Boundary control of long waves in nonlinear dispersive systems
DEFF Research Database (Denmark)
Hasan, Agus; Foss, Bjarne; Aamo, Ole Morten
2011-01-01
Unidirectional propagation of long waves in nonlinear dispersive systems may be modeled by the Benjamin-Bona-Mahony-Burgers equation, a third order partial differential equation incorporating linear dissipative and dispersive terms, as well as a term covering nonlinear wave phenomena. For higher...... orders of the nonlinearity, the equation may have unstable solitary wave solutions. Although it is a one dimensional problem, achieving a global result for this equation is not trivial due to the nonlinearity and the mixed partial derivative. In this paper, two sets of nonlinear boundary control laws...... that achieve global exponential stability and semi-global exponential stability are derived for both linear and nonlinear cases....
Long wave-short wave resonance in nonlinear negative refractive index media.
Chowdhury, Aref; Tataronis, John A
2008-04-18
We show that long wave-short wave resonance can be achieved in a second-order nonlinear negative refractive index medium when the short wave lies on the negative index branch. With the medium exhibiting a second-order nonlinear susceptibility, a number of nonlinear phenomena such as solitary waves, paired solitons, and periodic wave trains are possible or enhanced through the cascaded second-order effect. Potential applications include the generation of terahertz waves from optical pulses.
Numerical method of studying nonlinear interactions between long waves and multiple short waves
Institute of Scientific and Technical Information of China (English)
Xie Tao; Kuang Hai-Lan; William Perrie; Zou Guang-Hui; Nan Cheng-Feng; He Chao; Shen Tao; Chen Wei
2009-01-01
Although the nonlinear interactions between a single short gravity wave and a long wave can be solved analytically,the solution is less tractable in more general cases involving multiple short waves.In this work we present a numerical method of studying nonlinear interactions between a long wave and multiple short harmonic waves in infinitely deep water.Specifically,this method is applied to the calculation of the temporal and spatial evolutions of the surface elevations in which a given long wave interacts with several short harmonic waves.Another important application of our method is to quantitatively analyse the nonlinear interactions between an arbitrary short wave train and another short wave train.From simulation results,we obtain that the mechanism for the nonlinear interactions between one short wave train and another short wave train(expressed as wave train 2)leads to the energy focusing of the other short wave train(expressed as wave train 31.This mechanism Occurs on wave components with a narrow frequency bandwidth,whose frequencies are near that of wave train 3.
Directory of Open Access Journals (Sweden)
Shi Jing
2014-01-01
Full Text Available The solving processes of the homogeneous balance method, Jacobi elliptic function expansion method, fixed point method, and modified mapping method are introduced in this paper. By using four different methods, the exact solutions of nonlinear wave equation of a finite deformation elastic circular rod, Boussinesq equations and dispersive long wave equations are studied. In the discussion, the more physical specifications of these nonlinear equations, have been identified and the results indicated that these methods (especially the fixed point method can be used to solve other similar nonlinear wave equations.
Numerical simulation of nonlinear long waves interacting with arrays of emergent cylinders
Zainali, Amir; Weiss, Robert; Irish, Jennifer L; Yang, Yongqian
2016-01-01
We presented numerical simulation of long waves, interacting with arrays of emergent cylinders inside regularly spaced patches, representing discontinues patchy coastal vegetation. We employed the fully nonlinear and weakly dispersive Serre-Green-Naghdi equations (SGN) until the breaking process starts, while we changed the governing equations to nonlinear shallow water equations (NSW) at the vicinity of the breaking-wave peak and during the runup stage. We modeled the cylinders as physical boundaries rather than approximating them as macro-roughness friction. We showed that the cylinders provide protection for the areas behind them. However they might also cause amplification in local water depth in those areas. The presented results are extensively validated against the existing numerical and experimental data. Our results demonstrate the capability and reliability of our model in simulating wave interaction with emergent cylinders.
Institute of Scientific and Technical Information of China (English)
张卫国
2003-01-01
In this paper, we have obtained the bell-type and kink-type solitary wave solutions of the generalized symmetric regularized long-wave equations with high-order nonlinear terms by means of proper transformation and undetermined assumption method.
Diffractive waveplates for long wave infrared
Ouskova, Elena; Roberts, David; Tabiryan, Nelson; Steeves, D. M.; Kimball, B. R.
2017-05-01
We report about developing long-wave infrared diffractive optical components based on liquid crystals. The components show high efficiency and high transparency for the 10.6 μm wavelength of CO2 laser beam.
Dispersive internal long wave models
Energy Technology Data Exchange (ETDEWEB)
Camassa, R.; Choi, W.; Holm, D.D. [Los Alamos National Lab., NM (United States); Levermore, C.D.; Lvov, Y. [Univ. of Arizona, Tucson, AZ (United States)
1998-11-01
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at Los Alamos National Laboratory (LANL). This work is a joint analytical and numerical study of internal dispersive water wave propagation in a stratified two-layer fluid, a problem that has important geophysical fluid dynamics applications. Two-layer models can capture the main density-dependent effects because they can support, unlike homogeneous fluid models, the observed large amplitude internal wave motion at the interface between layers. The authors have derived new model equations using multiscale asymptotics in combination with the method they have developed for vertically averaging velocity and vorticity fields across fluid layers within the original Euler equations. The authors have found new exact conservation laws for layer-mean vorticity that have exact counterparts in the models. With this approach, they have derived a class of equations that retain the full nonlinearity of the original Euler equations while preserving the simplicity of known weakly nonlinear models, thus providing the theoretical foundation for experimental results so far unexplained.
Long wave polar modes in semiconductor heterostructures
Trallero-Giner, C; Garca̕-Moliner, F 0
1998-01-01
Long Wave Polar Modes in Semiconductor Heterostructures is concerned with the study of polar optical modes in semiconductor heterostructures from a phenomenological approach and aims to simplify the model of lattice dynamics calculations. The book provides useful tools for performing calculations relevant to anyone who might be interested in practical applications. The main focus of Long Wave Polar Modes in Semiconductor Heterostructures is planar heterostructures (quantum wells or barriers, superlattices, double barrier structures etc) but there is also discussion on the growing field of quan
A New General Algebraic Method and Its Application to Shallow Long Wave Approximate Equations
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A new general algebraic method is presented to uniformly construct a series of exact solutions for nonlinear evolution equations (NLEEs). For illustration, we apply the new method to shallow long wave approximate equations and successfully obtain abundant new exact solutions, which include rational solitary wave solutions and rational triangular periodic wave solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.
Hamiltonian long wave expansions for internal waves over a periodically varying bottom
Institute of Scientific and Technical Information of China (English)
ZHOU Hong-yan; PIAO Da-xiong
2008-01-01
We derive a Hamiltonian formulation for two-dimensional nonlinear long waves between two bodies of immiscible fluid with a periodic bottom.From the formulation and using the Hamiltonian perturbation theory,we obtain effective Boussinesq equations that describe the motion of bidirectional long waves and unidirectional equations that are similar to the KdV equation for the case in which the bottom possesses short length scale.The computations for these results are performed in the framework of an asymptotic analIysis of multiple scale operators.
New multi-soliton solutions and travelling wave solutions of the dispersive long-wave equations
Institute of Scientific and Technical Information of China (English)
张解放; 郭冠平; 吴锋民
2002-01-01
Using the extended homogeneous balance method, the (1+1)-dimensional dispersive Iong-wave equations have been solved. Starting from the homogeneous balance method, we have obtained a nonlinear transformation for simplifying a dispersive long-wave equation into a linear partial differential equation. Usually, we can obtain only a type of soliton-like solution. In this paper, we have further found some new multi-soliton solutions and exact travelling solutions of the dispersive long-wave equations from the linear partial equation.
Long-Wave Infrared Dyson Spectrometer
Johnson, William R.; Hook, Simon J.; Mouroulis, Pantazis Z.; Wilson, Daniel W.; Gunapala, Sarath D.; Hill, Cory J.; Mumolo, Jason M.; Eng, Bjorn T.
2008-01-01
Preliminary results are presented for an ultra compact long-wave infrared slit spectrometer based on the dyson concentric design. The dyson spectrometer has been integrated in a dewar environment with a quantum well infrared photodetecor (QWIP), concave electron beam fabricated diffraction grating and ultra precision slit. The entire system is cooled to cryogenic temperatures to maximize signal to noise ratio performance, hence eliminating thermal signal from transmissive elements and internal stray light. All of this is done while maintaining QWIP thermal control. A general description is given of the spectrometer, alignment technique and predicated performance. The spectrometer has been designed for optimal performance with respect to smile and keystone distortion. A spectral calibration is performed with NIST traceable targets. A 2-point non-uniformity correction is performed with a precision blackbody source to provide radiometric accuracy. Preliminary laboratory results show excellent agreement with modeled noise equivalent delta temperature and detector linearity over a broad temperature range.
Long Wave Infrared Cavity Enhanced Sensors
Energy Technology Data Exchange (ETDEWEB)
Taubman, Matthew S.; Scott, David C.; Cannon, Bret D.; Myers, Tanya L.; Munley, John T.; Nguyen, Vinh T.; Schultz, John F.
2005-12-01
The principal goal of Pacific Northwest National Laboratory's (PNNL's) long wave infrared (LWIR) cavity enhanced sensor (CES) task is to explore ultra-sensitive spectroscopic chemical sensing techniques and apply them to detecting proliferation of weapons of mass destruction (WMD). Our primary application is detecting signatures of WMD production, but LWIR CES techniques are also capable of detecting chemical weapons. The LWIR CES task is concerned exclusively with developing novel point sensors; stand-off detection is addressed by other PNNL tasks and projects. PNNL's LWIR CES research is distinguished from that done by others by the use quantum cascade lasers (QCLs) as the light source. QCLs are novel devices, and a significant fraction of our research has been devoted to developing the procedures and hardware required to implement them most effectively for chemical sensing. This report details the progress we have made on LWIR CES sensor development.
Generation of Long Waves using Non-Linear Digital Filters
DEFF Research Database (Denmark)
Høgedal, Michael; Frigaard, Peter; Christensen, Morten
1994-01-01
transform of the 1st order surface elevation and subsequently inverse Fourier transformed. Hence, the methods are unsuitable for real-time applications, for example where white noise are filtered digitally to obtain a wave spectrum with built-in stochastic variabillity. In the present paper an approximative...... method for including the correct 2nd order bound terms in such applications is presented. The technique utilizes non-liner digital filters fitted to the appropriate transfer function is derived only for bounded 2nd order subharmonics, as they laboratory experiments generally are considered the most...
2003-01-01
An efficient numerical method is developed for the numerical solution of non-linear wave equations typified by the regularized long wave equation (RLW) and its generalization (GRLW). The method developed uses a pseudo-spectral (Fourier transform) treatment of the space dependence together with a linearized implicit scheme in time. An important advantage to be gained from the use of this method, is the ability to vary the mesh length, thereby reducing the computational time. Using a linearized...
Long Wave Infrared Cavity Enhanced Sensors
Energy Technology Data Exchange (ETDEWEB)
Taubman, Matthew S.; Scott, David C.; Cannon, Bret D.; Myers, Tanya L.; Bonebrake, Christopher A.; Aker, Pam M.; Wojcik, Michael D.; Munley, John T.; Nguyen, Vinh T.; Schultz, John F.
2004-10-01
The principal goal of Pacific Northwest National Laboratory's (PNNL's) long wave infrared (LWIR) cavity enhanced sensor (CES) project is to explore ultra-sensitive spectroscopic techniques and apply them to the development of LWIR chemical sensors needed for detecting weapons proliferation. This includes detecting not only the weapons of mass destruction (WMDs) themselves, but also signatures of their production and/or detonation. The LWIR CES project is concerned exclusively with developing point sensors; other portions of PNNL's IR Sensors program address stand off detection. PNNL's LWIR CES research is distinguished from that done by others by the use quantum cascade lasers (QCLs) as the light source. QCLs are novel devices, and a significant fraction of our research has been devoted to developing the procedures and hardware required to implement them most effectively for chemical sensing. This report details the progress we have made on our LWIR CES sensor development. During FY02, PNNL investigated three LWIR CES implementations beginning with the easiest to implement, direct cavity-enhanced detection (simple CES), including a technique of intermediate difficulty, cavity-dithered phase-sensitive detection (FM recovery CES) through to the most complex technique, that of resonant sideband cavity-enhanced detection also known as noise-immune cavity-enhanced optical heterodyne molecular spectroscopy, or NICE-OHMS.
Long Wave Dynamics along a Convex Bottom
Didenkulova, Ira; Soomere, Tarmo
2008-01-01
Long linear wave transformation in the basin of varying depth is studied for a case of a convex bottom profile in the framework of one-dimensional shallow water equation. The existence of travelling wave solutions in this geometry and the uniqueness of this wave class is established through construction of a 1:1 transformation of the general 1D wave equation to the analogous wave equation with constant coefficients. The general solution of the Cauchy problem consists of two travelling waves propagating in opposite directions. It is found that generally a zone of a weak current is formed between these two waves. Waves are reflected from the coastline so that their profile is inverted with respect to the calm water surface. Long wave runup on a beach with this profile is studied for sine pulse, KdV soliton and N-wave. Shown is that in certain cases the runup height along the convex profile is considerably larger than for beaches with a linear slope. The analysis of wave reflection from the bottom containing a s...
New multisoliton solutions of the （2＋1） —dimensional dispersive long wave equations
Institute of Scientific and Technical Information of China (English)
JiefangZHANG; PingHAN
2001-01-01
Using the extension homogeneous balance method,we have obtained a nonlinear transformation to simplify the (2+1) dimensional dispersive long wave equations into a linear partial differential equation,and found some new special types of the multisoliton solutions and exact solutions of the linear partial differential equation.
Optical properties of PbIn6Te10 in the long-wave IR
Andreev, Yu M.; Badikov, V. V.; Ionin, A. A.; Kinyaevskiy, I. O.; Klimachev, Yu M.; Kotkov, A. A.; Lanskii, G. V.; Svetlichnyi, V. A.
2016-12-01
Optical properties of nonlinear PbIn6Te10 (PIT) crystal were studied for the first time within 30-1200 µm (0.2-15 THz) by FTIR and THz-TDS. It was found that PIT possesses the most attractive transparency features for efficient generation of long-wave mid-IR emission including 20-60 µm (5-15 THz) region by optical rectification. This crystal is also found useful for phase matched DFG generation into the long-wave THz region. In particular, by model study phase matched down-conversion of CO and CO2 laser lines into 130-1200 µm (0.3-2.3 THz) range is shown possible by ooe and eoe type of three wave interaction. Noncritical 90° phase matching for eoe type of interactions can be realized by selecting samples with specified composition.
Two-photon vibrational excitation of air by long-wave infrared laser pulses
Palastro, J P; Johnson, L A; Hafizi, B; Wahlstrand, J K; Milchberg, H M
2016-01-01
Ultrashort long-wave infrared (LWIR) laser pulses can resonantly excite vibrations in N2 and O2 through a two-photon transition. The absorptive, vibrational component of the ultrafast optical nonlinearity grows in time, starting smaller than, but quickly surpassing, the electronic, rotational, and vibrational refractive components. The growth of the vibrational component results in a novel mechanism of 3rd harmonic generation, providing an additional two-photon excitation channel, fundamental + 3rd harmonic. The original and emergent two-photon excitations drive the resonance exactly out of phase, causing spatial decay of the absorptive, vibrational nonlinearity. This nearly eliminates two-photon vibrational absorption. Here we present simulations and analytical calculations demonstrating how these processes modify the ultrafast optical nonlinearity in air. The results reveal nonlinear optical phenomena unique to the LWIR regime of ultrashort pulse propagation in atmosphere.
Long Waves Associated with Bichromatic Waves
Institute of Scientific and Technical Information of China (English)
DONG Guohai(董国海); YE Wenya(叶文亚); Nicholas Dodd
2001-01-01
A numerical model of low frequency waves is presented. The model is based on that of Roelvink (1993), but the numerical techniques used in the solution are based on the so-called Weighted-Average Flux (WAF) method withTime-Operator-Splitting (TOS) used for the treatment of the source terms. This method allows a small number ofcomputational points to be used, and is particularly efficient in modeling wave setup. The short wave (or primary wave)energy equation is solved with a traditional Lax-Wendroff technique. A nonlinear wave theory is introduced. The modeldescribed in this paper is found to be satisfactory in modeling low frequency waves associated with incident bichromaticwaves.
Long wave asymptote for the Landau Pomeranchuk Migdal effect
Koshelkin, A. V.
2004-01-01
It is shown that non-small angle multiple elastic scattering in matter leads to much stronger suppression of bremsstrahlung (BS) by high-energy particles in the long wave range of emission spectrum compared with the quenching predicted by Landau L D and Pomeranchuk I Ya (1953 Dokl. Akad. Nauk SSSR 92 535, 735) and Migdal A B (1954 Dokl. Akad. Nauk SSSR 96 49, 1956 Phys. Rev. 103 1811). This manifests itself as the rearrangement of the BS spectrum of soft photons in the far long wave region.
Institute of Scientific and Technical Information of China (English)
Chen Yong; Li Biao; Zhang Hong-Qing
2004-01-01
@@ An extended Jacobi elliptic function method is proposed for constructing the exact double periodic solutions of nonlinear partial differential equations (PDEs) in a unified way. It is shown that these solutions exactly degenerate to the many types of soliton solutions in a limited condition. The Wu-Zhang equation (which describes the (2+1)-dimensional dispersive long wave) is investigated by this means and more formal double periodic solutions are obtained.
Institute of Scientific and Technical Information of China (English)
WANG Qi; CHEN Yong; ZHANG Hong-Qing
2005-01-01
In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations. With the aid of symbolic computation, we apply the proposed method to solving the (1+1)-dimensional dispersive long wave equation and explicitly construct a series of exact solutions which include the rational form solitary wave solutions and elliptic doubly periodic wave solutions as special cases.
Extended Long Wave Hindcast inside Port Solutions to Minimize Resonance
Directory of Open Access Journals (Sweden)
Gabriel Diaz-Hernandez
2016-02-01
Full Text Available The present study shows a methodology to carry out a comprehensive study of port agitation and resonance analysis in Geraldton Harbor (Western Australia. The methodology described and applied here extends the short and long wave hindcast outside the harbor and towards the main basin. To perform such an analysis, and as the first stage of the methodology, it is necessary to determine, in detail, both the long and short wave characteristics, through a comprehensive methodology to obtain and to hindcast the full spectral data (short waves + long waves, for frequencies between 0.005 and 1 Hz. Twelve-year spectral hindcast wave data, at a location before the reef, have been modified analytically to include the energy input associated with infragravity waves. A decomposition technique based on the energy balance of the radiation stress of short waves is followed. Predictions for long wave heights and periods at different harbor locations are predicted and validated with data recorded during 2004 to 2009. This new database will ensure an accurate and reliable assessment of long wave hourly data (height, period and currents in any area within the main basin of the Port of Geraldton, for its present geometry. With this information, two main task will be completed: (1 undertake a forensic diagnosis of the present response of the harbor, identifying those forcing characteristics related to inoperability events; and (2 propose any layout solutions to minimize, change, dissipate/fade/vanish or positively modify the effects of long waves in the harbor, proposing different harbor geometry modifications. The goal is to identify all possible combinations of solutions that would minimize the current inoperability in the harbor. Different pre-designs are assessed in this preliminary study in order to exemplify the potential of the methodology.
Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations.
Islam, S M Rayhanul; Khan, Kamruzzaman; Akbar, M Ali
2015-01-01
In this paper, we implement the exp(-Φ(ξ))-expansion method to construct the exact traveling wave solutions for nonlinear evolution equations (NLEEs). Here we consider two model equations, namely the Korteweg-de Vries (KdV) equation and the time regularized long wave (TRLW) equation. These equations play significant role in nonlinear sciences. We obtained four types of explicit function solutions, namely hyperbolic, trigonometric, exponential and rational function solutions of the variables in the considered equations. It has shown that the applied method is quite efficient and is practically well suited for the aforementioned problems and so for the other NLEEs those arise in mathematical physics and engineering fields. PACS numbers: 02.30.Jr, 02.70.Wz, 05.45.Yv, 94.05.Fq.
Institute of Scientific and Technical Information of China (English)
WANG Qi; CHEN Yong; LI Biao; ZHANG Hong-Qing
2004-01-01
Based on the computerized symbolic Maple, we study two important nonlinear evolution equations, i.e.,the Hirota equation and the (1+1)-dimensional dispersive long wave equation by use of a direct and unified algebraic method named the general projective Riccati equation method to find more exact solutions to nonlinear differential equations. The method is more powerful than most of the existing tanh method. New and more general form solutions are obtained. The properties of the new formal solitary wave solutions are shown by some figures.
Mercury Cadmium Telluride Photoconductive Long Wave Infrared Linear Array Detectors
Directory of Open Access Journals (Sweden)
Risal Singh
2003-07-01
Full Text Available Mercury cadmium telluride (Hg1-x, CdxTe (MCT photoconductive long wave infrared linear arrays are still in demand due to several advantages. The linear array technology is well established, easier, economical and is quite relevant to thermal imaging even today. The scan thermal imaging systems based on this technology offer wider field of view coverage and capacity for higher resolution in the scan direction relative to staring systems that use expensive and yet to mature focal plane array detector technology. A critical review on photoconductive n-Hg1-x CdxTe linear array detector technology for the long wave infrared range has been presented. The emphasis lies on detector design and processing technology. The critical issues of diffusion and drift effects, Hi-Lo and heterostructure blocking contacts, surface passivation, and other related aspects have been considered from the detector design angle. The device processing technology aspects are of vital importance
Symmetries and casimir of an extended classical long wave system
Indian Academy of Sciences (India)
K M Tamizhmani; R Ilangovane; B Dubrovin
2013-04-01
In this paper, we derive Lie point, generalized, master and time-dependent symmetries of a dispersionless equation, which is an extension of a classical long wave system. This equation also admits an infinite-dimensional Lie algebraic structure of Virasoro-type, as in the dispersive integrable systems. We discuss the construction of a sequence of negative ranking symmetries through the property of uniformity in rank. More interestingly, we obtain the conserved quantities directly from the casimir of Poisson pencil.
New Conservative Schemes for Regularized Long Wave Equation
Institute of Scientific and Technical Information of China (English)
Tingchun Wang; Luming Zhang
2006-01-01
In this paper, two finite difference schemes are presented for initial-boundary value problems of Regularized Long-Wave(RLW) equation. They all have the advantages that there are discrete energies which are conserved. Convergence and stability of difference solutions with order O(h2 +τ2) are proved in the energy norm. Numerical experiment results demonstrate the effectiveness of the proposed schemes.
Tri-prong scheme for regularized long wave equation
Directory of Open Access Journals (Sweden)
M.M. Hosseini
2016-06-01
Full Text Available This paper witnesses the application of a tri-prong scheme comprising the well-known Variational Iteration (VIM, Adomian’s polynomials and an auxiliary parameter to obtain solutions of regularized long wave (RLW equation in large domain. Computational work elucidates the solution procedure appropriately and comparison with results by the standard variational iteration method shows that the auxiliary parameter proves very effective to control the convergence region of approximate solutions.
An Experimental and Numerical Study of Long Wave Run-Up on a Plane Beach
Directory of Open Access Journals (Sweden)
Ulrike Drähne
2015-12-01
Full Text Available This research is to facilitate the current understanding of long wave dynamics at coasts and during on-land propagation; experimental and numerical approaches are compared against existing analytical expressions for the long wave run-up. Leading depression sinusoidal waves are chosen to model these dynamics. The experimental study was conducted using a new pump-driven wave generator and the numerical experiments were carried out with a one-dimensional discontinuous Galerkin non-linear shallow water model. The numerical model is able to accurately reproduce the run-up elevation and velocities predicted by the theoretical expressions. Depending on the surf similarity of the generated waves and due to imperfections of the experimental wave generation, riding waves are observed in the experimental results. These artifacts can also be confirmed in the numerical study when the data from the physical experiments is assimilated. Qualitatively, scale effects associated with the experimental setting are discussed. Finally, shoreline velocities, run-up and run-down are determined and shown to largely agree with analytical predictions.
Kondratiev cycles and so-called long waves. The early research
J. Tinbergen (Jan)
1981-01-01
textabstractThis paper recalls some early work of the Dutch pioneers of long-wave research which anticipated many of the contemporary debates. Various explanations which have been advanced for the existence of long waves are reviewed, and the applicability of long-wave theories in a number of
Long-Wave Runup on a Plane Beach: An Experimental and Numerical Investigation
Vater, Stefan; Drähne, Ulrike; Goseberg, Nils; Beisiegel, Nicole; Behrens, Jörn
2016-04-01
In this study the runup generated by leading depression single sinusoidal waves as a very basic representation of a tsunami is investigated through physical and numerical experiments. The results are compared against existing analytical expressions for the long-wave runup of periodic sinusoidal waves. It can be shown that shallow water theory is applicable for the investigated type of waves. Furthermore, we demonstrate how such a comparative, inter-methodological work contributes to the understanding of shoreline motion of long waves. The produced data set may serve as a novel benchmark for leading depression sinusoidal waves. The experimental study was conducted using an innovative pump-driven wave generator that is capable of generating arbitrarily long waves which might even exceed the length of the wave flume. Due to the complex control problem for the chosen type of wave generator, spurious over-riding small-scale waves were unavoidable in some of the experiments. The numerical simulations were carried out with a one-dimensional Runge-Kutta discontinuous Galerkin (RKDG) non-linear shallow water model. It incorporates a high fidelity wetting and drying scheme. The sinusoidal waves are generated in a constant depth section attached to a linearly sloping beach, have periods between 20 and 100 seconds and surf similarity parameters between 4.4 and 15.6. In a first qualitative analysis the evolution of the runup elevation and velocity is compared. In order to quantify analytical, numerical and experimental data, the wave similarity measured by the Brier score, maximum run-up and run-down height, as well as run-up/run-down velocities are utilized as metrics. As a starting point, periodic and non-periodic clean sinusoidal waves are compared numerically to rule out differences due to the single sinusoidal wave generation in the wave flume. On further analysis, significant differences in experimental and analytically expected values are observed. However, with the
Normal Incident Long Wave Infrared Quantum Dash Quantum Cascade Photodetector
Wang, Feng-Jiao; Ren, Fei; Liu, Shu-Man; Zhuo, Ning; Zhai, Shen-Qiang; Liu, Jun-Qi; Liu, Feng-Qi; Wang, Zhan-Guo
2016-09-01
We demonstrate a quantum dash quantum cascade photodetector (QDash-QCD) by incorporating self-assembled InAs quantum dashes into the active region of a long wave infrared QCD. Sensitive photoresponse to normal incident light at 10 μm was observed, which is attributed to the intersubband (ISB) transitions in the quantum well/quantum dash (QW/QDash) hybrid absorption region and the following transfer of excited electrons on the extraction stair-like quantum levels separated by LO-phonon energy. The high density InAs quantum dashes were formed in the Stranski-Krastanow mode and stair-like levels were formed by a lattice matched InGaAs/InAlAs superlattice. A stable responsivity from 5 mA/W at 77 K to 3 mA/W at as high as 190 K was observed, which makes the QDash-QCD promising in high temperature operation.
Cultural Artifact Detection in Long Wave Infrared Imagery.
Energy Technology Data Exchange (ETDEWEB)
Anderson, Dylan Zachary [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Craven, Julia M. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ramon, Eric [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-01-01
Detection of cultural artifacts from airborne remotely sensed data is an important task in the context of on-site inspections. Airborne artifact detection can reduce the size of the search area the ground based inspection team must visit, thereby improving the efficiency of the inspection process. This report details two algorithms for detection of cultural artifacts in aerial long wave infrared imagery. The first algorithm creates an explicit model for cultural artifacts, and finds data that fits the model. The second algorithm creates a model of the background and finds data that does not fit the model. Both algorithms are applied to orthomosaic imagery generated as part of the MSFE13 data collection campaign under the spectral technology evaluation project.
Polarization characteristics of objects in long-wave infrared range.
Liu, Fei; Shao, Xiaopeng; Gao, Ying; Xiangli, Bin; Han, Pingli; Li, Guo
2016-02-01
Research on polarization characteristics of objects has become indispensable in the field of target detection. Though widespread studies on applying polarization to target detection and material identification exist, theoretical descriptions have varied widely in accuracy and completeness. Incomplete descriptions of polarization characteristics invariably result in poor demonstration of changes caused by macroscopic influence factors. For objects that are of finite surface, a comprehensive model is built to analyze the polarization characteristics of their thermal emission. With the Stokes theory and the superposition principle of light waves, the relation between the degree of linear polarization and the spatial geometrical parameters, such as the detection distance and the shape of objects, is discussed in the long-wave infrared range in detail. This model can be applied to analyze the linear polarization characteristics among different materials.
Design and fabrication of long wave infrared spectral filters
Carey, Victoria A.; McElhiney, Morgan E.; Gupta, Neelam; Jensen, Janet; Prather, Dennis W.; Mirotznik, Mark S.
2016-02-01
Multispectral and hyperspectral imaging in the long wave infrared (LWIR) spectral region has numerous applications in agriculture, astronomy20-22, medicine, and the sensing of dangerous chemical/biological agents23-25. One of the challenges of developing a spectral imaging system in the LWIR is the availability of spectral filters. We will report on three different design methods for realizing spectral filters in the LWIR. The first is an all-dielectric reflection filter based on the guidedmode resonance response. The second is a spatially-varying plasmonic structure that can be used to synthesize complicated spectral reflectance. The third is a Fabry-Perot design for tunable transmission. Numerical and experimental results will be presented.
Run-up amplification of transient long waves
Stefanakis, Themistoklis; Dutykh, Denys; Dias, Frédéric
2013-01-01
The extreme characteristics of long wave run-up are studied in this paper. First we give a brief overview of the existing theory which is mainly based on the hodograph transformation (Carrier & Greenspan, 1958). Then, using numerical simulations, we build on the work of Stefanakis et al. (2011) for an infinite sloping beach and we find that resonant run-up amplification of monochromatic waves is robust to spectral perturbations of the incoming wave and resonant regimes do exist for certain values of the frequency. In the setting of a finite beach attached to a constant depth region, resonance can only be observed when the incoming wavelength is larger than the distance from the undisturbed shoreline to the seaward boundary. Wavefront steepness is also found to play a role in wave run-up, with steeper waves reaching higher run-up values.
Long Wave Reflection and Transmission over A Sloping Step
Institute of Scientific and Technical Information of China (English)
Hsien-Kuo CHANG; Jin-Cheng LIOU
2004-01-01
This investigation examines long wave reflection and transmission induced by a sloping step. Bellman and Kalaba's(1959) invariant imbedding is introduced to find wave reflection. An alternative method matching both the surface elevation and its surface slope of each region at the junction is applied to the determination of wave reflection and transmission.The proposed methods are compared with the accurate numerical results of Porter and Porter (2000) and those of Mei(1983) for a vertical step. The wave reflection obtained for a mildly sloping step differs significantly from the result of Mei. The wave reflection is found to fluctuate owing to wave trapping for the mild sloping step. The height and the face slope of the step are important for determining wave reflection and transmission coefficients.
Sakkaravarthi, K; Kanna, T; Vijayajayanthi, M; Lakshmanan, M
2014-11-01
We consider a general multicomponent (2+1)-dimensional long-wave-short-wave resonance interaction (LSRI) system with arbitrary nonlinearity coefficients, which describes the nonlinear resonance interaction of multiple short waves with a long wave in two spatial dimensions. The general multicomponent LSRI system is shown to be integrable by performing the Painlevé analysis. Then we construct the exact bright multisoliton solutions by applying the Hirota's bilinearization method and study the propagation and collision dynamics of bright solitons in detail. Particularly, we investigate the head-on and overtaking collisions of bright solitons and explore two types of energy-sharing collisions as well as standard elastic collision. We have also corroborated the obtained analytical one-soliton solution by direct numerical simulation. Also, we discuss the formation and dynamics of resonant solitons. Interestingly, we demonstrate the formation of resonant solitons admitting breather-like (localized periodic pulse train) structure and also large amplitude localized structures akin to rogue waves coexisting with solitons. For completeness, we have also obtained dark one- and two-soliton solutions and studied their dynamics briefly.
Directory of Open Access Journals (Sweden)
E. Momoniat
2014-01-01
Full Text Available Two nonstandard finite difference schemes are derived to solve the regularized long wave equation. The criteria for choosing the “best” nonstandard approximation to the nonlinear term in the regularized long wave equation come from considering the modified equation. The two “best” nonstandard numerical schemes are shown to preserve conserved quantities when compared to an implicit scheme in which the nonlinear term is approximated in the usual way. Comparisons to the single solitary wave solution show significantly better results, measured in the L2 and L∞ norms, when compared to results obtained using a Petrov-Galerkin finite element method and a splitted quadratic B-spline collocation method. The growth in the error when simulating the single solitary wave solution using the two “best” nonstandard numerical schemes is shown to be linear implying the nonstandard finite difference schemes are conservative. The formation of an undular bore for both steep and shallow initial profiles is captured without the formation of numerical instabilities.
An economic policy for the fifth long wave
Directory of Open Access Journals (Sweden)
Angelo Reati
2004-12-01
Full Text Available The paper starts by reviewing some recent contributions on long waves, arguing that the present technological revolution in ICT is part of the broad phenomenon of a newlong wave. It follows that the main focus of economic policy should be to support the diffusion of the new technology and to favour the institutional changes required by such an objective. Four broad guidelines are suggested: i a Keynesian policy for demand going beyond the straitjacket of the Maastricht criteria and improving the income distribution in favour of employees; i a policy to re-establish the primacy of productive capital through systematic concerted open market operations to regulate financial liquidity; iii a reconstruction of the employment relationship that preserves the essential features of the "European social model" and a targeted flexibility of labour, that contrasts with the neoclassical all-out market flexibility; and iv a regime for intellectual property rights that avoids the drawbacks--both ethical and economic--of current US practices.
Normal Incident Long Wave Infrared Quantum Dash Quantum Cascade Photodetector.
Wang, Feng-Jiao; Ren, Fei; Liu, Shu-Man; Zhuo, Ning; Zhai, Shen-Qiang; Liu, Jun-Qi; Liu, Feng-Qi; Wang, Zhan-Guo
2016-12-01
We demonstrate a quantum dash quantum cascade photodetector (QDash-QCD) by incorporating self-assembled InAs quantum dashes into the active region of a long wave infrared QCD. Sensitive photoresponse to normal incident light at 10 μm was observed, which is attributed to the intersubband (ISB) transitions in the quantum well/quantum dash (QW/QDash) hybrid absorption region and the following transfer of excited electrons on the extraction stair-like quantum levels separated by LO-phonon energy. The high density InAs quantum dashes were formed in the Stranski-Krastanow mode and stair-like levels were formed by a lattice matched InGaAs/InAlAs superlattice. A stable responsivity from 5 mA/W at 77 K to 3 mA/W at as high as 190 K was observed, which makes the QDash-QCD promising in high temperature operation.
Long-wave infrared profile feature extractor (PFx) sensor
Sartain, Ronald B.; Aliberti, Keith; Alexander, Troy; Chiu, David
2009-05-01
The Long Wave Infrared (LWIR) Profile Feature Extractor (PFx) sensor has evolved from the initial profiling sensor that was developed by the University of Memphis (Near IR) and the Army Research Laboratory (visible). This paper presents the initial signatures of the LWIR PFx for human with and without backpacks, human with animal (dog), and a number of other animals. The current version of the LWIR PFx sensor is a diverging optical tripwire sensor. The LWIR PFx signatures are compared to the signatures of the Profile Sensor in the visible and Near IR spectral regions. The LWIR PFx signatures were collected with two different un-cooled micro bolometer focal plane array cameras, where the individual pixels were used as stand alone detectors (a non imaging sensor). This approach results in a completely passive, much lower bandwidth, much longer battery life, low weight, small volume sensor that provides sufficient information to classify objects into human Vs non human categories with a 98.5% accuracy.
Novel silicon lenses for long-wave infrared imaging
Kintz, Gregory; Stephanou, Philip; Petersen, Kurt
2016-05-01
The design, fabrication and performance of a novel silicon lens for Long Wave Infrared (LWIR) imaging are presented. The silicon lenses are planar in nature, and are created using standard wafer scale silicon micro-fabrication processes. The silicon batch processes are used to generate subwavelength structures that introduce spatially varying phase shifts in the incident light. We will show that the silicon lens designs can be extended to produce lenses of varying focal lengths and diameters, thus enabling IR imaging at significantly lower cost and reduced weight and form factor. An optical design program and a Finite-Difference Time-Domain (FDTD) simulation software tool are used to model the lens performance. The effects of polarization anisotropy are computed for the resultant subwavelength structures. Test samples with lenses with focal lengths in the range of 10 to 50 mm were fabricated. The test sample also included a prism structure, which is characterized by measuring the deflection of a CO2 laser beam and compared to theoretical beam deflection. The silicon lenses are used to produce an image on a VGA micro-bolometer array.
Velioǧlu, Deniz; Cevdet Yalçıner, Ahmet; Zaytsev, Andrey
2016-04-01
Tsunamis are huge waves with long wave periods and wave lengths that can cause great devastation and loss of life when they strike a coast. The interest in experimental and numerical modeling of tsunami propagation and inundation increased considerably after the 2011 Great East Japan earthquake. In this study, two numerical codes, FLOW 3D and NAMI DANCE, that analyze tsunami propagation and inundation patterns are considered. Flow 3D simulates linear and nonlinear propagating surface waves as well as long waves by solving three-dimensional Navier-Stokes (3D-NS) equations. NAMI DANCE uses finite difference computational method to solve 2D depth-averaged linear and nonlinear forms of shallow water equations (NSWE) in long wave problems, specifically tsunamis. In order to validate these two codes and analyze the differences between 3D-NS and 2D depth-averaged NSWE equations, two benchmark problems are applied. One benchmark problem investigates the runup of long waves over a complex 3D beach. The experimental setup is a 1:400 scale model of Monai Valley located on the west coast of Okushiri Island, Japan. Other benchmark problem is discussed in 2015 National Tsunami Hazard Mitigation Program (NTHMP) Annual meeting in Portland, USA. It is a field dataset, recording the Japan 2011 tsunami in Hilo Harbor, Hawaii. The computed water surface elevation and velocity data are compared with the measured data. The comparisons showed that both codes are in fairly good agreement with each other and benchmark data. The differences between 3D-NS and 2D depth-averaged NSWE equations are highlighted. All results are presented with discussions and comparisons. Acknowledgements: Partial support by Japan-Turkey Joint Research Project by JICA on earthquakes and tsunamis in Marmara Region (JICA SATREPS - MarDiM Project), 603839 ASTARTE Project of EU, UDAP-C-12-14 project of AFAD Turkey, 108Y227, 113M556 and 213M534 projects of TUBITAK Turkey, RAPSODI (CONCERT_Dis-021) of CONCERT
A (2+1)-Dimensional Dispersive Long Wave Hierarchy and its Integrable Couplings
Institute of Scientific and Technical Information of China (English)
Huanhe Dong
2007-01-01
Under the frame of the (2+1)-dimensional zero curvature equation and Tu model,the (2+1)-dimensional dispersive long wave hierarchy is obtained. Furthermore, the loop algebra is expanded into a larger one. Moreover, a class of integrable coupling system for dispersive long wave hierarchy and (2+1)-dimensional multi-component integrable system will be investigated.
Electronic crosstalk correction for terra long wave infrared photovoltaic bands
Sun, Junqiang; Madhavan, Sriharsha; Xiong, Xiaoxiong; Wang, Menghua
2014-11-01
The MODerate-resolution Imaging Spectroradiometer (MODIS) is one of the primary instruments in the National Aeronautics and Space Administration (NASA) Earth Observing System (EOS). The first MODIS instrument was launched in December 1999 on-board the Terra spacecraft. MODIS has 36 bands, among which 27-30 are Long Wave Infrared (LWIR) PhotoVoltaic (PV) bands covering a wavelength range from 6.72 μm to 9.73 μm. It has been found that there is severe contamination in Terra band 27 from other three bands due to crosstalk of signals among them. The crosstalk effect induces strong striping in the Earth View (EV) images and causes large long-term drift in the EV Brightness Temperature (BT) in the band. An algorithm using a linear approximation derived from on-orbit lunar observations has been developed to correct the crosstalk effect for band 27. It was demonstrated that the crosstalk correction can substantially reduce the striping in the EV images and significantly remove the long-term drift in the EV BT. In this paper, it is shown that other three LWIR PV bands are also contaminated by the crosstalk of signals among themselves. The effect induces strong striping artifacts and large long-term drifts in these bands as similarly observed in band 27. The crosstalk correction algorithm previously developed is applied to correct the crosstalk effect. It is demonstrated that the crosstalk correction successfully reduces the striping in the EV images and removes long-term drifts in the EV BT in bands 28-30 as was done similarly for band 27. The crosstalk correction algorithm can thus substantially improve both the image quality and radiometric accuracy of the LWIR PV bands Level 1B (L1B) products. The algorithm can be applied to other MODIS bands and/or other remote sensors that exhibit an electronic crosstalk effect.
Global smooth solutions in R3 to short wave-long wave interactions in magnetohydrodynamics
Frid, Hermano; Jia, Junxiong; Pan, Ronghua
2017-04-01
We consider a Benney-type system modeling short wave-long wave interactions in compressible viscous fluids under the influence of a magnetic field. Accordingly, this large system now consists of the compressible MHD equations coupled with a nonlinear Schrödinger equation along particle paths. We study the global existence of smooth solutions to the Cauchy problem in R3 when the initial data are small smooth perturbations of an equilibrium state. An important point here is that, instead of the simpler case having zero as the equilibrium state for the magnetic field, we consider an arbitrary non-zero equilibrium state B bar for the magnetic field. This is motivated by applications, e.g., Earth's magnetic field, and the lack of invariance of the MHD system with respect to either translations or rotations of the magnetic field. The usual time decay investigation through spectral analysis in this non-zero equilibrium case meets serious difficulties, for the eigenvalues in the frequency space are no longer spherically symmetric. Instead, we employ a recently developed technique of energy estimates involving evolution in negative Besov spaces, and combine it with the particular interplay here between Eulerian and Lagrangian coordinates.
Energy Technology Data Exchange (ETDEWEB)
Kong Cuicui [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)], E-mail: cuicuikong@yahoo.com.cn; Wang Dan; Song Lina; Zhang Hongqing [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)
2009-01-30
In this paper, with the aid of symbolic computation and a general ansaetz, we presented a new extended rational expansion method to construct new rational formal exact solutions to nonlinear partial differential equations. In order to illustrate the effectiveness of this method, we apply it to the MKDV-Burgers equation and the (2 + 1)-dimensional dispersive long wave equation, then several new kinds of exact solutions are successfully obtained by using the new ansaetz. The method can also be applied to other nonlinear partial differential equations.
Indian Academy of Sciences (India)
S De
2010-12-01
The predictability of planetary or ultra-long scale waves is limited by the large growth of errors in these scales in almost all the medium range forecast models. Understanding the cause for the enormous build up of error is, therefore, a necessary task for improving the prediction of planetary waves. A diagnostic analysis of the systematic error energetics has been performed in the Global Forecast System model to investigate the reasons for poor predictability of the lower tropospheric ultra-long waves (wavenumber bands 1 –4)in tropics using the analysis –forecast system of horizon- tal wind ﬁeld at 850 hPa level during the boreal summer period. For this purpose, systematic error energy is computed in spatial as well as in wavenumber domain. Non-linear inter-scale transfer of error has been formulated and evaluated through energy exchanges among participating triads. The study reveals that the error is generated in the prognostic model initially with a small magnitude at the different locations around tropical convergence zone (TCZ) attributed to the inaccuracy in representing different physical processes like cumulus convection applied in the model. At subsequent evolution of forecasts, error increases and spreads along the TCZ due to its non-linear advection to the higher scales and eventually to the ultra-long scales attributed to the inherent dynamics of the model evaluated through the process of wave –wave exchange of error energy in terms of the triad interactions. The continuous generation and then, non-linear propagation of error up to the planetary scales in the course of prediction increase the uncertainty in ultra-long scales which actually inhibit to predict accurately the planetary scale waves in tropics during medium range forecasts. This work suggests caveats to the modeler’s community in the predictability study of tropical ultra-long waves.
Hydroelastic analysis of ice shelves under long wave excitation
Papathanasiou, Theodosios; Karperaki, Angeliki; Theotokoglou, Efstathios; Belibassakis, Kostas
2014-05-01
The transient hydroelastic response of an ice shelf, under long wave forcing, is analysed by means of the Finite Element method. Our main goal is to provide a simple model for tsunami wave - ice shelf interaction, capable of reproducing, in an at least qualitative manner, the stress field induced in the ice shelf, when excited by a tsunami wave. The analysis is aimed to model ice calving caused by wave impact, as was the case after the Honsu 2011 incident [1]. Adopting several simplifying but realistic assumptions, the ice shelf is modeled as a variable thickness, Euler-Bernoulli, cantilever beam, while the 1+1 linear shallow water equations are employed for the hydrodynamic field representation, as described in [2]. The fixed cantilever beam resembles a constrained, continuous ice shelf extending into the ocean. The solution of such a system, for a freely floating plate, has been presented by Sturova [3], where a modal expansion of the hydroelastic response with respect to the dry modes of the beam has been used. Our solution approach is based on the development of a special hydroelastic finite element for the governing equations. Cases of constant and variable bathymetry are considered. Bending moment time profiles yield the maximum tensile stress at the upper and lower surfaces of the ice shelf, which is the critical parameter for crack initiation or propagation. As expected, maximum absolute bending moment values appear at the base of the ice shelf, where no deflection or rotation occurs. The fact that the wave is fully reflected on the vertical impermeable boundary, corresponding to the continental shelf under the base of the floe, leads to extreme focusing and thus extreme bending moment values. Finally, the case of cracked shelves has been considered with use of the elementary defective beam theory of Kienzler and Herrmann [4]. Future enhancement of the present model is proposed on the grounds of a higher order beam/plate theory and a 2-D formulation
Energy Technology Data Exchange (ETDEWEB)
Zheng Xuedong; Chen Yong; Zhang Hongqing
2003-05-12
Making use of a new generalized ansatzes, we present the generalized extended tanh-function method for constructing the exact solutions of nonlinear partial differential equations (NPDEs) in a unified way. Applying the generalized method, with the aid of MAPLE, we consider the Wu-Zhang equation (which describes (1+1)-dimensional dispersive long wave). As a result, we can successfully obtain the solitary wave solutions that can be found by the extended tanh-function method and the modified extended tanh-function method. More importantly, for the equation, we also obtain other new and more general solutions at the same time. The results include kink-profile solitary wave solutions, bell-profile solitary wave solutions, periodic wave solutions, rational solutions, singular solutions and other new formal solutions. As an illustrative sample, the properties of some soliton solutions for Wu-Zhang equation are shown by some figures.
Institute of Scientific and Technical Information of China (English)
CHENYong; WANGQi; LIBiao
2004-01-01
Making use of a new and more general ansatz, we present the generalized algebraic method to uniformly construct a series of new and general travelling wave solution for nonlinear partial differential equations. As an application of the method, we choose a (1+1)-dimensional dispersive long wave equation to illustrate the method. As a result, we can successfully obtain the solutions found by the method proposed by Fan [E. Fan, Comput. Phys. Commun. 153 (2003) 17] and find other new and more general solutions at the same time, which include polynomial solutions, exponential solutions, rational solutions, triangular periodic wave solutions, hyperbolic and soliton solutions, Jacobi and Weierstrass doubly periodic wave solutions.
Design of visible/long-wave infrared dual-band imaging optical system
Zhang, Lingzhi; Lai, Jianjun; Huang, Ying
2016-10-01
An efficient small size and low weight optical lens system covering the visible and long-wave infrared dual-band is designed. The chromatic aberration caused by the wide bands from visible to long-wave infrared is one of the tough problems though large efforts have been done in the related communities. In this paper, for materials used as the base of the achromatic design, we choose two suitable materials (Zns and Kbr) that allow transmission both of visible and long-wave infrared (LWIR) light. Though the two materials have proved the ability to correct three wavelengths for each spectral range, the correction from the materials compensation is not enough and aspheric even diffractive surface was selected to join this optical system for reducing the aberration. The design results show a good image quality for infrared band imaging while the corresponding visible imaging is acceptable to be used to extract the outline of objects.
Cubic Trigonometric B-spline Galerkin Methods for the Regularized Long Wave Equation
Irk, Dursun; Keskin, Pinar
2016-10-01
A numerical solution of the Regularized Long Wave (RLW) equation is obtained using Galerkin finite element method, based on Crank Nicolson method for the time integration and cubic trigonometric B-spline functions for the space integration. After two different linearization techniques are applied, the proposed algorithms are tested on the problems of propagation of a solitary wave and interaction of two solitary waves.
Variability In Long-Wave Runup as a Function of Nearshore Bathymetric Features
Energy Technology Data Exchange (ETDEWEB)
Dunkin, Lauren McNeill [Texas A & M Univ., College Station, TX (United States)
2010-05-01
Beaches and barrier islands are vulnerable to extreme storm events, such as hurricanes, that can cause severe erosion and overwash to the system. Having dunes and a wide beach in front of coastal infrastructure can provide protection during a storm, but the influence that nearshore bathymetric features have in protecting the beach and barrier island system is not completely understood. The spatial variation in nearshore features, such as sand bars and beach cusps, can alter nearshore hydrodynamics, including wave setup and runup. The influence of bathymetric features on long-wave runup can be used in evaluating the vulnerability of coastal regions to erosion and dune overtopping, evaluating the changing morphology, and implementing plans to protect infrastructure. In this thesis, long-wave runup variation due to changing bathymetric features as determined with the numerical model XBeach is quantified (eXtreme Beach behavior model). Wave heights are analyzed to determine the energy through the surfzone. XBeach assumes that coastal erosion at the land-sea interface is dominated by bound long-wave processes. Several hydrodynamic conditions are used to force the numerical model. The XBeach simulation results suggest that bathymetric irregularity induces significant changes in the extreme long-wave runup at the beach and the energy indicator through the surfzone.
Stability of Solitary Waves for Three Coupled Long Wave - Short Wave Interaction Equations
Borluk, H.; Erbay, S.
2009-01-01
In this paper we consider a three-component system of one dimensional long wave-short wave interaction equations. The system has two-parameter family of solitary wave solutions. We prove orbital stability of the solitary wave solutions using variational methods.
Holes and chaotic pulses of traveling waves coupled to a long-wave mode
Herrero, H; Herrero, Henar; Riecke, Hermann
1997-01-01
Localized traveling-wave pulses and holes, i.e. localized regions of vanishing wave amplitude, are investigated in a real Ginzburg-Landau equation coupled to a long-wave mode. In certain parameter regimes the pulses exhibit a Hopf bifurcation which leads to a breathing motion. Subsequently the oscillations undergo period-doubling bifurcations and become chaotic.
Holes and chaotic pulses of traveling waves coupled to a long-wave mode
Herrero, Henar; Riecke, Hermann
1997-02-01
It is shown that localized traveling-wave pulses and holes can be stabilized by a coupling to a long-wave mode. Simulations of suitable real Ginzburg-Landau equations reveal a small parameter regime in which the pulses exhibit a breathing motion (presumably related to a front bifurcation), which subsequently becomes chaotic via period-doubling bifurcations.
Review of Long Wave Dynamics over Reefs and into Ports with Implication for Port Operations
Directory of Open Access Journals (Sweden)
Ap van Dongeren
2016-02-01
Full Text Available This paper reviews the dynamics of infragravity (long-period waves over reef systems and the consequences of these waves for operations in ports located behind reefs with particular attention to Western Australia. Swells which originate in the Southern Ocean generate long (infragravity waves, which propagate to the coast. On the reef edge, the swell waves are largely dissipated, transferring energy to turbulence and heat but also in that process generating long wave energy. The remaining swell waves are dominated by the infragravity waves and propagate towards the mainland and into port basins where they cause moored ship motions with consequences for the operational downtime of the port’s operations. When contemplating solutions to mitigate the impact of the long wave problems, these may be addressed from two sides: from the load side (waves and the strength side (mooring. The former will be discussed in this paper.
New Complexiton Solutions of (1+1)-Dimensional Dispersive Long Wave Equation
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
By means of two different Riccati equations with different parameters as subequation in the components of finite rational expansion method, new complexiton solutions for the (1+1 )-dimensional dispersive long wave equation are successfully constructed, which include various combination of trigonometric periodic and hyperbolic function solutions, various combination of trigonometric periodic and rational function solutions, and various combination of hyperbolic and rational function solutions.
Li, Ben Q; Liu, Changhong
2011-01-15
A hybridization model for the localized surface plasmon resonance of a nanoshell is developed within the framework of long-wave approximation. Compared with the existing hybridization model derived from the hydrodynamic simulation of free electron gas, this approach is much simpler and gives identical results for a concentric nanoshell. Also, with this approach, the limitations associated with the original hybridization model are succinctly stated. Extension of this approach to hybridization modeling of more complicated structures such as multiplayered nanoshells is straightforward.
A simple formula for the net long-wave radiation flux in the southern Baltic Sea
Directory of Open Access Journals (Sweden)
Tomasz Zapadka
2001-09-01
Full Text Available This paper discusses problems of estimating the net long-wave radiation flux at the sea surface on the basis of easily measurable meteorological quantities (air and sea surface temperatures, near-surface water vapour pressure, cloudiness. Empirical data and existing formulae are compared. Additionally, an improved formula for the southern Baltic region is introduced, with a systematic error of less than 1 W -2 and a statistical error of less than 20 W -2.
Electronic Crosstalk in Aqua MODIS Long-Wave Infrared Photovoltaic Bands
Junqiang Sun; Menghua Wang
2016-01-01
Recent investigations have discovered that Terra MODerate-resolution Imaging Spectroradiometer (MODIS) long-wave infrared (LWIR) photovoltaic (PV) bands, bands 27–30, have strong crosstalk among themselves. The linear model developed to test the electronic crosstalk effect was instrumental in the first discovery of the effect in Terra MODIS band 27, and through subsequent investigations the model and the correction algorithm were tested further and established to be correct. It was shown that...
First Integral Method for Systems of (1+1-Dimensional Dispersive Long Wave
Directory of Open Access Journals (Sweden)
Jafar BIAZAR
2014-05-01
Full Text Available The First Integral method (FIM is applied to solve a dispersive long wave system. In this method the division theorem, as a statement in commutative Algebra has an important role. To show the ability and the efficiency of this approach an example is provided. Application of FIM to the illustrative example leads to six exact solutions, which it is shown that these six solutions are independent to each other. So there are six different exact solutions.
Non-completely elastic interactions in a (2+1)-dimensional dispersive long wave equation
Institute of Scientific and Technical Information of China (English)
Chen Wei-Lu; Zhang Wen-Ting; Zhang Li-Pu; Dai Chao-Qing
2012-01-01
With the help of a modified mapping method,we obtain two kinds of variable separation solutions with two arbitrary functions for the (2+1)-dimensional dispersive long wave equation.When selecting appropriate multi-valued functions in the variable separation solution,we investigate the interactions among special multi-dromions,dromion-like multi-peakons,and dromion-like multi-semifoldons,which all demonstrate non-completely elastic properties.
Technical considerations for designing low-cost, long-wave infrared objectives
Desroches, Gerard; Dalzell, Kristy; Robitaille, Blaise
2014-06-01
With the growth of uncooled infrared imaging in the consumer market, the balance between cost implications and performance criteria in the objective lens must be examined carefully. The increased availability of consumer-grade, long-wave infrared cameras is related to a decrease in military usage but it is also due to the decreasing costs of the cameras themselves. This has also driven up demand for low-cost, long-wave objectives that can resolve smaller pixels while maintaining high performance. Smaller pixels are traditionally associated with high cost objectives because of higher resolution requirements but, with careful consideration of all the requirements and proper selection of materials, costs can be moderated. This paper examines the cost/performance trade-off implications associated with optical and mechanical requirements of long-wave infrared objectives. Optical performance, f-number, field of view, distortion, focus range and thermal range all affect the cost of the objective. Because raw lens material cost is often the most expensive item in the construction, selection of the material as well as the shape of the lens while maintaining acceptable performance and cost targets were explored. As a result of these considerations, a low-cost, lightweight, well-performing objective was successfully designed, manufactured and tested.
Some New Exact Solutions to the Dispersive Long-Wave Equation in(2+1)-Dimensional Spaces
Institute of Scientific and Technical Information of China (English)
LI De-Sheng; ZHANG Hong-Qing
2003-01-01
In this paper, by using a further extended tanh method and symbolic computation system, some newsoliton-like and period form solutions of the dispersive long-wave equation in (2+1)-dimensional spaces are obtained.
Physical modeling of long-wave run-up mitigation using submerged breakwaters
Lee, Yu-Ting; Wu, Yun-Ta; Hwung, Hwung-Hweng; Yang, Ray-Yeng
2016-04-01
Natural hazard due to tsunami inundation inland has been viewed as a crucial issue for coastal engineering community. The 2004 India Ocean tsunami and the 2011 Tohoku earthquake tsunami were caused by mega scale earthquakes that brought tremendous catastrophe in the disaster regions. It is thus of great importance to develop innovative approach to achieve the reduction and mitigation of tsunami hazards. In this study, new experiments have been carried out in a laboratory-scale to investigate the physical process of long-wave through submerged breakwaters built upon a mild slope. Solitary-wave is employed to represent the characteristic of long-wave with infinite wavelength and wave period. Our goal is twofold. First of all, through changing the positions of single breakwater and multiple breakwaters upon a mild slope, the optimal locations of breakwaters can be pointed out by means of maximum run-up reduction. Secondly, through using a state-of-the-art measuring technique Bubble Image Velocimetry, which features non-intrusive and image-based measurement, the wave kinematics in the highly aerated region due to solitary-wave shoaling, breaking and uprush can be quantitated. Therefore, the mitigation of long-wave due to the construction of submerged breakwaters built upon a mild slope can be evaluated not only for imaging run-up and run-down characteristics but also for measuring turbulent velocity fields due to breaking wave. Although we understand the most devastating tsunami hazards cannot be fully mitigated with impossibility, this study is to provide quantitated information on what kind of artificial coastal structure that can withstand which level of wave loads.
Exotic Localized Coherent Structures of the (2+1)-Dimensional Dispersive Long-Wave Equation
Institute of Scientific and Technical Information of China (English)
ZHANG JieFang
2002-01-01
This article is concerned with the extended homogeneous balance method for studying thc abundantlocalized solution structures in the (2-k1)-dimensional dispersive long-wave equations uty + xx + (u2)xy/2 = 0, ηt +(u + u + uxy)x = 0. Starting from the homogeneous balance method, we find that the richness of the localized coherentstructures of the model is caused by the entrance of two variable-separated arbitrary functions. For some special selectionsof the arbitrary functions, it is shown that the localized structures of the model may be dromions, lumps, breathers,instantons and ring solitons.
Complexiton solutions of the (2+1)-dimensional dispersive long wave equation
Institute of Scientific and Technical Information of China (English)
Chen Yong; Fan En-Gui
2007-01-01
In this pager a pure algebraic method implemented in a computer algebraic system, named multiple Riccati equations rational expansion method, is presented to construct a novel class of complexiton solutions to integrable equations and nonintegrable equations. By solving the (2+1)-dimensional dispersive long wave equation, it obtains many new types of complexiton solutions such as various combination of trigonometric periodic and hyperbolic function solutions,various combination of trigonometric periodic and rational function solutions, various combination of hyperbolic and rational function solutions, etc.
Hollow Core Fiber Optics for Mid-Wave and Long-Wave Infrared Spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Kriesel, J.M.; Gat, N.; Bernacki, Bruce E.; Erikson, Rebecca L.; Cannon, Bret D.; Myers, Tanya L.; Bledt, Carlos M.; Harrington, J. A.
2011-06-01
The development and testing of hollow core glass waveguides (i.e., fiber optics) for use in Long-Wave Infrared (LWIR) spectroscopy systems is described. LWIR fiber optics are a key enabling technology needed to improve the utility and effectiveness of trace chemical detection systems based in the 8 to 12 micron region. This paper focuses on recent developments in hollow waveguide technology geared specifically for LWIR spectroscopy, including a reduction in both the length dependent loss and the bending loss while maintaining relatively high beam quality. Results will be presented from tests conducted with a Quantum Cascade Laser.
Institutional regimes, long wave systemic risk and great international crisis of 2008-2012
Directory of Open Access Journals (Sweden)
O’Hara Anthony Phillip
2012-01-01
Full Text Available This paper studies the relationship between long-term growth of GDP per capita, institutional regimes of accumulation (ROA, systemic risk and the Great International Crisis of 2008-2010. The principle hypothesis behind the work is that the ROA provides a foundation for long-term growth as a type of fundamental variable, and that this growth provides a buffer against systemic risk in the sense that sustainable growth provides resources for debt provision and employment stimulation. The emergence of a viable ROA is crucial for long waves of growth which stimulate both private sector profit and public sector tax receipts which (using conventional terminology reduce the structural deficit for both sectors. Low rates of long-term growth, therefore, provide a good indicator of the emergence of “long wave systemic risk” (LWSR, which left such nations vulnerable to uncertainty, financial crisis and recession. The paper investigates the inability of growth for various decades to “cover” instabilities associated with the Great Crisis, leading to high rates of LWSR, especially for European and North American nations that bore the brunt of the crisis.
Post-Colonial Africa and the World Economy: The Long Waves of Uneven Development
Directory of Open Access Journals (Sweden)
Fouad Makki
2015-08-01
Full Text Available The aim of this article is to examine the interactive dynamics of "Africa" and the "world economy" over the past half century. By relating the overarching developmental trajectory of the continent to the long-wave rhythms of the world economy, the article identifies three relatively articulated periods in the political economy of postcolonial Africa. The first, from circa 1960 to the late 1970s, was a period of state-led developmentalism enabled by the long postwar boom in the world economy and the embedded liberalism of the Bretton Woods system. A second period from circa 1980 to the turn of the new century was conditioned by the long downturn in the world-economy and a neo-li beral regime of accumulation that sought to re-structure and re-integrate Africa into a deregulated world market. The turn of the new millennium constitutes a new period in which neither the deep structural springs of the long downturn nor the neo-liberal project as such have been overcome; but their impact on Africa has been relativized by the emergence of East Asia as the new center of accumulation in the world economy. The resulting de-synchronization of the long-wave rhythms of the world economy has permitted a modest economic expansion in Africa within a largely extractive regime of accumulation and a wave of new enclosures that are profoundly reconstituting the social universe of Africa's primary producers.
The Development of Advanced Optical Fibers for Long-Wave Infrared Transmission
Directory of Open Access Journals (Sweden)
Pierre Lucas
2013-12-01
Full Text Available Long-wave infrared fibers are used in an increasing number of applications ranging from thermal imaging to bio-sensing. However, the design of optical fiber with low-loss in the far-infrared requires a combination of properties including good rheological characteristics for fiber drawing and low phonon energy for wide optical transparency, which are often mutually exclusive and can only be achieved through fine materials engineering. This paper presents strategies for obtaining low loss fibers in the far-infrared based on telluride glasses. The composition of the glasses is systematically investigated to obtained fibers with minimal losses. The fiber attenuation is shown to depend strongly on extrinsic impurity but also on intrinsic charge carrier populations in these low band-gap amorphous semiconductor materials.
Flag-based detection of weak gas signatures in long-wave infrared hyperspectral image sequences
Marrinan, Timothy; Beveridge, J. Ross; Draper, Bruce; Kirby, Michael; Peterson, Chris
2016-05-01
We present a flag manifold based method for detecting chemical plumes in long-wave infrared hyperspectral movies. The method encodes temporal and spatial information related to a hyperspectral pixel into a flag, or nested sequence of linear subspaces. The technique used to create the flags pushes information about the background clutter, ambient conditions, and potential chemical agents into the leading elements of the flags. Exploiting this temporal information allows for a detection algorithm that is sensitive to the presence of weak signals. This method is compared to existing techniques qualitatively on real data and quantitatively on synthetic data to show that the flag-based algorithm consistently performs better on data when the SINRdB is low, and beats the ACE and MF algorithms in probability of detection for low probabilities of false alarm even when the SINRdB is high.
Long-wave infrared functional brain imaging in human: a pilot study.
Joyal, Christian C; Henry, Mylene
2013-01-01
Although some authors suggest to use Long-Wave Infrared (LWIR) sensors to evaluate brain functioning, the link between emissions of LWIR and mental effort is not established. The goal of this pilot study was to determine whether frontal LWIR emissions vary during execution of neuropsychological tasks known to differentially activate the pre-frontal cortex (simple color presentations, induction of the Stroop effect, and a gambling task with real money). Surprisingly, LWIR emissions as measured with bilateral frontal sensors in 47 participants significantly differed between tasks, in the supposed direction (Colorpilot study suggests that investigations of convergent validity with other types of brain imaging techniques can be initiated with LWIR imaging. If confirmed, this technique would offer a simple and accessible method to evaluate frontal cortex activation.
Weakly nonlinear stability of ultra-thin slipping films
Institute of Scientific and Technical Information of China (English)
HU Guohui
2005-01-01
A weakly nonlinear theory is presented to study the effects of slippage on the stability of the ultra-thin polymer films.The nonlinear mathematical model is constructed for perturbations of small finite amplitude based on hydrodynamic equations with the long wave approximation. Results reveal that the nonlinearity always accelerates the rupture of the films. The influences of the slip length, film thickness, and initial amplitude of perturbations on the rupture of the films are investigated.
Institute of Scientific and Technical Information of China (English)
WEN Xiao-Yong
2009-01-01
With the aid of symbolic computation system Maple, some families of new rational variable separation solutions of the (2+1)-dimensional dispersive long wave equations are constructed by means of a function transformation, improved mapping approach, and variable separation approach, among which there are rational solitary wave solutions, periodic wave solutions and rational wave solutions.
Long-wave infrared imaging of vegetation for detecting leaking CO2 gas
Johnson, Jennifer E.; Shaw, Joseph A.; Lawrence, Rick; Nugent, Paul W.; Dobeck, Laura M.; Spangler, Lee H.
2012-01-01
The commercial development of uncooled-microbolometer, long-wave infrared (LWIR) imagers, combined with advanced radiometric calibration methods developed at Montana State University, has led to new uses of thermal imagery in remote sensing applications. One specific novel use of these calibrated imagers is imaging of vegetation for CO2 gas leak detection. During a four-week period in the summer of 2011, a CO2 leak was simulated in a test field run by the Zero Emissions Research and Technology Center in Bozeman, Montana. An LWIR imager was deployed on a scaffold before and during the CO2 release, viewing a vegetation test area that included regions of high and low CO2 flux. Increased root-level CO2 concentration caused plant stress that led to reduced thermal regulation of the vegetation, which was consistent with increased diurnal variation of IR emission observed in this study. In a linear regression, the IR data were found to have a strong relationship to the CO2 emission and to be consistent with the location of leaking CO2 gas. Reducing the continuous data set to one image per day weakened the regression fit, but maintained sufficient significance to indicate that this method could be implemented with once-daily airborne images.
Hollow core fiber optics for mid-wave and long-wave infrared spectroscopy
Kriesel, Jason M.; Gat, Nahum; Bernacki, Bruce E.; Erikson, Rebecca L.; Cannon, Bret D.; Myers, Tanya L.; Bledt, Carlos M.; Harrington, James A.
2011-05-01
We describe the development and testing of hollow core glass waveguides (i.e., fiber optics) for use in Mid-Wave Infrared (MWIR) and Long-Wave Infrared (LWIR) spectroscopy systems. Spectroscopy measurements in these wavelength regions (i.e., from 3 to 14 μm) are useful for detecting trace chemical compounds for a variety of security and defense related applications, and fiber optics are a key enabling technology needed to improve the utility and effectiveness of detection and calibration systems. Hollow glass fibers have the advantage over solid-core fibers (e.g., chalcogenide) in that they are less fragile, do not produce cladding modes, do not require angle cleaving or antireflection coatings to minimize laser feedback effects, and effectively transmit deeper into the infrared. This paper focuses on recent developments in hollow fiber technology geared specifically for infrared spectroscopy, including single mode beam delivery with relatively low bending loss. Results are presented from tests conducted using both Quantum Cascade Lasers (QCL) and CO2 lasers operating in the LWIR wavelength regime. Single-mode waveguides are shown to effectively deliver beams with relatively low loss (~ 1 dB/m) and relatively high beam quality. The fibers are also shown to effectively mode-filter the "raw" multi-mode output from a QCL, in effect damping out the higher order modes to produce a circularly symmetric Gaussian-like beam profile.
Parameterization of atmospheric long-wave emissivity in a mountainous site for all sky conditions
Directory of Open Access Journals (Sweden)
J. Herrero
2012-03-01
Full Text Available Long-wave radiation is an important component of the energy balance of the Earth's surface. The downward component, emitted by the clouds and aerosols in the atmosphere, is rarely measured, and is still not well understood. In mountainous areas, the models existing for its estimation through the emissivity of the atmosphere do not give good results, and worse still in the presence of clouds. In order to estimate this emissivity for any atmospheric state and in a mountainous site, we related it to the screen-level values of temperature, relative humidity and solar radiation. This permitted the obtaining of: (1 a new set of parametric equations and (2 the modification of the Brutsaert's equation for cloudy skies through the calibration of C factor to 0.34 and the parameterization of the cloud index N. Both fitted to the surface data measured at a weather station at a height of 2500 m a.s.l. in Sierra Nevada, Spain. This study analyzes separately three significant atmospheric states related to cloud cover, which were also deduced from the screen-level meteorological data. Clear and totally overcast skies are accurately represented by the new parametric expressions, while the intermediate situations corresponding to partly clouded skies, concentrate most of the dispersion in the measurements and, hence, the error in the simulation. Thus, the modeling of atmospheric emissivity is greatly improved thanks to the use of different equations for each atmospheric state.
Buried explosive hazard detection using forward-looking long-wave infrared imagery
Stone, K.; Keller, J. M.; Popescu, M.; Spain, C. J.
2011-06-01
Trainable size-contrast filters, similar to local dual-window RX anomaly detectors, utilizing the Bhattacharyya distance are used to detect buried explosive hazards in forward-looking long-wave infrared imagery. The imagery, captured from a moving vehicle, is geo-referenced, allowing projection of pixel coordinates into (UTM) Universal Transverse Mercator coordinates. Size-contrast filter detections for a particular frame are projected into UTM coordinates, and peaks are detected in the resulting density using the mean-shift algorithm. All peaks without a minimum number of detections in their local neighborhood are discarded. Peaks from individual frames are then combined into a single set of tentative hit locations, and the same mean-shift procedure is run on the resulting density. Peaks without a minimum number of hit locations in their local neighborhood are removed. The remaining peaks are declared as target locations. The mean-shift steps utilize both the spatial and temporal information in the imagery. Scoring is performed using ground truth locations in UTM coordinates. The size-contrast filter and mean-shift parameters are learned using a genetic algorithm which minimizes a multiobjective fitness function involving detection rate and false alarm rate. Performance of the proposed algorithm is evaluated on multiple lanes from a recent collection at a US Army test site.
Algorithm fusion in forward-looking long-wave infrared imagery for buried explosive hazard detection
Anderson, D. T.; Keller, James M.; Sjahputera, Ozy
2011-06-01
In this article, we propose a method to fuse multiple algorithms in a long wave infrared (LWIR) system in the context of forward looking buried explosive hazard detection. A pre-screener is applied first, which is an ensemble of local RX filters and mean shift clustering in UTM space. Hit correspondence is then performed with an algorithm based on corner detection, local binary patterns (LBP), multiple instance learning (MIL) and mean shift clustering in UTM space. Next, features from image chips are extracted from UTM confidence maps based on maximally stable extremal regions (MSERs) and Gaussian mixture models (GMMs). These sources are then fused using an ordered weighted average (OWA). While this fusion approach has yet to improve the overall positive detection rate in LWIR, we do demonstrate false alarm reduction. Targets that are not detected by our system are also not detected by a human under visual inspection. Experimental results are shown based on field data measurements from a US Army test site.
Directory of Open Access Journals (Sweden)
Özkan Güner
2014-01-01
Full Text Available We apply the functional variable method, exp-function method, and (G′/G-expansion method to establish the exact solutions of the nonlinear fractional partial differential equation (NLFPDE in the sense of the modified Riemann-Liouville derivative. As a result, some new exact solutions for them are obtained. The results show that these methods are very effective and powerful mathematical tools for solving nonlinear fractional equations arising in mathematical physics. As a result, these methods can also be applied to other nonlinear fractional differential equations.
Electronic Crosstalk in Aqua MODIS Long-Wave Infrared Photovoltaic Bands
Directory of Open Access Journals (Sweden)
Junqiang Sun
2016-09-01
Full Text Available Recent investigations have discovered that Terra MODerate-resolution Imaging Spectroradiometer (MODIS long-wave infrared (LWIR photovoltaic (PV bands, bands 27–30, have strong crosstalk among themselves. The linear model developed to test the electronic crosstalk effect was instrumental in the first discovery of the effect in Terra MODIS band 27, and through subsequent investigations the model and the correction algorithm were tested further and established to be correct. It was shown that the correction algorithm successfully mitigated the anomalous features in the calibration coefficients as well as the severe striping and the long-term drift in the Earth view (EV retrievals for the affected Terra bands. Here, the examination into Aqua MODIS using the established methodology confirms the existence of significant crosstalk contamination in its four LWIR PV, although the finding shows the overall effect to be of lesser degree. The crosstalk effect is characterized and the crosstalk correction coefficients are derived for all four Aqua LWIR PV bands via analysis of signal contamination in the lunar imagery. Sudden changes in the crosstalk contamination are clearly seen, as also in the Terra counterparts in previous investigations. These sudden changes are consistent with the sudden jumps observed in the linear calibration coefficients for many years, thus this latest finding provides an explanation to the long-standing but unexplained anomalies in the calibration coefficients of the four Aqua LWIR bands. It is also shown that the crosstalk contamination for these bands are of similar level for the two MODIS instruments in the early mission that can lead to as much as 2 K increase in brightness temperature for the affected bands, thus demonstrating significant impact on the science results already started at the early going. As Aqua MODIS is a legacy sensor, the crosstalk correction to its LWIR PV bands will be important to remove the impact of
Long Wave Flow Interaction with a Single Square Structure on a Sloping Beach
Directory of Open Access Journals (Sweden)
Gian C. Bremm
2015-08-01
Full Text Available In the context of dam breaks, tsunami, and flash floods, it is paramount to quantify the time-history of forces by the rapidly transient flow to vertical structures and the characteristics of the induced flow patterns. To resemble on-land tsunami-induced flow, a free-surface-piercing structure is exposed to long leading depression waves in a tsunami flume where long waves run up and down a 1:40 smooth and impermeable sloping beach after its generation by a volume-driven wave maker. The structure and its surrounding were monitored with force transducers, pressure gauges and cameras. Preparatory steady-state experiments were accomplished to determine the drag force coefficient of the square cylinder at various water depths. The flow during wave run-up and draw-down acting on the structure resulted in distinct flow pattern which were characteristic for the type of flow-structure interaction. Besides bow wave propagating upstream, a standing or partially-standing wave was observed in front of the structure together with a wake formation downstream, while a von Kármán vortex street developed during the deceleration phase of the flow motion and during draw-down. Force measurements indicated a sudden increase in the stream-wise total force starting with the arrival of the flow front during initial run-up. Lateral velocities showed significant oscillations in correlation with the von Kármán vortex street development. A comparison of the total measured base force with the analytically-calculated share of the drag force revealed that forces were prevailingly drag-dominated.
Absorption of Visible and Long-wave Radiation by Primary and Secondary Biogenic Aerosols.
Gaffney, J. S.; Marley, N. A.
2008-12-01
Field results for the 14C content of carbonaceous aerosols are presented that indicate significant biogenic sources of both primary and secondary aerosols in urban and regional environments. Samples collected in Mexico City and downwind of the urban area during the MILAGRO field study are compared with results reported previously in the literature indicating a significant amount of biogenic aerosols from both biomass burning and secondary photochemical production (e.g. terpene oxidations) are contributing to the overall carbonaceous aerosols in the optically active region of 0.1 to 1.0 micron. Samples in this size range collected on quartz fiber filters were also examined using an integrating sphere and FTIR diffuse reflectance techniques to obtain absorption spectra from 280 to the mid-IR. These data clearly indicate that the biogenic derived primary aerosols from agricultural and trash-burning, as well as secondary organic aerosols from isoprene and terpene oxidations will produce both UV-Visible (short-wave) absorbing substances as well as IR (long-wave) absorbing compounds including humic-like-substances (HULIS). With the anticipated increases in growing seasons (i.e. earlier springs and longer summers) the likely hood of increased fires (forest and grassland) as well as the continuing growth in agricultural burning activities, these primary sources are expected to increase and may play a role in heating of the atmosphere. The compound effects of these primary and secondary biogenic sources of absorbing aerosols to the total aerosol loading and regional climate will be discussed. This work was supported by the Office of Science (BER), U.S. Department of Energy, Grant No. DE-FG02-07ER64328 as part of the Atmospheric Science Program.
Institute of Scientific and Technical Information of China (English)
SONG Li-Na; ZHANG Hong-Qing
2007-01-01
In this work, by means of a generalized method and symbolic computation, we extend the Jacobi elliptic function rational expansion method to uniformly construct a series of stochastic wave solutions for stochastic evolution equations. To illustrate the effectiveness of our method, we take the (2+1)-dimensional stochastic dispersive long wave system as an example. We not only have obtained some known solutions, but also have constructed some new rational formal stochastic Jacobi elliptic function solutions.
Institute of Scientific and Technical Information of China (English)
黄文华; 张解放; 盛正卯
2002-01-01
The variable separation approach is used to find exact solutions of the (2+1)-dimensional long-wave-short-waveresonance interaction equation. The abundance of the coherent soliton structures of this model is introduced by theentrance of an arbitrary function of the seed solutions. For some special selections of the arbitrary function, it is shownthat the coherent soliton structures may be dromions, solitoffs, etc.
Silverberg, G.P.
2005-01-01
While long waves have been seriously discussed by economists for almost one hundred years, to date there is no scientific consensus that particular frequency components are in any way privileged in the undoubtedly fluctuating history of modern economic and political development. This is disappointing for two reasons. First, the demonstration that robust, well-defined periodic components existed would present us with a plausible tool for forecasting. And second, they could (and their purported...
Indian Academy of Sciences (India)
S M Bawiskar; M D Chipade; P V Puranik
2009-04-01
Analysis of ﬁfty four (1951-2004)years of daily energetics of zonal waves derived from NCEP/ NCAR wind ( and data and daily rainfall received over the Indian landmass (real time data) during southwest monsoon season (1 June-30 September)indicate that energetics (momentum transport and kinetic energy)of lower tropospheric ultra-long waves (waves 1 and 2)of low latitudes hold a key to intra-seasonal variability of monsoon rainfall over India. Correlation coefficient between climatology of daily (122 days)energetics of ultra-long waves and climatology of daily rainfall over Indian landmass is 0.9.The relation is not only signiﬁcant but also has a predictive potential.The normalised plot of both the series clearly indicates that the response period of rainfall to the energetics is of 5-10 days during the onset phase and 4-7 days during the withdrawal phase of monsoon over India.During the established phase of monsoon, both the series move hand-in-hand.Normalised plot of energetics of ultra-long waves and rainfall for individual year do not show marked deviation with respect to climatology.These results are ﬁrst of its kind and are useful for the short range forecast of rainfall over India.
Directory of Open Access Journals (Sweden)
Constantin Bota
2014-01-01
Full Text Available The paper presents the optimal homotopy perturbation method, which is a new method to find approximate analytical solutions for nonlinear partial differential equations. Based on the well-known homotopy perturbation method, the optimal homotopy perturbation method presents an accelerated convergence compared to the regular homotopy perturbation method. The applications presented emphasize the high accuracy of the method by means of a comparison with previous results.
Ultra-Trace Chemical Sensing with Long-Wave Infrared Cavity-Enhanced Spectroscopic Sensors
Energy Technology Data Exchange (ETDEWEB)
Taubman, Matthew S.; Myers, Tanya L.; Cannon, Bret D.; Williams, Richard M.; Schultz, John F.
2003-02-20
The infrared sensors task of Pacific Northwest National Laboratory's (PNNL's) Remote Spectroscopy Project (Task B of Project PL211) is focused on the science and technology of remote and in-situ spectroscopic chemical sensors for detecting proliferation and coun-tering terrorism. Missions to be addressed by remote chemical sensor development in-clude detecting proliferation of nuclear or chemical weapons, and providing warning of terrorist use of chemical weapons. Missions to be addressed by in-situ chemical sensor development include countering terrorism by screening luggage, personnel, and shipping containers for explosives, firearms, narcotics, chemical weapons, or chemical weapons residues, and mapping contaminated areas. The science and technology is also relevant to chemical weapons defense, air operations support, monitoring emissions from chemi-cal weapons destruction or industrial activities, law enforcement, medical diagnostics, and other applications. Sensors for most of these missions will require extreme chemical sensitivity and selectiv-ity because the signature chemicals of importance are expected to be present in low con-centrations or have low vapor pressures, and the ambient air is likely to contain pollutants or other chemicals with interfering spectra. Cavity-enhanced chemical sensors (CES) that draw air samples into optical cavities for laser-based interrogation of their chemical content promise real-time, in-situ chemical detection with extreme sensitivity to specified target molecules and superb immunity to spectral interference and other sources of noise. PNNL is developing CES based on quantum cascade (QC) lasers that operate in the mid-wave infrared (MWIR - 3 to 5 microns) and long-wave infrared (LWIR - 8 to 14 mi-crons), and CES based on telecommunications lasers operating in the short-wave infrared (SWIR - 1 to 2 microns). All three spectral regions are promising because smaller mo-lecular absorption cross sections in the SWIR
Institute of Scientific and Technical Information of China (English)
Xue-Wei Sun; Jie Peng; Ke-Qin Zhu
2012-01-01
The long wave stability of core-annular flow of power-law fluids with an axial pressure gradient is investigated at low Reynolds number.The interface between the two fluids is populated with an insoluble surfactant.The analytic solution for the growth rate of perturbation is obtained with long wave approximation.We are mainly concerned with the effects of shear-thinning/thickening property and interfacial surfactant on the flow stability.The results show that the influence of shear-thinning/thickening property accounts to the change of the capillary number.For a clean interface,the shear-thinning property enhances the capillary instability when the interface is close to the pipe wall.The converse is true when the interface is close to the pipe centerline.For shear-thickening fluids,the situation is reversed.When the interface is close to the pipe centerline,the capillary instability can be restrained due to the influence of surfactant.A parameter set can be found under which the flow is linearly stable.
An asymptotic approximation to the free-surface elevation around a cylinder in long waves
Morris-Thomas, Michael T
2013-01-01
Strong nonlinear effects are known to contribute to the wave run-up caused when a progressive wave impinges on a vertical surface piercing cylinder. The magnitude of the wave run-up is largely dependent on the coupling of the cylinder slenderness, $ka$, and wave steepness, $kA$, parameters. This present work proposes an analytical solution to the free-surface elevation around a circular cylinder in plane progressive waves. It is assumed throughout that the horizontal extent of the cylinder is much smaller than the incident wavelength and of the same order of magnitude as the incident wave amplitude. A perturbation expansion of the velocity potential and free-surface boundary condition is invoked and solved to third-order in terms of $ka$ and $kA$. The validity of this approach is investigated through a comparison with canonical second-order diffraction theory and existing experimental results. We find that for small $ka$, the long wavelength theory is valid up to $kA \\approx 0.16-0.2$ on the up wave side of t...
Long-wave analysis and control of the viscous Rayleigh-Taylor instability with electric fields
Cimpeanu, Radu; Anderson, Thomas; Petropoulos, Peter; Papageorgiou, Demetrios
2016-11-01
We investigate the electrostatic stabilization of a viscous thin film wetting the underside of a solid surface in the presence of a horizontally acting electric field. The competition between gravity, surface tension and the nonlocal effect of the applied electric field is captured analytically in the form of a nonlinear evolution equation. A semi-spectral solution strategy is employed to resolve the dynamics of the resulting partial differential equation. Furthermore, we conduct direct numerical simulations (DNS) of the Navier-Stokes equations and assess the accuracy of the obtained solutions when varying the electric field strength from zero up to the point when complete stabilization at the target finite wavelengths occurs. We employ DNS to examine the limitations of the asymptotically derived behavior in the context of increasing liquid film heights, with agreement found to be excellent even beyond the target lengthscales. Regimes in which the thin film assumption is no longer valid and droplet pinch-off occurs are then analyzed. Finally, the asymptotic and computational approaches are used in conjunction to identify efficient active control mechanisms allowing the manipulation of the fluid interface in light of engineering applications at small scales, such as mixing.
Kitaoka, T.; Sumi, T.
1994-01-01
The sensitiveness of white coated thermistor sensors and non-sensitiveness of the gold coated over white thermistor sensors (which have been manufactured by a vacuum evaporation process) to long wave radiation were ascertained by some simple experiments in-room and also by analyses of some results of experimental soundings. From results of analyses on the temperature discrepancies caused by long wave radiation, the possibility to sound the atmospheric ozone partial pressure by a radiosonde equipped with two kinds of sensors, sensitive and non-sensitive to the long wave radiation was suggested, and the test results of the newly developed software for the deduction of ozone partial pressure in upper layers was also shown. However, it was found that the following is the necessary condition to realize the purpose. The sounding should be made by a radiosonde equipped with three sensors, instead of two, one being non-sensitive to the long wave radiation perfectly, and the other two also non-sensitive partially to the downward one, with two different angles of exposure upward. It is essential for the realization of the purpose to get two different values of temperature discrepancies simultaneously observed by the three sensors mentioned above and to avoid the troublesome effects of the upward long wave radiation.
Cao, Yanpeng; Tisse, Christel-Loic
2014-02-01
In this Letter, we propose an efficient and accurate solution to remove temperature-dependent nonuniformity effects introduced by the imaging optics. This single-image-based approach computes optics-related fixed pattern noise (FPN) by fitting the derivatives of correction model to the gradient components, locally computed on an infrared image. A modified bilateral filtering algorithm is applied to local pixel output variations, so that the refined gradients are most likely caused by the nonuniformity associated with optics. The estimated bias field is subtracted from the raw infrared imagery to compensate the intensity variations caused by optics. The proposed method is fundamentally different from the existing nonuniformity correction (NUC) techniques developed for focal plane arrays (FPAs) and provides an essential image processing functionality to achieve completely shutterless NUC for uncooled long-wave infrared (LWIR) imaging systems.
Ag-Ag2S/reduced graphene oxide hybrids used as long-wave UV radiation emitting nanocomposites
Li, Wenyao; Xu, Ruoyu; Ling, Min; He, Guanjie
2017-10-01
We report a facile thermal decomposition approach to synthesize Ag-Ag2S/reduced graphene oxide (Ag-Ag2S/rGO), the Ag-Ag2S nanoparticles uniformly dispersed on reduced graphene oxide with diameters of 10-20 nm. The photoluminescence spectra of Ag-Ag2S/rGO showed two obvious emission peaks at 327 and 339 nm with the excitation wavelength at 287 nm. Compared with Ag-Ag2S heterostructured clusters with two peaks at 407 and 430 nm, it showed a big blue shift and higher intensity, which makes it a novel candidate for long-wave UV radiation emitting nanocomposite.
Powell, F C; Spiegel, G T; Muller, S A
1984-08-01
Psoralen and long-wave ultraviolet light A (PUVA) was used to treat 12 patients with parapsoriasis and 19 patients with mycosis fungoides. Excellent results were obtained in all 12 patients with parapsoriasis: 8 patients had complete clearing, 3 had more than 80% improvement, and 1 had considerable improvement. The response to PUVA in patients with mycosis fungoides varied according to the stage of the disease. Of 10 patients with early disease (stage I or II), 7 had complete clearing and the 3 others had more than 80% improvement. The nine patients with more advanced disease generally did not respond well to PUVA, with the exception of one patient with stage IV disease and one with stage V disease. PUVA may be the treatment of choice for parapsoriasis and is highly effective in the early stages of mycosis fungoides.
2011-01-01
Abstract HIV was first described as a "long-wave event" in 1990, well before the advent of antiretroviral therapy (ART). The pandemic was then seen as involving three curves: an HIV curve, an AIDS curve and a curve representing societal impact. Since the mid-2000's, free public delivery of life-saving ART has begun shifting HIV from a terminal disease to a chronic illness for those who can access and tolerate the medications. This increasing chronicity prompts revisiting HIV as a long-wave ev...
Nonlinear wavetrains in viscous conduits
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.).
正则长波方程的一个新的差分方法%A NEW FINITE DIFFERENCE METHOD FOR REGULARIZED LONG-WAVE EQUATION
Institute of Scientific and Technical Information of China (English)
张鲁明; 常谦顺
2000-01-01
In this paper, a finite difference method for a initial-boundary valueproblem of regularized long-wave equation was considered. A energyconservative finite difference scheme of three levels was proposed.Convergence and stability of difference solution were proved. The schemeneedn't iterate, thus, requires less CPU time. Numerical experimentresults demonstrate that the method is efficient and reliable.
This paper presents a depth-averaged two-dimensional shallow water model for simulating long waves in vegetated water bodies under breaking and non-breaking conditions. The effects of rigid vegetation are modelled in the form of drag and inertia forces as sink terms in the momentum equations. The dr...
Indian Academy of Sciences (India)
M D Chipade; J R Kulkarni; S M Bawiskar
2014-12-01
Analyses of 60 years (1949–2008) of monthly energetics of the zonal waves derived from NCEP/NCAR data indicate that ultra-long waves (waves 1 and 2) dominate the spectrum of lower tropospheric zonal waves during monsoon season (June–September). Westerlies over the Indian subcontinent are a source of energy to wave 1. Two oceanic anticyclones, one over Pacific and the other over Atlantic are sources of energy to wave 2. These two waves are inversely correlated. Climatology of the energetics of ultralong waves for the two epochs 1949–1978 (CLP1) and 1979–2008 (CLP2) of 30 years indicates that the intensity of wave 1 has decreased by about 33% whereas the intensity of wave 2 has increased by about 27%. Northward transport of sensible heat during CLP1 changes to southward during CLP2. Larger generation of zonal mean Available Potential Energy (APE) during CLP2 indicates more heating. A larger conversion of kinetic energy (KE) of wave 1 into APE of wave 1 leads to weakening of wave 1 during CLP2. In case of wave 2, lower rate of conversion of KE to APE leads to stronger wave 2 during CLP2. slagging and heating values of the coal has been found in this study.
Energy Technology Data Exchange (ETDEWEB)
Zhukovsii, K.; Nourani, Y.; Monte, L. [ENEA, Centro Ricerche Casaccia, S. Maria di Galeria, RM (Italy). Dipt. Energia
1999-07-01
In the present paper, the net long-wave radiation balance of the water-air environmental systems is analysed on the base of several semi-empirical approaches. Various theoretical models of infrared atmospheric radiation are reviewed. Factors, affecting their behavior are considered. Special attention is paid to physical conditions under which those models are applicable. Atmospheric and net infrared radiation fluxes are computed and compared under clear and cloudy sky. Results are presented in graphical form. Conclusions are made on the applicability of models considered for evaluating infrared radiation fluxes in environmental conditions of Central Italy. On the base of present analysis Anderson's model is chosen for future calculations of heat budget of lakes in Central Italy. [Italian] Nel presente rapporto viene analizzato il bilancio della radiazione infrarossa per i sistemi acquatici sulla base di alcune formule semi-empiriche. Vengono esaminati vari modelli della radiazione infrarossa atmosferica e i fattori che la influenzano. I flussi di radiazione infrarossa dall'atmosfera in condizioni di cielo sereno e nuvoloso vengono calcolati e confrontati. L'analisi dell'applicabilita' dei modelli considerati per il calcolo dei flussi di radiazione infrarossa in corrispondenza delle condizioni ambientali dell'Italia centrale suggerisce di scegliere il modello di Anderson per la valutazione del bilancio calorico die laghi vulcanici.
Energy Technology Data Exchange (ETDEWEB)
Jolley, Greg; Dehdashti Akhavan, Nima; Umana-Membreno, Gilberto; Antoszewski, Jarek; Faraone, Lorenzo [School of Electrical, Electronic and Computer Engineering, University of Western Australia, Perth, Western Australia 6009 (Australia)
2013-11-21
An electron transfer quantum well infrared photodetector (QWIP) consisting of repeating units of two coupled quantum wells (QWs) is capable of exhibiting a two color voltage dependent spectral response. However, significant electron transfer between the coupled QWs is required for spectral tuning, which may require the application of relatively high electric fields. Also, the band structure of coupled quantum wells is more complicated in comparison to a regular quantum well and, therefore, it is not always obvious if an electron transfer QWIP can be designed such that it meets specific performance characteristics. This paper presents a feasibility study of the electron transfer QWIP and its suitability for spectral tuning. Self consistent calculations have been performed of the bandstructure and the electric field that results from electron population within the quantum wells, from which the optical characteristics have been obtained. The band structure, spectral response, and the resonant final state energy locations have been compared with standard QWIPs. It is shown that spectral tuning in the long-wave infrared band can be achieved over a wide wavelength range of several microns while maintaining a relatively narrow spectral response FWHM. However, the total absorption strength is more limited in comparison to a standard QWIP, since the higher QW doping densities require much higher electric fields for electron transfer.
Du, Jia-Ren; Chen, Nian-Ke; Li, Xian-Bin; Xie, Sheng-Yi; Tian, Wei Quan; Wang, Xian-Yin; Tu, Hai-Ling; Sun, Hong-Bo
2016-02-01
Long-wave infrared (8-12 μm) transmitting materials play critical roles in space science and electronic science. However, the paradox between their mechanical strength and infrared transmitting performance seriously prohibits their applications in harsh external environment. From the experimental view, searching a good window material compatible with both properties is a vast trail-and-error engineering project, which is not readily achieved efficiently. In this work, we propose a very simple and efficient method to explore potential infrared window materials with suitable mechanical property by first-principles gene-like searching. Two hundred and fifty-three potential materials are evaluated to find their bulk modulus (for mechanical performance) and phonon vibrational frequency (for optical performance). Seven new potential candidates are selected, namely TiSe, TiS, MgS, CdF2, HgF2, CdO, and SrO. Especially, the performances of TiS and CdF2 can be comparable to that of the most popular commercial ZnS at high temperature. Finally, we propose possible ranges of infrared transmission for halogen, chalcogen and nitrogen compounds respectively to guide further exploration. The present strategy to explore IR window materials can significantly speed up the new development progress. The same idea can be used for other material rapid searching towards special functions and applications.
Institute of Scientific and Technical Information of China (English)
Qi Haiming; Zhang Xiaohua; Chen Hongjun; Sun Dongchang; Sun Yongtai
2009-01-01
A global localization system of in-pipe robot is introduced in this paper. Global position system (GPS) is applied to monitor the motion of robot along the whole pipeline which is equally divided into many segments by tracking stations. The definite segment in which robot existing can be detected and this is long-range localization. Ultra-long wave (ULW) is adopted to solve the problem of metallic shielding and realize effective communication between inside and outside of pipeline. ULW emitter is carried by robot. When the plant is broken or defects on pipe-wall are inspected, the robot will stop moving. Antenna array is presented and disposed upon the definite segment to search the accurate location of robot, and this is short-range localization. In this paper, five-antenna array is adopted and an effective linear signal fusion algorithm is presented. The localization precision reaches R<25cm. By tests in Shengli oil field, the whole system is verified with robust solutions.
The Long-Wave Infrared Earth Image as a Pointing Reference for Deep-Space Optical Communications
Biswas, A.; Piazzolla, S.; Peterson, G.; Ortiz, G. G.; Hemmati, H.
2006-11-01
Optical communications from space require an absolute pointing reference. Whereas at near-Earth and even planetary distances out to Mars and Jupiter a laser beacon transmitted from Earth can serve as such a pointing reference, for farther distances extending to the outer reaches of the solar system, the means for meeting this requirement remains an open issue. We discuss in this article the prospects and consequences of utilizing the Earth image sensed in the long-wave infrared (LWIR) spectral band as a beacon to satisfy the absolute pointing requirements. We have used data from satellite-based thermal measurements of Earth to synthesize images at various ranges and have shown the centroiding accuracies that can be achieved with prospective LWIR image sensing arrays. The nonuniform emissivity of Earth causes a mispointing bias error term that exceeds a provisional pointing budget allocation when using simple centroiding algorithms. Other issues related to implementing thermal imaging of Earth from deep space for the purposes of providing a pointing reference are also reported.
Institute of Scientific and Technical Information of China (English)
YAN ZhenYa
2002-01-01
Searching for special solitary wave solutions with compact support is of important significance in soliton theory. In this paper, to understand the role of nonlinear dispersion in pattern formation, a family of the regularized longwave Boussincsq equations with fully nonlinear dispersion (simply called R(m, n) equations), utt + a( un )xx + b(um )xxtt = 0(a, b const.), is studied. New solitary wave solutions with compact support of R(m, n) equations are found. In addition we find another compacton solutions of the two special cases, R(2, 2) equation and R(3, 3) equation. It is found that the nonlinear dispersion term in a nonlinear evolution equation is not a necessary condition of that it possesses compacton solutions.
Institute of Scientific and Technical Information of China (English)
Xu Chang-Zhi; He Bao-Gang; Zhang Jie-Fang
2004-01-01
A variable separation approach is proposed and extended to the (1+1)-dimensional physical system. The variable separation solutions of (1+1)-dimensional equations of long-wave-short-wave resonant interaction are obtained. Some special type of solutions such as soliton solution, non-propagating solitary wave solution, propagating solitary wave solution, oscillating solitary wave solution are found by selecting the arbitrary function appropriately.
Cabib, Dario; Lavi, Moshe; Gil, Amir; Ohel, Eran; Dolev, Jacob; Milman, Uri
2013-10-01
Spectral imagers in the Long Wave IR spectral range (8 to 12 microns) suffer from the problem of high production costs because the existing commercial cooled array detectors are expensive, and in fact they are prohibitively expensive for many applications. As a result, the drive to lower the cost of Long Wave IR spectral imagers is strong: this is the main motivation for CI to investigate a new design that allows these spectral imagers to be more affordable. One area of possible cost reduction without relinquishing the advantages of a cryogenically cooled detector is the method used to provide the spectral information. CI Systems has developed a long wave IR (7.7 to 12.3 micron) spectral imager concept using a Circular Variable Filter (CVF), (a proprietary component based on multiple layer interference filter technology) which has advantages over the interferometric Fourier Transform method commonly used in this spectral range. The CVF method has its own development challenges; however, once proven, this concept may be more suitable and affordable for applications in which a spectral resolution of 0.5% of the wavelength (or 50 nm at 10 μ) is required. The design of the optical system must minimize background signals without being cooled to cryogenic temperatures, so we called it VIrtually COld (or VICO). CI is in the final stages of prototype building and characterization. Present initial calibration results and measurement examples are given in this paper.
A Boussinesq model with alleviated nonlinearity and dispersion
Institute of Scientific and Technical Information of China (English)
ZHANG Dian-xin; TAO Jian-hua
2008-01-01
The classical Boussinesq equation is a weakly nonlinear and weakly dispersive equation, which has been widely applied to simulate wave propagation in off-coast shallow waters. A new form of the Boussinesq model for an uneven bottoms is derived in this paper. In the new model, nonlinearity is reduced without increasing the order of the highest derivative in the differential equations. Dispersion relationship of the model is improved to the order of Pade (2,2) by adjusting a parameter in the model based on the long wave approximation. Analysis of the linear dispersion, linear shoaling and nonlinearity of the present model shows that the performances in terms of nonlinearity, dispersion and shoaling of this model are improved. Numerical results obtained with the present model are in agreement with experimental data.
Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes
DEFF Research Database (Denmark)
Zhang, H.W.; Schäffer, Hemming Andreas
2007-01-01
An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....
Bloembergen, Nicolaas
1996-01-01
Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe
Energy Technology Data Exchange (ETDEWEB)
Geniet, F; Leon, J [Physique Mathematique et Theorique, CNRS-UMR 5825, 34095 Montpellier (France)
2003-05-07
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.
Lawson, Stefanie Lyn
2000-10-01
This dissertation presents the calibration and analysis of the Clementine long-wave infrared (LWIR) camera images. The scientific payload on the Clementine spacecraft included a LWIR camera with a single passband centered at a wavelength of 8.75 μm. The Clementine orbit deviated by +/-30° from Sun synchronous, and for two lunar months, dayside nadir-looking images were obtained near local noon. During the systematic mapping phase of the Clementine mission, approximately 220,000 thermal-infrared images of the lunar surface were obtained. I have completed the calibration of the LWIR camera. Here I present the various steps involved in the calibration routine and the associated uncertainty analysis. The LWIR calibration routine can be outlined as follows: convert measured data number values to radiance via a calibration equation; subtract a zero-flux background image from each lunar image; divide by a flatfield frame; identify bad pixels; smooth over only bad pixels; adjust radiances to reflect the absolute calibration; and convert radiances to brightness temperatures via the Planck function. Observed LWIR radiances can be converted to brightness temperatures, which provide information on various physical properties of the lunar surface. I also present here the LWIR global data set. The LWIR data from noontime orbits demonstrate that the Lambertian temperature model of cos1/4 (i) is a fair approximation for nadir-looking temperatures, rather than the cos1/6(i) behavior observed for ground-based measurements of the full Moon. Deviations from the Lambertian model are likely due to surface roughness effects. In an effort to understand the influence of large-scale topography on remote lunar surface measurements, I constructed a model which calculates the correlation between reflectance and temperature for a macroscopically rough surface with varying albedo. In this dissertation, LWIR temperatures are directly compared to Clementine ultraviolet-visible (UVVIS) camera 750
Soliton solutions to a few fractional nonlinear evolution equations in shallow water wave dynamics
Mirzazadeh, Mohammad; Ekici, Mehmet; Sonmezoglu, Abdullah; Ortakaya, Sami; Eslami, Mostafa; Biswas, Anjan
2016-05-01
This paper studies a few nonlinear evolution equations that appear with fractional temporal evolution and fractional spatial derivatives. These are Benjamin-Bona-Mahoney equation, dispersive long wave equation and Nizhnik-Novikov-Veselov equation. The extended Jacobi's elliptic function expansion method is implemented to obtain soliton and other periodic singular solutions to these equations. In the limiting case, when the modulus of ellipticity approaches zero or unity, these doubly periodic functions approach solitary waves or shock waves or periodic singular solutions emerge.
Periodic wavetrains for systems of coupled nonlinear Schrödinger equations
Indian Academy of Sciences (India)
Kwok W Chow; Derek W C Lal
2001-11-01
Exact, periodic wavetrains for systems of coupled nonlinear Schrödinger equations are obtained by the Hirota bilinear method and theta functions identities. Both the bright and dark soliton regimes are treated, and the solutions involve products of elliptic functions. The validity of these solutions is veriﬁed independently by a computer algebra software. The long wave limit is studied. Physical implications will be assessed.
Quasi-periodic and Non-periodic Waves in (2+1)-Dimensional Nonlinear Systems
Institute of Scientific and Technical Information of China (English)
TANG Xiao-Yan; LOU Sen-Yue
2005-01-01
New exact quasi-periodic and non-periodic solutions for the (2 + 1)-dimensional nonlinear systems are studied by means of the multi-linear variable separation approach (MLVSA) and the Jacobi elliptic functions with the space-time-dependent modulus. Though the result is valid for all the MLVSA solvable models, it is explicitly shown for the long-wave and short-wave interaction model.
2016-07-01
Advanced Research Projects Agency (DARPA) Dynamics-Enabled Frequency Sources (DEFYS) program is focused on the convergence of nonlinear dynamics and...Early work in this program has shown that nonlinear dynamics can provide performance advantages. However, the pathway from initial results to...dependent nonlinear stiffness observed in these devices. This work is ongoing, and will continue through the final period of this program . Reference 9
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
Nanda, Sudarsan
2013-01-01
"Nonlinear analysis" presents recent developments in calculus in Banach space, convex sets, convex functions, best approximation, fixed point theorems, nonlinear operators, variational inequality, complementary problem and semi-inner-product spaces. Nonlinear Analysis has become important and useful in the present days because many real world problems are nonlinear, nonconvex and nonsmooth in nature. Although basic concepts have been presented here but many results presented have not appeared in any book till now. The book could be used as a text for graduate students and also it will be useful for researchers working in this field.
Nonlinear wave-wave interactions and wedge waves
Institute of Scientific and Technical Information of China (English)
Ray Q.Lin; Will Perrie
2005-01-01
A tetrad mechanism for exciting long waves,for example edge waves,is described based on nonlinear resonant wave-wave interactions.In this mechanism,resonant interactions pass energy to an edge wave,from the three participating gravity waves.The estimated action flux into the edge wave can be orders of magnitude greater than the transfer fluxes derived from other competing mechanisms,such as triad interactions.Moreover,the numerical results show that the actual transfer rates into the edge wave from the three participating gravity waves are two-to three- orders of magnitude greater than bottom friction.
Sarkar, Jayati; Sharma, Ashutosh
2010-06-01
A general unified theory of field (van der Waals, electric, etc.)-induced surface instabilities in thin viscoelastic films that accounts for a destabilizing field and stabilizing effects of elastic strain and surface energy is presented. The present theory seamlessly covers the instability and its different regimes in films ranging from elastic to viscous, from adhesive (confined) to wetting (free surface), and from short- to long-wave instabilities. The critical conditions for the onset of instability are found to be strongly dependent on elastic properties such as the shear modulus of the film, but the dominant wavelength is strikingly independent of the film rheology. Different regimes based on a nondimensional parameter (gamma/mu h) are uncovered, where gamma is the surface energy, mu is the elastic shear modulus, and h is the film thickness. A short-wave, elasticlike response with wavelength lambda approximately = 2.96 h is obtained for gamma/mu h 1. Owing to their small critical thickness, wetting films destabilized by intermolecular forces always display long-wave instability regardless of their viscoelasticity. Furthermore, our numerical simulations based on energy minimization for unstable wetting elastic films show the formation of islands for ultrathin films and a morphological phase transition to holes embedded in the film for relatively thicker films. Unlike viscous films, however, unstable elastic films do not display a unique dominant wavelength but a bimodal distribution of wavelengths.
Yin, Yanchun; Chew, Andrew; Ren, Xiaoming; Li, Jie; Wang, Yang; Wu, Yi; Chang, Zenghu
2017-04-01
We present an approach for both efficient generation and amplification of 4-12 μm pulses by tailoring the phase matching of the nonlinear crystal Zinc Germanium Phosphide (ZGP) in a narrowband-pumped optical parametric chirped pulse amplifier (OPCPA) and a broadband-pumped dual-chirped optical parametric amplifier (DC-OPA), respectively. Preliminary experimental results are obtained for generating 1.8-4.2 μm super broadband spectra, which can be used to seed both the signal of the OPCPA and the pump of the DC-OPA. The theoretical pump-to-idler conversion efficiency reaches 27% in the DC-OPA pumped by a chirped broadband Cr2+:ZnSe/ZnS laser, enabling the generation of Terawatt-level 4-12 μm pulses with an available large-aperture ZGP. Furthermore, the 4-12 μm idler pulses can be compressed to sub-cycle pulses by compensating the tailored positive chirp of the idler pulses using the bulk compressor NaCl, and by indirectly controlling the higher-order idler phase through tuning the signal (2.4-4.0 μm) phase with a commercially available acousto-optic programmable dispersive filter (AOPDF). A similar approach is also described for generating high-energy 4-12 μm sub-cycle pulses via OPCPA pumped by a 2 μm Ho:YLF laser.
Soliton solution for nonlinear partial differential equations by cosine-function method
Energy Technology Data Exchange (ETDEWEB)
Ali, A.H.A. [Mathematics Department, Faculty of Science, Menoufia University, Shebein El-Koom (Egypt); Soliman, A.A. [Department of Mathematics, Faculty of Education (AL-Arish), Suez Canal University, AL-Arish 45111 (Egypt)], E-mail: asoliman_99@yahoo.com; Raslan, K.R. [Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo (Egypt)
2007-08-20
In this Letter, we established a traveling wave solution by using Cosine-function algorithm for nonlinear partial differential equations. The method is used to obtain the exact solutions for five different types of nonlinear partial differential equations such as, general equal width wave equation (GEWE), general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKdV), general improved Korteweg-de Vries equation (GIKdV), and Coupled equal width wave equations (CEWE), which are the important soliton equations.
Rogue waves: from nonlinear Schrödinger breather solutions to sea-keeping test.
Onorato, Miguel; Proment, Davide; Clauss, Günther; Klein, Marco
2013-01-01
Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during extreme ocean conditions using such breather solutions. In particular, we discuss a state of the art sea-keeping test in a 90-meter long wave tank by creating a Peregrine breather solution hitting a scaled chemical tanker and we discuss its potential devastating effects on the ship.
The effects of oppositely sloping boundaries with Ekman dissipation in a nonlinear baroclinic system
Weng, H.-Y.
1990-01-01
The present analytical and numerical examination of the effect of the slope Delta with dissipation delta on baroclinic flows in linear and nonlinear systems uses a modified Eady channel model with oppositely sloping top and bottom Ekman layers, and truncates the spectral wave solution up to six components. Comparisons are made wherever possible with results from beta-plane dissipative systems. In the linear system, the combined effect of Delta and delta strongly stabilizes long waves. In a nonlinear system without wave-wave interaction, Delta stabilizes the flow even for small delta and reduces the domain of vacillation while enlarging the domain of single-wave steady state.
Zhu, Hong-Ming; Pen, Ue-Li; Chen, Xuelei; Yu, Hao-Ran
2016-01-01
We present a direct approach to non-parametrically reconstruct the linear density field from an observed non-linear map. We solve for the unique displacement potential consistent with the non-linear density and positive definite coordinate transformation using a multigrid algorithm. We show that we recover the linear initial conditions up to $k\\sim 1\\ h/\\mathrm{Mpc}$ with minimal computational cost. This reconstruction approach generalizes the linear displacement theory to fully non-linear fields, potentially substantially expanding the BAO and RSD information content of dense large scale structure surveys, including for example SDSS main sample and 21cm intensity mapping.
Boyd, Robert W
2013-01-01
Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q
Directory of Open Access Journals (Sweden)
Whiteside Alan
2011-10-01
Full Text Available Abstract HIV was first described as a "long-wave event" in 1990, well before the advent of antiretroviral therapy (ART. The pandemic was then seen as involving three curves: an HIV curve, an AIDS curve and a curve representing societal impact. Since the mid-2000's, free public delivery of life-saving ART has begun shifting HIV from a terminal disease to a chronic illness for those who can access and tolerate the medications. This increasing chronicity prompts revisiting HIV as a long-wave event. First, with widespread availability of ART, the HIV curve will be higher and last longer. Moreover, if patterns in sub-Saharan Africa mirror experiences in the North, people on ART will live far longer lives but with new experiences of disability. Disability, broadly defined, can result from HIV, its related conditions, and from side effects of medications. Individual experiences of disability will vary. At a population level, however, we anticipate that experiences of disability will become a common part of living with HIV and, furthermore, may be understood as a variation of the second curve. In the original conceptualization, the second curve represented the transition to AIDS; in the era of treatment, we can expect a transition from HIV infection to HIV-related disability for people on ART. Many such individuals may eventually develop AIDS as well, but after a potentially long life that includes fluctuating episodes of illness, wellness and disability. This shift toward chronicity has implications for health and social service delivery, and requires a parallel shift in thinking regarding HIV-related disability. A model providing guidance on such a broader understanding of disability is the World Health Organization's International Classification of Functioning, Disability and Health (ICF. In contrast to a biomedical approach concerned primarily with diagnoses, the ICF includes attention to the impact of these diagnoses on people's lives and
Nixon, Stephanie A; Hanass-Hancock, Jill; Whiteside, Alan; Barnett, Tony
2011-10-20
HIV was first described as a "long-wave event" in 1990, well before the advent of antiretroviral therapy (ART). The pandemic was then seen as involving three curves: an HIV curve, an AIDS curve and a curve representing societal impact. Since the mid-2000's, free public delivery of life-saving ART has begun shifting HIV from a terminal disease to a chronic illness for those who can access and tolerate the medications. This increasing chronicity prompts revisiting HIV as a long-wave event. First, with widespread availability of ART, the HIV curve will be higher and last longer. Moreover, if patterns in sub-Saharan Africa mirror experiences in the North, people on ART will live far longer lives but with new experiences of disability. Disability, broadly defined, can result from HIV, its related conditions, and from side effects of medications. Individual experiences of disability will vary. At a population level, however, we anticipate that experiences of disability will become a common part of living with HIV and, furthermore, may be understood as a variation of the second curve. In the original conceptualization, the second curve represented the transition to AIDS; in the era of treatment, we can expect a transition from HIV infection to HIV-related disability for people on ART. Many such individuals may eventually develop AIDS as well, but after a potentially long life that includes fluctuating episodes of illness, wellness and disability. This shift toward chronicity has implications for health and social service delivery, and requires a parallel shift in thinking regarding HIV-related disability. A model providing guidance on such a broader understanding of disability is the World Health Organization's International Classification of Functioning, Disability and Health (ICF). In contrast to a biomedical approach concerned primarily with diagnoses, the ICF includes attention to the impact of these diagnoses on people's lives and livelihoods. The ICF also focuses on
Ruszczynski, Andrzej
2011-01-01
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates t
Fang, Zheng; Yi, Xinjian; Liu, Xiangyan; Zhang, Wei; Zhang, Tianxu
2013-08-01
We present a new optical system for infrared (IR) image-spectrum integration remote sensing. The purpose to develop this instrument is to find the key spectral characteristics of typical hot target and to explore a new intelligence fusion method for the recognition. When mounted on a two-dimensional rotation stage, it can track the suspected target by image processing, and then get its spectrum to do recognition. It is a dual-band system with long-wave infrared (LWIR) imaging and mid-wave infrared (MWIR) spectrum. An IR dichroic beamsplitter is used to divide wideband incident infrared into LWIR and MWIR. Compared to traditional infrared combined imaging and spectral-analysis instruments, it yields higher sensitivity for measuring the IR spectrum. The sensors for imaging and spectrum detection are separate, so high spatial resolution, frame rate, and spectrum resolution can all be obtained simultaneously.
Vandenrijt, Jean-François; Thizy, Cédric; Beaumont, Florent; Garcia, José; Martin, Laurent; Fabron, Christophe; Prieto, Eric; Maciaszek, Thierry; Georges, Marc P.
2015-08-01
We present digital holographic interferometry (DHI) in the long-wave infrared for monitoring the deformation under cryogenic conditions of a segmented focal plane array to be used in a space mission. The long wavelength was chosen for its ability to allow measurement of displacements 20 times larger than DHI in the visible and which were foreseen with the test object under such temperature changes. The specimen consists of 4x4 mosaic of detectors assembled on a frame. It was required to assess the global deformation of the ensemble, the deformation of each detector, and piston movements of each of them with respect to their neighbors. For that reason we incorporated the temporal phase unwrapping by capturing a sufficiently high number of holograms between which the phase does not suffer strong variations. At last since the specimen exhibit specular reflectivity at that wavelength, it is illuminated through a reflective diffuser.
Directory of Open Access Journals (Sweden)
Minqi Li
2015-08-01
Full Text Available In this paper we study the long-term movement of the profit rate and related variables in the UK, the US, Japan, and the Euro-zone. Since the mid-19th century there have been four long waves in the movement of the average profit rate and rate of accumulation. The average profit rate tended to fall between the late 19th century and the late 20th / early 21st century. The average profit share fell substantially in the transition from the UK hegemony to the US hegemony. The fall of the profit rateand profit share reflected rising wage and taxation costs. Our findings raise important questions regarding the future development of the capitalist world economy.
Directory of Open Access Journals (Sweden)
S. A. Kvitka
2014-02-01
An important part of the sustainable development of a country at present there is compliance governance development needs of economy (business and modern information society (civil society. Such trends can be noted in the modern history of Ukraine. Inconsistency actions of state institutions to the needs and expectations of the majority of the active population led to a mass protest movement . With the global information society, given the central role of Ukraine in the global balance of power between the main actors of the country, today , this has direct international intervention in the sequence out of the crisis in Ukraine . Meanwhile, since, according to periodization modern «long waves « in the world of instability phase ( prior to the structural crisis has only just begin, and subject to compliance with the requirements of Ukrainian state policy information society in Ukraine may avoid a catastrophic scenario.
Instability of coupled geostrophic density fronts and its nonlinear evolution
Scherer, Emilie; Zeitlin, Vladimir
Instability of coupled density fronts, and its fully nonlinear evolution are studied within the idealized reduced-gravity rotating shallow-water model. By using the collocation method, we benchmark the classical stability results on zero potential vorticity (PV) fronts and generalize them to non-zero PV fronts. In both cases, we find a series of instability zones intertwined with the stability regions along the along-front wavenumber axis, the most unstable modes being long wave. We then study the nonlinear evolution of the unstable modes with the help of a high-resolution well-balanced finite-volume numerical scheme by initializing it with the unstable modes found from the linear stability analysis. The most unstable long-wave mode evolves as follows: after a couple of inertial periods, the coupled fronts are pinched at some location and a series of weakly connected co-rotating elliptic anticyclonic vortices is formed, thus totally changing the character of the flow. The characteristics of these vortices are close to known rodon lens solutions. The shorter-wave unstable modes from the next instability zones are strongly concentrated in the frontal regions, have sharp gradients, and are saturated owing to dissipation without qualitatively changing the flow pattern.
In, Visarath; Longhini, Patrick; Kho, Andy; Neff, Joseph D.; Leung, Daniel; Liu, Norman; Meadows, Brian K.; Gordon, Frank; Bulsara, Adi R.; Palacios, Antonio
2012-12-01
The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz.
Energy Technology Data Exchange (ETDEWEB)
Turchetti, G. (Bologna Univ. (Italy). Dipt. di Fisica)
1989-01-01
Research in nonlinear dynamics is rapidly expanding and its range of applications is extending beyond the traditional areas of science where it was first developed. Indeed while linear analysis and modelling, which has been very successful in mathematical physics and engineering, has become a mature science, many elementary phenomena of intrinsic nonlinear nature were recently experimentally detected and investigated, suggesting new theoretical work. Complex systems, as turbulent fluids, were known to be governed by intrinsically nonlinear laws since a long time ago, but received purely phenomenological descriptions. The pioneering works of Boltzmann and Poincare, probably because of their intrinsic difficulty, did not have a revolutionary impact at their time; it is only very recently that their message is reaching a significant number of mathematicians and physicists. Certainly the development of computers and computer graphics played an important role in developing geometric intuition of complex phenomena through simple numerical experiments, while a new mathematical framework to understand them was being developed.
Seider, Warren D.; Ungar, Lyle H.
1987-01-01
Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…
Institute of Scientific and Technical Information of China (English)
张令元; 张金良; 王明亮
2006-01-01
By using the homogeneous balance principle(HBP), we derive a B(a)cklund transformation(BT) to the generalized dispersive long wave equation with variable coefficients.Based on the BT, we give many kinds of the exact solutions of the equation, such as, single solitary solutions, multi-soliton solutions and generalized exact solutions.
Bressan, L.; Tinti, S.
2016-01-01
This study presents a new method to analyse the properties of the sea-level signal recorded by coastal tide gauges in the long wave range that is in a window between wind/storm waves and tides and is typical of several phenomena like local seiches, coastal shelf resonances and tsunamis. The method consists of computing four specific functions based on the time gradient (slope) of the recorded sea level oscillations, namely the instantaneous slope (IS) as well as three more functions based on IS, namely the reconstructed sea level (RSL), the background slope (BS) and the control function (CF). These functions are examined through a traditional spectral fast Fourier transform (FFT) analysis and also through a statistical analysis, showing that they can be characterised by probability distribution functions PDFs such as the Student's t distribution (IS and RSL) and the beta distribution (CF). As an example, the method has been applied to data from the tide-gauge station of Siracusa, Italy.
Institute of Scientific and Technical Information of China (English)
Noarayanan Lakshmanan; Murali Kantharaj; Vallam Sundar
2012-01-01
Extreme coastal events require careful prediction of wave forces.Recent tsunamis have resulted in extensive damage of coastal structures.Such scenarios are the result of the action of long waves on structures.In this paper,the efficiency of vegetation as a buffer system in attenuating the incident ocean waves was studied through a well controlled experimental program.The study focused on the measurement of forces resulting from cnoidal waves on a model building mounted over a slope in the presence and absence of vegetation.The vegetative parameters,along with the width of the green belt,its position from the reference line,the diameter of the individual stems as well as the spacing between them,and their rigidity are varied so as to obtain a holistic view of the wave-vegetation interaction problem.The effect of vegetation on variations of dimensional forces with a Keulegan-Carpenter number (KC) was discussed in this paper.It has been shown that when vegetal patches are present in front of structure,the forces could be limited to within F*≤1,by a percentile of 92％,90％,55％,and 96％,respectively for gap ratios of 0.0,0.5,1.0,and 1.5.The force is at its maximum for the gap ratio of 1.0 and beyond which the forces start to diminish.
Bonelli, Giulio; Tanzini, Alessandro; Vasko, Petr
2014-01-01
We show that the exact partition function of U(N) six-dimensional gauge theory with eight supercharges on C^2 x S^2 provides the quantization of the integrable system of hydrodynamic type known as gl(N) periodic Intermediate Long Wave (ILW). We characterize this system as the hydrodynamic limit of elliptic Calogero-Moser integrable system. We compute the Bethe equations from the effective gauged linear sigma model on S^2 with target space the ADHM instanton moduli space, whose mirror computes the Yang-Yang function of gl(N) ILW. The quantum Hamiltonians are given by the local chiral ring observables of the six-dimensional gauge theory. As particular cases, these provide the gl(N) Benjamin-Ono and Korteweg-de Vries quantum Hamiltonians. In the four dimensional limit, we identify the local chiral ring observables with the conserved charges of Heisenberg plus W_N algebrae, thus providing a gauge theoretical proof of AGT correspondence.
Yang, Clayton S-C; Jin, Feng; Trivedi, Sudhir; Brown, Eiei; Hommerich, Uwe; Khurgin, Jacob B; Samuels, Alan C
2016-11-10
A mercury-cadmium-telluride linear array detection system that is capable of rapidly capturing (∼1-5 s) a broad spectrum of atomic and molecular laser-induced breakdown spectroscopy (LIBS) emissions in the long-wave infrared region (LWIR, ∼5.6-10 μm) was recently developed. Similar to the conventional ultraviolet-visible LIBS, a broadband emission spectrum of condensed phase samples covering a 5.6-10 μm spectral region could be acquired from just a single laser-induced micro-plasma. Intense and distinct atomic and molecular LWIR emission signatures of various solid inorganic energetic materials were readily observed and identified. Time resolved emissions of inorganic energetic materials were studied to assess the lifetimes of LWIR atomic and molecular emissions. The LWIR atomic emissions generally decayed fast on the scale of tens of microseconds, while the molecular signature emissions from target molecules excited by the laser-induced plasma appeared to be very long lived (∼millisecond). The time dependence of emission intensities and peak wavelengths of these signature emissions gave an insight into the origin and the environment of the emitting target species. Moreover, observed lifetimes of these LWIR emissions can be utilized for further optimization of the signal quality and detection limits of this technique.
Yang, Clayton S-C; Brown, Eiei; Kumi-Barimah, Eric; Hommerich, Uwe; Jin, Feng; Jia, Yingqing; Trivedi, Sudhir; D'souza, Arvind I; Decuir, Eric A; Wijewarnasuriya, Priyalal S; Samuels, Alan C
2015-11-20
In this work, we develop a mercury-cadmium-telluride linear array detection system that is capable of rapidly capturing (∼1-5 s) a broad spectrum of atomic and molecular laser-induced breakdown spectroscopy (LIBS) emissions in the long-wave infrared (LWIR) region (∼5.6-10 μm). Similar to the conventional UV-Vis LIBS, a broadband emission spectrum of condensed phase samples covering the whole 5.6-10 μm region can be acquired from just a single laser-induced microplasma or averaging a few single laser-induced microplasmas. Atomic and molecular signature emission spectra of solid inorganic and organic tablets and thin liquid films deposited on a rough asphalt surface are observed. This setup is capable of rapidly probing samples "as is" without the need of elaborate sample preparation and also offers the possibility of a simultaneous UV-Vis and LWIR LIBS measurement.
2015-01-01
From the Back Cover: The emphasis throughout the present volume is on the practical application of theoretical mathematical models helping to unravel the underlying mechanisms involved in processes from mathematical physics and biosciences. It has been conceived as a unique collection of abstract methods dealing especially with nonlinear partial differential equations (either stationary or evolutionary) that are applied to understand concrete processes involving some important applications re...
Wang, Nan; Wu, Jianghui; Meng, Hemin; Gao, Jiaobo; Fan, Zhe; Zhang, Mingxuan; Li, Yu; Li, Jianjun
2015-10-01
Interference imaging spectroscopy is the advanced subject among the infrared remote sensing, and it has become an important technique to detect spatial information and spectral information of targets. It has the advantages of high flux, high spectral resolution and high spatial resolution that can be used for detecting more details of the spectral and spatial information. Based on a Michelson interferometer with its mirrors replaced by corner-cubes, principles of a hand-held, static, long-wave infrared Fourier Transform(FT) imaging spectrometer using an uncooled microbolometer array are introduced. Because in such FT-based spectral imager, the interferogram is acquired over the whole field of the camera while the scene of interest scans the path difference range, vignetting should be strongly limited while keep the size of the interferometer as small as possible. Interferometer size is given and interferential light path is verified through TracePro software. First results of field and laboratory measurements using the spectral imager are presented. Remotely obtained spectrums collected with this instrument and with those of high precise Michelson spectrometer are compared, and the measured values turned out to be closely corresponded. The results, in turn, verified the feasibility of the systematic working mode. The resulting system tested here provides datacubes of up to 640×480 pixels over the 7.7~13μm spectral range, this wavelength range reveals important information about scenes such as gas or landmine detection, and the instrument has a spectral resolution of about 8cm-1 that fulfils the requirement for most targeted applications. Examples of sky and buildings detection are shown.
Indian Academy of Sciences (India)
R Sapra; S K Dhaka; V Panwar; R Bhatnagar; K Praveen Kumar; Y Shibagaki; M Venkat Ratnam; M Takahashi
2011-10-01
Relationship of outgoing long-wave radiation (OLR) with convective available potential energy (CAPE) and temperature at the 100-hPa pressure level is examined using daily radiosonde data for a period 1980–2006 over Delhi (28.3° N, 77.1°E) and Kolkata (22.3°N, 88.2°E), and during 1989–2005 over Cochin (10°N, 77°E) and Trivandrum (8.5°N, 77.0°E), India. Correlation coefficient (xy) between monthly OLR and CAPE shows a significant (∼ −0.45) anti-correlation at Delhi and Kolkata suggesting low OLR associated with high convective activity during summer (seasonal variation). Though, no significant correlation was found between OLR and CAPE at Cochin and Trivandrum (low latitude region); analysis of OLR and temperature (at 100-hPa) association suggests that low OLR peaks appear corresponding to low temperature at Delhi (xy ∼ 0.30) and Kolkata (xy ∼ 0.25) during summer. However, xy between OLR and temperature becomes opposite as we move towards low latitudes (∼8° – 10°N) due to strong solar cycle influence. Large scale components mainly ENSO and quasi-biennial oscillaton (QBO) that contributed to the 100-hPa temperature variability were also analyzed, which showed that ENSO variance is larger by a factor of two in comparison to QBO over Indian region. ENSO warm conditions cause warming at 100-hPa over Delhi and Darwin. However, due to strong QBO and solar signals in the equatorial region, ENSO signal seems less effective. QBO, ENSO, and solar cycle contribution in temperature are found location-dependent (latitudinal variability) responding in consonance with shifting in convective activity regime during El Niño, seasonal variability in the tropical easterly jet, and the solar irradiance.
Bagatin, E; Miot, H A; Soares, J L M; Sanudo, A; Afonso, J P J M; de Barros Junior, N; Talarico, S
2013-10-01
Cellulite refers to changes in skin relief on the thighs and buttocks of women, with a prevalence of 80-90%, causing dissatisfaction and search for treatment. Etiopathogenesis is multifactorial, as follows: herniation of the hypodermis towards the dermis, facilitated by perpendicular fibrous septa, changes in the dermal extracellular matrix, decreased adiponectin, genetic polymorphism, microcirculation alterations and inflammatory process. There are numerous therapeutic approaches, with little evidence of effectiveness. The long-wave infrared (LWIR) radiation interacts with water, improves microcirculation and stimulates metabolic processes. To date, the use of tissues with potential reflection of LWIR radiation has not been systematically investigated as adjuvant treatment for cellulite. To investigate the efficacy and safety of the treatment of cellulite through the use of compression stockings made with thread reflecting LWIR radiation. Clinical study of therapeutic intervention, controlled and double-blind, including 30 women, aging from 25 to 40 years, with cellulite of grades II and III on the thighs and buttocks who used compression stockings, "pantyhose" model, made with reflector thread of LWIR radiation, on only one randomized side. Women under other treatments for cellulite and with venous and/or blood insufficiencies were excluded. Evaluation of efficacy by clinical parameters, photographs, Dermatology Life Quality Index (DLQI), cutometry and high frequency ultrasonography and security by observation of adverse events and venous EcoDoppler recordings. DLQI scores showed significant reduction; the two-dimensional high-frequency ultrasonography showed an insignificant increase in dermal echogenicity as well as other efficacy parameters demonstrated no or slight improvement, with no differences between the sides exposed or not to LWIR; and there were no severe adverse events. Compression stockings, with or without thread reflector of LWIR, showed slight
Weakly Nonlinear Stability Analysis of a Thin Magnetic Fluid during Spin Coating
Directory of Open Access Journals (Sweden)
Cha'o-Kuang Chen
2010-01-01
Full Text Available This paper investigates the stability of a thin electrically conductive fluid under an applied uniform magnetic filed during spin coating. A generalized nonlinear kinematic model is derived by the long-wave perturbation method to represent the physical system. After linearizing the nonlinear evolution equation, the method of normal mode is applied to study the linear stability. Weakly nonlinear dynamics of film flow is studied by the multiple scales method. The Ginzburg-Landau equation is determined to discuss the necessary conditions of the various critical flow states, namely, subcritical stability, subcritical instability, supercritical stability, and supercritical explosion. The study reveals that the rotation number and the radius of the rotating circular disk generate similar destabilizing effects but the Hartmann number gives a stabilizing effect. Moreover, the optimum conditions can be found to alter stability of the film flow by controlling the applied magnetic field.
Directory of Open Access Journals (Sweden)
Emad A.-B. Abdel-Salam
2013-01-01
Full Text Available The fractional Riccati expansion method is proposed to solve fractional differential equations. To illustrate the effectiveness of the method, space-time fractional Korteweg-de Vries equation, regularized long-wave equation, Boussinesq equation, and Klein-Gordon equation are considered. As a result, abundant types of exact analytical solutions are obtained. These solutions include generalized trigonometric and hyperbolic functions solutions which may be useful for further understanding of the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time. The periodic and kink solutions are founded as special case.
Strongly nonlinear models for internal waves: an application for the dam-break problem
Chen, Shengqian
2016-01-01
Strongly nonlinear models of internal wave propagation for incompressible stratified Euler fluids are investigated numerically and analytically to determine the evolution of a class of initial conditions of interest in laboratory experiments. This class of step-like initial data severely tests the robustness of the models beyond their strict long-wave asymptotic validity, and model fidelity is assessed by direct numerical simulations (DNS) of the parent Euler system. It is found that the primary dynamics of near-solitary wave formation is remarkably well predicted by the models for both wave and fluid properties, at a fraction of the computational costs of the DNS code.
Nonlinear waves in a fluid-filled thin viscoelastic tube
Zhang, Shan-Yuan; Zhang, Tao
2010-11-01
In the present paper the propagation property of nonlinear waves in a thin viscoelastic tube filled with incompressible inviscid fluid is studied. The tube is considered to be made of an incompressible isotropic viscoelastic material described by Kelvin—Voigt model. Using the mass conservation and the momentum theorem of the fluid and radial dynamic equilibrium of an element of the tube wall, a set of nonlinear partial differential equations governing the propagation of nonlinear pressure wave in the solid—liquid coupled system is obtained. In the long-wave approximation the nonlinear far-field equations can be derived employing the reductive perturbation technique (RPT). Selecting the exponent α of the perturbation parameter in Gardner—Morikawa transformation according to the order of viscous coefficient η, three kinds of evolution equations with soliton solution, i.e. Korteweg—de Vries (KdV)—Burgers, KdV and Burgers equations are deduced. By means of the method of traveling-wave solution and numerical calculation, the propagation properties of solitary waves corresponding with these evolution equations are analysed in detail. Finally, as a example of practical application, the propagation of pressure pulses in large blood vessels is discussed.
Nonlinear waves in a fluid-filled thin viscoelastic tube
Institute of Scientific and Technical Information of China (English)
Zhang Shan-Yuan; Zhang Tao
2010-01-01
In the present paper the propagation property of nonlinear waves in a thin viscoelastic tube filled with incom-pressible inviscid fluid is studied. The tube is considered to be made of an incompressible isotropic viscoelastic material described by Kelvin-Voigt model. Using the mass conservation and the momentum theorem of the fluid and radial dynamic equilibrium of an element of the tube wall, a set of nonlinear partial differential equations governing the prop-agation of nonlinear pressure wave in the solid-liquid coupled system is obtained. In the long-wave approximation the nonlinear far-field equations can be derived employing the reductive perturbation technique (RPT). Selecting the expo-η, three kinds of evolution equations with soliton solution, i.e. Korteweg-de Vries (KdV)-Burgers, KdV and Burgers equations are deduced. By means of the method of traveling-wave solution and numerical calculation, the propagation properties of solitary waves corresponding with these evolution equations are analysed in detail. Finally, as a example of practical application, the propagation of pressure pulses in large blood vessels is discussed.
Ajaev; Davis
2000-02-01
Directional solidification of a dilute binary alloy in a Hele-Shaw cell is modeled by a long-wave nonlinear evolution equation with zero flux and contact-angle conditions at the walls. The basic steady-state solution and its linear stability criteria are found analytically, and the nonlinear system is solved numerically. Concave-down (toward the solid) interfaces under physically realistic conditions are found to be more unstable than the planar front. Weakly nonlinear analysis indicates that subcritical bifurcation is promoted, the domain of modulational instability is expanded and transition to three-dimensional patterns is delayed due to the contact-angle condition. In the strongly nonlinear regime fully three-dimensional steady-state solutions are found whose characteristic amplitude is larger than that for the two-dimensional problem. In the subcritical regime secondary bifurcation to stable solutions is promoted.
Rajasekar, Shanmuganathan
2016-01-01
This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques invo...
Institute of Scientific and Technical Information of China (English)
1996-01-01
3.1 A Unified Nonlinear Feedback Functional Method for Study Both Control and Synchronization of Spatiotemporal Chaos Fang Jinqing Ali M. K. (Department of Physics, The University of Lethbridge,Lethbridge, Alberta T1K 3M4,Canada) Two fundamental questions dominate future chaos control theories.The first is the problem of controlling hyperchaos in higher dimensional systems.The second question has yet to be addressed:the problem of controlling spatiotemporal chaos in a spatiotemporal system.In recent years, control and synchronization of spatiotemporal chaos and hyperchaos have became a much more important and challenging subject. The reason for this is the control and synchronism of such behaviours have extensive and great potential of interdisciplinary applications, such as security communication, information processing, medicine and so on. However, this subject is not much known and remains an outstanding open.
Nonlinear Materials Characterization Facility
Federal Laboratory Consortium — The Nonlinear Materials Characterization Facility conducts photophysical research and development of nonlinear materials operating in the visible spectrum to protect...
Nonlinear singular vectors and nonlinear singular values
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A novel concept of nonlinear singular vector and nonlinear singular value is introduced, which is a natural generalization of the classical linear singular vector and linear singular value to the nonlinear category. The optimization problem related to the determination of nonlinear singular vectors and singular values is formulated. The general idea of this approach is demonstrated by a simple two-dimensional quasigeostrophic model in the atmospheric and oceanic sciences. The advantage and its applications of the new method to the predictability, ensemble forecast and finite-time nonlinear instability are discussed. This paper makes a necessary preparation for further theoretical and numerical investigations.
Variational modelling of nonlinear water waves
Kalogirou, Anna; Bokhove, Onno
2015-11-01
Mathematical modelling of water waves is demonstrated by investigating variational methods. A potential flow water wave model is derived using variational techniques and extented to include explicit time-dependence, leading to non-autonomous dynamics. As a first example, we consider the problem of a soliton splash in a long wave channel with a contraction at its end, resulting after a sluice gate is removed at a finite time. The removal of the sluice gate is included in the variational principle through a time-dependent gravitational potential. A second example involving non-autonomous dynamics concerns the motion of a free surface in a vertical Hele-Shaw cell. Explicit time-dependence now enters the model through a linear damping term due to the effect of wall friction and a term representing the motion of an artificially driven wave pump. In both cases, the model is solved numerically using a Galerkin FEM and the numerical results are compared to wave structures observed in experiments. The water wave model is also adapted to accommodate nonlinear ship dynamics. The novelty is this case is the coupling between the water wave dynamics, the ship dynamics and water line dynamics on the ship. For simplicity, we consider a simple ship structure consisting of V-shaped cross-sections.
Weakly nonlinear simulation of planar stratified flows
Energy Technology Data Exchange (ETDEWEB)
King, Michael R. [Department of Chemical Engineering, University of Notre Dame, Notre Dame, Indiana 46556 (United States); McCready, Mark J. [Department of Chemical Engineering, University of Notre Dame, Notre Dame, Indiana 46556 (United States)
2000-01-01
The interfacial behavior of two-fluid, planar flows is studied by numerical integration of weakly-nonlinear amplitude equations derived via eigenfunction expansion of the governing equations. This study extends the range of classic Stuart-Landau theories by the inclusion of a spectrum of modes allowing all possible quadratic and cubic interactions. Results are obtained for four cases where linear and Stuart-Landau theories do not give a complete description; gas-liquid and oil-water pressure driven flow, matched-density liquid-liquid Couette flow, and the region of gas-liquid flow near resonance that switches from supercritical to subcritical. It is found that integration of amplitude equations gives better qualitative and quantitative agreement with experiments than Stuart-Landau theory. Further, the distinctively different behaviors of these systems can be understood in terms of the spectrum of nonlinear coefficients. In gas-liquid channel flow a low wave number wave is destabilized through quadratic interaction with the mean flow mode. For liquid-liquid Poiseuille flow, a low wave number wave is destabilized through cubic interactions with higher modes. For depth and viscosity ratios where liquid-liquid Couette flow is unstable to long waves and for which the growth rates are not too large, simulation results predict that the waves grow to a statistically steady state where there is no preferred wave number. Stabilization is provided by an apparently self-similar cascade of energy to higher modes that are linearly stable, explaining why no visible waves occur in experiments done in this region. While Stuart-Landau theory provides no prediction of wave amplitude above criticality for subcritical cases, simulations show that wave saturation at small amplitude is possible and suggests that subcritical predictions may not mean that steady waves do not exist. (c) 2000 American Institute of Physics.
NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS
Institute of Scientific and Technical Information of China (English)
PENG SHIGE
2005-01-01
This paper deals with nonlinear expectations. The author obtains a nonlinear generalization of the well-known Kolmogorov's consistent theorem and then use it to construct filtration-consistent nonlinear expectations via nonlinear Markov chains. Compared to the author's previous results, i.e., the theory of g-expectations introduced via BSDE on a probability space, the present framework is not based on a given probability measure. Many fully nonlinear and singular situations are covered. The induced topology is a natural generalization of Lp-norms and L∞-norm in linear situations.The author also obtains the existence and uniqueness result of BSDE under this new framework and develops a nonlinear type of von Neumann-Morgenstern representation theorem to utilities and present dynamic risk measures.
Surfactant and gravity dependent instability of two-layer Couette flows and its nonlinear saturation
Frenkel, Alexander L
2016-01-01
A horizontal flow of two immiscible fluid layers with different densities, viscosities and thicknesses, subject to vertical gravitational forces and with an insoluble surfactant present at the interface, is investigated. The base Couette flow is driven by the horizontal motion of the channel walls. Linear and nonlinear stages of the (inertialess) surfactant and gravity dependent long-wave instability are studied using the lubrication approximation, which leads to a system of coupled nonlinear evolution equations for the interface and surfactant disturbances. The linear stability is determined by an eigenvalue problem for the normal modes. The growth rates and the amplitudes of disturbances of the interface, surfactant, velocities, and pressures are found analytically. For each wavenumber, there are two active normal modes. For each mode, the instability threshold conditions in terms of the system parameters are determined. In particular, it transpires that for certain parametric ranges, even arbitrarily stron...
Di Biagio, Claudia; Formenti, Paola; Balkanski, Yves; Caponi, Lorenzo; Cazaunau, Mathieu; Pangui, Edouard; Journet, Emilie; Nowak, Sophie; Caquineau, Sandrine; Andreae, Meinrat O.; Kandler, Konrad; Saeed, Thuraya; Piketh, Stuart; Seibert, David; Williams, Earle; Doussin, Jean-François
2017-02-01
Modeling the interaction of dust with long-wave (LW) radiation is still a challenge because of the scarcity of information on the complex refractive index of dust from different source regions. In particular, little is known about the variability of the refractive index as a function of the dust mineralogical composition, which depends on the specific emission source, and its size distribution, which is modified during transport. As a consequence, to date, climate models and remote sensing retrievals generally use a spatially invariant and time-constant value for the dust LW refractive index. In this paper, the variability of the mineral dust LW refractive index as a function of its mineralogical composition and size distribution is explored by in situ measurements in a large smog chamber. Mineral dust aerosols were generated from 19 natural soils from 8 regions: northern Africa, the Sahel, eastern Africa and the Middle East, eastern Asia, North and South America, southern Africa, and Australia. Soil samples were selected from a total of 137 available samples in order to represent the diversity of sources from arid and semi-arid areas worldwide and to account for the heterogeneity of the soil composition at the global scale. Aerosol samples generated from soils were re-suspended in the chamber, where their LW extinction spectra (3-15 µm), size distribution, and mineralogical composition were measured. The generated aerosol exhibits a realistic size distribution and mineralogy, including both the sub- and super-micron fractions, and represents in typical atmospheric proportions the main LW-active minerals, such as clays, quartz, and calcite. The complex refractive index of the aerosol is obtained by an optical inversion based upon the measured extinction spectrum and size distribution. Results from the present study show that the imaginary LW refractive index (k) of dust varies greatly both in magnitude and spectral shape from sample to sample, reflecting the
Chen, Xianfeng; Zeng, Heping; Guo, Qi; She, Weilong
2015-01-01
This book presents an overview of the state of the art of nonlinear optics from weak light nonlinear optics, ultrafast nonlinear optics to electro-optical theory and applications. Topics range from the fundamental studies of the interaction between matter and radiation to the development of devices, components, and systems of tremendous commercial interest for widespread applications in optical telecommunications, medicine, and biotechnology.
Distributed nonlinear optical response
DEFF Research Database (Denmark)
Nikolov, Nikola Ivanov
2005-01-01
The purpose of the research presented here is to investigate basic physical properties in nonlinear optical materials with delayed or nonlocal nonlinearity. Soliton propagation, spectral broadening and the influence of the nonlocality or delay of the nonlinearity are the main focusses in the work...
Noncommutative Nonlinear Supersymmetry
Nishino, H; Nishino, Hitoshi; Rajpoot, Subhash
2002-01-01
We present noncommutative nonlinear supersymmetric theories. The first example is a non-polynomial Akulov-Volkov-type lagrangian with noncommutative nonlinear global supersymmetry in arbitrary space-time dimensions. The second example is the generalization of this lagrangian to Dirac-Born-Infeld lagrangian with nonlinear supersymmetry realized in dimensions D=2,3,4 and 6 (mod 8).
Fiber Nonlinearities: A Tutorial
Institute of Scientific and Technical Information of China (English)
Govind P. Agrawal
2003-01-01
Fiber nonlinearities have long been regarded as being mostly harmful for fiber-optic communication systems. Over the last few years, however, the nonlinear effects are increasingly being used for practical telecommunications applications,the Raman amplification being only one of the recent examples. In this tutorial I review the vario us nonlinear effects occurring in optical fibers from both standpoints..
Fiber Nonlinearities: A Tutorial
Institute of Scientific and Technical Information of China (English)
Govind; P.; Agrawal
2003-01-01
Fiber nonlinearities have long been regarded as being mostly harmful for fiber-optic communication systems. Over the last few years, however, the nonlinear effects are increasingly being used for practical telecommunications applications, the Raman amplification being only one of the recent examples. In this tutorial I review the various nonlinear effects occurring in optical fibers from both standpoints..
PBH tests for nonlinear systems
Kawano, Yu; Ohtsuka, Toshiyuki
2017-01-01
Recently, concepts of nonlinear eigenvalues and eigenvectors are introduced. In this paper, we establish connections between the nonlinear eigenvalues and nonlinear accessibility/observability. In particular, we provide a generalization of Popov- Belevitch-Hautus (PBH) test to nonlinear accessibilit
Nonlinear dynamics and complexity
Luo, Albert; Fu, Xilin
2014-01-01
This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.
Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities
Indian Academy of Sciences (India)
Antonella Fiacca; Nikolaos Matzakos; Nikolaos S Papageorgiou; Raffaella Servadei
2001-11-01
In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all $\\mathbb{R}$. Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed by the upper and lower solutions. Then we drop the requirement that the monotone nonlinearity is defined on all of $\\mathbb{R}$. This case is important because it covers variational inequalities. Using the theory of operators of monotone type we show that the problem has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth locally Lipschitz functionals we prove the existence of at least two nontrivial solutions (multiplicity theorem).
Electrical Performance Influence of Loading on Inverted Long-wave Antenna%加载对垂挂式长波天线电气性能影响的研究
Institute of Scientific and Technical Information of China (English)
宫烨; 翟琦; 蒋宇中
2016-01-01
在借鉴机载长波天线、气球天线和COCO天线的基础上,建立三种形式的垂挂式长波发信天线模型,然后就顶容性加载和电感加载两个方面研究顶容线数量以及电感加载位置、加感量等对天线电气性能的影响.仿真结果表明:顶容性加载和电感加载均能使天线的阻抗特性和辐射性能得到改善,且电感加载能够间接缩短天线物理长度.这一研究结果对改善长波天线电气性能、缩短天线物理长度等具有重要的指导意义.%Based on the airborne long-wave antenna, kptoon and COCO antenna. The three types of inverted long-wave antenna model are established. The influence of capacitive loading and inductance loading, particularly of the top-line number, inductance loading position and quantity on antenna electrical performance, is fairly studied. Simulation shows that the capacitive loading and inductance loading could improve impedance characteristic and radiation property of the antenna, while the inductance loading shortening the physical length of antenna. This research result has a guiding significance in electrical performance improvement and physical length shortening of the antenna.
Directory of Open Access Journals (Sweden)
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Ionescu, Tudor C.; Scherpen, Jacquelien M. A.
We study the notion of cross Gramians for nonlinear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain linearization results that correspond to the notion of a cross Gramian for symmetric linear systems. Furthermore, first steps towards relations with the singular value functions of the nonlinear Hankel operator are studied and yield promising results.
Directory of Open Access Journals (Sweden)
W. L. Fouché
1983-03-01
Full Text Available In this article we discuss some aspects of nonlinear functional analysis. It included reviews of Banach’s contraction theorem, Schauder’s fixed point theorem, globalising techniques and applications of homotopy theory to nonlinear functional analysis. The author emphasises that fundamentally new ideas are required in order to achieve a better understanding of phenomena which contain both nonlinear and definite infinite dimensional features.
Nonlinear Electrodynamics and QED
2003-01-01
The limits of linear electrodynamics are reviewed, and possible directions of nonlinear extension are explored. The central theme is that the qualitative character of the empirical successes of quantum electrodynamics must be used as a guide for understanding the nature of the nonlinearity of electrodynamics at the subatomic level. Some established theories of nonlinear electrodynamics, namely, those of Mie, Born, and Infeld are presented in the language of the modern geometrical and topologi...
Kono, Mitsuo
2010-01-01
A nonlinearity is one of the most important notions in modern physics. A plasma is rich in nonlinearities and provides a variety of behaviors inherent to instabilities, coherent wave structures and turbulence. The book covers the basic concepts and mathematical methods, necessary to comprehend nonlinear problems widely encountered in contemporary plasmas, but also in other fields of physics and current research on self-organized structures and magnetized plasma turbulence. The analyses make use of strongly nonlinear models solved by analytical techniques backed by extensive simulations and available experiments. The text is written for senior undergraduates, graduate students, lecturers and researchers in laboratory, space and fusion plasmas.
Nonlinear magnetic metamaterials.
Shadrivov, Ilya V; Kozyrev, Alexander B; van der Weide, Daniel W; Kivshar, Yuri S
2008-12-08
We study experimentally nonlinear tunable magnetic metamaterials operating at microwave frequencies. We fabricate the nonlinear metamaterial composed of double split-ring resonators where a varactor diode is introduced into each resonator so that the magnetic resonance can be tuned dynamically by varying the input power. We demonstrate that at higher powers the transmission of the metamaterial becomes power-dependent and, as a result, such metamaterial can demonstrate various nonlinear properties. In particular, we study experimentally the power-dependent shift of the transmission band and demonstrate nonlinearity-induced enhancement (or suppression) of wave transmission. (c) 2008 Optical Society of America
Organic nonlinear optical materials
Umegaki, S.
1987-01-01
Recently, it became clear that organic compounds with delocalized pi electrons show a great nonlinear optical response. Especially, secondary nonlinear optical constants of more than 2 digits were often seen in the molecular level compared to the existing inorganic crystals such as LiNbO3. The crystallization was continuously tried. Organic nonlinear optical crystals have a new future as materials for use in the applied physics such as photomodulation, optical frequency transformation, opto-bistabilization, and phase conjugation optics. Organic nonlinear optical materials, e.g., urea, O2NC6H4NH2, I, II, are reviewed with 50 references.
Nonlinearity-reduced interferometer
Wu, Chien-ming
2007-12-01
Periodic nonlinearity is a systematic error limiting the accuracy of displacement measurements at the nanometer level. It results from many causes such as the frequency mixing, polarization mixing, polarization-frequency mixing, and the ghost reflections. An interferometer having accuracy in displacement measurement of less than one-nanometer is necessary in nanometrology. To meet the requirement, the periodic nonlinearity should be less than deep sub-nanometer. In this paper, a nonlinearity-reduced interferometry has been proposed. Both the linear- and straightness-interferometer were tested. The developed interferometer demonstrated of a residual nonlinearity less than 25 pm.
Dimitrova, Zlatinka I
2015-01-01
We investigate flow of incompressible fluid in a cylindrical tube with elastic walls. The radius of the tube may change along its length. The discussed problem is connected to the blood flow in large human arteries and especially to nonlinear wave propagation due to the pulsations of the heart. The long-wave approximation for modeling of waves in blood is applied. The obtained model Korteweg-deVries equation possessing a variable coefficient is reduced to a nonlinear dynamical system of 3 first order differential equations. The low probability of arising of a solitary wave is shown. Periodic wave solutions of the model system of equations are studied and it is shown that the waves that are consequence of the irregular heart pulsations may be modeled by a sequence of parts of such periodic wave solutions.
Directory of Open Access Journals (Sweden)
Cha'o-Kuang Chen
2009-01-01
Full Text Available The main object of this paper is to study the weakly nonlinear hydrodynamic stability of the thin Newtonian fluid flowing on a rotating circular disk. A long-wave perturbation method is used to derive the nonlinear evolution equation for the film flow. The linear behaviors of the spreading wave are investigated by normal mode approach, and its weakly nonlinear behaviors are explored by the method of multiple scales. The Ginzburg-Landau equation is determined to discuss the necessary condition for the existence of such flow pattern. The results indicate that the superctitical instability region increases, and the subcritical stability region decreases with the increase of the rotation number or the radius of circular disk. It is found that the rotation number and the radius of circular disk not only play the significant roles in destabilizing the flow in the linear stability analysis but also shrink the area of supercritical stability region at high Reynolds number in the weakly nonlinear stability analysis.
Lasers for nonlinear microscopy.
Wise, Frank
2013-03-01
Various versions of nonlinear microscopy are revolutionizing the life sciences, almost all of which are made possible because of the development of ultrafast lasers. In this article, the main properties and technical features of short-pulse lasers used in nonlinear microscopy are summarized. Recent research results on fiber lasers that will impact future instruments are also discussed.
Eaton, D F
1991-07-19
The current state of materials development in nonlinear optics is summarized, and the promise of these materials is critically evaluated. Properties and important materials constants of current commercial materials and of new, promising, inorganic and organic molecular and polymeric materials with potential in second- and third-order nonlinear optical applications are presented.
Billings, S. A.
1988-03-01
Time and frequency domain identification methods for nonlinear systems are reviewed. Parametric methods, prediction error methods, structure detection, model validation, and experiment design are discussed. Identification of a liquid level system, a heat exchanger, and a turbocharge automotive diesel engine are illustrated. Rational models are introduced. Spectral analysis for nonlinear systems is treated. Recursive estimation is mentioned.
Ionescu, T. C.; Scherpen, J. M. A.; Korytowski, A; Malanowski, K; Mitkowski, W; Szymkat, M
2009-01-01
We study the notion of cross Gramians for nonlinear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Christiansen, Peter Leth; Torner, L.
1999-01-01
We show that with the quasi-phase-matching technique it is possible to fabricate stripes of nonlinearity that trap and guide light like waveguides. We investigate an array of such stripes and find that when the stripes are sufficiently narrow, the beam dynamics is governed by a quadratic nonlinear...
Controllability in nonlinear systems
Hirschorn, R. M.
1975-01-01
An explicit expression for the reachable set is obtained for a class of nonlinear systems. This class is described by a chain condition on the Lie algebra of vector fields associated with each nonlinear system. These ideas are used to obtain a generalization of a controllability result for linear systems in the case where multiplicative controls are present.
Menon, P. K. A.; Badgett, M. E.; Walker, R. A.
1992-01-01
Trajectory-control laws based on singular-perturbation theory and nonlinear dynamical modeling. Nonlinear maneuver autopilot commands flight-test trajectories of F-15 airplane. Underlying theory of controller enables separation of variables processed in fast and slow control loops, reducing amount of computation required.
Nonlinear optics and photonics
He, Guang S
2015-01-01
This book provides a comprehensive presentation on most of the major topics in nonlinear optics and photonics, with equal emphasis on principles, experiments, techniques, and applications. It covers many major new topics including optical solitons, multi-photon effects, nonlinear photoelectric effects, fast and slow light , and Terahertz photonics. Chapters 1-10 present the fundamentals of modern nonlinear optics, and could be used as a textbook with problems provided at the end of each chapter. Chapters 11-17 cover the more advanced topics of techniques and applications of nonlinear optics and photonics, serving as a highly informative reference for researchers and experts working in related areas. There are also 16 pages of color photographs to illustrate the visual appearances of some typical nonlinear optical effects and phenomena. The book could be adopted as a textbook for both undergraduates and graduate students, and serve as a useful reference work for researchers and experts in the fields of physics...
Lugiato, Luigi; Brambilla, Massimo
2015-01-01
Guiding graduate students and researchers through the complex world of laser physics and nonlinear optics, this book provides an in-depth exploration of the dynamics of lasers and other relevant optical systems, under the umbrella of a unitary spatio-temporal vision. Adopting a balanced approach, the book covers traditional as well as special topics in laser physics, quantum electronics and nonlinear optics, treating them from the viewpoint of nonlinear dynamical systems. These include laser emission, frequency generation, solitons, optically bistable systems, pulsations and chaos and optical pattern formation. It also provides a coherent and up-to-date treatment of the hierarchy of nonlinear optical models and of the rich variety of phenomena they describe, helping readers to understand the limits of validity of each model and the connections among the phenomena. It is ideal for graduate students and researchers in nonlinear optics, quantum electronics, laser physics and photonics.
Mitsotakis, Dimitrios; Assylbekuly, Aydar; Zhakebaev, Dauren
2016-01-01
In this Letter we consider long capillary-gravity waves described by a fully nonlinear weakly dispersive model. First, using the phase space analysis methods we describe all possible types of localized travelling waves. Then, we especially focus on the critical regime, where the surface tension is exactly balanced by the gravity force. We show that our long wave model with a critical Bond number admits stable travelling wave solutions with a singular crest. These solutions are usually referred to in the literature as peakons or peaked solitary waves. They satisfy the usual speed-amplitude relation, which coincides with Scott-Russel's empirical formula for solitary waves, while their decay rate is the same regardless their amplitude. Moreover, they can be of depression or elevation type independent of their speed. The dynamics of these solutions are studied as well.
Zweig, George
2016-05-01
An earlier paper characterizing the linear mechanical response of the organ of Corti [J. Acoust. Soc. Am. 138, 1102-1121 (2015)] is extended to the nonlinear domain. Assuming the existence of nonlinear oscillators nonlocally coupled through the pressure they help create, the oscillator equations are derived and examined when the stimuli are modulated tones and clicks. The nonlinearities are constrained by the requirements of oscillator stability and the invariance of zero crossings in the click response to changes in click amplitude. The nonlinear oscillator equations for tones are solved in terms of the fluid pressure that drives them, and its time derivative, presumably a proxy for forces created by outer hair cells. The pressure equation is reduced to quadrature, the integrand depending on the oscillators' responses. The resulting nonlocally coupled nonlinear equations for the pressure, and oscillator amplitudes and phases, are solved numerically in terms of the fluid pressure at the stapes. Methods for determining the nonlinear damping directly from measurements are described. Once the oscillators have been characterized from their tone and click responses, the mechanical response of the cochlea to natural sounds may be computed numerically. Signal processing inspired by cochlear mechanics opens up a new area of nonlocal nonlinear time-frequency analysis.
Agrawal, Govind P
2001-01-01
The Optical Society of America (OSA) and SPIE - The International Society for Optical Engineering have awarded Govind Agrawal with an honorable mention for the Joseph W. Goodman Book Writing Award for his work on Nonlinear Fiber Optics, 3rd edition.Nonlinear Fiber Optics, 3rd Edition, provides a comprehensive and up-to-date account of the nonlinear phenomena occurring inside optical fibers. It retains most of the material that appeared in the first edition, with the exception of Chapter 6, which is now devoted to the polarization effects relevant for light propagation in optical
Will Nonlinear Backcalculation Help?
DEFF Research Database (Denmark)
Ullidtz, Per
2000-01-01
demonstrates, that treating the subgrade as a nonlinear elastic material, can result in more realistic moduli and a much better agreement between measured and calculated stresses and strains.The response of nonlinear elastic materials can be calculated using the Finite Element Method (FEM). A much simpler...... approach is to use the Method of Equivalent Thicknesses (MET), modified for a nonlinear subgrade. The paper includes an example where moduli backcalculated using FEM, linear elastic theory and MET are compared. Stresses and strains predicted by the three methods are also compared to measured values...
Nonlinear graphene metamaterial
Nikolaenko, Andrey E; Atmatzakis, Evangelos; Luo, Zhiqiang; Shen, Ze Xiang; De Angelis, Francesco; Boden, Stuart A; Di Fabrizio, Enzo; Zheludev, Nikolay I
2012-01-01
We demonstrate that the broadband nonlinear optical response of graphene can be resonantly enhanced by more than an order of magnitude through hybridization with a plasmonic metamaterial,while retaining an ultrafast nonlinear response time of ~1 ps. Transmission modulation close to ~1% is seen at a pump uence of ~0.03 mJ/cm^2 at the wavelength of ~1600 nm. This approach allows to engineer and enhance graphene's nonlinearity within a broad wavelength range enabling applications in optical switching, mode-locking and pulse shaping.
Nonlinear Wave-Currents interactions in shallow water
Lannes, David
2015-01-01
We study here the propagation of long waves in the presence of vorticity. In the irrotational framework, the Green-Naghdi equations (also called Serre or fully nonlinear Boussinesq equations) are the standard model for the propagation of such waves. These equations couple the surface elevation to the vertically averaged horizontal velocity and are therefore independent of the vertical variable. In the presence of vorticity, the dependence on the vertical variable cannot be removed from the vorticity equation but it was however shown in [?] that the motion of the waves could be described using an extended Green-Naghdi system. In this paper we propose an analysis of these equations, and show that they can be used to get some new insight into wave-current interactions. We show in particular that solitary waves may have a drastically different behavior in the presence of vorticity and show the existence of solitary waves of maximal amplitude with a peak at their crest, whose angle depends on the vorticity. We als...
Multipolar nonlinear nanophotonics
Smirnova, Daria
2016-01-01
Nonlinear nanophotonics is a rapidly developing field with many useful applications for a design of nonlinear nanoantennas, light sources, nanolasers, sensors, and ultrafast miniature metadevices. A tight confinement of the local electromagnetic fields in resonant photonic nanostructures can boost nonlinear optical effects, thus offering versatile opportunities for subwavelength control of light. To achieve the desired functionalities, it is essential to gain flexible control over the near- and far-field properties of nanostructures. Thus, both modal and multipolar analyses are widely exploited for engineering nonlinear scattering from resonant nanoscale elements, in particular for enhancing the near-field interaction, tailoring the far-field multipolar interference, and optimization of the radiation directionality. Here, we review the recent advances in this recently emerged research field ranging from metallic structures exhibiting localized plasmonic resonances to hybrid metal-dielectric and all-dielectric...
Solitons in nonlinear lattices
Kartashov, Yaroslav V; Torner, Lluis
2010-01-01
This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of the nonlinearity, and their combinations with linear lattices. A majority of the results obtained, thus far, in this field and reviewed in this article are theoretical. Nevertheless, relevant experimental settings are surveyed too, with emphasis on perspectives for implementation of the theoretical predictions in the experiment. Physical systems discussed in the review belong to the realms of nonlinear optics (including artificial optical media, such as photonic crystals, and plasmonics) and Bose-Einstein condensation (BEC). The solitons are considered in one, two, and three dimensions (1D, 2D, and 3D). Basic properties of the solitons presented in the review are their existence, stability, and mobility. Although the field is still far from completion, general conclusions c...
Directory of Open Access Journals (Sweden)
Shakeeb Bin Hasan
2014-12-01
Full Text Available Contrary to traditional optical elements, plasmonic antennas made from nanostructured metals permit the localization of electromagnetic fields on length scales much smaller than the wavelength of light. This results in huge amplitudes for the electromagnetic field close to the antenna being conducive for the observation of nonlinear effects already at moderate pump powers. Thus, these antennas exhibit a promising potential to achieve optical frequency conversion and all-optical control of light at the nano-scale. This opens unprecedented opportunities for ultrafast nonlinear spectroscopy, sensing devices, on-chip optical frequency conversion, nonlinear optical metamaterials, and novel photon sources. Here, we review some of the recent advances in exploiting the potential of plasmonic antennas to realize robust nonlinear applications.
Leburn, Christopher; Reid, Derryck
2013-01-01
The field of ultrafast nonlinear optics is broad and multidisciplinary, and encompasses areas concerned with both the generation and measurement of ultrashort pulses of light, as well as those concerned with the applications of such pulses. Ultrashort pulses are extreme events – both in terms of their durations, and also the high peak powers which their short durations can facilitate. These extreme properties make them powerful experiment tools. On one hand, their ultrashort durations facilitate the probing and manipulation of matter on incredibly short timescales. On the other, their ultrashort durations can facilitate high peak powers which can drive highly nonlinear light-matter interaction processes. Ultrafast Nonlinear Optics covers a complete range of topics, both applied and fundamental in nature, within the area of ultrafast nonlinear optics. Chapters 1 to 4 are concerned with the generation and measurement of ultrashort pulses. Chapters 5 to 7 are concerned with fundamental applications of ultrasho...
DEFF Research Database (Denmark)
Nguyen-Duy, Khiem
and remains the prime source of energy in non-terrestrial applications such as those in sky-explorers. However, a renewable energy source is expensive, bulky, and its performance is weather dependent, which make testing of downstream converters very difficult. As a result, a nonlinear source emulator (NSE......) is a good solution to solve the problems associated with the use of real nonlinear sources in testing phases. However, a recent technical survey conducted during this work shows that most existing NSEs have only been concerned with simulating nonlinear systems in terrestrial applications. Furthermore......, their dynamic performance were not fast enough in order to imitate how a real nonlinear energy source would react under extreme conditions and operation modes. Particularly, a system in the sky can experience a step change of sunlight irradiation. Moreover, operation modes may include load step between nominal...
Introduction to nonlinear science
Nicolis, G
1995-01-01
One of the most unexpected results in science in recent years is that quite ordinary systems obeying simple laws can give rise to complex, nonlinear or chaotic, behavior. In this book, the author presents a unified treatment of the concepts and tools needed to analyze nonlinear phenomena and to outline some representative applications drawn from the physical, engineering, and biological sciences. Some of the interesting topics covered include: dynamical systems with a finite number of degrees of freedom, linear stability analysis of fixed points, nonlinear behavior of fixed points, bifurcation analysis, spatially distributed systems, broken symmetries, pattern formation, and chaotic dynamics. The author makes a special effort to provide a logical connection between ordinary dynamical systems and spatially extended systems, and to balance the emphasis on chaotic behavior and more classical nonlinear behavior. He also develops a statistical approach to complex systems and compares it to traditional deterministi...
Nonlinear magnetoinductive transmission lines
Lazarides, Nikos; Tsironis, G P
2011-01-01
Power transmission in one-dimensional nonlinear magnetic metamaterials driven at one end is investigated numerically and analytically in a wide frequency range. The nonlinear magnetic metamaterials are composed of varactor-loaded split-ring resonators which are coupled magnetically through their mutual inductances, forming thus a magnetoiductive transmission line. In the linear limit, significant power transmission along the array only appears for frequencies inside the linear magnetoinductive wave band. We present analytical, closed form solutions for the magnetoinductive waves transmitting the power in this regime, and their discrete frequency dispersion. When nonlinearity is important, more frequency bands with significant power transmission along the array may appear. In the equivalent circuit picture, the nonlinear magnetoiductive transmission line driven at one end by a relatively weak electromotive force, can be modeled by coupled resistive-inductive-capacitive (RLC) circuits with voltage-dependent cap...
Optimization under Nonlinear Constraints
1982-01-01
In this paper a timesaving method is proposed for maximizing likelihood functions when the parameter space is subject to nonlinear constraints, expressible as second order polynomials. The suggested approach is especially attractive when dealing with systems with many parameters.
Nonlinearity in nanomechanical cantilevers
DEFF Research Database (Denmark)
Villanueva Torrijo, Luis Guillermo; Karabalin, R. B.; Matheny, M. H.
2013-01-01
Euler-Bernoulli beam theory is widely used to successfully predict the linear dynamics of micro-and nanocantilever beams. However, its capacity to characterize the nonlinear dynamics of these devices has not yet been rigorously assessed, despite its use in nanoelectromechanical systems development....... These findings underscore the delicate balance between inertial and geometric nonlinear effects in the fundamental mode, and strongly motivate further work to develop theories beyond the Euler-Bernoulli approximation. DOI: 10.1103/PhysRevB.87.024304....... In this article, we report the first highly controlled measurements of the nonlinear response of nanomechanical cantilevers using an ultralinear detection system. This is performed for an extensive range of devices to probe the validity of Euler-Bernoulli theory in the nonlinear regime. We find that its...
Nonlinear Stokes Mueller Polarimetry
Samim, Masood; Barzda, Virginijus
2015-01-01
The Stokes Mueller polarimetry is generalized to include nonlinear optical processes such as second- and third-harmonic generation, sum- and difference-frequency generations. The overall algebraic form of the polarimetry is preserved, where the incoming and outgoing radiations are represented by column vectors and the intervening medium is represented by a matrix. Expressions for the generalized nonlinear Stokes vector and the Mueller matrix are provided in terms of coherency and correlation matrices, expanded by higher-dimensional analogues of Pauli matrices. In all cases, the outgoing radiation is represented by the conventional $4\\times 1$ Stokes vector, while dimensions of the incoming radiation Stokes vector and Mueller matrix depend on the order of the process being examined. In addition, relation between nonlinear susceptibilities and the measured Mueller matrices are explicitly provided. Finally, the approach of combining linear and nonlinear optical elements is discussed within the context of polarim...
Adaptive and Nonlinear Control
1992-02-29
in [22], we also applied the concept of zero dynamics to the problem of exact linearization of a nonlinear control system by dynamic feedback. Exact ...nonlinear systems, although it was well-known that the conditions for exact linearization are very stringent and consequently do not apply to a broad...29th IEEE Conference n Decision and Control, Invited Paper delivered by Dr. Gilliam. Exact Linearization of Zero Dynamics, 29th IEEE Conference on
Nonlinear Optics and Turbulence
1992-10-01
currently at Queen Mary College, London Patrick Dunne, (Ph.D., 1987, M.I.T., Hydrodynamic Stability, Nonlinear Waves), 1987-1988. Alecsander Dyachenko...U I I I U I I 3 9 3 V. BIOGRAPHIES A. FACULTY BRUCE BAYLY, 31, Ph.D. 1986, Princeton University. Postdoctoral visiting member 1986-88 at Courant...Caputo, A. C. Newell, and M. Shelley , "Nonlinear Wave Propagation Through a Random Medium and Soliton Tunneling", Integrable Systems and
Destefanis, V.; Kerlain, A.
2016-09-01
Minority-carrier lifetime measurements have been carried out on Hg0.77Cd0.23Te (111)B materials with gap suitable for detection in the Long-Wave Infrared (LWIR) band. The materials were grown on top of CdZnTe substrates using a liquid-phase epitaxy (LPE) process. From measurements done at 80 K, a clear difference in terms of minority-carrier lifetimes was obtained, as expected, between p-intrinsic (≤5 ns) and n-extrinsic doped samples (420 ns). Minority-carrier lifetimes were also measured as a function of temperature for the n-type samples. Auger-1-limited lifetimes were demonstrated over a wide temperature range (from 80 K to 300 K) with negligible Radiative or Shockley-Read-Hall lifetime contributions. Predictions of dark current densities are made from those lifetime measurements, assuming an Auger-1-limited lifetime. The agreement is very good between the predictions and dark current densities measured from p-on- n 640 × 512 pixels LWIR HgCdTe focal-plane arrays with 15- μm pitch from SOFRADIR, Agreement between predicted and measured dark currents and Rule'07 for LWIR is also demonstrated herein. Finally, minority-carrier lifetime measurements are demonstrated as a predictive method for focal-plane array performance. State-of-the-art dark currents from SOFRADIR p-on- n LWIR focal-plane arrays based upon high-quality HgCdTe materials are also illustrated.
Directory of Open Access Journals (Sweden)
Gila Notesco
2013-11-01
Full Text Available Remote-sensing platforms are often comprised of a cluster of different spectral range detectors or sensors to benefit from the spectral identification capabilities of each range. Missing data from these platforms, caused by problematic weather conditions, such as clouds, sensor failure, low temporal coverage or a narrow field of view (FOV, is one of the problems preventing proper monitoring of the Earth. One of the possible solutions is predicting a detector or sensor’s missing data using another detector/sensor. In this paper, we propose a new method of predicting spectral emissivity in the long-wave infrared (LWIR spectral region using the visible (VIS spectral region. The proposed method is suitable for two main scenarios of missing data: sensor malfunctions and narrow FOV. We demonstrate the usefulness and limitations of this prediction scheme using the airborne hyperspectral scanner (AHS sensor, which consists of both VIS and LWIR spectral regions, in a case study over the Sokolov area, Czech Republic.
Yang, Qianli; Pitkow, Xaq
2015-03-01
Most interesting natural sensory stimuli are encoded in the brain in a form that can only be decoded nonlinearly. But despite being a core function of the brain, nonlinear population codes are rarely studied and poorly understood. Interestingly, the few existing models of nonlinear codes are inconsistent with known architectural features of the brain. In particular, these codes have information content that scales with the size of the cortical population, even if that violates the data processing inequality by exceeding the amount of information entering the sensory system. Here we provide a valid theory of nonlinear population codes by generalizing recent work on information-limiting correlations in linear population codes. Although these generalized, nonlinear information-limiting correlations bound the performance of any decoder, they also make decoding more robust to suboptimal computation, allowing many suboptimal decoders to achieve nearly the same efficiency as an optimal decoder. Although these correlations are extremely difficult to measure directly, particularly for nonlinear codes, we provide a simple, practical test by which one can use choice-related activity in small populations of neurons to determine whether decoding is suboptimal or optimal and limited by correlated noise. We conclude by describing an example computation in the vestibular system where this theory applies. QY and XP was supported by a grant from the McNair foundation.
Nonlinear Multiantenna Detection Methods
Directory of Open Access Journals (Sweden)
Chen Sheng
2004-01-01
Full Text Available A nonlinear detection technique designed for multiple-antenna assisted receivers employed in space-division multiple-access systems is investigated. We derive the optimal solution of the nonlinear spatial-processing assisted receiver for binary phase shift keying signalling, which we refer to as the Bayesian detector. It is shown that this optimal Bayesian receiver significantly outperforms the standard linear beamforming assisted receiver in terms of a reduced bit error rate, at the expense of an increased complexity, while the achievable system capacity is substantially enhanced with the advent of employing nonlinear detection. Specifically, when the spatial separation expressed in terms of the angle of arrival between the desired and interfering signals is below a certain threshold, a linear beamformer would fail to separate them, while a nonlinear detection assisted receiver is still capable of performing adequately. The adaptive implementation of the optimal Bayesian detector can be realized using a radial basis function network. Two techniques are presented for constructing block-data-based adaptive nonlinear multiple-antenna assisted receivers. One of them is based on the relevance vector machine invoked for classification, while the other on the orthogonal forward selection procedure combined with the Fisher ratio class-separability measure. A recursive sample-by-sample adaptation procedure is also proposed for training nonlinear detectors based on an amalgam of enhanced -means clustering techniques and the recursive least squares algorithm.
Nonlinear systems in medicine.
Higgins, John P
2002-01-01
Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states.
Handbook of nonlinear optical crystals
Dmitriev, Valentin G; Nikogosyan, David N
1991-01-01
This Handbook of Nonlinear Optical Crystals provides a complete description of the properties and applications of nonlinear crystals In addition, it presents the most important equations for calculating the main parameters of nonlinear frequency converters This comprehensive reference work will be of great value to all scientists and engineers working in nonlinear optics, quantum electronics and laser physics
Nonlinear Approaches in Engineering Applications
Jazar, Reza
2012-01-01
Nonlinear Approaches in Engineering Applications focuses on nonlinear phenomena that are common in the engineering field. The nonlinear approaches described in this book provide a sound theoretical base and practical tools to design and analyze engineering systems with high efficiency and accuracy and with less energy and downtime. Presented here are nonlinear approaches in areas such as dynamic systems, optimal control and approaches in nonlinear dynamics and acoustics. Coverage encompasses a wide range of applications and fields including mathematical modeling and nonlinear behavior as applied to microresonators, nanotechnologies, nonlinear behavior in soil erosion,nonlinear population dynamics, and optimization in reducing vibration and noise as well as vibration in triple-walled carbon nanotubes. This book also: Provides a complete introduction to nonlinear behavior of systems and the advantages of nonlinearity as a tool for solving engineering problems Includes applications and examples drawn from the el...
Very Long Wave Length IR Detectors
2015-02-01
vertical mobilities for use in detector modeling and materials optimization. REFERENCES: 1. A. Rogalski, J. Antoszewski, and L. Faraone , J. Appl...A. Rogalski, J. Antoszewski, and L. Faraone J. Appl. Phys. 105, 091101 (2009) 3. G. J. Brown, Proceedings of SPIE 5783, 457 (2005). 4. D. L. Smith
Energy Technology Data Exchange (ETDEWEB)
Davis, C.G.
1990-01-01
The advent of nonlinear pulsation theory really coincides with the development of the large computers after the second world war. Christy and Stobbie were the first to make use of finite difference techniques on computers to model the bumps'' observed in the classical Cepheid light and velocity curves, the so-called Hertzsprung'' sequence. Following this work a more sophisticated analysis of the light and velocity curves from the models was made by Simon and Davis using Fourier techniques. Recently a simpler amplitude equation formalism has been developed that helps explain this resonance mechanism. The determination of Population I Cepheid masses by nonlinear methods will be discussed. For the lower mass objects, such as RR Lyrae and BL Her. stars, we find general agreement using evolutionary masses and nonlinear pulsation theory. An apparent difficulty of nonlinear pulsation theory occurs in the understanding of double'' mode pulsation, which will also be discussed. Recent studies in nonlinear pulsation theory have dealt with the question of mode selection, period doubling and the trends towards chaotic behavior such as is observed in the transition from W Virginis to RV Tauri-like stars. 10 refs., 1 fig., 2 tabs.
Nonlinear elastic waves in materials
Rushchitsky, Jeremiah J
2014-01-01
The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...
Nonlinear Dynamic Force Spectroscopy
Björnham, Oscar
2016-01-01
Dynamic force spectroscopy (DFS) is an experimental technique that is commonly used to assess information of the strength, energy landscape, and lifetime of noncovalent bio-molecular interactions. DFS traditionally requires an applied force that increases linearly with time so that the bio-complex under investigation is exposed to a constant loading rate. However, tethers or polymers can modulate the applied force in a nonlinear regime. For example, bacterial adhesion pili and polymers with worm-like chain properties are examples of structures that show nonlinear force responses. In these situations, the theory for traditional DFS cannot be readily applied. In this work we expand the theory for DFS to also include nonlinear external forces while still maintaining compatibility with the linear DFS theory. To validate the theory we modeled a bio-complex expressed on a stiff, an elastic and a worm-like chain polymer, using Monte Carlo methods, and assessed the corresponding rupture force spectra. It was found th...
Nonlinear optomechanical paddle nanocavities
Kaviani, Hamidreza; Wu, Marcelo; Ghobadi, Roohollah; Barclay, Paul E
2014-01-01
A photonic crystal optomechanical system combining strong nonlinear optomechanical coupling, low effective mass and large optical mode spacing is introduced. This nanoscale "paddle nanocavity" device supports mechanical resonances with effective mass of 300--600 fg which couple nonlinearly to co-localized optical modes with a quadratic optomechanical coupling coefficient $g^{(2)} > 2\\pi\\times400$ MHz/nm$^2$, and a two phonon to single photon optomechanical coupling rate $\\Delta \\omega_0 > 2\\pi\\times 16$ Hz. This coupling relies on strong phonon-photon interactions in a structure whose optical mode spectrum is highly non--degenerate. Simulations indicate that nonlinear optomechanical readout of thermally driven motion in these devices should be observable for T $> 50 $ mK, and that measurement of phonon shot noise is achievable.
Nonlinear dynamics of structures
Oller, Sergio
2014-01-01
This book lays the foundation of knowledge that will allow a better understanding of nonlinear phenomena that occur in structural dynamics. This work is intended for graduate engineering students who want to expand their knowledge on the dynamic behavior of structures, specifically in the nonlinear field, by presenting the basis of dynamic balance in non‐linear behavior structures due to the material and kinematics mechanical effects. Particularly, this publication shows the solution of the equation of dynamic equilibrium for structure with nonlinear time‐independent materials (plasticity, damage and frequencies evolution), as well as those time dependent non‐linear behavior materials (viscoelasticity and viscoplasticity). The convergence conditions for the non‐linear dynamic structure solution are studied, and the theoretical concepts and its programming algorithms are presented.
Nonlinear Photonic Crystal Fibers
DEFF Research Database (Denmark)
Hansen, Kim Per
2004-01-01
, leading to reduced mode confinement and dispersion flexibility. In this thesis, we treat the nonlinear photonic crystal fiber – a special sub-class of photonic crystal fibers, the core of which has a diameter comparable to the wavelength of the light guided in the fiber. The small core results in a large...... nonlinear coefficient and in various applications, it is therefore possible to reduce the required fiber lengths quite dramatically, leading to increased stability and efficiency. Furthermore, it is possible to design these fibers with zero-dispersion at previously unreachable wavelengths, paving the way...... for completely new applications, especially in and near the visible wavelength region. One such application is supercontinuum generation. Supercontinuum generation is extreme broadening of pulses in a nonlinear medium (in this case a small-core fiber), and depending on the dispersion of the fiber, it is possible...
Schmidt, Bruno E; Ernotte, Guilmot; Clerici, Matteo; Morandotti, Roberto; Ibrahim, Heide; Legare, Francois
2016-01-01
In the framework of linear optics, light fields do not interact with each other in a medium. Yet, when their field amplitude becomes comparable to the electron binding energies of matter, the nonlinear motion of these electrons emits new dipole radiation whose amplitude, frequency and phase differ from the incoming fields. Such high fields are typically achieved with ultra-short, femtosecond (1fs = 10-15 sec.) laser pulses containing very broad frequency spectra. Here, the matter not only couples incoming and outgoing fields but also causes different spectral components to interact and mix through a convolution process. In this contribution, we describe how frequency domain nonlinear optics overcomes the shortcomings arising from this convolution in conventional time domain nonlinear optics1. We generate light fields with previously inaccessible properties because the uncontrolled coupling of amplitudes and phases is turned off. For example, arbitrary phase functions are transferred linearly to the second har...
Nonlinear optomechanics with graphene
Shaffer, Airlia; Patil, Yogesh Sharad; Cheung, Hil F. H.; Wang, Ke; Vengalattore, Mukund
2016-05-01
To date, studies of cavity optomechanics have been limited to exploiting the linear interactions between the light and mechanics. However, investigations of quantum signal transduction, quantum enhanced metrology and manybody physics with optomechanics each require strong, nonlinear interactions. Graphene nanomembranes are an exciting prospect for realizing such studies due to their inherently nonlinear nature and low mass. We fabricate large graphene nanomembranes and study their mechanical and optical properties. By using dark ground imaging techniques, we correlate their eigenmode shapes with the measured dissipation. We study their hysteretic response present even at low driving amplitudes, and their nonlinear dissipation. Finally, we discuss ongoing efforts to use these resonators for studies of quantum optomechanics and force sensing. This work is supported by the DARPA QuASAR program through a Grant from the ARO.
Nonlinear Analysis of Buckling
Directory of Open Access Journals (Sweden)
Psotný Martin
2014-06-01
Full Text Available The stability analysis of slender web loaded in compression was presented. To solve this problem, a specialized computer program based on FEM was created. The nonlinear finite element method equations were derived from the variational principle of minimum of potential energy. To obtain the nonlinear equilibrium paths, the Newton-Raphson iteration algorithm was used. Corresponding levels of the total potential energy were defined. The peculiarities of the effects of the initial imperfections were investigated. Special attention was focused on the influence of imperfections on the post-critical buckling mode. The stable and unstable paths of the nonlinear solution were separated. Obtained results were compared with those gained using ANSYS system.
Nonlinear Metamaterials for Holography
Almeida, Euclides; Prior, Yehiam
2015-01-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multi-layer metamaterial holograms where by the nonlinear process of Third Harmonic Generation, a background free image is formed at a new frequency which is the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analyzed and prospects for future device applications are discussed.
Multidimensional nonlinear descriptive analysis
Nishisato, Shizuhiko
2006-01-01
Quantification of categorical, or non-numerical, data is a problem that scientists face across a wide range of disciplines. Exploring data analysis in various areas of research, such as the social sciences and biology, Multidimensional Nonlinear Descriptive Analysis presents methods for analyzing categorical data that are not necessarily sampled randomly from a normal population and often involve nonlinear relations. This reference not only provides an overview of multidimensional nonlinear descriptive analysis (MUNDA) of discrete data, it also offers new results in a variety of fields. The first part of the book covers conceptual and technical preliminaries needed to understand the data analysis in subsequent chapters. The next two parts contain applications of MUNDA to diverse data types, with each chapter devoted to one type of categorical data, a brief historical comment, and basic skills peculiar to the data types. The final part examines several problems and then concludes with suggestions for futu...
Nonlinear airship aeroelasticity
Bessert, N.; Frederich, O.
2005-12-01
The aeroelastic derivatives for today's aircraft are calculated in the concept phase using a standard procedure. This scheme has to be extended for large airships, due to various nonlinearities in structural and aerodynamic behaviour. In general, the structural model of an airship is physically as well as geometrically nonlinear. The main sources of nonlinearity are large deformations and the nonlinear material behaviour of membranes. The aerodynamic solution is also included in the nonlinear problem, because the deformed airship influences the surrounding flow. Due to these nonlinearities, the aeroelastic problem for airships can only be solved by an iterative procedure. As one possibility, the coupled aerodynamic and structural dynamic problem was handled using linked standard solvers. On the structural side, the Finite-Element program package ABAQUS was extended with an interface to the aerodynamic solver VSAERO. VSAERO is based on the aerodynamic panel method using potential flow theory. The equilibrium of the internal structural and the external aerodynamic forces leads to the structural response and a trimmed flight state for the specified flight conditions (e.g. speed, altitude). The application of small perturbations around a trimmed state produces reaction forces and moments. These constraint forces are then transferred into translational and rotational acceleration fields by performing an inertia relief analysis of the disturbed structural model. The change between the trimmed flight state and the disturbed one yields the respective aeroelastic derivatives. By including the calculated derivatives in the linearised equation of motion system, it is possible to judge the stability and controllability of the investigated airship.
Institute of Scientific and Technical Information of China (English)
丁风和; 哈媛媛
2012-01-01
Using OLR primary data downloaded from NASA website, throng the processing for two-dimensional space datum and simple point time-sequence datum, and consulting the earthquake catalog, the OLR temporal-spacial characteristics before 337 earthqaukes (Ms≥5) located in Inner Mongolia and its neighbor (N35°-55°, E95°-130°) region scince 1974 have been analyzed with OLR monthly mean field method and OLR monthly mean field anomaly method. It is discoved that, before 3-5 months of earthquakes, long-wave radiation (OLR) all appeared the obvious exceptionally change before many earthquakes; earthquake. In many positions the anomalies are also obvious before earthquake.%将NASA官方网站下载的OLR原始数据资料,处理为二维空间数据和单点时序数据,通过地震目录核实对比,利用OLR月平均场演变法和月平均场距平法分析1974年以来内蒙古及周边地区发生的337次地震事件(Ms≥5)前,长波辐射的时空变化特征.结果发现:在震前约3-5个月,在许多地震前长波辐射(0LR)出现明显的异常反映,许多点位在震前异常比较明显.
Agrawal, Govind
2012-01-01
Since the 4e appeared, a fast evolution of the field has occurred. The 5e of this classic work provides an up-to-date account of the nonlinear phenomena occurring inside optical fibers, the basis of all our telecommunications infastructure as well as being used in the medical field. Reflecting the big developments in research, this new edition includes major new content: slow light effects, which offers a reduction in noise and power consumption and more ordered network traffic-stimulated Brillouin scattering; vectorial treatment of highly nonlinear fibers; and a brand new chapter o
DEFF Research Database (Denmark)
Mosegaard, Klaus
2012-01-01
For non-linear inverse problems, the mathematical structure of the mapping from model parameters to data is usually unknown or partly unknown. Absence of information about the mathematical structure of this function prevents us from presenting an analytical solution, so our solution depends on our......-heuristics are inefficient for large-scale, non-linear inverse problems, and that the 'no-free-lunch' theorem holds. We discuss typical objections to the relevance of this theorem. A consequence of the no-free-lunch theorem is that algorithms adapted to the mathematical structure of the problem perform more efficiently than...
Fundamentals of nonlinear optics
Powers, Peter E
2011-01-01
Peter Powers's rigorous but simple description of a difficult field keeps the reader's attention throughout. … All chapters contain a list of references and large numbers of practice examples to be worked through. … By carefully working through the proposed problems, students will develop a sound understanding of the fundamental principles and applications. … the book serves perfectly for an introductory-level course for second- and third-order nonlinear optical phenomena. The author's writing style is refreshing and original. I expect that Fundamentals of Nonlinear Optics will fast become pop
Tunable nonlinear graphene metasurfaces
Smirnova, Daria A; Kivshar, Yuri S; Khanikaev, Alexander B
2015-01-01
We introduce the concept of nonlinear graphene metasurfaces employing the controllable interaction between a graphene layer and a planar metamaterial. Such hybrid metasurfaces support two types of subradiant resonant modes, asymmetric modes of structured metamaterial elements ("metamolecules") and graphene plasmons exhibiting strong mutual coupling and avoided dispersion crossing. High tunability of graphene plasmons facilitates strong interaction between the subradiant modes, modifying the spectral position and lifetime of the associated Fano resonances. We demonstrate that strong resonant interaction, combined with the subwavelength localization of plasmons, leads to the enhanced nonlinear response and high efficiency of the second-harmonic generation.
Nonlinear effects in optical fibers
Ferreira, Mario F
2011-01-01
Cutting-edge coverage of nonlinear phenomena occurring inside optical fibers Nonlinear fiber optics is a specialized part of fiber optics dealing with optical nonlinearities and their applications. As fiber-optic communication systems have become more advanced and complex, the nonlinear effects in optical fibers have increased in importance, as they adversely affect system performance. Paradoxically, the same nonlinear phenomena also offer the promise of addressing the bandwidth bottleneck for signal processing for future ultra-high speed optical networks. Nonlinear Effects in Optical Fiber
Nonlinear elliptic systems with exponential nonlinearities
Directory of Open Access Journals (Sweden)
Said El Manouni
2002-12-01
Full Text Available In this paper we investigate the existence of solutions for {gather*} -mathop{m div}( a(| abla u | ^N| abla u |^{N-2}u = f(x,u,v quad mbox{in } Omega -mathop{m div}(a(| abla v| ^N| abla v |^{N-2}v = g(x,u,v quad mbox{in } Omega u(x = v(x = 0 quad mbox{on }partial Omega. end{gather*} Where $Omega$ is a bounded domain in ${mathbb{R}}^N$, $Ngeq 2$, $f$ and $g$ are nonlinearities having an exponential growth on $Omega$ and $a$ is a continuous function satisfying some conditions which ensure the existence of solutions.
Nonlinearity and disorder: Classification and stability of nonlinear impurity modes
DEFF Research Database (Denmark)
Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole
2001-01-01
We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schrödinger equation and describe three types of no...
Generalized Nonlinear Yule Models
Lansky, Petr; Polito, Federico; Sacerdote, Laura
2016-10-01
With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.
Ritz, Christian; Parmigiani, Giovanni
2009-01-01
R is a rapidly evolving lingua franca of graphical display and statistical analysis of experiments from the applied sciences. This book provides a coherent treatment of nonlinear regression with R by means of examples from a diversity of applied sciences such as biology, chemistry, engineering, medicine and toxicology.
Gorban, A. N.; Karlin, I.V.
2003-01-01
Nonlinear kinetic equations are reviewed for a wide audience of specialists and postgraduate students in physics, mathematical physics, material science, chemical engineering and interdisciplinary research. Contents: The Boltzmann equation, Phenomenology and Quasi-chemical representation of the Boltzmann equation, Kinetic models, Discrete velocity models, Direct simulation, Lattice Gas and Lattice Boltzmann models, Minimal Boltzmann models for flows at low Knudsen number, Other kinetic equati...
Intramolecular and nonlinear dynamics
Energy Technology Data Exchange (ETDEWEB)
Davis, M.J. [Argonne National Laboratory, IL (United States)
1993-12-01
Research in this program focuses on three interconnected areas. The first involves the study of intramolecular dynamics, particularly of highly excited systems. The second area involves the use of nonlinear dynamics as a tool for the study of molecular dynamics and complex kinetics. The third area is the study of the classical/quantum correspondence for highly excited systems, particularly systems exhibiting classical chaos.
DEFF Research Database (Denmark)
Jørgensen, Michael Finn
1995-01-01
It is generally very difficult to solve nonlinear systems, and such systems often possess chaotic solutions. In the rare event that a system is completely solvable, it is said to integrable. Such systems never have chaotic solutions. Using the Inverse Scattering Transform Method (ISTM) two...
Nonlinear phased array imaging
Croxford, Anthony J.; Cheng, Jingwei; Potter, Jack N.
2016-04-01
A technique is presented for imaging acoustic nonlinearity within a specimen using ultrasonic phased arrays. Acoustic nonlinearity is measured by evaluating the difference in energy of the transmission bandwidth within the diffuse field produced through different focusing modes. The two different modes being classical beam forming, where delays are applied to different element of a phased array to physically focus the energy at a single location (parallel firing) and focusing in post processing, whereby one element at a time is fired and a focused image produced in post processing (sequential firing). Although these two approaches are linearly equivalent the difference in physical displacement within the specimen leads to differences in nonlinear effects. These differences are localized to the areas where the amplitude is different, essentially confining the differences to the focal point. Direct measurement at the focal point are however difficult to make. In order to measure this the diffuse field is used. It is a statistical property of the diffuse field that it represents the total energy in the system. If the energy in the diffuse field for both the sequential and parallel firing case is measured then the difference between these, within the input signal bandwidth, is largely due to differences at the focal spot. This difference therefore gives a localized measurement of where energy is moving out of the transmission bandwidth due to nonlinear effects. This technique is used to image fatigue cracks and other damage types undetectable with conventional linear ultrasonic measurements.
Generalized Nonlinear Yule Models
Lansky, Petr; Polito, Federico; Sacerdote, Laura
2016-11-01
With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.
Trirefringence in nonlinear metamaterials
De Lorenci, Vitorio A
2012-01-01
We study the propagation of electromagnetic waves in the limit of geometrical optics for a class of nearly transparent nonlinear uniaxial metamaterials for which their permittivity tensors present a negative principal component. Their permeability are assumed positive and dependent on the electric field. We show that light waves experience triple refraction -- trirefringence. Additionally to the ordinary wave, two extraordinary waves propagate in such media.
Borghi, M.; Castellan, C.; Signorini, S.; Trenti, A.; Pavesi, L.
2017-09-01
Silicon photonics is a technology based on fabricating integrated optical circuits by using the same paradigms as the dominant electronics industry. After twenty years of fervid development, silicon photonics is entering the market with low cost, high performance and mass-manufacturable optical devices. Until now, most silicon photonic devices have been based on linear optical effects, despite the many phenomenologies associated with nonlinear optics in both bulk materials and integrated waveguides. Silicon and silicon-based materials have strong optical nonlinearities which are enhanced in integrated devices by the small cross-section of the high-index contrast silicon waveguides or photonic crystals. Here the photons are made to strongly interact with the medium where they propagate. This is the central argument of nonlinear silicon photonics. It is the aim of this review to describe the state-of-the-art in the field. Starting from the basic nonlinearities in a silicon waveguide or in optical resonator geometries, many phenomena and applications are described—including frequency generation, frequency conversion, frequency-comb generation, supercontinuum generation, soliton formation, temporal imaging and time lensing, Raman lasing, and comb spectroscopy. Emerging quantum photonics applications, such as entangled photon sources, heralded single-photon sources and integrated quantum photonic circuits are also addressed at the end of this review.
Nonlinear fibre optics overview
DEFF Research Database (Denmark)
Travers, J. C.; Frosz, Michael Henoch; Dudley, J. M.
2010-01-01
, provides a background to the associated nonlinear optical processes, treats the generation mechanisms from continuous wave to femtosecond pulse pump regimes and highlights the diverse applications. A full discussion of numerical methods and comprehensive computer code are also provided, enabling readers...
Tsia, Kevin K.; Jalali, Bahram
2010-05-01
An intriguing optical property of silicon is that it exhibits a large third-order optical nonlinearity, with orders-ofmagnitude larger than that of silica glass in the telecommunication band. This allows efficient nonlinear optical interaction at relatively low power levels in a small footprint. Indeed, we have witnessed a stunning progress in harnessing the Raman and Kerr effects in silicon as the mechanisms for enabling chip-scale optical amplification, lasing, and wavelength conversion - functions that until recently were perceived to be beyond the reach of silicon. With all the continuous efforts developing novel techniques, nonlinear silicon photonics is expected to be able to reach even beyond the prior achievements. Instead of providing a comprehensive overview of this field, this manuscript highlights a number of new branches of nonlinear silicon photonics, which have not been fully recognized in the past. In particular, they are two-photon photovoltaic effect, mid-wave infrared (MWIR) silicon photonics, broadband Raman effects, inverse Raman scattering, and periodically-poled silicon (PePSi). These novel effects and techniques could create a new paradigm for silicon photonics and extend its utility beyond the traditionally anticipated applications.
Leitao, J C; Gerlach, M; Altmann, E G
2016-01-01
One of the most celebrated findings in complex systems in the last decade is that different indexes y (e.g., patents) scale nonlinearly with the population~x of the cities in which they appear, i.e., $y\\sim x^\\beta, \\beta \
Nonlinear Gravitational Lagrangians revisited
Magnano, Guido
2016-01-01
The Legendre transformation method, applied in 1987 to deal with purely metric gravitational Lagrangians with nonlinear dependence on the Ricci tensor, is extended to metric-affine models and is shown to provide a concise and insightful comparison of the dynamical content of the two variational frameworks.
Nonlinearities in Microwave Superconductivity
Ledenyov, Dimitri O.; Ledenyov, Viktor O.
2012-01-01
The research is focused on the modeling of nonlinear properties of High Temperature Superconducting (HTS) thin films, using Bardeen, Cooper, Schrieffer and Lumped Element Circuit theories, with purpose to enhance microwave power handling capabilities of microwave filters and optimize design of microwave circuits in micro- and nano- electronics.
Nonlinear tsunami generation mechanism
Directory of Open Access Journals (Sweden)
M. A. Nosov
2001-01-01
Full Text Available The nonlinear mechanism of long gravitational surface water wave generation by high-frequency bottom oscillations in a water layer of constant depth is investigated analytically. The connection between the surface wave amplitude and the parameters of bottom oscillations and source length is investigated.
DEFF Research Database (Denmark)
Mosekilde, Erik
Through a significant number of detailed and realistic examples this book illustrates how the insights gained over the past couple of decades in the fields of nonlinear dynamics and chaos theory can be applied in practice. Aomng the topics considered are microbiological reaction systems, ecological...
Terahertz semiconductor nonlinear optics
DEFF Research Database (Denmark)
Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias
2013-01-01
nonlinearity in doped semiconductors originates from the near-instantaneous heating of free electrons in the ponderomotive potential created by electric field of the THz pulse, leading to ultrafast increase of electron effective mass by intervalley scattering. Modification of effective mass in turn leads...
Nonlinear Optical Terahertz Technology Project
National Aeronautics and Space Administration — Our approach is based on high-Q optical WGM resonators made with a nonlinear crystal. Such resonators have been demonstrated to dramatically enhance nonlinear...
Phase retrieval using nonlinear diversity.
Lu, Chien-Hung; Barsi, Christopher; Williams, Matthew O; Kutz, J Nathan; Fleischer, Jason W
2013-04-01
We extend the Gerchberg-Saxton algorithm to phase retrieval in a nonlinear system. Using a tunable photorefractive crystal, we experimentally demonstrate the noninterferometric technique by reconstructing an unknown phase object from optical intensity measurements taken at different nonlinear strengths.
Strong nonlinear oscillators analytical solutions
Cveticanin, Livija
2017-01-01
This book outlines an analytical solution procedure of the pure nonlinear oscillator system, offering a solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter. Includes exercises.
Cubication of Conservative Nonlinear Oscillators
Belendez, Augusto; Alvarez, Mariela L.; Fernandez, Elena; Pascual, Immaculada
2009-01-01
A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear…
Terahertz Nonlinear Optics in Semiconductors
DEFF Research Database (Denmark)
Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias C.
2013-01-01
We demonstrate the nonlinear optical effects – selfphase modulation and saturable absorption of a single-cycle THz pulse in a semiconductor. Resulting from THz-induced modulation of Drude plasma, these nonlinear optical effects, in particular, lead to self-shortening and nonlinear spectral...
Fault Detection for Nonlinear Systems
DEFF Research Database (Denmark)
Stoustrup, Jakob; Niemann, H.H.
1998-01-01
The paper describes a general method for designing fault detection and isolation (FDI) systems for nonlinear processes. For a rich class of nonlinear systems, a nonlinear FDI system can be designed using convex optimization procedures. The proposed method is a natural extension of methods based...
Tassev, V. L.; Vangala, S.; Peterson, R.; Kimani, M.; Snure, M.; Markov, I.
2016-03-01
Frequency conversion in orientation-patterned quasi-phase matched materials is a leading approach for generating tunable mid- and long-wave coherent IR radiation for a wide variety of applications. A number of nonlinear optical materials are currently under intensive investigation. Due to their unique properties, chiefly wide IR transparency and high nonlinear susceptibility, GaAs and GaP are among the most promising. Compared to GaAs, GaP has the advantage of having higher thermal conductivity and significantly lower 2PA in the convenient pumping range of 1- 1.7 μm. HVPE growth of OPGaP, however, has encountered certain challenges: low quality and high price of commercially available GaP wafers; and strong parasitic nucleation during HVPE growth that reduces growth rate and aggravates layer quality, often leading to pattern overgrowth. Lessons learned from growing OPGaAs were not entirely helpful, leaving us to alternative solutions for both homoepitaxial growth and template preparation. We report repeatable one-step HVPE growth of up to 400 μm thick OPGaP with excellent domain fidelity deposited for first time on OPGaAs templates. The templates were prepared by wafer fusion bonding or MBE assisted polarity inversion technique. A close to equilibrium growth at such a large lattice mismatch (-3.6%) is itself noteworthy, especially when previously reported attempts (growth of OPZnSe on OPGaAs templates) at much smaller mismatch (+0.3%) have produced limited results. Combining the advantages of the two most promising materials, GaAs and GaP, is a solution that will accelerate the development of high power, tunable laser sources for the mid- and long-wave IR, and THz region.
Nonlinear electrostatic drift Kelvin-Helmholtz instability
Sharma, Avadhesh C.; Srivastava, Krishna M.
1993-01-01
Nonlinear analysis of electrostatic drift Kelvin-Helmholtz instability is performed. It is shown that the analysis leads to the propagation of the weakly nonlinear dispersive waves, and the nonlinear behavior is governed by the nonlinear Burger's equation.
Institute of Scientific and Technical Information of China (English)
李全勇; 李向天; 康玉思; 牟达
2013-01-01
The infrared scene simulator based on DMD provides the advanced means for the performance testing and evaluation of the infrared system. According to the working principle of DMD, the general scheme of infrared scene simulator is determined, that the illumination system is connected to projection system with the dichroic prism. The aberration properties and optical design and athermal design method of the projection optical system are discussed. A projection optical system is designed, which working waveband is 8~12μm long wave infrared band, F # is 2.8, the field of view is 3°. The projection system was athermalized by optical passive athermal design method at -40-60 ℃. The design result indicates that the optical transfer functions are close to the diffraction limit in the required temperature range, the image quality meet the design requirements, and the system has the characteristics with small loss radiation energy, high resolution and compact structure.%基于数字微镜器件(digital micromirror device，DMD)的红外景象模拟器能够为红外系统性能测试与评估提供先进的手段。根据 DMD 的工作原理，确定了以分光棱镜来连接照明系统和投影系统的红外景象模拟器总体方案。探讨了红外景象模拟器投影光学系统的像差特性、光学设计和无热化的设计方法，设计了一套工作在长波红外8～12μm，F#为2.8，视场角为3°的投影光学系统，并对该系统在−40～60℃之间进行光学被动式无热化设计。结果表明：该系统在所要求的温度范围内，光学传递函数均接近衍射极限，成像质量满足系统的设计要求，并具有辐射能量损失小、分辨率高、结构紧凑等特点。
Optothermal nonlinearity of silica aerogel
Braidotti, Maria Chiara; Fleming, Adam; Samuels, Michiel C; Di Falco, Andrea; Conti, Claudio
2016-01-01
We report on the characterization of silica aerogel thermal optical nonlinearity, obtained by z-scan technique. The results show that typical silica aerogels have nonlinear optical coefficient similar to that of glass $(\\simeq 10^{-12} $m$^2/$W), with negligible optical nonlinear absorption. The non\\-li\\-near coefficient can be increased to values in the range of $10^{-10} $m$^2/$W by embedding an absorbing dye in the aerogel. This value is one order of magnitude higher than that observed in the pure dye and in typical highly nonlinear materials like liquid crystals.
Essentials of nonlinear optics
Murti, Y V G S
2014-01-01
Current literature on Nonlinear Optics varies widely in terms of content, style, and coverage of specific topics, relative emphasis of areas and the depth of treatment. While most of these books are excellent resources for the researchers, there is a strong need for books appropriate for presenting the subject at the undergraduate or postgraduate levels in Universities. The need for such a book to serve as a textbook at the level of the bachelors and masters courses was felt by the authors while teaching courses on nonlinear optics to students of both science and engineering during the past two decades. This book has emerged from an attempt to address the requirement of presenting the subject at college level. A one-semester course covering the essentials can effectively be designed based on this.
Nonlinear metamaterials for holography
Almeida, Euclides; Bitton, Ora; Prior, Yehiam
2016-08-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three-dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years, it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multilayer metamaterial holograms. A background free image is formed at a new frequency--the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analysed and prospects for future device applications are discussed.
Nonlinear metamaterials for holography
Almeida, Euclides; Bitton, Ora
2016-01-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three-dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years, it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multilayer metamaterial holograms. A background free image is formed at a new frequency—the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analysed and prospects for future device applications are discussed. PMID:27545581
Van Leeuwen, Peter Jan; Reich, Sebastian
2015-01-01
This book contains two review articles on nonlinear data assimilation that deal with closely related topics but were written and can be read independently. Both contributions focus on so-called particle filters. The first contribution by Jan van Leeuwen focuses on the potential of proposal densities. It discusses the issues with present-day particle filters and explorers new ideas for proposal densities to solve them, converging to particle filters that work well in systems of any dimension, closing the contribution with a high-dimensional example. The second contribution by Cheng and Reich discusses a unified framework for ensemble-transform particle filters. This allows one to bridge successful ensemble Kalman filters with fully nonlinear particle filters, and allows a proper introduction of localization in particle filters, which has been lacking up to now.
Nonlinearity without Superluminality
Kent, A
2002-01-01
Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signalling. As Gisin and Polchinski first pointed out, this is not true for general nonlinear modifications of the Schroedinger equation. Excluding superluminal signalling has thus been taken to rule out most nonlinear versions of quantum theory. The no superluminal signalling constraint has also been used for alternative derivations of the optimal fidelities attainable for imperfect quantum cloning and other operations. These results apply to theories satisfying the rule that their predictions for widely separated and slowly moving entangled systems can be approximated by non-relativistic equations of motion with respect to a preferred time coordinate. This paper describes a natural way in which this rule might fail to hold. In particular, it is shown that quantum readout devices which di...
Monte Carlo and nonlinearities
Dauchet, Jérémi; Blanco, Stéphane; Caliot, Cyril; Charon, Julien; Coustet, Christophe; Hafi, Mouna El; Eymet, Vincent; Farges, Olivier; Forest, Vincent; Fournier, Richard; Galtier, Mathieu; Gautrais, Jacques; Khuong, Anaïs; Pelissier, Lionel; Piaud, Benjamin; Roger, Maxime; Terrée, Guillaume; Weitz, Sebastian
2016-01-01
The Monte Carlo method is widely used to numerically predict systems behaviour. However, its powerful incremental design assumes a strong premise which has severely limited application so far: the estimation process must combine linearly over dimensions. Here we show that this premise can be alleviated by projecting nonlinearities on a polynomial basis and increasing the configuration-space dimension. Considering phytoplankton growth in light-limited environments, radiative transfer in planetary atmospheres, electromagnetic scattering by particles and concentrated-solar-power-plant productions, we prove the real world usability of this advance on four test-cases that were so far regarded as impracticable by Monte Carlo approaches. We also illustrate an outstanding feature of our method when applied to sharp problems with interacting particles: handling rare events is now straightforward. Overall, our extension preserves the features that made the method popular: addressing nonlinearities does not compromise o...
Nonlinear Photonics 2014: introduction.
Akhmediev, N; Kartashov, Yaroslav
2015-01-12
International Conference "Nonlinear Photonics-2014" took place in Barcelona, Spain on July 27-31, 2014. It was a part of the "Advanced Photonics Congress" which is becoming a traditional notable event in the world of photonics. The current focus issue of Optics Express contains contributions from the participants of the Conference and the Congress. The articles in this focus issue by no means represent the total number of the congress contributions (around 400). However, it demonstrates wide range of topics covered at the event. The next conference of this series is to be held in 2016 in Australia, which is the home of many researchers working in the field of photonics in general and nonlinear photonics in particular.
Energy Technology Data Exchange (ETDEWEB)
Mitsotakis, Dimitrios, E-mail: dmitsot@gmail.com [Victoria University of Wellington, School of Mathematics, Statistics and Operations Research, PO Box 600, Wellington 6140 (New Zealand); Dutykh, Denys, E-mail: Denys.Dutykh@univ-savoie.fr [LAMA, UMR 5127 CNRS, Université Savoie Mont Blanc, Campus Scientifique, F-73376 Le Bourget-du-Lac Cedex (France); Assylbekuly, Aydar, E-mail: asylbekuly@mail.ru [Khoja Akhmet Yassawi International Kazakh–Turkish University, Faculty of Natural Science, Department of Mathematics, 161200 Turkestan (Kazakhstan); Zhakebayev, Dauren, E-mail: daurjaz@mail.ru [Al-Farabi Kazakh National University, Faculty of Mechanics and Mathematics, Department of Mathematical and Computer Modelling, 050000 Almaty (Kazakhstan)
2017-05-25
In this Letter we consider long capillary–gravity waves described by a fully nonlinear weakly dispersive model. First, using the phase space analysis methods we describe all possible types of localized travelling waves. Then, we especially focus on the critical regime, where the surface tension is exactly balanced by the gravity force. We show that our long wave model with a critical Bond number admits stable travelling wave solutions with a singular crest. These solutions are usually referred to in the literature as peakons or peaked solitary waves. They satisfy the usual speed-amplitude relation, which coincides with Scott–Russel's empirical formula for solitary waves, while their decay rate is the same regardless their amplitude. Moreover, they can be of depression or elevation type independent of their speed. The dynamics of these solutions are studied as well. - Highlights: • A model for long capillary–gravity weakly dispersive and fully nonlinear water waves is derived. • Shallow capillary–gravity waves are classified using phase plane analysis. • Peaked travelling waves are found in the critical regime. • The dynamics of peakons in Serre–Green–Naghdi equations is studied numerically.
Nonlinear fractional relaxation
Indian Academy of Sciences (India)
A Tofighi
2012-04-01
We deﬁne a nonlinear model for fractional relaxation phenomena. We use -expansion method to analyse this model. By studying the fundamental solutions of this model we ﬁnd that when → 0 the model exhibits a fast decay rate and when → ∞ the model exhibits a power-law decay. By analysing the frequency response we ﬁnd a logarithmic enhancement for the relative ratio of susceptibility.
Indian Academy of Sciences (India)
Ramaswamy Jaganathan; Sudeshna Sinha
2005-03-01
Motivated by studies on -deformed physical systems related to quantum group structures, and by the elements of Tsallis statistical mechanics, the concept of -deformed nonlinear maps is introduced. As a specific example, a -deformation procedure is applied to the logistic map. Compared to the canonical logistic map, the resulting family of -logistic maps is shown to have a wider spectrum of interesting behaviours, including the co-existence of attractors – a phenomenon rare in one-dimensional maps.
Controllability of nonlinear systems.
Sussmann, H. J.; Jurdjevic, V.
1972-01-01
Discussion of the controllability of nonlinear systems described by the equation dx/dt - F(x,u). Concepts formulated by Chow (1939) and Lobry (1970) are applied to establish criteria for F and its derivatives to obtain qualitative information on sets which can be obtained from x which denotes a variable of state in an arbitrary, real, analytical manifold. It is shown that controllability implies strong accessibility for a large class of manifolds including Euclidean spaces.-
Stochastic Nonlinear Aeroelasticity
2009-01-01
STOCHASTIC NONLINEAR AEROELASTICITY 5a. CONTRACT NUMBER In- house 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 0601102 6. AUTHOR(S) Philip S...ABSTRACT This report documents the culmination of in- house work in the area of uncertainty quantification and probabilistic techniques for... coff U∞ cs ea lw cw Figure 6: Wing and store geometry (left), wing box structural model (middle), flutter distribution (right
2007-03-01
IEEE Transactions on Automatic Control , AC- 48, pp. 1712-1723, (2003). [14] C.I. Byrnes, A. Isidori...Nonlinear internal models for output regulation,” IEEE Transactions on Automatic Control , AC-49, pp. 2244-2247, (2004). [15] C.I. Byrnes, F. Celani, A...approach,” IEEE Transactions on Automatic Control , 48 (Dec. 2003), 2172–2190. 2. C. I. Byrnes, “Differential Forms and Dynamical Systems,” to appear
Filamentation with nonlinear Bessel vortices.
Jukna, V; Milián, C; Xie, C; Itina, T; Dudley, J; Courvoisier, F; Couairon, A
2014-10-20
We present a new type of ring-shaped filaments featured by stationary nonlinear high-order Bessel solutions to the laser beam propagation equation. Two different regimes are identified by direct numerical simulations of the nonlinear propagation of axicon focused Gaussian beams carrying helicity in a Kerr medium with multiphoton absorption: the stable nonlinear propagation regime corresponds to a slow beam reshaping into one of the stationary nonlinear high-order Bessel solutions, called nonlinear Bessel vortices. The region of existence of nonlinear Bessel vortices is found semi-analytically. The influence of the Kerr nonlinearity and nonlinear losses on the beam shape is presented. Direct numerical simulations highlight the role of attractors played by nonlinear Bessel vortices in the stable propagation regime. Large input powers or small cone angles lead to the unstable propagation regime where nonlinear Bessel vortices break up into an helical multiple filament pattern or a more irregular structure. Nonlinear Bessel vortices are shown to be sufficiently intense to generate a ring-shaped filamentary ionized channel in the medium which is foreseen as opening the way to novel applications in laser material processing of transparent dielectrics.
Strongly nonlinear oscillators analytical solutions
Cveticanin, Livija
2014-01-01
This book provides the presentation of the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. The book presents the original author’s method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter is considered. Special attention is given to the one and two mass oscillatory systems with two-degrees-of-freedom. The criteria for the deterministic chaos in ideal and non-ideal pure nonlinear oscillators are derived analytically. The method for suppressing chaos is developed. Important problems are discussed in didactic exercises. The book is self-consistent and suitable as a textbook for students and also for profess...
Quantum well nonlinear microcavities
Oudar, J. L.; Kuszelewicz, R.; Sfez, B.; Pellat, D.; Azoulay, R.
We report on recent progress in reducing the power threshold of all-optical bistable quantum well vertical microcavities. Significant improvements are achieved through an increase of the cavity finesse, together with a reduction of the device active layer thickness. A critical intensity of 5 μW/μm 2 has been observed on a microcavity of finesse 250, with a nonlinear medium of only 18 GaAs quantum wells of 10 nm thickness. Further improvements of the Bragg mirror quality resulted in a finesse of 700 and a power-lifetime product of 15 fJ/μm 2. Microresonator pixellation allows to obtain 2-dimensional arrays. A thermally-induced alloy-mixing technique is described, which produced a 110 meV carrier confinement energy, together with a refractive index change of -.012, averaged over the 2.6 μm nonlinear medium thickness. The resulting electrical and optical confinement is shown to improve the nonlinear characteristics, by limiting lateral carrier diffusion and light diffraction.
Energy Technology Data Exchange (ETDEWEB)
Choi, W.; Camassa, R.
1998-12-31
The authors derive model equations that govern the evolution of internal gravity waves at the interface of two immiscible fluids. These models follow from the original Euler equations under the sole assumption that the waves are long compared to the undisturbed thickness of one of the fluid layers. No smallness assumption on the wave amplitude is made. Here the shallow water configuration is first considered, whereby the waves are taken to be long with respect to the total undisturbed thickness of the fluids. In part 2, the authors derive models for the configuration in which one of the two fluids has a thickness much larger than the wavelength. The fully nonlinear models contain the Korteweg-de Vries (KdV) equation and the intermediate-long-wave (ILW) equation, for shallow and deep water configurations respectively, as special cases in the limit of weak nonlinearity and unidirectional wave propagation. In particular, for a solitary wave of given amplitude, the characteristic wavelength is larger and the wave speed smaller than their counterparts for solitary wave solutions of the weakly nonlinear equations. These features are compared and found in overall good agreement with available experimental data for solitary waves of large amplitude in two-fluid systems.
De, Saumyendu; Sahai, Atul Kumar; Nath Goswami, Bhupendra
2013-04-01
energy and the scale interactions in terms of the wave-wave exchanges among nonlinear triads are formulated and the above hypothesis is tested through a diagnostic analysis of the error energetics in two different model predictions at the lower troposphere (850hPa). It has been revealed that nonlinear triad interactions lead to advection of errors from short and synoptic waves (wave number >10) to long waves (wave numbers 5 - 10) and from long waves to ultra-long waves (wave numbers 1 - 4) and is responsible for the rapid growth of errors in the planetary waves. The continuous generation and then, non-linear propagation of error upto the planetary scales in the course of prediction increase the uncertainty in ultra-long scales which actually inhibit to predict accurately the planetary scale waves in tropics during medium range forecasts. Unraveling this exact mechanism through which upscale transfer of errors take place may help us devising a method to limit the mixing of small scale error with the error in forecast of tropical Intra-seasonal Oscillations and improve the prediction of lower tropospheric ISOs. Keywords: Predictability, Systematic error energetics, Scale interactions, Triads, Intra-seasonal Oscillations. Reference: The YOTC Science Plan (2008) prepared by Duane Waliser and Mitch Moncrieff. A joint WCRP-WWRP/THORPEX International Initiative, WMO/TD-No. 1452, pp. 20. Baumhefner D P and Downey P 1978 Forecast intercomparisons from three numerical weather prediction models; Mon. Weather Rev. 106 1245 - 1279. Krishnamurti T N, Subramanium M, Oosteroff D K, Daughenbaugh G. 1990 Predictability of low frequency modes. Meteorol. Atmos. phys. 44 63 - 83.
Nonlinear robust hierarchical control for nonlinear uncertain systems
Directory of Open Access Journals (Sweden)
Leonessa Alexander
1999-01-01
Full Text Available A nonlinear robust control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving nominal system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear robust control strategy is developed that robustly stabilizes a given nonlinear system over a prescribed range of system uncertainty by robustly stabilizing a collection of nonlinear controlled uncertain subsystems. The robust switching nonlinear controller architecture is designed based on a generalized (lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized nominal system equilibria. The proposed framework robustly stabilizes a compact positively invariant set of a given nonlinear uncertain dynamical system with structured parametric uncertainty. Finally, the efficacy of the proposed approach is demonstrated on a jet engine propulsion control problem with uncertain pressure-flow map data.
Nonlinear scattering in plasmonic nanostructures
Chu, Shi-Wei
2016-09-01
Nonlinear phenomena provide novel light manipulation capabilities and innovative applications. Recently, we discovered nonlinear saturation on single-particle scattering of gold nanospheres by continuous-wave laser excitation and innovatively applied to improve microscopic resolution down to λ/8. However, the nonlinearity was limited to the green-orange plasmonic band of gold nanosphere, and the underlying mechanism has not yet been fully understood. In this work, we demonstrated that nonlinear scattering exists for various material/geometry combinations, thus expanding the applicable wavelength range. For near-infrared, gold nanorod is used, while for blue-violet, silver nanospheres are adopted. In terms of mechanism, the nonlinearity may originate from interband/intraband absorption, hot electron, or hot lattice, which are spectrally mixed in the case of gold nanosphere. For gold nanorod and silver nanosphere, nonlinear scattering occurs at plasmonic resonances, which are spectrally far from interband/intraband absorptions, so they are excluded. We found that the nonlinear index is much larger than possible contributions from hot electrons in literature. Therefore, we conclude that hot lattice is the major mechanism. In addition, we propose that similar to z-scan, which is the standard method to characterize nonlinearity of a thin sample, laser scanning microscopy should be adopted as the standard method to characterize nonlinearity from a nanostructure. Our work not only provides the physical mechanism of the nonlinear scattering, but also paves the way toward multi-color superresolution imaging based on non-bleaching plasmonic scattering.
Discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities
DEFF Research Database (Denmark)
Khare, A.; Rasmussen, Kim Ø; Salerno, M.
2006-01-01
A class of discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the saturable discrete nonlinear Schrodinger equation and the Ablowi......-Ladik equation. As a common property, these equations possess three kinds of exact analytical stationary solutions for which the Peierls-Nabarro barrier is zero. Several properties of these solutions, including stability, discrete breathers, and moving solutions, are investigated....
Dichromatic nonlinear eigenmodes in slab waveguide with chi(2) nonlinearity.
Darmanyan, S A; Nevière, M
2001-03-01
The existence of purely nonlinear eigenmodes in a waveguiding structure composed of a slab with quadratic nonlinearity surrounded by (non)linear claddings is reported. Modes having bright and dark solitonlike shapes and consisting of two mutually locked harmonics are identified. Asymmetrical modes are shown to exist in symmetrical environments. Constraints for the existence of the modes are derived in terms of parameters of guiding structure materials.
Nonlinear Schrodinger equation with chaotic, random, and nonperiodic nonlinearity
Cardoso, W B; Avelar, A T; Bazeia, D; Hussein, M S
2009-01-01
In this paper we deal with a nonlinear Schr\\"{o}dinger equation with chaotic, random, and nonperiodic cubic nonlinearity. Our goal is to study the soliton evolution, with the strength of the nonlinearity perturbed in the space and time coordinates and to check its robustness under these conditions. Comparing with a real system, the perturbation can be related to, e.g., impurities in crystalline structures, or coupling to a thermal reservoir which, on the average, enhances the nonlinearity. We also discuss the relevance of such random perturbations to the dynamics of Bose-Einstein Condensates and their collective excitations and transport.
Stolz, A; Markey, L; Francs, G Colas des; Bouhelier, A
2013-01-01
We introduce strongly-coupled optical gap antennas to interface optical radiation with current-carrying electrons at the nanoscale. The transducer relies on the nonlinear optical and electrical properties of an optical antenna operating in the tunneling regime. We discuss the underlying physical mechanisms controlling the conversion and demonstrate that a two-wire optical antenna can provide advanced optoelectronic functionalities beyond tailoring the electromagnetic response of a single emitter. Interfacing an electronic command layer with a nanoscale optical device may thus be facilitated by the optical rectennas discussed here.
Nonlinear surface electromagnetic phenomena
Ponath, H-E
1991-01-01
In recent years the physics of electromagnetic surface phenomena has developed rapidly, evolving into technologies for communications and industry, such as fiber and integrated optics. The variety of phenomena based on electromagnetism at surfaces is rich and this book was written with the aim of summarizing the available knowledge in selected areas of the field. The book contains reviews written by solid state and optical physicists on the nonlinear interaction of electromagnetic waves at and with surfaces and films. Both the physical phenomena and some potential applications are
Nonlinear electrodynamics with birefringence
Kruglov, S I
2015-01-01
A new model of nonlinear electrodynamics with three parameters is suggested. The phenomena of vacuum birefringence takes place when there is the external constant magnetic field. We calculate the indices of refraction for two polarizations of electromagnetic waves, parallel and perpendicular to the magnetic induction field. From the Bir\\'{e}fringence Magn\\'{e}tique du Vide (BMV) experiment one of the coefficients, $\\gamma\\approx 10^{-20}$ T$^{-2}$, was estimated. The canonical, symmetrical Belinfante energy-momentum tensors and dilatation current were obtained. The dilatation symmetry and the dual symmetry are broken in the model considered.
Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning
2001-01-01
Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which
Nonlinear dynamics in psychology
Directory of Open Access Journals (Sweden)
Stephen J. Guastello
2001-01-01
Full Text Available This article provides a survey of the applications of nonlinear dynamical systems theory to substantive problems encountered in the full scope of psychological science. Applications are organized into three topical areas – cognitive science, social and organizational psychology, and personality and clinical psychology. Both theoretical and empirical studies are considered with an emphasis on works that capture the broadest scope of issues that are of substantive interest to psychological theory. A budding literature on the implications of NDS principles in professional practice is reported also.
2009-11-18
analytic semigroup T(t) ~ eAl is exponentially stable (Notice that it is also a contraction semigroup ). 3. Be 3(U, Z) and P e £(W, 2) are bounded. 4. Ce...quite often in practice, .4 is self-adjoint. We also note that, since we assume (—A) is sectorial, we work with the semigroup exp(.4f) rather than...Uniform Output Regulation of Nonlinear Sys- tems: A convergent Dynamics Approach, Birkhauser, Boston, 2006. 23 135] A. Pazy, Semigroups of Linear
Directory of Open Access Journals (Sweden)
DJAIRO G. DEFIGUEIREDO
2000-12-01
Full Text Available In this paper we treat the question of the existence of solutions of boundary value problems for systems of nonlinear elliptic equations of the form - deltau = f (x, u, v,Ñu,Ñv, - deltav = g(x, u, v, Ñu, Ñv, in omega, We discuss several classes of such systems using both variational and topological methods. The notion of criticality takes into consideration the coupling, which plays important roles in both a priori estimates for the solutions and Palais-Smale conditions for the associated functional in the variational case.
Global Analysis of Nonlinear Dynamics
Luo, Albert
2012-01-01
Global Analysis of Nonlinear Dynamics collects chapters on recent developments in global analysis of non-linear dynamical systems with a particular emphasis on cell mapping methods developed by Professor C.S. Hsu of the University of California, Berkeley. This collection of contributions prepared by a diverse group of internationally recognized researchers is intended to stimulate interests in global analysis of complex and high-dimensional nonlinear dynamical systems, whose global properties are largely unexplored at this time. This book also: Presents recent developments in global analysis of non-linear dynamical systems Provides in-depth considerations and extensions of cell mapping methods Adopts an inclusive style accessible to non-specialists and graduate students Global Analysis of Nonlinear Dynamics is an ideal reference for the community of nonlinear dynamics in different disciplines including engineering, applied mathematics, meteorology, life science, computational science, and medicine.
Nonlinear evolution of drift instabilities
Energy Technology Data Exchange (ETDEWEB)
Lee, W.W.; Krommes, J.A.; Oberman, C.R.; Smith, R.A.
1984-01-01
The nonlinear evolution of collisionless drift instabilities in a shear-free magnetic field has been studied by means of gyrokinetic particle simulation as well as numerical integration of model mode-coupling equations. The purpose of the investigation is to identify relevant nonlinear mechanisms responsible for the steady-state drift wave fluctuations. It is found that the saturation of the instability is mainly caused by the nonlinear E x B convection of the resonant electrons and their associated velocity space nonlinearity. The latter also induces energy exchange between the competing modes, which, in turn, gives rise to enhanced diffusion. The nonlinear E x B convection of the ions, which contributes to the nonlinear frequency shift, is also an important ingredient for the saturation.
Rashidian Vaziri, Mohammad Reza
2013-07-10
In this paper, the Z-scan theory for nonlocal nonlinear media has been further developed when nonlinear absorption and nonlinear refraction appear simultaneously. To this end, the nonlinear photoinduced phase shift between the impinging and outgoing Gaussian beams from a nonlocal nonlinear sample has been generalized. It is shown that this kind of phase shift will reduce correctly to its known counterpart for the case of pure refractive nonlinearity. Using this generalized form of phase shift, the basic formulas for closed- and open-aperture beam transmittances in the far field have been provided, and a simple procedure for interpreting the Z-scan results has been proposed. In this procedure, by separately performing open- and closed-aperture Z-scan experiments and using the represented relations for the far-field transmittances, one can measure the nonlinear absorption coefficient and nonlinear index of refraction as well as the order of nonlocality. Theoretically, it is shown that when the absorptive nonlinearity is present in addition to the refractive nonlinearity, the sample nonlocal response can noticeably suppress the peak and enhance the valley of the Z-scan closed-aperture transmittance curves, which is due to the nonlocal action's ability to change the beam transverse dimensions.
长波紫外线照射对花背蟾蜍肾脏结构损伤%Impacts of long-wave ultraviolet radiation on kidney structure of Bufo Raddei
Institute of Scientific and Technical Information of China (English)
屈婷婷; 李丕鹏; 聂颖; 陆宇燕
2012-01-01
为研究长波紫外线对花背蟾蜍(Bufo raddei)肾脏的损伤,用波长为365 nm的长波紫外线(UVA)以352 μW·cm-2的辐射量对花背蟾蜍亚成体进行150、300和450 min的连续照射,分别在照射后立即、3、6、9、12和15 d取材,常规石蜡切片.结果表明:UVA照射后,3组不同照射时间的花背蟾蜍肾脏整体结构基本完整,但均出现肾小管管壁破裂,管径显著缩小,肾小囊消失,而300 min照射组的损伤则极为明显,其后依次为450 min照射组与150 min照射组,300与450 min照射组的肾小体塌陷程度较150 min照射组更为严重;经15 d的恢复,虽出现明显好转,但大多指标仍与对照组间存在极显著性差异;UVA对花背蟾蜍肾脏有着不可忽视的损伤,虽然具有一定的自我修复的能力,但在野外,紫外辐射的增强和植被的减少可导致两栖类遭受过度的紫外辐射,进而引起两栖类种群的衰减.%In order to study the damage of long-wave ultraviolet (UVA) on Bufo raddei kidney, three groups of Bufo raddeis juveniles were irradiated continuously by 365 nm UVA with a dosage of 352 μW · cm-2 for 150, 300, and 450 min, respectively, and the kidney after the irradiation was dissected immediately and 3, 6, 9, 12, and 15 days later, with its histological changes observed by general histological method. After the UVA radiation, the kidney structure was basically in integrity, except the fracture and visible constriction of renal tubule and the disappearance of renal capsule, which were most obvious in the 300 min group, followed by in 450 min group and in 150 min group. The damage to Malpigkian bodies was more serious in 300 and 450 min groups than in 150 min group. After 15 days recovery, though the damage was somewhat mitigated , most of the histological indices of the three experimental groups were significantly different from the control group. This study showed that the damage of UVA to B. raddei kidney could not be ignored in spite of
Topics on nonlinear generalized functions
Colombeau, J F
2011-01-01
The aim of this paper is to give the text of a recent introduction to nonlinear generalized functions exposed in my talk in the congress gf2011, which was asked by several participants. Three representative topics were presented: two recalls "Nonlinear generalized functions and their connections with distribution theory", "Examples of applications", and a recent development: "Locally convex topologies and compactness: a functional analysis of nonlinear generalized functions".
Nonlinear Ultrasonic Phased Array Imaging
Potter, J. N.; Croxford, A. J.; Wilcox, P. D.
2014-10-01
This Letter reports a technique for the imaging of acoustic nonlinearity. By contrasting the energy of the diffuse field produced through the focusing of an ultrasonic array by delayed parallel element transmission with that produced by postprocessing of sequential transmission data, acoustic nonlinearity local to the focal point is measured. Spatially isolated wave distortion is inferred without requiring interrogation of the wave at the inspection point, thereby allowing nonlinear imaging through depth.
Nonlinear ultrasonic phased array imaging
Potter, J N; Croxford, A.J.; Wilcox, P. D.
2014-01-01
This Letter reports a technique for the imaging of acoustic nonlinearity. By contrasting the energy of the diffuse field produced through the focusing of an ultrasonic array by delayed parallel element transmission with that produced by postprocessing of sequential transmission data, acoustic nonlinearity local to the focal point is measured. Spatially isolated wave distortion is inferred without requiring interrogation of the wave at the inspection point, thereby allowing nonlinear imaging t...
Research on Nonlinear Dynamical Systems.
1983-01-10
investigated fundamental aspects of functional differential equations, including qualitative questions (stability, nonlinear oscillations ), in 142,45,47,52...Bifurcation in the Duffing equation with several parameters, II. Proc. of the Royal Society of Edinburgh, Series A, 79A (1977), pp.317-326. 1I.J (with ;Ibtoas...Lecture Notes in Mathematics, Vol. 730 (1979). [54] Nonlinear oscillations in equations with delays. Proc. at A.M.S. 10th Summer Seminar on Nonlinear
Nonlinear ultrasonic phased array imaging.
Potter, J N; Croxford, A J; Wilcox, P D
2014-10-03
This Letter reports a technique for the imaging of acoustic nonlinearity. By contrasting the energy of the diffuse field produced through the focusing of an ultrasonic array by delayed parallel element transmission with that produced by postprocessing of sequential transmission data, acoustic nonlinearity local to the focal point is measured. Spatially isolated wave distortion is inferred without requiring interrogation of the wave at the inspection point, thereby allowing nonlinear imaging through depth.
Remote Atmospheric Nonlinear Optical Magnetometry
2014-04-28
Boyd , Nonlinear Optics (Elsevier, Burlington, MA, 2008). [13] M. Scully and S. Zubairy, Quantum Optics (Cambridge U. Press, Cambridge, UK, 1997...Naval Research Laboratory Washington, DC 20375-5320 NRL/MR/6703--14-9548 Remote Atmospheric Nonlinear Optical Magnetometry PhilliP SPrangle...b. ABSTRACT c. THIS PAGE 18. NUMBER OF PAGES 17. LIMITATION OF ABSTRACT Remote Atmospheric Nonlinear Optical Magnetometry Phillip Sprangle, Luke
Applications of nonlinear fiber optics
Agrawal, Govind
2008-01-01
* The only book describing applications of nonlinear fiber optics * Two new chapters on the latest developments: highly nonlinear fibers and quantum applications* Coverage of biomedical applications* Problems provided at the end of each chapterThe development of new highly nonlinear fibers - referred to as microstructured fibers, holey fibers and photonic crystal fibers - is the next generation technology for all-optical signal processing and biomedical applications. This new edition has been thoroughly updated to incorporate these key technology developments.The bo
Linearization of conservative nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Belendez, A; Alvarez, M L [Departamento de Fisica, IngenierIa de Sistemas y TeorIa de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E; Pascual, I [Departamento de Optica, FarmacologIa y AnatomIa, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es
2009-03-11
A linearization method of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force which allows us to obtain a frequency-amplitude relation which is valid not only for small but also for large amplitudes and, sometimes, for the complete range of oscillation amplitudes. Some conservative nonlinear oscillators are analysed to illustrate the usefulness and effectiveness of the technique.
Problems in nonlinear resistive MHD
Energy Technology Data Exchange (ETDEWEB)
Turnbull, A.D.; Strait, E.J.; La Haye, R.J.; Chu, M.S.; Miller, R.L. [General Atomics, San Diego, CA (United States)
1998-12-31
Two experimentally relevant problems can relatively easily be tackled by nonlinear MHD codes. Both problems require plasma rotation in addition to the nonlinear mode coupling and full geometry already incorporated into the codes, but no additional physics seems to be crucial. These problems discussed here are: (1) nonlinear coupling and interaction of multiple MHD modes near the B limit and (2) nonlinear coupling of the m/n = 1/1 sawtooth mode with higher n gongs and development of seed islands outside q = 1.
Asymptotics for dissipative nonlinear equations
Hayashi, Nakao; Kaikina, Elena I; Shishmarev, Ilya A
2006-01-01
Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.
Focus issue introduction: nonlinear optics.
Boulanger, Benoît; Cundiff, Steven T; Gauthier, Daniel J; Karlsson, Magnus; Lu, Yan-Qing; Norwood, Robert A; Skryabin, Dmitry; Taira, Takunori
2011-11-07
It is now fifty years since the original observation of second harmonic generation ushered in the field of nonlinear optics, close on the heels of the invention of the laser. This feature issue celebrates this anniversary with papers that span the range from new nonlinear optical materials, through the increasingly novel methods that have been developed for phase matching, to emerging areas such as nonlinear metamaterials and plasmonic enhancement of optical properties. It is clear that the next fifty years of nonlinear optics will witness a proliferation of new applications with increasing technological impact.
Nonlocal homogenization for nonlinear metamaterials
Gorlach, Maxim A; Lapine, Mikhail; Kivshar, Yuri S; Belov, Pavel A
2016-01-01
We present a consistent theoretical approach for calculating effective nonlinear susceptibilities of metamaterials taking into account both frequency and spatial dispersion. Employing the discrete dipole model, we demonstrate that effects of spatial dispersion become especially pronounced in the vicinity of effective permittivity resonance where nonlinear susceptibilities reach their maxima. In that case spatial dispersion may enable simultaneous generation of two harmonic signals with the same frequency and polarization but different wave vectors. We also prove that the derived expressions for nonlinear susceptibilities transform into the known form when spatial dispersion effects are negligible. In addition to revealing new physical phenomena, our results provide useful theoretical tools for analysing resonant nonlinear metamaterials.
Nonlinear Peltier effect in semiconductors
Zebarjadi, Mona; Esfarjani, Keivan; Shakouri, Ali
2007-09-01
Nonlinear Peltier coefficient of a doped InGaAs semiconductor is calculated numerically using the Monte Carlo technique. The Peltier coefficient is also obtained analytically for single parabolic band semiconductors assuming a shifted Fermi-Dirac electronic distribution under an applied bias. Analytical results are in agreement with numerical simulations. Key material parameters affecting the nonlinear behavior are doping concentration, effective mass, and electron-phonon coupling. Current density thresholds at which nonlinear behavior is observable are extracted from numerical data. It is shown that the nonlinear Peltier effect can be used to enhance cooling of thin film microrefrigerator devices especially at low temperatures.
Nonlinearities in Behavioral Macroeconomics.
Gomes, Orlando
2017-07-01
This article undertakes a journey across the literature on behavioral macroeconomics, with attention concentrated on the nonlinearities that the behavioral approach typically suggests or implies. The emphasis is placed on thinking the macro economy as a living organism, composed of many interacting parts, each one having a will of its own, which is in sharp contrast with the mechanism of the orthodox view (well represented by the neoclassical or new Keynesian dynamic stochastic general equilibrium - DSGE - model). The paper advocates that a thorough understanding of individual behavior in collective contexts is the only possible avenue to further explore macroeconomic phenomena and the often observed 'anomalies' that the benchmark DSGE macro framework is unable to explain or justify. After a reflection on the role of behavioral traits as a fundamental component of a new way of thinking the economy, the article proceeds with a debate on some of the most relevant frameworks in the literature that somehow link macro behavior and nonlinearities; covered subjects include macro models with disequilibrium rules, agent-based models that highlight interaction and complexity, evolutionary switching frameworks, and inattention based decision problems. These subjects have, as a fundamental point in common, the use of behavioral elements to transform existing interpretations of the economic reality, making it more evident how irregular fluctuations emerge and unfold on the aggregate.
Improved nonlinear prediction method
Adenan, Nur Hamiza; Md Noorani, Mohd Salmi
2014-06-01
The analysis and prediction of time series data have been addressed by researchers. Many techniques have been developed to be applied in various areas, such as weather forecasting, financial markets and hydrological phenomena involving data that are contaminated by noise. Therefore, various techniques to improve the method have been introduced to analyze and predict time series data. In respect of the importance of analysis and the accuracy of the prediction result, a study was undertaken to test the effectiveness of the improved nonlinear prediction method for data that contain noise. The improved nonlinear prediction method involves the formation of composite serial data based on the successive differences of the time series. Then, the phase space reconstruction was performed on the composite data (one-dimensional) to reconstruct a number of space dimensions. Finally the local linear approximation method was employed to make a prediction based on the phase space. This improved method was tested with data series Logistics that contain 0%, 5%, 10%, 20% and 30% of noise. The results show that by using the improved method, the predictions were found to be in close agreement with the observed ones. The correlation coefficient was close to one when the improved method was applied on data with up to 10% noise. Thus, an improvement to analyze data with noise without involving any noise reduction method was introduced to predict the time series data.
Nonlinear Response of Strong Nonlinear System Arisen in Polymer Cushion
Directory of Open Access Journals (Sweden)
Jun Wang
2013-01-01
Full Text Available A dynamic model is proposed for a polymer foam-based nonlinear cushioning system. An accurate analytical solution for the nonlinear free vibration of the system is derived by applying He's variational iteration method, and conditions for resonance are obtained, which should be avoided in the cushioning design.
Simplified Methods Applied to Nonlinear Motion of Spar Platforms
Energy Technology Data Exchange (ETDEWEB)
Haslum, Herbjoern Alf
2000-07-01
) are exposed to irregular seastates with long wave periods, linearly exited large amplitude heave resonance may occur. This is relevant for design seastates West of Shetland and in the Northern North Sea. (author)
Nonlinear Evolution of Ferroelectric Domains
Institute of Scientific and Technical Information of China (English)
WeiLU; Dai－NingFANG; 等
1997-01-01
The nonlinear evolution of ferroelectric domains is investigated in the paper and amodel is proposed which can be applied to numerical computation.Numerical results show that the model can accurately predict some nonlinear behavior and consist with those experimental results.
Nonlinear Electrodynamics and black holes
Breton, N; Breton, Nora; Garcia-Salcedo, Ricardo
2007-01-01
It is addressed the issue of black holes with nonlinear electromagnetic field, focussing mainly in the Born-Infeld case. The main features of these systems are described, for instance, geodesics, energy conditions, thermodynamics and isolated horizon aspects. Also are revised some black hole solutions of alternative nonlinear electrodynamics and its inconveniences.
Space curves, anholonomy and nonlinearity
Indian Academy of Sciences (India)
Radha Balakrishnan
2005-04-01
Using classical differential geometry, we discuss the phenomenon of anholonomy that gets associated with a static and a moving curve. We obtain the expressions for the respective geometric phases in the two cases and interpret them. We show that there is a close connection between anholonomy and nonlinearity in a wide class of nonlinear systems.
Balancing for unstable nonlinear systems
Scherpen, J.M.A.
1993-01-01
A previously obtained method of balancing for stable nonlinear systems is extended to unstable nonlinear systems. The similarity invariants obtained by the concept of LQG balancing for an unstable linear system can also be obtained by considering a past and future energy function of the system. By c
Nonlinear diffusion and superconducting hysteresis
Energy Technology Data Exchange (ETDEWEB)
Mayergoyz, I.D. [Univ. of Maryland, College Park, MD (United States)
1996-12-31
Nonlinear diffusion of electromagnetic fields in superconductors with ideal and gradual resistive transitions is studied. Analytical results obtained for linear and nonlinear polarizations of electromagnetic fields are reported. These results lead to various extensions of the critical state model for superconducting hysteresis.
Energy Technology Data Exchange (ETDEWEB)
Lallart, Mickael; Guyomar, Daniel, E-mail: mickael.lallart@insa-lyon.fr [LGEF, INSA-Lyon, Universite de Lyon, 8 rue de la Physique, F-69621 (France)
2011-10-29
The proliferation of wearable and left-behind devices has raised the issue of powering such systems. While primary batteries have been widely used in order to address this issue, recent trends have focused on energy harvesting products that feature high reliability and low maintenance issues. Among all the ambient sources available for energy harvesting, vibrations and heat have been of significant interest among the research community for small-scale devices. However, the conversion abilities of materials are still limited when dealing with systems featuring small dimensions. The purpose of this paper is to presents an up-to-date view of nonlinear approaches for increasing the efficiency of electromechanical and electrocaloric conversion mechanisms. From the modeling of the operation principles of the different architectures, a comparative analysis will be exposed, emphasizing the advantages and drawbacks of the presented concepts, in terms of maximal output power (under constant vibration magnitude or taking into account the damping effect), load independence, and implementation easiness.
Fainberg, B D
2015-01-01
Purely organic materials with negative and near-zero dielectric permittivity can be easily fabricated. Here we develop a theory of nonlinear non-steady-state organic plasmonics with strong laser pulses. The bistability response of the electron-vibrational model of organic materials in the condensed phase has been demonstrated. Non-steady-state organic plasmonics enable us to obtain near-zero dielectric permittivity during a short time. We have proposed to use non-steady-state organic plasmonics for the enhancement of intersite dipolar energy-transfer interaction in the quantum dot wire that influences on electron transport through nanojunctions. Such interactions can compensate Coulomb repulsions for particular conditions. We propose the exciton control of Coulomb blocking in the quantum dot wire based on the non-steady-state near-zero dielectric permittivity of the organic host medium.
2016-01-01
This volume brings together four lecture courses on modern aspects of water waves. The intention, through the lectures, is to present quite a range of mathematical ideas, primarily to show what is possible and what, currently, is of particular interest. Water waves of large amplitude can only be fully understood in terms of nonlinear effects, linear theory being not adequate for their description. Taking advantage of insights from physical observation, experimental evidence and numerical simulations, classical and modern mathematical approaches can be used to gain insight into their dynamics. The book presents several avenues and offers a wide range of material of current interest. Due to the interdisciplinary nature of the subject, the book should be of interest to mathematicians (pure and applied), physicists and engineers. The lectures provide a useful source for those who want to begin to investigate how mathematics can be used to improve our understanding of water wave phenomena. In addition, some of the...
Nonlinear estimation and classification
Hansen, Mark; Holmes, Christopher; Mallick, Bani; Yu, Bin
2003-01-01
Researchers in many disciplines face the formidable task of analyzing massive amounts of high-dimensional and highly-structured data This is due in part to recent advances in data collection and computing technologies As a result, fundamental statistical research is being undertaken in a variety of different fields Driven by the complexity of these new problems, and fueled by the explosion of available computer power, highly adaptive, non-linear procedures are now essential components of modern "data analysis," a term that we liberally interpret to include speech and pattern recognition, classification, data compression and signal processing The development of new, flexible methods combines advances from many sources, including approximation theory, numerical analysis, machine learning, signal processing and statistics The proposed workshop intends to bring together eminent experts from these fields in order to exchange ideas and forge directions for the future
Nonlinear transmission sputtering
Bitensky, I. S.; Sigmund, P.
1996-05-01
General expressions have been derived for the nonlinear yield of transmission sputtering for an incident polyatomic ion under the assumption that the molecule breaks up on entering the target and that sputter yields are enhanced due to proximity of atomic trajectories. Special attention is given to the case of negligible Coulomb explosion where projectile atoms penetrate independently. For weakly overlapping trajectories, the yield enhancement factor of a polyatomic molecule can be expressed by that of a diatom, amended with a correction for triple correlations if necessary. This expression is in good agreement with recent experimental findings on phenylalanine targets. Pertinent results on multiple scattering of atomic ions are reviewed and applied to independently-moving fragment atoms. The merits of measurements at variable layer thickness in addition to variable projectile energy are mentioned.
Perspectives on Nonlinear Filtering
Law, Kody
2015-01-07
The solution to the problem of nonlinear filtering may be given either as an estimate of the signal (and ideally some measure of concentration), or as a full posterior distribution. Similarly, one may evaluate the fidelity of the filter either by its ability to track the signal or its proximity to the posterior filtering distribution. Hence, the field enjoys a lively symbiosis between probability and control theory, and there are plenty of applications which benefit from algorithmic advances, from signal processing, to econometrics, to large-scale ocean, atmosphere, and climate modeling. This talk will survey some recent theoretical results involving accurate signal tracking with noise-free (degenerate) dynamics in high-dimensions (infinite, in principle, but say d between 103 and 108 , depending on the size of your application and your computer), and high-fidelity approximations of the filtering distribution in low dimensions (say d between 1 and several 10s).
Nonlinear rotordynamics analysis
Day, W. B.; Zalik, R. A.
1986-01-01
Three analytic consequences of the nonlinear Jeffcott equations are examined. The primary application of these analyses is directed toward understanding the excessive vibrations recorded in the Liquid Oxygen (LOX) pump of the Space Shuttle Main Engine (SSME) during hot firing ground testing. The first task is to provide bounds on the coefficients of the equations which delimit the two cases of numerical solution as a circle or an annulus. The second task examines the mathematical generalization to multiple forcing functions, which includes the special problems of mass imbalance, side force, rubbing, and combination of these forces. Finally, stability and boundedness of the steady-state solutions is discussed and related to the corresponding linear problem.
Nonlinearities in vegetation functioning
Ceballos-Núñez, Verónika; Müller, Markus; Metzler, Holger; Sierra, Carlos
2016-04-01
Given the current drastic changes in climate and atmospheric CO2 concentrations, and the role of vegetation in the global carbon cycle, there is increasing attention to the carbon allocation component in biosphere terrestrial models. Improving the representation of C allocation in models could be the key to having better predictions of the fate of C once it enters the vegetation and is partitioned to C pools of different residence times. C allocation has often been modeled using systems of ordinary differential equations, and it has been hypothesized that most models can be generalized with a specific form of a linear dynamical system. However, several studies have highlighted discrepancies between empirical observations and model predictions, attributing these differences to problems with model structure. Although efforts have been made to compare different models, the outcome of these qualitative assessments has been a conceptual categorization of them. In this contribution, we introduce a new effort to identify the main properties of groups of models by studying their mathematical structure. For this purpose, we performed a literature research of the relevant models of carbon allocation in vegetation and developed a database with their representation in symbolic mathematics. We used the Python package SymPy for symbolic mathematics as a common language and manipulated the models to calculate their Jacobian matrix at fixed points and their eigenvalues, among other mathematical analyses. Our preliminary results show a tendency of inverse proportionality between model complexity and size of time/space scale; complex interactions between the variables controlling carbon allocation in vegetation tend to operate at shorter time/space scales, and vice-versa. Most importantly, we found that although the linear structure is common, other structures with non-linearities have been also proposed. We, therefore, propose a new General Model that can accommodate these
Nonlinear field space cosmology
Mielczarek, Jakub; Trześniewski, Tomasz
2017-08-01
We consider the FRW cosmological model in which the matter content of the Universe (playing the role of an inflaton or quintessence) is given by a novel generalization of the massive scalar field. The latter is a scalar version of the recently introduced nonlinear field space theory, where the physical phase space of a given field is assumed to be compactified at large energies. For our analysis, we choose the simple case of a field with the spherical phase space and endow it with the generalized Hamiltonian analogous to the XXZ Heisenberg model, normally describing a system of spins in condensed matter physics. Subsequently, we study both the homogenous cosmological sector and linear perturbations of such a test field. In the homogenous sector, we find that nonlinearity of the field phase space is becoming relevant for large volumes of the Universe and can lead to a recollapse, and possibly also at very high energies, leading to the phase of a bounce. Quantization of the field is performed in the limit where the nontrivial nature of its phase space can be neglected, while there is a nonvanishing contribution from the Lorentz symmetry breaking term of the Hamiltonian. As a result, in the leading order of the XXZ anisotropy parameter, we find that the inflationary spectral index remains unmodified with respect to the standard case but the total amplitude of perturbations is subject to a correction. The Bunch-Davies vacuum state also becomes appropriately corrected. The proposed new approach is bringing cosmology and condensed matter physics closer together, which may turn out to be beneficial for both disciplines.
NONLINEAR STABILITY FOR EADY'S MODEL
Institute of Scientific and Technical Information of China (English)
LIU Yong-ming; QIU Ling-cun
2005-01-01
Poincaré type integral inequality plays an important role in the study of nonlinear stability ( in the sense of Arnold's second theorem) for three-dimensional quasigeostophic flow. The nonlinear stability of Eady's model is one of the most important cases in the application of the method. But the best nonlinear stability criterion obtained so far and the linear stability criterion are not coincident. The two criteria coincide only when the period of the channel is infinite.additional conservation law of momentum and by rigorous estimate of integral inequality. So the new nonlinear stability criterion was obtained, which shows that for Eady 's model in the periodic channel, the linear stable implies the nonlinear stable.
Nonlinear Waves in Complex Systems
DEFF Research Database (Denmark)
2007-01-01
The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations, it is the ......The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations......, it is the universality and robustness of the main models with respect to perturbations that developped the field. This is true for both continuous and discrete equations. In this volume we keep this broad view and draw new perspectives for nonlinear waves in complex systems. In particular we address energy flow...
Terahertz Nonlinearity in Graphene Plasmons
Jadidi, Mohammad M; Winnerl, Stephan; Sushkov, Andrei B; Drew, H Dennis; Murphy, Thomas E; Mittendorff, Martin
2015-01-01
Sub-wavelength graphene structures support localized plasmonic resonances in the terahertz and mid-infrared spectral regimes. The strong field confinement at the resonant frequency is predicted to significantly enhance the light-graphene interaction, which could enable nonlinear optics at low intensity in atomically thin, sub-wavelength devices. To date, the nonlinear response of graphene plasmons and their energy loss dynamics have not been experimentally studied. We measure and theoretically model the terahertz nonlinear response and energy relaxation dynamics of plasmons in graphene nanoribbons. We employ a THz pump-THz probe technique at the plasmon frequency and observe a strong saturation of plasmon absorption followed by a 10 ps relaxation time. The observed nonlinearity is enhanced by two orders of magnitude compared to unpatterned graphene with no plasmon resonance. We further present a thermal model for the nonlinear plasmonic absorption that supports the experimental results.
Fast Numerical Nonlinear Fourier Transforms
Wahls, Sander
2014-01-01
The nonlinear Fourier transform, which is also known as the forward scattering transform, decomposes a periodic signal into nonlinearly interacting waves. In contrast to the common Fourier transform, these waves no longer have to be sinusoidal. Physically relevant waveforms are often available for the analysis instead. The details of the transform depend on the waveforms underlying the analysis, which in turn are specified through the implicit assumption that the signal is governed by a certain evolution equation. For example, water waves generated by the Korteweg-de Vries equation can be expressed in terms of cnoidal waves. Light waves in optical fiber governed by the nonlinear Schr\\"dinger equation (NSE) are another example. Nonlinear analogs of classic problems such as spectral analysis and filtering arise in many applications, with information transmission in optical fiber, as proposed by Yousefi and Kschischang, being a very recent one. The nonlinear Fourier transform is eminently suited to address them ...
Properties of Nonlinear Dynamo Waves
Tobias, S. M.
1997-01-01
Dynamo theory offers the most promising explanation of the generation of the sun's magnetic cycle. Mean field electrodynamics has provided the platform for linear and nonlinear models of solar dynamos. However, the nonlinearities included are (necessarily) arbitrarily imposed in these models. This paper conducts a systematic survey of the role of nonlinearities in the dynamo process, by considering the behaviour of dynamo waves in the nonlinear regime. It is demonstrated that only by considering realistic nonlinearities that are non-local in space and time can modulation of the basic dynamo wave he achieved. Moreover, this modulation is greatest when there is a large separation of timescales provided by including a low magnetic Prandtl number in the equation for the velocity perturbations.
Cubication of conservative nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Belendez, Augusto; Alvarez, Mariela L [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, Elena; Pascual, Inmaculada [Departamento de Optica, FarmacologIa y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es
2009-09-15
A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A, while in a Taylor expansion of the restoring force these coefficients are independent of A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain an approximate frequency-amplitude relation as a function of the complete elliptic integral of the first kind. Some conservative nonlinear oscillators are analysed to illustrate the usefulness and effectiveness of this scheme.
Nonlinear Oscillators in Space Physics
Lester,Daniel; Thronson, Harley
2011-01-01
We discuss dynamical systems that produce an oscillation without an external time dependent source. Numerical results are presented for nonlinear oscillators in the Em1h's atmosphere, foremost the quasi-biennial oscillation (QBOl. These fluid dynamical oscillators, like the solar dynamo, have in common that one of the variables in a governing equation is strongly nonlinear and that the nonlinearity, to first order, has particular form. of 3rd or odd power. It is shown that this form of nonlinearity can produce the fundamental li'equency of the internal oscillation. which has a period that is favored by the dynamical condition of the fluid. The fundamental frequency maintains the oscillation, with no energy input to the system at that particular frequency. Nonlinearities of 2nd or even power could not maintain the oscillation.
Asymptotic expansions in nonlinear rotordynamics
Day, William B.
1987-01-01
This paper is an examination of special nonlinearities of the Jeffcott equations in rotordynamics. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot-firing ground testing. Deadband, side force, and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency, is defined and used to develop the solutions of the nonlinear Jeffcott equations as singular asymptotic expansions. This nonlinear natural frequency, which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies.
Nonlinear hyperbolic waves in multidimensions
Prasad, Phoolan
2001-01-01
The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. Since the 1993 publication of his work Propagation of a Curved Shock and Nonlinear Ray Theory, author Phoolan Prasad and his research group have made significant advances in the underlying theory of these phenomena. This volume presents their results and provides a self-contained account and gradual development of mathematical methods for studying successive positions of these fronts.Nonlinear Hyperbolic Waves in Multidimensions includes all introductory material on nonlinear hyperbolic waves and the theory of shock waves. The author derives the ray theory for a nonlinear wavefront, discusses kink phenomena, and develops a new theory for plane and curved shock propagation. He also derives a full set of conservation laws for a front propagating in two space dimensions, and uses these laws to obtain successive positions of a front with kinks. The treatment includes examples of the theory applied to converging wavefronts...
Analysis of Nonlinear Electromagnetic Metamaterials
Poutrina, Ekaterina; Smith, David R
2010-01-01
We analyze the properties of a nonlinear metamaterial formed by integrating nonlinear components or materials into the capacitive regions of metamaterial elements. A straightforward homogenization procedure leads to general expressions for the nonlinear susceptibilities of the composite metamaterial medium. The expressions are convenient, as they enable inhomogeneous system of scattering elements to be described as a continuous medium using the standard notation of nonlinear optics. We illustrate the validity and accuracy of our theoretical framework by performing measurements on a fabricated metamaterial sample composed of an array of split ring resonators (SRRs) with packaged varactors embedded in the capacitive gaps in a manner similar to that of Wang et al. [Opt. Express 16, 16058 (2008)]. Because the SRRs exhibit a predominant magnetic response to electromagnetic fields, the varactor-loaded SRR composite can be described as a magnetic material with nonlinear terms in its effective magnetic susceptibility...
The Nonlinear Analytical Envelope Equation in quadratic nonlinear crystals
Bache, Morten
2016-01-01
We here derive the so-called Nonlinear Analytical Envelope Equation (NAEE) inspired by the work of Conforti et al. [M. Conforti, A. Marini, T. X. Tran, D. Faccio, and F. Biancalana, "Interaction between optical fields and their conjugates in nonlinear media," Opt. Express 21, 31239-31252 (2013)], whose notation we follow. We present a complete model that includes $\\chi^{(2)}$ terms [M. Conforti, F. Baronio, and C. De Angelis, "Nonlinear envelope equation for broadband optical pulses in quadratic media," Phys. Rev. A 81, 053841 (2010)], $\\chi^{(3)}$ terms, and then extend the model to delayed Raman effects in the $\\chi^{(3)}$ term. We therefore get a complete model for ultrafast pulse propagation in quadratic nonlinear crystals similar to the Nonlinear Wave Equation in Frequency domain [H. Guo, X. Zeng, B. Zhou, and M. Bache, "Nonlinear wave equation in frequency domain: accurate modeling of ultrafast interaction in anisotropic nonlinear media," J. Opt. Soc. Am. B 30, 494-504 (2013)], but where the envelope is...
Breatherlike impurity modes in discrete nonlinear lattices
DEFF Research Database (Denmark)
Hennig, D.; Rasmussen, Kim; Tsironis, G. P.
1995-01-01
We investigate the properties of a disordered generalized discrete nonlinear Schrodinger equation, containing both diagonal and nondiagonal nonlinear terms. The equation models a Linear host lattice doped with nonlinear impurities. We find different types of impurity states that form itinerant...
Spatial solitons in nonlinear photonic crystals
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2000-01-01
We study solitons in one-dimensional quadratic nonlinear photonic crystals with periodic linear and nonlinear susceptibilities. We show that such crystals support stable bright and dark solitons, even when the effective quadratic nonlinearity is zero.......We study solitons in one-dimensional quadratic nonlinear photonic crystals with periodic linear and nonlinear susceptibilities. We show that such crystals support stable bright and dark solitons, even when the effective quadratic nonlinearity is zero....
Resource Letter NO-1: Nonlinear Optics
Garmire, Elsa
2011-03-01
This Resource Letter provides a guide to the literature on nonlinear optics. Books, journals, and websites are introduced that cover the general subject. Journal articles and websites are cited covering the following topics: second-order nonlinearities in transparent media including second-harmonic generation and optical parametric oscillation, third-order and higher nonlinearities, nonlinear refractive index, absorptive nonlinearities such as saturable absorption and multiphoton absorption, and scattering nonlinearities such as stimulated Raman scattering and stimulated Brillouin scattering. Steady-state and transient phenomena, fiber optics, solitons, nonlinear wave mixing, optical phase conjugation, nonlinear spectroscopy, and multiphoton microscopy are all outlined.
Neurodynamics: nonlinear dynamics and neurobiology.
Abarbanel, H D; Rabinovich, M I
2001-08-01
The use of methods from contemporary nonlinear dynamics in studying neurobiology has been rather limited.Yet, nonlinear dynamics has become a practical tool for analyzing data and verifying models. This has led to productive coupling of nonlinear dynamics with experiments in neurobiology in which the neural circuits are forced with constant stimuli, with slowly varying stimuli, with periodic stimuli, and with more complex information-bearing stimuli. Analysis of these more complex stimuli of neural circuits goes to the heart of how one is to understand the encoding and transmission of information by nervous systems.
Dissipative Nonlinear Dynamics in Holography
Basu, Pallab
2013-01-01
We look at the response of a nonlinearly coupled scalar field in an asymptotically AdS black brane geometry and find a behaviour very similar to that of known dissipative nonlinear systems like the chaotic pendulum. Transition to chaos proceeds through a series of period-doubling bifurcations. The presence of dissipation, crucial to this behaviour, arises naturally in a black hole background from the ingoing conditions imposed at the horizon. AdS/CFT translates our solution to a chaotic response of the operator dual to the scalar field. Our setup can also be used to study quench-like behaviour in strongly coupled nonlinear systems.
Acoustic-gravity nonlinear structures
Directory of Open Access Journals (Sweden)
D. Jovanović
2002-01-01
Full Text Available A catalogue of nonlinear vortex structures associated with acoustic-gravity perturbations in the Earth's atmosphere is presented. Besides the previously known Kelvin-Stewart cat's eyes, dipolar and tripolar structures, new solutions having the form of a row of counter-rotating vortices, and several weakly two-dimensional vortex chains are given. The existence conditions for these nonlinear structures are discussed with respect to the presence of inhomogeneities of the shear flows. The mode-coupling mechanism for the nonlinear generation of shear flows in the presence of linearly unstable acoustic-gravity waves, possibly also leading to intermittency and chaos, is presented.
Nonlinear effects in Thomson backscattering
Maroli, C.; Petrillo, V.; Tomassini, P.; Serafini, L.
2013-03-01
We analyze the nonlinear classical effects of the X/γ radiation produced by Thomson/Compton sources. We confirm the development of spectral fringes of the radiation on axis, which comports broadening, shift, and deformation of the spectrum. For the nominal parameters of the SPARC-LAB Thomson scattering and of the European Proposal for the gamma source ELI-NP, however, the radiation, when collected in the suitable acceptance angle, does not reveal many differences from that predicted by the linear model and the nonlinear redshift is subdominant with respect to the quantum recoil. An experiment aimed to the study of the nonlinearities is proposed on the SPARC-LAB source.
Nonlinear Dynamic Phenomena in Mechanics
Warminski, Jerzy; Cartmell, Matthew P
2012-01-01
Nonlinear phenomena should play a crucial role in the design and control of engineering systems and structures as they can drastically change the prevailing dynamical responses. This book covers theoretical and applications-based problems of nonlinear dynamics concerned with both discrete and continuous systems of interest in civil and mechanical engineering. They include pendulum-like systems, slender footbridges, shape memory alloys, sagged elastic cables and non-smooth problems. Pendulums can be used as a dynamic absorber mounted in high buildings, bridges or chimneys. Geometrical nonlinear
Nonlinear Optics: Principles and Applications
DEFF Research Database (Denmark)
Rottwitt, Karsten; Tidemand-Lichtenberg, Peter
As nonlinear optics further develops as a field of research in electromagnetic wave propagation, its state-of-the-art technologies will continue to strongly impact real-world applications in a variety of fields useful to the practicing scientist and engineer. From basic principles to examples...... of applications, Nonlinear Optics: Principles and Applications effectively bridges physics and mathematics with relevant applied material for real-world use. The book progresses naturally from fundamental aspects to illustrative examples, and presents a strong theoretical foundation that equips the reader...... and matter, this text focuses on the physical understanding of nonlinear optics, and explores optical material response functions in the time and frequency domain....
Oscillating solitons in nonlinear optics
Indian Academy of Sciences (India)
Lin Xiao-Gang; Liu Wen-Jun; Lei Ming
2016-03-01
Oscillating solitons are obtained in nonlinear optics. Analytical study of the variable coefficient nonlinear Schrödinger equation, which is used to describe the soliton propagation in those systems, is carried out using the Hirota’s bilinear method. The bilinear forms and analytic soliton solutions are derived, and the relevant properties and features of oscillating solitons are illustrated. Oscillating solitons are controlled by the reciprocal of the group velocity and Kerr nonlinearity. Results of this paper will be valuable to the study of dispersion-managed optical communication system and mode-locked fibre lasers.
Nonlinear dynamics: Challenges and perspectives
Indian Academy of Sciences (India)
M Lakshmanan
2005-04-01
The study of nonlinear dynamics has been an active area of research since 1960s, after certain path-breaking discoveries, leading to the concepts of solitons, integrability, bifurcations, chaos and spatio-temporal patterns, to name a few. Several new techniques and methods have been developed to understand nonlinear systems at different levels. Along with these, a multitude of potential applications of nonlinear dynamics have also been enunciated. In spite of these developments, several challenges, some of them fundamental and others on the efficacy of these methods in developing cutting edge technologies, remain to be tackled. In this article, a brief personal perspective of these issues is presented.
Femtosecond nonlinear polarization evolution based on cascade quadratic nonlinearities.
Liu, X; Ilday, F O; Beckwitt, K; Wise, F W
2000-09-15
We experimentally demonstrate that one can exploit nonlinear phase shifts produced in type I phase-mismatched second-harmonic generation to produce intensity-dependent polarization evolution with 100-fs pulses. An amplitude modulator based on nonlinear polarization rotation provides passive amplitude-modulation depth of up to ~50%. Applications of the amplitude and phase modulations to mode locking of femtosecond bulk and fiber lasers are promising and are discussed.
Intrinsic nonlinear response of surface plasmon polaritons
Im, Song-Jin; Kim, Gum-Hyok
2015-01-01
We offer a model to describe the intrinsic nonlinear response of surface plasmon polaritons (SPPs). Relation of the complex nonlinear coefficient of SPPs to the third-order nonlinear susceptibility of the metal is provided. As reported in a recent study, gold is highly lossy and simultaneously highly nonlinear due to interband absorption and interband thermo-modulation at a wavelength shorter than 700 nm. The effect of the high loss of the metal on the SPP nonlinear propagation is taken into account in our model. With the model we show difference in sign of real and imaginary parts between the nonlinear propagation coefficient and the nonlinear susceptibility of component material for the first time to our knowledge. Our model could have practical importance in studying plasmonic devices utilizing the nonlinear phase modulation and the nonlinear absorption of SPPs. For example, it allows one to extract the complex nonlinear susceptibility of gold through a measurement of SPP nonlinear propagation at the visib...
Deimling, Klaus
1985-01-01
topics. However, only a modest preliminary knowledge is needed. In the first chapter, where we introduce an important topological concept, the so-called topological degree for continuous maps from subsets ofRn into Rn, you need not know anything about functional analysis. Starting with Chapter 2, where infinite dimensions first appear, one should be familiar with the essential step of consider ing a sequence or a function of some sort as a point in the corresponding vector space of all such sequences or functions, whenever this abstraction is worthwhile. One should also work out the things which are proved in § 7 and accept certain basic principles of linear functional analysis quoted there for easier references, until they are applied in later chapters. In other words, even the 'completely linear' sections which we have included for your convenience serve only as a vehicle for progress in nonlinearity. Another point that makes the text introductory is the use of an essentially uniform mathematical languag...
Meyer, George
1997-01-01
The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of way points through which the aircraft trajectory must pass. The way points typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory which satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multi-dimensional, multi-axis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of possible operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordinatization, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions must be smooth. The guidance algorithm is based on the inversion of the pure feedback approximations, which is followed by iterative corrections for the effects of zero dynamics. The paper describes the structure and modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.
Whittam, A J
2001-01-01
susceptibility from 26 pm/V (same film without octadecanoic acid) to 40 pm/V. This increase in the second-order susceptibility occurred even though the amount of NLO-active dye was effectively diluted by the addition of the inactive octadecanoic acid. The wavelength of the absorption maximum ranged from 346-440 nm and there was direct correlation between the susceptibilities and the transparency of the films at the harmonic wavelength. Hemicyanine dyes were synthesised, with the general formulae: - (a) C sub 1 sub 8 H sub 3 sub 7 -A sup + -[CH=CH-C sub 6 H sub 4] sub x -N(CH sub 3) sub 2 I (b) C sub 1 sub 8 H sub 3 sub 7 -A sup + -[CH=CH] sub y -C sub 6 H sub 4 -N(CH sub 3) sub 2 I where A sup + is a pyridinium or isoquinolinium acceptor, and x = 1 or 2, and y = 1 or 2. The optically nonlinear dyes were investigated via the Langmuir-Blodgett (LB) technique. The dyes all produced isotherm data, with molecular areas of 22-60 A sup 2 per molecule, which are consistent with the cross-sectional areas of the chromo...
Nonlinear helical MHD instability
Energy Technology Data Exchange (ETDEWEB)
Zueva, N.M.; Solov' ev, L.S.
1977-07-01
An examination is made of the boundary problem on the development of MHD instability in a toroidal plasma. Two types of local helical instability are noted - Alfven and thermal, and the corresponding criteria of instability are cited. An evaluation is made of the maximum attainable kinetic energy, limited by the degree to which the law of conservation is fulfilled. An examination is made of a precise solution to a kinematic problem on the helical evolution of a cylindrical magnetic configuration at a given velocity distribution in a plasma. A numerical computation of the development of MHD instability in a plasma cylinder by a computerized solution of MHD equations is made where the process's helical symmetry is conserved. The development of instability is of a resonance nature. The instability involves the entire cross section of the plasma and leads to an inside-out reversal of the magnetic surfaces when there is a maximum unstable equilibrium configuration in the nonlinear stage. The examined instability in the tore is apparently stabilized by a magnetic hole when certain limitations are placed on the distribution of flows in the plasma. 29 references, 8 figures.
Design with Nonlinear Constraints
Tang, Chengcheng
2015-12-10
Most modern industrial and architectural designs need to satisfy the requirements of their targeted performance and respect the limitations of available fabrication technologies. At the same time, they should reflect the artistic considerations and personal taste of the designers, which cannot be simply formulated as optimization goals with single best solutions. This thesis aims at a general, flexible yet e cient computational framework for interactive creation, exploration and discovery of serviceable, constructible, and stylish designs. By formulating nonlinear engineering considerations as linear or quadratic expressions by introducing auxiliary variables, the constrained space could be e ciently accessed by the proposed algorithm Guided Projection, with the guidance of aesthetic formulations. The approach is introduced through applications in different scenarios, its effectiveness is demonstrated by examples that were difficult or even impossible to be computationally designed before. The first application is the design of meshes under both geometric and static constraints, including self-supporting polyhedral meshes that are not height fields. Then, with a formulation bridging mesh based and spline based representations, the application is extended to developable surfaces including origami with curved creases. Finally, general approaches to extend hard constraints and soft energies are discussed, followed by a concluding remark outlooking possible future studies.
Energy Technology Data Exchange (ETDEWEB)
Peeters, A. G.; Rath, F.; Buchholz, R.; Grosshauser, S. R.; Strintzi, D.; Weikl, A. [Physics Department, University of Bayreuth, Universitätsstrasse 30, Bayreuth (Germany); Camenen, Y. [Aix Marseille Univ, CNRS, PIIM, UMR 7345, Marseille (France); Candy, J. [General Atomics, PO Box 85608, San Diego, California 92186-5608 (United States); Casson, F. J. [CCFE, Culham Science Centre, Abingdon OX14 3DB, Oxon (United Kingdom); Hornsby, W. A. [Max Planck Institut für Plasmaphysik, Boltzmannstrasse 2 85748 Garching (Germany)
2016-08-15
It is shown that Ion Temperature Gradient turbulence close to the threshold exhibits a long time behaviour, with smaller heat fluxes at later times. This reduction is connected with the slow growth of long wave length zonal flows, and consequently, the numerical dissipation on these flows must be sufficiently small. Close to the nonlinear threshold for turbulence generation, a relatively small dissipation can maintain a turbulent state with a sizeable heat flux, through the damping of the zonal flow. Lowering the dissipation causes the turbulence, for temperature gradients close to the threshold, to be subdued. The heat flux then does not go smoothly to zero when the threshold is approached from above. Rather, a finite minimum heat flux is obtained below which no fully developed turbulent state exists. The threshold value of the temperature gradient length at which this finite heat flux is obtained is up to 30% larger compared with the threshold value obtained by extrapolating the heat flux to zero, and the cyclone base case is found to be nonlinearly stable. Transport is subdued when a fully developed staircase structure in the E × B shearing rate forms. Just above the threshold, an incomplete staircase develops, and transport is mediated by avalanche structures which propagate through the marginally stable regions.
Moyer, D.; De Luccia, F.; Haas, E.
2016-10-01
The Joint Polar Satellite System 1 (JPSS-1) is the follow on mission to the Suomi-National Polar-orbiting Partnership (SNPP) and provides critical weather and global climate products to the user community. A primary sensor on both JPSS-1 and S-NPP is the Visible-Infrared Imaging Radiometer Suite (VIIRS) with the Reflective Solar Band (RSB), Thermal Emissive Band (TEB) and Day Night Band (DNB) imagery providing a diverse spectral range of Earth observations. These VIIRS observation are radiometrically calibrated within the Sensor Data Records (SDRs) for use in Environmental Data Record (EDR) products such as Ocean Color/Chlorophyll (OCC) and Sea Surface Temperature (SST). Spectrally the VIIRS sensor can be broken down into 4 groups: the Visible Near Infra-Red (VNIR), Short-Wave Infra-Red (SWIR), Mid- Wave Infra-Red (MWIR) and Long-Wave Infra-Red (LWIR). The SWIR spectral bands on JPSS-1 VIIRS have a nonlinear response at low light levels affecting the calibration quality where Earth scenes are dark (like oceans). This anomalous behavior was not present on S-NPP VIIRS and will be a unique feature of the JPSS-1 VIIRS sensor. This paper will show the behavior of the SWIR response non-linearity on JPSS-1 VIIRS and potential mitigation approaches to limit its impact on the SDR and EDR products.
Nonlinear plasmonics at high temperatures
Directory of Open Access Journals (Sweden)
Sivan Yonatan
2017-01-01
Full Text Available We solve the Maxwell and heat equations self-consistently for metal nanoparticles under intense continuous wave (CW illumination. Unlike previous studies, we rely on experimentally-measured data for metal permittivity for increasing temperature and for the visible spectral range. We show that the thermal nonlinearity of the metal can lead to substantial deviations from the predictions of the linear model for the temperature and field distribution and, thus, can explain qualitatively the strong nonlinear scattering from such configurations observed experimentally. We also show that the incompleteness of existing data of the temperature dependence of the thermal properties of the system prevents reaching a quantitative agreement between the measured and calculated scattering data. This modeling approach is essential for the identification of the underlying physical mechanism responsible for the thermo-optical nonlinearity of the metal and should be adopted in all applications of high-temperature nonlinear plasmonics, especially for refractory metals, for both CW and pulsed illumination.
Nonlinear optics and organic materials
Energy Technology Data Exchange (ETDEWEB)
Shen, Y.R.
1994-07-01
We shall consider an interesting topic relating nonlinear optics and organic materials: how nonlinear optics can be used to study organic materials. One of the main differences between linear and nonlinear responses of a medium to incoming radiation is in their symmetries. It leads to the possibility that some properties of the medium could be more sensitively probed by nonlinear, rather than linear, optical means, or vise versa. A well-known example is that some vibrational modes of a medium could be Raman-active but infrared-inactive, and would be more readily observed by Raman scattering, which is a two-photon transition process. In this paper, we shall discuss, with the help of three examples, how we can use second harmonic generation (SHG) and sum frequency generation (SFG) to obtain unique information about a material. We shall focus on thin films, surfaces, and interfaces.
Nonlinear plasmonics at high temperatures
Sivan, Yonatan; Chu, Shi-Wei
2017-01-01
We solve the Maxwell and heat equations self-consistently for metal nanoparticles under intense continuous wave (CW) illumination. Unlike previous studies, we rely on experimentally-measured data for metal permittivity for increasing temperature and for the visible spectral range. We show that the thermal nonlinearity of the metal can lead to substantial deviations from the predictions of the linear model for the temperature and field distribution and, thus, can explain qualitatively the strong nonlinear scattering from such configurations observed experimentally. We also show that the incompleteness of existing data of the temperature dependence of the thermal properties of the system prevents reaching a quantitative agreement between the measured and calculated scattering data. This modeling approach is essential for the identification of the underlying physical mechanism responsible for the thermo-optical nonlinearity of the metal and should be adopted in all applications of high-temperature nonlinear plasmonics, especially for refractory metals, for both CW and pulsed illumination.
Nonlinear microstructured polymer optical fibres
DEFF Research Database (Denmark)
Frosz, Michael Henoch
. The combination of a small core size and zero-dispersion wavelength at the operating wavelength of widely available femtosecond Ti:sapphire lasers led to an extensive research in supercontinuum generation and other nonlinear effects in PCFs. It is crucial for the efficiency of many nonlinear mechanisms...... that the pump laser wavelength is close to the zero-dispersion wavelength and that the core size is small. Recently, work in fabricating PCFs from materials other than silica has intensified. One of the advantages of using alternative materials can be a higher inherent material nonlinearity, which...... to accurately obtain a small core size while maintaining small structural variations during fibre drawing. This talk will give a presentation of how the mPOFs are fabricated and the route to obtaining nonlinear effects in them....
Device Applications of Nonlinear Dynamics
Baglio, Salvatore
2006-01-01
This edited book is devoted specifically to the applications of complex nonlinear dynamic phenomena to real systems and device applications. While in the past decades there has been significant progress in the theory of nonlinear phenomena under an assortment of system boundary conditions and preparations, there exist comparatively few devices that actually take this rich behavior into account. "Device Applications of Nonlinear Dynamics" applies and exploits this knowledge to make devices which operate more efficiently and cheaply, while affording the promise of much better performance. Given the current explosion of ideas in areas as diverse as molecular motors, nonlinear filtering theory, noise-enhanced propagation, stochastic resonance and networked systems, the time is right to integrate the progress of complex systems research into real devices.
Nonlinear Inflaton Fragmentation after Preheating
Felder, G N; Felder, Gary N.; Kofman, Lev
2007-01-01
We consider the nonlinear dynamics of inflaton fragmentation during and after preheating in the simplest model of chaotic inflation. While the earlier regime of parametric resonant particle production and the later turbulent regime of interacting fields evolving towards equilibrium are well identified and understood, the short intermediate stage of violent nonlinear dynamics remains less explored. Lattice simulations of fully nonlinear preheating dynamics show specific features of this intermediate stage: occupation numbers of the scalar particles are peaked, scalar fields become significantly non-gaussian and the field dynamics become chaotic and irreversible. Visualization of the field dynamics in configuration space reveals that nonlinear interactions generate non-gaussian inflaton inhomogeneities with very fast growing amplitudes. The peaks of the inflaton inhomogeneities coincide with the peaks of the scalar field(s) produced by parametric resonance. When the inflaton peaks reach their maxima, they stop ...
Reconstruction of nonlinear wave propagation
Fleischer, Jason W; Barsi, Christopher; Wan, Wenjie
2013-04-23
Disclosed are systems and methods for characterizing a nonlinear propagation environment by numerically propagating a measured output waveform resulting from a known input waveform. The numerical propagation reconstructs the input waveform, and in the process, the nonlinear environment is characterized. In certain embodiments, knowledge of the characterized nonlinear environment facilitates determination of an unknown input based on a measured output. Similarly, knowledge of the characterized nonlinear environment also facilitates formation of a desired output based on a configurable input. In both situations, the input thus characterized and the output thus obtained include features that would normally be lost in linear propagations. Such features can include evanescent waves and peripheral waves, such that an image thus obtained are inherently wide-angle, farfield form of microscopy.
BRST charge for nonlinear algebras
Buchbinder, I L
2007-01-01
We study the construction of the classical nilpotent canonical BRST charge for the nonlinear gauge algebras where a commutator (in terms of Poisson brackets) of the constraints is a finite order polynomial of the constraints.
Nonlinear optics: the next decade.
Kivshar, Yuri S
2008-12-22
This paper concludes the Focus Serial assembled of invited papers in key areas of nonlinear optics (Editors: J.M. Dudley and R.W. Boyd), and it discusses new directions for future research in this field.
Nonlinear opto-mechanical pressure
Conti, Claudio
2014-01-01
A transparent material exhibits ultra-fast optical nonlinearity and is subject to optical pressure if irradiated by a laser beam. However, the effect of nonlinearity on optical pressure is often overlooked, even if a nonlinear optical pressure may be potentially employed in many applications, as optical manipulation, biophysics, cavity optomechanics, quantum optics, optical tractors, and is relevant in fundamental problems as the Abraham-Minkoswky dilemma, or the Casimir effect. Here we show that an ultra-fast nonlinear polarization gives indeed a contribution to the optical pressure that also is negative in certain spectral ranges; the theoretical analysis is confirmed by first-principles simulations. An order of magnitude estimate shows that the effect can be observable by measuring the deflection of a membrane made by graphene.
Nonlinear programming analysis and methods
Avriel, Mordecai
2012-01-01
This text provides an excellent bridge between principal theories and concepts and their practical implementation. Topics include convex programming, duality, generalized convexity, analysis of selected nonlinear programs, techniques for numerical solutions, and unconstrained optimization methods.
Nonlinear optics principles and applications
Li, Chunfei
2017-01-01
This book reflects the latest advances in nonlinear optics. Besides the simple, strict mathematical deduction, it also discusses the experimental verification and possible future applications, such as the all-optical switches. It consistently uses the practical unit system throughout. It employs simple physical images, such as "light waves" and "photons" to systematically explain the main principles of nonlinear optical effects. It uses the first-order nonlinear wave equation in frequency domain under the condition of “slowly varying amplitude approximation" and the classical model of the interaction between the light and electric dipole. At the same time, it also uses the rate equations based on the energy-level transition of particle systems excited by photons and the energy and momentum conservation principles to explain the nonlinear optical phenomenon. The book is intended for researchers, engineers and graduate students in the field of the optics, optoelectronics, fiber communication, information tech...
Hilbert complexes of nonlinear elasticity
Angoshtari, Arzhang; Yavari, Arash
2016-12-01
We introduce some Hilbert complexes involving second-order tensors on flat compact manifolds with boundary that describe the kinematics and the kinetics of motion in nonlinear elasticity. We then use the general framework of Hilbert complexes to write Hodge-type and Helmholtz-type orthogonal decompositions for second-order tensors. As some applications of these decompositions in nonlinear elasticity, we study the strain compatibility equations of linear and nonlinear elasticity in the presence of Dirichlet boundary conditions and the existence of stress functions on non-contractible bodies. As an application of these Hilbert complexes in computational mechanics, we briefly discuss the derivation of a new class of mixed finite element methods for nonlinear elasticity.
Studies of Nonlinear Problems. I
Fermi, E.; Pasta, J.; Ulam, S.
1955-05-01
A one-dimensional dynamical system of 64 particles with forces between neighbors containing nonlinear terms has been studied on the Los Alamos computer MANIAC I. The nonlinear terms considered are quadratic, cubic, and broken linear types. The results are analyzed into Fourier components and plotted as a function of time. The results show very little, if any, tendency toward equipartition of energy among the degrees of freedom.
Nonlinear magnetization dynamics in nanosystems
Mayergoyz, Isaak D; Serpico, Claudio
2014-01-01
As data transfer rates increase within the magnetic recording industry, improvements in device performance and reliability crucially depend on the thorough understanding of nonlinear magnetization dynamics at a sub-nanoscale level. This book offers a modern, stimulating approach to the subject of nonlinear magnetization dynamics by discussing important aspects such as the Landau-Lifshitz-Gilbert (LLG) equation, analytical solutions, and the connection between the general topological and structural aspects of dynamics. An advanced reference for the study and understanding of non
Nonlinear Observers for Gyro Calibration
Thienel, Julie; Sanner, Robert M.
2003-01-01
Nonlinear observers for gyro calibration are presented. The first observer estimates a constant gyro bias. The second observer estimates scale factor errors. The third observer estimates the gyro alignment for three orthogonal gyros. The convergence properties of all three observers are discussed. Additionally, all three observers are coupled with a nonlinear control algorithm. The stability of each of the resulting closed loop systems is analyzed. Simulated test results are presented for each system.
Nonlinear dynamics in atom optics
Energy Technology Data Exchange (ETDEWEB)
Chen Wenyu; Dyrting, S.; Milburn, G.J. [Queensland Univ., St. Lucia, QLD (Australia). Dept. of Physics
1996-12-31
In this paper theoretical work on classical and quantum nonlinear dynamics of cold atoms is reported. The basic concepts in nonlinear dynamics are reviewed and then applied to the motion of atoms in time-dependent standing waves and to the atomic bouncer. The quantum dynamics for the cases of regular and chaotic classical dynamics is described. The effect of spontaneous emission and external noise is also discussed. 104 refs., 1 tab., 21 figs.
A Nonlinear Transfer Operator Theorem
Pollicott, Mark
2017-02-01
In recent papers, Kenyon et al. (Ergod Theory Dyn Syst 32:1567-1584 2012), and Fan et al. (C R Math Acad Sci Paris 349:961-964 2011, Adv Math 295:271-333 2016) introduced a form of non-linear thermodynamic formalism based on solutions to a non-linear equation using matrices. In this note we consider the more general setting of Hölder continuous functions.
Nonlinear programming analysis and methods
Avriel, Mordecai
2003-01-01
Comprehensive and complete, this overview provides a single-volume treatment of key algorithms and theories. The author provides clear explanations of all theoretical aspects, with rigorous proof of most results. The two-part treatment begins with the derivation of optimality conditions and discussions of convex programming, duality, generalized convexity, and analysis of selected nonlinear programs. The second part concerns techniques for numerical solutions and unconstrained optimization methods, and it presents commonly used algorithms for constrained nonlinear optimization problems. This g
Nonlinear acoustics in biomedical ultrasound
Cleveland, Robin O.
2015-10-01
Ultrasound is widely used to image inside the body; it is also used therapeutically to treat certain medical conditions. In both imaging and therapy applications the amplitudes employed in biomedical ultrasound are often high enough that nonlinear acoustic effects are present in the propagation: the effects have the potential to be advantageous in some scenarios but a hindrance in others. In the case of ultrasound imaging the nonlinearity produces higher harmonics that result in images of greater quality. However, nonlinear effects interfere with the imaging of ultrasound contrast agents (typically micron sized bubbles with a strong nonlinear response of their own) and nonlinear effects also result in complications when derating of pressure measurements in water to in situ values in tissue. High intensity focused ultrasound (HIFU) is emerging as a non-invasive therapeutic modality which can result in thermal ablation of tissue. For thermal ablation, the extra effective attenuation resulting from nonlinear effects can result in enhanced heating of tissue if shock formation occurs in the target region for ablation - a highly desirable effect. However, if nonlinearity is too strong it can also result in undesired near-field heating and reduced ablation in the target region. The disruption of tissue (histotripsy) and fragmentation of kidney stones (lithotripsy) exploits shock waves to produce mechanically based effects, with minimal heating present. In these scenarios it is necessary for the waves to be of sufficient amplitude that a shock exists when the waveform reaches the target region. This talk will discuss how underlying nonlinear phenomenon act in all the diagnostic and therapeutic applications described above.
Nonlinear evolution equations in QCD
Stasto, A. M.
2004-01-01
The following lectures are an introduction to the phenomena of partonic saturation and nonlinear evolution equations in Quantum Chromodynamics. After a short introduction to the linear evolution, the problems of unitarity bound and parton saturation are discussed. The nonlinear Balitsky-Kovchegov evolution equation in the high energy limit is introduced, and the progress towards the understanding of the properties of its solution is reviewed. We discuss the concepts of the saturation scale, g...
Predictive simulation of nonlinear ultrasonics
Shen, Yanfeng; Giurgiutiu, Victor
2012-04-01
Most of the nonlinear ultrasonic studies to date have been experimental, but few theoretical predictive studies exist, especially for Lamb wave ultrasonic. Compared with nonlinear bulk waves and Rayleigh waves, nonlinear Lamb waves for structural health monitoring become more challenging due to their multi-mode dispersive features. In this paper, predictive study of nonlinear Lamb waves is done with finite element simulation. A pitch-catch method is used to interrogate a plate with a "breathing crack" which opens and closes under tension and compression. Piezoelectric wafer active sensors (PWAS) used as transmitter and receiver are modeled with coupled field elements. The "breathing crack" is simulated via "element birth and death" technique. The ultrasonic waves generated by the transmitter PWAS propagate into the structure, interact with the "breathing crack", acquire nonlinear features, and are picked up by the receiver PWAS. The features of the wave packets at the receiver PWAS are studied and discussed. The received signal is processed with Fast Fourier Transform to show the higher harmonics nonlinear characteristics. A baseline free damage index is introduced to assess the presence and the severity of the crack. The paper finishes with summary, conclusions, and suggestions for future work.
Leslie, Thomas M.
1993-01-01
A focused approach to development and evaluation of organic polymer films for use in optoelectronics is presented. The issues and challenges that are addressed include: (1) material synthesis, purification, and the tailoring of the material properties; (2) deposition of uniform thin films by a variety of methods; (3) characterization of material physical properties (thermal, electrical, optical, and electro-optical); and (4) device fabrication and testing. Photonic materials, devices, and systems were identified as critical technology areas by the Department of Commerce and the Department of Defense. This approach offers strong integration of basic material issues through engineering applications by the development of materials that can be exploited as the active unit in a variety of polymeric thin film devices. Improved materials were developed with unprecedented purity and stability. The absorptive properties can be tailored and controlled to provide significant improvement in propagation losses and nonlinear performance. Furthermore, the materials were incorporated into polymers that are highly compatible with fabrication and patterning processes for integrated optical devices and circuits. By simultaneously addressing the issues of materials development and characterization, keeping device design and fabrication in mind, many obstacles were overcome for implementation of these polymeric materials and devices into systems. We intend to considerably improve the upper use temperature, poling stability, and compatibility with silicon based devices. The principal device application that was targeted is a linear electro-optic modulation etalon. Organic polymers need to be properly designed and coupled with existing integrated circuit technology to create new photonic devices for optical communication, image processing, other laser applications such as harmonic generation, and eventually optical computing. The progression from microscopic sample to a suitable film
Nonlinear ultrasound wave propagation in thermoviscous fluids
DEFF Research Database (Denmark)
Sørensen, Mads Peter
coupled nonlinear partial differential equations, which resembles those of optical chi-2 materials. We think this result makes a remarkable link between nonlinear acoustics and nonlinear optics. Finally our analysis reveal an exact kink solution to the nonlinear acoustic problem. This kink solution...
New nonlinear optical materials based on ferrofluids
Energy Technology Data Exchange (ETDEWEB)
Huang, J P [Department of Physics, Fudan University, Shanghai 200433 (China); Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz (Germany); Institute of Theoretical Physics, Chinese University of Hong Kong, Shatin, NT, Hong Kong (China); Yu, K W [Department of Physics, Chinese University of Hong Kong, Shatin, NT, Hong Kong (China); Institute of Theoretical Physics, Chinese University of Hong Kong, Shatin, NT, Hong Kong (China)
2006-01-01
We exploit theoretically a new class of magneto-controlled nonlinear optical material based on ferrofluids in which ferromagnetic nanoparticles are coated with a nonmagnetic metallic nonlinear shell. Such an optical material can have anisotropic nonlinear optical properties and a giant enhancement of nonlinearity, as well as an attractive figure of merit.
Graphene - a rather ordinary nonlinear optical material
khurgin, Jacob B
2014-01-01
An analytical expression for the nonlinear refractive index of graphene has been derived and used to obtain the performance metrics of third order nonlinear devices using graphene as a nonlinear medium. None of the metrics is found to be superior to the existing nonlinear optical materials.
Nonlinear models for autoregressive conditional heteroskedasticity
DEFF Research Database (Denmark)
Teräsvirta, Timo
This paper contains a brief survey of nonlinear models of autore- gressive conditional heteroskedasticity. The models in question are parametric nonlinear extensions of the original model by Engle (1982). After presenting the individual models, linearity testing and parameter estimation...... are discussed. Forecasting volatility with nonlinear models is considered. Finally, parametric nonlinear models based on multi- plicative decomposition of the variance receive attention....
Focus issue introduction: nonlinear optics 2013.
Dadap, Jerry I; Karlsson, Magnus; Panoiu, Nicolae C
2013-12-16
Nonlinear Optics has continued to develop over the last few years at an extremely fast pace, with significant advances being reported in nonlinear optical metamaterials, optical signal processing, quantum optics, nonlinear optics at subwavelength scale, and biophotonics. These exciting new developments have generated significant potential for a broad spectrum of technological applications in which nonlinear-optical processes play a central role.
Standing waves for discrete nonlinear Schrodinger equations
Ming Jia
2016-01-01
The discrete nonlinear Schrodinger equation is a nonlinear lattice system that appears in many areas of physics such as nonlinear optics, biomolecular chains and Bose-Einstein condensates. By using critical point theory, we establish some new sufficient conditions on the existence results of standing waves for the discrete nonlinear Schrodinger equations. We give an appropriate example to illustrate the conclusion obtained.
BOOK REVIEW: Nonlinear Magnetohydrodynamics
Shafranov, V.
1998-08-01
Nonlinear magnetohydrodynamics by Dieter Biskamp is a thorough introduction to the physics of the most impressive non-linear phenomena that occur in conducting magnetoplasmas. The basic systems, in which non-trivial dynamic processes are observed, accompanied by changes of geometry of the magnetic field and the effects of energy transformation (magnetic energy into kinetic energy or the opposite effect in magnetic dynamos), are the plasma magnetic confinement systems for nuclear fusion and space plasmas, mainly the solar plasma. A significant number of the examples of the dynamic processes considered are taken from laboratory plasmas, for which an experimental check of the theory is possible. Therefore, though the book is intended for researchers and students interested in both laboratory, including nuclear fusion, and astrophysical plasmas, it is most probably closer to the first category of reader. In the Introduction the author notes that unlike the hydrodynamics of non-conducting fluids, where the phenomena caused by rapid fluid motions are the most interesting, for plasmas in a strong magnetic field the quasi-static configurations inside which the local dynamic processes occur are often the most important. Therefore, the reader will also find in this book rather traditional material on the theory of plasma equilibrium and stability in magnetic fields. In addition, it is notable that, as opposed to a linear theory, the non-linear theory, as a rule, cannot give quite definite explanations or predictions of phenomena, and consequently there are in the book many results obtained by consideration of numerical models with the use of supercomputers. The treatment of non-linear dynamics is preceded by Chapters 2 to 4, in which the basics of MHD theory are presented with an emphasis on the role of integral invariants of the magnetic helicity type, a derivation of the reduced MHD equations is given, together with examples of the exact solutions of the equilibrium
Complex motions and chaos in nonlinear systems
Machado, José; Zhang, Jiazhong
2016-01-01
This book brings together 10 chapters on a new stream of research examining complex phenomena in nonlinear systems—including engineering, physics, and social science. Complex Motions and Chaos in Nonlinear Systems provides readers a particular vantage of the nature and nonlinear phenomena in nonlinear dynamics that can develop the corresponding mathematical theory and apply nonlinear design to practical engineering as well as the study of other complex phenomena including those investigated within social science.
Compressed Sensing with Nonlinear Observations and Related Nonlinear Optimisation Problems
Blumensath, Thomas
2012-01-01
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured signals to be sampled far below the rate traditionally prescribed. Nearly all of the theory developed for Compressed Sensing signal recovery assumes that samples are taken using linear measurements. In this paper we instead address the Compressed Sensing recovery problem in a setting where the observations are non-linear. We show that, under conditions similar to those required in the linear setting, the Iterative Hard Thresholding algorithm can be used to accurately recover sparse or structured signals from few non-linear observations. Similar ideas can also be developed in a more general non-linear optimisation framework. In the second part of this paper we therefore present related result that show how this can be done under sparsity and union of subspaces constraints, wh...
Input saturation in nonlinear multivariable processes resolved by nonlinear decoupling
Directory of Open Access Journals (Sweden)
Jens G. Balchen
1995-04-01
Full Text Available A new method is presented for the resolution of the problem of input saturation in nonlinear multivariable process control by means of elementary nonlinear decoupling (END. Input saturation can have serious consequences particularly in multivariable control because it may lead to very undesirable system behaviour and quite often system instability. Many authors have searched for systematic techniques for designing multivariable control systems in which saturation may occur in any of the control variables (inputs, manipulated variables. No generally accepted method seems to have been presented so far which gives a solution in closed form. The method of elementary nonlinear decoupling (END can be applied directly to the case of saturation control variables by deriving as many control strategies as there are combinations of saturating control variables. The method is demonstrated by the multivariable control of a simulated Fluidized Catalytic Cracker (FCC with very convincing results.
Nonlinear graphene plasmonics (Conference Presentation)
Cox, Joel D.; Marini, Andrea; Garcia de Abajo, Javier F.
2016-09-01
The combination of graphene's intrinsically-high nonlinear optical response with its ability to support long-lived, electrically tunable plasmons that couple strongly with light has generated great expectations for application of the atomically-thin material to nanophotonic devices. These expectations are mainly reinforced by classical analyses performed using the response derived from extended graphene, neglecting finite-size and nonlocal effects that become important when the carbon layer is structured on the nanometer scale in actual device designs. Based on a quantum-mechanical description of graphene using tight-binding electronic states combined with the random-phase approximation, we show that finite-size effects produce large contributions that increase the nonlinear response associated with plasmons in nanostructured graphene to significantly higher levels than previously thought, particularly in the case of Kerr-type optical nonlinearities. Motivated by this finding, we discuss and compare saturable absorption in extended and nanostructured graphene, with or without plasmonic enhancement, within the context of passive mode-locking for ultrafast lasers. We also explore the possibility of high-harmonic generation in doped graphene nanoribbons and nanoislands, where illumination by an infrared pulse of moderate intensity, tuned to a plasmon resonance, is predicted to generate light at harmonics of order 13 or higher, extending over the visible and UV regimes. Our atomistic description of graphene's nonlinear optical response reveals its complex nature in both extended and nanostructured systems, while further supporting the exceptional potential of this material for nonlinear nanophotonic devices.
Introduction to nonlinear dispersive equations
Linares, Felipe
2015-01-01
This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research. The second edition of Introdu...
Nonlinear plasmonics at high temperatures
Sivan, Yonatan
2016-01-01
We solve the Maxwell and heat equations self-consistently for metal nanoparticles under intense continuous wave (CW) illumination. Unlike previous studies, we rely on {\\em experimentally}-measured data for the metal permittivity for increasing temperature and for the visible spectral range. We show that the thermal nonlinearity of the metal can lead to substantial deviations from the predictions of the linear model for the temperature and field distribution, and thus, can explain qualitatively the strong nonlinear scattering from such configurations observed experimentally. We also show that the incompleteness of existing data of the temperature dependence of the thermal properties of the system prevents reaching a quantitative agreement between the measured and calculated scattering data. This modelling approach is essential for the identification of the underlying physical mechanism responsible for the thermo-optical nonlinearity of the metal and should be adopted in all applications of high temperature non...
Nonlinear Multigrid for Reservoir Simulation
DEFF Research Database (Denmark)
Christensen, Max la Cour; Eskildsen, Klaus Langgren; Engsig-Karup, Allan Peter
2016-01-01
A feasibility study is presented on the effectiveness of applying nonlinear multigrid methods for efficient reservoir simulation of subsurface flow in porous media. A conventional strategy modeled after global linearization by means of Newton’s method is compared with an alternative strategy...... modeled after local linearization, leading to a nonlinear multigrid method in the form of the full-approximation scheme (FAS). It is demonstrated through numerical experiments that, without loss of robustness, the FAS method can outperform the conventional techniques in terms of algorithmic and numerical...... efficiency for a black-oil model. Furthermore, the use of the FAS method enables a significant reduction in memory usage compared with conventional techniques, which suggests new possibilities for improved large-scale reservoir simulation and numerical efficiency. Last, nonlinear multilevel preconditioning...
Nonlinear photoacoustic spectroscopy of hemoglobin
Energy Technology Data Exchange (ETDEWEB)
Danielli, Amos; Maslov, Konstantin; Favazza, Christopher P.; Xia, Jun; Wang, Lihong V., E-mail: LHWANG@WUSTL.EDU [Optical Imaging Laboratory, Department of Biomedical Engineering, Washington University in St. Louis, One Brookings Drive, St. Louis, Missouri 63130 (United States)
2015-05-18
As light intensity increases in photoacoustic imaging, the saturation of optical absorption and the temperature dependence of the thermal expansion coefficient result in a measurable nonlinear dependence of the photoacoustic (PA) signal on the excitation pulse fluence. Here, under controlled conditions, we investigate the intensity-dependent photoacoustic signals from oxygenated and deoxygenated hemoglobin at varied optical wavelengths and molecular concentrations. The wavelength and concentration dependencies of the nonlinear PA spectrum are found to be significantly greater in oxygenated hemoglobin than in deoxygenated hemoglobin. These effects are further influenced by the hemoglobin concentration. These nonlinear phenomena provide insights into applications of photoacoustics, such as measurements of average inter-molecular distances on a nm scale or with a tuned selection of wavelengths, a more accurate quantitative PA tomography.
Nonlinear Waves in Complex Systems
DEFF Research Database (Denmark)
2007-01-01
The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations......, it is the universality and robustness of the main models with respect to perturbations that developped the field. This is true for both continuous and discrete equations. In this volume we keep this broad view and draw new perspectives for nonlinear waves in complex systems. In particular we address energy flow...... in Fourier space and equipartition, the role of inhomogeneities and complex geometry and the importance of coupled systems....
Nonlinear dynamics in biological systems
Carballido-Landeira, Jorge
2016-01-01
This book presents recent research results relating to applications of nonlinear dynamics, focusing specifically on four topics of wide interest: heart dynamics, DNA/RNA, cell mobility, and proteins. The book derives from the First BCAM Workshop on Nonlinear Dynamics in Biological Systems, held in June 2014 at the Basque Center of Applied Mathematics (BCAM). At this international meeting, researchers from different but complementary backgrounds, including molecular dynamics, physical chemistry, bio-informatics and biophysics, presented their most recent results and discussed the future direction of their studies using theoretical, mathematical modeling and experimental approaches. Such was the level of interest stimulated that the decision was taken to produce this publication, with the organizers of the event acting as editors. All of the contributing authors are researchers working on diverse biological problems that can be approached using nonlinear dynamics. The book will appeal especially to applied math...
Nonlinear microrheology of living cells
Kollmannsberger, Philip; Fabry, Ben
2009-01-01
The linear rheology of adherent cells is characterized by a power-law creep or stress relaxation response, and proportionality between stiffness and internal prestress. It is unknown whether these observations hold in the physiologically relevant nonlinear regime. We used magnetic tweezers microrheology to measure the time- and force-dependent nonlinear creep response of adherent cells. Cell deformations in response to a stepwise increasing force applied to cytoskeletally bound magnetic beads were analyzed with a nonlinear superposition approach. The creep response followed a weak power law regardless of force. Stiffness and power law exponent both increased with force, indicating stress stiffening as well as fluidization of the cytoskeleton. Softer cells showed a more pronounced stress stiffening, which is quantitatively explained by their smaller internal prestress. Stiffer and more elastic cells showed a more pronounced force-induced fluidization, consistent with predictions from soft glassy rheology. Thes...
A NONLINEAR FEASIBILITY PROBLEM HEURISTIC
Directory of Open Access Journals (Sweden)
Sergio Drumond Ventura
2015-04-01
Full Text Available In this work we consider a region S ⊂ given by a finite number of nonlinear smooth convex inequalities and having nonempty interior. We assume a point x 0 is given, which is close in certain norm to the analytic center of S, and that a new nonlinear smooth convex inequality is added to those defining S (perturbed region. It is constructively shown how to obtain a shift of the right-hand side of this inequality such that the point x 0 is still close (in the same norm to the analytic center of this shifted region. Starting from this point and using the theoretical results shown, we develop a heuristic that allows us to obtain the approximate analytic center of the perturbed region. Then, we present a procedure to solve the problem of nonlinear feasibility. The procedure was implemented and we performed some numerical tests for the quadratic (random case.
Nonlinear Deformable-body Dynamics
Luo, Albert C J
2010-01-01
"Nonlinear Deformable-body Dynamics" mainly consists in a mathematical treatise of approximate theories for thin deformable bodies, including cables, beams, rods, webs, membranes, plates, and shells. The intent of the book is to stimulate more research in the area of nonlinear deformable-body dynamics not only because of the unsolved theoretical puzzles it presents but also because of its wide spectrum of applications. For instance, the theories for soft webs and rod-reinforced soft structures can be applied to biomechanics for DNA and living tissues, and the nonlinear theory of deformable bodies, based on the Kirchhoff assumptions, is a special case discussed. This book can serve as a reference work for researchers and a textbook for senior and postgraduate students in physics, mathematics, engineering and biophysics. Dr. Albert C.J. Luo is a Professor of Mechanical Engineering at Southern Illinois University, Edwardsville, IL, USA. Professor Luo is an internationally recognized scientist in the field of non...
Nonlinear Resistivity for Magnetohydrodynamical Models
Lingam, Manasvi; Pfefferlé, David; Comisso, Luca; Bhattacharjee, Amitava
2016-01-01
A nonlinear current-dependent resistivity that accurately accounts for the collisional electron-ion momentum transfer rate is derived. It is shown that the Spitzer resistivity overestimates the resistivity in certain observationally relevant regimes. The nonlinear resistivity computed herein is a strictly decreasing function of the current, in contrast to some notable previous proposals. The relative importance of the new expression with respect to the well-established electron inertia and Hall terms is also examined. The subtle implications of this current-dependent resistivity are discussed in the context of plasma systems and phenomena such as magnetic reconnection.
Time Series with Tailored Nonlinearities
Raeth, C
2015-01-01
It is demonstrated how to generate time series with tailored nonlinearities by inducing well- defined constraints on the Fourier phases. Correlations between the phase information of adjacent phases and (static and dynamic) measures of nonlinearities are established and their origin is explained. By applying a set of simple constraints on the phases of an originally linear and uncor- related Gaussian time series, the observed scaling behavior of the intensity distribution of empirical time series can be reproduced. The power law character of the intensity distributions being typical for e.g. turbulence and financial data can thus be explained in terms of phase correlations.
Topics in nonlinear functional analysis
Nirenberg, Louis
2001-01-01
Since its first appearance as a set of lecture notes published by the Courant Institute in 1974, this book served as an introduction to various subjects in nonlinear functional analysis. The current edition is a reprint of these notes, with added bibliographic references. Topological and analytic methods are developed for treating nonlinear ordinary and partial differential equations. The first two chapters of the book introduce the notion of topological degree and develop its basic properties. These properties are used in later chapters in the discussion of bifurcation theory (the possible br
Finite elements of nonlinear continua
Oden, J T
2000-01-01
Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view.The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical s
Nonlinear Control of Heartbeat Models
Directory of Open Access Journals (Sweden)
Witt Thanom
2011-02-01
Full Text Available This paper presents a novel application of nonlinear control theory to heartbeat models. Existing heartbeat models are investigated and modified by incorporating the control input as a pacemaker to provide the control channel. A nonlinear feedback linearization technique is applied to force the output of the systems to generate artificial electrocardiogram (ECG signal using discrete data as the reference inputs. The synthetic ECG may serve as a flexible signal source to assess the effectiveness of a diagnostic ECG signal-processing device.
Edge detection by nonlinear dynamics
Energy Technology Data Exchange (ETDEWEB)
Wong, Yiu-fai
1994-07-01
We demonstrate how the formulation of a nonlinear scale-space filter can be used for edge detection and junction analysis. By casting edge-preserving filtering in terms of maximizing information content subject to an average cost function, the computed cost at each pixel location becomes a local measure of edgeness. This computation depends on a single scale parameter and the given image data. Unlike previous approaches which require careful tuning of the filter kernels for various types of edges, our scheme is general enough to be able to handle different edges, such as lines, step-edges, corners and junctions. Anisotropy in the data is handled automatically by the nonlinear dynamics.
Generation of nonlinear vortex precursors
Chen, Yue-Yue; Liu, Chengpu
2016-01-01
We numerically study the propagation of a few-cycle pulse carrying orbital angular momentum (OAM) through a dense atomic system. Nonlinear precursors consisting of high-order vortex har- monics are generated in the transmitted field due to ultrafast Bloch oscillation. The nonlinear precursors survive to propagation effects and are well separated with the main pulse, which provide a straightforward way of measuring precursors. By the virtue of carrying high-order OAM, the obtained vortex precursors as information carriers have potential applications in optical informa- tion and communication fields where controllable loss, large information-carrying capacity and high speed communication are required.
Stability analysis of nonlinear systems
Lakshmikantham, Vangipuram; Martynyuk, Anatoly A
2015-01-01
The book investigates stability theory in terms of two different measure, exhibiting the advantage of employing families of Lyapunov functions and treats the theory of a variety of inequalities, clearly bringing out the underlying theme. It also demonstrates manifestations of the general Lyapunov method, showing how this technique can be adapted to various apparently diverse nonlinear problems. Furthermore it discusses the application of theoretical results to several different models chosen from real world phenomena, furnishing data that is particularly relevant for practitioners. Stability Analysis of Nonlinear Systems is an invaluable single-sourse reference for industrial and applied mathematicians, statisticians, engineers, researchers in the applied sciences, and graduate students studying differential equations.
Higher dimensional nonlinear massive gravity
Do, Tuan Q
2016-01-01
Inspired by a recent ghost-free nonlinear massive gravity in four-dimensional spacetime, we study its higher dimensional scenarios. As a result, we are able to show the constant-like behavior of massive graviton terms for some well-known metrics such as the Friedmann-Lemaitre-Robertson-Walker, Bianchi type I, and Schwarzschild-Tangherlini-(A)dS metrics in a specific five-dimensional nonlinear massive gravity under an assumption that its fiducial metrics are compatible with physical ones. In addition, some simple cosmological solutions of the five-dimensional massive gravity will be figured out consistently.
Wave equation with concentrated nonlinearities
Noja, Diego; Posilicano, Andrea
2004-01-01
In this paper we address the problem of wave dynamics in presence of concentrated nonlinearities. Given a vector field $V$ on an open subset of $\\CO^n$ and a discrete set $Y\\subset\\RE^3$ with $n$ elements, we define a nonlinear operator $\\Delta_{V,Y}$ on $L^2(\\RE^3)$ which coincides with the free Laplacian when restricted to regular functions vanishing at $Y$, and which reduces to the usual Laplacian with point interactions placed at $Y$ when $V$ is linear and is represented by an Hermitean m...
Field guide to nonlinear optics
Powers, Peter E
2013-01-01
Optomechanics is a field of mechanics that addresses the specific design challenges associated with optical systems. This [i]Field Guide [/i]describes how to mount optical components, as well as how to analyze a given design. It is intended for practicing optical and mechanical engineers whose work requires knowledge in both optics and mechanics. This Field Guide is designed for those looking for a condensed and concise source of key concepts, equations, and techniques for nonlinear optics. Topics covered include technologically important effects, recent developments in nonlinear optics
Stability analysis of nonlinear systems with slope restricted nonlinearities.
Liu, Xian; Du, Jiajia; Gao, Qing
2014-01-01
The problem of absolute stability of Lur'e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP) lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.
Stability Analysis of Nonlinear Systems with Slope Restricted Nonlinearities
Directory of Open Access Journals (Sweden)
Xian Liu
2014-01-01
Full Text Available The problem of absolute stability of Lur’e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.
Nonlinearity and nonclassicality in a nanomechanical resonator
Energy Technology Data Exchange (ETDEWEB)
Teklu, Berihu [Clermont Universite, Blaise Pascal University, CNRS, PHOTON-N2, Institut Pascal, Aubiere Cedex (France); Universita degli Studi di Milano, Dipartimento di Fisica, Milano (Italy); Ferraro, Alessandro; Paternostro, Mauro [Queen' s University, Centre for Theoretical Atomic, Molecular, and Optical Physics, School of Mathematics and Physics, Belfast (United Kingdom); Paris, Matteo G.A. [Universita degli Studi di Milano, Dipartimento di Fisica, Milano (Italy)
2015-12-15
We address quantitatively the relationship between the nonlinearity of a mechanical resonator and the nonclassicality of its ground state. In particular, we analyze the nonclassical properties of the nonlinear Duffing oscillator (being driven or not) as a paradigmatic example of a nonlinear nanomechanical resonator. We first discuss how to quantify the nonlinearity of this system and then show that the nonclassicality of the ground state, as measured by the volume occupied by the negative part of the Wigner function, monotonically increases with the nonlinearity in all the working regimes addressed in our study. Our results show quantitatively that nonlinearity is a resource to create nonclassical states in mechanical systems. (orig.)
Analysis of Wave Nonlinear Dispersion Relation
Institute of Scientific and Technical Information of China (English)
LI Rui-jie; TAO Jian-fu
2005-01-01
The nonlinear dispersion relations and modified relations proposed by Kirby and Hedges have the limitation of intermediate minimum value. To overcome the shortcoming, a new nonlinear dispersion relation is proposed. Based on the summarization and comparison of existing nonlinear dispersion relations, it can be found that the new nonlinear dispersion relation not only keeps the advantages of other nonlinear dispersion relations, but also significantly reduces the relative errors of the nonlinear dispersion relations for a range of the relative water depth of 1＜kh＜1.5 and has sufficient accuracy for practical purposes.
Topology optimization of nonlinear optical devices
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard
2011-01-01
This paper considers the design of nonlinear photonic devices. The nonlinearity stems from a nonlinear material model with a permittivity that depends on the local time-averaged intensity of the electric field. A finite element model is developed for time-harmonic wave propagation and an incremen......This paper considers the design of nonlinear photonic devices. The nonlinearity stems from a nonlinear material model with a permittivity that depends on the local time-averaged intensity of the electric field. A finite element model is developed for time-harmonic wave propagation...
Cieslinski, Jan L.; Ferapontov, Eugene V.; Kitaev, Alexander V.; Nimmo, Jonathan J. C.
2009-10-01
-component dispersionless Boussinesq-type system. T E Kouloukas and V G Papageorgiou introduce a family of nonparametric Yang-Baxter maps obtained by re-factorization of matrix polynomials of first degree. These maps are Poisson with respect to the Sklyanin bracket, and their degenerations are connected to known integrable systems on quad-graphs. S V Manakov and P M Santini apply a novel version of the inverse scattering transform based on Lax pairs in multidimensional commuting vector fields to the heavenly and Pavlov equations, establishing that their localized solutions evolve without breaking, and constructing the long-time behaviour of the corresponding Cauchy problems. Discretizations of integrable geometric models depend heavily on the coordinates used. M Nieszporski and A Sym show how to discretize Bianchi surfaces (associated with an elliptic version of the Ernst equation) in arbitrary parametrization. C Rogers and A Szereszewski study the Bäcklund transformation for L-isothermic surfaces in the original Bianchi formulation. They establish a connection between this transformation and a nonhomogeneous linear Schrödinger equation and construct a class of generalized Dupin cyclides. W K Schief, A Szereszewski and C Rogers study a classical system of equilibrium equations for shell membranes. Various examples of viable membrane geometries lead to remarkable geometric configurations such as generalized Dupin cyclides and L-minimal surfaces. A Sergyeyev constructs infinite hierarchies of nonlocal higher symmetries for the oriented associativity equations using the spectral problem. The hierarchies in question generalize those constructed by Chen, Kontsevich and Schwarz for the WDVV equations. J Shiraishi and Y Tutiya study an integro-differential equation which generalizes the periodic intermediate long wave equation. The kernel of the singular integral involved is a second order difference of the Weierstrass ζ-function. Using Sato's formulation, the authors
Non-linear canonical correlation
van der Burg, Eeke; de Leeuw, Jan
1983-01-01
Non-linear canonical correlation analysis is a method for canonical correlation analysis with optimal scaling features. The method fits many kinds of discrete data. The different parameters are solved for in an alternating least squares way and the corresponding program is called CANALS. An
DEFF Research Database (Denmark)
Andersen, Steffen; Harrison, Glenn W.; Hole, Arne Risa
2012-01-01
We develop an extension of the familiar linear mixed logit model to allow for the direct estimation of parametric non-linear functions defined over structural parameters. Classic applications include the estimation of coefficients of utility functions to characterize risk attitudes and discountin...
Impurity solitons with quadratic nonlinearities
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Torres, Juan P-; Torner, Lluis
1998-01-01
We fmd families of solitary waves mediated by parametric mixing in quadratic nonlinear media that are localized at point-defect impurities. Solitons localized at attractive impurities are found to be dynamically stable. It is shown that localization at the impurity modifies strongly the soliton p...
Stochastic nonlinear differential equations. I
Heilmann, O.J.; Kampen, N.G. van
1974-01-01
A solution method is developed for nonlinear differential equations having the following two properties. Their coefficients are stochastic through their dependence on a Markov process. The magnitude of the fluctuations, multiplied with their auto-correlation time, is a small quantity. Under these co
Badikyan, Karen
2016-01-01
The nonlinear theory of relyativistic strophotron is developed. Classical equations of motion are averaged over fast oscillations. The slow motion phase and saturation parameter are found different from usual undulator oscillation parameters. In the strong field approximation the analytical expression of gain is found on higher harmonics of main resonance frequency.
Observation of Nonlinear Compton Scattering
Energy Technology Data Exchange (ETDEWEB)
Kotseroglou, T.
2003-12-19
This experiment tests Quantum Electrodynamics in the strong field regime. Nonlinear Compton scattering has been observed during the interaction of a 46.6 GeV electron beam with a 10{sup 18} W/cm{sup 2} laser beam. The strength of the field achieved was measured by the parameter {eta} = e{var_epsilon}{sub rms}/{omega}mc = 0.6. Data were collected with infrared and green laser photons and circularly polarized laser light. The timing stabilization achieved between the picosecond laser and electron pulses has {sigma}{sub rms} = 2 ps. A strong signal of electrons that absorbed up to 4 infrared photons (or up to 3 green photons) at the same point in space and time, while emitting a single gamma ray, was observed. The energy spectra of the scattered electrons and the nonlinear dependence of the electron yield on the field strength agreed with the simulation over 3 orders of magnitude. The detector could not resolve the nonlinear Compton scattering from the multiple single Compton scattering which produced rates of scattered electrons of the same order of magnitude. Nevertheless, a simulation has studied this difference and concluded that the scattered electron rates observed could not be accounted for only by multiple ordinary Compton scattering; nonlinear Compton scattering processes are dominant for n {ge} 3.
Nonlinear Optics of Hexaphenyl Nanofibers
DEFF Research Database (Denmark)
Balzer, Frank; Al-Shamery, Katharina; Neuendorf, Rolf
2003-01-01
measurements reveal that the nonlinear optical transition dipole moment is oriented with an angle of 75° with respect to the needles long axes. The absolute value of the macroscopic second-order susceptibility, averaged over a size distribution of p-6P nanoaggregates, is estimated to be of the order of 6...
Nonlinear intravascular ultrasound contrast imaging
Goertz, David E.; Frijlink, Martijn E.; de Jong, N.; van der Steen, Antonius F.W.
2006-01-01
Nonlinear contrast agent imaging with intravascular ultrasound (IVUS) is investigated using a prototype IVUS system and an experimental small bubble contrast agent. The IVUS system employed a mechanically scanned single element transducer and was operated at a 20 MHz transmit frequency (F20) for
Quantum nonlinear optics without photons
Stassi, Roberto; Macrı, Vincenzo; Kockum, Anton Frisk; Di Stefano, Omar; Miranowicz, Adam; Savasta, Salvatore; Nori, Franco
2017-08-01
Spontaneous parametric down-conversion is a well-known process in quantum nonlinear optics in which a photon incident on a nonlinear crystal spontaneously splits into two photons. Here we propose an analogous physical process where one excited atom directly transfers its excitation to a pair of spatially separated atoms with probability approaching 1. The interaction is mediated by the exchange of virtual rather than real photons. This nonlinear atomic process is coherent and reversible, so the pair of excited atoms can transfer the excitation back to the first one: the atomic analog of sum-frequency generation of light. The parameters used to investigate this process correspond to experimentally demonstrated values in ultrastrong circuit quantum electrodynamics. This approach can be extended to realize other nonlinear interatomic processes, such as four-atom mixing, and is an attractive architecture for the realization of quantum devices on a chip. We show that four-qubit mixing can efficiently implement quantum repetition codes and, thus, can be used for error-correction codes.
Cosmological effects of nonlinear electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Novello, M [Instituto de Cosmologia Relatividade Astrofisica (ICRA-Brasil/CBPF), Rua Dr Xavier Sigaud, 150, CEP 22290-180, Rio de Janeiro (Brazil); Goulart, E [Instituto de Cosmologia Relatividade Astrofisica (ICRA-Brasil/CBPF), Rua Dr Xavier Sigaud, 150, CEP 22290-180, Rio de Janeiro (Brazil); Salim, J M [Instituto de Cosmologia Relatividade Astrofisica (ICRA-Brasil/CBPF), Rua Dr Xavier Sigaud, 150, CEP 22290-180, Rio de Janeiro (Brazil); Bergliaffa, S E Perez [Departamento de Fisica Teorica, Universidade do Estado do Rio de Janeiro, R. Sao Francisco Xavier, 524, Maracana, CEP 20559-900, Rio de Janeiro (Brazil)
2007-06-07
It will be shown that a given realization of nonlinear electrodynamics, used as a source of Einstein's equations, generates a cosmological model with interesting features, namely a phase of current cosmic acceleration, and the absence of an initial singularity, thus pointing to a way of solving two important problems in cosmology.
On Nonlinear Higher Spin Curvature
Manvelyan, Ruben(Yerevan Physics Institute, Alikhanian Br. St. 2, Yerevan, 0036, Armenia); Mkrtchyan, Karapet; Rühl, Werner; Tovmasyan, Murad
2011-01-01
We present the first nonlinear term of the higher spin curvature which is covariant with respect to deformed gauge transformations that are linear in the field. We consider in detail the case of spin 3 after presenting spin 2 as an example, and then construct the general spin s quadratic term of the deWit-Freedman curvature.
On nonlinear higher spin curvature
Energy Technology Data Exchange (ETDEWEB)
Manvelyan, Ruben, E-mail: manvel@physik.uni-kl.d [Department of Physics, Erwin Schroedinger Strasse, Technical University of Kaiserslautern, Postfach 3049, 67653 Kaiserslautern (Germany); Yerevan Physics Institute, Alikhanian Br. Str. 2, 0036 Yerevan (Armenia); Mkrtchyan, Karapet, E-mail: karapet@yerphi.a [Department of Physics, Erwin Schroedinger Strasse, Technical University of Kaiserslautern, Postfach 3049, 67653 Kaiserslautern (Germany); Yerevan Physics Institute, Alikhanian Br. Str. 2, 0036 Yerevan (Armenia); Ruehl, Werner, E-mail: ruehl@physik.uni-kl.d [Department of Physics, Erwin Schroedinger Strasse, Technical University of Kaiserslautern, Postfach 3049, 67653 Kaiserslautern (Germany); Tovmasyan, Murad, E-mail: mtovmasyan@ysu.a [Yerevan Physics Institute, Alikhanian Br. Str. 2, 0036 Yerevan (Armenia)
2011-05-09
We present the first nonlinear term of the higher spin curvature which is covariant with respect to deformed gauge transformations that are linear in the field. We consider the case of spin 3 after presenting spin 2 as an example, and then construct the general spin s quadratic term of the de Wit-Freedman curvature.
Nonlinear smoothing for random fields
Aihara, Shin Ichi; Bagchi, Arunabha
1995-01-01
Stochastic nonlinear elliptic partial differential equations with white noise disturbances are studied in the countably additive measure set up. Introducing the Onsager-Machlup function to the system model, the smoothing problem for maximizing the modified likelihood functional is solved and the exp
Practical stability of nonlinear systems
Lakshmikantham, Vangipuram; Martynyuk, Anatolii Andreevich
1990-01-01
This is the first book that deals with practical stability and its development. It presents a systematic study of the theory of practical stability in terms of two different measures and arbitrary sets and demonstrates the manifestations of general Lyapunov's method by showing how this effective technique can be adapted to investigate various apparently diverse nonlinear problems including control systems and multivalued differential equations.
The virial theorem for nonlinear problems
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Colima (Mexico); Fernandez, Francisco M [INIFTA (UNLP, CCT La Plata-CONICET), Division Quimica Teorica, Blvd 113 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)], E-mail: paolo.amore@gmail.com, E-mail: fernande@quimica.unlp.edu.ar
2009-09-15
We show that the virial theorem provides a useful simple tool for approximating nonlinear problems. In particular, we consider conservative nonlinear oscillators and obtain the same main result derived earlier from the expansion in Chebyshev polynomials. (letters and comments)
Nonlinear rheological models for structured interfaces
Sagis, L.M.C.
2010-01-01
The GENERIC formalism is a formulation of nonequilibrium thermodynamics ideally suited to develop nonlinear constitutive equations for the stress–deformation behavior of complex interfaces. Here we develop a GENERIC model for multiphase systems with interfaces displaying nonlinear viscoelastic stres
International Conference on Applications in Nonlinear Dynamics
Longhini, Patrick; Palacios, Antonio
2017-01-01
This book presents collaborative research works carried out by experimentalists and theorists around the world in the field of nonlinear dynamical systems. It provides a forum for applications of nonlinear systems while solving practical problems in science and engineering. Topics include: Applied Nonlinear Optics, Sensor, Radar & Communication Signal Processing, Nano Devices, Nonlinear Biomedical Applications, Circuits & Systems, Coupled Nonlinear Oscillator, Precision Timing Devices, Networks, and other contemporary topics in the general field of Nonlinear Science. This book provides a comprehensive report of the various research projects presented at the International Conference on Applications in Nonlinear Dynamics (ICAND 2016) held in Denver, Colorado, 2016. It can be a valuable tool for scientists and engineering interested in connecting ideas and methods in nonlinear dynamics with actual design, fabrication and implementation of engineering applications or devices.
Hamiltonian realizations of nonlinear adjoint operators
Fujimoto, Kenji; Scherpen, Jacquelien M.A.; Gray, W. Steven
2002-01-01
This paper addresses the issue of state-space realizations for nonlinear adjoint operators. In particular, the relationships between nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are established. Then, characterizations of the adjoints of control
Hamiltonian Realizations of Nonlinear Adjoint Operators
Fujimoto, Kenji; Scherpen, Jacquelien M.A.; Gray, W. Steven
2000-01-01
This paper addresses state-space realizations for nonlinear adjoint operators. In particular the relationship among nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are clarified. The characterization of controllability, observability and Hankel ope
Nonlinear Least Squares for Inverse Problems
Chavent, Guy
2009-01-01
Presents an introduction into the least squares resolution of nonlinear inverse problems. This title intends to develop a geometrical theory to analyze nonlinear least square (NLS) problems with respect to their quadratic wellposedness, that is, both wellposedness and optimizability
Nonlinear dynamics by mode superposition
Energy Technology Data Exchange (ETDEWEB)
Nickell, R.E.
1976-01-01
A mode superposition technique for approximately solving nonlinear initial-boundary-value problems of structural dynamics is discussed, and results for examples involving large deformation are compared to those obtained with implicit direct integration methods such as the Newmark generalized acceleration and Houbolt backward-difference operators. The initial natural frequencies and mode shapes are found by inverse power iteration with the trial vectors for successively higher modes being swept by Gram-Schmidt orthonormalization at each iteration. The subsequent modal spectrum for nonlinear states is based upon the tangent stiffness of the structure and is calculated by a subspace iteration procedure that involves matrix multiplication only, using the most recently computed spectrum as an initial estimate. Then, a precise time integration algorithm that has no artificial damping or phase velocity error for linear problems is applied to the uncoupled modal equations of motion. Squared-frequency extrapolation is examined for nonlinear problems as a means by which these qualities of accuracy and precision can be maintained when the state of the system (and, thus, the modal spectrum) is changing rapidly. The results indicate that a number of important advantages accrue to nonlinear mode superposition: (a) there is no significant difference in total solution time between mode superposition and implicit direct integration analyses for problems having narrow matric half-bandwidth (in fact, as bandwidth increases, mode superposition becomes more economical), (b) solution accuracy is under better control since the analyst has ready access to modal participation factors and the ratios of time step size to modal period, and (c) physical understanding of nonlinear dynamic response is improved since the analyst is able to observe the changes in the modal spectrum as deformation proceeds.
Interaction nonlinearity in asphalt binders
Motamed, Arash; Bhasin, Amit; Liechti, Kenneth M.
2012-05-01
Asphalt mixtures are complex composites that comprise aggregate, asphalt binder, and air. Several research studies have shown that the mechanical behavior of the asphalt mixture is strongly influenced by the matrix, i.e. the asphalt binder. Characterization and a thorough understanding of the binder behavior is the first and crucial step towards developing an accurate constitutive model for the composite. Accurate constitutive models for the constituent materials are critical to ensure accurate performance predictions at a material and structural level using micromechanics. This paper presents the findings from a systematic investigation into the nature of the linear and nonlinear response of asphalt binders subjected to different types of loading using the Dynamic Shear Rheometer (DSR). Laboratory test data show that a compressive normal force is generated in an axially constrained specimen subjected to torsional shear. This paper investigates the source of this normal force and demonstrates that the asphalt binder can dilate when subjected to shear loads. This paper also presents the findings from a study conducted to investigate the source of the nonlinearity in the asphalt binder. Test results demonstrate that the application of cyclic shear loads results in the development of a normal force and a concomitant reduction in the dynamic shear modulus. This form of nonlinear response is referred to as an "interaction nonlinearity". A combination of experimental and analytical tools is used to demonstrate and verify the presence of this interaction nonlinearity in asphalt binders. The findings from this study highlight the importance of modeling the mechanical behavior of asphalt binders based on the overall stress state of the material.
Nonlinear Michelson interferometer for improved quantum metrology
Luis, Alfredo; Rivas, Ángel
2015-08-01
We examine quantum detection via a Michelson interferometer embedded in a gas with Kerr nonlinearity. This nonlinear interferometer is illuminated by pulses of classical light. This strategy combines the robustness against practical imperfections of classical light with the improvement provided by nonlinear processes. Regarding ultimate quantum limits, we stress that, as a difference with linear schemes, the nonlinearity introduces pulse duration as a new variable into play along with the energy resources.
Detecting the Nonlinearity of Fish Acoustic Signals
Institute of Scientific and Technical Information of China (English)
REN Xinmin; YIN Li
2006-01-01
This paper discusses the nonlinearity of fish acoustic signals by using the surrogate data method.We compare the difference of three test statistics - time-irreversibility Trey, correlation dimension D2 and auto mutual information function Ⅰbetween the original data and the surrogate data.We come to the conclusion that there exists nonlinearity in the fish acoustic signals and there exist deterministic nonlinear components; therefore nonlinear dynamic theory can be used to analyze fish acoustic signals.
Nonlinear Markov Control Processes and Games
2012-11-15
further research we indicated possible extensions to state spaces with nontrivial geometry, to the controlled nonlinear quantum dynamic semigroups and...space nonlinear Markov semigroup is a one-parameter semigroup of (possibly nonlinear) transformations of the unit simplex in n-dimensional Euclidean...certain mixing property of nonlinear transition probabilities. In case of the semigroup parametrized by continuous time one defines its generator as the
Nonlinear metrology with a quantum interface
Napolitano, M.; Mitchell, M. W.
2009-01-01
We describe nonlinear quantum atom-light interfaces and nonlinear quantum metrology in the collective continuous variable formalism. We develop a nonlinear effective Hamiltonian in terms of spin and polarization collective variables and show that model Hamiltonians of interest for nonlinear quantum metrology can be produced in $^{87}$Rb ensembles. With these Hamiltonians, metrologically relevant atomic properties, e.g. the collective spin, can be measured better than the "Heisenberg limit" $\\...
Nonlinear Michelson interferometer for improved quantum metrology
Luis Aina, Alfredo; Rivas Vargas, Ángel
2015-01-01
We examine quantum detection via a Michelson interferometer embedded in a gas with Kerr nonlinearity. This nonlinear interferometer is illuminated by pulses of classical light. This strategy combines the robustness against practical imperfections of classical light with the improvement provided by nonlinear processes. Regarding ultimate quantum limits, we stress that, as a difference with linear schemes, the nonlinearity introduces pulse duration as a new variable into play along with the ene...
Standing waves for discrete nonlinear Schrodinger equations
Directory of Open Access Journals (Sweden)
Ming Jia
2016-07-01
Full Text Available The discrete nonlinear Schrodinger equation is a nonlinear lattice system that appears in many areas of physics such as nonlinear optics, biomolecular chains and Bose-Einstein condensates. By using critical point theory, we establish some new sufficient conditions on the existence results of standing waves for the discrete nonlinear Schrodinger equations. We give an appropriate example to illustrate the conclusion obtained.
Nonlinear Young integrals via fractional calculus
Hu, Yaozhong (1961-); Le, Khoa
2015-01-01
For H\\"older continuous functions $W(t,x)$ and $\\varphi_t$, we define nonlinear integral $\\int_a^b W(dt, \\varphi_t)$ via fractional calculus. This nonlinear integral arises naturally in the Feynman-Kac formula for stochastic heat equations with random coefficients. We also define iterated nonlinear integrals.
Nonlinear approaches in engineering applications 2
Jazar, Reza N
2013-01-01
Provides updated principles and applications of the nonlinear approaches in solving engineering and physics problems Demonstrates how nonlinear approaches may open avenues to better, safer, cheaper systems with less energy consumption Has a strong emphasis on the application, physical meaning, and methodologies of nonlinear approaches in different engineering and science problems
Nonlinear quasimodes near elliptic periodic geodesics
Albin, Pierre; Marzuola, Jeremy L; Thomann, Laurent
2011-01-01
We consider the nonlinear Schr\\"odinger equation on a compact manifold near an elliptic periodic geodesic. Using a geometric optics construction, we construct quasimodes to a nonlinear stationary problem which are highly localized near the periodic geodesic. We show the nonlinear Schr\\"odinger evolution of such a quasimode remains localized near the geodesic, at least for short times.
Nonlinear time series modelling: an introduction
Simon M. Potter
1999-01-01
Recent developments in nonlinear time series modelling are reviewed. Three main types of nonlinear models are discussed: Markov Switching, Threshold Autoregression and Smooth Transition Autoregression. Classical and Bayesian estimation techniques are described for each model. Parametric tests for nonlinearity are reviewed with examples from the three types of models. Finally, forecasting and impulse response analysis is developed.
Variational principles for nonlinear piezoelectric materials
Energy Technology Data Exchange (ETDEWEB)
Rodriguez-Ramos, R.; Guinovart-Diaz, R. [Universidad de la Habana, Facultad de Matematica y Computacion, Vedado, Habana (Cuba); Pobedria, B.E. [Moscow State University M. V. Lomonosov, Composites Department, Moscow (Russian Federation); Padilla, P. [Universidad Nacional Autonoma de Mexico, Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas (IIMAS), Cd. Universitaria, Mexico D.F. (Mexico); Bravo-Castillero, J. [Universidad de la Habana, Facultad de Matematica y Computacion, Vedado, Habana (Cuba); Campus Estado de Mexico. Division de Arquitectura e Ingenieria, Instituto Tecnologico de Estudios Superiores de Monterrey, Atizapan de Zaragoza, Estado de Mexico (Mexico); Maugin, G.A. [Universite Pierre et Marie Curie. Case 162, UMR 7607 CNRS, Laboratoire de Modelisation en Mecanique, Paris Cedex 05 (France)
2004-12-01
In the present paper, we consider the behavior of nonlinear piezoelectric materials by generalization for this case of the Hashin-Shtrikman variational principles. The new general formulation used here differs from others, because, it gives the possibility to evaluate the upper and lower Hashin-Shtrikman bounds for specific physical nonlinearities of piezoelectric materials. Geometrical nonlinearities are not considered. (orig.)
Unsymmetrical squaraines for nonlinear optical materials
Marder, Seth R. (Inventor); Chen, Chin-Ti (Inventor); Cheng, Lap-Tak (Inventor)
1996-01-01
Compositions for use in non-linear optical devices. The compositions have first molecular electronic hyperpolarizability (.beta.) either positive or negative in sign and therefore display second order non-linear optical properties when incorporated into non-linear optical devices.
Nonlinear parametric instability of wind turbine wings
DEFF Research Database (Denmark)
Larsen, Jesper Winther; Nielsen, Søren R.K.
2006-01-01
Nonlinear rotor dynamic is characterized by parametric excitation of both linear and nonlinear terms caused by centrifugal and Coriolis forces when formulated in a moving frame of reference. Assuming harmonically varying support point motions from the tower, the nonlinear parametric instability...
On balanced truncation for symmetric nonlinear systems
Fujimoto, K.; Scherpen, Jacqueline M.A.
2014-01-01
This paper is concerned with model order reduction based on balanced realization for symmetric nonlinear systems. A new notion of symmetry for nonlinear systems was characterized recently. It plays an important role in linear systems theory and is expected to provide new insights to nonlinear system
Introducing Nonlinear Pricing into Consumer Choice Theory.
DeSalvo, Joseph S.; Huq, Mobinul
2002-01-01
Describes and contrasts nonlinear and linear pricing in consumer choice theory. Discusses the types of nonlinear pricing: block-declining tariff, two-part tariff, three-part tariff, and quality discounts or premia. States that understanding nonlinear pricing enhances student comprehension of consumer choice theory. Suggests teaching the concept in…
Nonlinear parametric instability of wind turbine wings
DEFF Research Database (Denmark)
Larsen, Jesper Winther; Nielsen, Søren R.K.
2006-01-01
Nonlinear rotor dynamic is characterized by parametric excitation of both linear and nonlinear terms caused by centrifugal and Coriolis forces when formulated in a moving frame of reference. Assuming harmonically varying support point motions from the tower, the nonlinear parametric instability o...
Solitons in quadratic nonlinear photonic crystals
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2001-01-01
We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities, which can be defocusing, and we numerically find previously unknown soliton families...
Common large innovations across nonlinear time series
Ph.H.B.F. Franses (Philip Hans); R. Paap (Richard)
2002-01-01
textabstractWe propose a multivariate nonlinear econometric time series model, which can be used to examine if there is common nonlinearity across economic variables. The model is a multivariate censored latent effects autoregression. The key feature of this model is that nonlinearity appears as sep
Nonlinear observer design for a nonlinear string/cable FEM model using contraction theory
DEFF Research Database (Denmark)
Turkyilmaz, Yilmaz; Jouffroy, Jerome; Egeland, Olav
Contraction theory is a recently developed nonlinear analysis tool which may be useful for solving a variety of nonlinear control problems. In this paper, using Contraction theory, a nonlinear observer is designed for a general nonlinear cable/string FEM (Finite Element Method) model. The cable...
Nonlinear observer design for a nonlinear string/cable FEM model using contraction theory
DEFF Research Database (Denmark)
Turkyilmaz, Yilmaz; Jouffroy, Jerome; Egeland, Olav
Contraction theory is a recently developed nonlinear analysis tool which may be useful for solving a variety of nonlinear control problems. In this paper, using Contraction theory, a nonlinear observer is designed for a general nonlinear cable/string FEM (Finite Element Method) model. The cable...
Processing Approach of Non-linear Adjustment Models in the Space of Non-linear Models
Institute of Scientific and Technical Information of China (English)
LI Chaokui; ZHU Qing; SONG Chengfang
2003-01-01
This paper investigates the mathematic features of non-linear models and discusses the processing way of non-linear factors which contributes to the non-linearity of a nonlinear model. On the basis of the error definition, this paper puts forward a new adjustment criterion, SGPE.Last, this paper investigates the solution of a non-linear regression model in the non-linear model space and makes the comparison between the estimated values in non-linear model space and those in linear model space.
Energy Technology Data Exchange (ETDEWEB)
Zhang, G.M. [China Center of Advanced Science and Technology (CCAST), Beijing, BJ (China)]|[Suzhou Univ. (China). Dept. of Physics
1996-04-01
In this note we consider the geometrical effects of a percolating system on the nonlinear transport properties in a superconductor-normal conductor nonlinear resistor network. For realistic composites, the nonlinearity may play an important role in the electrical transport phenomena. A typical example consists of studying a nonlinear composite medium in which an inclusion with nonlinear current-field (J-E) characteristics is randomly embedded in a host with either linear or nonlinear J-E response. For such a system, substantial progress in studies of the effective nonlinear response has been made in the past few years. 24 refs.
Nonlinear acoustic propagation in rectangular ducts
Nayfeh, A. H.; Tsai, M.-S.
1974-01-01
The method of multiple scales is used to obtain a second-order uniformly valid expansion for nonlinear acoustic wave propagation in a rectangular duct whose walls are treated with a nonlinear acoustic material. The wave propagation in the duct is characterized by the unsteady nonlinear Euler equations. The results show that nonlinear materials attenuate sound more than linear materials except at high acoustic frequencies. The nonlinear materials produce higher and combination tones which have higher attenuation rates than the fundamentals. Moreover, the attenuation rates of the fundamentals increase with increasing amplitude.
The Effective AC Response of Nonlinear Composites
Institute of Scientific and Technical Information of China (English)
WEI En-Bo; GU Guo-Qing
2001-01-01
A perturbative approach is used to study the AC response of nonlinear composite media, which obey a current-field relation of the form J = σ E + χ|E|2 E with components having nonlinear response at finite frequencies. For a sinusoidal applied field, we extend the local potential in terms of sinusoidal components at fundamental frequency and high-order harmonic frequencies to treat the nonlinear composites. For nonlinear composite media vith a low concentrations of spherical inclusions, we give the formulae of the nonlinear effective AC susceptibility χ*3ω at the third harmonic frequency.
Nonlinear fiber optics formerly quantum electronics
Agrawal, Govind
1995-01-01
The field of nonlinear fiber optics has grown substantially since the First Edition of Nonlinear Fiber Optics, published in 1989. Like the First Edition, this Second Edition is a comprehensive, tutorial, and up-to-date account of nonlinear optical phenomena in fiber optics. It synthesizes widely scattered research material and presents it in an accessible manner for students and researchers already engaged in or wishing to enter the field of nonlinear fiber optics. Particular attention is paid to the importance of nonlinear effects in the design of optical fiber communication systems. This is
Nonlinear phononics using atomically thin membranes
Midtvedt, Daniel; Isacsson, Andreas; Croy, Alexander
2014-09-01
Phononic crystals and acoustic metamaterials are used to tailor phonon and sound propagation properties by utilizing artificial, periodic structures. Analogous to photonic crystals, phononic band gaps can be created, which influence wave propagation and, more generally, allow engineering of the acoustic properties of a system. Beyond that, nonlinear phenomena in periodic structures have been extensively studied in photonic crystals and atomic Bose-Einstein condensates in optical lattices. However, creating nonlinear phononic crystals or nonlinear acoustic metamaterials remains challenging and only few examples have been demonstrated. Here, we show that atomically thin and periodically pinned membranes support coupled localized modes with nonlinear dynamics. The proposed system provides a platform for investigating nonlinear phononics.
Advances in nonlinear optical materials and devices
Byer, Robert L.
1991-01-01
The recent progress in the application of nonlinear techniques to extend the frequency of laser sources has come from the joint progress in laser sources and in nonlinear materials. A brief summary of the progress in diode pumped solid state lasers is followed by an overview of progress in nonlinear frequency extension by harmonic generation and parametric processes. Improved nonlinear materials including bulk crystals, quasiphasematched interactions, guided wave devices, and quantum well intersubband studies are discussed with the idea of identifying areas of future progress in nonlinear materials and devices.
The nonlinear piezoelectric tuned vibration absorber
Soltani, P.; Kerschen, G.
2015-07-01
This paper proposes a piezoelectric vibration absorber, termed the nonlinear piezoelectric tuned vibration absorber (NPTVA), for the mitigation of nonlinear resonances of mechanical systems. The new feature of the NPTVA is that its nonlinear restoring force is designed according to a principle of similarity, i.e., the NPTVA should be an electrical analog of the nonlinear host system. Analytical formulas for the NPTVA parameters are derived using the homotopy perturbation method. Doing so, a nonlinear generalization of Den Hartog’s equal-peak tuning rule is developed for piezoelectric vibration absorbers.
CHAOTIC BELT PHENOMENA IN NONLINEAR ELASTIC BEAM
Institute of Scientific and Technical Information of China (English)
张年梅; 杨桂通
2003-01-01
The chaotic motions of axial compressed nonlinear elastic beam subjected totransverse load were studied. The damping force in the system is nonlinear. Consideringmaterial and geometric nonlinearity, nonlinear governing equation of the system wasderived. By use of nonlinear Galerkin method, differential dynamic system was set up.Melnikov method was used to analyze the characters of the system. The results showed thatchaos may occur in the system when the load parameters P0 and f satisfy some conditions.The zone of chaotic motion was belted. The route from subharmonic bifurcation to chaoswas analyzed. The critical conditions that chaos occurs were determined.
Spin squeezing in nonlinear spin coherent states
Wang, Xiaoguang
2001-01-01
We introduce the nonlinear spin coherent state via its ladder operator formalism and propose a type of nonlinear spin coherent state by the nonlinear time evolution of spin coherent states. By a new version of spectroscopic squeezing criteria we study the spin squeezing in both the spin coherent state and nonlinear spin coherent state. The results show that the spin coherent state is not squeezed in the x, y, and z directions, and the nonlinear spin coherent state may be squeezed in the x and...
Generalized solutions of nonlinear partial differential equations
Rosinger, EE
1987-01-01
During the last few years, several fairly systematic nonlinear theories of generalized solutions of rather arbitrary nonlinear partial differential equations have emerged. The aim of this volume is to offer the reader a sufficiently detailed introduction to two of these recent nonlinear theories which have so far contributed most to the study of generalized solutions of nonlinear partial differential equations, bringing the reader to the level of ongoing research.The essence of the two nonlinear theories presented in this volume is the observation that much of the mathematics concernin
DEFF Research Database (Denmark)
Du, Yigang
without iteration steps. The ASA is implemented in combination with Field II and extended to simulate the pulsed ultrasound fields. The simulated results from a linear array transducer are made by the ASA based on Field II, and by a released non-linear simulation program- Abersim, respectively....... The calculation speed of the ASA is increased approximately by a factor of 140. For the second harmonic point spread function the error of the full width is 1.5% at -6 dB and 6.4% at -12 dB compared to Abersim. To further investigate the linear and non-linear ultrasound fields, hydrophone measurements.......3% relative to the measurement from a 1 inch diameter transducer. A preliminary study for harmonic imaging using synthetic aperture sequential beamforming (SASB) has been demonstrated. A wire phantom underwater measurement is made by an experimental synthetic aperture real-time ultrasound scanner (SARUS...
Energy Technology Data Exchange (ETDEWEB)
Max-Planck-Institut fur Quantenoptik; Goulielmakis, E.; Schultze, M.; Hofstetter, M.; Yakovlev, V. S.; Gagnon, J.; Uiberacker, M.; Aquila, A. L.; gullikson, E. M.; attwood, D. T.; Kienberger, R.; Krausz, F.; Kleineberg, U.
2008-11-05
Nonlinear optics plays a central role in the advancement of optical science and laser-based technologies. We report on the confinement of the nonlinear interaction of light with matter to a single wave cycle and demonstrate its utility for time-resolved and strong-field science. The electric field of 3.3-femtosecond, 0.72-micron laser pulses with a controlled and measured waveform ionizes atoms near the crests of the central wave cycle, with ionization being virtually switched off outside this interval. Isolated sub-100-attosecond pulses of extreme ultraviolet light (photon energy {approx} 80 electron volts), containing {approx} 0.5 nanojoule of energy, emerge from the interaction with a conversion efficiency of {approx} 10{sup -6}. These tools enable the study of the precision control of electron motion with light fields and electron-electron interactions with a resolution approaching the atomic unit of time ({approx} 24 attoseconds).
New approaches to nonlinear waves
2016-01-01
The book details a few of the novel methods developed in the last few years for studying various aspects of nonlinear wave systems. The introductory chapter provides a general overview, thematically linking the objects described in the book. Two chapters are devoted to wave systems possessing resonances with linear frequencies (Chapter 2) and with nonlinear frequencies (Chapter 3). In the next two chapters modulation instability in the KdV-type of equations is studied using rigorous mathematical methods (Chapter 4) and its possible connection to freak waves is investigated (Chapter 5). The book goes on to demonstrate how the choice of the Hamiltonian (Chapter 6) or the Lagrangian (Chapter 7) framework allows us to gain a deeper insight into the properties of a specific wave system. The final chapter discusses problems encountered when attempting to verify the theoretical predictions using numerical or laboratory experiments. All the chapters are illustrated by ample constructive examples demonstrating the app...
Nonlinear ion trap stability analysis
Energy Technology Data Exchange (ETDEWEB)
Mihalcea, Bogdan M; Visan, Gina G, E-mail: bmihal@infim.r [Institute for Laser, Plasma and Radiation Physics (INFLPR), Atomistilor Str. Nr. 409, 077125 Magurele-Bucharest, Jud. Ilfov (Romania)
2010-09-01
This paper investigates the dynamics of an ion confined in a nonlinear Paul trap. The equation of motion for the ion is shown to be consistent with the equation describing a damped, forced Duffing oscillator. All perturbing factors are taken into consideration in the approach. Moreover, the ion is considered to undergo interaction with an external electromagnetic field. The method is based on numerical integration of the equation of motion, as the system under investigation is highly nonlinear. Phase portraits and Poincare sections show that chaos is present in the associated dynamics. The system of interest exhibits fractal properties and strange attractors. The bifurcation diagrams emphasize qualitative changes of the dynamics and the onset of chaos.
Understanding nonlinear effects and losses
Energy Technology Data Exchange (ETDEWEB)
Irwin, J.
1995-10-01
With the planned construction of a large hadron collider (LHC) and a major upgrade of LEP (LEP-II) at CERN, a {Phi}-factory at Frascatti, and B-factories at SLAC (PEP-II) and KEK (KEK-B), we are now entering new energy and intensity regimes in both electron and proton circular colliders. Understanding and accurately estimating dynamic apertures and particle loss rates under both injection and colliding beam conditions is of primary importance. This paper summarizes discussions on Understanding Nonlinear Effects and Losses that took place in Working Group Three at the September 1994 Conference on Nonlinear Dynamics in Particle Accelerators at Arcidosso, Italy. Questions addressed were: {open_quotes}What do simulations indicate as the underlying causes of particle loss?{close_quotes} and {open_quotes}Do experiments agree with simulations-and if not, why not?{close_quotes} Special attention was given to a discrepancy between dynamic aperture measurements and theoretical predictions at HERA.
Nonlinear effects in asymmetric catalysis.
Satyanarayana, Tummanapalli; Abraham, Susan; Kagan, Henri B
2009-01-01
There is a need for the preparation of enantiomerically pure compounds for various applications. An efficient approach to achieve this goal is asymmetric catalysis. The chiral catalyst is usually prepared from a chiral auxiliary, which itself is derived from a natural product or by resolution of a racemic precursor. The use of non-enantiopure chiral auxiliaries in asymmetric catalysis seems unattractive to preparative chemists, since the anticipated enantiomeric excess (ee) of the reaction product should be proportional to the ee value of the chiral auxiliary (linearity). In fact, some deviation from linearity may arise. Such nonlinear effects can be rich in mechanistic information and can be synthetically useful (asymmetric amplification). This Review documents the advances made during the last decade in the use of nonlinear effects in the area of organometallic and organic catalysis.
Some nonlinear space decomposition algorithms
Energy Technology Data Exchange (ETDEWEB)
Tai, Xue-Cheng; Espedal, M. [Univ. of Bergen (Norway)
1996-12-31
Convergence of a space decomposition method is proved for a general convex programming problem. The space decomposition refers to methods that decompose a space into sums of subspaces, which could be a domain decomposition or a multigrid method for partial differential equations. Two algorithms are proposed. Both can be used for linear as well as nonlinear elliptic problems and they reduce to the standard additive and multiplicative Schwarz methods for linear elliptic problems. Two {open_quotes}hybrid{close_quotes} algorithms are also presented. They converge faster than the additive one and have better parallelism than the multiplicative method. Numerical tests with a two level domain decomposition for linear, nonlinear and interface elliptic problems are presented for the proposed algorithms.
Directory of Open Access Journals (Sweden)
Leonardo José Gonçalves Aguiar
2011-06-01
Full Text Available A radiação de onda longa proveniente da atmosfera (Lin é a componente do balanço de radiação mais difícil de ser medida. Na Amazônia praticamente não existem medidas regulares dessa componente, mesmo sendo uma importante variável no cálculo do balanço de radiação à superfície e muito usada para alimentar modelos climáticos. Tendo em vista a necessidade desses dados, o objetivo do presente trabalho é avaliar o desempenho de sete equações na estimativa da Lin para dias de céu claro em áreas de floresta (Reserva Biológica do Jaru, 10º4'48''S; 61º55'48''W e de pastagem (Fazenda Nossa Senhora, 10º45'S; 62º21'W no sudoeste da Amazônia. Medidas de radiação de onda longa atmosférica realizadas no período de junho de 2005 a maio de 2006 foram comparadas com as estimativas. As equações testadas tiveram desempenho satisfatório apenas durante a estação seca. As condições de alta nebulosidade, dominantes na estação chuvosa, restringiram a quantidade de dados utilizados na avaliação das equações. As equações que utilizam informações de temperatura do ar e pressão de vapor d'água para a estimativa da Lin tiveram melhor desempenho em relação às que utilizam apenas a temperatura do ar. As equações de Brutsaert (1975, Idso (1981 e Prata (1996 foram as que apresentaram melhor desempenho, apresentando os maiores índices de concordância, e sendo, portanto, as equações mais indicadas para a estimativa da radiação de onda longa atmosférica no sudoeste da Amazônia.Atmospheric long wave radiation (Lin is the most difficult component of the radiation budget to be measured. In Amazonia there are very few regular measurements of this component, even though it is an important variable in the calculation of the surface radiation balance and frequently used in climate models. Given the need for such data, the objective of this study is to evaluate the performance of seven equations used for the estimation of Lin
Nonlinear Control of Magnetic Bearings
Institute of Scientific and Technical Information of China (English)
Khac Duc Do; Dang Hoe Nguyen; Thanh Binh Nguyen
2010-01-01
In this paper, recent results controling nonlinear systems with output tracking error constraints are applied to the design of new tracking controllers for magnetic bearings. The proposed controllers can force the rotor to track a bounded and sufficiently smooth refer-ence trajectory asymptotically and guarantee non-contactedness be-tween the rotor and the stator of the magnetic bearings. Simulation results are included to illustrate the effectiveness of the proposed con-trollers.
LINEAR AND NONLINEAR SEMIDEFINITE PROGRAMMING
Directory of Open Access Journals (Sweden)
Walter Gómez Bofill
2014-12-01
Full Text Available This paper provides a short introduction to optimization problems with semidefinite constraints. Basic duality and optimality conditions are presented. For linear semidefinite programming some advances by dealing with degeneracy and the semidefinite facial reduction are discussed. Two relatively recent areas of application are presented. Finally a short overview of relevant literature on algorithmic approaches for efficiently solving linear and nonlinear semidefinite programming is provided.
CMOS Nonlinear Signal Processing Circuits
2010-01-01
The chapter describes various nonlinear signal processing CMOS circuits, including a high reliable WTA/LTA, simple MED cell, and low-voltage arbitrary order extractor. We focus the discussion on CMOS analog circuit design with reliable, programmable capability, and low voltage operation. It is a practical problem when the multiple identical cells are required to match and realized within a single chip using a conventional process. Thus, the design of high-reliable circuit is indeed needed. Th...
Lagrangian description of nonlinear chromatography
Institute of Scientific and Technical Information of China (English)
LIANG Heng; LIU Xiaolong
2004-01-01
Under the framework of non-equilibrium thermodynamic separation theory (NTST), Local Lagrangian approach (LLA) was proposed to deal with the essential issues of the convection and diffusion (shock waves) phenomena in nonlinear chromatography with recursion equations based on the three basic theorems, Lagrangian description, continuity axiom and local equilibrium assumption (LEA). This approach remarkably distinguished from the system of contemporary chromatographic theories (Eulerian description-partial differential equations), and can felicitously match modern cybernetics.
Dynamical Imaging using Spatial Nonlinearity
2014-01-29
Imin )/ (Imax + Imin ) = 0.15 for detection of the bars (from maxima to central dip). For our experimental measurements, the best linear visibility is...Statistical theory for incoherent light propagation in nonlinear media, Physical Review E, 65 (2002) 035602. [52] M.J. Bastiaans, Application of the...1238. [53] M.E. Testorf, B.M. Hennelly, J. Ojeda-Castañeda, Phase-space optics : fundamentals and applications , McGraw-Hill, New York, 2010. [54] K.H
Nonlinear input-output systems
Hunt, L. R.; Luksic, Mladen; Su, Renjeng
1987-01-01
Necessary and sufficient conditions that the nonlinear system dot-x = f(x) + ug(x) and y = h(x) be locally feedback equivalent to the controllable linear system dot-xi = A xi + bv and y = C xi having linear output are found. Only the single input and single output case is considered, however, the results generalize to multi-input and multi-output systems.
Robust nonlinear regression in applications
Lim, Changwon; Sen, Pranab K.; Peddada, Shyamal D.
2013-01-01
Robust statistical methods, such as M-estimators, are needed for nonlinear regression models because of the presence of outliers/influential observations and heteroscedasticity. Outliers and influential observations are commonly observed in many applications, especially in toxicology and agricultural experiments. For example, dose response studies, which are routinely conducted in toxicology and agriculture, sometimes result in potential outliers, especially in the high dose gr...
Nonlinear Acoustic Characterization of Targets
2008-01-01
matching so as to transmit as much energy as possible into the test object. In addition to this limitation, ultrasound is only able to measure range by...metric arrays for standoff analysis of targets. In 1982, Yoneyama[4] discussed the nonlinear interaction of ultrasound with air as the “scattering of... cavitation effect. This produces a rectification at higher frequencies just as a diode does in an electrical circuit. This natural rectification allows
Transformation design and nonlinear Hamiltonians
Brougham, Thomas; Jex, Igor
2009-01-01
We study a class of nonlinear Hamiltonians, with applications in quantum optics. The interaction terms of these Hamiltonians are generated by taking a linear combination of powers of a simple `beam splitter' Hamiltonian. The entanglement properties of the eigenstates are studied. Finally, we show how to use this class of Hamiltonians to perform special tasks such as conditional state swapping, which can be used to generate optical cat states and to sort photons.