. The soliton management, especially the synchronized dispersive and nonlinear management in optical fibers is discussed. It is found that in the situation without external potential, the synchronized dispersive and nonlinear management can keep the integrability of the nonlinear Schrödinger equation; this suggests that in optical fibers, the synchronized dispersive and nonlinear management can control and maintain the propagation of a multi-soliton. - Highlights: • We consider a unified model for soliton management by an integrable integro-differential Schrödinger equation. • Using Lax pair, the N-fold Darboux transformation for the equation is presented. • The multi-soliton management is considered. • The synchronized dispersive and nonlinear management is suggested

Efficient uncertainty quantification of a fully nonlinear and dispersive water wave model with random inputs

DEFF Research Database (Denmark)

Bigoni, Daniele; Engsig-Karup, Allan Peter; Eskilsson, Claes

2016-01-01

A major challenge in next-generation industrial applications is to improve numerical analysis by quantifying uncertainties in predictions. In this work we present a formulation of a fully nonlinear and dispersive potential flow water wave model with random inputs for the probabilistic description...... at different points in the parameter space, allowing for the reuse of existing simulation software. The choice of the applied methods is driven by the number of uncertain input parameters and by the fact that finding the solution of the considered model is computationally intensive. We revisit experimental...... benchmarks often used for validation of deterministic water wave models. Based on numerical experiments and assumed uncertainties in boundary data, our analysis reveals that some of the known discrepancies from deterministic simulation in comparison with experimental measurements could be partially explained...

Analysis of second order harmonic distortion due to transmitter non-linearity and chromatic and modal dispersion of optical OFDM SSB modulated signals in SMF-MMF fiber links

Science.gov (United States)

Patel, Dhananjay; Singh, Vinay Kumar; Dalal, U. D.

2017-01-01

Single mode fibers (SMF) are typically used in Wide Area Networks (WAN), Metropolitan Area Networks (MAN) and also find applications in Radio over Fiber (RoF) architectures supporting data transmission in Fiber to the Home (FTTH), Remote Antenna Units (RAUs), in-building networks etc. Multi-mode fibers (MMFs) with low cost, ease of installation and low maintenance are predominantly (85-90%) deployed in-building networks providing data access in local area networks (LANs). The transmission of millimeter wave signals through the SMF in WAN and MAN, along with the reuse of MMF in-building networks will not levy fiber reinstallation cost. The transmission of the millimeter waves experiences signal impairments due to the transmitter non-linearity and modal dispersion of the MMF. The MMF exhibiting large modal dispersion limits the bandwidth-length product of the fiber. The second and higher-order harmonics present in the optical signal fall within the system bandwidth. This causes degradation in the received signal and an unwanted radiation of power at the RAU. The power of these harmonics is proportional to the non-linearity of the transmitter and the modal dispersion of the MMF and should be maintained below the standard values as per the international norms. In this paper, a mathematical model is developed for Second-order Harmonic Distortion (HD2) generated due to non-linearity of the transmitter and chromatic-modal dispersion of the SMF-MMF optic link. This is also verified using a software simulation. The model consists of a Mach Zehnder Modulator (MZM) that generates two m-QAM OFDM Single Sideband (SSB) signals based on phase shift of the hybrid coupler (90° and 120°). Our results show that the SSB signal with 120° hybrid coupler has suppresses the higher-order harmonics and makes the system more robust against the HD2 in the SMF-MMF optic link.

Collapse of nonlinear Langmuir waves

International Nuclear Information System (INIS)

Malkin, V.M.

1986-01-01

The dispersion of sufficiently intensive Langmuir waves is determined by intrinsic (electron) nonlinearity. During Langmuir collapse the wave energy density required for the appearance of electron nonlinearity is attained, generally speaking, prior to the development of dissipative processes. Up to now, the effect of electron nonlinearity on the collapse dynamics and spectrum of strong Langmuir turbulence ( which may be very appreciable ) has not been studied extensively because of the difficulty of describing nonlinear Langmuir waves. In the present paper the positive determinacy of the electron nonlinear hamiltonian is proven, the increment of modulation instability of a nonlinear Langmuir wave cluster localized in a cavity is calculated, and the universal law of their collapse is found

Nonlinear waves in solar plasmas - a review

International Nuclear Information System (INIS)

Ballai, I

2006-01-01

Nonlinearity is a direct consequence of large scale dynamics in the solar plasmas. When nonlinear steepening of waves is balanced by dispersion, solitary waves are generated. In the vicinity of resonances, waves can steepen into nonlinear waves influencing the efficiency of energy deposition. Here we review recent theoretical breakthroughs that have lead to a greater understanding of many aspects of nonlinear waves arising in homogeneous and inhomogeneous solar plasmas

Establishment of regression dependences. Linear and nonlinear dependences

International Nuclear Information System (INIS)

Onishchenko, A.M.

1994-01-01

The main problems of determination of linear and 19 types of nonlinear regression dependences are completely discussed. It is taken into consideration that total dispersions are the sum of measurement dispersions and parameter variation dispersions themselves. Approaches to all dispersions determination are described. It is shown that the least square fit gives inconsistent estimation for industrial objects and processes. The correction methods by taking into account comparable measurement errors for both variable give an opportunity to obtain consistent estimation for the regression equation parameters. The condition of the correction technique application expediency is given. The technique for determination of nonlinear regression dependences taking into account the dependence form and comparable errors of both variables is described. 6 refs., 1 tab

Highly Nonlinear and Birefringent Spiral Photonic Crystal Fiber

Directory of Open Access Journals (Sweden)

S. Revathi

2014-01-01

Full Text Available We propose and design a spiral photonic crystal fiber with elliptical air holes for achieving high birefringence, large nonlinearity, and negative dispersion. The structure is designed using chalcogenide glass (As2S3 for different ellipticity ratios of air holes in the cladding and the effect on various properties is observed. The proposed structure has birefringence of the order 10−2, nonlinearity of 26739.42 W−1 m−1, and dispersion of −1136.69 at 0.85 μm. An accurate numerical approach based on finite element method is used for the design and simulation of the structure. Due to high birefringence and negative dispersion, the proposed structure can be used for polarization control and dispersion compensation, respectively.

Nonlinear wave equation in frequency domain: accurate modeling of ultrafast interaction in anisotropic nonlinear media

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...... nonlinearities, delayed Raman effects, and anisotropic nonlinearities. The full potential of this wave equation is demonstrated by investigating simulations of solitons generated in the process of ultrafast cascaded second-harmonic generation. We show that a balance in the soliton delay can be achieved due...

Effects of intermode nonlinearity and intramode nonlinearity on modulation instability in randomly birefringent two-mode optical fibers

Science.gov (United States)

Li, Jin Hua; Xu, Hui; Sun, Ting Ting; Pei, Shi Xin; Ren, Hai Dong

2018-05-01

We analyze in detail the effects of the intermode nonlinearity (IEMN) and intramode nonlinearity (IRMN) on modulation instability (MI) in randomly birefringent two-mode optical fibers (RB-TMFs). In the anomalous dispersion regime, the MI gain enhances significantly as the IEMN and IRMN coefficients increases. In the normal dispersion regime, MI can be generated without the differential mode group delay (DMGD) effect, as long as the IEMN coefficient between two distinct modes is above a critical value, or the IRMN coefficient inside a mode is below a critical value. This critical IEMN (IRMN) coefficient depends strongly on the given IRMN (IEMN) coefficient and DMGD for a given nonlinear RB-TMF structure, and is independent on the input total power, the power ratio distribution and the group velocity dispersion (GVD) ratio between the two modes. On the other hand, in contrast to the MI band arising from the pure effect of DMGD in the normal dispersion regime, where MI vanishes after a critical total power, the generated MI band under the combined effects of IEMN and IRMN without DMGD exists for any total power and enhances with the total power. The MI analysis is verified numerically by launching perturbed continuous waves (CWs) with wave propagation method.

Ageing of the nonlinear optical susceptibility in soft matter

International Nuclear Information System (INIS)

Ghofraniha, N; Conti, C; Leonardo, R Di; Ruzicka, B; Ruocco, G

2007-01-01

We investigate the nonlinear optics response of a colloidal dispersion undergoing dynamics slowing down with age, by using Z-scan and dynamic light scattering measurements. We study the high optical nonlinearity of an organic dye (rhodamine B) dispersed in a water-clay (laponite) suspension. We consider different clay concentrations (2.0-2.6 wt%) experiencing dynamics arrest. We find that (i) the concentration dependent exponential growth of both mean relaxation time and nonlinear absorption coefficient can be individually scaled to a master curve and (ii) the scaling times are the same for the two physical quantities. These findings indicate that the optical nonlinear susceptibility exhibits the same ageing universal scaling behaviour, typical of disordered out of equilibrium systems

Weakly nonlinear dispersion and stop-band effects for periodic structures

DEFF Research Database (Denmark)

Sorokin, Vladislav; Thomsen, Jon Juel

of frequency band-gaps, i.e. frequency ranges in which elastic waves cannot propagate. Most existing analytical methods in the field are based on Floquet theory [1]; e.g. this holds for the classical Hill’s method of infinite determinants [1,2], and themethod of space-harmonics [3]. However, application...... 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...... to be accounted for.The paper deals with analytically predicting dynamic response for nonlinear elastic structures with a continuous periodic variation in structural properties. Specifically, for a Bernoulli-Euler beam with aspatially continuous modulation of structural properties in the axial direction...

Optical bullets and "rockets" in nonlinear dissipative systems and their transformations and interactions.

Science.gov (United States)

Soto-Crespo, J M; Grelu, Philippe; Akhmediev, Nail

2006-05-01

We demonstrate the existence of stable optical light bullets in nonlinear dissipative media for both cases of normal and anomalous chromatic dispersion. The prediction is based on direct numerical simulations of the (3+1)-dimensional complex cubic-quintic Ginzburg-Landau equation. We do not impose conditions of spherical or cylindrical symmetry. Regions of existence of stable bullets are determined in the parameter space. Beyond the domain of parameters where stable bullets are found, unstable bullets can be transformed into "rockets" i.e. bullets elongated in the temporal domain. A few examples of the interaction between two optical bullets are considered using spatial and temporal interaction planes.

Development of a code to simulate dispersion of atmospheric released tritium gas in the environmental media and to evaluate doses. TRIDOSE

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)

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

Linear and nonlinear modeling of light propagation in hollow-core photonic crystal fiber

DEFF Research Database (Denmark)

Roberts, John; Lægsgaard, Jesper

2009-01-01

Hollow core photonic crystal fibers (HC-PCFs) find applications which include quantum and non-linear optics, gas detection and short high-intensity laser pulse delivery. Central to most applications is an understanding of the linear and nonlinear optical properties. These require careful modeling....... The intricacies of modeling various forms of HC-PCF are reviewed. An example of linear dispersion engineering, aimed at reducing and flattening the group velocity dispersion, is then presented. Finally, a study of short high intensity pulse delivery using HC-PCF in both dispersive and nonlinear (solitonic...

Ring vortex solitons in nonlocal nonlinear media

DEFF Research Database (Denmark)

Briedis, D.; Petersen, D.E.; Edmundson, D.

2005-01-01

We study the formation and propagation of two-dimensional vortex solitons, i.e. solitons with a phase singularity, in optical materials with a nonlocal focusing nonlinearity. We show that nonlocality stabilizes the dynamics of an otherwise unstable vortex beam. This occurs for either single...... 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....

Nonlinear propagation of ultrashort laser pulses in transparent media

International Nuclear Information System (INIS)

Vincotte, A.

2006-10-01

We present different aspects of the propagation of ultrashort laser pulses in transparent media. First, we derive the propagation equations starting from the Maxwell equations. We remind of the main physical phenomena undergone by ultrashort and powerful laser pulses. First self-focusing occurs, owing to the Kerr response of the medium. This self-focusing is stopped by plasma generation from the laser-induced ionization of the ambient atoms. The propagation of the wave generates a super-continuum through self-phase modulation. We recall the main results concerning the simple and multiple filamentation of an intense wave, induced by the beam inhomogeneities and which take place as soon as the beam power is above critical. In a second part, we investigate the influence of high-order nonlinearities on the propagation of the beam and especially on its filamentation pattern. To control the multi-filamentation process, we investigate in a third part the propagation of beams with special designs, namely; Gradient- and vortex-shaped beams. We justify the robustness of this latter kind of optical objects. Eventually, we investigate multi-filamentation patterns of femtosecond pulses in a fog tube and in cells of ethanol doped with coumarin, for different beam configurations. (author)

Chemotaxis and flow disorder shape microbial dispersion in porous media

Science.gov (United States)

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.

Broadband Nonlinear Signal Processing in Silicon Nanowires

DEFF Research Database (Denmark)

Yvind, Kresten; Pu, Minhao; Hvam, Jørn Märcher

The fast non-linearity of silicon allows Tbit/s optical signal processing. By choosing suitable dimensions of silicon nanowires their dispersion can be tailored to ensure a high nonlinearity at power levels low enough to avoid significant two-photon abso We have fabricated low insertion...

Spatiotemporal solitons in quadratic nonlinear media

Indian Academy of Sciences (India)

Optical solitons are localized electromagnetic waves that propagate stably in .... conversion generates a nonlinear phase shift ∆ΦNL at the FH frequency. ... to incidence on the SHG crystal (lithium iodate or barium borate, cut for type-I interac-.

Contribution of Higher-Order Dispersion to Nonlinear Electron-Acoustic Solitary Waves in a Relativistic Electron Beam Plasma System

International Nuclear Information System (INIS)

Zahran, M.A.; El-Shewy, E.K.

2008-01-01

The nonlinear properties of solitary wave structures are reported in an unmagnetized collisionless plasma comprising of cold relativistic electron fluid, Maxwellian hot electrons, relativistic electron beam, and stationary ions. The Korteweg--de Vries (KdV) equation has been derived using a reductive perturbation theory. As the wave amplitude increases, the width and velocity of the soliton deviate from the prediction of the KdV equation i.e. the breakdown of the KdV approximation. On the other hand, to overcome this weakness we extend our analysis to obtain the KdV equation with fifth-order dispersion term. The solution of the resulting equation has been obtained

Dispersion of the linear and nonlinear optical susceptibilities of the CuAl(S1−xSex)2 mixed chaclcopyrite compounds

International Nuclear Information System (INIS)

Reshak, A. H.; Brik, M. G.; Auluck, S.

2014-01-01

Based on the electronic band structure, we have calculated the dispersion of the linear and nonlinear optical susceptibilities for the mixed CuAl(S 1−x Se 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 (CuAlS 2 ), 1.9 eV (CuAl(S 0.75 Se 0.25 ) 2 ), 1.7 eV (CuAl(S 0.5 Se 0.5 ) 2 ), 1.5 eV (CuAl(S 0.25 Se 0.75 ) 2 ), and 1.4 eV (CuAlSe 2 ) 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 ε 2 xx (ω) and ε 2 zz (ω)/ε 2 xx (ω), ε 2 yy (ω), and ε 2 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 CuAlS 2 and CuAlSe 2 exhibit | χ 123 (2) (−2ω;ω;ω) | as the dominant component, while the mixed alloys exhibit | χ 111 (2) (−2ω;ω;ω) | as the dominant component. The features of | χ 123 (2) (−2ω;ω;ω) | and | χ 111 (2) (−2ω;ω;ω) | spectra were analyzed on the basis of the absorptive part of the corresponding dielectric function ε 2 (ω) as a function of both ω/2 and ω.

SIMULATION OF FORWARD AND BACKWARD WAVES EVOLUTION OF FEW-CYCLE PULSES PROPAGATING IN AN OPTICAL WAVEGUIDE WITH DISPERSION AND CUBIC NONLINEARITY OF ELECTRONIC AND ELECTRONIC-VIBRATION NATURE

Directory of Open Access Journals (Sweden)

L. S. Konev

2015-09-01

Full Text Available Numerical method for calculation of forward and backward waves of intense few-cycle laser pulses propagating in an optical waveguide with dispersion and cubic nonlinearity of electronic and electronic-vibration nature is described. Simulations made with the implemented algorithm show that accounting for Raman nonlinearity does not lead to qualitative changes in behavior of the backward wave. Speaking about quantitative changes, the increase of efficiency of energy transfer from the forward wave to the backward wave is observed. Presented method can be also used to simulate interaction of counterpropagating pulses.

Nonlinear surface waves at ferrite-metamaterial waveguide structure

Science.gov (United States)

Hissi, Nour El Houda; Mokhtari, Bouchra; Eddeqaqi, Noureddine Cherkaoui; Shabat, Mohammed Musa; Atangana, Jacques

2016-09-01

A new ferrite slab made of a metamaterial (MTM), surrounded by a nonlinear cover cladding and a ferrite substrate, was shown to support unusual types of electromagnetic surface waves. We impose the boundary conditions to derive the dispersion relation and others necessary to formulate the proposed structure. We analyse the dispersion properties of the nonlinear surface waves and we calculate the associated propagation index and the film-cover interface nonlinearity. In the calculation, several sets of the permeability of the MTM are considered. Results show that the waves behaviour depends on the values of the permeability of the MTM, the thickness of the waveguide and the film-cover interface nonlinearity. It is also shown that the use of the singular solutions to the electric field equation allows to identify several new properties of surface waves which do not exist in conventional waveguide.

Explicit formulation of second and third order optical nonlinearity in the FDTD framework

Science.gov (United States)

Varin, Charles; Emms, Rhys; Bart, Graeme; Fennel, Thomas; Brabec, Thomas

2018-01-01

The finite-difference time-domain (FDTD) method is a flexible and powerful technique for rigorously solving Maxwell's equations. However, three-dimensional optical nonlinearity in current commercial and research FDTD softwares requires solving iteratively an implicit form of Maxwell's equations over the entire numerical space and at each time step. Reaching numerical convergence demands significant computational resources and practical implementation often requires major modifications to the core FDTD engine. In this paper, we present an explicit method to include second and third order optical nonlinearity in the FDTD framework based on a nonlinear generalization of the Lorentz dispersion model. A formal derivation of the nonlinear Lorentz dispersion equation is equally provided, starting from the quantum mechanical equations describing nonlinear optics in the two-level approximation. With the proposed approach, numerical integration of optical nonlinearity and dispersion in FDTD is intuitive, transparent, and fully explicit. A strong-field formulation is also proposed, which opens an interesting avenue for FDTD-based modelling of the extreme nonlinear optics phenomena involved in laser filamentation and femtosecond micromachining of dielectrics.

Diffractons: Solitary Waves Created by Diffraction in Periodic Media

KAUST Repository

Ketcheson, David I.

2015-03-31

A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. These solitary waves depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation in the sound speed of the medium. A high-order homogenized model confirms this effective dispersive behavior, and its solutions agree well with those obtained by direct simulation of the variable-coefficient system. These waves are observed to be long-time stable, globally attracting solutions that arise in general as solutions to nonlinear wave problems with periodically varying sound speed. They share some properties with known classes of solitary waves but possess important differences as well.

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

Dispersivity in heterogeneous permeable media

International Nuclear Information System (INIS)

Chesnut, D.A.

1994-01-01

When one fluid displaces another through a one-dimensional porous medium, the composition changes from pure displacing fluid at the inlet to pure displaced fluid some distance downstream. The distance over which an arbitrary percentage of this change occurs is defined as the mixing zone length, which increases with increasing average distance traveled by the displacement front. For continuous injection, the mixing zone size can be determined from a breakthrough curve as the time required for the effluent displacing fluid concentration to change from, say, 10% to 90%. In classical dispersion theory, the mixing zone grows in proportion to the square root of the mean distance traveled, or, equivalently, to the square root of the mean breakthrough time. In a multi-dimensional heterogeneous medium, especially at field scales, the size of the mixing zone grows almost linearly with mean distance or travel time. If an observed breakthrough curve is forced to fit the, clinical theory, the resulting effective dispersivity, instead of being constant, also increases almost linearly with the spatial or temporal scale of the problem. This occurs because the heterogeneity in flow properties creates a corresponding velocity distribution along the different flow pathways from the inlet to the outlet of the system. Mixing occurs mostly at the outlet, or wherever the fluid is sampled, rather than within the medium. In this paper, we consider the effects. of this behavior on radionuclide or other contaminant migration

Dispersivity in heterogeneous permeable media

International Nuclear Information System (INIS)

Chesnut, D.A.

1994-01-01

When one fluid displaces another through a one-dimensional porous medium, the composition changes from pure displacing fluid at the inlet to pure displaced fluid some distance downstream. The distance over which an arbitrary percentage (typically 80%) of this change occurs is defined as the mixing zone length, which increases with increasing average distance traveled by the displacement front. Alternatively, for continuous injection, the mixing zone size can be determined from a breakthrough curve as the time required for the effluent displacing fluid concentration to change from, say, 10% to 90%. In classical dispersion theory, the mixing zone grows in proportion to the square root of the mean distance traveled, or, equivalently, to the square root of the mean breakthrough time. In a multi-dimensional heterogeneous medium, especially at field scales, the size of the mixing zone grows almost linearly with mean distance or travel time. If an observed breakthrough curve is forced to fit the classical theory, the resulting effective dispersivity, instead of being constant, also increases almost linearly with the spatial or temporal scale of the problem. This occurs because the heterogeneity in flow properties creates a corresponding velocity distribution along the different flow pathways from the inlet to the outlet of the system. Mixing occurs mostly at the outlet, or wherever the fluid is sampled, rather than within the medium. In this paper, we consider the effects of this behavior on radionuclide or other contaminant migration

Nonlinear Electron Waves in Strongly Magnetized Plasmas

DEFF Research Database (Denmark)

Pécseli, Hans; Juul Rasmussen, Jens

1980-01-01

Weakly nonlinear dispersive electron waves in strongly magnetized plasma are considered. A modified nonlinear Schrodinger equation is derived taking into account the effect of particles resonating with the group velocity of the waves (nonlinear Landau damping). The possibility of including the ion...... dynamics in the analysis is also demonstrated. As a particular case the authors investigate nonlinear waves in a strongly magnetized plasma filled wave-guide, where the effects of finite geometry are important. The relevance of this problem to laboratory experiments is discussed....

High-power laser radiation in atmospheric aerosols: Nonlinear optics of aerodispersed media

Science.gov (United States)

Zuev, V. E.; Zemlianov, A. A.; Kopytin, Iu. D.; Kuzikovskii, A. V.

The bulk of this book contains the results of investigations carried out at the Institute of Atmospheric Optics, Siberian Branch, USSR Academy of Science with the participation of the authors. The microphysical and optical characteristics of atmospheric aerosols are considered, taking into account light scattering by a single aerosol particle, light scattering by a system of particles, the scattering phase matrix, light scattering by clouds and fogs, light scattering by hazes, and scattering phase functions of polydispersed aerosols. Other topics studies are related to low-energy (subexplosive) effects of radiation on individual particles, the formation of clear zones in clouds and fogs due to the vaporization of droplets under regular regimes, self-action of a wave beam in a water aerosol under conditions of regular droplet vaporization, laser beam propagation through an explosively evaporating water-droplet aerosol, the propagation of high-power laser radiation through hazes, the ionization and optical breakdown in aerosol media, and laser monitoring of a turbid atmosphere using nonlinear effects.

The nonlinear CWFA [Cherenkov Wakefield Accelerator

International Nuclear Information System (INIS)

Schoessow, P.

1989-01-01

The possible use of nonlinear media to enhance the performance of the Cherenkov Wakefield Accelerator (CWFA) is considered. Numerical experiments have been performed using a new wakefield code which demonstrate larger gradients and transformer ratios in the nonlinear CWFA than are obtained in the linear case. 7 refs., 3 figs

Nonlinearly preconditioned semismooth Newton methods for variational inequality solution of two-phase flow in porous media

KAUST Repository

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.

Nonlinearly preconditioned semismooth Newton methods for variational inequality solution of two-phase flow in porous media

KAUST Repository

Yang, Haijian; Sun, Shuyu; Yang, Chao

2016-01-01

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.

Energetic mid-IR femtosecond pulse generation by self-defocusing soliton-induced dispersive waves in a bulk quadratic nonlinear crystal

DEFF Research Database (Denmark)

Zhou, Binbin; Guo, Hairun; Bache, Morten

2015-01-01

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 with...... 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....... 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...

Optical rogue waves and soliton turbulence in nonlinear fibre optics

DEFF Research Database (Denmark)

Genty, G.; Dudley, J. M.; de Sterke, C. M.

2009-01-01

We examine optical rogue wave generation in nonlinear fibre propagation in terms of soliton turbulence. We show that higher-order dispersion is sufficient to generate localized rogue soliton structures, and Raman scattering effects are not required.......We examine optical rogue wave generation in nonlinear fibre propagation in terms of soliton turbulence. We show that higher-order dispersion is sufficient to generate localized rogue soliton structures, and Raman scattering effects are not required....

Visible continuum pulses based on enhanced dispersive wave generation for endogenous fluorescence imaging.

Science.gov (United States)

Cui, Quan; Chen, Zhongyun; Liu, Qian; Zhang, Zhihong; Luo, Qingming; Fu, Ling

2017-09-01

In this study, we demonstrate endogenous fluorescence imaging using visible continuum pulses based on 100-fs Ti:sapphire oscillator and a nonlinear photonic crystal fiber. Broadband (500-700 nm) and high-power (150 mW) continuum pulses are generated through enhanced dispersive wave generation by pumping femtosecond pulses at the anomalous dispersion region near zero-dispersion wavelength of high-nonlinear photonic crystal fibers. We also minimize the continuum pulse width by determining the proper fiber length. The visible-wavelength two-photon microscopy produces NADH and tryptophan images of mice tissues simultaneously. Our 500-700 nm continuum pulses support extending nonlinear microscopy to visible wavelength range that is inaccessible to 100-fs Ti:sapphire oscillators and other applications requiring visible laser pulses.

Solitons and Weakly Nonlinear Waves in Plasmas

DEFF Research Database (Denmark)

Pécseli, Hans

1985-01-01

Theoretical descriptions of solitons and weakly nonlinear waves propagating in plasma media are reviewed, with particular attention to the Korteweg-de Vries (KDV) equation and the Nonlinear Schrödinger equation (NLS). The modifications of these basic equations due to the effects of resonant...

Nonlinear modulation of torsional waves in elastic rod. [Instability

Energy Technology Data Exchange (ETDEWEB)

Hirao, M; Sugimoto, N [Osaka Univ., Toyonaka (Japan). Faculty of Engineering Science

1977-06-01

Nonlinear Schroedinger equation, which describes the nonlinear modulation of dispersive torsional waves in an elastic rod of circular cross-section, is derived by the derivative expansion method. It is found, for the lowest dispersive mode, that the modulational instability occurs except in the range of the carrier wavenumber, 2.799nonlinear Schroedinger equation is no longer valid. In this case, another system of equations is derived, which governs both the wave amplitudes involved in this resonance between the fundamental torsional and its second-harmonic longitudinal modes.

Nonlinear density waves in a marginally stable gravitating disk

International Nuclear Information System (INIS)

Korchagin, V.I.

1986-01-01

The evolution of short nonlinear density waves in a disk at the stability limit is studied for arbitrary values of the radial wave number k/sub r/. For waves with wave numbers that do not lie at the minimum of the dispersion curve, the behavior of the amplitude is described by a nonlinear parabolic equation; however, stationary soliton solutions cannot exist in such a system since there is no dispersion spreading of a packet. For wave numbers lying at the minimum of the dispersion curve, soliton structures with determined amplitude are possible. In stable gravitating disks and in a disk at the stability limit, two physically different types of soliton can exist

A collective variable approach and stabilization for dispersion-managed optical solitons in the quintic complex Ginzburg-Landau equation as perturbations of the nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Fewo, S I; Kenfack-Jiotsa, A; Kofane, T C

2006-01-01

With the help of the one-dimensional quintic complex Ginzburg-Landau equation (CGLE) as perturbations of the nonlinear Schroedinger equation (NLSE), we derive the equations of motion of pulse parameters called collective variables (CVs), of a pulse propagating in dispersion-managed (DM) fibre optic links. The equations obtained are investigated numerically in order to view the evolution of pulse parameters along the propagation distance, and also to analyse effects of initial amplitude and width on the propagating pulse. Nonlinear gain is shown to be beneficial in stabilizing DM solitons. A fully numerical simulation of the one-dimensional quintic CGLE as perturbations of NLSE finally tests the results of the CV theory. A good agreement is observed between both methods

Design considerations for multi component molecular-polymeric nonlinear optical materials

Energy Technology Data Exchange (ETDEWEB)

Singer, K.D. (Case Western Reserve Univ., Cleveland, OH (USA). Dept. of Physics); Kuzyk, M.G. (Washington State Univ., Pullman, WA (USA). Dept. of Physics); Fang, T.; Holland, W.R. (AT and T Bell Labs., Princeton, NJ (USA)); Cahill, P.A. (Sandia National Labs., Albuquerque, NM (USA))

1990-01-01

We review our work on multi component polymeric nonlinear optical materials. These materials consist of nonlinear optical molecules incorporated in a polymeric host. A cross-linked triazine polymer incorporating a dicyanovinyl terminated azo dye was found to be relatively stable at 85{degree} and posses an electro-optic coefficient of 11pm/V. We have also observed the zero dispersion condition in a new anomalous dispersion dye for phase matched second harmonic generation, and expect efficient conversion to the blue. A squarylium dye, ISQ, has been found to posses a large third order nonlinearity, and may display two-level behavior. 24 refs., 11 figs.

Naturally stable Sagnac-Michelson nonlinear interferometer.

Science.gov (United States)

Lukens, Joseph M; Peters, Nicholas A; Pooser, Raphael C

2016-12-01

Interferometers measure a wide variety of dynamic processes by converting a phase change into an intensity change. Nonlinear interferometers, making use of nonlinear media in lieu of beamsplitters, promise substantial improvement in the quest to reach the ultimate sensitivity limits. Here we demonstrate a new nonlinear interferometer utilizing a single parametric amplifier for mode mixing-conceptually, a nonlinear version of the conventional Michelson interferometer with its arms collapsed together. We observe up to 99.9% interference visibility and find evidence for noise reduction based on phase-sensitive gain. Our configuration utilizes fewer components than previous demonstrations and requires no active stabilization, offering new capabilities for practical nonlinear interferometric-based sensors.

Dispersion of contaminants in saturated porous media

International Nuclear Information System (INIS)

Moltyaner, G.L.; Poisson, J.M.

1987-10-01

The main objective of this paper is to outline the experimental and theoretical investigations performed in an attempt to validate the applicability of finite element based numerical models for the prediction of the behaviour of a conservative tracer at the Twin Lake aquifer, Chalk River Nuclear Laboratories, Chalk River, Ontario. The essential point is that the 3/4 of a million data points obtained at the Twin Lake site from a 40 m natural gradient tracer test provide a unique opportunity for quantifying the system variability and for testing finite element models of the dispersion process. The subject of this discussion is the advection-dispersion model of contaminant transport - its equation and solution by the Galerkin finite element method. The report gives a brief description of the experimental data and the methods for the estimation of transport parameters. Scales of averaging associated with the conceptual formulation of the dispersion process, measurement of process variables, parameter estimation and the numerical models are discussed. The compatibility between the scales is emphasized as a major requirement for predictive modelling. The developed finite element model of the radioiodine transport describes the overall behaviour of the tracer plume but lacks the capability to simulate the fingerlike spreading of the plume due to the fact that the grid does not have an adequately fine space discretization. Unfortunately, a refinement of the grid spacing is limited by the size of the site computer memory. For the advection-dominated transport, as that encountered at the Twin Lake aquifer, the failure to satisfy fine mesh requirement causes numerical dispersion. In general, it was concluded that the conventional finite element model may produce accurate simulation of the tracer cloud provided that the adequately fine space discretization of the grid compatible with the support scale of measurements and the adequately fine time discretization are made. This

Numerical study of fractional nonlinear Schrodinger equations

KAUST Repository

Klein, Christian

2014-10-08

Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By an appropriate choice of the dispersive exponent, both mass and energy sub- and supercritical regimes can be identified. This allows us to study the possibility of finite time blow-up versus global existence, the nature of the blow-up, the stability and instability of nonlinear ground states and the long-time dynamics of solutions. The latter is also studied in a semiclassical setting. Moreover, we numerically construct ground state solutions of the fractional nonlinear Schrödinger equation.

Soliton solutions to the fifth-order Korteweg-de Vries equation and their applications to surface and internal water waves

Science.gov (United States)

Khusnutdinova, K. R.; Stepanyants, Y. A.; Tranter, M. R.

2018-02-01

We study solitary wave solutions of the fifth-order Korteweg-de Vries equation which contains, besides the traditional quadratic nonlinearity and third-order dispersion, additional terms including cubic nonlinearity and fifth order linear dispersion, as well as two nonlinear dispersive terms. An exact solitary wave solution to this equation is derived, and the dependence of its amplitude, width, and speed on the parameters of the governing equation is studied. It is shown that the derived solution can represent either an embedded or regular soliton depending on the equation parameters. The nonlinear dispersive terms can drastically influence the existence of solitary waves, their nature (regular or embedded), profile, polarity, and stability with respect to small perturbations. We show, in particular, that in some cases embedded solitons can be stable even with respect to interactions with regular solitons. The results obtained are applicable to surface and internal waves in fluids, as well as to waves in other media (plasma, solid waveguides, elastic media with microstructure, etc.).

Synthesis, characterization and non-linear optical response of organophilic carbon dots

KAUST Repository

Bourlinos, Athanasios B.

2013-09-01

For the first time ever we report the nonlinear optical (NLO) properties of carbon dots (C-dots). The C-dots for these experiments were synthesized by mild pyrolysis of lauryl gallate. The resulting C-dots bear lauryl chains and, hence, are highly dispersible in polar organic solvents, like chloroform. Dispersions in CHCl3 show significant NLO response. Specifically, the C-dots show negative nonlinear absorption coefficient and negative nonlinear refraction. Using suspensions with different concentrations these parameters are quantified and compared to those of fullerene a well-known carbon molecule with proven NLO response. © 2013 Elsevier Ltd. All rights reserved.

Synthesis, characterization and non-linear optical response of organophilic carbon dots

KAUST Repository

Bourlinos, Athanasios B.; Karakassides, Michael A.; Kouloumpis, Antonios; Gournis, Dimitrios; Bakandritsos, Aristides; Papagiannouli, Irene; Aloukos, Panagiotis; Couris, Stelios; Hola, Katerina; Zboril, Radek; Krysmann, Marta; Giannelis, Emmanuel P.

2013-01-01

For the first time ever we report the nonlinear optical (NLO) properties of carbon dots (C-dots). The C-dots for these experiments were synthesized by mild pyrolysis of lauryl gallate. The resulting C-dots bear lauryl chains and, hence, are highly dispersible in polar organic solvents, like chloroform. Dispersions in CHCl3 show significant NLO response. Specifically, the C-dots show negative nonlinear absorption coefficient and negative nonlinear refraction. Using suspensions with different concentrations these parameters are quantified and compared to those of fullerene a well-known carbon molecule with proven NLO response. © 2013 Elsevier Ltd. All rights reserved.

Relativistic invariance of dispersion-relations and their associated wave-operators and Green-functions

International Nuclear Information System (INIS)

Censor, Dan

2010-01-01

Identifying invariance properties helps in simplifying calculations and consolidating concepts. Presently the Special Relativistic invariance of dispersion relations and their associated scalar wave operators is investigated for general dispersive homogeneous linear media. Invariance properties of the four-dimensional Fourier-transform integrals is demonstrated, from which the invariance of the scalar Green-function is inferred. Dispersion relations and the associated group velocities feature in Hamiltonian ray tracing theory. The derivation of group velocities for moving media from the dispersion relation for these media at rest is discussed. It is verified that the group velocity concept satisfies the relativistic velocity-addition formula. In this respect it is considered to be 'real', i.e., substantial, physically measurable, and not merely a mathematical artifact. Conversely, if we assume the group velocity to be substantial, it follows that the dispersion relation must be a relativistic invariant. (orig.)

A generalized auxiliary equation method and its application to nonlinear Klein-Gordon and generalized nonlinear Camassa-Holm equations

International Nuclear Information System (INIS)

Yomba, Emmanuel

2008-01-01

With the aid of symbolic computation, a generalized auxiliary equation method is proposed to construct more general exact solutions to two types of NLPDEs. First, we present new family of solutions to a nonlinear Klein-Gordon equation, by using this auxiliary equation method including a new first-order nonlinear ODE with six-degree nonlinear term proposed by Sirendaoreji. Then, we apply an indirect F-function method very close to the F-expansion method to solve the generalized Camassa-Holm equation with fully nonlinear dispersion and fully nonlinear convection C(l,n,p). Taking advantage of the new first-order nonlinear ODE with six degree nonlinear term, this indirect F-function method is used to map the solutions of C(l,n,p) equations to those of that nonlinear ODE. As a result, we can successfully obtain in a unified way, many exact solutions

Coupled nonlinear oscillators

Energy Technology Data Exchange (ETDEWEB)

Chandra, J; Scott, A C

1983-01-01

Topics discussed include transitions in weakly coupled nonlinear oscillators, singularly perturbed delay-differential equations, and chaos in simple laser systems. Papers are presented on truncated Navier-Stokes equations in a two-dimensional torus, on frequency locking in Josephson point contacts, and on soliton excitations in Josephson tunnel junctions. Attention is also given to the nonlinear coupling of radiation pulses to absorbing anharmonic molecular media, to aspects of interrupted coarse-graining in stimulated excitation, and to a statistical analysis of long-term dynamic irregularity in an exactly soluble quantum mechanical model.

Tellurite composite microstructured optical fibers with ultra-flattened and zero dispersion

Science.gov (United States)

Duan, Zhongchao; Liao, Meisong; Tomas, Kohoutek; Tong, Hoangtuan; Asano, Koji; Suzuki, Takenobu; Ohishi, Yasutake

2012-04-01

We report the fabrication of tellurite composite microstructured optical fiber (CMOF) with ultra-flattened zero dispersion (+/-3 ps/nm/Km) over 200nm band. To obtain this dispersion profile together with high nonlinearity, one ring of air holes and two layers of glass cladding are employed in the tellurite CMOF. The core of fiber is made of TeO2-Li2O-WO3 -MoO3-Nb2O5 (TLWMN) tellurite glass which possesses high linear and nonlinear refractive indices. The refractive index (n) at 1544nm and nonlinear refractive index (n2) of TLWMN glass is 2.08 and 3.78×10-11 esu, respectively. TeO2-ZnO-Na2O-La2O3 (TZNL) glass with n of 1.96 at 1544 nm and TeO2-ZnO-Li2O-Na2O-P2O5 (TZLNP) glass with low refractive index n of 1.63 at 1544 nm are used as the first cladding and the second cladding, respectively. Six small air holes are located between the core and the first glass cladding. Such kind of fiber with ~1.7 μm core and ~0.6 μm air holes are fabricated by a rod-in-tube method. The chromatic dispersion of the fiber is calculated by the fully vectorial finite difference method (FV-FDM) and becomes (+/-3 ps/nm/Km) in the wide range from 1.53 μm to 1.72 μm. And the nonlinear coefficient of present fiber is about 3.47 m-1W-1 which is much higher than that of silica MOFs. Furthermore, broad and flattened supercontinuum generation is demonstrated in 30-cm-long fiber with femtosecond laser pumping at 1557 nm. This kind of fiber has promising potential in nonlinear applications owing to the high nonlinearity and flattened dispersion profile.

Nonlinear acoustic waves in micro-inhomogeneous solids

CERN Document Server

Nazarov, Veniamin

2014-01-01

Nonlinear Acoustic Waves in Micro-inhomogeneous Solids covers the broad and dynamic branch of nonlinear acoustics, presenting a wide variety of different phenomena from both experimental and theoretical perspectives. The introductory chapters, written in the style of graduate-level textbook, present a review of the main achievements of classic nonlinear acoustics of homogeneous media. This enables readers to gain insight into nonlinear wave processes in homogeneous and micro-inhomogeneous solids and compare it within the framework of the book. The subsequent eight chapters covering: Physical m

Anomalous dispersion in correlated porous media: a coupled continuous time random walk approach

Science.gov (United States)

Comolli, Alessandro; Dentz, Marco

2017-09-01

We study the causes of anomalous dispersion in Darcy-scale porous media characterized by spatially heterogeneous hydraulic properties. Spatial variability in hydraulic conductivity leads to spatial variability in the flow properties through Darcy's law and thus impacts on solute and particle transport. We consider purely advective transport in heterogeneity scenarios characterized by broad distributions of heterogeneity length scales and point values. Particle transport is characterized in terms of the stochastic properties of equidistantly sampled Lagrangian velocities, which are determined by the flow and conductivity statistics. The persistence length scales of flow and transport velocities are imprinted in the spatial disorder and reflect the distribution of heterogeneity length scales. Particle transitions over the velocity length scales are kinematically coupled with the transition time through velocity. We show that the average particle motion follows a coupled continuous time random walk (CTRW), which is fully parameterized by the distribution of flow velocities and the medium geometry in terms of the heterogeneity length scales. The coupled CTRW provides a systematic framework for the investigation of the origins of anomalous dispersion in terms of heterogeneity correlation and the distribution of conductivity point values. We derive analytical expressions for the asymptotic scaling of the moments of the spatial particle distribution and first arrival time distribution (FATD), and perform numerical particle tracking simulations of the coupled CTRW to capture the full average transport behavior. Broad distributions of heterogeneity point values and lengths scales may lead to very similar dispersion behaviors in terms of the spatial variance. Their mechanisms, however are very different, which manifests in the distributions of particle positions and arrival times, which plays a central role for the prediction of the fate of dissolved substances in

On nonlinear periodic drift waves

International Nuclear Information System (INIS)

Kauschke, U.; Schlueter, H.

1990-09-01

Nonlinear periodic drift waves are investigated on the basis of a simple perturbation scheme for both the amplitude and inverse frequency. The coefficients for the generation of the forced harmonics are derived, a nonlinear dispersion relation is suggested and a criterion for the onset of the modulational instability is obtained. The results are compared with the ones obtained with the help of a standard KBM-treatment. Moreover cnoidal drift waves are suggested and compared to an experimental observation. (orig.)

Quantum optics of dispersive dielectric media

International Nuclear Information System (INIS)

Lenac, Z.

2003-01-01

We quantize the electromagnetic field in a polar medium starting with the fundamental equations of motion. In our model the medium is described by a Lorenz-type dielectric function ε(r,ω) appropriate, e.g., for ionic crystals, metals, and inert dielectrics. There are no restrictions on the spatial behavior of the dielectric function, i.e., there can be many different polar media with arbitrary shapes. We assume no losses in our system so the dielectric function for the whole space is assumed as real. The quantization procedure is based on an expansion of the total field (transverse and longitudinal) in terms of the coupled (polariton) eigenmodes, and this approach incorporates all previous results derived for similar but restricted systems (e.g., without spatial or frequency dependence of coupled modes). Within the same model, we also quantize the Hamiltonian of a nonretarded electromagnetic field in polar media. Particular attention is paid to the derivation of the orthogonality and closure relations, which are used in a discussion of the fundamental (equal-time) commutation relations between the conjugate field operators

Characterization and enhanced nonlinear optical limiting response in carbon nanodots dispersed in solid-state hybrid organically modified silica gel glasses

Science.gov (United States)

Huang, Li; Zheng, Chan; Guo, Qiaohang; Huang, Dongdong; Wu, Xiukai; Chen, Ling

2018-02-01

Freely dispersed carbon nanodots (CNDs) were introduced into a 3-glycidoxy-propyltrimethoxysilane modified silicate gel glass (i.e. an organically modified silica or ORMOSIL) by a highly efficient and simple sol-gel process, which could be easily extended to prepare functional molecules/nanoparticles solid state optoelectronic devices. Scanning electron microscope imaging, Fourier transform infrared spectroscopy, pore structure measurements, ultraviolet-visible spectroscopy, and fluorescence spectroscopy were used to investigate the surface characteristics, structure, texture, and linear optical properties of the CND/SiO2 ORMOSIL gel glasses. Images and UV/Vis spectra confirmed the successful dispersion of CNDs in the ORMOSIL gel glass. The surface characteristics and pore structure of the host SiO2 matrix were markedly changed through the introduction of the CNDs. The linear optical properties of the guest CNDs were also affected by the sol-gel procedure. The nonlinear optical (NLO) properties of the CNDs were investigated by a nanosecond open-aperture Z-scan technique at 532 nm both in liquid and solid matrices. We found that the NLO response of the CNDs was considerably improved after their incorporation into the ORMOSIL gel glasses. Possible enhancement mechanisms were also explored. The nonlinear extinction coefficient gradually increased while the optical limiting (OL) threshold decreased as the CND doping level was increased. This result suggests that the NLO and OL properties of the composite gel glasses can be optimized by tuning the concentration of CNDs in the gel glass matrix. Our findings show that CND/SiO2 ORMOSIL gel glasses are promising candidates for optical limiters to protect sensitive instruments and human eyes from damage caused by high power lasers.

Dynamical soil-structure interactions: influence of soil behaviour nonlinearities

International Nuclear Information System (INIS)

Gandomzadeh, Ali

2011-01-01

The interaction of the soil with the structure has been largely explored the assumption of material and geometrical linearity of the soil. Nevertheless, for moderate or strong seismic events, the maximum shear strain can easily reach the elastic limit of the soil behavior. Considering soil-structure interaction, the nonlinear effects may change the soil stiffness at the base of the structure and therefore energy dissipation into the soil. Consequently, ignoring the nonlinear characteristics of the dynamic soil-structure interaction (DSSI) this phenomenon could lead to erroneous predictions of structural response. The goal of this work is to implement a fully nonlinear constitutive model for soils into a numerical code in order to investigate the effect of soil nonlinearity on dynamic soil structure interaction. Moreover, different issues are taken into account such as the effect of confining stress on the shear modulus of the soil, initial static condition, contact elements in the soil-structure interface, etc. During this work, a simple absorbing layer method based on a Rayleigh/Caughey damping formulation, which is often already available in existing Finite Element softwares, is also presented. The stability conditions of the wave propagation problems are studied and it is shown that the linear and nonlinear behavior are very different when dealing with numerical dispersion. It is shown that the 10 points per wavelength rule, recommended in the literature for the elastic media is not sufficient for the nonlinear case. The implemented model is first numerically verified by comparing the results with other known numerical codes. Afterward, a parametric study is carried out for different types of structures and various soil profiles to characterize nonlinear effects. Different features of the DSSI are compared to the linear case: modification of the amplitude and frequency content of the waves propagated into the soil, fundamental frequency, energy dissipation in

Optical rogue waves generation in a nonlinear metamaterial

Science.gov (United States)

Onana Essama, Bedel Giscard; Atangana, Jacques; Biya-Motto, Frederick; Mokhtari, Bouchra; Cherkaoui Eddeqaqi, Noureddine; Kofane, Timoleon Crepin

2014-11-01

We investigate the behavior of electromagnetic wave which propagates in a metamaterial for negative index regime. The optical pulse propagation is described by the nonlinear Schrödinger equation with cubic-quintic nonlinearities, second- and third-order dispersion effects. The behavior obtained for negative index regime is compared to that observed for positive index regime. The characterization of electromagnetic wave uses some pulse parameters obtained analytically and called collective coordinates such as amplitude, temporal position, width, chirp, frequency shift and phase. Six frequency ranges have been pointed out where a numerical evolution of collective coordinates and their stability are studied under a typical example to verify our analysis. It appears that a robust soliton due to a perfect compensation process between second-order dispersion and cubic-nonlinearity is presented at each frequency range for both negative and positive index regimes. Thereafter, the stability of the soliton pulse and physical conditions leading to optical rogue waves generation are discussed at each frequency range for both regimes, when third-order dispersion and quintic-nonlinearity come into play. We have demonstrated that collective coordinates give much useful information on external and internal behavior of rogue events. Firstly, we determine at what distance begins the internal excitation leading to rogue waves. Secondly, what kind of internal modification and how it modifies the system in order to build-up rogue events. These results lead to a best comprehension of the mechanism of rogue waves generation. So, it clearly appears that the rogue wave behavior strongly depends on nonlinearity strength of distortion, frequency and regime considered.

Nonlinear theory of the free-electron laser

International Nuclear Information System (INIS)

Chian, A.C.-L.; Padua Brito Serbeto, A. de.

1984-01-01

A theory of Raman free-electron laser using a circularly polarized electromagnetic pump is investigated. Coupled wave equations that describe both linear and nonlinear evolution of stimulated Raman scattering are derived. The dispersion relation and the growth rate for the parametric instability are obtained. Nonlinear processes that may lead to saturation of the free-electron laser are discussed. (Author) [pt

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....

Global solutions of nonlinear Schrödinger equations

CERN Document Server

Bourgain, J

1999-01-01

This volume presents recent progress in the theory of nonlinear dispersive equations, primarily the nonlinear Schrödinger (NLS) equation. The Cauchy problem for defocusing NLS with critical nonlinearity is discussed. New techniques and results are described on global existence and properties of solutions with large Cauchy data. Current research in harmonic analysis around Strichartz's inequalities and its relevance to nonlinear PDE is presented. Several topics in NLS theory on bounded domains are reviewed. Using the NLS as an example, the book offers comprehensive insight on current research r

Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes

DEFF Research Database (Denmark)

Zhang, H.W.; Schäffer, Hemming Andreas

2007-01-01

An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....

Slow light pulse propagation in dispersive media

DEFF Research Database (Denmark)

Nielsen, Torben Roland; Mørk, Jesper; Lavrinenko, Andrei

2009-01-01

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...... rights reserved....

Phase noise of dispersion-managed solitons

International Nuclear Information System (INIS)

Spiller, Elaine T.; Biondini, Gino

2009-01-01

We quantify noise-induced phase deviations of dispersion-managed solitons (DMS) in optical fiber communications and femtosecond lasers. We first develop a perturbation theory for the dispersion-managed nonlinear Schroedinger equation (DMNLSE) in order to compute the noise-induced mean and variance of the soliton parameters. We then use the analytical results to guide importance-sampled Monte Carlo simulations of the noise-driven DMNLSE. Comparison of these results with those from the original unaveraged governing equations confirms the validity of the DMNLSE as a model for many dispersion-managed systems and quantify the increased robustness of DMS with respect to noise-induced phase jitter.

Nonlinear parity readout with a microwave photodetector

Science.gov (United States)

Schöndorf, M.; Wilhelm, F. K.

2018-04-01

Robust high-fidelity parity measurement is an important operation in many applications of quantum computing. In this work we show how in a circuit QED architecture, one can measure parity in a single shot at very high contrast by taking advantage of the nonlinear behavior of a strongly driven microwave cavity coupled to one or multiple qubits. We work in a nonlinear dispersive regime treated in an exact dispersive transformation. We show that appropriate tuning of experimental parameters leads to very high contrast in the cavity and therefore to a high-efficiency parity readout with a microwave photon counter or another amplitude detector. These tuning conditions are based on nonlinearity and are hence more robust than previously described linear tuning schemes. In the first part of the paper we show in detail how to achieve this for two-qubit parity measurements and extend this to N qubits in the second part of the paper. We also study the quantum nondemolition character of the protocol.

Precise calculations in simulations of the interaction of low energy neutrons with nano-dispersed media

International Nuclear Information System (INIS)

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

Precise calculations in simulations of the interaction of low energy neutrons with nano-dispersed media

Science.gov (United States)

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.

Coulombic interactions and multicomponent ionic dispersion during transport of charged species in heterogeneous porous media

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...... occurred. To quantitatively interpret the outcomes of our laboratory experiments in the spatially variable flow fields we developed a two dimensional numerical model based on a multicomponent formulation, on charge conservation and on the accurate description of transverse dispersion. The results...... of the multicomponent transport simulations were compared with the high-resolution (5 mm spacing) concentration measurements of the ionic species at the outlet of the flow-through domain. The excellent agreement between the measured concentrations and the results of purely forward numerical simulations demonstrates...

Precise calculations in simulations of the interaction of low energy neutrons with nano-dispersed media

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.

SPP propagation in nonlinear glass-metal interface

KAUST Repository

Sagor, Rakibul Hasan

2011-12-01

The non-linear propagation of Surface-Plasmon-Polaritons (SPP) in single interface of metal and chalcogenide glass (ChG) is considered. A time domain simulation algorithm is developed using the Finite Difference Time Domain (FDTD) method. The general polarization algorithm incorporated in the auxiliary differential equation (ADE) is used to model frequency-dependent dispersion relation and third-order nonlinearity of ChG. The main objective is to observe the nonlinear behavior of SPP propagation and study the dynamics of the whole structure. © 2011 IEEE.

Theoretical and numerical characterization of a 40 Gbps long-haul multi-channel transmission system with dispersion compensation

Directory of Open Access Journals (Sweden)

Kaikai Xu

2015-08-01

Full Text Available When updating the 10 Gbps optical transmission system to 40 Gbps, the main limits are chromatic dispersion, nonlinear effect, especially the interactions of dispersion and intra-channel nonlinearity. To optimize the performance of standard WDM in a 40 Gbps four-channel transmission system, numerical simulations are carried out to compare three different dispersion compensation techniques (without compensation; periodic dispersion compensation at the front end; and dispensation compensation all at the end of the system by means of highly dispersed pulses for chromatic dispersion on a terrestrial 40 Gbps system. Both the loss and dispersion of the transmission fiber are periodically compensated, since two dispersive elements are placed at the input and the output ends of a compensation period. Due to the interplay between dispersion, nonlinearity and signal power, and the effect of dispersion on the pulse evolution, the pulse compress can be optimized and the system performance can be improved to compare with the system with either pre- or post-dispersion compensation. On comparing pre- and post-compensation methods, it is found that the latter is superior to the former. Further performance optimization includes how to properly match the EDFA power and length of the fiber.

Simulating dispersion in porous media and the influence of segmentation on stagnancy in carbonates

Science.gov (United States)

Gray, F.; Cen, J.; Shah, S. M.; Crawshaw, J. P.; Boek, E. S.

2016-11-01

Understanding the transport of chemical components in porous media is fundamentally important to many reservoir processes such as contaminant transport and reactive flows involved in CO2 sequestration. Carbonate rocks in particular present difficulties for pore-scale simulations because they contain large amounts of sub-micron porosity. In this work, we introduce a new hybrid simulation model to calculate hydrodynamic dispersion in pore-scale images of real porous media and use this to elucidate the origins and behaviour of stagnant zones arising in transport simulations using micro-CT images of carbonates. For this purpose a stochastic particle model for simulating the transport of a solute is coupled to a Lattice-Boltzmann algorithm to calculate the flow field. The particle method incorporates second order spatial and temporal resolution to resolve finer features of the domain. We demonstrate how dispersion coefficients can be accurately obtained in capillaries, where corresponding analytical solutions are available, even when these are resolved to just a few lattice units. Then we compute molecular displacement distributions for pore-spaces of varying complexity: a pack of beads; a Bentheimer sandstone; and a Portland carbonate. Our calculated propagator distributions are compared directly with recent experimental PFG-NMR propagator distributions (Scheven et al., 2005; Mitchell et al., 2008), the latter excluding spin relaxation mechanisms. We observe that the calculated transport propagators can be quantitatively compared with the experimental distribution, provided that spin relaxations in the experiment are excluded, and good agreement is found for both the sandstone and the carbonate. However, due to the absence of explicit micro-porosity from the carbonate pore space image used for flow field simulations we note that there are fundamental differences in the physical origins of the stagnant zones for micro-porous rocks between simulation and experiment. We

Wave-equation dispersion inversion

KAUST Repository

Li, Jing

2016-12-08

We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained from Rayleigh waves recorded by vertical-component geophones. Similar to wave-equation traveltime tomography, the complicated surface wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the phase-velocity and frequency domains. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2-D or 3-D S-wave velocity models. This procedure, denoted as wave-equation dispersion inversion (WD), does not require the assumption of a layered model and is significantly less prone to the cycle-skipping problems of full waveform inversion. The synthetic and field data examples demonstrate that WD can approximately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic data and the inversion of dispersion curves associated with Love waves.

Nonlinear dynamics: Challenges and perspectives

Indian Academy of Sciences (India)

fields such as economics, social dynamics and so on [6–10]. These nonlinear ..... developing all-optical computers in homogeneous bulk media such as pho- ... suggestions have been given to develop effective chaos-based cryptographic.

Methodological Challenges by (New Media. An Essay on Perspectives and Possible Consequences

Directory of Open Access Journals (Sweden)

Christian Wessely

2015-11-01

Full Text Available The classical concept of media analysis depends to a large extent on linearity, but modern interactive media are mostly non-linear. Roger Odin has suggested a method for working with such interactive media; however, the approach he suggests creates a new problem. What would be an appropriate way to deal with the dilemma of balancing sufficient intersubjectivity and concessions to non-linearity?

Simulations of fluid flow through porous media based on cellular automata and non-linear dynamics

Energy Technology Data Exchange (ETDEWEB)

Paulson, K V

1992-05-15

A study is being carried out to apply cellular automata and non-linear dynamics in the construction of efficient and accurate computer simulations of multiphase fluid flow through porous media, with the objective of application to reservoir modelling for hydrocarbon recovery. An algorithm based on Boolean operations has been developed which transforms a PC clone into a highly efficient vector processor capable of cellular automata simulation of single fluid flow through two-dimensional rock matrix models of varying porosities. Macroscopic flow patterns have been established through spatial and temporal averaging with no floating point operations. Permeabilities of the different models have been calculated. Hardware allows the algorithm to function on dual processors on a PC platform using a video recording and editing facility. Very encouraging results have been obtained. 4 figs.

Drift vortices in continuous media

International Nuclear Information System (INIS)

Chernousenko, V.M.; Chernenko, I.V.; Chernyshenko, S.V.

1989-01-01

The work is devoted to investigation into the problems of large-scale cortex drift and generation in continuous media based on the solution of notably non-linear differential equations. Using the capability of the modern computer technique it is possible to consider a series of cases with regard to medium viscosity and its inhomogeneity and with regard to three-dimensional vortex nature. Based on the solutions obtained the large-scale steady-state vortex generation processes are considered. The results can be used when studying non-linear phenomena in plasma and processes of substance and energy transfer in non-equilibrium media. 16 refs.; 5 figs

Dispersion relation of linearly polarized strong electromagnetic waves

Energy Technology Data Exchange (ETDEWEB)

Ferrari, A; Massaglia, S [Consiglio Nazionale delle Ricerche, Turin (Italy). Lab. di Cosmo-Geofisica; Dobrowolny, M [Comitato Nazionale per l' Energia Nucleaire, Frascati (Italy). Lab. Plasma Spazio

1975-12-15

A numerical study is presented of the dispersion relation of linearly polarized strong electromagnetic waves in a cold electron plasma. The nonlinear effects introduced by the relativistic motion of electrons are: (1) the dispersion relation depends explicitly on the field strength ..cap alpha..=eE/sub 0//mc..omega../sub 0/, and (2) the propagation of modes with frequencies below the formal electron plasma frequency is allowed.

Quantum treatment of field propagation in a fiber near the zero dispersion wavelength

Science.gov (United States)

Safaei, A.; Bassi, A.; Bolorizadeh, M. A.

2018-05-01

In this report, we present a quantum theory describing the propagation of the electromagnetic radiation in a fiber in the presence of the third order dispersion coefficient. We obtained the quantum photon-polariton field, hence, we provide herein a coupled set of operator forms for the corresponding nonlinear Schrödinger equations when the third order dispersion coefficient is included. Coupled stochastic nonlinear Schrödinger equations were obtained by applying a positive P-representation that governs the propagation and interaction of quantum solitons in the presence of the third-order dispersion term. Finally, to reduce the fluctuations near solitons in the first approximation, we developed coupled stochastic linear equations.

Channel Capacity Calculation at Large SNR and Small Dispersion within Path-Integral Approach

Science.gov (United States)

Reznichenko, A. V.; Terekhov, I. S.

2018-04-01

We consider the optical fiber channel modelled by the nonlinear Shrödinger equation with additive white Gaussian noise. Using Feynman path-integral approach for the model with small dispersion we find the first nonzero corrections to the conditional probability density function and the channel capacity estimations at large signal-to-noise ratio. We demonstrate that the correction to the channel capacity in small dimensionless dispersion parameter is quadratic and positive therefore increasing the earlier calculated capacity for a nondispersive nonlinear optical fiber channel in the intermediate power region. Also for small dispersion case we find the analytical expressions for simple correlators of the output signals in our noisy channel.

Bright breathers in nonlinear left-handed metamaterial lattices

Science.gov (United States)

Koukouloyannis, V.; Kevrekidis, P. G.; Veldes, G. P.; Frantzeskakis, D. J.; DiMarzio, D.; Lan, X.; Radisic, V.

2018-02-01

In the present work, we examine a prototypical model for the formation of bright breathers in nonlinear left-handed metamaterial lattices. Utilizing the paradigm of nonlinear transmission lines, we build a relevant lattice and develop a quasi-continuum multiscale approximation that enables us to appreciate both the underlying linear dispersion relation and the potential for bifurcation of nonlinear states. We focus here, more specifically, on bright discrete breathers which bifurcate from the lower edge of the linear dispersion relation at wavenumber k=π . Guided by the multiscale analysis, we calculate numerically both the stable inter-site centered and the unstable site-centered members of the relevant family. We quantify the associated stability via Floquet analysis and the Peierls-Nabarro barrier of the energy difference between these branches. Finally, we explore the dynamical implications of these findings towards the potential mobility or lack thereof (pinning) of such breather solutions.

Vibrational mechanics nonlinear dynamic effects, general approach, applications

CERN Document Server

Blekhman, Iliya I

2000-01-01

This important book deals with vibrational mechanics - the new, intensively developing section of nonlinear dynamics and the theory of nonlinear oscillations. It offers a general approach to the study of the effect of vibration on nonlinear mechanical systems.The book presents the mathematical apparatus of vibrational mechanics which is used to describe such nonlinear effects as the disappearance and appearance under vibration of stable positions of equilibrium and motions (i.e. attractors), the change of the rheological properties of the media, self-synchronization, self-balancing, the vibrat

Nonlinear and turbulent processes in physics. Volume 2. Nonlinear effects in various areas of science

Energy Technology Data Exchange (ETDEWEB)

Sagdeev, R Z

1984-01-01

The results of theoretical and experimental investigations of nonlinear and turbulent phenomena from a wide range of fields in physics are presented in reviews and reports. Topics examined include localized vortex formations in an ideal fluid, phase transitions in crystals, spatially nonuniform structures in condensed matter, solitons in molecular systems, the migration of quasi-particles in easily deformed crystals, bifurcations and dissipative structures in distributed kinetic systems, and structures in a nonlinear burning medium. Consideration is given to macroscopic motion generation in nonequilibrium media, the interaction of bulk and surface wave trains, near-threshold instabilities in hydrodynamics, solitons in nonlinear elastic rods with variable characteristics, the generation of solitons and vortices from chaos, and nonlinear electromagnetic-wave dissipation in an electron system.

Experimental research on dispersion parameters of ground water around the area of CIAE

International Nuclear Information System (INIS)

Yu Jun

1993-01-01

The dispersion are important parameters in modeling the migration of pollutant in the ground water. Due to the complexity of geological media, variant dispersion is expected according to the difference of the geological media. Three parts are included in physical simulation in the laboratory column, tracer experiment in the field and the prediction of dispersion using the stochastic model. Experimental results show that the dispersion obtained in the column are three orders of magnitude smaller than that obtained in the field. Using the field values of conductivity and stochastic theory, the calculated asymptotic longitudinal and lateral dispersion are 370 and 0.45 meters respectively and the correlation length is 400 meters approximately. Using the dispersion obtained from the formula in the paper can enhance the precision of the model prediction, the distance heeded to reach the Fick's dispersion is 6 km approximately

THEORETICAL EVALUATION OF NONLINEAR EFFECTS ON OPTICAL WDM NETWORKS WITH VARIOUS FIBER TYPES

Directory of Open Access Journals (Sweden)

YASIN M. KARFAA

2010-09-01

Full Text Available A theoretical study is carried out to evaluate the performance of an opticalwavelength division multiplexing (WDM network transmission system in the presenceof crosstalk due to optical fiber nonlinearities. The most significant nonlinear effects inthe optical fiber which are Cross-Phase Modulation (XPM, Four-Wave Mixing (FWM,and Stimulated Raman Scattering (SRS are investigated. Four types of optical fiber areincluded in the analysis; these are: single-mode fiber (SMF, dispersion compensationfiber (DCF, non-zero dispersion fiber (NZDF, and non-zero dispersion shifted fiber(NZDSF. The results represent the standard deviation of nonlinearity induced crosstalknoise power due to FWM and SRS, XPM power penalty for SMF, DCF, NZDF, andNZDSF types of fiber, besides the Bit Error Rate (BER for the three nonlinear effectsusing standard fiber type (SMF. It is concluded that three significant fiber nonlinearitiesare making huge limitations against increasing the launched power which is desired,otherwise, lower values of launched power limit network expansion including length,distance, covered areas, and number of users accessing the WDM network, unlesssuitable precautions are taken to neutralize the nonlinear effects. Besides, various fibertypes are not behaving similarly towards network parameters.

Constraints on small-scale cosmological fluctuations from SNe lensing dispersion

International Nuclear Information System (INIS)

Ben-Dayan, Ido; Takahashi, Ryuichi

2015-04-01

We provide predictions on small-scale cosmological density power spectrum from supernova lensing dispersion. Parameterizing the primordial power spectrum with running α and running of running β of the spectral index, we exclude large positive α and β parameters which induce too large lensing dispersions over current observational upper bound. We ran cosmological N-body simulations of collisionless dark matter particles to investigate non-linear evolution of the primordial power spectrum with positive running parameters. The initial small-scale enhancement of the power spectrum is largely erased when entering into the non-linear regime. For example, even if the linear power spectrum at k>10 hMpc -1 is enhanced by 1-2 orders of magnitude, the enhancement much decreases to a factor of 2-3 at late time (z≤1.5). Therefore, the lensing dispersion induced by the dark matter fluctuations weakly constrains the running parameters. When including baryon-cooling effects (which strongly enhance the small-scale clustering), the constraint is comparable or tighter than the PLANCK constraint, depending on the UV cut-off. Further investigations of the non-linear matter spectrum with baryonic processes is needed to reach a firm constraint.

Threshold effect under nonlinear limitation of the intensity of high-power light

International Nuclear Information System (INIS)

Tereshchenko, S A; Podgaetskii, V M; Gerasimenko, A Yu; Savel'ev, M S

2015-01-01

A model is proposed to describe the properties of limiters of high-power laser radiation, which takes into account the threshold character of nonlinear interaction of radiation with the working medium of the limiter. The generally accepted non-threshold model is a particular case of the threshold model if the threshold radiation intensity is zero. Experimental z-scan data are used to determine the nonlinear optical characteristics of media with carbon nanotubes, polymethine and pyran dyes, zinc selenide, porphyrin-graphene and fullerene-graphene. A threshold effect of nonlinear interaction between laser radiation and some of investigated working media of limiters is revealed. It is shown that the threshold model more adequately describes experimental z-scan data. (nonlinear optical phenomena)

Rogue waves generation in a left-handed nonlinear transmission line with series varactor diodes

Science.gov (United States)

Onana Essama, B. G.; Atangana, J.; Biya Motto, F.; Mokhtari, B.; Cherkaoui Eddeqaqi, N.; Kofane, Timoleon C.

2014-07-01

We investigate the electromagnetic wave behavior and its characterization using collective variables technique. Second-order dispersion, first- and second-order nonlinearities, which strongly act in a left-handed nonlinear transmission line with series varactor diodes, are taken into account. Four frequency ranges have been found. The first one gives the so-called energetic soliton due to a perfect combination of second-order dispersion and first-order nonlinearity. The second frequency range presents a dispersive soliton leading to the collapse of the electromagnetic wave at the third frequency range. But the fourth one shows physical conditions which are able to provoke the appearance of wave trains generation with some particular waves, the rogue waves. Moreover, we demonstrate that the number of rogue waves increases with frequency. The soliton, thereafter, gains a relative stability when second-order nonlinearity comes into play with some specific values in the fourth frequency range. Furthermore, the stability conditions of the electromagnetic wave at high frequencies have been also discussed.

Computing in nonlinear media and automata collectives

CERN Document Server

Adamatzky, Andrew

2001-01-01

Reaction-diffusion, excitation, and computation. Subdivision of space. Computation on and with graphs. Computational universality of excitable media. Phenomenology of lattice excitation and emergence of computation.

Longitudinal dispersion coefficients for numerical modeling of groundwater solute transport in heterogeneous formations

DEFF Research Database (Denmark)

Lee, Jonghyun; Rolle, Massimo; Kitanidis, Peter K.

2018-01-01

Most recent research on hydrodynamic dispersion in porous media has focused on whole-domain dispersion while other research is largely on laboratory-scale dispersion. This work focuses on the contribution of a single block in a numerical model to dispersion. Variability of fluid velocity and conc...

Nonlinear tunneling of bright and dark rogue waves in combined nonlinear Schrödinger and Maxwell-Bloch systems

Science.gov (United States)

Raju, Thokala Soloman; Pal, Ritu

2018-05-01

We derive the analytical rogue wave solutions for the generalized inhomogeneous nonlinear Schrödinger-Maxwell-Bloch (GINLS-MB) equation describing the pulse propagation in erbium-doped fibre system. Then by suitably choosing the inhomogeneous parameters, we delineate the tunneling properties of rogue waves through dispersion and nonlinearity barriers or wells. Finally, we demonstrate the propagating characteristics of optical solitons by considering their tunneling through periodic barriers by the proper choice of external potential.

Nonlinear theory of localized standing waves

OpenAIRE

Denardo, Bruce; Larraza, Andrés; Putterman, Seth; Roberts, Paul

1992-01-01

An investigation of the nonlinear dispersive equations of continuum mechanics reveals localized standing-wave solutions that are domain walls between regions of different wave number. These states can appear even when the dispersion law is a single-valued function of the wave number. In addition, we calculate solutions for kinks in cutoff and noncutoff modes, as well as cutoff breather solitons. Division of Engineering and Geophysics of the Office of Basic Energy Science of U.S. DOE for su...

Nonlinear elastic longitudinal strain-wave propagation in a plate with nonequilibrium laser-generated point defects

International Nuclear Information System (INIS)

Mirzade, Fikret Kh.

2005-01-01

The propagation of longitudinal strain wave in a plate with quadratic nonlinearity of elastic continuum was studied in the context of a model that takes into account the joint dynamics of elastic displacements in the medium and the concentration of the nonequilibrium laser-induced point defects. The input equations of the problem are reformulated in terms of only the total displacements of the medium points. In this case, the presence of structural defects manifests itself in the emergence of a delayed response of the system to the propagation of the strain-related perturbations, which is characteristic of media with relaxation or memory. The model equations describing the nonlinear displacement wave were derived with allowance made for the values of the relaxation parameter. The influence of the generation and relaxation of lattice defects on the propagation of this wave was analyzed. It is shown that, for short relaxation times of defects, the strain can propagate in the form of shock fronts. In the case of longer relaxation times, shock waves do not form and the strain wave propagates only in the form of solitary waves or a train of solitons. The contributions of the finiteness of the defect-recombination rate to linear and nonlinear elastic modulus, and spatial dispersion are determined

Phonon dispersion evolution in uniaxially strained aluminum crystal

Science.gov (United States)

Parthasarathy, Ranganathan; Misra, Anil; Aryal, Sitaram; Ouyang, Lizhi

2018-04-01

The influence of loading upon the phonon dispersion of crystalline materials could be highly nonlinear with certain particular trends that depend upon the loading path. In this paper, we have calculated the influence of [100] uniaxial strain on the phonon dispersion and group velocities in fcc aluminum using second moments of position obtained from molecular dynamics (MD) simulation at 300 K. In contrast to nonlinear monotonic variation of both longitudinal and transverse phonon frequencies along the Δ , Λ and Σ lines of the first Brillouin zone under tension, transverse phonon branches along the Λ line show inflection at specific wavevectors when the compressive strain exceeds 5%. Further, the longitudinal group velocities along the high-symmetry Δ line vary non-monotonically with strain, reaching a minimum at 5% compressive strain. Throughout the strain range studied, the equilibrium positions of atoms displace in an affine manner preserving certain static structural symmetry. We attribute the anomalies in the phonon dispersion to the non-affine evolution of second moments of atomic position, and the associated plateauing of force constants under the applied strain path.

Time-Reversal Generation of Rogue Waves

Science.gov (United States)

Chabchoub, Amin; Fink, Mathias

2014-03-01

The formation of extreme localizations in nonlinear dispersive media can be explained and described within the framework of nonlinear evolution equations, such as the nonlinear Schrödinger equation (NLS). Within the class of exact NLS breather solutions on a finite background, which describe the modulational instability of monochromatic wave trains, the hierarchy of rational solutions localized in both time and space is considered to provide appropriate prototypes to model rogue wave dynamics. Here, we use the time-reversal invariance of the NLS to propose and experimentally demonstrate a new approach to constructing strongly nonlinear localized waves focused in both time and space. The potential applications of this time-reversal approach include remote sensing and motivated analogous experimental analysis in other nonlinear dispersive media, such as optics, Bose-Einstein condensates, and plasma, where the wave motion dynamics is governed by the NLS.

Bright solitons for a generalized nonautonomous nonlinear equation in a nonlinear inhomogeneous fiber

Science.gov (United States)

Xie, Xi-Yang; Tian, Bo; Liu, Lei; Guan, Yue-Yang; Jiang, Yan

2017-06-01

In this paper, we investigate a generalized nonautonomous nonlinear equation, which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber. Under certain integrable constraints, bilinear forms, bright one- and two-soliton solutions are obtained. Via certain transformation, we investigate the properties of the solitons with the first-order dispersion parameter σ1(x, t), second-order dispersion parameter σ2(x, t), third-order dispersion parameter σ3(x, t), phase modulation and gain (loss) v(x, t). Soliton propagation and collision are graphically presented and analyzed: One soliton is shown to maintain its amplitude and width during the propagation. When we choose σ1(x, t), σ2(x, t) and σ3(x, t) differently, travelling direction of the soliton is found to alter. v(x, t) is observed to affect the amplitude of the soliton. Head-on collision between the two solitons is presented with σ1(x, t), σ2(x, t), σ3(x, t) and v(x, t) as the constants, and solitons' amplitudes are the same before and after the collision. When σ1(x, t), σ2(x, t) and σ3(x, t) are chosen as certain functions, the solitons' traveling directions change during the collision. v(x, t) can influence the amplitudes of the two solitons.

Nonlinear Displacement Discontinuity Model for Generalized Rayleigh Wave in Contact Interface

Energy Technology Data Exchange (ETDEWEB)

Kim, No Hyu; Yang, Seung Yong [Korea University of Technology and Education, Cheonan (Korea, Republic of)

2007-12-15

Imperfectly jointed interface serves as mechanical waveguide for elastic waves and gives rise to two distinct kinds of guided wave propagating along the interface. Contact acoustic nonlinearity (CAN) is known to plays major role in the generation of these interface waves called generalized Rayleigh waves in non-welded interface. Closed crack is modeled as non-welded interface that has nonlinear discontinuity condition in displacement across its boundary. Mathematical analysis of boundary conditions and wave equation is conducted to investigate the dispersive characteristics of the interface waves. Existence of the generalized Rayleigh wave(interface wave) in nonlinear contact interface is verified in theory where the dispersion equation for the interface wave is formulated and analyzed. It reveals that the interface waves have two distinct modes and that the phase velocity of anti-symmetric wave mode is highly dependent on contact conditions represented by linear and nonlinear dimensionless specific stiffness

Nonlinear Displacement Discontinuity Model for Generalized Rayleigh Wave in Contact Interface

International Nuclear Information System (INIS)

Kim, No Hyu; Yang, Seung Yong

2007-01-01

Imperfectly jointed interface serves as mechanical waveguide for elastic waves and gives rise to two distinct kinds of guided wave propagating along the interface. Contact acoustic nonlinearity (CAN) is known to plays major role in the generation of these interface waves called generalized Rayleigh waves in non-welded interface. Closed crack is modeled as non-welded interface that has nonlinear discontinuity condition in displacement across its boundary. Mathematical analysis of boundary conditions and wave equation is conducted to investigate the dispersive characteristics of the interface waves. Existence of the generalized Rayleigh wave(interface wave) in nonlinear contact interface is verified in theory where the dispersion equation for the interface wave is formulated and analyzed. It reveals that the interface waves have two distinct modes and that the phase velocity of anti-symmetric wave mode is highly dependent on contact conditions represented by linear and nonlinear dimensionless specific stiffness

Solitons and nonlinear waves in space plasmas

International Nuclear Information System (INIS)

Stasiewicz, K.

2005-01-01

Recent measurements made on the ESA/NASA Cluster mission to the Earth's magnetosphere have provided first detailed measurements of magnetosonic solitons in space. The solitons represent localized enhancements of the magnetic field by a factor of 2-10, or depressions down to 10% of the ambient field. The magnetic field signatures are associated with density depressions/enhancements A two-fluid model of nonlinear electron and ion inertial waves in anisotropic plasmas explains the main properties of these structures. It is shown that warm plasmas support four types of nonlinear waves, which correspond to four linear modes: Alfvenic, magnetosonic, sound, and electron inertial waves. Each of these nonlinear modes has slow and fast versions. It is shown by direct integration that the exponential growth rate of nonlinear modes is balanced by the ion and electron dispersion leading to solutions in the form of trains of solitons or cnoidal waves. By using a novel technique of phase portraits it is shown how the dispersive properties of electron and ion inertial waves change at the transition between warm and hot plasmas, and how trains of solitons ('' mirror modes '') are produced in a hot, anisotropic plasma. The applicability of the model is illustrated with data from Cluster spacecraft. (author)

Interaction trajectory of solitons in nonlinear media with an arbitrary degree of nonlocality

International Nuclear Information System (INIS)

Dai, Zhiping; Yang, Zhenjun; Ling, Xiaohui; Zhang, Shumin; Pang, Zhaoguang

2016-01-01

The interaction trajectory of solitons in nonlocal nonlinear media is investigated. A simple differential equation describing the interaction trajectories is derived based on the light ray equation. Numerical calculations are carried out to illustrate the interaction trajectories with different parameters. The results show that the degree of nonlocality greatly affects the interaction of solitons. For a strongly nonlocal case, the interaction trajectory can be described by a cosine function. Analytical expressions describing the trajectory and the oscillation period are obtained. For generally and weakly nonlocal cases, the interaction trajectories still oscillate periodically, however it is no longer sinusoidal and the oscillation period increases with the nonlocal degree decreasing. In addition, the trajectory of two solitons launched with a relative angle at the entrance plane is investigated. It is found that there exists a critical angle. When the initial relative angle is larger than the critical angle, the two solitons do not collide on propagation. The influence of the degree of nonlocality on the critical angle is also discussed.

Investigation of odd-order nonlinear susceptibilities in atomic vapors

Energy Technology Data Exchange (ETDEWEB)

Yan, Yaqi [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi’an Jiaotong University, Xi’an 710049 (China); Shaanxi Key Laboratory of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Teaching and Research Section of Maths and Physics, Guangzhou Commanding Academy of Chinese People’s Armed Police Force, Guangzhou, 510440 (China); Wu, Zhenkun; Si, Jinhai; Yan, Lihe; Zhang, Yiqi; Yuan, Chenzhi; Sun, Jia [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi’an Jiaotong University, Xi’an 710049 (China); Shaanxi Key Laboratory of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Zhang, Yanpeng, E-mail: ypzhang@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi’an Jiaotong University, Xi’an 710049 (China); Shaanxi Key Laboratory of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China)

2013-06-15

We theoretically deduce the macroscopic symmetry constraints for arbitrary odd-order nonlinear susceptibilities in homogeneous media including atomic vapors for the first time. After theoretically calculating the expressions using a semiclassical method, we demonstrate that the expressions for third- and fifth-order nonlinear susceptibilities for undressed and dressed four- and six-wave mixing (FWM and SWM) in atomic vapors satisfy the macroscopic symmetry constraints. We experimentally demonstrate consistence between the macroscopic symmetry constraints and the semiclassical expressions for atomic vapors by observing polarization control of FWM and SWM processes. The experimental results are in reasonable agreement with our theoretical calculations. -- Highlights: •The macroscopic symmetry constraints are deduced for homogeneous media including atomic vapors. •We demonstrate that odd-order nonlinear susceptibilities satisfy the constraints. •We experimentally demonstrate the deduction in part.

Chromatic dispersion effects in ultra-low coherence interferometry

Energy Technology Data Exchange (ETDEWEB)

Lychagov, V V; Ryabukho, V P [N.G.Chernyshevsky Saratov State University (Russian Federation)

2015-06-30

We consider the properties of an interference signal shift from zero-path-difference position in the presence of an uncompensated dispersive layer in one of the interferometer arms. It is experimentally shown that in using an ultra-low coherence light source, the formation of the interference signal is also determined by the group velocity dispersion, which results in a nonlinear dependence of the position of the interference signal on the geometrical thickness of the dispersive layer. The discrepancy in the dispersive layer and compensator refractive indices in the third decimal place is experimentally shown to lead to an interference signal shift that is an order of magnitude greater than the pulse width. (interferometry)

Oscillating solitons in nonlinear optics

Indian Academy of Sciences (India)

... are derived, and the relevant properties and features of oscillating solitons are illustrated. Oscillating solitons are controlled by the reciprocal of the group velocity and Kerr nonlinearity. Results of this paper will be valuable to the study of dispersion-managed optical communication system and mode-locked fibre lasers.

A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation

KAUST Repository

Wu, Zedong

2018-04-05

Numerical simulation of the acoustic wave equation in either isotropic or anisotropic media is crucial to seismic modeling, imaging and inversion. Actually, it represents the core computation cost of these highly advanced seismic processing methods. However, the conventional finite-difference method suffers from severe numerical dispersion errors and S-wave artifacts when solving the acoustic wave equation for anisotropic media. We propose a method to obtain the finite-difference coefficients by comparing its numerical dispersion with the exact form. We find the optimal finite difference coefficients that share the dispersion characteristics of the exact equation with minimal dispersion error. The method is extended to solve the acoustic wave equation in transversely isotropic (TI) media without S-wave artifacts. Numerical examples show that the method is is highly accurate and efficient.

Separation Transformation and New Exact Solutions of the (N + 1)-dimensional Dispersive Double sine-Gordon Equation

International Nuclear Information System (INIS)

Tian Ye; Chen Jing; Zhang Zhifei

2012-01-01

In this paper, the separation transformation approach is extended to the (N + 1)-dimensional dispersive double sine-Gordon equation arising in many physical systems such as the spin dynamics in the B phase of 3 He superfluid. This equation is first reduced to a set of partial differential equations and a nonlinear ordinary differential equation. Then the general solutions of the set of partial differential equations are obtained and the nonlinear ordinary differential equation is solved by F-expansion method. Finally, many new exact solutions of the (N + 1)-dimensional dispersive double sine-Gordon equation are constructed explicitly via the separation transformation. For the case of N > 2, there is an arbitrary function in the exact solutions, which may reveal more novel nonlinear structures in the high-dimensional dispersive double sine-Gordon equation.

Bulk nonlinear elastic strain waves in a bar with nanosize inclusions

DEFF Research Database (Denmark)

Gula, Igor A.; Samsonov (†), Alexander M.

2018-01-01

We propose a mathematical model for propagation of the long nonlinearly elastic longitudinal strain waves in a bar, which contains nanoscale structural inclusions. The model is governed by a nonlinear doubly dispersive equation (DDE) with respect to the one unknown longitudinal strain function. We...

Even and odd combinations of nonlinear coherent states

International Nuclear Information System (INIS)

De los Santos-Sanchez, O; Recamier, J

2011-01-01

In this work we present some statistical properties of even and odd combinations of nonlinear coherent states associated with two nonlinear potentials; one supporting a finite number of bound states and the other supporting an infinite number of bound states, within the framework of an f-deformed algebra. We calculate their normalized variance and the temporal evolution of their dispersion relations using nonlinear coherent states defined as (a) eigensates of the deformed annihilation operator and (b) those states created by the application of a deformed displacement operator upon the ground state of the oscillator.

A simple homogeneous model for regular and irregular metallic wire media samples

Science.gov (United States)

Kosulnikov, S. Y.; Mirmoosa, M. S.; Simovski, C. R.

2018-02-01

To simplify the solution of electromagnetic problems with wire media samples, it is reasonable to treat them as the samples of a homogeneous material without spatial dispersion. The account of spatial dispersion implies additional boundary conditions and makes the solution of boundary problems difficult especially if the sample is not an infinitely extended layer. Moreover, for a novel type of wire media - arrays of randomly tilted wires - a spatially dispersive model has not been developed. Here, we introduce a simplistic heuristic model of wire media samples shaped as bricks. Our model covers WM of both regularly and irregularly stretched wires.

URANIUM BISMUTHIDE DISPERSION IN MOLTEN METAL

Science.gov (United States)

Teitel, R.J.

1959-10-27

The formation of intermetallic bismuth compounds of thorium or uranium dispersed in a liquid media containing bismuth and lead is described. A bismuthide of uranium dispersed in a liquid metal medium is formed by dissolving uranium in composition of lead and bismuth containing less than 80% lead and lowering the temperature of the composition to a temperature below the point at which the solubility of uranium is exceeded and above the melting point of the composition.

Effect of P T symmetry on nonlinear waves for three-wave interaction models in the quadratic nonlinear media

Science.gov (United States)

Shen, Yujia; Wen, Zichao; Yan, Zhenya; Hang, Chao

2018-04-01

We study the three-wave interaction that couples an electromagnetic pump wave to two frequency down-converted daughter waves in a quadratic optical crystal and P T -symmetric potentials. P T symmetric potentials are shown to modulate stably nonlinear modes in two kinds of three-wave interaction models. The first one is a spatially extended three-wave interaction system with odd gain-and-loss distribution in the channel. Modulated by the P T -symmetric single-well or multi-well Scarf-II potentials, the system is numerically shown to possess stable soliton solutions. Via adiabatical change of system parameters, numerical simulations for the excitation and evolution of nonlinear modes are also performed. The second one is a combination of P T -symmetric models which are coupled via three-wave interactions. Families of nonlinear modes are found with some particular choices of parameters. Stable and unstable nonlinear modes are shown in distinct families by means of numerical simulations. These results will be useful to further investigate nonlinear modes in three-wave interaction models.

Axial dispersion via shear-enhanced diffusion in colloidal suspensions

KAUST Repository

Griffiths, I. M.

2012-03-01

The familiar example of Taylor dispersion of molecular solutes is extended to describe colloidal suspensions, where the fluctuations that contribute to dispersion arise from hydrodynamic interactions. The generic scheme is illustrated for a suspension of particles in a pressure-driven pipe flow, with a concentration-dependent diffusivity that captures both the shear-induced and Brownian contributions. The effect of the cross-stream migration via shear-induced diffusion is shown to dramatically reduce the axial dispersion predicted by classical Taylor dispersion for a molecular solute. Analytic and numerical solutions are presented that illustrate the effect of the concentration dependence of this nonlinear hydrodynamic mechanism. Copyright © EPLA, 2012.

Nonlocal description of X waves in quadratic nonlinear materials

DEFF Research Database (Denmark)

Larsen, Peter Ulrik Vingaard; Sørensen, Mads Peter; Bang, Ole

2006-01-01

We study localized light bullets and X-waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multi-dimensional nonlinear waves. For X-waves we show that a local cascading limit in terms of a nonlinear Schrodinger equation...

RESEARCH OF LINEAR AND NONLINEAR PROCESSES AT FEMTOSECOND LASER RADIATION PROPAGATION IN THE MEDIUM SIMULATING THE HUMAN EYE VITREOUS

Directory of Open Access Journals (Sweden)

P. Y. Rogov

2015-09-01

Full Text Available The paper deals with mathematical model of linear and nonlinear processes occurring at the propagation of femtosecond laser pulses in the vitreous of the human eye. Methods of computing modeling are applied for the nonlinear spectral equation solution describing the dynamics of a two-dimensional TE-polarized radiation in a homogeneous isotropic medium with cubic fast-response nonlinearity without the usage of slowly varying envelope approximation. Environments close to the optical media parameters of the eye were used for the simulation. The model of femtosecond radiation propagation takes into account the process dynamics for dispersion broadening of pulses in time and the occurence of the self-focusing near the retina when passing through the vitreous body of the eye. Dependence between the pulse duration on the retina has been revealed and the duration of the input pulse and the values of power density at which there is self-focusing have been found. It is shown that the main mechanism of radiation damage with the use of titanium-sapphire laser is photoionization. The results coincide with those obtained by the other scientists, and are usable for creation Russian laser safety standards for femtosecond laser systems.

Theoretical analysis of open aperture reflection Z-scan on materials with high-order optical nonlinearities

International Nuclear Information System (INIS)

Petris, Adrian I.; Vlad, Valentin I.

2010-03-01

We present a theoretical analysis of open aperture reflection Z-scan in nonlinear media with third-, fifth-, and higher-order nonlinearities. A general analytical expression for the normalized reflectance when third-, fifth- and higher-order optical nonlinearities are excited is derived and its consequences on RZ-scan in media with high-order nonlinearities are discussed. We show that by performing RZ-scan experiments at different incident intensities it is possible to put in evidence the excitation of different order nonlinearities in the medium. Their contributions to the overall nonlinear response can be discriminated by using formulas derived by us. A RZ-scan numerical simulation using these formulas and data taken from literature, measured by another method for the third-, fifth-, and seventh-order nonlinear refractive indices of As 2 S 3 chalcogenide glass, is performed. (author)

All-optical control of group velocity dispersion in tellurite photonic crystal fibers.

Science.gov (United States)

Liu, Lai; Tian, Qijun; Liao, Meisong; Zhao, Dan; Qin, Guanshi; Ohishi, Yasutake; Qin, Weiping

2012-12-15

We demonstrate all-optical control of group velocity dispersion (GVD) via optical Kerr effect in highly nonlinear tellurite photonic crystal fibers. The redshift of the zero-dispersion wavelength is over 307 nm, measured by soliton self-frequency shift cancellation, when the pump peak power of a 1.56 μm femtosecond fiber laser is increased to 11.6 kW. The all-optical control of GVD not only offers a new platform for constructing all-optical-control photonic devices but also promises a new class of experiments in nonlinear fiber optics and light-matter interactions.

Impurity solitons with quadratic nonlinearities

DEFF Research Database (Denmark)

Clausen, Carl A. Balslev; Torres, Juan P-; Torner, Lluis

1998-01-01

We fmd families of solitary waves mediated by parametric mixing in quadratic nonlinear media that are localized at point-defect impurities. Solitons localized at attractive impurities are found to be dynamically stable. It is shown that localization at the impurity modifies strongly the soliton...

Quantitative characterization of nanoparticle agglomeration within biological media

International Nuclear Information System (INIS)

Hondow, Nicole; Brydson, Rik; Wang, Peiyi; Holton, Mark D.; Brown, M. Rowan; Rees, Paul; Summers, Huw D.; Brown, Andy

2012-01-01

Quantitative analysis of nanoparticle dispersion state within biological media is essential to understanding cellular uptake and the roles of diffusion, sedimentation, and endocytosis in determining nanoparticle dose. The dispersion of polymer-coated CdTe/ZnS quantum dots in water and cell growth medium with and without fetal bovine serum was analyzed by transmission electron microscopy (TEM) and dynamic light scattering (DLS) techniques. Characterization by TEM of samples prepared by plunge freezing the blotted solutions into liquid ethane was sensitive to the dispersion state of the quantum dots and enabled measurement of agglomerate size distributions even in the presence of serum proteins where DLS failed. In addition, TEM showed a reduced packing fraction of quantum dots per agglomerate when dispersed in biological media and serum compared to just water, highlighting the effect of interactions between the media, serum proteins, and the quantum dots. The identification of a heterogeneous distribution of quantum dots and quantum dot agglomerates in cell growth medium and serum by TEM will enable correlation with the previously reported optical metrology of in vitro cellular uptake of this quantum dot dispersion. In this paper, we present a comparative study of TEM and DLS and show that plunge-freeze TEM provides a robust assessment of nanoparticle agglomeration state.

Holographic characterization of colloidal particles in turbid media

Science.gov (United States)

Cheong, Fook Chiong; Kasimbeg, Priya; Ruffner, David B.; Hlaing, Ei Hnin; Blusewicz, Jaroslaw M.; Philips, Laura A.; Grier, David G.

2017-10-01

Holographic particle characterization uses in-line holographic microscopy and the Lorenz-Mie theory of light scattering to measure the diameter and the refractive index of individual colloidal particles in their native dispersions. This wealth of information has proved invaluable in fields as diverse as soft-matter physics, biopharmaceuticals, wastewater management, and food science but so far has been available only for dispersions in transparent media. Here, we demonstrate that holographic characterization can yield precise and accurate results even when the particles of interest are dispersed in turbid media. By elucidating how multiple light scattering contributes to image formation in holographic microscopy, we establish the range conditions under which holographic characterization can reliably probe turbid samples. We validate the technique with measurements on model colloidal spheres dispersed in commercial nanoparticle slurries.

Modulation stability and dispersive optical soliton solutions of higher order nonlinear Schrödinger equation and its applications in mono-mode optical fibers

Science.gov (United States)

Arshad, Muhammad; Seadawy, Aly R.; Lu, Dianchen

2018-01-01

In mono-mode optical fibers, the higher order non-linear Schrödinger equation (NLSE) describes the propagation of enormously short light pulses. We constructed optical solitons and, solitary wave solutions of higher order NLSE mono-mode optical fibers via employing modified extended mapping method which has important applications in Mathematics and physics. Furthermore, the formation conditions are also given on parameters in which optical bright and dark solitons can exist for this media. The moment of the obtained solutions are also given graphically, that helps to realize the physical phenomena's of this model. The modulation instability analysis is utilized to discuss the model stability, which verifies that all obtained solutions are exact and stable. Many other such types of models arising in applied sciences can also be solved by this reliable, powerful and effective method. The method can also be functional to other sorts of higher order nonlinear problems in contemporary areas of research.

Robust Multiscale Iterative Solvers for Nonlinear Flows in Highly Heterogeneous Media

KAUST Repository

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.

Group-velocity matched nonlinear photonic crystal fibers

DEFF Research Database (Denmark)

Bache, Morten; Lægsgaard, Jesper; Bang, Ole

2006-01-01

A quadratic nonlinear index-guiding silica PCF is optimized for efficient second-harmonic generation through dispersion calculations. Zero group-velocity mismatch is possible for any pump wavelength above 780 nm. Very high conversion efficiencies and bandwidths are found....

Soliton interaction in quadratic and cubic bulk media

DEFF Research Database (Denmark)

Johansen, Steffen Kjær; Bang, Ole

2000-01-01

Summary form only given. The understanding of how and to what extend the cubic nonlinearity affects beam propagation and spatial soliton formation in quadratic media is of vital importance in fundamental and applied nonlinear physics. We consider beam propagation under type-I SHG conditions...... in lossless bulk second order nonlinear optical materials with a nonvanishing third order nonlinearity. It is known that in pure second order systems a single soliton can never collapse whereas in systems with both nonlinearities and that stable single soliton propagation can only in some circumstances...

Finite elements of nonlinear continua

CERN Document Server

Oden, John Tinsley

1972-01-01

Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view.The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical s

Saturable absorption in detonation nanodiamond dispersions

Science.gov (United States)

Vanyukov, Viatcheslav; Mikheev, Gennady; Mogileva, Tatyana; Puzyr, Alexey; Bondar, Vladimir; Lyashenko, Dmitry; Chuvilin, Andrey

2017-07-01

We report on a saturable absorption in aqueous dispersions of nanodiamonds with femtosecond laser pulse excitation at a wavelength of 795 nm. The open aperture Z-scan experiments reveal that in a wide range of nanodiamond particle sizes and concentrations, a light-induced increase of transmittance occurs. The transmittance increase originates from the saturation of light absorption and is associated with a light absorption at 1.5 eV by graphite and dimer chains (Pandey dimer chains). The obtained key nonlinear parameters of nanodiamond dispersions are compared with those of graphene and carbon nanotubes, which are widely used for the mode-locking.

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...

Nonlinear reflection of shock shear waves in soft elastic media.

Science.gov (United States)

Pinton, Gianmarco; Coulouvrat, François; Gennisson, Jean-Luc; Tanter, Mickaël

2010-02-01

For fluids, the theoretical investigation of shock wave reflection has a good agreement with experiments when the incident shock Mach number is large. But when it is small, theory predicts that Mach reflections are physically unrealistic, which contradicts experimental evidence. This von Neumann paradox is investigated for shear shock waves in soft elastic solids with theory and simulations. The nonlinear elastic wave equation is approximated by a paraxial wave equation with a cubic nonlinear term. This equation is solved numerically with finite differences and the Godunov scheme. Three reflection regimes are observed. Theory is developed for shock propagation by applying the Rankine-Hugoniot relations and entropic constraints. A characteristic parameter relating diffraction and non-linearity is introduced and its theoretical values are shown to match numerical observations. The numerical solution is then applied to von Neumann reflection, where curved reflected and Mach shocks are observed. Finally, the case of weak von Neumann reflection, where there is no reflected shock, is examined. The smooth but non-monotonic transition between these three reflection regimes, from linear Snell-Descartes to perfect grazing case, provides a solution to the acoustical von Neumann paradox for the shear wave equation. This transition is similar to the quadratic non-linearity in fluids.

Upscaling solute transport in naturally fractured porous media with the continuous time random walk method

Energy Technology Data Exchange (ETDEWEB)

Geiger, S.; Cortis, A.; Birkholzer, J.T.

2010-04-01

Solute transport in fractured porous media is typically 'non-Fickian'; that is, it is characterized by early breakthrough and long tailing and by nonlinear growth of the Green function-centered second moment. This behavior is due to the effects of (1) multirate diffusion occurring between the highly permeable fracture network and the low-permeability rock matrix, (2) a wide range of advection rates in the fractures and, possibly, the matrix as well, and (3) a range of path lengths. As a consequence, prediction of solute transport processes at the macroscale represents a formidable challenge. Classical dual-porosity (or mobile-immobile) approaches in conjunction with an advection-dispersion equation and macroscopic dispersivity commonly fail to predict breakthrough of fractured porous media accurately. It was recently demonstrated that the continuous time random walk (CTRW) method can be used as a generalized upscaling approach. Here we extend this work and use results from high-resolution finite element-finite volume-based simulations of solute transport in an outcrop analogue of a naturally fractured reservoir to calibrate the CTRW method by extracting a distribution of retention times. This procedure allows us to predict breakthrough at other model locations accurately and to gain significant insight into the nature of the fracture-matrix interaction in naturally fractured porous reservoirs with geologically realistic fracture geometries.

Nonlinear waves and pattern dynamics

CERN Document Server

Pelinovsky, Efim; Mutabazi, Innocent

2018-01-01

This book addresses the fascinating phenomena associated with nonlinear waves and spatio-temporal patterns. These appear almost everywhere in nature from sand bed forms to brain patterns, and yet their understanding still presents fundamental scientific challenges. The reader will learn here, in particular, about the current state-of-the art and new results in: Nonlinear water waves: resonance, solitons, focusing, Bose-Einstein condensation, as well as and their relevance for the sea environment (sea-wind interaction, sand bed forms, fiber clustering) Pattern formation in non-equilibrium media: soap films, chimera patterns in oscillating media, viscoelastic Couette-Taylor flow, flow in the wake behind a heated cylinder, other pattern formation. The editors and authors dedicate this book to the memory of Alexander Ezersky, Professor of Fluid Mechanics at the University of Caen Normandie (France) from September 2007 to July 2016. Before 2007, he had served as a Senior Scientist at the Institute of Applied Physi...

Construction of a single/multiple wavelength RZ optical pulse source at 40 GHz by use of wavelength conversion in a high-nonlinearity DSF-NOLM

DEFF Research Database (Denmark)

Yu, Jianjun; Yujun, Qian; Jeppesen, Palle

2001-01-01

A single or multiple wavelength RZ optical pulse source at 40 GHz is successfully obtained by using wavelength conversion in a nonlinear optical loop mirror consisting of high nonlinearity-dispersion shifted fiber.......A single or multiple wavelength RZ optical pulse source at 40 GHz is successfully obtained by using wavelength conversion in a nonlinear optical loop mirror consisting of high nonlinearity-dispersion shifted fiber....

Nonlinear phonons in high-Tc superconductors mixed crystals

International Nuclear Information System (INIS)

Gadzhiev, B.R.; Dzhavadov, N.A.

1998-01-01

The integrodifferential kinetic equation which is a generalization of the Landau-Ginzburg formalism is introduced. The peculiarities of nonlinear kinetics are investigated by entering the nonlocal function, which is a quantitative measure of time dispersion. The classification nonlocal function is made by its Hausdorff dimensionality d c . It is shown that in the case d c c =1, the relaxation equation is the equation of damping harmonic oscillator. In the case d c >1, the relaxation equation contains the time derivation arbitrary high order. After linearization of the corresponding dynamic equations near the corresponding nonlinear static equations the dispersion and then after spatial averaging, temperature and frequency dependency of corresponding dynamic susceptibility have been determined. It is shown that in the cases d c c >1 the temperature evolution system alongside with the soft mode is accompanied by the modes which depend nonlinearly on the temperature. The physical nature of quasiscattering in the incommensurate phases of layered crystals is studied. The obtained theoretical results are applied to the layered HTSC crystals. (author)

Simultaneous spatial and temporal focusing: a route towards confined nonlinear materials processing

Science.gov (United States)

Kammel, Robert; Bergner, Klaus; Thomas, Jens; Ackermann, Roland; Skupin, Stefan; Nolte, Stefan

2016-03-01

Ultrashort pulse lasers enable reliable and versatile high precision ablation and surface processing of various materials such as metals, polymers and semiconductors. However, when modifications deep inside the bulk of transparent media are required, nonlinear pulse material interactions can decrease the precision, since weak focusing and the long propagation of the intense pulses within the nonlinear media may induce Kerr self-focusing, filamentation and white light generation. In order to improve the precision of those modifications, simultaneous spatial and temporal focusing (SSTF) allows to reduce detrimental nonlinear interactions, because the ultrashort pulse duration is only obtained at the focus, while outside of the focal region the continuously increasing pulse duration strongly reduces the pulse intensity. In this paper, we review the fundamental concepts of this technology and provide an overview of its applications for purposes of multiphoton microscopy and laser materials processing. Moreover, numerical simulations on the nonlinear pulse propagation within transparent media illustrate the linear and nonlinear pulse propagation, highlighting the differences between conventional focusing and SSTF. Finally, fs-laser induced modifications in gelatine are presented to compare nonlinear side-effects caused by conventional focusing and SSTF. With conventional focusing the complex interplay of self-focusing and filamentation induces strongly inhomogeneous, elongated disruptions. In contrast, disruptions induced by SSTF are homogeneously located at the focal plane and reduced in length by a factor >2, which is in excellent agreement with the numerical simulations of the nonlinear pulse propagation and might favor SSTF for demanding applications such as intraocular fs-laser surgery.

Evaluation of third order nonlinear optical parameters of CdS/PVA nanocomposite

International Nuclear Information System (INIS)

Sharma, Mamta; Tripathi, S. K.

2015-01-01

CdS nanoparticles dispersed in PVA are prepared by Chemical method at room temperature. The nonlinear optical parameters such as nonlinear absorption (β), nonlinear refractive index (n 2 ) and nonlinear susceptibility (χ 3 ) are calculated for this sample by using Z-scan technique. CdS/PVA samples show the two photon absorption mechanism. The third order nonlinear susceptibility is calculated from n 2 and β and is found to be of the order of 10 −7 – 10 −8 m 2 /V 2 . The larger value of third order nonlinear susceptibility is due to dielectric and quantum confinement effect

Nonlinear optical studies of curcumin metal derivatives with cw laser

Energy Technology Data Exchange (ETDEWEB)

Henari, F. Z., E-mail: fzhenari@rcsi-mub.com; Cassidy, S. [Department of Basic Medical Sciences, Royal College of Surgeons in Ireland, Medical University of Bahrain (Bahrain)

2015-03-30

We report on measurements of the nonlinear refractive index and nonlinear absorption coefficients for curcumin and curcumin metal complexes of boron, copper, and iron at different wavelengths using the Z-scan technique. These materials are found to be novel nonlinear media. It was found that the addition of metals slightly influences its nonlinearity. These materials show a large negative nonlinear refractive index of the order of 10{sup −7} cm{sup 2}/W and negative nonlinear absorption of the order of 10{sup −6} cm/W. The origin of the nonlinearity was investigated by comparison of the formalism that is known as the Gaussian decomposition model with the thermal lens model. The optical limiting behavior based on the nonlinear refractive index was also investigated.

Nonlinear optical studies of curcumin metal derivatives with cw laser

International Nuclear Information System (INIS)

Henari, F. Z.; Cassidy, S.

2015-01-01

We report on measurements of the nonlinear refractive index and nonlinear absorption coefficients for curcumin and curcumin metal complexes of boron, copper, and iron at different wavelengths using the Z-scan technique. These materials are found to be novel nonlinear media. It was found that the addition of metals slightly influences its nonlinearity. These materials show a large negative nonlinear refractive index of the order of 10 −7 cm 2 /W and negative nonlinear absorption of the order of 10 −6 cm/W. The origin of the nonlinearity was investigated by comparison of the formalism that is known as the Gaussian decomposition model with the thermal lens model. The optical limiting behavior based on the nonlinear refractive index was also investigated

Collapse of solitary excitations in the nonlinear Schrödinger equation with nonlinear damping and white noise

DEFF Research Database (Denmark)

Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Rasmussen, Kim

1996-01-01

in an exponentially decreasing width of the solution in the long-time limit. We also find that a sufficiently large noise variance may cause an initially localized distribution to spread instead of contracting, and that the critical variance necessary to cause dispersion will for small damping be the same......We study the effect of adding noise and nonlinear damping in the two-dimensional nonlinear Schrodinger equation (NLS). Using a collective approach, we find that for initial conditions where total collapse occurs in the unperturbed NLS, the presence of the damping term will instead...

Controlling nonlinear waves in excitable media

International Nuclear Information System (INIS)

Puebla, Hector; Martin, Roland; Alvarez-Ramirez, Jose; Aguilar-Lopez, Ricardo

2009-01-01

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.

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.

Influence of biofilms on transport properties in porous media

Science.gov (United States)

Davit, Y.

2015-12-01

Microbial activity and biofilm growth in porous media can drastically modify transport properties such as permeability, longitudinal and transverse dispersion or effective reaction rates. Understanding these effects has proven to be a considerable challenge. Advances in this field have been hindered by the difficulty of modeling and visualizing these multi-phase non-linear effects across a broad range of spatial and temporal scales. To address these issues, we are developing a strategy that combines imaging techniques based on x-ray micro-tomography with homogenization of pore-scale transport equations. Here, we review recent progress in x-ray imaging of biofilms in porous media, with a particular focus on the contrast agents that are used to differentiate between the fluid and biofilm phases. We further show how the 3D distribution of the different phases can be used to extract specific information about the biofilm and how effective properties can be calculated via the resolution of closure problems. These closure problems are obtained using the method of volume averaging and must be adapted to the problem of interest. In hydrological systems, we show that a generic formulation for reactive solute transport is based on a domain decomposition approach at the micro-scale yielding macro-scale models reminiscent of multi-rate mass transfer approaches.

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

Porous media geometry and transports

CERN Document Server

Adler, Pierre

1992-01-01

The goal of ""Porous Media: Geometry and Transports"" is to provide the basis of a rational and modern approach to porous media. This book emphasizes several geometrical structures (spatially periodic, fractal, and random to reconstructed) and the three major single-phase transports (diffusion, convection, and Taylor dispersion).""Porous Media"" serves various purposes. For students it introduces basic information on structure and transports. Engineers will find this book useful as a readily accessible assemblage of al the major experimental results pertaining to single-phase tr

Bright and dark solitons in the normal dispersion regime of inhomogeneous optical fibers: Soliton interaction and soliton control

International Nuclear Information System (INIS)

Liu Wenjun; Tian Bo; Xu Tao; Sun Kun; Jiang Yan

2010-01-01

Symbolically investigated in this paper is a nonlinear Schroedinger equation with the varying dispersion and nonlinearity for the propagation of optical pulses in the normal dispersion regime of inhomogeneous optical fibers. With the aid of the Hirota method, analytic one- and two-soliton solutions are obtained. Relevant properties of physical and optical interest are illustrated. Different from the previous results, both the bright and dark solitons are hereby derived in the normal dispersion regime of the inhomogeneous optical fibers. Moreover, different dispersion profiles of the dispersion-decreasing fibers can be used to realize the soliton control. Finally, soliton interaction is discussed with the soliton control confirmed to have no influence on the interaction. The results might be of certain value for the study of the signal generator and soliton control.

Effect of nonlocal dispersion on self-interacting excitations

DEFF Research Database (Denmark)

Christiansen, Peter Leth; Rasmussen, Kim; Gaididei, Yu.B.

1996-01-01

The dynamics of self-interacting quasiparticles in 1Dsystems with long-range dispersive interactions isexpressed in terms of a nonlocal nonlinear Schrödingerequation. Two branches of stationary solutions are found.The new branch which contains a cusp soliton is shown to beunstable and blowup...

Radionuclide transport in fractured media

International Nuclear Information System (INIS)

Williams, M.M.R.

1993-01-01

Until recently, the classical advective-dispersive transport equation was considered to be an adequate model for describing the motion of a solute (e.g. radionuclides) in porous and fractured media. In this model, the dispersion coefficient is either obtained from a microscopic model of the porous medium or by carefully controlled experiments. As a result of such experiments, a large body of data has been accumulated on the dispersivity. Detailed examination of these data has resulted in a curious phenomenon being discovered; namely, that the longitudinal dispersion length is 'scale-dependent'. That is to say the value deduced depends on the 'size' of the experiment, i.e. on the distance over which measurements are made. Several interesting attempts have been made to develop theories which explain this phenomenon, all based on treating the velocity of the water in the porous medium as a spatially random variable, but retaining the advective-dispersive balance equation. In this work we present an entirely new approach to the problem of solute transport in fractured media based upon an analogy with neutron transport. The new method has several advantages over the previous theories and these will be explained below. Results from the new theory are in agreement with experimental trends and do not require any further adjustment to explain the scale-dependent effect

Langmuir wave dispersion relation in non-Maxwellian plasmas

International Nuclear Information System (INIS)

Ouazene, M.; Annou, R.

2010-01-01

The Langmuir wave dispersion relation is derived in partially ionized plasmas, where free electrons are confined to move in a nearest neighbor ions' potential well. The equilibrium velocity distribution function experiences then, a departure from Maxwell distribution function. The effect of the non-Maxwellian character of the distribution function on the Langmuir phase and group velocities as well as the phase matching conditions and the nonlinear growth rate of decay instability is investigated. The proposed Langmuir wave dispersion relation is relevant to dense and cryogenic plasmas.

Evaluation of third order nonlinear optical parameters of CdS/PVA nanocomposite

Energy Technology Data Exchange (ETDEWEB)

Sharma, Mamta [Department of Physics, Center of Advanced Study in Physics, Panjab University, Chandigarh-160014 (India); Department of Applied Sciences (Physics), UIET, Panjab University, Chandigarh-160014 (India); Tripathi, S. K., E-mail: surya@pu.ac.in, E-mail: surya-tr@yahoo.com [Department of Physics, Center of Advanced Study in Physics, Panjab University, Chandigarh-160014 (India)

2015-06-24

CdS nanoparticles dispersed in PVA are prepared by Chemical method at room temperature. The nonlinear optical parameters such as nonlinear absorption (β), nonlinear refractive index (n{sub 2}) and nonlinear susceptibility (χ{sup 3}) are calculated for this sample by using Z-scan technique. CdS/PVA samples show the two photon absorption mechanism. The third order nonlinear susceptibility is calculated from n{sub 2} and β and is found to be of the order of 10{sup −7} – 10{sup −8} m{sup 2}/V{sup 2}. The larger value of third order nonlinear susceptibility is due to dielectric and quantum confinement effect.

Dispersion and shape engineered plasmonic nanosensors

Science.gov (United States)

Jeong, Hyeon-Ho; Mark, Andrew G.; Alarcón-Correa, Mariana; Kim, Insook; Oswald, Peter; Lee, Tung-Chun; Fischer, Peer

2016-04-01

Biosensors based on the localized surface plasmon resonance (LSPR) of individual metallic nanoparticles promise to deliver modular, low-cost sensing with high-detection thresholds. However, they continue to suffer from relatively low sensitivity and figures of merit (FOMs). Herein we introduce the idea of sensitivity enhancement of LSPR sensors through engineering of the material dispersion function. Employing dispersion and shape engineering of chiral nanoparticles leads to remarkable refractive index sensitivities (1,091 nm RIU-1 at λ=921 nm) and FOMs (>2,800 RIU-1). A key feature is that the polarization-dependent extinction of the nanoparticles is now characterized by rich spectral features, including bipolar peaks and nulls, suitable for tracking refractive index changes. This sensing modality offers strong optical contrast even in the presence of highly absorbing media, an important consideration for use in complex biological media with limited transmission. The technique is sensitive to surface-specific binding events which we demonstrate through biotin-avidin surface coupling.

The influence of organic matter content and media compaction on the dispersal of entomopathogenic nematodes with different foraging strategies.

Science.gov (United States)

Kapranas, Apostolos; Maher, Abigail M D; Griffin, Christine T

2017-12-01

In laboratory experiments, we investigated how media with varying ratio of peat:sand and two levels of compaction influence dispersal success of entomopathogenic nematode (EPN) species with different foraging strategies: Steinernema carpocapsae (ambusher), Heterorhabditis downesi (cruiser) and Steinernema feltiae (intermediate). Success was measured by the numbers of nematodes moving through a 4 cm column and invading a wax moth larva. We found that both compaction and increasing peat content generally decreased EPN infective juvenile (IJ) success for all three species. Of the three species, H. downesi was the least affected by peat content, and S. carpocapsae was the most adversely influenced by compaction. In addition, sex ratios of the invading IJs of the two Steinernema species were differentially influenced by peat content, and in the case of S. feltiae, sex ratio was also affected by compaction. This indicates that dispersal of male and female IJs is differentially affected by soil parameters and that this differentiation is species-specific. In conclusion, our study shows that organic matter: sand ratio and soil compaction have a marked influence on EPN foraging behaviour with implications for harnessing them as biological pest control agents.

Nonlinear tunneling of optical soliton in 3 coupled NLS equation with symbolic computation

Energy Technology Data Exchange (ETDEWEB)

Mani Rajan, M.S., E-mail: senthilmanirajanofc@gmail.com [Department of Physics, Anna University, Madurai Region, Ramanathapuram (India); Mahalingam, A. [Department of Physics, Anna University, Chennai - 600 025 (India); Uthayakumar, A. [Department of Physics, Presidency College, Chennai - 600 005 (India)

2014-07-15

We investigated the soliton solution for N coupled nonlinear Schrödinger (CNLS) equations. These equations are coupled due to the cross-phase-modulation (CPM). Lax pair of this system is obtained via the Ablowitz–Kaup–Newell–Segur (AKNS) scheme and the corresponding Darboux transformation is constructed to derive the soliton solution. One and two soliton solutions are generated. Using two soliton solutions of 3 CNLS equation, nonlinear tunneling of soliton for both with and without exponential background has been discussed. Finally cascade compression of optical soliton through multi-nonlinear barrier has been discussed. The obtained results may have promising applications in all-optical devices based on optical solitons, study of soliton propagation in birefringence fiber systems and optical soliton with distributed dispersion and nonlinearity management. -- Highlights: •We consider the nonlinear tunneling of soliton in birefringence fiber. •3-coupled NLS (CNLS) equation with variable coefficients is considered. •Two soliton solutions are obtained via Darboux transformation using constructed Lax pair. •Soliton tunneling through dispersion barrier and well are investigated. •Finally, cascade compression of soliton has been achieved.

Derivation of an applied nonlinear Schroedinger equation

Energy Technology Data Exchange (ETDEWEB)

Pitts, Todd Alan [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Laine, Mark Richard [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Schwarz, Jens [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Rambo, Patrick K. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Karelitz, David B. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

2015-01-01

We derive from first principles a mathematical physics model useful for understanding nonlinear optical propagation (including filamentation). All assumptions necessary for the development are clearly explained. We include the Kerr effect, Raman scattering, and ionization (as well as linear and nonlinear shock, diffraction and dispersion). We explain the phenomenological sub-models and each assumption required to arrive at a complete and consistent theoretical description. The development includes the relationship between shock and ionization and demonstrates why inclusion of Drude model impedance effects alters the nature of the shock operator. Unclassified Unlimited Release

Nonlinear self-modulation of ion-acoustic waves

International Nuclear Information System (INIS)

Ikezi, H.; Schwarzenegger, K.; Simons, A.L.; Ohsawa, Y.; Kamimura, T.

1978-01-01

The nonlinear evolution of an ion-acoustic wave packet is studied. Experimentally, it is found that (i) nonlinear phase modulation develops in the wave packet; (ii) the phase modulation, together with the dispersion effect, causes expansion and breaking of the wave packet; (iii) the ions trapped in the troughs of the wave potential introduce self-phase modulation; and (iv) the ion-acoustic wave is stable with respect to the modulational instability. Computer simulations have reproduced the experimental results. The physical picture and the model equation describing the wave evolution are discussed

Absorption and scattering coefficients estimation in two-dimensional participating media using the generalized maximum entropy and Levenberg-Marquardt methods; Estimacion del coeficiente de absorcion y dispersion en medios participantes bidimensionales utilizando el metodo de maxima entropia generalizada y el metodo Levenberg-Marquardt

Energy Technology Data Exchange (ETDEWEB)

Berrocal T, Mariella J. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear]|[Universidad Nacional de Ingenieria, Lima (Peru); Roberty, Nilson C. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear; Silva Neto, Antonio J. [Universidade do Estado, Nova Friburgo, RJ (Brazil). Instituto Politecnico. Dept. de Engenharia Mecanica e Energia]|[Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear

2002-07-01

The solution of inverse problems in participating media where there is emission, absorption and dispersion of the radiation possesses several applications in engineering and medicine. The objective of this work is to estimative the coefficients of absorption and dispersion in two-dimensional heterogeneous participating media, using in independent form the Generalized Maximum Entropy and Levenberg Marquardt methods. Both methods are based on the solution of the direct problem that is modeled by the Boltzmann equation in cartesian geometry. Some cases testes are presented. (author)

Method of model reduction and multifidelity models for solute transport in random layered porous media

Energy Technology Data Exchange (ETDEWEB)

Xu, Zhijie; Tartakovsky, Alexandre M.

2017-09-01

This work presents a hierarchical model for solute transport in bounded layered porous media with random permeability. The model generalizes the Taylor-Aris dispersion theory to stochastic transport in random layered porous media with a known velocity covariance function. In the hierarchical model, we represent (random) concentration in terms of its cross-sectional average and a variation function. We derive a one-dimensional stochastic advection-dispersion-type equation for the average concentration and a stochastic Poisson equation for the variation function, as well as expressions for the effective velocity and dispersion coefficient. We observe that velocity fluctuations enhance dispersion in a non-monotonic fashion: the dispersion initially increases with correlation length λ, reaches a maximum, and decreases to zero at infinity. Maximum enhancement can be obtained at the correlation length about 0.25 the size of the porous media perpendicular to flow.

The use of nonlinear regression analysis for integrating pollutant concentration measurements with atmospheric dispersion modeling for source term estimation

International Nuclear Information System (INIS)

Edwards, L.L.; Freis, R.P.; Peters, L.G.; Gudiksen, P.H.; Pitovranov, S.E.

1993-01-01

The accuracy associated with assessing the environmental consequences of an accidental release of radioactivity is highly dependent on the knowledge of the source term characteristics, which are generally poorly known. The development of an automated numerical technique that integrates the radiological measurements with atmospheric dispersion modeling for more accurate source term estimation is reported. Often, this process of parameter estimation is performed by an emergency response assessor, who takes an intelligent first guess at the model parameters, then, comparing the model results with whatever measurements are available, makes an intuitive, informed next guess of the model parameters. This process may be repeated any number of times until the assessor feels that the model results are reasonable in terms of the measured observations. A new approach, based on a nonlinear least-squares regression scheme coupled with the existing Atmospheric Release Advisory Capability three-dimensional atmospheric dispersion models, is to supplement the assessor's intuition with automated mathematical methods that do not significantly increase the response time of the existing predictive models. The viability of the approach is evaluated by estimation of the known SF 6 tracer release rates associated with the Mesoscale Atmospheric Transport Studies tracer experiments conducted at the Savannah River Laboratory during 1983. These 19 experiments resulted in 14 successful, separate tracer releases with sampling of the tracer plumes along the cross-plume arc situated ∼30 km from the release site

Nonlinear phenomena in collisionless plasmas. Progress report, September 1, 1974--August 31, 1975

International Nuclear Information System (INIS)

Aamodt, R.E.

1975-01-01

The nonlinear evolution of unstable collective modes common to conventional mirror machines is being analyzed in order to evaluate measurable saturation amplitudes, spectrum properties, and concomitant particle loss rates. The nonlinear dispersion relation for the classic drift-cone mode, including nonlinear E x B VECTOR convective cells is presently being evaluated to find its self-saturation properties. Large amplitude rf heating mechanisms, localized mode nonlinearities, and propagation and amplification of transverse modes in collisionless inhomogeneous plasmas have also been partially evaluated. (U.S.)

Optimization for nonlinear inverse problem

International Nuclear Information System (INIS)

Boyadzhiev, G.; Brandmayr, E.; Pinat, T.; Panza, G.F.

2007-06-01

The nonlinear inversion of geophysical data in general does not yield a unique solution, but a single model, representing the investigated field, is preferred for an easy geological interpretation of the observations. The analyzed region is constituted by a number of sub-regions where the multi-valued nonlinear inversion is applied, which leads to a multi-valued solution. Therefore, combining the values of the solution in each sub-region, many acceptable models are obtained for the entire region and this complicates the geological interpretation of geophysical investigations. In this paper are presented new methodologies, capable to select one model, among all acceptable ones, that satisfies different criteria of smoothness in the explored space of solutions. In this work we focus on the non-linear inversion of surface waves dispersion curves, which gives structural models of shear-wave velocity versus depth, but the basic concepts have a general validity. (author)

Role of geomechanically grown fractures on dispersive transport in heterogeneous geological formations

NARCIS (Netherlands)

Nick, H.M.; Paluszny, A.; Blunt, M.J.; Matthai, S.K.

2011-01-01

A second order in space accurate implicit scheme for time-dependent advection-dispersion equations and a discrete fracture propagation model are employed to model solute transport in porous media.We study the impact of the fractures on mass transport and dispersion. To model flowand transport,

Nonlinearities in Periodic Structures and Metamaterials

CERN Document Server

Denz, Cornelia; Kivshar, Yuri S

2010-01-01

Optical information processing of the future is associated with a new generation of compact nanoscale optical devices operating entirely with light. Moreover, adaptive features such as self-guiding, reconfiguration and switching become more and more important. Nonlinear devices offer an enormous potential for these applications. Consequently, innovative concepts for all-optical communication and information technologies based on nonlinear effects in photonic-crystal physics and nanoscale devices as metamaterials are of high interest. This book focuses on nonlinear optical phenomena in periodic media, such as photonic crystals, optically-induced, adaptive lattices, atomic lattices or metamaterials. The main purpose is to describe and overview new physical phenomena that result from the interplay between nonlinearities and structural periodicities and is a guide to actual and future developments for the expert reader in optical information processing, as well as in the physics of cold atoms in optical lattices.

Study of large nonlinear change phase in Hibiscus Sabdariffa

Science.gov (United States)

Trejo-Durán, M.; Alvarado-Méndez, E.; Andrade-Lucio, J. A.; Rojas-Laguna, R.; Vázquez-Guevara, M. A.

2015-09-01

High intensities electromagnetic energy interacting with organic media gives rise to nonlinear optical effects. Hibiscus Sabdariffa is a flower whose concentrated solution presents interesting nonlinear optical properties. This organic material shows an important self-phase modulation with changes bigger than 2π. We present a diffraction ring patterns study of the Hibiscus Sabdariffa solution. Numerical results of transmittance, with refraction and simultaneous absorption, are shown.

Enhanced index and negative dispersion without absorption in driven cascade media

International Nuclear Information System (INIS)

Hu Xiangming; Xu Jun

2004-01-01

In this paper we investigate the dispersive and absorptive properties of a system of three-level cascade atoms driven by a strong coherent field. Three characteristic features are found. First, for the same set of atom-light interaction parameters, the indices of refraction are large at three different frequencies where the absorption vanishes. These three frequencies are determined by the resonance transition frequencies between dressed states produced by the strong driving field. Second, negative dispersion without absorption, which leads to superluminal light propagation, is achievable in the central resonance structure of the dispersion spectrum. Third, the whole absorption spectrum displays, in general, three pairs of absorption peaks and three pairs of gain (negative absorption) peaks. The minimal spacing between dressed states determines whether the outer adjacent gain peaks are separated from each other

A dispersion model of transport media in radiotracer investigations on selected chemical installations

International Nuclear Information System (INIS)

Iller, E.

1999-01-01

Tracer investigations of media transport through chemical reactors play a significant role in the chemical technology. They provide the basis for the determination of some important process parameters, such as flow character of the transported medium, degree of utilisation of the reactor volume during chemical transitions of substrates or even indicate possible mechanisms of chemical reactions. Determination of the medium flow characteristics is closely connected with the mathematical description of the process - a mathematical model of transport. The method of assessment of radiotracers suitability for the investigation of distillation processes presented in this paper allows to determine, in a simple manner, the parameters of distillation characteristics of the radionuclides, the average distillation temperature, the range of distillation temperatures, a suitable radiochemical purity. These parameters precisely determine the behavior of tracers to be expected in a wide range of variable conditions of the distillation process. Applications of tracer tested in such a manner to the investigations of dynamics of media in the industrial rectification columns has resulted in obtaining a dependable evaluation of the performance of these columns in a wide range of changes of their operational parameters. Particular attention has been paid to dynamics of the liquid [phase on the column plate. A dispersion model of liquid flow with hold-up zones has been proposed for the description of the liquid phase transport in the plate - overall assembly.The model consists of a number of flow and stagnant zones, with mass transfer between them. Another example of practical application of results from radiotracer investigation is an analysis of of phase dynamics in the installations designed for the process of liquefaction of Polish coals by means of their catalytic hydrogenation. For the analysis of phase transport in a reaction vessel various mathematical models were applied with

Nonlinear dynamics of drift structures in a magnetized dissipative plasma

International Nuclear Information System (INIS)

Aburjania, G. D.; Rogava, D. L.; Kharshiladze, O. A.

2011-01-01

A study is made of the nonlinear dynamics of solitary vortex structures in an inhomogeneous magnetized dissipative plasma. A nonlinear transport equation for long-wavelength drift wave structures is derived with allowance for the nonuniformity of the plasma density and temperature equilibria, as well as the magnetic and collisional viscosity of the medium and its friction. The dynamic equation describes two types of nonlinearity: scalar (due to the temperature inhomogeneity) and vector (due to the convectively polarized motion of the particles of the medium). The equation is fourth order in the spatial derivatives, in contrast to the second-order Hasegawa-Mima equations. An analytic steady solution to the nonlinear equation is obtained that describes a new type of solitary dipole vortex. The nonlinear dynamic equation is integrated numerically. A new algorithm and a new finite difference scheme for solving the equation are proposed, and it is proved that the solution so obtained is unique. The equation is used to investigate how the initially steady dipole vortex constructed here behaves unsteadily under the action of the factors just mentioned. Numerical simulations revealed that the role of the vector nonlinearity is twofold: it helps the dispersion or the scalar nonlinearity (depending on their magnitude) to ensure the mutual equilibrium and, thereby, promote self-organization of the vortical structures. It is shown that dispersion breaks the initial dipole vortex into a set of tightly packed, smaller scale, less intense monopole vortices-alternating cyclones and anticyclones. When the dispersion of the evolving initial dipole vortex is weak, the scalar nonlinearity symmetrically breaks a cyclone-anticyclone pair into a cyclone and an anticyclone, which are independent of one another and have essentially the same intensity, shape, and size. The stronger the dispersion, the more anisotropic the process whereby the structures break: the anticyclone is more intense

The collapse of acoustic waves in dispersive media

International Nuclear Information System (INIS)

Kuznetsov, E.A.; Musher, S.L.; Shafarenko, A.V.

1983-01-01

The existence of the collapse of acoustic waves with a positive dispersion is demonstrated. A qualitative description of wave collapse, based on the analysis of invariants, is proposed. Through the use of a numerical simulation, it is established that, in the Kadomtsev-Petviashvili three-dimensional equation, collapse is accompanied by the formation of a weakly turbulent background by the wave radiation from the cavity

Solute transport through porous media using asymptotic dispersivity

Indian Academy of Sciences (India)

ber of processes and porous media properties including convective transport .... existence of regions within the porous medium in which there is minimum advective flow. .... concentration at x = L. The initial and the exit boundary conditions can be .... rial was cleaned, washed and dried to ensure that the material free from ...

Spatiotemporal electromagnetic soliton and spatial ring formation in nonlinear metamaterials

International Nuclear Information System (INIS)

Zhang Jinggui; Wen Shuangchun; Xiang Yuanjiang; Wang Youwen; Luo Hailu

2010-01-01

We present a systematic investigation of ultrashort electromagnetic pulse propagation in metamaterials (MMs) with simultaneous cubic electric and magnetic nonlinearity. We predict that spatiotemporal electromagnetic solitons may exist in the positive-index region of a MM with focusing nonlinearity and anomalous group velocity dispersion (GVD), as well as in the negative-index region of the MM with defocusing nonlinearity and normal GVD. The experimental circumstances for generating and manipulating spatiotemporal electromagnetic solitons can be created by elaborating appropriate MMs. In addition, we find that, in the negative-index region of a MM, a spatial ring may be formed as the electromagnetic pulse propagates for focusing nonlinearity and anomalous GVD; while the phenomenon of temporal splitting of the electromagnetic pulse may appear for the same case except for the defocusing nonlinearity. Finally, we demonstrate that the nonlinear magnetization makes the sign of effective electric nonlinear effect switchable due to the combined action of electric and magnetic nonlinearity, exerting a significant influence on the propagation of electromagnetic pulses.

Nonlinear acoustics of water-saturated marine sediments

DEFF Research Database (Denmark)

Jensen, Leif Bjørnø

1976-01-01

Interest in the acoustic qualities of water-saturated marine sediments has increased considerably during recent years. The use of sources of high-intensity sound in oil propsecting, in geophysical and geological studies of bottom and subbottom materials and profiles and recently in marine...... archaeology has emphasized the need of information about the nonlinear acoustic qualities of water-saturated marine sediments. While the acoustic experiments and theoretical investigations hitherto performed have concentrated on a determination of the linear acoustic qualities of water-saturated marine...... sediments, their parameters of nonlinear acoustics are still unexplored. The strong absorption, increasing about linearly with frequency, found in most marine sediments and the occurrence of velocity dispersion by some marine sediments restrict the number of nonlinear acoustic test methods traditionally...

Solitary waves on nonlinear elastic rods. I

DEFF Research Database (Denmark)

Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.

1984-01-01

Acoustic waves on elastic rods with circular cross section are governed by improved Boussinesq equations when transverse motion and nonlinearity in the elastic medium are taken into account. Solitary wave solutions to these equations have been found. The present paper treats the interaction betwe...... nonlinearity. The balance between dispersion and nonlinearity in the equation is investigated.......Acoustic waves on elastic rods with circular cross section are governed by improved Boussinesq equations when transverse motion and nonlinearity in the elastic medium are taken into account. Solitary wave solutions to these equations have been found. The present paper treats the interaction between...... the solitary waves numerically. It is demonstrated that the waves behave almost like solitons in agreement with the fact that the improved Boussinesq equations are nearly integrable. Thus three conservation theorems can be derived from the equations. A new subsonic quasibreather is found in the case of a cubic...

Interactions of solitons in Bragg gratings with dispersive reflectivity in a cubic-quintic medium

Science.gov (United States)

Dasanayaka, Sahan; Atai, Javid

2011-08-01

Interactions between quiescent solitons in Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity are systematically investigated. In a previous work two disjoint families of solitons were identified in this model. One family can be viewed as the generalization of the Bragg grating solitons in Kerr nonlinearity with dispersive reflectivity (Type 1). On the other hand, the quintic nonlinearity is dominant in the other family (Type 2). For weak to moderate dispersive reflectivity, two in-phase solitons will attract and collide. Possible collision outcomes include merger to form a quiescent soliton, formation of three solitons including a quiescent one, separation after passing through each other once, asymmetric separation after several quasielastic collisions, and soliton destruction. Type 2 solitons are always destroyed by collisions. Solitons develop sidelobes when dispersive reflectivity is strong. In this case, it is found that the outcome of the interactions is strongly dependent on the initial separation of solitons. Solitons with sidelobes will collide only if they are in-phase and their initial separation is below a certain critical value. For larger separations, both in-phase and π-out-of-phase Type 1 and Type 2 solitons may either repel each other or form a temporary bound state that subsequently splits into two separating solitons. Additionally, in the case of Type 2 solitons, for certain initial separations, the bound state disintegrates into a single moving soliton.

Analytical study for the ability of nonlinear transmission lines to generate solitons

International Nuclear Information System (INIS)

Mostafa, S.I.

2009-01-01

The ability of the nonlinear transmission lines (NLTL) has been studied analytically, in this paper to generate solitons and to cause waveform spreading. This can be achieved by balancing nonlinearity and dispersion. A new technique of improved tanh method (ITM) and improved sech methods (ISM) is applied to the nonlinear partial differential equation that describes the NLTL. It is found that the parameters of the transmission line play an important role in controlling the shape of the soliton.

Ion acoustic waves in pair-ion plasma: Linear and nonlinear analyses

International Nuclear Information System (INIS)

Saeed, R.; Mushtaq, A.

2009-01-01

Linear and nonlinear properties of low frequency ion acoustic wave (IAW) in pair-ion plasma in the presence of electrons are investigated. The dispersion relation and Kadomtsev-Petviashvili equation for linear/nonlinear IAW are derived from sets of hydrodynamic equations where the ion pairs are inertial while electrons are Boltzmannian. The dispersion curves for various concentrations of electrons are discussed and compared with experimental results. The predicted linear IAW propagates at the same frequencies as those of the experimentally observed IAW if n e0 ∼10 4 cm -3 . It is found that nonlinear profile of the ion acoustic solitary waves is significantly affected by the percentage ratio of electron number density and temperature. It is also determined that rarefactive solitary waves can propagate in this system. It is hoped that the results presented in this study would be helpful in understanding the salient features of the finite amplitude localized ion acoustic solitary pulses in a laboratory fullerene plasma.

Multi-shocks generation and collapsing instabilities induced by competing nonlinearities

KAUST Repository

Crosta, Matteo; Trillo, Stefano; Fratalocchi, Andrea

2012-01-01

We investigate dispersive shock dynamics in materials with competing cubic-quintic nonlinearities. Whitham theory of modulation, hydrodynamic analysis and numerics demonstrate a rich physical scenario, ranging from multi-shock generation to collapse.

Bivariational calculations for radiation transfer in an inhomogeneous participating media

International Nuclear Information System (INIS)

El Wakil, S.A.; Machali, H.M.; Haggag, M.H.; Attia, M.T.

1986-07-01

Equations for radiation transfer are obtained for dispersive media with space dependent albedo. Bivariational bound principle is used to calculate the reflection and transmission coefficients for such media. Numerical results are given and compared. (author)

Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials.

Science.gov (United States)

Kourakis, I; Shukla, P K

2005-07-01

We investigate the nonlinear propagation of electromagnetic waves in left-handed materials. For this purpose, we consider a set of coupled nonlinear Schrödinger (CNLS) equations, which govern the dynamics of coupled electric and magnetic field envelopes. The CNLS equations are used to obtain a nonlinear dispersion, which depicts the modulational stability profile of the coupled plane-wave solutions in left-handed materials. An exact (in)stability criterion for modulational interactions is derived, and analytical expressions for the instability growth rate are obtained.

On reflection from interfaces with some spatially dispersive metamaterials

International Nuclear Information System (INIS)

Nefedov, Igor; Viitanen, Ari; Tretyakov, Sergei

2006-01-01

Plane-wave reflection from interfaces with single and double wire media is considered. Such media exhibit strong spatial dispersion even at very low frequencies which causes appearance of additional waves. The problem of additional boundary conditions (ABC) in application to wire media is discussed and an ABC-free approach, known in solid state physics, is used. Expressions for the fields and Poynting vectors of refracted waves are derived. The directions and values of the power density flow of refracted waves are found and conservation of the power flow through the interface is checked

A finite parallel zone model to interpret and extend Giddings' coupling theory for the eddy-dispersion in porous chromatographic media.

Science.gov (United States)

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. Copyright © 2013 Elsevier B.V. All rights reserved.

Comparative Study of FDTD-Adopted Numerical Algorithms for Kerr Nonlinearities

DEFF Research Database (Denmark)

Maksymov, Ivan S.; Sukhorukov, Andrey A.; Lavrinenko, Andrei

2011-01-01

Accurate finite-difference time-domain (FDTD) modeling of optical pulse propagation in nonlinear media usually implies the use of auxiliary differential equation (ADE) techniques. The updating of electric field in full-vectorial 3-D ADE FDTD modeling of the optical Kerr effect and two-photon abso...... approaches. Such schemes can significantly reduce the CPU time for nonlinear computations, especially in 3-D models....

Electronegative nonlinear oscillating modes in plasmas

Science.gov (United States)

Panguetna, Chérif Souleman; Tabi, Conrad Bertrand; Kofané, Timoléon Crépin

2018-02-01

The emergence of nonlinear modulated waves is addressed in an unmagnetized electronegative plasma made of Boltzmann electrons, Boltzmann negative ions and cold mobile positive ions. The reductive perturbation method is used to reduce the dynamics of the whole system to a cubic nonlinear Schrödinger equation, whose the nonlinear and dispersion coefficients, P and Q, are function of the negative ion parameters, namely the negative ion concentration ratio (α) and the electron-to-negative ion temperature ratio (σn). It is observed that these parameters importantly affect the formation of modulated ion-acoustic waves, either as exact solutions or via the activation of modulational instability. Especially, the theory of modulational instability is used to show the correlation between the parametric analysis and the formation of modulated solitons, obtained here as bright envelopes and kink-wave solitons.

Chi 3 dispersion in planar tantalum pentoxide waveguides in the telecommunications window.

Science.gov (United States)

Chen, Ruiqi Y; Charlton, Martin D B; Lagoudakis, Pavlos G

2009-04-01

We report on the dispersion of the third-order nonlinear susceptibility (chi(3) or "Chi 3") in planar Ta2O5 waveguides in the telecommunications spectral window. We utilize the observation of third-harmonic generation under ultrashort pulsed excitation as a reference-free characterization method of chi(3) and obtain a large nonlinear coefficient, 2x10(-13) esu, at 1550 nm. Our observation of efficient third-harmonic generation in Ta2O5 waveguides in the telecoms window reveals the potential of this material system in high-speed integrated nonlinear optical switches.

An Extended Newmark-FDTD Method for Complex Dispersive Media

Directory of Open Access Journals (Sweden)

Yu-Qiang Zhang

2018-01-01

Full Text Available Based on polarizability in the form of a complex quadratic rational function, a novel finite-difference time-domain (FDTD approach combined with the Newmark algorithm is presented for dealing with a complex dispersive medium. In this paper, the time-stepping equation of the polarization vector is derived by applying simultaneously the Newmark algorithm to the two sides of a second-order time-domain differential equation obtained from the relation between the polarization vector and electric field intensity in the frequency domain by the inverse Fourier transform. Then, its accuracy and stability are discussed from the two aspects of theoretical analysis and numerical computation. It is observed that this method possesses the advantages of high accuracy, high stability, and a wide application scope and can thus be applied to the treatment of many complex dispersion models, including the complex conjugate pole residue model, critical point model, modified Lorentz model, and complex quadratic rational function.

Diffusion and sorption in particles and two-dimensional dispersion in a porous media

International Nuclear Information System (INIS)

Rasmuson, A.

1980-01-01

A solution of the two-dimensional differential equation of dispersion from a disk source, coupled with a differential equation of diffusion and sorption in particles, is developed. The solution is obtained by the successive use of the Laplace and the Hankel transforms and is given in the form of an infinite double-integral. If the lateral dispersion is negligible, the solution is shown to simplify to a solution presented earlier. Dimensionless quantities are introduced. A steady-state condition is obtained after long time. This is investigated in some detail. An expression is derived for the highest concentration which may be expected at a point in space. An important relation is obtained when longitudinal dispersion is neglected. The solution for any value of the lateral dispersion coefficient and radial distance from the source is then obtained by simple multiplication of a solution for no lateral dispersion with the steady-state value. A method for integrating the infinite double integral is given. Some typical examples are shown. (Auth.)

Fast and accurate modeling of nonlinear pulse propagation in graded-index multimode fibers.

Science.gov (United States)

Conforti, Matteo; Mas Arabi, Carlos; Mussot, Arnaud; Kudlinski, Alexandre

2017-10-01

We develop a model for the description of nonlinear pulse propagation in multimode optical fibers with a parabolic refractive index profile. It consists of a 1+1D generalized nonlinear Schrödinger equation with a periodic nonlinear coefficient, which can be solved in an extremely fast and efficient way. The model is able to quantitatively reproduce recently observed phenomena like geometric parametric instability and broadband dispersive wave emission. We envisage that our equation will represent a valuable tool for the study of spatiotemporal nonlinear dynamics in the growing field of multimode fiber optics.

Shocks, singularities and oscillations in nonlinear optics and fluid mechanics

CERN Document Server

Santo, Daniele; Lannes, David

2017-01-01

The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory (stability, relaxation) and fluid mechanics (boundary layers, water waves, Euler equations, geophysical flows, etc.). It is a valuable resource for researchers in these fields. .

Preparation and optical properties of gold-dispersed BaTiO3 thin films

Energy Technology Data Exchange (ETDEWEB)

Kineri, T; Mori, M [TDK Corp., Tokyo (Japan). R and D Center; Kadono, K; Sakaguchi, T; Miya, M; Wakabayashi, H [Osaka National Research Inst., Osaka (Japan); Tsuchiya, T [Science Univ. of Tokyo, Tokyo (Japan). Faculty of Industrial Science and Technology

1993-12-01

Recently, metal or semiconductor-doped glasses were widely studied because of their large resonant third-order nonlinearity. These glasses are utilized in an optical information field as all optical logic devices in the future. The gold-doped glass films or thin layers have a large third-order nonlinear susceptibility [chi] and are prepared by r.f. sputtering method, etc. The optical properties, particularly the refractive index or dielectric constant of the matrix, are very important for the optical nonlinearity of these materials. In this study, gold-dispersed BaTiO3 thin films and gold-dispersed SiO2 thin films are prepared using r.f. magnetron sputtering method, and the optical properties of the films are compared. The [chi] of the films are measured and the effect of the matrix of the films on [chi] is investigated. The headings in the paper are: Introduction, Experimental procedure, Results, Discussion, and Conclusion. 13 refs., 9 figs.

Exact solutions to a nonlinear dispersive model with variable coefficients

International Nuclear Information System (INIS)

Yin Jun; Lai Shaoyong; Qing Yin

2009-01-01

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.

Observation of Self-Cavitating Envelope Dispersive Shock Waves in Yttrium Iron Garnet Thin Films

Science.gov (United States)

Janantha, P. A. Praveen; Sprenger, Patrick; Hoefer, Mark A.; Wu, Mingzhong

2017-07-01

The formation and properties of envelope dispersive shock wave (DSW) excitations from repulsive nonlinear waves in a magnetic film are studied. Experiments involve the excitation of a spin wave step pulse in a low-loss magnetic Y3Fe5O12 thin film strip, in which the spin wave amplitude increases rapidly, realizing the canonical Riemann problem of shock theory. Under certain conditions, the envelope of the spin wave pulse evolves into a DSW that consists of an expanding train of nonlinear oscillations with amplitudes increasing from front to back, terminated by a black soliton. The onset of DSW self-cavitation, indicated by a point of zero power and a concomitant 180° phase jump, is observed for sufficiently large steps, indicative of the bidirectional dispersive hydrodynamic nature of the DSW. The experimental observations are interpreted with theory and simulations of the nonlinear Schrödinger equation.

Nonlinear coherent structures in granular crystals

Science.gov (United States)

Chong, C.; Porter, Mason A.; Kevrekidis, P. G.; Daraio, C.

2017-10-01

The study of granular crystals, which are nonlinear metamaterials that consist of closely packed arrays of particles that interact elastically, is a vibrant area of research that combines ideas from disciplines such as materials science, nonlinear dynamics, and condensed-matter physics. Granular crystals exploit geometrical nonlinearities in their constitutive microstructure to produce properties (such as tunability and energy localization) that are not conventional to engineering materials and linear devices. In this topical review, we focus on recent experimental, computational, and theoretical results on nonlinear coherent structures in granular crystals. Such structures—which include traveling solitary waves, dispersive shock waves, and discrete breathers—have fascinating dynamics, including a diversity of both transient features and robust, long-lived patterns that emerge from broad classes of initial data. In our review, we primarily discuss phenomena in one-dimensional crystals, as most research to date has focused on such scenarios, but we also present some extensions to two-dimensional settings. Throughout the review, we highlight open problems and discuss a variety of potential engineering applications that arise from the rich dynamic response of granular crystals.

Analysis of fractional non-linear diffusion behaviors based on Adomian polynomials

Directory of Open Access Journals (Sweden)

Wu Guo-Cheng

2017-01-01

Full Text Available A time-fractional non-linear diffusion equation of two orders is considered to investigate strong non-linearity through porous media. An equivalent integral equation is established and Adomian polynomials are adopted to linearize non-linear terms. With the Taylor expansion of fractional order, recurrence formulae are proposed and novel numerical solutions are obtained to depict the diffusion behaviors more accurately. The result shows that the method is suitable for numerical simulation of the fractional diffusion equations of multi-orders.