NASA Astrophysics Data System (ADS)
Dakova, D.; Dakova, A.; Slavchev, V.; Staykov, P.; Kovachev, L.
2016-01-01
In last two decades the phenomena resulting from the evolution of ultra-short laser pulses in nonlinear dispersive medium actively are being studied. The most commonly used equation for describing the dynamics of optical pulses in one-dimensional and planar waveguides is the standard nonlinear Schrodinger equation (NSE). It works very well for nanosecond and picosecond laser pulses, but in the frames of femtosecond optics, it is necessary two additional terms to be included. They are responsible for higher order of linear dispersion and dispersion of nonlinearity. These effects are significant in the range of ultra-short light pulses. In the present paper, it is presented a theoretical model of the propagation of optical solitons. We found an exact analytical soliton solution of the modified NSE, including third order of linear dispersion and dispersion of nonlinearity. It is possible to observe a soliton as a result of the dynamic balance between effects of higher order of dispersion and nonlinearity.
NASA Astrophysics Data System (ADS)
Li, Ping-Wah
1994-12-01
In his paper [J. Acoust. Soc. Am. 77, 2050 (1985)] Blackstock presented a generalized Burgers equation for the propagation of one-dimensional weakly nonlinear waves in various media. His results, and the approach he employed there, however, are limited to harmonic waves. In this paper, we present a general approach to model nonlinear waves of more general wave forms that propagate in media with arbitrary absorption and dispersion relations. The resulting equation is again called the generalized Burgers equation (to follow the terminology of the literature). It is found that steady shock solutions for various media can be described by the corresponding simplified version of the equation. An efficient numerical method by means of spectral analysis is developed for solving the generalized Burgers equation. Typical results exemplified by the case of a sinusoidal wave source are also reported in this paper.
NASA Astrophysics Data System (ADS)
Nikitenkova, S.; Singh, N.; Stepanyants, Y.
2015-12-01
In this paper, we revisit the problem of modulation stability of quasi-monochromatic wave-trains propagating in a media with the double dispersion occurring both at small and large wavenumbers. We start with the shallow-water equations derived by Shrira [Izv., Acad. Sci., USSR, Atmos. Ocean. Phys. (Engl. Transl.) 17, 55-59 (1981)] which describes both surface and internal long waves in a rotating fluid. The small-scale (Boussinesq-type) dispersion is assumed to be weak, whereas the large-scale (Coriolis-type) dispersion is considered as without any restriction. For unidirectional waves propagating in one direction, only the considered set of equations reduces to the Gardner-Ostrovsky equation which is applicable only within a finite range of wavenumbers. We derive the nonlinear Schrödinger equation (NLSE) which describes the evolution of narrow-band wave-trains and show that within a more general bi-directional equation the wave-trains, similar to that derived from the Ostrovsky equation, are also modulationally stable at relatively small wavenumbers k < kc and unstable at k > kc, where kc is some critical wavenumber. The NLSE derived here has a wider range of applicability: it is valid for arbitrarily small wavenumbers. We present the analysis of coefficients of the NLSE for different signs of coefficients of the governing equation and compare them with those derived from the Ostrovsky equation. The analysis shows that for weakly dispersive waves in the range of parameters where the Gardner-Ostrovsky equation is valid, the cubic nonlinearity does not contribute to the nonlinear coefficient of NLSE; therefore, the NLSE can be correctly derived from the Ostrovsky equation.
Nikitenkova, S; Singh, N; Stepanyants, Y
2015-12-01
In this paper, we revisit the problem of modulation stability of quasi-monochromatic wave-trains propagating in a media with the double dispersion occurring both at small and large wavenumbers. We start with the shallow-water equations derived by Shrira [Izv., Acad. Sci., USSR, Atmos. Ocean. Phys. (Engl. Transl.) 17, 55-59 (1981)] which describes both surface and internal long waves in a rotating fluid. The small-scale (Boussinesq-type) dispersion is assumed to be weak, whereas the large-scale (Coriolis-type) dispersion is considered as without any restriction. For unidirectional waves propagating in one direction, only the considered set of equations reduces to the Gardner-Ostrovsky equation which is applicable only within a finite range of wavenumbers. We derive the nonlinear Schrödinger equation (NLSE) which describes the evolution of narrow-band wave-trains and show that within a more general bi-directional equation the wave-trains, similar to that derived from the Ostrovsky equation, are also modulationally stable at relatively small wavenumbers k < kc and unstable at k > kc, where kc is some critical wavenumber. The NLSE derived here has a wider range of applicability: it is valid for arbitrarily small wavenumbers. We present the analysis of coefficients of the NLSE for different signs of coefficients of the governing equation and compare them with those derived from the Ostrovsky equation. The analysis shows that for weakly dispersive waves in the range of parameters where the Gardner-Ostrovsky equation is valid, the cubic nonlinearity does not contribute to the nonlinear coefficient of NLSE; therefore, the NLSE can be correctly derived from the Ostrovsky equation.
NASA Astrophysics Data System (ADS)
Kapoyko, Yury A.; Drozdov, Arkadiy A.; Kozlov, Sergei A.; Zhang, Xi-Cheng
2016-09-01
Simple arithmetic dependencies of the velocity of the mass center motion and the root-mean-square duration of initially single-cycle, two-cycle, and Gaussian pulses with a random number of oscillations under the pulse envelope are derived depending on their center frequency, initial duration, and peak field amplitude, as well as on dispersive and nonlinear characteristics of homogeneous isotropic dielectric media. In media with normal group dispersion, it is shown that due to nonresonant dispersion the square of the few-cycle pulse duration increases with distance inversely proportional to the fourth power of the number of input pulse cycles. In media with normal group dispersion, the square of the pulse duration is inversely proportional to the number of input pulse cycles due to cubic nonlinearity. In media with anomalous group dispersion, it is shown that due to cubic nonlinearity, few-cycle pulse self-compression decreases with the reduction of the number of cycles in the initial pulse. This pulse self-compression effect has a threshold nature and terminates at a fixed number of cycles of the input pulse. Such a number of cycles is determined by the input intensity and the central frequency of the pulse, as well as by the dispersive and nonlinear characteristics of the medium.
Aseeva, N. V. Gromov, E. M.; Tyutin, V. V.
2015-12-15
The dynamics of high-frequency field solitons is considered using the extended nonhomogeneous nonlinear Schrödinger equation with induced scattering from damped low-frequency waves (pseudoinduced scattering). This scattering is a 3D analog of the stimulated Raman scattering from temporal spatially homogeneous damped low-frequency modes, which is well known in optics. Spatial inhomogeneities of secondorder linear dispersion and cubic nonlinearity are also taken into account. It is shown that the shift in the 3D spectrum of soliton wavenumbers toward the short-wavelength region is due to nonlinearity increasing in coordinate and to decreasing dispersion. Analytic results are confirmed by numerical calculations.
ACOUSTIC RECTIFICATION IN DISPERSIVE MEDIA
Cantrell, John H.
2009-03-03
It is shown that the shapes of acoustic radiation-induced static strain and displacement pulses (rectified acoustic pulses) are defined locally by the energy density of the generating waveform. Dispersive properties are introduced analytically by assuming that the rectified pulses are functionally dependent on a phase factor that includes both dispersive and nonlinear terms. The dispersion causes an evolutionary change in the shape of the energy density profile that leads to the generation of solitons experimentally observed in fused silica.
NASA Technical Reports Server (NTRS)
Goorjian, Peter M.; Taflove, Allen
1992-01-01
The initial results for femtosecond electromagnetic soliton propagation and collision obtained from first principles, i.e., by a direct time integration of Maxwell's equations are reported. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit the modeling of 2D and 3D optical soliton propagation, scattering, and switching from the full-vector Maxwell's equations.
Apparatus and Methods Using Highly Optically Dispersive Media
2011-08-02
e.g., semicon- ductor compounds (e.g., CdSSe), nonlinear crystals (e.g., KTP, BBO, LiN03), crystals (e.g., Ruby, Alexandrite ); e) integrated...e.g., KTP, BBO, LiN03), crystals (e.g., Ruby, Alexandrite ), and 50 other known solid media. 5) Integrated lightwave structures; the dispersion can
Nonlinear dispersive similariton: spectral interferometric study
Zeytunyan, A S; Khachikyan, T J; Palandjan, K A; Esayan, G L; Muradyan, L Kh
2010-06-23
A similariton formed in a passive optical fibre is experimentally found and investigated by spectral interferometry completely characterising the complex radiation field. A nonlinear dispersive character of similariton formation leads to chirp linearisation and spectrotemporal similarity of this similariton. (nonlinear optical phenomena)
Electromagnetic energy momentum in dispersive media
Philbin, T. G.
2011-01-15
The standard derivations of electromagnetic energy and momentum in media take Maxwell's equations as the starting point. It is well known that for dispersive media this approach does not directly yield exact expressions for the energy and momentum densities. Although Maxwell's equations fully describe electromagnetic fields, the general approach to conserved quantities in field theory is not based on the field equations, but rather on the action. Here an action principle for macroscopic electromagnetism in dispersive, lossless media is used to derive the exact conserved energy-momentum tensor. The time-averaged energy density reduces to Brillouin's simple formula when the fields are monochromatic. The time-averaged momentum density for monochromatic fields corresponds to the familiar Minkowski expression DxB, but for general fields in dispersive media the momentum density does not have the Minkowski value. The results are unaffected by the debate over momentum balance in light-matter interactions.
Dispersivity in heterogeneous permeable media
Chesnut, D.A.
1994-01-01
When one fluid displaces another through a one-dimensional porous medium, the composition changes from pure displacing fluid at the inlet to pure displaced fluid some distance downstream. The distance over which an arbitrary percentage of this change occurs is defined as the mixing zone length, which increases with increasing average distance traveled by the displacement front. For continuous injection, the mixing zone size can be determined from a breakthrough curve as the time required for the effluent displacing fluid concentration to change from, say, 10% to 90%. In classical dispersion theory, the mixing zone grows in proportion to the square root of the mean distance traveled, or, equivalently, to the square root of the mean breakthrough time. In a multi-dimensional heterogeneous medium, especially at field scales, the size of the mixing zone grows almost linearly with mean distance or travel time. If an observed breakthrough curve is forced to fit the, clinical theory, the resulting effective dispersivity, instead of being constant, also increases almost linearly with the spatial or temporal scale of the problem. This occurs because the heterogeneity in flow properties creates a corresponding velocity distribution along the different flow pathways from the inlet to the outlet of the system. Mixing occurs mostly at the outlet, or wherever the fluid is sampled, rather than within the medium. In this paper, we consider the effects. of this behavior on radionuclide or other contaminant migration.
Phase space distributions tailored for dispersive media.
Petruccelli, Jonathan C; Alonso, Miguel A
2010-05-01
New phase space distributions are proposed for describing pulse propagation in dispersive media for one spatial dimension. These distributions depend on time, position, and velocity, so that the pulse's spatial propagation or temporal evolution is described by a free-particle-like transformation followed by integration over velocity. Examples are considered for approximate Lorentz-model dielectrics and metallic waveguides.
Nonlinear Acoustics in a Dispersive Continuum: Random Waves, Radiation Pressure, and Quantum Noise.
1983-03-01
Karpman , Nonlinear Waves in Dispersive Media, Pergamon Press, New York, 1975, p. 76. 26. R. Beyers, Nonlinear Acoustics, U.S. Government Printing...20301 U. S. Army Research nffice 2 copies Box 12211 Research Triangle Park tlorth Carolina 27709 Defense Technical Information Center 12 copies Cameron
Dark periodic lattices in nonlinear liquid media
NASA Astrophysics Data System (ADS)
Alvarado-Méndez, Edgar; Trejo-Durán, Mónica; Cano-Lara, Miroslava; Huerta-Mascotte, Eduardo; Castaňo, Víctor M.
2007-11-01
Experimental evidence of the formation of one- and two-dimensional dark periodic lattices in a negative Kerr-type nonlinear liquid media is presented. Bright periodic lattices propagate throughout two nonlinear liquids [alcohol with rhodamine (R6G), and acetone with R6G] as the negative nonlinear refractive index forms a dark periodic lattice. Our experiments demonstrate that the nonlinearity increases with the optical power and that a proper selection of the period leads to self-phase modulation of the lattice.
Relativistic radiation transport in dispersive media
Kichenassamy, S.; Krikorian, R.A.
1985-10-15
A general-relativistic radiative transfer equation in an isotropic, weakly absorbing, nonmagnetized dispersive medium is derived using the kinetic-theoretical approach and the relativistic Hamiltonian theory of geometrical optics in those media. It yields the generally accepted classical equation in the special-relativistic approximation and in stationary conditions. The influence of the gravitational field and of space-time variations of the refractive index n on the radiation distribution is made explicit in the case of spherical symmetry.
Generalized dispersive wave emission in nonlinear fiber optics.
Webb, K E; Xu, Y Q; Erkintalo, M; Murdoch, S G
2013-01-15
We show that the emission of dispersive waves in nonlinear fiber optics is not limited to soliton-like pulses propagating in the anomalous dispersion regime. We demonstrate, both numerically and experimentally, that pulses propagating in the normal dispersion regime can excite resonant dispersive radiation across the zero-dispersion wavelength into the anomalous regime.
Nonlinear lattice waves in heterogeneous media
NASA Astrophysics Data System (ADS)
Laptyeva, T. V.; Ivanchenko, M. V.; Flach, S.
2014-12-01
We discuss recent advances in the understanding of the dynamics of nonlinear lattice waves in heterogeneous media, which enforce complete wave localization in the linear wave equation limit, especially Anderson localization for random potentials, and Aubry-André localization for quasiperiodic potentials. Additional nonlinear terms in the wave equations can either preserve the phase-coherent localization of waves, or destroy it through nonintegrability and deterministic chaos. Spreading wave packets are observed to show universal features in their dynamics which are related to properties of nonlinear diffusion equations.
Nonlinear flow in porous media
NASA Astrophysics Data System (ADS)
Rojas, Sergio Jesus
1998-07-01
Numerical solutions of the Navier-Stokes equations in two-dimensional quasi-periodic and quasi-isotropic random media were obtained to analyze the local and large scale aspects of finite Reynolds number flow. For Reynolds number less than one, the results show a first correction to Darcy's law which is cubic in the Darcy (averaged) velocity, while for Reynolds number greater than one, the results are in agreement with Forchheimer equation. That is, the correction to Darcy's law is quadratic in the average (Darcy) velocity. The cubic correction to Darcy's law support Mei and Auriault's (1991) theoretical study, based on homogenization theory. In addition, the results show support to a unifying empirical equation describing fluid flow in porous media of similar structure, first proposed by Beavers and Sparrow (1969). Also, the results show agreement, except by a multiplicative constant, with Sangani and Acrivos (1982) equation for the drag on dilute array of cylinders.
Nonlinear Poisson equation for heterogeneous media.
Hu, Langhua; Wei, Guo-Wei
2012-08-22
The Poisson equation is a widely accepted model for electrostatic analysis. However, the Poisson equation is derived based on electric polarizations in a linear, isotropic, and homogeneous dielectric medium. This article introduces a nonlinear Poisson equation to take into consideration of hyperpolarization effects due to intensive charges and possible nonlinear, anisotropic, and heterogeneous media. Variational principle is utilized to derive the nonlinear Poisson model from an electrostatic energy functional. To apply the proposed nonlinear Poisson equation for the solvation analysis, we also construct a nonpolar solvation energy functional based on the nonlinear Poisson equation by using the geometric measure theory. At a fixed temperature, the proposed nonlinear Poisson theory is extensively validated by the electrostatic analysis of the Kirkwood model and a set of 20 proteins, and the solvation analysis of a set of 17 small molecules whose experimental measurements are also available for a comparison. Moreover, the nonlinear Poisson equation is further applied to the solvation analysis of 21 compounds at different temperatures. Numerical results are compared to theoretical prediction, experimental measurements, and those obtained from other theoretical methods in the literature. A good agreement between our results and experimental data as well as theoretical results suggests that the proposed nonlinear Poisson model is a potentially useful model for electrostatic analysis involving hyperpolarization effects.
Nonlinear Poisson Equation for Heterogeneous Media
Hu, Langhua; Wei, Guo-Wei
2012-01-01
The Poisson equation is a widely accepted model for electrostatic analysis. However, the Poisson equation is derived based on electric polarizations in a linear, isotropic, and homogeneous dielectric medium. This article introduces a nonlinear Poisson equation to take into consideration of hyperpolarization effects due to intensive charges and possible nonlinear, anisotropic, and heterogeneous media. Variational principle is utilized to derive the nonlinear Poisson model from an electrostatic energy functional. To apply the proposed nonlinear Poisson equation for the solvation analysis, we also construct a nonpolar solvation energy functional based on the nonlinear Poisson equation by using the geometric measure theory. At a fixed temperature, the proposed nonlinear Poisson theory is extensively validated by the electrostatic analysis of the Kirkwood model and a set of 20 proteins, and the solvation analysis of a set of 17 small molecules whose experimental measurements are also available for a comparison. Moreover, the nonlinear Poisson equation is further applied to the solvation analysis of 21 compounds at different temperatures. Numerical results are compared to theoretical prediction, experimental measurements, and those obtained from other theoretical methods in the literature. A good agreement between our results and experimental data as well as theoretical results suggests that the proposed nonlinear Poisson model is a potentially useful model for electrostatic analysis involving hyperpolarization effects. PMID:22947937
Amplitude-dependent Lamb wave dispersion in nonlinear plates.
Packo, Pawel; Uhl, Tadeusz; Staszewski, Wieslaw J; Leamy, Michael J
2016-08-01
The paper presents a perturbation approach for calculating amplitude-dependent Lamb wave dispersion in nonlinear plates. Nonlinear dispersion relationships are derived in closed form using a hyperelastic stress-strain constitutive relationship, the Green-Lagrange strain measure, and the partial wave technique integrated with a Lindstedt-Poincaré perturbation approach. Solvability conditions are derived using an operator formalism with inner product projections applied against solutions to the adjoint problem. When applied to the first- and second-order problems, these solvability conditions lead to amplitude-dependent, nonlinear dispersion corrections for frequency as a function of wavenumber. Numerical simulations verify the predicted dispersion shifts for an example nonlinear plate. The analysis and identification of amplitude-dependent, nonlinear Lamb wave dispersion complements recent research focusing on higher harmonic generation and internally resonant waves, which require precise dispersion relationships for frequency-wavenumber matching.
Improved fiber nonlinearity mitigation in dispersion managed optical OFDM links
NASA Astrophysics Data System (ADS)
Tamilarasan, Ilavarasan; Saminathan, Brindha; Murugappan, Meenakshi
2017-02-01
Fiber nonlinearity is seen as a capacity limiting factor in OFDM based dispersion managed links since the Four Wave Mixing effects become enhanced due to the high PAPR. In this paper, the authors have compared the linear and nonlinear PAPR reduction techniques for fiber nonlinearity mitigation in OFDM based dispersion managed links. In the existing optical systems, linear transform techniques such as SLM and PTS have been implemented to reduce nonlinear effects. In the proposed study, superior performance of the L2-by-3 nonlinear transform technique is demonstrated for PAPR reduction to mitigate fiber nonlinearities. The performance evaluation is carried out by interfacing multiple simulators. The results of both linear and nonlinear transform techniques have been compared and the results show that nonlinear transform technique outperforms the linear transform in terms of nonlinearity mitigation and improved BER performance.
Dispersion and nonlinear effects in OFDM-RoF system
NASA Astrophysics Data System (ADS)
Alhasson, Bader H.; Bloul, Albe M.; Matin, M.
2010-08-01
The radio-over-fiber (RoF) network has been a proven technology to be the best candidate for the wireless-access technology, and the orthogonal frequency division multiplexing (OFDM) technique has been established as the core technology in the physical layer of next generation wireless communication system, as a result OFDM-RoF has drawn attentions worldwide and raised many new research topics recently. At the present time, the trend of information industry is towards mobile, wireless, digital and broadband. The next generation network (NGN) has motivated researchers to study higher-speed wider-band multimedia communication to transmit (voice, data, and all sorts of media such as video) at a higher speed. The NGN would offer services that would necessitate broadband networks with bandwidth higher than 2Mbit/s per radio channel. Many new services emerged, such as Internet Protocol TV (IPTV), High Definition TV (HDTV), mobile multimedia and video stream media. Both speed and capacity have been the key objectives in transmission. In the meantime, the demand for transmission bandwidth increased at a very quick pace. The coming of 4G and 5G era will provide faster data transmission and higher bit rate and bandwidth. Taking advantages of both optical communication and wireless communication, OFDM Radio over Fiber (OFDM-RoF) system is characterized by its high speed, large capacity and high spectral efficiency. However, up to the present there are some problems to be solved, such as dispersion and nonlinearity effects. In this paper we will study the dispersion and nonlinearity effects and their elimination in OFDM-radio-over-fiber system.
Nonlinear and Dispersive Optical Pulse Propagation
NASA Astrophysics Data System (ADS)
Dijaili, Sol Peter
In this dissertation, there are basically four novel contributions to the field of picosecond pulse propagation and measurement. The first contribution is the temporal ABCD matrix which is an analog of the traditional ABCD ray matrices used in Gaussian beam propagation. The temporal ABCD matrix allows for the easy calculation of the effects of linear chirp or group velocity dispersion in the time domain. As with Gaussian beams in space, there also exists a complete Hermite-Gaussian basis in time whose propagation can be tracked with the temporal ABCD matrices. The second contribution is the timing synchronization between a colliding pulse mode-locked dye laser and a gain-switched Fabry-Perot type AlGaAs laser diode that has achieved less than 40 femtoseconds of relative timing jitter by using a pulsed optical phase lock loop (POPLL). The relative timing jitter was measured using the error voltage of the feedback loop. This method of measurement is accurate since the frequencies of all the timing fluctuations fall within the loop bandwidth. The novel element is a broad band optical cross-correlator that can resolve femtosecond time delay errors between two pulse trains. The third contribution is a novel dispersive technique of determining the nonlinear frequency sweep of a picosecond pulse with relatively good accuracy. All the measurements are made in the time domain and hence there is no time-bandwidth limitation to the accuracy. The fourth contribution is the first demonstration of cross -phase modulation in a semiconductor laser amplifier where a variable chirp was observed. A simple expression for the chirp imparted on a weak signal pulse by the action of a strong pump pulse is derived. A maximum frequency excursion of 16 GHz due to the cross-phase modulation was measured. A value of 5 was found for alpha _{xpm} which is a factor for characterizing the cross-phase modulation in a similar manner to the conventional linewidth enhancement factor, alpha.
Dispersion of Sound in Dilute Suspensions with Nonlinear Particle Relaxation
NASA Technical Reports Server (NTRS)
Kandula, Max
2010-01-01
The theory accounting for nonlinear particle relaxation (viscous and thermal) has been applied to the prediction of dispersion of sound in dilute suspensions. The results suggest that significant deviations exist for sound dispersion between the linear and nonlinear theories at large values of Omega(Tau)(sub d), where Omega is the circular frequency, and Tau(sub d) is the Stokesian particle relaxation time. It is revealed that the nonlinear effect on the dispersion coefficient due to viscous contribution is larger relative to that of thermal conduction
Plasma metamaterials as cloaking and nonlinear media
NASA Astrophysics Data System (ADS)
Sakai, O.; Yamaguchi, S.; Bambina, A.; Iwai, A.; Nakamura, Y.; Tamayama, Y.; Miyagi, S.
2017-01-01
Plasma metamaterials, composites of low-temperature plasmas and periodic functional microstructures, work as cloaking and nonlinear media. Due to functions of the microstructures like negative permeability, electromagnetic waves in and around plasma metamaterials propagate in a quite different manner from the case with the conventional space in which relative permeability is positive and unity. Using plasmas and plasma metamaterials, we achieve various controls of microwave propagating paths such as unidirectionality and cloaking in the two- or 3D spaces. For instance, a concentric plasma layer makes wave propagation unidirectional, and waves propagate in different routes when they start inside or outside the concentric layer. Furthermore, due to spatial permittivity gradient and anisotropic refractive index, electromagnetic waves detour in plasma metamaterial layers. Another significant point that plasma metamaterials can realize is nonlinearity. When we study high-power electromagnetic waves propagating in them, we observe several properties describable in terms of nonlinear dynamics and nonlinear photonics. Microwaves beyond threshold energy trigger bifurcations in plasma permittivity, and the second harmonic wave detected simultaneously is generated with strong emission levels. Such electromagnetic wave propagation is achieved with advantages over other materials, since plasmas and metallic microstructures work in harmony and in synergy.
Nonlinearity compensation using dispersion-folded digital backward propagation.
Zhu, Likai; Li, Guifang
2012-06-18
A computationally efficient dispersion-folded (D-folded) digital backward propagation (DBP) method for nonlinearity compensation of dispersion-managed fiber links is proposed. At the optimum power level of long-haul fiber transmission, the optical waveform evolution along the fiber is dominated by the chromatic dispersion. The optical waveform and, consequently, the nonlinear behavior of the optical signal repeat at locations of identical accumulated dispersion. Hence the DBP steps can be folded according to the accumulated dispersion. Experimental results show that for 6,084 km single channel transmission, the D-folded DBP method reduces the computation by a factor of 43 with negligible penalty in performance. Simulation of inter-channel nonlinearity compensation for 13,000 km wavelength-division multiplexing (WDM) transmission shows that the D-folded DBP method can reduce the computation by a factor of 37.
Compact bright pulse and ultrashort-pulse in the nonlinear Kerr-like media
NASA Astrophysics Data System (ADS)
Pokam Nguewawe, Chancelor; Yemele, David; Donkeng, Hatou-Yvelin; Kofane, Timoléon Crépin
2017-02-01
The extended nonlinear Schrödinger equation describing the propagation of light beam in the weak nonlocal nonlinear media in general, and in the optical fibers with nearly instantaneous nonlinear response of the medium in particular, is investigated. In the zero-dispersion limit, we show that the system exhibits stable stationary compact bright pulse with an arbitrary nonlinear phase-shift both for the focusing and the defocusing media. However, in the presence of the large linear dispersion, this compact pulse become unstable and may be either disintegrate or transform into the ultrashort bright pulse according to whether the system operates in the normal or in the anomalous region. The exact analytical expressions of these two pulses are derived and the results checked through numerical simulations.
FDTD scattered field formulation for scatterers in stratified dispersive media.
Olkkonen, Juuso
2010-03-01
We introduce a simple scattered field (SF) technique that enables finite difference time domain (FDTD) modeling of light scattering from dispersive objects residing in stratified dispersive media. The introduced SF technique is verified against the total field scattered field (TFSF) technique. As an application example, we study surface plasmon polariton enhanced light transmission through a 100 nm wide slit in a silver film.
Measurement of the Acoustic Nonlinearity Parameter for Biological Media.
NASA Astrophysics Data System (ADS)
Cobb, Wesley Nelson
In vitro measurements of the acoustic nonlinearity parameter are presented for several biological media. With these measurements it is possible to predict the distortion of a finite amplitude wave in biological tissues of current diagnostic and research interest. The measurement method is based on the finite amplitude distortion of a sine wave that is emmitted by a piston source. The growth of the second harmonic component of this wave is measured by a piston receiver which is coaxial with and has the same size as the source. The experimental measurements and theory are compared in order to determine the nonlinearity parameter. The density, sound speed, and attenuation for the medium are determined in order to make this comparison. The theory developed for this study accounts for the influence of both diffraction and attenuation on the experimental measurements. The effects of dispersion, tissue inhomogeneity and gas bubbles within the excised tissues are studied. To test the measurement method, experimental results are compared with established values for the nonlinearity parameter of distilled water, ethylene glycol and glycerol. The agreement between these values suggests that the measurement uncertainty is (+OR-) 5% for liquids and (+OR-) 10% for solid tissues. Measurements are presented for dog blood and bovine serum albumen as a function of concentration. The nonlinearity parameters for liver, kidney and spleen are reported for both human and canine tissues. The values for the fresh tissues displayed little variation (6.8 to 7.8). Measurements for fixed, normal and cirrhotic tissues indicated that the nonlinearity parameter does not depend strongly on pathology. However, the values for fixed tissues were somewhat higher than those of the fresh tissues.
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.
Angular radiation transfer in inhomogeneous dispersive media
NASA Astrophysics Data System (ADS)
Saad, E. A.; El Ghazaly, A. A.; Krim, M. S. Abdel
1988-10-01
The equation of radiative transfer for an inhomogeneous dispersive finite medium subject to general boundary conditions is solved. The Padé approximation technique is used to calculate the angular distribution of radiation. Numerical results for the [0/1] Padé approximant lead to numerical results that compare with the exact results.
Optical dispersive shock waves in defocusing colloidal media
NASA Astrophysics Data System (ADS)
An, X.; Marchant, T. R.; Smyth, N. F.
2017-03-01
The propagation of an optical dispersive shock wave, generated from a jump discontinuity in light intensity, in a defocusing colloidal medium is analysed. The equations governing nonlinear light propagation in a colloidal medium consist of a nonlinear Schrödinger equation for the beam and an algebraic equation for the medium response. In the limit of low light intensity, these equations reduce to a perturbed higher order nonlinear Schrödinger equation. Solutions for the leading and trailing edges of the colloidal dispersive shock wave are found using modulation theory. This is done for both the perturbed nonlinear Schrödinger equation and the full colloid equations for arbitrary light intensity. These results are compared with numerical solutions of the colloid equations.
Soliton solutions with power-law nonlinearity in inhomogeneous media
NASA Astrophysics Data System (ADS)
Dai, Chao-Qing; Yu, Fang-Bo
2013-04-01
We construct the relation between the variable coefficient nonlinear Schrödinger equations with power-law nonlinearity and the constant coefficient one via a transformation. Based on this transformation, we analytically obtain the closed-form bright and dark soliton solutions for variable coefficient nonlinear Schrödinger equations with power-law nonlinearity, third-order dispersion and self-steepening effect. The dynamic behaviors of bright and dark solitons in dispersion-decreasing fibers with hyperbolic, exponential, linear, logarithmic and Gaussian profiles are analyzed.
Nonlinear Dispersive ALFVÉN Waves in Magnetoplasmas
NASA Astrophysics Data System (ADS)
Shukla, P. K.; Eliasson, B.; Stenflo, L.; Bingham, R.
2008-03-01
Large amplitude Alfvén waves are frequently found in magnetized space and laboratory plasmas. Our objective here is to discuss the linear and nonlinear properties of dispersive Alfvén waves (DAWs) in a uniform magnetoplasma. We first consider the effects of finite frequency (ω/ωci) and ion gyroradius on inertial and kinetic Alfvén waves, where ωci is the ion gyrofrequency. Next, we focus on nonlinear effects caused by the dispersive Alfvén waves. Such effects include the plasma density enhancement and depression by the Alfvén wave ponderomotive force, nonlinear interactions among the DAWs, the generation of zonal flows by the DAWs, as well as the electron and ion heating due to wave-particle interactions. The relevance of our investigation to the appearance of nonlinear dispersive Alfvén waves in the Earth's auroral acceleration region, in the solar corona, and in the Large Plasma Device (LAPD) at UCLA is discussed.
Nonlinear Cherenkov radiation at the interface of two different nonlinear media.
Zhao, Xiaohui; Zheng, Yuanlin; Ren, Huaijin; An, Ning; Deng, Xuewei; Chen, Xianfeng
2016-06-13
We discuss the nonlinear response due to the spatial modulation of the second-order susceptibility at the interface between two nonlinear media, and experimentally demonstrate that the nonlinear Cherenkov radiation is enhanced by the interface of two nonlinear crystals with a large disparity in χ^{(2)}. In our experiment, the intensity of the nonlinear Cherenkov radiation generated at the nonlinear interface was approximately 4 to 10 times that at the crystal boundary. This result suggests potential applications to efficient frequency conversion.
Variance of Dispersion Coefficients in Heterogeneous Porous Media
NASA Astrophysics Data System (ADS)
Dentz, Marco; De Barros, Felipe P. J.
2013-04-01
We study the dispersion of a passive solute in heterogeneous porous media using a stochastic modeling approach. Heterogeneity on one hand leads to an increase of solute spreading, which is described by the well-known macrodispersion phenomenon. On the other hand, it induces uncertainty about the dispersion behavior, which is quantified by ensemble averages over suitably defined dispersion coefficients in single medium realizations. We focus here on the sample to sample fluctuations of dispersion coefficients about their ensemble mean values for solutes evolving from point-like and extended source distributions in d = 2 and d = 3 spatial dimensions. The definition of dispersion coefficients in single medium realizations for finite source sizes is not unique, unlike for point-like sources. Thus, we first discuss a series of dispersion measures, which describe the extension of the solute plume, as well as dispersion measures that quantify the solute dispersion relative to the injection point. The sample to sample fluctuations of these observables are quantified in terms of the variance with respect to their ensemble averages. We find that the ensemble averages of these dispersion measures may be identical, their fluctuation behavior, however, may be very different. This is quantified using perturbation expansions in the fluctuations of the random flow field. We derive explicit expressions for the time evolution of the variance of the dispersion coefficients. The characteristic time scale for the variance evolution is given by the typical dispersion time over the characteristic heterogeneity scale and the dimensions of the source. We find that the dispersion variances asymptotically decrease to zero in d = 3 dimensions, which means, the dispersion coefficients are self-averaging observables, at least for moderate heterogeneity. In d = 2 dimensions, the variance converges towards a finite asymptotic value that is independent of the source distribution. Dispersion is not
Fidelity and fidelity susceptibility of pulses in dispersive media
Wang Ligang; Gu Shijian
2009-07-15
Motivated by the growing importance of the fidelity and fidelity susceptibility (FS) in quantum critical phenomena, we use these concepts to describe the pulse propagation inside the dispersive media. It is found that there is a dramatic change in the fidelity and the FS of the pulse at a critical propagation distance inside a dispersive medium, and whether such a dramatic change for a light pulse occurs or not strongly depends on both the dispersive strength of the media and the pulse property. We study in detail about the changes in the fidelity and the FS for both a smooth and a truncated Gaussian pulse through the abnormal and normal dispersive media, where the group velocities are well defined. Our results show that both the fidelity and the FS could be very useful to determine whether the pulse is completely distorted or not at the critical distance; therefore it would be very helpful to find the maximal effective propagation region of the pulse's group velocity, in terms of the changes in the pulse's fidelity and FS.
Influence of Chemotaxis on Bacterial Dispersion in Porous Media
NASA Astrophysics Data System (ADS)
Ford, R. M.; Narayanaswamy, K.; Wood, B. D.
2007-12-01
Bioremediation of groundwater is limited by the degree to which microorganisms and pollutants are mixed together in the subsurface environment. Good mixing is difficult to achieve because of the structure of geological media and the unavailability of external mixing devices. Chemotaxis, which is the ability of motile bacteria to sense chemical concentration gradients in their local surroundings and swim toward higher concentrations of attractants, could potentially enhance the mixing and expedite the biodegradation process. The chemotactic migration on the pore-scale could eventually result in greater dispersion at the field-scale. In this study, the volume averaging method was used to derive an expression that accounts for chemotactic responses to local chemical gradients in the dispersion coefficient at larger scales. We will present results where the upscaling scheme was applied to problems with well defined hydraulic conditions such as a series of inline cylinders, and well-defined chemical gradients. In general, increasing the attractant gradients resulted in greater bacterial dispersion coefficients. Engineering correlations were developed to relate the enhanced dispersion to dimensionless groups such as the Peclet number and a dimensionless chemotactic driving force defined in this work. It was found that under certain constraints, the effect of chemotaxis was to increase the dispersion coefficient by an additional term that was a linear function of the chemotactic driving force, i.e. E=Dbulk+α v+ β σ, where Dbulk is the bulk diffusion coefficient, v is the fluid velocity, σ is the dimensionless chemotactic driving force we defined, and α and β are appropriate dispersivities. This study will improve our physical understanding of how chemotaxis impacts dispersion and allow us to quantify dispersion in terms of bacterial properties and structure of the geologic media. The engineering correlations that result are critical for improving our assessment and
Ultratransparent Media and Transformation Optics with Shifted Spatial Dispersions
NASA Astrophysics Data System (ADS)
Luo, Jie; Yang, Yuting; Yao, Zhongqi; Lu, Weixin; Hou, Bo; Hang, Zhi Hong; Chan, C. T.; Lai, Yun
2016-11-01
By using pure dielectric photonic crystals, we demonstrate the realization of ultratransparent media, which allow near 100% transmission of light for all incident angles and create aberration-free virtual images. The ultratransparency effect is well explained by spatially dispersive effective medium theory for photonic crystals, and verified by both simulations and proof-of-principle microwave experiments. Designed with shifted elliptical equal frequency contours, such ultratransparent media not only provide a low-loss and feasible platform for transformation optics devices at optical frequencies, but also enable new freedom for phase manipulation beyond the local medium framework.
Ultratransparent Media and Transformation Optics with Shifted Spatial Dispersions.
Luo, Jie; Yang, Yuting; Yao, Zhongqi; Lu, Weixin; Hou, Bo; Hang, Zhi Hong; Chan, C T; Lai, Yun
2016-11-25
By using pure dielectric photonic crystals, we demonstrate the realization of ultratransparent media, which allow near 100% transmission of light for all incident angles and create aberration-free virtual images. The ultratransparency effect is well explained by spatially dispersive effective medium theory for photonic crystals, and verified by both simulations and proof-of-principle microwave experiments. Designed with shifted elliptical equal frequency contours, such ultratransparent media not only provide a low-loss and feasible platform for transformation optics devices at optical frequencies, but also enable new freedom for phase manipulation beyond the local medium framework.
Electret processes in disordered systems based on liquid dispersion media
NASA Astrophysics Data System (ADS)
Shcherbachenko, L. A.; Maksimova, N. T.; Komarov, E. S.; Ruzhnikov, L. I.; Karnakov, V. A.; Baryshnikov, E. S.; Krasnov, D. A.; Troshev, A. A.; Baryshnikov, D. S.; Ezhova, L. I.
2012-10-01
Electret-thermal analysis (ETA) of disordered systems based on dispersed media is carried out. It is shown that the method of thermally stimulated currents makes it possible to estimate the structural changes occurring in a liquid dispersion medium. It is found that liquid water in a free state exhibits the electret properties. The observed multiple peaks on the thermally stimulated current curve are the evidence of the multicomponent nature of the "free water" system. The mechanisms of processes leading to the formation of the electret state in such systems are considered.
Averaged model for momentum and dispersion in hierarchical porous media.
Chabanon, Morgan; David, Bertrand; Goyeau, Benoît
2015-08-01
Hierarchical porous media are multiscale systems, where different characteristic pore sizes and structures are encountered at each scale. Focusing the analysis to three pore scales, an upscaling procedure based on the volume-averaging method is applied twice, in order to obtain a macroscopic model for momentum and diffusion-dispersion. The effective transport properties at the macroscopic scale (permeability and dispersion tensors) are found to be explicitly dependent on the mesoscopic ones. Closure problems associated to these averaged properties are numerically solved at the different scales for two types of bidisperse porous media. Results show a strong influence of the lower-scale porous structures and flow intensity on the macroscopic effective transport properties.
Dark spatial solitons splitting in logarithmically saturable nonlinear media
NASA Astrophysics Data System (ADS)
Zhang, Yuhong; Liu, Baoyuan; Lu, Keqing; Liu, Wangyun; Han, Jun
2014-12-01
We numerically simulate the evolution of the dark-notch-bearing optical beam in the logarithmically saturable nonlinear media based on beam propagation method (BPM). The simulation results indicate that the multiple dark spatial solitons are deep, possible in this type of nonlinear media. The number of multiple dark spatial solitons depends on the width of the dark notch, the initial conditions and the peak intensity of the initial input beam. Under the odd and even initial conditions, the odd and even number sequence of multiple dark spatial solitons can be obtained, respectively. For an input beam with fixed optical intensity, the number of dark solitons increases with the width of the initial input dark notch. The behavior of the multiple dark solitons in this type of media is similar to that in a photorefractive nonlinear crystal.
Mechanisms of anomalous dispersion in flow through heterogeneous porous media
NASA Astrophysics Data System (ADS)
Tyukhova, Alina; Dentz, Marco; Kinzelbach, Wolfgang; Willmann, Matthias
2016-11-01
We study the origins of anomalous dispersion in heterogeneous porous media in terms of the medium and flow properties. To identify and quantify the heterogeneity controls, we focus on porous media which are organized in assemblies of equally sized conductive inclusions embedded in a constant conductivity matrix. We study the behavior of particle arrival times for different conductivity distributions and link the statistical medium characteristics to large-scale transport using a continuous time random walk (CTRW) approach. The CTRW models particle motion as a sequence of transitions in space and time. We derive an explicit map of the conductivity onto the transition time distribution. The derived CTRW model predicts solute transport based on the conductivity distribution and the characteristic heterogeneity length. In this way, heavy tails in solute arrival times and anomalous particle dispersion as measured by the centered mean square displacement are directly related to the medium properties. These findings shed light on the mechanisms of anomalous dispersion in heterogeneous porous media, and provide a basis for the predictive modeling of large-scale transport.
Demi, L; van Dongen, K W A; Verweij, M D
2011-03-01
Experimental data reveals that attenuation is an important phenomenon in medical ultrasound. Attenuation is particularly important for medical applications based on nonlinear acoustics, since higher harmonics experience higher attenuation than the fundamental. Here, a method is presented to accurately solve the wave equation for nonlinear acoustic media with spatially inhomogeneous attenuation. Losses are modeled by a spatially dependent compliance relaxation function, which is included in the Westervelt equation. Introduction of absorption in the form of a causal relaxation function automatically results in the appearance of dispersion. The appearance of inhomogeneities implies the presence of a spatially inhomogeneous contrast source in the presented full-wave method leading to inclusion of forward and backward scattering. The contrast source problem is solved iteratively using a Neumann scheme, similar to the iterative nonlinear contrast source (INCS) method. The presented method is directionally independent and capable of dealing with weakly to moderately nonlinear, large scale, three-dimensional wave fields occurring in diagnostic ultrasound. Convergence of the method has been investigated and results for homogeneous, lossy, linear media show full agreement with the exact results. Moreover, the performance of the method is demonstrated through simulations involving steered and unsteered beams in nonlinear media with spatially homogeneous and inhomogeneous attenuation.
Stabilization of vortex solitons in nonlocal nonlinear media
Minzoni, Antonmaria A.; Smyth, Noel F.; Worthy, Annette L.; Kivshar, Yuri S.
2007-12-15
We study the evolution of vortex solitons in optical media with a nonlocal nonlinear response. We employ a modulation theory for the vortex parameters based on an averaged Lagrangian, and analyze the azimuthal evolution of both the vortex width and diffractive radiation. We describe analytically the physical mechanism for vortex stabilization due to the long-range nonlocal nonlinear response, the effect observed earlier in numerical simulations only.
Asymmetric partially coherent solitons in saturable nonlinear media.
Litchinitser, N M; Królikowski, W; Akhmediev, N N; Agrawal, G P
1999-08-01
We investigate theoretically properties of partially coherent solitons in optical nonlinear media with slow saturable nonlinearity. We have found numerically that such a medium can support spatial solitons which are asymmetric in shape and are composed of only a finite number of modes associated with the self-induced waveguide. It is shown that these asymmetric spatial solitons can propagate many diffraction lengths without changes, but that collisions change their shape and may split them apart.
Studies on dispersive stabilization of porous media flows
NASA Astrophysics Data System (ADS)
Daripa, Prabir; Gin, Craig
2016-08-01
Motivated by a need to improve the performance of chemical enhanced oil recovery (EOR) processes, we investigate dispersive effects on the linear stability of three-layer porous media flow models of EOR for two different types of interfaces: permeable and impermeable interfaces. Results presented are relevant for the design of smarter interfaces in the available parameter space of capillary number, Peclet number, longitudinal and transverse dispersion, and the viscous profile of the middle layer. The stabilization capacity of each of these two interfaces is explored numerically and conditions for complete dispersive stabilization are identified for each of these two types of interfaces. Key results obtained are (i) three-layer porous media flows with permeable interfaces can be almost completely stabilized by diffusion if the optimal viscous profile is chosen, (ii) flows with impermeable interfaces can also be almost completely stabilized for short time, but become more unstable at later times because diffusion flattens out the basic viscous profile, (iii) diffusion stabilizes short waves more than long waves which leads to a "turning point" Peclet number at which short and long waves have the same growth rate, and (iv) mechanical dispersion further stabilizes flows with permeable interfaces but in some cases has a destabilizing effect for flows with impermeable interfaces, which is a surprising result. These results are then used to give a comparison of the two types of interfaces. It is found that for most values of the flow parameters, permeable interfaces suppress flow instability more than impermeable interfaces.
On a class of nonlinear dispersive-dissipative interactions
Rosenau, P.
1997-07-29
The authors study the prototypical, genuinely nonlinear, equation; u{sub t} + a(u{sup m}){sub x} + (u{sup n}){sub xxx} = {mu}(u{sup k}){sub xx}, a, {mu} = consts., which encompasses a wide variety of dissipative-dispersive interactions. The parametric surface k = (m + n)/2 separates diffusion dominated from dissipation dominated phenomena. On this surface dissipative and dispersive effects are in detailed balance for all amplitudes. In particular, the m = n + 2 = k + 1 subclass can be transformed into a form free of convection and dissipation making it accessible to theoretical studies. Both bounded and unbounded oscillations are found and certain exact solutions are presented. When a = (2{mu}3/){sup 2} the map yields a linear equation; rational, periodic and aperiodic solutions are constructed.
Modeling highly-dispersive transparency in planar nonlinear metamaterials
NASA Astrophysics Data System (ADS)
Potravkin, N. N.; Makarov, V. A.; Perezhogin, I. A.
2017-02-01
We consider propagation of light in planar optical metamaterial, which basic element is composed of two silver stripes, and it possesses strong dispersion in optical range. Our method of numerical modeling allows us to take into consideration the nonlinearity of the material and the effects of light self-action without considerable increase of the calculation time. It is shown that plasmonic resonances originating in such a structure result in multiple enhancement of local field and high sensitivity of the transmission coefficient to the intensity of incident monochromatic wave.
Saturation-dependent solute dispersivity in porous media: Pore-scale processes
NASA Astrophysics Data System (ADS)
Raoof, A.; Hassanizadeh, S. M.
2013-04-01
It is known that in variably saturated porous media, dispersion coefficient depends on Darcy velocity and water saturation. In one-dimensional flow, it is commonly assumed that the dispersion coefficient is a linear function of velocity. The coefficient of proportionality, called the dispersivity, is considered to depend on saturation. However, there is not much known about its dependence on saturation. In this study, we investigate, using a pore network model, how the longitudinal dispersivity varies nonlinearly with saturation. We schematize the porous medium as a network of pore bodies and pore throats with finite volumes. The pore space is modeled using the multidirectional pore-network concept, which allows for a distribution of pore coordination numbers. This topological property together with the distribution of pore sizes are used to mimic the microstructure of real porous media. The dispersivity is calculated by solving the mass balance equations for solute concentration in all network elements and averaging the concentrations over a large number of pores. We have introduced a new formulation of solute transport within pore space, where we account for different compartments of residual water within drained pores. This formulation makes it possible to capture the effect of limited mixing due to partial filling of the pores under variably saturated conditions. We found that dispersivity increases with the decrease in saturation, it reaches a maximum value, and then decreases with further decrease in saturation. To show the capability of our formulation to properly capture the effect of saturation on solute dispersion, we applied it to model the results of a reported experimental study.
Beam steering and routing in quadratic nonlinear media
Aceves, A.B.; Santos, M.C.; Torner, L.
1997-04-01
We show how the spatial phase modulation of weak second-harmonic signals controls the overall direction of propagation of spatial solitons in quadratic nonlinear media. We investigate numerically such a process and discuss its applications to all-optical beam routing. 5 refs., 3 figs.
Nonlinear ultrasonic propagation in biological media.
Dunn, F.; Law, W. K.; Frizzell, L. A.
1982-01-01
The nonlinearity parameter B/A for several biological materials was determined by measuring the amplitude of the second harmonic pressure as a function of distance from the source and the amplitude of the fundamental at the source. The B/A values for bovine serum albumin and haemoglobin solutions were found to increase approximately linearly with solution concentration. Blood and homogenized liver exhibit a B/A value similar to a haemoglobin solution of the same dry weight, but whole liver has a greater B/A value. PMID:6950775
Superfluid light in bulk nonlinear media
Carusotto, Iacopo
2014-01-01
We review how the paraxial approximation naturally leads to a hydrodynamic description of light propagation in a bulk Kerr nonlinear medium in terms of a wave equation analogous to the Gross–Pitaevskii equation for the order parameter of a superfluid. The main features of the many-body collective dynamics of the fluid of light in this propagating geometry are discussed: generation and observation of Bogoliubov sound waves in the fluid of light is first described. Experimentally accessible manifestations of superfluidity are then highlighted. Perspectives in view of realizing analogue models of gravity are finally given. PMID:25197252
Spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity
Golubkov, A A; Makarov, Vladimir A
2011-11-30
We present a brief review of the results of fifty years of development efforts in spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity. The recent original results obtained by the authors show the fundamental possibility of determining, from experimental data, the coordinate dependences of complex quadratic susceptibility tensor components of a onedimensionally inhomogeneous (along the z axis) medium with an arbitrary frequency dispersion, if the linear dielectric properties of the medium also vary along the z axis and are described by a diagonal tensor of the linear dielectric constant. It is assumed that the medium in question has the form of a plane-parallel plate, whose surfaces are perpendicular to the direction of the inhomogeneity. Using the example of several components of the tensors X{sup (2)}(z, {omega}{sub 1} {+-} {omega}{sub 2}; {omega}{sub 1}, {+-} {omega}{sub 2}), we describe two methods for finding their spatial profiles, which differ in the interaction geometry of plane monochromatic fundamental waves with frequencies {omega}{sub 1} and {omega}{sub 2}. The both methods are based on assessing the intensity of the waves propagating from the plate at the sum or difference frequency and require measurements over a range of angles of incidence of the fundamental waves. Such measurements include two series of additional estimates of the intensities of the waves generated under special conditions by using the test and additional reference plates, which eliminates the need for complicated phase measurements of the complex amplitudes of the waves at the sum (difference) frequency.
Ultrasonic wave velocity in the restructuring of disperse media
NASA Astrophysics Data System (ADS)
Koltsova, I. S.; Khomutova, A. S.; Deinega, M. A.
2016-03-01
The ultrasonic wave velocities in the restructuring of disperse media were measured using interference and pulsed techniques and the coefficient of reflection in suspensions of starch, Al2O3, and SiO2 particles, glass bulbs, their porous sediments, and composites of Fe3O4 particles in 10% gelatin aqueous solution at a frequency of 3 MHz. The experiments showed alternating variation in the concentration velocity coefficient during the transition of the dispersed phase concentration from the subpercolation to percolation region. The minimum ultrasonic wave velocity in the region of discrete clusters correlates with the ratio between the particle and matrix densities. The results obtained are explained using the Isakovich, Chaban, Rytov, Biot, Hausdorff, and other theories.
The Numerical Solution of Acoustic Propagation through Dispersive Moving Media
2010-06-01
domain version [3] of the Kramer- Kronig relationships (K-K), [6] he arrived at a general form for the operator. Szabo’s operator was originally...for longitudinal and shear wave propagation in viscoelastic media,” J. Acoust. Soc. Am. 107, 2437-2446, 2000. [6] R. D. L. Kronig , “On the theory...domain representation of the Kramers- Kronig dispersion relations,” J. Acoust. Soc. Am. 108, 2114-2119, 2000. [8] G. V. Norton and J. C. Novarini
Interface modes at step edges of media with anisotropic dispersion
NASA Astrophysics Data System (ADS)
Toedt, Jan-Niklas; Mansfeld, Sebastian; Mellem, Daniel; Hansen, Wolfgang; Heitmann, Detlef; Mendach, Stefan
2016-05-01
Time-resolved scanning Kerr microscopy data are presented that illustrate the refraction and total reflection of spin waves in a Ni80Fe20 film at a film-thickness step. In our experiments spin waves are excited with microwaves on coplanar wave guides. By changing the orientation of an externally applied magnetic field, we can manipulate the group velocity of the wave and hence control the angle of incidence on the step. An interface mode bound at the step is observed, when the magnetic field vector is perpendicular to the step. We point out the general conditions under which such interface modes can be expected in media with strongly anisotropic dispersion.
Magnetoviscous effect in ferrofluids with different dispersion media
NASA Astrophysics Data System (ADS)
Borin, D. Yu; Korolev, V. V.; Ramazanova, A. G.; Odenbach, S.; Balmasova, O. V.; Yashkova, V. I.; Korolev, D. V.
2016-10-01
Ferrofluids based on magnetite nanoparticles dispersed in different carrier media (dialkyldiphenyl and polyethylsiloxane) have been synthesized using mixed surfactants (oleic acid, stearic acid and alkenyl succinic anhydride). Magnetic properties of the samples and a change of their shear viscosities in an applied magnetic field have been studied in order to evaluate an influence of the carrier medium on a magnetoviscous effect. A significance of the interaction of the carrier medium and surfactant with a consideration of the magnetic and rheological behavior of ferrofluids was demonstrated.
Nonlinear self-focus of pulsed-wave beams in Kerr media
Judkins, J.B.
1992-12-31
A modified finite-difference time-domain method for solving Maxwell`s equations in nonlinear media is presented. This method allows for a finite response time to be incorporated in the medium, physically creating dispersion and absorption mechanisms. The technique models electromagnetic fields in two space dimensions and time and encompasses both the TE{sub z} and TM{sub z} set of decoupled field equations. Aspects of an ultra-short pulsed Gaussian beam are studied in a variety of linear and nonlinear environments to demonstrate that the methods developed here can be used efficaciously in the modeling of pulses in complex problem space geometries even when nonlinearities are present.
Radiating dispersive shock waves in non-local optical media
El, Gennady A.
2016-01-01
We consider the step Riemann problem for the system of equations describing the propagation of a coherent light beam in nematic liquid crystals, which is a general system describing nonlinear wave propagation in a number of different physical applications. While the equation governing the light beam is of defocusing nonlinear Schrödinger (NLS) equation type, the dispersive shock wave (DSW) generated from this initial condition has major differences from the standard DSW solution of the defocusing NLS equation. In particular, it is found that the DSW has positive polarity and generates resonant radiation which propagates ahead of it. Remarkably, the velocity of the lead soliton of the DSW is determined by the classical shock velocity. The solution for the radiative wavetrain is obtained using the Wentzel–Kramers–Brillouin approximation. It is shown that for sufficiently small initial jumps the nematic DSW is asymptotically governed by a Korteweg–de Vries equation with the fifth-order dispersion, which explicitly shows the resonance generating the radiation ahead of the DSW. The constructed asymptotic theory is shown to be in good agreement with the results of direct numerical simulations. PMID:27118911
Peiponen, Kai-Erik; Saarinen, Jarkko J.; Svirko, Yuri
2004-04-01
Dispersion relations and sum rules for nonlinear susceptibilities are derived using complex analysis and especially the concept of a meromorphic function. The dispersion relations and sum rules provide frames to investigate the consistency between the theory and experiments.
NASA Astrophysics Data System (ADS)
Muniruzzaman, Muhammad; Haberer, Christina; Grathwohl, Peter; Rolle, Massimo
2014-05-01
We study the influence of Coulombic effects on transport of charged species in saturated porous media in advection-dominated flow regimes. We focus on transverse hydrodynamic dispersion and we performed quasi two-dimensional flow-through experiments in homogeneous and spatially variable flow fields to investigate transport of dilute electrolyte solutions. The experiments were conducted at flow velocities (1.0, 1.5 and 6 m/day) where advection is the dominant mass transfer process. High-resolution measurements at the outlet were performed to determine the concentration of different cations and anions. In order to interpret the laboratory experiments we develop a two-dimensional numerical model. The adopted modeling approach is based on a multicomponent formulation, charge conservation, and the accurate description of local transverse dispersion. The latter entails a non-linear dependence of the transverse dispersion coefficient on the flow velocity as well as a compound-specific dependence on the molecular diffusion of the transported solutes. The model was benchmarked by comparing the results of the 2D steady-state multicomponent simulations with 1D transient results of PHREEQC in homogeneous scenarios, and it was successively used to quantitatively evaluate the experimental results in both homogeneous and heterogeneous porous media. Our experimental and modeling results show that Coulombic cross-coupling of dispersive fluxes of charged species in porous media significantly affects the lateral displacement of charged ions in both homogeneous and heterogeneous flow-through systems. Such effects are remarkable not only in diffusion-dominated but also in advection-dominated flow regimes.
Quantum and classical optics of dispersive and absorptive structured media
NASA Astrophysics Data System (ADS)
Bhat, Navin Andrew Rama
This thesis presents a Hamiltonian formulation of the electromagnetic fields in structured (inhomogeneous) media of arbitrary dimensionality, with arbitrary material dispersion and absorption consistent with causality. The method is based on an identification of the photonic component of the polariton modes of the system. Although the medium degrees of freedom are introduced in an oscillator model, only the macroscopic response of the medium appears in the derived eigenvalue equation for the polaritons. For both the discrete transparent-regime spectrum and the continuous absorptive-regime spectrum, standard codes for photonic modes in nonabsorptive systems can easily be leveraged to calculate polariton modes. Two applications of the theory are presented: pulse propagation and spontaneous parametric down-conversion (SPDC). In the propagation study, the dynamics of the nonfluctuating part of a classical-like pulse are expressed in terms of a Schrodinger equation for a polariton effective field. The complex propagation parameters of that equation can be obtained from the same generalized dispersion surfaces typically used while neglecting absorption, without incurring additional computational complexity. As an example I characterize optical pulse propagation in an Au/MgF 2 metallodielectric stack, using the empirical response function, and elucidate the various roles of Bragg scattering, interband absorption and field expulsion. Further, I derive the Beer coefficient in causal structured media. The SPDC calculation is rigorous, captures the full 3D physics, and properly incorporates linear dispersion. I obtain an expression for the down-converted state, quantify pair-production properties, and characterize the scaling behavior of the SPDC energy. Dispersion affects the normalization of the polariton modes, and calculations of the down-conversion efficiency that neglect this can be off by 100% or more for common media regardless of geometry if the pump is near the band
Slow and fast light propagation in nonlinear Kerr media.
NASA Astrophysics Data System (ADS)
Yang, Qiguang; Ma, Seongmin; Wang, Huitian; Jung, S. S.
2005-04-01
Sub- and superluminal propagation of light pulse in Kerr materials has been investigated. Group velocities as slow as much less than 1 millimeter per second to as fast as negative several hundreds meters per second can be easily obtained in Kerr medium, which possesses large nonlinear refractive index and long relaxation time, such as Cr doped Alexandrite, Ruby, and GdAlO3. The physical mechanism is the strong highly dispersive coupling between different frequency components of the pulse. The new mechanism of slowing down pulses as well as producing superluminal pulses enlarges the very specific materials to all kinds of nonlinear optical materials.
Dispersion of nonresonant third-order nonlinearities in Silicon Carbide
De Leonardis, Francesco; Soref, Richard A.; Passaro, Vittorio M. N.
2017-01-01
In this paper we present a physical discussion of the indirect two-photon absorption (TPA) occuring in silicon carbide with either cubic or wurtzite structure. Phonon-electron interaction is analyzed by finding the phonon features involved in the process as depending upon the crystal symmetry. Consistent physical assumptions about the phonon-electron scattering mechanisms are proposed in order to give a mathematical formulation to predict the wavelength dispersion of TPA and the Kerr nonlinear refractive index n2. The TPA spectrum is investigated including the effects of band nonparabolicity and the influence of the continuum exciton. Moreover, a parametric analysis is presented in order to fit the experimental measurements. Finally, we have estimated the n2 in a large wavelength range spanning the visible to the mid-IR region. PMID:28098223
Dispersion of nonresonant third-order nonlinearities in Silicon Carbide.
De Leonardis, Francesco; Soref, Richard A; Passaro, Vittorio M N
2017-01-18
In this paper we present a physical discussion of the indirect two-photon absorption (TPA) occuring in silicon carbide with either cubic or wurtzite structure. Phonon-electron interaction is analyzed by finding the phonon features involved in the process as depending upon the crystal symmetry. Consistent physical assumptions about the phonon-electron scattering mechanisms are proposed in order to give a mathematical formulation to predict the wavelength dispersion of TPA and the Kerr nonlinear refractive index n2. The TPA spectrum is investigated including the effects of band nonparabolicity and the influence of the continuum exciton. Moreover, a parametric analysis is presented in order to fit the experimental measurements. Finally, we have estimated the n2 in a large wavelength range spanning the visible to the mid-IR region.
Dispersion of nonresonant third-order nonlinearities in Silicon Carbide
NASA Astrophysics Data System (ADS)
de Leonardis, Francesco; Soref, Richard A.; Passaro, Vittorio M. N.
2017-01-01
In this paper we present a physical discussion of the indirect two-photon absorption (TPA) occuring in silicon carbide with either cubic or wurtzite structure. Phonon-electron interaction is analyzed by finding the phonon features involved in the process as depending upon the crystal symmetry. Consistent physical assumptions about the phonon-electron scattering mechanisms are proposed in order to give a mathematical formulation to predict the wavelength dispersion of TPA and the Kerr nonlinear refractive index n2. The TPA spectrum is investigated including the effects of band nonparabolicity and the influence of the continuum exciton. Moreover, a parametric analysis is presented in order to fit the experimental measurements. Finally, we have estimated the n2 in a large wavelength range spanning the visible to the mid-IR region.
Nonlinear plasmonic dispersion and coupling analysis in the symmetric graphene sheets waveguide
Jiang, Xiangqian; Yuan, Haiming; Sun, Xiudong
2016-01-01
We study the nonlinear dispersion and coupling properties of the graphene-bounded dielectric slab waveguide at near-THz/THz frequency range, and then reveal the mechanism of symmetry breaking in nonlinear graphene waveguide. We analyze the influence of field intensity and chemical potential on dispersion relation, and find that the nonlinearity of graphene affects strongly the dispersion relation. As the chemical potential decreases, the dispersion properties change significantly. Antisymmetric and asymmetric branches disappear and only symmetric one remains. A nonlinear coupled mode theory is established to describe the dispersion relations and its variation, which agrees with the numerical results well. Using the nonlinear couple model we reveal the reason of occurrence of asymmetric mode in the nonlinear waveguide. PMID:27976749
Nonlinear plasmonic dispersion and coupling analysis in the symmetric graphene sheets waveguide.
Jiang, Xiangqian; Yuan, Haiming; Sun, Xiudong
2016-12-15
We study the nonlinear dispersion and coupling properties of the graphene-bounded dielectric slab waveguide at near-THz/THz frequency range, and then reveal the mechanism of symmetry breaking in nonlinear graphene waveguide. We analyze the influence of field intensity and chemical potential on dispersion relation, and find that the nonlinearity of graphene affects strongly the dispersion relation. As the chemical potential decreases, the dispersion properties change significantly. Antisymmetric and asymmetric branches disappear and only symmetric one remains. A nonlinear coupled mode theory is established to describe the dispersion relations and its variation, which agrees with the numerical results well. Using the nonlinear couple model we reveal the reason of occurrence of asymmetric mode in the nonlinear waveguide.
Nonlinear plasmonic dispersion and coupling analysis in the symmetric graphene sheets waveguide
NASA Astrophysics Data System (ADS)
Jiang, Xiangqian; Yuan, Haiming; Sun, Xiudong
2016-12-01
We study the nonlinear dispersion and coupling properties of the graphene-bounded dielectric slab waveguide at near-THz/THz frequency range, and then reveal the mechanism of symmetry breaking in nonlinear graphene waveguide. We analyze the influence of field intensity and chemical potential on dispersion relation, and find that the nonlinearity of graphene affects strongly the dispersion relation. As the chemical potential decreases, the dispersion properties change significantly. Antisymmetric and asymmetric branches disappear and only symmetric one remains. A nonlinear coupled mode theory is established to describe the dispersion relations and its variation, which agrees with the numerical results well. Using the nonlinear couple model we reveal the reason of occurrence of asymmetric mode in the nonlinear waveguide.
Stabilization of vortex beams in Kerr media by nonlinear absorption
NASA Astrophysics Data System (ADS)
Porras, Miguel A.; Carvalho, Márcio; Leblond, Hervé; Malomed, Boris A.
2016-11-01
We elaborate a solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form robust tubular filaments in transparent dielectrics as common as air, water, and optical glasses at sufficiently high intensities. We also show that the tubular, rotating, and specklelike filamentation regimes, previously observed in experiments with axicon-generated Bessel beams, can be explained as manifestations of the stability or instability of a specific nonlinear Bessel-vortex state, which is fully identified.
1986-04-30
TenCate , who is supported by ONR Contract NOOO I 4-84-K-0574, in the completion of work on pure tones that interact in higher order modes of a...rectangular duct.26 Through collaboration with TenCate , Lind has acquired experience with the same experimental apparatus that he will use beginning I June...34 J. Acoust. Soc. " .. Am. 65.1127-1133(1979). 36. J. A TenCate and K F. Hamilton, "Dispersive nonlinear wave interactions in a rectangular duct," In
Nonlinear light-matter interactions in engineered optical media
NASA Astrophysics Data System (ADS)
Litchinitser, Natalia
In this talk, we consider fundamental optical phenomena at the interface of nonlinear and singular optics in artificial media, including theoretical and experimental studies of linear and nonlinear light-matter interactions of vector and singular optical beams in metamaterials. We show that unique optical properties of metamaterials open unlimited prospects to ``engineer'' light itself. Thanks to their ability to manipulate both electric and magnetic field components, metamaterials open new degrees of freedom for tailoring complex polarization states and orbital angular momentum (OAM) of light. We will discuss several approaches to structured light manipulation on the nanoscale using metal-dielectric, all-dielectric and hyperbolic metamaterials. These new functionalities, including polarization and OAM conversion, beam magnification and de-magnification, and sub-wavelength imaging using novel non-resonant hyperlens are likely to enable a new generation of on-chip or all-fiber structured light applications. The emergence of metamaterials also has a strong potential to enable a plethora of novel nonlinear light-matter interactions and even new nonlinear materials. In particular, nonlinear focusing and defocusing effects are of paramount importance for manipulation of the minimum focusing spot size of structured light beams necessary for nanoscale trapping, manipulation, and fundamental spectroscopic studies. Colloidal suspensions offer as a promising platform for engineering polarizibilities and realization of large and tunable nonlinearities. We will present our recent studies of the phenomenon of spatial modulational instability leading to laser beam filamentation in an engineered soft-matter nonlinear medium. Finally, we introduce so-called virtual hyperbolic metamaterials formed by an array of plasma channels in air as a result of self-focusing of an intense laser pulse, and show that such structure can be used to manipulate microwave beams in a free space. This
All-fiber nonlinearity- and dispersion-managed dissipative soliton nanotube mode-locked laser
Zhang, Z.; Popa, D. Wittwer, V. J.; Milana, S.; Hasan, T.; Jiang, Z.; Ferrari, A. C.; Ilday, F. Ö.
2015-12-14
We report dissipative soliton generation from an Yb-doped all-fiber nonlinearity- and dispersion-managed nanotube mode-locked laser. A simple all-fiber ring cavity exploits a photonic crystal fiber for both nonlinearity enhancement and dispersion compensation. The laser generates stable dissipative solitons with large linear chirp in the net normal dispersion regime. Pulses that are 8.7 ps long are externally compressed to 118 fs, outperforming current nanotube-based Yb-doped fiber laser designs.
All-fiber nonlinearity- and dispersion-managed dissipative soliton nanotube mode-locked laser
NASA Astrophysics Data System (ADS)
Zhang, Z.; Popa, D.; Wittwer, V. J.; Milana, S.; Hasan, T.; Jiang, Z.; Ferrari, A. C.; Ilday, F. Ö.
2015-12-01
We report dissipative soliton generation from an Yb-doped all-fiber nonlinearity- and dispersion-managed nanotube mode-locked laser. A simple all-fiber ring cavity exploits a photonic crystal fiber for both nonlinearity enhancement and dispersion compensation. The laser generates stable dissipative solitons with large linear chirp in the net normal dispersion regime. Pulses that are 8.7 ps long are externally compressed to 118 fs, outperforming current nanotube-based Yb-doped fiber laser designs.
Wave velocity dispersion and attenuation in media exhibiting internal oscillations
NASA Astrophysics Data System (ADS)
Frehner, Marcel; Steeb, Holger; Schmalholz, Stefan M.
2010-05-01
Understanding the dynamical and acoustical behavior of porous and heterogeneous rocks is of great importance in geophysics, e.g. earthquakes, and for various seismic engineering applications, e.g. hydrocarbon exploration. Within a heterogeneous medium oscillations with a characteristic resonance frequency, depending on the mass and internal length of the heterogeneity, can occur. When excited, heterogeneities can self-oscillate with their natural frequency. Another example of internal oscillations is the dynamical behavior of non-wetting fluid blobs or fluid patches in residually saturated pore spaces. Surface tension forces or capillary forces act as the restoring force that drives the oscillation. Whatever mechanism is involved, an oscillatory phenomena within a heterogeneous medium will have an effect on acoustic or seismic waves propagating through such a medium, i.e. wave velocity dispersion and frequency-dependent attenuation. We present two models for media exhibiting internal oscillations and discuss the frequency-dependent wave propagation mechanism. Both models give similar results: (1) The low-frequency (i.e. quasi-static) limit for the phase velocity is identical with the Gassmann-Wood limit and the high-frequency limit is larger than this value and (2) Around the resonance frequency a very strong phase velocity change and the largest attenuation occurs. (1) Model for a homogeneous medium exhibiting internal oscillations We present a continuum model for an acoustic medium exhibiting internal damped oscillations. The obvious application of this model is water containing oscillating gas bubbles, providing the material and model parameters for this study. Two physically based momentum interaction terms between the two inherent constituents are used: (1) A purely elastic term of oscillatory nature that scales with the volume of the bubbles and (2) A viscous term that scales with the specific surface of the bubble. The model is capable of taking into account
Controlling Spatiotemporal Chaos in Active Dissipative-Dispersive Nonlinear Systems
NASA Astrophysics Data System (ADS)
Gomes, Susana; Pradas, Marc; Kalliadasis, Serafim; Papageorgiou, Demetrios; Pavliotis, Grigorios
2015-11-01
We present a novel generic methodology for the stabilization and control of infinite-dimensional dynamical systems exhibiting low-dimensional spatiotemporal chaos. The methodology is exemplified with the generalized Kuramoto-Sivashinsky equation, the simplest possible prototype that retains that fundamental elements of any nonlinear process involving wave evolution. The equation is applicable on a wide variety of systems including falling liquid films and plasma waves with dispersion due to finite banana width. We show that applying the appropriate choice of time-dependent feedback controls via blowing and suction, we are able to stabilize and/or control all stable or unstable solutions, including steady solutions, travelling waves and spatiotemporal chaos, but also use the controls obtained to stabilize the solutions to more general long wave models. We acknowledge financial support from Imperial College through a Roth PhD studentship, Engineering and Physical Sciences Research Council of the UK through Grants No. EP/H034587, EP/J009636, EP/K041134, EP/L020564 and EP/L024926 and European Research Council via Advanced Grant No. 247031.
Cai, Yangjian; Lin, Qiang; Ge, Di
2002-10-01
By adopting a new tensor method, we derived an analytical propagation formula for the cross-spectral density of partially coherent twisted anisotropic Gaussian Schell-model (GSM) beams through dispersive and absorbing media. Using the derived formula, we studied the evolution properties and spectrum properties of twisted anisotropic GSM beams in dispersive and absorbing media. The results show that the dispersive and absorbing media have strong influences on the propagation properties of twisted anisotropic GSM beams and their spectrum evolution. Our method provides a simple and convenient way to study the propagation of twisted anisotropic GSM beams in media with complex refractive index.
NASA Astrophysics Data System (ADS)
Hopkins, James; Gaudette, Jamie; Mehta, Priyanth
2013-10-01
With the advent of digital signal processing (DSP) in optical transmitters and receivers, the ability to finely tune the ratio of pre and post dispersion compensation can be exploited to best mitigate the nonlinear penalties caused by the Kerr effect. A portion of the nonlinear penalty in optical communication channels has been explained by an increase in peak to average power ratio (PAPR) inherent in highly dispersed signals. The standard approach for minimizing these impairments applies 50% pre dispersion compensation and 50% post dispersion compensation, thereby decreasing average PAPR along the length of the cable, as compared with either 100% pre or post dispersion compensation. In this paper we demonstrate that simply considering the net accumulated dispersion, and applying 50/50 pre/post dispersion is not necessarily the best way to minimize PAPR and subsequent Kerr nonlinearities. Instead, we consider the cumulative dispersion along the entire length of the cable, and, taking into account this additional information, derive an analytic formula for the minimization of PAPR. Alignment with simulation and experimental measurements is presented using a commercially available 100Gb/s dual-polarization binary phase-shift-keying (DP-BPSK) coherent modem, with transmitter and receiver DSP. Measurements are provided from two different 5000km dispersion managed Submarine test-beds, as well as a 3800km terrestrial test-bed with a mixture of SMF-28 and TWRS optical fiber. This method is shown to deviate significantly from the conventional 50/50 method described above, in dispersion managed communications systems, and more closely aligns with results obtained from simulation and data collected from laboratory test-beds.
The Whitham approach to dispersive shocks in systems with cubic-quintic nonlinearities
NASA Astrophysics Data System (ADS)
Crosta, M.; Trillo, S.; Fratalocchi, A.
2012-09-01
By employing a rigorous approach based on the Whitham modulation theory, we investigate dispersive shock waves arising in a high-order nonlinear Schrödinger equation with competing cubic and quintic nonlinear responses. This model finds important applications in both nonlinear optics and Bose-Einstein condensates. Our theory predicts the formation of dispersive shocks with totally controllable properties, encompassing both steering and compression effects. Numerical simulations confirm these results perfectly. Quite remarkably, shock tuning can be achieved in the regime of a very small high order, i.e. quintic, nonlinearity.
Flow and dispersion in anisotropic porous media: A lattice-Boltzmann study
NASA Astrophysics Data System (ADS)
Maggiolo, D.; Picano, F.; Guarnieri, M.
2016-10-01
Given their capability of spreading active chemical species and collecting electricity, porous media made of carbon fibers are extensively used as diffusion layers in energy storage systems, such as redox flow batteries. In spite of this, the dispersion dynamics of species inside porous media is still not well understood and often lends itself to different interpretations. Actually, the microscopic design of efficient porous media, which can potentially and effectively improve the performances of flow batteries, is still an open challenge. The present study aims to investigate the effect of fibrous media micro-structure on dispersion, in particular the effect of fiber orientation on drag and dispersion dynamics. Several lattice-Boltzmann simulations of flows through differently oriented fibrous media coupled with Lagrangian simulations of particle tracers have been performed. Results show that orienting fibers preferentially along the streamwise direction minimizes the drag and maximizes the dispersion, which is the most desirable condition for diffusion layers in flow batteries' applications.
Christodoulides, D N; Joseph, R L
1984-06-01
The propagation of nonlinear optical pulses in fibers is discussed, taking into account physical effects arising from nonlinearity, dispersion, and transverse confinement. The wave equation is solved by treating the radial dependence of the field in an exact way. The conditions supporting bright solitary waves are presented and compared with previous results.
High-order FDTD methods for transverse electromagnetic systems in dispersive inhomogeneous media.
Zhao, Shan
2011-08-15
This Letter introduces a novel finite-difference time-domain (FDTD) formulation for solving transverse electromagnetic systems in dispersive media. Based on the auxiliary differential equation approach, the Debye dispersion model is coupled with Maxwell's equations to derive a supplementary ordinary differential equation for describing the regularity changes in electromagnetic fields at the dispersive interface. The resulting time-dependent jump conditions are rigorously enforced in the FDTD discretization by means of the matched interface and boundary scheme. High-order convergences are numerically achieved for the first time in the literature in the FDTD simulations of dispersive inhomogeneous media.
NONLINEAR OPTICAL PHENOMENA: Dispersive regime of spectral compression
NASA Astrophysics Data System (ADS)
Kutuzyan, A. A.; Mansuryan, T. G.; Esayan, G. L.; Akopyan, R. S.; Muradyan, Kh
2008-04-01
The role of the group velocity dispersion in the spectral compression of subpicosecond laser pulses is analysed based on numerical and experimental studies. It is shown that the group velocity dispersion in an optical fibre can substantially change the physical pattern of the spectral compression process.
Local computational strategies for predicting wave propagation in nonlinear media
NASA Astrophysics Data System (ADS)
Leamy, Michael J.; Autrusson, Thibaut B.; Staszewski, Wieslaw J.; Uhl, Tadeusz; Packo, Pawel
2014-03-01
Two local computational strategies for modeling elastic wave propagation, namely the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE), are compared and contrasted in analyzing bulk waves in two-dimensional nonlinear media. Each strategy formulates the problem from the perspective of a cell and its local interactions with other cells, leading to robust treatments of anisotropy, heterogeneity, and nonlinearity. The local approach also enables straight-forward parallelization on high performance computing clusters. While the two share a common local perspective, they differ in two major respects. The first is that CAFE employs both rectangular and triangular cells, while LISA considers only rectangular. The second is that LISA appeared much earlier than CAFE (early 1990's versus late 2000's), and as such has been developed to a much greater degree with a multitude of material models, cell-to-cell interactions, loading possibilities, and boundary treatments. A hybrid approach which combines the two is of great interest since the non-uniform mesh capability of the CAFE triangular cell can be readily coupled to LISA's rectangular grids, taking advantage of the built-in LISA features on the uniform portion of the domain. For linear material domains, the hybrid implementation appears straight-forward since both methods have been shown to recover the same equations in the rectangular case. For nonlinear material domains, the formulations cannot be put into a one-to-one correspondence, and hybrid implementation may be more problematic. This paper addresses these differences by first presenting the underlying formulations, and then computing results for growth of a second harmonic in an introduced bulk pressure wave. Rectangular cells are used in both LISA and CAFE. Results from both approaches are compared to an approximate, analytical solution based on a two-scale field representation. Differences in the LISA and CAFE computed
Nonlinear acoustics in a dispersive continuum: Random waves, radiation pressure, and quantum noise
NASA Astrophysics Data System (ADS)
Cabot, M. A.
The nonlinear interaction of sound with sound is studied using dispersive hydrodynamics which derived from a variational principle and the assumption that the internal energy density depends on gradients of the mass density. The attenuation of sound due to nonlinear interaction with a background is calculated and is shown to be sensitive to both the nature of the dispersion and decay bandwidths. The theoretical results are compared to those of low temperature helium experiments. A kinetic equation which described the nonlinear self-inter action of a background is derived. When a Deybe-type cutoff is imposed, a white noise distribution is shown to be a stationary distribution of the kinetic equation. The attenuation and spectrum of decay of a sound wave due to nonlinear interaction with zero point motion is calculated. In one dimension, the dispersive hydrodynamic equations are used to calculate the Langevin and Rayleigh radiation pressures of wave packets and solitary waves.
Abe, H.; Okuda, H.
1994-06-01
We study linear and nonlinear properties of a new computer simulation model developed to study the propagation of electromagnetic waves in a dielectric medium in the linear and nonlinear regimes. The model is constructed by combining a microscopic model used in the semi-classical approximation for the dielectric media and the particle model developed for the plasma simulations. It is shown that the model may be useful for studying linear and nonlinear wave propagation in the dielectric media.
NASA Astrophysics Data System (ADS)
Rajan, M. S. Mani
2016-08-01
In this manuscript, the ultrashort soliton pulse propagation through nonlinear tunneling in cubic quintic media is investigated. The effect of chirping on propagation characteristics of the soliton pulse is analytically investigated using similarity transformation. In particular, we investigate the propagation dynamics of ultrashort soliton pulse through dispersion barrier for both chirp and chirp-free soliton. By investigating the obtained soliton solution, we found that chirping has strong influence on soliton dynamics such as pulse compression with amplification. These two important dynamics of chirped soliton in cubic quintic media open new possibilities to improve the solitonic communication system. Moreover, we surprisingly observe that a dispersion well is formed for the chirped case whereas a barrier is formed for the chirp-free case, which has certain applications in the construction of logic gate devices to achieve ultrafast switching.
Strojan, Klemen; Leonardi, Adrijana; Bregar, Vladimir B; Križaj, Igor; Svete, Jurij; Pavlin, Mojca
2017-01-01
Protein corona of nanoparticles (NPs), which forms when these particles come in to contact with protein-containing fluids, is considered as an overlooked factor in nanomedicine. Through numerous studies it has been becoming increasingly evident that it importantly dictates the interaction of NPs with their surroundings. Several factors that determine the compositions of NPs protein corona have been identified in recent years, but one has remained largely ignored-the composition of media used for dispersion of NPs. Here, we determined the effect of dispersion media on the composition of protein corona of polyacrylic acid-coated cobalt ferrite NPs (PAA NPs) and silica NPs. Our results confirmed some of the basic premises such as NPs type-dependent specificity of the protein corona. But more importantly, we demonstrated the effect of the dispersion media on the protein corona composition. The differences between constituents of the media used for dispersion of NPs, such as divalent ions and macromolecules were responsible for the differences in protein corona composition formed in the presence of fetal bovine serum (FBS). Our results suggest that the protein corona composition is a complex function of the constituents present in the media used for dispersion of NPs. Regardless of the dispersion media and FBS concentration, majority of proteins from either PAA NPs or silica NPs coronas were involved in the process of transport and hemostasis. Interestingly, corona of silica NPs contained three complement system related proteins: complement factor H, complement C3 and complement C4 while PAA NPs bound only one immune system related protein, α-2-glycoprotein. Importantly, relative abundance of complement C3 protein in corona of silica NPs was increased when NPs were dispersed in NaCl, which further implies the relevance of dispersion media used to prepare NPs.
Strojan, Klemen; Leonardi, Adrijana; Bregar, Vladimir B.; Križaj, Igor; Svete, Jurij; Pavlin, Mojca
2017-01-01
Protein corona of nanoparticles (NPs), which forms when these particles come in to contact with protein-containing fluids, is considered as an overlooked factor in nanomedicine. Through numerous studies it has been becoming increasingly evident that it importantly dictates the interaction of NPs with their surroundings. Several factors that determine the compositions of NPs protein corona have been identified in recent years, but one has remained largely ignored—the composition of media used for dispersion of NPs. Here, we determined the effect of dispersion media on the composition of protein corona of polyacrylic acid-coated cobalt ferrite NPs (PAA NPs) and silica NPs. Our results confirmed some of the basic premises such as NPs type-dependent specificity of the protein corona. But more importantly, we demonstrated the effect of the dispersion media on the protein corona composition. The differences between constituents of the media used for dispersion of NPs, such as divalent ions and macromolecules were responsible for the differences in protein corona composition formed in the presence of fetal bovine serum (FBS). Our results suggest that the protein corona composition is a complex function of the constituents present in the media used for dispersion of NPs. Regardless of the dispersion media and FBS concentration, majority of proteins from either PAA NPs or silica NPs coronas were involved in the process of transport and hemostasis. Interestingly, corona of silica NPs contained three complement system related proteins: complement factor H, complement C3 and complement C4 while PAA NPs bound only one immune system related protein, α-2-glycoprotein. Importantly, relative abundance of complement C3 protein in corona of silica NPs was increased when NPs were dispersed in NaCl, which further implies the relevance of dispersion media used to prepare NPs. PMID:28052135
Are There Optical Solitary Wave Solutions in Linear Media with Group Velocity Dispersion?
NASA Technical Reports Server (NTRS)
Li, Zhonghao; Zhou, Guosheng
1996-01-01
A generalized exact optical bright solitary wave solution in a three dimensional dispersive linear medium is presented. The most interesting property of the solution is that it can exist in the normal group-velocity-dispersion (GVD) region. In addition, another peculiar feature is that it may achieve a condition of 'zero-dispersion' to the media so that a solitary wave of arbitrarily small amplitude may be propagated with no dependence on is pulse width.
Laine, T A; Friberg, A T
2000-06-01
We investigate electromagnetic wave reflection and propagation in layered Kerr structures by introducing a method based on the application of canonical perturbation theory to fields in nonlinear media. Via the Hamilton-Jacobi formalism of classical mechanics, the waves in linear layers are expressed with constant canonical variables. The nonlinearity is treated as a small perturbation that modifies the constant invariants. We explicitly evaluate the nonlinear fields correct to first order by perturbation and compare the results to a rigorous nonlinear thin-layer model. Both polarizations, TE and TM, are considered separately. An exact quadrature solution of the nonlinear field in TM polarization is derived. We show that with weak nonlinearities the perturbative technique yields simple and accurate analytical expressions for the nonlinear fields. The results give physical insight into the use of nonlinear media for controlling the scattered fields in layered structures.
Nonlinear dispersive evolution of coherent trapped particle structures in collisionless plasmas
NASA Astrophysics Data System (ADS)
Mandal, Debraj; Sharma, Devendra
2016-10-01
The nonlinear limit of the collective perturbations in plasma is characterized by the onset of amplitude dependence in the wave dispersion. In a special class of nonlinear effects having origin in plasma kinetic theory, this amplitude dependence is removed only by collisions such that perturbations have no linear counterpart in collisionless limit and must follow a nonlinear dispersion relation (NDR). Exploring whether these fundamentally nonlinear perturbations can be driven unstable without entropy production might transform the character of the linear threshold based operating mechanism of the plasma turbulence that relies on well defined discrete spectrum prescribed by the linear plasma dispersion. In our multiscale, exact mass ratio, kinetic simulations the evolution of fundamentally nonlinear trapped particle structures is explored on both fast and slow ion and electron acoustic branches of the associated Nonlinear dispersion relation, respectively. The propagating structures that mutually interact exhibit a near continuum of the phase velocities and show microscopic evolution of the separatrix between streaming and trapped particle regions in the phase space, describing the subtle continuity between discrete and continuum bases of the plasma turbulence.
Ultrashort Pulse Effects in Semiconductor Amplifiers & in Dispersive Media
1994-03-31
they lead to the two dimensional nonlinear Schr ~ dinger equation with a focusing nonlinear- ity. This equation has singularities, corresponding to a...behavior of a device we would like to have model equations , derived from the underlying physics, which do not require that the full range of time scale:s...solver to integrate full vector Maxwell in one two or three dimensions. At this time that equation is being integrated coupled to a simple two oscillator
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.
Simulations and Theory of Density-Dependent Dispersion in Weakly Heterogeneous Porous Media
NASA Astrophysics Data System (ADS)
Landman, A.; Schotting, R. J.
2004-12-01
The effect of density gradients on dispersive mixing of miscible fluids is studied. Density gradients not only affect dispersive transport for unstable flow, but also can significantly affect dispersion under stable conditions. For vertical displacements, laboratory experiments show a reduction of the longitudinal dispersivity under the influence of stabilizing density gradients. Linear Fick's law for the dispersive flux is inadequate to model these experiments. Therefore, alternative theories have been developed that incorporate the effect of density gradients. In this study, accurate numerical simulations of vertical displacements in weakly heterogeneous porous columns are performed. The numerical results confirm experimental observations. Furthermore, the computed concentration profiles are used to validate nonlinear dispersion theories applicable for high density gradients. A comparison is made with the stochastic theory of Welty and Gelhar, with homogenization theory, and with the nonlinear dispersion theory of Hassanizadeh and Leijnse. For small variances in log k, the stochastic and homogenization theory lead to reasonably good predictions of the computed concentration profiles and variances, without any fitting. In the theory of Hassanizadeh and Leijnse a fitting parameter is involved. This nonlinear dispersion parameter is not a true medium parameter, as it is found to be dependent on the flow rate and on the travel distance.
The dispersion and aggregation of graphene oxide in aqueous media
NASA Astrophysics Data System (ADS)
Wang, Meng; Niu, Yang; Zhou, Jihan; Wen, Hao; Zhang, Zhenyu; Luo, Da; Gao, Dongliang; Yang, Juan; Liang, Dehai; Li, Yan
2016-07-01
Graphene oxide (GO), as a typical two-dimensional material, possesses a range of oxygen-containing groups and shows surfactant and/or polyelectrolyte-like characteristics. Herein, GO sheets with narrow size distribution were prepared by an ultracentrifugation-based process and the aggregation behaviour of GO in pure water and an electrolyte aqueous solution were studied using laser light scattering (LLS). When adding common electrolytes, such as NaCl and MgCl2, into the GO dispersions, aggregation occurs and irreversible coagulation eventually occurs too. However, the GO dispersion can still remain stable when adding excess AlCl3. The zeta potential of the GO dispersion changes from negative to positive after the addition of access AlCl3, indicating that electrostatic repulsion is still responsible for the dispersion of GO, which is in good agreement with the LLS results. This finding on the dispersion of GO may be applied in the solution processing of GO. It also expands the scope of the design and preparation of new GO-based hybrid materials with different functions.Graphene oxide (GO), as a typical two-dimensional material, possesses a range of oxygen-containing groups and shows surfactant and/or polyelectrolyte-like characteristics. Herein, GO sheets with narrow size distribution were prepared by an ultracentrifugation-based process and the aggregation behaviour of GO in pure water and an electrolyte aqueous solution were studied using laser light scattering (LLS). When adding common electrolytes, such as NaCl and MgCl2, into the GO dispersions, aggregation occurs and irreversible coagulation eventually occurs too. However, the GO dispersion can still remain stable when adding excess AlCl3. The zeta potential of the GO dispersion changes from negative to positive after the addition of access AlCl3, indicating that electrostatic repulsion is still responsible for the dispersion of GO, which is in good agreement with the LLS results. This finding on the
Non-Linear Noise Contributions in Highly Dispersive Optical Transmission Systems
NASA Astrophysics Data System (ADS)
Matera, Francesco
2016-01-01
This article reports an analytical investigation, confirmed by numerical simulations, about the non-linear noise contribution in single-channel systems adopting generic modulation-detection formats in long links with both managed and unmanaged dispersion compensation and its impact in system performance. This noise contribution is expressed in terms of a pulse non-linear interaction length and permits a simple calculation of the Q-factor. Results point out the dependence of this non-linear noise on the number of amplifiers spans, N, according to the adopted chromatic dispersion compensation scheme, the modulation-detection format, and the signal baud rate. It is also shown how the effects of polarization multiplexing can be taken into account and how this single-channel non-linear noise contribution can be used in a wavelength-division multiplexing (WDM) environment.
Nonlinear coupling of left and right handed circularly polarized dispersive Alfvén wave
Sharma, R. P. Sharma, Swati Gaur, Nidhi
2014-07-15
The nonlinear phenomena are of prominent interests in understanding the particle acceleration and transportation in the interplanetary space. The ponderomotive nonlinearity causing the filamentation of the parallel propagating circularly polarized dispersive Alfvén wave having a finite frequency may be one of the mechanisms that contribute to the heating of the plasmas. The contribution will be different of the left (L) handed mode, the right (R) handed mode, and the mix mode. The contribution also depends upon the finite frequency of the circularly polarized waves. In the present paper, we have investigated the effect of the nonlinear coupling of the L and R circularly polarized dispersive Alfvén wave on the localized structures formation and the respective power spectra. The dynamical equations are derived in the presence of the ponderomotive nonlinearity of the L and R pumps and then studied semi-analytically as well as numerically. The ponderomotive nonlinearity accounts for the nonlinear coupling between both the modes. In the presence of the adiabatic response of the density fluctuations, the nonlinear dynamical equations satisfy the modified nonlinear Schrödinger equation. The equations thus obtained are solved in solar wind regime to study the coupling effect on localization and the power spectra. The effect of coupling is also studied on Faraday rotation and ellipticity of the wave caused due to the difference in the localization of the left and the right modes with the distance of propagation.
One-dimensional dispersion phenomena in terms of fractional media
NASA Astrophysics Data System (ADS)
Sumelka, W.; Zaera, R.; Fernández-Sáez, J.
2016-09-01
It is well know that structured solids present dispersive behaviour which cannot be captured by the classical continuum mechanics theories. A canonical problem in which this can be seen is the wave propagation in the Born-Von Karman lattice. In this paper the dispersive effects in a 1D structured solid is analysed using the Fractional Continuum Mechanics (FCM) approach previously proposed by Sumelka (2013). The formulation uses the Riesz-Caputo (RC) fractional derivative and introduces two phenomenological/material parameters: 1) the size of non-local surrounding lf, which plays the role of the lattice spacing; and 2) the order of fractional continua α, which can be devised as a fitting parameter. The results obtained with this approach have been compared with the reference dispersion curve of Born-Von Karman lattice, and the capability of the fractional model to capture the size effects present in the dynamic behaviour of discrete systems has been proved.
Dispersive and dissipative nonlinear structures in degenerate Fermi-Dirac Pauli quantum plasma
NASA Astrophysics Data System (ADS)
Sahu, Biswajit; Sinha, Anjana; Roychoudhury, Rajkumar
2016-09-01
We study the interplay between dispersion due to the electron degeneracy parameter and dissipation caused by plasma resistivity, in degenerate Fermi-Dirac Pauli quantum plasma. Considering relativistic degeneracy pressure for electrons, we investigate both arbitrary and small amplitude nonlinear structures. The corresponding trajectories are also plotted in the phase plane. The linear analysis for the dispersion relation yields interesting features. The present work is anticipated to be of physical relevance in the study of compact magnetized astrophysical objects like white dwarfs.
2015-01-01
In vitro toxicity assessment of engineered nanomaterials (ENM), the most common testing platform for ENM, requires prior ENM dispersion, stabilization, and characterization in cell culture media. Dispersion inefficiencies and active aggregation of particles often result in polydisperse and multimodal particle size distributions. Accurate characterization of important properties of such polydisperse distributions (size distribution, effective density, charge, mobility, aggregation kinetics, etc.) is critical for understanding differences in the effective dose delivered to cells as a function of time and dispersion conditions, as well as for nano–bio interactions. Here we have investigated the utility of tunable nanopore resistive pulse sensing (TRPS) technology for characterization of four industry relevant ENMs (oxidized single-walled carbon nanohorns, carbon black, cerium oxide and nickel nanoparticles) in cell culture media containing serum. Harvard dispersion and dosimetry platform was used for preparing ENM dispersions and estimating delivered dose to cells based on dispersion characterization input from dynamic light scattering (DLS) and TRPS. The slopes of cell death vs administered and delivered ENM dose were then derived and compared. We investigated the impact of serum protein content, ENM concentration, and cell medium on the size distributions. The TRPS technology offers higher resolution and sensitivity compared to DLS and unique insights into ENM size distribution and concentration, as well as particle behavior and morphology in complex media. The in vitro dose–response slopes changed significantly for certain nanomaterials when delivered dose to cells was taken into consideration, highlighting the importance of accurate dispersion and dosimetry in in vitro nanotoxicology. PMID:25093451
Tuning the nonlinear response of (6,5)-enriched single-wall carbon nanotubes dispersions
NASA Astrophysics Data System (ADS)
Aréstegui, O. S.; Silva, E. C. O.; Baggio, A. L.; Gontijo, R. N.; Hickmann, J. M.; Fantini, C.; Alencar, M. A. R. C.; Fonseca, E. J. S.
2017-04-01
Ultrafast nonlinear optical properties of (6,5)-enriched single-wall carbon nanotubes (SWCNTs) dispersions are investigated using the thermally managed Z-scan technique. As the (6,5) SWCNTs presented a strong resonance in the range of 895-1048 nm, the nonlinear refractive index (n2) and the absorption coefficients (β) measurements were performed tuning the laser exactly around absorption peak of the (6,5) SWCNTs. It is observed that the nonlinear response is very sensitive to the wavelength and the spectral behavior of n2 is strongly correlated to the tubes one-photon absorption band, presenting also a peak when the laser photon energy is near the tube resonance energy. This result suggests that a suitable selection of nanotubes types may provide optimized nonlinear optical responses in distinct regions of the electromagnetic spectrum. Analysis of the figures of merit indicated that this material is promising for ultrafast nonlinear optical applications under near infrared excitation.
Asymptotic solutions of weakly nonlinear, dispersive wave-propagation problems by Fourier analysis
Srinivasan, R.
1989-01-01
A perturbation method based on Fourier analysis and multiple scales is introduced for solving weakly nonlinear, dispersive wave propagation problems with Fourier transformable initial conditions. Asymptotic solutions are derived for the weakly nonlinear cubic Schroedinger (NLS) equation with variable coefficients and the weakly nonlinear Kortewegde-Vries (KdV) equation; the results for the NLS equation are verified by comparison with numerical solutions. In the special case of constant coefficients, the asymptotic solution for the weakly nonlinear NLS equation agrees to leading order with previously derived results in the literature; in general, this is not true to higher orders. Therefore previous asymptotic results for the strongly nonlinear Schroedinger equation can be valid only for restricted initial conditions. Similar conclusions apply to the KdV equation.
Chakrabarti, Nikhil; Maity, Chandan; Schamel, Hans
2011-04-08
Compressional waves in a magnetized plasma of arbitrary resistivity are treated with the lagrangian fluid approach. An exact nonlinear solution with a nontrivial space and time dependence is obtained with boundary conditions as in Harris' current sheet. The solution shows competition among hydrodynamic convection, magnetic field diffusion, and dispersion. This results in a collapse of density and the magnetic field in the absence of dispersion. The dispersion effects arrest the collapse of density but not of the magnetic field. A possible application is in the early stage of magnetic star formation.
Nonlinear Behavior Of Saturated Porous Media Under External Impact
NASA Astrophysics Data System (ADS)
Perepechko, Y.
2005-12-01
This paper deals with nonlinear behavior of liquid saturated porous media in gravity filed under external impact. The continuum is assumed to be a two-velocity medium; it consists of a deformable porous matrix (with Maxwell's reology) and a Newtonian liquid that saturates this matrix. The energy dissipation in this model takes place due the interface friction between the solid matrix and saturating liquid, and also through relaxation of inelastic shear stress in the porous matrix. The elaborated nonisothermal mathematical model for this kind of medium is a thermodynamically consistent and closed model. Godunov's explicit difference scheme was used for computer simulation; the method implies numerical simulation for discontinuity decay in flux calculations. As an illustrative example, we consider the formation of dissipation structures in a plain layer of that medium after pulse or periodic impact on the background of liquid filtration through the porous matrix. At the process beginning, one can observe elastic behavior of the porous matrix. Deformation spreading through the saturated porous matrix occurs almost without distortions and produces a channel-shaped zone of stretching with a high porosity. Later on, dissipation processes and reology properties of porous medium causes the diffusion of this channel. We also observe a correlation between the liquid distribution (porosity for the solid matrix) and dilatancy fields; this allows us to restore the dilatancy field from the measured fluid saturation of the medium. This work was supported by the RFBR (Grant No. 04-05-64107), the Presidium of SB RAS (Grant 106), the President's Grants (NSh-2118.2003.5, NSh-1573.2003.5).
Microscopic Models for Electromagnetic Wave Propagation in Highly Dispersive Media
1990-06-18
rotations, the effects of pressure and temperature and to show the classes of density fluctuations in I which give spatial dispersion, ie, the k- dependance ...complex plane the response e (co, Q) lives on some Riemann surface which is determined by the k- dependance . 2. Talks and Publications Three talks were...sources of 1- dependance (k- dependance in Fourier transform variables) have been identified. One is bubbles or cavitation which scatter the propagating
Charalampidis, E G; Kevrekidis, P G; Frantzeskakis, D J; Malomed, B A
2016-08-01
We consider a two-component, two-dimensional nonlinear Schrödinger system with unequal dispersion coefficients and self-defocusing nonlinearities, chiefly with equal strengths of the self- and cross-interactions. In this setting, a natural waveform with a nonvanishing background in one component is a vortex, which induces an effective potential well in the second component, via the nonlinear coupling of the two components. We show that the potential well may support not only the fundamental bound state, but also multiring excited radial state complexes for suitable ranges of values of the dispersion coefficient of the second component. We systematically explore the existence, stability, and nonlinear dynamics of these states. The complexes involving the excited radial states are weakly unstable, with a growth rate depending on the dispersion of the second component. Their evolution leads to transformation of the multiring complexes into stable vortex-bright solitons ones with the fundamental state in the second component. The excited states may be stabilized by a harmonic-oscillator trapping potential, as well as by unequal strengths of the self- and cross-repulsive nonlinearities.
Nonlinear effect of dispersal rate on spatial synchrony of predator-prey cycles.
Fox, Jeremy W; Legault, Geoffrey; Legault, Geoff; Vasseur, David A; Einarson, Jodie A
2013-01-01
Spatially-separated populations often exhibit positively correlated fluctuations in abundance and other population variables, a phenomenon known as spatial synchrony. Generation and maintenance of synchrony requires forces that rapidly restore synchrony in the face of desynchronizing forces such as demographic and environmental stochasticity. One such force is dispersal, which couples local populations together, thereby synchronizing them. Theory predicts that average spatial synchrony can be a nonlinear function of dispersal rate, but the form of the dispersal rate-synchrony relationship has never been quantified for any system. Theory also predicts that in the presence of demographic and environmental stochasticity, realized levels of synchrony can exhibit high variability around the average, so that ecologically-identical metapopulations might exhibit very different levels of synchrony. We quantified the dispersal rate-synchrony relationship using a model system of protist predator-prey cycles in pairs of laboratory microcosms linked by different rates of dispersal. Paired predator-prey cycles initially were anti-synchronous, and were subject to demographic stochasticity and spatially-uncorrelated temperature fluctuations, challenging the ability of dispersal to rapidly synchronize them. Mean synchrony of prey cycles was a nonlinear, saturating function of dispersal rate. Even extremely low rates of dispersal (<0.4% per prey generation) were capable of rapidly bringing initially anti-synchronous cycles into synchrony. Consistent with theory, ecologically-identical replicates exhibited very different levels of prey synchrony, especially at low to intermediate dispersal rates. Our results suggest that even the very low rates of dispersal observed in many natural systems are sufficient to generate and maintain synchrony of cyclic population dynamics, at least when environments are not too spatially heterogeneous.
Coherent propagation of waves in dilute random media with weak nonlinearity
Wellens, Thomas; Gremaud, Benoit
2009-12-15
We develop a diagrammatic theory for transport of waves in dilute disordered media with weak nonlinearity. We first represent the solution of the nonlinear wave equation as a nonlinear Born series. From this, we construct nonlinear ladder and crossed diagrams for the average wave intensity. Then, we sum up the diagrammatic series completely, i.e., nonperturbatively in the strength of the nonlinearity, and thereby obtain integral equations describing both nonlinear diffusive transport and coherent backscattering of the average intensity. As main result, we find that the nonlinearity significantly influences the magnitude of the coherent backscattering effect. Depending on the type of nonlinearity, coherent backscattering is either enhanced or suppressed, as compared to the linear case.
NASA Astrophysics Data System (ADS)
Yu, Changyuan
Chromatic dispersion, polarization mode dispersion (PMD) and nonlinear effects are important issues on the physical layer of high-speed reconfigurable WDM optical fiber communication systems. For beyond 10 Gbit/s optical fiber transmission system, it is essential that chromatic dispersion and PMD be well managed by dispersion monitoring and compensation. One the other hand, dispersive and nonlinear effects in optical fiber systems can also be beneficial and has applications on pulse management, all-optical signal processing and network function, which will be essential for high bite-rate optical networks and replacing the expensive optical-electrical-optical (O/E/O) conversion. In this Ph.D. dissertation, we present a detailed research on dispersive and nonlinear effects in high-speed optical communication systems. We have demonstrated: (i) A novel technique for optically compensating the PMD-induced RF power fading that occurs in single-sideband (SSB) subcarrier-multiplexed systems. By aligning the polarization states of the optical carrier and the SSB, RF power fading due to all orders of PMD can be completely compensated. (ii) Chromatic-dispersion-insensitive PMD monitoring by using a narrowband FBG notch filter to recover the RF clock power for 10Gb/s NRZ data, and apply it as a control signal for PMD compensation. (iii) Chirp-free high-speed optical pulse generation with a repetition rate of 160 GHz (which is four times of the frequency of the electrical clock) using a phase modulator and polarization maintaining (PM) fiber. (iv) Polarization-insensitive all-optical wavelength conversion based on four-wave mixing in dispersion-shifted fiber (DSF) with a fiber Bragg grating and a Faraday rotator mirror. (v) Width-tunable optical RZ pulse train generation based on four-wave mixing in highly-nonlinear fiber. By electrically tuning the delay between two pump pulse trains, the pulse-width of a generated pulse train is continuously tuned. (vi) A high-speed all
Noncontact thermoacoustic detection of targets embedded in dispersive media
NASA Astrophysics Data System (ADS)
Boyle, Kevin C.; Nan, Hao; Khuri-Yakub, Butrus T.; Arbabian, Amin
2016-10-01
A microwave-induced thermoacoustic detection system for embedded targets in lossy media is presented. The system achieves reliable detection of 5 cm × 5 cm × 2 cm targets embedded in a large Agarose sample at a 20 cm acoustic standoff. Repeated measurements across different target and sample configurations confirm the system's ability to distinguish between a target signal and a baseline control signal generated by the package without embedded targets. Post-processing techniques including filtering and baseline signal characterization further improve detection performance.
RADIONUCLIDE DISPERSION RATES BY AEOLIAN, FLUVIAL, AND POROUS MEDIA TRANSPORT
J. Walton; P. Goodell; C. Brashears; D. French; A. Kelts
2005-07-11
Radionuclide transport was measured from high grade uranium ore boulders near the Nopal I Site, Chihuahua, Mexico. High grade uranium ore boulders were left behind after removal of a uranium ore stockpile at the Prior High Grade Stockpile (PHGS). During the 25 years when the boulder was present, radionuclides were released and transported by sheetflow during precipitation events, wind blown resuspension, and infiltration into the unsaturated zone. In this study, one of the boulders was removed, followed by grid sampling of the surrounding area. Measured gamma radiation levels in three dimensions were used to derive separate dispersion rates by the three transport mechanisms.
Zhang, Ya-Ni; Ren, Li-Yong; Gong, Yong-Kang; Li, Xiao-Hui; Wang, Lei-Ran; Sun, Chuan-Dong
2010-06-01
We have proposed a novel type of photonic crystal fiber (PCF) with low dispersion and high nonlinearity for four-wave mixing. This type of fiber is composed of a solid silica core and a cladding with a squeezed hexagonal lattice elliptical airhole along the fiber length. Its dispersion and nonlinearity coefficient are investigated simultaneously by using the full vectorial finite element method. Numerical results show that the proposed highly nonlinear low-dispersion fiber has a total dispersion as low as +/-2.5 ps nm(-1) km(-1) over an ultrabroad wavelength range from 1.43 to 1.8 microm, and the corresponding nonlinearity coefficient and birefringence are about 150 W(-1) km(-1) and 2.5x10(-3) at 1.55 microm, respectively. The proposed PCF with low ultraflattened dispersion, high nonlinearity, and high birefringence can have important application in four-wave mixing.
Long time behavior of some nonlinear dispersive equations
NASA Astrophysics Data System (ADS)
Deng, Yu
This thesis is divided into two parts. The first part consists of Chapters 2 and 3, in which we study the random data theory for the Benjamin-Ono equation on the periodic domain. In Chapter 2 we shall prove the invariance of the Gibbs measure associated to the Hamiltonian E1 of the equation, which was constructed in [49]. Despite the fact that the support of the Gibbs measure contains very rough functions that are not even in L2, we have successfully established the global dynamics by combining probabilistic arguments, Xs,b type estimates and the hidden structure of the equation. In Chapter 3, which is joint work with N. Tzvetkov and N. Visciglia, we extend this invariance result to the weighted Gaussian measures associated with the higher order conservation laws E2 and E3, thus completing the collection of invariant measures (except for the white noise), given the result of [51]. The second part concerns the global behavior of solutions to quasilinear dispersive systems in Rd with suitably small data. In Chapter 4 we shall prove global existence and scattering for small data solutions to systems of quasilinear Klein-Gordon equations with arbitrary speed and mass in 3 D, which extends the results in [20] and [32]. Moreover, the methods introduced here are quite general, and can be applied in a number of different situations. In Chapter 5, we briefly discuss how these methods, together with other techniques, are used in recent joint work with A. Ionescu and B. Pausader to study the 2D Euler-Maxwell system.
Real-space Hopfield diagonalization of inhomogeneous dispersive media
NASA Astrophysics Data System (ADS)
Gubbin, Christopher R.; Maier, Stefan A.; De Liberato, Simone
2016-11-01
We introduce a real-space technique able to extend the standard Hopfield approach commonly used in quantum polaritonics to the case of inhomogeneous lossless materials interacting with the electromagnetic field. We derive the creation and annihilation polaritonic operators for the system normal modes as linear, space-dependent superpositions of the microscopic light and matter fields. We prove their completeness and invert the Hopfield transformation expressing the microscopic fields as functions of the polaritonic operators. As an example, we apply our approach to the case of a planar interface between vacuum and a polar dielectric, showing how we can consistently treat both propagative and surface modes, and express their nonlinear interactions, arising from phonon anharmonicity, as polaritonic scattering terms. We also show that our theory, including the proof of completeness, can be naturally extended to the case of dissipative materials.
NASA Astrophysics Data System (ADS)
Purvinis, Georgeanne M.
Organic crystals and certain polymer films, such as ionically self-assembled monolayer (ISAM) films, are lossy and anisotropic. These materials may have a large chi(2) nonlinear response, and thus are conceivably capable of efficient second order processes. Anomalous dispersion phase-matched second harmonic generation (ADPM-SHG) in organic media is a second order wavelength conversion process that phase matches like-order modes in a waveguide (ex: TM0o → TM02o ), thus maximizing the overlap integral. Demonstration of ADPM-SHG in economical and easily fabricated polymer ISAM film is the ultimate experimental goal of this research. In order to achieve demonstration of ADPM-SHG in an ISAM film, both theoretical and material research contributions are accomplished. The predominant analysis approaches in literature are based on the finite element method, which is approximate and computationally intensive, thus prohibiting arbitrary crystallographic media orientations in devices. This restricted treatment in the literature may be insufficient with ISAM films, as SHG occurs in a spectral region of residual absorption, the film is uniaxial, and the optic axis may not be aligned the waveguide coordinate system. Thus, the theory objectives of the dissertation research are: (1) develop an exact solution for finding the polarization states in lossy anisotropic media using a new complex orthogonal similarity transformation with the complex symmetric impermeability tensor, (2) develop a rigorous transverse resonance analysis to find the eigenmodes of general lossy anisotropic planar waveguides with arbitrary principal axes orientations, and (3) integrate the results of steps 1--2 to determine the conversion efficiency of an ISAM planar waveguide using ADPM-SHG, thus illustrating the importance of the dissertation research by highlighting the errors resulting in algorithms published in other works. Experimentally, the dissertation focuses on designing anionic and cationic
Analytical solution for the advection-dispersion transport equation in layered media
Technology Transfer Automated Retrieval System (TEKTRAN)
The advection-dispersion transport equation with first-order decay was solved analytically for multi-layered media using the classic integral transform technique (CITT). The solution procedure used an associated non-self-adjoint advection-diffusion eigenvalue problem that had the same form and coef...
Construction of the wave operator for non-linear dispersive equations
NASA Astrophysics Data System (ADS)
Tsuruta, Kai Erik
In this thesis, we will study non-linear dispersive equations. The primary focus will be on the construction of the positive-time wave operator for such equations. The positive-time wave operator problem arises in the study of the asymptotics of a partial differential equation. It is a map from a space of initial data X into itself, and is loosely defined as follows: Suppose that for a solution ψlin to the dispersive equation with no non-linearity and initial data ψ +, there exists a unique solution ψ to the non-linear equation with initial data ψ0 such that ψ behaves as ψ lin as t → infinity. Then the wave operator is the map W+ that takes ψ + to ψ0. By its definition, W+ is injective. An important additional question is whether or not the map is also surjective. If so, then every non-linear solution emanating from X behaves, in some sense, linearly as it evolves (this is known as asymptotic completeness). Thus, there is some justification for treating these solutions as their much simpler linear counterparts. The main results presented in this thesis revolve around the construction of the wave operator(s) at critical non-linearities. We will study the "semi-relativistic" Schrodinger equation as well as the Klein-Gordon-Schrodinger system on R2 . In both cases, we will impose fairly general quadratic non-linearities for which conservation laws cannot be relied upon. These non-linearities fall below the scaling required to employ such tools as the Strichartz estimates. We instead adapt the "first iteration method" of Jang, Li, and Zhang to our setting which depends crucially on the critical decay of the non-linear interaction of the linear evolution. To see the critical decay in our problem, careful analysis is needed to treat the regime where one has spatial and/or time resonance.
Light propagation in media with a highly nonlinear response: An analytical study
NASA Astrophysics Data System (ADS)
Tatarinova, Larisa L.; Garcia, Martin E.
2011-04-01
The problem of light propagation in highly nonlinear media is studied with the help of a recently introduced systematic approach to the analytical solution of equations of nonlinear optics [L.L. Tatarinova, M.E. Garcia, Exact solutions of the eikonal equations describing self-focusing in highly nonlinear geometrical optics, Phys. Rev. A 78 (2008) 021806(R)(1-4)]. Numerous particular cases of media exhibiting high-order nonlinear refractive indices are considered. We obtain analytical expressions for determining the self-focusing position and a new exact expression for calculating the filament intensity. The constructed solutions allowed us to revise a so-called self-focusing scaling law, i.e., the functional dependence of the self-focusing position on the initial light peak intensity. It was demonstrated that this dependence is governed by the form of the nonlinear refractive index and not by the laser beam shape at the boundary.
NASA Astrophysics Data System (ADS)
Wu, Yan; Xie, Qiongtao; Zhong, Honghua; Wen, Linghua; Hai, Wenhua
2013-05-01
We investigate algebraic bright and vortex solitons in self-defocusing (SDF) media with a type of spatially inhomogeneous nonlinearity. For a specific choice of the nonlinearity parameters, certain exact analytical solutions for algebraic bright and vortex solitons have been constructed. By applying the linear stability analysis, the stability regions of these algebraic solitons are obtained numerically. In addition, we show analytically that a homogeneous SDF nonlinearity superposed by a localized self-focusing nonlinearity can support exact algebraic bright solitons under certain conditions.
Strongly nonlinear evolution of low-frequency wave packets in a dispersive plasma
NASA Technical Reports Server (NTRS)
Vasquez, Bernard J.
1993-01-01
The evolution of strongly nonlinear, strongly modulated wave packets is investigated in a dispersive plasma using a hybrid numerical code. These wave packets have amplitudes exceeding the strength of the external magnetic field, along which they propagate. Alfven (left helicity) wave packets show strong steepening for p < 1, while fast (fight heIicity) wave packets hardly steepen for any beta. Substantial regions of opposite helicity form on the leading side of steepened Alfven wave packets. This behavior differs qualitatively from that exhibited by the solutions to the derivative nonlinear Schrodinger (DNLS) equation.
On a hierarchy of nonlinearly dispersive generalized Korteweg - de Vries evolution equations
Christov, Ivan C.
2015-08-20
We propose a hierarchy of nonlinearly dispersive generalized Korteweg–de Vries (KdV) evolution equations based on a modification of the Lagrangian density whose induced action functional the KdV equation extremizes. Two recent nonlinear evolution equations describing wave propagation in certain generalized continua with an inherent material length scale are members of the proposed hierarchy. Like KdV, the equations from the proposed hierarchy possess Hamiltonian structure. Unlike KdV, the solutions to these equations can be compact (i.e., they vanish outside of some open interval) and, in addition, peaked. Implicit solutions for these peaked, compact traveling waves (“peakompactons”) are presented.
Conditioning-induced elastic nonlinearity in hysteretic media
NASA Astrophysics Data System (ADS)
Gliozzi, A. S.; Scalerandi, M.; Antonaci, P.; Bruno, C. L. E.
2010-08-01
The definition and measurement of the nonlinear elastic properties of a sample is of great importance for a large number of applications, including characterization of material performances and damage detection. However, such measurements are often influenced by spurious effects due to a combination of nonlinearity and nonequilibrium phenomena. We will present experimental data to show how nonlinearity due to small cracks in concrete samples increases as a consequence of conditioning, i.e., after having perturbed them with a constant amplitude excitation. In addition, our experimental data highlight "memory effects," i.e., they show that when the excitation is removed, the elastic modulus does not return instantaneously to the initial value.
Measurements of nonlinear refractive index in scattering media
Samineni, Prathyush; Perret, Zachary; Warren, Warren S.; Fischer, Martin C.
2012-01-01
We have recently developed a spectral re-shaping technique to simultaneously measure nonlinear refractive index and nonlinear absorption. In this technique, the information about the nonlinearities is encoded in the frequency domain, rather than in the spatial domain as in the conventional Z-scan method. Here we show that frequency encoding is much more robust with respect to scattering. We compare spectral re-shaping and Z-scan measurements in a highly scattering environment and show that reliable spectral re-shaping measurements can be performed even in a regime that precludes standard Z-scans. PMID:20588401
NASA Astrophysics Data System (ADS)
Cortinez, J. M.; Valocchi, A. J.; Herrera, P. A.
2013-12-01
Because of the finite size of numerical grids, it is very difficult to correctly account for processes that occur at different spatial scales to accurately simulate the migration of conservative and reactive compounds dissolved in groundwater. In one hand, transport processes in heterogeneous porous media are controlled by local-scale dispersion associated to transport processes at the pore-scale. On the other hand, variations of velocity at the continuum- or Darcy-scale produce spreading of the contaminant plume, which is referred to as macro-dispersion. Furthermore, under some conditions both effects interact, so that spreading may enhance the action of local-scale dispersion resulting in higher mixing, dilution and reaction rates. Traditionally, transport processes at different spatial scales have been included in numerical simulations by using a single dispersion coefficient. This approach implicitly assumes that the separate effects of local-dispersion and macro-dispersion can be added and represented by a unique effective dispersion coefficient. Moreover, the selection of the effective dispersion coefficient for numerical simulations usually do not consider the filtering effect of the grid size over the small-scale flow features. We have developed a multi-scale Lagragian numerical method that allows using two different dispersion coefficients to represent local- and macro-scale dispersion. This technique considers fluid particles that carry solute mass and whose locations evolve according to a deterministic component given by the grid-scale velocity and a stochastic component that corresponds to a block-effective macro-dispersion coefficient. Mass transfer between particles due to local-scale dispersion is approximated by a meshless method. We use our model to test under which transport conditions the combined effect of local- and macro-dispersion are additive and can be represented by a single effective dispersion coefficient. We also demonstrate that for
Xia, Cen; Liu, Xiang; Chandrasekhar, S; Fontaine, N K; Zhu, Likai; Li, G
2014-03-10
We demonstrate nonlinearity compensation of 37.5-GHz-spaced 128-Gb/s PDM-QPSK signals using dispersion-folded digital-backward-propagation and a spectrally-sliced receiver that simultaneously receives three WDM signals, showing mitigation of intra-channel and inter-channel nonlinear effects in a 2560-km dispersion-managed TWRS-fiber link. Intra-channel and adjacent inter-channel nonlinear compensation gains when WDM channels are fully populated in the C-band are estimated based on the GN-model.
Rius, Manuel; Bolea, Mario; Mora, José; Ortega, Beatriz; Capmany, José
2015-05-18
We experimentally demonstrate, for the first time, a chirped microwave pulses generator based on the processing of an incoherent optical signal by means of a nonlinear dispersive element. Different capabilities have been demonstrated such as the control of the time-bandwidth product and the frequency tuning increasing the flexibility of the generated waveform compared to coherent techniques. Moreover, the use of differential detection improves considerably the limitation over the signal-to-noise ratio related to incoherent processing.
Modeling Solution of Nonlinear Dispersive Partial Differential Equations using the Marker Method
Jerome L.V. Lewandowski
2005-01-25
A new method for the solution of nonlinear dispersive partial differential equations is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details.
Low-Dispersion Scheme for Nonlinear Acoustic Waves in Nonuniform Flow
NASA Technical Reports Server (NTRS)
Baysal, Oktay; Kaushik, Dinesh K.; Idres, Moumen
1997-01-01
The linear dispersion-relation-preserving scheme and its boundary conditions have been extended to the nonlinear Euler equations. This allowed computing, a nonuniform flowfield and a nonlinear acoustic wave propagation in such a medium, by the same scheme. By casting all the equations, boundary conditions, and the solution scheme in generalized curvilinear coordinates, the solutions were made possible for non-Cartesian domains and, for the better deployment of the grid points, nonuniform grid step sizes could be used. It has been tested for a number of simple initial-value and periodic-source problems. A simple demonstration of the difference between a linear and nonlinear propagation was conducted. The wall boundary condition, derived from the momentum equations and implemented through a pressure at a ghost point, and the radiation boundary condition, derived from the asymptotic solution to the Euler equations, have proven to be effective for the nonlinear equations and nonuniform flows. The nonreflective characteristic boundary conditions also have shown success but limited to the nonlinear waves in no mean flow, and failed for nonlinear waves in nonuniform flow.
Solitons supported by localized nonlinearities in periodic media
Dror, Nir; Malomed, Boris A.
2011-03-15
Nonlinear periodic systems, such as photonic crystals and Bose-Einstein condensates (BEC's) loaded into optical lattices, are often described by the nonlinear Schroedinger or Gross-Pitaevskii equation with a sinusoidal potential. Here, we consider a model based on such a periodic potential, with the nonlinearity (attractive or repulsive) concentrated either at a single point or at a symmetric set of two points, which are represented, respectively, by a single {delta} function or a combination of two {delta} functions. With the attractive or repulsive sign of the nonlinearity, this model gives rise to ordinary solitons or gap solitons (GS's), which reside, respectively, in the semi-infinite or finite gaps of the system's linear spectrum, being pinned to the {delta} functions. Physical realizations of these systems are possible in optics and BEC's, using diverse variants of the nonlinearity management. First, we demonstrate that the single {delta} function multiplying the nonlinear term supports families of stableregular solitons in the self-attractive case, while a family of solitons supported by the attractive {delta} function in the absence of the periodic potential is completely unstable. In addition, we show that the {delta} function can support stable GS's in the first finite band gap in both the self-attractive and repulsive models. The stability analysis for the GS's in the second finite band gap is reported too, for both signs of the nonlinearity. Alongside the numerical analysis, analytical approximations are developed for the solitons in the semi-infinite and first two finite gaps, with the single {delta} function positioned at a minimum or maximum of the periodic potential. In the model with the symmetric set of two {delta} functions, we study the effect of the spontaneous symmetry breaking of the pinned solitons. Two configurations are considered, with the {delta} functions set symmetrically with respect to the minimum or maximum of the underlying
On the interaction between gravity forces and hydrodynamic dispersion in heterogeneous porous media
NASA Astrophysics Data System (ADS)
Schotting, R.; Landman, A.; Egorov, A.; Demidov, D.
2005-12-01
In a series of independently conducted vertical displacement experiments in porous columns (The Netherlands, Germany and Australia), a peculiar phenomenon has been observed. If the resident fluid, i.e. fresh water is displaced by a saltwater solution with a higher density, the effective dispersion coefficient deacreases significantly as compared to the tracer case, where both the resident and invading fluids have (almost) identical densities. The higher the density contrast between the two fluids, the more the dispersion coefficient decreases as compared to the classical Fickian xase. This phenomenon cannot be theoretically described and modelled using classical linear Fick's Law for the dispersive mass flux. Several attempts were made to formulate adequate new theories to incorporate these density effects. Hassanizadeh extended Fick's Law with a second-order nonlinear term, including a new dispersion parameter. Although very good agreement with the aforemnetioned experiments could be achieved, this theory is not able to explain and include the underlying physics of this phenomenon. The decrease of the dispersion coefficient is the result of the interaction between gravity forces and density variations at the displacement front, due to local small-scale heterogeneities. With this phenomenon in mind, several alternative nonlinear theories have been proposed. We mention Welty and Gelhar (stochastic approach), Egorov and Demidov (homogenisation at the Darcy- scale), Demidov (homogenisation at the pore-scale). All theories have in common that the resulting nonlinear dispersion coefficient is a function of the density gradient and not of the absolute density. All of the aforementioned theories have been tested against carefully conducted massive numerical experiments, and if possible, against laboratory experiments. The results of the comparisons will be presented, and future research directions will be indicated.
Pseudospectral modeling and dispersion analysis of Rayleigh waves in viscoelastic media
Zhang, K.; Luo, Y.; Xia, J.; Chen, C.
2011-01-01
Multichannel Analysis of Surface Waves (MASW) is one of the most widely used techniques in environmental and engineering geophysics to determine shear-wave velocities and dynamic properties, which is based on the elastic layered system theory. Wave propagation in the Earth, however, has been recognized as viscoelastic and the propagation of Rayleigh waves presents substantial differences in viscoelastic media as compared with elastic media. Therefore, it is necessary to carry out numerical simulation and dispersion analysis of Rayleigh waves in viscoelastic media to better understand Rayleigh-wave behaviors in the real world. We apply a pseudospectral method to the calculation of the spatial derivatives using a Chebyshev difference operator in the vertical direction and a Fourier difference operator in the horizontal direction based on the velocity-stress elastodynamic equations and relations of linear viscoelastic solids. This approach stretches the spatial discrete grid to have a minimum grid size near the free surface so that high accuracy and resolution are achieved at the free surface, which allows an effective incorporation of the free surface boundary conditions since the Chebyshev method is nonperiodic. We first use an elastic homogeneous half-space model to demonstrate the accuracy of the pseudospectral method comparing with the analytical solution, and verify the correctness of the numerical modeling results for a viscoelastic half-space comparing the phase velocities of Rayleigh wave between the theoretical values and the dispersive image generated by high-resolution linear Radon transform. We then simulate three types of two-layer models to analyze dispersive-energy characteristics for near-surface applications. Results demonstrate that the phase velocity of Rayleigh waves in viscoelastic media is relatively higher than in elastic media and the fundamental mode increases by 10-16% when the frequency is above 10. Hz due to the velocity dispersion of P
Zibar, Darko; Winther, Ole; Franceschi, Niccolo; Borkowski, Robert; Caballero, Antonio; Arlunno, Valeria; Schmidt, Mikkel N; Gonzales, Neil Guerrero; Mao, Bangning; Ye, Yabin; Larsen, Knud J; Monroy, Idelfonso Tafur
2012-12-10
In this paper, we show numerically and experimentally that expectation maximization (EM) algorithm is a powerful tool in combating system impairments such as fibre nonlinearities, inphase and quadrature (I/Q) modulator imperfections and laser linewidth. The EM algorithm is an iterative algorithm that can be used to compensate for the impairments which have an imprint on a signal constellation, i.e. rotation and distortion of the constellation points. The EM is especially effective for combating non-linear phase noise (NLPN). It is because NLPN severely distorts the signal constellation and this can be tracked by the EM. The gain in the nonlinear system tolerance for the system under consideration is shown to be dependent on the transmission scenario. We show experimentally that for a dispersion managed polarization multiplexed 16-QAM system at 14 Gbaud a gain in the nonlinear system tolerance of up to 3 dB can be obtained. For, a dispersion unmanaged system this gain reduces to 0.5 dB.
Nonlinear interaction of long dispersive Kelvin waves in deep natural basins
NASA Astrophysics Data System (ADS)
Budnev, Nikolay M.; Lovtsov, Sergey V.; Portyanskaya, Inna A.; Rastegin, Alexey E.; Rubtsov, Valeriy Yu.
2010-05-01
Nonlinear phenomena are of great importance for complete understanding of dynamical processes in fluids. However, direct studies of hydrodynamic equations seem to be very hard just due to nonlinear terms. Many approaches to nonlinear dispersive waves are related to the technique of multiple scales. It is one of most seminal ways to obtain those models that combine possibility of analytic investigation with actual effects of nonlinearity. Consideration of long Kelvin waves within the linear theory is well known issue of geophysical hydrodynamics. An influence of boundary effects leads to dispersion of Kelvin waves. At the same time, mutual balance between dispersive and nonlinear terms in motion equations can provide a formation of stable localized structures so-called solitary waves. When stratification is essential, different vertical modes of oscillation are typically excited. Corresponding analysis of vertical structure for solitary Rossby waves has been developed in many works, mainly due to Redekopp. But proper treatment of large-scale Kelvin waves seems to be not indicated in the literature. The principal aim of our work is to fill this lacuna. The present work has been partially inspired by temperature monitoring data obtained in south area of Lake Baikal. Under conditions of winter stratification, specific displacements of fragments of temperature profile from up to down were observed within upper layer. It is valuable that a shape of moving fragment remains almost undistorted. After ending this temperature decreasing, the temperature profile was rectified to initial shape. In all the years of observations, vertical displacements reach several tens of meters with duration of several days. These phenomena were interpreted as manifestation of long dispersive Kelvin waves, especially due to direction of propagation along the coastline. Regularly observed displacements from up to down may be evidences for nonlinear character of wave dynamics. Indeed, internal
Thomsen, Jon Juel
2016-01-01
The paper deals with analytically predicting the effects of weak nonlinearity on the dispersion relation and frequency band-gaps of a periodic Bernoulli–Euler beam performing bending oscillations. Two cases are considered: (i) large transverse deflections, where nonlinear (true) curvature, nonlinear material and nonlinear inertia owing to longitudinal motions of the beam are taken into account, and (ii) mid-plane stretching nonlinearity. A novel approach is employed, the method of varying amplitudes. As a result, the isolated as well as combined effects of the considered sources of nonlinearities are revealed. It is shown that nonlinear inertia has the most substantial impact on the dispersion relation of a non-uniform beam by removing all frequency band-gaps. Explanations of the revealed effects are suggested, and validated by experiments and numerical simulation. PMID:27118899
Neural Network Associative Memory Using Non-Linear Holographic Storage Media
1989-12-01
T’,?T Cýy’ ( AFIT/GEO/ENG/89D-3 AD-A214 340 L NEURAL NETWORK ASSOCIATIVE MEMORY USING NON-LINEAR HOLOGRAPHIC STORAGE MEDIA I THESIS I Presented to...order approximations of the required gain were provided. - - -In= unazn A FIT/GEO/ENG/89D-3 NEURAL NETWORK ASSOCIATIVE MEMORY USING NON-LINEAR...approxi- mations of the required gain were provided. vi NEURAL NETWORK ASSOCIATIVE MEMORY USING NON-LINEAR HOLOGRAPHIC STORAGE MEDIA I. Introduction The
Quan, Li; Liu, Xiaozhou; Gong, Xiufen
2012-10-01
High efficiency of the second-harmonic and sum-frequency generation can be obtained in optical superlattice by using the conventional quasi-phase-matched (QPM) method. Although this trick can be played on the acoustic wave, the media with negative nonlinear parameters are not common in acoustics. Furthermore, the QPM method used in acoustic metamaterials has been less studied. In this work, a protocol is provided to realize the QPM method by using nonlinear complementary media in acoustic metamaterials in order to obtain large backward second-harmonic generation. Compared with the conventional method, the method gains a broader bandwidth and can be used in both acoustic and electromagnetic waves.
Comparison of equations for the EDTD solution in anisotropic and dispersive media
Burke, G.J.; Steich, D.J.
1997-01-01
The recursive-convolution solution for anisotropic and dispersive media was seen to yield accurate results for reflection from ferrite slabs up to a frequency limit set by the sampling interval. Depending on the application, the results shown might be considered usable up to about 300 GHz, which corresponds to about 13 cells per wavelength. Results at still higher frequencies might be usable when a time delay or frequency shift due to dispersion can be tolerated. Several different forms of the update equations were considered which can result from different approximations in reducing the continuous equations to discrete form.
Proposal and design of Airy-based rocket pulses for invariant propagation in lossy dispersive media.
Preciado, Miguel A; Sugden, Kate
2012-12-01
A novel (to our knowledge) kind of Airy-based pulse with an invariant propagation in lossy dispersive media is proposed. The basic principle is based on an optical energy trade-off between different parts of the pulse caused by the chromatic dispersion, which is used to compensate the attenuation losses of the propagation medium. Although the ideal concept of the proposed pulses implies infinite pulse energy, the numerical simulations show that practical finite energy pulses can be designed to obtain a partially invariant propagation over a finite distance of propagation.
Localization of light in a parabolically bending waveguide array in thermal nonlinear media.
Ye, Fangwei; Dong, Liangwei; Hu, Bambi
2009-03-01
A parabolically longitudinally bending waveguide array imprinted into thermal nonlinear media is found to support the localized stationary solitons. The localization results from the suppression of a curvature effect by the nonlinearity with an infinite-range nonlocality. The localization criterion is given analytically. Solitons propagate stably along a curved trajectory without bending loss, and their locations are significantly influenced by the waveguide curvature. These solitons represent the first example of stationary localized solitons encountered in curved waveguides.
Modulational instability in nonlocal media with competing non-Kerr nonlinearities
NASA Astrophysics Data System (ADS)
Tiofack, C. G. Latchio; Tagwo, H.; Dafounansou, O.; Mohamadou, A.; Kofane, T. C.
2015-12-01
We investigate analytically and numerically the modulational instability (MI) and propagation properties of light in nonlocal media with competing cubic-quintic nonlinearities where the response functions are assumed to be equal. By using the linear stability analysis, the generic properties of the MI gain spectra are demonstrated for the exponential and rectangular response functions. Special attention is paid to investigate the competition between the spatial scale of the cubic and quintic nonlinearities. For media with exponential response function, we have obtained the range of the wave numbers where instability occurs. It is found that the increase in the absolute value of the quintic nonlinearity suppresses the instability in the regime where the cubic nonlinearity prevails over the quintic one and promotes its development in the opposite case. For media with negative response function, additional MI bands are excited at higher wave numbers when the width of the nonlocal response function exceeds a certain threshold. In the regime where the quintic nonlinearity is dominant, the increase in the absolute value of the quintic coefficient leads to the enhancement of the gain value and the movement of the maximum gain to higher wave numbers. On the other hand, in the case of the predominance of the cubic nonlinearity, the position of the maximum gain bands move to lower wave numbers and MI domain becomes increasingly narrows when the quintic term increases. The numerical simulations fully confirm our analytical results.
Gorkovenko, A. I.; Plekhanov, A. I.; Simanchuk, A. E.; Yakimanskiy, A. V.; Nosova, G. I.; Solovskaya, N. A.; Smirnov, N. N.
2014-12-14
Detailed investigations of the quadratic nonlinear response of a series of new polyimides with covalently attached chromophore DR13 are performed by the Maker fringes method in the range of fundamental wavelength from 850 to 1450 nm. Polymer films with thickness of 100–400 nm were spin-coated on glass substrates and corona poled. For these materials, the maximum values of the second harmonic generation coefficients d{sub 33} are 80–120 pm/V. A red shift of the nonlinear response dispersion with respect to the linear absorption spectrum was observed for the DR13 chromophore. The temperature dependences of linear absorption and nonlinear coefficients d{sub 33} for studied structures are observed. It was found that the temperature changes of the absorption spectra lead to appreciable contribution to the value of the nonlinear coefficient d{sub 33}. The demonstrated high temperature stability (up to 120 °C) of chromophore-containing polyimide thin films makes it possible to eliminate the degradation of their nonlinear optical properties in the future applications of such structures.
Environmental Consequences of Nanotechnologies: Nanoparticle Dispersion in Aqueous Media: SOP-T-1
2015-02-01
ER D C/ EL S R- 15 -2 Environmental Consequences of Nanotechnologies Nanoparticle Dispersion in Aqueous Media: SOP-T-1 En vi ro nm en...Consequences of Nanotechnologies Scientific Operating Procedure SOP-T-1 Jessica G. Coleman, Alan J. Kennedy, and Ashley R. Harmon Environmental...EQT) Research Program titled “Environmental Consequences of Nanotechnologies .” Procedures link to the ERDC NanoGRID (Guidance for Risk Informed
Z-scan for thin media with more than one nonlocal nonlinear response.
Irivas, B A Martinez; Carrasco, M L Arroyo; Otero, M M Mendez; García, R Ramos; Castillo, M D Iturbe
2016-06-13
A model to characterize the response of a thin media that can exhibit more than one nonlocal nonlinear response when it is illuminated with a Gaussian beam in a z-scan experiment is proposed. The model considers that these nonlocal contributions can be treated as independent contributions in the refractive or absorptive nonlinear response. Numerical results for two nonlocal nonlinear contributions with different magnitudes between them are presented. Experimental results obtained from a hydrogenated amorphous silicon sample are used to corroborate this model.
Finite-difference and finite-volume methods for nonlinear standing ultrasonic waves in fluid media.
Vanhille, C; Conde, C; Campos-Pozuelo, C
2004-04-01
In the framework of the application of high-power ultrasonics in industrial processing in fluid media, the mathematical prediction of the acoustical parameters inside resonators should improve the development of practical systems. This can be achieved by the use of numerical tools able to treat the nonlinear acoustics involved in these phenomena. In particular, effects like nonlinear distortion and nonlinear attenuation are fundamental in applications. In this paper, three one-dimensional numerical models in the time domain for calculating the nonlinear acoustic field inside a one-dimensional resonant cavity are presented and compared. They are based on the finite-difference and the finite-volume methods. These different algorithms solve the differential equations, from the linear up to the strongly nonlinear case (including weak shock). Some physical results obtained from the modelling of ultrasonic waves and a comparison of the efficiency of the different algorithms are presented.
Upscaling of Solute Transport in Heterogeneous Media with Non-uniform Flow and Dispersion Fields
Xu, Zhijie; Meakin, Paul
2013-10-01
An analytical and computational model for non-reactive solute transport in periodic heterogeneous media with arbitrary non-uniform flow and dispersion fields within the unit cell of length ε is described. The model lumps the effect of non-uniform flow and dispersion into an effective advection velocity Ve and an effective dispersion coefficient De. It is shown that both Ve and De are scale-dependent (dependent on the length scale of the microscopic heterogeneity, ε), dependent on the Péclet number Pe, and on a dimensionless parameter α that represents the effects of microscopic heterogeneity. The parameter α, confined to the range of [-0.5, 0.5] for the numerical example presented, depends on the flow direction and non-uniform flow and dispersion fields. Effective advection velocity Ve and dispersion coefficient De can be derived for any given flow and dispersion fields, and . Homogenized solutions describing the macroscopic variations can be obtained from the effective model. Solutions with sub-unit-cell accuracy can be constructed by homogenized solutions and its spatial derivatives. A numerical implementation of the model compared with direct numerical solutions using a fine grid, demonstrated that the new method was in good agreement with direct solutions, but with significant computational savings.
Controlled opacity in a class of nonlinear dielectric media
NASA Astrophysics Data System (ADS)
Bittencourt, E.; Camargo, G. H. S.; De Lorenci, V. A.; Klippert, R.
2017-03-01
Motivated by new technologies for designing and tailoring metamaterials, we seek properties for certain classes of nonlinear optical materials that allow room for a reversibly controlled opacity-to-transparency phase transition through the application of external electromagnetic fields. We examine some mathematically simple models for the dielectric parameters of the medium and compute the relevant geometric quantities that describe the speed and polarization of light rays.
Observation of surface dark solitons in nonlocal nonlinear media.
Gao, XingHui; Wang, Jing; Zhou, Luohong; Yang, ZhenJun; Ma, Xuekai; Lu, Daquan; Guo, Qi; Hu, Wei
2014-07-01
We investigated surface dark solitons (SDSs) at the interface between a self-defocusing nonlocal nonlinear medium and a linear medium, both theoretically and experimentally. We demonstrate that fundamental and higher-order SDSs can exist when the linear refractive index of the self-defocusing medium is much greater than that of the linear medium. The fundamental and second-order solitons are observed at the interface between air and a weakly absorbing liquid.
Oskooi, Ardavan; Johnson, Steven G.
2011-04-01
We show that some previous proposals for perfectly matched layer (PML) absorbers in anisotropic media or for waveguides at oblique incidence are not, in fact true PMLs; in previous work we similarly showed a failure of several PML proposals for periodic media (photonic crystals). We therefore argue that a more careful validation scheme is required for PML proposals, in contrast to past authors who have typically checked only that reflections are small for a fixed resolution, and suggest a simple validation scheme that can be readily applied to any PML proposal regardless of derivation or implementation. We demonstrate this test for a corrected, unsplit-field PML valid for anisotropic, dispersive media, implemented in both planewave-expansion and finite-difference time-domain (FDTD) methods.
Finite difference methods for transient signal propagation in stratified dispersive media
NASA Technical Reports Server (NTRS)
Lam, D. H.
1975-01-01
Explicit difference equations are presented for the solution of a signal of arbitrary waveform propagating in an ohmic dielectric, a cold plasma, a Debye model dielectric, and a Lorentz model dielectric. These difference equations are derived from the governing time-dependent integro-differential equations for the electric fields by a finite difference method. A special difference equation is derived for the grid point at the boundary of two different media. Employing this difference equation, transient signal propagation in an inhomogeneous media can be solved provided that the medium is approximated in a step-wise fashion. The solutions are generated simply by marching on in time. It is concluded that while the classical transform methods will remain useful in certain cases, with the development of the finite difference methods described, an extensive class of problems of transient signal propagating in stratified dispersive media can be effectively solved by numerical methods.
Plant Roots Increase Bacterivorous Nematode Dispersion through Nonuniform Glass-bead Media.
Trap, Jean; Bernard, Laetitia; Brauman, Alain; Pablo, Anne-Laure; Plassard, Claude; Ranoarisoa, Mahafaka Patricia; Blanchart, Eric
2015-12-01
Dispersion of bacterivorous nematodes in soil is a crucial ecological process that permits settlement and exploitation of new bacterial-rich patches. Although plant roots, by modifying soil structure, are likely to influence this process, they have so far been neglected. In this study, using an original three-compartment microcosm experimental design and polyvinyl chloride (PVC) bars to mimic plant roots, we tested the ability of roots to improve the dispersion of bacterivorous nematode populations through two wet, nonuniform granular (glass bead) media imitating contrasting soil textures. We showed that artificial roots increased migration time of bacterivorous nematode populations in the small-bead medium, suggesting that plant roots may play an important role in nematode dispersion in fine-textured soils or when soil compaction is high.
Plant Roots Increase Bacterivorous Nematode Dispersion through Nonuniform Glass-bead Media
Trap, Jean; Bernard, Laetitia; Brauman, Alain; Pablo, Anne-Laure; Plassard, Claude; Ranoarisoa, Mahafaka Patricia; Blanchart, Eric
2015-01-01
Dispersion of bacterivorous nematodes in soil is a crucial ecological process that permits settlement and exploitation of new bacterial-rich patches. Although plant roots, by modifying soil structure, are likely to influence this process, they have so far been neglected. In this study, using an original three-compartment microcosm experimental design and polyvinyl chloride (PVC) bars to mimic plant roots, we tested the ability of roots to improve the dispersion of bacterivorous nematode populations through two wet, nonuniform granular (glass bead) media imitating contrasting soil textures. We showed that artificial roots increased migration time of bacterivorous nematode populations in the small-bead medium, suggesting that plant roots may play an important role in nematode dispersion in fine-textured soils or when soil compaction is high. PMID:26941457
Dispersive effects on the multi-layer porous media flows with permeable and impermeable interfaces
NASA Astrophysics Data System (ADS)
Daripa, Prabir; Gin, Craig
2016-11-01
We investigate dispersive effects on the linear stability of multi-layer porous media flow models of enhanced oil recovery for two different types of interfaces: permeable and impermeable interfaces. Results presented are relevant for the design of smarter interfaces in the available parameter space of Capillary number, Peclet number, longitudinal and transverse dispersion and the viscous profile of the middle layer. The stabilization capacity of each of these two interfaces is explored numerically and conditions for complete dispersive stabilization are identified for each of these two types of interfaces. Several key results will be presented including our finding that for most values of the flow parameters, permeable interfaces suppress flow instability more than impermeable interfaces. Time permitting, full simulation results will also be presented. NSF Grant # DMS-1522782 and QNRF NPRP Grant 08-777-1-141.
Integration of nonlinearity-management and dispersion-management for pulses in fiber-optic links
NASA Astrophysics Data System (ADS)
Driben, Rodislav; Malomed, Boris A.; Mahlab, Uri
2004-03-01
We introduce a model of a long-haul fiber-optic link that uses a combination of the nonlinearity- and dispersion-compensation (management) to stabilize nonsoliton pulses. The compensation of the accumulated fiber nonlinearity, and simultaneously pulse reshaping, which helps to suppress the inter-symbol interference (ISI, i.e., blurring of blank spaces between adjacent pulses), are performed by second-harmonic-generating modules, which are periodically inserted together with amplifiers. We demonstrate that the dispersion-management (DM), which was not included in an earlier considered model, drastically improves stability of the pulses. The stable-transmission length for an isolated pulse, which was less than 10 fiber spans with the use of the nonlinearity-management only, becomes indefinitely long. It is demonstrated too that the pulse is quite robust against fluctuations of its initial parameters, and the scheme operates efficiently in a very broad parameter range. The interaction between pulses can be safely suppressed for the transmission distance exceeding 16 spans (≃1000 km). The smallest temporal separation between adjacent pulses, which is necessary to prevent the ISI, attains a minimum in the case of moderate DM, similar to known results for the DM solitons. The mutually-induced distortion of co-propagating pulses being accounted for by the emission of radiation, a plausible way to further increase the stable-transmission limit is to introduce bandpass filters.
Dispersion relation equation preserving FDTD method for nonlinear cubic Schrödinger equation
NASA Astrophysics Data System (ADS)
Sheu, Tony W. H.; Le Lin
2015-10-01
In this study we aim to solve the cubic nonlinear Schrödinger (CNLS) equation by the method of fractional steps. Over a time step from tn to tn+1, the linear part of the Schrödinger equation is solved firstly through four time integration steps. In this part of the simulation, the explicit symplectic scheme of fourth order accuracy is adopted to approximate the time derivative term. The second-order spatial derivative term in the linear Schrödinger equation is approximated by centered scheme. The resulting symplectic and space centered difference scheme renders an optimized numerical dispersion relation equation. In the second part of the simulation, the solution of the nonlinear equation is computed exactly thanks to the embedded invariant nature within each time increment. The proposed semi-discretized difference scheme underlying the modified equation analysis of second kind and the method of dispersion error minimization has been assessed in terms of the spatial modified wavenumber or the temporal angular frequency resolution. Several problems have been solved to show that application of this new finite difference scheme for the calculation of one- and two-dimensional Schrödinger equations can deemed conserve Hamiltonian quantities and preserve dispersion relation equation (DRE).
Bright solitons in nonlinear media with a self-defocusing double-well nonlinearity
NASA Astrophysics Data System (ADS)
Xie, Qiongtao; Wang, Linmao; Wang, Yizhen; Shen, Zhenjiang; Fu, Jun
2014-12-01
We show that stable bright solitons can appear in a medium with spatially inhomogeneous self-defocusing (SDF) nonlinearity of a double-well structure. For a specific choice of the nonlinearity parameters, we obtain exact analytical solutions for the fundamental bright solitons. By making use of the linear stability analysis, the stability region in the parameter space for the exact fundamental bright soliton is obtained numerically. We also show the bifurcation from an antisymmetric to an asymmetric bright soliton for the SDF double-well nonlinearity.
Nonlinear Gamow vectors, shock waves, and irreversibility in optically nonlocal media
NASA Astrophysics Data System (ADS)
Gentilini, Silvia; Braidotti, Maria Chiara; Marcucci, Giulia; DelRe, Eugenio; Conti, Claudio
2015-08-01
Dispersive shock waves dominate wave-breaking phenomena in Hamiltonian systems. In the absence of loss, these highly irregular and disordered waves are potentially reversible. However, no experimental evidence has been given about the possibility of inverting the dynamics of a dispersive shock wave and turn it into a regular wavefront. Nevertheless, the opposite scenario, i.e., a smooth wave generating turbulent dynamics, is well studied and observed in experiments. Here we introduce a theoretical formulation for the dynamics in a highly nonlocal and defocusing medium described by the nonlinear Schroedinger equation. Our theory unveils a mechanism that enhances the degree of irreversibility. This mechanism explains why a dispersive shock cannot be reversed in evolution even for an arbitrarily small amount of loss. Our theory is based on the concept of nonlinear Gamow vectors, i.e., power-dependent generalizations of the counterintuitive and hereto-elusive exponentially decaying states in Hamiltonian systems. We theoretically show that nonlinear Gamow vectors play a fundamental role in nonlinear Schroedinger models: They may be used as a generalized basis for describing the dynamics of the shock waves and affect the degree of irreversibility of wave-breaking phenomena. Gamow vectors allow analytical calculation of the amount of breaking of time reversal with a quantitative agreement with numerical solutions. We also show that a nonlocal, nonlinear optical medium may act as a simulator for the experimental investigation of quantum irreversible models, as the reversed harmonic oscillator.
NASA Astrophysics Data System (ADS)
Li, Jin Hua; Chan, Hiu Ning; Chiang, Kin Seng; Chow, Kwok Wing
2015-11-01
Breathers and rogue waves of special coupled nonlinear Schrödinger systems (the Manakov equations) are studied analytically. These systems model the orthogonal polarization modes in an optical fiber with randomly varying birefringence. Studies earlier in the literature had shown that rogue waves can occur in these Manakov systems with dispersion and nonlinearity of opposite signs, and that the criterion for the existence of rogue waves correlates closely with the onset of modulation instability. In the present work the Hirota bilinear transform is employed to calculate the breathers (pulsating modes), and rogue waves are obtained as a long wave limit of such breathers. In terms of wave profiles, a 'black' rogue wave (intensity dropping to zero) and the transition to a four-petal configuration are elucidated analytically. Sufficiently strong modulation instabilities of the background may overwhelm or mask the development of the rogue waves, and such thresholds are correlated to actual physical properties of optical fibers. Numerical simulations on the evolution of breathers are performed to verify the prediction of the analytical formulations.
Propagation of a Laguerre-Gaussian correlated Schell-model beam in strongly nonlocal nonlinear media
NASA Astrophysics Data System (ADS)
Qiu, Yunli; Chen, Zhaoxi; He, Yingji
2017-04-01
Analytical expressions for the cross-spectral density function and the second-order moments of the Wigner distribution function of a Laguerre-Gaussian correlated Schell-model (LGCSM) beam propagating in strongly nonlocal nonlinear media are derived. The propagation properties, such as beam irradiance, beam width, the spectral degree of coherence and the propagation factor of a LGCSM beam inside the media are investigated in detail. The effect of the beam parameters and the input power on the evolution properties of a LGCSM is illustrated numerically. It is found that the beam width varies periodically or keeps invariant for a certain proper input power. And both the beam irradiance and the spectral degree of coherence of the LGCSM beam change periodically with the propagation distance for the arbitrary input power which however has no influence on the propagation factor. The coherent length and the mode order mainly affect the evolution speed of the LGCSM beam in strongly nonlocal nonlinear media.
NASA Astrophysics Data System (ADS)
Hasan, Md. Rabiul; Anower, Md. Shamim; Hasan, Md. Imran
2016-05-01
A simple hexagonal photonic crystal fiber is proposed to simultaneously achieve ultrahigh birefringence, large nonlinear coefficient, and two zero dispersion wavelengths (ZDWs). The finite element method with circular perfectly matched layer boundary condition is used to simulate the designed structure. Simulation results show that it is possible to achieve two closely lying ZDWs of 1.08 and 1.29 μm for x-polarization with 0.88 and 1.20 μm for y-polarization modes, respectively. In addition, an ultrahigh birefringence of 3.15×10-2 and a high nonlinear coefficient of 58 W-1 km-1 are also obtained at the excitation wavelength of 1.55 μm. The proposed fiber can have important applications in supercontinuum generation, parametric amplification, four-wave mixing, and optical sensors design.
Active Resonator Reset in the Nonlinear Dispersive Regime of Circuit QED
NASA Astrophysics Data System (ADS)
Bultink, C. C.; Rol, M. A.; O'Brien, T. E.; Fu, X.; Dikken, B. C. S.; Dickel, C.; Vermeulen, R. F. L.; de Sterke, J. C.; Bruno, A.; Schouten, R. N.; DiCarlo, L.
2016-09-01
We present two pulse schemes to actively deplete measurement photons from a readout resonator in the nonlinear dispersive regime of circuit QED. One method uses digital feedback conditioned on the measurement outcome, while the other is unconditional. In the absence of analytic forms and symmetries to exploit in this nonlinear regime, the depletion pulses are numerically optimized using the Powell method. We speed up photon depletion by more than six inverse resonator linewidths, saving approximately 1650 ns compared to depletion by waiting. We quantify the benefit by emulating an ancilla qubit performing repeated quantum-parity checks in a repetition code. Fast depletion increases the mean number of cycles to a spurious error detection event from order 1 to 75 at a 1 -μ s cycle time.
NASA Astrophysics Data System (ADS)
Sen, Pranay K.; Kumar, Abhay; Sen, Pratima
1999-06-01
Using semiclassical time dependent perturbation treatment, the coherence radiation-semiconductor interaction under ultrashort pulsed near band-gap resonant excitation regime has been analytically investigated in a narrow direct-gap semiconductor waveguide structure. The role of excitonic effect is incorporated to study transient pulse propagation effects in GAs/AlGaAs waveguide duly irradiated by a 100 fs Ti:Sapphire laser. Nonlinear Schroedinger equation is employed to examine the role of group velocity dispersion and nonlinear optical effect on the transmission characteristics of the pulse at various excitation intensities and waveguide lengths. The results suggest the occurrence of pulse break-up and pulse narrowing during propagation of the pulse through the GaAs/AlGaAs waveguide.
NASA Astrophysics Data System (ADS)
Rhén, Christin; Isacsson, Andreas
2017-01-01
The harmonic oscillator is one of the most widely used model systems in physics: an indispensable theoretical tool in a variety of fields. It is well known that an otherwise linear oscillator can attain novel and nonlinear features through interaction with another dynamical system. We investigate such an interacting system: a superconducting LC-circuit dispersively coupled to a superconducting quantum interference device (SQUID). We find that the SQUID phase behaves as a classical two-level system, whose two states correspond to one linear and one nonlinear regime for the LC-resonator. As a result, the circuit’s response to forcing can become multistable. The strength of the nonlinearity is tuned by the level of noise in the system, and increases with decreasing noise. This tunable nonlinearity could potentially find application in the field of sensitive detection, whereas increased understanding of the classical harmonic oscillator is relevant for studies of the quantum-to-classical crossover of Jaynes-Cummings systems.
Rhén, Christin; Isacsson, Andreas
2017-01-01
The harmonic oscillator is one of the most widely used model systems in physics: an indispensable theoretical tool in a variety of fields. It is well known that an otherwise linear oscillator can attain novel and nonlinear features through interaction with another dynamical system. We investigate such an interacting system: a superconducting LC-circuit dispersively coupled to a superconducting quantum interference device (SQUID). We find that the SQUID phase behaves as a classical two-level system, whose two states correspond to one linear and one nonlinear regime for the LC-resonator. As a result, the circuit’s response to forcing can become multistable. The strength of the nonlinearity is tuned by the level of noise in the system, and increases with decreasing noise. This tunable nonlinearity could potentially find application in the field of sensitive detection, whereas increased understanding of the classical harmonic oscillator is relevant for studies of the quantum-to-classical crossover of Jaynes-Cummings systems. PMID:28120946
Nonlinear dynamics of direction-selective recurrent neural media.
Xie, Xiaohui; Giese, Martin A
2002-05-01
The direction selectivity of cortical neurons can be accounted for by asymmetric lateral connections. Such lateral connectivity leads to a network dynamics with characteristic properties that can be exploited for distinguishing in neurophysiological experiments this mechanism for direction selectivity from other possible mechanisms. We present a mathematical analysis for a class of direction-selective neural models with asymmetric lateral connections. Contrasting with earlier theoretical studies that have analyzed approximations of the network dynamics by neglecting nonlinearities using methods from linear systems theory, we study the network dynamics with nonlinearity taken into consideration. We show that asymmetrically coupled networks can stabilize stimulus-locked traveling pulse solutions that are appropriate for the modeling of the responses of direction-selective neurons. In addition, our analysis shows that outside a certain regime of stimulus speeds the stability of these solutions breaks down, giving rise to lurching activity waves with specific spatiotemporal periodicity. These solutions, and the bifurcation by which they arise, cannot be easily accounted for by classical models for direction selectivity.
Symmetries of the TDNLS equations for weakly nonlinear dispersive MHD waves
NASA Technical Reports Server (NTRS)
Webb, G. M.; Brio, M.; Zank, G. P.
1995-01-01
In this paper we consider the symmetries and conservation laws for the TDNLS equations derived by Hada (1993) and Brio, Hunter and Johnson, to describe the propagation of weakly nonlinear dispersive MHD waves in beta approximately 1 plasmas. The equations describe the interaction of the Alfven and magnetoacoustic modes near the triple umbilic, where the fast magnetosonic, slow magnetosonic and Alfven speeds coincide and a(g)(exp 2) = V(A)(exp 2) where a(g) is the gas sound speed and V(A) is the Alfven speed. We discuss Lagrangian and Hamiltonian formulations, and similarity solutions for the equations.
Influence of wavelength-dependent-loss on dispersive wave in nonlinear optical fibers.
Herrera, Rodrigo Acuna
2012-11-01
In this work, we study numerically the influence of wavelength-dependent loss on the generation of dispersive waves (DWs) in nonlinear fiber. This kind of loss can be obtained, for instance, by the acousto-optic effect in fiber optics. We show that this loss lowers DW frequency in an opposite way that the Raman effect does. Also, we see that the Raman effect does not change the DW frequency too much when wavelength-dependent loss is included. Finally, we show that the DW frequency is not practically affected by fiber length.
NASA Astrophysics Data System (ADS)
Qiao, Yaojun; Li, Ming; Yang, Qiuhong; Xu, Yanfei; Ji, Yuefeng
2015-01-01
Closed-form expressions of nonlinear interference of dense wavelength-division-multiplexed (WDM) systems with dispersion managed transmission (DMT) are derived. We carry out a simulative validation by addressing an ample and significant set of the Nyquist-WDM systems based on polarization multiplexed quadrature phase-shift keying (PM-QPSK) subcarriers at a baud rate of 32 Gbaud per channel. Simulation results show the simple closed-form analytical expressions can provide an effective tool for the quick and accurate prediction of system performance in DMT coherent optical systems.
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.
On the closure of circular holes in nonlinear viscous media.
NASA Astrophysics Data System (ADS)
Cornet, Jan; Dabrowski, Marcin; Schmid, Daniel
2016-04-01
Many rocks exhibit viscous behaviors which have to be taken into account in applications ranging from wellbores creeping during drilling to salt caves or hard rock mine tunnels shrinking with time. We address all these different cases using a unified configuration. We consider a 2D plane strain problem where a circular hole, representing the wellbore, the cave or the mine tunnel depending on the application, is embedded in an infinite incompressible non-linear viscous material. The problem is purely mechanical. Not only the rheological model used here is well suited for real formations but it can also represent many different sorts of rocks like salts, shales, quartzite and even ice. The major difference between the applications concerns the relevant time scales and they must therefore be separated according to that. For short timescale applications like wellbore creep during drilling it is first necessary to determine whether an elastic component must or must not be taken into account. This analysis is carried out using a non-linear viscoelastic Maxwell model. If it is acknowledged that a purely viscous rheology is enough, as can be the case for salts, then we can proceed with our unified configuration. We start by considering the case where the medium is isotropic and where pressure boundary conditions are prescribed both at the hole rim and at infinity. This problem is 1D due to axial symmetry. Analytical solutions to very similar problems have already been provided and we compare the solution we have derived to the existing ones. We show that our solution is consistent and that we recover similar results to the ones derived for comparable rheologies. Using MILAMIN, a fast finite element code, we investigate further two cases which lead to angular dependency and stress concentrations around the hole. In the first case we add a deviatoric stress at infinity and we study the impact of this extra stress on the solution. It is important to understand this parameter
The permeability of poly-disperse porous media and effective particle size
NASA Astrophysics Data System (ADS)
Markicevic, B. I.; Preston, C.; Osterroth, S.; Iliev, O.; Hurwitz, M.
2015-11-01
The interactions between the fluid and solid phases in porous media account for the openness and length of the flow path that the fluid needs to travel within. The same reasoning applies for both mono- and poly-disperse media, and is reflected in the adoption of the same permeability models. The only difference is that an effective particle size diameter has to be used for the poly-disperse samples. A filtration experiment is used to form a particle layer, filter cake, consisting of particles of different sizes. Both inflow and outflow particle size distribution are measured by particle counting method, and from their difference, the particle size distribution in the cake is determined. In a set of experiments, the filtration history is altered by changing (i) filtration medium; (ii) suspension flow rate; and (iii) particle concentration, where in all cases investigated the cake permeability remains constant. In order to predict the permeability of poly-disperse cake from the analytical models, the particle size distribution moments are calculated, and the permeability is found for each moment. Comparing the experimental to the analytical permeability values the effective particle size is found, where the permeability calculated by using the harmonic mean of the particle size distribution reproduces the permeability experimental value best. Finally, in the parametric study, reducing the cake porosity and/or lowering the particle retention shifts effective particle size used in the permeability model toward higher moments of the particle size distribution function.
Self-Organization of Light in Optical Media with Competing Nonlinearities
NASA Astrophysics Data System (ADS)
Maucher, F.; Pohl, T.; Skupin, S.; Krolikowski, W.
2016-04-01
We study the propagation of light beams through optical media with competing nonlocal nonlinearities. We demonstrate that the nonlocality of competing focusing and defocusing nonlinearities gives rise to self-organization and stationary states with stable hexagonal intensity patterns, akin to transverse crystals of light filaments. Signatures of this long-range ordering are shown to be observable in the propagation of light in optical waveguides and even in free space. We consider a specific form of the nonlinear response that arises in atomic vapor upon proper light coupling. Yet, the general phenomenon of self-organization is a generic consequence of competing nonlocal nonlinearities, and may, hence, also be observed in other settings.
Inexact Picard iterative scheme for steady-state nonlinear diffusion in random heterogeneous media.
Mohan, P Surya; Nair, Prasanth B; Keane, Andy J
2009-04-01
In this paper, we present a numerical scheme for the analysis of steady-state nonlinear diffusion in random heterogeneous media. The key idea is to iteratively solve the nonlinear stochastic governing equations via an inexact Picard iteration scheme, wherein the nonlinear constitutive law is linearized using the current guess of the solution. The linearized stochastic governing equations are then spatially discretized and approximately solved using stochastic reduced basis projection schemes. The approximation to the solution process thus obtained is used as the guess for the next iteration. This iterative procedure is repeated until an appropriate convergence criterion is met. Detailed numerical studies are presented for diffusion in a square domain for varying degrees of nonlinearity. The numerical results are compared against benchmark Monte Carlo simulations, and it is shown that the proposed approach provides good approximations for the response statistics at modest computational effort.
Spatiotemporal solitons in birefringent media near the zero-dispersion point
NASA Astrophysics Data System (ADS)
Fitrakis, E. P.; Nistazakis, H. E.; Malomed, B. A.; Frantzeskakis, D. J.; Kevrekidis, P. G.
2006-09-01
We present a new species of spatiotemporal solitons (STSs, alias light bullets) that may be formed through the interaction of two waves with different polarizations in a birefringent Kerr medium near the point at which the second-order group-velocity dispersion (GVD) vanishes in the presence of a uniform cw background in one component. The analysis is based on an asymptotic reduction of the two cross-phase, modulation-coupled (2+1)-dimensional nonlinear Schrödinger equations, incorporating the third-order GVD to the Davey-Stewartson (DS) systems of type I or II for the self-defocusing and focusing Kerr nonlinearity, respectively. The STSs are then predicted following the pattern of the dromion solutions of the DS-I system and lump solitons of the DS-II system. Strictly speaking, the solitons are unstable, but they are shown to be stable objects on experimentally relevant scales of the propagation distance.
Nonlinear acoustic pulse propagation in dispersive sediments using fractional loss operators.
Maestas, Joseph T; Collis, Jon M
2016-03-01
The nonlinear progressive wave equation (NPE) is a time-domain formulation of the Euler fluid equations designed to model low-angle wave propagation using a wave-following computational domain. The wave-following frame of reference permits the simulation of long-range propagation and is useful in modeling blast wave effects in the ocean waveguide. Existing models do not take into account frequency-dependent sediment attenuation, a feature necessary for accurately describing sound propagation over, into, and out of the ocean sediment. Sediment attenuation is addressed in this work by applying lossy operators to the governing equation that are based on a fractional Laplacian. These operators accurately describe frequency-dependent attenuation and dispersion in typical ocean sediments. However, dispersion within the sediment is found to be a secondary process to absorption and effectively negligible for ranges of interest. The resulting fractional NPE is benchmarked against a Fourier-transformed parabolic equation solution for a linear case, and against the analytical Mendousse solution to Burgers' equation for the nonlinear case. The fractional NPE is then used to investigate the effects of attenuation on shock wave propagation.
Sputtered stoichiometric TeO2 glass films: Dispersion of linear and nonlinear optical properties
NASA Astrophysics Data System (ADS)
D'Amore, Franco; Di Giulio, Massimo; Pietralunga, Silvia M.; Zappettini, Andrea; Nasi, Lucia; Rigato, Valentino; Martinelli, Mario
2003-08-01
We report on the optical characterization of TeO2 amorphous films deposited by radio-frequency (rf) reactive sputtering. X-ray diffraction, electronic microscopy, and Rutherford backscattering analysis have been performed in order to assess the structural and compositional properties of the samples. The linear optical characterization has been performed by variable angle spectroscopic ellipsometry at wavelengths between 260 and 1700 nm, leading to determination of the dispersion of the complex refractive index for sputtered tellurium dioxide. In the spectral range of transparency, between 1700 and 500 nm, refractive index values ranging from 2.05 to 2.16 have been obtained. The dispersion of the complex third-order nonlinear optical coefficient of the sample has been evaluated in the near-infrared spectral range by third harmonic generation measurements. The out-of-resonance value of the χ(3) coefficient for TeO2 is in the range between 1.2×10-12 and 1.4×10-12 esu. The conjugation of optical transparency, high nonlinear refractive index and the possibility of growing films of good optical quality, make rf sputtered TeO2 a promising material for the implementation of devices for the processing of optical communication signals.
Nonlinear dynamics in flow through unsaturated fractured-porous media: Status and perspectives
Faybishenko, Boris
2002-11-27
The need has long been recognized to improve predictions of flow and transport in partially saturated heterogeneous soils and fractured rock of the vadose zone for many practical applications, such as remediation of contaminated sites, nuclear waste disposal in geological formations, and climate predictions. Until recently, flow and transport processes in heterogeneous subsurface media with oscillating irregularities were assumed to be random and were not analyzed using methods of nonlinear dynamics. The goals of this paper are to review the theoretical concepts, present the results, and provide perspectives on investigations of flow and transport in unsaturated heterogeneous soils and fractured rock, using the methods of nonlinear dynamics and deterministic chaos. The results of laboratory and field investigations indicate that the nonlinear dynamics of flow and transport processes in unsaturated soils and fractured rocks arise from the dynamic feedback and competition between various nonlinear physical processes along with complex geometry of flow paths. Although direct measurements of variables characterizing the individual flow processes are not technically feasible, their cumulative effect can be characterized by analyzing time series data using the models and methods of nonlinear dynamics and chaos. Identifying flow through soil or rock as a nonlinear dynamical system is important for developing appropriate short- and long-time predictive models, evaluating prediction uncertainty, assessing the spatial distribution of flow characteristics from time series data, and improving chemical transport simulations. Inferring the nature of flow processes through the methods of nonlinear dynamics could become widely used in different areas of the earth sciences.
Double resonant processes in 1D nonlinear periodic media
NASA Astrophysics Data System (ADS)
Kuzmiak, Vladimir; Konotop, Vladimir
2001-03-01
We consider one-dimensional periodic structure consisting of alternating layers fabricated from the materials possessing \\chi^(2) nonlinearity and assume that the filling fraction and the dielectric permittivities of the slabs are chosen in such a way that resonant contions for the generation for the second and third harmonic are satisfied simultaneously. The possibility of such process is demonstrated in the structure consisting of the alternating slabs of AlGaAs and InSb. The wave evolution is described in terms of envelope function approach. By taking account three resonant waves one obtains a system of coupled-mode differential equations. One of the solutions which is of special importance is that of having a constant amplitude and the first and third harmonic having zero amplitude. We analyze the stability of the solutions and show that the use of the double resonance allows one to obtain difference generation. A particular example of such a process is fractional conversion ω arrow (2/3)ω which takes place with the participation of the mode with the frequency ω/3.
Dispersion coefficients for the interaction of Cs atom with different material media
NASA Astrophysics Data System (ADS)
Kaur, Kiranpreet; Kaur, Jasmeet; Sahoo, B. K.; Arora, Bindiya
2016-10-01
Motivated by a large number of applications, the dispersion (C3) coefficients for the interaction of a Cs atom with different material media such as Au (metal), Si (semiconductor) and various dielectric surfaces like vitreous SiO2, SiNx, sapphire and YAG are determined using accurate values of the dynamic polarizabilities of the Cs atom obtained employing the relativistic coupled-cluster approach and the dynamic dielectric constants of the walls. Moreover, we also give the retardation function in the graphical representation as functions of separation distances to describe the interaction potentials between the Cs atom with the above considered material media. For the easy access to the interaction potentials at a given distance of separation, we give a simple working functional fitting form for the retardation functions in terms of four fitting parameters that are quoted for the respective medium.
Full 3D dispersion curve solutions for guided waves in generally anisotropic media
NASA Astrophysics Data System (ADS)
Hernando Quintanilla, F.; Lowe, M. J. S.; Craster, R. V.
2016-02-01
Dispersion curves of guided waves provide valuable information about the physical and elastic properties of waves propagating within a given waveguide structure. Algorithms to accurately compute these curves are an essential tool for engineers working in non-destructive evaluation and for scientists studying wave phenomena. Dispersion curves are typically computed for low or zero attenuation and presented in two or three dimensional plots. The former do not always provide a clear and complete picture of the dispersion loci and the latter are very difficult to obtain when high values of attenuation are involved and arbitrary anisotropy is considered in single or multi-layered systems. As a consequence, drawing correct and reliable conclusions is a challenging task in the modern applications that often utilize multi-layered anisotropic viscoelastic materials. These challenges are overcome here by using a spectral collocation method (SCM) to robustly find dispersion curves in the most complicated cases of high attenuation and arbitrary anisotropy. Solutions are then plotted in three-dimensional frequency-complex wavenumber space, thus gaining much deeper insight into the nature of these problems. The cases studied range from classical examples, which validate this approach, to new ones involving materials up to the most general triclinic class for both flat and cylindrical geometry in multi-layered systems. The apparent crossing of modes within the same symmetry family in viscoelastic media is also explained and clarified by the results. Finally, the consequences of the centre of symmetry, present in every crystal class, on the solutions are discussed.
Discrete multipole dark solitons in saturable nonlinearity media with parity-time symmetric lattices
NASA Astrophysics Data System (ADS)
Shi, Zhiwei; Xue, Jing; Xing, Zhu; Li, Yang; Li, Huagang
2017-02-01
We investigate numerically the existence and stability of discrete multipole dark solitons in saturable nonlinearity media with parity-time (PT) symmetric lattices. The dipole and triple solitons share the same existence domain associated with the propagation constant, gain-loss coefficient and the degree of saturable nonlinearity. However, the solitons stably propagate in a different area of the aforementioned three parameters. The beam power monotonously increases with the increase of propagation constant and the saturable degree, but gently decreases with the gain-loss coefficient. Moreover, the power of the triple solitons is higher than that of dipole solitons under the same conditions.
Nonlinear effects associated with dispersive Alfvén waves in plasmas
NASA Astrophysics Data System (ADS)
Shukla, P. K.; Stenflo, L.; Bingham, R.; Eliasson, B.
2004-12-01
Large amplitude Alfvén waves are frequently found in magnetized space and laboratory plasmas. Our objective here is to discuss the linear and nonlinear properties of dispersive Alfvén waves (DAWs) in a uniform magnetoplasma. We first consider finite frequency (ω/ωci) and ion gyroradius effects on inertial and kinetic Alfvén waves, where ωci is the ion gyrofrequency. Next, we focus on nonlinear effects caused by DAWs. Such effects include plasma density enhancement and depression by the Alfvén wave ponderomotive force, electron Joule heating by the thermal Alfvén wave force, the generation of zonal flows due to the shear Alfvén wave mode couplings as well as the formation of localized Alfvénic structures and Alfvénic vortices. The relevance of our investigation to the appearance of nonlinear Alfvén waves in the Earth's auroral acceleration region, in the solar corona and in the large plasma device at UCLA is discussed.
NASA Astrophysics Data System (ADS)
Horst, Allison M.; Ji, Zhaoxia; Holden, Patricia A.
2012-08-01
Nanoparticle exposure in toxicity studies requires that nanoparticles are bioavailable by remaining highly dispersed in culture media. However, reported dispersion approaches are variable, mostly study-specific, and not transferable owing to their empirical basis. Furthermore, many published approaches employ proteinaceous dispersants in rich laboratory media, both of which represent end members in environmental scenarios. Here, a systematic approach was developed to disperse initially agglomerated TiO2 nanoparticles (Aeroxide® TiO2 P25, Evonik, NJ; primary particle size range 6.4-73.8 nm) in oligotrophic culture medium for environmentally relevant bacterial toxicity studies. Based on understanding particle-particle interactions in aqueous media and maintaining environmental relevance, the approach involves (1) quantifying the relationship between pH and zeta potential to determine the point of zero charge of select nanoparticles in water; (2) nominating, then testing and selecting, environmentally relevant stabilizing agents; and (3) dispersing via "condition and capture" whereby stock dry powder nanoparticles are sonicated in pre-conditioned (with base, or acid, plus stabilizing agent) water, then diluted into culture media. The "condition and capture" principle is transferable to other nanoparticle and media chemistries: simultaneously, mechanically and electrostatically, nanoparticles can be dispersed with surrounding stabilizers that coat and sterically hinder reagglomeration in the culture medium.
Unifying diffusion and seepage for nonlinear gas transport in multiscale porous media
NASA Astrophysics Data System (ADS)
Song, Hongqing; Wang, Yuhe; Wang, Jiulong; Li, Zhengyi
2016-09-01
We unify the diffusion and seepage process for nonlinear gas transport in multiscale porous media via a proposed new general transport equation. A coherent theoretical derivation indicates the wall-molecule and molecule-molecule collisions drive the Knudsen and collective diffusive fluxes, and constitute the system pressure across the porous media. A new terminology, nominal diffusion coefficient can summarize Knudsen and collective diffusion coefficients. Physical and numerical experiments show the support of the new formulation and provide approaches to obtain the diffusion coefficient and permeability simultaneously. This work has important implication for natural gas extraction and greenhouse gases sequestration in geological formations.
NASA Astrophysics Data System (ADS)
Zhang, Di; Capoglu, Ilker; Li, Yue; Cherkezyan, Lusik; Chandler, John; Spicer, Graham; Subramanian, Hariharan; Taflove, Allen; Backman, Vadim
2016-06-01
Combining finite-difference time-domain (FDTD) methods and modeling of optical microscopy modalities, we previously developed an open-source software package called Angora, which is essentially a "microscope in a computer." However, the samples being simulated were limited to nondispersive media. Since media dispersions are common in biological samples (such as cells with staining and metallic biomarkers), we have further developed a module in Angora to simulate samples having complicated dispersion properties, thereby allowing the synthesis of microscope images of most biological samples. We first describe a method to integrate media dispersion into FDTD, and we validate the corresponding Angora dispersion module by applying Mie theory, as well as by experimentally imaging gold microspheres. Then, we demonstrate how Angora can facilitate the development of optical imaging techniques with a case study.
Nonlinear coda wave analysis of hysteretic elastic behavior in strongly scattering media
NASA Astrophysics Data System (ADS)
Ouarabi, M. Ait; Boubenider, F.; Gliozzi, A. S.; Scalerandi, M.
2016-10-01
Strongly scattering elastic media, such as consolidated granular materials, respond to ultrasonic pulse excitations with a long response signal with peculiar properties. The portion of the signal at late times, termed coda, is due to multiple scattering. It contains information about the elastic properties of the material, and it has been proven to be very sensitive to small variations in the modulus. Here we propose a technique based on a nonlinear analysis of the coda of a signal, which might be applied to quantify the nonlinear elastic response in consolidated granular media exhibiting a hysteretic elastic behavior. The method proposed allows for an intrinsic definition of the reference signal which is normally needed for applying coda-based methods.
NASA Astrophysics Data System (ADS)
Luo, Ting
As optical communications approach more data bandwidth, longer transmission distance, and more reconfigurability, dispersion, nonlinearity and polarization-dependent effects are becoming key issues for future all-optical fiber optic systems and networks. For ≥10 Gbit/s optical fiber transmission systems, it is critical that chromatic dispersion and polarization-mode-dispersion be well monitored and compensated using some type of dispersion monitoring and compensation. On the other hand, dispersive and nonlinear effects in optical fiber systems can also be beneficial and have applications on pulse management, all-optical signal processing and network function, which will be essential for high bite-rate optical networks and replacing the expensive optical-electrical-optical (O/E/O) conversion. In this Ph.D. dissertation, we present a detailed research on dispersion, nonlinearity, and polarization-dependent effects in high-speed optical communication systems. We have demonstrated: (i) A dynamic channel-spacing tunable multi-wavelength Erbium-doped fiber laser; (ii) Chromatic-dispersion-insensitive PMD monitoring by tracking the radio-frequency extracted from the vestigial-sideband; (iii) A method for simultaneous chromatic and polarization-mode dispersions monitoring by adding a frequency-shifted carrier; (iv) Polarization-insensitive optical parametric amplification by depolarizing the pump; (v) All optical chromatic dispersion monitoring potential for ultra-high speed (>40 Gbit/s) optical systems using cross-phase modulation in a highly nonlinear fiber; (vi) A novel fiber-based autocorrelator using polarimetric four-wave mixing effect and a tunable differential-group-delay element; (vii) A simple all-fiber-based autocorrelator by measuring the degree-of-polarization; and (viii) Reduction of pattern dependent data distortion in a stimulated Brillouin scattering based slow light element. These techniques will play key roles in future high-speed dynamic WDM optical
Suppression of two-photon resonantly enhanced nonlinear processes in extended media
Garrett, W.R.; Moore, M.A.; Payne, M.G.; Wunderlich, R.K.
1988-11-01
On the basis of combined experimental and theoretical studies of nonlinear processes associated with two-photon excitations near 3d and 4d states in Na, we show how resonantly enhanced stimulated hyper-Raman emission, parametric four-wave mixing processes and total resonant two-photon absorption can become severely suppressed through the actions of internally generated fields on the total atomic response in extended media. 7 refs., 3 figs.
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.
Javan, N. Sepehri Homami, S. H. H.
2015-02-15
Self-guided nonlinear propagation of intense circularly-polarized electromagnetic waves in a hot electron-positron-ion magnetoplasma is studied. Using a relativistic fluid model, a nonlinear equation is derived, which describes the interaction of the electromagnetic wave with the plasma in the quasi-neutral approximation. Transverse Eigen modes, the nonlinear dispersion relation and the group velocity are obtained. Results show that the transverse profile in the case of magnetized plasma with cylindrical symmetry has a radially damping oscillatory form. Effect of applying external magnetic fields, existence of the electron-positron pairs, changing the amplitude of the electromagnetic wave, and its polarization on the nonlinear dispersion relation and Eigen modes are studied.
On incremental non-linearity in granular media: phenomenological and multi-scale views
NASA Astrophysics Data System (ADS)
Darve, Félix; Nicot, François
2005-12-01
On the basis of fundamental constitutive laws such as elasticity, perfect plasticity, and pure viscosity, many elasto-viscoplastic constitutive relations have been developed since the 1970s through phenomenological approaches. In addition, a few more recent micro-mechanical models based on multi-scale approaches are now able to describe the main macroscopic features of the mechanical behaviour of granular media. The purpose of this paper is to compare a phenomenological constitutive relation and a micro-mechanical model with respect to a basic issue regularly raised about granular assemblies: the incrementally non-linear character of their behaviour. It is shown that both phenomenological and micro-mechanical models exhibit an incremental non-linearity. In addition, the multi-scale approach reveals that the macroscopic incremental non-linearity could stem from the change in the regime of local contacts between particles (from plastic regime to elastic regime) in terms of the incremental macroscopic loading direction. Copyright
1992-02-13
Self-diffusion studies of Se in CdSe and chemical interdiffusion studies of Se in CdTe, on the other hand, revealed diffusivities on the order of 107...pp. 922-933 (1990). - 23 - 10. R. S. Fiegelson and R. S. Route, "Improved yield of Bridgman grown AgGaSe 2 crystals using shaped crucibles," J. Cryst...and F. G. Storz, "Linear and nonlinear optical properties of ZnGeP2 and CdSe ," Appl. Phys. Lett. 18, pp. 301-303 (1971). 50. K. L. Vodopyanov, L. A
Ramirez, E V Garcia; Carrasco, M L Arroyo; Otero, M M Mendez; Cerda, S Chavez; Castillo, M D Iturbe
2010-10-11
In this work we present a simple model that can be used to calculate the far field intensity distributions when a Gaussian beam cross a thin sample of nonlinear media but the response can be nonlocal.
1988-09-01
decomposed into a series of associated aperiodic solitary waves, as can be achieved for solutions of the KdV equation [11], is still under investigation. 3...The organization of the paper is as follows: In Section 2, we discuss aperiodic and periodic solitary wave solutions of a model equation with...Periodic Solitary Wave Solutions of the Nonlinear Klein Gordon Equation without Dispersion We shall take, as our model equation , the nonlinear Klein
Tracing Analytic Ray Curves for Light and Sound Propagation in Non-Linear Media.
Mo, Qi; Yeh, Hengchin; Manocha, Dinesh
2016-11-01
The physical world consists of spatially varying media, such as the atmosphere and the ocean, in which light and sound propagates along non-linear trajectories. This presents a challenge to existing ray-tracing based methods, which are widely adopted to simulate propagation due to their efficiency and flexibility, but assume linear rays. We present a novel algorithm that traces analytic ray curves computed from local media gradients, and utilizes the closed-form solutions of both the intersections of the ray curves with planar surfaces, and the travel distance. By constructing an adaptive unstructured mesh, our algorithm is able to model general media profiles that vary in three dimensions with complex boundaries consisting of terrains and other scene objects such as buildings. Our analytic ray curve tracer with the adaptive mesh improves the efficiency considerably over prior methods. We highlight the algorithm's application on simulation of visual and sound propagation in outdoor scenes.
Synthesis of Silver Nanoparticles Dispersed in Various Aqueous Media Using Laser Ablation
Tajdidzadeh, M.; Azmi, B. Z.; Yunus, W. Mahmood M.; Talib, Z. Abidin; Sadrolhosseini, A. R.; Karimzadeh, K.; Gene, S. A.; Dorraj, M.
2014-01-01
The particle size, morphology, and stability of Ag-NPs were investigated in the present study. A Q-Switched Nd: YAG pulsed laser (λ = 532 nm, 360 mJ/pulse) was used for ablation of a pure Ag plate for 30 min to prepare Ag-NPs in the organic compound such as ethylene glycol (EG) and biopolymer such as chitosan. The media (EG, chitosan) permitted the making of NPs with well dispersed and average size of Ag-NPs in EG is about 22 nm and in chitosan is about 10 nm in spherical form. Particle size, morphology, and stability of NPs were compared with distilled water as a reference. The stability of the samples was studied by measuring UV-visible absorption spectra of samples after one month. The result indicated that the formation efficiency of NPs in chitosan was higher than other media and NPs in chitosan solution were more stable than other media during one month storage. This method for synthesis of silver NPs could be as a green method due to its environmentally friendly nature. PMID:25295298
Pantsyrnaya, T; Blanchard, F; Delaunay, S; Goergen, J L; Guédon, E; Guseva, E; Boudrant, J
2011-03-01
In the present study surfactant addition with the help of either a mechanical dispersion or a thermal treatment was applied in order to increase the solubility and the bioavailability of phenanthrene in aqueous media, and therefore to promote its biodegradation. Among four tested surfactants (Tween 80, Brij 30, sodium dodecyl sulphate and rhamnolipids), Brij 30 (0.5 gL(-1)) showed the best results allowing us to attain about 20 mgL(-1) of soluble phenanthrene. An additional thermal treatment at 60°C for 24h, 200 rpm permitted to increase the solubility of phenanthrene in the presence of Brij 30 (0.5 gL(-1)) to about 30 mgL(-1). Higher dispersions of phenanthrene particles as well as the reduction of their size were obtained using Ultra-Turrax and French press. The biodegradation of phenanthrene by Pseudomonas putida was then investigated. The reduction of size of phenanthrene particles by mechanical dispersion did not influence its biodegradation, suggesting that P. putida consumed only soluble phenanthrene. The addition of Brij 30 (0.5 gL(-1)) permitted to obtain more phenanthrene metabolized. The use of Brij 30 coupled with a transitory heating of phenanthrene-containing medium at 60°C led to an even more complete biodegradation. This might be a promising way to enhance biodegradation of PAHs.
Nonlinear effects related to circularly polarized dispersive Alfvén waves
NASA Astrophysics Data System (ADS)
Sharma, Swati; Gaur, Nidhi; Sharma, R. P.
2016-09-01
In situ measurements of solar wind have strongly implicated its turbulent behavior. The observed power spectra report a breakpoint around length scales of the order of ion scales. As one of the responsible mechanisms for the observed steepening in power spectrum, our approach includes a right circularly polarized dispersive Alfvén wave (DAW) with finite frequency correction which, when subjected to transverse collapse/filamentation instability, may possibly result in steepening of spectrum and progressive transfer of energy from larger scales to smaller scales. We have studied the nonlinear effects associated with coupling of DAW with kinetic Alfvén wave in solar wind at 1 A.U. The formation of localized structures provides a clue about the emergence of turbulence. Numerical simulation is performed to study localization and power spectral density of the field and density fluctuations. The results show steeper spectrum indicating transfer of large scale turbulent energy down to small scales.
Dispersion and absorption in one-dimensional nonlinear lattices: A resonance phonon approach
NASA Astrophysics Data System (ADS)
Xu, Lubo; Wang, Lei
2016-09-01
Based on the linear response theory, we propose a resonance phonon (r-ph) approach to study the renormalized phonons in a few one-dimensional nonlinear lattices. Compared with the existing anharmonic phonon (a-ph) approach, the dispersion relations derived from this approach agree with the expectations of the effective phonon (e-ph) theory much better. The application is also largely extended, i.e., it is applicable in many extreme situations, e.g., high frequency, high temperature, etc., where the existing one can hardly work. Furthermore, two separated phonon branches (one acoustic and one optical) with a clear gap in between can be observed by the r-ph approach in a diatomic anharmonic lattice. While only one combined branch can be detected in the same lattice with both the a-ph approach and the e-ph theory.
Transmission of pulses in a dispersion-managed fiber link with extra nonlinear segments
NASA Astrophysics Data System (ADS)
Driben, Rodislav; Malomed, Boris A.; Chu, P. L.
2005-01-01
We introduce an extended version of the dispersion-management (DM) model, which includes an extra nonlinear element, and consider transmission of return-to-zero pulses in this system (they are not solitons). The pulses feature self-compression, accompanied by generation of side peaks (in the temporal domain). An optimal transmission distance, zopt, is identified, up to which the pulse continues to compress itself (the eventual width-compression factor is ≃2), while the amplitude of the side peaks remains small enough. The distance zopt virtually does not depend on the strength S of the DM part of the system in the interval 1.5 < S < 11, but it is sensitive to the nonlinearity strength in the extra segment. The system provides essentially stronger suppression of the noise-induced jitter of the pulses than the ordinary DM model. The most important issue is interaction between adjacent pulses, which is a basic difficulty in the case of DM solitons. In a broad parameter region, the system provides effective isolation between pulses. The minimum initial temporal distance between them, necessary for the isolation, is quite small, slightly larger than 1.5 the pulse's width. The transmission actually improves the quality of multi-pulse arrays, as it leads to deepening of hiatuses between originally overlapping pulses.
Frequency dispersion of the first hyperpolarizabilities of reference molecules for nonlinear optics
Wergifosse, Marc de; Champagne, Benoît; Castet, Frédéric
2015-05-21
The frequency dispersion of the hyper-Rayleigh scattering first hyperpolarizabilities (β{sub HRS}) of five reference molecules for nonlinear optics, namely, carbon tetrachloride, chloroform, dichloromethane, acetonitrile, and trichloroacetonitrile, is described using the coupled-cluster singles and doubles quadratic response function (CCSD-QRF) as well as approximate schemes. Comparisons to approximate schemes in which the frequency dispersion is evaluated as either a multiplicative or an additive correction to the static hyperpolarizability yield the following observations: (i) errors of the order of 10% or less are usually encountered when using the multiplicative scheme for photon energies far from the lowest dipole-allowed excitation energies, (ii) spurious cases cannot be excluded as evidenced by carbon tetrachloride where the multiplicative scheme predicts a decrease of β{sub HRS} in contradiction to the increase obtained using the CCSD-QRF method, and (iii) the additive scheme is at best as reliable as the multiplicative approximation. The two-state approximation presents the advantage of correcting the wrong behavior of the additive and multiplicative schemes for carbon tetrachloride, but it is not an improved solution for the other compounds, while the question of selecting the appropriate dominant excited state remains unanswered. Finally, a new β{sub xyz} value of 18.9 a.u. is proposed for carbon tetrachloride in gas phase at λ = 1064 nm, to be compared with the measured 16.9 ± 1.4 a.u. value due to Shelton.
ERIC Educational Resources Information Center
Gutenko, Gregory
For a new course in media editing at the University of Missouri at Kansas City, a nonlinear, affordable AVID Media Suite Pro system was selected for the student video laboratory, a textbook was chosen, and an instructor was trained. However, there were difficulties concerning the acquisition, delivery, setup, and debugging of the editing…
Sun, Hongguang; Zhang, Yong; Chen, Wen; Reeves, Donald M
2014-02-01
Field and numerical experiments of solute transport through heterogeneous porous and fractured media show that the growth of contaminant plumes may not exhibit constant scaling, and may instead transition between diffusive states (i.e., superdiffusion, subdiffusion, and Fickian diffusion) at various transport scales. These transitions are likely attributed to physical properties of the medium, such as spatial variations in medium heterogeneity. We refer to this transitory dispersive behavior as "transient dispersion", and propose a variable-index fractional-derivative model (FDM) to describe the underlying transport dynamics. The new model generalizes the standard constant-index FDM which is limited to stationary heterogeneous media. Numerical methods including an implicit Eulerian method (for spatiotemporal transient dispersion) and a Lagrangian solver (for multiscaling dispersion) are utilized to produce variable-index FDM solutions. The variable-index FDM is then applied to describe transient dispersion observed at two field tracer tests and a set of numerical experiments. Results show that 1) uranine transport at the small-scale Grimsel test site transitions from strong subdispersion to Fickian dispersion, 2) transport of tritium at the regional-scale Macrodispersion Experimental (MADE) site transitions from near-Fickian dispersion to strong superdispersion, and 3) the conservative particle transport through regional-scale discrete fracture network transitions from superdispersion to Fickian dispersion. The variable-index model can efficiently quantify these transitions, with the scale index varying linearly in time or space.
Yang, Shan; Ganikhanov, Feruz
2013-11-15
We propose and experimentally demonstrate a method that is capable of resolving both real and imaginary parts of third-order nonlinearity (χ(3)) in the vicinity of Raman resonances. Dispersion of χ(3) can be obtained from a medium probed within microscopic volumes with a spectral resolution of better than 0.10 cm(-1).
Tho, Ingunn; Liepold, Bernd; Rosenberg, Joerg; Maegerlein, Markus; Brandl, Martin; Fricker, Gert
2010-04-16
The objective of the study was to characterise the aqueous dispersions of ritonavir melt extrudates. More specifically to look into the particular system formed when melt extrudate of a poorly soluble drug dissolved in a hydrophilic polymer matrix containing a surfactant is dispersed in an aqueous medium. Melt extrudates with and without ritonavir were studied. The drug containing extrudate was confirmed to be molecular dispersions of drug in a polymer/surfactant matrix. Particulate dispersions were formed in water from both drug and placebo extrudates. The dispersions were investigated with respect to mean particle size and particle size distribution (photon correlation spectroscopy and optical particle counting), surface charge (zeta potential), particle composition (ultracentrifugation), tendency to form aggregates and precipitate (turbidity), in vitro dissolution rate and drug release. It was concluded that dispersion of melt extrudates in aqueous medium give rise to nano/micro-dispersions. The stability of the nano/micro-dispersion is sensitive to anions and may be subjected to association/aggregation/flocculation as time proceeds after preparation of dispersion. Melt extrudate showed improved dissolution rate and drug release properties compared to crystalline raw material. From studies of single components and physical mixtures of the formulation composition it can be concluded that the drug delivery system itself, namely solid dispersion prepared by melt extrusion technology, plays a key role for the formation of the observed particles.
Forty-five degree backscattering-mode nonlinear absorption imaging in turbid media
NASA Astrophysics Data System (ADS)
Cui, Liping; Knox, Wayne H.
2010-03-01
Two-color nonlinear absorption imaging has been previously demonstrated with endogenous contrast of hemoglobin and melanin in turbid media using transmission-mode detection and a dual-laser technology approach. For clinical applications, it would be generally preferable to use backscattering mode detection and a simpler single-laser technology. We demonstrate that imaging in backscattering mode in turbid media using nonlinear absorption can be obtained with as little as 1-mW average power per beam with a single laser source. Images have been achieved with a detector receiving backscattered light at a 45-deg angle relative to the incoming beams' direction. We obtain images of capillary tube phantoms with resolution as high as 20 μm and penetration depth up to 0.9 mm for a 300-μm tube at SNR ~1 in calibrated scattering solutions. Simulation results of the backscattering and detection process using nonimaging optics are demonstrated. A Monte Carlo-based method shows that the nonlinear signal drops exponentially as the depth increases, which agrees well with our experimental results. Simulation also shows that with our current detection method, only 2% of the signal is typically collected with a 5-mm-radius detector.
NASA Astrophysics Data System (ADS)
Ouyang, Wei; Mao, Weijian; Li, Wuqun; Zhang, Pan
2016-11-01
An approach for approximate direct quadratic nonlinear inversion in two-parameter (density and bulk modulus) heterogeneous acoustic media is being presented and discussed in this paper. The approach consists of two parts: the first is a linear generalized Radon transform (GRT) migration procedure based on the weighted true-amplitude summation of pre-stack seismic scattered data that is adapted to a virtually arbitrary observing system, and the second is a non-iterative quadratic inversion operation, produced from the explicit expression of amplitude radiation pattern that is acting on the migrated data. This ensures the asymptotic inversion can continue to simultaneously locate the discontinuities and reconstruct the size of the discontinuities in the perturbation parameters describing the acoustic media. We identify that the amplitude radiation pattern is the binary quadratic combination of the parameters in the process of formulating nonlinear inverse scattering problems based on second-order Born approximation. The coefficients of the quadratic terms are computed by appropriately handling the double scattering effects. These added quadratic terms provide a better amplitude correction for the parameters inversion. Through numerical tests, we show that for strong perturbations, the errors of the linear inversion are significant and unacceptable. In contrast, the quadratic nonlinear inversion can give fairly accurate inversion results and keep almost the same computational complexity as conventional GRT liner inversion.
NASA Astrophysics Data System (ADS)
Ouyang, Wei; Mao, Weijian; Li, Wuqun; Zhang, Pan
2017-02-01
An approach for approximate direct quadratic non-linear inversion in two-parameter (density and bulk modulus) heterogeneous acoustic media is being presented and discussed in this paper. The approach consists of two parts: the first is a linear generalized Radon transform (GRT) migration procedure based on the weighted true-amplitude summation of pre-stack seismic scattered data that is adapted to a virtually arbitrary observing system, and the second is a non-iterative quadratic inversion operation, produced from the explicit expression of amplitude radiation pattern that is acting on the migrated data. This ensures the asymptotic inversion can continue to simultaneously locate the discontinuities and reconstruct the size of the discontinuities in the perturbation parameters describing the acoustic media. We identify that the amplitude radiation pattern is the binary quadratic combination of the parameters in the process of formulating non-linear inverse scattering problems based on second-order Born approximation. The coefficients of the quadratic terms are computed by appropriately handling the double scattering effects. These added quadratic terms provide a better amplitude correction for the parameters inversion. Through numerical tests, we show that for strong perturbations, the errors of the linear inversion are significant and unacceptable. In contrast, the quadratic non-linear inversion can give fairly accurate inversion results and keep almost the same computational complexity as conventional GRT liner inversion.
Artem’ev, V. A.; Nezvanov, A. Yu.; Nesvizhevsky, V. V.
2016-01-15
We discuss properties of the interaction of slow neutrons with nano-dispersed media and their application for neutron reflectors. In order to increase the accuracy of model simulation of the interaction of neutrons with nanopowders, we perform precise quantum mechanical calculation of potential scattering of neutrons on single nanoparticles using the method of phase functions. We compare results of precise calculations with those performed within first Born approximation for nanodiamonds with the radius of 2–5 nm and for neutron energies 3 × 10{sup -7}–10{sup -3} eV. Born approximation overestimates the probability of scattering to large angles, while the accuracy of evaluation of integral characteristics (cross sections, albedo) is acceptable. Using Monte-Carlo method, we calculate albedo of neutrons from different layers of piled up diamond nanopowder.
NASA Astrophysics Data System (ADS)
Artem'ev, V. A.; Nezvanov, A. Yu.; Nesvizhevsky, V. V.
2016-01-01
We discuss properties of the interaction of slow neutrons with nano-dispersed media and their application for neutron reflectors. In order to increase the accuracy of model simulation of the interaction of neutrons with nanopowders, we perform precise quantum mechanical calculation of potential scattering of neutrons on single nanoparticles using the method of phase functions. We compare results of precise calculations with those performed within first Born approximation for nanodiamonds with the radius of 2-5 nm and for neutron energies 3 × 10-7-10-3 eV. Born approximation overestimates the probability of scattering to large angles, while the accuracy of evaluation of integral characteristics (cross sections, albedo) is acceptable. Using Monte-Carlo method, we calculate albedo of neutrons from different layers of piled up diamond nanopowder.
Self-organization of frozen light in near-zero-index media with cubic nonlinearity
NASA Astrophysics Data System (ADS)
Marini, A.; García de Abajo, F. J.
2016-02-01
Optical beams are generally unbound in bulk media, and propagate with a velocity approximately amounting to the speed of light in free-space. Guidance and full spatial confinement of light are usually achieved by means of waveguides, mirrors, resonators, and photonic crystals. Here we theoretically demonstrate that nonlinear self-organization can be exploited to freeze optical beams in bulk near-zero-index media, thus enabling three-dimensional self-trapping of still light without the need of optical resonators. Light is stopped to a standstill owing to the divergent wavelength and the vanishing group velocity, effectively rendering, through nonlinearity, a positive-epsilon trapping cavity carved in an otherwise slightly-negative-epsilon medium. By numerically solving Maxwell’s equations, we find a soliton-like family of still azimuthal doughnuts, which we further study through an adiabatic perturbative theory that describes soliton evaporation in lossy media or condensation in actively pumped materials. Our results suggest applications in optical data processing and storage, quantum optical memories, and soliton-based lasers without cavities. Additionally, near-zero-index conditions can also be found in the interplanetary medium and in the atmosphere, where we provide a complementary explanation to the rare phenomenon of ball-lightning.
Self-organization of frozen light in near-zero-index media with cubic nonlinearity
Marini, A.; García de Abajo, F. J.
2016-01-01
Optical beams are generally unbound in bulk media, and propagate with a velocity approximately amounting to the speed of light in free-space. Guidance and full spatial confinement of light are usually achieved by means of waveguides, mirrors, resonators, and photonic crystals. Here we theoretically demonstrate that nonlinear self-organization can be exploited to freeze optical beams in bulk near-zero-index media, thus enabling three-dimensional self-trapping of still light without the need of optical resonators. Light is stopped to a standstill owing to the divergent wavelength and the vanishing group velocity, effectively rendering, through nonlinearity, a positive-epsilon trapping cavity carved in an otherwise slightly-negative-epsilon medium. By numerically solving Maxwell’s equations, we find a soliton-like family of still azimuthal doughnuts, which we further study through an adiabatic perturbative theory that describes soliton evaporation in lossy media or condensation in actively pumped materials. Our results suggest applications in optical data processing and storage, quantum optical memories, and soliton-based lasers without cavities. Additionally, near-zero-index conditions can also be found in the interplanetary medium and in the atmosphere, where we provide a complementary explanation to the rare phenomenon of ball-lightning. PMID:26847877
NASA Technical Reports Server (NTRS)
Lobashov, A. A.; Mostepanenko, V. M.
1993-01-01
The theory of quantum effects in nonlinear dielectric media is developed. The nonlinear dielectric media is influenced by an external pumping field. The diagonalization of the Hamiltonian of a quantized field is obtained by the canonical Bogoliubov transformations. The transformations allow us to obtain the general expressions for the number of created photons and for the degree of squeezing. In the case of a plane pumping wave, for example, the results are calculated by using the zero order of the secular perturbation theory, with small parameters characterizing the medium nonlinearity. The Heisenberg equations of motion are obtained for non-stationary case and a commonly used Hamiltonian is derived from the first principles of quantum electrodynamics.
Yi, Xiaogang; Wu, Jian; Li, Yan; Li, Wei; Hong, Xiaobin; Guo, Hongxiang; Zuo, Yong; Lin, Jintong
2012-12-03
Considering the polarization mode dispersion(PMD), the transmission penalty induced by nonlinear signal-noise interactions (NSNI) between the amplified spontaneous emission noise (ASE) and the information signal is investigated numerically for 40(100)G dispersion-managed(DM) polarization-multiplexed quadrature phase-shift keying (PM-QPSK) systems. We show that for single-channel PM-QPSK systems, PMD is helpful to reduce the NSNI-induced penalty. For multi-channel PM-QPSK system, however, the NSNI-induced nonlinear penalty is significantly enhanced by PMD, especially at low bit-rate. Our results show that due to the NSNI, the reduction of allowed input power that gives 1-dB Q penalty after 1600-km nonlinear transmission will increase from 1dB without PMD to 3.7dB with PMD for 42.8-Gbit/s coherent return-to-zero (RZ)-PM-QPSK systems.
Makarov, V A; Petnikova, V M; Shuvalov, V V
2015-09-30
Three unusual classes of particular analytical solutions to a system of four nonlinear equations are found for slowly varying complex amplitudes of circularly polarised components of the electric field. The system describes the self-action and interaction of two elliptically polarised plane waves collinearly propagating in an isotropic medium with second-order frequency dispersion and spatial dispersion of cubic nonlinearity. The solutions correspond to self-consistent combinations of two elliptically polarised cnoidal waves whose mutually orthogonal polarisation components vary in accordance with pairwise identical laws during propagation. At the same time, the amplitudes of the component with the same circular polarisation are proportional to two different elliptic Jacobi functions with the same periods. (nonlinear optical phenomena)
Dispersion in porous media, continuous-time random walks, and percolation.
Sahimi, Muhammad
2012-01-01
A promising approach to the modeling of anomalous (non-Gaussian) dispersion in flow through heterogeneous porous media is the continuous-time random walk (CTRW) method. In such a formula on the waiting time distribution ψ(t) is usually assumed to be given by ψ(t)∼t-1-α, with α fitted to the experimental data. The exponent α is also related to the power-law growth of the mean-square displacement of the solute with the time t
Hybrid dispersive media with controllable wave propagation: A new take on smart materials
NASA Astrophysics Data System (ADS)
Bergamini, Andrea E.; Zündel, Manuel; Flores Parra, Edgar A.; Delpero, Tommaso; Ruzzene, Massimo; Ermanni, Paolo
2015-10-01
In this paper, we report on the wave transmission characteristics of a hybrid one dimensional (1D) medium. The hybrid characteristic is the result of the coupling between a 1D mechanical waveguide in the form of an elastic beam, supporting the propagation of transverse waves and a discrete electrical transmission line, consisting of a series of inductors connected to ground through capacitors. The capacitors correspond to a periodic array of piezoelectric patches that are bonded to the beam and that couple the two waveguides. The coupling leads to a hybrid medium that is characterized by a coincidence condition for the frequency/wavenumber value corresponding to the intersection of the branches of the two waveguides. In the frequency range centered at coincidence, the hybrid medium features strong attenuation of wave motion as a result of the energy transfer towards the electrical transmission line. This energy transfer, and the ensuing attenuation of wave motion, is alike the one obtained through internal resonating units of the kind commonly used in metamaterials. However, the distinct shape of the dispersion curves suggests how this energy transfer is not the result of a resonance and is therefore fundamentally different. This paper presents the numerical investigation of the wave propagation in the considered media, it illustrates experimental evidence of wave transmission characteristics and compares the performance of the considered configuration with that of internal resonating metamaterials. In addition, the ability to conveniently tune the dispersion properties of the electrical transmission line is exploited to adapt the periodicity of the domain and to investigate diatomic periodic configurations that are characterized by a richer dispersion spectrum and broader bandwidth of wave attenuation at coincidence. The medium consisting of mechanical, piezoelectric, and analog electronic elements can be easily interfaced to digital devices to offer a novel
Hybrid dispersive media with controllable wave propagation: A new take on smart materials
Bergamini, Andrea E.; Zündel, Manuel; Flores Parra, Edgar A.; Ermanni, Paolo; Delpero, Tommaso; Ruzzene, Massimo
2015-10-21
In this paper, we report on the wave transmission characteristics of a hybrid one dimensional (1D) medium. The hybrid characteristic is the result of the coupling between a 1D mechanical waveguide in the form of an elastic beam, supporting the propagation of transverse waves and a discrete electrical transmission line, consisting of a series of inductors connected to ground through capacitors. The capacitors correspond to a periodic array of piezoelectric patches that are bonded to the beam and that couple the two waveguides. The coupling leads to a hybrid medium that is characterized by a coincidence condition for the frequency/wavenumber value corresponding to the intersection of the branches of the two waveguides. In the frequency range centered at coincidence, the hybrid medium features strong attenuation of wave motion as a result of the energy transfer towards the electrical transmission line. This energy transfer, and the ensuing attenuation of wave motion, is alike the one obtained through internal resonating units of the kind commonly used in metamaterials. However, the distinct shape of the dispersion curves suggests how this energy transfer is not the result of a resonance and is therefore fundamentally different. This paper presents the numerical investigation of the wave propagation in the considered media, it illustrates experimental evidence of wave transmission characteristics and compares the performance of the considered configuration with that of internal resonating metamaterials. In addition, the ability to conveniently tune the dispersion properties of the electrical transmission line is exploited to adapt the periodicity of the domain and to investigate diatomic periodic configurations that are characterized by a richer dispersion spectrum and broader bandwidth of wave attenuation at coincidence. The medium consisting of mechanical, piezoelectric, and analog electronic elements can be easily interfaced to digital devices to offer a novel
On the existence of optical vortex solitons propagating in saturable nonlinear media
NASA Astrophysics Data System (ADS)
Medina, Luciano
2017-01-01
In this paper, an existence theory is established for ring-profiled optical vortex solitons. We consider such solitons in the context of an electromagnetic light wave propagating in a self-focusing nonlinear media and governed by a nonlinear Schrödinger type equation. A variational principle and constrained minimization approach is used to prove the existence of positive solutions for an undetermined wave propagation constant. We provide a series of explicit estimates related to the wave propagation constant, a prescribed energy flux, and vortex winding number. Further, on a Nehari manifold, the existence of positive solutions for a wide range of parameter values is proved. We also provide numerical analysis to illustrate the behavior of the soliton's amplitude and wave propagation constant with respect to a prescribed energy flux and vortex winding number.
Non-Linear Stability of an Electrified Plane Interface in Porous Media
NASA Astrophysics Data System (ADS)
El-Dib, Yusry O.; Moatimid, Galal M.
2004-03-01
The non-linear electrohydrodynamic stability of capillary-gravity waves on the interface between two semi-infinite dielectric fluids is investigated. The system is stressed by a vertical electric field in the presence of surface charges. The work examines a few representative porous media configurations. The analysis includes Rayleigh-Taylor and Kelvin-Helmholtz instabilities. The boundary - value problem leads to a non-linear equation governing the surface evolution. Taylor theory is adopted to expand this equation, in the light of multiple scales, in order to obtain a non-linear Schr¨odinger equation describing the behavior of the perturbed interface. The latter equation, representing the amplitude of the quasi-monochromatic traveling wave, is used to describe the stability criteria. These criteria are discussed both analytically and numerically. In order to identifiy regions of stability and instability, the electric field intensity is plotted versus the wave number. Through a linear stability approach it is found that Darcy's coefficients have a destabilizing influence, while in the non-linear scope these coefficients as well as the electric field intensity play a dual role on the stability.
Ziółkowski, Andrzej
2014-12-15
Nonlinear light propagation in photorefractive media can be analyzed by numerical methods. The presented numerical approach has regard to the effects of time nonlocality. Two algorithms are presented, and compared in terms of physical results and computing times. The possibility to address the issue of time nonlocality in two ways is attributed to the fact that, it is possible to completely separate carrier dynamics evaluation and wave equation calculation. This in turn, allows to choose a short integration time for carrier dynamics and a longer one to solve the wave equation. The tests of the methods were carried out for a one-carrier model that describes most of photorefractive media, and for a model with bipolar transport and hot electron effect, used in descriptions of semiconductor materials.
MeDiA: Mean Distance Association and Its Applications in Nonlinear Gene Set Analysis.
Peng, Hesen; Ma, Junjie; Bai, Yun; Lu, Jianwei; Yu, Tianwei
2015-01-01
Probabilistic association discovery aims at identifying the association between random vectors, regardless of number of variables involved or linear/nonlinear functional forms. Recently, applications in high-dimensional data have generated rising interest in probabilistic association discovery. We developed a framework based on functions on the observation graph, named MeDiA (Mean Distance Association). We generalize its property to a group of functions on the observation graph. The group of functions encapsulates major existing methods in association discovery, e.g. mutual information and Brownian Covariance, and can be expanded to more complicated forms. We conducted numerical comparison of the statistical power of related methods under multiple scenarios. We further demonstrated the application of MeDiA as a method of gene set analysis that captures a broader range of responses than traditional gene set analysis methods.
Nonlinearity-mediated soliton ejection from trapping potentials in nonlocal media
Ye Fangwei; Kartashov, Yaroslav V.; Torner, Lluis; Hu Bambi
2010-08-15
We address the properties of optical solitons in thermal nonlinear media with a local refractive index defect that is capable of trapping solitons launched close to the sample boundary despite the boundary-mediated forces that tend to deflect all beams toward the center of the sample. We show that while such forces become more pronounced with an increasing of the input beam power the defect can trap only light below a critical power above which solitons are ejected. The dynamics of soliton ejection and the subsequent propagation may be controlled.
Bright solitons in defocusing media with spatial modulation of the quintic nonlinearity
NASA Astrophysics Data System (ADS)
Zeng, Jianhua; Malomed, Boris A.
2012-09-01
It has been recently demonstrated that self-defocusing (SDF) media with cubic nonlinearity, whose local coefficient grows from the center to the periphery fast enough, support stable bright solitons without the use of any linear potential. Our objective is to test the genericity of this mechanism for other nonlinearities, by applying it to one- and two-dimensional (1D and 2D) quintic SDF media. The models may be implemented in optics (in particular, in colloidal suspensions of nanoparticles), and the 1D model may be applied to the description of the Tonks-Girardeau gas of ultracold bosons. In 1D, the nonlinearity-modulation function is taken as g0+sinh2βx. This model admits a subfamily of exact solutions for fundamental solitons. Generic soliton solutions are constructed in a numerical form and also by means of the Thomas-Fermi and variational approximations (TFA and VA). In particular, a new ansatz for the VA is proposed, in the form of “raised sech,” which provides for an essentially better accuracy than the usual Gaussian ansatz. The stability of all the fundamental (nodeless) 1D solitons is established through the computation of the corresponding eigenvalues for small perturbations and also verified by direct simulations. Higher-order 1D solitons with two nodes have a limited stability region, all the modes with more than two nodes being unstable. It is concluded that the recently proposed inverted Vakhitov-Kolokolov stability criterion for fundamental bright solitons in systems with SDF nonlinearities holds here too. Particular exact solutions for 2D solitons are produced as well.
NASA Astrophysics Data System (ADS)
Kim, Bong-Sik
Three dimensional (3D) Navier-Stokes-alpha equations are considered for uniformly rotating geophysical fluid flows (large Coriolis parameter f = 2O). The Navier-Stokes-alpha equations are a nonlinear dispersive regularization of usual Navier-Stokes equations obtained by Lagrangian averaging. The focus is on the existence and global regularity of solutions of the 3D rotating Navier-Stokes-alpha equations and the uniform convergence of these solutions to those of the original 3D rotating Navier-Stokes equations for large Coriolis parameters f as alpha → 0. Methods are based on fast singular oscillating limits and results are obtained for periodic boundary conditions for all domain aspect ratios, including the case of three wave resonances which yields nonlinear "2½-dimensional" limit resonant equations for f → 0. The existence and global regularity of solutions of limit resonant equations is established, uniformly in alpha. Bootstrapping from global regularity of the limit equations, the existence of a regular solution of the full 3D rotating Navier-Stokes-alpha equations for large f for an infinite time is established. Then, the uniform convergence of a regular solution of the 3D rotating Navier-Stokes-alpha equations (alpha ≠ 0) to the one of the original 3D rotating NavierStokes equations (alpha = 0) for f large but fixed as alpha → 0 follows; this implies "shadowing" of trajectories of the limit dynamical systems by those of the perturbed alpha-dynamical systems. All the estimates are uniform in alpha, in contrast with previous estimates in the literature which blow up as alpha → 0. Finally, the existence of global attractors as well as exponential attractors is established for large f and the estimates are uniform in alpha.
Mechanical balance laws for fully nonlinear and weakly dispersive water waves
NASA Astrophysics Data System (ADS)
Kalisch, Henrik; Khorsand, Zahra; Mitsotakis, Dimitrios
2016-10-01
The Serre-Green-Naghdi system is a coupled, fully nonlinear system of dispersive evolution equations which approximates the full water wave problem. The system is known to describe accurately the wave motion at the surface of an incompressible inviscid fluid in the case when the fluid flow is irrotational and two-dimensional. The system is an extension of the well known shallow-water system to the situation where the waves are long, but not so long that dispersive effects can be neglected. In the current work, the focus is on deriving mass, momentum and energy densities and fluxes associated with the Serre-Green-Naghdi system. These quantities arise from imposing balance equations of the same asymptotic order as the evolution equations. In the case of an even bed, the conservation equations are satisfied exactly by the solutions of the Serre-Green-Naghdi system. The case of variable bathymetry is more complicated, with mass and momentum conservation satisfied exactly, and energy conservation satisfied only in a global sense. In all cases, the quantities found here reduce correctly to the corresponding counterparts in both the Boussinesq and the shallow-water scaling. One consequence of the present analysis is that the energy loss appearing in the shallow-water theory of undular bores is fully compensated by the emergence of oscillations behind the bore front. The situation is analyzed numerically by approximating solutions of the Serre-Green-Naghdi equations using a finite-element discretization coupled with an adaptive Runge-Kutta time integration scheme, and it is found that the energy is indeed conserved nearly to machine precision. As a second application, the shoaling of solitary waves on a plane beach is analyzed. It appears that the Serre-Green-Naghdi equations are capable of predicting both the shape of the free surface and the evolution of kinetic and potential energy with good accuracy in the early stages of shoaling.
Clobert, J.; Danchin, E.; Dhondt, A.A.; Nichols, J.D.
2001-01-01
The ability of species to migrate and disperse is a trait that has interested ecologists for many years. Now that so many species and ecosystems face major environmental threats from habitat fragmentation and global climate change, the ability of species to adapt to these changes by dispersing, migrating, or moving between patches of habitat can be crucial to ensuring their survival. This book provides a timely and wide-ranging overview of the study of dispersal and incorporates much of the latest research. The causes, mechanisms, and consequences of dispersal at the individual, population, species and community levels are considered. The potential of new techniques and models for studying dispersal, drawn from molecular biology and demography, is also explored. Perspectives and insights are offered from the fields of evolution, conservation biology and genetics. Throughout the book, theoretical approaches are combined with empirical data, and care has been taken to include examples from as wide a range of species as possible.
2007-09-01
dispersive media, electromagnetic Debye model [23] of orientational polarization phenomena [24] transient propagation , ultrawideband radar . and the Rocard...airframes), the remote detection of buried structures (such as landmines and lED’s), ionospheric pulse propagation (for remote sensing from an orbiting... ionospheric pulse propagation (for remote sensing from an orbiting satellite), as well as the problem of ultrawideband electromagnetic pulse exposure
Alpatova, Alla L; Shan, Wenqian; Babica, Pavel; Upham, Brad L; Rogensues, Adam R; Masten, Susan J; Drown, Edward; Mohanty, Amar K; Alocilja, Evangelyn C; Tarabara, Volodymyr V
2010-01-01
As the range of applications for carbon nanotubes (CNTs) rapidly expands, understanding the effect of CNTs on prokaryotic and eukaryotic cell systems has become an important research priority, especially in light of recent reports of the facile dispersion of CNTs in a variety of aqueous systems including natural water. In this study, single-walled carbon nanotubes (SWCNTs) were dispersed in water using a range of natural (gum arabic, amylose, Suwannee River natural organic matter) and synthetic (polyvinyl pyrrolidone, Triton X-100) dispersing agents (dispersants) that attach to the CNT surface non-covalently via different physiosorption mechanisms. The charge and the average effective hydrodynamic diameter of suspended SWCNTs as well as the concentration of exfoliated SWCNTs in the dispersion were found to remain relatively stable over a period of 4 weeks. The cytotoxicity of suspended SWCNTs was assessed as a function of dispersant type and exposure time (up to 48 h) using general viability bioassay with Escherichia coli and using neutral red dye uptake (NDU) bioassay with WB-F344 rat liver epithelia cells. In the E. coli viability bioassays, three types of growth media with different organic loadings and salt contents were evaluated. When the dispersant itself was non-toxic, no losses of E. coli and WB-F344 viability were observed. The cell viability was affected only by SWCNTs dispersed using Triton X-100, which was cytotoxic in SWCNT-free (control) solution. The epigenetic toxicity of dispersed CNTs was evaluated using gap junction intercellular communication (GJIC) bioassay applied to WB-F344 rat liver epithelial cells. With all SWCNT suspensions except those where SWCNTs were dispersed using Triton X-100 (wherein GJIC could not be measured because the sample was cytotoxic), no inhibition of GJIC in the presence of SWCNTs was observed. These results suggest a strong dependence of the toxicity of SWCNT suspensions on the toxicity of the dispersant and point to
Two-component vector solitons in defocusing Kerr-type media with spatially modulated nonlinearity
Zhong, Wei-Ping; Belić, Milivoj
2014-12-15
We present a class of exact solutions to the coupled (2+1)-dimensional nonlinear Schrödinger equation with spatially modulated nonlinearity and a special external potential, which describe the evolution of two-component vector solitons in defocusing Kerr-type media. We find a robust soliton solution, constructed with the help of Whittaker functions. For specific choices of the topological charge, the radial mode number and the modulation depth, the solitons may exist in various forms, such as the half-moon, necklace-ring, and sawtooth vortex-ring patterns. Our results show that the profile of such solitons can be effectively controlled by the topological charge, the radial mode number, and the modulation depth. - Highlights: • Two-component vector soliton clusters in defocusing Kerr-type media are reported. • These soliton clusters are constructed with the help of Whittaker functions. • The half-moon, necklace-ring and vortex-ring patterns are found. • The profile of these solitons can be effectively controlled by three soliton parameters.
Li, Ming; Zhang, Fan; Chen, Zhangyuan; Xu, Anshi
2008-12-22
We propose a diverse vestigial-sideband-filtering feed forward equalizer and decision feedback equalizer (DVSB-FFE-DFE), which is capable of compensating residual chromatic dispersion (CD) as well as mitigating fiber nonlinearity in on-off keying (OOK) systems. In DVSBFFE-DFE, the upper and the lower VSB filtered signals are jointly equalized with FFE followed by DFE. Simulation results show that in a 42.7 Gbit/s nonreturn-to-zero OOK system, DVSB-FFE-DFE can effectively mitigate the required optical signal-to-noise ratio penalty induced by residual CD and fiber nonlinearity.
NASA Astrophysics Data System (ADS)
Islam, Md. Ibadul; Khatun, Maksuda; Ahmed, Kawsar
2017-02-01
This paper presents dispersion tailoring of photonic crystal fibers creating artificial defect along one of the regular square axes. A finite element method (FEM) has been enforced for numerical investigation of several guiding properties of the PCF covering a broad wavelength range about 1340-1640 nm over the telecommunication windows. According to simulation, the proposed PCF has obtained a strictly single-mode fiber, which has an ultra-high negative dispersion of about -584.60 to -2337.60 ps/(nm-km) and also possible to cover the highest nonlinearity order of 131.91 W-1 km-1 under the operating wavelength. Moreover, the proposed PCF structure experimentally focuses on higher nonlinear coefficient, which successfully compensates the chromatic dispersion of standard single mode in entire band of interest and greatly applicable to the optical transmission system. Additionally, the single mode behavior of S-PCF is explicated by employing V parameter. In our dispersion sensitive analysis, this fiber is significantly more robust due to successfully achieve ultra-high negative dispersion, which gains more promiscuous compared to the prior best results.
Simulating dispersion in porous media and the influence of segmentation on stagnancy in carbonates
NASA Astrophysics Data System (ADS)
Gray, F.; Cen, J.; Shah, S. M.; Crawshaw, J. P.; Boek, E. S.
2016-11-01
Understanding the transport of chemical components in porous media is fundamentally important to many reservoir processes such as contaminant transport and reactive flows involved in CO2 sequestration. Carbonate rocks in particular present difficulties for pore-scale simulations because they contain large amounts of sub-micron porosity. In this work, we introduce a new hybrid simulation model to calculate hydrodynamic dispersion in pore-scale images of real porous media and use this to elucidate the origins and behaviour of stagnant zones arising in transport simulations using micro-CT images of carbonates. For this purpose a stochastic particle model for simulating the transport of a solute is coupled to a Lattice-Boltzmann algorithm to calculate the flow field. The particle method incorporates second order spatial and temporal resolution to resolve finer features of the domain. We demonstrate how dispersion coefficients can be accurately obtained in capillaries, where corresponding analytical solutions are available, even when these are resolved to just a few lattice units. Then we compute molecular displacement distributions for pore-spaces of varying complexity: a pack of beads; a Bentheimer sandstone; and a Portland carbonate. Our calculated propagator distributions are compared directly with recent experimental PFG-NMR propagator distributions (Scheven et al., 2005; Mitchell et al., 2008), the latter excluding spin relaxation mechanisms. We observe that the calculated transport propagators can be quantitatively compared with the experimental distribution, provided that spin relaxations in the experiment are excluded, and good agreement is found for both the sandstone and the carbonate. However, due to the absence of explicit micro-porosity from the carbonate pore space image used for flow field simulations we note that there are fundamental differences in the physical origins of the stagnant zones for micro-porous rocks between simulation and experiment. We
NASA Astrophysics Data System (ADS)
Chrysikopoulos, Constantinos V.; Manariotis, Ioannis D.; Syngouna, Vasiliki I.
2014-05-01
Accurate prediction of colloid and biocolloid transport in porous media relies heavily on usage of suitable dispersion coefficients. The widespread procedure for dispersion coefficient determination consists of conducting conservative tracer experiments and subsequently fitting the collected breakthrough data with a selected advection-dispersion transport model. The fitted dispersion coefficient is assumed to characterize the porous medium and is often used thereafter to analyze experimental results obtained from the same porous medium with other solutes, colloids, and biocolloids. The classical advection-dispersion equation implies that Fick's first law of diffusion adequately describes the dispersion process, or that the dispersive flux is proportional to the concentration gradient. Therefore, the above-described procedure inherently assumes that the dispersive flux of all solutes, colloids and biocolloids under the same flow field conditions is exactly the same. Furthermore, the available mathematical models for colloid and biocoloid transport in porous media do not adequately account for gravity effects. Here an extensive laboratory study was undertaken in order to assess whether the dispersivity, which traditionally has been considered to be a property of the porous medium, is dependent on colloid particle size, interstitial velocity and length scale. The breakthrough curves were successfully simulated with a mathematical model describing colloid and biocolloid transport in homogeneous, water saturated porous media. The results demonstrated that the dispersivity increases very slowly with increasing interstitial velocity, and increases with column length. Furthermore, contrary to earlier results, which were based either on just a few experimental observations or experimental conditions leading to low mass recoveries, dispersivity was positively correlated with colloid particle size. Also, transport experiments were performed with biocolloids (bacteriophages:
NASA Astrophysics Data System (ADS)
Lee, C. T.; Lee, C. C.
2015-04-01
This paper introduces a systematic approach to investigate a higher order nonlinear dispersive wave equation for modeling different wave modes. We present both the conventional KdV-type soliton and anomaly type solitons for the equation. We also show the conservation laws and Hamiltonian structures for the equation. Our results suggest that the underlying equation has more interacting soliton phenomena than one would have known for the classical KdV and Boussinesq equation.
NASA Astrophysics Data System (ADS)
Baskonus, Haci Mehmet; Bulut, Hasan
2015-10-01
In this study, we have studied to obtain some new analytical solutions to the (1 + 1)-dimensional nonlinear Dispersive Modified Benjamin-Bona-Mahony equation by using modified exp-function method. We have submitted the general structure of modified exp-function method. We have founded some new analytical solutions such as hyperbolic and rational function solutions. Afterward, we have plotted 2D and 3D surfaces of analytical solutions obtained in this study by using computer programming wolfram Mathematica 9.
Chow, K K; Shu, C; Lin, Chinlon; Bjarklev, A
2005-10-31
We demonstrate extinction ratio improvement by using pump-modulated four-wave mixing in a dispersion-flattened nonlinear photonic crystal fiber. A 6-dB improvement in the extinction ratio of a degraded return-to-zero signal has been achieved. A power penalty improvement of 3 dB at 10(-9) bit-error-rate level is obtained in the 10 Gb/s bit-error-rate measurements.
NASA Astrophysics Data System (ADS)
Zimmerling, Jörn; Wei, Lei; Urbach, Paul; Remis, Rob
2016-06-01
In this paper we present a Krylov subspace model-order reduction technique for time- and frequency-domain electromagnetic wave fields in linear dispersive media. Starting point is a self-consistent first-order form of Maxwell's equations and the constitutive relation. This form is discretized on a standard staggered Yee grid, while the extension to infinity is modeled via a recently developed global complex scaling method. By applying this scaling method, the time- or frequency-domain electromagnetic wave field can be computed via a so-called stability-corrected wave function. Since this function cannot be computed directly due to the large order of the discretized Maxwell system matrix, Krylov subspace reduced-order models are constructed that approximate this wave function. We show that the system matrix exhibits a particular physics-based symmetry relation that allows us to efficiently construct the time- and frequency-domain reduced-order models via a Lanczos-type reduction algorithm. The frequency-domain models allow for frequency sweeps meaning that a single model provides field approximations for all frequencies of interest and dominant field modes can easily be determined as well. Numerical experiments for two- and three-dimensional configurations illustrate the performance of the proposed reduction method.
Coupling micro-CT with computer simulations to analyze dispersion in porous media
NASA Astrophysics Data System (ADS)
Sobhani, Sadaf; Dunnmon, Jared; Werer, Michael
2015-11-01
In recent years, table-top X-ray Computed Tomography (XCT) systems have been utilized to analyze various samples with a resolution on the order of 1 μm -100 μm . In this study, we explore the use of these systems both in extracting high-resolution topologies of porous structures for use as inputs into computational simulations and in directly characterizing gas dispersion within such structures using fluoroscopic imaging of dense gaseous tracers. The opaque-solid environment and small pore-scale effects in porous media restrict the use of conventional imaging techniques, thereby making XCT a potentially useful diagnostic technique for understanding internal flows in porous and optically inaccessible structures. In the present work, we extract the topology of various reticulated porous foams from 3D XCT data and perform numerical simulations of the flow inside these structures. Permeability and tortuosity, which are key parameters in volume-averaged models are evaluated from the resulting flow fields and knowledge of the solid structure.
NASA Astrophysics Data System (ADS)
Yankovskii, A. P.
2015-03-01
On the basis of an algorithm of time steps, a method to simulate the creep is developed for rib-reinforced composite media made of nonlinear hereditary phase materials whose behavior is described by the Rabotnov theory. The technique proposed allows one, at discrete moments of time, to consider such a composition as nonlinear elastic with the initial stress state. The use of an iterative process of the type of the method of variable elasticity parameters allowed us to linearize the governing relationships and to reduce the problem of calculation of creep of the composite media at discrete points in time to a series of linear elastic problems of the mechanics of composites.
NASA Astrophysics Data System (ADS)
Sun, Y. W.; Liu, C.; Chan, K. L.; Xie, P. H.; Liu, W. Q.; Zeng, Y.; Wang, S. M.; Huang, S. H.; Chen, J.; Wang, Y. P.; Si, F. Q.
2013-08-01
In this paper, we present an optimized analysis algorithm for non-dispersive infrared (NDIR) to in situ monitor stack emissions. The proposed algorithm simultaneously compensates for nonlinear absorption and cross interference among different gases. We present a mathematical derivation for the measurement error caused by variations in interference coefficients when nonlinear absorption occurs. The proposed algorithm is derived from a classical one and uses interference functions to quantify cross interference. The interference functions vary proportionally with the nonlinear absorption. Thus, interference coefficients among different gases can be modeled by the interference functions whether gases are characterized by linear or nonlinear absorption. In this study, the simultaneous analysis of two components (CO2 and CO) serves as an example for the validation of the proposed algorithm. The interference functions in this case can be obtained by least-squares fitting with third-order polynomials. Experiments show that the results of cross interference correction are improved significantly by utilizing the fitted interference functions when nonlinear absorptions occur. The dynamic measurement ranges of CO2 and CO are improved by about a factor of 1.8 and 3.5, respectively. A commercial analyzer with high accuracy was used to validate the CO and CO2 measurements derived from the NDIR analyzer prototype in which the new algorithm was embedded. The comparison of the two analyzers show that the prototype works well both within the linear and nonlinear ranges.
NASA Astrophysics Data System (ADS)
Fu, Libi; Song, Weiguo; Lo, Siuming
2017-01-01
Emergencies involved in mass events are related to a variety of factors and processes. An important factor is the transmission of information on danger that has an influence on nonlinear crowd dynamics during the process of crowd dispersion. Due to much uncertainty in this process, there is an urgent need to propose a method to investigate the influence. In this paper, a novel fuzzy-theory-based method is presented to study crowd dynamics under the influence of information transmission. Fuzzy functions and rules are designed for the ambiguous description of human states. Reasonable inference is employed to decide the output values of decision making such as pedestrian movement speed and directions. Through simulation under four-way pedestrian situations, good crowd dispersion phenomena are achieved. Simulation results under different conditions demonstrate that information transmission cannot always induce successful crowd dispersion in all situations. This depends on whether decision strategies in response to information on danger are unified and effective, especially in dense crowds. Results also suggest that an increase in drift strength at low density and the percentage of pedestrians, who choose one of the furthest unoccupied Von Neumann neighbors from the dangerous source as the drift direction at high density, is helpful in crowd dispersion. Compared with previous work, our comprehensive study improves an in-depth understanding of nonlinear crowd dynamics under the effect of information on danger.
Hermite-Gaussian stationary solutions in strongly nonlocal nonlinear optical media
NASA Astrophysics Data System (ADS)
Zhong, Lanhua; Yang, Jing; Ren, Zhanmei; Guo, Qi
2017-01-01
Approximate analytical stationary solutions (SSs) of a cluster of Hermite-Gaussian (HG) shape is obtained in strongly nonlocal nonlinear media by the variational approach. The evolution of the HG SSs shows that when the order n ⩽ 3, they propagate stably and form solitons; otherwise, when n ⩾ 4, they always propagate unstably and evolve into self-trapped speckle-like beams. However, all these SSs maintain nearly invariant statistic beam-width during their propagation. Furthermore, when the input power deviates from the so-called critical power, the unstable HG beam will adjust its beam-width to form a new self-trapped beam, unlike the soliton which will turn to be a breather. But the average beam-widths are independent of the stability of the propagation of the HG SSs.
A 2D spring model for the simulation of ultrasonic wave propagation in nonlinear hysteretic media.
Delsanto, P P; Gliozzi, A S; Hirsekorn, M; Nobili, M
2006-07-01
A two-dimensional (2D) approach to the simulation of ultrasonic wave propagation in nonclassical nonlinear (NCNL) media is presented. The approach represents the extension to 2D of a previously proposed one dimensional (1D) Spring Model, with the inclusion of a PM space treatment of the intersticial regions between grains. The extension to 2D is of great practical relevance for its potential applications in the field of quantitative nondestructive evaluation and material characterization, but it is also useful, from a theoretical point of view, to gain a better insight of the interaction mechanisms involved. The model is tested by means of virtual 2D experiments. The expected NCNL behaviors are qualitatively well reproduced.
Popov, A.K.; Myslivets, S.A.; George, Thomas F.
2005-04-01
Specific features of nonlinear interference processes at quantum transitions in near- and fully resonant Doppler-broadened optically dense media are studied. The possibility of all-optical switching of the medium to opaque or, alternatively, to absolutely transparent, or even to strongly amplifying states is explored, which is controlled by a small variation of two driving or probe radiations and does not require any change of the level populations. Optimum conditions for inversionless amplification of short-wavelength radiation above the oscillation threshold at the expense of the longer-wavelength control fields are investigated. The feasibility of overcoming the fundamental limitation on a velocity-interval of resonantly coupled molecules imposed by the Doppler effect is shown, based on quantum coherence.
NASA Astrophysics Data System (ADS)
Kujawska, T.; Wójcik, J.; Nowicki, A.
Knowledge of the acoustic nonlinearity parameter, B/A, of biological fluids or soft tissues is necessary whenever high intensity pressure fields are induced. A numerical model recently developed in our lab is capable of fast predicting the nonlinear distortion of pulsed finite-amplitude acoustic waves generated from axisymmetric sources propagating through multilayer attenuating media. Quantitative analysis of the obtained results enabled developing the alternative method for determination of the B/A of biological media. First, the method involves measuring the nonlinear waveform distortion of the tone burst propagating through water. Then, it involves numerical modeling (in frequency domain) using the Time-Averaged Wave Envelope (TAWE) approach. The numerical simulation results are fitted to the experimental data by adjusting the source boundary conditions to determine accurately the source pressure, effective radius and apodization function being the input parameters to the numerical solver. Next, the method involves measuring the nonlinear distortion of idem tone burst passing through the two-layer system of parallel media. Then, we numerically model nonlinear distortion in two-layer system of media in frequency domain under experimental boundary conditions. The numerical simulation results are fitted to the experimental data by adjusting the B/A value of the tested material. Values of the B/A for 1.3-butanediol at both the ambient (25°C) and physiological (36.6°C) temperatures were determined. The obtained result (B/A = 10.5 ± 5% at 25°C) is in a good agreement with that available in literature. The B/A = 11.5 ± 5% at 36.6°C was determined.
NASA Astrophysics Data System (ADS)
Sun, Y.-W.; Liu, C.; Chan, K.-L.; Xie, P.-H.; Liu, W.-Q.; Zeng, Y.; Wang, S.-M.; Huang, S.-H.; Chen, J.; Wang, Y.-P.; Si, F.-Q.
2013-02-01
In this paper, we present an optimized analysis algorithm for non-dispersive infrared (NDIR) to monitor stack emissions. The newly developed analysis algorithm simultaneously compensates for nonlinear absorption and cross-interference between different gases. We present a mathematical derivation for the measurement error caused by variations in interference coefficients when nonlinear absorption occurs. The optimized algorithm is derived from a classical one and uses interference functions to quantify cross-interference. The interference functions vary proportionally with the nonlinear absorption. Thus, interference coefficients among different gases can be modeled by the interference functions whether gases are characterized by linear or nonlinear absorption. In this study, the simultaneous analysis of two components (CO2 and CO) serves as an example for the validation of the optimized algorithm. The interference functions in this case can be obtained by least-squares fitting with three-order polynomials. Experiments show that the results of cross-interference correction are improved significantly by utilizing fitted interference functions when nonlinear absorptions occur. The dynamic measurement ranges of CO2 and CO are improved by about a factor of 1.8 and 3.5, respectively. A commercial NDIR multi-gas analyzer with high accuracy was used to validate the CO and CO2 measurements derived from the NDIR analyzer prototype in which the new cross-interference correction algorithm was embedded. Both measurements well agreed.
Nonlinear localized modes in PT-symmetric optical media with competing gain and loss
Midya, Bikashkali; Roychoudhury, Rajkumar
2014-02-15
The existence and stability of the nonlinear spatial localized modes are investigated in parity-time symmetric optical media characterized by a generic complex hyperbolic refractive index distribution with competing gain and loss profile. The exact analytical expression of the localized modes are found for all values of the competing parameter and in the presence of both the self-focusing and self-defocusing Kerr nonlinearity. The effects of competing gain/loss profile on the stability structure of these localized modes are discussed with the help of linear stability analysis followed by the direct numerical simulation of the governing equation. The spatial localized modes in two-dimensional geometry as well as the transverse power-flow density associated with these localized modes are also examined. -- Highlights: • Existence of localized modes is investigated in PT-symmetric complex potentials. • Exact analytical expression of the localized modes is obtained. • Effect of gain/loss profile on the stability of these localized modes is discussed. • Localized modes in 2D and associated transverse power-flow density are also examined.
Bull, Larry; Budd, Adam; Stone, Christopher; Uroukov, Ivan; de Lacy Costello, Ben; Adamatzky, Andrew
2008-01-01
We propose that the behavior of nonlinear media can be controlled automatically through evolutionary learning. By extension, forms of unconventional computing (viz., massively parallel nonlinear computers) can be realized by such an approach. In this initial study a light-sensitive subexcitable Belousov-Zhabotinsky reaction in which a checkerboard image, composed of cells of varying light intensity projected onto the surface of a thin silica gel impregnated with a catalyst and indicator, is controlled using a learning classifier system. Pulses of wave fragments are injected into the checkerboard grid, resulting in rich spatiotemporal behavior, and a learning classifier system is shown to be able to direct the fragments to an arbitrary position through dynamic control of the light intensity within each cell in both simulated and real chemical systems. Similarly, a learning classifier system is shown to be able to control the electrical stimulation of cultured neuronal networks so that they display elementary learning. Results indicate that the learned stimulation protocols identify seemingly fundamental properties of in vitro neuronal networks. Use of another learning scheme presented in the literature confirms that such fundamental behavioral characteristics of a given network must be considered in training experiments.
Multiphase continuum model to describe dynamic loading effects in nonlinear porous media
Swift, R.P.; Burton, D.E.; Bryan, J.B.; Glenn, H.D.
1985-03-01
A multiphase constitutive model that couples nonlinear deformation to porous flow has been developed for numerical analyses of dynamic behavior of geological media. The model has been incorporated into the explicit finite-difference code TENSOR and applied to examine the phenomenology associated with contained explosions and nuclear surface cratering in a coral geology. For contained explosions in nearly saturated media, the model predicts a region of liquefaction to exist adjacent to the cavity. This region is markedly enhanced for the case of total saturation and the associated pore pressure buildup indicate that the stability of the residual stress field may be threatened. Based on plausible assumptions about the geology and the constitutive relations of coral, we have shown that the multiphase constitutive model can relate subsidence to calculational parameters such as peak effective stress. Most of the observed volume of the Koa crater at the Pacific Proving Grounds can be accounted for by late time consolidation of the damaged coral. 21 refs., 10 figs.
Coupled periodic waves with opposite dispersions in a nonlinear optical fiber
NASA Astrophysics Data System (ADS)
Tsang, S. C.; Nakkeeran, K.; Malomed, Boris A.; Chow, K. W.
2005-05-01
Using the Hirota's method and elliptic θ-functions, we obtain three families of exact periodic (cnoidal) wave solutions for two nonlinear Schrödinger (NLS) equations coupled by XPM (cross-phase-modulation) terms, with a ratio σ of the XPM and SPM (self-phase-modulation) coefficients. Unlike the previous works, we obtain the solutions for the case when the coefficients of the group-velocity-dispersion (GVD) in the coupled equations have opposite signs. In the limit of the infinite period, the solutions with σ > 1 carry over into inverted bound states of bright and dark solitons in the normal- and anomalous-GVD modes (known as "symbiotic solitons"), while the infinite-period solution with σ < 1 is an uninverted bound state (also an unstable one). The case of σ = 2 is of direct interest to fiber-optic telecommunications, as it corresponds to a scheme with a pulse stream in an anomalous-GVD payload channel stabilized by a concomitant strong periodic signal in a mate normal-GVD channel. The case of arbitrary σ may be implemented in a dual-core waveguide. To understand the stability of the coupled waves, we first analytically explore the modulational stability of CW (constant-amplitude) solutions, concluding that they may be completely stable for σ ⩾ 1, provided that the absolute value of the GVD coefficient is smaller in the anomalous-GVD mode than in the normal-GVD one, and certain auxiliary conditions on the amplitudes are met. The stability of the exact cnoidal-wave solutions is tested in direct simulations. We infer that, while, strictly speaking, in the practically significant case of σ = 2 all the solutions are unstable, in many cases the instability may be strongly attenuated, rendering the above-mentioned paired channels scheme usable. In particular, the instability is milder for a smaller period of the wave pattern, and/or if the anomalous GVD is weaker than the normal GVD in the mate channel. When the instability sets in, it first initiates quasi
NASA Astrophysics Data System (ADS)
Rasmussen, K. Ø.; Christiansen, P. L.; Johansson, M.; Gaididei, Yu. B.; Mingaleev, S. F.
1998-03-01
A one-dimensional discrete nonlinear Schrödinger (DNLS) model with the power dependence, r- s on the distance r, of dispersive interactions is proposed. The stationary states of the system are studied both analytically and numerically. Two kinds of trial functions, exp-like and sech-like are exploited and the results of both approaches are compared. Both on-site and inter-site stationary states are investigated. It is shown that for s sufficiently large all features of the model are qualitatively the same as in the DNLS model with nearest-neighbor interaction. For s less than some critical value, scr, there is an interval of bistability where two stable stationary states exist at each excitation number. The bistability of on-site solitons may occur for dipole-dipole dispersive interaction ( s = 3), while scr for inter-site solitions is close to 2.1. In the framework of the DNLS equation with nearest-neighbor coupling we discuss the stability of highly localized, “breather-like”, excitations under the influence of thermal fluctuations. Numerical analysis shows that the lifetime of the breather is always finite and in a large parameter region inversely proportional to the noise variance for fixed damping and nonlinearity. We also find that the decay rate of the breather decreases with increasing nonlinearity and with increasing damping.
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.
Prakash, Deo; Shaaban, E.R.; Shapaan, M.; Mohamed, S.H.; Othman, A.A.; Verma, K.D.
2016-08-15
Highlights: • Combined experimental and theoretical researches on ZnSe Thin Films. • The film thickness and refractive index were determined using envelope method. • The absorption coefficient and the energy gap were calculated. • Dispersion parameters were determined using Wemple-DiDomenico relation. • The third order susceptibility and nonlinear refractive index were calculated. - Abstract: Zinc selenide (ZnSe) thin films with different thicknesses were evaporated onto glass substrates using the thermal evaporation technique. X-ray diffraction analysis confirmed that both the film and powder have cubic zinc-blende structure. The fundamental optical parameters like absorption coefficient, extinction coefficient and band gap were evaluated in transparent region of transmittance and reflectance spectrum. The optical transition of the films was found to be allowed, where the energy gap increased from 2.576 to 2.702 eV with increasing film thickness. Also, the refractive index value increase with increasing film thickness. The refractive indices evaluated through envelope method were extrapolated by Cauchy dispersion relationship over the whole spectra range. Additionally, the dispersion of refractive index was determined in terms of Wemple-DiDomenico single oscillator model. Third order susceptibility and nonlinear refractive index were determined for different thickness of ZnSe thin films.
Williams, Ross; Cherin, Emmanuel; Lam, Toby Y J; Tavakkoli, Jahangir; Zemp, Roger J; Foster, F Stuart
2006-11-21
Nonlinear propagation has been demonstrated to have a significant impact on ultrasound imaging. An efficient computational algorithm is presented to simulate nonlinear ultrasound propagation through layered liquid and tissue-equivalent media. Results are compared with hydrophone measurements. This study was undertaken to investigate the role of nonlinear propagation in high frequency ultrasound micro-imaging. The acoustic field of a focused transducer (20 MHz centre frequency, f-number 2.5) was simulated for layered media consisting of water and tissue-mimicking phantom, for several wide-bandwidth source pulses. The simulation model accounted for the effects of diffraction, attenuation and nonlinearity, with transmission and refraction at layer boundaries. The parameter of nonlinearity, B/A, of the water and tissue-mimicking phantom were assumed to be 5.2 and 7.4, respectively. The experimentally measured phantom B/A value found using a finite-amplitude insert-substitution method was shown to be 7.4 +/- 0.6. Relative amounts of measured second and third harmonic pressures as a function of the fundamental pressures at the focus were in good agreement with simulations. Agreement within 3% was found between measurements and simulations of the beam widths of the fundamental and second harmonic signals following propagation through the tissue phantom. The results demonstrate significant nonlinear propagation effects for high frequency imaging beams.
NASA Astrophysics Data System (ADS)
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
Li, Xiaolin; Zhang, Fan; Chen, Zhangyuan; Xu, Anshi
2007-12-24
We numerically investigate XPM effect and XPM-induced nonlinear phase noise in both RZ-DPSK and multi-format (RZ-DPSK and RZ-OOK) WDM systems operating at 40 Gbit/s with different dispersion maps. The relative strength of XPM effect and XPM-induced nonlinear phase noise is discussed for both RZ-DPSK and multi-format WDM transmission. With optimum dispersion mapping, XPM and XPM-induced nonlinear phase noise from neighboring channels carrying either OOK or DPSK signals can both be effectively suppressed.
NASA Astrophysics Data System (ADS)
Seadawy, Aly R.
2017-01-01
The propagation of three-dimensional nonlinear irrotational flow of an inviscid and incompressible fluid of the long waves in dispersive shallow-water approximation is analyzed. The problem formulation of the long waves in dispersive shallow-water approximation lead to fifth-order Kadomtsev-Petviashvili (KP) dynamical equation by applying the reductive perturbation theory. By using an extended auxiliary equation method, the solitary travelling-wave solutions of the two-dimensional nonlinear fifth-order KP dynamical equation are derived. An analytical as well as a numerical solution of the two-dimensional nonlinear KP equation are obtained and analyzed with the effects of external pressure flow.
NASA Astrophysics Data System (ADS)
Selima, Ehab S.; Seadawy, Aly R.; Yao, Xiaohua
2016-12-01
The three-dimensional (3-D) nonlinear and dispersive PDEs system for surface waves propagating at undisturbed water surface under the gravity force and surface tension effects are studied. By applying the reductive perturbation method, we derive the (2 + 1) -dimensions form of the Davey-Stewartson (DS) system for the modulation of 2-D harmonic waves. By using the simplest equation method, we find exact traveling wave solutions and a general form of the multiple-soliton solution of the DS model. The dispersion analysis as well as the conservation law of the DS system are discussed. It is revealed that the consistency of the results with the conservation of the potential energy increases with increasing Ursell parameter. Also, the stability of the ODEs form of the DS system is presented by using the phase portrait method.
Enhancement of a nano cavity lifetime by induced slow light and nonlinear dispersions.
Grinberg, P; Bencheikh, K; Brunstein, M; Yacomotti, A M; Dumeige, Y; Sagnes, I; Raineri, F; Bigot, L; Levenson, J A
2012-11-19
We start from a 2D photonic crystal nanocavity with moderate Q-factor and dynamically increase it by two order of magnitude by the joint action of coherent population oscillations and nonlinear refractive index.
NASA Astrophysics Data System (ADS)
Zhao, Tongtong; Lou, Shuqin; Su, Wei; Wang, Xin
2016-01-01
We propose an As2Se3-based highly nonlinear photonic quasi-crystal fiber with dual zero-dispersion wavelengths (ZDWs). Using a full-vector finite element method, the proposed fiber is optimized to obtain high nonlinear coefficient, low confinement loss and two zero-dispersion points by optimizing the structure parameters. Numerical results demonstrate that the proposed photonic quasi-crystal fiber (PQF) has dual ZDWs and the nonlinear coefficient up to 2600 W-1 km-1 within the wavelength range from 2 to 5.5 μm. Due to the introduction of the large air holes in the third ring of the proposed fiber, the ability of confining the fundamental mode field can be improved effectively and thus the low confinement loss can be obtained. The proposed PQF with high nonlinearity and dual ZDWs will have a number of potential applications in four-wave mixing, super-continuum generation, and higher-order dispersion effects.
NASA Astrophysics Data System (ADS)
Ye, S.; Sleep, B. E.
2012-12-01
The effects of biofilm growth on the flow and transport in porous media were investigated in an anaerobic two-dimensional coarse sand-filled cell. The cell was inoculated with a mixed microbial culture fed methanol. Biomass concentrations attached to the sand and suspended in the water in the cell were determined by protein analysis. The biofilm thickness on individual sand grains was investigated with confocal laser scanning microscopy (CLSM). The biofilm thickness for individual sand grains had a range of mean values from 59 to 316 microns in this study. To investigate the implications of the variability of biofilm thicknesses, four models were used to calculate reductions in porous media permeability as a function of biofilm thickness. Taylor's model (Taylor et al., 1990) predicted a reduction by a factor ranging from 14 to 5000 from minimum to maximum mean biofilm thickness. Vandevivere's Model (Vandevivere et al.,1995) predicted a reduction in permeability by a factor ranging from 769 to 3846 from minimum to maximum mean biofilm thickness. Seki's model (Seki and Miyazaki, 2001) could not be applied in this study. Clement's model (Clement et al., 1996) predicted a reduction ranging from 1 to 1.14 over the range of biomass levels observed in the cell. To investigate the implications of the variability of biofilm thicknesses for dispersivity, Taylor and Jaffe's models (1990) were used to calculate increase in porous media dispersivity as a function of biofilm thickness. The model predicted an increase in dispersivity by a factor ranging from 20 to 1883 by a simplified dispersivity model and a factor ranging from 4 to 85 by a dispersivity model based on a cut-and-random-rejoin type model of pore geometry from minimum to maximum mean biofilm thickness. Acknowledgements Funding for this research from US Dupont Company, and also from NSFC40872155, 40725010 and 41030746 is gratefully acknowledged. References: Clement, T.P., Hooker, B.S. and Skeen, R.S., 1996
Interaction trajectory of solitons in nonlinear media with an arbitrary degree of nonlocality
Dai, Zhiping; Yang, Zhenjun; Ling, Xiaohui; Zhang, Shumin; Pang, Zhaoguang
2016-03-15
The interaction trajectory of solitons in nonlocal nonlinear media is investigated. A simple differential equation describing the interaction trajectories is derived based on the light ray equation. Numerical calculations are carried out to illustrate the interaction trajectories with different parameters. The results show that the degree of nonlocality greatly affects the interaction of solitons. For a strongly nonlocal case, the interaction trajectory can be described by a cosine function. Analytical expressions describing the trajectory and the oscillation period are obtained. For generally and weakly nonlocal cases, the interaction trajectories still oscillate periodically, however it is no longer sinusoidal and the oscillation period increases with the nonlocal degree decreasing. In addition, the trajectory of two solitons launched with a relative angle at the entrance plane is investigated. It is found that there exists a critical angle. When the initial relative angle is larger than the critical angle, the two solitons do not collide on propagation. The influence of the degree of nonlocality on the critical angle is also discussed.
An efficient distribution method for nonlinear transport problems in stochastic porous media
NASA Astrophysics Data System (ADS)
Ibrahima, F.; Tchelepi, H.; Meyer, D. W.
2015-12-01
Because geophysical data are inexorably sparse and incomplete, stochastic treatments of simulated responses are convenient to explore possible scenarios and assess risks in subsurface problems. In particular, understanding how uncertainties propagate in porous media with nonlinear two-phase flow is essential, yet challenging, in reservoir simulation and hydrology. We give a computationally efficient and numerically accurate method to estimate the one-point probability density (PDF) and cumulative distribution functions (CDF) of the water saturation for the stochastic Buckley-Leverett problem when the probability distributions of the permeability and porosity fields are available. The method draws inspiration from the streamline approach and expresses the distributions of interest essentially in terms of an analytically derived mapping and the distribution of the time of flight. In a large class of applications the latter can be estimated at low computational costs (even via conventional Monte Carlo). Once the water saturation distribution is determined, any one-point statistics thereof can be obtained, especially its average and standard deviation. Moreover, rarely available in other approaches, yet crucial information such as the probability of rare events and saturation quantiles (e.g. P10, P50 and P90) can be derived from the method. We provide various examples and comparisons with Monte Carlo simulations to illustrate the performance of the method.
Density Waves in Saturn's Rings: Non-linear Dispersion and Moon Libration Effects
NASA Astrophysics Data System (ADS)
Sremcevic, Miodrag; Stewart, G. R.; Albers, N.; Colwell, J. E.; Esposito, L. W.
2008-05-01
We analyze strong spiral density waves in stellar occultations by Saturn's A ring observed with the Cassini Ultraviolet Imaging Spectrograph (UVIS) and find that waves dispersion relation exhibits a clear deviation from the linear trend. All waves examined here reveal an intrinsic quadratic radial dependence on the wavenumber. We provide evidence that the deviation from the linear trend is caused by the ring's pressure term acting against the self-gravity of the ring particles. From the observed dispersion relation and using the theory of Goldreich and Tremaine (1978, 1979, ApJ) where the pressure is parameterized as p=σ c2, we measure the velocity dispersion c=2-5 mm/s in the A ring. Additionally, in all first order Pandora waves the dispersion relation exhibits a wiggly structure. Comparing 60 stellar UVIS occultations between 2004 and 2008 we infer that this wavenumber oscillation propagates away from the resonance location with a period of about 600 days. This inferred period is consistent with the 3:2 near corotation resonance between Pandora and Mimas (French et al., 2003, Icarus). The observed libration in wavenumber allows us to accurately measure the group velocity in the rings and obtain independent estimates of both surface density and velocity dispersion of the rings.
Robertson, Scott; Leonhardt, Ulf
2014-11-01
Hawking radiation has become experimentally testable thanks to the many analog systems which mimic the effects of the event horizon on wave propagation. These systems are typically dominated by dispersion and give rise to a numerically soluble and stable ordinary differential equation only if the rest-frame dispersion relation Ω^{2}(k) is a polynomial of relatively low degree. Here we present a new method for the calculation of wave scattering in a one-dimensional medium of arbitrary dispersion. It views the wave equation as an integral equation in Fourier space, which can be solved using standard and efficient numerical techniques.
Phased-array cancellation of nonlinear FWM in coherent OFDM dispersive multi-span links.
Nazarathy, Moshe; Khurgin, Jacob; Weidenfeld, Rakefet; Meiman, Yehuda; Cho, Pak; Noe, Reinhold; Shpantzer, Isaac; Karagodsky, Vadim
2008-09-29
We develop an analytic model of Coherent Optical Orthogonal Frequency Division Multiplexing (OFDM) propagation and detection over multi-span long-haul fiber links, comprehensively and rigorously analyzing the impairments due the combined effects of FWM, Dispersion and ASE noise. Consistent with prior work of Innoe and Schadt in the WDM context, our new closed-form expressions for the total FWM received power fluctuations in the wake of dispersive phase mismatch in OFDM transmission, indicate that the FWM contributions of the multitude of spans build-up on a phased-array basis. For particular ultra-long haul link designs, the effectiveness of dispersion in reducing FWM is far greater than previously assumed in OFDM system analysis. The key is having the dominant FWM intermodulation products due to the multiple spans, destructively interfere, mutually cancelling their FWM intermodulation products, analogous to operating at the null of a phased-array antenna system. By applying the new analysis tools, this mode of effectively mitigating the FWM impairment, is shown under specific dispersion and spectral management conditions, to substantially suppress the FWM power fluctuations. Accounting for the phased-array concept and applying the compact OFDM design formulas developed here, we analyzed system performance of a 40 Gbps coherent OFDM system, over standard G.652 fiber, with cyclic prefix based electronic dispersion compensation but no optical compensation along the link. The transmission range for 10-3 target BER is almost tripled from 2560 km to 6960 km, relative to a reference system performing optical dispersion compensation in every span (ideally accounting for FWM and ASE noise and the cyclic prefix overhead, but excluding additional impairments).
Magnetic resonance imaging measurements evidence weak dispersion in homogeneous porous media
NASA Astrophysics Data System (ADS)
Lehoux, A. P.; Rodts, S.; Faure, P.; Michel, E.; Courtier-Murias, D.; Coussot, P.
2016-11-01
We measure the dispersion coefficient through homogeneous bead or sand packings at different flow rates from direct magnetic resonance imaging (MRI) visualizations of the transport characteristics of a pulse of paramagnetic nanoparticles. Through two-dimensional imaging we observe homogeneous dispersion inside the sample, but we show that entrance effects may induce significant radial heterogeneities, which would affect the interpretation of the breakthrough curve. Another MRI approach then provides quantitative measurements of the evolution in time of the longitudinal particle distribution in the sample. These data can be analyzed to deduce the coefficient of dispersion independently of entrance effects. The values obtained for this "effective" dispersion coefficient are almost ten times lower than the commonly accepted values.
Nonlinear wavelength conversion in photonic crystal fibers with three zero-dispersion points
Stark, S. P.; Biancalana, F.; Podlipensky, A.; St. J. Russell, P.
2011-02-15
In this theoretical study, we show that a simple endlessly single-mode photonic crystal fiber can be designed to yield, not just two, but three zero-dispersion wavelengths. The presence of a third dispersion zero creates a rich phase-matching topology, enabling enhanced control over the spectral locations of the four-wave-mixing and resonant-radiation bands emitted by solitons and short pulses. The greatly enhanced flexibility in the positioning of these bands has applications in wavelength conversion, supercontinuum generation, and pair-photon sources for quantum optics.
Dispersion of nonresonant third-order nonlinearities in GeSiSn ternary alloys
De Leonardis, Francesco; Troia, Benedetto; Soref, Richard A.; Passaro, Vittorio M. N.
2016-01-01
Silicon (Si), tin (Sn), and germanium (Ge) alloys have attracted research attention as direct band gap semiconductors with applications in electronics and optoelectronics. In particular, GeSn field effect transistors can exhibit very high performance in terms of power reduction and operating speed because of the high electron drift mobility, while the SiGeSn system can be constructed using CMOS-compatible techniques to realize lasers, LED, and photodetectors. The wide Si, Ge and Sn transparencies allow the use of binary and ternary alloys extended to mid-IR wavelengths, where nonlinearities can also be employed. However, neither theoretical or experimental predictions of nonlinear features in SiGeSn alloys are reported in the literature. For the first time, a rigorous and detailed physical investigation is presented to estimate the two photon absorption (TPA) coefficient and the Kerr refractive index for the SiGeSn alloy up to 12 μm. The TPA spectrum, the effective TPA wavelength cut-off, and the Kerr nonlinear refractive index have been determined as a function of alloy compositions. The promising results achieved can pave the way to the demonstration of on-chip nonlinear-based applications, including mid-IR spectrometer-on-a-chip, all-optical wavelength down/up-conversion, frequency comb generation, quantum-correlated photon-pair source generation and supercontinuum source creation, as well as Raman lasing. PMID:27622979
Dispersion of nonresonant third-order nonlinearities in GeSiSn ternary alloys
NASA Astrophysics Data System (ADS)
de Leonardis, Francesco; Troia, Benedetto; Soref, Richard A.; Passaro, Vittorio M. N.
2016-09-01
Silicon (Si), tin (Sn), and germanium (Ge) alloys have attracted research attention as direct band gap semiconductors with applications in electronics and optoelectronics. In particular, GeSn field effect transistors can exhibit very high performance in terms of power reduction and operating speed because of the high electron drift mobility, while the SiGeSn system can be constructed using CMOS-compatible techniques to realize lasers, LED, and photodetectors. The wide Si, Ge and Sn transparencies allow the use of binary and ternary alloys extended to mid-IR wavelengths, where nonlinearities can also be employed. However, neither theoretical or experimental predictions of nonlinear features in SiGeSn alloys are reported in the literature. For the first time, a rigorous and detailed physical investigation is presented to estimate the two photon absorption (TPA) coefficient and the Kerr refractive index for the SiGeSn alloy up to 12 μm. The TPA spectrum, the effective TPA wavelength cut-off, and the Kerr nonlinear refractive index have been determined as a function of alloy compositions. The promising results achieved can pave the way to the demonstration of on-chip nonlinear-based applications, including mid-IR spectrometer-on-a-chip, all-optical wavelength down/up-conversion, frequency comb generation, quantum-correlated photon-pair source generation and supercontinuum source creation, as well as Raman lasing.
Dispersion Effects in Nonlinear Light Propagation in 1-D Fiber Gratings
2007-11-02
Fundamentos Matemáticos E.T.S.I. Aeronáuticos Universidad Politécnica de Madrid 28040 Madrid, SPAIN Contents 1 Introduction...is based on the analysis and numerical simulations of the so-called nonlinear coupled mode equations (NLCME). This system of equations accounts for the
NASA Astrophysics Data System (ADS)
Fujioka, J.; Espinosa, A.
2015-11-01
In this article, we show that if the nonlinear Schrödinger (NLS) equation is generalized by simultaneously taking into account higher-order dispersion, a quintic nonlinearity, and self-steepening terms, the resulting equation is interesting as it has exact soliton solutions which may be (depending on the values of the coefficients) stable or unstable, standard or "embedded," fixed or "moving" (i.e., solitons which advance along the retarded-time axis). We investigate the stability of these solitons by means of a modified version of the Vakhitov-Kolokolov criterion, and numerical tests are carried out to corroborate that these solitons respond differently to perturbations. It is shown that this generalized NLS equation can be derived from a Lagrangian density which contains an auxiliary variable, and Noether's theorem is then used to show that the invariance of the action integral under infinitesimal gauge transformations generates a whole family of conserved quantities. Finally, we study if this equation has the Painlevé property.
Fujioka, J; Espinosa, A
2015-11-01
In this article, we show that if the nonlinear Schrödinger (NLS) equation is generalized by simultaneously taking into account higher-order dispersion, a quintic nonlinearity, and self-steepening terms, the resulting equation is interesting as it has exact soliton solutions which may be (depending on the values of the coefficients) stable or unstable, standard or "embedded," fixed or "moving" (i.e., solitons which advance along the retarded-time axis). We investigate the stability of these solitons by means of a modified version of the Vakhitov-Kolokolov criterion, and numerical tests are carried out to corroborate that these solitons respond differently to perturbations. It is shown that this generalized NLS equation can be derived from a Lagrangian density which contains an auxiliary variable, and Noether's theorem is then used to show that the invariance of the action integral under infinitesimal gauge transformations generates a whole family of conserved quantities. Finally, we study if this equation has the Painlevé property.
Modeling dispersion in three-dimensional heterogeneous fractured media at Yucca Mountain.
McKenna, Sean A; Walker, Douglas D; Arnold, Bill
2003-01-01
Highly resolved numerical simulations are conducted to evaluate the longitudinal and transverse dispersivities proposed for use in the larger-scale Yucca Mountain saturated zone (SZ) site-scale model. Two different stochastic continuum models (SCM) that define the spatial variability of permeability are inferred from the observed fracture characteristics and the measured permeabilities. These models are created with a combination of indicator geostatistics and boolean simulation that allow for modeling different correlation lengths and anisotropy ratios at different permeability thresholds as well as the inclusion of large, high-permeability features. Longitudinal and transverse (horizontal and vertical) dispersion through the permeability realizations is evaluated for both distributed and focused source geometries using groundwater flow and streamline particle tracking. These numerical results are compared to behavior predicted by an analytical solution and to dispersivities estimated by an expert panel. Early time transport results are significantly non-Gaussian due to the strong heterogeneity of the fractured medium. At late times, travel distances of 23 correlation lengths, the longitudinal and transverse horizontal dispersivity results are well approximated by the analytical solution and the expert elicitation estimates. The calculated transverse vertical dispersivity values are smaller than those estimated from the analytical solution. Inclusion of high-permeability features of the same size as the model domain with a distributed planar source creates extreme values of the longitudinal and transverse horizontal dispersivity.
Effective Block-Scale Dispersion and Its Self-Averaging Behavior in Heterogeneous Porous Media
NASA Astrophysics Data System (ADS)
de Barros, Felipe; Dentz, Marco
2015-04-01
Upscaled (effective) dispersion coefficients in spatially heterogeneous flow fields must (1) account for the sub-scale variability that is filtered out by homogenization and (2) be modeled as a random function to incorporate the uncertainty associated with non-ergodic solute bodies. In this study, we use the framework developed in de Barros and Rubin (2011) [de Barros F.P.J. and Rubin Y., Modelling of block-scale macrodispersion as a random function. Journal of Fluid Mechanics 676 (2011): 514-545] to develop novel semi-analytical expressions for the first two statistical moments of the block-effective dispersion coefficients in three-dimensional spatially random flow fields as a function of the key characteristic length scales defining the transport problem. The derived expressions are based on perturbation theory and limited to weak-to-mild heterogeneity and uniform-in-the-mean steady state flow fields. The semi-analytical solutions provide physical insights of the main controlling factors influencing the temporal scaling of the dispersion coefficient of the solute body and its self-averaging dispersion behavior. Our results illustrate the relevance of the joint influence of the block-scale and local-scale dispersion in diminishing the macrodispersion variance under non-ergodic conditions. The impact of the statistical anisotropy ratio in the block-effective macrodispersion self-averaging behavior is also investigated. The analysis performed in this work has implications in numerical modeling and grid design.
Characterizing dispersivity and stagnation in porous media using NMR flow propagators
NASA Astrophysics Data System (ADS)
Singer, P. M.; Mitchell, J.; Fordham, E. J.
2016-09-01
Low-field nuclear magnetic resonance (NMR) displacement probability distributions (flow propagators) are presented for water flowing through heterogeneous porous materials. Four sedimentary rocks have been chosen as example systems: Dolostone, Bentheimer sandstone, Berea sandstone, and Indiana limestone (in order of decreasing permeability). The fluid displacement is characterized by pre-asymptotic Stokes' flow and so the probability distributions are bimodal, with peaks corresponding to stagnant fluid in dead-end pores and flowing fluid in the connected porosity. Cut-off Gaussian functions are used to fit the flowing and stagnant peaks independently. An effective dispersivity length scale Lv (also known as the mixing length scale) is estimated by fitting the portion of the probability distribution corresponding to the flowing fluid. For the relatively homogeneous Bentheimer sandstone, the ratio of effective dispersivity length scale to effective transport diameter dt is Lv /dt ≈ 16 , which is an order of magnitude larger than for randomly packed glass beads where Lv /dt ≈ 1.8 . We compare these dispersivity parameters to similar values extracted from a cumulant analysis of the entire propagator. Fitting a cut-off Gaussian avoids the usual complications of analyzing dispersion in the presence of the ubiquitous stagnant fluid, and results in a clear demonstration of the influence of long-range heterogeneities on the dispersivity for flow in real sedimentary rocks.
Characterizing dispersivity and stagnation in porous media using NMR flow propagators.
Singer, P M; Mitchell, J; Fordham, E J
2016-09-01
Low-field nuclear magnetic resonance (NMR) displacement probability distributions (flow propagators) are presented for water flowing through heterogeneous porous materials. Four sedimentary rocks have been chosen as example systems: Dolostone, Bentheimer sandstone, Berea sandstone, and Indiana limestone (in order of decreasing permeability). The fluid displacement is characterized by pre-asymptotic Stokes' flow and so the probability distributions are bimodal, with peaks corresponding to stagnant fluid in dead-end pores and flowing fluid in the connected porosity. Cut-off Gaussian functions are used to fit the flowing and stagnant peaks independently. An effective dispersivity length scale Lv (also known as the mixing length scale) is estimated by fitting the portion of the probability distribution corresponding to the flowing fluid. For the relatively homogeneous Bentheimer sandstone, the ratio of effective dispersivity length scale to effective transport diameter dt is Lv/dt≈16, which is an order of magnitude larger than for randomly packed glass beads where Lv/dt≈1.8. We compare these dispersivity parameters to similar values extracted from a cumulant analysis of the entire propagator. Fitting a cut-off Gaussian avoids the usual complications of analyzing dispersion in the presence of the ubiquitous stagnant fluid, and results in a clear demonstration of the influence of long-range heterogeneities on the dispersivity for flow in real sedimentary rocks.
Westergaard, Philip G; Christensen, Bjarke T R; Tieri, David; Matin, Rastin; Cooper, John; Holland, Murray; Ye, Jun; Thomsen, Jan W
2015-03-06
As an alternative to state-of-the-art laser frequency stabilization using ultrastable cavities, it has been proposed to exploit the nonlinear effects from coupling of atoms with a narrow transition to an optical cavity. Here, we have constructed such a system and observed nonlinear phase shifts of a narrow optical line by a strong coupling of a sample of strontium-88 atoms to an optical cavity. The sample temperature of a few mK provides a domain where the Doppler energy scale is several orders of magnitude larger than the narrow linewidth of the optical transition. This makes the system sensitive to velocity dependent multiphoton scattering events (Dopplerons) that affect the cavity field transmission and phase. By varying the number of atoms and the intracavity power, we systematically study this nonlinear phase signature which displays roughly the same features as for much lower temperature samples. This demonstration in a relatively simple system opens new possibilities for alternative routes to laser stabilization at the sub-100 mHz level and superradiant laser sources involving narrow-line atoms. The understanding of relevant motional effects obtained here has direct implications for other atomic clocks when used in relation to ultranarrow clock transitions.
A new formulation of the dispersion tensor in homogeneous porous media
NASA Astrophysics Data System (ADS)
Valdés-Parada, Francisco J.; Lasseux, Didier; Bellet, Fabien
2016-04-01
Dispersion is the result of two mass transport processes, namely molecular diffusion, which is a pure mixing effect and hydrodynamic dispersion, which combines mixing and spreading. The identification of each contribution is crucial and is often misinterpreted. Traditionally, under a volume averaging framework, a single closure problem is solved and the resulting fields are substituted into diffusive and dispersive filters. However the diffusive filter (that leads to the effective diffusivity) allows passing information from convection, which leads to an incorrect definition of the effective medium coefficients composing the total dispersion tensor. In this work, we revisit the definitions of the effective diffusivity and hydrodynamic dispersion tensors using the method of volume averaging. Our analysis shows that, in the context of laminar flow with or without inertial effects, two closure problems need to be computed in order to correctly define the corresponding effective medium coefficients. The first closure problem is associated to momentum transport and needs to be solved for a prescribed Reynolds number and flow orientation. The second closure problem is related to mass transport and it is solved first with a zero Péclet number and second with the required Péclet number and flow orientation. All the closure problems are written using closure variables only as required by the upscaling method. The total dispersion tensor is shown to depend on the microstructure, macroscopic flow angles, the cell (or pore) Péclet number and the cell (or pore) Reynolds number. It is non-symmetric in the general case. The condition for quasi-symmetry is highlighted. The functionality of the longitudinal and transverse components of this tensor with the flow angle is investigated for a 2D model porous structure obtaining consistent results with previous studies.
NASA Astrophysics Data System (ADS)
Ibrahima, Fayadhoi; Meyer, Daniel; Tchelepi, Hamdi
2016-04-01
Because geophysical data are inexorably sparse and incomplete, stochastic treatments of simulated responses are crucial to explore possible scenarios and assess risks in subsurface problems. In particular, nonlinear two-phase flows in porous media are essential, yet challenging, in reservoir simulation and hydrology. Adding highly heterogeneous and uncertain input, such as the permeability and porosity fields, transforms the estimation of the flow response into a tough stochastic problem for which computationally expensive Monte Carlo (MC) simulations remain the preferred option.We propose an alternative approach to evaluate the probability distribution of the (water) saturation for the stochastic Buckley-Leverett problem when the probability distributions of the permeability and porosity fields are available. We give a computationally efficient and numerically accurate method to estimate the one-point probability density (PDF) and cumulative distribution functions (CDF) of the (water) saturation. The distribution method draws inspiration from a Lagrangian approach of the stochastic transport problem and expresses the saturation PDF and CDF essentially in terms of a deterministic mapping and the distribution and statistics of scalar random fields. In a large class of applications these random fields can be estimated at low computational costs (few MC runs), thus making the distribution method attractive. Even though the method relies on a key assumption of fixed streamlines, we show that it performs well for high input variances, which is the case of interest. Once the saturation distribution is determined, any one-point statistics thereof can be obtained, especially the saturation average and standard deviation. Moreover, the probability of rare events and saturation quantiles (e.g. P10, P50 and P90) can be efficiently derived from the distribution method. These statistics can then be used for risk assessment, as well as data assimilation and uncertainty reduction
NASA Astrophysics Data System (ADS)
Gorokhovskii, A. V.; Gorshkov, N. V.; Burmistrov, I. N.; Goffman, V. G.; Tret'yachenko, E. V.; Sevryugin, A. V.; Fedorov, F. S.; Kovyneva, N. N.
2016-06-01
The electrical properties of dispersions of a powdered ferroelectric nanocomposite based on ilmenite (FeTiO3) and hollandite (K1.46Ti7.2Fe0.8O16) in dioctyl phthalate have been studied by impedance spectroscopy techniques in a frequency range of 10-1-106 Hz. The influence of stabilizing additives of cationic and anionic surfactants and iron acetylacetonate on the permittivity, conductivity, and dielectric losses was determined for dispersions containing 40 mass % of the solid composite. The influence of composition on the mechanisms of relaxation processes in the system is discussed.
Robertson, Scott
2014-11-01
Analog gravity experiments make feasible the realization of black hole space-times in a laboratory setting and the observational verification of Hawking radiation. Since such analog systems are typically dominated by dispersion, efficient techniques for calculating the predicted Hawking spectrum in the presence of strong dispersion are required. In the preceding paper, an integral method in Fourier space is proposed for stationary 1+1-dimensional backgrounds which are asymptotically symmetric. Here, this method is generalized to backgrounds which are different in the asymptotic regions to the left and right of the scattering region.
NASA Astrophysics Data System (ADS)
Zhang, Guo-Bao; Ma, Ruyun
2014-10-01
This paper is concerned with the traveling wave solutions and the spreading speeds for a nonlocal dispersal equation with convolution-type crossing-monostable nonlinearity, which is motivated by an age-structured population model with time delay. We first prove the existence of traveling wave solution with critical wave speed c = c*. By introducing two auxiliary monotone birth functions and using a fluctuation method, we further show that the number c = c* is also the spreading speed of the corresponding initial value problem with compact support. Then, the nonexistence of traveling wave solutions for c < c* is established. Finally, by means of the (technical) weighted energy method, we prove that the traveling wave with large speed is exponentially stable, when the initial perturbation around the wave is relatively small in a weighted norm.
Acelas, Nancy Y; Martin, Benjamin D; López, Diana; Jefferson, Bruce
2015-01-01
Hydrated ferric oxide (HFeO), hydrated zirconium oxide (HZrO) and hydrated copper oxide (HCuO) were immobilized within a microporous anion exchange resin (IRA-400), forming hybrid media for enhanced phosphate removal from aqueous systems. Empirical data from batch kinetic trials fitted the pseudo second order mechanism for chemical adsorption and each media was rate limited by intraparticle diffusion overall. These models were also used to predict the adsorption rate constants and the equilibrium adsorption capacities, which ranged from 26.51 to 30.44 mgP g(-1), and from 24.15 to 27.90 mgP g(-1) of media for the calculated and experimental capacities, respectively. The phosphate adsorption behavior by the hybrid materials fit both the Langmuir and Freundlich adsorption isotherms (R(2)>0.94), and the maximum adsorption capacities were 111.1 mgP g(-1) for HFeO, 91.74 mgP g(-1) for HZrO and 74.07 mgP g(-1) for HCuO. The effect of competing ions such as sulfate reduced these capacities to 18.52 mgP g(-1) for HFeO and 18.97 mgP g(-1) for HZrO. Despite this decrease, HFeO was capable of reducing the phosphate in a real wastewater matrix by 83%, and the HZrO media was able to reduce it by 86%, suggesting that such hybrid media have the potential for application at full scale.
NASA Astrophysics Data System (ADS)
Rudenko, O. V.; Hedberg, C. M.
2015-01-01
The stationary profile in the focal region of a focused nonlinear acoustic wave is described. Three models following from the Khokhlov-Zabolotskaya (KZ) equation with three independent variables are used: (i) the simplified one-dimensional Ostrovsky-Vakhnenko equation, (ii) the system of equations for paraxial series expansion of the acoustic field in powers of transverse coordinates, and (iii) the KZ equation reduced to two independent variables. The structure of the last equation is analogous to the Westervelt equation. Linearization through the Legendre transformation and reduction to the well-studied Euler-Tricomi equation is shown. At high intensities the stationary profiles are periodic sequences of arc sections having singularities of derivative in their matching points. The occurrence of arc profiles was pointed out by Makov. These appear in different nonlinear systems with low-frequency dispersion. Profiles containing discontinuities (shock fronts) change their form while passing through the focal region and are non-stationary waves. The numerical estimations of maximum pressure and intensity in the focus agree with computer calculations and experimental measurements.
On the Role of Osmosis for Non-Linear Shock Waves f Pressure and Solute in Porous Media
NASA Astrophysics Data System (ADS)
Kanivesky, Roman; Salusti, Ettore; Caserta, Arrigo
2013-04-01
A novel non-Osanger model focusing on non-linear mechanic and chemo-poroelastic coupling of fluids and solute in porous rocks is developed based on the modern wave theory. Analyzing in 1-D a system of two adjacent rocks with different conditions we obtain two coupled non-linear equations for fluid pressure and solute (salt or pollutants) concentration, evolving under the action of strong stress from one "source" rock towards the other rock. Their solutions allow to identify quick non-linear solitary (Burgers) waves of coupled fluid pressure and solute density, that are different from diffusive or perturbative solutions found in other analyses. The strong transient waves for low permeability porous media, such as clay and shale, are analyzed in detail. For medium and high-permeability porous media (sandstones) this model is also tentatively applied. Indeed in recent works of Alexander (1990) and Hart(2009) is supported the presence of small osmotic phenomena in other rocks where osmosis was previously ignored. An attempt to apply our model to soils in Calabria (Italy), such as clastic marine and fluvial deposits as well as discontinuous remnants of Miocene and Pliocene carbonate and terrigeneous deposits, is also discussed.
NASA Astrophysics Data System (ADS)
Choudhury, Raja Roy; Choudhury, Arundhati Roy; Ghose, Mrinal Kanti
2013-09-01
To characterize nonlinear optical fiber, a semi-analytical formulation using variational principle and the Nelder-Mead Simplex method for nonlinear unconstrained minimization is proposed. The number of optimizing parameters in order to optimize core parameter U has been increased to incorporate more flexibility in the formulation of an innovative form of fundamental modal field. This formulation provides accurate analytical expressions for modal dispersion parameter (g) of optical fiber with Kerr nonlinearity. The minimization of core parameter (U), which involves Kerr nonlinearity through the nonstationary expression of propagation constant, is carried out by the Nelder-Mead Simplex method of nonlinear unconstrained minimization, suitable for problems with nonsmooth functions as the method does not require any derivative information. This formulation has less computational burden for calculation of modal parameters than full numerical methods.
Tardajos, Myriam G; Aranaz, Inmaculada; Sayar, Filiz; Elvira, Carlos; Reinecke, Helmut; Piskin, Erhan; Gallardo, Alberto
2012-04-03
The differential reactivity of methylmethacrylate (MMA) and vinylpyrrolidone (VP) in free radical copolymerization, with stirring in methanol, renders an emulsified two phase system. The dispersed and continuous liquid phases contain copolymers rich in MMA and VP, respectively. When Fe(3)O(4) magnetic nanoparticles (mNPs) stabilized with tetramethylammonium hydroxide are added to this emulsion, the mNPs are located in the continuous phase. Very small chemical changes in the methacrylic or vinylic chains are able to guide the mNP toward the interface or to the inside of the dispersed phase since quite a selective functionalization of each phase may be achieved separately. Thus, a small addition of methacrylic acid as comonomer (0.5% molar) guides all of the mNPs to the interface while a 0.5% molar of sulfopropyl methacrylate induces the migration of all mNPs to the dispersed phase. When 0.5% molar of a VP derivative bearing sulfonate functionality is added, the mNPs are found both in the interface and in the continuous phase. The addition of water allows solid MMA-based microspheres to be obtained incorporating the mNPs selectively either at the surface or in the core.
The Wave Processes in the Media Having Inelastic Hysteresis with Saturation of The Nonlinear Loss
NASA Astrophysics Data System (ADS)
Nazarov, V. E.; Kiyashko, S. B.
2016-07-01
We study theoretically the nonlinear wave processes during excitation of a longitudinal harmonic wave in an unbounded medium and the rod resonator with inelastic hysteresis and saturation of the amplitude-dependent loss. The nonlinear-wave characteristics in such systems, namely, the amplitude-dependent loss, variation in the wave-propagation velocity, the resonant-frequency shift, and the higher-harmonic amplitudes are determined. The results of the theoretical and experimental studies of nonlinear effects in the rod resonator of annealed polycrystalline copper are compared. The effective parameters of the hysteretic nonlinearity of this metal are evaluated.
Dietrich, Scott; Mayer, William; Byrnes, Sean; ...
2015-02-20
The effects of microwave radiation on transport properties of atomically thin La2-xSrxCuO₄ films were studied in the 0.1-20 GHz frequency range. Resistance changes induced by microwaves were investigated at different temperatures (8–15 K) near the superconducting transition. A strong decrease of the nonlinear response is observed within a few GHz of a cutoff frequency νcut ≈ 2GHz. The expected frequency dependence vastly underestimates the sharpness of this drop. Numerical simulations that assume ac response to follow dc V-I characteristics of the films reproduce well the low frequency behavior, but fail above νcut. Thus, high-frequency radiation is much less effective inmore » inducing vortex-antivortex dissociation in the oscillating superconducting condensate.« less
Dietrich, Scott; Mayer, William; Byrnes, Sean; Vitkalov, Sergey; Sergeev, A.; Bollinger, Anthony T.; Božović, Ivan
2015-02-20
The effects of microwave radiation on transport properties of atomically thin La_{2-x}Sr_{x}CuO₄ films were studied in the 0.1-20 GHz frequency range. Resistance changes induced by microwaves were investigated at different temperatures (8–15 K) near the superconducting transition. A strong decrease of the nonlinear response is observed within a few GHz of a cutoff frequency ν_{cut} ≈ 2GHz. The expected frequency dependence vastly underestimates the sharpness of this drop. Numerical simulations that assume ac response to follow dc V-I characteristics of the films reproduce well the low frequency behavior, but fail above ν_{cut}. Thus, high-frequency radiation is much less effective in inducing vortex-antivortex dissociation in the oscillating superconducting condensate.
NASA Astrophysics Data System (ADS)
Faccio, Daniele; Clerici, Matteo; Averchi, Alessandro; Lotti, Antonio; Jedrkiewicz, Ottavia; Dubietis, Audrius; Tamosauskas, Gintaras; Couairon, Arnaud; Bragheri, Francesca; Papazoglou, Dimitris; Tzortzakis, Stelios; di Trapani, Paolo
2008-09-01
We study ultrashort laser-pulse propagation and filamentation dynamics in dispersive Kerr media. We identify the regime for which the filamentation threshold (Pth) is considerably higher than the critical power (Pcr) for monochromatic beam collapse in pure Kerr media. In particular, we compare the threshold for the formation of filaments with that for the formation of X -waves. At powers Pcr
dispersion, and no filaments or X -waves are formed. At P⩾Pth , we observe X -wave formation and a weak filamentation regime. At P≫Pth , we observe both X -waves and fully formed filaments.
Tao, Wei; Bao, Hongchun; Gu, Min
2011-05-01
Real-time monitoring the variation of chlorophyll distributions and cellular structures in leaves during plant growth provides important information for understanding the physiological statuses of plants. Two-photon-excited autofluorescence imaging and second harmonic generation imaging of leaves can be used for monitoring the nature intrinsic fluorophores distribution and cellular structures of leaves by the use of the near-infrared region of light which has minimal light absorption by endogenous molecules and thus increases tissue penetration. However, the two-photon absorption peak of intrinsic fluorophores of a ficus benjamina leaf is 50 nm away from the second harmonic generation excitation wavelength, which cannot be effectively excited by a femtosecond laser beam with one central wavelength. This paper shows that a highly polarized supercontinuum light generated from a birefringent nonlinear photonic crystal fiber with two zero-dispersion wavelengths can effectively excite two-photon autofluorescence as well as second harmonic generation signals for simultaneously monitoring intrinsic fluorophore distributions and non-centrosymmetric structures of leaves.
NASA Astrophysics Data System (ADS)
Leble, Sergei B.
S.B. Leble's book deals with nonlinear waves and their propagation in metallic and dielectric waveguides and media with stratification. The underlying nonlinear evolution equations (NEEs) are derived giving also their solutions for specific situations. The reader will find new elements to the traditional approach. Various dispersion and relaxation laws for different guides are considered as well as the explicit form of projection operators, NEEs, quasi-solitons and of Darboux transforms. Special points relate to: 1. the development of a universal asymptotic method of deriving NEEs for guide propagation; 2. applications to the cases of stratified liquids, gases, solids and plasmas with various nonlinearities and dispersion laws; 3. connections between the basic problem and soliton- like solutions of the corresponding NEEs; 4. discussion of details of simple solutions in higher- order nonsingular perturbation theory.
NASA Astrophysics Data System (ADS)
Li, Xiaobo; Dong, Liangguo; Zhao, Qun
2014-12-01
Seismic wave propagation in patchy-saturated porous media is studied by numerical simulation in time domain at the seismic frequency band (1-1000 Hz). The models consist of hundreds of representative elementary volumes (REVs), where the REV is partially saturated with water and gas pockets. Seismic modelling experiments are implemented in a traditional way, with ‘periodic’ boundary conditions applied to get rid of undrained boundary conditions at the outer edges of the REVs. The characteristics of confining pressure, induced pore pressure, solid particle velocities and Darcy filtration velocities are analysed. The snapshots show that strong pore pressure gradients are generated across the interface between gas and water phases, and significant fluid flow occurs. The conversion of a fast P-wave into a dissipating slow P-wave takes place at seismic frequencies, and the converted slow P-wave diffuses strongly in both gas- and water-saturated phases. These numerical results can help us to understand the loss mechanism at seismic frequencies. Then, P-wave attenuation and velocity dispersion of a heterogeneous REV are calculated during traditional seismic modelling at seismic frequencies. The numerical results show good agreement with theoretical predictions obtained from patchy saturation theory. Furthermore, the effects of different fluid distributions on P-wave attenuation and velocity dispersion are analysed numerically. A series of experiments are implemented by considering large, small and random gas-patchy inclusions. The decrease of gas pocket size makes the peak frequency move towards high frequencies. Random distribution of gas patches may affect both the peak attenuation and peak frequencies. Seismic attenuation caused by Biot global flow, elastic scattering and wave-induced fluid flow (WIFF) associated with patchy saturation are computed numerically. The results show that the contribution of Biot’s global flow and scattering to the overall attenuation
Dual-Lagrangian description adapted to quantum optics in dispersive and dissipative dielectric media
NASA Astrophysics Data System (ADS)
Drezet, Aurélien
2016-11-01
We develop a dual description of quantum optics adapted to dielectric systems without magnetic property. Our formalism, which is shown to be equivalent to the standard one within some dipolar approximations discussed in the article, is applied to the description of polaritons in dielectric media. We show that the dual formalism leads to the Huttner-Barnett equations [B. Huttner and S. M. Barnett, Phys. Rev. A 46, 4306 (1992), 10.1103/PhysRevA.46.4306] for QED in dielectric systems. More generally, we discuss the role of electromagnetic duality in the quantization procedure for optical systems and derive the structure of the dynamical laws in the various representations.
NASA Astrophysics Data System (ADS)
Rauter, N.; Lammering, R.
2015-04-01
In order to detect micro-structural damages accurately new methods are currently developed. A promising tool is the generation of higher harmonic wave modes caused by the nonlinear Lamb wave propagation in plate like structures. Due to the very small amplitudes a cumulative effect is used. To get a better overview of this inspection method numerical simulations are essential. Previous studies have developed the analytical description of this phenomenon which is based on the five-constant nonlinear elastic theory. The analytical solution has been approved by numerical simulations. In this work first the nonlinear cumulative wave propagation is simulated and analyzed considering micro-structural cracks in thin linear elastic isotropic plates. It is shown that there is a cumulative effect considering the S1-S2 mode pair. Furthermore the sensitivity of the relative acoustical nonlinearity parameter regarding those damages is validated. Furthermore, an influence of the crack size and orientation on the nonlinear wave propagation behavior is observed. In a second step the micro-structural cracks are replaced by a nonlinear material model. Instead of the five-constant nonlinear elastic theory hyperelastic material models that are implemented in commonly used FEM software are used to simulate the cumulative effect of the higher harmonic Lamb wave generation. The cumulative effect as well as the different nonlinear behavior of the S1-S2 and S2-S4 mode pairs are found by using these hyperelastic material models. It is shown that, both numerical simulations, which take into account micro-structural cracks on the one hand and nonlinear material on the other hand, lead to comparable results. Furthermore, in comparison to the five-constant nonlinear elastic theory the use of the well established hyperelastic material models like Neo-Hooke and Mooney-Rivlin are a suitable alternative to simulate the cumulative higher harmonic generation.
NASA Astrophysics Data System (ADS)
Glasgow, Scott Alan; Corson, John; Verhaaren, Chris
2010-07-01
Free energies of dissipative media are reviewed. Then we use free-energy-optimal excitation and de-excitation fields to generate a dielectric’s time-reversal spectrum, with several properties: a) The spectrum generalizes the time-reversal parity from “even” and “odd” of conservative systems to an interval [-1,+1] of “time-reversal eigenvalues” λ in dissipative media. b) It yields eigenmodes that are complete: any state of the medium is optimally excitable or de-excitable by them. c) These excitations are orthogonal with respect to the work function of the medium and, so, d) characterize field excitations for the given medium that, when superimposed, only do work on the medium, not on each other via the medium-field interaction mechanism. Notions of en masse potential and kinetic energy in the dissipative medium arise through even (λ=+1) and odd (λ=-1) parity, but also other energy notions via alternative parity (|λ|<1) under time reversal.
Light generation at the anomalous dispersion high energy range of a nonlinear opal film.
Botey, Muriel; Maymó, Marc; Molinos-Gómez, Alberto; Dorado, Luis; Depine, Ricardo A; Lozano, Gabriel; Mihi, Agustín; Míguez, Hernán; Martorell, Jordi
2009-07-20
We study experimentally and theoretically light propagation and generation at the high energy range of a close-packed fcc photonic crystal of polystyrene spheres coated with a nonlinear material. We observe an enhancement of the second harmonic generation of light that may be explained on the basis of amplification effects arising from propagation at anomalous group velocities. Theoretical calculations are performed to support this assumption. The vector KKR method we use allows us to determine, from the linear response of the crystal, the behavior of the group velocity in our finite photonic structures when losses introduced by absorption or scattering by defects are taken into account assuming a nonzero imaginary part for the dielectric constant. In such structures, we predict large variations of the group velocity for wavelengths on the order or smaller than the lattice constant of the structure, where an anomalous group velocity behavior is associated with the flat bands of the photonic band structure. We find that a direct relation may be established between the group velocity reduction and the enhancement of a light generation processes such as the second harmonic generation we consider. However, frequencies for which the enhancement is found, in the finite photonic crystals we use, do not necessarily coincide with the frequencies of flat high energy bands.
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.
Zhang, Y.; Xu, Y.; Xia, J.
2011-01-01
We analyse dispersion and attenuation of surface waves at free surfaces of possible vacuum/poroelastic media: permeable-'open pore', impermeable-'closed pore' and partially permeable boundaries, which have not been previously reported in detail by researchers, under different surface-permeable, viscous-damping, elastic and fluid-flowing conditions. Our discussion is focused on their characteristics in the exploration-seismic frequency band (a few through 200 Hz) for near-surface applications. We find two surface-wave modes exist, R1 waves for all conditions, and R2 waves for closed-pore and partially permeable conditions. For R1 waves, velocities disperse most under partially permeable conditions and least under the open-pore condition. High-coupling damping coefficients move the main dispersion frequency range to high frequencies. There is an f1 frequency dependence as a constant-Q model for attenuation at high frequencies. R1 waves for the open pore are most sensitive to elastic modulus variation, but least sensitive to tortuosities variation. R1 waves for partially permeable surface radiate as non-physical waves (Im(k) < 0) at low frequencies. For R2 waves, velocities are slightly lower than the bulk slow P2 waves. At low frequencies, both velocity and attenuation are diffusive of f1/2 frequency dependence, as P2 waves. It is found that for partially permeable surfaces, the attenuation displays -f1 frequency dependence as frequency increasing. High surface permeability, low-coupling damping coefficients, low Poisson's ratios, and low tortuosities increase the slope of the -f1 dependence. When the attenuation coefficients reach 0, R2 waves for partially permeable surface begin to radiate as non-physical waves. ?? 2011 The Authors Geophysical Journal International ?? 2011 RAS.
Chen, Yong; Yan, Zhenya
2016-03-22
Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields.
Chen, Yong; Yan, Zhenya
2016-01-01
Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields. PMID:27002543
Gagnon, Yakir L; Kröger, Ronald H H; Söderberg, Bo
2010-04-21
Color dispersion, i.e., the dependency of refractive index of any transparent material on the wavelength of light, has important consequences for the function of optical instruments and animal eyes. Using a multi-objective goal attainment optimization algorithm, a dispersion model was successfully fitted to measured refractive indices of various ocular media and the longitudinal chromatic aberration determined by laser-scanning in the crystalline lens of the African cichlid fish, Astatotilapia burtoni. The model describes the effects of color dispersion in fish lenses and may be applicable to the eyes of other vertebrates as well.
Casanova, Axelle; Carriere, Marie; Herlin-Boime, Nathalie
2011-02-01
In this paper, results concerning the dispersion by different ways of a very common industrial titania NP (Degussa P25 produced in ton quantities). When dispersed in water, the suspensions of NP appear stable for weeks. When transferred in the cell culture medium (DMEM) or if directly dispersed in DMEM, strong evolution of size is seen as well as sedimentation. To address this problem and avoid direct aggregation, when going to DMEM, a "surfactant" relevant with biological studies (FBS) prior to transfer in DMEM (or other cell media) can be used. The main results are presented here.
Nonlinearization and waves in bounded media: old wine in a new bottle
NASA Astrophysics Data System (ADS)
Mortell, Michael P.; Seymour, Brian R.
2017-02-01
We consider problems such as a standing wave in a closed straight tube, a self-sustained oscillation, damped resonance, evolution of resonance and resonance between concentric spheres. These nonlinear problems, and other similar ones, have been solved by a variety of techniques when it is seen that linear theory fails. The unifying approach given here is to initially set up the appropriate linear difference equation, where the difference is the linear travel time. When the linear travel time is replaced by a corrected nonlinear travel time, the nonlinear difference equation yields the required solution.
Pikal, M J; Lukes, A L
1976-09-01
The gravimetric Knudsen method for vapor pressure measurement may be subject to serious systematic errors when the sample: (a) consists of the volatile component dispersed in an inert porous matrix and/or (b) contains a dissolved polymeric solute. Vaporization of water present as an impurity in the matrix may result in an appreciable "background" mass loss, and "nonequilibrium effects" may be present; i.e., The vapor of interest may be unable to escape from the sample rapidly enough to maintain the equilibrium vapor pressure in the Knudsen cell. Methods for eliminating the interference due to background effects are described, and a theoretical analysis of nonequilibrium effects is presented. The essential validity of the theories for nonequilibrium effects and the effectiveness of the methods for circumventing background effects were verified by experimental studies with molded nitroglycerin tablets. With nitroglycerin tablets, accurate Knudsen vapor pressure data may be obtained using the modified procedures and data analysis presented in this report.
NASA Astrophysics Data System (ADS)
Schoofs, Stan; Trompert, Ron A.; Hansen, Ulrich
2000-03-01
Horizontally layered structures can develop in porous or partially molten environments, such as hydrothermal systems, magmatic intrusions and the early Earth's mantle. The porosity φ of these natural environments is typically small. Since dissolved chemical elements unlike heat cannot diffuse through the solid rocks, heat and solute influence the interstitial fluid density in a different manner: heat advects slower than solute through the liquid by the factor φ, while diffusion of heat through the bulk porous medium is larger by the factor φ-1 times the ratio between the thermal and chemical diffusivities. By performing numerical experiments in which a rigid low-porosity medium is heated from below, we have studied the formation and evolution of layers in an initially stably stratified liquid. Growth of a convective layer through convective entrainment, the formation of a stable density interface on top of the layer and destabilization of the next layer are intimately linked. By monitoring the heat (solute) fluxes, it is observed that the transport of heat (solute) across the interface changes from convective entrainment towards a regime in which transfer is purely diffusive (dispersive). Because this transition occurs before the stage at which the lower layer arrives at the thermal equilibrium, we conclude that the layer growth stops when the density interface on top has grown sufficiently strong to keep the ascending plumes in the lower layer from convectively entraining more fluid from above. A simple balance between the most important forces, exerted on a fluid parcel in the lower layer, is proposed to determine this transition. This force balance also indicates whether a density interface keeps intact, migrates upwards or breaks down during the further evolution of the layered sequence. Finally, mechanical dispersion tends to increase transport of chemically dissolved elements across the density interface. Since this reduces the density difference between
NASA Astrophysics Data System (ADS)
Doney, Robert L.; Agui, Juan H.; Sen, Surajit
2009-09-01
Rapid absorption of impulses using light-weight, small, reusable systems is a challenging problem. An axially aligned set of progressively shrinking elastic spheres, a "tapered chain," has been shown to be a versatile and scalable shock absorber in earlier simulational, theoretical, and experimental works by several authors. We have recently shown (see R. L. Doney and S. Sen, Phys. Rev. Lett. 97, 155502 (2006)) that the shock absorption ability of a tapered chain can be dramatically enhanced by placing small interstitial grains between the regular grains in the tapered chain systems. Here we focus on a detailed study of the problem introduced in the above mentioned letter, present extensive dynamical simulations using parameters for a titanium-aluminum-vanadium alloy Ti6Al4V, derive attendant hard-sphere analyses based formulae to describe energy dispersion, and finally discuss some preliminary experimental results using systems with chrome spheres and small Nitinol interstitial grains to present the underlying nonlinear dynamics of this so-called decorated tapered granular alignment. We are specifically interested in small systems, comprised of several grains. This is because in real applications, mass and volume occupied must inevitably be minimized. Our conclusion is that the decorated tapered chain offers enhanced energy dispersion by locking in much of the input energy in the grains of the tapered chain rather than in the small interstitial grains. Thus, the present study offers insights into how the shock absorption capabilities of these systems can be pushed even further by improving energy absorption capabilities of the larger grains in the tapered chains. We envision that these scalable, decorated tapered chains may be used as shock absorbing components in body armor, armored vehicles, building applications and in perhaps even in applications in rehabilitation science.
A self-consistent theory of localization in nonlinear random media
NASA Astrophysics Data System (ADS)
Cherroret, Nicolas
2017-01-01
The self-consistent theory of localization is generalized to account for a weak quadratic nonlinear potential in the wave equation. For spreading wave packets, the theory predicts the destruction of Anderson localization by the nonlinearity and its replacement by algebraic subdiffusion, while classical diffusion remains unaffected. In 3D, this leads to the emergence of a subdiffusion-diffusion transition in place of the Anderson transition. The accuracy and the limitations of the theory are discussed.
Gilles, L; Moloney, J V; Vázquez, L
1999-07-01
The dynamical evolution of an intense ultrashort sub-10-fs two-cycle optical pulse is considered as it propagates through a transparent third-order dielectric medium characterized by three resonance lines and a finite sub-fs relaxation time of the electronic nonlinearity. Numerical integration of the full Maxwell's equations incorporating triple-resonance Lorentz linear dispersion and Debye nonlinear dispersion, for a linearly polarized electromagnetic pulse centered at lambda(0)=1.24 microm in the normal dispersion region near the zero dispersion wavelength, shows the formation of shocks occurring on the optical cycle due to the generation of optical harmonics. The finite relaxation time of the nonlinear electronic response (sub-fs time scale) (i) slows down the steepening rate of the optical cycle; (ii) does not limit the generation of strongly phase matched optical harmonics, and consequently the development of infinitely sharp edges on the optical cycle producing its breaking when linear dispersion is not included; (iii) reduces the production of phase matched harmonics and consequently the sharpening of the jumps when dispersion is present, compared to the case of an instantaneous nonlinear response; and (iv) reduces the harmonic spectrum spreading and modulation at later times on the appearance of self-steepening of the electric field envelope.
Kumar, Shiva; Shao, Jing; Liang, Xiaojun
2014-12-29
In the presence of pre-dispersion, an exact solution of nonlinear Schrödinger equation (NLSE) is derived for impulse input. The phase factor of the exact solution is obtained in a closed form using the exponential integral. The nonlinear interaction among periodically placed impulses launched at the input is investigated, and the condition under which these pulses do not exchange energy is examined. It is found that if the complex weights of the impulses at the input have a secant-hyperbolic envelope and a proper chirp factor, they will propagate over long distances without exchanging energy. To describe their interaction, a discrete version of NLSE is derived. The derived equation is a form of discrete self-trapping (DST) equation, which is found to admit fundamental and higher order soliton solutions in the presence of high pre-dispersion. Nonlinear eigenmodes derived here may be useful for description of signal propagation and nonlinear interaction in highly pre-dispersion fiber-optic systems.
NASA Astrophysics Data System (ADS)
Manikandan, K.; Senthilvelan, M.
2016-07-01
We construct spatiotemporal localized envelope solutions of a (3 + 1)-dimensional nonlinear Schrödinger equation with varying coefficients such as dispersion, nonlinearity and gain parameters through similarity transformation technique. The obtained localized rational solutions can serve as prototypes of rogue waves in different branches of science. We investigate the characteristics of constructed localized solutions in detail when it propagates through six different dispersion profiles, namely, constant, linear, Gaussian, hyperbolic, logarithm, and exponential. We also obtain expressions for the hump and valleys of rogue wave intensity profiles for these six dispersion profiles and study the trajectory of it in each case. Further, we analyze how the intensity of another localized solution, namely, breather, changes when it propagates through the aforementioned six dispersion profiles. Our studies reveal that these localized solutions co-exist with the collapsing solutions which are already found in the (3 + 1)-dimensional nonlinear Schrödinger equation. The obtained results will help to understand the corresponding localized wave phenomena in related fields.
NASA Astrophysics Data System (ADS)
Wang, L. Y.; Xu, W. C.; Luo, Z. C.; Cao, W. J.; Luo, A. P.; Dong, J. L.; Wang, H. Y.
2011-10-01
We experimentally demonstrate a passively Q-switched mode-locking (QML) operation in an Erbium-doped fiber ring laser with net normal dispersion by using nonlinear polarization rotation technique. A 2 m long section of dispersion compensating fiber (DCF) with extra large positive dispersion was inserted into the cavity to ensure the fiber laser working in the region of net positive dispersion. By carefully adjusting the polarization controller, both uniform dissipative mode-locking pulses with fundamental repetition rate and QML pulse trains with tunable repetition rate from 71.58 to 98.83 kHz are achieved. It is found that the QML operation is caused by the interaction between the polarization state of the pulse and the intracavity polarizer.
Tu, Yaoquan; Zhang, Qiong; Agren, Hans
2007-04-12
We demonstrate a complete procedure for simulations of electric field poled polymeric nonlinear optical systems with the purpose to evaluate the macroscopic electro-optic coefficients. The simulations cover the electric field poling effects on the chromophore order at the liquid state, the cooling procedure from the liquid to the solid state in the presence of the poling field, and the back-relaxation of the system after the removal of the field. We use Disperse Red chromophore molecules doped in a poly(methyl methacrylate) matrix for a numerical demonstration of the total procedure. On the basis of the simulation results, the polymer mobility and the static properties of the dopant chromophores are derived. In the liquid state, the chromophore molecules are closer to the side chains than to the backbones of the polymer matrix, and after the simulated annealing, the polymer matrix tends to be closely packed, leading to a significant change in the polymer structure around the chromophore molecules. Besides predicting the absolute macroscopic electro-optic coefficient values, the results are used to derive the microscopic origin of these values in terms of geometric and electronic structure, loading, poling, and back-relaxation effects, thereby aiding to establish design principles for optimum guest-host configurations.
Benisti, D; Strozzi, D J; Gremillet, L
2007-05-08
The kinetic nonlinear dispersion relation, and frequency shift {delta}{omega}{sub srs}, of a plasma wave driven by stimulated Raman scattering (SRS) are presented. Our theoretical calculations are fully electromagnetic, and use an adiabatic expression for the electron susceptibility which accounts for the change in phase velocity as the wave grows. When k{lambda}{sub D} {approx}> 0.35 (k being the plasma wave number and {lambda}{sub D} the Debye length), {delta}{omega}{sub srs} is significantly larger than could be inferred by assuming that the wave is freely propagating. Our theory is in excellent agreement with 1-D Eulerian Vlasov-Maxwell simulations when 0.3 {le} k{lambda}{sub D} {le} 0.58, and allows discussion of previously proposed mechanisms for Raman saturation. In particular, we find that no 'loss of resonance' of the plasma wave would limit the Raman growth rate, and that saturation through a phase detuning between the plasma wave and the laser drive is mitigated by wave number shifts.
NASA Astrophysics Data System (ADS)
Li, Boxiao; Tchelepi, Hamdi A.
2015-09-01
Nonlinear convergence problems in numerical reservoir simulation can lead to unacceptably large computational time and are often the main impediment to performing simulation studies of large-scale problems. We analyze the nonlinearity of the discrete transport (mass conservation) equation for immiscible, incompressible, two-phase flow in porous media in the presence of viscous, buoyancy, and capillary forces. Although simulation problems are multi-dimensional with large numbers of cells and variables, we find that the essence of the nonlinear behavior can be understood by studying the discretized (numerical) flux function for the interface between two cells. The numerical flux is expressed in terms of the saturations of the two cells. Discontinuities in the first-order derivative of the flux function (referred to as kinks) and inflection lines are identified as the cause of convergence difficulty. These critical features (kinks and inflections) change the curvature of the numerical flux function abruptly, and can lead to overshoots, oscillations, or divergence in Newton iterations. Based on our understanding of the nonlinearity, a nonlinear solver is developed, referred to as the Numerical Trust Region (NTR) solver. The solver is able to guide the Newton iterations safely and efficiently through the different saturation 'trust-regions' delineated by the kinks and inflections. Specifically, overshoots and oscillations that often lead to convergence failure are avoided. Numerical examples demonstrate that our NTR solver has superior convergence performance compared with existing methods. In particular, convergence is achieved for a wide range of timestep sizes and Courant-Friedrichs-Lewy (CFL) numbers spanning several orders of magnitude. In addition, a discretization scheme is proposed for handling heterogeneities in capillary-pressure-saturation relationship. The scheme has less degree of nonlinearity compared with the standard Single-point Phase-based Upstream
Modulational instability in two-component discrete media with cubic-quintic nonlinearity.
Baizakov, B B; Bouketir, A; Messikh, A; Umarov, B A
2009-04-01
The effect of cubic-quintic nonlinearity and associated intercomponent couplings on the modulational instability (MI) of plane-wave solutions of the two-component discrete nonlinear Schrödinger (DNLS) equation is considered. Conditions for the onset of MI are revealed and the growth rate of small perturbations is analytically derived. For the same set of initial parameters as equal amplitudes of plane waves and intercomponent coupling coefficients, the effect of quintic nonlinearity on MI is found to be essentially stronger than the effect of cubic nonlinearity. Analytical predictions are supported by numerical simulations of the underlying coupled cubic-quintic DNLS equation. Relevance of obtained results to dense Bose-Einstein condensates (BECs) in deep optical lattices, when three-body processes are essential, is discussed. In particular, the phase separation under the effect of MI in a two-component repulsive BEC loaded in a deep optical lattice is predicted and found in numerical simulations. Bimodal light propagation in waveguide arrays fabricated from optical materials with non-Kerr nonlinearity is discussed as another possible physical realization for the considered model.
Self-similar optical pulses in competing cubic-quintic nonlinear media with distributed coefficients
Zhang Jiefang; Tian Qing; Wang Yueyue; Dai Chaoqing; Wu Lei
2010-02-15
We present a systematic analysis of the self-similar propagation of optical pulses within the framework of the generalized cubic-quintic nonlinear Schroedinger equation with distributed coefficients. By appropriately choosing the relations between the distributed coefficients, we not only retrieve the exact self-similar solitonic solutions, but also find both the approximate self-similar Gaussian-Hermite solutions and compact solutions. Our analytical and numerical considerations reveal that proper choices of the distributed coefficients could make the unstable solitons stable and could restrict the nonlinear interaction between the neighboring solitons.
NASA Astrophysics Data System (ADS)
Szczepanek, Jan; Kardaś, Tomasz; Nejbauer, Michał; Radzewicz, Czesław; Stepanenko, Yuriy
2016-03-01
In this paper we report an all-PM-fiber laser amplifier system seeded by an all-normal-dispersion oscillator mode-locked with a Nonlinear Optical Loop Mirror (NOLM). The presented all-normal-dispersion cavity works in a dissipative soliton regime and delivers highly-chirped, high energy pulses above 2.5 nJ with full width at half maximum below 200 fs. The ultrafast oscillator followed by the all-PM-fiber amplifying stage delivered pulses with the energy of 42.5 nJ and time duration below 190 fs. The electrical field of optical pulses from the system was reconstructed using the SPIDER technique. The influence of nonlinear processes on the pulse temporal envelope was investigated.
Siegrist, R.L.; Smuin, D.R.; Korte, N.E.; Greene, D.W.; Pickering, D.A.; Lowe, K.S.; Strong-Gunderson, J.
2000-08-01
Chlorocarbons like trichloroethylene (TCE) are common contaminants of concern at US Department of Energy (DOE) facilities and industrial sites across the US and abroad. These contaminants of concern are present in source areas and in soil and ground water plumes as dissolved or sorbed phase constituents as well as dense nonaqueous-phase liquids (DNAPLs). These DNAPL compounds can be released to the environment through a variety of means including leaks in storage tanks and transfer lines, spills during transportation, and land treatment of wastes. When DNAPL compounds are present in low permeability media (LPM) like silt and clay layers or deposits, there are major challenges with assessment of their behavior and implementation of effective in situ remediation technologies. This report describes a field demonstration that was conducted at the Portsmouth Gaseous Diffusion Plant (PORTS) Clean Test Site (CTS) to evaluate the feasibility of permeation and dispersal of reagents into LPM. Various reagents and tracers were injected at seven test cells primarily to evaluate the feasibility of delivery, but also to evaluate the effects of the injected reagents on LPM. The various reagents and tracers were injected at the PORTS CTS using a multi-port injection system (MPIS) developed and provided by Hayward Baker Environmental, Inc.
Tu, Haohua; Liu, Yuan; Liu, Xiaomin; Turchinovich, Dmitry; Lægsgaard, Jesper; Boppart, Stephen A.
2012-01-01
Dispersion-flattened dispersion-decreased all-normal dispersion (DFDD-ANDi) photonic crystal fibers have been identified as promising candidates for high-spectral-power coherent supercontinuum (SC) generation. However, the effects of the unintentional birefringence of the fibers on the SC generation have been ignored. This birefringence is widely present in nonlinear non-polarization maintaining fibers with a typical core size of 2 µm, presumably due to the structural symmetry breaks introduced in the fiber drawing process. We find that an intrinsic form-birefringence on the order of 10−5 profoundly affects the SC generation in a DFDD-ANDi photonic crystal fiber. Conventional simulations based on the scalar generalized nonlinear Schrödinger equation (GNLSE) fail to reproduce the prominent observed features of the SC generation in a short piece (9-cm) of this fiber. However, these features can be qualitatively or semi-quantitatively understood by the coupled GNLSE that takes into account the form-birefringence. The nonlinear polarization effects induced by the birefringence significantly distort the otherwise simple spectrotemporal field of the SC pulses. We therefore propose the fabrication of polarization-maintaining DFDD-ANDi fibers to avoid these adverse effects in pursuing a practical coherent fiber SC laser. PMID:22274457
Domingue, Scott R.; Bartels, Randy A.
2013-01-01
The intrinsic weak birefringence in all-normal dispersion highly nonlinear fiber, particularly ultra-high-numerical-aperture fiber, generates supercontinuum with long term polarization instabilities, even for seed pulses launched along the perceived slow axis of the fiber. Highly co/anti-correlated fluctuations in energy between regions of power spectral density mask the extent of the spectral noise in total integrated power measurements. The instability exhibits a seed pulse power threshold above which the output polarization state of the supercontinuum seeds from noise. Eliminating this instability through the utilization of nonlinear fiber with a large designed birefringence, encourages the exploration of compression schemes and seed sources. Here, we include an analysis of the difficulties for seeding supercontinuum with the highly attractive ANDi-type lasers. Lastly, we introduce an intuitive approach for understanding supercontinuum development and evolution. By modifying the traditional characteristic dispersion and nonlinear lengths to track pulse properties within the nonlinear fiber, we find simple, descriptive handles for supercontinuum evolution. PMID:23736583
Analytical theory for the propagation of laser beams in nonlinear media
Tatarinova, Larisa L.; Garcia, Martin E.
2007-10-15
The propagation of a laser beam of intensity I in a nonlinear medium with a refractive index n(I) of arbitrary form is studied. In particular, the influence of the functional form n=n(I) on self-focusing and self-trapping is investigated. Starting from the propagation equations and using symmetry considerations and the Bogoliubov renormalization group approach, we derive a general equation relating the self-focusing distance, the intensity, and n(I). For different polynomial dependences of n(I) on I, we construct analytical solutions for the spatial intensity profile I(r) for an initially collimated Gaussian beam inside the medium. We also explicitly analyze the case of nonlinear self-focusing accompanied by multiphoton ionization. For particular (already studied) cases, we considerably improve the accuracy of the results with respect to previous semianalytical studies and obtain very good agreement with recent numerical simulations.
Nonlinear optical processing with Fabry-Perot interferometers containing phase recording media
NASA Technical Reports Server (NTRS)
Bartholomew, B. J.; Lee, S. H.
1980-01-01
New techniques in nonlinear optical processing are explored, based on the operation of intensity level selection as performed by a Fabry-Perot interferometer containing a phase object. The image being processed is recorded on a medium between the mirrors as a spatially varying phase shift less than pi. The interferometer only transmits light through those portions of the object that corresponds to a single value of the phase and hence to a single intensity level in the input. More complicated operations such as thresholding and analog-to-digital conversion are performed by modulating the light source as the different levels are selected. Photoresist and lithium niobate have been used as phase objects, and experimental data for both are presented. Three kinds of Fabry-Perot interferometers have been used to demonstrate nonlinear processing using coherent and incoherent light. Color images have been produced with black and white inputs and white light illumination.
Nonlinear generation mechanism for the vortical electric field in magnetized plasma media
Aburjania, G. D.
2007-10-15
A physical mechanism and nonlinear mathematical formalism for study of generation and further amplification of the vortical electric field in the magnetized plasma are proposed. A modulation instability process in a plasma medium is considered in a strong constant magnetic field. The plasmon condensate is modulated not by a low-frequency ionic sound as is usually done, but by the beating of two high-frequency transverse electromagnetic waves propagating along the external magnetic field. Conditions in which aperiodic instability occurs are found and its increment is defined. This instability leads to a decrease in the scale of Langmuir turbulence along the external magnetic field and to the generation of electromagnetic fields. Dissipative property of the medium increases an amplitude threshold of the pumping waves. It is shown that for sufficiently large amplitudes of pumping waves the effect described in the paper is the defining nonlinear process.
Thermalization and Bose-Einstein condensation of quantum light in bulk nonlinear media
NASA Astrophysics Data System (ADS)
Chiocchetta, A.; Larré, P.-É.; Carusotto, I.
2016-07-01
We study the thermalization and the Bose-Einstein condensation of a paraxial, spectrally narrow beam of quantum light propagating in a lossless bulk Kerr medium. The spatiotemporal evolution of the quantum optical field is ruled by a Heisenberg equation analogous to the quantum nonlinear Schrödinger equation of dilute atomic Bose gases. Correspondingly, in the weak-nonlinearity regime, the phase-space density evolves according to the Boltzmann equation. Expressions for the thermalization time and for the temperature and the chemical potential of the eventual Bose-Einstein distribution are found. After discussing experimental issues, we introduce an optical setup allowing the evaporative cooling of a guided beam of light towards Bose-Einstein condensation. This might serve as a novel source of coherent light.
Feng, Xian; Poletti, Francesco; Camerlingo, Angela; Parmigiani, Francesca; Horak, Peter; Petropoulos, Periklis; Loh, Wei H; Richardson, David J
2009-10-26
We report the fabrication of an all-solid highly nonlinear microstructured optical fiber. The structured preform was made by glass extrusion using two types of commercial lead silicate glasses that provide high index-contrast. Effectively single-moded guidance was observed in the fiber at 1.55 microm. The effective nonlinearity and the propagation loss at this wavelength were measured to be 120 W(-1)km(-1) and 0.8 dB/m, respectively. Numerical simulations indicate that the fiber is dispersion-shifted with a zero-dispersion-wavelength of 1475 nm and a dispersion slope of 0.16 ps/nm(2)/km respectively at 1.55 microm. These predictions are consistent with the experimentally determined dispersion of + 12.5 ps/nm/km at 1.55 microm. Tunable and efficient four-wave-mixing based wavelength conversion was demonstrated at wavelengths around 1.55 microm using a 1.5m-length of the fiber.
Double-hump solitary waves in quadratically nonlinear media with loss and gain
NASA Astrophysics Data System (ADS)
Darmanyan, S.; Crasovan, L.; Lederer, F.
2000-03-01
We report the existence of a family of bright chirped localized waves in quadratic media with loss and gain. It is shown that the fundamental field component of the symbiotic solitary wave may exhibit a double-hump shape. The conditions of the solitary wave's existence are identified. Numerical experiments disclose different scenarios of instability as well as domains of rather robust behavior of these objects upon propagation.
Nonlinear optical limiting based on energy and charge transfer in fullerene-containing media
NASA Astrophysics Data System (ADS)
Belousova, I. M.; Danilov, V. V.; Videnichev, D. A.; Gogoleva, N. G.; Ermolaeva, G. M.; Kislyakov, I. M.; Gryaznova, M. V.; Buersing, H.; Walter, D.; Eberle, B.; Ebert, R.
2009-09-01
The optical limiting efficiency and the possibility of extending the spectral and time ranges of optical limiters based on fullerene-containing media are studied. The optical limiting of pulses of different durations in solutions of C60 and higher fullerenes, the triplet—triplet transfer in multicomponent fullerene-containing solutions, and the electron transfer in the C60-tetramethylbenzidine-perylene system are investigated.
Phase- and group-matched nonlinear interactions mediated by multiple filamentation in Kerr media
Faccio, D.; Lotti, A.; Dubietis, A.; Tamosauskas, G.; Valiulis, G.; Piskarskas, A.; Polesana, P.; Di Trapani, P.; Couairon, A.
2007-11-15
Laser-pulse filamentation in Kerr media induced by a strongly elliptic input beam leads to breakup into a periodic array of filaments. In the plane of the filament array we observe strong Stokes and anti-Stokes emission at large angles. For 1 ps input pulses the measured angles are found to support two different phase-matching configurations: one nontransversally phase matched and the other perfectly phase matched. Shorter 200 fs pulses give rise to group-velocity-matched Raman conversion.
Mathematical Problems of Nonlinear Wave Propagation and of Waves in Heterogeneous Media.
1986-10-22
Landau type by examining secondary bifurcation. Professor Venakides has completed two papers on the Korteweg -de Vries equation . One shows how step-like...Venakldes The Zero Dispersion Limit of the Korteweg -de Vries Equation for Initial Potentials with Non-trivial Reflection Coefficient Pub: Comm. Pure...Keller The oic dimensional Schr6dingcr equation is solved asymptotically for scattering of a particle by a potential barrier and for botnid staLes of a
Kwon, Dongwook; Park, Jonghoon; Park, Jaehong; Choi, Seo Yeon; Yoon, Tae Hyun
2014-01-01
The extrinsic physicochemical properties of nanoparticles (NPs), such as hydrodynamic size, surface charge, surface functional group, and colloidal stabilities, in toxicity testing media are known to have a significant influence on in vitro toxicity assessments. Therefore, interpretation of nanotoxicity test results should be based on reliable characterization of the NPs’ extrinsic properties in actual toxicity testing media. Here, we present a set of physicochemical characterization results for commercially available ZnO NPs, including core diameter, hydrodynamic diameter, surface charges, and colloidal stabilities, in two in vitro toxicity testing media (Roswell Park Memorial Institute [RPMI] and Dulbecco’s Modified Eagle’s Medium [DMEM]), as well as simple cell viability assay results for selected ZnO NPs. Four commercially available and manufactured ZnO NPs, with different core sizes, were used in this study, and their surface charge was modified with five different surface coating materials (sodium citrate, tris(2-aminoethyl)amine, poly(acrylic acid), poly(allylamine hydrochloride), and poly-L-lysine hydrochloride). The results showed that ZnO NPs were better dispersed in cell culture media via surface modification with positively or negatively charged molecules. Moreover, in the presence of fetal bovine serum (FBS) in RPMI and DMEM media, ZnO NPs were found even better dispersed for a longer period (at least 48 hours). For the HeLa cells exposed to ZnO NPs in DMEM media without FBS, surface charge-dependent cytotoxicity trends were observed, while these trends were not observed for those cells cultured in FBS-containing media. This confirmed the important roles of surface-modifying compounds and of surface charge on the resultant cytotoxicities of NPs. PMID:25565826
NASA Astrophysics Data System (ADS)
Yang, Haijian; Sun, Shuyu; Yang, Chao
2017-03-01
Most existing methods for solving two-phase flow problems in porous media do not take the physically feasible saturation fractions between 0 and 1 into account, which often destroys the numerical accuracy and physical interpretability of the simulation. To calculate the solution without the loss of this basic requirement, we introduce a variational inequality formulation of the saturation equilibrium with a box inequality constraint, and use a conservative finite element method for the spatial discretization and a backward differentiation formula with adaptive time stepping for the temporal integration. The resulting variational inequality system at each time step is solved by using a semismooth Newton algorithm. To accelerate the Newton convergence and improve the robustness, we employ a family of adaptive nonlinear elimination methods as a nonlinear preconditioner. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm. A comparison is also included to show the superiority of the proposed fully implicit approach over the classical IMplicit Pressure-Explicit Saturation (IMPES) method in terms of the time step size and the total execution time measured on a parallel computer.
Coexistence of synchrony and incoherence in oscillatory media under nonlinear global coupling
Schmidt, Lennart; García-Morales, Vladimir; Schönleber, Konrad; Krischer, Katharina
2014-03-15
We report a novel mechanism for the formation of chimera states, a peculiar spatiotemporal pattern with coexisting synchronized and incoherent domains found in ensembles of identical oscillators. Considering Stuart-Landau oscillators, we demonstrate that a nonlinear global coupling can induce this symmetry breaking. We find chimera states also in a spatially extended system, a modified complex Ginzburg-Landau equation. This theoretical prediction is validated with an oscillatory electrochemical system, the electro-oxidation of silicon, where the spontaneous formation of chimeras is observed without any external feedback control.
Scaling laws for the response of nonlinear elastic media with implications for cell mechanics.
Shokef, Yair; Safran, Samuel A
2012-04-27
We show how strain stiffening affects the elastic response to internal forces, caused either by material defects and inhomogeneities or by active forces that molecular motors generate in living cells. For a spherical force dipole in a material with a strongly nonlinear strain energy density, strains change sign with distance, indicating that, even around a contractile inclusion or molecular motor, there is radial compression; it is only at a long distance that one recovers the linear response in which the medium is radially stretched. Scaling laws with irrational exponents relate the far-field renormalized strain to the near-field strain applied by the inclusion or active force.
NASA Technical Reports Server (NTRS)
Smith, David D.
2002-01-01
This talk will review the linear and nonlinear optical properties of metal nanoparticles and dielectric microparticles, with an emphasis on local field effects, and whispering gallery modes (WGMs), as well as the conjunction of these two effects for enhanced Raman. In particular, enhanced optical properties that result from electromagnetic coupling effects will be discussed in the context of Mie scattering from concentric spheres and bispheres. Predictions of mode splitting and photonic bandgaps in micro-spheres will be presented and will be shown to be analogous to effects that occur in coupled resonator optical waveguides (CROW). Slow and fast light in SCISSOR / CROW configurations will also be discussed.
NASA Astrophysics Data System (ADS)
de la Garza-Rubí, R. M. A.; Güizado-Rodríguez, M.; Mayorga-Cruz, D.; Basurto-Pensado, M. A.; Guerrero-Álvarez, J. A.; Ramos-Ortiz, G.; Rodríguez, M.; Maldonado, J. L.
2015-08-01
A copolymer of 3-hexylthiophene and thiophene functionalized with disperse red 1, poly(3-HT-co-TDR1), was synthesized. Chemical structure, molecular weight distribution, optical and thermal properties of this copolymer were characterized by NMR, FT-IR, UV-vis, GPC and DSC-TGA. An optical nonlinear analysis by Z-scan method was also performed for both continuous wave (CW) and pulsed laser pumping. In the CW regime the nonlinearities were evaluated in solid films, and a negative nonlinear refractive index in the range 2.7-4.1 × 10-4 cm2/W was obtained. These values are notoriously high and allowed to observe self-defocusing effects at very low laser intensities: below 1 mW. Further, nonlinear self-phase modulation patterns, during laser irradiation, were also observed. In the pulsed excitation the nonlinear response was evaluated in solution resulting in large two-photon absorption cross section of 5725 GM for the whole copolymer chain and with a value of 232 GM per repeated monomeric unit.
NASA Astrophysics Data System (ADS)
Riaz, Amir; Tchelepi, Hamdi A.
2004-12-01
Linear stability analysis of immiscible displacements is carried out for both viscously and gravitationally unstable two-phase flows in porous media with very large adverse viscosity ratios. Capillary dispersion is the proper dissipative mechanism in this case which sets both the preferred length scale and the band width of the spectrum of unstable length scales. The growth rate, the most dangerous and the cutoff wavenumbers, all scale linearly with the capillary number. We show that the instability is governed by fluid properties across the shock rather than those across the full Buckley-Leverett profile. The shock total mobility ratio provides a sufficient condition for the onset of instability; however, it is not an appropriate criterion for predicting the magnitude of the growth rate, particularly for large viscosity ratios. The details of the relative permeability functions are observed to have a significant influence on the stability characteristics. For neutrally buoyant flows the maximum growth rate scales linearly with the viscosity ratio while the most dangerous and the cutoff wavenumbers scale with the square root of the viscosity ratio. In the case of displacements with density contrast, the maximum growth rate scales with the square of the unstable gravity number while the most dangerous and the cutoff wavenumbers scale with an exponent of 1.2, for all viscosity ratios. A marginal stability curve is computed for stable and unstable regions in the parameter space of the viscosity ratio and the gravity number. It is found that flows with unstable viscosity contrasts are more readily stabilized with buoyancy as compared to the viscous stabilization of gravitationally unstable flows.
Exact solutions of optical pulse propagation in nonlinear meta-materials
NASA Astrophysics Data System (ADS)
Nanda, Lipsa
2017-01-01
An analytical and simulation based method has been used to exactly solve the nonlinear wave propagation in bulk media exhibiting frequency dependent dielectric susceptibility and magnetic permeability. The method has been further extended to investigate the intensity distribution in a nonlinear meta-material with negative refractive index where both ɛ and μ are dispersive and negative in nature.
Creation of vortices by torque in multidimensional media with inhomogeneous defocusing nonlinearity
Driben, Rodislav; Meier, Torsten; Malomed, Boris A.
2015-01-01
Recently, a new class of nonlinear systems was introduced, in which the self-trapping of fundamental and vortical localized modes in space of dimension D is supported by cubic self-repulsion with a strength growing as a function of the distance from the center, r, at any rate faster that rD. These systems support robust 2D and 3D modes which either do not exist or are unstable in other nonlinear systems. Here we demonstrate a possibility to create solitary vortices in this setting by applying a phase-imprinting torque to the ground state. Initially, a strong torque completely destroys the ground state. However, contrary to usual systems, where the destruction is irreversible, the present ones demonstrate a rapid restabilization and the creation of one or several shifted vortices orbiting the center. For the sake of comparison, we show analytically that, in the linear system with a 3D trapping potential, the action of a torque on the ground state is inefficient and creates only even-vorticity states with a small probability. PMID:25800140
Balzer, Jan C; Döpke, Benjamin; Brenner, Carsten; Klehr, Andreas; Erbert, Götz; Tränkle, Günther; Hofmann, Martin R
2014-07-28
We analyze the influence of second and third order intracavity dispersion on a passively mode-locked diode laser by introducing a spatial light modulator (SLM) into the external cavity. The dispersion is optimized for chirped pulses with highest possible spectral bandwidth that can be externally compressed to the sub picosecond range. We demonstrate that the highest spectral bandwidth is achieved for a combination of second and third order dispersion. With subsequent external compression pulses with a duration of 437 fs are generated.
NASA Astrophysics Data System (ADS)
Miller, C. T.; Kees, C. E.
2002-12-01
Time integration methods that adapt in both the order of approximation and time step have been shown to provide efficient solutions for Richards' equation. In this work, we extend the same method of lines approach to solve a set of two-phase flow formulations and address some mass conservation issues from the previous work. We analyze these formulations and the nonlinear systems that result from applying the integration methods, placing particular emphasis on their index, range of applicability, and mass conservation characteristics. We conduct numerical experiments to study the behavior of the numerical models for three test problems. We demonstrate that higher order integration in time is more efficient than standard low-order methods for a variety of practical grids and integration tolerances, that the adaptive scheme successfully varies the step size in response to changing conditions, and that mass balance can be maintained efficiently using variable-order integration and an appropriately chosen numerical model formulation.
NASA Astrophysics Data System (ADS)
Beaudoin, Anthony; de Dreuzy, Jean-Raynald; Erhel, Jocelyne
2010-12-01
We investigate the influences of pore-scale dispersion and of larger-scale permeability heterogeneities on the macrodispersion without the molecular diffusion. Permeability follows a lognormal exponentially correlated distribution characterized by its correlation length λ and its lognormal variance σ2. Macrodispersion is evaluated numerically by using parallel simulations on grids of characteristic size ranging from 200λ to 1600λ. We note αL and αT the pore-scale longitudinal and transversal dispersivities. For αL/λ < 10-2 and αT/λ < 10-3, the influence of pore-scale dispersion on the macrodispersion is smaller than 5% of the macrodispersion due only to permeability heterogeneities. Larger dispersivities (αL/λ ≥ 10-2 or αT/λ ≥ 10-3) induce larger effects than those obtained by the semianalytical expression of Salandin and Fiorotto (1998) for σ2 > 1. The effects of local dispersion on the longitudinal macrodispersion remain limited to 25% at most of the macrodispersion due only to permeability heterogeneities. For σ2 > 1, isotropic local dispersion induces a reduction of the longitudinal macrodispersion, whereas anisotropic local dispersion lets it increase. The longitudinal and transverse local dispersions induce opposite effects on the longitudinal macrodispersion, which are respectively an increase and a reduction. The transverse macrodispersion null without local dispersion or molecular diffusion becomes strictly positive with local dispersion. Because of the velocity field heterogeneities, it is amplified by a factor of 2 to 50 from the grid scale to the macro scale. The transverse dispersion is triggered by both longitudinal and transverse local dispersions. A reduction of a factor of 2 of the transverse local dispersion at fixed longitudinal local dispersion yields only a reduction of a factor of 4 at most of the transverse macrodispersion for σ2 ≥ 2.25.
Nonlinear spatial focusing in random layered media by spectral pulse shaping
NASA Astrophysics Data System (ADS)
Han, Alex C.; Milner, Valery
2016-02-01
We demonstrate numerically a method of focusing two-photon fields inside one-dimensional random media. The approach is based on coherent control of backscattering achieved by adaptive spectral pulse shaping. The spectral phases of a femtosecond laser pulse are adjusted for the constructive interference of its backward-traveling components, resulting in an enhanced reflection from within the random system. A delayed forward-propagating second pulse overlaps with the controlled reflection, increasing the interpulse multiphoton field at a location determined by the delay between the two pulses. The technique is shown to be robust against the variations of the disorder and to work with realistic pulse-shaping parameters, hence enabling applications in controlling random lasing and multiphoton imaging in scattering materials.
Cai, Jun-Hao; Chen, He; Chen, Sheng-Ping; Hou, Jing
2017-02-20
We present the results of numerical simulations of dissipative soliton generation using nonlinear Schrödinger equations in an all-normal-dispersion (ANDi) mode-locked fiber laser based on a nonlinear optical loop mirror (NOLM). Firstly, systematic and computationally intensive analysis of the pulse state distributions in two-dimensional parameter spaces of an ANDi fiber laser was conducted. In addition, we determined that unstable non-vanishing regions including pulsation and noise-like pulses are directly related to the saturable absorptions of NOLMs and that two critical filter bandwidths separate those regions from stable ones. Finally, we found that the multi-pulsing power threshold can be maximized by using an optimal optical filter bandwidth.
NASA Astrophysics Data System (ADS)
Chandra, S.; Vardhanan, A. Vishnu; Gangopadhyay, R.
2007-11-01
Optical phase conjugation (OPC) and distributed Raman amplifier (DRA) combination (OPC-DRA) is demonstrated as a potential enabling solution for simultaneous reduction of fiber non-linearities and dispersion compensation of a sub-carrier multiplexed (SCM) optical transmission link. The present work is focused on the use of OPC-DRA combination for system performance improvement in terms of composite second order distortion (CSO) and carrier to noise ratio (CNR) of the SCM link. The analysis further shows that, introduction of DRA with proper pumping scheme significantly reduce fiber non-linearity resulting in improvement of the system performance in terms of CNR, compared to the situation where only mid-way optical phase conjugation is used.
Antiplane wave scattering from a cylindrical cavity in pre-stressed nonlinear elastic media
Shearer, Tom; Parnell, William J.; Abrahams, I. David
2015-01-01
The effect of a longitudinal stretch and a pressure-induced inhomogeneous radial deformation on the scattering of antiplane elastic waves from a cylindrical cavity is determined. Three popular nonlinear strain energy functions are considered: the neo-Hookean, the Mooney–Rivlin and a two-term Arruda–Boyce model. A new method is developed to analyse and solve the governing wave equations. It exploits their properties to determine an asymptotic solution in the far-field, which is then used to derive a boundary condition to numerically evaluate the equations local to the cavity. This method could be applied to any linear ordinary differential equation whose inhomogeneous coefficients tend to a constant as its independent variable tends to infinity. The effect of the pre-stress is evaluated by considering the scattering cross section. A longitudinal stretch is found to decrease the scattered power emanating from the cavity, whereas a compression increases it. The effect of the pressure difference depends on the strain energy function employed. For a Mooney–Rivlin material, a cavity inflation increases the scattered power and a deflation decreases it; for a neo-Hookean material, the scattering cross section is unaffected by the radial deformation; and for a two-term Arruda–Boyce material, both inflation and deflation are found to decrease the scattered power. PMID:26543398
Antiplane wave scattering from a cylindrical cavity in pre-stressed nonlinear elastic media.
Shearer, Tom; Parnell, William J; Abrahams, I David
2015-10-08
The effect of a longitudinal stretch and a pressure-induced inhomogeneous radial deformation on the scattering of antiplane elastic waves from a cylindrical cavity is determined. Three popular nonlinear strain energy functions are considered: the neo-Hookean, the Mooney-Rivlin and a two-term Arruda-Boyce model. A new method is developed to analyse and solve the governing wave equations. It exploits their properties to determine an asymptotic solution in the far-field, which is then used to derive a boundary condition to numerically evaluate the equations local to the cavity. This method could be applied to any linear ordinary differential equation whose inhomogeneous coefficients tend to a constant as its independent variable tends to infinity. The effect of the pre-stress is evaluated by considering the scattering cross section. A longitudinal stretch is found to decrease the scattered power emanating from the cavity, whereas a compression increases it. The effect of the pressure difference depends on the strain energy function employed. For a Mooney-Rivlin material, a cavity inflation increases the scattered power and a deflation decreases it; for a neo-Hookean material, the scattering cross section is unaffected by the radial deformation; and for a two-term Arruda-Boyce material, both inflation and deflation are found to decrease the scattered power.
Ahmad, Harith; Dernaika, Mohamad; Harun, Sulaiman Wadi
2014-09-22
This paper describes a proposal and successful demonstration of a dual wavelength all-fiber passively Q-switched erbium-doped fiber ring laser. The Q-switch operation was realized by using a nonlinear loop mirror that incorporated an unbalanced dispersion-decreasing taper fiber to act as a saturable absorber without additional elements. This setup enabled a fiber ring laser to achieve a performance of 48.7 kHz repetition rate with pulse duration of around 3.2 μs and approximate pulse energy of 20 nJ.
Tu, Haohua; Liu, Yuan; Lægsgaard, Jesper; Sharma, Utkarsh; Siegel, Martin; Kopf, Daniel; Boppart, Stephen A.
2010-01-01
We quantitatively predict the observed continuum-like spectral broadening in a 90-mm weakly birefringent all-normal dispersion-flattened photonic crystal fiber pumped by 1041-nm 229-fs 76-MHz pulses from a solid-state Yb:KYW laser. The well-characterized continuum pulses span a bandwidth of up to 300 nm around the laser wavelength, allowing high spectral power density pulse shaping useful for various coherent control applications. We also identify the nonlinear polarization effect that limits the bandwidth of these continuum pulses, and therefore report the path toward a series of attractive alternative broadband coherent optical sources. PMID:21197060
Hartmann, Nanna B; Jensen, Keld Alstrup; Baun, Anders; Rasmussen, Kirsten; Rauscher, Hubert; Tantra, Ratna; Cupi, Denisa; Gilliland, Douglas; Pianella, Francesca; Riego Sintes, Juan M
2015-01-01
Selecting appropriate ways of bringing engineered nanoparticles (ENP) into aqueous dispersion is a main obstacle for testing, and thus for understanding and evaluating, their potential adverse effects to the environment and human health. Using different methods to prepare (stock) dispersions of the same ENP may be a source of variation in the toxicity measured. Harmonization and standardization of dispersion methods applied in mammalian and ecotoxicity testing are needed to ensure a comparable data quality and to minimize test artifacts produced by modifications of ENP during the dispersion preparation process. Such harmonization and standardization will also enhance comparability among tests, labs, and studies on different types of ENP. The scope of this review was to critically discuss the essential parameters in dispersion protocols for ENP. The parameters are identified from individual scientific studies and from consensus reached in larger scale research projects and international organizations. A step-wise approach is proposed to develop tailored dispersion protocols for ecotoxicological and mammalian toxicological testing of ENP. The recommendations of this analysis may serve as a guide to researchers, companies, and regulators when selecting, developing, and evaluating the appropriateness of dispersion methods applied in mammalian and ecotoxicity testing. However, additional experimentation is needed to further document the protocol parameters and investigate to what extent different stock dispersion methods affect ecotoxicological and mammalian toxicological responses of ENP.
NASA Technical Reports Server (NTRS)
Huang, N. E.; Tung, C.-C.
1977-01-01
The influence of the directional distribution of wave energy on the dispersion relation is calculated numerically using various directional wave spectrum models. The results indicate that the dispersion relation varies both as a function of the directional energy distribution and the direction of propagation of the wave component under consideration. Furthermore, both the mean deviation and the random scatter from the linear approximation increase as the energy spreading decreases. Limited observational data are compared with the theoretical results. The agreement is favorable.
NASA Astrophysics Data System (ADS)
Navarrete, Alvaro; Paredes, Angel; Salgueiro, José R.; Michinel, Humberto
2017-01-01
We analyze theoretically the Schrödinger-Poisson equation in two transverse dimensions in the presence of a Kerr term. The model describes the nonlinear propagation of optical beams in thermo-optical media and can be regarded as an analog system for a self-gravitating self-interacting wave. We compute numerically the family of radially symmetric ground-state bright stationary solutions for focusing and defocusing local nonlinearity, keeping in both cases a focusing nonlocal nonlinearity. We also analyze excited states and oscillations induced by fixing the temperature at the borders of the material. We provide simulations of soliton interactions, drawing analogies with the dynamics of galactic cores in the scalar field dark-matter scenario.
Observation of Dispersive Shock Waves, Solitons, and Their Interactions in Viscous Fluid Conduits.
Maiden, Michelle D; Lowman, Nicholas K; Anderson, Dalton V; Schubert, Marika E; Hoefer, Mark A
2016-04-29
Dispersive shock waves and solitons are fundamental nonlinear excitations in dispersive media, but dispersive shock wave studies to date have been severely constrained. Here, we report on a novel dispersive hydrodynamic test bed: the effectively frictionless dynamics of interfacial waves between two high viscosity contrast, miscible, low Reynolds number Stokes fluids. This scenario is realized by injecting from below a lighter, viscous fluid into a column filled with high viscosity fluid. The injected fluid forms a deformable pipe whose diameter is proportional to the injection rate, enabling precise control over the generation of symmetric interfacial waves. Buoyancy drives nonlinear interfacial self-steepening, while normal stresses give rise to the dispersion of interfacial waves. Extremely slow mass diffusion and mass conservation imply that the interfacial waves are effectively dissipationless. This enables high fidelity observations of large amplitude dispersive shock waves in this spatially extended system, found to agree quantitatively with a nonlinear wave averaging theory. Furthermore, several highly coherent phenomena are investigated including dispersive shock wave backflow, the refraction or absorption of solitons by dispersive shock waves, and the multiphase merging of two dispersive shock waves. The complex, coherent, nonlinear mixing of dispersive shock waves and solitons observed here are universal features of dissipationless, dispersive hydrodynamic flows.
Observation of Dispersive Shock Waves, Solitons, and Their Interactions in Viscous Fluid Conduits
NASA Astrophysics Data System (ADS)
Maiden, Michelle D.; Lowman, Nicholas K.; Anderson, Dalton V.; Schubert, Marika E.; Hoefer, Mark A.
2016-04-01
Dispersive shock waves and solitons are fundamental nonlinear excitations in dispersive media, but dispersive shock wave studies to date have been severely constrained. Here, we report on a novel dispersive hydrodynamic test bed: the effectively frictionless dynamics of interfacial waves between two high viscosity contrast, miscible, low Reynolds number Stokes fluids. This scenario is realized by injecting from below a lighter, viscous fluid into a column filled with high viscosity fluid. The injected fluid forms a deformable pipe whose diameter is proportional to the injection rate, enabling precise control over the generation of symmetric interfacial waves. Buoyancy drives nonlinear interfacial self-steepening, while normal stresses give rise to the dispersion of interfacial waves. Extremely slow mass diffusion and mass conservation imply that the interfacial waves are effectively dissipationless. This enables high fidelity observations of large amplitude dispersive shock waves in this spatially extended system, found to agree quantitatively with a nonlinear wave averaging theory. Furthermore, several highly coherent phenomena are investigated including dispersive shock wave backflow, the refraction or absorption of solitons by dispersive shock waves, and the multiphase merging of two dispersive shock waves. The complex, coherent, nonlinear mixing of dispersive shock waves and solitons observed here are universal features of dissipationless, dispersive hydrodynamic flows.
2010-03-01
finally discuss some preliminary experimental results using systems with chrome spheres and small Nitinol interstitial grains to present the... Nitinol interstitial grains to present the underlying nonlinear dynamics of this so-called decorated tapered granular alignment. We are specifically...second was the DTC setup. In this case, small Nitinol 2.38 mm diameter particles were in- troduced between the main STC particles so that NDTC=9. 53 The
Seth J. Putterman
2006-01-10
FINAL REPORT ON : NON-LINEAR WAVES IN CONTINUOUS MEDIA Doe DE FG03-87ER13686 (001312-001) Submitted January 10, 2006 by Seth J. Putterman 310-8252269 Physics Department University of California Los Angeles, CA 90095 puherman@ritva.physics.ucla.edu NON-LINEAR WAVES IN CONTINUOUS MEDIA I am happy to report that this project has been a big success. For over 10 years the DOE [Division of Materials Sciences and Engineering] has funded our research program on the overarching theme of spontaneous energy focusing phenomena. These effects occur when a nonlinear macroscopic system is excited so as to drive it far from equilibrium. The subsequent relaxation to equilibrium does not occur smoothly but instead is accompanied by the formation of structured domains where the energy density is highly concentrated. A signature example is picosecond sonoluminescence [1] wherein a smooth sound wave has its energy density focused by 12 orders of magnitude to generate a clock-like string of picosecond flashes of ultraviolet light. Our earlier work on solitons [2] demonstrated how uniform surface waves break up into stable localized structures. Our experimental work on turbulence produced photos of localized structures lying many standard deviations outside the range of gaussian statistics[3]. This effect is referred to as intermittency. Our recent work on friction finds its motivation in those theories of sonoluminescence which invoke frictional electricity. In its most common form this is the generation of a spark when we touch a doorknob after walking over a carpet. Our reading of the literature on this subject indicated that frictional electricity like sonoluminescence is not understood. So to probe triboelectrification we set up a modern version of an experiment performed by Bernoulli in 1700. Here sparking is caused by the rubbing of glass against mercury. We indeed observed flashes of light which were accompanied by events of stick-slip friction at the interface between the
NASA Astrophysics Data System (ADS)
Xia, Ya-Rong; Xin, Xiang-Peng; Zhang, Shun-Li
2017-01-01
This paper mainly discusses the (2+1)-dimensional modified dispersive water-wave (MDWW) system which will be proved nonlinear self-adjointness. This property is applied to construct conservation laws corresponding to the symmetries of the system. Moreover, via the truncated Painlevé analysis and consistent tanh-function expansion (CTE) method, the soliton-cnoidal periodic wave interaction solutions and corresponding images will be eventually achieved. Supported by National Natural Science Foundation of China under Grant Nos. 11371293, 11505090, the Natural Science Foundation of Shaanxi Province under Grant No. 2014JM2-1009, Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No. BS2015SF009 and the Science and Technology Innovation Foundation of Xi’an under Grant No. CYX1531WL41
NASA Astrophysics Data System (ADS)
Hammer, Daniel X.; Noojin, Gary D.; Thomas, Robert J.; Stolarski, David J.; Rockwell, Benjamin A.; Welch, Ashley J.
1999-06-01
Spectrally resolved white-light interferometry (SRWLI) was used to measure the wavelength dependence of refractive index (i.e., dispersion) for various ocular components. The accuracy of the technique was assessed by measurement of fused silica and water, the refractive indices of which have been measured at several different wavelengths. The dispersion of bovine and rabbit aqueous and vitreous humor was measured from 400 to 1100 nm. Also, the dispersion was measured from 400 to 700 nm for aqueous and vitreous humor extracted from goat and rhesus monkey eyes. For the humors, the dispersion did not deviate significantly from water. In an additional experiment, the dispersion of aqueous and vitreous humor that had aged up to a month was compared to freshly harvested material. No difference was found between the fresh and aged media. An unsuccessful attempt was also made to use the technique for dispersion measurement of bovine cornea and lens. Future refinement may allow measurement of the dispersion of cornea and lens across the entire visible and near-infrared wavelength band. The principles of white- light interferometry including image analysis, measurement accuracy, and limitations of the technique, are discussed. In addition, alternate techniques and previous measurements of ocular dispersion are reviewed.
Chitgarha, Mohammad Reza; Khaleghi, Salman; Ziyadi, Morteza; Mohajerin-Ariaei, Amirhossein; Almaiman, Ahmed; Daab, Wajih; Rogawski, Devora; Tur, Moshe; Touch, Joseph D; Langrock, Carsten; Fejer, Martin M; Willner, Alan E
2014-05-15
We propose and demonstrate an all-optical phase noise reduction scheme that uses optical nonlinear mixing and tunable optical delays to suppress the low-speed phase noise induced by laser linewidth. By utilizing the phase conjugate copy of the original signal and two narrow-linewidth optical pumps, the phase noise induced by laser linewidth can be reduced by a factor of ∼5 for a laser with 500-MHz phase noise bandwidth. The error-vector-magnitude can be improved from ∼30% to ∼14% for the same laser linewidth for 40-Gbit/s quadrature phase shift keying signal.
NASA Astrophysics Data System (ADS)
Xiao, Xiaosheng; Hua, Yi
2016-10-01
All-normal-dispersion (ANDi) mode-locked Yb-doped fiber laser is a promising seed source for supercontinuum (SC) generation, due to its compact structure and broadband output. The influences of output ports of the ANDi laser mode-locked by nonlinear polarization rotation (NPR), on the generated SC are investigated. Two output ports of ANDi laser are considered, one of which is the conventional nonlinear polarization rotation (NPR) port and the other is extracted from a coupler after the NPR port. It is found that, the SC originated from the coupler port is much broader than that from the NPR port, which is validated by lots of experiments with different output parameters. Furthermore, the conclusion is verified and generalized to general ANDi lasers by numerical simulations, because the output pulse from coupler port could be cleaner than that from NPR port. Besides, there are no significant differences in the phase coherence and temporal stability between the SCs generated from both ports. Hence for the SC generation based on ANDi laser, it is preferred to use the pulse of coupler port (i.e. pulse after NPR port) serving as the seed source.
Sanz-Prat, Alicia; Lu, Chuanhe; Amos, Richard T; Finkel, Michael; Blowes, David W; Cirpka, Olaf A
2016-09-01
the two types of biomass at late times. Results obtained by mapping the exposure-time based results to the two-dimensional domain are compared with simulations based on the two-dimensional, spatially explicit advection-dispersion-reaction equation. Once quasi-steady state has been reached, we find a good agreement in terms of the chemical-compound concentrations between the two approaches inside the reactive zones, whereas the exposure-time based model is not able to capture reactions occurring in the zones with zero electron-donor release. We conclude that exposure-time models provide good approximations of nonlinear bio-reactive transport when transverse mixing is not the overall controlling process and all reactions are essentially restricted to distinct reactive zones.
NASA Astrophysics Data System (ADS)
Sanz-Prat, Alicia; Lu, Chuanhe; Amos, Richard T.; Finkel, Michael; Blowes, David W.; Cirpka, Olaf A.
2016-09-01
the two types of biomass at late times. Results obtained by mapping the exposure-time based results to the two-dimensional domain are compared with simulations based on the two-dimensional, spatially explicit advection-dispersion-reaction equation. Once quasi-steady state has been reached, we find a good agreement in terms of the chemical-compound concentrations between the two approaches inside the reactive zones, whereas the exposure-time based model is not able to capture reactions occurring in the zones with zero electron-donor release. We conclude that exposure-time models provide good approximations of nonlinear bio-reactive transport when transverse mixing is not the overall controlling process and all reactions are essentially restricted to distinct reactive zones.
Dispersive shock waves and modulation theory
NASA Astrophysics Data System (ADS)
El, G. A.; Hoefer, M. A.
2016-10-01
There is growing physical and mathematical interest in the hydrodynamics of dissipationless/dispersive media. Since G.B. Whitham's seminal publication fifty years ago that ushered in the mathematical study of dispersive hydrodynamics, there has been a significant body of work in this area. However, there has been no comprehensive survey of the field of dispersive hydrodynamics. Utilizing Whitham's averaging theory as the primary mathematical tool, we review the rich mathematical developments over the past fifty years with an emphasis on physical applications. The fundamental, large scale, coherent excitation in dispersive hydrodynamic systems is an expanding, oscillatory dispersive shock wave or DSW. Both the macroscopic and microscopic properties of DSWs are analyzed in detail within the context of the universal, integrable, and foundational models for uni-directional (Korteweg-de Vries equation) and bi-directional (Nonlinear Schrödinger equation) dispersive hydrodynamics. A DSW fitting procedure that does not rely upon integrable structure yet reveals important macroscopic DSW properties is described. DSW theory is then applied to a number of physical applications: superfluids, nonlinear optics, geophysics, and fluid dynamics. Finally, we survey some of the more recent developments including non-classical DSWs, DSW interactions, DSWs in perturbed and inhomogeneous environments, and two-dimensional, oblique DSWs.
Nonlinear Waves in Waveguides with Stratification.
NASA Astrophysics Data System (ADS)
Leble, Sergei B.
S.B. Leble's book deals with nonlinear waves and their propagation in metallic and dielectric waveguides and media with stratification. The underlying nonlinear evolution equations (NEEs) are derived giving also their solutions for specific situations. The reader will find new elements to the traditional approach. Various dispersion and relaxation laws for different guides are considered as well as the explicit form of projection operators, NEEs, quasi-solitons and of Darboux transforms. Special points relate to: 1. the development of a universal asymptotic method of deriving NEEs for guide propagation; 2. applications to the cases of stratified liquids, gases, solids and plasmas with various nonlinearities and dispersion laws; 3. connections between the basic problem and soliton- like solutions of the corresponding NEEs; 4. discussion of details of simple solutions in higher- order nonsingular perturbation theory.
Reshak, A. H.; Brik, M. G.; Auluck, S.
2014-09-14
Based on the electronic band structure, we have calculated the dispersion of the linear and nonlinear optical susceptibilities for the mixed CuAl(S{sub 1–x}Se{sub x})₂ chaclcopyrite compounds with x=0.0, 0.25, 0.5, 0.75, and 1.0. Calculations are performed within the Perdew-Becke-Ernzerhof general gradient approximation. The investigated compounds possess a direct band gap of about 2.2 eV (CuAlS₂), 1.9 eV (CuAl(S₀.₇₅Se₀.₂₅)₂), 1.7 eV (CuAl(S₀.₅Se₀.₅)₂), 1.5 eV (CuAl(S₀.₂₅Se₀.₇₅)₂), and 1.4 eV (CuAlSe₂) which tuned to make them optically active for the optoelectronics and photovoltaic applications. These results confirm that substituting S by Se causes significant band gaps' reduction. The optical function's dispersion ε₂{sup xx}(ω) and ε₂{sup zz}(ω)/ε₂{sup xx}(ω), ε₂{sup yy}(ω), and ε₂{sup zz}(ω) was calculated and discussed in detail. To demonstrate the effect of substituting S by Se on the complex second-order nonlinear optical susceptibility tensors, we performed detailed calculations for the complex second-order nonlinear optical susceptibility tensors, which show that the neat parents compounds CuAlS₂ and CuAlSe₂ exhibit | χ₁₂₂²}(-2ω;ω;ω) | as the dominant component, while the mixed alloys exhibit | χ₁₁₁²(-2ω;ω;ω) | as the dominant component. The features of | χ₁₂₃²}(-2ω;ω;ω) | and | χ{sub 111}²}(-2ω;ω;ω) | spectra were analyzed on the basis of the absorptive part of the corresponding dielectric function ε₂(ω) as a function of both ω/2 and ω.
NASA Astrophysics Data System (ADS)
Wu, Zhenkun; Gu, Yuzong
2016-12-01
The propagation of two-dimensional beams is analytically and numerically investigated in strongly nonlocal nonlinear media (SNNM) based on the ABCD matrix. The two-dimensional beams reported in this paper are described by the product of the superposition of generalized Laguerre-Gaussian (LG), Hermite-Gaussian (HG), Bessel-Gaussian (BG), and circular Airy (CA) beams, carrying an orbital angular momentum (OAM). Owing to OAM and the modulation of SNNM, we find that the propagation of these two-dimensional beams exhibits complete rotation and periodic inversion: the spatial intensity profile first extends and then diminishes, and during the propagation the process repeats to form a breath-like phenomenon.
NASA Astrophysics Data System (ADS)
Ostrosablina, A. A.; Sidorov, A. I.
2005-07-01
This paper presents the experimental and theoretical results of a study of the interaction of pulsed laser radiation with thick composite media containing nanoparticles of vanadium dioxide (VO2). It establishes that the reversible semiconductor-metal phase transition that occurs in VO2 nanoparticles under the action of radiation can produce self-defocusing of radiation in the visible and near-IR regions because of the formation of a photoinduced dynamic lens. An analysis is carried out of how the radiation intensity affects the dynamics of these processes. It is shown that photoinduced absorption and scattering play a role in forming the nonlinear optical response.
NASA Astrophysics Data System (ADS)
Zheng, Jie-Ning; Li, Shan-Shan; Ma, Xiaohong; Chen, Fang-Yi; Wang, Ai-Jun; Chen, Jian-Rong; Feng, Jiu-Ju
2014-09-01
Well-defined core-shell gold-palladium@palladium nanocrystals (AuPd@Pd) are facilely prepared by a simple and green wet-chemical method at 25 °C. A Good's buffer, 2-[4-(2-hydroxyethyl)-1-piperazinyl] ethanesulfonic acid (HEPES), is used as a reducing agent and a shape-directing agent, while there is no template, seed, organic solvent, or surfactant involved. The AuPd@Pd nanocrystals are uniformly dispersed on graphene nanosheets by ultrasonication, resulting in the formation of graphene supported AuPd@Pd (G-AuPd@Pd). The as-prepared nanocomposites exhibit the improved catalytic activity, good tolerance, and better stability for oxygen reduction reaction (ORR) and methanol oxidation reaction (MOR) in alkaline media, compared with the G-Pd and commercial Pd black catalysts. The as-developed method may provide a promising pathway for large-scale fabrication of AuPd-based catalysts.
Itoh, Tomomichi; Fukutani, Kaori; Hino, Masato; Ihara, Eiji; Inoue, Kenzo
2009-02-15
The effects of polystyrene-b-poly(aminomethyl styrene) (PS(n)-b-PAMS(m)) stabilizers on the particle size (D(n)) and size distribution (PSD) in dispersion polymerization of styrene were investigated. The block copolymers, PS(n)-b-PAMS(m), were prepared as follows: (i) atom transfer radical polymerization (ATRP) of styrene (PS-Br), (ii) ATRP of vinylbenzylphthalimide with the PS-Br (PS-b-PVBP), and (iii) treatment of the PS-b-PVBP with hydrazine. When the dispersion polymerization of styrene proceeded at 60 degrees C in ethanol with PS(19)-b-PAMS(130) stabilizer, spherical polystyrene particles with D(n)=0.91 microm (PSD=1.01) were obtained. The particle size was strongly affected by the copolymer composition. With an increase in PAMS block length from m=54 to 100 in PS(17)-b-PAMS(m), particle diameter became smaller from 1.55 to 0.91 microm. On the other hand, an increase in the length from m=20 to 82 in PS(34)-b-PAMS(m)s caused an increase in particle size from 0.35 to 0.70 microm. Titration of the particles suggests that 14-81% of stabilizers used in the polymerization system were attached on the polystyrene particle surfaces, depending on the composition of the block copolymers. Thus, for the dispersion polymerization of styrene, PS(n)-b-PAMS(m) block copolymers have both functions as a stabilizer during polymerization and surface-modification sites of polystyrene particles.
Nonlinear electrostatic drift Kelvin-Helmholtz instability
NASA Technical Reports Server (NTRS)
Sharma, Avadhesh C.; Srivastava, Krishna M.
1993-01-01
Nonlinear analysis of electrostatic drift Kelvin-Helmholtz instability is performed. It is shown that the analysis leads to the propagation of the weakly nonlinear dispersive waves, and the nonlinear behavior is governed by the nonlinear Burger's equation.
Parker, Jack C; Kim, Ungtae
2015-11-01
The mono-continuum advection-dispersion equation (mADE) is commonly regarded as unsuitable for application to media that exhibit rapid breakthrough and extended tailing associated with diffusion between high and low permeability regions. This paper demonstrates that the mADE can be successfully used to model such conditions if certain issues are addressed. First, since hydrodynamic dispersion, unlike molecular diffusion, cannot occur upstream of the contaminant source, models must be formulated to prevent "back-dispersion." Second, large variations in aquifer permeability will result in differences between volume-weighted average concentration (resident concentration) and flow-weighted average concentration (flux concentration). Water samples taken from wells may be regarded as flux concentrations, while soil samples may be analyzed to determine resident concentrations. While the mADE is usually derived in terms of resident concentration, it is known that a mADE of the same mathematical form may be written in terms of flux concentration. However, when solving the latter, the mathematical transformation of a flux boundary condition applied to the resident mADE becomes a concentration type boundary condition for the flux mADE. Initial conditions must also be consistent with the form of the mADE that is to be solved. Thus, careful attention must be given to the type of concentration data that is available, whether resident or flux concentrations are to be simulated, and to boundary and initial conditions. We present 3-D analytical solutions for resident and flux concentrations, discuss methods of solving numerical models to obtain resident and flux concentrations, and compare results for hypothetical problems. We also present an upscaling method for computing "effective" dispersivities and other mADE model parameters in terms of physically meaningful parameters in a diffusion-limited mobile-immobile model. Application of the latter to previously published studies of
Reshak, Ali H; Stys, D; Auluck, S; Kityk, I V
2011-02-21
As a starting point for our calculation of 3-methyl-4-phenyl-5-(2-pyridyl)-1,2,4-triazole we used the XRD data obtained by C. Liu, Z. Wang, H. Xiao, Y. Lan, X. Li, S. Wang, Jie Tang, Z. Chen, J. Chem. Crystallogr., 2009 39 881. The structure was optimized by minimization of the forces acting on the atoms keeping the lattice parameters fixed with the experimental values. Using the relaxed geometry we have performed a comprehensive theoretical investigation of dispersion of the linear and nonlinear optical susceptibilities of 3-methyl-4-phenyl-5-(2-pyridyl)-1,2,4-triazole using the full potential linear augmented plane wave method. The local density approximation by Ceperley-Alder (CA) exchange-correlation potential was applied. The full potential calculations show that this material possesses a direct energy gap of 3.4 eV for the original experimental structure and 3.2 eV for the optimized structure. We have calculated the complex's dielectric susceptibility ε(ω) dispersion, its zero-frequency limit ε(1)(0) and the birefringence. We find that a 3-methyl-4-phenyl-5-(2-pyridyl)-1,2,4-triazole crystal possesses a negative birefringence at the low-frequency limit Δn(0) which is equal to about -0.182 (-0.192) and at λ = 1064 nm is -0.193 (-0.21) for the non-optimized structure (optimized one), respectively. We also report calculations of the complex second-order optical susceptibility dispersions for the principal tensor components: χ(ω), χ(ω) and χ(ω). The intra- and inter-band contributions to these susceptibilities are evaluated. The calculated total second order susceptibility tensor components at the low-frequency limit |χ(0)| and |χ(ω)| at λ = 1064 nm for all the three tensor components are evaluated. We established that the calculated microscopic second order hyperpolarizability, β(ijk), the vector component along the dipole moment direction, at the low-frequency limit and at λ = 1064 nm, for the dominant component |χ(ω)| is 4.99 × 10(-30) esu
Manikandan, K; Senthilvelan, M
2016-07-01
We construct spatiotemporal localized envelope solutions of a (3 + 1)-dimensional nonlinear Schrödinger equation with varying coefficients such as dispersion, nonlinearity and gain parameters through similarity transformation technique. The obtained localized rational solutions can serve as prototypes of rogue waves in different branches of science. We investigate the characteristics of constructed localized solutions in detail when it propagates through six different dispersion profiles, namely, constant, linear, Gaussian, hyperbolic, logarithm, and exponential. We also obtain expressions for the hump and valleys of rogue wave intensity profiles for these six dispersion profiles and study the trajectory of it in each case. Further, we analyze how the intensity of another localized solution, namely, breather, changes when it propagates through the aforementioned six dispersion profiles. Our studies reveal that these localized solutions co-exist with the collapsing solutions which are already found in the (3 + 1)-dimensional nonlinear Schrödinger equation. The obtained results will help to understand the corresponding localized wave phenomena in related fields.
2013-11-06
the nonlinear parametric processes in the AFB KTP plates, see Fig. 3. The pump beam at 539 nm is an output generated by a MOPO system (10 Hz, 5 ns...ps pulse width) is from an output of Master Oscillator/Power Oscillator ( MOPO ), with wide range wavelength tenability. The pump beam is split into
NASA Astrophysics Data System (ADS)
Lan, Chao-feng; Li, Feng-chen; Chen, Huan; Lu, Di; Yang, De-sen; Zhang, Meng
2015-06-01
Based on the Burgers equation and Manley-Rowe equation, the derivation about nonlinear interaction of the acoustic waves has been done in this paper. After nonlinear interaction among the low-frequency weak waves and the pump wave, the analytical solutions of acoustic waves' amplitude in the field are deduced. The relationship between normalized energy of high-frequency and the change of acoustic energy before and after the nonlinear interaction of the acoustic waves is analyzed. The experimental results about the changes of the acoustic energy are presented. The study shows that new frequencies are generated and the energies of the low-frequency are modulated in a long term by the pump waves, which leads the energies of the low-frequency acoustic waves to change in the pulse trend in the process of the nonlinear interaction of the acoustic waves. The increase and decrease of the energies of the low-frequency are observed under certain typical conditions, which lays a foundation for practical engineering applications.
Time-Reversal of Nonlinear Water Waves
NASA Astrophysics Data System (ADS)
Chabchoub, Amin; Ducrozet, Guillaume; Fink, Mathias
2016-11-01
Time-reversal (TR) refocusing of hydrodynamic nonlinear waves can be discussed within the framework of the nonlinear Schrödinger equation (NLS). Indeed, exact solutions of the latter weakly nonlinear evolution equation can be used to study the applicability and limitations of wave refocusing using TR mirrors in hydrodynamics. Recent laboratory experiments confirmed the applicability of TR approach to breathers, known to model extreme and doubly-localized wave configurations. In order to study the range of validity of the TR approach to nonlinear waves, a numerical study using a unidirectional numerical water wave tank, implemented by the higher-order spectral method, reveals new insights to the problem. The validity of the TR approach is assessed over a diversity of NLS configurations, ranging from stationary envelope and breathing solutions, pointing out the importance of higher-order dispersive and particularly nonlinear effects in the refocusing of these hydrodynamic localized structures. Due to the interdisciplinary nature of the approach several applications in other nonlinear dispersive physical media may result in addition to evident usage in the field of ocean engineering.
Hansson, T; Lisak, M; Anderson, D
2012-02-10
It is shown that the evolution equations describing partially coherent wave propagation in noninstantaneous Kerr media are integrable and have an infinite number of invariants. A recursion relation for generating these invariants is presented, and it is demonstrated how to express them in the coherent density, self-consistent multimode, mutual coherence, and Wigner formalisms.
Spatiotemporal soliton supported by parity-time symmetric potential with competing nonlinearities
NASA Astrophysics Data System (ADS)
Xu, Si-Liu; Zhao, Yuan; Petrović, Nikola Z.; Belić, Milivoj R.
2016-07-01
We construct explicit spatiotemporal or light bullet (LB) solutions to the (3 + 1)-dimensional nonlinear Schrödinger equation (NLSE) with inhomogeneous diffraction/dispersion and nonlinearity in the presence of parity-time (PT) symmetric potential with competing nonlinearities. The solution is based on the similarity transformation, by which the initial inhomogeneous problem is reduced to the standard NLSE with constant coefficients but with redefined variables and potential. Transmission characteristics of LB solutions, such as the phase change, half width and chirp, are studied in the media with exponentially decreasing diffraction/dispersion and with periodic modulation. Our outcomes demonstrate that diffraction/dispersion and nonlinearity management can prolong the stability of LBs in a PT potential.
NASA Astrophysics Data System (ADS)
Yankovskii, A. P.
2015-05-01
An indirect verification of a structural model describing the creep of a composite medium reinforced by honeycombs and made of nonlinear hereditary phase materials obeying the Rabotnov theory of creep is presented. It is shown that the structural model proposed is trustworthy and can be used in practical calculations. For different kinds of loading, creep curves for a honeycomb core made of a D16T aluminum alloy are calculated.
NASA Astrophysics Data System (ADS)
Gómez-Sosa, Gustavo; Ogawa, Takeshi; Isoshima, Takashi; Hara, Masahiko
The second-order nonlinear optical susceptibilities χ(2) of two isomeric polymers containing an azo dye, Disperse Red 19, were determined by the first-order electroabsorption spectroscopy (EAS), and compared with values previously obtained by SHG measurements. The para-polymer was found to have higher susceptibility than the corresponding meta-polymer. χ(2) were found to be 5-6 × 10-8 esu, which are comparable to those obtained by the Maker Fringe method.
NASA Astrophysics Data System (ADS)
Krutyansky, Leonid M.; Brysev, Andrew P.; Klopotov, Roman V.; Pernod, Philippe J.; Preobrazhensky, Vladimir L.; Yan, Xiang; Hamilton, Mark F.
2003-10-01
Acoustical imaging in complex media (e.g., biological tissue) can be affected by phase aberrations introduced in a wave during propagation. Wave phase conjugation (WPC) of ultrasound is known for its ability to compensate for phase distortions due to inhomogeneity of the propagation medium, and it can be used for improvement of acoustical imaging under these conditions. In a nonlinear medium harmonics are generated during propagation of an intense beam of ultrasound, and this principle is used in tissue harmonic imaging. The parametric method of WPC permits phase conjugation of a selected frequency component of the probe beam. In this way the peculiarities of WPC can be combined with advantages of harmonic imaging. Automated WPC-focusing of the conjugated second-harmonic component of a focused nonlinear probe beam is studied experimentally and theoretically for the case of a homogeneous medium, and experimentally for a medium with pseudo-random inhomogeneities. The generated conjugate wave can also be sufficiently intense to generate higher-order harmonics, which display enhanced focusing. Improvement of a C-scan harmonic imaging system operating in an inhomogeneous medium is provided as an example.
NASA Astrophysics Data System (ADS)
Wang, W. B.; Wang, F.; Yu, Q.; Zhang, X.; Lu, Y. X.; Gu, J.
2016-11-01
We propose and experimentally demonstrate a bidirectional erbium-doped fiber laser delivering dispersion-managed soliton (DMS) and Q-switched pulse based on a graphene-polyvinyl alcohol (PVA) and nonlinear optical loop mirror (NOLM) saturable absorbers (SAs). In proposed structure, the DMS is achieved in clockwise (CW) direction and Q-switched pulse is obtained in counter-clockwise (CCW) direction. By properly adjusting the intracavity attenuators (ATT) and polarizer controllers (PCs), DMS in the CW direction and Q-switched pulse in the CCW direction can be obtained, respectively or simultaneously. The DMS with full width at half maximum (FWHM) of ~480 fs, signal to noise ratio (SNR) of ~60 dB and repetition frequency about 3.907 MHz is obtained. The Q-switched pulse is established at a pump power of 180 mW with a repetition rate of ~43.5 kHz and FWHM of ~8.18 μs. When the pump power is increased to 700 mW, Q-switched pulse with a repetition rate of ~107.1 kHz and FWHM of ~2.15 μs is generated. When the two type pulses are formed simultaneously, the maximum repetition rate of Q-switched pulse is 55.8 kHz and minimum FWHM is 2.81 μs, the DMS can be formed by properly adjusting PC and ATT in this case. To the best of our knowledge, it is the first time that Q-switched pulse and DMS have been acquired respectively or simultaneously in a fiber laser.
NASA Astrophysics Data System (ADS)
Martin, Elly; Treeby, Bradley E.
2015-10-01
To increase the effectiveness of high intensity focused ultrasound (HIFU) treatments, prediction of ultrasound propagation in biological tissues is essential, particularly where bones are present in the field. This requires complex full-wave computational models which account for nonlinearity, absorption, and heterogeneity. These models must be properly validated but there is a lack of analytical solutions which apply in these conditions. Experimental validation of the models is therefore essential. However, accurate measurement of HIFU fields is not trivial. Our aim is to establish rigorous methods for obtaining reference data sets with which to validate tissue realistic simulations of ultrasound propagation. Here, we present preliminary measurements which form an initial validation of simulations performed using the k-Wave MATLAB toolbox. Acoustic pressure was measured on a plane in the field of a focused ultrasound transducer in free field conditions to be used as a Dirichlet boundary condition for simulations. Rectangular and wedge shaped olive oil scatterers were placed in the field and further pressure measurements were made in the far field for comparison with simulations. Good qualitative agreement was observed between the measured and simulated nonlinear pressure fields.
Stability analysis of dissolution-driven convection in porous media
NASA Astrophysics Data System (ADS)
Emami-Meybodi, Hamid
2017-01-01
We study the stability of dissolution-driven convection in the presence of a capillary transition zone and hydrodynamic dispersion in a saturated anisotropic porous medium, where the solute concentration is assumed to decay via a first-order chemical reaction. While the reaction enhances stability by consuming the solute, porous media anisotropy, hydrodynamic dispersion, and capillary transition zone destabilize the diffusive boundary layer that is unstably formed in a gravitational field. We perform linear stability analysis, based on the quasi-steady-state approximation, to assess critical times, critical wavenumbers, and neutral stability curves as a function of anisotropy ratio, dispersivity ratio, dispersion strength, material parameter, Bond number, Damköhler number, and Rayleigh number. The results show that the diffusive boundary layer becomes unstable in anisotropic porous media where both the capillary transition zone and dispersion are considered, even if the geochemical reaction is significantly large. Using direct numerical simulations, based on the finite difference method, we study the nonlinear dynamics of the system by examining dissolution flux, interaction of convective fingers, and flow topology. The results of nonlinear simulations confirm the predictions from the linear stability analysis and reveal that the fingering pattern is significantly influenced by combined effects of reaction, anisotropy, dispersion, and capillarity. Finally, we draw conclusions on implications of our results on carbon dioxide sequestration in deep saline aquifers.
Chen, W; Holm, S
2004-04-01
Frequency-dependent attenuation typically obeys an empirical power law with an exponent ranging from 0 to 2. The standard time-domain partial differential equation models can describe merely two extreme cases of frequency-independent and frequency-squared dependent attenuations. The otherwise nonzero and nonsquare frequency dependency occurring in many cases of practical interest is thus often called the anomalous attenuation. In this study, a linear integro-differential equation wave model was developed for the anomalous attenuation by using the space-fractional Laplacian operation, and the strategy is then extended to the nonlinear Burgers equation. A new definition of the fractional Laplacian is also introduced which naturally includes the boundary conditions and has inherent regularization to ease the hypersingularity in the conventional fractional Laplacian. Under the Szabo's smallness approximation, where attenuation is assumed to be much smaller than the wave number, the linear model is found consistent with arbitrary frequency power-law dependency.
Envelope Solitons in Acoustically Dispersive Vitreous Silica
NASA Technical Reports Server (NTRS)
Cantrell, John H.; Yost, William T.
2012-01-01
Acoustic radiation-induced static strains, displacements, and stresses are manifested as rectified or dc waveforms linked to the energy density of an acoustic wave or vibrational mode via the mode nonlinearity parameter of the material. An analytical model is developed for acoustically dispersive media that predicts the evolution of the energy density of an initial waveform into a series of energy solitons that generates a corresponding series of radiation-induced static strains (envelope solitons). The evolutionary characteristics of the envelope solitons are confirmed experimentally in Suprasil W1 vitreous silica. The value (-11.9 plus or minus 1.43) for the nonlinearity parameter, determined from displacement measurements of the envelope solitons via a capacitive transducer, is in good agreement with the value (-11.6 plus or minus 1.16) obtained independently from acoustic harmonic generation measurements. The agreement provides strong, quantitative evidence for the validity of the model.
NASA Astrophysics Data System (ADS)
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.
Chabchoub, A.; Kibler, B.; Finot, C.; Millot, G.; Onorato, M.; Dudley, J.M.; Babanin, A.V.
2015-10-15
The dynamics of waves in weakly nonlinear dispersive media can be described by the nonlinear Schrödinger equation (NLSE). An important feature of the equation is that it can be derived in a number of different physical contexts; therefore, analogies between different fields, such as for example fiber optics, water waves, plasma waves and Bose–Einstein condensates, can be established. Here, we investigate the similarities between wave propagation in optical Kerr media and water waves. In particular, we discuss the modulation instability (MI) in both media. In analogy to the water wave problem, we derive for Kerr-media the Benjamin–Feir index, i.e. a nondimensional parameter related to the probability of formation of rogue waves in incoherent wave trains.
Nonlinear acoustic wave equations with fractional loss operators.
Prieur, Fabrice; Holm, Sverre
2011-09-01
Fractional derivatives are well suited to describe wave propagation in complex media. When introduced in classical wave equations, they allow a modeling of attenuation and dispersion that better describes sound propagation in biological tissues. Traditional constitutive equations from solid mechanics and heat conduction are modified using fractional derivatives. They are used to derive a nonlinear wave equation which describes attenuation and dispersion laws that match observations. This wave equation is a generalization of the Westervelt equation, and also leads to a fractional version of the Khokhlov-Zabolotskaya-Kuznetsov and Burgers' equations.
NASA Astrophysics Data System (ADS)
Shukla, P. K.; Bingham, R.; Stenflo, L.; Dawson, J. M.
1996-01-01
Starting in 1989 we have created a forum at the International Centre for Theoretical Physics, Trieste, where scientists from different parts of the world can meet and exchange information in the frontier areas of physics. In the three previous meetings, we focused on large amplitude waves and fields in plasmas, the physics of dusty plasmas, and wave-particle interactions and energization in plasmas. In 1995, we came up with a fresh idea of organizing somewhat enlarged but still well focused research topics that are cross-disciplinary. Thus, the usual 'fourth-week activity' of the Plasma Physics College at the ICTP was replaced by an International Topical Workshop on Plasma Physics: Coherent Processes in Nonlinear Media, which was held at the ICTP during the period 16-20 October, 1995. This provided us an opportunity to draw eminent speakers from many closely related fields such as plasma physics, fluid dynamics, nonlinear optics, and astrophysics. The Workshop was attended by 82 delegates from 34 countries, and the participation from the industrial and the developing countries was about half each. The programme included 4 review and 29 topical invited lectures. In addition, about 30 contributed papers were presented as posters in two sessions. The latter were created in order to give opportunities to younger physicists for displaying the results of their recent work and to obtain constructive comments from the other participants. During the five days at the ICTP, we focused on almost all the various aspects of nonlinear phenomena that are common in different branches of science. The review and topical lectures as well as the posters dealt with the most recent advances in coherent nonlinear processes in space and astrophysical plasmas, in fluids and optics, in low temperature dusty plasmas, as well as in laser produced and magnetically confined laboratory plasmas. The focus was on the physics of various types of waves and their generation mechanisms, the development
NASA Astrophysics Data System (ADS)
Splinter, Robert; Svenson, Robert H.; Sosa, Eduardo; Buchele d'Avila, Andre Luiz; Scanavacca, Mauricio; Pruitt, Ernest; Kasell, Jackie H.
2003-02-01
When irradiating particular biological media in general there will be a range of optical properties to deal with, with respect to the irradiating wavelength, and the respective tissues that make up the organ under treatment or being imaged. In addition to this we saw changing optical properties under influence of denaturization, dehydration and carbonization. We also observed optical nonlinearities that are irradiance dependent, in addition to the birefringence which affects the light distribution throughout the tissue differently than the polarization birefringence used in optical polarization microscopy. In the treatment of ventricular tachycardia with laser photocoagulation the success of the procedure depends on whether sufficient energy has been directed to the relevant region of the myocardium to ablate the entire arrhythmogenic focus. A new high power diode laser operating in the near infrared was used in an animal infarct model and in human arrhythmia ablation. The light distribution measured for Chagasic heart tissues at the diode laser wavelength demonstrated the key potential to create controlled deep photocoagulation lesions. From our observations we may conclude that the diode laser - catheter combination offers significant potential for the elimination of arrhythmia's resulting from Chagas disease.
Ginn, T R; Murphy, E M; Chilakapati, A; Seeboonruang, U
2001-03-01
Aerobic biodegradation of benzoate by Pseudomonas cepacia sp. in a saturated heterogeneous porous medium was simulated using the stochastic-convective reaction (SCR) approach. A laboratory flow cell was randomly packed with low permeability silt-size inclusions in a high permeability sand matrix. In the SCR upscaling approach, the characteristics of the flow field are determined by the breakthrough of a conservative tracer. Spatial information on the actual location of the heterogeneities is not used. The mass balance equations governing the nonlinear and multicomponent reactive transport are recast in terms of reactive transports in each of a finite number of discrete streamtubes. The streamtube ensemble members represent transport via a steady constant average velocity per streamtube and a conventional Fickian dispersion term, and their contributions to the observed breakthroughs are determined by flux-averaging the streamtube solute concentrations. The resulting simulations were compared to those from a high-resolution deterministic simulation of the reactive transport, and to alternative ensemble representations involving (i) effective Fickian travel time distribution function, (ii) purely convective streamtube transport, and (iii) streamtube ensemble subset simulations. The results of the SCR simulation compare favorably to that of a sophisticated high-resolution deterministic approach.
NASA Astrophysics Data System (ADS)
Ginn, T. R.; Murphy, E. M.; Chilakapati, A.; Seeboonruang, U.
2001-03-01
Aerobic biodegradation of benzoate by Pseudomonas cepacia sp. in a saturated heterogeneous porous medium was simulated using the stochastic-convective reaction (SCR) approach. A laboratory flow cell was randomly packed with low permeability silt-size inclusions in a high permeability sand matrix. In the SCR upscaling approach, the characteristics of the flow field are determined by the breakthrough of a conservative tracer. Spatial information on the actual location of the heterogeneities is not used. The mass balance equations governing the nonlinear and multicomponent reactive transport are recast in terms of reactive transports in each of a finite number of discrete streamtubes. The streamtube ensemble members represent transport via a steady constant average velocity per streamtube and a conventional Fickian dispersion term, and their contributions to the observed breakthroughs are determined by flux-averaging the streamtube solute concentrations. The resulting simulations were compared to those from a high-resolution deterministic simulation of the reactive transport, and to alternative ensemble representations involving (i) effective Fickian travel time distribution function, (ii) purely convective streamtube transport, and (iii) streamtube ensemble subset simulations. The results of the SCR simulation compare favorably to that of a sophisticated high-resolution deterministic approach.
Nonlinear TE-polarized SPPs on a graphene cladded parallel plate waveguide
NASA Astrophysics Data System (ADS)
Wu, Yuexiang; Dai, Xiaoyu; Xiang, Yuanjiang; Fan, Dianyuan
2017-03-01
We consider the transverse electric (TE) surface plasmon polaritons (SPPs) supported by a graphene parallel plate waveguide bounded by Kerr-type nonlinear media in the mid-infrared and terahertz frequencies. Through theoretical analysis of the exact dispersion relations, we reveal the existence conditions of the even mode and odd mode of nonlinear TE SPPs in this system. To be specific, if the linear permittivity of the nonlinear cladding is larger than the permittivity of the core, it only supports the even mode and two branches of the dispersion curve exist. However, when the linear permittivity of the nonlinear cladding is smaller than the permittivity of the core, both even and odd modes can be supported. Moreover, it is found that the propagation constant of even and odd modes decreases with the increasing Fermi energy of graphene.
Adams, J
2002-08-09
New crystalline materials were investigated for applications in frequency conversion of near-infrared wavelengths and as gain media for tunable mid-infrared solid-state lasers. GaCa{sub 4}O(BO{sub 3}){sub 3} (GdCOB), YCa{sub 4}O(BO{sub 3}){sub 3} (YCOB), LaCa{sub 4}O(BO{sub 3}){sub 3} (LaCOB), and Gd{sub 0.275}Y{sub 0.725}Ca{sub 4}O(BO{sub 3}){sub 3} were characterized for frequency conversion of 1 {micro}m lasers. For type I doubling at 1064 nm, LaCOB, GdCOB, and YCOB were found to have effective coupling coefficients (d{sub eff}) of 0.52 {+-} 0.05, 0.78 {+-} 0.06, and 1.12 {+-} 0.07 pm/V, respectively. LaCOB was measured to have angular and thermal sensitivities of 1224 {+-} 184 (cm-rad){sup -1} and < 0.10 (cm-{sup o}C){sup -1}, respectively. The effective coupling coefficient for type II noncritically phasematched (NCPM) doubling at 1064 nm in Gd{sub 0.275}Y{sub 0.725}Ca{sub 4}O(BO{sub 3}){sub 3} was measured to be 0.37 {+-} 0.04 pm/V. We predict LaCOB to have a type I NCPM fundamental wavelength of 1042 {+-} 1.5 nm. Due to its low angular and thermal sensitivities for doubling near 1047 nm, LaCOB has potential for frequency doubling of high-average power Nd:LiYF{sub 4} and Yb:Sr{sub 5}(P0{sub 4}){sub 3}F lasers. LaCOB, GdCOB, and YCOB were also investigated for optical parametric oscillator applications and we determined that they may have potential in a Ti:sapphire pumped oscillator. The effective linear electro-optic coefficients (r{sub eff}) were measured along dielectric directions in YCOB and a maximum r{sub eff} of 10.8 pm/V was found. For a crystal with a 5:1 aspect ratio, the corresponding half-wave voltage at 1064 nm would be 19.6 kV. Therefore a Pockels cell composed of two YCOB crystals with 5:1 aspect ratios would have a required half-wave voltage <10 kV. Moderate coupling coefficients (3 x KH{sub 2}PO{sub 4}), low thermal sensitivities, ease of growth to large sizes, non-hygroscopicity, and favorable polishing and coating characteristics make La
NASA Astrophysics Data System (ADS)
Liu, Hong-Zhun; Sun, Xiao-Quan; Chen, Li-Jiang
2014-07-01
This article shows that all novel exact solutions in the commented paper are not admitted by the original generalized Klein-Gordon equation and active-dissipative dispersive media equation. In addition, we present general solutions of certain auxiliary equation with sixth-degree nonlinear term. Then, based on above general solutions, we find that five cases in their Table 1 is shown to be incorrect.
Dispersive wave emission from wave breaking.
Conforti, Matteo; Trillo, Stefano
2013-10-01
We show that pulses undergoing wave breaking in nonlinear weakly dispersive fibers radiate, owing to phase-matching (assisted by higher-order dispersion) of linear dispersive waves with the shock-wave front. Our theoretical results perfectly explain the radiation observed recently from pulses propagating in the normal dispersion (i.e., nonsolitonic) regime.
Nonlinear Hysteretic Torsional Waves
NASA Astrophysics Data System (ADS)
Cabaret, J.; Béquin, P.; Theocharis, G.; Andreev, V.; Gusev, V. E.; Tournat, V.
2015-07-01
We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters.
Nonlinear Hysteretic Torsional Waves.
Cabaret, J; Béquin, P; Theocharis, G; Andreev, V; Gusev, V E; Tournat, V
2015-07-31
We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters.
Dark three-sister rogue waves in normally dispersive optical fibers with random birefringence.
Chen, Shihua; Soto-Crespo, Jose M; Grelu, Philippe
2014-11-03
We investigate dark rogue wave dynamics in normally dispersive birefringent optical fibers, based on the exact rational solutions of the coupled nonlinear Schrödinger equations. Analytical solutions are derived up to the second order via a nonrecursive Darboux transformation method. Vector dark "three-sister" rogue waves as well as their existence conditions are demonstrated. The robustness against small perturbations is numerically confirmed in spite of the onset of modulational instability, offering the possibility to observe such extreme events in normal optical fibers with random birefringence, or in other Manakov-type vector nonlinear media.
Bilayer dispersion-flattened waveguides with four zero-dispersion wavelengths.
Guo, Yuhao; Jafari, Zeinab; Agarwal, Anu M; Kimerling, Lionel C; Li, Guifang; Michel, Jurgen; Zhang, Lin
2016-11-01
We propose a new type of bilayer dispersion-flattened waveguides that have four zero-dispersion wavelengths. Low and flat dispersion can be achieved by using two different material combinations, with a much smaller index contrast as compared to the previously proposed slot-assisted dispersion-flattened waveguides. Without using a nano-slot, dispersion becomes less sensitive to waveguide dimensions, which is highly desirable for high-yield device fabrication. Ultra-low dispersion, high nonlinearity, and fabrication-friendly design would make it promising for practical implementation of nonlinear photonic functions. The proposed waveguide configuration deepens our understanding of the dispersion flattening principle.
1993-03-21
University Press , to be published). No patents have resulted from this research. Accesion For NTIS CRA&M DTIC TAB By ..................... .. . . . *Avdi; c 2 ...Sherinan,"Asymptotic Theory of Pulse Propagation in Absorbing and Dispersive Dielectrics," (Invited Paper), Review of Radio Science, 1990-1992 ( Oxford
Mid-infrared dispersive waves generation in a birefringent fluorotellurite microstructured fiber
NASA Astrophysics Data System (ADS)
Yao, Chuanfei; Zhao, Zhipeng; Jia, Zhixu; Li, Qing; Hu, Minglie; Qin, Guanshi; Ohishi, Yasutake; Qin, Weiping
2016-09-01
Tunable mid-infrared dispersive waves are generated in a birefringent fluorotellurite microstructured fiber (FTMF) pumped by a 1560 nm femtosecond fiber laser. The FTMF have two zero-dispersion wavelengths (ZDWs) for each polarization axis. The second ZDWs for the fast and slow axes of the FTMF are 2224 and 2042 nm, respectively. As the pump laser is polarized along the fast (or slow) axis of the FTMF, tunable mid-infrared dispersive waves from 2680 to 2725 nm (or from 2260 to 2400 nm) are generated in the FTMF when the Raman soliton meets the second zero-dispersion wavelength of the fast (or slow) axis with increasing the pump power. Our results show that the designed FTMFs are promising nonlinear media for generating tunable mid-infrared light sources.
Kwok, C H; Chow, C W; Tsang, H K; Lin, Chinlon; Bjarklev, A
2006-06-15
We study the conversion bandwidth of the cross-polarization-modulation (XPoIM)-based wavelength conversion scheme with a dispersion-flattened highly nonlinear photonic-crystal fiber for signals with a nonreturn-to-zero (NRZ) modulation format. Both theoretical and experimental results show that the conversion bandwidth can be extended to cover a very wide band, including S-, C-, and L-bands for 10 Gbit/s NRZ signals (a total bandwidth of 120 nm is experimentally demonstrated). We also study the theoretical bandwidth limit for 40 Gbit/s NRZ signals. A significant extension of the conversion bandwidth using the XPoIM approach compared with the four-wave mixing approach previously reported is demonstrated.
NASA Astrophysics Data System (ADS)
Wu, Wenjue; Zhou, Yue; Sun, Ji; Dai, Yitang; Yin, Feifei; Dai, Jian; Xu, Kun
2016-11-01
We proposed a mode-locked all-polarization-maintaining erbium-doped fiber laser base on a nonlinear amplifying loop mirror (NALM). The laser can generate 1.6 ps pulses at 1550 nm with the energy of 1 nJ that can be compressed down to 100 fs with the compressor outside the cavity. The repetition rate of the output pulse is 12MHz. Such configuration of laser is easier controlled and self starting long term operation, and is highly desirable for industrial applications, such as micro-machining.
Reshak, Ali H; Auluck, S; Kityk, I V
2009-02-26
We have performed ab inito theoretical calculations of the electronic structure and the linear and nonlinear optical susceptibilities for calcium neodymium oxyborate Ca4NdO(BO3)3 using two approximations for the exchange correlation (XC) potentials, the local density approximation (LDA) and the generalized gradient approximation (GGA). Our calculations show that this compound is metallic-like, with density of states at the Fermi energy E(F), N(E(F)), of 5.95 and 10.33 states/Ry-cell or bare electronic specific heat coefficients of 1.03 and 1.79 mJ/mol-K2 for LDA and GGA, respectively. The overlap between the valence and conduction bands is strong, resulting in metallic behavior. We found that Nd-s/p/d, Ca-s/p, B-p, and O-s/p states controlled the overlapping around E(F). The effect of LDA and GGA on the band structure, density of states, and linear optical properties is very small, while for the nonlinear optical properties, it is very pronounced. Our calculations show that χ(111)(2)(ω) is the dominant component for both LDA and GGA. We find opposite signs of the contributions of the 2ω and 1ω inter/intraband to the real and imaginary parts for the dominant component throughout the wide optical frequency range.
NASA Astrophysics Data System (ADS)
Jasinski, Jerzy
2015-05-01
In the paper propagation of axially-symmetric (1+2)D beam in nonlinear medium with dual-power nonlinearity is analyzed. The ordinary differential equation for transverse stationary profile of the propagating field is derived and solved using a perturbation technique. The simple analytical formulas for the three lowest order solutions are obtained. They describe fields of algebraic profiles. The zero order solution satisfies exactly the nonlinear Schrödinger equation in (1+2)D case. Higher order solutions are determined by propagation constant and describe fields of different initial amplitude. The accuracy of approximation and stability of the obtained solutions are discussed.
Sackey, Isaac; Da Ros, Francesco; Jazayerifar, Mahmoud; Richter, Thomas; Meuer, Christian; Nölle, Markus; Molle, Lutz; Peucheret, Christophe; Petermann, Klaus; Schubert, Colja
2014-11-03
We present experimental and numerical investigations of Kerr nonlinearity compensation in a 400-km standard single-mode fiber link with distributed Raman amplification with backward pumping. A dual-pump polarization-independent fiber-based optical parametric amplifier is used for mid-link spectral inversion of 5 × 28-GBd polarization-multiplexed 16-QAM signals. Signal quality factor (Q-factor) improvements of 1.1 dB and 0.8 dB were obtained in the cases of a single-channel and a five-channel wavelength-division multiplexing (WDM) system, respectively. The experimental results are compared to numerical simulations with good agreement. It is also shown with simulations that a maximum transmission reach of 2400 km enabled by the optical phase conjugator is possible for the WDM signal.
Ultrafast nonlinear optofluidics in selectively liquid-filled photonic crystal fibers.
Vieweg, M; Gissibl, T; Pricking, S; Kuhlmey, B T; Wu, D C; Eggleton, B J; Giessen, H
2010-11-22
Selective filling of photonic crystal fibers with different media enables a plethora of possibilities in linear and nonlinear optics. Using two-photon direct-laser writing we demonstrate full flexibility of individual closing of holes and subsequent filling of photonic crystal fibers with highly nonlinear liquids. We experimentally demonstrate solitonic supercontinuum generation over 600 nm bandwidth using a compact femtosecond oscillator as pump source. Encapsulating our fibers at the ends we realize a compact ultrafast nonlinear optofluidic device. Our work is fundamentally important to the field of nonlinear optics as it provides a new platform for investigations of spatio-temporal nonlinear effects and underpins new applications in sensing and communications. Selective filling of different linear and nonlinear liquids, metals, gases, gain media, and liquid crystals into photonic crystal fibers will be the basis of new reconfigurable and versatile optical fiber devices with unprecedented performance. Control over both temporal and spatial dispersion as well as linear and nonlinear coupling will lead to the generation of spatial-temporal solitons, so-called optical bullets.
Dark- and bright-rogue-wave solutions for media with long-wave-short-wave resonance.
Chen, Shihua; Grelu, Philippe; Soto-Crespo, J M
2014-01-01
Exact explicit rogue-wave solutions of intricate structures are presented for the long-wave-short-wave resonance equation. These vector parametric solutions feature coupled dark- and bright-field counterparts of the Peregrine soliton. Numerical simulations show the robustness of dark and bright rogue waves in spite of the onset of modulational instability. Dark fields originate from the complex interplay between anomalous dispersion and the nonlinearity driven by the coupled long wave. This unusual mechanism, not available in scalar nonlinear wave equation models, can provide a route to the experimental realization of dark rogue waves in, for instance, negative index media or with capillary-gravity waves.
Novotny, Laura A.; Jurcisek, Joseph A.; Ward, Michael O.; Jordan, Zachary B.; Goodman, Steven D.; Bakaletz, Lauren O.
2015-01-01
Summary Despite resulting in a similar overall outcome, unlike antibodies directed against the DNABII protein, integration host factor (IHF), which induce catastrophic structural collapse of biofilms formed by nontypeable Haemophilus influenzae (NTHI), those directed against a recombinant soluble form of PilA [the majority subunit of Type IV pili (Tfp) produced by NTHI], mediated gradual ‘top-down’ dispersal of NTHI from biofilms. This dispersal occurred via a mechanism that was dependent upon expression of both PilA (and by inference, Tfp) and production of AI-2 quorum signaling molecules by LuxS. The addition of rsPilA to a biofilm-targeted therapeutic vaccine formulation comprised of IHF plus the powerful adjuvant dmLT, and delivered via a non-invasive transcutaneous immunization route, induced an immune response that targeted two important determinants essential for biofilm formation by NTHI. This resulted in significantly earlier eradication of NTHI from both planktonic and adherent populations in the middle ear, disruption of mucosal biofilms already resident within middle ears prior to immunization, and rapid resolution of signs of disease in an animal model of experimental otitis media. These data support continued development of this novel combinatorial immunization approach for resolution and/or prevention of multiple diseases of the respiratory tract caused by NTHI. PMID:25597921
Novotny, Laura A; Jurcisek, Joseph A; Ward, Michael O; Jordan, Zachary B; Goodman, Steven D; Bakaletz, Lauren O
2015-04-01
Despite resulting in a similar overall outcome, unlike antibodies directed against the DNABII protein, integration host factor (IHF), which induce catastrophic structural collapse of biofilms formed by nontypeable Haemophilus influenzae (NTHI), those directed against a recombinant soluble form of PilA [the majority subunit of Type IV pili (Tfp) produced by NTHI], mediated gradual 'top-down' dispersal of NTHI from biofilms. This dispersal occurred via a mechanism that was dependent upon expression of both PilA (and by inference, Tfp) and production of AI-2 quorum signaling molecules by LuxS. The addition of rsPilA to a biofilm-targeted therapeutic vaccine formulation comprised of IHF plus the powerful adjuvant dmLT and delivered via a noninvasive transcutaneous immunization route induced an immune response that targeted two important determinants essential for biofilm formation by NTHI. This resulted in significantly earlier eradication of NTHI from both planktonic and adherent populations in the middle ear, disruption of mucosal biofilms already resident within middle ears prior to immunization and rapid resolution of signs of disease in an animal model of experimental otitis media. These data support continued development of this novel combinatorial immunization approach for resolution and/or prevention of multiple diseases of the respiratory tract caused by NTHI.
NASA Astrophysics Data System (ADS)
Wang, Pengcheng; Zhou, Yingke; Hu, Min; Chen, Jian
2017-01-01
Nitrogen-doped carbon nanotube supporting NiO nanoparticles were synthesized by a chemical precipitation process coupled with subsequent calcination. The morphology and structure of the composites were characterized by transmission electron microscopy (TEM), X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS), and the electrochemical performance was evaluated using cyclic voltammetry and chronoamperometric technique. The effects of nitrogen doping, calcination temperature and content of NiO nanoparticles on the electrocatalytic activity toward methanol oxidation were systematically studied. The results show that the uniformly dispersed ultrafine NiO nanoparticles supported on nitrogen-doped carbon nanotube are obtained after calcination at 400 °C. The optimized composite catalysts present high electrocatalytic activity, fast charge-transfer process, excellent accessibility and stability for methanol oxidation reaction, which are promising for application in the alkaline direct methanol fuel cells.
NASA Astrophysics Data System (ADS)
Yan, Zhenya; Wen, Zichao; Hang, Chao
2015-08-01
We present a unified theoretical study of the bright solitons governed by self-focusing and defocusing nonlinear Schrödinger (NLS) equations with generalized parity-time- (PT ) symmetric Scarff-II potentials. Particularly, a PT -symmetric k -wave-number Scarff-II potential and a multiwell Scarff-II potential are considered, respectively. For the k -wave-number Scarff-II potential, the parameter space can be divided into different regions, corresponding to unbroken and broken PT symmetry and the bright solitons for self-focusing and defocusing Kerr nonlinearities. For the multiwell Scarff-II potential the bright solitons can be obtained by using a periodically space-modulated Kerr nonlinearity. The linear stability of bright solitons with PT -symmetric k -wave-number and multiwell Scarff-II potentials is analyzed in detail using numerical simulations. Stable and unstable bright solitons are found in both regions of unbroken and broken PT symmetry due to the existence of the nonlinearity. Furthermore, the bright solitons in three-dimensional self-focusing and defocusing NLS equations with a generalized PT -symmetric Scarff-II potential are explored. This may have potential applications in the field of optical information transmission and processing based on optical solitons in nonlinear dissipative but PT -symmetric systems.
Time-reversal of nonlinear waves: Applicability and limitations
NASA Astrophysics Data System (ADS)
Ducrozet, G.; Fink, M.; Chabchoub, A.
2016-09-01
Time-reversal (TR) refocusing of waves is one of the fundamental principles in wave physics. Using the TR approach, time-reversal mirrors can physically create a time-reversed wave that exactly refocus back, in space and time, to its original source regardless of the complexity of the medium as if time were going backward. Laboratory experiments have proved that this approach can be applied not only in acoustics and electromagnetism, but also in the field of linear and nonlinear water waves. Studying the range of validity and limitations of the TR approach may determine and quantify its range of applicability in hydrodynamics. In this context, we report a numerical study of hydrodynamic time-reversal using a unidirectional numerical wave tank, implemented by the nonlinear high-order spectral method, known to accurately model the physical processes at play, beyond physical laboratory restrictions. The applicability of the TR approach is assessed over a variety of hydrodynamic localized and pulsating structures' configurations, pointing out the importance of high-order dispersive and particularly nonlinear effects in the refocusing of hydrodynamic stationary envelope solitons and breathers. We expect that the results may motivate similar experiments in other nonlinear dispersive media and encourage several applications with particular emphasis on the field of ocean engineering.
Compactons in Nonlinear Schroedinger Lattices with Strong Nonlinearity Management
Abdullaev, F. Kh.; Kevrekidis, P. G.; Salerno, M.
2010-09-10
The existence of compactons in the discrete nonlinear Schroedinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. In the averaged discrete nonlinear Schroedinger equation, the resulting effective interwell tunneling depends on the modulation parameters and on the field amplitude. This introduces nonlinear dispersion in the system and can lead to a prototypical realization of single- or multisite stable discrete compactons in nonlinear optical waveguide and Bose-Einstein condensate arrays. These structures can dynamically arise out of Gaussian or compactly supported initial data.
NASA Astrophysics Data System (ADS)
Tariq, Kalim Ul-Haq; Seadawy, A. R.
The Boussinesq equation with dual dispersion and modified Korteweg-de Vries-Kadomtsev-Petviashvili equations describe weakly dispersive and small amplitude waves propagating in a quasi three-dimensional media. In this article, we study the analytical Bright-Dark solitary wave solutions for (3 + 1)-dimensional Breaking soliton equation, Boussinesq equation with dual dispersion and modified Korteweg-de Vries-Kadomtsev-Petviashvili equation have been extracted. These results hold numerous travelling wave solutions that are of key importance in elucidating some physical circumstance. The technique can also be functional to other sorts of nonlinear evolution equations in contemporary areas of research.
Finite elements of nonlinear continua.
NASA Technical Reports Server (NTRS)
Oden, J. T.
1972-01-01
The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.
NASA Astrophysics Data System (ADS)
Hui, Zhan-Qiang; Zhang, Bo; Zhang, Jian-Guo
2016-04-01
All-optical NRZ-to-RZ format conversion with a function of wavelength multicasting is proposed in this paper, which is realized by exploiting cross-phase modulation (XPM) and four-wave-mixing (FWM) in a dispersion-flattened highly nonlinear photonic crystal fiber (DF-HNL-PCF). The designed format converter is experimentally demonstrated, for which the 1-to-4 wavelength multicasting is achieved simultaneously by filtering out two FWM idler waves and both blue-chirped and red-chirped components of the broadened NRZ spectrum induced by XPM. Moreover, the wavelength tunability and dynamic characteristics of the proposed NRZ-to-RZ format converter are also exploited using the different central wavelengths of an optical clock signal and varying the input optical power at a DF-HNL-PCF in our experiment. It is shown that the designed format converter can possess a wide range of operational wavelength over 17 nm, an optimal extinction ratio of 11.6 dB, and a Q-factor of 7.1, respectively. Since the proposed scheme uses an optical fiber-based configuration and is easy for implementation, it can be very useful for future applications in advanced fiber-optic communication networks.
NASA Astrophysics Data System (ADS)
Liu, Chongxuan; Szecsody, Jim E.; Zachara, John M.; Ball, William P.
The generalized integral transform technique (GITT) is applied to solve the one-dimensional advection-dispersion equation (ADE) in heterogeneous porous media coupled with either linear or nonlinear sorption and decay. When both sorption and decay are linear, analytical solutions are obtained using the GITT for one-dimensional ADEs with spatially and temporally variable flow and dispersion coefficient and arbitrary initial and boundary conditions. When either sorption or decay is nonlinear the solutions to ADEs with the GITT are hybrid analytical-numerical. In both linear and nonlinear cases, the forward and inverse integral transforms for the problems described in the paper are apparent and straightforward. Some illustrative examples with linear sorption and decay are presented to demonstrate the application and check the accuracy of the derived analytical solutions. The derived hybrid analytical-numerical solutions are checked against a numerical approach and demonstratively applied to a nonlinear transport example, which simulates a simplified system of iron oxide bioreduction with nonlinear sorption and nonlinear reaction kinetics.
NASA Astrophysics Data System (ADS)
Chen, Yi-Xiang; Xu, Zhou-Xiang; Jiang, Yun-Feng; Shi, Jin; Xu, Fang-Qian
2015-07-01
We obtain exact spatial localized mode solutions of a (2+1)-dimensional nonlinear Schrödinger equation with constant diffraction and cubic-quintic nonlinearity in Script PScript T-symmetric potential, and study the linear stability of these solutions. Based on these results, we further derive exact spatial localized mode solutions in a cubic-quintic medium with harmonic and Script PScript T-symmetric potentials. Moreover, the dynamical behaviors of spatial localized modes in the exponential diffraction decreasing waveguide and the periodic distributed amplification system are investigated. Supported by the Project of Technology Office in Zhejiang Province under Grant No. 2014C32006, the Special Foundation for theoretical physics Research Program of China under Grant No. 11447124, National Natural Science Foundation of China under Grant No. 11374254 and the Higher School Visiting Scholar Development under Grant No. FX2013103
NASA Astrophysics Data System (ADS)
Tereshchenko, S. A.; Savelyev, M. S.; Podgaetsky, V. M.; Gerasimenko, A. Yu.; Selishchev, S. V.
2016-09-01
A threshold model is described which permits one to determine the properties of limiters for high-powered laser light. It takes into account the threshold characteristics of the nonlinear optical interaction between the laser beam and the limiter working material. The traditional non-threshold model is a particular case of the threshold model when the limiting threshold is zero. The nonlinear characteristics of carbon nanotubes in liquid and solid media are obtained from experimental Z-scan data. Specifically, the nonlinear threshold effect was observed for aqueous dispersions of nanotubes, but not for nanotubes in solid polymethylmethacrylate. The threshold model fits the experimental Z-scan data better than the non-threshold model. Output characteristics were obtained that integrally describe the nonlinear properties of the optical limiters.
1991-05-22
elastoplastic moduli and the elastic constants of the material . 14.~~I NIUMMC oENE PAGES Micromechanics; Constitutive Law; Granular Media; Sand...research effort has been conducted on constitutive and micromechanical modelling of granular soil. This includes: 1) the development of a new constitutive ...U5WStaneee 0"e a" (R". 2 19) 0" sa Lug &" % jI& The report consists of three volumes, as follows: Volume I: "A Constitutive Law for Granular Materials
NASA Astrophysics Data System (ADS)
Vinogradova, O. P.; Ostrosablina, A. A.; Sidorov, A. I.
2006-02-01
This paper presents the experimental and theoretical results of a study of the interaction of pulsed laser radiation with thick composite media containing nanoparticles of vanadium dioxide (VO2). It is established that the reversible semiconductor-metal phase transition that occurs in the VO2 nanoparticles under the action of radiation can produce self-focusing of the mid-IR radiation by the formation of a photoinduced dynamic lens. An analysis is carried out of how the radiation intensity affects the dynamics of the given process.
NASA Astrophysics Data System (ADS)
Madvaliev, U.; Salikhov, T. Kh.; Sharifov, D. M.
2006-06-01
A perturbation theory is put forward that describes the effect of thermal nonlinearity due to the temperature dependence of the thermophysical parameters of high-absorption systems with a low thermal conductivity on the parameters of the photoacoustic signal detected by the gas microphone technique. It is found that the dependence of the photoacoustic signal amplitude on incident beam intensity I 0 stems from the dependence of the illuminated surface temperature on I 0. This dependence is a complicated function instead of being a simple quadratic function as was expected. In the limiting cases (μsβ ≪ 1 and μsβ ≫ 1), this contribution to the photoacoustic signal amplitude is described by simple expressions, which are convenient for determining the thermal coefficients of the thermophysical parameters of the medium. It is found that the thermal nonlinearity significantly affects the photoacoustic signal phase in the frequency region meeting the condition μsβ ˜ 1. In the above limiting cases, its effect is insignificant. A theory of generation of the photoacoustic signal second harmonic is proposed. The second harmonic is related to the temperature dependence of the thermophysical parameters of the buffer gas and sample. It is shown that the amplitude of the signal is a quadratic function of the incident beam intensity and varies with its frequency as ω-3/2 for μsβ ≫ 1 and ω-5/2 for μsβ ≪ 1.
Migration of dispersive GPR data
Powers, M.H.; Oden, C.P.; ,
2004-01-01
Electrical conductivity and dielectric and magnetic relaxation phenomena cause electromagnetic propagation to be dispersive in earth materials. Both velocity and attenuation may vary with frequency, depending on the frequency content of the propagating energy and the nature of the relaxation phenomena. A minor amount of velocity dispersion is associated with high attenuation. For this reason, measuring effects of velocity dispersion in ground penetrating radar (GPR) data is difficult. With a dispersive forward model, GPR responses to propagation through materials with known frequency-dependent properties have been created. These responses are used as test data for migration algorithms that have been modified to handle specific aspects of dispersive media. When either Stolt or Gazdag migration methods are modified to correct for just velocity dispersion, the results are little changed from standard migration. For nondispersive propagating wavefield data, like deep seismic, ensuring correct phase summation in a migration algorithm is more important than correctly handling amplitude. However, the results of migrating model responses to dispersive media with modified algorithms indicate that, in this case, correcting for frequency-dependent amplitude loss has a much greater effect on the result than correcting for proper phase summation. A modified migration is only effective when it includes attenuation recovery, performing deconvolution and migration simultaneously.
New avenues for phase matching in nonlinear hyperbolic metamaterials.
Duncan, C; Perret, L; Palomba, S; Lapine, M; Kuhlmey, B T; de Sterke, C Martijn
2015-03-11
Nonlinear optical processes, which are of paramount importance in science and technology, involve the generation of new frequencies. This requires phase matching to avoid that light generated at different positions interferes destructively. Of the two original approaches to achieve this, one relies on birefringence in optical crystals, and is therefore limited by the dispersion of naturally occurring materials, whereas the other, quasi-phase-matching, requires direct modulation of material properties, which is not universally possible. To overcome these limitations, we propose to exploit the unique dispersion afforded by hyperbolic metamaterials, where the refractive index can be arbitrarily large. We systematically analyse the ensuing opportunities and demonstrate that hyperbolic phase matching can be achieved with a wide range of material parameters, offering access to the use of nonlinear media for which phase matching cannot be achieved by other means. With the rapid development in the fabrication of hyperbolic metamaterials, our approach is destined to bring significant advantages over conventional techniques for the phase matching of a variety of nonlinear processes.
Calculations of precursor propagation in dispersive dielectrics.
Bacon, Larry Donald
2003-08-01
The present study is a numerical investigation of the propagation of electromagnetic transients in dispersive media. It considers propagation in water using Debye and composite Rocard-Powles-Lorentz models for the complex permittivity. The study addresses this question: For practical transmitted spectra, does precursor propagation provide any features that can be used to advantage over conventional signal propagation in models of dispersive media of interest? A companion experimental study is currently in progress that will attempt to measure the effects studied here.
Dement'ev, Aleksandr S; Demin, I; Murauskas, E; Slavinskis, S
2011-02-28
Efficient compression of focused {approx}0.9-ns pulses of a miniature Nd:YAG laser to less than 60 ps is experimentally obtained at their interaction with counterpropagating pulses of the same carrier frequency and width in CCl{sub 4}. In this case, electrostriction interaction (amplification) begins not from the level of spontaneous-scattering noise; therefore, the counterpropagating pulses can be compressed at pump pulse energies below the stimulated Brillouin scattering (SBS) threshold energies. When counterpropagating seed pulses are used, the energy and temporal stability of compressed pulses are several times higher, and their time jitter is smaller than that for SBS compression from the level of spontaneous-scattering noise. (nonlinear optical phenomena)
NASA Astrophysics Data System (ADS)
Louis, Hélène; Odent, Vincent; Louvergneaux, Eric
2016-04-01
Shock waves are well-known nonlinear waves, displaying an abrupt discontinuity. Observation can be made in a lot of physical fields, as in water wave, plasma and nonlinear optics. Shock waves can either break or relax through either catastrophic or regularization phenomena. In this work, we restrain our study to dispersive shock waves. This regularization phenomenon implies the emission of dispersive waves. We demonstrate experimentally and numerically the generation of spatial dispersive shock waves in a nonlocal focusing media. The generation of dispersive shock wave in a focusing media is more problematic than in a defocusing one. Indeed, the modulational instability has to be frustrated to observe this phenomenon. In 2010, the dispersive shock wave was demonstrated experimentally in a focusing media with a partially coherent beam [1]. Another way is to use a nonlocal media [2]. The impact of nonlocality is more important than the modulational instability frustration. Here, we use nematic liquid crystals (NLC) as Kerr-like nonlocal medium. To achieve shock formation, we use the Riemann condition as initial spatial condition (edge at the beam entrance of the NLC cell). In these experimental conditions, we generate, experimentally and numerically, shock waves that relax through the emission of dispersive waves. Associated with this phenomenon, we evidence the emergence of a localized wave that travels through the transverse beam profile. The beam steepness, which is a good indicator of the shock formation, is maximal at the shock point position. This latter follows a power law versus the injected power as in [3]. Increasing the injected power, we found multiple shock points. We have good agreements between the numerical simulations and the experimental results. [1] W. Wan, D. V Dylov, C. Barsi, and J. W. Fleischer, Opt. Lett. 35, 2819 (2010). [2] G. Assanto, T. R. Marchant, and N. F. Smyth, Phys. Rev. A - At. Mol. Opt. Phys. 78, 1 (2008). [3] N. Ghofraniha, L. S
Cascaded Second-Order Nonlinearities in Waveguides.
NASA Astrophysics Data System (ADS)
Sundheimer, Michael Lee
The cascaded second-order nonlinearity arising from the second-harmonic generation process in noncentrosymmetric media is a novel approach to achieving the nonlinear phase shifts required for all-optical signal processing. The research presented in this dissertation demonstrated and measured the cascaded second-order nonlinearity for the first time in viable integrated optical waveguide formats. Cascaded self-phase modulation was measured in potassium titanyl phosphate (KTiOPO_4 or KTP) segmented quasi-phasematched waveguides at wavelengths near 855 nm and in the optical fiber telecommunications window near 1.585 μm using picosecond and femtosecond pulses, respectively. Spectral modulation and broadening were observed on the output fundamental spectrum and compared to predictions from pulsed second -harmonic generation theory under conditions of group-velocity mismatch (temporal walk-off) and group-velocity dispersion. Peak cascaded phase shifts of the fundamental of approximately pi at 855 nm were inferred with 690 W of peak guided power. Peak cascaded phase shifts of approximately pi/2 were inferred at 1.585 μm with 760 W of peak power in the guide. Direct interferometric measurements of the magnitude and sign of the cascaded nonlinear phase shift of the fundamental were performed in temperature-tuned lithium niobate (LiNbO _3) channel waveguides at 1.32 mum. The cascaded phase shift was shown to change sign upon passing through the phasematching condition, as required by theory. Peak cascaded phase shifts of +0.53 pi and -0.13 pi were measured for 86 W peak power in these waveguides. A non-uniform temperature profile along the waveguide led to a non-uniform wavevector-mismatch along the guide, resulting in an enhanced positive phase shift and an increased temperature bandwidth for the phase shift. The phase shifts achieved in this research are large enough to be suitable for some all-optical signal processing functions.
Recurrence of initial state of nonlinear ion waves
Abe, K.; Satofuka, N.
1981-06-01
By solving the Korteweg--deVries equation in a wide range of the ratio between the nonlinearity and the dispersion, the recurrence of the initial state of the ion wave is examined. The recurrence is assured of taking place only when the dispersion of the initial ion wave predominates over the nonlinearity. If the initial wave has strong nonlinearity compared with the dispersion, the recurrence is indistinct, and the initial monochromatic wave evolves to a turbulent state.
Fractional power-law spatial dispersion in electrodynamics
Tarasov, Vasily E.; Trujillo, Juan J.
2013-07-15
Electric fields in non-local media with power-law spatial dispersion are discussed. Equations involving a fractional Laplacian in the Riesz form that describe the electric fields in such non-local media are studied. The generalizations of Coulomb’s law and Debye’s screening for power-law non-local media are characterized. We consider simple models with anomalous behavior of plasma-like media with power-law spatial dispersions. The suggested fractional differential models for these plasma-like media are discussed to describe non-local properties of power-law type. -- Highlights: •Plasma-like non-local media with power-law spatial dispersion. •Fractional differential equations for electric fields in the media. •The generalizations of Coulomb’s law and Debye’s screening for the media.
Solutions of the cylindrical nonlinear Maxwell equations.
Xiong, Hao; Si, Liu-Gang; Ding, Chunling; Lü, Xin-You; Yang, Xiaoxue; Wu, Ying
2012-01-01
Cylindrical nonlinear optics is a burgeoning research area which describes cylindrical electromagnetic wave propagation in nonlinear media. Finding new exact solutions for different types of nonlinearity and inhomogeneity to describe cylindrical electromagnetic wave propagation is of great interest and meaningful for theory and application. This paper gives exact solutions for the cylindrical nonlinear Maxwell equations and presents an interesting connection between the exact solutions for different cylindrical nonlinear Maxwell equations. We also provide some examples and discussion to show the application of the results we obtained. Our results provide the basis for solving complex systems of nonlinearity and inhomogeneity with simple systems.
Dissipative effects in nonlinear Klein-Gordon dynamics
NASA Astrophysics Data System (ADS)
Plastino, A. R.; Tsallis, C.
2016-03-01
We consider dissipation in a recently proposed nonlinear Klein-Gordon dynamics that admits exact time-dependent solutions of the power-law form e_qi(kx-wt) , involving the q-exponential function naturally arising within the nonextensive thermostatistics (e_qz \\equiv [1+(1-q)z]1/(1-q) , with e_1^z=ez ). These basic solutions behave like free particles, complying, for all values of q, with the de Broglie-Einstein relations p=\\hbar k , E=\\hbar ω and satisfying a dispersion law corresponding to the relativistic energy-momentum relation E2 = c^2p2 + m^2c4 . The dissipative effects explored here are described by an evolution equation that can be regarded as a nonlinear generalization of the celebrated telegraph equation, unifying within one single theoretical framework the nonlinear Klein-Gordon equation, a nonlinear Schrödinger equation, and the power-law diffusion (porous-media) equation. The associated dynamics exhibits physically appealing traveling solutions of the q-plane wave form with a complex frequency ω and a q-Gaussian square modulus profile.
1987-09-25
for the Korteweg - deVries equation . In order to understand the effects of a slowly varying medium, Luke [1] in 1966 utilized themethod of multiple... Korteweg - deVries type equations [7]. For clarity, we note that after using (4.9) and VkJ : 0 [see (7.6)] the equation for the modulated phase shift O(X,T...dispersive oscillatory waves are analyzed for Korteweg - deVries type partial differential equations with slowly varying coefficients and arbitrary
ERIC Educational Resources Information Center
Vennebush, G. Patrick
2004-01-01
Media Clips aims to offer readers contemporary, authentic applications of quantitative reasoning based on print or electronic media. Clips may be in text or graphic format, and clip sources may be either print or electronic media.
Shen, Y.R.; Chen, C.K.; de Castro, A.R.B.
1980-01-01
Surface electromagnetic waves are waves propagating along the interface of two media. Their existence was predicted by Sommerfield in 1909. In recent years, interesting applications have been found in the study of overlayers and molecular adsorption on surfaces, in probing of phase transitions, and in measurements of refractive indices. In the laboratory, the nonlinear interaction of surface electromagnetic waves were studied. The preliminary results of this recent venture in this area are presented.
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.
Asphaltene dispersants as demulsification aids
Manek, M.B.
1995-11-01
Destabilization of petroleum asphaltenes may cause a multitude of problems in crude oil recovery and production. One major problem is their agglomeration at the water-oil interface of crude oil emulsions. Once agglomeration occurs, destabilized asphaltenes can form a thick pad in the dehydration equipment, which significantly reduces the demulsification rate. Certain polymeric dispersants increase asphaltene solubilization in hydrocarbon media, and when used in conjunction with emulsion breakers, facilitate the demulsification process. Two case studies are presented that demonstrate how asphaltene dispersants can efficiently inhibit pad formation and help reduce demulsifier dosage. Criteria for dispersant application and selection are discussed, which include the application of a novel laboratory technique to assess asphaltene stabilization in the crude oil. The technique monitors asphaltene agglomeration while undergoing titration with an incompatible solvent (precipitant). The method was used to evaluate stabilization of asphaltenes in the crude oil and to screen asphaltene dispersants.
Hata, Shigefumi; Nakao, Hiroya; Mikhailov, Alexander S.
2014-01-01
As shown by Alan Turing in 1952, differential diffusion may destabilize uniform distributions of reacting species and lead to emergence of patterns. While stationary Turing patterns are broadly known, the oscillatory instability, leading to traveling waves in continuous media and sometimes called the wave bifurcation, remains less investigated. Here, we extend the original analysis by Turing to networks and apply it to ecological metapopulations with dispersal connections between habitats. Remarkably, the oscillatory Turing instability does not lead to wave patterns in networks, but to spontaneous development of heterogeneous oscillations and possible extinction of species. We find such oscillatory instabilities for all possible food webs with three predator or prey species, under various assumptions about the mobility of individual species and nonlinear interactions between them. Hence, the oscillatory Turing instability should be generic and must play a fundamental role in metapopulation dynamics, providing a common mechanism for dispersal-induced destabilization of ecosystems. PMID:24394959
NASA Astrophysics Data System (ADS)
Hata, Shigefumi; Nakao, Hiroya; Mikhailov, Alexander S.
2014-01-01
As shown by Alan Turing in 1952, differential diffusion may destabilize uniform distributions of reacting species and lead to emergence of patterns. While stationary Turing patterns are broadly known, the oscillatory instability, leading to traveling waves in continuous media and sometimes called the wave bifurcation, remains less investigated. Here, we extend the original analysis by Turing to networks and apply it to ecological metapopulations with dispersal connections between habitats. Remarkably, the oscillatory Turing instability does not lead to wave patterns in networks, but to spontaneous development of heterogeneous oscillations and possible extinction of species. We find such oscillatory instabilities for all possible food webs with three predator or prey species, under various assumptions about the mobility of individual species and nonlinear interactions between them. Hence, the oscillatory Turing instability should be generic and must play a fundamental role in metapopulation dynamics, providing a common mechanism for dispersal-induced destabilization of ecosystems.
ERIC Educational Resources Information Center
Budiansky, Stephen
1980-01-01
This article discusses the need for more accurate and complete input data and field verification of the various models of air pollutant dispension. Consideration should be given to changing the form of air quality standards based on enhanced dispersion modeling techniques. (Author/RE)
Instability of two-dimensional solitons and vortices in defocusing media
NASA Astrophysics Data System (ADS)
Kuznetsov, E. A.; Rasmussen, J. Juul
1995-05-01
In the framework of the three-dimensional nonlinear Schrödinger equation the instability of two-dimensional solitons and vortices is demonstrated. The soliton instability can be considered as the analog of the Kadomtsev-Petviashvili instability (Dokl. Akad. Nauk SSSR 192, 753 (1970) [Sov. Phys. Dokl. 15, 539 (1970)]) of one-dimensional acoustic solitons in media with positive dispersion. For large distances between the vortices, this instability transforms into the Crow instability [AIAA J. 8, 2172 (1970)] of two vortex filaments with opposite circulations.
Wave-equation dispersion inversion
NASA Astrophysics Data System (ADS)
Li, Jing; Feng, Zongcai; Schuster, Gerard
2017-03-01
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.
1989-06-15
following surprising situation. Namely associated with the integrable nonlinear Schrodinger equations are standard numerical schemes which exhibit at...36. An Initial Boundary Value Problem for the Nonlinear Schrodinger Equations , A.S. Fokas, Physica D March 1989. 37. Evolution Theory, Periodic... gravity waves and wave excitation phenomena related to moving pressure distributions; numerical approximation and computation; nonlinear optics; and
NASA Technical Reports Server (NTRS)
Frost, W.; Christensen, L. S.; Collins, F. G.; Camp, D. W.
1980-01-01
A study of economically viable techniques for dispersing warm fog at commercial airports is presented. Five fog dispersion techniques are examined: evaporation suppression, downwash, mixing, seeding with hygroscopic material, thermal techniques, and charged particle techniques. Thermal techniques, although effective, were found to be too expensive for routine airport operations, and detrimental to the environment. Seeding or helicopter downwash are practical for small-scale or temporary fog clearing, but are probably not useful for airport operations on a routine basis. Considerable disagreement exists on the capability of charged particle techniques, which stems from the fact that different assumptions and parameter values are used in the analytical models. Recommendations resulting from the review of this technique are listed, and include: experimental measurements of the parameters in question; a study to ascertain possible safety hazards, such as increased electrical activity or fuel ignition during refueling operations which could render charged particle techniques impractical; and a study of a single charged particle generator.
Spatial Beam Dynamics Mediated by Hybrid Nonlinearity
NASA Astrophysics Data System (ADS)
Zhang, Peng; Lou, Cibo; Hu, Yi; Liu, Sheng; Zhao, Jianlin; Xu, Jingjun; Chen, Zhigang
We provide a brief overview of recent progresses on the study of a new type of nonlinearity, named hybrid nonlinearity: the coexistence of self-focusing and self-defocusing nonlinearities in the same material under identical conditions. Such hybrid nonlinearity is established in a nonconventionally biased photorefractive crystal, which offers enhanced anisotropy and nonlocality, leading to a variety of unusual nonlinear beam dynamics in both continuous and discrete regimes. In homogenous media, elliptical optical solitons, stabilization of nonlinear optical vortices, as well as orientation-induced transition between bright and dark solitons are demonstrated. In discrete media, hybrid nonlinearity enables the creation of an ionic-type photonic lattice with alternating positive and negative optical potentials, which in turn enables the reconfiguration of lattice structures and Brillouin zones for band-gap engineering and light manipulation. Moreover, a host of nonlinear discrete localized states mediated by such hybrid nonlinearity are uncovered, including elliptical discrete solitons and "saddle" solitons. The novel concept of hybrid nonlinearity opens a door for exploring spatial beam dynamics and related nonlinear phenomena in anisotropic nonlinear systems beyond optics.
Strasburger, Victor C
2010-11-01
The American Academy of Pediatrics recognizes that exposure to mass media (eg, television, movies, video and computer games, the Internet, music lyrics and videos, newspapers, magazines, books, advertising) presents health risks for children and adolescents but can provide benefits as well. Media education has the potential to reduce the harmful effects of media and accentuate the positive effects. By understanding and supporting media education, pediatricians can play an important role in reducing harmful effects of media on children and adolescents.
NASA Astrophysics Data System (ADS)
Geniet, F.; Leon, J.
2003-05-01
A nonlinear system possessing a natural forbidden band gap can transmit energy of a signal with a frequency in the gap, as recently shown for a nonlinear chain of coupled pendulums (Geniet and Leon 2002 Phys. Rev. Lett. 89 134102). This process of nonlinear supratransmission, occurring at a threshold that is exactly predictable in many cases, is shown to have a simple experimental realization with a mechanical chain of pendulums coupled by a coil spring. It is then analysed in more detail. First we go to different (nonintegrable) systems which do sustain nonlinear supratransmission. Then a Josephson transmission line (a one-dimensional array of short Josephson junctions coupled through superconducting wires) is shown to also sustain nonlinear supratransmission, though being related to a different class of boundary conditions, and despite the presence of damping, finiteness, and discreteness. Finally, the mechanism at the origin of nonlinear supratransmission is found to be a nonlinear instability, and this is briefly discussed here.
Soliton trapping of dispersive waves in photonic crystal fiber with two zero dispersive wavelengths.
Wang, Weibin; Yang, Hua; Tang, Pinghua; Zhao, Chujun; Gao, Jing
2013-05-06
Based on the generalized nonlinear Schrödinger equation, we present a numerical study of trapping of dispersive waves by solitons during supercontinuum generation in photonic crystal fibers pumped with femtosecond pulses in the anomalous dispersion region. Numerical simulation results show that the generated supercontinuum is bounded by two branches of dispersive waves, namely blue-shifted dispersive waves (B-DWs) and red-shifted dispersive waves (R-DWs). We find a novel phenomenon that not only B-DWs but also R-DWs can be trapped by solitons across the zero-dispersion wavelength when the group-velocity matching between the soliton and the dispersive wave is satisfied, which may led to the generation of new spectral components via mixing of solitons and dispersive waves. Mixing of solitons with dispersive waves has been shown to play an important role in shaping not only the edge of the supercontinuum, but also its central part around the higher zero-dispersion wavelength. Further, we show that the phenomenon of soliton trapping of dispersive waves in photonic crystal fibers with two zero-dispersion wavelengths has a very close relationship with pumping power and the interval between two zero-dispersion wavelengths. In order to clearly display the evolution of soliton trapping of dispersive waves, the spectrogram of output pulses is observed using cross-correlation frequency-resolved optical gating technique (XFROG).
Tunneling induced absorption with competing Nonlinearities
Peng, Yandong; Yang, Aihong; Xu, Yan; Wang, Peng; Yu, Yang; Guo, Hongju; Ren, Tingqi
2016-01-01
We investigate tunneling induced nonlinear absorption phenomena in a coupled quantum-dot system. Resonant tunneling causes constructive interference in the nonlinear absorption that leads to an increase of more than an order of magnitude over the maximum absorption in a coupled quantum dot system without tunneling. Resonant tunneling also leads to a narrowing of the linewidth of the absorption peak to a sublinewidth level. Analytical expressions show that the enhanced nonlinear absorption is largely due to the fifth-order nonlinear term. Competition between third- and fifth-order nonlinearities leads to an anomalous dispersion of the total susceptibility. PMID:27958303
Nonlinear wavetrains in viscous conduits
NASA Astrophysics Data System (ADS)
Maiden, Michelle; Hoefer, Mark
2016-11-01
Viscous fluid conduits provide an ideal system for the study of dissipationless, dispersive hydrodynamics. A dense, viscous fluid serves as the background medium through which a lighter, less viscous fluid buoyantly rises. If the interior fluid is continuously injected, a deformable pipe forms. The long wave interfacial dynamics are well-described by a dispersive nonlinear partial differential equation. In this talk, experiments, numerics, and asymptotics of the viscous fluid conduit system will be presented. Structures at multiple length scales are discussed, including solitons, dispersive shock waves, and periodic waves. Modulations of periodic waves will be explored in the weakly nonlinear regime with the Nonlinear Schrödinger (NLS) equation. Modulational instability (stability) is identified for sufficiently short (long) periodic waves due to a change in dispersion curvature. These asymptotic results are confirmed by numerical simulations of perturbed nonlinear periodic wave solutions. Also, numerically observed are envelope bright and dark solitons well approximated by NLS. This work was partially supported by NSF CAREER DMS-1255422 (M.A.H.) and NSF GRFP (M.D.M.).
Analysis of linear and nonlinear effects in optical fiber
NASA Astrophysics Data System (ADS)
Jurečka, Stanislav; Scholtz, Łubomír.; Ladányi, Libor; Müllerová, Jarmila
2016-12-01
The propagation of optical pulses in dispersive nonlinear fibers is studied by using an adaptive split step Fourier method. Propagation of optical pulse is described by a generalized nonlinear Schrödinger equation. Various initial pulse shapes can be used, impact of group velocity dispersion up to the fourth-order dispersion, self phase modulation and their interplay are studied in connection with the dispersion and nonlinear length parameters. Properties of propagating field are analyzed in time and in frequency domain. For pulse propagation in telecommunication applications the results of implemented solutions are in good agreement with experiments.
Anomalous dispersions of `hedgehog' particles
NASA Astrophysics Data System (ADS)
Bahng, Joong Hwan; Yeom, Bongjun; Wang, Yichun; Tung, Siu On; Hoff, J. Damon; Kotov, Nicholas
2015-01-01
Hydrophobic particles in water and hydrophilic particles in oil aggregate, but can form colloidal dispersions if their surfaces are chemically camouflaged with surfactants, organic tethers, adsorbed polymers or other particles that impart affinity for the solvent and increase interparticle repulsion. A different strategy for modulating the interaction between a solid and a liquid uses surface corrugation, which gives rise to unique wetting behaviour. Here we show that this topographical effect can also be used to disperse particles in a wide range of solvents without recourse to chemicals to camouflage the particles' surfaces: we produce micrometre-sized particles that are coated with stiff, nanoscale spikes and exhibit long-term colloidal stability in both hydrophilic and hydrophobic media. We find that these `hedgehog' particles do not interpenetrate each other with their spikes, which markedly decreases the contact area between the particles and, therefore, the attractive forces between them. The trapping of air in aqueous dispersions, solvent autoionization at highly developed interfaces, and long-range electrostatic repulsion in organic media also contribute to the colloidal stability of our particles. The unusual dispersion behaviour of our hedgehog particles, overturning the notion that like dissolves like, might help to mitigate adverse environmental effects of the use of surfactants and volatile organic solvents, and deepens our understanding of interparticle interactions and nanoscale colloidal chemistry.
Magnetic particle dispersion in polymer solution
NASA Astrophysics Data System (ADS)
Jeon, Kwang Seoung
Magnetic particle dispersions were prepared in order to observe the effect of particle surface properties, concentration and functional group of binder, milling time, and solvent on dispersion properties. Rheology and transverse susceptibility measurements were used to characterize the dispersion quality of the magnetic paints macroscopically and microscopically, respectively. In this study, by applying the acid-base concept, methods to optimize magnetic dispersions were established. Initially, interaction between acid-base sites on particles and binder was investigated by poisoning the sites with chemicals, then quantifying each type of adsorption (hydrogen and chemical adsorption) using thermogravimetric analysis. With this fundamental information, effects of typical dispersion parameters were investigated. The acid base interaction between binder solution and particles was related to the magnetic and rheological properties of magnetic inks. The results have significant implications for high density particulate media where dispersion will become increasingly important.
Spatiotemporal control of light by Bloch-mode dispersion in multi-core fibers.
Rasmussen, Per Dalgaard; Sukhorukov, Andrey A; Neshev, Dragomir N; Krolikowski, Wieslaw; Bang, Ole; Laegsgaard, Jesper; Kivshar, Yuri S
2008-04-14
We study theoretically the dispersion properties of Bloch modes and nonlinearly-induced defect states in two-dimensional waveguide arrays. We define the conditions for achieving anomalous group-velocity dispersion and discuss possibilities for generation of spatiotemporal solitons.
ERIC Educational Resources Information Center
Journal of Chemical Education, 1981
1981-01-01
Summarizes papers presented at the Sixth Biennial Conference on Chemical Education describing new media and gadgets, particularly models, computers, and other media. A bibliography of 15 presented papers on these topics is attached. (CS)
Strasburger, V C
1999-01-01
For decades, media violence has been viewed as largely a Western problem. New studies indicate that Indian children have increasing access to the media and that media violence will subject them to the same problems as Western children: imitation, desensitization, fear, and inappropriate attitudes about violence and aggression. Solutions exist but will have to be implemented within the next decade to protect Indian children and adolescents from the harmful effects of media violence.
Spectral Hole Burning via Kerr Nonlinearity
NASA Astrophysics Data System (ADS)
Khan, Anwar Ali; Abdul Jabar, M. S.; Jalaluddin, M.; Bacha, Bakht Amin; Iftikhar, Ahmad
2015-10-01
Spectral hole burning is investigated in an optical medium in the presence of Doppler broadening and Kerr nonlinearity. The Kerr nonlinearity generates coherent hole burning in the absorption spectrum. The higher order Kerr nonlinearity enhances the typical lamb dip of the hole. Normal dispersion in the hole burning region while Steep anomalous dispersion between the two hole burning regions also enhances with higher order Kerr effect. A large phase shift creates large delay or advancement in the pulse propagation while no distortion is observed in the pulse. These results provide significant steps to improve optical memory, telecom devices, preservation of information and image quality. Supported by Higher Education Commission (HEC) of Pakistan
Dispersion of a Nonwetting Liquid in a Disordered Nanoporous Medium
NASA Astrophysics Data System (ADS)
Borman, V. D.; Belogorlov, A. A.; Grekhov, A. M.; Tronin, V. N.; Alexeev, K. P.
A dispersion transition in the Fluka 100 C8 and Fluka 100 C18 hydrophobic silica gels close in the structural characteristics has been studied. Nonlinear dependences of the volume of the trapped liquid on the degree of filling, which have not yet been observed at the interaction of nonwetting liquids with nanoporous media, have been revealed. Two critical temperatures Tc1 ≈ 330 K and Tc2 ≈ 340 K have been found for the Fluka 100 C18/water system. At a temperature above Tc1, a transition occurs at a degree of filling of 0.5 from the state of the system with a linear increase in the volume of the trapped liquid with the degree of filling to the state in which the dispersion transition occurs at a degree of filling of 0.5. At temperatures above Tc2, the fraction of the trapped liquid is small and independent of the temperature and degree of filling. When Fluka 100 C8 is filled with water, no abrupt change in the volume of the trapped liquid with an increase in the degree of filling has been detected in the temperature range under study T = 300-360 K. In this case, a linear increase in the volume of the trapped liquid with the degree of filling has been observed.
ERIC Educational Resources Information Center
Downtown Business Quarterly, 1998
1998-01-01
This theme issue explores lower Manhattan's burgeoning "New Media" industry, a growing source of jobs in lower Manhattan. The first article, "New Media Manpower Issues" (Rodney Alexander), addresses manpower, training, and workforce demands faced by new media companies in New York City. The second article, "Case Study:…
ERIC Educational Resources Information Center
Marklund, Inger, Ed.; Hanse, Mona-Britt, Ed.
1984-01-01
The Swedish Media Panel is a research program about children and young persons and their use of mass media. The aim of the ten-year (1975-1985) project is to explain how media habits originate, how they change as children grow older, what factors on the part of children themselves and in their surroundings may be connected with a certain use of…
2010-05-01
4 Table 2: Traditional Media Usage (% of consumers ...media can be described in terms of content authors and passive consumers . Traditional media sources have dominated the landscape of news distribution...delivering software as a continually-updated service that gets better the more people use it, consuming and remixing data from multiple sources
NASA Astrophysics Data System (ADS)
Kato, Kiyoshi; Umemura, Nobuhiro; Petrov, Valentin
2017-03-01
This paper reports the Sellmeier and thermo-optic dispersion formulas for CdGa2S4 that provide excellent reproduction of the temperature-dependent phase-matching conditions in Hg0.35Cd0.65Ga2S4 and Hg0.51Cd0.49Ga2S4 for second-harmonic generation (SHG) and sum-frequency generation (SFG) in the 0.897-10.5910 μm spectral range coupled with Sellmeier and thermo-optic dispersion formulas for HgGa2S4 presented in our previous papers (Kato et al., 2016 [1]; Umemura et al., 2012 [2]).
Beam Combining by Phase Transition Nonlinear Media
1990-02-01
metastable region of spontaneous nucleation. " the measurement of SBS and DFWM in the transient (short pulse) regime in NCPF. • the demonstration of SRS with...heat capacity measurements , it is observed that simple fluids can be superheated more than expected on the basis of classical nucleation theory. In its... tetrafluoromethane 14 CF4 -45.45 37.43 * boron trifluoride BF 3 -12.26 49.2 T ethylene C2IH4 9.91 50.5 F wN <-- carbonyl fluoride CF20 14.7 33.52
Beam Combining by Phase Transition Nonlinear Media.
1988-03-04
F hT argon Ar -122 48 * methane CH4 -82.3 45.8 F krypton Kr -63.6 54.3 * tetrafluoromethane 14 CF4 -45.45 37.43 * boron trifluoride BF3 -12.26 49.2 T...From visual observation and heat capacity measurements , it is observed that simple fluids can be superheated more than expected on the basis of...required SBS red shift and beam quality measurements , we obtained a collimated reflection which was threshold sensitive, which occurred with and without
Quantum optical rotatory dispersion
Tischler, Nora; Krenn, Mario; Fickler, Robert; Vidal, Xavier; Zeilinger, Anton; Molina-Terriza, Gabriel
2016-01-01
The phenomenon of molecular optical activity manifests itself as the rotation of the plane of linear polarization when light passes through chiral media. Measurements of optical activity and its wavelength dependence, that is, optical rotatory dispersion, can reveal information about intricate properties of molecules, such as the three-dimensional arrangement of atoms comprising a molecule. Given a limited probe power, quantum metrology offers the possibility of outperforming classical measurements. This has particular appeal when samples may be damaged by high power, which is a potential concern for chiroptical studies. We present the first experiment in which multiwavelength polarization-entangled photon pairs are used to measure the optical activity and optical rotatory dispersion exhibited by a solution of chiral molecules. Our work paves the way for quantum-enhanced measurements of chirality, with potential applications in chemistry, biology, materials science, and the pharmaceutical industry. The scheme that we use for probing wavelength dependence not only allows one to surpass the information extracted per photon in a classical measurement but also can be used for more general differential measurements. PMID:27713928
Quantum optical rotatory dispersion.
Tischler, Nora; Krenn, Mario; Fickler, Robert; Vidal, Xavier; Zeilinger, Anton; Molina-Terriza, Gabriel
2016-10-01
The phenomenon of molecular optical activity manifests itself as the rotation of the plane of linear polarization when light passes through chiral media. Measurements of optical activity and its wavelength dependence, that is, optical rotatory dispersion, can reveal information about intricate properties of molecules, such as the three-dimensional arrangement of atoms comprising a molecule. Given a limited probe power, quantum metrology offers the possibility of outperforming classical measurements. This has particular appeal when samples may be damaged by high power, which is a potential concern for chiroptical studies. We present the first experiment in which multiwavelength polarization-entangled photon pairs are used to measure the optical activity and optical rotatory dispersion exhibited by a solution of chiral molecules. Our work paves the way for quantum-enhanced measurements of chirality, with potential applications in chemistry, biology, materials science, and the pharmaceutical industry. The scheme that we use for probing wavelength dependence not only allows one to surpass the information extracted per photon in a classical measurement but also can be used for more general differential measurements.
NASA Astrophysics Data System (ADS)
Picozzi, A.; Garnier, J.; Hansson, T.; Suret, P.; Randoux, S.; Millot, G.; Christodoulides, D. N.
2014-09-01
The nonlinear propagation of coherent optical fields has been extensively explored in the framework of nonlinear optics, while the linear propagation of incoherent fields has been widely studied in the framework of statistical optics. However, these two fundamental fields of optics have been mostly developed independently of each other, so that a satisfactory understanding of statistical nonlinear optics is still lacking. This article is aimed at reviewing a unified theoretical formulation of statistical nonlinear optics on the basis of the wave turbulence theory, which provides a nonequilibrium thermodynamic description of the system of incoherent nonlinear waves. We consider the nonlinear Schrödinger equation as a representative model accounting either for a nonlocal or a noninstantaneous nonlinearity, as well as higher-order dispersion effects. Depending on the amount of nonlocal (noninstantaneous) nonlinear interaction and the amount of inhomogeneous (nonstationary) statistics of the incoherent wave, different types of kinetic equations are derived and discussed. In the spatial domain, when the incoherent wave exhibits inhomogeneous statistical fluctuations, different forms of the (Hamiltonian) Vlasov equation are obtained depending on the amount of nonlocality. This Vlasov approach describes the processes of incoherent modulational instability and localized incoherent soliton structures. In the temporal domain, the causality property inherent to the response function leads to a kinetic formulation analogous to the weak Langmuir turbulence equation, which describes nonlocalized spectral incoherent solitons. In the presence of a highly noninstantaneous response, this formulation reduces to a family of singular integro-differential kinetic equations (e.g., Benjamin-Ono equation), which describe incoherent dispersive shock waves. Conversely, a non-stationary statistics leads to a (non-Hamiltonian) long-range Vlasov formulation, whose self-consistent potential is
URANIUM BISMUTHIDE DISPERSION IN MOLTEN METAL
Teitel, R.J.
1959-10-27
The formation of intermetallic bismuth compounds of thorium or uranium dispersed in a liquid media containing bismuth and lead is described. A bismuthide of uranium dispersed in a liquid metal medium is formed by dissolving uranium in composition of lead and bismuth containing less than 80% lead and lowering the temperature of the composition to a temperature below the point at which the solubility of uranium is exceeded and above the melting point of the composition.
Continuous control of the nonlinearity phase for harmonic generations.
Li, Guixin; Chen, Shumei; Pholchai, Nitipat; Reineke, Bernhard; Wong, Polis Wing Han; Pun, Edwin Yue Bun; Cheah, Kok Wai; Zentgraf, Thomas; Zhang, Shuang
2015-06-01
The capability of locally engineering the nonlinear optical properties of media is crucial in nonlinear optics. Although poling is the most widely employed technique for achieving locally controlled nonlinearity, it leads only to a binary nonlinear state, which is equivalent to a discrete phase change of π in the nonlinear polarizability. Here, inspired by the concept of spin-rotation coupling, we experimentally demonstrate nonlinear metasurfaces with homogeneous linear optical properties but spatially varying effective nonlinear polarizability with continuously controllable phase. The continuous phase control over the local nonlinearity is demonstrated for second and third harmonic generation by using nonlinear metasurfaces consisting of nanoantennas of C3 and C4 rotational symmetries, respectively. The continuous phase engineering of the effective nonlinear polarizability enables complete control over the propagation of harmonic generation signals. Therefore, this method seamlessly combines the generation and manipulation of harmonic waves, paving the way for highly compact nonlinear nanophotonic devices.
NASA Astrophysics Data System (ADS)
Schmid, K. S.; Geiger, S.; Sorbie, K. S.
2013-05-01
This paper presents higher order methods for the numerical modeling of two-phase flow with simultaneous transport and adsorption of viscosifying species within the individual phases in permeable porous media. The numerical scheme presented addresses the three major challenges in simulating this process. Firstly, the component transport is strongly coupled with the viscous and capillary forces that act on the movement of the carrier phase. The discretization of the capillary parts is especially difficult since its effect on flow yields non-linear parabolic conservation equations. These are amenable to non-linear finite elements (FEs), while the capillary contribution on the component transport is first-order hyperbolic, where classical FEs are unsuitable. We solve this efficiently by a Strang splitting that uses finite volumes (FVs) with explicit time-stepping for the viscous parts and a combined finite element-finite volume (FEFV) scheme with implicit time-stepping for the capillary parts. Secondly, the components undergo hydrodynamic dispersion and discerning between numerical and physical dispersion is essential. We develop higher-order formulations for the phase and component fluxes that keep numerical dispersion low and combine them with implicit FEs such that the non-linearities of the dispersion tensor are fully incorporated. Thirdly, subsurface permeable media show strong spatial heterogeneity, with coefficients varying over many orders of magnitude and geometric complexity that make the use of unstructured grids essential. In this work, we employ node-centered FVs that combine their ability to resolve flow with the flexibility of FEs. Numerical examples of increasing complexity are presented that demonstrate the convergence and robustness of our approach and prove its versatility for highly heterogeneous, and geometrically complex fractured porous media.
A dispersion flattened tellurite composite holey fiber
NASA Astrophysics Data System (ADS)
Liao, Meisong; Duan, ZhongChao; Gao, Weiqing; Yan, Xin; Suzuki, Takenobu; Ohishi, Yasutake
2012-02-01
Highly nonlinear tellurite holey fiber can be transparent from visible to 5 μm. Its nonlinearity can be higher than highly nonlinear silica fiber by more than one order of magnitude. However, the dispersion of tellurite holey fiber is difficult to tailor because of the difficulties in fabrication. Tellurite glass shows a low viscosity at the fiber drawing temperature. Moreover the viscosity decreases sharply with increasing temperature. Tellurite holey fiber with a complex microstructure could be subject to heavy deformation during fabrication process. So far most tellurite highly nonlinear holey fibers just have a simple structure which results in an unflattened dispersion. It cancels the advantage of high nonlinearity greatly in practical applications. In this work we try to develop a dispersion flattened tellurite composite holey fiber (TCHF). The holey structure of the TCHF is composed of only one ring of holes, so the heavy deformation, which probably occurs for tellurite complex microstructured fiber during the fabrication process, can be avoided. Since the holey structure is simple, to improve the flexibility in tailoring dispersion, we use two kinds of tellurite glasses which have different refractive-indices to design and fabricate the TCHF. The holes are formed by two tellurite glasses. The fiber can be fabricated by a simple rod-in-tube method. By using this structure the dispersion is engineered to be the most flattened for the highly nonlinear soft glass fiber within 1.5-1.6 μm. More than one octave supercontinuum generation, mainly broadened by self phase modulation, is demonstrated by using the fabricated TCHF.
Dispersive properties of multisymplectic integrators
NASA Astrophysics Data System (ADS)
Schober, C. M.; Wlodarczyk, T. H.
2008-05-01
Multisymplectic (MS) integrators, i.e. numerical schemes which exactly preserve a discrete space-time symplectic structure, are a new class of structure preserving algorithms for solving Hamiltonian PDEs. In this paper we examine the dispersive properties of MS integrators for the linear wave and sine-Gordon equations. In particular a leapfrog in space and time scheme (a member of the Lobatto Runge-Kutta family of methods) and the Preissman box scheme are considered. We find the numerical dispersion relations are monotonic and that the sign of the group velocity is preserved. The group velocity dispersion (GVD) is found to provide significant information and succinctly explain the qualitative differences in the numerical solutions obtained with the different schemes. Further, the numerical dispersion relations for the linearized sine-Gordon equation provides information on the ability of the MS integrators to capture the sine-Gordon dynamics. We are able to link the numerical dispersion relations to the total energy of the various methods, thus providing information on the coarse grid behavior of MS integrators in the nonlinear regime.
Media Monday tip sheet builds Spartanburg's media relations.
Rees, Tom
2005-01-01
Media Monday is published weekly and sent to area newsrooms by the Spartanburg Regional Healthcare System, Spartanburg, S.C. The news and feature tip sheet was started in 1998 in order to disperse a lot of information with a limited number of staff.
Compactons in nonlinear Schrödinger lattices with strong nonlinearity management.
Abdullaev, F Kh; Kevrekidis, P G; Salerno, M
2010-09-10
The existence of compactons in the discrete nonlinear Schrödinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. In the averaged discrete nonlinear Schrödinger equation, the resulting effective interwell tunneling depends on the modulation parameters and on the field amplitude. This introduces nonlinear dispersion in the system and can lead to a prototypical realization of single- or multisite stable discrete compactons in nonlinear optical waveguide and Bose-Einstein condensate arrays. These structures can dynamically arise out of Gaussian or compactly supported initial data.
Folded digital backward propagation for dispersion-managed fiber-optic transmission.
Zhu, Likai; Li, Guifang
2011-03-28
In periodically dispersion managed long-haul transmission systems, waveform distortion is dominated by chromatic dispersion. As a result of the periodic waveform evolution, the nonlinear behavior also repeats itself in every dispersion period. It is shown that, under the weakly nonlinear assumption, nonlinear effects accumulated in a large number (K) of spans can be approximated by nonlinear effects accumulated in a single span with the same dispersion map and K times the nonlinearity. Thus, significant savings in computational load can be achieved in digital compensation of fiber nonlinearity using folded digital backward propagation (DBP). Simulation results show that the required computation for DBP of dispersion managed transoceanic transmission systems can be reduced by up to 2 orders of magnitude with negligible penalty using folded DBP.
Physical models of polarization mode dispersion
Menyuk, C.R.; Wai, P.K.A.
1995-12-31
The effect of randomly varying birefringence on light propagation in optical fibers is studied theoretically in the parameter regime that will be used for long-distance communications. In this regime, the birefringence is large and varies very rapidly in comparison to the nonlinear and dispersive scale lengths. We determine the polarization mode dispersion, and we show that physically realistic models yield the same result for polarization mode dispersion as earlier heuristic models that were introduced by Poole. We also prove an ergodic theorem.
Nonlinear waves: Dynamics and evolution
NASA Astrophysics Data System (ADS)
Gaponov-Grekhov, A. V.; Rabinovich, M. I.
Papers on nonlinear waves are presented, covering topics such as the history of studies on nonlinear dynamics since Poincare, attractors, pattern formation and the dynamics of two-dimensional structures in nonequilibirum dissipative media, the onset of spatial chaos in one-dimensional systems, and self-organization phenomena in laser thermochemistry. Additional topics include criteria for the existence of moving structures in two-component reaction-diffusion systems, space-time structures in optoelectronic devices, stimulated scattering and surface structures, and distributed wave collapse in the nonlinear Schroedinger equation. Consideration is also given to dimensions and entropies in multidimensional systems, measurement methods for correlation dimensions, quantum localization and dynamic chaos, self-organization in bacterial cells and populations, nonlinear phenomena in condensed matter, and the origin and evolutionary dynamics of Uranian rings.
Nonlinear and quantum atom optics.
Rolston, S L; Phillips, W D
2002-03-14
Coherent matter waves in the form of Bose-Einstein condensates have led to the development of nonlinear and quantum atom optics - the de Broglie wave analogues of nonlinear and quantum optics with light. In nonlinear atom optics, four-wave mixing of matter waves and mixing of combinations of light and matter waves have been observed; such progress culminated in the demonstration of phase-coherent matter-wave amplification. Solitons represent another active area in nonlinear atom optics: these non-dispersing propagating modes of the equation that governs Bose-Einstein condensates have been created experimentally, and observed subsequently to break up into vortices. Quantum atom optics is concerned with the statistical properties and correlations of matter-wave fields. A first step in this area is the measurement of reduced number fluctuations in a Bose-Einstein condensate partitioned into a series of optical potential wells.
Dispersion Method Using Focused Ultrasonic Field
NASA Astrophysics Data System (ADS)
Jungsoon Kim,; Moojoon Kim,; Kanglyel Ha,; Minchul Chu,
2010-07-01
The dispersion of powders into liquids has become one of the most important techniques in high-tech industries and it is a common process in the formulation of various products, such as paint, ink, shampoo, beverages, and polishing media. In this study, an ultrasonic system with a cylindrical transducer is newly introduced for pure nanoparticle dispersion. The acoustics pressure field and the characteristics of the shock pulse caused by cavitation are investigated. The frequency spectrum of the pulse from the collapse of air bubbles in the cavitation is analyzed theoretically. It was confirmed that a TiO2 water suspension can be dispersed effectively using the suggested system.
Dispersive solitons in magneto-optic waveguides
NASA Astrophysics Data System (ADS)
Vega-Guzman, Jose; Ullah, Malik Zaka; Asma, Mir; Zhou, Qin; Biswas, Anjan
2017-03-01
This paper obtains bright, dark and singular dispersive optical soliton solutions with magneto-optic waveguides. The governing equation is the coupled Schrödinger-Hirota equation. The existence criteria of these solitons are also presented. Both Kerr law and power law of nonlinearity are considered.
Single-cycle coherent terahertz-pulse propagation in rigid-rotor molecular media
NASA Astrophysics Data System (ADS)
Marskar, Robert; Ã-sterberg, Ulf L.
2015-08-01
We theoretically analyze linear and nonlinear coherent propagation of linearly polarized, plane-wave, resonant single-cycle terahertz pulses through spatially extended rigid-rotor molecular media. Our model incorporates mixed state medium preparation, nonperturbative nonlinearities, saturation, coherence, memory effects, and propagation, but ignores the effects of damping. Explicit solutions are reported in the linear propagation regime. These solutions are the multilevel superposition of linear, single-cycle 0 π pulses, and appear as temporal beats in the time domain. For media initially in thermal equilibrium, the pulse and molecular beats are dispersive and broaden temporally with increased propagation distance. In the simplified limit of equal rotational line strength (an idealized situation), the emitted impulses are exact temporal copies of the input pulse. An efficient, scalable computational method for solving the reduced multilevel Maxwell-Bloch equations for molecular media is reported. This method is based on a standard differential method for the propagation equation together with an operator splitting method for the Bloch equations. It invokes neither the slowly varying envelope (SVEA) or rotating wave approximations (RWA), and incorporates a large number of possible energy eigenstates (we solve for 7744 levels). Case studies of nonlinear single-cycle pulse propagation are then provided by means of computer solutions. In the nonlinear regime, we observe strong molecular orientations and suppression of the pulse and orientational revivals predicted by linear theory. For sufficiently strong pulses, coherent bleaching effects lead to increased transmission of the driving pulse, which also bears signs of self-modulation and carrier-shock formation.
NASA Astrophysics Data System (ADS)
Naveed, M.; Kawamoto, K.; Hamamoto, S.; Sakaki, T.; Moldrup, P.; Komatsu, T.
2010-12-01
The transport and fate of gases in the soil are governed by gas advection, diffusion and dispersion phenomena. Among three gas transport phenomena, gas dispersion is least understood. Main objective of this study is to investigate the gas dispersion phenomena, emphasising on the effect of moisture content, sand particle shape, particle size, particle size distribution, and scale dependency on gas dispersion. One dimensional laboratory column experiments, in an apparatus consisting of an acrylic column attached to inlet and outlet chambers (Hamamoto et al., SSAJ, 2009), were conducted for the measurements of gas dispersion coefficient (DH). Various types of sands (Narita and Toyoura sands from Japan, and Granusils and Accusands from United States) and glass beads with variable moisture contents were used as porous media. Shape of the sand particles were characterized in terms of sphericity and roundness. The changes in the oxygen concentration within the soil column and in the inlet and outlet chambers were monitored. In addition the air pressure at inlet and middle of the soil column was also monitored to ensure the uniform density of porous media along the column. The measured breakthrough curves were fitted with the analytical solution of the advection dispersion equation to determine dispersion coefficients. The measured dispersion coefficient (DH) showed linear increase with pore velocity (u0). Measured dispersivity (λ= DH/u0) increases with decrease in air filled porosity induced by adding moisture contents in sands. Its values varies from 0 to 3 cm on decreasing air filled porosity from 0.50 (air dry) to 0.25 (field capacity). Shape of the sand particles has no significant effect on gas dispersion. When gas dispersion phenomena was studied on different shape of the sand particles at various air filled porosities, it was found that for angular sand particles initially gas dispersivity increases more rapidly as compared to rounded sand particles and finally
Power-law spatial dispersion from fractional Liouville equation
Tarasov, Vasily E.
2013-10-15
A microscopic model in the framework of fractional kinetics to describe spatial dispersion of power-law type is suggested. The Liouville equation with the Caputo fractional derivatives is used to obtain the power-law dependence of the absolute permittivity on the wave vector. The fractional differential equations for electrostatic potential in the media with power-law spatial dispersion are derived. The particular solutions of these equations for the electric potential of point charge in this media are considered.
Instability in poroelastic media
NASA Astrophysics Data System (ADS)
Pramanik, Satyajit; Wettlaufer, John
2016-11-01
Fluid flow in deformable porous materials, which play significant role in different biological and geological systems of wide range of scales, is a highly nonlinear problem. Feedback from the elastic deformation of the solid skeleton on the fluid flow and vice-versa gives rise to pattern formation in the porosity structure of the skeleton. We view some of these patterns as instabilities of the coupled fluid-solid system. Due to highly nonlinear nature of the problem, very little has been understood about this instability. Here, we use a minimal poroelastic theory to understand the pattern formation in a fluid-saturated poroelastic material and discuss the similarities/differences with viscous fingering in non-deformable porous media.
Instability of nonlinear waves with close wavenumbers
NASA Astrophysics Data System (ADS)
Babanin, Alexander; Babanina, Anna; Chalikov, Dmitry
2013-04-01
Evolution of bichromatic waves represents a substantial interest in fluid mechanics, oceanography and maritime engineering, as well as in other fields of physics. In this presentation, evolution of surface water waves will be considered in the context of how close the bichromatic wave modes can be in the frequency/wavenumber space before the dynamics of their interactions changes, if it does. In this regard, the topic may be relevant across various applications for nonlinear waves in dispersive media. The study is conducted by means of the fully nonlinear one-dimensional model for gravity water waves by Chalikov & Sheinin. This approach is based on a non-stationary conformal mapping, which allows the equations of potential flow with the inclusion of a free surface to be written in a surface-following coordinate system. This transformation does not impose any restrictions on the shape of the surface, except that it has to be possible to represent this surface in terms of a Fourier series. The model accuracy and energy conservation within the evolving wave trains is very high, it is determined by the computer precision. We show that interaction of two monochromatic waves at the water surface enters a different dynamic regime if their wavenumbers become very close. Downshifting of the initial wave energy and growth of the first mode occur in the course of evolution of the two waves, depending on wave steepness and dk/k. Behaviour of these features change if dk/k<0.0025: both downshifting and growth rate become independent of dk/k, and the growth rates increases by orders of magnitude.
Blow-up of a hyperbolic equation of viscoelasticity with supercritical nonlinearities
NASA Astrophysics Data System (ADS)
Guo, Yanqiu; Rammaha, Mohammad A.; Sakuntasathien, Sawanya
2017-02-01
We investigate a hyperbolic PDE, modeling wave propagation in viscoelastic media, under the influence of a linear memory term of Boltzmann type, and a nonlinear damping modeling friction, as well as an energy-amplifying supercritical nonlinear source:
Ultrabroadband Dispersive Radiation by Spatiotemporal Oscillation of Multimode Waves.
Wright, Logan G; Wabnitz, Stefan; Christodoulides, Demetrios N; Wise, Frank W
2015-11-27
In nonlinear dynamical systems, qualitatively distinct phenomena occur depending continuously on the size of the bounded domain containing the system. For nonlinear waves, a multimode waveguide is a bounded three-dimensional domain, allowing observation of dynamics impossible in open settings. Here we study radiation emitted by bounded nonlinear waves: the spatiotemporal oscillations of solitons in multimode fiber generate multimode dispersive waves over an ultrabroadband spectral range. This work suggests routes to sources of coherent electromagnetic waves with unprecedented spectral range.
Single-mode dispersive waves and soliton microcomb dynamics
NASA Astrophysics Data System (ADS)
Yi, Xu; Yang, Qi-Fan; Zhang, Xueyue; Yang, Ki Youl; Li, Xinbai; Vahala, Kerry
2017-03-01
Dissipative Kerr solitons are self-sustaining optical wavepackets in resonators. They use the Kerr nonlinearity to both compensate dispersion and offset optical loss. Besides providing insights into nonlinear resonator physics, they can be applied in frequency metrology, precision clocks, and spectroscopy. Like other optical solitons, the dissipative Kerr soliton can radiate power as a dispersive wave through a process that is the optical analogue of Cherenkov radiation. Dispersive waves typically consist of an ensemble of optical modes. Here, a limiting case is studied in which the dispersive wave is concentrated into a single cavity mode. In this limit, its interaction with the soliton induces hysteresis behaviour in the soliton's spectral and temporal properties. Also, an operating point of enhanced repetition-rate stability occurs through balance of dispersive-wave recoil and Raman-induced soliton-self-frequency shift. The single-mode dispersive wave can therefore provide quiet states of soliton comb operation useful in many applications.
Nonlinear gravity waves in the water flow with inhomogeneous vorticity
NASA Astrophysics Data System (ADS)
Abrashkin, Anatoly; Pelinovsky, Efim
2016-04-01
Nonlinear Schrodinger equation is derived for weakly modulated nonlinear wave packets in the infinite-depth water flow with inhomogeneous vorticity. Governing 2-D equations are written in Lagrangian variables. Nonlinear Schrodinger equation is obtained in the third order of perturbation theory taking into account weak non-uniform vortex current. Two limiting cases are analyzed. The first one corresponds to the uniform surface flow and is described by the classic nonlinear Schrodinger equation allowed the modulational instability. The second one is the Gerstner's wave packet. In this limiting case the nonlinear term is absent confirming known fact that nonlinear Gerstner's wave has the linear dispersion relation.
Nonlinear traveling wave solution for the MJO skeleton model
NASA Astrophysics Data System (ADS)
Chen, S.; Stechmann, S. N.
2014-12-01
Recently, a minimal dynamical model is presented for capturing MJO's fundamental features. The model is a nonlinear oscillator model for the MJO skeleton and it involves interactions between convection, moisture and circulation. I will present the exact nonlinear traveling wave solutions for the model based on its energy conservation. The exact nonlinear solution provides for an explicit comparison of features between linear and nonlinear waves such as dispersion relations and traveling wave speeds. Moreover, the nonlinear solutions, compared with the linear ones, produce a narrow region of active convection and a wider region of suppressed convection. These predictions offer nonlinear MJO features that could potentially be targets of observational investigations.