Similarity solutions of some two-space-dimensional nonlinear wave evolution equations

NASA Technical Reports Server (NTRS)

Redekopp, L. G.

1980-01-01

Similarity reductions of the two-space-dimensional versions of the Korteweg-de Vries, modified Korteweg-de Vries, Benjamin-Davis-Ono, and nonlinear Schroedinger equations are presented, and some solutions of the reduced equations are discussed. Exact dispersive solutions of the two-dimensional Korteweg-de Vries equation are obtained, and the similarity solution of this equation is shown to be reducible to the second Painleve transcendent.

The soliton transform and a possible application to nonlinear Alfven waves in space

NASA Technical Reports Server (NTRS)

Hada, T.; Hamilton, R. L.; Kennel, C. F.

1993-01-01

The inverse scattering transform (IST) based on the derivative nonlinear Schroedinger (DNLS) equation is applied to a complex time series of nonlinear Alfven wave data generated by numerical simulation. The IST describes the long-time evolution of quasi-parallel Alfven waves more efficiently than the Fourier transform, which is adapted to linear rather than nonlinear problems. When dissipation is added, so the conditions for the validity of the DNLS are not strictly satisfied, the IST continues to provide a compact description of the wavefield in terms of a small number of decaying envelope solitons.

Derivation of an applied nonlinear Schroedinger equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pitts, Todd Alan; Laine, Mark Richard; Schwarz, Jens

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

Dark and grey compressional dispersive Alfven solitons in plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shukla, P. K.; Eliasson, B.; Stenflo, L.

2011-06-15

The amplitude modulation of compressional dispersive Alfven (CDA) waves in a low-{beta} plasma is considered. It is shown that the dynamics of modulated CDA waves is governed by a cubic nonlinear Schroedinger equation, which depicts the formation of a dark/grey envelope CDA soliton.

Multigrid techniques for nonlinear eigenvalue probems: Solutions of a nonlinear Schroedinger eigenvalue problem in 2D and 3D

NASA Technical Reports Server (NTRS)

Costiner, Sorin; Taasan, Shlomo

1994-01-01

This paper presents multigrid (MG) techniques for nonlinear eigenvalue problems (EP) and emphasizes an MG algorithm for a nonlinear Schrodinger EP. The algorithm overcomes the mentioned difficulties combining the following techniques: an MG projection coupled with backrotations for separation of solutions and treatment of difficulties related to clusters of close and equal eigenvalues; MG subspace continuation techniques for treatment of the nonlinearity; an MG simultaneous treatment of the eigenvectors at the same time with the nonlinearity and with the global constraints. The simultaneous MG techniques reduce the large number of self consistent iterations to only a few or one MG simultaneous iteration and keep the solutions in a right neighborhood where the algorithm converges fast.

Observation of Quasi-Two-Dimensional Nonlinear Interactions in a Drift-Wave Streamer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yamada, T.; Nagashima, Y.; Itoh, S.-I.

2010-11-26

A streamer, which is a bunching of drift-wave fluctuations, and its mediator, which generates the streamer by coupling with other fluctuations, have been observed in a cylindrical magnetized plasma. Their radial structures were investigated in detail by using the biphase analysis. Their quasi-two-dimensional structures were revealed to be equivalent with a pair of fast and slow modes predicted by a nonlinear Schroedinger equation based on the Hasegawa-Mima model.

Extremely Fast Numerical Integration of Ocean Surface Wave Dynamics: Building Blocks for a Higher Order Method

DTIC Science & Technology

2006-09-30

equation known as the Kadomtsev - Petviashvili (KP) equation ): (ηt + coηx +αηηx + βη )x +γηyy = 0 (4) where γ = co / 2 . The KdV equation ...using the spectral formulation of the Kadomtsev - Petviashvili equation , a standard equation for nonlinear, shallow water wave dynamics that is a... Petviashvili and nonlinear Schroedinger equations and higher order corrections have been developed as prerequisites to coding the Boussinesq and Euler

Quantum spatial propagation of squeezed light in a degenerate parametric amplifier

NASA Technical Reports Server (NTRS)

Deutsch, Ivan H.; Garrison, John C.

1992-01-01

Differential equations which describe the steady state spatial evolution of nonclassical light are established using standard quantum field theoretic techniques. A Schroedinger equation for the state vector of the optical field is derived using the quantum analog of the slowly varying envelope approximation (SVEA). The steady state solutions are those that satisfy the time independent Schroedinger equation. The resulting eigenvalue problem then leads to the spatial propagation equations. For the degenerate parametric amplifier this method shows that the squeezing parameter obey nonlinear differential equations coupled by the amplifier gain and phase mismatch. The solution to these differential equations is equivalent to one obtained from the classical three wave mixing steady state solution to the parametric amplifier with a nondepleted pump.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dubrovsky, V. G.; Topovsky, A. V.

New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u{sup (n)}, n= 1, Horizontal-Ellipsis , N are constructed via Zakharov and Manakov {partial_derivative}-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u{sup (n)} and calculated by {partial_derivative}-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schroedinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums ofmore » special solutions u{sup (n)}. It is shown that the sums u=u{sup (k{sub 1})}+...+u{sup (k{sub m})}, 1 Less-Than-Or-Slanted-Equal-To k{sub 1} < k{sub 2} < Horizontal-Ellipsis < k{sub m} Less-Than-Or-Slanted-Equal-To N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schroedinger equation and can serve as model potentials for electrons in planar structures of modern electronics.« less

Reduction of the equation for lower hybrid waves in a plasma to a nonlinear Schroedinger equation

NASA Technical Reports Server (NTRS)

Karney, C. F. F.

1977-01-01

Equations describing the nonlinear propagation of waves in an anisotropic plasma are rarely exactly soluble. However it is often possible to make approximations that reduce the exact equations into a simpler equation. The use of MACSYMA to make such approximations, and so reduce the equation describing lower hybrid waves into the nonlinear Schrodinger equation which is soluble by the inverse scattering method is demonstrated. MACSYMA is used at several stages in the calculation only because there is a natural division between calculations that are easiest done by hand, and those that are easiest done by machine.

Modulational-instability-induced supercontinuum generation with saturable nonlinear response

DOE Office of Scientific and Technical Information (OSTI.GOV)

Raja, R. Vasantha Jayakantha; Porsezian, K.; Nithyanandan, K.

2010-07-15

We theoretically investigate the supercontinuum generation (SCG) on the basis of modulational instability (MI) in liquid-core photonic crystal fibers (LCPCF) with CS{sub 2}-filled central core. The effect of saturable nonlinearity of LCPCF on SCG in the femtosecond regime is studied using an appropriately modified nonlinear Schroedinger equation. We also compare the MI induced spectral broadening with SCG obtained by soliton fission. To analyze the quality of the pulse broadening, we study the coherence of the SC pulse numerically. It is evident from the numerical simulation that the response of the saturable nonlinearity suppresses the broadening of the pulse. We alsomore » observe that the MI induced SCG in the presence of saturable nonlinearity degrades the coherence of the SCG pulse when compared to unsaturated medium.« less

Topics in strong Langmuir turbulence

NASA Technical Reports Server (NTRS)

Nicholson, D. R.

1983-01-01

Progress in two approaches to the study of strong Langmuir turbulence is reported. In two spatial dimensions, numerical solution of the Zakharov equations yields a steady state involving linear growth, linear damping, and a collection of coherent, long-lived entities which might loosely be called solitons. In one spatial dimension, a statistical theory is applied to the cubically nonlinear Schroedinger equation and is solved analytically in a special case.

Topics in strong Langmuir turbulence

NASA Technical Reports Server (NTRS)

Nicholson, D. R.

1982-01-01

Progress in two approaches to the study of strong Langmuir turbulence is reported. In two spatial dimensions, numerical solution of the Zakharov equations yields a steady state involving linear growth, linear damping, and a collection of coherent, long-lived entities which might loosely be called solitons. In one spatial dimension, a statistical theory is applied to the cubically nonlinear Schroedinger equation and is solved analytically in a special case.

A new fourth-order Fourier-Bessel split-step method for the extended nonlinear Schroedinger equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nash, Patrick L.

2008-01-10

Fourier split-step techniques are often used to compute soliton-like numerical solutions of the nonlinear Schroedinger equation. Here, a new fourth-order implementation of the Fourier split-step algorithm is described for problems possessing azimuthal symmetry in 3 + 1-dimensions. This implementation is based, in part, on a finite difference approximation {delta}{sub perpendicular} {sup FDA} of 1/r ({partial_derivative})/({partial_derivative}r) r({partial_derivative})/({partial_derivative}r) that possesses an associated exact unitary representation of e{sup i/2{lambda}}{sup {delta}{sub perpendicular}{sup FDA}}. The matrix elements of this unitary matrix are given by special functions known as the associated Bessel functions. Hence the attribute Fourier-Bessel for the method. The Fourier-Bessel algorithm is shown tomore » be unitary and unconditionally stable. The Fourier-Bessel algorithm is employed to simulate the propagation of a periodic series of short laser pulses through a nonlinear medium. This numerical simulation calculates waveform intensity profiles in a sequence of planes that are transverse to the general propagation direction, and labeled by the cylindrical coordinate z. These profiles exhibit a series of isolated pulses that are offset from the time origin by characteristic times, and provide evidence for a physical effect that may be loosely termed normal mode condensation. Normal mode condensation is consistent with experimentally observed pulse filamentation into a packet of short bursts, which may occur as a result of short, intense irradiation of a medium.« less

A numerical and experimental study on the nonlinear evolution of long-crested irregular waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goullet, Arnaud; Choi, Wooyoung; Division of Ocean Systems Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701

2011-01-15

The spatial evolution of nonlinear long-crested irregular waves characterized by the JONSWAP spectrum is studied numerically using a nonlinear wave model based on a pseudospectral (PS) method and the modified nonlinear Schroedinger (MNLS) equation. In addition, new laboratory experiments with two different spectral bandwidths are carried out and a number of wave probe measurements are made to validate these two wave models. Strongly nonlinear wave groups are observed experimentally and their propagation and interaction are studied in detail. For the comparison with experimental measurements, the two models need to be initialized with care and the initialization procedures are described. Themore » MNLS equation is found to approximate reasonably well for the wave fields with a relatively smaller Benjamin-Feir index, but the phase error increases as the propagation distance increases. The PS model with different orders of nonlinear approximation is solved numerically, and it is shown that the fifth-order model agrees well with our measurements prior to wave breaking for both spectral bandwidths.« less

Prolongation structures of nonlinear evolution equations. II

NASA Technical Reports Server (NTRS)

Estabrook, F. B.; Wahlquist, H. D.

1976-01-01

The prolongation structure of a closed ideal of exterior differential forms is further discussed, and its use illustrated by application to an ideal (in six dimensions) representing the cubically nonlinear Schroedinger equation. The prolongation structure in this case is explicitly given, and recurrence relations derived which support the conjecture that the structure is open - i.e., does not terminate as a set of structure relations of a finite-dimensional Lie group. We introduce the use of multiple pseudopotentials to generate multiple Baecklund transformation, and derive the double Baecklund transformation. This symmetric transformation concisely expresses the (usually conjectured) theorem of permutability, which must consequently apply to all solutions irrespective of asymptotic constraints.

Comment on 'Nonlinear band structure in Bose-Einstein condensates: Nonlinear Schroedinger equation with a Kronig-Penney potential'

DOE Office of Scientific and Technical Information (OSTI.GOV)

Danshita, Ippei; Department of Physics, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555; Tsuchiya, Shunji

2007-07-15

In their recent paper [Phys. Rev. A 71, 033622 (2005)], Seaman et al. studied Bloch states of the condensate wave function in a Kronig-Penney potential and calculated the band structure. They argued that the effective mass is always positive when a swallowtail energy loop is present in the band structure. In this Comment, we reexamine their argument by actually calculating the effective mass. It is found that there exists a region where the effective mass is negative even when a swallowtail is present. Based on this fact, we discuss the interpretation of swallowtails in terms of superfluidity.

Initial study of Schroedinger eigenmaps for spectral target detection

NASA Astrophysics Data System (ADS)

Dorado-Munoz, Leidy P.; Messinger, David W.

2016-08-01

Spectral target detection refers to the process of searching for a specific material with a known spectrum over a large area containing materials with different spectral signatures. Traditional target detection methods in hyperspectral imagery (HSI) require assuming the data fit some statistical or geometric models and based on the model, to estimate parameters for defining a hypothesis test, where one class (i.e., target class) is chosen over the other classes (i.e., background class). Nonlinear manifold learning methods such as Laplacian eigenmaps (LE) have extensively shown their potential use in HSI processing, specifically in classification or segmentation. Recently, Schroedinger eigenmaps (SE), which is built upon LE, has been introduced as a semisupervised classification method. In SE, the former Laplacian operator is replaced by the Schroedinger operator. The Schroedinger operator includes by definition, a potential term V that steers the transformation in certain directions improving the separability between classes. In this regard, we propose a methodology for target detection that is not based on the traditional schemes and that does not need the estimation of statistical or geometric parameters. This method is based on SE, where the potential term V is taken into consideration to include the prior knowledge about the target class and use it to steer the transformation in directions where the target location in the new space is known and the separability between target and background is augmented. An initial study of how SE can be used in a target detection scheme for HSI is shown here. In-scene pixel and spectral signature detection approaches are presented. The HSI data used comprise various target panels for testing simultaneous detection of multiple objects with different complexities.

Distribution-valued initial data for the complex Ginzburg-Landau equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Levermore, C.D.; Oliver, M.

1997-11-01

The generalized complex Ginzburg-Landau (CGL) equation with a nonlinearity of order 2{sigma} + 1 in d spatial dimensions has a unique local classical solution for distributional initial data in the Sobolev space H{sup q} provided that q > d/2 - 1/{sigma}. This result directly corresponds to a theorem for the nonlinear Schroedinger (NLS) equation which has been proved by Cazenave and Weissler in 1990. While the proof in the NLS case relies on Besov space techniques, it is shown here that for the CGL equation, the smoothing properties of the linear semigroup can be eased to obtain an almost optimalmore » result by elementary means. 1 fig.« less

Extremely Fast Numerical Integration of Ocean Surface Wave Dynamics

DTIC Science & Technology

2007-09-30

sub-processor must be added as shown in the blue box of Fig. 1. We first consider the Kadomtsev - Petviashvili (KP) equation ηt + coηx +αηηx + βη ...analytic integration of the so-called “soliton equations ,” I have discovered how the GFT can be used to solved higher order equations for which study...analytical study and extremely fast numerical integration of the extended nonlinear Schroedinger equation for fully three dimensional wave motion

Vortex Nucleation in a Dissipative Variant of the Nonlinear Schroedinger Equation Under Rotation

DTIC Science & Technology

2014-12-01

dark solitons ) and vortices. Early soliton experiments of about 15 years ago observed the motion of a dark soliton towards the edge of the trap [27...of dark soliton oscillations in a unitary Fermi gas [30]. A number of the- oretical studies have provided relevant explanation for this phenomenology...in atomic BECs [31, 32, 33, 34, 35, 36, 37, 38, 39]. In particular, it has been identified in these works that the dark soliton follows an anti

Shock Waves in a Bose-Einstein Condensate

NASA Technical Reports Server (NTRS)

Kulikov, Igor; Zak, Michail

2005-01-01

A paper presents a theoretical study of shock waves in a trapped Bose-Einstein condensate (BEC). The mathematical model of the BEC in this study is a nonlinear Schroedinger equation (NLSE) in which (1) the role of the wave function of a single particle in the traditional Schroedinger equation is played by a space- and time-dependent complex order parameter (x,t) proportional to the square root of the density of atoms and (2) the atoms engage in a repulsive interaction characterized by a potential proportional to | (x,t)|2. Equations that describe macroscopic perturbations of the BEC at zero temperature are derived from the NLSE and simplifying assumptions are made, leading to equations for the propagation of sound waves and the transformation of sound waves into shock waves. Equations for the speeds of shock waves and the relationships between jumps of velocity and density across shock fronts are derived. Similarities and differences between this theory and the classical theory of sound waves and shocks in ordinary gases are noted. The present theory is illustrated by solving the equations for the example of a shock wave propagating in a cigar-shaped BEC.

Relativistic extension of the Kay-Moses method for constructing transparent potentials in quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Toyama, F.M.; Nogami, Y.; Zhao, Z.

1993-02-01

For the Dirac equation in one space dimension with a potential of the Lorentz scalar type, we present a complete solution for the problem of constructing a transparent potential. This is a relativistic extension of the Kay-Moses method which was developed for the nonrelativistic Schroedinger equation. There is an infinite family of transparent potentials. The potentials are all related to solutions of a class of coupled, nonlinear Dirac equations. In addition, it is argued that an admixture of a Lorentz vector component in the potential impairs perfect transparency.

Construction of stable explicit finite-difference schemes for Schroedinger type differential equations

NASA Technical Reports Server (NTRS)

Mickens, Ronald E.

1989-01-01

A family of conditionally stable, forward Euler finite difference equations can be constructed for the simplest equation of Schroedinger type, namely u sub t - iu sub xx. Generalization of this result to physically realistic Schroedinger type equations is presented.

Thomas-Fermi approximation for a condensate with higher-order interactions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thoegersen, M.; Jensen, A. S.; Zinner, N. T.

We consider the ground state of a harmonically trapped Bose-Einstein condensate within the Gross-Pitaevskii theory including the effective-range corrections for a two-body zero-range potential. The resulting nonlinear Schroedinger equation is solved analytically in the Thomas-Fermi approximation neglecting the kinetic-energy term. We present results for the chemical potential and the condensate profiles, discuss boundary conditions, and compare to the usual Thomas-Fermi approach. We discuss several ways to increase the influence of effective-range corrections in experiment with magnetically tunable interactions. The level of tuning required could be inside experimental reach in the near future.

Dark soliton interaction of spinor Bose-Einstein condensates in an optical lattice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li Zaidong; Li Qiuyan

2007-08-15

We study the magnetic soliton dynamics of spinor Bose-Einstein condensates in an optical lattice which results in an effective Hamiltonian of anisotropic pseudospin chain. An equation of nonlinear Schroedinger type is derived and exact magnetic soliton solutions are obtained analytically by means of Hirota method. Our results show that the critical external field is needed for creating the magnetic soliton in spinor Bose-Einstein condensates. The soliton size, velocity and shape frequency can be controlled in practical experiment by adjusting the magnetic field. Moreover, the elastic collision of two solitons is investigated in detail.

Integrability and structural stability of solutions to the Ginzburg-Landau equation

NASA Technical Reports Server (NTRS)

Keefe, Laurence R.

1986-01-01

The integrability of the Ginzburg-Landau equation is studied to investigate if the existence of chaotic solutions found numerically could have been predicted a priori. The equation is shown not to possess the Painleveproperty, except for a special case of the coefficients that corresponds to the integrable, nonlinear Schroedinger (NLS) equation. Regarding the Ginzburg-Landau equation as a dissipative perturbation of the NLS, numerical experiments show all but one of a family of two-tori solutions, possessed by the NLS under particular conditions, to disappear under real perturbations to the NLS coefficients of O(10 to the -6th).

Spectral Target Detection using Schroedinger Eigenmaps

NASA Astrophysics Data System (ADS)

Dorado-Munoz, Leidy P.

Applications of optical remote sensing processes include environmental monitoring, military monitoring, meteorology, mapping, surveillance, etc. Many of these tasks include the detection of specific objects or materials, usually few or small, which are surrounded by other materials that clutter the scene and hide the relevant information. This target detection process has been boosted lately by the use of hyperspectral imagery (HSI) since its high spectral dimension provides more detailed spectral information that is desirable in data exploitation. Typical spectral target detectors rely on statistical or geometric models to characterize the spectral variability of the data. However, in many cases these parametric models do not fit well HSI data that impacts the detection performance. On the other hand, non-linear transformation methods, mainly based on manifold learning algorithms, have shown a potential use in HSI transformation, dimensionality reduction and classification. In target detection, non-linear transformation algorithms are used as preprocessing techniques that transform the data to a more suitable lower dimensional space, where the statistical or geometric detectors are applied. One of these non-linear manifold methods is the Schroedinger Eigenmaps (SE) algorithm that has been introduced as a technique for semi-supervised classification. The core tool of the SE algorithm is the Schroedinger operator that includes a potential term that encodes prior information about the materials present in a scene, and enables the embedding to be steered in some convenient directions in order to cluster similar pixels together. A completely novel target detection methodology based on SE algorithm is proposed for the first time in this thesis. The proposed methodology does not just include the transformation of the data to a lower dimensional space but also includes the definition of a detector that capitalizes on the theory behind SE. The fact that target pixels and those similar pixels are clustered in a predictable region of the low-dimensional representation is used to define a decision rule that allows one to identify target pixels over the rest of pixels in a given image. In addition, a knowledge propagation scheme is used to combine spectral and spatial information as a means to propagate the "potential constraints" to nearby points. The propagation scheme is introduced to reinforce weak connections and improve the separability between most of the target pixels and the background. Experiments using different HSI data sets are carried out in order to test the proposed methodology. The assessment is performed from a quantitative and qualitative point of view, and by comparing the SE-based methodology against two other detection methodologies that use linear/non-linear algorithms as transformations and the well-known Adaptive Coherence/Cosine Estimator (ACE) detector. Overall results show that the SE-based detector outperforms the other two detection methodologies, which indicates the usefulness of the SE transformation in spectral target detection problems.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu Wenjun; Tian Bo, E-mail: tian.bupt@yahoo.com.c; State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100191

2010-08-15

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

Adiabatic Berry phase in an atom-molecule conversion system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fu Libin; Center for Applied Physics and Technology, Peking University, Beijing 100084; Liu Jie, E-mail: liu_jie@iapcm.ac.c

2010-11-15

We investigate the Berry phase of adiabatic quantum evolution in the atom-molecule conversion system that is governed by a nonlinear Schroedinger equation. We find that the Berry phase consists of two parts: the usual Berry connection term and a novel term from the nonlinearity brought forth by the atom-molecule coupling. The total geometric phase can be still viewed as the flux of the magnetic field of a monopole through the surface enclosed by a closed path in parameter space. The charge of the monopole, however, is found to be one third of the elementary charge of the usual quantized monopole.more » We also derive the classical Hannay angle of a geometric nature associated with the adiabatic evolution. It exactly equals minus Berry phase, indicating a novel connection between Berry phase and Hannay angle in contrast to the usual derivative form.« less

Number-phase minimum-uncertainty state with reduced number uncertainty in a Kerr nonlinear interferometer

NASA Astrophysics Data System (ADS)

Kitagawa, M.; Yamamoto, Y.

1987-11-01

An alternative scheme for generating amplitude-squeezed states of photons based on unitary evolution which can properly be described by quantum mechanics is presented. This scheme is a nonlinear Mach-Zehnder interferometer containing an optical Kerr medium. The quasi-probability density (QPD) and photon-number distribution of the output field are calculated, and it is demonstrated that the reduced photon-number uncertainty and enhanced phase uncertainty maintain the minimum-uncertainty product. A self-phase-modulation of the single-mode quantized field in the Kerr medium is described based on localized operators. The spatial evolution of the state is demonstrated by QPD in the Schroedinger picture. It is shown that photon-number variance can be reduced to a level far below the limit for an ordinary squeezed state, and that the state prepared using this scheme remains a number-phase minimum-uncertainty state until the maximum reduction of number fluctuations is surpassed.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kanna, T.; Vijayajayanthi, M.; Lakshmanan, M.

The bright soliton solutions of the mixed coupled nonlinear Schroedinger equations with two components (2-CNLS) with linear self- and cross-coupling terms have been obtained by identifying a transformation that transforms the corresponding equation to the integrable mixed 2-CNLS equations. The study on the collision dynamics of bright solitons shows that there exists periodic energy switching, due to the coupling terms. This periodic energy switching can be controlled by the new type of shape changing collisions of bright solitons arising in a mixed 2-CNLS system, characterized by intensity redistribution, amplitude dependent phase shift, and relative separation distance. We also point outmore » that this system exhibits large periodic intensity switching even with very small linear self-coupling strengths.« less

Nonphasematched broadband THz amplification and reshaping in a dispersive chi(3) medium.

PubMed

Koys, Martin; Noskovicova, Eva; Velic, Dusan; Lorenc, Dusan

2017-06-12

We theoretically investigate non-phasematched broadband THz amplification in dispersive chi(3) media. A short 100 fs pump pulse is interacting with a temporally matched second harmonic pulse and a weak THz signal through the four wave mixing process and a significant broadband THz amplification and reshaping is observed. The pulse evolution dynamics is explored by numerically solving a set of generalized Nonlinear Schroedinger equations. The influence of incident pulse chirp, pulse duration and the role of wavelength, THz seed frequency and losses are evaluated separately. It is found that a careful choice of incident parameters can provide a broadband THz output and/or a significant increase of THz peak power.

Schroedinger's Wave Structure of Matter (WSM)

NASA Astrophysics Data System (ADS)

Wolff, Milo; Haselhurst, Geoff

2009-10-01

The puzzling electron is due to the belief that it is a discrete particle. Einstein deduced this structure was impossible since Nature does not allow the discrete particle. Clifford (1876) rejected discrete matter and suggested structures in `space'. Schroedinger, (1937) also eliminated discrete particles writing: What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. Particles are just schaumkommen (appearances). He rejected wave-particle duality. Schroedinger's concept was developed by Milo Wolff and Geoff Haselhurst (SpaceAndMotion.com) using the Scalar Wave Equation to find spherical wave solutions in a 3D quantum space. This WSM, the origin of all the Natural Laws, contains all the electron's properties including the Schroedinger Equation. The origin of Newton's Law F=ma is no longer a puzzle; It originates from Mach's principle of inertia (1883) that depends on the space medium and the WSM. Carver Mead (1999) at CalTech used the WSM to design Intel micro-chips correcting errors of Maxwell's magnetic Equations. Applications of the WSM also describe matter at molecular dimensions: alloys, catalysts, biology and medicine, molecular computers and memories. See ``Schroedinger's Universe'' - at Amazon.com

The Universe according to Schroedinger and Milo

NASA Astrophysics Data System (ADS)

Wolff, Milo

2009-10-01

The puzzling electron is due to the belief that it is a discrete particle. Schroedinger, (1937) eliminated discrete particles writing: What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. Particles are just schaumkommen (appearances). Thus he rejected wave-particle duality. Schroedinger's concept was developed by Milo Wolff using a Scalar Wave Equation in 3D quantum space to find wave solutions. The resulting Wave Structure of Matter (WSM) contains all the electron's properties including the Schroedinger Equation. Further, Newton's Law F=ma is no longer a puzzle; It originates from Mach's principle of inertia (1883) that depends on the space medium and the WSM. These the origin of all the Natural Laws. Carver Mead (1999) at CalTech used the WSM to design Intel micro-chips and to correct errors of Maxwell's Equations. Applications of the WSM describe matter at molecular dimensions: Industrial alloys, catalysts, biology and medicine, molecular computers and memories. See book ``Schroedinger's Universe'' - at Amazon.com. Pioneers of the WSM are growing rapidly. Some are: SpaceAndMotion.com, QuantumMatter.com, treeincarnation.com/audio/milowolff.htm, daugerresearch.com/orbitals/index.shtml, glafreniere.com/matter.html =A new Universe.

Newtonian semiclassical gravity in three ontological quantum theories that solve the measurement problem: Formalisms and empirical predictions

NASA Astrophysics Data System (ADS)

Derakhshani, Maaneli

In this thesis, we consider the implications of solving the quantum measurement problem for the Newtonian description of semiclassical gravity. First we review the formalism of the Newtonian description of semiclassical gravity based on standard quantum mechanics---the Schroedinger-Newton theory---and two well-established predictions that come out of it, namely, gravitational 'cat states' and gravitationally-induced wavepacket collapse. Then we review three quantum theories with 'primitive ontologies' that are well-known known to solve the measurement problem---Schroedinger's many worlds theory, the GRW collapse theory with matter density ontology, and Nelson's stochastic mechanics. We extend the formalisms of these three quantum theories to Newtonian models of semiclassical gravity and evaluate their implications for gravitational cat states and gravitational wavepacket collapse. We find that (1) Newtonian semiclassical gravity based on Schroedinger's many worlds theory is mathematically equivalent to the Schroedinger-Newton theory and makes the same predictions; (2) Newtonian semiclassical gravity based on the GRW theory differs from Schroedinger-Newton only in the use of a stochastic collapse law, but this law allows it to suppress gravitational cat states so as not to be in contradiction with experiment, while allowing for gravitational wavepacket collapse to happen as well; (3) Newtonian semiclassical gravity based on Nelson's stochastic mechanics differs significantly from Schroedinger-Newton, and does not predict gravitational cat states nor gravitational wavepacket collapse. Considering that gravitational cat states are experimentally ruled out, but gravitational wavepacket collapse is testable in the near future, this implies that only the latter two are viable theories of Newtonian semiclassical gravity and that they can be experimentally tested against each other in future molecular interferometry experiments that are anticipated to be capable of testing the gravitational wavepacket collapse prediction.

Vibrational Schroedinger Cats

NASA Technical Reports Server (NTRS)

Kis, Z.; Janszky, J.; Vinogradov, An. V.; Kobayashi, T.

1996-01-01

The optical Schroedinger cat states are simple realizations of quantum states having nonclassical features. It is shown that vibrational analogues of such states can be realized in an experiment of double pulse excitation of vibrionic transitions. To track the evolution of the vibrational wave packet we derive a non-unitary time evolution operator so that calculations are made in a quasi Heisenberg picture.

Schroedinger operators with the q-ladder symmetry algebras

NASA Technical Reports Server (NTRS)

Skorik, Sergei; Spiridonov, Vyacheslav

1994-01-01

A class of the one-dimensional Schroedinger operators L with the symmetry algebra LB(+/-) = q(+/-2)B(+/-)L, (B(+),B(-)) = P(sub N)(L), is described. Here B(+/-) are the 'q-ladder' operators and P(sub N)(L) is a polynomial of the order N. Peculiarities of the coherent states of this algebra are briefly discussed.

Schroedinger's Wave Structure of Matter (WSM)

NASA Astrophysics Data System (ADS)

Wolff, Milo

2009-05-01

The puzzling electron is due to the belief that it is a discrete particle. Einstein deduced this structure impossible since Nature does not match the discrete particle. Clifford (1876) rejected discrete matter and suggested structures in `space'. Schroedinger, (1937) also eliminated discrete particles writing: What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. Particles are just schaumkommen (appearances). He rejected wave-particle duality. Schroedinger's concept was developed by Milo Wolff and Geoff Haselhurst (http://www.SpaceAndMotion.com) using the Scalar Wave Equation to find spherical wave solutions in a 3D quantum space. This WSM is the origin of all the Natural Laws; thus it contains all the electron's properties including the Schroedinger Equation. The origin of Newton's Law F=ma is no longer a puzzle; it is shown to originate from Mach's principle of inertia (1883) that depends on the space medium. Carver Mead (1999) applied the WSM to design Intel micro-chips correcting errors of Maxwell's magnetic Equations. Applications of the WSM describe matter at molecular dimensions: alloys, catalysts, the mechanisms of biology and medicine, molecular computers and memories. See http://www.amazon.com/Schro at Amazon.com.

Quantum mechanical streamlines. I - Square potential barrier

NASA Technical Reports Server (NTRS)

Hirschfelder, J. O.; Christoph, A. C.; Palke, W. E.

1974-01-01

Exact numerical calculations are made for scattering of quantum mechanical particles hitting a square two-dimensional potential barrier (an exact analog of the Goos-Haenchen optical experiments). Quantum mechanical streamlines are plotted and found to be smooth and continuous, to have continuous first derivatives even through the classical forbidden region, and to form quantized vortices around each of the nodal points. A comparison is made between the present numerical calculations and the stationary wave approximation, and good agreement is found between both the Goos-Haenchen shifts and the reflection coefficients. The time-independent Schroedinger equation for real wavefunctions is reduced to solving a nonlinear first-order partial differential equation, leading to a generalization of the Prager-Hirschfelder perturbation scheme. Implications of the hydrodynamical formulation of quantum mechanics are discussed, and cases are cited where quantum and classical mechanical motions are identical.

‘Schroedinger’s Cat’ Molecules Give Rise to Exquisitely Detailed Movies

ScienceCinema

None

2018-01-16

One of the most famous mind-twisters of the quantum world is the thought experiment known as “Schroedinger’s Cat,” in which a cat placed in a box and potentially exposed to poison is simultaneously dead and alive until someone opens the box and peeks inside. Scientists have known for a long time that an atom or molecule can also be in two different states at once. Now researchers at the Stanford PULSE Institute and the Department of Energy’s SLAC National Accelerator Laboratory have exploited this Schroedinger’s Cat behavior to create X-ray movies of atomic motion with much more detail than ever before.

Rogue waves in terms of multi-point statistics and nonequilibrium thermodynamics

NASA Astrophysics Data System (ADS)

Hadjihosseini, Ali; Lind, Pedro; Mori, Nobuhito; Hoffmann, Norbert P.; Peinke, Joachim

2017-04-01

Ocean waves, which lead to rogue waves, are investigated on the background of complex systems. In contrast to deterministic approaches based on the nonlinear Schroedinger equation or focusing effects, we analyze this system in terms of a noisy stochastic system. In particular we present a statistical method that maps the complexity of multi-point data into the statistics of hierarchically ordered height increments for different time scales. We show that the stochastic cascade process with Markov properties is governed by a Fokker-Planck equation. Conditional probabilities as well as the Fokker-Planck equation itself can be estimated directly from the available observational data. This stochastic description enables us to show several new aspects of wave states. Surrogate data sets can in turn be generated allowing to work out different statistical features of the complex sea state in general and extreme rogue wave events in particular. The results also open up new perspectives for forecasting the occurrence probability of extreme rogue wave events, and even for forecasting the occurrence of individual rogue waves based on precursory dynamics. As a new outlook the ocean wave states will be considered in terms of nonequilibrium thermodynamics, for which the entropy production of different wave heights will be considered. We show evidence that rogue waves are characterized by negative entropy production. The statistics of the entropy production can be used to distinguish different wave states.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Podoshvedov, S. A., E-mail: podoshvedov@mail.ru

A method to generate Schroedinger cat states in free propagating optical fields based on the use of displaced states (or displacement operators) is developed. Some optical schemes with photon-added coherent states are studied. The schemes are modifications of the general method based on a sequence of displacements and photon additions or subtractions adjusted to generate Schroedinger cat states of a larger size. The effects of detection inefficiency are taken into account.

Atomic Schroedinger cat-like states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Enriquez-Flores, Marco; Rosas-Ortiz, Oscar; Departamento de Fisica, Cinvestav, A.P. 14-740, Mexico D.F. 07000

2010-10-11

After a short overview of the basic mathematical structure of quantum mechanics we analyze the Schroedinger's antinomic example of a living and dead cat mixed in equal parts. Superpositions of Glauber kets are shown to approximate such macroscopic states. Then, two-level atomic states are used to construct mesoscopic kittens as appropriate linear combinations of angular momentum eigenkets for j = 1/2. Some general comments close the present contribution.

Quantum theory of rotational isomerism and Hill equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ugulava, A.; Toklikishvili, Z.; Chkhaidze, S.

2012-06-15

The process of rotational isomerism of linear triatomic molecules is described by the potential with two different-depth minima and one barrier between them. The corresponding quantum-mechanical equation is represented in the form that is a special case of the Hill equation. It is shown that the Hill-Schroedinger equation has a Klein's quadratic group symmetry which, in its turn, contains three invariant subgroups. The presence of these subgroups makes it possible to create a picture of energy spectrum which depends on a parameter and has many merging and branch points. The parameter-dependent energy spectrum of the Hill-Schroedinger equation, like Mathieu-characteristics, containsmore » branch points from the left and from the right of the demarcation line. However, compared to the Mathieu-characteristics, in the Hill-Schroedinger equation spectrum the 'right' points are moved away even further for some distance that is the bigger, the bigger is the less deep well. The asymptotic wave functions of the Hill-Schroedinger equation for the energy values near the potential minimum contain two isolated sharp peaks indicating a possibility of the presence of two stable isomers. At high energy values near the potential maximum, the height of two peaks decreases, and between them there appear chaotic oscillations. This form of the wave functions corresponds to the process of isomerization.« less

A general formula for Rayleigh-Schroedinger perturbation energy utilizing a power series expansion of the quantum mechanical Hamiltonian

DOE Office of Scientific and Technical Information (OSTI.GOV)

Herbert, J.M.

1997-02-01

Perturbation theory has long been utilized by quantum chemists as a method for approximating solutions to the Schroedinger equation. Perturbation treatments represent a system`s energy as a power series in which each additional term further corrects the total energy; it is therefore convenient to have an explicit formula for the nth-order energy correction term. If all perturbations are collected into a single Hamiltonian operator, such a closed-form expression for the nth-order energy correction is well known; however, use of a single perturbed Hamiltonian often leads to divergent energy series, while superior convergence behavior is obtained by expanding the perturbed Hamiltonianmore » in a power series. This report presents a closed-form expression for the nth-order energy correction obtained using Rayleigh-Schroedinger perturbation theory and a power series expansion of the Hamiltonian.« less

The harmonic oscillator and the position dependent mass Schroedinger equation: isospectral partners and factorization operators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Morales, J.; Ovando, G.; Pena, J. J.

2010-12-23

One of the most important scientific contributions of Professor Marcos Moshinsky has been his study on the harmonic oscillator in quantum theory vis a vis the standard Schroedinger equation with constant mass [1]. However, a simple description of the motion of a particle interacting with an external environment such as happen in compositionally graded alloys consist of replacing the mass by the so-called effective mass that is in general variable and dependent on position. Therefore, honoring in memoriam Marcos Moshinsky, in this work we consider the position-dependent mass Schrodinger equations (PDMSE) for the harmonic oscillator potential model as former potentialmore » as well as with equi-spaced spectrum solutions, i.e. harmonic oscillator isospectral partners. To that purpose, the point canonical transformation method to convert a general second order differential equation (DE), of Sturm-Liouville type, into a Schroedinger-like standard equation is applied to the PDMSE. In that case, the former potential associated to the PDMSE and the potential involved in the Schroedinger-like standard equation are related through a Riccati-type relationship that includes the equivalent of the Witten superpotential to determine the exactly solvable positions-dependent mass distribution (PDMD)m(x). Even though the proposed approach is exemplified with the harmonic oscillator potential, the procedure is general and can be straightforwardly applied to other DEs.« less

Ab initio calculation of proton-coupled electron transfer rates using the external-potential representation: A ubiquinol complex in solution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yamamoto, Takeshi; Kato, Shigeki

2007-06-14

In quantum-mechanical/molecular-mechanical (QM/MM) treatment of chemical reactions in condensed phases, one solves the electronic Schroedinger equation for the solute (or an active site) under the electrostatic field from the environment. This Schroedinger equation depends parametrically on the solute nuclear coordinates R and the external electrostatic potential V. This fact suggests that one may use R and V as natural collective coordinates for describing the entire system, where V plays the role of collective solvent variables. In this paper such an (R,V) representation of the QM/MM canonical ensemble is described, with particular focus on how to treat charge transfer processes inmore » this representation. As an example, the above method is applied to the proton-coupled electron transfer of a ubiquinol analog with phenoxyl radical in acetonitrile solvent. Ab initio free-energy surfaces are calculated as functions of R and V using the reference interaction site model self-consistent field method, the equilibrium points and the minimum free-energy crossing point are located in the (R,V) space, and then the kinetic isotope effects (KIEs) are evaluated approximately. The results suggest that a stiffer proton potential at the transition state may be responsible for unusual KIEs observed experimentally for related systems.« less

Scattering transform for nonstationary Schroedinger equation with bidimensionally perturbed N-soliton potential

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.

2006-12-15

In the framework of the extended resolvent approach the direct and inverse scattering problems for the nonstationary Schroedinger equation with a potential being a perturbation of the N-soliton potential by means of a generic bidimensional smooth function decaying at large spaces are introduced and investigated. The initial value problem of the Kadomtsev-Petviashvili I equation for a solution describing N wave solitons on a generic smooth decaying background is then linearized, giving the time evolution of the spectral data.

Solving the Schroedinger Equation of Atoms and Molecules without Analytical Integration Based on the Free Iterative-Complement-Interaction Wave Function

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakatsuji, H.; Nakashima, H.; Department of Synthetic Chemistry and Biological Chemistry, Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510

2007-12-14

A local Schroedinger equation (LSE) method is proposed for solving the Schroedinger equation (SE) of general atoms and molecules without doing analytic integrations over the complement functions of the free ICI (iterative-complement-interaction) wave functions. Since the free ICI wave function is potentially exact, we can assume a flatness of its local energy. The variational principle is not applicable because the analytic integrations over the free ICI complement functions are very difficult for general atoms and molecules. The LSE method is applied to several 2 to 5 electron atoms and molecules, giving an accuracy of 10{sup -5} Hartree in total energy.more » The potential energy curves of H{sub 2} and LiH molecules are calculated precisely with the free ICI LSE method. The results show the high potentiality of the free ICI LSE method for developing accurate predictive quantum chemistry with the solutions of the SE.« less

Quantum theory and chemistry: Two propositions

NASA Technical Reports Server (NTRS)

Aronowitz, S.

1980-01-01

Two propositions concerning quantum chemistry are proposed. First, it is proposed that the nonrelativistic Schroedinger equation, where the Hamiltonian operator is associated with an assemblage of nuclei and electrons, can never be arranged to yield specific molecules in the chemists' sense. It is argued that this result is a necessary condition if the Schroedinger has relevancy to chemistry. Second, once a system is in a particular state with regard to interactions among its components (the assemblage of nuclei and electrons), it cannot spontaneously eliminate any of those interactions. This leads to a subtle form of irreversibility.

The thermal-wave model: A Schroedinger-like equation for charged particle beam dynamics

NASA Technical Reports Server (NTRS)

Fedele, Renato; Miele, G.

1994-01-01

We review some results on longitudinal beam dynamics obtained in the framework of the Thermal Wave Model (TWM). In this model, which has recently shown the capability to describe both longitudinal and transverse dynamics of charged particle beams, the beam dynamics is ruled by Schroedinger-like equations for the beam wave functions, whose squared modulus is proportional to the beam density profile. Remarkably, the role of the Planck constant is played by a diffractive constant epsilon, the emittance, which has a thermal nature.

The 'hard problem' and the quantum physicists. Part 1: the first generation.

PubMed

Smith, C U M

2006-07-01

All four of the most important figures in the early twentieth-century development of quantum physics-Niels Bohr, Erwin Schroedinger, Werner Heisenberg and Wolfgang Pauli-had strong interests in the traditional mind-brain, or 'hard,' problem. This paper reviews their approach to this problem, showing the influence of Bohr's complementarity thesis, the significance of Schroedinger's small book, 'What is life?,' the updated Platonism of Heisenberg and, perhaps most interesting of all, the interaction of Carl Jung and Wolfgang Pauli in the latter's search for a unification of mind and matter.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sanchez-Arriaga, G.; Hada, T.; Nariyuki, Y.

The triple-degenerate derivative nonlinear Schroedinger (TDNLS) system modified with resistive wave damping and growth is truncated to study the coherent coupling of four waves, three Alfven and one acoustic, near resonance. In the conservative case, the truncation equations derive from a time independent Hamiltonian function with two degrees of freedom. Using a Poincare map analysis, two parameters regimes are explored. In the first regime we check how the modulational instability of the TDNLS system affects to the dynamics of the truncation model, while in the second one the exact triple degenerated case is discussed. In the dissipative case, the truncationmore » model gives rise to a six dimensional flow with five free parameters. Computing some bifurcation diagrams the dependence with the sound to Alfven velocity ratio as well as the Alfven modes involved in the truncation is analyzed. The system exhibits a wealth of dynamics including chaotic attractor, several kinds of bifurcations, and crises. The truncation model was compared to numerical integrations of the TDNLS system.« less

On the heat trace of Schroedinger operators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Banuelos, R.; Sa Barreto, A.

1995-12-31

Trace formulae for heat kernels of Schroedinger operators have been widely studied in connection with spectral and scattering theory. They have been used to obtain information about a potential from its spectrum, or from its scattering data, and vice-versa. Using elementary Fourier transform methods we obtain a formula for the general coefficient in the asymptotic expansion of the trace of the heat kernel of the Schroedinger operator {minus}{Delta} + V, as t {down_arrow} 0, with V {element_of} S(R{sup n}), the class of functions with rapid decay at infinity. In dimension n = 1 a recurrent formula for the general coefficientmore » in the expansion is obtained in [6]. However the KdV methods used there do not seem to generalize to higher dimension. Using the formula of [6] and the symmetry of some integrals, Y. Colin de Verdiere has computed the first four coefficients for potentials in three space dimensions. Also in [1] a different method is used to compute heat coefficients for differential operators on manifolds. 14 refs.« less

Solving the electron and electron-nuclear Schroedinger equations for the excited states of helium atom with the free iterative-complement-interaction method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakashima, Hiroyuki; Hijikata, Yuh; Nakatsuji, Hiroshi

2008-04-21

Very accurate variational calculations with the free iterative-complement-interaction (ICI) method for solving the Schroedinger equation were performed for the 1sNs singlet and triplet excited states of helium atom up to N=24. This is the first extensive applications of the free ICI method to the calculations of excited states to very high levels. We performed the calculations with the fixed-nucleus Hamiltonian and moving-nucleus Hamiltonian. The latter case is the Schroedinger equation for the electron-nuclear Hamiltonian and includes the quantum effect of nuclear motion. This solution corresponds to the nonrelativistic limit and reproduced the experimental values up to five decimal figures. Themore » small differences from the experimental values are not at all the theoretical errors but represent the physical effects that are not included in the present calculations, such as relativistic effect, quantum electrodynamic effect, and even the experimental errors. The present calculations constitute a small step toward the accurately predictive quantum chemistry.« less

General method of solving the Schroedinger equation of atoms and molecules

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakatsuji, Hiroshi

2005-12-15

We propose a general method of solving the Schroedinger equation of atoms and molecules. We first construct the wave function having the exact structure, using the ICI (iterative configuration or complement interaction) method and then optimize the variables involved by the variational principle. Based on the scaled Schroedinger equation and related principles, we can avoid the singularity problem of atoms and molecules and formulate a general method of calculating the exact wave functions in an analytical expansion form. We choose initial function {psi}{sub 0} and scaling g function, and then the ICI method automatically generates the wave function that hasmore » the exact structure by using the Hamiltonian of the system. The Hamiltonian contains all the information of the system. The free ICI method provides a flexible and variationally favorable procedure of constructing the exact wave function. We explain the computational procedure of the analytical ICI method routinely performed in our laboratory. Simple examples are given using hydrogen atom for the nuclear singularity case, the Hooke's atom for the electron singularity case, and the helium atom for both cases.« less

Positive phase space distributions and uncertainty relations

NASA Technical Reports Server (NTRS)

Kruger, Jan

1993-01-01

In contrast to a widespread belief, Wigner's theorem allows the construction of true joint probabilities in phase space for distributions describing the object system as well as for distributions depending on the measurement apparatus. The fundamental role of Heisenberg's uncertainty relations in Schroedinger form (including correlations) is pointed out for these two possible interpretations of joint probability distributions. Hence, in order that a multivariate normal probability distribution in phase space may correspond to a Wigner distribution of a pure or a mixed state, it is necessary and sufficient that Heisenberg's uncertainty relation in Schroedinger form should be satisfied.

Magnetotail dynamics under isobaric constraints

NASA Technical Reports Server (NTRS)

Birn, Joachim; Schindler, Karl; Janicke, Lutz; Hesse, Michael

1994-01-01

Using linear theory and nonlinear MHD simulations, we investigate the resistive and ideal MHD stability of two-dimensional plasma configurations under the isobaric constraint dP/dt = 0, which in ideal MHD is equivalent to conserving the pressure function P = P(A), where A denotes the magnetic flux. This constraint is satisfied for incompressible modes, such as Alfven waves, and for systems undergoing energy losses. The linear stability analysis leads to a Schroedinger equation, which can be investigated by standard quantum mechanics procedures. We present an application to a typical stretched magnetotail configuration. For a one-dimensional sheet equilibrium characteristic properties of tearing instability are rediscovered. However, the maximum growth rate scales with the 1/7 power of the resistivity, which implies much faster growth than for the standard tearing mode (assuming that the resistivity is small). The same basic eigen-mode is found also for weakly two-dimensional equilibria, even in the ideal MHD limit. In this case the growth rate scales with the 1/4 power of the normal magnetic field. The results of the linear stability analysis are confirmed qualitatively by nonlinear dynamic MHD simulations. These results suggest the interesting possibility that substorm onset, or the thinning in the late growth phase, is caused by the release of a thermodynamic constraint without the (immediate) necessity of releasing the ideal MHD constraint. In the nonlinear regime the resistive and ideal developments differ in that the ideal mode does not lead to neutral line formation without the further release of the ideal MHD constraint; instead a thin current sheet forms. The isobaric constraint is critically discussed. Under perhaps more realistic adiabatic conditions the ideal mode appears to be stable but could be driven by external perturbations and thus generate the thin current sheet in the late growth phase, before a nonideal instability sets in.

Nonlinear Schroedinger Approximations for Partial Differential Equations with Quadratic and Quasilinear Terms

NASA Astrophysics Data System (ADS)

Cummings, Patrick

We consider the approximation of solutions of two complicated, physical systems via the nonlinear Schrodinger equation (NLS). In particular, we discuss the evolution of wave packets and long waves in two physical models. Due to the complicated nature of the equations governing many physical systems and the in-depth knowledge we have for solutions of the nonlinear Schrodinger equation, it is advantageous to use approximation results of this kind to model these physical systems. The approximations are simple enough that we can use them to understand the qualitative and quantitative behavior of the solutions, and by justifying them we can show that the behavior of the approximation captures the behavior of solutions to the original equation, at least for long, but finite time. We first consider a model of the water wave equations which can be approximated by wave packets using the NLS equation. We discuss a new proof that both simplifies and strengthens previous justification results of Schneider and Wayne. Rather than using analytic norms, as was done by Schneider and Wayne, we construct a modified energy functional so that the approximation holds for the full interval of existence of the approximate NLS solution as opposed to a subinterval (as is seen in the analytic case). Furthermore, the proof avoids problems associated with inverting the normal form transform by working with a modified energy functional motivated by Craig and Hunter et al. We then consider the Klein-Gordon-Zakharov system and prove a long wave approximation result. In this case there is a non-trivial resonance that cannot be eliminated via a normal form transform. By combining the normal form transform for small Fourier modes and using analytic norms elsewhere, we can get a justification result on the order 1 over epsilon squared time scale.

Some Exact Results for the Schroedinger Wave Equation with a Time Dependent Potential

NASA Technical Reports Server (NTRS)

Campbell, Joel

2009-01-01

The time dependent Schroedinger equation with a time dependent delta function potential is solved exactly for many special cases. In all other cases the problem can be reduced to an integral equation of the Volterra type. It is shown that by knowing the wave function at the origin, one may derive the wave function everywhere. Thus, the problem is reduced from a PDE in two variables to an integral equation in one. These results are used to compare adiabatic versus sudden changes in the potential. It is shown that adiabatic changes in the p otential lead to conservation of the normalization of the probability density.

A new fundamental model of moving particle for reinterpreting Schroedinger equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Umar, Muhamad Darwis

2012-06-20

The study of Schroedinger equation based on a hypothesis that every particle must move randomly in a quantum-sized volume has been done. In addition to random motion, every particle can do relative motion through the movement of its quantum-sized volume. On the other way these motions can coincide. In this proposed model, the random motion is one kind of intrinsic properties of the particle. The every change of both speed of randomly intrinsic motion and or the velocity of translational motion of a quantum-sized volume will represent a transition between two states, and the change of speed of randomly intrinsicmore » motion will generate diffusion process or Brownian motion perspectives. Diffusion process can take place in backward and forward processes and will represent a dissipative system. To derive Schroedinger equation from our hypothesis we use time operator introduced by Nelson. From a fundamental analysis, we find out that, naturally, we should view the means of Newton's Law F(vector sign) = ma(vector sign) as no an external force, but it is just to describe both the presence of intrinsic random motion and the change of the particle energy.« less

Conformal mapping and bound states in bent waveguides

NASA Astrophysics Data System (ADS)

Sadurní, E.; Schleich, W. P.

2010-12-01

Is it possible to trap a quantum particle in an open geometry? In this work we deal with the boundary value problem of the stationary Schroedinger (or Helmholtz) equation within a waveguide with straight segments and a rectangular bending. The problem can be reduced to a one-dimensional matrix Schroedinger equation using two descriptions: oblique modes and conformal coordinates. We use a corner-corrected WKB formalism to find the energies of the one-dimensional problem. It is shown that the presence of bound states is an effect due to the boundary alone, with no classical counterpart for this geometry. The conformal description proves to be simpler, as the coupling of transversal modes is not essential in this case.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nekrasov, Nikita; ITEP, Moscow; Shatashvili, Samson

Supersymmetric vacua of two dimensional N = 4 gauge theories with matter, softly broken by the twisted masses down to N = 2, are shown to be in one-to-one correspondence with the eigenstates of integrable spin chain Hamiltonians. Examples include: the Heisenberg SU(2)XXX spin chain which is mapped to the two dimensional U(N) theory with fundamental hypermultiplets, the XXZ spin chain which is mapped to the analogous three dimensional super-Yang-Mills theory compactified on a circle, the XYZ spin chain and eight-vertex model which are related to the four dimensional theory compactified on T{sup 2}. A consequence of our correspondence ismore » the isomorphism of the quantum cohomology ring of various quiver varieties, such as cotangent bundles to (partial) flag varieties and the ring of quantum integrals of motion of various spin chains. The correspondence extends to any spin group, representations, boundary conditions, and inhomogeneity, it includes Sinh-Gordon and non-linear Schroedinger models as well as the dynamical spin chains like Hubbard model. Compactifications of four dimensional N = 2 theories on a two-sphere lead to the instanton-corrected Bethe equations.« less

Design of HIFU transducers for generating specified nonlinear ultrasound fields

PubMed Central

Rosnitskiy, Pavel B.; Yuldashev, Petr V.; Sapozhnikov, Oleg A.; Maxwell, Adam; Kreider, Wayne; Bailey, Michael R.; Khokhlova, Vera A.

2016-01-01

Various clinical applications of high intensity focused ultrasound (HIFU) have different requirements for the pressure levels and degree of nonlinear waveform distortion at the focus. The goal of this work was to determine transducer design parameters that produce either a specified shock amplitude in the focal waveform or specified peak pressures while still maintaining quasilinear conditions at the focus. Multi-parametric nonlinear modeling based on the KZK equation with an equivalent source boundary condition was employed. Peak pressures, shock amplitudes at the focus, and corresponding source outputs were determined for different transducer geometries and levels of nonlinear distortion. Results are presented in terms of the parameters of an equivalent single-element, spherically shaped transducer. The accuracy of the method and its applicability to cases of strongly focused transducers were validated by comparing the KZK modeling data with measurements and nonlinear full-diffraction simulations for a single-element source and arrays with 7 and 256 elements. The results provide look-up data for evaluating nonlinear distortions at the focus of existing therapeutic systems as well as for guiding the design of new transducers that generate specified nonlinear fields. PMID:27775904

Solving the Schroedinger equation for helium atom and its isoelectronic ions with the free iterative complement interaction (ICI) method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakashima, Hiroyuki; Nakatsuji, Hiroshi

2007-12-14

The Schroedinger equation was solved very accurately for helium atom and its isoelectronic ions (Z=1-10) with the free iterative complement interaction (ICI) method followed by the variational principle. We obtained highly accurate wave functions and energies of helium atom and its isoelectronic ions. For helium, the calculated energy was -2.903 724 377 034 119 598 311 159 245 194 404 446 696 905 37 a.u., correct over 40 digit accuracy, and for H{sup -}, it was -0.527 751 016 544 377 196 590 814 566 747 511 383 045 02 a.u. These results prove numerically that with the free ICImore » method, we can calculate the solutions of the Schroedinger equation as accurately as one desires. We examined several types of scaling function g and initial function {psi}{sub 0} of the free ICI method. The performance was good when logarithm functions were used in the initial function because the logarithm function is physically essential for three-particle collision area. The best performance was obtained when we introduce a new logarithm function containing not only r{sub 1} and r{sub 2} but also r{sub 12} in the same logarithm function.« less

Simulations of nonlinear continuous wave pressure fields in FOCUS

NASA Astrophysics Data System (ADS)

Zhao, Xiaofeng; Hamilton, Mark F.; McGough, Robert J.

2017-03-01

The Khokhlov - Zabolotskaya - Kuznetsov (KZK) equation is a parabolic approximation to the Westervelt equation that models the effects of diffraction, attenuation, and nonlinearity. Although the KZK equation is only valid in the far field of the paraxial region for mildly focused or unfocused transducers, the KZK equation is widely applied in medical ultrasound simulations. For a continuous wave input, the KZK equation is effectively modeled by the Bergen Code [J. Berntsen, Numerical Calculations of Finite Amplitude Sound Beams, in M. F. Hamilton and D. T. Blackstock, editors, Frontiers of Nonlinear Acoustics: Proceedings of 12th ISNA, Elsevier, 1990], which is a finite difference model that utilizes operator splitting. Similar C++ routines have been developed for FOCUS, the `Fast Object-Oriented C++ Ultrasound Simulator' (http://www.egr.msu.edu/˜fultras-web) to calculate nonlinear pressure fields generated by axisymmetric flat circular and spherically focused ultrasound transducers. This new routine complements an existing FOCUS program that models nonlinear ultrasound propagation with the angular spectrum approach [P. T. Christopher and K. J. Parker, J. Acoust. Soc. Am. 90, 488-499 (1991)]. Results obtained from these two nonlinear ultrasound simulation approaches are evaluated and compared for continuous wave linear simulations. The simulation results match closely in the farfield of the paraxial region, but the results differ in the nearfield. The nonlinear pressure field generated by a spherically focused transducer with a peak surface pressure of 0.2MPa radiating in a lossy medium with β = 3.5 is simulated, and the computation times are also evaluated. The nonlinear simulation results demonstrate acceptable agreement in the focal zone. These two related nonlinear simulation approaches are now included with FOCUS to enable convenient simulations of nonlinear pressure fields on desktop and laptop computers.

Design of HIFU Transducers for Generating Specified Nonlinear Ultrasound Fields.

PubMed

Rosnitskiy, Pavel B; Yuldashev, Petr V; Sapozhnikov, Oleg A; Maxwell, Adam D; Kreider, Wayne; Bailey, Michael R; Khokhlova, Vera A

2017-02-01

Various clinical applications of high-intensity focused ultrasound have different requirements for the pressure levels and degree of nonlinear waveform distortion at the focus. The goal of this paper is to determine transducer design parameters that produce either a specified shock amplitude in the focal waveform or specified peak pressures while still maintaining quasi-linear conditions at the focus. Multiparametric nonlinear modeling based on the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation with an equivalent source boundary condition was employed. Peak pressures, shock amplitudes at the focus, and corresponding source outputs were determined for different transducer geometries and levels of nonlinear distortion. The results are presented in terms of the parameters of an equivalent single-element spherically shaped transducer. The accuracy of the method and its applicability to cases of strongly focused transducers were validated by comparing the KZK modeling data with measurements and nonlinear full diffraction simulations for a single-element source and arrays with 7 and 256 elements. The results provide look-up data for evaluating nonlinear distortions at the focus of existing therapeutic systems as well as for guiding the design of new transducers that generate specified nonlinear fields.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jentschura, Ulrich D.; National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8401; Mohr, Peter J.

We describe the calculation of hydrogenic (one-loop) Bethe logarithms for all states with principal quantum numbers n{<=}200. While, in principle, the calculation of the Bethe logarithm is a rather easy computational problem involving only the nonrelativistic (Schroedinger) theory of the hydrogen atom, certain calculational difficulties affect highly excited states, and in particular states for which the principal quantum number is much larger than the orbital angular momentum quantum number. Two evaluation methods are contrasted. One of these is based on the calculation of the principal value of a specific integral over a virtual photon energy. The other method relies directlymore » on the spectral representation of the Schroedinger-Coulomb propagator. Selected numerical results are presented. The full set of values is available at arXiv.org/quant-ph/0504002.« less

A comparative study of Laplacians and Schroedinger- Lichnerowicz-Weitzenboeck identities in Riemannian and antisymplectic geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Batalin, Igor A.; I.E. Tamm Theory Division, P.N. Lebedev Physics Institute, Russian Academy of Sciences, 53 Leninsky Prospect, Moscow 119991; Bering, Klaus

2009-07-15

We introduce an antisymplectic Dirac operator and antisymplectic gamma matrices. We explore similarities between, on one hand, the Schroedinger-Lichnerowicz formula for spinor bundles in Riemannian spin geometry, which contains a zeroth-order term proportional to the Levi-Civita scalar curvature, and, on the other hand, the nilpotent, Grassmann-odd, second-order {delta} operator in antisymplectic geometry, which, in general, has a zeroth-order term proportional to the odd scalar curvature of an arbitrary antisymplectic and torsion-free connection that is compatible with the measure density. Finally, we discuss the close relationship with the two-loop scalar curvature term in the quantum Hamiltonian for a particle in amore » curved Riemannian space.« less

Numerical analysis of spectral properties of coupled oscillator Schroedinger operators. I - Single and double well anharmonic oscillators

NASA Technical Reports Server (NTRS)

Isaacson, D.; Isaacson, E. L.; Paes-Leme, P. J.; Marchesin, D.

1981-01-01

Several methods for computing many eigenvalues and eigenfunctions of a single anharmonic oscillator Schroedinger operator whose potential may have one or two minima are described. One of the methods requires the solution of an ill-conditioned generalized eigenvalue problem. This method has the virtue of using a bounded amount of work to achieve a given accuracy in both the single and double well regions. Rigorous bounds are given, and it is proved that the approximations converge faster than any inverse power of the size of the matrices needed to compute them. The results of computations for the g:phi(4):1 theory are presented. These results indicate that the methods actually converge exponentially fast.

Symbolic derivation of high-order Rayleigh-Schroedinger perturbation energies using computer algebra: Application to vibrational-rotational analysis of diatomic molecules

DOE Office of Scientific and Technical Information (OSTI.GOV)

Herbert, John M.

1997-01-01

Rayleigh-Schroedinger perturbation theory is an effective and popular tool for describing low-lying vibrational and rotational states of molecules. This method, in conjunction with ab initio techniques for computation of electronic potential energy surfaces, can be used to calculate first-principles molecular vibrational-rotational energies to successive orders of approximation. Because of mathematical complexities, however, such perturbation calculations are rarely extended beyond the second order of approximation, although recent work by Herbert has provided a formula for the nth-order energy correction. This report extends that work and furnishes the remaining theoretical details (including a general formula for the Rayleigh-Schroedinger expansion coefficients) necessary formore » calculation of energy corrections to arbitrary order. The commercial computer algebra software Mathematica is employed to perform the prohibitively tedious symbolic manipulations necessary for derivation of generalized energy formulae in terms of universal constants, molecular constants, and quantum numbers. As a pedagogical example, a Hamiltonian operator tailored specifically to diatomic molecules is derived, and the perturbation formulae obtained from this Hamiltonian are evaluated for a number of such molecules. This work provides a foundation for future analyses of polyatomic molecules, since it demonstrates that arbitrary-order perturbation theory can successfully be applied with the aid of commercially available computer algebra software.« less

Lattice Simulations in MOM v.s. Schroedinger Functional Scheme and Triality

DOE Office of Scientific and Technical Information (OSTI.GOV)

Furui, Sadataka

The QCD beta function extracted from polarized electron proton scattering data obtained at JLab and the lattice simulation in the MOM scheme suggest that the critical flavor number for the presence of IR fixed point is about three. In analyses of Schroedinger functional scheme, however, critical flavor number for the presence of IR fixed point and the conformality is larger than nine.In the QCD analysis, when quarks are expressed in quaternion basis, the product of quaternions are expressed by octonions and the octonion posesses the triality symmetry. Since the triality has the effect of multiplying the falvor number, it couldmore » explain the apparent large critical flavor number in the Schroedinger functinal scheme. In this scheme, larger degrees of freedom in adjusting data of different scales on the boundary are necessary than in the MOM scheme.In weak interaction, there is no clear lepton-flavor violation except in the neutrino oscillation. If the triality is assigned to the lepton flavors(e,{mu} and {tau}) and they are assumed to be exact symmetry, or the electro-magnetic interaction preserves tiality, but the strong interaction is triality blind, there is a possibility of explaining the neutrino oscillation through triality mixing of the matter field.The self energy of gluons, ghost and gauge bosons due to self-dual gauge fields and leptonic decays of B,D and D{sub s} mesons are discussed.« less

Nonlinear propagation analysis of few-optical-cycle pulses for subfemtosecond compression and carrier envelope phase effect

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mizuta, Yo; Nagasawa, Minoru; Ohtani, Morimasa

2005-12-15

A numerical approach called Fourier direct method (FDM) is applied to nonlinear propagation of optical pulses with the central wavelength 800 nm, the width 2.67-12.00 fs, and the peak power 25-6870 kW in a fused-silica fiber. Bidirectional propagation, delayed Raman response, nonlinear dispersion (self-steepening, core dispersion), as well as correct linear dispersion are incorporated into 'bidirectional propagation equations' which are derived directly from Maxwell's equations. These equations are solved for forward and backward waves, instead of the electric-field envelope as in the nonlinear Schroedinger equation (NLSE). They are integrated as multidimensional simultaneous evolution equations evolved in space. We investigate, bothmore » theoretically and numerically, the validity and the limitation of assumptions and approximations used for deriving the NLSE. Also, the accuracy and the efficiency of the FDM are compared quantitatively with those of the finite-difference time-domain numerical approach. The time-domain size 500 fs and the number of grid points in time 2048 are chosen to investigate numerically intensity spectra, spectral phases, and temporal electric-field profiles up to the propagation distance 1.0 mm. On the intensity spectrum of a few-optical-cycle pulses, the self-steepening, core dispersion, and the delayed Raman response appear as dominant, middle, and slight effects, respectively. The delayed Raman response and the core dispersion reduce the effective nonlinearity. Correct linear dispersion is important since it affects the intensity spectrum sensitively. For the compression of femtosecond optical pulses by the complete phase compensation, the shortness and the pulse quality of compressed pulses are remarkably improved by the intense initial peak power rather than by the short initial pulse width or by the propagation distance longer than 0.1 mm. They will be compressed as short as 0.3 fs below the damage threshold of fused-silica fiber 6 MW. It is demonstrated that the carrier envelope phase (CEP) causes the difference on the temporal electric-field profile and the intensity spectrum for the initial peak power of the order of megawatts. At the propagation distance longer than the coherence length for third-order harmonics, the difference grows in the spectral components around the third-order and higher-order harmonics. The CEP can be a sensitive marker to monitor the evolution of nonlinear optical process by a few-optical-cycle electric-field wave-packet source.« less

Absorbing boundaries in numerical solutions of the time-dependent Schroedinger equation on a grid using exterior complex scaling

DOE Office of Scientific and Technical Information (OSTI.GOV)

He, F.; Ruiz, C.; Becker, A.

We study the suppression of reflections in the numerical simulation of the time-dependent Schroedinger equation for strong-field problems on a grid using exterior complex scaling (ECS) as an absorbing boundary condition. It is shown that the ECS method can be applied in both the length and the velocity gauge as long as appropriate approximations are applied in the ECS transformation of the electron-field coupling. It is found that the ECS method improves the suppression of reflection as compared to the conventional masking function technique in typical simulations of atoms exposed to an intense laser pulse. Finally, we demonstrate the advantagemore » of the ECS technique to avoid unphysical artifacts in the evaluation of high harmonic spectra.« less

Analytical solutions of the Schroedinger equation for a two-dimensional exciton in magnetic field of arbitrary strength

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hoang-Do, Ngoc-Tram; Hoang, Van-Hung; Le, Van-Hoang

2013-05-15

The Feranchuk-Komarov operator method is developed by combining with the Levi-Civita transformation in order to construct analytical solutions of the Schroedinger equation for a two-dimensional exciton in a uniform magnetic field of arbitrary strength. As a result, analytical expressions for the energy of the ground and excited states are obtained with a very high precision of up to four decimal places. Especially, the precision is uniformly stable for the whole range of the magnetic field. This advantage appears due to the consideration of the asymptotic behaviour of the wave-functions in strong magnetic field. The results could be used for variousmore » physical analyses and the method used here could also be applied to other atomic systems.« less

Question 1: origin of life and the living state.

PubMed

Kauffman, Stuart

2007-10-01

The aim of this article is to discuss four topics: First, the origin of molecular reproduction. Second, the origin of agency - the capacity of a system to act on its own behalf. Agency is a stunning feature of human and some wider range of life. Third, to discuss a still poorly articulated feature of life noticed by the philosopher Immanuel Kant over 200 years ago: A self propagating organization of process. We have no theory for this aspect of life, yet it is central to life. Fourth, I will discuss constraints, as in Schroedinger's aperiodic crystal (Schroedinger E, What is life? The physical aspect of the living cell, 1944), as information, part of the total non-equilibrium union of matter, energy, work, work cycles, constraints, and information that appear to comprise the living state.

Perturbation method for the second-order nonlinear effect of focused acoustic field around a scatterer in an ideal fluid.

PubMed

Liu, Gang; Jayathilake, Pahala Gedara; Khoo, Boo Cheong

2014-02-01

Two nonlinear models are proposed to investigate the focused acoustic waves that the nonlinear effects will be important inside the liquid around the scatterer. Firstly, the one dimensional solutions for the widely used Westervelt equation with different coordinates are obtained based on the perturbation method with the second order nonlinear terms. Then, by introducing the small parameter (Mach number), a dimensionless formulation and asymptotic perturbation expansion via the compressible potential flow theory is applied. This model permits the decoupling between the velocity potential and enthalpy to second order, with the first potential solutions satisfying the linear wave equation (Helmholtz equation), whereas the second order solutions are associated with the linear non-homogeneous equation. Based on the model, the local nonlinear effects of focused acoustic waves on certain volume are studied in which the findings may have important implications for bubble cavitation/initiation via focused ultrasound called HIFU (High Intensity Focused Ultrasound). The calculated results show that for the domain encompassing less than ten times the radius away from the center of the scatterer, the non-linear effect exerts a significant influence on the focused high intensity acoustic wave. Moreover, at the comparatively higher frequencies, for the model of spherical wave, a lower Mach number may result in stronger nonlinear effects. Copyright © 2013 Elsevier B.V. All rights reserved.

Probing the interior of a solid volume with time reversal and nonlinear elastic wave spectroscopy.

PubMed

Le Bas, P Y; Ulrich, T J; Anderson, B E; Guyer, R A; Johnson, P A

2011-10-01

A nonlinear scatterer is simulated in the body of a sample and demonstrates a technique to locate and define the elastic nature of the scatterer. Using the principle of time reversal, elastic wave energy is focused at the interface between blocks of optical grade glass and aluminum. Focusing of energy at the interface creates nonlinear wave scattering that can be detected on the sample perimeter with time-reversal mirror elements. The nonlinearly generated scattered signal is bandpass filtered about the nonlinearly generated components, time reversed and broadcast from the same mirror elements, and the signal is focused at the scattering location on the interface. © 2011 Acoustical Society of America

Subsonic and Supersonic Effects in Bose-Einstein Condensate

NASA Technical Reports Server (NTRS)

Zak, Michail

2003-01-01

A paper presents a theoretical investigation of subsonic and supersonic effects in a Bose-Einstein condensate (BEC). The BEC is represented by a time-dependent, nonlinear Schroedinger equation that includes terms for an external confining potential term and a weak interatomic repulsive potential proportional to the number density of atoms. From this model are derived Madelung equations, which relate the quantum phase with the number density, and which are used to represent excitations propagating through the BEC. These equations are shown to be analogous to the classical equations of flow of an inviscid, compressible fluid characterized by a speed of sound (g/Po)1/2, where g is the coefficient of the repulsive potential and Po is the unperturbed mass density of the BEC. The equations are used to study the effects of a region of perturbation moving through the BEC. The excitations created by a perturbation moving at subsonic speed are found to be described by a Laplace equation and to propagate at infinite speed. For a supersonically moving perturbation, the excitations are found to be described by a wave equation and to propagate at finite speed inside a Mach cone.

Blow-up profile to the solutions of two-coupled Schroedinger equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen Jianqing; Guo Boling

2009-02-15

The model of the following two-coupled Schroedinger equations, i{sub t}+(1/2){delta}u=(g{sub 11}|u|{sup 2p}+g|u|{sup p-1}|v|{sup p+1})uu, (t,x)(set-membership sign)R{sub +}xR{sup N}, and iv{sub t}+(1/2){delta}v=(g|u|{sup p+1}|v|{sup p-1}+g{sub 22}|v|{sup 2p})v, (t,x)(set-membership sign)R{sub +}xR{sup N}, is proposed in the study of the Bose-Einstein condensates [Mitchell, et al., ''Self-traping of partially spatially incoherent light,'' Phys. Rev. Lett. 77, 490 (1996)]. We prove that for suitable initial data and p the solution blows up exactly like {delta} function. As a by-product, we prove that similar phenomenon occurs for the critical two-coupled Schroedinger equations with harmonic potential [Perez-Garcia, V. M. and Beitia, T. B., ''Sybiotic solitons in heteronuclear multicomponentmore » Bose-Einstein condensates,'' Phys. Rev. A 72, 033620 (2005)], iu{sub t}+(1/2){delta}u=({omega}/2)|x|{sup 2}u+(g{sub 11}|u|{sup 2p}+g|u|{sup p-1}|v|{sup p+1})u, x(set-membership sign)R{sup N}, and iv{sub t}+(1/2){delta}v=({omega}/2)|x|{sup 2}v+(g|u|{sup p+1}|v|{sup p-1}+g{sub 22}|v|{sup 2p})v, x(set-membership sign)R{sup N}.« less

Effect of nonlinear absorption on self focusing of short laser pulse in a plasma

NASA Astrophysics Data System (ADS)

Kumar, Ashok

2012-06-01

Paraxial theory of self focusing of short pulse laser in a plasma under transient and saturating effects of nonlinearity and nonlinear absorption is developed. The absorption is averaged over the cross-section of the beam and is different for different time segments of the pulse. The electron temperature includes cumulative effect of previous history of temporal profile of pulse intensity, however, the ambipolar diffusion is taken to be faster than the heating time. The relaxation effect causes self-distortion of the pulse temporal profile where as the nonlinear absorption weakens self focusing. For the pulses of duration comparable to the electron ion collision time, the front part of the pulse gets defocused where as the latter part undergoes periodic self focusing.

Waveguides with Absorbing Boundaries: Nonlinearity Controlled by an Exceptional Point and Solitons

NASA Astrophysics Data System (ADS)

Midya, Bikashkali; Konotop, Vladimir V.

2017-07-01

We reveal the existence of continuous families of guided single-mode solitons in planar waveguides with weakly nonlinear active core and absorbing boundaries. Stable propagation of TE and TM-polarized solitons is accompanied by attenuation of all other modes, i.e., the waveguide features properties of conservative and dissipative systems. If the linear spectrum of the waveguide possesses exceptional points, which occurs in the case of TM polarization, an originally focusing (defocusing) material nonlinearity may become effectively defocusing (focusing). This occurs due to the geometric phase of the carried eigenmode when the surface impedance encircles the exceptional point. In its turn, the change of the effective nonlinearity ensures the existence of dark (bright) solitons in spite of focusing (defocusing) Kerr nonlinearity of the core. The existence of an exceptional point can also result in anomalous enhancement of the effective nonlinearity. In terms of practical applications, the nonlinearity of the reported waveguide can be manipulated by controlling the properties of the absorbing cladding.

Some Thoughts on Stability in Nonlinear Periodic Focusing Systems

DOE R&D Accomplishments Database

McMillan, E. M.

1967-09-05

A brief discussion is given of the long-term stability of particle motions through periodic focusing structures containing lumped nonlinear elements. A method is presented whereby one can specify the nonlinear elements in such a way as to generate a variety of structures in which the motion has long-term stability.

Operator based integration of information in multimodal radiological search mission with applications to anomaly detection

NASA Astrophysics Data System (ADS)

Benedetto, J.; Cloninger, A.; Czaja, W.; Doster, T.; Kochersberger, K.; Manning, B.; McCullough, T.; McLane, M.

2014-05-01

Successful performance of radiological search mission is dependent on effective utilization of mixture of signals. Examples of modalities include, e.g., EO imagery and gamma radiation data, or radiation data collected during multiple events. In addition, elevation data or spatial proximity can be used to enhance the performance of acquisition systems. State of the art techniques in processing and exploitation of complex information manifolds rely on diffusion operators. Our approach involves machine learning techniques based on analysis of joint data- dependent graphs and their associated diffusion kernels. Then, the significant eigenvectors of the derived fused graph Laplace and Schroedinger operators form the new representation, which provides integrated features from the heterogeneous input data. The families of data-dependent Laplace and Schroedinger operators on joint data graphs, shall be integrated by means of appropriately designed fusion metrics. These fused representations are used for target and anomaly detection.

Degenerate RS perturbation theory. [Rayleigh-Schroedinger energies and wave functions

NASA Technical Reports Server (NTRS)

Hirschfelder, J. O.; Certain, P. R.

1974-01-01

A concise, systematic procedure is given for determining the Rayleigh-Schroedinger energies and wave functions of degenerate states to arbitrarily high orders even when the degeneracies of the various states are resolved in arbitrary orders. The procedure is expressed in terms of an iterative cycle in which the energy through the (2n + 1)-th order is expressed in terms of the partially determined wave function through the n-th order. Both a direct and an operator derivation are given. The two approaches are equivalent and can be transcribed into each other. The direct approach deals with the wave functions (without the use of formal operators) and has the advantage that it resembles the usual treatment of nondegenerate perturbations and maintains close contact with the basic physics. In the operator approach, the wave functions are expressed in terms of infinite-order operators which are determined by the successive resolution of the space of the zeroth-order functions.

Nonlinear effects in the radiation force generated by amplitude-modulated focused beams

NASA Astrophysics Data System (ADS)

González, Nuria; Jiménez, Noé; Redondo, Javier; Roig, Bernardino; Picó, Rubén; Sánchez-Morcillo, Víctor; Konofagou, Elisa E.; Camarena, Francisco

2012-10-01

Harmonic Motion Imaging (HMI) uses an amplitude-modulated (AM) beam to induce an oscillatory radiation force before, during and after ablation. In this paper, the findings from a numerical analysis of the effects related with the nonlinear propagation of AM focused ultrasonic beams in water on the radiation force and the location of its maxima will be presented. The numerical modeling is performed using the KZK nonlinear parabolic equation. The radiation force is generated by a focused transducer with a gain of 18, a carrier frequency of 1 MHz and a modulation frequency of 25 kHz. The modulated excitation generates a spatially-invariant force proportional to the intensity. Regarding the nonlinear wave propagation, the force is no longer proportional to the intensity, reaching a factor of eight between the nonlinear and linear estimations. Also, a 9 mm shift in the on-axis force peak occurs when the initial pressure increased from 1 to 300 kPa. This spatial shift, due to the nonlinear effects, becomes dynamic in AM focused beams, as the different signal periods have different amplitudes. This study shows that both the value and the spatial position of the force peak are affected by the nonlinear propagation of the ultrasonic waves.

Enhanced focus steering abilities of multi-element therapeutic arrays operating in nonlinear regimes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yuldashev, P., E-mail: petr@acs366.phys.msu.ru; Ilyin, S.; Gavrilov, L.

2015-10-28

Steering abilities of a typical HIFU therapeutic array operated in linear and nonlinear regimes were compared using numerical simulation with the 3D Westervelt equation. The array included 256 elements of 1.2 MHz frequency and 6.6 mm diameter distributed in a quasi-random pattern over a spherical shell with a 130 mm aperture and a focal length of 120 mm. In the case of linear focusing, thermal effects are proportional to the intensity level and the criterion for safe array operation is that the intensity in the grating lobes should be less than 10% of the intensity in the main focus. Inmore » the case of nonlinear focusing, the heating effect is no longer proportional to intensity; therefore the heat deposition rate was chosen as the relevant metric, using the same 10% threshold for the secondary lobe in comparison with the focal maximum. When steering the focus, the same linearly predicted intensity level at the main focus was maintained by increasing the array power. Numerical simulations of the acoustic field were performed for nonlinear propagation both in water and in tissue. It was shown that for shock-forming conditions in the main focus, the steering range of safe electronic focusing is larger than that for linear propagation conditions. Nonlinear sonication regimes therefore can be used to enlarge tissue volumes that can be sonicated using electronic steering of the focus of HIFU arrays.« less

Nonlinear focal shift beyond the geometrical focus in moderately focused acoustic beams.

PubMed

Camarena, Francisco; Adrián-Martínez, Silvia; Jiménez, Noé; Sánchez-Morcillo, Víctor

2013-08-01

The phenomenon of the displacement of the position along the axis of the pressure, intensity, and radiation force maxima of focused acoustic beams under increasing driving voltages (nonlinear focal shift) is studied for the case of a moderately focused beam. The theoretical and experimental results show the existence of this shift along the axis when the initial pressure in the transducer increases until the acoustic field reaches the fully developed nonlinear regime of propagation. Experimental data show that at high amplitudes and for moderate focusing, the position of the on-axis pressure maximum and radiation force maximum can surpass the geometrical focal length. On the contrary, the on-axis pressure minimum approaches the transducer under increasing driving voltages, increasing the distance between the positive and negative peak pressure in the beam. These results are in agreement with numerical KZK model predictions and the existed data of other authors and can be explained according to the effect of self-refraction characteristic of the nonlinear regime of propagation.

Some Thoughts on Stability in Nonlinear Periodic Focusing Systems [Addendum

DOE R&D Accomplishments Database

McMillan, Edwin M.

1968-03-29

Addendum to September 5, 1967 report with the same title and with the abstract: A brief discussion is given of the long-term stability of particle motions through periodic focusing structures containing lumped nonlinear elements. A method is presented whereby one can specify the nonlinear elements in such a way as to generate a variety of structures in which the motion has long-term stability.

Super-nonlinear fluorescence microscopy for high-contrast deep tissue imaging

NASA Astrophysics Data System (ADS)

Wei, Lu; Zhu, Xinxin; Chen, Zhixing; Min, Wei

2014-02-01

Two-photon excited fluorescence microscopy (TPFM) offers the highest penetration depth with subcellular resolution in light microscopy, due to its unique advantage of nonlinear excitation. However, a fundamental imaging-depth limit, accompanied by a vanishing signal-to-background contrast, still exists for TPFM when imaging deep into scattering samples. Formally, the focusing depth, at which the in-focus signal and the out-of-focus background are equal to each other, is defined as the fundamental imaging-depth limit. To go beyond this imaging-depth limit of TPFM, we report a new class of super-nonlinear fluorescence microscopy for high-contrast deep tissue imaging, including multiphoton activation and imaging (MPAI) harnessing novel photo-activatable fluorophores, stimulated emission reduced fluorescence (SERF) microscopy by adding a weak laser beam for stimulated emission, and two-photon induced focal saturation imaging with preferential depletion of ground-state fluorophores at focus. The resulting image contrasts all exhibit a higher-order (third- or fourth- order) nonlinear signal dependence on laser intensity than that in the standard TPFM. Both the physical principles and the imaging demonstrations will be provided for each super-nonlinear microscopy. In all these techniques, the created super-nonlinearity significantly enhances the imaging contrast and concurrently extends the imaging depth-limit of TPFM. Conceptually different from conventional multiphoton processes mediated by virtual states, our strategy constitutes a new class of fluorescence microscopy where high-order nonlinearity is mediated by real population transfer.

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

NASA Astrophysics Data System (ADS)

Kharin, Nikolay A.

2001-05-01

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

Problems in Nonlinear Acoustics: Pulsed Finite Amplitude Sound Beams, Nonlinear Propagation of Sound in Layered Media, Time Domain Solutions for Focused Sound Beams, Focusing of Sound with an Ellipsoidal Mirror, and Modeling Finite Amplitude Propagation in Waveguides.

DTIC Science & Technology

1991-08-01

performed entirely in the time domain, solves the KZK (Khokhlov-Zabolotskaya-Kuznetsov) nonlinear parabolic wdve equation for pulsed, axisymmetric...finite amplitude sound beams. The KZK equation accounts for the combined effects of nonlinearity, diffraction and thermoviscous absorption on the...those used by Naze Tjotta, Tjotta, and Vefring to produce Fig. 7 of Ref. 4 with a frequency domain numerical solution of the KZK equation. However

Nonlinear aspects of acoustic radiation force in biomedical applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ostrovsky, Lev, E-mail: Lev.A.Ostrovsky@noaa.gov; Tsyuryupa, Sergey; Sarvazyan, Armen, E-mail: armen@artannlabs.com

In the past decade acoustic radiation force (ARF) became a powerful tool in numerous biomedical applications. ARF from a focused ultrasound beam acts as a virtual “finger” for remote probing of internal anatomical structures and obtaining diagnostic information. This presentation deals with generation of shear waves by nonlinear focused beams. Albeit the ARF has intrinsically nonlinear origin, in most cases the primary ultrasonic wave was considered in the linear approximation. In this presentation, we consider the effects of nonlinearly distorted beams on generation of shear waves by such beams.

Nonlinear aspects of acoustic radiation force in biomedical applications

NASA Astrophysics Data System (ADS)

Ostrovsky, Lev; Tsyuryupa, Sergey; Sarvazyan, Armen

2015-10-01

In the past decade acoustic radiation force (ARF) became a powerful tool in numerous biomedical applications. ARF from a focused ultrasound beam acts as a virtual "finger" for remote probing of internal anatomical structures and obtaining diagnostic information. This presentation deals with generation of shear waves by nonlinear focused beams. Albeit the ARF has intrinsically nonlinear origin, in most cases the primary ultrasonic wave was considered in the linear approximation. In this presentation, we consider the effects of nonlinearly distorted beams on generation of shear waves by such beams.

Solitons in a nonlinear model of spin transport in helical molecules

NASA Astrophysics Data System (ADS)

Albares, P.; Díaz, E.; Cerveró, Jose M.; Domínguez-Adame, F.; Diez, E.; Estévez, P. G.

2018-02-01

We study an effective integrable nonlinear model describing an electron moving along the axis of a deformable helical molecule. The helical conformation of dipoles in the molecular backbone induces an unconventional Rashba-like interaction that couples the electron spin with its linear momentum. In addition, a focusing nonlinearity arises from the electron-lattice interaction, enabling the formation of a variety of stable solitons such as bright solitons, breathers, and rogue waves. A thorough study of the soliton solutions for both focusing and defocusing nonlinear interaction is presented and discussed.

Nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating embedded in water

NASA Astrophysics Data System (ADS)

Jiménez, N.; Romero-García, V.; Picó, R.; Garcia-Raffi, L. M.; Staliunas, K.

2015-11-01

We report the nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating immersed in water. In the linear regime, the system presents high focal gain (32 dB), with a narrow beam-width and intense side lobes as it is common in focusing by Fresnel-like lenses. Activating the nonlinearity of the host medium by using high amplitude incident waves, the focusing properties of the lens dramatically change. Theoretical predictions show that the focal gain of the system extraordinary increases in the strongly nonlinear regime (Mach number of 6.1 × 10-4). Particularly, the harmonic generation is locally activated at the focal spot, and the second harmonic beam is characterized by strongly reduced side-lobes and an excellent beam profile as experiments show in agreement with theory. The results can motivate applications in medical therapy or second harmonic imaging.

Albert Einstein and the Quantum Riddle

ERIC Educational Resources Information Center

Lande, Alfred

1974-01-01

Derives a systematic structure contributing to the solution of the quantum riddle in Einstein's sense by deducing quantum mechanics from the postulates of symmetry, correspondence, and covariance. Indicates that the systematic presentation is in agreement with quantum mechanics established by Schroedinger, Born, and Heisenberg. (CC)

Rigid rotators. [deriving the time-independent energy states associated with rotational motions of the molecule

NASA Technical Reports Server (NTRS)

1976-01-01

The two-particle, steady-state Schroedinger equation is transformed to center of mass and internuclear distance vector coordinates, leading to the free particle wave equation for the kinetic energy motion of the molecule and a decoupled wave equation for a single particle of reduced mass moving in a spherical potential field. The latter describes the vibrational and rotational energy modes of the diatomic molecule. For fixed internuclear distance, this becomes the equation of rigid rotator motion. The classical partition function for the rotator is derived and compared with the quantum expression. Molecular symmetry effects are developed from the generalized Pauli principle that the steady-state wave function of any system of fundamental particles must be antisymmetric. Nuclear spin and spin quantum functions are introduced and ortho- and para-states of rotators, along with their degeneracies, are defined. Effects of nuclear spin on entropy are deduced. Next, rigid polyatomic rotators are considered and the partition function for this case is derived. The patterns of rotational energy levels for nonlinear molecules are discussed for the spherical symmetric top, for the prolate symmetric top, for the oblate symmetric top, and for the asymmetric top. Finally, the equilibrium energy and specific heat of rigid rotators are derived.

Measurement of nonlinear refractive index and ionization rates in air using a wavefront sensor.

PubMed

Schwarz, Jens; Rambo, Patrick; Kimmel, Mark; Atherton, Briggs

2012-04-09

A wavefront sensor has been used to measure the Kerr nonlinear focal shift of a high intensity ultrashort pulse beam in a focusing beam geometry while accounting for the effects of plasma-defocusing. It is shown that plasma-defocusing plays a major role in the nonlinear focusing dynamics and that measurements of Kerr nonlinearity and ionization are coupled. Furthermore, this coupled effect leads to a novel way that measures the laser ionization rates in air under atmospheric conditions as well as Kerr nonlinearity. The measured nonlinear index n₂ compares well with values found in the literature and the measured ionization rates could be successfully benchmarked to the model developed by Perelomov, Popov, and Terentev (PPT model) [Sov. Phys. JETP 50, 1393 (1966)].

Universality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schrödinger Equation

NASA Astrophysics Data System (ADS)

Tikan, Alexey; Billet, Cyril; El, Gennady; Tovbis, Alexander; Bertola, Marco; Sylvestre, Thibaut; Gustave, Francois; Randoux, Stephane; Genty, Goëry; Suret, Pierre; Dudley, John M.

2017-07-01

We report experimental confirmation of the universal emergence of the Peregrine soliton predicted to occur during pulse propagation in the semiclassical limit of the focusing nonlinear Schrödinger equation. Using an optical fiber based system, measurements of temporal focusing of high power pulses reveal both intensity and phase signatures of the Peregrine soliton during the initial nonlinear evolution stage. Experimental and numerical results are in very good agreement, and show that the universal mechanism that yields the Peregrine soliton structure is highly robust and can be observed over a broad range of parameters.

Post-filament self-trapping of ultrashort laser pulses.

PubMed

Mitrofanov, A V; Voronin, A A; Sidorov-Biryukov, D A; Andriukaitis, G; Flöry, T; Pugžlys, A; Fedotov, A B; Mikhailova, J M; Panchenko, V Ya; Baltuška, A; Zheltikov, A M

2014-08-15

Laser filamentation is understood to be self-channeling of intense ultrashort laser pulses achieved when the self-focusing because of the Kerr nonlinearity is balanced by ionization-induced defocusing. Here, we show that, right behind the ionized region of a laser filament, ultrashort laser pulses can couple into a much longer light channel, where a stable self-guiding spatial mode is sustained by the saturable self-focusing nonlinearity. In the limiting regime of negligibly low ionization, this post-filamentation beam dynamics converges to a large-scale beam self-trapping scenario known since the pioneering work on saturable self-focusing nonlinearities.

Dark-bright quadratic solitons with a focusing effective Kerr nonlinearity

NASA Astrophysics Data System (ADS)

Chen, Manna; Ping, Xiaorou; Liang, Guo; Guo, Qi; Lu, Daquan; Hu, Wei

2018-01-01

Dark solitons are traditionally considered to exist in defocusing Kerr nonlinearity media. We investigate dark quadratic solitons with a focusing effective Kerr nonlinearity and a sine-oscillatory nonlocal response. A nonlinear refractive index with a focusing sine-oscillatory response leads to a defocusing effect with a strong degree of nonlocality, which causes the formation of dark solitons. By analyzing the modulational instability, we determine the parameter domain for dark quadratic solitons with a stable background and numerically obtain dark-bright soliton solutions in the form of pairs, which avoid radiative phenomena. Based on a numerical simulation, we find that all dark-bright soliton pairs are unstable after a relatively long propagation distance, and their stabilities are affected by the soliton interval and the degree of nonlocality.

Analysis of radial and longitudinal force of plasma wakefield generated by a chirped pulse laser

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghasemi, Leila; Afhami, Saeedeh; Eslami, Esmaeil, E-mail: eeslami@iust.ac.ir

2015-08-15

In present paper, the chirp effect of an electromagnetic pulse via an analytical model of wakefield generation is studied. Different types of chirps are employed in this study. Our results show that by the use of nonlinear chirped pulse the longitudinal wakefield and focusing force is stronger than that of linear chirped pulse. It is indicated that quadratic nonlinear chirped pulses are globally much efficient than periodic nonlinear chirped pulses. Our calculations also predict that in nonlinear chirped pulse case, the overlap of focusing and accelerating regions is broader than that achieved in linear chirped pulse.

The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schroedinger equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leung Shingyu, E-mail: masyleung@ust.h; Qian Jianliang, E-mail: qian@math.msu.ed

2010-11-20

We propose the backward phase flow method to implement the Fourier-Bros-Iagolnitzer (FBI)-transform-based Eulerian Gaussian beam method for solving the Schroedinger equation in the semi-classical regime. The idea of Eulerian Gaussian beams has been first proposed in . In this paper we aim at two crucial computational issues of the Eulerian Gaussian beam method: how to carry out long-time beam propagation and how to compute beam ingredients rapidly in phase space. By virtue of the FBI transform, we address the first issue by introducing the reinitialization strategy into the Eulerian Gaussian beam framework. Essentially we reinitialize beam propagation by applying themore » FBI transform to wavefields at intermediate time steps when the beams become too wide. To address the second issue, inspired by the original phase flow method, we propose the backward phase flow method which allows us to compute beam ingredients rapidly. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithms.« less

Soliton-plasma nonlinear dynamics in mid-IR gas-filled hollow-core fibers.

PubMed

Selim Habib, Md; Markos, Christos; Bang, Ole; Bache, Morten

2017-06-01

We investigate numerically soliton-plasma interaction in a noble-gas-filled silica hollow-core anti-resonant fiber pumped in the mid-IR at 3.0 μm. We observe multiple soliton self-compression stages due to distinct stages where either the self-focusing or the self-defocusing nonlinearity dominates. Specifically, the parameters may be tuned so the competing plasma self-defocusing nonlinearity only dominates over the Kerr self-focusing nonlinearity around the soliton self-compression stage, where the increasing peak intensity on the leading pulse edge initiates a competing self-defocusing plasma nonlinearity acting nonlocally on the trailing edge, effectively preventing soliton formation there. As the plasma switches off after the self-compression stage, self-focusing dominates again, initiating another soliton self-compression stage in the trailing edge. This process is accompanied by supercontinuum generation spanning 1-4 μm. We find that the spectral coherence drops as the secondary compression stage is initiated.

Numerical simulation and comparison of nonlinear self-focusing based on iteration and ray tracing

NASA Astrophysics Data System (ADS)

Li, Xiaotong; Chen, Hao; Wang, Weiwei; Ruan, Wangchao; Zhang, Luwei; Cen, Zhaofeng

2017-05-01

Self-focusing is observed in nonlinear materials owing to the interaction between laser and matter when laser beam propagates. Some of numerical simulation strategies such as the beam propagation method (BPM) based on nonlinear Schrödinger equation and ray tracing method based on Fermat's principle have applied to simulate the self-focusing process. In this paper we present an iteration nonlinear ray tracing method in that the nonlinear material is also cut into massive slices just like the existing approaches, but instead of paraxial approximation and split-step Fourier transform, a large quantity of sampled real rays are traced step by step through the system with changing refractive index and laser intensity by iteration. In this process a smooth treatment is employed to generate a laser density distribution at each slice to decrease the error caused by the under-sampling. The characteristics of this method is that the nonlinear refractive indices of the points on current slice are calculated by iteration so as to solve the problem of unknown parameters in the material caused by the causal relationship between laser intensity and nonlinear refractive index. Compared with the beam propagation method, this algorithm is more suitable for engineering application with lower time complexity, and has the calculation capacity for numerical simulation of self-focusing process in the systems including both of linear and nonlinear optical media. If the sampled rays are traced with their complex amplitudes and light paths or phases, it will be possible to simulate the superposition effects of different beam. At the end of the paper, the advantages and disadvantages of this algorithm are discussed.

Mathematical Tools for Image Reconstruction

DTIC Science & Technology

1991-07-01

l.Diffuse tomography 2.Concentrating a signal in the physical and spectral domains. 3.New explicit solutions for the Kadomtsev - Petviashvili equation 4...the case of the Schroedinger equation it was possible to "beat Heisenberg" with piecewise linear potentials. Finally let me say that the paper Some

Nonlinear absorption in biological tissue for high intensity focused ultrasound.

PubMed

Liu, Xiaozhou; Li, Junlun; Gong, Xiufen; Zhang, Dong

2006-12-22

In recent years the propagation of the high intensity focused ultrasound (HIFU) in biological tissue is an interesting area due to its potential applications in non-invasive treatment of disease. The base principle of these applications is the heat effect generated by ultrasound absorption. In order to control therapeutic efficiency, it is important to evaluate the heat generation in biological tissue irradiated by ultrasound. In his paper, based on the Khokhlov-Zabolotkaya-Kuznetsov (KZK) equation in frequency-domain, the numerical simulations of nonlinear absorption in biological tissues for high intensity focused ultrasound are performed. We find that ultrasound thermal transfer effect will be enhanced with the increasing of initial acoustic intensity due to the high harmonic generation. The concept of extra absorption factor is introduced to describe nonlinear absorption in biological tissue for HIFU. The theoretical results show that the heat deposition induced by the nonlinear theory can be nearly two times as large as that predicated by linear theory. Then, the influence of the diffraction effect on the position of the focus in HIFU is investigated. It is shown that the sound focus moves toward the transducer compared with the geometry focus because of the diffraction of the sound wave. The position of the maximum heat deposition is shifted to the geometry focus with the increase of initial acoustic intensity because the high harmonics are less diffraction. Finally, the temperature in the porcine fat tissue changing with the time is predicated by Pennes' equation and the experimental results verify the nonlinear theoretical prediction.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lipkin, H.J.

Overwhelming experimental evidence for quarks as real physical constituents of hadrons along with the QCD analogs of the Balmer Formula, Bohr Atom and Schroedinger Equation already existed in 1966 but was dismissed as heresy. ZGS experiments played an important role in the quark revolution. This role is briefly reviewed and subsequent progress in quark physics is described.

Critical power for self-focusing of optical beam in absorbing media

NASA Astrophysics Data System (ADS)

Qi, Pengfei; Zhang, Lin; Lin, Lie; Zhang, Nan; Wang, Yan; Liu, Weiwei

2018-04-01

Self-focusing effects are of central importance for most nonlinear optical effects. The critical power for self-focusing is commonly investigated theoretically without considering a material’s absorption. Although this is practicable for various materials, investigating the critical power for self-focusing in media with non-negligible absorption is also necessary, because this is the situation usually met in practice. In this paper, the simple analytical expressions describing the relationships among incident power, absorption coefficient and focal position are provided by a simple physical model based on the Fermat principle. Expressions for the absorption dependent critical power are also derived; these can play important roles in experimental and applied research on self-focusing-related nonlinear optical phenomena in absorbing media. Numerical results, based on the nonlinear wave equation—and which can predict experimental results perfectly—are also presented, and agree quantitatively with the analytical results proposed in this paper.

Dam break problem for the focusing nonlinear Schrödinger equation and the generation of rogue waves

NASA Astrophysics Data System (ADS)

El, G. A.; Khamis, E. G.; Tovbis, A.

2016-09-01

We propose a novel, analytically tractable, scenario of the rogue wave formation in the framework of the small-dispersion focusing nonlinear Schrödinger (NLS) equation with the initial condition in the form of a rectangular barrier (a ‘box’). We use the Whitham modulation theory combined with the nonlinear steepest descent for the semi-classical inverse scattering transform, to describe the evolution and interaction of two counter-propagating nonlinear wave trains—the dispersive dam break flows—generated in the NLS box problem. We show that the interaction dynamics results in the emergence of modulated large-amplitude quasi-periodic breather lattices whose amplitude profiles are closely approximated by the Akhmediev and Peregrine breathers within certain space-time domain. Our semi-classical analytical results are shown to be in excellent agreement with the results of direct numerical simulations of the small-dispersion focusing NLS equation.

Subdiffraction focusing of scanning beams by a negative-refraction layer combined with a nonlinear layer.

PubMed

Husakou, A; Herrmann, J

2006-11-13

We evaluate the possibility to focus scanning light beams below the diffraction limit by using the combination of a nonlinear material with a Kerr-type nonlinearity or two-photon absorption to create seed evanescent components of the beam and a negative-refraction material to enhance them. Superfocusing to spots with a FWHM in the range of 0.2 lambda is theoretically predicted both in the context of the effective-medium theory and by the direct numerical solution of Maxwell equations for an inhomogeneous pho-tonic crystal. The evolution of the transverse spectrum and the dependence of superfocusing on the parameters of the negative-refraction material are also studied. We show that the use of a Kerr-type nonlinear layer for the creation of seed evanescent components yields focused spots with a higher intensity compared with those obtained by the application of a saturable absorber.

Terahertz generation by relativistic ponderomotive focusing of two co-axial Gaussian laser beams propagating in ripple density plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kumar, Subodh; Singh, Ram Kishor, E-mail: ram007kishor@gmail.com; Sharma, R. P.

Terahertz (THz) generation by beating of two co-axial Gaussian laser beams, propagating in ripple density plasma, has been studied when both ponderomotive and relativistic nonlinearities are operative. When the two lasers co-propagate in rippled density plasma, electrons acquire a nonlinear velocity at beat frequency in the direction transverse to the direction of propagation. This nonlinear oscillatory velocity couples with the density ripple to generate a nonlinear current, which in turn generates THz radiation at the difference frequency. The necessary phase matching condition is provided by the density ripple. Relativistic ponderomotive focusing of the two lasers and its effects on yieldmore » of the generated THz amplitude have been discussed. Numerical results show that conversion efficiency of the order of 10{sup −3} can be achieved in the terahertz radiation generation with relativistic ponderomotive focusing.« less

Nonlinear propagation of phase-conjugate focused sound beams in water

NASA Astrophysics Data System (ADS)

Brysev, A. P.; Krutyansky, L. M.; Preobrazhensky, V. L.; Pyl'nov, Yu. V.; Cunningham, K. B.; Hamilton, M. F.

2000-07-01

Nonlinear propagation of phase-conjugate, focused, ultrasound beams is studied. Measurements are presented of harmonic amplitudes along the axis and in the focal plane of the conjugate beam, and of the waveform and spectrum at the focus. A maximum peak pressure of 3.9 MPa was recorded in the conjugate beam. The measurements are compared with simulations based on the KZK equation, and satisfactory agreement is obtained.

Molecular orientation sensitive second harmonic microscopy by radially and azimuthally polarized light

PubMed Central

Ehmke, Tobias; Nitzsche, Tim Heiko; Knebl, Andreas; Heisterkamp, Alexander

2014-01-01

We demonstrate the possibility to switch the z-polarization component of the illumination in the vicinity of the focus of high-NA objective lenses by applying radially and azimuthally polarized incident light. The influence of the field distribution on nonlinear effects was first investigated by the means of simulations. These were performed for high-NA objective lenses commonly used in nonlinear microscopy. Special attention is paid to the influence of the polarization of the incoming field. For linearly, circularly and radially polarized light a considerable polarization component in z-direction is generated by high NA focusing. Azimuthal polarization is an exceptional case: even for strong focusing no z-component arises. Furthermore, the influence of the input polarization on the intensity contributing to the nonlinear signal generation was computed. No distinct difference between comparable input polarization states was found for chosen thresholds of nonlinear signal generation. Differences in signal generation for radially and azimuthally polarized vortex beams were experimentally evaluated in native collagen tissue (porcine cornea). The findings are in good agreement with the theoretical predictions and display the possibility to probe the molecular orientation along the optical axis of samples with known nonlinear properties. The combination of simulations regarding the nonlinear response of materials and experiments with different sample orientations and present or non present z-polarization could help to increase the understanding of nonlinear signal formation in yet unstudied materials. PMID:25071961

Propagation of intense short laser pulses in the atmosphere.

PubMed

Sprangle, P; Peñano, J R; Hafizi, B

2002-10-01

The propagation of short, intense laser pulses in the atmosphere is investigated theoretically and numerically. A set of three-dimensional (3D), nonlinear propagation equations is derived, which includes the effects of dispersion, nonlinear self-focusing, stimulated molecular Raman scattering, multiphoton and tunneling ionization, energy depletion due to ionization, relativistic focusing, and ponderomotively excited plasma wakefields. The instantaneous frequency spread along a laser pulse in air, which develops due to various nonlinear effects, is analyzed and discussed. Coupled equations for the power, spot size, and electron density are derived for an intense ionizing laser pulse. From these equations we obtain an equilibrium for a single optical-plasma filament, which involves a balancing between diffraction, nonlinear self-focusing, and plasma defocusing. The equilibrium is shown to require a specific distribution of power along the filament. It is found that in the presence of ionization a self-guided optical filament is not realizable. A method for generating a remote spark in the atmosphere is proposed, which utilizes the dispersive and nonlinear properties of air to cause a low-intensity chirped laser pulse to compress both longitudinally and transversely. For optimally chosen parameters, we find that the transverse and longitudinal focal lengths can be made to coincide, resulting in rapid intensity increase, ionization, and white light generation in a localized region far from the source. Coupled equations for the laser spot size and pulse duration are derived, which can describe the focusing and compression process in the low-intensity regime. More general examples involving beam focusing, compression, ionization, and white light generation near the focal region are studied by numerically solving the full set of 3D, nonlinear propagation equations.

Hidden algebra method (quasi-exact-solvability in quantum mechanics)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Turbiner, Alexander; Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apartado, Postal 70-543, 04510 Mexico, D. F.

1996-02-20

A general introduction to quasi-exactly-solvable problems of quantum mechanics is presented. Main attention is given to multidimensional quasi-exactly-solvable and exactly-solvable Schroedinger operators. Exact-solvability of the Calogero and Sutherland N-body problems ass ociated with an existence of the hidden algebra slN is discussed extensively.

The "Hard Problem" and the Quantum Physicists. Part 1: The First Generation

ERIC Educational Resources Information Center

Smith, C. U. M.

2006-01-01

All four of the most important figures in the early twentieth-century development of quantum physics--Niels Bohr, Erwin Schroedinger, Werner Heisenberg and Wolfgang Pauli--had strong interests in the traditional mind--brain, or "hard," problem. This paper reviews their approach to this problem, showing the influence of Bohr's complementarity…

How Accurately Does the Free Complement Wave Function of a Helium Atom Satisfy the Schroedinger Equation?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakashima, Hiroyuki; Nakatsuji, Hiroshi

2008-12-12

The local energy defined by H{psi}/{psi} must be equal to the exact energy E at any coordinate of an atom or molecule, as long as the {psi} under consideration is exact. The discrepancy from E of this quantity is a stringent test of the accuracy of the calculated wave function. The H-square error for a normalized {psi}, defined by {sigma}{sup 2}{identical_to}<{psi}|(H-E){sup 2}|{psi}>, is also a severe test of the accuracy. Using these quantities, we have examined the accuracy of our wave function of a helium atom calculated using the free complement method that was developed to solve the Schroedinger equation.more » Together with the variational upper bound, the lower bound of the exact energy calculated using a modified Temple's formula ensured the definitely correct value of the helium fixed-nucleus ground state energy to be -2.903 724 377 034 119 598 311 159 245 194 4 a.u., which is correct to 32 digits.« less

A full vectorial generalized discontinuous Galerkin beam propagation method (GDG-BPM) for nonsmooth electromagnetic fields in waveguides

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fan Kai; Cai Wei; Ji Xia

2008-07-20

In this paper, we propose a new full vectorial generalized discontinuous Galerkin beam propagation method (GDG-BPM) to accurately handle the discontinuities in electromagnetic fields associated with wave propagations in inhomogeneous optical waveguides. The numerical method is a combination of the traditional beam propagation method (BPM) with a newly developed generalized discontinuous Galerkin (GDG) method [K. Fan, W. Cai, X. Ji, A generalized discontinuous Galerkin method (GDG) for Schroedinger equations with nonsmooth solutions, J. Comput. Phys. 227 (2008) 2387-2410]. The GDG method is based on a reformulation, using distributional variables to account for solution jumps across material interfaces, of Schroedinger equationsmore » resulting from paraxial approximations of vector Helmholtz equations. Four versions of the GDG-BPM are obtained for either the electric or magnetic field components. Modeling of wave propagations in various optical fibers using the full vectorial GDG-BPM is included. Numerical results validate the high order accuracy and the flexibility of the method for various types of interface jump conditions.« less

Schroedinger's immortal cat

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peres, A.

1988-01-01

The purpose of this paper is to review and clarify the quantum measurement problem. The latter originates in the ambivalent nature of the observer: Although the observer is not described by the Schroedinger equation, it should nevertheless be possible to quantize him and include him in the wave function if quantum theory is universally valid. The problem is to prove that no contradiction may arise in these two conflicting descriptions. The proof invokes the notion of irreversibility. The validity of the latter is questionable, because the standard rationale for classical irreversibility, namely mixing and coarse graining, does not apply tomore » quantum theory. There is no chaos in a closed, finite quantum system. However, when a system is large enough, it cannot be perfectly isolated from it environment, namely from external (or even internal) degrees of freedom which are not fully accounted for in the Hamiltonian of that system. As a consequence, the long-range evolution of such a quantum system is essentially unpredictable. It follows that the notion of irreversibility is a valid one in quantum theory and the measurement problem can be brought to a satisfactory solution.« less

Niels Bohr's discussions with Albert Einstein, Werner Heisenberg, and Erwin Schroedinger: the origins of the principles of uncertainty and complementarity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mehra, J.

1987-05-01

In this paper, the main outlines of the discussions between Niels Bohr with Albert Einstein, Werner Heisenberg, and Erwin Schroedinger during 1920-1927 are treated. From the formulation of quantum mechanics in 1925-1926 and wave mechanics in 1926, there emerged Born's statistical interpretation of the wave function in summer 1926, and on the basis of the quantum mechanical transformation theory - formulated in fall 1926 by Dirac, London, and Jordan - Heisenberg formulated the uncertainty principle in early 1927. At the Volta Conference in Como in September 1927 and at the fifth Solvay Conference in Brussels the following month, Bohr publiclymore » enunciated his complementarity principle, which had been developing in his mind for several years. The Bohr-Einstein discussions about the consistency and completeness of quantum mechanics and of physical theory as such - formally begun in October 1927 at the fifth Solvay Conference and carried on at the sixth Solvay Conference in October 1930 - were continued during the next decades. All these aspects are briefly summarized.« less

Generalized Nonlinear Chirp Scaling Algorithm for High-Resolution Highly Squint SAR Imaging.

PubMed

Yi, Tianzhu; He, Zhihua; He, Feng; Dong, Zhen; Wu, Manqing

2017-11-07

This paper presents a modified approach for high-resolution, highly squint synthetic aperture radar (SAR) data processing. Several nonlinear chirp scaling (NLCS) algorithms have been proposed to solve the azimuth variance of the frequency modulation rates that are caused by the linear range walk correction (LRWC). However, the azimuth depth of focusing (ADOF) is not handled well by these algorithms. The generalized nonlinear chirp scaling (GNLCS) algorithm that is proposed in this paper uses the method of series reverse (MSR) to improve the ADOF and focusing precision. It also introduces a high order processing kernel to avoid the range block processing. Simulation results show that the GNLCS algorithm can enlarge the ADOF and focusing precision for high-resolution highly squint SAR data.

Introduction to Focus Issue: nonlinear and stochastic physics in biology.

PubMed

Bahar, Sonya; Neiman, Alexander B; Jung, Peter; Kurths, Jürgen; Schimansky-Geier, Lutz; Showalter, Kenneth

2011-12-01

Frank Moss was a leading figure in the study of nonlinear and stochastic processes in biological systems. His work, particularly in the area of stochastic resonance, has been highly influential to the interdisciplinary scientific community. This Focus Issue pays tribute to Moss with articles that describe the most recent advances in the field he helped to create. In this Introduction, we review Moss's seminal scientific contributions and introduce the articles that make up this Focus Issue.

A novel design for maskless direct laser writing nanolithography: Combination of diffractive optical element and nonlinear absorption inorganic resists

NASA Astrophysics Data System (ADS)

Zha, Yikun; Wei, Jingsong; Gan, Fuxi

2013-09-01

Maskless laser direct writing lithography has been applied in the fabrication of optical elements and electric-optical devices. With the development of technology, the feature size of the elements and devices is required to reduce down to nanoscale. Increasing the numerical aperture of converging lens and shortening the laser wavelength are good methods to obtain the small spot and reduce the feature size to nanoscale, while this will cause the reduction of the depth of focus. The reduction of depth of focus will lead to some difficulties in the focusing and tracking servo controlling during the high speed laser direct writing lithography. In this work, the combination of the diffractive optical elements and the nonlinear absorption inorganic resist thin films cannot only extend the depth of focus, but also reduce the feature size of the lithographic marks down to nanoscale. By using the five-zone annular phase-only binary pupil filter as the diffractive optical elements and AgInSbTe as the nonlinear absorption inorganic resist thin film, the depth of focus cannot only extend to 7.39 times that of the focused spot, but also reduce the lithographic feature size down to 54.6 nm. The ill-effect of sidelobe on the lithography is also eliminated by the nonlinear reverse saturable absorption and the phase change threshold lithographic characteristics.

Effect of marine derived deoxyribonucleic acid on nonlinear optical properties of PicoGreen dye

NASA Astrophysics Data System (ADS)

Pradeep, C.; Mathew, S.; Nithyaja, B.; Radhakrishnan, P.; Nampoori, V. P. N.

2013-06-01

We have investigated the effect of DNA on nonlinear absorption of PicoGreen dye using single beam open aperture Z-scan technique in nanosecond regime. We observed reverse saturable absorption at 532 nm for PicoGreen without DNA. In the presence of DNA, the sample begins to behave like saturable absorbers and this effect increased as the concentration of DNA was increased. The dye-intercalated DNA showed SA characteristics near the focus but exhibited RSA characteristics at the focus. Theoretical analysis has been performed using a two-photon absorption model based on nonlinear absorption coefficient and saturation intensity. Such tailoring of optical nonlinear absorption in PicoGreen makes it a potential candidate for photonic application.

Numerical Simulation of Focused Shock Shear Waves in Soft Solids and a Two-Dimensional Nonlinear Homogeneous Model of the Brain

PubMed Central

Giammarinaro, B.; Coulouvrat, F.; Pinton, G.

2016-01-01

Shear waves that propagate in soft solids, such as the brain, are strongly nonlinear and can develop into shock waves in less than one wavelength. We hypothesize that these shear shock waves could be responsible for certain types of traumatic brain injuries (TBI) and that the spherical geometry of the skull bone could focus shear waves deep in the brain, generating diffuse axonal injuries. Theoretical models and numerical methods that describe nonlinear polarized shear waves in soft solids such as the brain are presented. They include the cubic nonlinearities that are characteristic of soft solids and the specific types of nonclassical attenuation and dispersion observed in soft tissues and the brain. The numerical methods are validated with analytical solutions, where possible, and with self-similar scaling laws where no known solutions exist. Initial conditions based on a human head X-ray microtomography (CT) were used to simulate focused shear shock waves in the brain. Three regimes are investigated with shock wave formation distances of 2.54 m, 0.018 m, and 0.0064 m. We demonstrate that under realistic loading scenarios, with nonlinear properties consistent with measurements in the brain, and when the shock wave propagation distance and focal distance coincide, nonlinear propagation can easily overcome attenuation to generate shear shocks deep inside the brain. Due to these effects, the accelerations in the focal are larger by a factor of 15 compared to acceleration at the skull surface. These results suggest that shock wave focusing could be responsible for diffuse axonal injuries. PMID:26833489

Suppression of Space Charge Induced Beam Halo in Nonlinear Focusing Channel

DOE PAGES

Batygin, Yuri Konstantinovich; Scheinker, Alexander; Kurennoy, Sergey; ...

2016-01-29

An intense non-uniform particle beam exhibits strong emittance growth and halo formation in focusing channels due to nonlinear space charge forces of the beam. This phenomenon limits beam brightness and results in particle losses. The problem is connected with irreversible distortion of phase space volume of the beam in conventional focusing structures due to filamentation in phase space. Emittance growth is accompanied by halo formation in real space, which results in inevitable particle losses. We discuss a new approach for solving a self-consistent problem for a matched non-uniform beam in two-dimensional geometry. The resulting solution is applied to the problemmore » of beam transport, while avoiding emittance growth and halo formation by the use of nonlinear focusing field. Conservation of a beam distribution function is demonstrated analytically and by particle-in-cell simulation for a beam with a realistic beam distribution.« less

Problems in Nonlinear Acoustics: Parametric Receiving Arrays, Focused Finite Amplitude Sound, & Noncollinear Tone-Noise Interactions

DTIC Science & Technology

1987-07-01

fields (see also Chapter 4 of Ref. 22). Like our investigation, theirs is based on the Khokhlov-Zabolotskaya-Kuznetsov ( KZK ) equa- tion [23,24...25,26], also based on the KZK e(iualiou, is limited to weakly nonlinear systems. However, the practical case of a focused circular source with gain of...iment. The demonstrated abihty of the KZK equation to accurately model focused sound fields from reahstic sources [i.e., having abrupt edges and

On the theory of self-focusing of powerful wave beams in nonhomogeneous media

NASA Technical Reports Server (NTRS)

Yerokhin, N. S.; Fadeyev, A. P.

1983-01-01

The stationary self-focusing of the Gauss wave beam is considered in a nonhomogeneous medium in the case of local nonlinearity. Equations of the aberrationless approximation for the beam width, the field on the beam axis and the refraction factor are integrated on a computer. Self-focusing in dependence of the nonlinearity level and initial divergence, the dissipation, the length of nonhomogeneity of the dielectric permittivity nondisturbed by a beam, and the diffraction parameter are investigated.

Focusing of Shear Shock Waves

NASA Astrophysics Data System (ADS)

Giammarinaro, Bruno; Espíndola, David; Coulouvrat, François; Pinton, Gianmarco

2018-01-01

Focusing is a ubiquitous way to transform waves. Recently, a new type of shock wave has been observed experimentally with high-frame-rate ultrasound: shear shock waves in soft solids. These strongly nonlinear waves are characterized by a high Mach number, because the shear wave velocity is much slower, by 3 orders of magnitude, than the longitudinal wave velocity. Furthermore, these waves have a unique cubic nonlinearity which generates only odd harmonics. Unlike longitudinal waves for which only compressional shocks are possible, shear waves exhibit cubic nonlinearities which can generate positive and negative shocks. Here we present the experimental observation of shear shock wave focusing, generated by the vertical motion of a solid cylinder section embedded in a soft gelatin-graphite phantom to induce linearly vertically polarized motion. Raw ultrasound data from high-frame-rate (7692 images per second) acquisitions in combination with algorithms that are tuned to detect small displacements (approximately 1 μ m ) are used to generate quantitative movies of gel motion. The features of shear shock wave focusing are analyzed by comparing experimental observations with numerical simulations of a retarded-time elastodynamic equation with cubic nonlinearities and empirical attenuation laws for soft solids.

Second harmonic generation by self-focusing of intense hollow Gaussian laser beam in collisionless plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Purohit, Gunjan, E-mail: gunjan75@gmail.com; Rawat, Priyanka; Gauniyal, Rakhi

2016-01-15

The effect of self focused hollow Gaussian laser beam (HGLB) (carrying null intensity in center) on the excitation of electron plasma wave (EPW) and second harmonic generation (SHG) has been investigated in collisionless plasma, where relativistic-ponderomotive and only relativistic nonlinearities are operative. The relativistic change of electron mass and the modification of the background electron density due to ponderomotive nonlinearity lead to self-focusing of HGLB in plasma. Paraxial ray theory has been used to derive coupled equations for the self focusing of HGLB in plasma, generation of EPW, and second harmonic. These coupled equations are solved analytically and numerically tomore » study the laser intensity in the plasma, electric field associated with the excited EPW, and the power of SHG. Second harmonic emission is generated due to nonlinear coupling between incident HGLB and EPW satisfying the proper phase matching conditions. The results show that the effect of including the ponderomotive nonlinearity is significant on the generation of EPW and second harmonic. The electric field associated with EPW and the power of SHG are found to be highly sensitive to the order of the hollow Gaussian beam.« less

Semiclassical limit of the focusing NLS: Whitham equations and the Riemann-Hilbert Problem approach

NASA Astrophysics Data System (ADS)

Tovbis, Alexander; El, Gennady A.

2016-10-01

The main goal of this paper is to put together: a) the Whitham theory applicable to slowly modulated N-phase nonlinear wave solutions to the focusing nonlinear Schrödinger (fNLS) equation, and b) the Riemann-Hilbert Problem approach to particular solutions of the fNLS in the semiclassical (small dispersion) limit that develop slowly modulated N-phase nonlinear wave in the process of evolution. Both approaches have their own merits and limitations. Understanding of the interrelations between them could prove beneficial for a broad range of problems involving the semiclassical fNLS.

Self-focusing and defocusing of Gaussian laser beams in collisional inhomogeneous plasmas with linear density and temperature ramps

NASA Astrophysics Data System (ADS)

Hashemzadeh, M.

2018-01-01

Self-focusing and defocusing of Gaussian laser beams in collisional inhomogeneous plasmas are investigated in the presence of various laser intensities and linear density and temperature ramps. Considering the ponderomotive force and using the momentum transfer and energy equations, the nonlinear electron density is derived. Taking into account the paraxial approximation and nonlinear electron density, a nonlinear differential equation, governing the focusing and defocusing of the laser beam, is obtained. Results show that in the absence of ramps the laser beam is focused between a minimum and a maximum value of laser intensity. For a certain value of laser intensity and initial electron density, the self-focusing process occurs in a temperature range which reaches its maximum at turning point temperature. However, the laser beam is converged in a narrow range for various amounts of initial electron density. It is indicated that the σ2 parameter and its sign can affect the self-focusing process for different values of laser intensity, initial temperature, and initial density. Finally, it is found that although the electron density ramp-down diverges the laser beam, electron density ramp-up improves the self-focusing process.

Generalized Nonlinear Chirp Scaling Algorithm for High-Resolution Highly Squint SAR Imaging

PubMed Central

He, Zhihua; He, Feng; Dong, Zhen; Wu, Manqing

2017-01-01

This paper presents a modified approach for high-resolution, highly squint synthetic aperture radar (SAR) data processing. Several nonlinear chirp scaling (NLCS) algorithms have been proposed to solve the azimuth variance of the frequency modulation rates that are caused by the linear range walk correction (LRWC). However, the azimuth depth of focusing (ADOF) is not handled well by these algorithms. The generalized nonlinear chirp scaling (GNLCS) algorithm that is proposed in this paper uses the method of series reverse (MSR) to improve the ADOF and focusing precision. It also introduces a high order processing kernel to avoid the range block processing. Simulation results show that the GNLCS algorithm can enlarge the ADOF and focusing precision for high-resolution highly squint SAR data. PMID:29112151

Interactions of nonlocal dark solitons under competing cubic-quintic nonlinearities.

PubMed

Chen, Wei; Shen, Ming; Kong, Qian; Shi, Jielong; Wang, Qi; Krolikowski, Wieslaw

2014-04-01

We investigate analytically and numerically the interactions of dark solitons under competing nonlocal cubic and local quintic nonlinearities. It is shown that the self-defocusing quintic nonlinearity will strengthen the attractive interaction and decrease the relative distance between solitons, whereas the self-focusing quintic nonlinearity will enhance the repulsive interaction and increase soliton separation. We demonstrate these results by approximate variational approach and direct numerical simulation.

Laser damage metrology in biaxial nonlinear crystals using different test beams

NASA Astrophysics Data System (ADS)

Hildenbrand, Anne; Wagner, Frank R.; Akhouayri, Hassan; Natoli, Jean-Yves; Commandre, Mireille

2008-01-01

Laser damage measurements in nonlinear optical crystals, in particular in biaxial crystals, may be influenced by several effects proper to these materials or greatly enhanced in these materials. Before discussion of these effects, we address the topic of error bar determination for probability measurements. Error bars for the damage probabilities are important because nonlinear crystals are often small and expensive, thus only few sites are used for a single damage probability measurement. We present the mathematical basics and a flow diagram for the numerical calculation of error bars for probability measurements that correspond to a chosen confidence level. Effects that possibly modify the maximum intensity in a biaxial nonlinear crystal are: focusing aberration, walk-off and self-focusing. Depending on focusing conditions, propagation direction, polarization of the light and the position of the focus point in the crystal, strong aberrations may change the beam profile and drastically decrease the maximum intensity in the crystal. A correction factor for this effect is proposed, but quantitative corrections are not possible without taking into account the experimental beam profile after the focusing lens. The characteristics of walk-off and self-focusing have quickly been reviewed for the sake of completeness of this article. Finally, parasitic second harmonic generation may influence the laser damage behavior of crystals. The important point for laser damage measurements is that the amount of externally observed SHG after the crystal does not correspond to the maximum amount of second harmonic light inside the crystal.

Second harmonic generation of q-Gaussian laser beam in preformed collisional plasma channel with nonlinear absorption

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gupta, Naveen, E-mail: naveens222@rediffmail.com; Singh, Arvinder, E-mail: arvinder6@lycos.com; Singh, Navpreet, E-mail: navpreet.nit@gmail.com

2015-11-15

This paper presents a scheme for second harmonic generation of an intense q-Gaussian laser beam in a preformed parabolic plasma channel, where collisional nonlinearity is operative with nonlinear absorption. Due to nonuniform irradiance of intensity along the wavefront of the laser beam, nonuniform Ohmic heating of plasma electrons takes place. Due to this nonuniform heating of plasma, the laser beam gets self-focused and produces strong density gradients in the transverse direction. The generated density gradients excite an electron plasma wave at pump frequency that interacts with the pump beam to produce its second harmonics. The formulation is based on amore » numerical solution of the nonlinear Schrodinger wave equation in WKB approximation followed by moment theory approach. A second order nonlinear differential equation governing the propagation dynamics of the laser beam with distance of propagation has been obtained and is solved numerically by Runge Kutta fourth order technique. The effect of nonlinear absorption on self-focusing of the laser beam and conversion efficiency of its second harmonics has been investigated.« less

Maximal amplitudes of finite-gap solutions for the focusing Nonlinear Schrödinger Equation

NASA Astrophysics Data System (ADS)

Bertola, M.; Tovbis, A.

2017-09-01

Finite-gap (algebro-geometric) solutions to the focusing Nonlinear Schrödinger Equation (fNLS) i ψ_t + ψ_{xx} + 2|ψ|^2ψ=0, are quasi-periodic solutions that represent nonlinear multi-phase waves. In general, a finite-gap solution for (0-1) is defined by a collection of Schwarz symmetrical spectral bands and of real constants (initial phases), associated with the corresponding bands. In this paper we prove an interesting new formula for the maximal amplitude of a finite-gap solution to the focusing Nonlinear Schrödinger equation with given spectral bands: the amplitude does not exceed the sum of the imaginary parts of all the endpoints in the upper half plane. In the case of the straight vertical bands, that amounts to the half of the sum of the length of all the bands. The maximal amplitude will be attained for certain choices of the initial phases. This result is an important part of a criterion for the potential presence of the rogue waves in finite-gap solutions with a given set of spectral endpoints, obtained in Bertola et al. (Proc R Soc A, 2016. doi: 10.1098/rspa.2016.0340). A similar result was also obtained for the defocusing Nonlinear Schrödinger equation.

Effect of nonlinearity on lesion formation for high-intensity focused ultrasound (HIFU) exposures

NASA Astrophysics Data System (ADS)

Lee, Paul; Lizzi, Frederic L.; Ketterling, Jeffrey A.; Vecchio, Christopher J.

2004-05-01

This study examined the effects of nonlinear propagation phenomena on two types of HIFU transducers (5 MHz) being used for thermal treatments of disease. The first transducer is a 5-element annular array. The second is a transducer with a 5-strip electrode; its multilobed focused beam is designed to efficiently produce broad, paddle-shaped lesions. The beam patterns of these transducers were computed using a variety of excitation patterns for electronic focusing of the annular array and variation of lesion size for the strip-electrode transducer. A range of intensities was studied to determine how nonlinear propagation affects the beam shape, constituent frequency content, grating lobes, etc. These 3D computations used a finite-amplitude beam propagation model that combined the angular spectrum method and Burger's equation to compute the diffraction and nonlinear effects, respectively. Computed beam patterns were compared with hydrophone measurements for each transducer. The linear and nonlinear beam patterns were used to compute the absorbed thermal dose, and the bioheat equation was evaluated to calculate 3D temperature rises and geometry of induced lesions. Computed lesion sizes and shapes were compared to in vitro lesions created by each HIFU transducer. [Work supported by NCI and NHLBI Grant 5R01 CA84588.

Generation and control of sound bullets with a nonlinear acoustic lens.

PubMed

Spadoni, Alessandro; Daraio, Chiara

2010-04-20

Acoustic lenses are employed in a variety of applications, from biomedical imaging and surgery to defense systems and damage detection in materials. Focused acoustic signals, for example, enable ultrasonic transducers to image the interior of the human body. Currently however the performance of acoustic devices is limited by their linear operational envelope, which implies relatively inaccurate focusing and low focal power. Here we show a dramatic focusing effect and the generation of compact acoustic pulses (sound bullets) in solid and fluid media, with energies orders of magnitude greater than previously achievable. This focusing is made possible by a tunable, nonlinear acoustic lens, which consists of ordered arrays of granular chains. The amplitude, size, and location of the sound bullets can be controlled by varying the static precompression of the chains. Theory and numerical simulations demonstrate the focusing effect, and photoelasticity experiments corroborate it. Our nonlinear lens permits a qualitatively new way of generating high-energy acoustic pulses, which may improve imaging capabilities through increased accuracy and signal-to-noise ratios and may lead to more effective nonintrusive scalpels, for example, for cancer treatment.

Generation and control of sound bullets with a nonlinear acoustic lens

PubMed Central

Spadoni, Alessandro; Daraio, Chiara

2010-01-01

Acoustic lenses are employed in a variety of applications, from biomedical imaging and surgery to defense systems and damage detection in materials. Focused acoustic signals, for example, enable ultrasonic transducers to image the interior of the human body. Currently however the performance of acoustic devices is limited by their linear operational envelope, which implies relatively inaccurate focusing and low focal power. Here we show a dramatic focusing effect and the generation of compact acoustic pulses (sound bullets) in solid and fluid media, with energies orders of magnitude greater than previously achievable. This focusing is made possible by a tunable, nonlinear acoustic lens, which consists of ordered arrays of granular chains. The amplitude, size, and location of the sound bullets can be controlled by varying the static precompression of the chains. Theory and numerical simulations demonstrate the focusing effect, and photoelasticity experiments corroborate it. Our nonlinear lens permits a qualitatively new way of generating high-energy acoustic pulses, which may improve imaging capabilities through increased accuracy and signal-to-noise ratios and may lead to more effective nonintrusive scalpels, for example, for cancer treatment. PMID:20368461

Control of polarization rotation in nonlinear propagation of fully structured light

NASA Astrophysics Data System (ADS)

Gibson, Christopher J.; Bevington, Patrick; Oppo, Gian-Luca; Yao, Alison M.

2018-03-01

Knowing and controlling the spatial polarization distribution of a beam is of importance in applications such as optical tweezing, imaging, material processing, and communications. Here we show how the polarization distribution is affected by both linear and nonlinear (self-focusing) propagation. We derive an analytical expression for the polarization rotation of fully structured light (FSL) beams during linear propagation and show that the observed rotation is due entirely to the difference in Gouy phase between the two eigenmodes comprising the FSL beams, in excellent agreement with numerical simulations. We also explore the effect of cross-phase modulation due to a self-focusing (Kerr) nonlinearity and show that polarization rotation can be controlled by changing the eigenmodes of the superposition, and physical parameters such as the beam size, the amount of Kerr nonlinearity, and the input power. Finally, we show that by biasing cylindrical vector beams to have elliptical polarization, we can vary the polarization state from radial through spiral to azimuthal using nonlinear propagation.

Gaussian variational ansatz in the problem of anomalous sea waves: Comparison with direct numerical simulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ruban, V. P., E-mail: ruban@itp.ac.ru

2015-05-15

The nonlinear dynamics of an obliquely oriented wave packet on a sea surface is analyzed analytically and numerically for various initial parameters of the packet in relation to the problem of the so-called rogue waves. Within the Gaussian variational ansatz applied to the corresponding (1+2)-dimensional hyperbolic nonlinear Schrödinger equation (NLSE), a simplified Lagrangian system of differential equations is derived that describes the evolution of the coefficients of the real and imaginary quadratic forms appearing in the Gaussian. This model provides a semi-quantitative description of the process of nonlinear spatiotemporal focusing, which is one of the most probable mechanisms of roguemore » wave formation in random wave fields. The system of equations is integrated in quadratures, which allows one to better understand the qualitative differences between linear and nonlinear focusing regimes of a wave packet. Predictions of the Gaussian model are compared with the results of direct numerical simulation of fully nonlinear long-crested waves.« less

Experimental observation of disorder induced self-focusing in optical fibers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leonetti, Marco, E-mail: marco.leonetti@roma1.infn.it; Karbasi, Salman; Mafi, Arash

2014-10-27

We observed disorder induced focusing nonlinearity activated by a monochromatic light beam in optical fibers composed by two kinds of plastics. The two materials, arranged in disordered fashion, support modes with a degree of localization which increases with the intensity of the optical beam. The temporal response of the optical fiber demonstrates the thermal origin of this nonlinearity. Measurements of the localization length as a function of the input power with broadband and monochromatic inputs show the effectiveness of focusing action with respect to the case of homogeneous fibers.

Effect of exponential density transition on self-focusing of q-Gaussian laser beam in collisionless plasma

NASA Astrophysics Data System (ADS)

Valkunde, Amol T.; Vhanmore, Bandopant D.; Urunkar, Trupti U.; Gavade, Kusum M.; Patil, Sandip D.; Takale, Mansing V.

2018-05-01

In this work, nonlinear aspects of a high intensity q-Gaussian laser beam propagating in collisionless plasma having upward density ramp of exponential profiles is studied. We have employed the nonlinearity in dielectric function of plasma by considering ponderomotive nonlinearity. The differential equation governing the dimensionless beam width parameter is achieved by using Wentzel-Kramers-Brillouin (WKB) and paraxial approximations and solved it numerically by using Runge-Kutta fourth order method. Effect of exponential density ramp profile on self-focusing of q-Gaussian laser beam for various values of q is systematically carried out and compared with results Gaussian laser beam propagating in collisionless plasma having uniform density. It is found that exponential plasma density ramp causes the laser beam to become more focused and gives reasonably interesting results.

Long-term, correlated emittance decrease in intense, high-brightness induction linacs

NASA Astrophysics Data System (ADS)

Carlsten, Bruce E.

1999-09-01

Simulations of high-brightness induction linacs often show a slow, long-term emittance decrease as the beam is matched from the electron gun into the linac. Superimposed on this long-term decrease are rapid emittance oscillations. These effects can be described in terms of correlations in the beam's radial phase space. The rapid emittance oscillations are due to transverse plasma oscillations, which stay nearly in phase for different radial positions within the beam. The initial emittance, just after the electron gun, is dominated by nonlinear focusing within the gun introduced by the anode exit hole. Due to the large space-charge force of an intense electron beam, the focusing of the beam through the matching section introduces an effective nonlinear force (from the change in the particles' potential energies) which counteracts the nonlinearities from the electron gun, leading to an average, long-term emittance decrease. Not all of the initial nonlinearity is removed by the matching procedure, and there are important consequences both for emittance measurements using solenoid focal length scans and for focusing the electron beam to a target.

The parallel-sequential field subtraction techniques for nonlinear ultrasonic imaging

NASA Astrophysics Data System (ADS)

Cheng, Jingwei; Potter, Jack N.; Drinkwater, Bruce W.

2018-04-01

Nonlinear imaging techniques have recently emerged which have the potential to detect cracks at a much earlier stage and have sensitivity to particularly closed defects. This study utilizes two modes of focusing: parallel, in which the elements are fired together with a delay law, and sequential, in which elements are fired independently. In the parallel focusing, a high intensity ultrasonic beam is formed in the specimen at the focal point. However, in sequential focusing only low intensity signals from individual elements enter the sample and the full matrix of transmit-receive signals is recorded; with elastic assumptions, both parallel and sequential images are expected to be identical. Here we measure the difference between these images formed from the coherent component of the field and use this to characterize nonlinearity of closed fatigue cracks. In particular we monitor the reduction in amplitude at the fundamental frequency at each focal point and use this metric to form images of the spatial distribution of nonlinearity. The results suggest the subtracted image can suppress linear features (e.g., back wall or large scatters) and allow damage to be detected at an early stage.

Nonlinear Pedagogy and Its Role in Encouraging Twenty-First Century Competencies through Physical Education: A Singapore Experience

ERIC Educational Resources Information Center

Lee, Miriam Chang Yi; Chow, Jia Yi; Button, Chris; Tan, Clara Wee Keat

2017-01-01

Nonlinear Pedagogy is an exploratory approach to teaching and learning Physical Education that can be potentially effective to help children acquire relevant twenty-first century competencies. Underpinned by Ecological Dynamics, the focus of Nonlinear Pedagogy is on the learner and includes the provision of less prescriptive instructions and…

Final Technical Report: Collaborative Research Center for Nonlinear Simulation of Energetic Particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berk, Herbert L.

2018-02-15

The study of this project focused on developing a reduced nonlinear model to describe chirping processes in a fusion plasma. A successful method was developed with results clear enough to allow an analytic theory to be developed that replicates the long term response of a nonlinear phase space structure immersed in the MHD continnuum.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Flego, S.P.; Plastino, A.; Universitat de les Illes Balears and IFISC-CSIC, 07122 Palma de Mallorca

We explore intriguing links connecting Hellmann-Feynman's theorem to a thermodynamics information-optimizing principle based on Fisher's information measure. - Highlights: > We link a purely quantum mechanical result, the Hellmann-Feynman theorem, with Jaynes' information theoretical reciprocity relations. > These relations involve the coefficients of a series expansion of the potential function. > We suggest the existence of a Legendre transform structure behind Schroedinger's equation, akin to the one characterizing thermodynamics.

Effective equations for the quantum pendulum from momentous quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hernandez, Hector H.; Chacon-Acosta, Guillermo; Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, Artificios 40, Mexico D. F. 01120

In this work we study the quantum pendulum within the framework of momentous quantum mechanics. This description replaces the Schroedinger equation for the quantum evolution of the system with an infinite set of classical equations for expectation values of configuration variables, and quantum dispersions. We solve numerically the effective equations up to the second order, and describe its evolution.

Quantum leaps in philosophy of mind: Reply to Bourget'scritique

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stapp, Henry P.

2004-07-26

David Bourget has raised some conceptual and technical objections to my development of von Neumann's treatment of the Copenhagen idea that the purely physical process described by the Schroedinger equation must be supplemented by a psychophysical process called the choice of the experiment by Bohr and Process 1 by von Neumann. I answer here each of Bourget's objections.

Hidden algebra method (quasi-exact-solvability in quantum mechanics)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Turbiner, A.

1996-02-01

A general introduction to quasi-exactly-solvable problems of quantum mechanics is presented. Main attention is given to multidimensional quasi-exactly-solvable and exactly-solvable Schroedinger operators. Exact-solvability of the Calogero and Sutherland {ital N}-body problems ass ociated with an existence of the hidden algebra {ital sl}{sub {ital N}} is discussed extensively. {copyright} {ital 1996 American Institute of Physics.}

Quantum Entanglement in Optical Lattice Systems

DTIC Science & Technology

2015-02-18

Zitterbewegung oscillation was first predicted by Schroedinger in 1930 for relativistic Dirac electrons where it arises from the interference...magnetic gradient. The gradient affected the Rabi cycling rate, leading to a phase winding along the long axis of the cigar -shaped BEC. While the single...approach is applicable to spherically symmetric, strictly two- dimensional, strictly one-dimensional, cigar -shaped, and pancake-shaped traps and has

Uncertainty relations, zero point energy and the linear canonical group

NASA Technical Reports Server (NTRS)

Sudarshan, E. C. G.

1993-01-01

The close relationship between the zero point energy, the uncertainty relations, coherent states, squeezed states, and correlated states for one mode is investigated. This group-theoretic perspective enables the parametrization and identification of their multimode generalization. In particular the generalized Schroedinger-Robertson uncertainty relations are analyzed. An elementary method of determining the canonical structure of the generalized correlated states is presented.

The quantum universe

NASA Astrophysics Data System (ADS)

Hey, Anthony J. G.; Walters, Patrick

This book provides a descriptive, popular account of quantum physics. The basic topics addressed include: waves and particles, the Heisenberg uncertainty principle, the Schroedinger equation and matter waves, atoms and nuclei, quantum tunneling, the Pauli exclusion principle and the elements, quantum cooperation and superfluids, Feynman rules, weak photons, quarks, and gluons. The applications of quantum physics to astrophyics, nuclear technology, and modern electronics are addressed.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Paavola, Janika; Hall, Michael J. W.; Paris, Matteo G. A.

The transition from quantum to classical, in the case of a quantum harmonic oscillator, is typically identified with the transition from a quantum superposition of macroscopically distinguishable states, such as the Schroedinger-cat state, into the corresponding statistical mixture. This transition is commonly characterized by the asymptotic loss of the interference term in the Wigner representation of the cat state. In this paper we show that the quantum-to-classical transition has different dynamical features depending on the measure for nonclassicality used. Measures based on an operatorial definition have well-defined physical meaning and allow a deeper understanding of the quantum-to-classical transition. Our analysismore » shows that, for most nonclassicality measures, the Schroedinger-cat state becomes classical after a finite time. Moreover, our results challenge the prevailing idea that more macroscopic states are more susceptible to decoherence in the sense that the transition from quantum to classical occurs faster. Since nonclassicality is a prerequisite for entanglement generation our results also bridge the gap between decoherence, which is lost only asymptotically, and entanglement, which may show a ''sudden death''. In fact, whereas the loss of coherences still remains asymptotic, we emphasize that the transition from quantum to classical can indeed occur at a finite time.« less

Position dependent mass Schroedinger equation and isospectral potentials: Intertwining operator approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Midya, Bikashkali; Roy, B.; Roychoudhury, R.

2010-02-15

Here, we have studied first- and second-order intertwining approaches to generate isospectral partner potentials of position dependent (effective) mass Schroedinger equation. The second-order intertwiner is constructed directly by taking it as second-order linear differential operator with position dependent coefficients, and the system of equations arising from the intertwining relationship is solved for the coefficients by taking an ansatz. A complete scheme for obtaining general solution is obtained, which is valid for any arbitrary potential and mass function. The proposed technique allows us to generate isospectral potentials with the following spectral modifications: (i) to add new bound state(s), (ii) to removemore » bound state(s), and (iii) to leave the spectrum unaffected. To explain our findings with the help of an illustration, we have used point canonical transformation to obtain the general solution of the position dependent mass Schrodinger equation corresponding to a potential and mass function. It is shown that our results are consistent with the formulation of type A N-fold supersymmetry [T. Tanaka, J. Phys. A 39, 219 (2006); A. Gonzalez-Lopez and T. Tanaka, J. Phys. A 39, 3715 (2006)] for the particular cases N=1 and N=2, respectively.« less

Practical recursive solution of degenerate Rayleigh-Schroedinger perturbation theory and application to high-order calculations of the Zeeman effect in hydrogen

DOE Office of Scientific and Technical Information (OSTI.GOV)

Silverstone, H.J.; Moats, R.K.

1981-04-01

With the aim of high-order calculations, a new recursive solution for the degenerate Rayleigh-Schroedinger perturbation-theory wave function and energy has been derived. The final formulas, chi/sup (N/)/sub sigma/ = R/sup () -sigma/summation/sup N/-1/sub k/ = 0 H/sup (sigma+1+k/)/sub sigma+1/chi/sup (N/-1-k), E/sup (N/+sigma) = <0Vertical BarH/sup (N/+sigma)/sub sigma+1/Vertical Bar0> + < 0Vertical Barsummation/sup N/-2/sub k/ = 0H/sup (sigma+1+k/)/sub sigma+1/ Vertical Barchi/sup (N/-1-k)>,which involve new Hamiltonian-related operators H/sup (sigma+k/)/sub sigma/ and H/sup( sigma+k/)/sub sigma/, strongly resemble the standard nondegenerate recursive formulas. As an illustration, the perturbed energy coefficients for the 3s-3d/sub 0/ states of hydrogen in the Zeeman effect have been calculatedmore » recursively through 87th order in the square of the magnetic field. Our treatment is compared with that of Hirschfelder and Certain (J. Chem. Phys. 60, 1118 (1974)), and some relative advantages of each are pointed out.« less

Near-planar TS waves and longitudinal vortices in channel flow: Nonlinear interaction and focusing

NASA Technical Reports Server (NTRS)

Hall, P.; Smith, F. T.

1989-01-01

The nonlinear interaction between planar or near-planar Tollmien-Schlichting waves and longitudinal vortices, induced or input, is considered theoretically for channel flows at high Reynolds numbers. Several kinds of nonlinear interaction, dependent on the input amplitudes and wavenumbers or on previously occurring interactions, are found and inter-related. The first, Type 1, is studied the most here and it usually produces spanwise focusing of both the wave and the vortex motion, within a finite scaled time, along with enhancement of both their amplitudes. This then points to the nonlinear interaction Type 2 where new interactive effects come into force to drive the wave and the vortex nonlinearly. Types 3, 4 correspond to still higher amplitudes, with 3 being related to 2, while 4 is connected with a larger-scale interaction 5 studied in an allied paper. Both 3, 4 are subsets of the full three-dimensional triple-deck-lie interaction, 6. The strongest nonlinear interactions are those of 4, 5, 6 since they alter the mean-flow profile substantially, i.e., by an 0(1) relative amount. All the types of nonlinear interaction however can result in the formation of focussed responses in the sense of spanwise concentrations and/or amplifications of vorticity and wave amplitude.

Simulation of non-linear acoustic field and thermal pattern of phased-array high-intensity focused ultrasound (HIFU).

PubMed

Wang, Mingjun; Zhou, Yufeng

2016-08-01

HIFU becomes an effective and non-invasive modality of solid tumour/cancer ablation. Simulation of the non-linear acoustic wave propagation using a phased-array transducer in multiple layered media using different focusing strategies and the consequent lesion formation are essential in HIFU planning in order to enhance the efficacy and efficiency of treatment. An angular spectrum approach with marching fractional steps was applied in the wave propagation from phased-array HIFU transducer, and diffraction, attenuation, and non-linearity effects were accounted for by a second-order operator splitting scheme. The simulated distributions of the first three harmonics along and transverse to the transducer axis were compared to the hydrophone measurements. The bioheat equation was used to simulate the subsequent temperature elevation using the deposited acoustic energy, and lesion formation was determined by the thermal dose. Better agreement was found between the measured harmonics distribution and simulation using the proposed algorithm than the Khokhlov-Zabozotskaya-Kuznetsov equation. Variable focusing of the phased-array transducer (geometric focusing, transverse shifting and the generation of multiple foci) can be simulated successfully. The shifting and splitting of focus was found to result in significantly less temperature elevation at the focus and the subsequently, the smaller lesion size, but the larger grating lobe grating lobe in the pre-focal region. The proposed algorithm could simulate the non-linear wave propagation from the source with arbitrary shape and distribution of excitation through multiple tissue layers in high computation accuracy. The performance of phased-array HIFU can be optimised in the treatment planning.

Nonlinear Light Dynamics in Multi-Core Structures

DTIC Science & Technology

2017-02-27

be generated in continuous- discrete optical media such as multi-core optical fiber or waveguide arrays; localisation dynamics in a continuous... discrete nonlinear system. Detailed theoretical analysis is presented of the existence and stability of the discrete -continuous light bullets using a very...and pulse compression using wave collapse (self-focusing) energy localisation dynamics in a continuous- discrete nonlinear system, as implemented in a

The Recommendations for Linear Measurement Techniques on the Measurements of Nonlinear System Parameters of a Joint.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, Scott A; Catalfamo, Simone; Brake, Matthew R. W.

2017-01-01

In the study of the dynamics of nonlinear systems, experimental measurements often convolute the response of the nonlinearity of interest and the effects of the experimental setup. To reduce the influence of the experimental setup on the deduction of the parameters of the nonlinearity, the response of a mechanical joint is investigated under various experimental setups. These experiments first focus on quantifying how support structures and measurement techniques affect the natural frequency and damping of a linear system. The results indicate that support structures created from bungees have negligible influence on the system in terms of frequency and damping ratiomore » variations. The study then focuses on the effects of the excitation technique on the response for a linear system. The findings suggest that thinner stingers should not be used, because under the high force requirements the stinger bending modes are excited adding unwanted torsional coupling. The optimal configuration for testing the linear system is then applied to a nonlinear system in order to assess the robustness of the test configuration. Finally, recommendations are made for conducting experiments on nonlinear systems using conventional/linear testing techniques.« less

Full 3D modelling of pulse propagation enables efficient nonlinear frequency conversion with low energy laser pulses in a single-element tripler.

PubMed

Kardaś, Tomasz M; Nejbauer, Michał; Wnuk, Paweł; Resan, Bojan; Radzewicz, Czesław; Wasylczyk, Piotr

2017-02-22

Although new optical materials continue to open up access to more and more wavelength bands where femtosecond laser pulses can be generated, light frequency conversion techniques are still indispensable in filling the gaps on the ultrafast spectral scale. With high repetition rate, low pulse energy laser sources (oscillators) tight focusing is necessary for a robust wave mixing and the efficiency of broadband nonlinear conversion is limited by diffraction as well as spatial and temporal walk-off. Here we demonstrate a miniature third harmonic generator (tripler) with conversion efficiency exceeding 30%, producing 246 fs UV pulses via cascaded second order processes within a single laser beam focus. Designing this highly efficient and ultra compact frequency converter was made possible by full 3-dimentional modelling of propagation of tightly focused, broadband light fields in nonlinear and birefringent media.

Laser-pulse compression in a collisional plasma under weak-relativistic ponderomotive nonlinearity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Singh, Mamta; Gupta, D. N., E-mail: dngupta@physics.du.ac.in

We present theory and numerical analysis which demonstrate laser-pulse compression in a collisional plasma under the weak-relativistic ponderomotive nonlinearity. Plasma equilibrium density is modified due to the ohmic heating of electrons, the collisions, and the weak relativistic-ponderomotive force during the interaction of a laser pulse with plasmas. First, within one-dimensional analysis, the longitudinal self-compression mechanism is discussed. Three-dimensional analysis (spatiotemporal) of laser pulse propagation is also investigated by coupling the self-compression with the self-focusing. In the regime in which the laser becomes self-focused due to the weak relativistic-ponderomotive nonlinearity, we provide results for enhanced pulse compression. The results show thatmore » the matched interplay between self-focusing and self-compression can improve significantly the temporal profile of the compressed pulse. Enhanced pulse compression can be achieved by optimizing and selecting the parameters such as collision frequency, ion-temperature, and laser intensity.« less

Bandwidth Limitations in Characterization of High Intensity Focused Ultrasound Fields in the Presence of Shocks

NASA Astrophysics Data System (ADS)

Khokhlova, V. A.; Bessonova, O. V.; Soneson, J. E.; Canney, M. S.; Bailey, M. R.; Crum, L. A.

2010-03-01

Nonlinear propagation effects result in the formation of weak shocks in high intensity focused ultrasound (HIFU) fields. When shocks are present, the wave spectrum consists of hundreds of harmonics. In practice, shock waves are modeled using a finite number of harmonics and measured with hydrophones that have limited bandwidths. The goal of this work was to determine how many harmonics are necessary to model or measure peak pressures, intensity, and heat deposition rates of the HIFU fields. Numerical solutions of the Khokhlov-Zabolotskaya-Kuznetzov-type (KZK) nonlinear parabolic equation were obtained using two independent algorithms, compared, and analyzed for nonlinear propagation in water, in gel phantom, and in tissue. Measurements were performed in the focus of the HIFU field in the same media using fiber optic probe hydrophones of various bandwidths. Experimental data were compared to the simulation results.

Full 3D modelling of pulse propagation enables efficient nonlinear frequency conversion with low energy laser pulses in a single-element tripler

NASA Astrophysics Data System (ADS)

Kardaś, Tomasz M.; Nejbauer, Michał; Wnuk, Paweł; Resan, Bojan; Radzewicz, Czesław; Wasylczyk, Piotr

2017-02-01

Although new optical materials continue to open up access to more and more wavelength bands where femtosecond laser pulses can be generated, light frequency conversion techniques are still indispensable in filling the gaps on the ultrafast spectral scale. With high repetition rate, low pulse energy laser sources (oscillators) tight focusing is necessary for a robust wave mixing and the efficiency of broadband nonlinear conversion is limited by diffraction as well as spatial and temporal walk-off. Here we demonstrate a miniature third harmonic generator (tripler) with conversion efficiency exceeding 30%, producing 246 fs UV pulses via cascaded second order processes within a single laser beam focus. Designing this highly efficient and ultra compact frequency converter was made possible by full 3-dimentional modelling of propagation of tightly focused, broadband light fields in nonlinear and birefringent media.

Nonlinear light-matter interactions in engineered optical media

NASA Astrophysics Data System (ADS)

Litchinitser, Natalia

In this talk, we consider fundamental optical phenomena at the interface of nonlinear and singular optics in artificial media, including theoretical and experimental studies of linear and nonlinear light-matter interactions of vector and singular optical beams in metamaterials. We show that unique optical properties of metamaterials open unlimited prospects to ``engineer'' light itself. Thanks to their ability to manipulate both electric and magnetic field components, metamaterials open new degrees of freedom for tailoring complex polarization states and orbital angular momentum (OAM) of light. We will discuss several approaches to structured light manipulation on the nanoscale using metal-dielectric, all-dielectric and hyperbolic metamaterials. These new functionalities, including polarization and OAM conversion, beam magnification and de-magnification, and sub-wavelength imaging using novel non-resonant hyperlens are likely to enable a new generation of on-chip or all-fiber structured light applications. The emergence of metamaterials also has a strong potential to enable a plethora of novel nonlinear light-matter interactions and even new nonlinear materials. In particular, nonlinear focusing and defocusing effects are of paramount importance for manipulation of the minimum focusing spot size of structured light beams necessary for nanoscale trapping, manipulation, and fundamental spectroscopic studies. Colloidal suspensions offer as a promising platform for engineering polarizibilities and realization of large and tunable nonlinearities. We will present our recent studies of the phenomenon of spatial modulational instability leading to laser beam filamentation in an engineered soft-matter nonlinear medium. Finally, we introduce so-called virtual hyperbolic metamaterials formed by an array of plasma channels in air as a result of self-focusing of an intense laser pulse, and show that such structure can be used to manipulate microwave beams in a free space. This work was supported by the Army Research Office Awards (W911NF-15-1-0146, W911NF-11-1-0297).

Nonlinear Photonics 2014: introduction.

PubMed

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.

Optical super-resolution effect induced by nonlinear characteristics of graphene oxide films

NASA Astrophysics Data System (ADS)

Zhao, Yong-chuang; Nie, Zhong-quan; Zhai, Ai-ping; Tian, Yan-ting; Liu, Chao; Shi, Chang-kun; Jia, Bao-hua

2018-01-01

In this work, we focus on the optical super-resolution effect induced by strong nonlinear saturation absorption (NSA) of graphene oxide (GO) membranes. The third-order optical nonlinearities are characterized by the canonical Z-scan technique under femtosecond laser (wavelength: 800 nm, pulse width: 100 fs) excitation. Through controlling the applied femtosecond laser energy, NSA of the GO films can be tuned continuously. The GO film is placed at the focal plane as a unique amplitude filter to improve the resolution of the focused field. A multi-layer system model is proposed to present the generation of a deep sub-wavelength spot associated with the nonlinearity of GO films. Moreover, the parameter conditions to achieve the best resolution (˜λ/6) are determined entirely. The demonstrated results here are useful for high density optical recoding and storage, nanolithography, and super-resolution optical imaging.

Fiber bundle phase conjugate mirror

DOEpatents

Ward, Benjamin G.

2012-05-01

An improved method and apparatus for passively conjugating the phases of a distorted wavefronts resulting from optical phase mismatch between elements of a fiber laser array are disclosed. A method for passively conjugating a distorted wavefront comprises the steps of: multiplexing a plurality of probe fibers and a bundle pump fiber in a fiber bundle array; passing the multiplexed output from the fiber bundle array through a collimating lens and into one portion of a non-linear medium; passing the output from a pump collection fiber through a focusing lens and into another portion of the non-linear medium so that the output from the pump collection fiber mixes with the multiplexed output from the fiber bundle; adjusting one or more degrees of freedom of one or more of the fiber bundle array, the collimating lens, the focusing lens, the non-linear medium, or the pump collection fiber to produce a standing wave in the non-linear medium.

Focus issue introduction: nonlinear photonics.

PubMed

Akhmediev, Nail; Rottwitt, Karsten

2012-11-19

It is now 23 years since the first Topical Meeting "Nonlinear Guided Wave Phenomena" (Houston, TX, February 2-4, 1989) has been organised by George Stegeman and Allan Boardman with support of the Optical Society of America. These series of the OSA conferences known as NLGW, continued under the name "Nonlinear Photonics" starting from 2007. The latest one, in Colorado Springs in June 17-21, 2012 has been a great success despite the fierce fires advancing around the city at the time of the conference. This Focus issue is a collection of several papers presented at the conference with extended content submitted to Optics Express. Although this collection is small in comparison to the total number of papers presented at the conference, it gives a flavor of the topics considered at the meeting. It is also worthy to mention here that the next meeting "Nonlinear Photonics" is planned to be held in Barcelona - one of the main European centers on this subject.

FOCUSING OF HIGH POWER ULTRASOUND BEAMS AND LIMITING VALUES OF SHOCK WAVE PARAMETERS

PubMed Central

Bessonova, O.V.; Khokhlova, V.A.; Bailey, M.R.; Canney, M.S.; Crum, L.A.

2009-01-01

In this work, the influence of nonlinear and diffraction effects on amplification factors of focused ultrasound systems is investigated. The limiting values of acoustic field parameters obtained by focusing of high power ultrasound are studied. The Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation was used for the numerical modeling. Solutions for the nonlinear acoustic field were obtained at output levels corresponding to both pre- and post- shock formation conditions in the focal area of the beam in a weakly dissipative medium. Numerical solutions were compared with experimental data as well as with known analytic predictions. PMID:20161349

FOCUSING OF HIGH POWER ULTRASOUND BEAMS AND LIMITING VALUES OF SHOCK WAVE PARAMETERS.

PubMed

Bessonova, O V; Khokhlova, V A; Bailey, M R; Canney, M S; Crum, L A

2009-07-21

In this work, the influence of nonlinear and diffraction effects on amplification factors of focused ultrasound systems is investigated. The limiting values of acoustic field parameters obtained by focusing of high power ultrasound are studied. The Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation was used for the numerical modeling. Solutions for the nonlinear acoustic field were obtained at output levels corresponding to both pre- and post- shock formation conditions in the focal area of the beam in a weakly dissipative medium. Numerical solutions were compared with experimental data as well as with known analytic predictions.

Focusing of high power ultrasound beams and limiting values of shock wave parameters

NASA Astrophysics Data System (ADS)

Bessonova, O. V.; Khokhlova, V. A.; Bailey, M. R.; Canney, M. S.; Crum, L. A.

2009-10-01

In this work, the influence of nonlinear and diffraction effects on amplification factors of focused ultrasound systems is investigated. The limiting values of acoustic field parameters obtained by focusing of high power ultrasound are studied. The Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation was used for the numerical modeling. Solutions for the nonlinear acoustic field were obtained at output levels corresponding to both pre- and post-shock formation conditions in the focal area of the beam in a weakly dissipative medium. Numerical solutions were compared with experimental data as well as with known analytic predictions.

Focusing of a dark hollow Gaussian electromagnetic beam in a magnetoplasma

NASA Astrophysics Data System (ADS)

Sodha, Mahendra Singh; Mishra, S. K.; Misra, Shikha

2009-12-01

This paper presents an analysis and subsequent discussion of the self focusing of a dark hollow Gaussian electromagnetic beam (HGB) in a magnetoplasma, considering ponderomotive and collisional nonlinearities. A paraxial-like approach, in which the relevant parameters are expanded in terms of radial distance from the maximum of the irradiance rather than that from the axis, has been adopted to analyze the propagation of the HGB. The nature of self focusing is highlighted through the critical curves as a plot of dimensionless radius versus power of the beam. The effect of the magnetic field and the nature of the nonlinearity on self focusing of various order HGBs has also been explored.

Nonlinear Wavefront Control with All-Dielectric Metasurfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Lei; Kruk, Sergey; Koshelev, Kirill

Metasurfaces, two-dimensional lattices of nanoscale resonators, offer unique opportunities for functional flat optics and allow the control of the transmission, reflection, and polarization of a wavefront of light. Recently, all-dielectric metasurfaces reached remarkable efficiencies, often matching or out-performing conventional optical elements. The exploitation of the nonlinear optical response of metasurfaces offers a paradigm shift in nonlinear optics, and dielectric nonlinear metasurfaces are expected to enrich subwavelength photonics by enhancing substantially nonlinear response of natural materials combined with the efficient control of the phase of nonlinear waves. Here, we suggest a novel and rather general approach for engineering the wavefront ofmore » parametric waves of arbitrary complexity generated by a nonlinear metasurface. We design all-dielectric nonlinear metasurfaces, achieve a highly efficient wavefront control of a third-harmonic field, and demonstrate the generation of nonlinear beams at a designed angle and the generation of nonlinear focusing vortex beams. Lastly, our nonlinear metasurfaces produce phase gradients over a full 0–2π phase range with a 92% diffraction efficiency.« less

Nonlinear Wavefront Control with All-Dielectric Metasurfaces.

PubMed

Wang, Lei; Kruk, Sergey; Koshelev, Kirill; Kravchenko, Ivan; Luther-Davies, Barry; Kivshar, Yuri

2018-06-13

Metasurfaces, two-dimensional lattices of nanoscale resonators, offer unique opportunities for functional flat optics and allow the control of the transmission, reflection, and polarization of a wavefront of light. Recently, all-dielectric metasurfaces reached remarkable efficiencies, often matching or out-performing conventional optical elements. The exploitation of the nonlinear optical response of metasurfaces offers a paradigm shift in nonlinear optics, and dielectric nonlinear metasurfaces are expected to enrich subwavelength photonics by enhancing substantially nonlinear response of natural materials combined with the efficient control of the phase of nonlinear waves. Here, we suggest a novel and rather general approach for engineering the wavefront of parametric waves of arbitrary complexity generated by a nonlinear metasurface. We design all-dielectric nonlinear metasurfaces, achieve a highly efficient wavefront control of a third-harmonic field, and demonstrate the generation of nonlinear beams at a designed angle and the generation of nonlinear focusing vortex beams. Our nonlinear metasurfaces produce phase gradients over a full 0-2π phase range with a 92% diffraction efficiency.

Nonlinear Wavefront Control with All-Dielectric Metasurfaces

DOE PAGES

Wang, Lei; Kruk, Sergey; Koshelev, Kirill; ...

2018-05-11

Metasurfaces, two-dimensional lattices of nanoscale resonators, offer unique opportunities for functional flat optics and allow the control of the transmission, reflection, and polarization of a wavefront of light. Recently, all-dielectric metasurfaces reached remarkable efficiencies, often matching or out-performing conventional optical elements. The exploitation of the nonlinear optical response of metasurfaces offers a paradigm shift in nonlinear optics, and dielectric nonlinear metasurfaces are expected to enrich subwavelength photonics by enhancing substantially nonlinear response of natural materials combined with the efficient control of the phase of nonlinear waves. Here, we suggest a novel and rather general approach for engineering the wavefront ofmore » parametric waves of arbitrary complexity generated by a nonlinear metasurface. We design all-dielectric nonlinear metasurfaces, achieve a highly efficient wavefront control of a third-harmonic field, and demonstrate the generation of nonlinear beams at a designed angle and the generation of nonlinear focusing vortex beams. Lastly, our nonlinear metasurfaces produce phase gradients over a full 0–2π phase range with a 92% diffraction efficiency.« less

Hidden Statistics of Schroedinger Equation

NASA Technical Reports Server (NTRS)

Zak, Michail

2011-01-01

Work was carried out in determination of the mathematical origin of randomness in quantum mechanics and creating a hidden statistics of Schr dinger equation; i.e., to expose the transitional stochastic process as a "bridge" to the quantum world. The governing equations of hidden statistics would preserve such properties of quantum physics as superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods.

Two atoms in an anisotropic harmonic trap

DOE Office of Scientific and Technical Information (OSTI.GOV)

Idziaszek, Z.; Centrum Fizyki Teoretycznej, Polska Akademia Nauk, 02-668 Warsaw; Calarco, T.

2005-05-15

We consider the system of two interacting atoms confined in axially symmetric harmonic trap. Within the pseudopotential approximation, we solve the Schroedinger equation exactly, discussing the limits of quasi-one-and quasi-two-dimensional geometries. Finally, we discuss the application of an energy-dependent pseudopotential, which allows us to extend the validity of our results to the case of tight traps and large scattering lengths.

Introduction to the Contributions of A. Temkin and R. J. Drachman to Atomic Physics

NASA Technical Reports Server (NTRS)

Bhatia, A.K.

2007-01-01

Their work, as is the work of most atomic theorists, is concerned with solving the Schroedinger equation accurately for wave function in cases where there is no exact analytical solution. In particular, Temkin is associated with electron scattering from atoms and ions. When he started there already were a number of methods to study the scattering of electrons from atoms.

Course 4: Anyons

NASA Astrophysics Data System (ADS)

Myrheim, J.

Contents 1 Introduction 1.1 The concept of particle statistics 1.2 Statistical mechanics and the many-body problem 1.3 Experimental physics in two dimensions 1.4 The algebraic approach: Heisenberg quantization 1.5 More general quantizations 2 The configuration space 2.1 The Euclidean relative space for two particles 2.2 Dimensions d=1,2,3 2.3 Homotopy 2.4 The braid group 3 Schroedinger quantization in one dimension 4 Heisenberg quantization in one dimension 4.1 The coordinate representation 5 Schroedinger quantization in dimension d ≥ 2 5.1 Scalar wave functions 5.2 Homotopy 5.3 Interchange phases 5.4 The statistics vector potential 5.5 The N-particle case 5.6 Chern-Simons theory 6 The Feynman path integral for anyons 6.1 Eigenstates for position and momentum 6.2 The path integral 6.3 Conjugation classes in SN 6.4 The non-interacting case 6.5 Duality of Feynman and Schroedinger quantization 7 The harmonic oscillator 7.1 The two-dimensional harmonic oscillator 7.2 Two anyons in a harmonic oscillator potential 7.3 More than two anyons 7.4 The three-anyon problem 8 The anyon gas 8.1 The cluster and virial expansions 8.2 First and second order perturbative results 8.3 Regularization by periodic boundary conditions 8.4 Regularization by a harmonic oscillator potential 8.5 Bosons and fermions 8.6 Two anyons 8.7 Three anyons 8.8 The Monte Carlo method 8.9 The path integral representation of the coefficients GP 8.10 Exact and approximate polynomials 8.11 The fourth virial coefficient of anyons 8.12 Two polynomial theorems 9 Charged particles in a constant magnetic field 9.1 One particle in a magnetic field 9.2 Two anyons in a magnetic field 9.3 The anyon gas in a magnetic field 10 Interchange phases and geometric phases 10.1 Introduction to geometric phases 10.2 One particle in a magnetic field 10.3 Two particles in a magnetic field 10.4 Interchange of two anyons in potential wells 10.5 Laughlin's theory of the fractional quantum Hall effect

The parallel-sequential field subtraction technique for coherent nonlinear ultrasonic imaging

NASA Astrophysics Data System (ADS)

Cheng, Jingwei; Potter, Jack N.; Drinkwater, Bruce W.

2018-06-01

Nonlinear imaging techniques have recently emerged which have the potential to detect cracks at a much earlier stage than was previously possible and have sensitivity to partially closed defects. This study explores a coherent imaging technique based on the subtraction of two modes of focusing: parallel, in which the elements are fired together with a delay law and sequential, in which elements are fired independently. In the parallel focusing a high intensity ultrasonic beam is formed in the specimen at the focal point. However, in sequential focusing only low intensity signals from individual elements enter the sample and the full matrix of transmit-receive signals is recorded and post-processed to form an image. Under linear elastic assumptions, both parallel and sequential images are expected to be identical. Here we measure the difference between these images and use this to characterise the nonlinearity of small closed fatigue cracks. In particular we monitor the change in relative phase and amplitude at the fundamental frequencies for each focal point and use this nonlinear coherent imaging metric to form images of the spatial distribution of nonlinearity. The results suggest the subtracted image can suppress linear features (e.g. back wall or large scatters) effectively when instrumentation noise compensation in applied, thereby allowing damage to be detected at an early stage (c. 15% of fatigue life) and reliably quantified in later fatigue life.

Integrated nonlinear photonics. Emerging applications and ongoing challenges - A mini review

DOE PAGES

Hendrickson, Scott M.; Foster, Amy C.; Camacho, Ryan M.; ...

2014-11-26

In this paper, we provide a review of recent progress in integrated nonlinear photonics with a focus on emerging applications in all-optical signal processing, ultra-low-power all-optical switching, and quantum information processing.

Nonlinear coherent structures in granular crystals

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Characterization of nonlinear ultrasound fields of 2D therapeutic arrays

PubMed Central

Yuldashev, Petr V.; Kreider, Wayne; Sapozhnikov, Oleg A.; Farr, Navid; Partanen, Ari; Bailey, Michael R.; Khokhlova, Vera

2015-01-01

A current trend in high intensity focused ultrasound (HIFU) technologies is to use 2D focused phased arrays that enable electronic steering of the focus, beamforming to avoid overheating of obstacles (such as ribs), and better focusing through inhomogeneities of soft tissue using time reversal methods. In many HIFU applications, the acoustic intensity in situ can reach thousands of W/cm2 leading to nonlinear propagation effects. At high power outputs, shock fronts develop in the focal region and significantly alter the bioeffects induced. Clinical applications of HIFU are relatively new and challenges remain for ensuring their safety and efficacy. A key component of these challenges is the lack of standard procedures for characterizing nonlinear HIFU fields under operating conditions. Methods that combine low-amplitude pressure measurements and nonlinear modeling of the pressure field have been proposed for axially symmetric single element transducers but have not yet been validated for the much more complex 3D fields generated by therapeutic arrays. Here, the method was tested for a clinical HIFU source comprising a 256-element transducer array. A numerical algorithm based on the Westervelt equation was used to enable 3D full-diffraction nonlinear modeling. With the acoustic holography method, the magnitude and phase of the acoustic field were measured at a low power output and used to determine the pattern of vibrations at the surface of the array. This pattern was then scaled to simulate a range of intensity levels near the elements up to 10 W/cm2. The accuracy of modeling was validated by comparison with direct measurements of the focal waveforms using a fiber-optic hydrophone. Simulation results and measurements show that shock fronts with amplitudes up to 100 MPa were present in focal waveforms at clinically relevant outputs, indicating the importance of strong nonlinear effects in ultrasound fields generated by HIFU arrays. PMID:26203345

Laser induced white lighting of tungsten filament

NASA Astrophysics Data System (ADS)

Strek, W.; Tomala, R.; Lukaszewicz, M.

2018-04-01

The sustained bright white light emission of thin tungsten filament was induced under irradiation with focused beam of CW infrared laser diode. The broadband emission centered at 600 nm has demonstrated the threshold behavior on excitation power. Its intensity increased non-linearly with excitation power. The emission occurred only from the spot of focused beam of excitation laser diode. The white lighting was accompanied by efficient photocurrent flow and photoelectron emission which both increased non-linearly with laser irradiation power.

Study of Nonlinear Propagation of Ultrashort Laser Pulses and Its Application to Harmonic Generation

NASA Astrophysics Data System (ADS)

Weerawarne, Darshana L.

Laser filamentation, which is one of the exotic nonlinear optical phenomena, is self-guidance of high-power laser beams due to the dynamic balance between the optical Kerr effect (self-focusing) and other nonlinear effects such as plasma defocusing. It has many applications including supercontinuum generation (SCG), high-order harmonic generation (HHG), lightning guiding, stand-off sensing, and rain making. The main focus of this work is on studying odd-order harmonic generation (HG) (i.e., 3o, 5o, 7o, etc., where o is the angular frequency) in centrosymmetric media while a high-power, ultrashort harmonic-driving pulse undergoes nonlinear propagation such as laser filamentation. The investigation of highly-controversial nonlinear indices of refraction by measuring low-order HG in air is carried out. Furthermore, time-resolved (i.e., pump-probe) experiments and significant harmonic enhancements are presented and a novel HG mechanism based on higher-order nonlinearities is proposed to explain the experimental results. C/C++ numerical simulations are used to solve the nonlinear Schrodinger equation (NLSE) which supports the experimental findings. Another project which I have performed is selective sintering using lasers. Short-pulse lasers provide a fascinating tool for material processing, especially when the conventional oven-based techniques fail to process flexible materials for smart energy/electronics applications. I present experimental and theoretical studies on laser processing of nanoparticle-coated flexible materials, aiming to fabricate flexible electronic devices.

Nonlinear effects of electromagnetic forces on primary resonance of a levitated elastic bar supported by high- Tc superconducting bearings

NASA Astrophysics Data System (ADS)

Iori, T.; Ogawa, S.; Sugiura, T.

2007-10-01

This research investigates nonlinear dynamics of an elastic body supported at both its ends by electromagnetic forces between superconductors and magnets. We focus on the primary resonance of each eigenmode under vertical excitation of superconducting bulks. Experiment and numerical analysis show the softening tendency in the resonance of the 3rd mode consisting of mainly deflection and slightly translation. This nonlinear response can be theoretically explained only by nonlinear coupling between the 1st and 3rd modes through their quadratic terms.

Characterizing nonlinearity in invasive EEG recordings from temporal lobe epilepsy

NASA Astrophysics Data System (ADS)

Casdagli, M. C.; Iasemidis, L. D.; Sackellares, J. C.; Roper, S. N.; Gilmore, R. L.; Savit, R. S.

Invasive electroencephalographic (EEG) recordings from depth and subdural electrodes, performed in eight patients with temporal lobe epilepsy, are analyzed using a variety of nonlinear techniques. A surrogate data technique is used to find strong evidence for nonlinearities in epileptogenic regions of the brain. Most of these nonlinearities are characterized as “spiking” by a wavelet analysis. A small fraction of the nonlinearities are characterized as “recurrent” by a nonlinear prediction algorithm. Recurrent activity is found to occur in spatio-temporal patterns related to the location of the epileptogenic focus. Residual delay maps, used to characterize “lag-one nonlinearity”, are remarkably stationary for a given electrode, and exhibit striking variations among electrodes. The clinical and theoretical implications of these results are discussed.

Reflection and Transmission of a Focused Finite Amplitude Sound Beam Incident on a Curved Interface

NASA Astrophysics Data System (ADS)

Makin, Inder Raj Singh

Reflection and transmission of a finite amplitude focused sound beam at a weakly curved interface separating two fluid-like media are investigated. The KZK parabolic wave equation, which accounts for thermoviscous absorption, diffraction, and nonlinearity, is used to describe the high intensity focused beam. The first part of the work deals with the quasilinear analysis of a weakly nonlinear beam after its reflection and transmission from a curved interface. A Green's function approach is used to define the field integrals describing the primary and the nonlinearly generated second harmonic beam. Closed-form solutions are obtained for the primary and second harmonic beams when a Gaussian amplitude distribution at the source is assumed. The second part of the research uses a numerical frequency domain solution of the KZK equation for a fully nonlinear analysis of the reflected and transmitted fields. Both piston and Gaussian sources are considered. Harmonic components generated in the medium due to propagation of the focused beam are evaluated, and formation of shocks in the reflected and transmitted beams is investigated. A finite amplitude focused beam is observed to be modified due to reflection and transmission from a curved interface in a manner distinct from that in the case of a small signal beam. Propagation curves, beam patterns, phase plots and time waveforms for various parameters defining the source and media pairs are presented, highlighting the effect of the interface curvature on the reflected and transmitted beams. Relevance of the current work to biomedical applications of ultrasound is discussed.

Single-photon nonlinearities in the propagation of focused beams through dense atomic clouds

NASA Astrophysics Data System (ADS)

Wang, Yidan; Gorshkov, Alexey; Gullans, Michael

2017-04-01

We theoretically study single-photon nonlinearities realized when a highly focused Gaussian beam passes through a dense atomic cloud. In this system, strong dipole-dipole interactions arise between closely spaced atoms and significantly affect light propagation. We find that the highly focused Gaussian beam can be treated as an effective one-dimensional waveguide, which simplifies the calculation of photon transmission and correlation functions. The formalism we develop is also applicable to the case where additional atom-atom interactions, such as interactions between Rydberg atoms, are involved. This work was supported by the ARL, NSF PFC at the JQI, AFOSR, NSF PIF, ARO, and AFOSR MURI.

Variational analysis of SPM- and IPM-based interactions in cubic non-local nonlinear media

NASA Astrophysics Data System (ADS)

Maleshkov, G.; Bezuhanov, Kalojan; Dreischuh, Aleksander A.

2005-04-01

We analytically show the non-locality of cubic nonlinear media causes an increase of the critical power for self- and induced focusing and influences the condition for signal beam attraction/repulsion in an off-axis geometry.

Quantized expected returns in terms of dividend yield at the money

NASA Astrophysics Data System (ADS)

Dieng, Lamine

2011-03-01

We use the Bachelier (additive model) and the Black-Scholes (multiplicative model) as our models for the stock price movement for an investor who has entered into an America call option contract. We assume the investor to pay certain dividend yield on the expected rate of returns from buying stocks. In this work, we also assume the stock price to be initially in the out of the money state and eventually will move up through at the money state to the deep in the money state where the expected future payoffs and returns are positive for the stock holder. We call a singularity point at the money because the expected payoff vanishes at this point. Then, using martingale, supermartingale and Markov theories we obtain the Bachelier-type of the Black-Scholes and the Black-Scholes equations which we hedge in the limit where the change of the expected payoff of the call option is extremely small. Hence, by comparison we obtain the time-independent Schroedinger equation in Quantum Mechanics. We solve completely the time independent Schroedinger equation for both models to obtain the expected rate of returns and the expected payoffs for the stock holder at the money. We find the expected rate of returns to be quantized in terms of the dividend yield.

Autofocus and fusion using nonlinear correlation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cabazos-Marín, Alma Rocío; Álvarez-Borrego, Josué, E-mail: josue@cicese.mx; Coronel-Beltrán, Ángel

2014-10-06

In this work a new algorithm is proposed for auto focusing and images fusion captured by microscope's CCD. The proposed algorithm for auto focusing implements the spiral scanning of each image in the stack f(x, y){sub w} to define the V{sub w} vector. The spectrum of the vector FV{sub w} is calculated by fast Fourier transform. The best in-focus image is determined by a focus measure that is obtained by the FV{sub 1} nonlinear correlation vector, of the reference image, with each other FV{sub W} images in the stack. In addition, fusion is performed with a subset of selected imagesmore » f(x, y){sub SBF} like the images with best focus measurement. Fusion creates a new improved image f(x, y){sub F} with the selection of pixels of higher intensity.« less

Nonlinear Absorption and Heating of Dense Plasmas.

DTIC Science & Technology

plasma focus both illuminated by a high intensity CO2 laser. Results indicate the previously noted increases in absorption due to the inclusion of the nonlinear saturation mechanism. The previously obtained increases in absorption with increasing density scale height and decreasing temperatures are also recovered. The

The Strong Effects Of On-Axis Focal Shift And Its Nonlinear Variation In Ultrasound Beams Radiated By Low Fresnel Number Transducers

NASA Astrophysics Data System (ADS)

Makov, Y. N.; Espinosa, V.; Sánchez-Morcillo, V. J.; Ramis, J.; Cruañes, J.; Camarena, F.

2006-05-01

On the basis of theoretical concepts, an accurate and complete experimental and numerical examination of the on-axis distribution and the corresponding temporal profiles for low-Fresnel-number focused ultrasound beams under increasing transducer input voltage has been performed. For a real focusing transducer with sufficiently small Fresnel number, a strong initial (linear) shift of the main on-axis pressure maximum from geometrical focal point towards the transducer, and its following displacement towards the focal point and backward motion as the driving transducer voltage increase until highly nonlinear regimes were fixed. The simultaneous monitoring of the temporal waveform modifications determines the real roles and interplay between different nonlinear effects (refraction and attenuation) in the observed dynamics of on-axis pressure maximum. The experimental results are in good agreement with numerical solutions of KZK equation, confirming that the observed dynamic shift of the maximum pressure point is related only to the interplay between diffraction, dissipation and nonlinearity of the acoustic wave.

Nonlinear optical waves with the second Painleve transcendent shape of envelope in Kerr media

NASA Astrophysics Data System (ADS)

Shcherbakov, Alexandre S.; Tepichin Rodriguez, Eduardo; Sanchez Sanchez, Mauro

2004-05-01

Nonlinear optical wave packets with the second Painleve transcendent shape of envelope are revealed in Kerr media, manifesting weakly focusing cubic nonlinearity, square-law dispersion, and linear losses. When the state of nonlinear optical transmission is realized, two possible types of boundary conditions turn out to be satisfied for these wave packets. The propagation of initially unchirped optical wave packets under consideration could be supported by lossless medium in both normal and anomalous dispersion regimes. At the same time initially chirped optical waves with the second Painleve transcendent shape in low-loss medium and need matching the magnitude of optical losses by the dispersion and nonlinear properties of that medium.

Proof of Concept for an Ultrasensitive Technique to Detect and Localize Sources of Elastic Nonlinearity Using Phononic Crystals.

PubMed

Miniaci, M; Gliozzi, A S; Morvan, B; Krushynska, A; Bosia, F; Scalerandi, M; Pugno, N M

2017-05-26

The appearance of nonlinear effects in elastic wave propagation is one of the most reliable and sensitive indicators of the onset of material damage. However, these effects are usually very small and can be detected only using cumbersome digital signal processing techniques. Here, we propose and experimentally validate an alternative approach, using the filtering and focusing properties of phononic crystals to naturally select and reflect the higher harmonics generated by nonlinear effects, enabling the realization of time-reversal procedures for nonlinear elastic source detection. The proposed device demonstrates its potential as an efficient, compact, portable, passive apparatus for nonlinear elastic wave sensing and damage detection.

Nonlinear refractive index measurements and self-action effects in Roselle-Hibiscus Sabdariffa solutions

NASA Astrophysics Data System (ADS)

Henari, F. Z.; Al-Saie, A.

2006-12-01

We report the observation of self-action phenomena, such as self-focusing, self-defocusing, self-phase modulation and beam fanning in Roselle-Hibiscus Sabdariffa solutions. This material is found to be a new type of natural nonlinear media, and the nonlinear reflective index coefficient has been determined using a Z-scan technique and by measuring the critical power for the self-trapping effect. Z-scan measurements show that this material has a large negative nonlinear refractive index, n 2 = 1 × 10-4 esu. A comparison between the experimental n 2 values and the calculated thermal value for n 2 suggests that the major contribution to nonlinear response is of thermal origin.

Polarization Shaping for Control of Nonlinear Propagation.

PubMed

Bouchard, Frédéric; Larocque, Hugo; Yao, Alison M; Travis, Christopher; De Leon, Israel; Rubano, Andrea; Karimi, Ebrahim; Oppo, Gian-Luca; Boyd, Robert W

2016-12-02

We study the nonlinear optical propagation of two different classes of light beams with space-varying polarization-radially symmetric vector beams and Poincaré beams with lemon and star topologies-in a rubidium vapor cell. Unlike Laguerre-Gauss and other types of beams that quickly experience instabilities, we observe that their propagation is not marked by beam breakup while still exhibiting traits such as nonlinear confinement and self-focusing. Our results suggest that, by tailoring the spatial structure of the polarization, the effects of nonlinear propagation can be effectively controlled. These findings provide a novel approach to transport high-power light beams in nonlinear media with controllable distortions to their spatial structure and polarization properties.

Self-Organization of Light in Optical Media with Competing Nonlinearities.

PubMed

Maucher, F; Pohl, T; Skupin, S; Krolikowski, W

2016-04-22

We study the propagation of light beams through optical media with competing nonlocal nonlinearities. We demonstrate that the nonlocality of competing focusing and defocusing nonlinearities gives rise to self-organization and stationary states with stable hexagonal intensity patterns, akin to transverse crystals of light filaments. Signatures of this long-range ordering are shown to be observable in the propagation of light in optical waveguides and even in free space. We consider a specific form of the nonlinear response that arises in atomic vapor upon proper light coupling. Yet, the general phenomenon of self-organization is a generic consequence of competing nonlocal nonlinearities, and may, hence, also be observed in other settings.

3D Multispecies Nonlinear Perturbative Particle Simulation of Intense Nonneutral Particle Beams (Research supported by the Department of Energy and the Short Pulse Spallation Source Project and LANSCE Division of LANL.)

NASA Astrophysics Data System (ADS)

Qin, Hong; Davidson, Ronald C.; Lee, W. Wei-Li

1999-11-01

The Beam Equilibrium Stability and Transport (BEST) code, a 3D multispecies nonlinear perturbative particle simulation code, has been developed to study collective effects in intense charged particle beams described self-consistently by the Vlasov-Maxwell equations. A Darwin model is adopted for transverse electromagnetic effects. As a 3D multispecies perturbative particle simulation code, it provides several unique capabilities. Since the simulation particles are used to simulate only the perturbed distribution function and self-fields, the simulation noise is reduced significantly. The perturbative approach also enables the code to investigate different physics effects separately, as well as simultaneously. The code can be easily switched between linear and nonlinear operation, and used to study both linear stability properties and nonlinear beam dynamics. These features, combined with 3D and multispecies capabilities, provides an effective tool to investigate the electron-ion two-stream instability, periodically focused solutions in alternating focusing fields, and many other important problems in nonlinear beam dynamics and accelerator physics. Applications to the two-stream instability are presented.

Design of HIFU transducers to generate specific nonlinear ultrasound fields.

PubMed

Khokhlova, Vera A; Yuldashev, Petr V; Rosnitskiy, Pavel B; Maxwell, Adam D; Kreider, Wayne; Bailey, Michael R; Sapozhnikov, Oleg A

2016-01-01

Various clinical applications of high intensity focused ultrasound (HIFU) have different requirements on the pressure level and degree of nonlinear waveform distortion at the focus. Applications that utilize nonlinear waves with developed shocks are of growing interest, for example, for mechanical disintegration as well as for accelerated thermal ablation of tissue. In this work, an inverse problem of determining transducer parameters to enable formation of shocks with desired amplitude at the focus is solved. The solution was obtained by performing multiple direct simulations of the parabolic Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation for various parameters of the source. It is shown that results obtained within the parabolic approximation can be used to describe the focal region of single element spherical sources as well as complex transducer arrays. It is also demonstrated that the focal pressure level at which fully developed shocks are formed mainly depends on the focusing angle of the source and only slightly depends on its aperture and operating frequency. Using the simulation results, a 256-element HIFU array operating at 1.5 MHz frequency was designed for a specific application of boiling-histotripsy that relies on the presence of 90-100 MPa shocks at the focus. The size of the array elements and focusing angle of the array were chosen to satisfy technical limitations on the intensity at the array elements and desired shock amplitudes in the focal waveform. Focus steering capabilities of the array were analysed using an open-source T-Array software developed at Moscow State University.

Design of HIFU Transducers to Generate Specific Nonlinear Ultrasound Fields

NASA Astrophysics Data System (ADS)

Khokhlova, Vera A.; Yuldashev, Petr V.; Rosnitskiy, Pavel B.; Maxwell, Adam D.; Kreider, Wayne; Bailey, Michael R.; Sapozhnikov, Oleg A.

Various clinical applications of high intensity focused ultrasound (HIFU) have different requirements on the pressure level and degree of nonlinear waveform distortion at the focus. Applications that utilize nonlinear waves with developed shocks are of growing interest, for example, for mechanical disintegration as well as for accelerated thermal ablation oftissue. In this work, an inverse problem of determining transducer parameters to enable formation of shockswith desired amplitude at the focus is solved. The solution was obtained by performing multipledirect simulations of the parabolic Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation for various parameters of the source. It is shown that results obtained within the parabolic approximation can be used to describe the focal region of single element spherical sourcesas well as complex transducer arrays. It is also demonstrated that the focal pressure level at which fully developed shocksare formed mainly depends on the focusing angle of the source and only slightly depends on its aperture and operating frequency. Using the simulation results, a 256-element HIFU array operating at 1.5 MHz frequency was designed for a specific application of boiling-histotripsy that relies on the presence of 90-100 MPa shocks at the focus. The size of the array elements and focusing angle of the array were chosen to satisfy technical limitations on the intensity at the array elements and desired shock amplitudes in the focal waveform. Focus steering capabilities of the array were analysed using an open-source T-Array software developed at Moscow State University.

Perpendicular Diffusion Coefficient of Comic Rays: The Presence of Weak Adiabatic Focusing

NASA Astrophysics Data System (ADS)

Wang, J. F.; Qin, G.; Ma, Q. M.; Song, T.; Yuan, S. B.

2017-08-01

The influence of adiabatic focusing on particle diffusion is an important topic in astrophysics and plasma physics. In the past, several authors have explored the influence of along-field adiabatic focusing on the parallel diffusion of charged energetic particles. In this paper, using the unified nonlinear transport theory developed by Shalchi and the method of He and Schlickeiser, we derive a new nonlinear perpendicular diffusion coefficient for a non-uniform background magnetic field. This formula demonstrates that the particle perpendicular diffusion coefficient is modified by along-field adiabatic focusing. For isotropic pitch-angle scattering and the weak adiabatic focusing limit, the derived perpendicular diffusion coefficient is independent of the sign of adiabatic focusing characteristic length. For the two-component model, we simplify the perpendicular diffusion coefficient up to the second order of the power series of the adiabatic focusing characteristic quantity. We find that the first-order modifying factor is equal to zero and that the sign of the second order is determined by the energy of the particles.

On solutions of the fifth-order dispersive equations with porous medium type non-linearity

NASA Astrophysics Data System (ADS)

Kocak, Huseyin; Pinar, Zehra

2018-07-01

In this work, we focus on obtaining the exact solutions of the fifth-order semi-linear and non-linear dispersive partial differential equations, which have the second-order diffusion-like (porous-type) non-linearity. The proposed equations were not studied in the literature in the sense of the exact solutions. We reveal solutions of the proposed equations using the classical Riccati equations method. The obtained exact solutions, which can play a key role to simulate non-linear waves in the medium with dispersion and diffusion, are illustrated and discussed in details.

Nonlinear Dynamics and the Growth of Literature.

ERIC Educational Resources Information Center

Tabah, Albert N.

1992-01-01

Discussion of nonlinear dynamic mechanisms focuses on whether information production and dissemination can be described by similar mechanisms. The exponential versus linear growth of literature is discussed, the time factor is considered, an example using literature from the field of superconductivity is given, and implications for information…

Subwavelength nonlinear phase control and anomalous phase matching in plasmonic metasurfaces

NASA Astrophysics Data System (ADS)

Almeida, Euclides; Shalem, Guy; Prior, Yehiam

2016-01-01

Metasurfaces, and in particular those containing plasmonic-based metallic elements, constitute an attractive set of materials with a potential for replacing standard bulky optical elements. In recent years, increasing attention has been focused on their nonlinear optical properties, particularly in the context of second and third harmonic generation and beam steering by phase gratings. Here, we harness the full phase control enabled by subwavelength plasmonic elements to demonstrate a unique metasurface phase matching that is required for efficient nonlinear processes. We discuss the difference between scattering by a grating and by subwavelength phase-gradient elements. We show that for such interfaces an anomalous phase-matching condition prevails, which is the nonlinear analogue of the generalized Snell's law. The subwavelength phase control of optical nonlinearities paves the way for the design of ultrathin, flat nonlinear optical elements. We demonstrate nonlinear metasurface lenses, which act both as generators and as manipulators of the frequency-converted signal.

The Effect of Crack Orientation on the Nonlinear Interaction of a P-wave with an S-wave

DOE PAGES

TenCate, J. A.; Malcolm, A. E.; Feng, X.; ...

2016-06-06

Cracks, joints, fluids, and other pore-scale structures have long been hypothesized to be the cause of the large elastic nonlinearity observed in rocks. It is difficult to definitively say which pore-scale features are most important, however, because of the difficulty in isolating the source of the nonlinear interaction. In this work, we focus on the influence of cracks on the recorded nonlinear signal and in particular on how the orientation of microcracks changes the strength of the nonlinear interaction. We do this by studying the effect of orientation on the measurements in a rock with anisotropy correlated with the presencemore » and alignment of microcracks. We measure the nonlinear response via the traveltime delay induced in a low-amplitude P wave probe by a high-amplitude S wave pump. We find evidence that crack orientation has a significant effect on the nonlinear signal.« less

Localized solutions of Lugiato-Lefever equations with focused pump.

PubMed

Cardoso, Wesley B; Salasnich, Luca; Malomed, Boris A

2017-12-04

Lugiato-Lefever (LL) equations in one and two dimensions (1D and 2D) accurately describe the dynamics of optical fields in pumped lossy cavities with the intrinsic Kerr nonlinearity. The external pump is usually assumed to be uniform, but it can be made tightly focused too-in particular, for building small pixels. We obtain solutions of the LL equations, with both the focusing and defocusing intrinsic nonlinearity, for 1D and 2D confined modes supported by the localized pump. In the 1D setting, we first develop a simple perturbation theory, based in the sech ansatz, in the case of weak pump and loss. Then, a family of exact analytical solutions for spatially confined modes is produced for the pump focused in the form of a delta-function, with a nonlinear loss (two-photon absorption) added to the LL model. Numerical findings demonstrate that these exact solutions are stable, both dynamically and structurally (the latter means that stable numerical solutions close to the exact ones are found when a specific condition, necessary for the existence of the analytical solution, does not hold). In 2D, vast families of stable confined modes are produced by means of a variational approximation and full numerical simulations.

Development of a Nonlinear Acoustic Phased Array and its Interaction with Thin Plates

NASA Astrophysics Data System (ADS)

Anzel, Paul; Donahue, Carly; Daraio, Chiara

2015-03-01

Numerous technologies are based on the principle of focusing acoustic energy. We propose a new device to focus sound waves which exploits highly nonlinear dynamics. The advantages of this device are the capability of generating very highly powerful acoustic pulses and potential operation in high-temperature environments where traditional piezoelectrics may fail. This device is composed of rows of ball bearings placed in contact with a medium of interest and with an actuator on the top. Elastic spherical particles have a contact force that grows with their relative displacement to the three-halves power (Hertzian contact). When several spheres are placed in a row, the particles support the propagation of ``solitary waves''--strong, compact stress-wave pulses whose tendency to disperse is counteracted by the nonlinearity of the sphere's contact force. We present results regarding the experimental operation of the device and its comparison to theory and numerical simulations. We will show how well this system is capable of focusing energy at various locations in the medium, and the limits imposed by pre-compression. Finally, the effects of timing error on energy focusing will be demonstrated. This research has been supported by a NASA Space Technology Research Fellowship.

A boundary condition to the Khokhlov-Zabolotskaya equation for modeling strongly focused nonlinear ultrasound fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rosnitskiy, P., E-mail: pavrosni@yandex.ru; Yuldashev, P., E-mail: petr@acs366.phys.msu.ru; Khokhlova, V., E-mail: vera@acs366.phys.msu.ru

2015-10-28

An equivalent source model was proposed as a boundary condition to the nonlinear parabolic Khokhlov-Zabolotskaya (KZ) equation to simulate high intensity focused ultrasound (HIFU) fields generated by medical ultrasound transducers with the shape of a spherical shell. The boundary condition was set in the initial plane; the aperture, the focal distance, and the initial pressure of the source were chosen based on the best match of the axial pressure amplitude and phase distributions in the Rayleigh integral analytic solution for a spherical transducer and the linear parabolic approximation solution for the equivalent source. Analytic expressions for the equivalent source parametersmore » were derived. It was shown that the proposed approach allowed us to transfer the boundary condition from the spherical surface to the plane and to achieve a very good match between the linear field solutions of the parabolic and full diffraction models even for highly focused sources with F-number less than unity. The proposed method can be further used to expand the capabilities of the KZ nonlinear parabolic equation for efficient modeling of HIFU fields generated by strongly focused sources.« less

Single-Particle Quantum Dynamics in a Magnetic Lattice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Venturini, Marco

2001-02-01

We study the quantum dynamics of a spinless charged-particle propagating through a magnetic lattice in a transport line or storage ring. Starting from the Klein-Gordon equation and by applying the paraxial approximation, we derive a Schroedinger-like equation for the betatron motion. A suitable unitary transformation reduces the problem to that of a simple harmonic oscillator. As a result we are able to find an explicit expression for the particle wavefunction.

Transition from linear- to nonlinear-focusing regime in filamentation

PubMed Central

Lim, Khan; Durand, Magali; Baudelet, Matthieu; Richardson, Martin

2014-01-01

Laser filamentation in gases is often carried out in the laboratory with focusing optics to better stabilize the filament, whereas real-world applications of filaments frequently involve collimated or near-collimated beams. It is well documented that geometrical focusing can alter the properties of laser filaments and, consequently, a transition between a collimated and a strongly focused filament is expected. Nevertheless, this transition point has not been identified. Here, we propose an analytical method to determine the transition, and show that it corresponds to an actual shift in the balance of physical mechanisms governing filamentation. In high-NA conditions, filamentation is primarily governed by geometrical focusing and plasma effects, while the Kerr nonlinearity plays a more significant role as NA decreases. We find the transition between the two regimes to be relatively insensitive to the intrinsic laser parameters, and our analysis agrees well with a wide range of parameters found in published literature. PMID:25434678

Mechanics of the acoustic radiation force in tissue-like solids

NASA Astrophysics Data System (ADS)

Dontsov, Egor V.

The acoustic radiation force (ARF) is a phenomenon affiliated with the nonlinear effects of high-intensity wave propagation. It represents the mean momentum transfer from the sound wave to the medium, and allows for an effective computation of the mean motion (e.g. acoustic streaming in fluids) induced by a high-intensity sound wave. Nowadays, the high-intensity focused ultrasound is frequently used in medical diagnosis applications due to its ability to "push" inside the tissue with the radiation body force and facilitate the local quantification of tissue's viscoelastic properties. The main objectives of this study include: i) the theoretical investigation of the ARF in fluids and tissue-like solids generated respectively by the amplitude modulated plane wave and focused ultrasound; ii) computation of the nonlinear acoustic wave propagation when the amplitude of the focused ultrasound field is modulated by a low-frequency signal, and iii) modeling of the ARF-induced motion in tissue-like solids for the purpose of quantifying their nonlinear elasticity via the magnitude of the ARF. Regarding the first part, a comparison with the existing theory of the ARF reveals a number of key features that are brought to light by the new formulation, including the contributions to the ARF of ultrasound modulation and thermal expansion, as well as the precise role of constitutive nonlinearities in generating the sustained body force in tissue-like solids by a focused ultrasound beam. In the second part, the hybrid time-frequency domain algorithm for the numerical analysis of the nonlinear wave equation is proposed. The approach is validated by comparing the results to the finite-difference modeling in time domain. Regarding the third objective, the Fourier transform approach is used to compute the ARF-induced shear wave motion in tissue-mimicking phantoms. A comparison between the experiment (tests performed at the Mayo Clinic) and model permitted the estimation of a particular coefficient of nonlinear tissue elasticity from the amplitude of the ARF-generated shear waves. For completeness, the ARF estimates of this coefficient are verified via an established technique known as acoustoelasticity.

Simulations for the Test Flight of an Experimental HALE Aircraft

DTIC Science & Technology

2011-06-01

as a plant representation for HALE aircraft control design. It focuses on a reduced number of states to represent the complex nonlinear problem...Atkins, Ella M., Shearer, Christopher M. and Nathan A. Pitcher . “X-HALE: A Very Flexible UAV for Nonlinear Aeroelastic Tests.” (AIAA 2010-2715), April

Coherent source interaction, third-order nonlinear response of synthesized PEG coated magnetite nanoparticles in polyethylene glycol and its application

NASA Astrophysics Data System (ADS)

Gopal, S. Veena; Chitrambalam, S.; Joe, I. Hubert

2018-01-01

Third-order nonlinear response of synthesized polyethylene glycol coated Fe3O4 nanoparticles dispersed in a suitable solvent, polyethylene glycol has been studied. The structural characterization of the synthesized magnetite nanoparticles were carried out. The linear optical property of the synthesized magnetite nanoparticles was investigated using UV-visible technique. Both closed and open aperture Z-scan techniques have been performed at 532 nm with pulse width 5 ns and repetition rate 10 Hz. It was found that polyethylene glycol coated magnetite exhibits reverse saturable absorption, with significant nonlinear absorption coefficient. Two-photon absorption intensity dependent positive nonlinear refraction coefficients indicate self focusing phenomena. Results show that higher concentration gives better nonlinear and optical limiting properties.

Numerical Simulations of Self-Focused Pulses Using the Nonlinear Maxwell Equations

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1994-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations. Abstract of a proposed paper for presentation at the meeting NONLINEAR OPTICS: Materials, Fundamentals, and Applications, Hyatt Regency Waikaloa, Waikaloa, Hawaii, July 24-29, 1994, Cosponsored by IEEE/Lasers and Electro-Optics Society and Optical Society of America

Time reversal focusing of high amplitude sound in a reverberation chamber.

PubMed

Willardson, Matthew L; Anderson, Brian E; Young, Sarah M; Denison, Michael H; Patchett, Brian D

2018-02-01

Time reversal (TR) is a signal processing technique that can be used for intentional sound focusing. While it has been studied in room acoustics, the application of TR to produce a high amplitude focus of sound in a room has not yet been explored. The purpose of this study is to create a virtual source of spherical waves with TR that are of sufficient intensity to study nonlinear acoustic propagation. A parameterization study of deconvolution, one-bit, clipping, and decay compensation TR methods is performed to optimize high amplitude focusing and temporal signal focus quality. Of all TR methods studied, clipping is shown to produce the highest amplitude focal signal. An experiment utilizing eight horn loudspeakers in a reverberation chamber is done with the clipping TR method. A peak focal amplitude of 9.05 kPa (173.1 dB peak re 20 μPa) is achieved. Results from this experiment indicate that this high amplitude focusing is a nonlinear process.

Rogue waves for a discrete (2+1)-dimensional Ablowitz-Ladik equation in the nonlinear optics and Bose-Einstein condensation

NASA Astrophysics Data System (ADS)

Wu, Xiao-Yu; Tian, Bo; Chai, Han-Peng; Du, Zhong

2018-03-01

Under investigation in this paper is a discrete (2+1)-dimensional Ablowitz-Ladik equation, which is used to model the nonlinear waves in the nonlinear optics and Bose-Einstein condensation. Employing the Kadomtsev-Petviashvili hierarchy reduction, we obtain the rogue wave solutions in terms of the Gramian. We graphically study the first-, second- and third-order rogue waves with the influence of the focusing coefficient and coupling strength. When the value of the focusing coefficient increases, both the peak of the rogue wave and background decrease. When the value of the coupling strength increases, the rogue wave raises and decays in a shorter time. High-order rogue waves are exhibited as one single highest peak and some lower humps, and such lower humps are shown as the triangular and circular patterns.

The existence of periodic solutions for nonlinear beam equations on Td by a para-differential method

NASA Astrophysics Data System (ADS)

Chen, Bochao; Li, Yong; Gao, Yixian

2018-05-01

This paper focuses on the construction of periodic solutions of nonlinear beam equations on the $d$-dimensional tori. For a large set of frequencies, we demonstrate that an equivalent form of the nonlinear equations can be obtained by a para-differential conjugation. Given the non-resonant conditions on each finite dimensional subspaces, it is shown that the periodic solutions can be constructed for the block diagonal equation by a classical iteration scheme.

Modal method for Second Harmonic Generation in nanostructures

NASA Astrophysics Data System (ADS)

Héron, S.; Pardo, F.; Bouchon, P.; Pelouard, J.-L.; Haïdar, R.

2015-05-01

Nanophotonic devices show interesting features for nonlinear response enhancement but numerical tools are mandatory to fully determine their behaviour. To address this need, we present a numerical modal method dedicated to nonlinear optics calculations under the undepleted pump approximation. It is brie y explained in the frame of Second Harmonic Generation for both plane waves and focused beams. The nonlinear behaviour of selected nanostructures is then investigated to show comparison with existing analytical results and study the convergence of the code.

Nonlinear Thomson scattering of a relativistically strong tightly focused ultrashort laser pulse

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vais, O. E.; Bochkarev, S. G., E-mail: bochkar@sci.lebedev.ru; Bychenkov, V. Yu.

The problem of nonlinear Thomson scattering of a relativistically strong linearly polarized ultrashort laser pulse tightly focused into a spot with a diameter of D{sub F} ≳ λ (where λ is the laser wavelength) is solved. The energy, spectral, and angular distributions of radiation generated due to Thomson scattering from test electrons located in the focal region are found. The characteristics of scattered radiation are studied as functions of the tightness of laser focusing and the initial position of test particles relative to the center of the focal region for a given laser pulse energy. It is demonstrated that themore » ultratight focusing is not optimal for obtaining the brightest and hardest source of secondary electromagnetic radiation. The hardest and shortest radiation pulse is generated when the beam waist diameter is ≃10λ.« less

Design of HIFU transducers to generate specific nonlinear ultrasound fields

PubMed Central

Khokhlova, Vera A.; Yuldashev, Petr V.; Rosnitskiy, Pavel B.; Maxwell, Adam D.; Kreider, Wayne; Bailey, Michael R.; Sapozhnikov, Oleg A.

2017-01-01

Various clinical applications of high intensity focused ultrasound (HIFU) have different requirements on the pressure level and degree of nonlinear waveform distortion at the focus. Applications that utilize nonlinear waves with developed shocks are of growing interest, for example, for mechanical disintegration as well as for accelerated thermal ablation of tissue. In this work, an inverse problem of determining transducer parameters to enable formation of shocks with desired amplitude at the focus is solved. The solution was obtained by performing multiple direct simulations of the parabolic Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation for various parameters of the source. It is shown that results obtained within the parabolic approximation can be used to describe the focal region of single element spherical sources as well as complex transducer arrays. It is also demonstrated that the focal pressure level at which fully developed shocks are formed mainly depends on the focusing angle of the source and only slightly depends on its aperture and operating frequency. Using the simulation results, a 256-element HIFU array operating at 1.5 MHz frequency was designed for a specific application of boiling-histotripsy that relies on the presence of 90–100 MPa shocks at the focus. The size of the array elements and focusing angle of the array were chosen to satisfy technical limitations on the intensity at the array elements and desired shock amplitudes in the focal waveform. Focus steering capabilities of the array were analysed using an open-source T-Array software developed at Moscow State University. PMID:28580038

Quasi-Maximum Likelihood Estimation of Structural Equation Models with Multiple Interaction and Quadratic Effects

ERIC Educational Resources Information Center

Klein, Andreas G.; Muthen, Bengt O.

2007-01-01

In this article, a nonlinear structural equation model is introduced and a quasi-maximum likelihood method for simultaneous estimation and testing of multiple nonlinear effects is developed. The focus of the new methodology lies on efficiency, robustness, and computational practicability. Monte-Carlo studies indicate that the method is highly…

Presence of nonlinearity in intracranial EEG recordings: detected by Lyapunov exponents

NASA Astrophysics Data System (ADS)

Liu, Chang-Chia; Shiau, Deng-Shan; Chaovalitwongse, W. Art; Pardalos, Panos M.; Sackellares, J. C.

2007-11-01

In this communication, we performed nonlinearity analysis in the EEG signals recorded from patients with temporal lobe epilepsy (TLE). The largest Lyapunov exponent (Lmax) and phase randomization surrogate data technique were employed to form the statistical test. EEG recordings were acquired invasively from three patients in six brain regions (left and right temporal depth, sub-temporal and orbitofrontal) with 28-32 depth electrodes placed in depth and subdural of the brain. All three patients in this study have unilateral epileptic focus region on the right hippocampus(RH). Nonlinearity was detected by comparing the Lmax profiles of the EEG recordings to its surrogates. The nonlinearity was seen in all different states of the patient with the highest found in post-ictal state. Further our results for all patients exhibited higher degree of differences, quantified by paired t-test, in Lmax values between original and its surrogate from EEG signals recorded from epileptic focus regions. The results of this study demonstrated the Lmax is capable to capture spatio-temporal dynamics that may not be able to detect by linear measurements in the intracranial EEG recordings.

EPR: Some History and Clarification

NASA Astrophysics Data System (ADS)

Fine, Arthur

2002-04-01

Locality, separation and entanglement 1930s style. We’ll explore the background to the 1935 paper by Einstein, Podolsky and Rosen, how it was composed, the actual argument of the paper, the principles used, and how the paper was received by Schroedinger, and others.We’ll also look at Bohr’s response: the extent to which Bohr connects with what Einstein was after in EPR and the extent to EPR marks a shift in Bohr’s thinking about the quantum theory.

The Schwinger Variational Method

NASA Technical Reports Server (NTRS)

Huo, Winifred M.

1995-01-01

Variational methods have proven invaluable in theoretical physics and chemistry, both for bound state problems and for the study of collision phenomena. For collisional problems they can be grouped into two types: those based on the Schroedinger equation and those based on the Lippmann-Schwinger equation. The application of the Schwinger variational (SV) method to e-molecule collisions and photoionization has been reviewed previously. The present chapter discusses the implementation of the SV method as applied to e-molecule collisions.

Quantum mechanics from an equivalence principle

DOE Office of Scientific and Technical Information (OSTI.GOV)

Faraggi, A.E.; Matone, M.

1997-05-15

The authors show that requiring diffeomorphic equivalence for one-dimensional stationary states implies that the reduced action S{sub 0} satisfies the quantum Hamilton-Jacobi equation with the Planck constant playing the role of a covariantizing parameter. The construction shows the existence of a fundamental initial condition which is strictly related to the Moebius symmetry of the Legendre transform and to its involutive character. The universal nature of the initial condition implies the Schroedinger equation in any dimension.

Review of the inverse scattering problem at fixed energy in quantum mechanics

NASA Technical Reports Server (NTRS)

Sabatier, P. C.

1972-01-01

Methods of solution of the inverse scattering problem at fixed energy in quantum mechanics are presented. Scattering experiments of a beam of particles at a nonrelativisitic energy by a target made up of particles are analyzed. The Schroedinger equation is used to develop the quantum mechanical description of the system and one of several functions depending on the relative distance of the particles. The inverse problem is the construction of the potentials from experimental measurements.

Quantum Sets and Clifford Algebras

NASA Astrophysics Data System (ADS)

Finkelstein, David

1982-06-01

The mathematical language presently used for quantum physics is a high-level language. As a lowest-level or basic language I construct a quantum set theory in three stages: (1) Classical set theory, formulated as a Clifford algebra of “ S numbers” generated by a single monadic operation, “bracing,” Br = {…}. (2) Indefinite set theory, a modification of set theory dealing with the modal logical concept of possibility. (3) Quantum set theory. The quantum set is constructed from the null set by the familiar quantum techniques of tensor product and antisymmetrization. There are both a Clifford and a Grassmann algebra with sets as basis elements. Rank and cardinality operators are analogous to Schroedinger coordinates of the theory, in that they are multiplication or “ Q-type” operators. “ P-type” operators analogous to Schroedinger momenta, in that they transform the Q-type quantities, are bracing (Br), Clifford multiplication by a set X, and the creator of X, represented by Grassmann multiplication c( X) by the set X. Br and its adjoint Br* form a Bose-Einstein canonical pair, and c( X) and its adjoint c( X)* form a Fermi-Dirac or anticanonical pair. Many coefficient number systems can be employed in this quantization. I use the integers for a discrete quantum theory, with the usual complex quantum theory as limit. Quantum set theory may be applied to a quantum time space and a quantum automaton.

Hunting for Snarks in Quantum Mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hestenes, David

2009-12-08

A long-standing debate over the interpretation of quantum mechanics has centered on the meaning of Schroedinger's wave function {psi} for an electron. Broadly speaking, there are two major opposing schools. On the one side, the Copenhagen school(led by Bohr, Heisenberg and Pauli) holds that {psi} provides a complete description of a single electron state; hence the probability interpretation of {psi}{psi}* expresses an irreducible uncertainty in electron behavior that is intrinsic in nature. On the other side, the realist school(led by Einstein, de Broglie, Bohm and Jaynes) holds that {psi} represents a statistical ensemble of possible electron states; hence it ismore » an incomplete description of a single electron state. I contend that the debaters have overlooked crucial facts about the electron revealed by Dirac theory. In particular, analysis of electron zitterbewegung(first noticed by Schroedinger) opens a window to particle substructure in quantum mechanics that explains the physical significance of the complex phase factor in {psi}. This led to a testable model for particle substructure with surprising support by recent experimental evidence. If the explanation is upheld by further research, it will resolve the debate in favor of the realist school. I give details. The perils of research on the foundations of quantum mechanics have been foreseen by Lewis Carroll in The Hunting of the Snark{exclamation_point}.« less

Nonlinear ultrasonics for material state awareness

NASA Astrophysics Data System (ADS)

Jacobs, L. J.

2014-02-01

Predictive health monitoring of structural components will require the development of advanced sensing techniques capable of providing quantitative information on the damage state of structural materials. By focusing on nonlinear acoustic techniques, it is possible to measure absolute, strength based material parameters that can then be coupled with uncertainty models to enable accurate and quantitative life prediction. Starting at the material level, this review will present current research that involves a combination of sensing techniques and physics-based models to characterize damage in metallic materials. In metals, these nonlinear ultrasonic measurements can sense material state, before the formation of micro- and macro-cracks. Typically, cracks of a measurable size appear quite late in a component's total life, while the material's integrity in terms of toughness and strength gradually decreases due to the microplasticity (dislocations) and associated change in the material's microstructure. This review focuses on second harmonic generation techniques. Since these nonlinear acoustic techniques are acoustic wave based, component interrogation can be performed with bulk, surface and guided waves using the same underlying material physics; these nonlinear ultrasonic techniques provide results which are independent of the wave type used. Recent physics-based models consider the evolution of damage due to dislocations, slip bands, interstitials, and precipitates in the lattice structure, which can lead to localized damage.

Nonlinear flight control design using backstepping methodology

NASA Astrophysics Data System (ADS)

Tran, Thanh Trung

The subject of nonlinear flight control design using backstepping control methodology is investigated in the dissertation research presented here. Control design methods based on nonlinear models of the dynamic system provide higher utility and versatility because the design model more closely matches the physical system behavior. Obtaining requisite model fidelity is only half of the overall design process, however. Design of the nonlinear control loops can lessen the effects of nonlinearity, or even exploit nonlinearity, to achieve higher levels of closed-loop stability, performance, and robustness. The goal of the research is to improve control quality for a general class of strict-feedback dynamic systems and provide flight control architectures to augment the aircraft motion. The research is divided into two parts: theoretical control development for the strict-feedback form of nonlinear dynamic systems and application of the proposed theory for nonlinear flight dynamics. In the first part, the research is built on two components: transforming the nonlinear dynamic model to a canonical strict-feedback form and then applying backstepping control theory to the canonical model. The research considers a process to determine when this transformation is possible, and when it is possible, a systematic process to transfer the model is also considered when practical. When this is not the case, certain modeling assumptions are explored to facilitate the transformation. After achieving the canonical form, a systematic design procedure for formulating a backstepping control law is explored in the research. Starting with the simplest subsystem and ending with the full system, pseudo control concepts based on Lyapunov control functions are used to control each successive subsystem. Typically each pseudo control must be solved from a nonlinear algebraic equation. At the end of this process, the physical control input must be re-expressed in terms of the physical states by eliminating the pseudo control transformations. In the second part, the research focuses on nonlinear control design for flight dynamics of aircraft motion. Some assumptions on aerodynamics of the aircraft are addressed to transform full nonlinear flight dynamics into the canonical strict-feedback form. The assumptions are also analyzed, validated, and compared to show the advantages and disadvantages of the design models. With the achieved models, investigation focuses on formulating the backstepping control laws and provides an advanced control algorithm for nonlinear flight dynamics of the aircraft. Experimental and simulation studies are successfully implemented to validate the proposed control method. Advancement of nonlinear backstepping control theory and its application to nonlinear flight control are achieved in the dissertation research.

The Buoyancy Budget With a Nonlinear Equation of State

NASA Astrophysics Data System (ADS)

Hieronymus, M. H.; Nycander, J.

2012-12-01

There has been a number of studies focusing on different aspects of having a nonlinear equation of state for seawater. Amongst other things it has been shown that the nonlinear equation of state has implications for the oceanic energy budget and that nonlinear processes can be a significant source of dense water production. This presentation will focus on the oceanic buoyancy budget. The nonlinear equation of state of seawater can introduce a sink or source of buoyancy when water parcels of unequal salinities and temperatures are mixed. A common example is the process known as cabbeling, which is responsible for forming a water mass that is denser than the original constituents in a mixture of two water masses with equal densities but different salinities and temperatures. This presentation will contain quantitative estimates of these nonlinear effects on the buoyancy budget of the global ocean. Because of these nonlinear effects there is a net sink of buoyancy in the oceans interior and the size of this sink can be determined from the buoyancy fluxes at the ocean boundaries. These boundary buoyancy fluxes are calculated using two surface heat flux climatologies one based on in situ measurements, the other on a reanalysis and in both cases using a nonlinear equation of state. The presentation also treats the buoyancy budget in the State of the art ocean model Nucleus for European Modelling of the Ocean (NEMO) and the results from NEMO are seen to be in good agreement with the buoyancy budgets based on the heat flux climatologies. Using the ocean model is a good complement to the surface flux climatologies, because in NEMO the buoyancy fluxes can be evaluated at all vertical model levels. This means that the vertical distribution of the buoyancy sink can be looked into. The results from NEMO shows that in large parts of the ocean the nonlinear buoyancy sink is the largest contribution to the buoyancy budget.

Influence of light absorption on relativistic self-focusing of Gaussian laser beam in cold quantum plasma

NASA Astrophysics Data System (ADS)

Patil, S. D.; Valkunde, A. T.; Vhanmore, B. D.; Urunkar, T. U.; Gavade, K. M.; Takale, M. V.

2018-05-01

When inter particle distance is comparable to the de Broglies wavelength of charged particles, quantum effects in plasmas are unavoidable. We have exploited an influence of light absorption on self-focusing of Gaussian laser beam in cold quantum plasma by considering relativistic nonlinearity. Nonlinear differential equation governing beam-width parameter has been established by using parabolic equation approach under paraxial and WKB approximations. The effect of light absorption on variation of beam-width parameter with dimensionless distance of propagation is presented graphically and discussed. It is found that light absorption plays vital role in weakening the relativistic self-focusing of laser beam during propagation in cold quantum plasma and gives reasonably interesting results.

Research on Nonlinear Time Series Forecasting of Time-Delay NN Embedded with Bayesian Regularization

NASA Astrophysics Data System (ADS)

Jiang, Weijin; Xu, Yusheng; Xu, Yuhui; Wang, Jianmin

Based on the idea of nonlinear prediction of phase space reconstruction, this paper presented a time delay BP neural network model, whose generalization capability was improved by Bayesian regularization. Furthermore, the model is applied to forecast the imp&exp trades in one industry. The results showed that the improved model has excellent generalization capabilities, which not only learned the historical curve, but efficiently predicted the trend of business. Comparing with common evaluation of forecasts, we put on a conclusion that nonlinear forecast can not only focus on data combination and precision improvement, it also can vividly reflect the nonlinear characteristic of the forecasting system. While analyzing the forecasting precision of the model, we give a model judgment by calculating the nonlinear characteristic value of the combined serial and original serial, proved that the forecasting model can reasonably 'catch' the dynamic characteristic of the nonlinear system which produced the origin serial.

Nonlinear bias analysis and correction of microwave temperature sounder observations for FY-3C meteorological satellite

NASA Astrophysics Data System (ADS)

Hu, Taiyang; Lv, Rongchuan; Jin, Xu; Li, Hao; Chen, Wenxin

2018-01-01

The nonlinear bias analysis and correction of receiving channels in Chinese FY-3C meteorological satellite Microwave Temperature Sounder (MWTS) is a key technology of data assimilation for satellite radiance data. The thermal-vacuum chamber calibration data acquired from the MWTS can be analyzed to evaluate the instrument performance, including radiometric temperature sensitivity, channel nonlinearity and calibration accuracy. Especially, the nonlinearity parameters due to imperfect square-law detectors will be calculated from calibration data and further used to correct the nonlinear bias contributions of microwave receiving channels. Based upon the operational principles and thermalvacuum chamber calibration procedures of MWTS, this paper mainly focuses on the nonlinear bias analysis and correction methods for improving the calibration accuracy of the important instrument onboard FY-3C meteorological satellite, from the perspective of theoretical and experimental studies. Furthermore, a series of original results are presented to demonstrate the feasibility and significance of the methods.

A novel method for predicting the power outputs of wave energy converters

NASA Astrophysics Data System (ADS)

Wang, Yingguang

2018-03-01

This paper focuses on realistically predicting the power outputs of wave energy converters operating in shallow water nonlinear waves. A heaving two-body point absorber is utilized as a specific calculation example, and the generated power of the point absorber has been predicted by using a novel method (a nonlinear simulation method) that incorporates a second order random wave model into a nonlinear dynamic filter. It is demonstrated that the second order random wave model in this article can be utilized to generate irregular waves with realistic crest-trough asymmetries, and consequently, more accurate generated power can be predicted by subsequently solving the nonlinear dynamic filter equation with the nonlinearly simulated second order waves as inputs. The research findings demonstrate that the novel nonlinear simulation method in this article can be utilized as a robust tool for ocean engineers in their design, analysis and optimization of wave energy converters.

Marshall N. Rosenbluth Outstanding Doctoral Thesis Award Talk: The Ultrafast Nonlinear Response of Air Molecules and its Effect on Femtosecond Laser Plasma Filaments in Atmosphere

NASA Astrophysics Data System (ADS)

Chen, Yu-Hsin

2012-10-01

When exceeding the critical power Pcr, an intense laser pulse propagating in a gas collapses into one or multiple ``filaments,'' which can extend meters in length with weakly ionized plasma and local intensity ˜ 10^13 W/cm^2 radially confined in a diameter of < 100 μm [1]. While it has been generally accepted the nonlinear self-focusing of the laser pulse leading to beam collapse is stabilized by plasma generation [2], neither the field-induced nonlinearity nor the plasma generation had been directly measured. This uncertainty has given rise to recent controversy about whether plasma generation does indeed counteract the positive nonlinearity [3, 4]. For even a basic understanding of femtosecond filamentation and for applications, the focusing and defocusing mechanisms---nonlinear self-focusing and ionization---must be understood. By employing a single-shot, time-resolved technique based on spectral interferometry [5] to study the constituents of air, it is found that the rotational responses in O2 and N2 are the dominant nonlinear effect in filamentary propagation when the laser pulse duration is longer than ˜ 100fs. Furthermore, we find that the instantaneous nonlinearity scales linearly up to the ionization threshold [6], eliminating any possibility of an ionization-free negative stabilization [3] of filamentation. This is confirmed by space-resolved electron density measurements in meter-long filaments produced with different pulse durations, using optical interferometry with a grazing-incidence, ps-delayed probe [7].[4pt] [1] A. Braun et al., Opt. Lett. 20, 73 (1995).[0pt] [2] A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).[0pt] [3] V. Loriot et al., Opt. Express 17, 13429 (2009).[0pt] [4] P. B'ejot et al., Phys. Rev. Lett. 104, 103903 (2010).[0pt] [5] Y.-H. Chen et al., Opt. Express 15, 7458 (2007); Opt. Express 15, 11341 (2007).[0pt] [6] J. K. Wahlstrand et al., Phys. Rev. Lett. 107, 103901 (2011).[0pt] [7] Y.-H. Chen et al., Phys. Rev. Lett. 105, 215005 (2010).

Dark solitons, modulation instability and breathers in a chain of weakly nonlinear oscillators with cyclic symmetry

NASA Astrophysics Data System (ADS)

Fontanela, F.; Grolet, A.; Salles, L.; Chabchoub, A.; Hoffmann, N.

2018-01-01

In the aerospace industry the trend for light-weight structures and the resulting complex dynamic behaviours currently challenge vibration engineers. In many cases, these light-weight structures deviate from linear behaviour, and complex nonlinear phenomena can be expected. We consider a cyclically symmetric system of coupled weakly nonlinear undamped oscillators that could be considered a minimal model for different cyclic and symmetric aerospace structures experiencing large deformations. The focus is on localised vibrations that arise from wave envelope modulation of travelling waves. For the defocussing parameter range of the approximative nonlinear evolution equation, we show the possible existence of dark solitons and discuss their characteristics. For the focussing parameter range, we characterise modulation instability and illustrate corresponding nonlinear breather dynamics. Furthermore, we show that for stronger nonlinearity or randomness in initial conditions, transient breather-type dynamics and decay into bright solitons appear. The findings suggest that significant vibration localisation may arise due to mechanisms of nonlinear modulation dynamics.

Nonlinear parallel momentum transport in strong electrostatic turbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Lu, E-mail: luwang@hust.edu.cn; Wen, Tiliang; Diamond, P. H.

2015-05-15

Most existing theoretical studies of momentum transport focus on calculating the Reynolds stress based on quasilinear theory, without considering the nonlinear momentum flux-〈v{sup ~}{sub r}n{sup ~}u{sup ~}{sub ∥}〉. However, a recent experiment on TORPEX found that the nonlinear toroidal momentum flux induced by blobs makes a significant contribution as compared to the Reynolds stress [Labit et al., Phys. Plasmas 18, 032308 (2011)]. In this work, the nonlinear parallel momentum flux in strong electrostatic turbulence is calculated by using a three dimensional Hasegawa-Mima equation, which is relevant for tokamak edge turbulence. It is shown that the nonlinear diffusivity is smaller thanmore » the quasilinear diffusivity from Reynolds stress. However, the leading order nonlinear residual stress can be comparable to the quasilinear residual stress, and so may be important to intrinsic rotation in tokamak edge plasmas. A key difference from the quasilinear residual stress is that parallel fluctuation spectrum asymmetry is not required for nonlinear residual stress.« less

Third-Order Optical Nonlinearities of Squarylium Dyes with Benzothiazole Donor Groups Measured Using the Picosecond Z-Scan Technique

NASA Astrophysics Data System (ADS)

Li, Zhong-Yu; Xu, Song; Chen, Zi-Hui; Zhang, Fu-Shi; Kasatani, Kazuo

2011-08-01

Third-order optical nonlinearities of two squarylium dyes with benzothiazole donor groups (BSQ1 and BSQ2) in chloroform solution are measured by a picosecond Z-scan technique at 532 nm. It is found that the two compounds show the saturation absorption and nonlinear self-focus refraction effect. The molecular second hyperpolarizabilities are calculated to be 7.46 × 10-31 esu and 5.01 × 10-30 esu for BSQ1 and BSQ2, respectively. The large optical nonlinearities of squarylium dyes can be attributed to their rigid and intramolecular charge transfer structure. The difference in γ values is attributed to the chloro group of benzene rings of BSQ2 and the one-photon resonance effect. It is found that the third-order nonlinear susceptibilities of two squarylium dyes are mainly determined by the real parts of χ(3), and the large optical nonlinearities of studied squarylium dyes can be attributed to the nonlinear refraction.

Out-of-Focus Projector Calibration Method with Distortion Correction on the Projection Plane in the Structured Light Three-Dimensional Measurement System.

PubMed

Zhang, Jiarui; Zhang, Yingjie; Chen, Bo

2017-12-20

The three-dimensional measurement system with a binary defocusing technique is widely applied in diverse fields. The measurement accuracy is mainly determined by out-of-focus projector calibration accuracy. In this paper, a high-precision out-of-focus projector calibration method that is based on distortion correction on the projection plane and nonlinear optimization algorithm is proposed. To this end, the paper experimentally presents the principle that the projector has noticeable distortions outside its focus plane. In terms of this principle, the proposed method uses a high-order radial and tangential lens distortion representation on the projection plane to correct the calibration residuals caused by projection distortion. The final accuracy parameters of out-of-focus projector were obtained using a nonlinear optimization algorithm with good initial values, which were provided by coarsely calibrating the parameters of the out-of-focus projector on the focal and projection planes. Finally, the experimental results demonstrated that the proposed method can accuracy calibrate an out-of-focus projector, regardless of the amount of defocusing.

Perpendicular Diffusion Coefficient of Comic Rays: The Presence of Weak Adiabatic Focusing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, J. F.; Ma, Q. M.; Song, T.

The influence of adiabatic focusing on particle diffusion is an important topic in astrophysics and plasma physics. In the past, several authors have explored the influence of along-field adiabatic focusing on the parallel diffusion of charged energetic particles. In this paper, using the unified nonlinear transport theory developed by Shalchi and the method of He and Schlickeiser, we derive a new nonlinear perpendicular diffusion coefficient for a non-uniform background magnetic field. This formula demonstrates that the particle perpendicular diffusion coefficient is modified by along-field adiabatic focusing. For isotropic pitch-angle scattering and the weak adiabatic focusing limit, the derived perpendicular diffusionmore » coefficient is independent of the sign of adiabatic focusing characteristic length. For the two-component model, we simplify the perpendicular diffusion coefficient up to the second order of the power series of the adiabatic focusing characteristic quantity. We find that the first-order modifying factor is equal to zero and that the sign of the second order is determined by the energy of the particles.« less

Revisiting the investor sentiment-stock returns relationship: A multi-scale perspective using wavelets

NASA Astrophysics Data System (ADS)

Lao, Jiashun; Nie, He; Jiang, Yonghong

2018-06-01

This paper employs SBW proposed by Baker and Wurgler (2006) to investigate the nonlinear asymmetric Granger causality between investor sentiment and stock returns for US economy while considering different time-scales. The wavelet method is utilized to decompose time series of investor sentiment and stock returns at different time-scales to focus on the local analysis of different time horizons of investors. The linear and nonlinear asymmetric Granger methods are employed to examine the Granger causal relationship on similar time-scales. We find evidence of strong bilateral linear and nonlinear asymmetric Granger causality between longer-term investor sentiment and stock returns. Furthermore, we observe the positive nonlinear causal relationship from stock returns to investor sentiment and the negative nonlinear causal relationship from investor sentiment to stock returns.

Nonlinear effective theory of dark energy

NASA Astrophysics Data System (ADS)

Cusin, Giulia; Lewandowski, Matthew; Vernizzi, Filippo

2018-04-01

We develop an approach to parametrize cosmological perturbations beyond linear order for general dark energy and modified gravity models characterized by a single scalar degree of freedom. We derive the full nonlinear action, focusing on Horndeski theories. In the quasi-static, non-relativistic limit, there are a total of six independent relevant operators, three of which start at nonlinear order. The new nonlinear couplings modify, beyond linear order, the generalized Poisson equation relating the Newtonian potential to the matter density contrast. We derive this equation up to cubic order in perturbations and, in a companion article [1], we apply it to compute the one-loop matter power spectrum. Within this approach, we also discuss the Vainshtein regime around spherical sources and the relation between the Vainshtein scale and the nonlinear scale for structure formation.

Laser beam self-focusing in turbulent dissipative media.

PubMed

Hafizi, B; Peñano, J R; Palastro, J P; Fischer, R P; DiComo, G

2017-01-15

A high-power laser beam propagating through a dielectric in the presence of fluctuations is subject to diffraction, dissipation, and optical Kerr nonlinearity. A method of moments was applied to a stochastic, nonlinear enveloped wave equation to analyze the evolution of the long-term spot radius. For propagation in atmospheric turbulence described by a Kolmogorov-von Kármán spectral density, the analysis was benchmarked against field experiments in the low-power limit and compared with simulation results in the high-power regime. Dissipation reduced the effect of self-focusing and led to chromatic aberration.

Final Report---Optimization Under Nonconvexity and Uncertainty: Algorithms and Software

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jeff Linderoth

2011-11-06

the goal of this work was to develop new algorithmic techniques for solving large-scale numerical optimization problems, focusing on problems classes that have proven to be among the most challenging for practitioners: those involving uncertainty and those involving nonconvexity. This research advanced the state-of-the-art in solving mixed integer linear programs containing symmetry, mixed integer nonlinear programs, and stochastic optimization problems. The focus of the work done in the continuation was on Mixed Integer Nonlinear Programs (MINLP)s and Mixed Integer Linear Programs (MILP)s, especially those containing a great deal of symmetry.

Moderately nonlinear ultrasound propagation in blood-mimicking fluid.

PubMed

Kharin, Nikolay A; Vince, D Geoffrey

2004-04-01

In medical diagnostic ultrasound (US), higher than-in-water nonlinearity of body fluids and tissue usually does not produce strong nonlinearly distorted waves because of the high absorption. The relative influence of absorption and nonlinearity can be characterized by the Gol'dberg number Gamma. There are two limiting cases in nonlinear acoustics: weak waves (Gamma < 1) or strong waves (Gamma > 1). However, at diagnostic frequencies in tissue and body fluids, the nonlinear effects and effects of absorption more likely are comparable (Gol'dberg number Gamma approximately 1). The aim of this work was to study the nonlinear propagation of a moderately nonlinear US second harmonic signal in a blood-mimicking fluid. Quasilinear solutions to the KZK equation are presented, assuming radiation from a flat and geometrically focused circular Gaussian source. The solutions are expressed in a new simplified closed form and are in very good agreement with those of previous studies measuring and modeling Gaussian beams. The solutions also show good agreement with the measurements of the beams produced by commercially available transducers, even without special Gaussian shading.

Nonlinear guiding of picosecond CO2 laser pulses in atmosphere(Conference Presentation)

NASA Astrophysics Data System (ADS)

Tochitsky, Sergei

2017-05-01

During the last 20 years much attention has been given to the study of propagation of short intense laser pulses for which the peak power exceeds the critical power of self-focusing, Pcr. For a laser power P < Pcr, a dynamic equilibrium between the Kerr self-focusing, diffraction and defocusing caused by laser-ionized plasma result in the production of a high intensity laser filament in air within which a variety of nonlinear optical phenomena are observed. However, research in the 0.8-1 μm range so far has shown a fundamental limitation of guided energy to a few mJ transported within an 100 μm single channel. A long-wavelength, 0 10 μm CO2 laser is a promising candidate for nonlinear guiding because expected high Pcr values according to the modeling should allow for the increase of energy (and therefore power) in a self-guided beam from mJ (GW) to few Joules (TW). During the last decade a significant progress has been achieved in amplification of picosecond pulses to terawatt and recently to <10 TW power level at UCLA and ATF BNL. Such powerful 10 μm lasers open possibility for nonlinear propagation studies in an atmospheric window with high transmission. As a natural first step in a our program on picosecond CO2 laser filamentation, we have made first measurements of Kerr coefficients of air and air constituents around 10 μm. We also undertook direct measurements of n2 of air by analyzing nonlinear self-focusing in air using a 3 ps, 600 GW pulses of the BNL CO2 laser.

Nonlinear mechanical response of the extracellular matrix: learning from articular cartilage

NASA Astrophysics Data System (ADS)

Kearns, Sarah; Das, Moumita

2015-03-01

We study the mechanical structure-function relations in the extracellular matrix (ECM) with focus on nonlinear shear and compression response. As a model system, our study focuses on the ECM in articular cartilage tissue which has two major mechanobiological components: a network of the biopolymer collagen that acts as a stiff, reinforcing matrix, and a flexible aggrecan network that facilitates deformability. We model this system as a double network hydrogel made of interpenetrating networks of stiff and flexible biopolymers respectively. We study the linear and nonlinear mechanical response of the model ECM to shear and compression forces using a combination of rigidity percolation theory and energy minimization approaches. Our results may provide useful insights into the design principles of the ECM as well as biomimetic hydrogels that are mechanically robust and can, at the same time, easily adapt to cues in their surroundings.

Self-Inversion of the Image of a Small-Scale Opaque Object in the Process of Focusing of the Illuminating Beam in an Absorbing Medium

NASA Astrophysics Data System (ADS)

Bubis, E. L.; Lozhrkarev, V. V.; Stepanov, A. N.; Smirnov, A. I.; Martynov, V. O.; Mal'shakova, O. A.; Silin, D. E.; Gusev, S. A.

2017-03-01

We describe the process of adaptive self-inversion of an image (nonlinear switching) of smallscale opaque object, when the amplitude-modulated laser beam, which illuminates it, is focused in a weakly absorbing medium. It is shown that, despite the nonlocal character of the process, which is due to thermal nonlinearity, the brightness-inverse image is characterized by acceptable quality and a high conversion coefficient. It is shown that the coefficient of conversion of the original image to the inverse one depends on the ratio of the object dimensions and the size of the illuminating beam, and decreases sharply for relatively large objects. The obtained experimental data agree with the numerical calculations. Inversion of the images of several model objects and microdefects in a nonlinear KDP crystal is demonstrated.

Reservoir Computing Beyond Memory-Nonlinearity Trade-off.

PubMed

Inubushi, Masanobu; Yoshimura, Kazuyuki

2017-08-31

Reservoir computing is a brain-inspired machine learning framework that employs a signal-driven dynamical system, in particular harnessing common-signal-induced synchronization which is a widely observed nonlinear phenomenon. Basic understanding of a working principle in reservoir computing can be expected to shed light on how information is stored and processed in nonlinear dynamical systems, potentially leading to progress in a broad range of nonlinear sciences. As a first step toward this goal, from the viewpoint of nonlinear physics and information theory, we study the memory-nonlinearity trade-off uncovered by Dambre et al. (2012). Focusing on a variational equation, we clarify a dynamical mechanism behind the trade-off, which illustrates why nonlinear dynamics degrades memory stored in dynamical system in general. Moreover, based on the trade-off, we propose a mixture reservoir endowed with both linear and nonlinear dynamics and show that it improves the performance of information processing. Interestingly, for some tasks, significant improvements are observed by adding a few linear dynamics to the nonlinear dynamical system. By employing the echo state network model, the effect of the mixture reservoir is numerically verified for a simple function approximation task and for more complex tasks.

Nonlinear waveguide optics and photonic crystal fibers.

PubMed

Knight, J C; Skryabin, D V

2007-11-12

Focus Serial: Frontiers of Nonlinear Optics

A Simple Model for Nonlinear Confocal Ultrasonic Beams

NASA Astrophysics Data System (ADS)

Zhang, Dong; Zhou, Lin; Si, Li-Sheng; Gong, Xiu-Fen

2007-01-01

A confocally and coaxially arranged pair of focused transmitter and receiver represents one of the best geometries for medical ultrasonic imaging and non-invasive detection. We develop a simple theoretical model for describing the nonlinear propagation of a confocal ultrasonic beam in biological tissues. On the basis of the parabolic approximation and quasi-linear approximation, the nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation is solved by using the angular spectrum approach. Gaussian superposition technique is applied to simplify the solution, and an analytical solution for the second harmonics in the confocal ultrasonic beam is presented. Measurements are performed to examine the validity of the theoretical model. This model provides a preliminary model for acoustic nonlinear microscopy.

System Identification for Nonlinear Control Using Neural Networks

NASA Technical Reports Server (NTRS)

Stengel, Robert F.; Linse, Dennis J.

1990-01-01

An approach to incorporating artificial neural networks in nonlinear, adaptive control systems is described. The controller contains three principal elements: a nonlinear inverse dynamic control law whose coefficients depend on a comprehensive model of the plant, a neural network that models system dynamics, and a state estimator whose outputs drive the control law and train the neural network. Attention is focused on the system identification task, which combines an extended Kalman filter with generalized spline function approximation. Continual learning is possible during normal operation, without taking the system off line for specialized training. Nonlinear inverse dynamic control requires smooth derivatives as well as function estimates, imposing stringent goals on the approximating technique.

Solitonic characteristics of Airy beam nonlinear propagation

NASA Astrophysics Data System (ADS)

Bouchet, Thomas; Marsal, Nicolas; Sciamanna, Marc; Wolfersberger, Delphine

2018-05-01

We analyze the nonlinear propagation of a one-dimensional Airy beam. Under nonlinear focusing conditions, the Airy beam splits into a weak accelerating structure and a beam that has been named an "off-shooting soliton." Experimental measurements and numerical results related to the off-shooting Airy beam are compared to soliton theoretical profiles and a good agreement is found in terms of transverse shape, width, and amplitude. We identify the different parameters to generate an Airy beam off-shooting soliton and demonstrate that its profile is also preserved through propagation over long distances.

The role of acoustic nonlinearity in tissue heating behind a rib cage using a high-intensity focused ultrasound phased array

NASA Astrophysics Data System (ADS)

Yuldashev, Petr V.; Shmeleva, Svetlana M.; Ilyin, Sergey A.; Sapozhnikov, Oleg A.; Gavrilov, Leonid R.; Khokhlova, Vera A.

2013-04-01

The goal of this study was to investigate theoretically the effects of nonlinear propagation in a high-intensity focused ultrasound (HIFU) field produced by a therapeutic phased array and the resultant heating of tissue behind a rib cage. Three configurations of focusing were simulated: in water, in water with ribs in the beam path and in water with ribs backed by a layer of soft tissue. The Westervelt equation was used to model the nonlinear HIFU field, and a 1 MHz phased array consisting of 254 circular elements was used as a boundary condition to the model. The temperature rise in tissue was modelled using the bioheat equation, and thermally necrosed volumes were calculated using the thermal dose formulation. The shapes of lesions predicted by the modelling were compared with those previously obtained in in vitro experiments at low-power sonications. Intensity levels at the face of the array elements that corresponded to the formation of high-amplitude shock fronts in the focal region were determined as 10 W cm-2 in the free field in water and 40 W cm-2 in the presence of ribs. It was shown that exposures with shocks provided a substantial increase in tissue heating, and its better spatial localization in the main focal region only. The relative effects of overheating ribs and splitting of the focus due to the periodic structure of the ribs were therefore reduced. These results suggest that utilizing nonlinear propagation and shock formation effects can be beneficial for inducing confined HIFU lesions when irradiating through obstructions such as ribs. Design of compact therapeutic arrays to provide maximum power outputs with lower intensity levels at the elements is necessary to achieve shock wave regimes for clinically relevant sonication depths in tissue.

The role of acoustic nonlinearity in tissue heating behind the rib cage using high intensity focused ultrasound phased array

PubMed Central

Yuldashev, Petr V.; Shmeleva, Svetlana M.; Ilyin, Sergey A.; Sapozhnikov, Oleg A.; Gavrilov, Leonid R.; Khokhlova, Vera A.

2013-01-01

The goal of this study was to investigate theoretically the effects of nonlinear propagation in a high intensity focused ultrasound (HIFU) field produced by a therapeutic phased array and the resultant heating of tissue behind a rib cage. Three configurations of focusing were simulated: in water, in water with ribs in the beam path, and in water with ribs backed by a layer of soft tissue. The Westervelt equation was used to model the nonlinear HIFU field and a 1 MHz phased array consisting of 254 circular elements was used as a boundary condition to the model. The temperature rise in tissue was modelled using the bioheat equation, and thermally necrosed volumes were calculated using the thermal dose formulation. The shapes of lesions predicted by the modelling were compared with those previously obtained in in vitro experiments at low power sonications. Intensity levels at the face of the array elements that corresponded to formation of high amplitude shock fronts in the focal region were determined as 10 W·cm−2 in the free field in water and 40 W·cm−2 in the presence of ribs. It was shown that exposures with shocks provided a substantial increase in tissue heating, and its better spatial localization in the main focal region only. The relative effects of overheating ribs and splitting of the focus due to the periodic structure of the ribs were therefore reduced. These results suggest that utilizing nonlinear propagation and shock formation effects can be beneficial for inducing confined HIFU lesions when irradiating through obstructions such as ribs. Design of compact therapeutic arrays to provide maximum power outputs with lower intensity levels at the elements is necessary to achieve shock wave regimes for clinically relevant sonication depths in tissue. PMID:23528338

S-matrix method for the numerical determination of bound states.

NASA Technical Reports Server (NTRS)

Bhatia, A. K.; Madan, R. N.

1973-01-01

A rapid numerical technique for the determination of bound states of a partial-wave-projected Schroedinger equation is presented. First, one needs to integrate the equation only outwards as in the scattering case, and second, the number of trials necessary to determine the eigenenergy and the corresponding eigenfunction is considerably less than in the usual method. As a nontrivial example of the technique, bound states are calculated in the exchange approximation for the e-/He+ system and l equals 1 partial wave.

Quantum Algorithms for Computational Physics: Volume 3 of Lattice Gas Dynamics

DTIC Science & Technology

2007-01-03

time- dependent state |q(t)〉 of a two- energy level quantum mechanical system, which is a fermionic qubit and is governed by the Schroedinger wave...on-site ket of size 2B |Ψ〉 total system ket of size 2Q 2.2 The quantum state in the number representation From the previous section, a time- dependent ...duration depend on the particular experimental realization, so that the natural coupling along with the program of externally applied pulses together

Multicharmed Baryon Production in High Energy Nuclear Collisions

NASA Astrophysics Data System (ADS)

Zhao, Jiaxing; Zhuang, Pengfei

2017-03-01

We study nuclear medium effect on multicharmed baryon production in relativistic heavy ion collisions. By solving the three-quark Schroedinger equation at finite temperature, we calculate the wave functions and Wigner functions for doubly and triply charmed baryons Ξ_{cc} and Ω_{ccc}. Their production in nuclear collisions is largely enhanced due to the combination of uncorrelated charm quarks in the quark-gluon plasma. It is most probable to discover these new particles in heavy ion collisions at the RHIC and LHC energies.

Numerical study of a confocal ultrasonic setup for creation of cavitation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lafond, Maxime, E-mail: maxime.lafond@inserm.fr; Chavrier, Françoise; Prieur, Fabrice

2015-10-28

Acoustic cavitation is used for various therapeutic applications such as local enhancement of drug delivery, histotripsy or hyperthermia. One of the utmost important parameter for cavitation creation is the rarefaction pressure. The typical magnitude of the rarefaction pressure required to initiate cavitation from gas dissolved in tissue is beyond the range of the megapascal. Because nonlinear effects need to be taken into account, a numerical simulator based on the Westervelt equation was used to study the pressure waveform and the acoustic field generated by a setup for creation of cavitation consisting of two high intensity focused ultrasound transducers mounted confocally.more » At constant acoustic power, simulations with only one and both transducers from the confocal setup showed that the distortion of the pressure waveform due to the combined effects of nonlinearity and diffraction is less pronounced when both confocal transducers are used. Consequently, the confocal setup generates a greater peak negative pressure at focus which is more favorable for cavitation initiation. Comparison between the confocal setup and a single transducer with the same total emitting surface puts in evidence the role of the spatial separation of the two beams. Furthermore, it has been previously shown that the location of the peak negative pressure created by a single transducer shifts from focus towards the transducers in the presence of nonlinear effects. The simulator was used to study a configuration where the acoustical axes of transducers intersect on the peak negative pressure instead of the geometrical focus. For a representative confocal setup, namely moderate nonlinear effects, a 2% increase of the peak negative pressure and 8% decrease of the peak positive pressure resulted from this configuration. These differences tend to increase by increasing nonlinear effects. Although the optimal position of the transducers varies with the nonlinear regimen, the intersection point remains the location of the peak negative pressure in any case. Thus, unlike the location of the peak negative pressure for a single transducer can shift by a few millimeters, the focal point of a confocal device is independent of the power. This point is particularly important for therapeutic applications, frequently requiring high spatial accuracy. An experiment conducted shows that cavitation creation can be achieved easier with confocal ultrasound.« less

Numerical simulations of self-focusing of ultrafast laser pulses

NASA Astrophysics Data System (ADS)

Fibich, Gadi; Ren, Weiqing; Wang, Xiao-Ping

2003-05-01

Simulation of nonlinear propagation of intense ultrafast laser pulses is a hard problem, because of the steep spatial gradients and the temporal shocks that form during the propagation. In this study we adapt the iterative grid distribution method of Ren and Wang [J. Comput. Phys. 159, 246 (2000)] to solve the two-dimensional nonlinear Schrödinger equation with normal time dispersion, space-time focusing, and self-steepening. Our simulations show that, after the asymmetric temporal pulse splitting, the rear peak self-focuses faster than the front one. As a result, the collapse of the rear peak is arrested before that of the front peak. Unlike what has sometimes been conjectured, however, collapse of the two peaks is not arrested through multiple splittings, but rather through temporal dispersion.

Time-Reversal Generation of Rogue Waves

NASA Astrophysics Data System (ADS)

Chabchoub, Amin; Fink, Mathias

2014-03-01

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

Computational aspects in high intensity ultrasonic surgery planning.

PubMed

Pulkkinen, A; Hynynen, K

2010-01-01

Therapeutic ultrasound treatment planning is discussed and computational aspects regarding it are reviewed. Nonlinear ultrasound simulations were solved with a combined frequency domain Rayleigh and KZK model. Ultrasonic simulations were combined with thermal simulations and were used to compute heating of muscle tissue in vivo for four different focused ultrasound transducers. The simulations were compared with measurements and good agreement was found for large F-number transducers. However, at F# 1.9 the simulated rate of temperature rise was approximately a factor of 2 higher than the measured ones. The power levels used with the F# 1 transducer were too low to show any nonlinearity. The simulations were used to investigate the importance of nonlinarities generated in the coupling water, and also the importance of including skin in the simulations. Ignoring either of these in the model would lead to larger errors. Most notably, the nonlinearities generated in the water can enhance the focal temperature by more than 100%. The simulations also demonstrated that pulsed high power sonications may provide an opportunity to significantly (up to a factor of 3) reduce the treatment time. In conclusion, nonlinear propagation can play an important role in shaping the energy distribution during a focused ultrasound treatment and it should not be ignored in planning. However, the current simulation methods are accurate only with relatively large F-numbers and better models need to be developed for sharply focused transducers. Copyright 2009 Elsevier Ltd. All rights reserved.

Chaos, patterns, coherent structures, and turbulence: Reflections on nonlinear science.

PubMed

Ecke, Robert E

2015-09-01

The paradigms of nonlinear science were succinctly articulated over 25 years ago as deterministic chaos, pattern formation, coherent structures, and adaptation/evolution/learning. For chaos, the main unifying concept was universal routes to chaos in general nonlinear dynamical systems, built upon a framework of bifurcation theory. Pattern formation focused on spatially extended nonlinear systems, taking advantage of symmetry properties to develop highly quantitative amplitude equations of the Ginzburg-Landau type to describe early nonlinear phenomena in the vicinity of critical points. Solitons, mathematically precise localized nonlinear wave states, were generalized to a larger and less precise class of coherent structures such as, for example, concentrated regions of vorticity from laboratory wake flows to the Jovian Great Red Spot. The combination of these three ideas was hoped to provide the tools and concepts for the understanding and characterization of the strongly nonlinear problem of fluid turbulence. Although this early promise has been largely unfulfilled, steady progress has been made using the approaches of nonlinear science. I provide a series of examples of bifurcations and chaos, of one-dimensional and two-dimensional pattern formation, and of turbulence to illustrate both the progress and limitations of the nonlinear science approach. As experimental and computational methods continue to improve, the promise of nonlinear science to elucidate fluid turbulence continues to advance in a steady manner, indicative of the grand challenge nature of strongly nonlinear multi-scale dynamical systems.

Equations for description of nonlinear standing waves in constant-cross-sectioned resonators.

PubMed

Bednarik, Michal; Cervenka, Milan

2014-03-01

This work is focused on investigation of applicability of two widely used model equations for description of nonlinear standing waves in constant-cross-sectioned resonators. The investigation is based on the comparison of numerical solutions of these model equations with solutions of more accurate model equations whose validity has been verified experimentally in a number of published papers.

Nonlinear Eulerian Thermoelasticity for Anisotropic Crystals

DTIC Science & Technology

2013-08-01

the applied pressure. However, some crystalline materials such as ceramics and hard minerals may retain significant shear strength at finite strain...which elastic properties have been measured. Benefits of using Eulerian strain measures for nonlinear elasticity of isotropic materials were extolled by...highly symmetric anharmonic properties . Deviations may be expected for highly anisotropic materials , as shown in Section 4. This work is focused

Nonlinear Electromagnetic Waves and Spherical Arc-Polarized Waves in Space Plasmas

NASA Technical Reports Server (NTRS)

Tsurutani, B.; Ho, Christian M.; Arballo, John K.; Lakhina, Gurbax S.; Glassmeier, Karl-Heinz; Neubauer, Fritz M.

1997-01-01

We review observations of nonlinear plasma waves detected by interplanetary spacecraft. For this paper we will focus primarily on the phase-steepened properties of such waves. Plasma waves at comet Giacobini-Zinner measured by the International Cometary Explorer (ICE), at comets Halley and Grigg-Skjellerup measured by Giotto, and interplanetary Alfven waves measured by Ulysses, will be discussed and intercompared.

Synthesis, characterization and theoretical investigations of the structure, electronic properties and third-order nonlinearity optics (NLO) of M(DPIP)2

NASA Astrophysics Data System (ADS)

Li, Kang; Tang, Guodong; Kou, ShanShan; Culnane, Lance F.; Zhang, Yu; Song, Yinglin; Li, Rongqing; Wei, Changmei

2015-03-01

Three complexes of M(DPIP)2 (M = Cu, Co, Zn as 1, 2, 3) were synthesized and characterized by elemental analysis, IR, UV-Vis, thermogravimetry, and X-ray diffraction. Their nonlinear optical properties were measured by the Z-scan technique and yielded a normalized transmittance of about 70% for complex 1 (45 μJ pulse), and 93% for complex 3 (68 μJ pulse at the focus point). The nonlinear absorption coefficient, β, is 1.4 × 10-11 m/W for 1 and 5.6 × 10-13 m/W for 3, and the third-order nonlinear refraction index, n2, is 1.0 × 10-18 m2/W for 3. Complex 1 shows self-defocusing property, while complex 3 exhibits self-focusing property. The thermogravimetric results show that the frame structure of compounds 1-3 begin to collapse at 400, 250 and 280 °C, respectively, which suggests that they elicit excellent thermal stability. This research aims to provide better understanding of these compounds, and offer preliminary explanations for the significant differences between compounds 1-3, in order to potentially help in the designing of future novel materials with NLO properties.

Mach stem formation in reflection and focusing of weak shock acoustic pulses.

PubMed

Karzova, Maria M; Khokhlova, Vera A; Salze, Edouard; Ollivier, Sébastien; Blanc-Benon, Philippe

2015-06-01

The aim of this study is to show the evidence of Mach stem formation for very weak shock waves with acoustic Mach numbers on the order of 10(-3) to 10(-2). Two representative cases are considered: reflection of shock pulses from a rigid surface and focusing of nonlinear acoustic beams. Reflection experiments are performed in air using spark-generated shock pulses. Shock fronts are visualized using a schlieren system. Both regular and irregular types of reflection are observed. Numerical simulations are performed to demonstrate the Mach stem formation in the focal region of periodic and pulsed nonlinear beams in water.

Self-focusing and defocusing of Gaussian laser beams in collisional underdense magnetized plasmas with considering the nonlinear ohmic heating and ponderomotive force effects

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ettehadi Abari, Mehdi; Sedaghat, Mahsa; Shokri, Babak, E-mail: b-shokri@sbu.ac.ir

2015-10-15

The propagation characteristics of a Gaussian laser beam in collisional magnetized plasma are investigated by considering the ponderomotive and ohmic heating nonlinearities. Here, by taking into account the effect of the external magnetic field, the second order differential equation of the dimensionless beam width parameter is solved numerically. Furthermore, the nonlinear dielectric permittivity of the mentioned plasma medium in the paraxial approximation and its dependence on the propagation characteristics of the Gaussian laser pulse is obtained, and its variation in terms of the dimensionless plasma length is analyzed at different initial normalized plasma and cyclotron frequencies. The results show thatmore » the dimensionless beam width parameter is strongly affected by the initial plasma frequency, magnetic strength, and laser pulse intensity. Furthermore, it is found that there exists a certain intensity value below which the laser pulse tends to self focus, while the beam diverges above of this value. In addition, the results confirm that, by increasing the plasma and cyclotron frequencies (plasma density and magnetic strength), the self-focusing effect can occur intensively.« less

Building Blocks for Reliable Complex Nonlinear Numerical Simulations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Mansour, Nagi N. (Technical Monitor)

2002-01-01

This talk describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.

Building Blocks for Reliable Complex Nonlinear Numerical Simulations

NASA Technical Reports Server (NTRS)

Yee, H. C.

2005-01-01

This chapter describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations.

Nonlinearity analysis of measurement model for vision-based optical navigation system

NASA Astrophysics Data System (ADS)

Li, Jianguo; Cui, Hutao; Tian, Yang

2015-02-01

In the autonomous optical navigation system based on line-of-sight vector observation, nonlinearity of measurement model is highly correlated with the navigation performance. By quantitatively calculating the degree of nonlinearity of the focal plane model and the unit vector model, this paper focuses on determining which optical measurement model performs better. Firstly, measurement equations and measurement noise statistics of these two line-of-sight measurement models are established based on perspective projection co-linearity equation. Then the nonlinear effects of measurement model on the filter performance are analyzed within the framework of the Extended Kalman filter, also the degrees of nonlinearity of two measurement models are compared using the curvature measure theory from differential geometry. Finally, a simulation of star-tracker-based attitude determination is presented to confirm the superiority of the unit vector measurement model. Simulation results show that the magnitude of curvature nonlinearity measurement is consistent with the filter performance, and the unit vector measurement model yields higher estimation precision and faster convergence properties.

Building Blocks for Reliable Complex Nonlinear Numerical Simulations. Chapter 2

NASA Technical Reports Server (NTRS)

Yee, H. C.; Mansour, Nagi N. (Technical Monitor)

2001-01-01

This chapter describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.

An exponential decay model for mediation.

PubMed

Fritz, Matthew S

2014-10-01

Mediation analysis is often used to investigate mechanisms of change in prevention research. Results finding mediation are strengthened when longitudinal data are used because of the need for temporal precedence. Current longitudinal mediation models have focused mainly on linear change, but many variables in prevention change nonlinearly across time. The most common solution to nonlinearity is to add a quadratic term to the linear model, but this can lead to the use of the quadratic function to explain all nonlinearity, regardless of theory and the characteristics of the variables in the model. The current study describes the problems that arise when quadratic functions are used to describe all nonlinearity and how the use of nonlinear functions, such as exponential decay, address many of these problems. In addition, nonlinear models provide several advantages over polynomial models including usefulness of parameters, parsimony, and generalizability. The effects of using nonlinear functions for mediation analysis are then discussed and a nonlinear growth curve model for mediation is presented. An empirical example using data from a randomized intervention study is then provided to illustrate the estimation and interpretation of the model. Implications, limitations, and future directions are also discussed.

Nonlinear defect localized modes and composite gray and anti-gray solitons in one-dimensional waveguide arrays with dual-flip defects

NASA Astrophysics Data System (ADS)

Liu, Yan; Guan, Yefeng; Li, Hai; Luo, Zhihuan; Mai, Zhijie

2017-08-01

We study families of stationary nonlinear localized modes and composite gray and anti-gray solitons in a one-dimensional linear waveguide array with dual phase-flip nonlinear point defects. Unstaggered fundamental and dipole bright modes are studied when the defect nonlinearity is self-focusing. For the fundamental modes, symmetric and asymmetric nonlinear modes are found. Their stable areas are studied using different defect coefficients and their total power. For the nonlinear dipole modes, the stability conditions of this type of mode are also identified by different defect coefficients and the total power. When the defect nonlinearity is replaced by the self-defocusing one, staggered fundamental and dipole bright modes are created. Finally, if we replace the linear waveguide with a full nonlinear waveguide, a new type of gray and anti-gray solitons, which are constructed by a kink and anti-kink pair, can be supported by such dual phase-flip defects. In contrast to the usual gray and anti-gray solitons formed by a single kink, their backgrounds on either side of the gray hole or bright hump have the same phase.

An Exponential Decay Model for Mediation

PubMed Central

Fritz, Matthew S.

2013-01-01

Mediation analysis is often used to investigate mechanisms of change in prevention research. Results finding mediation are strengthened when longitudinal data are used because of the need for temporal precedence. Current longitudinal mediation models have focused mainly on linear change, but many variables in prevention change nonlinearly across time. The most common solution to nonlinearity is to add a quadratic term to the linear model, but this can lead to the use of the quadratic function to explain all nonlinearity, regardless of theory and the characteristics of the variables in the model. The current study describes the problems that arise when quadratic functions are used to describe all nonlinearity and how the use of nonlinear functions, such as exponential decay, addresses many of these problems. In addition, nonlinear models provide several advantages over polynomial models including usefulness of parameters, parsimony, and generalizability. The effects of using nonlinear functions for mediation analysis are then discussed and a nonlinear growth curve model for mediation is presented. An empirical example using data from a randomized intervention study is then provided to illustrate the estimation and interpretation of the model. Implications, limitations, and future directions are also discussed. PMID:23625557

Experiences on p-Version Time-Discontinuous Galerkin's Method for Nonlinear Heat Transfer Analysis and Sensitivity Analysis

NASA Technical Reports Server (NTRS)

Hou, Gene

2004-01-01

The focus of this research is on the development of analysis and sensitivity analysis equations for nonlinear, transient heat transfer problems modeled by p-version, time discontinuous finite element approximation. The resulting matrix equation of the state equation is simply in the form ofA(x)x = c, representing a single step, time marching scheme. The Newton-Raphson's method is used to solve the nonlinear equation. Examples are first provided to demonstrate the accuracy characteristics of the resultant finite element approximation. A direct differentiation approach is then used to compute the thermal sensitivities of a nonlinear heat transfer problem. The report shows that only minimal coding effort is required to enhance the analysis code with the sensitivity analysis capability.

Symmetry-Breaking Bifurcation in the Nonlinear Schrödinger Equation with Symmetric Potentials

NASA Astrophysics Data System (ADS)

Kirr, E.; Kevrekidis, P. G.; Pelinovsky, D. E.

2011-12-01

We consider the focusing (attractive) nonlinear Schrödinger (NLS) equation with an external, symmetric potential which vanishes at infinity and supports a linear bound state. We prove that the symmetric, nonlinear ground states must undergo a symmetry breaking bifurcation if the potential has a non-degenerate local maxima at zero. Under a generic assumption we show that the bifurcation is either a subcritical or supercritical pitchfork. In the particular case of double-well potentials with large separation, the power of nonlinearity determines the subcritical or supercritical character of the bifurcation. The results are obtained from a careful analysis of the spectral properties of the ground states at both small and large values for the corresponding eigenvalue parameter.

Few-cycle solitons and supercontinuum generation with cascaded quadratic nonlinearities in unpoled lithium niobate ridge waveguides.

PubMed

Guo, Hairun; Zeng, Xianglong; Zhou, Binbin; Bache, Morten

2014-03-01

Formation and interaction of few-cycle solitons in a lithium niobate ridge waveguide are numerically investigated. The solitons are created through a cascaded phase-mismatched second-harmonic generation process, which induces a dominant self-defocusing Kerr-like nonlinearity on the pump pulse. The inherent material self-focusing Kerr nonlinearity is overcome over a wide wavelength range, and self-defocusing solitons are supported from 1100 to 1900 nm, covering the whole communication band. Single cycle self-compressed solitons and supercontinuum generation spanning 1.3 octaves are observed when pumped with femtosecond nanojoule pulses at 1550 nm. The waveguide is not periodically poled, as quasi-phase-matching would lead to detrimental nonlinear effects impeding few-cycle soliton formation.

Two-dimensional solitons in conservative and parity-time-symmetric triple-core waveguides with cubic-quintic nonlinearity

NASA Astrophysics Data System (ADS)

Feijoo, David; Zezyulin, Dmitry A.; Konotop, Vladimir V.

2015-12-01

We analyze a system of three two-dimensional nonlinear Schrödinger equations coupled by linear terms and with the cubic-quintic (focusing-defocusing) nonlinearity. We consider two versions of the model: conservative and parity-time (PT ) symmetric. These models describe triple-core nonlinear optical waveguides, with balanced gain and losses in the PT -symmetric case. We obtain families of soliton solutions and discuss their stability. The latter study is performed using a linear stability analysis and checked with direct numerical simulations of the evolutional system of equations. Stable solitons are found in the conservative and PT -symmetric cases. Interactions and collisions between the conservative and PT -symmetric solitons are briefly investigated, as well.

Adaptive nonlinear control for autonomous ground vehicles

NASA Astrophysics Data System (ADS)

Black, William S.

We present the background and motivation for ground vehicle autonomy, and focus on uses for space-exploration. Using a simple design example of an autonomous ground vehicle we derive the equations of motion. After providing the mathematical background for nonlinear systems and control we present two common methods for exactly linearizing nonlinear systems, feedback linearization and backstepping. We use these in combination with three adaptive control methods: model reference adaptive control, adaptive sliding mode control, and extremum-seeking model reference adaptive control. We show the performances of each combination through several simulation results. We then consider disturbances in the system, and design nonlinear disturbance observers for both single-input-single-output and multi-input-multi-output systems. Finally, we show the performance of these observers with simulation results.

Fast prediction of pulsed nonlinear acoustic fields from clinically relevant sources using Time-Averaged Wave Envelope approach: comparison of numerical simulations and experimental results

PubMed Central

Wójcik, J.; Kujawska, T.; Nowicki, A.; Lewin, P.A.

2008-01-01

The primary goal of this work was to verify experimentally the applicability of the recently introduced Time-Averaged Wave Envelope (TAWE) method [1] as a tool for fast prediction of four dimensional (4D) pulsed nonlinear pressure fields from arbitrarily shaped acoustic sources in attenuating media. The experiments were performed in water at the fundamental frequency of 2.8 MHz for spherically focused (focal length F = 80 mm) square (20 × 20 mm) and rectangular (10 × 25 mm) sources similar to those used in the design of 1D linear arrays operating with ultrasonic imaging systems. The experimental results obtained with 10-cycle tone bursts at three different excitation levels corresponding to linear, moderately nonlinear and highly nonlinear propagation conditions (0.045, 0.225 and 0.45 MPa on-source pressure amplitude, respectively) were compared with those yielded using the TAWE approach [1]. The comparison of the experimental results and numerical simulations has shown that the TAWE approach is well suited to predict (to within ± 1 dB) both the spatial-temporal and spatial-spectral pressure variations in the pulsed nonlinear acoustic beams. The obtained results indicated that implementation of the TAWE approach enabled shortening of computation time in comparison with the time needed for prediction of the full 4D pulsed nonlinear acoustic fields using a conventional (Fourier-series) approach [2]. The reduction in computation time depends on several parameters, including the source geometry, dimensions, fundamental resonance frequency, excitation level as well as the strength of the medium nonlinearity. For the non-axisymmetric focused transducers mentioned above and excited by a tone burst corresponding to moderately nonlinear and highly nonlinear conditions the execution time of computations was 3 and 12 hours, respectively, when using a 1.5 GHz clock frequency, 32-bit processor PC laptop with 2 GB RAM memory, only. Such prediction of the full 4D pulsed field is not possible when using conventional, Fourier-series scheme as it would require increasing the RAM memory by at least 2 orders of magnitude. PMID:18474387

Nonlinear plasmonic imaging techniques and their biological applications

NASA Astrophysics Data System (ADS)

Deka, Gitanjal; Sun, Chi-Kuang; Fujita, Katsumasa; Chu, Shi-Wei

2017-01-01

Nonlinear optics, when combined with microscopy, is known to provide advantages including novel contrast, deep tissue observation, and minimal invasiveness. In addition, special nonlinearities, such as switch on/off and saturation, can enhance the spatial resolution below the diffraction limit, revolutionizing the field of optical microscopy. These nonlinear imaging techniques are extremely useful for biological studies on various scales from molecules to cells to tissues. Nevertheless, in most cases, nonlinear optical interaction requires strong illumination, typically at least gigawatts per square centimeter intensity. Such strong illumination can cause significant phototoxicity or even photodamage to fragile biological samples. Therefore, it is highly desirable to find mechanisms that allow the reduction of illumination intensity. Surface plasmon, which is the collective oscillation of electrons in metal under light excitation, is capable of significantly enhancing the local field around the metal nanostructures and thus boosting up the efficiency of nonlinear optical interactions of the surrounding materials or of the metal itself. In this mini-review, we discuss the recent progress of plasmonics in nonlinear optical microscopy with a special focus on biological applications. The advancement of nonlinear imaging modalities (including incoherent/coherent Raman scattering, two/three-photon luminescence, and second/third harmonic generations that have been amalgamated with plasmonics), as well as the novel subdiffraction limit imaging techniques based on nonlinear behaviors of plasmonic scattering, is addressed.

A constructive nonlinear array (CNA) method for barely visible impact detection in composite materials

NASA Astrophysics Data System (ADS)

Malfense Fierro, Gian Piero; Meo, Michele

2017-04-01

Currently there are numerous phased array techniques such as Full Matrix Capture (FMC) and Total Focusing Method (TFM) that provide good damage assessment for composite materials. Although, linear methods struggle to evaluate and assess low levels of damage, while nonlinear methods have shown great promise in early damage detection. A sweep and subtraction evaluation method coupled with a constructive nonlinear array method (CNA) is proposed in order to assess damage specific nonlinearities, address issues with frequency selection when using nonlinear ultrasound imaging techniques and reduce equipment generated nonlinearities. These methods were evaluated using multiple excitation locations on an impacted composite panel with a complex damage (barely visible impact damage). According to various recent works, damage excitation can be accentuated by exciting at local defect resonance (LDR) frequencies; although these frequencies are not always easily determinable. The sweep methodology uses broadband excitation to determine both local defect and material resonances, by assessing local defect generated nonlinearities using a laser vibrometer it is possible to assess which frequencies excite the complex geometry of the crack. The dual effect of accurately determining local defect resonances, the use of an image subtraction method and the reduction of equipment based nonlinearities using CNA result in greater repeatability and clearer nonlinear imaging (NIM).

Adaptive wavefront shaping for controlling nonlinear multimode interactions in optical fibres

NASA Astrophysics Data System (ADS)

Tzang, Omer; Caravaca-Aguirre, Antonio M.; Wagner, Kelvin; Piestun, Rafael

2018-06-01

Recent progress in wavefront shaping has enabled control of light propagation inside linear media to focus and image through scattering objects. In particular, light propagation in multimode fibres comprises complex intermodal interactions and rich spatiotemporal dynamics. Control of physical phenomena in multimode fibres and its applications are in their infancy, opening opportunities to take advantage of complex nonlinear modal dynamics. Here, we demonstrate a wavefront shaping approach for controlling nonlinear phenomena in multimode fibres. Using a spatial light modulator at the fibre input, real-time spectral feedback and a genetic algorithm optimization, we control a highly nonlinear multimode stimulated Raman scattering cascade and its interplay with four-wave mixing via a flexible implicit control on the superposition of modes coupled into the fibre. We show versatile spectrum manipulations including shifts, suppression, and enhancement of Stokes and anti-Stokes peaks. These demonstrations illustrate the power of wavefront shaping to control and optimize nonlinear wave propagation.

Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos.

PubMed

Basko, D M

2014-02-01

We study the discrete nonlinear Schröinger equation with weak disorder, focusing on the regime when the nonlinearity is, on the one hand, weak enough for the normal modes of the linear problem to remain well resolved but, on the other, strong enough for the dynamics of the normal mode amplitudes to be chaotic for almost all modes. We show that in this regime and in the limit of high temperature, the macroscopic density ρ satisfies the nonlinear diffusion equation with a density-dependent diffusion coefficient, D(ρ) = D(0)ρ(2). An explicit expression for D(0) is obtained in terms of the eigenfunctions and eigenvalues of the linear problem, which is then evaluated numerically. The role of the second conserved quantity (energy) in the transport is also quantitatively discussed.

Bearing defect signature analysis using advanced nonlinear signal analysis in a controlled environment

NASA Technical Reports Server (NTRS)

Zoladz, T.; Earhart, E.; Fiorucci, T.

1995-01-01

Utilizing high-frequency data from a highly instrumented rotor assembly, seeded bearing defect signatures are characterized using both conventional linear approaches, such as power spectral density analysis, and recently developed nonlinear techniques such as bicoherence analysis. Traditional low-frequency (less than 20 kHz) analysis and high-frequency envelope analysis of both accelerometer and acoustic emission data are used to recover characteristic bearing distress information buried deeply in acquired data. The successful coupling of newly developed nonlinear signal analysis with recovered wideband envelope data from accelerometers and acoustic emission sensors is the innovative focus of this research.

Proceedings of the Conference on Moments and Signal

NASA Astrophysics Data System (ADS)

Purdue, P.; Solomon, H.

1992-09-01

The focus of this paper is (1) to describe systematic methodologies for selecting nonlinear transformations for blind equalization algorithms (and thus new types of cumulants), and (2) to give an overview of the existing blind equalization algorithms and point out their strengths as well as weaknesses. It is shown that all blind equalization algorithms belong in one of the following three categories, depending where the nonlinear transformation is being applied on the data: (1) the Bussgang algorithms, where the nonlinearity is in the output of the adaptive equalization filter; (2) the polyspectra (or Higher-Order Spectra) algorithms, where the nonlinearity is in the input of the adaptive equalization filter; and (3) the algorithms where the nonlinearity is inside the adaptive filter, i.e., the nonlinear filter or neural network. We describe methodologies for selecting nonlinear transformations based on various optimality criteria such as MSE or MAP. We illustrate that such existing algorithms as Sato, Benveniste-Goursat, Godard or CMA, Stop-and-Go, and Donoho are indeed special cases of the Bussgang family of techniques when the nonlinearity is memoryless. We present results that demonstrate the polyspectra-based algorithms exhibit faster convergence rate than Bussgang algorithms. However, this improved performance is at the expense of more computations per iteration. We also show that blind equalizers based on nonlinear filters or neural networks are more suited for channels that have nonlinear distortions.

Non-Linear Editing for the Smaller College-Level Production Program, Rev. 2.0.

ERIC Educational Resources Information Center

Tetzlaff, David

This paper focuses on a specific topic and contention: Non-linear editing earns its place in a liberal arts setting because it is a superior tool to teach the concepts of how moving picture discourse is constructed through editing. The paper first points out that most students at small liberal arts colleges are not going to wind up working…

3-D zebrafish embryo image filtering by nonlinear partial differential equations.

PubMed

Rizzi, Barbara; Campana, Matteo; Zanella, Cecilia; Melani, Camilo; Cunderlik, Robert; Krivá, Zuzana; Bourgine, Paul; Mikula, Karol; Peyriéras, Nadine; Sarti, Alessandro

2007-01-01

We discuss application of nonlinear PDE based methods to filtering of 3-D confocal images of embryogenesis. We focus on the mean curvature driven and the regularized Perona-Malik equations, where standard as well as newly suggested edge detectors are used. After presenting the related mathematical models, the practical results are given and discussed by visual inspection and quantitatively using the mean Hausdorff distance.

Physics and applications of atmospheric nonlinear optics and filamentation.

PubMed

Kasparian, Jérôme; Wolf, Jean-Pierre

2008-01-07

We review the properties and applications of ultrashort laser pulses in the atmosphere, with a particular focus on filamentation. Filamentation is a non-linear propagation regime specific of ultrashort and ultraintense laser pulses in the atmosphere. Typical applications include remote sensing of atmospheric gases and aerosols, lightning control, laser-induced spectroscopy, coherent anti-stokes Raman scattering, and the generation of sub-THz radiation.

Opto-mechanical analysis of nonlinear elastomer membrane deformation under hydraulic pressure for variable-focus liquid-filled microlenses.

PubMed

Choi, Seung Tae; Son, Byeong Soo; Seo, Gye Won; Park, Si-Young; Lee, Kyung-Sick

2014-03-10

Nonlinear large deformation of a transparent elastomer membrane under hydraulic pressure was analyzed to investigate its optical performance for a variable-focus liquid-filled membrane microlens. In most membrane microlenses, actuators control the hydraulic pressure of optical fluid so that the elastomer membrane together with the internal optical fluid changes its shape, which alters the light path of the microlens to adapt its optical power. A fluid-structure interaction simulation was performed to estimate the transient behavior of the microlens under the operation of electroactive polymer actuators, demonstrating that the viscosity of the optical fluid successfully stabilizes the fluctuations within a fairly short period of time during dynamic operations. Axisymmetric nonlinear plate theory was used to calculate the deformation profile of the membrane under hydrostatic pressure, with which optical characteristics of the membrane microlens were estimated. The effects of gravitation and viscoelastic behavior of the elastomer membrane on the optical performance of the membrane microlens were also evaluated with finite element analysis.

Optical Response of Metal Nanoantennas to Femtosecond Pulses

NASA Astrophysics Data System (ADS)

Biswas, Sushmita; Heberle, Albert

2007-03-01

Nanoscale metal antennas are promising devices for focusing light down to dimensions much smaller than the wavelength of light. This focusing can lead to strong optical enhancement of the response of single molecules or quantum dots placed in the antenna gap, as well as strong nonlinearities. The optical response of such antenna, however, is not well understood yet. Here, we will present results of our investigations of the linear and nonlinear optical response of silver nanoscale bowtie antennas to excitation with near-infrared pulses from a femtosecond Ti:sapphire laser. The antennas were fabricated with electron beam lithography and a lift-of process on glass substrates and semiconductor materials. They have lengths of a few hundred nanometers and gaps between 10 and 100 nanometers. We will discuss polarization dependence of the excitation sensitivity, second harmonic generation and other nonlinear effects. References: [1] P. Muhlschlegel et al., Science ,1607(2005). [2] J.N. Farahani et al., Phys. Rev. Lett. 95,017402(2005).

Solution of the lossy nonlinear Tricomi equation with application to sonic boom focusing

NASA Astrophysics Data System (ADS)

Salamone, Joseph A., III

Sonic boom focusing theory has been augmented with new terms that account for mean flow effects in the direction of propagation and also for atmospheric absorption/dispersion due to molecular relaxation due to oxygen and nitrogen. The newly derived model equation was numerically implemented using a computer code. The computer code was numerically validated using a spectral solution for nonlinear propagation of a sinusoid through a lossy homogeneous medium. An additional numerical check was performed to verify the linear diffraction component of the code calculations. The computer code was experimentally validated using measured sonic boom focusing data from the NASA sponsored Superboom Caustic and Analysis Measurement Program (SCAMP) flight test. The computer code was in good agreement with both the numerical and experimental validation. The newly developed code was applied to examine the focusing of a NASA low-boom demonstration vehicle concept. The resulting pressure field was calculated for several supersonic climb profiles. The shaping efforts designed into the signatures were still somewhat evident despite the effects of sonic boom focusing.

Focusing high-squint and large-baseline one-stationary bistatic SAR data using keystone transform and enhanced nonlinear chirp scaling based on an ellipse model

NASA Astrophysics Data System (ADS)

Zhong, Hua; Zhang, Song; Hu, Jian; Sun, Minhong

2017-12-01

This paper deals with the imaging problem for one-stationary bistatic synthetic aperture radar (BiSAR) with high-squint, large-baseline configuration. In this bistatic configuration, accurate focusing of BiSAR data is a difficult issue due to the relatively large range cell migration (RCM), severe range-azimuth coupling, and inherent azimuth-geometric variance. To circumvent these issues, an enhanced azimuth nonlinear chirp scaling (NLCS) algorithm based on an ellipse model is investigated in this paper. In the range processing, a method combining deramp operation and keystone transform (KT) is adopted to remove linear RCM completely and mitigate range-azimuth cross-coupling. In the azimuth focusing, an ellipse model is established to analyze and depict the characteristic of azimuth-variant Doppler phase. Based on the new model, an enhanced azimuth NLCS algorithm is derived to focus one-stationary BiSAR data. Simulating results exhibited at the end of this paper validate the effectiveness of the proposed algorithm.

Air-Coupled Vibrometry

NASA Astrophysics Data System (ADS)

Döring, D.; Solodov, I.; Busse, G.

Sound and ultrasound in air are the products of a multitude of different processes and thus can be favorable or undesirable phenomena. Development of experimental tools for non-invasive measurements and imaging of airborne sound fields is of importance for linear and nonlinear nondestructive material testing as well as noise control in industrial or civil engineering applications. One possible solution is based on acousto-optic interaction, like light diffraction imaging. The diffraction approach usually requires a sophisticated setup with fine optical alignment barely applicable in industrial environment. This paper focuses on the application of the robust experimental tool of scanning laser vibrometry, which utilizes commercial off-the-shelf equipment. The imaging technique of air-coupled vibrometry (ACV) is based on the modulation of the optical path length by the acoustic pressure of the sound wave. The theoretical considerations focus on the analysis of acousto-optical phase modulation. The sensitivity of the ACV in detecting vibration velocity was estimated as ~1 mm/s. The ACV applications to imaging of linear airborne fields are demonstrated for leaky wave propagation and measurements of ultrasonic air-coupled transducers. For higher-intensity ultrasound, the classical nonlinear effect of the second harmonic generation was measured in air. Another nonlinear application includes a direct observation of the nonlinear air-coupled emission (NACE) from the damaged areas in solid materials. The source of the NACE is shown to be strongly localized around the damage and proposed as a nonlinear "tag" to discern and image the defects.

Laser beam propagation in nematic liquid crystals at the temperature close to the nematicisotropic critical point.

PubMed

Chen, Yu-Jen; Lin, Yu-Sung; Jiang, I-Min; Tsai, Ming-Shan

2008-03-17

This study investigates the optical nonlinearity of beam propagation in homogeneously aligned nematic liquid crystal (NLC) cells at a temperature close to the nematic-isotropic temperature (TNI). The undulate propagation mode with convergent and divergent loops appearing alternately is reported and the thermally enhanced optical reorientation nonlinearity at the focus is described. The optically induced phase transition exists along the pump beam direction. With the application of the conscopic technique, the arrangements of LC at the focus are proposed in this study. Results of this study demonstrate that the evolution of the LC configuration was affected by the pump beam based on the analysis of conoscopic patterns.

Nonlinear side effects of fs pulses inside corneal tissue during photodisruption

NASA Astrophysics Data System (ADS)

Heisterkamp, A.; Ripken, T.; Mamom, T.; Drommer, W.; Welling, H.; Ertmer, W.; Lubatschowski, H.

In order to evaluate the potential for refractive surgery, fs laser pulses of 150-fs pulse duration were used to process corneal tissue of dead and living animal eyes. By focusing the laser radiation down to spot sizes of several microns, very precise cuts could be achieved inside the treated cornea, accompanied with minimum collateral damage to the tissue by thermal or mechanical effects. During histo-pathological analysis by light and transmission electron microscopy considerable side effects of fs photodisruption were found. Due to the high intensities at the focal region several nonlinear effects occurred. Self-focusing, photodissociation, UV-light production were observed, leading to streak formation inside the cornea.

Axial–transversal coupling in the free nonlinear vibrations of Timoshenko beams with arbitrary slenderness and axial boundary conditions

PubMed Central

Rega, Giuseppe

2016-01-01

The nonlinear free oscillations of a straight planar Timoshenko beam are investigated analytically by means of the asymptotic development method. Attention is focused for the first time, to the best of our knowledge, on the nonlinear coupling between the axial and the transversal oscillations of the beam, which are decoupled in the linear regime. The existence of coupled and uncoupled motion is discussed. Furthermore, the softening versus hardening nature of the backbone curves is investigated in depth. The results are summarized by means of behaviour charts that illustrate the different possible classes of motion in the parameter space. New, and partially unexpected, phenomena, such as the changing of the nonlinear behaviour from softening to hardening by adding/removing the axial vibrations, are highlighted. PMID:27436974

Semiclassical approximations in the coherent-state representation

NASA Technical Reports Server (NTRS)

Kurchan, J.; Leboeuf, P.; Saraceno, M.

1989-01-01

The semiclassical limit of the stationary Schroedinger equation in the coherent-state representation is analyzed simultaneously for the groups W1, SU(2), and SU(1,1). A simple expression for the first two orders for the wave function and the associated semiclassical quantization rule is obtained if a definite choice for the classical Hamiltonian and expansion parameter is made. The behavior of the modulus of the wave function, which is a distribution function in a curved phase space, is studied for the three groups. The results are applied to the quantum triaxial rotor.

Einstein and the Quantum: The Secret Life of EPR

NASA Astrophysics Data System (ADS)

Fine, Arthur

2006-05-01

Locality, separation and entanglement -- 1930s style. Starting with Solvay 1927, we'll explore the background to the 1935 paper by Einstein, Podolsky and Rosen: how it was composed, the actual argument and principles used, and how the paper was received by Schroedinger, and others. We'll also look at Bohr's response: the extent to which Bohr connects with what Einstein was after in EPR and the extent to which EPR marks a shift in Bohr's thinking about the quantum theory. Time permitting, we will contrast EPR with Bell's theorem.

Uncertainty relation for non-Hamiltonian quantum systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tarasov, Vasily E.

2013-01-15

General forms of uncertainty relations for quantum observables of non-Hamiltonian quantum systems are considered. Special cases of uncertainty relations are discussed. The uncertainty relations for non-Hamiltonian quantum systems are considered in the Schroedinger-Robertson form since it allows us to take into account Lie-Jordan algebra of quantum observables. In uncertainty relations, the time dependence of quantum observables and the properties of this dependence are discussed. We take into account that a time evolution of observables of a non-Hamiltonian quantum system is not an endomorphism with respect to Lie, Jordan, and associative multiplications.

The divine clockwork: Bohr's correspondence principle and Nelson's stochastic mechanics for the atomic elliptic state

DOE Office of Scientific and Technical Information (OSTI.GOV)

Durran, Richard; Neate, Andrew; Truman, Aubrey

2008-03-15

We consider the Bohr correspondence limit of the Schroedinger wave function for an atomic elliptic state. We analyze this limit in the context of Nelson's stochastic mechanics, exposing an underlying deterministic dynamical system in which trajectories converge to Keplerian motion on an ellipse. This solves the long standing problem of obtaining Kepler's laws of planetary motion in a quantum mechanical setting. In this quantum mechanical setting, local mild instabilities occur in the Keplerian orbit for eccentricities greater than (1/{radical}(2)) which do not occur classically.

Ramsey's method of separated oscillating fields and its application to gravitationally induced quantum phase shifts

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abele, H.; Jenke, T.; Leeb, H.

2010-03-15

We propose to apply Ramsey's method of separated oscillating fields to the spectroscopy of the quantum states in the gravity potential above a horizontal mirror. This method allows a precise measurement of quantum mechanical phaseshifts of a Schroedinger wave packet bouncing off a hard surface in the gravitational field of the Earth. Measurements with ultracold neutrons will offer a sensitivity to Newton's law or hypothetical short-ranged interactions, which is about 21 orders of magnitude below the energy scale of electromagnetism.

Fatigue crack damage detection using subharmonic component with nonlinear boundary condition

NASA Astrophysics Data System (ADS)

Wu, Weiliang; Shen, Yanfeng; Qu, Wenzhong; Xiao, Li; Giurgiutiu, Victor

2015-03-01

In recent years, researchers have focused on structural health monitoring (SHM) and damage detection techniques using nonlinear vibration and nonlinear ultrasonic methods. Fatigue cracks may exhibit contact acoustic nonlinearity (CAN) with distinctive features such as superharmonics and subharmonics in the power spectrum of the sensing signals. However, challenges have been noticed in the practical applications of the harmonic methods. For instance, superharmonics can also be generated by the piezoelectric transducers and the electronic equipment; super/subharmonics may also stem from the nonlinear boundary conditions such as structural fixtures and joints. It is hard to tell whether the nonlinear features come from the structural damage or the intrinsic nonlinear boundary conditions. The objective of this paper is to demonstrate the application of nonlinear ultrasonic subharmonic method for detecting fatigue cracks with nonlinear boundary conditions. The fatigue crack was qualitatively modeled as a single-degree-of-freedom (SDOF) system with non-classical hysteretic nonlinear interface forces at both sides of the crack surfaces. The threshold of subharmonic generation was studied, and the influence of crack interface parameters on the subharmonic resonance condition was investigated. The different threshold behaviors between the nonlinear boundary condition and the fatigue crack was found, which can be used to distinguish the source of nonlinear subharmonic features. To evaluate the proposed method, experiments of an aluminum plate with a fatigue crack were conducted to quantitatively verify the subharmonic resonance range. Two surface-bonded piezoelectric transducers were used to generate and receive ultrasonic wave signals. The fatigue damage was characterized in terms of a subharmonic damage index. The experimental results demonstrated that the subharmonic component of the sensing signal can be used to detect the fatigue crack and further distinguish it from inherent nonlinear boundary conditions.

Fatigue crack damage detection using subharmonic component with nonlinear boundary condition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Weiliang, E-mail: wwl@whu.edu.cn; Qu, Wenzhong, E-mail: qwz@whu.edu.cn, E-mail: xiaoli6401@126.com; Xiao, Li, E-mail: qwz@whu.edu.cn, E-mail: xiaoli6401@126.com

In recent years, researchers have focused on structural health monitoring (SHM) and damage detection techniques using nonlinear vibration and nonlinear ultrasonic methods. Fatigue cracks may exhibit contact acoustic nonlinearity (CAN) with distinctive features such as superharmonics and subharmonics in the power spectrum of the sensing signals. However, challenges have been noticed in the practical applications of the harmonic methods. For instance, superharmonics can also be generated by the piezoelectric transducers and the electronic equipment; super/subharmonics may also stem from the nonlinear boundary conditions such as structural fixtures and joints. It is hard to tell whether the nonlinear features come frommore » the structural damage or the intrinsic nonlinear boundary conditions. The objective of this paper is to demonstrate the application of nonlinear ultrasonic subharmonic method for detecting fatigue cracks with nonlinear boundary conditions. The fatigue crack was qualitatively modeled as a single-degree-of-freedom (SDOF) system with non-classical hysteretic nonlinear interface forces at both sides of the crack surfaces. The threshold of subharmonic generation was studied, and the influence of crack interface parameters on the subharmonic resonance condition was investigated. The different threshold behaviors between the nonlinear boundary condition and the fatigue crack was found, which can be used to distinguish the source of nonlinear subharmonic features. To evaluate the proposed method, experiments of an aluminum plate with a fatigue crack were conducted to quantitatively verify the subharmonic resonance range. Two surface-bonded piezoelectric transducers were used to generate and receive ultrasonic wave signals. The fatigue damage was characterized in terms of a subharmonic damage index. The experimental results demonstrated that the subharmonic component of the sensing signal can be used to detect the fatigue crack and further distinguish it from inherent nonlinear boundary conditions.« less

A modeling approach to predict acoustic nonlinear field generated by a transmitter with an aluminum lens.

PubMed

Fan, Tingbo; Liu, Zhenbo; Chen, Tao; Li, Faqi; Zhang, Dong

2011-09-01

In this work, the authors propose a modeling approach to compute the nonlinear acoustic field generated by a flat piston transmitter with an attached aluminum lens. In this approach, the geometrical parameters (radius and focal length) of a virtual source are initially determined by Snell's refraction law and then adjusted based on the Rayleigh integral result in the linear case. Then, this virtual source is used with the nonlinear spheroidal beam equation (SBE) model to predict the nonlinear acoustic field in the focal region. To examine the validity of this approach, the calculated nonlinear result is compared with those from the Westervelt and (Khokhlov-Zabolotskaya-Kuznetsov) KZK equations for a focal intensity of 7 kW/cm(2). Results indicate that this approach could accurately describe the nonlinear acoustic field in the focal region with less computation time. The proposed modeling approach is shown to accurately describe the nonlinear acoustic field in the focal region. Compared with the Westervelt equation, the computation time of this approach is significantly reduced. It might also be applicable for the widely used concave focused transmitter with a large aperture angle.

Nonlinear imaging (NIM) of barely visible impact damage (BVID) in composite panels using a semi and full air-coupled linear and nonlinear ultrasound technique

NASA Astrophysics Data System (ADS)

Malfense Fierro, Gian Piero; Meo, Michele

2018-03-01

Two non-contact methods were evaluated to address the reliability and reproducibility concerns affecting industry adoption of nonlinear ultrasound techniques for non-destructive testing and evaluation (NDT/E) purposes. A semi and a fully air-coupled linear and nonlinear ultrasound method was evaluated by testing for barely visible impact damage (BVID) in composite materials. Air coupled systems provide various advantages over contact driven systems; such as: ease of inspection, no contact and lubrication issues and a great potential for non-uniform geometry evaluation. The semi air-coupled setup used a suction attached piezoelectric transducer to excite the sample and an array of low-cost microphones to capture the signal over the inspection area, while the second method focused on a purely air-coupled setup, using an air-coupled transducer to excite the structure and capture the signal. One of the issues facing nonlinear and any air-coupled systems is transferring enough energy to stimulate wave propagation and in the case of nonlinear ultrasound; damage regions. Results for both methods provided nonlinear imaging (NIM) of damage regions using a sweep excitation methodology, with the semi aircoupled system providing clearer results.

Identification of nonlinear modes using phase-locked-loop experimental continuation and normal form

NASA Astrophysics Data System (ADS)

Denis, V.; Jossic, M.; Giraud-Audine, C.; Chomette, B.; Renault, A.; Thomas, O.

2018-06-01

In this article, we address the model identification of nonlinear vibratory systems, with a specific focus on systems modeled with distributed nonlinearities, such as geometrically nonlinear mechanical structures. The proposed strategy theoretically relies on the concept of nonlinear modes of the underlying conservative unforced system and the use of normal forms. Within this framework, it is shown that without internal resonance, a valid reduced order model for a nonlinear mode is a single Duffing oscillator. We then propose an efficient experimental strategy to measure the backbone curve of a particular nonlinear mode and we use it to identify the free parameters of the reduced order model. The experimental part relies on a Phase-Locked Loop (PLL) and enables a robust and automatic measurement of backbone curves as well as forced responses. It is theoretically and experimentally shown that the PLL is able to stabilize the unstable part of Duffing-like frequency responses, thus enabling its robust experimental measurement. Finally, the whole procedure is tested on three experimental systems: a circular plate, a chinese gong and a piezoelectric cantilever beam. It enable to validate the procedure by comparison to available theoretical models as well as to other experimental identification methods.

Power requirements reducing of FBG based all-optical switching

NASA Astrophysics Data System (ADS)

Scholtz, Ľubomír.; Solanská, Michaela; Ladányi, Libor; Müllerová, Jarmila

2017-12-01

Although Fiber Bragg gratings (FBGs) are well known devices, their using as all-optical switching elements has been still examined. Current research is focused on optimization of their properties for their using in future all-optical networks. The main problem are high switching intensities needed for achieving the changes of the transmission state. Over several years switching intensities have been reduced from hundreds of GW/cm2 to tens of MW/cm2 by selecting appropriate gratings and signal parameters or using suitable materials. Two principal nonlinear effects with similar power requirements can result in the bistable transmission/reflection of an input optical pulse. In the self-phase modulation (SPM) regime switching is achieved by the intense probe pulse itself. Using cross-phase modulation (XPM) a strong pump alters the FBG refractive index experienced by a weak probe pulse. As a result of this the detuning of the probe pulse from the center of the photonic band gap occurs. Using of XPM the effect of modulation instability is reduced. Modulation instability which is the main SPM degradation mechanism. We focused on nonlinear FBGs based on chalcogenide glasses which are very often used in various applications. Thanks to high nonlinear parameters chalcogenide glasses are suitable candidates for reducing switching intensities of nonlinear FBGs.

Nonlinear derating of high-intensity focused ultrasound beams using Gaussian modal sums.

PubMed

Dibaji, Seyed Ahmad Reza; Banerjee, Rupak K; Soneson, Joshua E; Myers, Matthew R

2013-11-01

A method is introduced for using measurements made in water of the nonlinear acoustic pressure field produced by a high-intensity focused ultrasound transducer to compute the acoustic pressure and temperature rise in a tissue medium. The acoustic pressure harmonics generated by nonlinear propagation are represented as a sum of modes having a Gaussian functional dependence in the radial direction. While the method is derived in the context of Gaussian beams, final results are applicable to general transducer profiles. The focal acoustic pressure is obtained by solving an evolution equation in the axial variable. The nonlinear term in the evolution equation for tissue is modeled using modal amplitudes measured in water and suitably reduced using a combination of "source derating" (experiments in water performed at a lower source acoustic pressure than in tissue) and "endpoint derating" (amplitudes reduced at the target location). Numerical experiments showed that, with proper combinations of source derating and endpoint derating, direct simulations of acoustic pressure and temperature in tissue could be reproduced by derating within 5% error. Advantages of the derating approach presented include applicability over a wide range of gains, ease of computation (a single numerical quadrature is required), and readily obtained temperature estimates from the water measurements.

Nonlinear Optics and Solitons in Photonic Crystal Fibres

NASA Astrophysics Data System (ADS)

Skryabin, Dmitry V.; Wadsworth, William J.

The fibre optics revolution in communication technologies followed the 1950's demonstration of the glass fibres with dielectric cladding [1]. Transmission applications of fibre optics have become a dominant modern day technology not least because nonlinearities present in - or introduced into - glass and enhanced by the tight focusing of the fibre modes allow for numerous light processing techniques, such as amplification, frequency conversion, pulse shaping, and many others. For these reasons, and because of the rich fundamental physics behind it, nonlinear fibre optics has become a blossoming discipline in its own right [1]. The 1990's witnessed another important development in fibre optics. Once again it came from a new approach to the fibre cladding, comprising a periodic pattern of air holes separated by glass membranes forming a photonic crystal structure [2, 3]. This prompted the name Photonic Crystal Fibres (PCFs). The fascinating story behind the invention of PCF and research into various fibre designs can be found, e.g., in [4]. Our aim here is to review the role played by PCFs in nonlinear and quantum optics, which is becoming the mainstream of the PCF related research and applications. Our focus will be on the areas where PCFs have brought to life effects and applications which were previously difficult, impossible to observe or simply not thought about.

Synthesis, characterization and theoretical investigations of the structure, electronic properties and third-order nonlinearity optics (NLO) of M(DPIP)₂.

PubMed

Li, Kang; Tang, Guodong; Kou, ShanShan; Culnane, Lance F; Zhang, Yu; Song, Yinglin; Li, Rongqing; Wei, Changmei

2015-03-15

Three complexes of M(DPIP)2 (M=Cu, Co, Zn as 1, 2, 3) were synthesized and characterized by elemental analysis, IR, UV-Vis, thermogravimetry, and X-ray diffraction. Their nonlinear optical properties were measured by the Z-scan technique and yielded a normalized transmittance of about 70% for complex 1 (45 μJ pulse), and 93% for complex 3 (68 μJ pulse at the focus point). The nonlinear absorption coefficient, β, is 1.4×10(-11) m/W for 1 and 5.6×10(-13) m/W for 3, and the third-order nonlinear refraction index, n2, is 1.0×10(-18) m(2)/W for 3. Complex 1 shows self-defocusing property, while complex 3 exhibits self-focusing property. The thermogravimetric results show that the frame structure of compounds 1-3 begin to collapse at 400, 250 and 280°C, respectively, which suggests that they elicit excellent thermal stability. This research aims to provide better understanding of these compounds, and offer preliminary explanations for the significant differences between compounds 1-3, in order to potentially help in the designing of future novel materials with NLO properties. Copyright © 2014 Elsevier B.V. All rights reserved.

Analytic and computational modelling of super-radiant pulse compression in plasma and comparisons with experiment

NASA Astrophysics Data System (ADS)

Shvets, Gennady; Kalmykov, Serguei; Dreher, Matthias; Meyer-Ter-Vehn, Juergen

2003-10-01

The strongly non-linear regime of Raman backscattering [1,2] holds the promise of compressing long low-intensity laser beams into ultra-short high intensity pulses. As the short pulse is amplified by the long counter-propagating pump via backscattering the pump off the nonlinear plasma wave, its duration shrinks and intensity grows. The increase of the bandwidth of the amplified pulse only occurs in the nonlinear amplification regime, and is its most telling signature. Recent experiments at MPQ carried out in the strongly nonlinear regime reveal two previously unobserved features: (i) bandwidth expansion, and (ii) breakdown of the initially smooth amplified pulse into several spikes. Using semi-analytic model and particle-in-cell simulations, we explain the multiple pulse formation by the synchrotron motion of plasma electrons in the ponderomotive potential. Self-similar solutions consisting of multiple spikes are derived, and their nonlinear frequency shifts evaluated. The nonlinear focusing of the pulse by the pump is predicted and compared with experimental observations. [1] G. Shvets et. al., Phys. Rev. Lett. 81, 4879 (1998). [2] A. Pukhov, Rep. Progr. Phys. 66, 47 (1998).

Effect of nonlinearity saturation on hot-image formation in cascaded saturable nonlinear medium slabs

NASA Astrophysics Data System (ADS)

Wang, Youwen; Dai, Zhiping; Ling, Xiaohui; Chen, Liezun; Lu, Shizhuan; You, Kaiming

2016-11-01

In high-power laser system such as Petawatt lasers, the laser beam can be intense enough to result in saturation of nonlinear refraction index of medium. Based on the standard linearization method of small-scale self-focusing and the split-step Fourier numerical calculation method, we present analytical and simulative investigations on the hot-image formation in cascaded saturable nonlinear medium slabs, to disclose the effect of nonlinearity saturation on the distribution and intensity of hot images. The analytical and simulative results are found in good agreement. It is shown that, saturable nonlinearity does not change the distribution of hot images, while may greatly affect the intensity of hot images, i.e., for a given saturation light intensity, with the intensity of the incident laser beam, the intensity of hot images firstly increases monotonously and eventually reaches a saturation; for the incident laser beam of a given intensity, with the saturation light intensity lowering, the intensity of hot images decreases rapidly, even resulting in a few hot images too weak to be visible.

Measurement of ultrafast optical Kerr effect of Ge-Sb-Se chalcogenide slab waveguides by the beam self-trapping technique

NASA Astrophysics Data System (ADS)

Kuriakose, Tintu; Baudet, Emeline; Halenkovič, Tomáš; Elsawy, Mahmoud M. R.; Němec, Petr; Nazabal, Virginie; Renversez, Gilles; Chauvet, Mathieu

2017-11-01

We present a reliable and original experimental technique based on the analysis of beam self-trapping to measure ultrafast optical nonlinearities in planar waveguides. The technique is applied to the characterization of Ge-Sb-Se chalcogenide films that allow Kerr induced self-focusing and soliton formation. Linear and nonlinear optical constants of three different chalcogenide waveguides are studied at 1200 and 1550 nm in femtosecond regime. Waveguide propagation loss and two photon absorption coefficients are determined by transmission analysis. Beam broadening and narrowing results are compared with simulations of the nonlinear Schrödinger equation solved by BPM method to deduce the Kerr n2 coefficients. Kerr optical nonlinearities obtained by our original technique compare favorably with the values obtained by Z-scan technique. Nonlinear refractive index as high as (69 ± 11) × 10-18m2 / W is measured in Ge12.5Sb25Se62.5 at 1200 nm with low nonlinear absorption and low propagation losses which reveals the great characteristics of our waveguides for ultrafast all optical switching and integrated photonic devices.

Spatiotemporal chaos and two-dimensional dissipative rogue waves in Lugiato-Lefever model

NASA Astrophysics Data System (ADS)

Panajotov, Krassimir; Clerc, Marcel G.; Tlidi, Mustapha

2017-06-01

Driven nonlinear optical cavities can exhibit complex spatiotemporal dynamics. We consider the paradigmatic Lugiato-Lefever model describing driven nonlinear optical resonator. This model is one of the most-studied nonlinear equations in optics. It describes a large spectrum of nonlinear phenomena from bistability, to periodic patterns, localized structures, self-pulsating localized structures and to a complex spatiotemporal behavior. The model is considered also as prototype model to describe several optical nonlinear devices such as Kerr media, liquid crystals, left handed materials, nonlinear fiber cavity, and frequency comb generation. We focus our analysis on a spatiotemporal chaotic dynamics in one-dimension. We identify a route to spatiotemporal chaos through an extended quasiperiodicity. We have estimated the Kaplan-Yorke dimension that provides a measure of the strange attractor complexity. Likewise, we show that the Lugiato-Leferver equation supports rogues waves in two-dimensional settings. We characterize rogue-wave formation by computing the probability distribution of the pulse height. Contribution to the Topical Issue "Theory and Applications of the Lugiato-Lefever Equation", edited by Yanne K. Chembo, Damia Gomila, Mustapha Tlidi, Curtis R. Menyuk.

Non-linear effects in bunch compressor of TARLA

NASA Astrophysics Data System (ADS)

Yildiz, Hüseyin; Aksoy, Avni; Arikan, Pervin

2016-03-01

Transport of a beam through an accelerator beamline is affected by high order and non-linear effects such as space charge, coherent synchrotron radiation, wakefield, etc. These effects damage form of the beam, and they lead particle loss, emittance growth, bunch length variation, beam halo formation, etc. One of the known non-linear effects on low energy machine is space charge effect. In this study we focus on space charge effect for Turkish Accelerator and Radiation Laboratory in Ankara (TARLA) machine which is designed to drive InfraRed Free Electron Laser covering the range of 3-250 µm. Moreover, we discuss second order effects on bunch compressor of TARLA.

Linear and Nonlinear Time Reverse Acoustics in Geomaterials

NASA Astrophysics Data System (ADS)

Sutin, A.; Johnson, P. A.; Tencate, J.

2004-12-01

Linear and Nonlinear Time Reverse Acoustics in Geomaterials P. A. Johnson, A.Sutin and J. TenCate Time Reversal Acoustics (TRA) is one of the most interesting topics to have emerged in modern acoustics in the last 40 years. Much of the seminal research in this area has been carried out by the group at the Laboratoire Ondes et Acoustique at the University of Paris 7, who have demonstrated the ability and robustness of TRA (using Time Reversal Mirrors) to provide spatial control and focusing of an ultrasonic beam (e.g. Fink, 1999). The ability to obtain highly focused signals with TRA has numerous applications, including lithotripsy, ultrasonic brain surgery, nondestructive evaluation and underwater acoustic communication. Notably, the study of time reversal in solids and in the earth is still relatively new. The problem is fundamentally different from the purely acoustic one due to the excitation and propagation of both compressional (bulk) and shear waves as well as the scattering and potentially high dissipation of the medium. We conducted series of TRA experiments in different solids using direct-coupled transducers on solids in tandem with a large bandwidth laser vibrometer detector. A typical time reversal experiment was carried out using the following steps (Sutin et al. 2004a). Laboratory experiments were conducted in different geomaterials of different shapes and sizes, including Carrera marble, granite and Berea sandstone. We observed that, in spite of potentially huge numbers of wave conversions (e.g., compressional to shear, shear to compressional, compressional/shear to surface waves, etc.) for each reflection at each free surface, time reversal still provides significant spatial and temporal focusing in these different geophysical materials. The typical size of the focal area is approximately equivalent to the shear wavelength and the focal area, but becomes larger with increasing wave attenuation (Sutin et al. 2004a; Delsanto et al., 2003)). The TR-induced focusing of wave energy at a point in space and time is ideal from the perspective of enhancing elastic wave, nonlinear response (for example, higher harmonic generation or wave modulation effects). We call this technique Nonlinear Time Reverse Acoustics (NLTRA) (Sutin et a. 2004b). We investigated the harmonic generation in TRA signals focused above a small crack (2mm) in a glass cube. Large second harmonic amplitudes were observed above the crack. Scanning of the surface by applying the laser vibrometer simultaneous with TRA focusing of the signal to an array of corresponding scanning points provided nonlinear imaging of the surface, showing all cracks in the scanned region. References: Delsanto, P. P., P. A. Johnson, M. Scalerandi, J. A. TenCate, LISA simulations of time-reversed acoustic and elastic wave experiments, J. of Physics D: Applied Physics 35, 3145-3152, (2003). M. Fink, Time Reversed Acoustics, Scientific American, 91-97 (1999). Sutin, A., J. TenCate and P. A. Johnson, Single-channel time reversal in elastic solids, J. Acoust. Soc. Am., in press (2004a). Sutin, A., P. Johnson, and J. TenCate, Development of nonlinear time reverse acoustics (NLTRA) method for crack detection in solids, Proceedings of the World Congress on Acoustics (Paris) [http://www.sfa.asso.fr/wcu2003/] 121-124 (2003b).

Light focusing using epsilon-near-zero metamaterials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu, Weiren, E-mail: weiren.zhu@monash.edu; Premaratne, Malin; Si, Li-Ming, E-mail: lms@bit.edu.cn

2013-11-15

We present a strategy of focusing light using epsilon-near-zero metamaterials with embedded dielectric cylinder. The focusing mechanism is analytically investigated, and its accuracy is substantiated by rigorous full-wave simulations. It is found that the focusing intensity is highly depend on the embedded medium and its size, and the magnetic field amplitude of the focused beam itself can reach as high as 98.2 times the incident field. Owing to its versatility, the proposed light focusing system is sure to find applications in fields such as bio-sensing and in nonlinear optics.

Free-carrier-induced soliton fission unveiled by in situ measurements in nanophotonic waveguides

DOE Office of Scientific and Technical Information (OSTI.GOV)

Husko, Chad; Wulf, Matthias; Lefrancois, Simon

Solitons are localized waves formed by a balance of focusing and defocusing effects. These nonlinear waves exist in diverse forms of matter yet exhibit similar properties including stability, periodic recurrence and particle-like trajectories. One important property is soliton fission, a process by which an energetic higher-order soliton breaks apart due to dispersive or nonlinear perturbations. Here we demonstrate through both experiment and theory that nonlinear photocarrier generation can induce soliton fission. Using near-field measurements, we directly observe the nonlinear spatial and temporal evolution of optical pulses in situ in a nanophotonic semiconductor waveguide. We develop an analytic formalism describing themore » free-carrier dispersion (FCD) perturbation and show the experiment exceeds the minimum threshold by an order of magnitude. We confirm these observations with a numerical nonlinear Schrodinger equation model. Finally, these results provide a fundamental explanation and physical scaling of optical pulse evolution in free-carrier media and could enable improved supercontinuum sources in gas based and integrated semiconductor waveguides.« less

Mobility of discrete multibreathers in the exciton dynamics of the Davydov model with saturable nonlinearities.

PubMed

Tchinang Tchameu, J D; Togueu Motcheyo, A B; Tchawoua, C

2014-10-01

We show that the state of amide-I excitations in proteins is modeled by the discrete nonlinear Schrödinger equation with saturable nonlinearities. This is done by extending the Davydov model to take into account the competition between local compression and local dilatation of the lattice, thus leading to the interplay between self-focusing and defocusing saturable nonlinearities. Site-centered (sc) mode and/or bond-centered mode like discrete multihump soliton (DMHS) solutions are found numerically and their stability is analyzed. As a result, we obtained the existence and stability diagrams for all observed types of sc DMHS solutions. We also note that the stability of sc DMHS solutions depends not only on the value of the interpeak separation but also on the number of peaks, while their counterpart having at least one intersite soliton is instable. A study of mobility is achieved and it appears that, depending on the higher-order saturable nonlinearity, DMHS-like mechanism for vibrational energy transport along the protein chain is possible.

Transition Theory and Experimental Comparisons on (I) Amplification into Streets and (II) a Strongly Nonlinear Break-up Criterion

NASA Astrophysics Data System (ADS)

Smith, F. T.; Bowles, R. I.

1992-10-01

The two stages I, II are studied by using recent nonlinear theory and then compared with the experiments of Nishioka et al. (1979) on the transition of plane Poiseuille flow. The first stage I starts at low amplitude from warped input, which is deformed through weakly nonlinear interaction into a blow-up in amplitude and phase accompanied by spanwise focusing into streets. This leads into the strongly nonlinear stage II. It holds for a broad range of interactive boundary layers and related flows, to all of which the nonlinear break-up criterion applies. The experimental comparisons on I, II for channel flow overall show encouraging quantitative agreement, supporting recent comparisons (in the boundary-layer setting) of the description of stage I in Stewart & Smith (1992) with the experiments of Klebanoff & Tidstrom (1959) and of the break-up criterion of Smith (1988a) with the computations of Peridier et al. (1991 a, b).

Free-carrier-induced soliton fission unveiled by in situ measurements in nanophotonic waveguides

DOE PAGES

Husko, Chad; Wulf, Matthias; Lefrancois, Simon; ...

2016-04-15

Solitons are localized waves formed by a balance of focusing and defocusing effects. These nonlinear waves exist in diverse forms of matter yet exhibit similar properties including stability, periodic recurrence and particle-like trajectories. One important property is soliton fission, a process by which an energetic higher-order soliton breaks apart due to dispersive or nonlinear perturbations. Here we demonstrate through both experiment and theory that nonlinear photocarrier generation can induce soliton fission. Using near-field measurements, we directly observe the nonlinear spatial and temporal evolution of optical pulses in situ in a nanophotonic semiconductor waveguide. We develop an analytic formalism describing themore » free-carrier dispersion (FCD) perturbation and show the experiment exceeds the minimum threshold by an order of magnitude. We confirm these observations with a numerical nonlinear Schrodinger equation model. Finally, these results provide a fundamental explanation and physical scaling of optical pulse evolution in free-carrier media and could enable improved supercontinuum sources in gas based and integrated semiconductor waveguides.« less

Efficient Nonlinear Atomization Model for Thin 3D Free Liquid Films

NASA Astrophysics Data System (ADS)

Mehring, Carsten

2007-03-01

Reviewed is a nonlinear reduced-dimension thin-film model developed by the author and aimed at the prediction of spray formation from thin films such as those found in gas-turbine engines (e.g., prefilming air-blast atomizers), heavy-fuel-oil burners (e.g., rotary-cup atomizers) and in the paint industry (e.g., flat-fan atomizers). Various implementations of the model focusing on different model-aspects, i.e., effect of film geometry, surface tension, liquid viscosity, coupling with surrounding gas-phase flow, influence of long-range intermolecular forces during film rupture are reviewed together with a validation of the nonlinear wave propagation characteristics predicted by the model for inviscid planar films using a two-dimensional vortex- method. An extension and generalization of the current nonlinear film model for implementation into a commercial flow- solver is outlined.

Nonlinear propagation in ultrasonic fields: measurements, modelling and harmonic imaging.

PubMed

Humphrey, V F

2000-03-01

In high amplitude ultrasonic fields, such as those used in medical ultrasound, nonlinear propagation can result in waveform distortion and the generation of harmonics of the initial frequency. In the nearfield of a transducer this process is complicated by diffraction effects associated with the source. The results of a programme to study the nonlinear propagation in the fields of circular, focused and rectangular transducers are described, and comparisons made with numerical predictions obtained using a finite difference solution to the Khokhlov-Zabolotskaya-Kuznetsov (or KZK) equation. These results are extended to consider nonlinear propagation in tissue-like media and the implications for ultrasonic measurements and ultrasonic heating are discussed. The narrower beamwidths and reduced side-lobe levels of the harmonic beams are illustrated and the use of harmonics to form diagnostic images with improved resolution is described.

Performance analysis of smart laminated composite plate integrated with distributed AFC material undergoing geometrically nonlinear transient vibrations

NASA Astrophysics Data System (ADS)

Shivakumar, J.; Ashok, M. H.; Khadakbhavi, Vishwanath; Pujari, Sanjay; Nandurkar, Santosh

2018-02-01

The present work focuses on geometrically nonlinear transient analysis of laminated smart composite plates integrated with the patches of Active fiber composites (AFC) using Active constrained layer damping (ACLD) as the distributed actuators. The analysis has been carried out using generalised energy based finite element model. The coupled electromechanical finite element model is derived using Von Karman type nonlinear strain displacement relations and a first-order shear deformation theory (FSDT). Eight-node iso-parametric serendipity elements are used for discretization of the overall plate integrated with AFC patch material. The viscoelastic constrained layer is modelled using GHM method. The numerical results shows the improvement in the active damping characteristics of the laminated composite plates over the passive damping for suppressing the geometrically nonlinear transient vibrations of laminated composite plates with AFC as patch material.

Nonlinear Relaxation in Population Dynamics

NASA Astrophysics Data System (ADS)

Cirone, Markus A.; de Pasquale, Ferdinando; Spagnolo, Bernardo

We analyze the nonlinear relaxation of a complex ecosystem composed of many interacting species. The ecological system is described by generalized Lotka-Volterra equations with a multiplicative noise. The transient dynamics is studied in the framework of the mean field theory and with random interaction between the species. We focus on the statistical properties of the asymptotic behaviour of the time integral of the ith population and on the distribution of the population and of the local field.

Gregorian optical system with non-linear optical technology for protection against intense optical transients

DOEpatents

Ackermann, Mark R [Albuquerque, NM; Diels, Jean-Claude M [Albuquerque, NM

2007-06-26

An optical system comprising a concave primary mirror reflects light through an intermediate focus to a secondary mirror. The secondary mirror re-focuses the image to a final image plane. Optical limiter material is placed near the intermediate focus to optically limit the intensity of light so that downstream components of the optical system are protected from intense optical transients. Additional lenses before and/or after the intermediate focus correct optical aberrations.

A new perspective on Quantum Finance using the Black-Scholes pricing model

NASA Astrophysics Data System (ADS)

Dieng, Lamine

2007-03-01

Options are known to be divided into two types, the first type is called a call option and the second type is called a put option and these options are offered to stock holders in order to hedge their positions against risky fluctuations of the stock price. It is important to mention that due to fluctuations of the stock price, options can be found sometimes deep in the money, at the money and out of the money. A deep in the money option is described when the option's holder has a positive expected payoff, at the money option is when the option's holder has a zero expected payoff and an out of the money option is when the payoff is negative. In this work, we will assume the stock price to be described by the well known Black-Scholes model or sometimes called the multiplicative model. Using Ito calculus, Martingale and supermartingale theories, we investigated the Black-Scholes pricing equation at the money (X(stock price)= K (strike price)) when the expected payoff of the options holder is zero. We also hedged the Black-Scholes pricing equation in the limit when delta is zero to obtain the non-relativistic time independent Schroedinger equation in quantum mechanics. We compared the two equations and found the diffusion constant to be a function of the stock price in contrast to the Bachelier model we have worked on earlier. We solved the Schroedinger equation and found a dependence between interest rate, volatility and strike price at the money.

Implementation of spatial overlap modulation nonlinear optical microscopy using an electro-optic deflector

PubMed Central

Isobe, Keisuke; Kawano, Hiroyuki; Kumagai, Akiko; Miyawaki, Atsushi; Midorikawa, Katsumi

2013-01-01

A spatial overlap modulation (SPOM) technique is a nonlinear optical microscopy technique which enhances the three-dimensional spatial resolution and rejects the out-of-focus background limiting the imaging depth inside a highly scattering sample. Here, we report on the implementation of SPOM in which beam pointing modulation is achieved by an electro-optic deflector. The modulation and demodulation frequencies are enhanced to 200 kHz and 400 kHz, respectively, resulting in a 200-fold enhancement compared with the previously reported system. The resolution enhancement and suppression of the out-of-focus background are demonstrated by sum-frequency-generation imaging of pounded granulated sugar and deep imaging of fluorescent beads in a tissue-like phantom, respectively. PMID:24156055

Rogue periodic waves of the focusing nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Chen, Jinbing; Pelinovsky, Dmitry E.

2018-02-01

Rogue periodic waves stand for rogue waves on a periodic background. The nonlinear Schrödinger equation in the focusing case admits two families of periodic wave solutions expressed by the Jacobian elliptic functions dn and cn. Both periodic waves are modulationally unstable with respect to long-wave perturbations. Exact solutions for the rogue periodic waves are constructed by using the explicit expressions for the periodic eigenfunctions of the Zakharov-Shabat spectral problem and the Darboux transformations. These exact solutions generalize the classical rogue wave (the so-called Peregrine's breather). The magnification factor of the rogue periodic waves is computed as a function of the elliptic modulus. Rogue periodic waves constructed here are compared with the rogue wave patterns obtained numerically in recent publications.

Rogue periodic waves of the focusing nonlinear Schrödinger equation.

PubMed

Chen, Jinbing; Pelinovsky, Dmitry E

2018-02-01

Rogue periodic waves stand for rogue waves on a periodic background. The nonlinear Schrödinger equation in the focusing case admits two families of periodic wave solutions expressed by the Jacobian elliptic functions dn and cn . Both periodic waves are modulationally unstable with respect to long-wave perturbations. Exact solutions for the rogue periodic waves are constructed by using the explicit expressions for the periodic eigenfunctions of the Zakharov-Shabat spectral problem and the Darboux transformations. These exact solutions generalize the classical rogue wave (the so-called Peregrine's breather). The magnification factor of the rogue periodic waves is computed as a function of the elliptic modulus. Rogue periodic waves constructed here are compared with the rogue wave patterns obtained numerically in recent publications.

Effects of Higher-Order Relativistic Nonlinearity and Wakefield During a Moderately Intense Laser Pulse Propagation in a Plasma Channel

NASA Astrophysics Data System (ADS)

Liu, Ming-Ping; Liu, Bing-Bing; Liu, San-Qiu; Zhang, Fu-Yang; Liu, Jie

2013-08-01

Using a variational approach, the propagation of a moderately intense laser pulse in a parabolic preformed plasma channel is investigated. The effects of higher-order relativistic nonlinearity (HRN) and wakefield are included. The effect of HRN serves as an additional defocusing mechanism and has the same order of magnitude in the spot size as that of the transverse wakefield (TWF). The effect of longitudinal wakefield is much larger than those of HRN and TWF for an intense laser pulse with the pulse length equaling the plasma wavelength. The catastrophic focusing of the laser spot size would be prevented in the present of HRN and then it varies with periodic focusing oscillations.

Using bivariate signal analysis to characterize the epileptic focus: the benefit of surrogates.

PubMed

Andrzejak, R G; Chicharro, D; Lehnertz, K; Mormann, F

2011-04-01

The disease epilepsy is related to hypersynchronous activity of networks of neurons. While acute epileptic seizures are the most extreme manifestation of this hypersynchronous activity, an elevated level of interdependence of neuronal dynamics is thought to persist also during the seizure-free interval. In multichannel recordings from brain areas involved in the epileptic process, this interdependence can be reflected in an increased linear cross correlation but also in signal properties of higher order. Bivariate time series analysis comprises a variety of approaches, each with different degrees of sensitivity and specificity for interdependencies reflected in lower- or higher-order properties of pairs of simultaneously recorded signals. Here we investigate which approach is best suited to detect putatively elevated interdependence levels in signals recorded from brain areas involved in the epileptic process. For this purpose, we use the linear cross correlation that is sensitive to lower-order signatures of interdependence, a nonlinear interdependence measure that integrates both lower- and higher-order properties, and a surrogate-corrected nonlinear interdependence measure that aims to specifically characterize higher-order properties. We analyze intracranial electroencephalographic recordings of the seizure-free interval from 29 patients with an epileptic focus located in the medial temporal lobe. Our results show that all three approaches detect higher levels of interdependence for signals recorded from the brain hemisphere containing the epileptic focus as compared to signals recorded from the opposite hemisphere. For the linear cross correlation, however, these differences are not significant. For the nonlinear interdependence measure, results are significant but only of moderate accuracy with regard to the discriminative power for the focal and nonfocal hemispheres. The highest significance and accuracy is obtained for the surrogate-corrected nonlinear interdependence measure.

Focus scanning with feedback control for fiber-optic nonlinear endomicroscopy (Conference Presentation)

NASA Astrophysics Data System (ADS)

Li, Ang; Liang, Wenxuan; Li, Xingde

2017-02-01

Fiber-optic nonlinear endomicroscopy represents a strong promise to enable translation of nonlinear microscopy technologies to in vivo applications, particularly imaging of internal organs. Two-dimensional imaging beam scanning has been accomplished by using fiber-optic scanners or MEMS scanners. Yet nonlinear endomicroscopy still cannot perform rapid and reliable depth or focus scanning while maintaining a small form factor. Shape memory alloy (SMA) wire had shown promise in extending 2D endoscopic imaging to the third dimension. By Joule heating, the SMA wire would contract and move the endomicroscope optics to change beam focus. However, this method suffered from hysteresis, and was susceptible to change in ambient temperature, making it difficult to achieve accurate and reliable depth scanning. Here we present a feedback-controlled SMA actuator which addressed these challenges. The core of the feedback loop was a Hall effect sensor. By measuring the magnetic flux density from a tiny magnet attached to the SMA wire, contraction distance of the SMA wire could be tracked in real time. The distance was then fed to the PID algorithm running in a microprocessor, which computed the error between the command position and the current position of the actuator. The current running through the SMA wire was adjusted accordingly. Our feedback-controlled SMA actuator had a tube-like shape with outer diameter of 5.5 mm and length of 25 mm, and was designed to house the endomicroscope inside. Initial test showed that it allowed more than 300 microns of travel distance, with an average positioning error of less than 2 microns. 3D imaging experiments with the endomicroscope is underway, and its imaging performance will be assessed and discussed.

Using bivariate signal analysis to characterize the epileptic focus: The benefit of surrogates

NASA Astrophysics Data System (ADS)

Andrzejak, R. G.; Chicharro, D.; Lehnertz, K.; Mormann, F.

2011-04-01

The disease epilepsy is related to hypersynchronous activity of networks of neurons. While acute epileptic seizures are the most extreme manifestation of this hypersynchronous activity, an elevated level of interdependence of neuronal dynamics is thought to persist also during the seizure-free interval. In multichannel recordings from brain areas involved in the epileptic process, this interdependence can be reflected in an increased linear cross correlation but also in signal properties of higher order. Bivariate time series analysis comprises a variety of approaches, each with different degrees of sensitivity and specificity for interdependencies reflected in lower- or higher-order properties of pairs of simultaneously recorded signals. Here we investigate which approach is best suited to detect putatively elevated interdependence levels in signals recorded from brain areas involved in the epileptic process. For this purpose, we use the linear cross correlation that is sensitive to lower-order signatures of interdependence, a nonlinear interdependence measure that integrates both lower- and higher-order properties, and a surrogate-corrected nonlinear interdependence measure that aims to specifically characterize higher-order properties. We analyze intracranial electroencephalographic recordings of the seizure-free interval from 29 patients with an epileptic focus located in the medial temporal lobe. Our results show that all three approaches detect higher levels of interdependence for signals recorded from the brain hemisphere containing the epileptic focus as compared to signals recorded from the opposite hemisphere. For the linear cross correlation, however, these differences are not significant. For the nonlinear interdependence measure, results are significant but only of moderate accuracy with regard to the discriminative power for the focal and nonfocal hemispheres. The highest significance and accuracy is obtained for the surrogate-corrected nonlinear interdependence measure.

Wave propagation in ordered, disordered, and nonlinear photonic band gap materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lidorikis, Elefterios

Photonic band gap materials are artificial dielectric structures that give the promise of molding and controlling the flow of optical light the same way semiconductors mold and control the electric current flow. In this dissertation the author studied two areas of photonic band gap materials. The first area is focused on the properties of one-dimensional PBG materials doped with Kerr-type nonlinear material, while, the second area is focused on the mechanisms responsible for the gap formation as well as other properties of two-dimensional PBG materials. He first studied, in Chapter 2, the general adequacy of an approximate structure model inmore » which the nonlinearity is assumed to be concentrated in equally-spaced very thin layers, or 6-functions, while the rest of the space is linear. This model had been used before, but its range of validity and the physical reasons for its limitations were not quite clear yet. He performed an extensive examination of many aspects of the model's nonlinear response and comparison against more realistic models with finite-width nonlinear layers, and found that the d-function model is quite adequate, capturing the essential features in the transmission characteristics. The author found one exception, coming from the deficiency of processing a rigid bottom band edge, i.e. the upper edge of the gaps is always independent of the refraction index contrast. This causes the model to miss-predict that there are no soliton solutions for a positive Kerr-coefficient, something known to be untrue.« less

Harmonic generation of Lamb waves

NASA Astrophysics Data System (ADS)

Ing, Ros Kiri

2002-11-01

Lamb waves are dispersive waves that propagate following a number of distinct modes that depend on the values of the central frequency and frequency band. According to such properties and using the time-reversal process, it is shown that the hyperfocusing effect may be experienced [R. K. Ing and M. Fink, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 1032-1043 (1998)]. Such a focusing effect both relates the time recompression of the dispersive Lamb waves and constructive interference on the focus point of the modes involved. The hyperfocusing effect is interesting because it allows the amplitude of the Lamb waves to reach huge values on the focus point. In our experiments, Lamb waves with normal amplitudes of micrometer values have been achieved on the free surface of a Duralumin plate of 3 mm thickness. By analyzing the Lamb waves in the neighborhood of the focus point using the 2-D Fourier transform technique, a nonlinear process of harmonic generation is then observed--the fundamental frequency component is centered at 1.5 MHz. This nonlinear process is under study and quantified.

Generation of terahertz radiation by intense hollow Gaussian laser beam in magnetised plasma under relativistic-ponderomotive regime

NASA Astrophysics Data System (ADS)

Rawat, Priyanka; Rawat, Vinod; Gaur, Bineet; Purohit, Gunjan

2017-07-01

This paper explores the self-focusing of hollow Gaussian laser beam (HGLB) in collisionless magnetized plasma and its effect on the generation of THz radiation in the presence of relativistic-ponderomotive nonlinearity. The relativistic change of electron mass and electron density perturbation due to the ponderomotive force leads to self-focusing of the laser beam in plasma. Nonlinear coupling between the intense HGLB and electron plasma wave leads to generation of THz radiation in plasma. Resonant excitation of THz radiation at different frequencies of laser and electron plasma wave satisfies proper phase matching conditions. Appropriate expressions for the beam width parameter of the laser beam and the electric vector of the THz wave have been evaluated under the paraxial-ray and Wentzel-Kramers Brillouin approximations. It is found that the yield of THz amplitude depends on the focusing behaviour of laser beam, magnetic field, and background electron density. Numerical simulations have been carried out to investigate the effect of laser and plasma parameters on self-focusing of the laser beam and further its effect on the efficiency of the generated THz radiation.

Diode end pumped laser and harmonic generator using same

NASA Technical Reports Server (NTRS)

Byer, Robert L. (Inventor); Dixon, George J. (Inventor); Kane, Thomas J. (Inventor)

1988-01-01

A second harmonic, optical generator is disclosed in which a laser diode produces an output pumping beam which is focused by means of a graded, refractive index rod lens into a rod of lasant material, such as Nd:YAG, disposed within an optical resonator to pump the lasant material and to excite the optical resonator at a fundamental wavelength. A non-linear electro-optic material such as MgO:LiNbO.sub.3 is coupled to the excited, fundamental mode of the optical resonator to produce a non-linear interaction with the fundamental wavelength producing a harmonic. In one embodiment, the gain medium and the non-linear material are disposed within an optical resonator defined by a pair of reflectors, one of which is formed on a face of the gain medium and the second of which is formed on a face of the non-linear medium. In another embodiment, the non-linear, electro-optic material is doped with the lasant ion such that the gain medium and the non-linear doubling material are co-extensive in volume. In another embodiment, a non-linear, doubling material is disposed in an optical resonator external of the laser gai medium for improved stability of the second harmonic generation process. In another embodiment, the laser gain medium andthe non-linear material are bonded together by means of an optically transparent cement to form a mechanically stable, monolithic structure. In another embodiment, the non-linear material has reflective faces formed thereon to define a ring resonator to decouple reflections from the non-linear medium back to the gain medium for improved stability.

From solitons to rogue waves in nonlinear left-handed metamaterials.

PubMed

Shen, Yannan; Kevrekidis, P G; Veldes, G P; Frantzeskakis, D J; DiMarzio, D; Lan, X; Radisic, V

2017-03-01

In the present work, we explore soliton and roguelike wave solutions in the transmission line analog of a nonlinear left-handed metamaterial. The nonlinearity is expressed through a voltage-dependent, symmetric capacitance motivated by recently developed ferroelectric barium strontium titanate thin-film capacitor designs. We develop both the corresponding nonlinear dynamical lattice and its reduction via a multiple scales expansion to a nonlinear Schrödinger (NLS) model for the envelope of a given carrier wave. The reduced model can feature either a focusing or a defocusing nonlinearity depending on the frequency (wave number) of the carrier. We then consider the robustness of different types of solitary waves of the reduced model within the original nonlinear left-handed medium. We find that both bright and dark solitons persist in a suitable parametric regime, where the reduction to the NLS model is valid. Additionally, for suitable initial conditions, we observe a rogue wave type of behavior that differs significantly from the classic Peregrine rogue wave evolution, including most notably the breakup of a single Peregrine-like pattern into solutions with multiple wave peaks. Finally, we touch upon the behavior of generalized members of the family of the Peregrine solitons, namely, Akhmediev breathers and Kuznetsov-Ma solitons, and explore how these evolve in the left-handed transmission line.

We should be using nonlinear indices when relating heart-rate dynamics to cognition and mood

PubMed Central

Young, Hayley; Benton, David

2015-01-01

Both heart rate (HR) and brain functioning involve the integrated output of a multitude of regulatory mechanisms, that are not quantified adequately by linear approximations such as means and standard deviations. It was therefore considered whether non-linear measures of HR complexity are more strongly associated with cognition and mood. Whilst resting, the inter-beat (R-R) time series of twenty-one males and twenty-four females were measured for five minutes. The data were summarised using time, frequency and nonlinear complexity measures. Attention, memory, reaction times, mood and cortisol levels were assessed. Nonlinear HR indices captured additional information, enabling a greater percentage of the variance in behaviour to be explained. On occasions non-linear indices were related to aspects for behaviour, for example focused attention and cortisol production, when time or frequency indices were not. These effects were sexually dimorphic with HR complexity being more strongly associated with the behaviour of females. It was concluded that nonlinear rather than linear methods of summarizing the HR times series offers a novel way of relating brain functioning and behaviour. It should be considered whether non-linear measures of HR complexity can be used as a biomarker of the integrated functioning of the brain. PMID:26565560

Effect of reduction time on third order optical nonlinearity of reduced graphene oxide

NASA Astrophysics Data System (ADS)

Sreeja, V. G.; Vinitha, G.; Reshmi, R.; Anila, E. I.; Jayaraj, M. K.

2017-04-01

We report the influence of reduction time on structural, linear and nonlinear optical properties of reduced graphene oxide (rGO) thin films synthesized by spin coating method. We observed that the structural, linear and nonlinear optical properties can be tuned with reduction time in GO is due to the increased structural ordering because of the restoration of sp2 carbon atoms with the time of reduction. The nonlinear absorption studies by open aperture Z-scan technique exhibited a saturable absorption. The nonlinear refraction studies showed the self de focusing nature of rGO by closed aperture Z scan technique. The nonlinear absorption coefficient and saturation intensity varies with the time for reduction of GO which is attributed to the depletion of valence band and the conduction band filling effect. Our results emphasize duration for reduction of GO dependent optical nonlinearity of rGO thin films to a great extent and explore its applications Q switched mode locking laser systems for generating ultra short laser pulses and in optical sensors. The rGO coated films were characterized by X-Ray diffraction method (XRD), Fourier transform infrared spectroscopy (FTIR), Raman spectroscopy, UV-Vis absorption spectroscopy (UV-Vis), Photoluminescence (PL) and Scanning electron microscope (SEM) measurements.

Quantum-limited amplification with a nonlinear cavity detector

NASA Astrophysics Data System (ADS)

Laflamme, C.; Clerk, A. A.

2011-03-01

We consider the quantum measurement properties of a driven cavity with a Kerr-type nonlinearity that is used to amplify a dispersively coupled input signal. Focusing on an operating regime that is near a bifurcation point, we derive simple asymptotic expressions describing the cavity’s noise and response. We show that the cavity’s backaction and imprecision noise allow for quantum-limited linear amplification and position detection only if one is able to utilize the sizable correlations between these quantities. This is possible when one amplifies a nonresonant signal but is not possible in quantum nondemolition qubit detection. We also consider the possibility of using the nonlinear cavity’s backaction for cooling a mechanical mode.

Influence of damped propagation of dopant on the static and frequency-dependent third nonlinear polarizability of quantum dot

NASA Astrophysics Data System (ADS)

Pal, Suvajit; Ghosh, Manas

2014-07-01

We investigate the profiles of diagonal components of static and frequency-dependent third nonlinear (γxxxx and γyyyy) polarizability of repulsive impurity doped quantum dots. The dopant impurity potential takes a GAUSSIAN form. We have considered propagation of the dopant within an environment that damps the motion. The study focuses on role of damping strength on the diagonal components of both static and frequency-dependent third nonlinear polarizability of the doped system. The doped system is further exposed to an external electric field of given intensity. Damping subtly modulates the dot-impurity interaction and fabricates the polarizability components in a noticeable manner.

Nonlinear absorption and optical limiting in gold-precipitated glasses induced by a femtosecond laser

NASA Astrophysics Data System (ADS)

Qu, Shiliang; Gao, Yachen; Jiang, Xiongwei; Zeng, Huidan; Song, Yinglin; Qiu, Jianrong; Zhu, Congshan; Hirao, K.

2003-09-01

Nonlinear absorptions of Au nanoparticles precipitated silicate glasses by irradiation of a focused femtosecond pulsed laser were investigated using Z-scan technique with 8 ns pulses at 532 nm. Optical limiting (OL) effects in such glasses have been also measured. It is observed that the behaviors of transition from saturable absorption to reverse saturable absorption and the OL performances for different samples are significantly different, which depend drastically on the irradiation power density of the femtosecond laser used for the Au nanoparticles precipitation in the glass. Strong nonlinear absorptions in these samples are mainly attributed to the surface plasmon resonance (SPR) and free carrier absorptions of the precipitated Au nanoparticles.

Nonlinear Gravitational and Radiation Aspects in Nanoliquid with Exponential Space Dependent Heat Source and Variable Viscosity

NASA Astrophysics Data System (ADS)

Gireesha, B. J.; Kumar, P. B. Sampath; Mahanthesh, B.; Shehzad, S. A.; Abbasi, F. M.

2018-05-01

The nonlinear convective flow of kerosene-Alumina nanoliquid subjected to an exponential space dependent heat source and temperature dependent viscosity is investigated here. This study is focuses on augmentation of heat transport rate in liquid propellant rocket engine. The kerosene-Alumina nanoliquid is considered as the regenerative coolant. Aspects of radiation and viscous dissipation are also covered. Relevant nonlinear system is solved numerically via RK based shooting scheme. Diverse flow fields are computed and examined for distinct governing variables. We figured out that the nanoliquid's temperature increased due to space dependent heat source and radiation aspects. The heat transfer rate is higher in case of changeable viscosity than constant viscosity.

Non-linear effects in bunch compressor of TARLA

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yildiz, Hüseyin, E-mail: huseyinyildiz006@gmail.com, E-mail: huseyinyildiz@gazi.edu.tr; Aksoy, Avni; Arikan, Pervin

2016-03-25

Transport of a beam through an accelerator beamline is affected by high order and non-linear effects such as space charge, coherent synchrotron radiation, wakefield, etc. These effects damage form of the beam, and they lead particle loss, emittance growth, bunch length variation, beam halo formation, etc. One of the known non-linear effects on low energy machine is space charge effect. In this study we focus on space charge effect for Turkish Accelerator and Radiation Laboratory in Ankara (TARLA) machine which is designed to drive InfraRed Free Electron Laser covering the range of 3-250 µm. Moreover, we discuss second order effects onmore » bunch compressor of TARLA.« less

Nonlinear Gravitational and Radiation Aspects in Nanoliquid with Exponential Space Dependent Heat Source and Variable Viscosity

NASA Astrophysics Data System (ADS)

Gireesha, B. J.; Kumar, P. B. Sampath; Mahanthesh, B.; Shehzad, S. A.; Abbasi, F. M.

2018-02-01

The nonlinear convective flow of kerosene-Alumina nanoliquid subjected to an exponential space dependent heat source and temperature dependent viscosity is investigated here. This study is focuses on augmentation of heat transport rate in liquid propellant rocket engine. The kerosene-Alumina nanoliquid is considered as the regenerative coolant. Aspects of radiation and viscous dissipation are also covered. Relevant nonlinear system is solved numerically via RK based shooting scheme. Diverse flow fields are computed and examined for distinct governing variables. We figured out that the nanoliquid's temperature increased due to space dependent heat source and radiation aspects. The heat transfer rate is higher in case of changeable viscosity than constant viscosity.

Spiraling elliptic Laguerre-Gaussian soliton in isotropic nonlocal competing cubic-quintic nonlinear media

NASA Astrophysics Data System (ADS)

Wang, Qing; Li, JingZhen; Xie, WeiXin

2018-06-01

This paper introduce a kind of spiraling elliptic Laguerre-Gaussian (SELG) soliton which has complicated structures in its profile and phase, and find that it can be formed in nonlocal cubic, quantic and competing cubic-quintic nonlinear media, respectively. The different-order SELG solitons with the same ellipticity have the same rotation period, cross-term phase coefficient, critical power and different critical orbital angular momentums (OAM). However, with the increase of ellipticity, the rotation period, cross-term phase coefficient, critical power and OAM are all increased. In particular, there are bistable SELG solitons stemmed by the competing effect between self-focusing cubic and self-defocusing quintic nonlinearities.

Discrete retardance second harmonic generation ellipsometry.

PubMed

Dehen, Christopher J; Everly, R Michael; Plocinik, Ryan M; Hedderich, Hartmut G; Simpson, Garth J

2007-01-01

A new instrument was constructed to perform discrete retardance nonlinear optical ellipsometry (DR-NOE). The focus of the design was to perform second harmonic generation NOE while maximizing sample and application flexibility and minimizing data acquisition time. The discrete retardance configuration results in relatively simple computational algorithms for performing nonlinear optical ellipsometric analysis. NOE analysis of a disperse red 19 monolayer yielded results that were consistent with previously reported values for the same surface system, but with significantly reduced acquisition times.

Ring formation in self-focusing of electromagnetic beams in plasmas

NASA Astrophysics Data System (ADS)

Faisal, M.; Mishra, S. K.; Verma, M. P.; Sodha, M. S.

2007-10-01

This article presents a paraxial theory of ring formation as an initially Gaussian beam propagates in a nonlinear plasma, characterized by significant collisional or ponderomotive nonlinearity. Regions in the axial irradiance-(beamwidth)-2 space, for which the ring formation occurs and the paraxial theory is valid, have been characterized; for typical points in these regions the dependence of the beam width parameter and the radial distribution of irradiance on the distance has been specifically investigated and discussed.

Nonlinear Schrödinger equations for Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Galati, Luigi; Zheng, Shijun

2013-10-01

The Gross-Pitaevskii equation, or more generally the nonlinear Schrödinger equation, models the Bose-Einstein condensates in a macroscopic gaseous superfluid wave-matter state in ultra-cold temperature. We provide analytical study of the NLS with L2 initial data in order to understand propagation of the defocusing and focusing waves for the BEC mechanism in the presence of electromagnetic fields. Numerical simulations are performed for the two-dimensional GPE with anisotropic quadratic potentials.

Leaky, Pulsating Laser-Plasma Filaments in the Nonlinear Schrödinger Equation Approximation

NASA Astrophysics Data System (ADS)

Johnston, Tudor Wyatt

1996-11-01

For studying self-focusing and filamention of electromagnetic beams in plasmas (and other media) (including laser beams in ICF plasmas) with power well over the critical value for self-focusing, considerable success has recently been achieved using the well-known nonlinear Schrodinger equation with "saturating" nonlinearities (i.e. those for which the nonlinearity is not infinite even if the field becomes indefinitely large). High-power beams with noticeable structure can indeed break up into numerous filaments, but these filaments emerge from the phase of filament creation in states rather close to the known filament equilibria. This is seen to be due to the loss of excess power from the filaments as they are forming and pulsating, so that each filament thus tends to condense to an equilibrium state. Analysis of filaments near equilibrium is thus seen to be more relevant than anticipated, but radiation from the filament(s) can often play an important role. Concepts have been borrowed from normal quantum mechanics (e.g. Bohr oscillations at the appropriate Rabi frequency) to explain the oscillation spectrum and whether significant radiation damping is present. Apparent momentum transfer during multiple filament creation seems common. Some discussion is given of the application of this kind of analysis to the radial confinement of sub-picosecond laser pulses over distances of tens of meters. (François Vidal (INRS) is the major collaborator in this work.)

Nanomaterial-enhanced frequency combs (Conference Presentation)

NASA Astrophysics Data System (ADS)

Armani, Andrea M.; Castro-Beltran, Rigoberto; Diep, Vinh; Gungor, Eda; Shen, Xiaoqin; Soltani, Soheil

2017-02-01

Optical cavities are able to confine and store specific wavelengths of light, acting as optical amplifiers at those wavelengths. Because the amount of amplification is directly related to the cavity quality factor (Q) (or the cavity finesse), frequency comb research has focused on high-Q and ultra-high Q microcavities fabricated from a range of materials using a variety of methods. In all cases, the comb generation relies on a nonlinear process known as parametric frequency conversion which is based on a third order nonlinear interaction and which results in four wave mixing (FWM). Clearly, this approach requires significant optical power, which was the original motivation for using ultra-high-Q cavities. In fact, the majority of research to date has focused on pursuing increasingly high Q factors. However, another strategy is to improve the nonlinearity of the resonator through intelligently designing materials for this application. In the present work, a suite of nanomaterials (organic and inorganic) have been intelligently designed with the explicit purpose to enhance the nonlinearity of the resonator and reducing the threshold for frequency comb generation in the near-IR. The nanomaterials do not change the structure of the comb and only act to reduce the comb threshold. The silica microcavity is used as a testbed for initial demonstration and verification purposes. However, the fundamental strategy is translatable to other whispering gallery mode cavities.

Weakly Nonlinear Description of Parametric Instabilities in Vibrating Flows

NASA Technical Reports Server (NTRS)

Knobloch, E.; Vega, J. M.

1999-01-01

This project focuses on the effects of weak dissipation on vibrational flows in microgravity and in particular on (a) the generation of mean flows through viscous effects and their reaction on the flows themselves, and (b) the effects of finite group velocity and dispersion on the resulting dynamics in large domains. The basic mechanism responsible for the generation of such flows is nonlinear and was identified by Schlichting [21] and Longuet-Higgins. However, only recently has it become possible to describe such flows self-consistently in terms of amplitude equations for the parametrically excited waves coupled to a mean flow equation. The derivation of these equations is nontrivial because the limit of zero viscosity is singular. This project focuses on various aspects of this singular problem (i.e., the limit C equivalent to (nu)((g)(h(exp 3)))exp -1/2 << 1,where nu is the kinematic viscosity and h is the liquid depth) in the weakly nonlinear regime. A number of distinct cases is identified depending on the values of the Bond number, the size of the nonlinear terms, distance above threshold and the length scales of interest. The theory provides a quantitative explanation of a number of experiments on the vibration modes of liquid bridges and related experiments on parametric excitation of capillary waves in containers of both small and large aspect ratio. The following is a summary of results obtained thus far.

Perturbative and Ab-Initio Calculations of Electrical Susceptibilities of Atoms

NASA Astrophysics Data System (ADS)

Spott, Andrew

Perturbative nonlinear optics consists of many powerful predictive theoretical methods, including the perturbative series of observables related to the interaction of light with matter. The light intensity limits of such series have been studied in the past for highly nonlinear processes such as above threshold ionization and high harmonic generation. A more recent debate focuses on the limits of applicability of perturbation theory for the nonlinear electrical susceptibility and the nonlinear index of refraction of atoms, which are important parameters to study, for example, for filamentation of laser pulses in nonlinear media. In this thesis we analyze theoretical predictions for the electrical susceptibility of atoms for the transition from the perturbative to the nonperturbative intensity regime. To this end, we apply a numerical basis state method that allows us to perform respective calculations in the framework of perturbation theory as well as using ab-initio methods. The results let us identify the intensity at which the application of perturbation theory breaks down. Furthermore, we provide an analysis of the nonlinear susceptibility as a function of time during the interaction with the laser pulse and find that theoretical predictions are in good agreement with recent experimental data.

Non-Linear Approach in Kinesiology Should Be Preferred to the Linear--A Case of Basketball.

PubMed

Trninić, Marko; Jeličić, Mario; Papić, Vladan

2015-07-01

In kinesiology, medicine, biology and psychology, in which research focus is on dynamical self-organized systems, complex connections exist between variables. Non-linear nature of complex systems has been discussed and explained by the example of non-linear anthropometric predictors of performance in basketball. Previous studies interpreted relations between anthropometric features and measures of effectiveness in basketball by (a) using linear correlation models, and by (b) including all basketball athletes in the same sample of participants regardless of their playing position. In this paper the significance and character of linear and non-linear relations between simple anthropometric predictors (AP) and performance criteria consisting of situation-related measures of effectiveness (SE) in basketball were determined and evaluated. The sample of participants consisted of top-level junior basketball players divided in three groups according to their playing time (8 minutes and more per game) and playing position: guards (N = 42), forwards (N = 26) and centers (N = 40). Linear (general model) and non-linear (general model) regression models were calculated simultaneously and separately for each group. The conclusion is viable: non-linear regressions are frequently superior to linear correlations when interpreting actual association logic among research variables.

Magnetic field induced changes in linear and nonlinear optical properties of Ti incorporated Cr2O3 nanostructured thin film

NASA Astrophysics Data System (ADS)

Baraskar, Priyanka; Chouhan, Romita; Agrawal, Arpana; Choudhary, R. J.; Sen, Pranay K.; Sen, Pratima

2018-03-01

We report the magnetic field effect on the linear and nonlinear optical properties of pulse laser ablated Ti-incorporated Cr2O3 nanostructured thin film. Optical properties have been experimentally analyzed under Voigt geometry by performing ultraviolet-visible spectroscopy and closed aperture Z-scan technique using a continuous wave He-Ne laser source. Nonlinear optical response reveals a single peak-valley feature in the far field diffraction pattern in absence of magnetic field (B = 0) confirming self-defocussing effect. This feature switches to a valley-peak configuration for B = 5000G, suggesting self-focusing effect. For B ≤ 750G, oscillations were observed revealing the occurrence of higher order nonlinearity. Origin of nonlinearity is attributed to the near resonant d-d transitions observed from the broad peak occurring around 2 eV. These transitions are of magnetic origin and get modified under the application of external magnetic field. Our results suggest that magnetic field can be used as an effective tool to monitor the sign of optical nonlinearity and hence the thermal expansion in Ti-incorporated Cr2O3 nanostructured thin film.

Chirped Peregrine solitons in a class of cubic-quintic nonlinear Schrödinger equations.

PubMed

Chen, Shihua; Baronio, Fabio; Soto-Crespo, Jose M; Liu, Yi; Grelu, Philippe

2016-06-01

We shed light on the fundamental form of the Peregrine soliton as well as on its frequency chirping property by virtue of a pertinent cubic-quintic nonlinear Schrödinger equation. An exact generic Peregrine soliton solution is obtained via a simple gauge transformation, which unifies the recently-most-studied fundamental rogue-wave species. We discover that this type of Peregrine soliton, viable for both the focusing and defocusing Kerr nonlinearities, could exhibit an extra doubly localized chirp while keeping the characteristic intensity features of the original Peregrine soliton, hence the term chirped Peregrine soliton. The existence of chirped Peregrine solitons in a self-defocusing nonlinear medium may be attributed to the presence of self-steepening effect when the latter is not balanced out by the third-order dispersion. We numerically confirm the robustness of such chirped Peregrine solitons in spite of the onset of modulation instability.

Observation of ion acoustic multi-Peregrine solitons in multicomponent plasma with negative ions

NASA Astrophysics Data System (ADS)

Pathak, Pallabi; Sharma, Sumita K.; Nakamura, Y.; Bailung, H.

2017-12-01

The evolution of the multi-Peregrine soliton is investigated in a multicomponent plasma and found to be critically dependent on the initial bound state. Formation and splitting of Peregrine soliton, broadening of the frequency spectra provide clear evidence of nonlinear-dispersive focusing due to modulational instability, a generic mechanism for rogue wave formation in which amplitude and phase modulation grow as a result of interplay between nonlinearity and anomalous dispersion. We have shown that initial perturbation parameters (amplitude & temporal length) critically determine the number of solitons evolution. It is also found that a sufficiently long wavelength perturbation of high amplitude invoke strong nonlinearity to generate a supercontinuum state. Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT) analysis of the experimental time series data clearly indicate the spatio-temporal localization and spectral broadening. We consider a model based on the frame work of Nonlinear Schrodinger equation (NLSE) to explain the experimental observations.

An experimental nonlinear low dynamic stiffness device for shock isolation

NASA Astrophysics Data System (ADS)

Francisco Ledezma-Ramirez, Diego; Ferguson, Neil S.; Brennan, Michael J.; Tang, Bin

2015-07-01

The problem of shock generated vibration is very common in practice and difficult to isolate due to the high levels of excitation involved and its transient nature. If not properly isolated it could lead to large transmitted forces and displacements. Typically, classical shock isolation relies on the use of passive stiffness elements to absorb energy by deformation and some damping mechanism to dissipate residual vibration. The approach of using nonlinear stiffness elements is explored in this paper, focusing in providing an isolation system with low dynamic stiffness. The possibilities of using such a configuration for a shock mount are studied experimentally following previous theoretical models. The model studied considers electromagnets and permanent magnets in order to obtain nonlinear stiffness forces using different voltage configurations. It is found that the stiffness nonlinearities could be advantageous in improving shock isolation in terms of absolute displacement and acceleration response when compared with linear elastic elements.

The use of normal forms for analysing nonlinear mechanical vibrations

PubMed Central

Neild, Simon A.; Champneys, Alan R.; Wagg, David J.; Hill, Thomas L.; Cammarano, Andrea

2015-01-01

A historical introduction is given of the theory of normal forms for simplifying nonlinear dynamical systems close to resonances or bifurcation points. The specific focus is on mechanical vibration problems, described by finite degree-of-freedom second-order-in-time differential equations. A recent variant of the normal form method, that respects the specific structure of such models, is recalled. It is shown how this method can be placed within the context of the general theory of normal forms provided the damping and forcing terms are treated as unfolding parameters. The approach is contrasted to the alternative theory of nonlinear normal modes (NNMs) which is argued to be problematic in the presence of damping. The efficacy of the normal form method is illustrated on a model of the vibration of a taut cable, which is geometrically nonlinear. It is shown how the method is able to accurately predict NNM shapes and their bifurcations. PMID:26303917

Wide localized solutions of the parity-time-symmetric nonautonomous nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Meza, L. E. Arroyo; Dutra, A. de Souza; Hott, M. B.; Roy, P.

2015-01-01

By using canonical transformations we obtain localized (in space) exact solutions of the nonlinear Schrödinger equation (NLSE) with cubic and quintic space and time modulated nonlinearities and in the presence of time-dependent and inhomogeneous external potentials and amplification or absorption (source or drain) coefficients. We obtain a class of wide localized exact solutions of NLSE in the presence of a number of non-Hermitian parity-time (PT )-symmetric external potentials, which are constituted by a mixing of external potentials and source or drain terms. The exact solutions found here can be applied to theoretical studies of ultrashort pulse propagation in optical fibers with focusing and defocusing nonlinearities. We show that, even in the presence of gain or loss terms, stable solutions can be found and that the PT symmetry is an important feature to guarantee the conservation of the average energy of the system.

Echodentography based on nonlinear time reversal tomography: Ultrasonic nonlinear signature identification

NASA Astrophysics Data System (ADS)

Santos, Serge Dos; Farova, Zuzana; Kus, Vaclav; Prevorovsky, Zdenek

2012-05-01

This paper examines possibilities of using Nonlinear Elastic Wave Spectroscopy (NEWS) methods in dental investigations. Themain task consisted in imaging cracks or other degradation signatures located in dentin close to the Enamel-Dentine Junction (EDJ). NEWS approach was investigated experimentally with a new bi-modal acousto-optic set-up based on the chirp-coded nonlinear ultrasonic time reversal (TR) concepts. Complex internal structure of the tooth is analyzed by the TR-NEWS procedure adapted to tomography-like imaging of the tooth damages. Ultrasonic instrumentation with 10 MHz bandwidth has been set together including laser vibrometer used to detect responses of the tooth on its excitation carried out by a contact piezoelectric transducer. Bi-modal TR-NEWS images of the tooth were created before and after focusing, which resulted from the time compression. The polar B-scan of the tooth realized with TR-NEWS procedure is suggested to be applied as a new echodentography imaging.

Oscillatory Dynamics of One-Dimensional Homogeneous Granular Chains

NASA Astrophysics Data System (ADS)

Starosvetsky, Yuli; Jayaprakash, K. R.; Hasan, Md. Arif; Vakakis, Alexander F.

The acoustics of the homogeneous granular chains has been studied extensively both numerically and experimentally in the references cited in the previous chapters. This chapter focuses on the oscillatory behavior of finite dimensional homogeneous granular chains. It is well known that normal vibration modes are the building blocks of the vibrations of linear systems due to the applicability of the principle of superposition. One the other hand, nonlinear theory is deprived of such a general superposition principle (although special cases of nonlinear superpositions do exist), but nonlinear normal modes ‒ NNMs still play an important role in the forced and resonance dynamics of these systems. In their basic definition [1], NNMs were defined as time-periodic nonlinear oscillations of discrete or continuous dynamical systems where all coordinates (degrees-of-freedom) oscillate in-unison with the same frequency; further extensions of this definition have been considered to account for NNMs of systems with internal resonances [2]...

Spin-orbit optical cross-phase-modulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brasselet, Etienne

2010-12-15

We show experimentally that optical phase singularities (PSs) can be written and erased, locally and in a controllable manner, into a light beam using the giant Kerr optical nonlinearities of liquid crystals. The method relies on the nonlinear optical spin-orbit coupling experienced by a collimated probe beam when a collinear focused pump beam imprints a radial birefringent pattern into a nematic film. In addition, experimental data are quantitatively described, accounting for the elastic anisotropy of the material and its nonlocal spatial response to the pump light field. Since we show that the optical intensity of a light beam (the 'pump')more » controls the phase of another beam (the 'probe') in a singular fashion (i.e., with the generation of a screw PS) via their interaction in a nonlinear medium that involves spin-orbit coupling, we dubbed such a nonlinear optical process as spin-orbit optical cross-phase-modulation.« less

Bright breathers in nonlinear left-handed metamaterial lattices

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Numerical simulation of ultrasound-thermotherapy combining nonlinear wave propagation with broadband soft-tissue absorption.

PubMed

Ginter, S

2000-07-01

Ultrasound (US) thermotherapy is used to treat tumours, located deep in human tissue, by heat. It features by the application of high intensity focused ultrasound (HIFU), high local temperatures of about 90 degrees C and short treating time of a few seconds. Dosage of the therapy remains a problem. To get it under control, one has to know the heat source, i.e. the amount of absorbed US power, which shows nonlinear influences. Therefore, accurate simulations are essential. In this paper, an improved simulation model is introduced which enables accurate investigations of US thermotherapy. It combines nonlinear US propagation effects, which lead to generation of higher harmonics, with a broadband frequency-power law absorption typical for soft tissue. Only the combination of both provides a reliable calculation of the generated heat. Simulations show the influence of nonlinearities and broadband damping for different source signals on the absorbed US power density distribution.

Experimental Measurement of the Nonlinear Interaction between Counterpropagating Alfv'en Waves in the LaPD

NASA Astrophysics Data System (ADS)

Schroeder, J. W. R.; Drake, D. J.; Howes, G. G.; Skiff, F.; Kletzing, C. A.; Carter, T. A.; Dorfman, S.; Auerbach, D.

2012-10-01

Turbulence plays an important role in the transport of mass and energy in many space and astrophysical plasmas ranging from galaxy clusters to Earth's magnetosphere. One active topic of research is the application of idealized Alfv'enic turbulence models to plasma conditions relevant to space and astrophysical plasmas. Alfv'enic turbulence models based on incompressible magnetohydrodynamics (MHD) contain a nonlinear interaction that drives the cascade of energy to smaller scales. We describe experiments at the Large Plasma Device (LaPD) that focus on the interaction of an Alfv'en wave traveling parallel to the mean magnetic field with a counterpropagating Alfv'en wave. Theory predicts the nonlinear interaction of the two primary waves will produce a secondary daughter Alfv'en wave. In this study, we present the first experimental identification of the daughter wave generated by nonlinear interactions between the primary Alfv'en waves.

Thermal conductance of suspended nanoribbons: interplay between strain and interatomic potential nonlinearity

NASA Astrophysics Data System (ADS)

Barreto, Roberto; Florencia Carusela, M.; Monastra, Alejandro G.

2017-10-01

We investigate the role that nonlinearity in the interatomic potential has on the thermal conductance of a suspended nanoribbon when it is subjected to a longitudinal strain. To focus on the first cubic and quartic nonlinear terms of a general potential, we propose an atomic system based on an α-β Fermi-Pasta-Ulam nearest neighbor interaction. We perform classical molecular dynamics simulations to investigate the contribution of longitudinal, transversal and flexural modes to the thermal conductance as a function of the α-β parameters and the applied strain. We compare the cases where atoms are allowed to vibrate only in plane (2D) with the case of vibrations in and out of plane (3D). We find that the dependence of conductance on α and β relies on a crossover phenomenon between linear/nonlinear delocalized/localized flexural and transversal modes, driven by an on/off switch of the strain.

Nonlinear force feedback control of piezoelectric-hydraulic pump actuator for automotive transmission shift control

NASA Astrophysics Data System (ADS)

Kim, Gi-Woo; Wang, K. W.

2008-03-01

In recent years, researchers have investigated the feasibility of utilizing piezoelectric-hydraulic pump based actuation systems for automotive transmission controls. This new concept could eventually reduce the complexity, weight, and fuel consumption of the current transmissions. In this research, we focus on how to utilize this new approach on the shift control of automatic transmissions (AT), which generally requires pressure profiling for friction elements during the operation. To illustrate the concept, we will consider the 1--> 2 up shift control using band brake friction elements. In order to perform the actuation force tracking for AT shift control, nonlinear force feedback control laws are designed based on the sliding mode theory for the given nonlinear system. This paper will describe the modeling of the band brake actuation system, the design of the nonlinear force feedback controller, and simulation and experimental results for demonstration of the new concept.

Adaptive Fuzzy Tracking Control for a Class of MIMO Nonlinear Systems in Nonstrict-Feedback Form.

PubMed

Chen, Bing; Lin, Chong; Liu, Xiaoping; Liu, Kefu

2015-12-01

This paper focuses on the problem of fuzzy adaptive control for a class of multiinput and multioutput (MIMO) nonlinear systems in nonstrict-feedback form, which contains the strict-feedback form as a special case. By the condition of variable partition, a new fuzzy adaptive backstepping is proposed for such a class of nonlinear MIMO systems. The suggested fuzzy adaptive controller guarantees that the proposed control scheme can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking errors eventually converge to a small neighborhood around the origin. The main advantage of this paper is that a control approach is systematically derived for nonlinear systems with strong interconnected terms which are the functions of all states of the whole system. Simulation results further illustrate the effectiveness of the suggested approach.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hendrickson, Scott M.; Foster, Amy C.; Camacho, Ryan M.

In this paper, we provide a review of recent progress in integrated nonlinear photonics with a focus on emerging applications in all-optical signal processing, ultra-low-power all-optical switching, and quantum information processing.

Theoretical study of dissociative recombination of Cl{sub 2}{sup +}

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang Mingwu; Graduate School of Chinese Academy of Sciences, Beijing 100039; Department of Physics, Stockholm University, S-106 91 Stockholm

Theoretical studies of low-energy electron collisions with Cl{sub 2}{sup +} leading to direct dissociative recombination are presented. The relevant potential energy curves and autoionization widths are calculated by combining electron scattering calculations using the complex Kohn variational method with multireference configuration interaction structure calculations. The dynamics on the four lowest resonant states of all symmetries is studied by the solution of a driven Schroedinger equation. The thermal rate coefficient for dissociative recombination of Cl{sub 2}{sup +} is calculated and the influence on the thermal rate coefficient from vibrational excited target ions is investigated.

Transport methods and interactions for space radiations

NASA Technical Reports Server (NTRS)

Wilson, John W.; Townsend, Lawrence W.; Schimmerling, Walter S.; Khandelwal, Govind S.; Khan, Ferdous S.; Nealy, John E.; Cucinotta, Francis A.; Simonsen, Lisa C.; Shinn, Judy L.; Norbury, John W.

1991-01-01

A review of the program in space radiation protection at the Langley Research Center is given. The relevant Boltzmann equations are given with a discussion of approximation procedures for space applications. The interaction coefficients are related to solution of the many-body Schroedinger equation with nuclear and electromagnetic forces. Various solution techniques are discussed to obtain relevant interaction cross sections with extensive comparison with experiments. Solution techniques for the Boltzmann equations are discussed in detail. Transport computer code validation is discussed through analytical benchmarking, comparison with other codes, comparison with laboratory experiments and measurements in space. Applications to lunar and Mars missions are discussed.

Manifold alignment with Schroedinger eigenmaps

NASA Astrophysics Data System (ADS)

Johnson, Juan E.; Bachmann, Charles M.; Cahill, Nathan D.

2016-05-01

The sun-target-sensor angle can change during aerial remote sensing. In an attempt to compensate BRDF effects in multi-angular hyperspectral images, the Semi-Supervised Manifold Alignment (SSMA) algorithm pulls data from similar classes together and pushes data from different classes apart. SSMA uses Laplacian Eigenmaps (LE) to preserve the original geometric structure of each local data set independently. In this paper, we replace LE with Spatial-Spectral Schoedinger Eigenmaps (SSSE) which was designed to be a semisupervised enhancement to the to extend the SSMA methodology and improve classification of multi-angular hyperspectral images captured over Hog Island in the Virginia Coast Reserve.

Self-channeling of high-power laser pulses through strong atmospheric turbulence

NASA Astrophysics Data System (ADS)

Peñano, J.; Palastro, J. P.; Hafizi, B.; Helle, M. H.; DiComo, G. P.

2017-07-01

We present an unusual example of truly long-range propagation of high-power laser pulses through strong atmospheric turbulence. A form of nonlinear self-channeling is achieved when the laser power is close to the self-focusing power of air and the transverse dimensions of the pulse are smaller than the coherence diameter of turbulence. In this mode, nonlinear self-focusing counteracts diffraction, and turbulence-induced spreading is greatly reduced. Furthermore, the laser intensity is below the ionization threshold so that multiphoton absorption and plasma defocusing are avoided. Simulations show that the pulse can propagate many Rayleigh lengths (several kilometers) while maintaining a high intensity. In the presence of aerosols, or other extinction mechanisms that deplete laser energy, the pulse can be chirped to maintain the channeling.

Nearly spherical constant power detonation waves driven by focused radiation

NASA Technical Reports Server (NTRS)

George, Y. H.

1973-01-01

Shape and inner flow of a tridimensional spark are studied. The spark is created by focusing a laser beam in a gas. A second order fully non-linear equation is derived for the radial velocity on the axis of symmetry in the neighborhood of the origin. Solutions to that equation display the existence of a forbidden region near the focus, thus indicating the limits of applicability of a small perturbation solution.

NONLINEAR AND FIBER OPTICS: Self-similar solution obtained by self-focusing of annular laser beams

NASA Astrophysics Data System (ADS)

Azimov, B. S.; Platonenko, Viktor T.; Sagatov, M. M.

1991-03-01

A numerical modeling is reported of steady-state self-focusing of an annular beam with thin "walls." An approximate similar solution is found to describe well the relationships observed in the numerical experiment for a special selection of the input parameters of the beam. This solution is used to estimate the focal length. Such self-similar self-focusing is shown to affect the whole power of the beam.

A DERATING METHOD FOR THERAPEUTIC APPLICATIONS OF HIGH INTENSITY FOCUSED ULTRASOUND

PubMed Central

Bessonova, O.V.; Khokhlova, V.A.; Canney, M.S.; Bailey, M.R.; Crum, L.A.

2010-01-01

Current methods of determining high intensity focused ultrasound (HIFU) fields in tissue rely on extrapolation of measurements in water assuming linear wave propagation both in water and in tissue. Neglecting nonlinear propagation effects in the derating process can result in significant errors. In this work, a new method based on scaling the source amplitude is introduced to estimate focal parameters of nonlinear HIFU fields in tissue. Focal values of acoustic field parameters in absorptive tissue are obtained from a numerical solution to a KZK-type equation and are compared to those simulated for propagation in water. Focal waveforms, peak pressures, and intensities are calculated over a wide range of source outputs and linear focusing gains. Our modeling indicates, that for the high gain sources which are typically used in therapeutic medical applications, the focal field parameters derated with our method agree well with numerical simulation in tissue. The feasibility of the derating method is demonstrated experimentally in excised bovine liver tissue. PMID:20582159

Gaussian representation of high-intensity focused ultrasound beams.

PubMed

Soneson, Joshua E; Myers, Matthew R

2007-11-01

A method for fast numerical simulation of high-intensity focused ultrasound beams is derived. The method is based on the frequency-domain representation of the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, and assumes for each harmonic a Gaussian transverse pressure distribution at all distances from the transducer face. The beamwidths of the harmonics are constrained to vary inversely with the square root of the harmonic number, and as such this method may be viewed as an extension of a quasilinear approximation. The technique is capable of determining pressure or intensity fields of moderately nonlinear high-intensity focused ultrasound beams in water or biological tissue, usually requiring less than a minute of computer time on a modern workstation. Moreover, this method is particularly well suited to high-gain simulations since, unlike traditional finite-difference methods, it is not subject to resolution limitations in the transverse direction. Results are shown to be in reasonable agreement with numerical solutions of the full KZK equation in both tissue and water for moderately nonlinear beams.

A derating method for therapeutic applications of high intensity focused ultrasound

NASA Astrophysics Data System (ADS)

Bessonova, O. V.; Khokhlova, V. A.; Canney, M. S.; Bailey, M. R.; Crum, L. A.

2010-05-01

Current methods of determining high intensity focused ultrasound (HIFU) fields in tissue rely on extrapolation of measurements in water assuming linear wave propagation both in water and in tissue. Neglecting nonlinear propagation effects in the derating process can result in significant errors. A new method based on scaling the source amplitude is introduced to estimate focal parameters of nonlinear HIFU fields in tissue. Focal values of acoustic field parameters in absorptive tissue are obtained from a numerical solution to a KZK-type equation and are compared to those simulated for propagation in water. Focal wave-forms, peak pressures, and intensities are calculated over a wide range of source outputs and linear focusing gains. Our modeling indicates, that for the high gain sources which are typically used in therapeutic medical applications, the focal field parameters derated with our method agree well with numerical simulation in tissue. The feasibility of the derating method is demonstrated experimentally in excised bovine liver tissue.

A DERATING METHOD FOR THERAPEUTIC APPLICATIONS OF HIGH INTENSITY FOCUSED ULTRASOUND.

PubMed

Bessonova, O V; Khokhlova, V A; Canney, M S; Bailey, M R; Crum, L A

2010-01-01

Current methods of determining high intensity focused ultrasound (HIFU) fields in tissue rely on extrapolation of measurements in water assuming linear wave propagation both in water and in tissue. Neglecting nonlinear propagation effects in the derating process can result in significant errors. In this work, a new method based on scaling the source amplitude is introduced to estimate focal parameters of nonlinear HIFU fields in tissue. Focal values of acoustic field parameters in absorptive tissue are obtained from a numerical solution to a KZK-type equation and are compared to those simulated for propagation in water. Focal waveforms, peak pressures, and intensities are calculated over a wide range of source outputs and linear focusing gains. Our modeling indicates, that for the high gain sources which are typically used in therapeutic medical applications, the focal field parameters derated with our method agree well with numerical simulation in tissue. The feasibility of the derating method is demonstrated experimentally in excised bovine liver tissue.

Conference on Non-linear Phenomena in Mathematical Physics: Dedicated to Cathleen Synge Morawetz on her 85th Birthday. The Fields Institute, Toronto, Canada September 18-20, 2008. Sponsors: Association for Women in Mathematics, Inc. and The Fields Institute

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lewis, Jennifer

2012-10-15

This scientific meeting focused on the legacy of Cathleen S. Morawetz and the impact that her scientific work on transonic flow and the non-linear wave equation has had in recent progress on different aspects of analysis for non-linear wave, kinetic and quantum transport problems associated to mathematical physics. These are areas where the elements of continuum, statistical and stochastic mechanics, and their interplay, have counterparts in the theory of existence, uniqueness and stability of the associated systems of equations and geometric constraints. It was a central event for the applied and computational analysis community focusing on Partial Differential Equations. Themore » goal of the proposal was to honor Cathleen Morawetz, a highly successful woman in mathematics, while encouraging beginning researchers. The conference was successful in show casing the work of successful women, enhancing the visibility of women in the profession and providing role models for those just beginning their careers. The two-day conference included seven 45-minute lectures and one day of six 45-minute lectures, and a poster session for junior participants. The conference program included 19 distinguished speakers, 10 poster presentations, about 70 junior and senior participants and, of course, the participation of Cathleen Synge Morawetz. The conference celebrated Morawetz's paramount contributions to the theory of non-linear equations in gas dynamics and their impact in the current trends of nonlinear phenomena in mathematical physics, but also served as an awareness session of current women's contribution to mathematics.« less

Derivation of the Effective Nonlinear Schrodinger Equations for Dark and Power Law Spatial Plasmon-Polariton Solitons Using Nano Self-Focusing

DTIC Science & Technology

2011-03-01

An e?ective Nonlinear Schr?dinger Equation for propagation is derived for optical dark and power law spatial solitons at the subwavelength with a... soliton amplitude profiles are displayed as a hyperbolic secant function and hold there profile at short distances on the order of centimeters. Dark ...spatial solitons are similar but have hyperbolic tangent type profiles. Dark spatial solitons were first observed by Jerominek in 1985 and Belanger and

Rypina Receives 2008 Donald L. Turcotte Award

NASA Astrophysics Data System (ADS)

2008-12-01

Irina Rypina has been awarded the Donald L. Turcotte Award, given annually to recent Ph.D. recipients for outstanding dissertation research that contributes directly to the field of nonlinear geophysics. Rypina's thesis is entitled ``Lagrangian coherent structures and transport in two-dimensional incompressible flows with oceanographic and atmospheric applications.'' She will be formally presented with the award at the Nonlinear Geophysics Focus Group Reception during the 2008 AGU Fall Meeting, which will be held 15-19 December in San Francisco, Calif.

1984 European Conference on Optics, Optical Systems and Applications, Amsterdam, Netherlands, October 9-12, 1984, Proceedings

NASA Astrophysics Data System (ADS)

Boelger, B.; Ferwerda, H. A.

Various papers on optics, optical systems, and their applications are presented. The general topics addressed include: laser systems, optical and electrooptical materials and devices; novel spectroscopic techniques and applications; inspection, remote sensing, velocimetry, and gauging; optical design and image formation; holography, image processing, and storage; and integrated and fiber optics. Also discussed are: nonlinear optics; nonlinear photorefractive materials; scattering and diffractions applications in materials processing, deposition, and machining; medical and biological applications; and focus on industry.

A Numerical Study of Automated Dynamic Relaxation for Nonlinear Static Tensioned Structures.

DTIC Science & Technology

1987-10-01

sytem f dscree fnit element equations, i.e., an algebraic system. The form of these equa- tions is the same for all nonlinear kinematic structures that...the first phase the solu- tion to the static, prestress configuration is sought. This phase is also referred to as form finding, shape finding, or the...does facilitate stability of the numerical solution. The system of equations, which is the focus of the solution methods presented, is formed by a

Thickness Gauging of Single-Layer Conductive Materials with Two-Point Non Linear Calibration Algorithm

NASA Technical Reports Server (NTRS)

Fulton, James P. (Inventor); Namkung, Min (Inventor); Simpson, John W. (Inventor); Wincheski, Russell A. (Inventor); Nath, Shridhar C. (Inventor)

1998-01-01

A thickness gauging instrument uses a flux focusing eddy current probe and two-point nonlinear calibration algorithm. The instrument is small and portable due to the simple interpretation and operational characteristics of the probe. A nonlinear interpolation scheme incorporated into the instrument enables a user to make highly accurate thickness measurements over a fairly wide calibration range from a single side of nonferromagnetic conductive metals. The instrument is very easy to use and can be calibrated quickly.

On implicit abstract neutral nonlinear differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hernández, Eduardo, E-mail: lalohm@ffclrp.usp.br; O’Regan, Donal, E-mail: donal.oregan@nuigalway.ie

2016-04-15

In this paper we continue our developments in Hernández and O’Regan (J Funct Anal 261:3457–3481, 2011) on the existence of solutions for abstract neutral differential equations. In particular we extend the results in Hernández and O’Regan (J Funct Anal 261:3457–3481, 2011) for the case of implicit nonlinear neutral equations and we focus on applications to partial “nonlinear” neutral differential equations. Some applications involving partial neutral differential equations are presented.

PharmML in Action: an Interoperable Language for Modeling and Simulation

PubMed Central

Bizzotto, R; Smith, G; Yvon, F; Kristensen, NR; Swat, MJ

2017-01-01

PharmML1 is an XML‐based exchange format2, 3, 4 created with a focus on nonlinear mixed‐effect (NLME) models used in pharmacometrics,5, 6 but providing a very general framework that also allows describing mathematical and statistical models such as single‐subject or nonlinear and multivariate regression models. This tutorial provides an overview of the structure of this language, brief suggestions on how to work with it, and use cases demonstrating its power and flexibility. PMID:28575551

Nonlinear acoustics in biomedical ultrasound

NASA Astrophysics Data System (ADS)

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.

Girsanov's transformation based variance reduced Monte Carlo simulation schemes for reliability estimation in nonlinear stochastic dynamics

NASA Astrophysics Data System (ADS)

Kanjilal, Oindrila; Manohar, C. S.

2017-07-01

The study considers the problem of simulation based time variant reliability analysis of nonlinear randomly excited dynamical systems. Attention is focused on importance sampling strategies based on the application of Girsanov's transformation method. Controls which minimize the distance function, as in the first order reliability method (FORM), are shown to minimize a bound on the sampling variance of the estimator for the probability of failure. Two schemes based on the application of calculus of variations for selecting control signals are proposed: the first obtains the control force as the solution of a two-point nonlinear boundary value problem, and, the second explores the application of the Volterra series in characterizing the controls. The relative merits of these schemes, vis-à-vis the method based on ideas from the FORM, are discussed. Illustrative examples, involving archetypal single degree of freedom (dof) nonlinear oscillators, and a multi-degree of freedom nonlinear dynamical system, are presented. The credentials of the proposed procedures are established by comparing the solutions with pertinent results from direct Monte Carlo simulations.

Nonlinear evolution equations for surface plasmons for nano-focusing at a Kerr/metallic interface and tapered waveguide

NASA Astrophysics Data System (ADS)

Crutcher, Sihon H.; Osei, Albert; Biswas, Anjan

2012-06-01

Maxwell's equations for a metallic and nonlinear Kerr interface waveguide at the nanoscale can be approximated to a (1+1) D Nonlinear Schrodinger type model equation (NLSE) with appropriate assumptions and approximations. Theoretically, without losses or perturbations spatial plasmon solitons profiles are easily produced. However, with losses, the amplitude or beam profile is no longer stationary and adiabatic parameters have to be considered to understand propagation. For this model, adiabatic parameters are calculated considering losses resulting in linear differential coupled integral equations with constant definite integral coefficients not dependent on the transverse and longitudinal coordinates. Furthermore, by considering another configuration, a waveguide that is an M-NL-M (metal-nonlinear Kerr-metal) that tapers, the tapering can balance the loss experienced at a non-tapered metal/nonlinear Kerr interface causing attenuation of the beam profile, so these spatial plasmon solitons can be produced. In this paper taking into consideration the (1+1)D NLSE model for a tapered waveguide, we derive a one soliton solution based on He's Semi-Inverse Variational Principle (HPV).

Investigation of giant Kerr nonlinearity in quantum cascade lasers using mid-infrared femtosecond pulses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cai, Hong; Liu, Sheng; Department of Physics, University of Maryland, Baltimore County

2015-02-02

We study the Kerr nonlinearity of quantum cascade lasers (QCLs) by coupling resonant and off-resonant mid-infrared (mid-IR) femtosecond (fs) pulses into an active QCL waveguide. We observe an increase in the spectral width of the transmitted fs pulses as the coupled mid-infrared (mid-IR) pulse power increases. This is explained by the self-phase modulation effect due to the large Kerr nonlinearity of QCL waveguides. We further confirm this effect by observing the intensity dependent far-field profile of the transmitted mid-IR pulses, showing the pulses undergo self-focusing as they propagate through the active QCL due to the intensity dependent refractive index. Wemore » experimentally estimate the nonlinear refractive index n{sub 2} of a QCL to be ∼8 × 10{sup −9 }cm{sup 2}/W using the far-field beam profile of the transmitted pulses. The finite-difference time-domain simulations of QCL waveguides with Kerr nonlinearity incorporated show similar behavior to the experimental results.« less

Non-linear dynamic analysis of geared systems, part 2

NASA Technical Reports Server (NTRS)

Singh, Rajendra; Houser, Donald R.; Kahraman, Ahmet

1990-01-01

A good understanding of the steady state dynamic behavior of a geared system is required in order to design reliable and quiet transmissions. This study focuses on a system containing a spur gear pair with backlash and periodically time-varying mesh stiffness, and rolling element bearings with clearance type non-linearities. A dynamic finite element model of the linear time-invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and force vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solution with the finite element model results. Several key system parameters such as mean load and damping ratio are identified and their effects on the non-linear frequency response are evaluated quantitatively. Other fundamental issues such as the dynamic coupling between non-linear modes, dynamic interactions between component non-linearities and time-varying mesh stiffness, and the existence of subharmonic and chaotic solutions including routes to chaos have also been examined in depth.

GEOPHYSICS, ASTRONOMY AND ASTROPHYSICS: Numerical method of studying nonlinear interactions between long waves and multiple short waves

NASA Astrophysics Data System (ADS)

Xie, Tao; Kuang, Hai-Lan; William, Perrie; Zou, Guang-Hui; Nan, Cheng-Feng; He, Chao; Shen, Tao; Chen, Wei

2009-07-01

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 3). This mechanism occurs on wave components with a narrow frequency bandwidth, whose frequencies are near that of wave train 3.

Nonlinear interactions in mixing layers and compressible heated round jets. Ph.D. Thesis Final Report

NASA Technical Reports Server (NTRS)

Jarrah, Yousef Mohd

1989-01-01

The nonlinear interactions between a fundamental instability mode and both its harmonics and the changing mean flow are studied using the weakly nonlinear stability theory of Stuart and Watson, and numerical solutions of coupled nonlinear partial differential equations. The first part focuses on incompressible cold (or isothermal; constant temperature throughout) mixing layers, and for these, the first and second Landau constants are calculated as functions of wavenumber and Reynolds number. It is found that the dominant contribution to the Landau constants arises from the mean flow changes and not from the higher harmonics. In order to establish the range of validity of the weakly nonlinear theory, the weakly nonlinear and numerical solutions are compared and the limitation of each is discussed. At small amplitudes and at low-to-moderate Reynolds numbers, the two results compare well in describing the saturation of the fundamental, the distortion of the mean flow, and the initial stages of vorticity roll-up. At larger amplitudes, the interaction between the fundamental, second harmonic, and the mean flow is strongly nonlinear and the numerical solution predicts flow oscillations, whereas the weakly nonlinear theory yields saturation. In the second part, the weakly nonlinear theory is extended to heated (or nonisothermal; mean temperature distribution) subsonic round jets where quadratic and cubic nonlinear interactions are present, and the Landau constants also depend on jet temperature ratio, Mach number and azimuthal mode number. Under exponential growth and nonlinear saturation, it is found that heating and compressibility suppress the growth of instability waves, that the first azimuthal mode is the dominant instability mode, and that the weakly nonlinear solution describes the early stages of the roll-up of an axisymmetric shear layer. The receptivity of a typical jet flow to pulse type input disturbance is also studied by solving the initial value problem and then examining the behavior of the long-time solution.

Towards improved NDE and SHM methodologies incorporating nonlinear structural features

NASA Astrophysics Data System (ADS)

Chillara, Vamshi Krishna

Ultrasound is widely employed in Nondestructive Evaluation (NDE) and Structural Health Monitoring (SHM) applications to detect and characterize damage/defects in materials. In particular, ultrasonic guided waves are considered a foremost candidate for in-situ monitoring applications. Conventional ultrasonic techniques rely on changes/discontinuities in linear elastic material properties, namely the Young's modulus and shear modulus to detect damage. On the other hand, nonlinear ultrasonic techniques that rely on micro-scale nonlinear material/structural behavior are proven to be sensitive to damage induced microstructural changes that precede macro-scale damage and are hence capable of early damage detection. The goal of this thesis is to investigate the capabilities of nonlinear guided waves --- a fusion of nonlinear ultrasonic techniques with the guided wave methodologies for early damage detection. To that end, the thesis focuses on two important aspects of the problem: 1. Wavemechanics - deals with ultrasonic guided wave propagation in nonlinear waveguides; 2. Micromechanics - deals with correlating ultrasonic response with micro-scale nonlinear material behavior. For the development of efficient NDE and SHM methodologies that incorporate nonlinear structural features, a detailed understanding of the above aspects is indispensable. In this thesis, the wavemechanics aspect of the problem is dealt with from both theoretical and numerical standpoints. A generalized theoretical framework is developed to study higher harmonic guided waves in plates. This was employed to study second harmonic guided waves in pipes using a large-radius asymptotic approximation. Second harmonic guided waves in plates are studied from a numerical standpoint. Theoretical predictions are validated and some key aspects of higher harmonic generation in waveguides are outlined. Finally, second harmonic guided waves in plates with inhomogeneous and localized nonlinearities are studied and some important aspects of guided wave mode selection are addressed. The other part of the work focused on developing a micromechanics based understanding of ultrasonic higher harmonic generation. Three important aspects of micro-scale material behavior, namely tension-compression asymmetry, shearnormal coupling and deformation induced asymmetry are identified and their role in ultrasonic higher harmonic generation is discussed. Tension-compression asymmetry is identified to cause second (even) harmonic generation in materials. Then, shearnormal coupling is identified to cause generation of secondary waves of different polarity than the primary waves. In addition, deformation induced anisotropy due to the presence of residual stress/strain and its contribution to ultrasonic higher harmonic generation is qualitatively discussed. Also, the tension-compression asymmetry in the material is quantified using an energy based measure. The above measure is employed to develop a homogenization based approach amenable to multi-scale analysis to correlate microstructure with ultrasonic higher harmonic generation. Finally, experimental investigations concerning third harmonic SH wave generation in plates are carried out and the effect of load and temperature changes on nonlinear ultrasonic measurements are discussed in the context of SHM. It was found that while nonlinear ultrasound is sensitive to micro-scale damage, the relative nonlinearity parameter may not always be the best measure to quantify the nonlinearity as it is subject to spurious effects from changes in environmental factors such as loads and temperature.

Nonlinear structures and anomalous transport in partially magnetized E×B plasmas

DOE PAGES

Janhunen, Salomon; Smolyakov, Andrei; Chapurin, Oleksandr; ...

2017-12-29

Nonlinear dynamics of the electron-cyclotron instability driven by the electron E x B current in a crossed electric and magnetic field is studied. In the nonlinear regime, the instability proceeds by developing a large amplitude coherent wave driven by the energy input from the fundamental cyclotron resonance. Further evolution shows the formation of the long wavelength envelope akin to the modulational instability. Simultaneously, the ion density shows the development of a high-k content responsible for wave focusing and sharp peaks on the periodic cnoidal wave structure. Here, it is shown that the anomalous electron transport (along the direction of themore » applied electric field) is dominated by the long wavelength part of the turbulent spectrum.« less

Chirped self-similar optical pulses in tapered centrosymmetric nonlinear waveguides doped with resonant impurities

NASA Astrophysics Data System (ADS)

He, J. R.; Xu, S. L.; Xue, L.

2017-11-01

Exact chirped self-similar optical pulses propagating in tapered centrosymmetric nonlinear waveguides doped with resonant impurities are reported. The propagation behaviors of the pulses are studied by tailoring of the tapering function. Numerical simulations and stability analysis reveal that the tapering can be used to postpone the wave dispersion and the addition of a small cubic self-focusing term to the governing equation could stabilize the chirped bright pulses. An example of possible experimental protocol that may generate the pulses in realistic waveguides is given. The obtained chirped self-similar optical pulses are particularly useful in the design of amplifying or attenuating pulse compressors for chirped solitary waves in tapered centrosymmetric nonlinear waveguides doped with resonant impurities.

Assessing first-order emulator inference for physical parameters in nonlinear mechanistic models

USGS Publications Warehouse

Hooten, Mevin B.; Leeds, William B.; Fiechter, Jerome; Wikle, Christopher K.

2011-01-01

We present an approach for estimating physical parameters in nonlinear models that relies on an approximation to the mechanistic model itself for computational efficiency. The proposed methodology is validated and applied in two different modeling scenarios: (a) Simulation and (b) lower trophic level ocean ecosystem model. The approach we develop relies on the ability to predict right singular vectors (resulting from a decomposition of computer model experimental output) based on the computer model input and an experimental set of parameters. Critically, we model the right singular vectors in terms of the model parameters via a nonlinear statistical model. Specifically, we focus our attention on first-order models of these right singular vectors rather than the second-order (covariance) structure.

On controlling networks of limit-cycle oscillators

NASA Astrophysics Data System (ADS)

Skardal, Per Sebastian; Arenas, Alex

2016-09-01

The control of network-coupled nonlinear dynamical systems is an active area of research in the nonlinear science community. Coupled oscillator networks represent a particularly important family of nonlinear systems, with applications ranging from the power grid to cardiac excitation. Here, we study the control of network-coupled limit cycle oscillators, extending the previous work that focused on phase oscillators. Based on stabilizing a target fixed point, our method aims to attain complete frequency synchronization, i.e., consensus, by applying control to as few oscillators as possible. We develop two types of controls. The first type directs oscillators towards larger amplitudes, while the second does not. We present numerical examples of both control types and comment on the potential failures of the method.

Higher-order modulation instability in nonlinear fiber optics.

PubMed

Erkintalo, Miro; Hammani, Kamal; Kibler, Bertrand; Finot, Christophe; Akhmediev, Nail; Dudley, John M; Genty, Goëry

2011-12-16

We report theoretical, numerical, and experimental studies of higher-order modulation instability in the focusing nonlinear Schrödinger equation. This higher-order instability arises from the nonlinear superposition of elementary instabilities, associated with initial single breather evolution followed by a regime of complex, yet deterministic, pulse splitting. We analytically describe the process using the Darboux transformation and compare with experiments in optical fiber. We show how a suitably low frequency modulation on a continuous wave field induces higher-order modulation instability splitting with the pulse characteristics at different phases of evolution related by a simple scaling relationship. We anticipate that similar processes are likely to be observed in many other systems including plasmas, Bose-Einstein condensates, and deep water waves. © 2011 American Physical Society

Linear and nonlinear properties of photonic crystal fibers filled with nematic liquid crystals

NASA Astrophysics Data System (ADS)

Brzdąkiewicz, K. A.; Laudyn, U. A.; Karpierz, M. A.; Woliński, T. R.; Wójcik, J.

2006-12-01

We investigate linear and nonlinear light propagation in the photonic crystal fibers infiltrated with nematic liquid crystals. Such a photonic structure, with periodic modulation of refractive index, which could be additionally controlled by the temperature and by the optical power, allows for the study of discrete optical phenomena. Our theoretical investigations, carried out with the near infrared wavelength of 830 nm, for both focusing and defocusing Kerr-type nonlinearity, show the possibility of the transverse light localization, which can result in the discrete soliton generation. In addition, we present the preliminary experimental results on the linear light propagation in the photonic crystal fiber with the glycerin-water solution and 6CHBT nematics, as the guest materials.

Comparative methods to assess harmonic response of nonlinear piezoelectric energy harvesters interfaced with AC and DC circuits

NASA Astrophysics Data System (ADS)

Lan, Chunbo; Tang, Lihua; Harne, Ryan L.

2018-05-01

Nonlinear piezoelectric energy harvester (PEH) has been widely investigated during the past few years. Among the majority of these researches, a pure resistive load is used to evaluate power output. To power conventional electronics in practical application, the alternating current (AC) generated by nonlinear PEH needs to be transformed into a direct current (DC) and rectifying circuits are required to interface the device and electronic load. This paper aims at exploring the critical influences of AC and DC interface circuits on nonlinear PEH. As a representative nonlinear PEH, we fabricate and evaluate a monostable PEH in terms of generated power and useful operating bandwidth when it is connected to AC and DC interface circuits. Firstly, the harmonic balance analysis and equivalent circuit representation method are utilized to tackle the modeling of nonlinear energy harvesters connected to AC and DC interface circuits. The performances of the monostable PEH connected to these interface circuits are then analyzed and compared, focusing on the influences of the varying load, excitation and electromechanical coupling strength on the nonlinear dynamics, bandwidth and harvested power. Subsequently, the behaviors of the monostable PEH with AC and DC interface circuits are verified by experiment. Results indicate that both AC and DC interface circuits have a peculiar influence on the power peak shifting and operational bandwidth of the monostable PEH, which is quite different from that on the linear PEH.

A deep belief network with PLSR for nonlinear system modeling.

PubMed

Qiao, Junfei; Wang, Gongming; Li, Wenjing; Li, Xiaoli

2018-08-01

Nonlinear system modeling plays an important role in practical engineering, and deep learning-based deep belief network (DBN) is now popular in nonlinear system modeling and identification because of the strong learning ability. However, the existing weights optimization for DBN is based on gradient, which always leads to a local optimum and a poor training result. In this paper, a DBN with partial least square regression (PLSR-DBN) is proposed for nonlinear system modeling, which focuses on the problem of weights optimization for DBN using PLSR. Firstly, unsupervised contrastive divergence (CD) algorithm is used in weights initialization. Secondly, initial weights derived from CD algorithm are optimized through layer-by-layer PLSR modeling from top layer to bottom layer. Instead of gradient method, PLSR-DBN can determine the optimal weights using several PLSR models, so that a better performance of PLSR-DBN is achieved. Then, the analysis of convergence is theoretically given to guarantee the effectiveness of the proposed PLSR-DBN model. Finally, the proposed PLSR-DBN is tested on two benchmark nonlinear systems and an actual wastewater treatment system as well as a handwritten digit recognition (nonlinear mapping and modeling) with high-dimension input data. The experiment results show that the proposed PLSR-DBN has better performances of time and accuracy on nonlinear system modeling than that of other methods. Copyright © 2017 Elsevier Ltd. All rights reserved.

PREFACE: Physics and Mathematics of Nonlinear Phenomena 2013 (PMNP2013)

NASA Astrophysics Data System (ADS)

Konopelchenko, B. G.; Landolfi, G.; Martina, L.; Vitolo, R.

2014-03-01

Modern theory of nonlinear integrable equations is nowdays an important and effective tool of study for numerous nonlinear phenomena in various branches of physics from hydrodynamics and optics to quantum filed theory and gravity. It includes the study of nonlinear partial differential and discrete equations, regular and singular behaviour of their solutions, Hamitonian and bi- Hamitonian structures, their symmetries, associated deformations of algebraic and geometrical structures with applications to various models in physics and mathematics. The PMNP 2013 conference focused on recent advances and developments in Continuous and discrete, classical and quantum integrable systems Hamiltonian, critical and geometric structures of nonlinear integrable equations Integrable systems in quantum field theory and matrix models Models of nonlinear phenomena in physics Applications of nonlinear integrable systems in physics The Scientific Committee of the conference was formed by Francesco Calogero (University of Rome `La Sapienza', Italy) Boris A Dubrovin (SISSA, Italy) Yuji Kodama (Ohio State University, USA) Franco Magri (University of Milan `Bicocca', Italy) Vladimir E Zakharov (University of Arizona, USA, and Landau Institute for Theoretical Physics, Russia) The Organizing Committee: Boris G Konopelchenko, Giulio Landolfi, Luigi Martina, Department of Mathematics and Physics `E De Giorgi' and the Istituto Nazionale di Fisica Nucleare, and Raffaele Vitolo, Department of Mathematics and Physics `E De Giorgi'. A list of sponsors, speakers, talks, participants and the conference photograph are given in the PDF. Conference photograph

Method and system for training dynamic nonlinear adaptive filters which have embedded memory

NASA Technical Reports Server (NTRS)

Rabinowitz, Matthew (Inventor)

2002-01-01

Described herein is a method and system for training nonlinear adaptive filters (or neural networks) which have embedded memory. Such memory can arise in a multi-layer finite impulse response (FIR) architecture, or an infinite impulse response (IIR) architecture. We focus on filter architectures with separate linear dynamic components and static nonlinear components. Such filters can be structured so as to restrict their degrees of computational freedom based on a priori knowledge about the dynamic operation to be emulated. The method is detailed for an FIR architecture which consists of linear FIR filters together with nonlinear generalized single layer subnets. For the IIR case, we extend the methodology to a general nonlinear architecture which uses feedback. For these dynamic architectures, we describe how one can apply optimization techniques which make updates closer to the Newton direction than those of a steepest descent method, such as backpropagation. We detail a novel adaptive modified Gauss-Newton optimization technique, which uses an adaptive learning rate to determine both the magnitude and direction of update steps. For a wide range of adaptive filtering applications, the new training algorithm converges faster and to a smaller value of cost than both steepest-descent methods such as backpropagation-through-time, and standard quasi-Newton methods. We apply the algorithm to modeling the inverse of a nonlinear dynamic tracking system 5, as well as a nonlinear amplifier 6.

On intrinsic nonlinear particle motion in compact synchrotrons

NASA Astrophysics Data System (ADS)

Hwang, Kyung Ryun

Due to the low energy and small curvature characteristics of compact synchrotrons, there can be unexpected features that were not present or negligible in high energy accelerators. Nonlinear kinetics, fringe field effect, and space charge effect are those features which become important for low energy and small curvature accelerators. Nonlinear kinematics can limit the dynamics aperture for compact machine even if it consists of all linear elements. The contribution of the nonlinear kinematics on nonlinear optics parameters are first derived. As the dipole bending radius become smaller, the dipole fringe field effect become stronger. Calculation of the Lie map generator and corresponding mapping equation of dipole fringe field is presented. It is found that the higher order nonlinear potential is inverse proportional to powers of fringe field extent and correction to focusing and low order nonlinear potential is proportional to powers of fringe field extent. The fringe field also found to cause large closed orbit deviation for compact synchrotrons. The 2:1 and 4:1 space charge resonances are known to cause beam loss, emittance growth and halo formation for low energy high intensity beams. By numerical simulations, we observe a higher order 6:2 space charge resonance, which can successfully be understood by the concatenation of 2:1 and 4:1 resonances via canonical perturbation. We also develop an explicit symplectic tracking method for compact electrostatic storage rings and explore the feasibility of electric dipole moment (EDM) measurements.

A semi-active H∞ control strategy with application to the vibration suppression of nonlinear high-rise building under earthquake excitations.

PubMed

Yan, Guiyun; Chen, Fuquan; Wu, Yingxiong

2016-01-01

Different from previous researches which mostly focused on linear response control of seismically excited high-rise buildings, this study aims to control nonlinear seismic response of high-rise buildings. To this end, a semi-active control strategy, in which H∞ control algorithm is used and magneto-rheological dampers are employed for an actuator, is presented to suppress the nonlinear vibration. In this strategy, a modified Kalman-Bucy observer which is suitable for the proposed semi-active strategy is developed to obtain the state vector from the measured semi-active control force and acceleration feedback, taking into account of the effects of nonlinearity, disturbance and uncertainty of controlled system parameters by the observed nonlinear accelerations. Then, the proposed semi-active H∞ control strategy is applied to the ASCE 20-story benchmark building when subjected to earthquake excitation and compared with the other control approaches by some control criteria. It is indicated that the proposed semi-active H∞ control strategy provides much better control performances by comparison with the semi-active MPC and Clipped-LQG control approaches, and can reduce nonlinear seismic response and minimize the damage in the buildings. Besides, it enhances the reliability of the control performance when compared with the active control strategy. Thus, the proposed semi-active H∞ control strategy is suitable for suppressing the nonlinear vibration of high-rise buildings.

A heuristic neural network initialization scheme for modeling nonlinear functions in engineering mechanics: continuous development

NASA Astrophysics Data System (ADS)

Pei, Jin-Song; Mai, Eric C.

2007-04-01

This paper introduces a continuous effort towards the development of a heuristic initialization methodology for constructing multilayer feedforward neural networks to model nonlinear functions. In this and previous studies that this work is built upon, including the one presented at SPIE 2006, the authors do not presume to provide a universal method to approximate arbitrary functions, rather the focus is given to the development of a rational and unambiguous initialization procedure that applies to the approximation of nonlinear functions in the specific domain of engineering mechanics. The applications of this exploratory work can be numerous including those associated with potential correlation and interpretation of the inner workings of neural networks, such as damage detection. The goal of this study is fulfilled by utilizing the governing physics and mathematics of nonlinear functions and the strength of the sigmoidal basis function. A step-by-step graphical procedure utilizing a few neural network prototypes as "templates" to approximate commonly seen memoryless nonlinear functions of one or two variables is further developed in this study. Decomposition of complex nonlinear functions into a summation of some simpler nonlinear functions is utilized to exploit this prototype-based initialization methodology. Training examples are presented to demonstrate the rationality and effciency of the proposed methodology when compared with the popular Nguyen-Widrow initialization algorithm. Future work is also identfied.

Introduction to nonlinear acoustics

NASA Astrophysics Data System (ADS)

Bjørnø, Leif

2010-01-01

A brief review of the basic principles of fluid mechanics needed for development of linear and nonlinear ultrasonic concepts will be given. The fundamental equations of nonlinear ultrasonics will be derived and their physical properties explained. It will be shown how an originally monochromatic finite-amplitude ultrasonic wave, due to nonlinear effects, will distort during its propagation in time and space to form higher harmonics to its fundamental frequency. The concepts of shock formation will be presented. The material nonlinearity, described by the nonlinearity parameter B/A of the material, and the convective nonlinearity, described by the ultrasonic Mach Number, will be explained. Two procedures for determination of B/A will briefly be described and some B/A-values characterizing biological materials will be presented. Shock formation, described by use of the Goldberg Number,and Ultrasonic Saturation will be discussed.. An introduction to focused ultrasonic fields will be given and it will be shown how the ultrasonic intensity will vary axially and laterally in and near the focal region and how the field parameters of interest to biomedical applications may be described by use of the KZK-Model. Finally, an introduction will be given to the parametric acoustic array formed by mixing and interaction of two monochromatic, finite-amplitude ultrasonic waves in a liquid and the potentials of this mixing process in biomedical ultrasound will briefly be mentioned.

A Laboratory-Based Nonlinear Dynamics Course for Science and Engineering Students.

ERIC Educational Resources Information Center

Sungar, N.; Sharpe, J. P.; Moelter, M. J.; Fleishon, N.; Morrison, K.; McDill, J.; Schoonover, R.

2001-01-01

Describes the implementation of a new laboratory-based, interdisciplinary undergraduate course on linear dynamical systems. Focuses on geometrical methods and data visualization techniques. (Contains 20 references.) (Author/YDS)

Characterization of a Multi-element Clinical HIFU System Using Acoustic Holography and Nonlinear Modeling

PubMed Central

Kreider, Wayne; Yuldashev, Petr V.; Sapozhnikov, Oleg A.; Farr, Navid; Partanen, Ari; Bailey, Michael R.; Khokhlova, Vera A.

2014-01-01

High-intensity focused ultrasound (HIFU) is a treatment modality that relies on the delivery of acoustic energy to remote tissue sites to induce thermal and/or mechanical tissue ablation. To ensure the safety and efficacy of this medical technology, standard approaches are needed for accurately characterizing the acoustic pressures generated by clinical ultrasound sources under operating conditions. Characterization of HIFU fields is complicated by nonlinear wave propagation and the complexity of phased-array transducers. Previous work has described aspects of an approach that combines measurements and modeling, and here we demonstrate this approach for a clinical phased array transducer. First, low-amplitude hydrophone measurements were performed in water over a scan plane between the array and the focus. Second, these measurements were used to holographically reconstruct the surface vibrations of the transducer and to set a boundary condition for a 3-D acoustic propagation model. Finally, nonlinear simulations of the acoustic field were carried out over a range of source power levels. Simulation results were compared to pressure waveforms measured directly by hydrophone at both low and high power levels, demonstrating that details of the acoustic field including shock formation are quantitatively predicted. PMID:25004539

Waveguide fabrication in PMMA using a modified cavity femtosecond oscillator

NASA Astrophysics Data System (ADS)

Wang, Ke; Klimov, Denis; Kolber, Zbigniew

2007-09-01

Poly Methyl Methacrylate (PMMA) is an advantageous material than glass in oceanographic sensing applications because of its inhospitality for marine organisms. Waveguide sensors fabricated in PMMA are often used to measure the parameters in ocean such as PH, CO II, O II concentrations, etc. A tightly-focused femtosecond laser is often used to produce such a waveguide or even more complicated structures through the nonlinear effect in the bulk of PMMA, with pulse energy at μJ or mJ level. And such a laser system requires the amplifier from chirped-pulse amplification (CPA). The oscillator itself can produce pulse energy only at nJ level which is under the threshold of nonlinear effect. However, in our experiment, a modification to the oscillator cavity, which elongates the cavity length approximately 3 times and as a result, decreases the repetition rate from 93mHz to 32 mHz, can increase the pulse energy to 15 nJ. Under a tight focusing lens (100x 1.40 microscope objective), such an intensity exceeds the nonlinear threshold of PMMA. Thus, waveguide can be fabricated in PMMA using only a femtosecond oscillator and oceanographic sensors can be also made by this simple technique.

Porous elastic system with nonlinear damping and sources terms

NASA Astrophysics Data System (ADS)

Freitas, Mirelson M.; Santos, M. L.; Langa, José A.

2018-02-01

We study the long-time behavior of porous-elastic system, focusing on the interplay between nonlinear damping and source terms. The sources may represent restoring forces, but may also be focusing thus potentially amplifying the total energy which is the primary scenario of interest. By employing nonlinear semigroups and the theory of monotone operators, we obtain several results on the existence of local and global weak solutions, and uniqueness of weak solutions. Moreover, we prove that such unique solutions depend continuously on the initial data. Under some restrictions on the parameters, we also prove that every weak solution to our system blows up in finite time, provided the initial energy is negative and the sources are more dominant than the damping in the system. Additional results are obtained via careful analysis involving the Nehari Manifold. Specifically, we prove the existence of a unique global weak solution with initial data coming from the "good" part of the potential well. For such a global solution, we prove that the total energy of the system decays exponentially or algebraically, depending on the behavior of the dissipation in the system near the origin. We also prove the existence of a global attractor.

Electron Acceleration by Beating of Two Intense Cross-Focused Hollow Gaussian Laser Beams in Plasma

NASA Astrophysics Data System (ADS)

Mahmoud, Saleh T.; Gauniyal, Rakhi; Ahmad, Nafis; Rawat, Priyanka; Purohit, Gunjan

2018-01-01

This paper presents propagation of two cross-focused intense hollow Gaussian laser beams (HGBs) in collisionless plasma and its effect on the generation of electron plasma wave (EPW) and electron acceleration process, when relativistic and ponderomotive nonlinearities are simultaneously operative. Nonlinear differential equations have been set up for beamwidth of laser beams, power of generated EPW, and energy gain by electrons using WKB and paraxial approximations. Numerical simulations have been carried out to investigate the effect of typical laser-plasma parameters on the focusing of laser beams in plasmas and further its effect on power of excited EPW and acceleration of electrons. It is observed that focusing of two laser beams in plasma increases for higher order of hollow Gaussian beams, which significantly enhanced the power of generated EPW and energy gain. The amplitude of EPW and energy gain by electrons is found to enhance with an increase in the intensity of laser beams and plasma density. This study will be useful to plasma beat wave accelerator and in other applications requiring multiple laser beams. Supported by United Arab Emirates University for Financial under Grant No. UPAR (2014)-31S164

Simulation of nonlinear propagation of biomedical ultrasound using pzflex and the Khokhlov-Zabolotskaya-Kuznetsov Texas code

PubMed Central

Qiao, Shan; Jackson, Edward; Coussios, Constantin C.; Cleveland, Robin O.

2016-01-01

Nonlinear acoustics plays an important role in both diagnostic and therapeutic applications of biomedical ultrasound and a number of research and commercial software packages are available. In this manuscript, predictions of two solvers available in a commercial software package, pzflex, one using the finite-element-method (FEM) and the other a pseudo-spectral method, spectralflex, are compared with measurements and the Khokhlov-Zabolotskaya-Kuznetsov (KZK) Texas code (a finite-difference time-domain algorithm). The pzflex methods solve the continuity equation, momentum equation and equation of state where they account for nonlinearity to second order whereas the KZK code solves a nonlinear wave equation with a paraxial approximation for diffraction. Measurements of the field from a single element 3.3 MHz focused transducer were compared with the simulations and there was good agreement for the fundamental frequency and the harmonics; however the FEM pzflex solver incurred a high computational cost to achieve equivalent accuracy. In addition, pzflex results exhibited non-physical oscillations in the spatial distribution of harmonics when the amplitudes were relatively low. It was found that spectralflex was able to accurately capture the nonlinear fields at reasonable computational cost. These results emphasize the need to benchmark nonlinear simulations before using codes as predictive tools. PMID:27914432

Simulation of nonlinear propagation of biomedical ultrasound using pzflex and the Khokhlov-Zabolotskaya-Kuznetsov Texas code.

PubMed

Qiao, Shan; Jackson, Edward; Coussios, Constantin C; Cleveland, Robin O

2016-09-01

Nonlinear acoustics plays an important role in both diagnostic and therapeutic applications of biomedical ultrasound and a number of research and commercial software packages are available. In this manuscript, predictions of two solvers available in a commercial software package, pzflex, one using the finite-element-method (FEM) and the other a pseudo-spectral method, spectralflex, are compared with measurements and the Khokhlov-Zabolotskaya-Kuznetsov (KZK) Texas code (a finite-difference time-domain algorithm). The pzflex methods solve the continuity equation, momentum equation and equation of state where they account for nonlinearity to second order whereas the KZK code solves a nonlinear wave equation with a paraxial approximation for diffraction. Measurements of the field from a single element 3.3 MHz focused transducer were compared with the simulations and there was good agreement for the fundamental frequency and the harmonics; however the FEM pzflex solver incurred a high computational cost to achieve equivalent accuracy. In addition, pzflex results exhibited non-physical oscillations in the spatial distribution of harmonics when the amplitudes were relatively low. It was found that spectralflex was able to accurately capture the nonlinear fields at reasonable computational cost. These results emphasize the need to benchmark nonlinear simulations before using codes as predictive tools.

Simulations and model of the nonlinear Richtmyer–Meshkov instability

DOE PAGES

Dimonte, Guy; Ramaprabhu, P.

2010-01-21

The nonlinear evolution of the Richtmyer-Meshkov (RM) instability is investigated using numerical simulations with the FLASH code in two-dimensions (2D). The purpose of the simulations is to develop an empiricial nonlinear model of the RM instability that is applicable to inertial confinement fusion (ICF) and ejecta formation, namely, at large Atwood number A and scaled initial amplitude kh o (k ≡ wavenumber) of the perturbation. The FLASH code is first validated with a variety of RM experiments that evolve well into the nonlinear regime. They reveal that bubbles stagnate when they grow by an increment of 2/k and that spikesmore » accelerate for A > 0.5 due to higher harmonics that focus them. These results are then compared with a variety of nonlinear models that are based on potential flow. We find that the models agree with simulations for moderate values of A < 0.9 and kh o< 1, but not for the larger values that characterize ICF and ejecta formation. We thus develop a new nonlinear empirical model that captures the simulation results consistent with potential flow for a broader range of A and kh o. Our hope is that such empirical models concisely capture the RM simulations and inspire more rigorous solutions.« less

Nonlinear structured-illumination enhanced temporal focusing multiphoton excitation microscopy with a digital micromirror device.

PubMed

Cheng, Li-Chung; Lien, Chi-Hsiang; Da Sie, Yong; Hu, Yvonne Yuling; Lin, Chun-Yu; Chien, Fan-Ching; Xu, Chris; Dong, Chen Yuan; Chen, Shean-Jen

2014-08-01

In this study, the light diffraction of temporal focusing multiphoton excitation microscopy (TFMPEM) and the excitation patterning of nonlinear structured-illumination microscopy (NSIM) can be simultaneously and accurately implemented via a single high-resolution digital micromirror device. The lateral and axial spatial resolutions of the TFMPEM are remarkably improved through the second-order NSIM and projected structured light, respectively. The experimental results demonstrate that the lateral and axial resolutions are enhanced from 397 nm to 168 nm (2.4-fold) and from 2.33 μm to 1.22 μm (1.9-fold), respectively, in full width at the half maximum. Furthermore, a three-dimensionally rendered image of a cytoskeleton cell featuring ~25 nm microtubules is improved, with other microtubules at a distance near the lateral resolution of 168 nm also able to be distinguished.

Species difference in the mechanism of nonlinear pharmacokinetics of E2074, a novel sodium channel inhibitor, in rats, dogs, and monkeys.

PubMed

Nagaya, Yoko; Takenaka, Osamu; Kusano, Kazutomi; Yoshimura, Tsutomu

2013-05-01

New chemical entities often exhibit nonlinear pharmacokinetics (PK) profiles in experimental animals. However, the number of studies that have focused on species differences in nonlinear PK is very limited; thus, the aim of this study was to clarify the mechanism of the nonlinear PK of E2074 (2-[(2R)-2-fluoro-3-{(3r)-[(3-fluorobenzyl)oxy]-8-azabicyclo[3.2.1]oct-8-yl}propyl]-4,5-dimethyl-2,4-dihydro-3H-1,2,4-triazol-3-one), a novel sodium channel inhibitor, in rats, dogs, and monkeys. Nonlinear PK profiles with more than dose-proportional increases of Cmax and area under the plasma concentration curve were observed in all species after oral administration. The Michaelis-Menten constant (Km) values of hepatic microsomal metabolism were 7.23 and 0.41 μM in rats and dogs in vitro, respectively, which were lower than the unbound maximum plasma concentrations after oral administration in vivo, indicating that the nonlinear PK in rats and dogs was attributable to the saturation of hepatic metabolism. However, we do not believe that the saturation of hepatic metabolism was the mechanism of nonlinearity in monkeys because of the high Km value (42.44 μM) observed in liver microsomes. Intestinal metabolism was observed in monkey intestinal microsomes but not in rats and dogs, and the nonlinear PK in monkeys was diminished by inhibition of intestinal metabolism with a concomitant oral dose of ketoconazole. These results suggest that saturation of the intestinal metabolism is the potential mechanism of nonlinearity in monkeys. P-glycoprotein was not involved in the nonlinear PK profiles in any species. In conclusion, the mechanism of the nonlinear PK of E2074 is species dependent, with the saturation of hepatic metabolism in rats and dogs and that of intestinal metabolism in monkeys being the primary cause.

A new treatment for predicting the self-excited vibrations of nonlinear systems with frictional interfaces: The Constrained Harmonic Balance Method, with application to disc brake squeal

NASA Astrophysics Data System (ADS)

Coudeyras, N.; Sinou, J.-J.; Nacivet, S.

2009-01-01

Brake squeal noise is still an issue since it generates high warranty costs for the automotive industry and irritation for customers. Key parameters must be known in order to reduce it. Stability analysis is a common method of studying nonlinear phenomena and has been widely used by the scientific and the engineering communities for solving disc brake squeal problems. This type of analysis provides areas of stability versus instability for driven parameters, thereby making it possible to define design criteria. Nevertheless, this technique does not permit obtaining the vibrating state of the brake system and nonlinear methods have to be employed. Temporal integration is a well-known method for computing the dynamic solution but as it is time consuming, nonlinear methods such as the Harmonic Balance Method (HBM) are preferred. This paper presents a novel nonlinear method called the Constrained Harmonic Balance Method (CHBM) that works for nonlinear systems subject to flutter instability. An additional constraint-based condition is proposed that omits the static equilibrium point (i.e. the trivial static solution of the nonlinear problem that would be obtained by applying the classical HBM) and therefore focuses on predicting both the Fourier coefficients and the fundamental frequency of the stationary nonlinear system. The effectiveness of the proposed nonlinear approach is illustrated by an analysis of disc brake squeal. The brake system under consideration is a reduced finite element model of a pad and a disc. Both stability and nonlinear analyses are performed and the results are compared with a classical variable order solver integration algorithm. Therefore, the objectives of the following paper are to present not only an extension of the HBM (CHBM) but also to demonstrate an application to the specific problem of disc brake squeal with extensively parametric studies that investigate the effects of the friction coefficient, piston pressure, nonlinear stiffness and structural damping.

Intensification of the impact of high-intensity focused ultrasound (HIFU) with special spatiotemporal modulation

NASA Astrophysics Data System (ADS)

Gusev, V. A.; Rudenko, O. V.

2013-01-01

The principle of forming a special form of powerful acoustic signals is proposed, which makes it possible to ensure precise spatiotemporal beam focusing. The introduction of a transverse-coordinate-dependent local wave frequency is suggested, due to which the equality of the formation lengths of a discontinuity for all rays is achieved. This thereby ensures an increase in nonlinear absorption; as a result, the temperature and radiation action of focused ultrasound on the medium increase.

Maximizing the optical network capacity

PubMed Central

Bayvel, Polina; Maher, Robert; Liga, Gabriele; Shevchenko, Nikita A.; Lavery, Domaniç; Killey, Robert I.

2016-01-01

Most of the digital data transmitted are carried by optical fibres, forming the great part of the national and international communication infrastructure. The information-carrying capacity of these networks has increased vastly over the past decades through the introduction of wavelength division multiplexing, advanced modulation formats, digital signal processing and improved optical fibre and amplifier technology. These developments sparked the communication revolution and the growth of the Internet, and have created an illusion of infinite capacity being available. But as the volume of data continues to increase, is there a limit to the capacity of an optical fibre communication channel? The optical fibre channel is nonlinear, and the intensity-dependent Kerr nonlinearity limit has been suggested as a fundamental limit to optical fibre capacity. Current research is focused on whether this is the case, and on linear and nonlinear techniques, both optical and electronic, to understand, unlock and maximize the capacity of optical communications in the nonlinear regime. This paper describes some of them and discusses future prospects for success in the quest for capacity. PMID:26809572

An NN-Based SRD Decomposition Algorithm and Its Application in Nonlinear Compensation

PubMed Central

Yan, Honghang; Deng, Fang; Sun, Jian; Chen, Jie

2014-01-01

In this study, a neural network-based square root of descending (SRD) order decomposition algorithm for compensating for nonlinear data generated by sensors is presented. The study aims at exploring the optimized decomposition of data 1.00,0.00,0.00 and minimizing the computational complexity and memory space of the training process. A linear decomposition algorithm, which automatically finds the optimal decomposition of N subparts and reduces the training time to 1N and memory cost to 1N, has been implemented on nonlinear data obtained from an encoder. Particular focus is given to the theoretical access of estimating the numbers of hidden nodes and the precision of varying the decomposition method. Numerical experiments are designed to evaluate the effect of this algorithm. Moreover, a designed device for angular sensor calibration is presented. We conduct an experiment that samples the data of an encoder and compensates for the nonlinearity of the encoder to testify this novel algorithm. PMID:25232912

Impact of nonlinear distortion on acoustic radiation force elastography.

PubMed

Draudt, Andrew B; Cleveland, Robin O

2011-11-01

High-intensity focused ultrasound (HIFU) produces an acoustic radiation force that induces tissue displacement, which can be measured by monitoring time shifts in the backscattered signals from interrogation pulses. If the pulse occurs simultaneously with the HIFU, the arrival time of the backscatter will be biased because nonlinearity associated with the HIFU changes the local sound speed. Measurements of the pressure field using 1.1 MHz HIFU and a 7.5 MHz pulse in water exhibited a nonlinearly induced apparent displacement (NIAD) that varied with the HIFU pressure, propagation distance and the timing of the pulse relative to the HIFU. Nonlinear simulations employing the KZK equation predicted NIADs that agreed with measurements. Experiments with chicken breast demonstrated a NIAD with magnitude similar to that expected from the radiation force. Finally it was shown that if two pulses were fired with different phases relative to the HIFU, then upon averaging, the NIAD could be mitigated. Copyright © 2011 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

Several new directions for ultrafast fiber lasers [Invited].

PubMed

Fu, Walter; Wright, Logan G; Sidorenko, Pavel; Backus, Sterling; Wise, Frank W

2018-04-16

Ultrafast fiber lasers have the potential to make applications of ultrashort pulses widespread - techniques not only for scientists, but also for doctors, manufacturing engineers, and more. Today, this potential is only realized in refractive surgery and some femtosecond micromachining. The existing market for ultrafast lasers remains dominated by solid-state lasers, primarily Ti:sapphire, due to their superior performance. Recent advances show routes to ultrafast fiber sources that provide performance and capabilities equal to, and in some cases beyond, those of Ti:sapphire, in compact, versatile, low-cost devices. In this paper, we discuss the prospects for future ultrafast fiber lasers built on new kinds of pulse generation that capitalize on nonlinear dynamics. We focus primarily on three promising directions: mode-locked oscillators that use nonlinearity to enhance performance; systems that use nonlinear pulse propagation to achieve ultrashort pulses without a mode-locked oscillator; and multimode fiber lasers that exploit nonlinearities in space and time to obtain unparalleled control over an electric field.

Nonlinear Talbot Effect and Its Applications

NASA Astrophysics Data System (ADS)

Yang, Zhening

2018-03-01

Talbot effect, a lenless self-imaging phenomenon, was first discovered in 1836 by H.F. Talbot. The conventional Talbott effect has been studied for over a hundred years. Recently, the rapid development of optical superlattices has brought a great breakthrough in Talbot effect research. A nonlinear self-imaging phenomenon was found in the periodically poled LiTaO3 (PPLT) crystals. [1][2][3] This nonlinear Talbot effect has applications not only in optics but also in many other fields. For example, the phenomenon is realized by frequency-doubled beams, which offers people a new way to enhance the spatial resolution of the self-images of periodic objects. And by observing the self-image of the second harmonic (SH) field on the sample surface, people can detect the domain structure in the crystal without damaging the sample. Throughout this review paper, an overview of nonlinear Talbot effect and two applications of this phenomenon is presented. Breakthroughs like achieving a super-focused spot and realizing an acousto-optic tunable SH Talbot illuminator will be introduced as well.

A nonlinear vibration isolator achieving high-static-low-dynamic stiffness and tunable anti-resonance frequency band

NASA Astrophysics Data System (ADS)

Sun, Xiuting; Jing, Xingjian

2016-12-01

This study investigates theoretically and experimentally a vibration isolator constructed by an n-layer Scissor-Like Structure (SLS), focusing on the analysis and design of nonlinear stiffness and damping characteristics for advantageous isolation performance in both orthogonal directions. With the mathematical modeling, the influence incurred by different structural parameters on system isolation performance is studied. It is shown that, (a) nonlinear high-static-low-dynamic stiffness and damping characteristics can be seen such that the system can achieve good isolation performance in both directions, (b) an anti-resonance frequency band exists due to the coupling effect between the linear and nonlinear stiffness in the two orthogonal directions within the structure, and (c) all these performances are designable with several structural parameters. The advantages of the proposed system are shown through comparisons with an existing quasi-zero-stiffness vibration isolator (QZS-VI) and a traditional mass-spring-damper vibration isolator (MSD-VI), and further validated by experimental results.

Nonlinear evolution of magnetic flux ropes. I - Low-beta limit

NASA Technical Reports Server (NTRS)

Osherovich, V. A.; Farrugia, C. J.; Burlaga, L. F.

1993-01-01

We study the nonlinear self-similar evolution of a cylindrical magnetic flux tube with two components of the magnetic field, axial and azimuthal. We restrict ourselves to the case of a plasma of low beta. Introducing a special class of configurations we call 'separable fields', we reduce the problem to an ordinary differential equation. Two cases are to be distinguished: (1) when the total field minimizes on the symmetry axis, the magnetic configuration inexorably collapses, and (2) when, on the other hand, the total field maximizes on the symmetry axis, the magnetic configuration behaves analogously to a nonlinear oscillator. Here we focus on the latter case. The effective potential of the motion contains two terms: a strong repulsive term and a weak restoring term associated with the pinch. We solve the nonlinear differential equation of motion numerically and find that the period of oscillations grows exponentially with the energy of the oscillator. Our treatment emphasizes the role of the force-free configuration as the lowest potential energy state about which the system oscillates.

Sub-wavelength modulation of χ (2) optical nonlinearity in organic thin films

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yan, Yixin; Yuan, Yakun; Wang, Baomin

Modulating the second-order nonlinear optical susceptibility (χ (2)) of materials at the nanoscale represents an ongoing technological challenge for a variety of integrated frequency conversion and nonlinear nanophotonic applications. Here we exploit the large hyperpolarizability of intermolecular charge transfer states, naturally aligned at an organic semiconductor donor–acceptor (DA) interface, as a means to control the magnitude and sign of χ (2) at the nanoscale. Focusing initially on a single pentacene-C 60 DA interface, we confirm that the charge transfer transition is strongly aligned orthogonal to the heterojunction and find that it is responsible for a large interfacial nonlinearity probed viamore » second harmonic generation that is sufficient to achieve d 33 > 10pm V –1, when incorporated in a non-centrosymmetric DA multilayer stack. Lastly, using grating-shadowed oblique-angle deposition to laterally structure the DA interface distribution in such multilayers subsequently enables the demonstration of a χ (2) grating with 280 nm periodicity, which is the shortest reported to date.« less

Stationary waves on nonlinear quantum graphs. II. Application of canonical perturbation theory in basic graph structures.

PubMed

Gnutzmann, Sven; Waltner, Daniel

2016-12-01

We consider exact and asymptotic solutions of the stationary cubic nonlinear Schrödinger equation on metric graphs. We focus on some basic example graphs. The asymptotic solutions are obtained using the canonical perturbation formalism developed in our earlier paper [S. Gnutzmann and D. Waltner, Phys. Rev. E 93, 032204 (2016)2470-004510.1103/PhysRevE.93.032204]. For closed example graphs (interval, ring, star graph, tadpole graph), we calculate spectral curves and show how the description of spectra reduces to known characteristic functions of linear quantum graphs in the low-intensity limit. Analogously for open examples, we show how nonlinear scattering of stationary waves arises and how it reduces to known linear scattering amplitudes at low intensities. In the short-wavelength asymptotics we discuss how genuine nonlinear effects may be described using the leading order of canonical perturbation theory: bifurcation of spectral curves (and the corresponding solutions) in closed graphs and multistability in open graphs.

Stochastic Modeling and Analysis of Multiple Nonlinear Accelerated Degradation Processes through Information Fusion

PubMed Central

Sun, Fuqiang; Liu, Le; Li, Xiaoyang; Liao, Haitao

2016-01-01

Accelerated degradation testing (ADT) is an efficient technique for evaluating the lifetime of a highly reliable product whose underlying failure process may be traced by the degradation of the product’s performance parameters with time. However, most research on ADT mainly focuses on a single performance parameter. In reality, the performance of a modern product is usually characterized by multiple parameters, and the degradation paths are usually nonlinear. To address such problems, this paper develops a new s-dependent nonlinear ADT model for products with multiple performance parameters using a general Wiener process and copulas. The general Wiener process models the nonlinear ADT data, and the dependency among different degradation measures is analyzed using the copula method. An engineering case study on a tuner’s ADT data is conducted to demonstrate the effectiveness of the proposed method. The results illustrate that the proposed method is quite effective in estimating the lifetime of a product with s-dependent performance parameters. PMID:27509499

Stochastic Modeling and Analysis of Multiple Nonlinear Accelerated Degradation Processes through Information Fusion.

PubMed

Sun, Fuqiang; Liu, Le; Li, Xiaoyang; Liao, Haitao

2016-08-06

Accelerated degradation testing (ADT) is an efficient technique for evaluating the lifetime of a highly reliable product whose underlying failure process may be traced by the degradation of the product's performance parameters with time. However, most research on ADT mainly focuses on a single performance parameter. In reality, the performance of a modern product is usually characterized by multiple parameters, and the degradation paths are usually nonlinear. To address such problems, this paper develops a new s-dependent nonlinear ADT model for products with multiple performance parameters using a general Wiener process and copulas. The general Wiener process models the nonlinear ADT data, and the dependency among different degradation measures is analyzed using the copula method. An engineering case study on a tuner's ADT data is conducted to demonstrate the effectiveness of the proposed method. The results illustrate that the proposed method is quite effective in estimating the lifetime of a product with s-dependent performance parameters.

Sub-wavelength modulation of χ(2) optical nonlinearity in organic thin films

NASA Astrophysics Data System (ADS)

Yan, Yixin; Yuan, Yakun; Wang, Baomin; Gopalan, Venkatraman; Giebink, Noel C.

2017-01-01

Modulating the second-order nonlinear optical susceptibility (χ(2)) of materials at the nanoscale represents an ongoing technological challenge for a variety of integrated frequency conversion and nonlinear nanophotonic applications. Here we exploit the large hyperpolarizability of intermolecular charge transfer states, naturally aligned at an organic semiconductor donor-acceptor (DA) interface, as a means to control the magnitude and sign of χ(2) at the nanoscale. Focusing initially on a single pentacene-C60 DA interface, we confirm that the charge transfer transition is strongly aligned orthogonal to the heterojunction and find that it is responsible for a large interfacial nonlinearity probed via second harmonic generation that is sufficient to achieve d33>10 pm V-1, when incorporated in a non-centrosymmetric DA multilayer stack. Using grating-shadowed oblique-angle deposition to laterally structure the DA interface distribution in such multilayers subsequently enables the demonstration of a χ(2) grating with 280 nm periodicity, which is the shortest reported to date.

Computational process to study the wave propagation In a non-linear medium by quasi- linearization

NASA Astrophysics Data System (ADS)

Sharath Babu, K.; Venkata Brammam, J.; Baby Rani, CH

2018-03-01

Two objects having distinct velocities come into contact an impact can occur. The impact study i.e., in the displacement of the objects after the impact, the impact force is function of time‘t’ which is behaves similar to compression force. The impact tenure is very short so impulses must be generated subsequently high stresses are generated. In this work we are examined the wave propagation inside the object after collision and measured the object non-linear behavior in the one-dimensional case. Wave transmission is studied by means of material acoustic parameter value. The objective of this paper is to present a computational study of propagating pulsation and harmonic waves in nonlinear media using quasi-linearization and subsequently utilized the central difference scheme. This study gives focus on longitudinal, one- dimensional wave propagation. In the finite difference scheme Non-linear system is reduced to a linear system by applying quasi-linearization method. The computed results exhibit good agreement on par with the selected non-liner wave propagation.

Nonlinear optical properties and excited state dynamics of sandwich-type mixed (phthalocyaninato)(Schiff-base) triple-decker complexes: Effect of rare earth atom

NASA Astrophysics Data System (ADS)

Li, Zhongguo; Gao, Feng; Xiao, Zhengguo; Wu, Xingzhi; Zuo, Jinglin; Song, Yinglin

2018-07-01

The third-order nonlinear optical properties of two di-lanthanide (Ln = Tb and Dy) sandwich complexes with mixed phthalocyanine and Schiff-base ligands were studied using Z-scan technique at 532 nm with 20 ps and 4 ns pulses. Both complexes exhibit reverse saturable absorption and self-focusing effect in ps regime, while the second-order hyperpolarizability decreases from Dy to Tb. Interestingly, the Tb triple-decker complexes show larger nonlinear absorption than Dy complexes on ns timescale. The time-resolved pump-probe measurements demonstrate that the nonlinear optical response was caused by excited-state mechanism related to the five-level model, while the singlet state lifetime of Dy complexes is 3 times shorter than that of Tb complexes. Our results indicate the lanthanide ions play a critical role in the photo-physical properties of triple-decker phthalocyanine complexes for their application as optical limiting materials.

Sub-wavelength modulation of χ (2) optical nonlinearity in organic thin films

DOE PAGES

Yan, Yixin; Yuan, Yakun; Wang, Baomin; ...

2017-01-27

Modulating the second-order nonlinear optical susceptibility (χ (2)) of materials at the nanoscale represents an ongoing technological challenge for a variety of integrated frequency conversion and nonlinear nanophotonic applications. Here we exploit the large hyperpolarizability of intermolecular charge transfer states, naturally aligned at an organic semiconductor donor–acceptor (DA) interface, as a means to control the magnitude and sign of χ (2) at the nanoscale. Focusing initially on a single pentacene-C 60 DA interface, we confirm that the charge transfer transition is strongly aligned orthogonal to the heterojunction and find that it is responsible for a large interfacial nonlinearity probed viamore » second harmonic generation that is sufficient to achieve d 33 > 10pm V –1, when incorporated in a non-centrosymmetric DA multilayer stack. Lastly, using grating-shadowed oblique-angle deposition to laterally structure the DA interface distribution in such multilayers subsequently enables the demonstration of a χ (2) grating with 280 nm periodicity, which is the shortest reported to date.« less

Quantum dynamics by the constrained adiabatic trajectory method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leclerc, A.; Jolicard, G.; Guerin, S.

2011-03-15

We develop the constrained adiabatic trajectory method (CATM), which allows one to solve the time-dependent Schroedinger equation constraining the dynamics to a single Floquet eigenstate, as if it were adiabatic. This constrained Floquet state (CFS) is determined from the Hamiltonian modified by an artificial time-dependent absorbing potential whose forms are derived according to the initial conditions. The main advantage of this technique for practical implementation is that the CFS is easy to determine even for large systems since its corresponding eigenvalue is well isolated from the others through its imaginary part. The properties and limitations of the CATM are exploredmore » through simple examples.« less

Phase space quantum mechanics - Direct

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nasiri, S.; Sobouti, Y.; Taati, F.

2006-09-15

Conventional approach to quantum mechanics in phase space (q,p), is to take the operator based quantum mechanics of Schroedinger, or an equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher level of abstraction, in which the independence and the symmetric role of q and p is maintained throughout, and at once arrive at phase space state functions. Upon reduction to the q- or p-space the proposed formalism gives the conventional quantum mechanics, however, with a definite rule for ordering of factors of noncommuting observables. Further conceptual and practical merits of themore » formalism are demonstrated throughout the text.« less

The FEM-R-Matrix Approach: Use of Mixed Finite Element and Gaussian Basis Sets for Electron Molecule Collisions

NASA Technical Reports Server (NTRS)

Thuemmel, Helmar T.; Huo, Winifred M.; Langhoff, Stephen R. (Technical Monitor)

1995-01-01

For the calculation of electron molecule collision cross sections R-matrix methods automatically take advantage of the division of configuration space into an inner region (I) bounded by radius tau b, where the scattered electron is within the molecular charge cloud and the system is described by an correlated Configuration Interaction (CI) treatment in close analogy to bound state calculations, and an outer region (II) where the scattered electron moves in the long-range multipole potential of the target and efficient analytic methods can be used for solving the asymptotic Schroedinger equation plus boundary conditions.

High-order harmonic generation by atoms in a few-cycle laser pulse: Carrier-envelope phase and many-electron effects

DOE Office of Scientific and Technical Information (OSTI.GOV)

Frolov, M. V.; Manakov, N. L.; Silaev, A. A.

2011-02-15

Analytic formulas describing high-order harmonic generation (HHG) by atoms in a short laser pulse are obtained quantum mechanically in the tunneling limit. These results provide analytic expressions of the three-step HHG scenario, as well as of the returning electron wave packet, in a few-cycle pulse. Our results agree well with those of numerical solutions of the time-dependent Schroedinger equation for the H atom, while for Xe they predict many-electron atomic dynamics features in few-cycle HHG spectra and significant dependence of these features on the carrier-envelope phase of a laser pulse.

Analysis of a semiclassical model for rotational transition probabilities. [in highly nonequilibrium flow of diatomic molecules

NASA Technical Reports Server (NTRS)

Deiwert, G. S.; Yoshikawa, K. K.

1975-01-01

A semiclassical model proposed by Pearson and Hansen (1974) for computing collision-induced transition probabilities in diatomic molecules is tested by the direct-simulation Monte Carlo method. Specifically, this model is described by point centers of repulsion for collision dynamics, and the resulting classical trajectories are used in conjunction with the Schroedinger equation for a rigid-rotator harmonic oscillator to compute the rotational energy transition probabilities necessary to evaluate the rotation-translation exchange phenomena. It is assumed that a single, average energy spacing exists between the initial state and possible final states for a given collision.

Experimental demonstration of a quantum annealing algorithm for the traveling salesman problem in a nuclear-magnetic-resonance quantum simulator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen Hongwei; High Magnetic Field Laboratory, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031; Kong Xi

The method of quantum annealing (QA) is a promising way for solving many optimization problems in both classical and quantum information theory. The main advantage of this approach, compared with the gate model, is the robustness of the operations against errors originated from both external controls and the environment. In this work, we succeed in demonstrating experimentally an application of the method of QA to a simplified version of the traveling salesman problem by simulating the corresponding Schroedinger evolution with a NMR quantum simulator. The experimental results unambiguously yielded the optimal traveling route, in good agreement with the theoretical prediction.

Application of wave mechanics theory to fluid dynamics problems: Fundamentals

NASA Technical Reports Server (NTRS)

Krzywoblocki, M. Z. V.

1974-01-01

The application of the basic formalistic elements of wave mechanics theory is discussed. The theory is used to describe the physical phenomena on the microscopic level, the fluid dynamics of gases and liquids, and the analysis of physical phenomena on the macroscopic (visually observable) level. The practical advantages of relating the two fields of wave mechanics and fluid mechanics through the use of the Schroedinger equation constitute the approach to this relationship. Some of the subjects include: (1) fundamental aspects of wave mechanics theory, (2) laminarity of flow, (3) velocity potential, (4) disturbances in fluids, (5) introductory elements of the bifurcation theory, and (6) physiological aspects in fluid dynamics.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cao, Jianjun; Shen, Dongyi; Feng, Yaming

Negative refraction has attracted much interest for its promising capability in imaging applications. Such an effect can be implemented by negative index meta-materials, however, which are usually accompanied by high loss and demanding fabrication processes. Recently, alternative nonlinear approaches like phase conjugation and four wave mixing have shown advantages of low-loss and easy-to-implement, but associated problems like narrow accepting angles can still halt their practical applications. Here, we demonstrate theoretically and experimentally a scheme to realize negative refraction by nonlinear difference frequency generation with wide tunability, where a thin Beta barium borate slice serves as a negative refraction layer bendingmore » the input signal beam to the idler beam at a negative angle. Furthermore, we realize optical focusing effect using such nonlinear negative refraction, which may enable many potential applications in imaging science.« less

A programmable nonlinear acoustic metamaterial

NASA Astrophysics Data System (ADS)

Yang, Tianzhi; Song, Zhi-Guang; Clerkin, Eoin; Zhang, Ye-Wei; Sun, Jia-He; Su, Yi-Shu; Chen, Li-Qun; Hagedorn, Peter

2017-09-01

Acoustic metamaterials with specifically designed lattices can manipulate acoustic/elastic waves in unprecedented ways. Whereas there are many studies that focus on passive linear lattice, with non-reconfigurable structures. In this letter, we present the design, theory and experimental demonstration of an active nonlinear acoustic metamaterial, the dynamic properties of which can be modified instantaneously with reversibility. By incorporating active and nonlinear elements in a single unit cell, a real-time tunability and switchability of the band gap is achieved. In addition, we demonstrate a dynamic "editing" capability for shaping transmission spectra, which can be used to create the desired band gap and resonance. This feature is impossible to achieve in passive metamaterials. These advantages demonstrate the versatility of the proposed device, paving the way toward smart acoustic devices, such as logic elements, diode and transistor.

Non-linear associations between laryngo-pharyngeal symptoms of gastro-oesophageal reflux disease: clues from artificial intelligence analysis

PubMed Central

Grossi, E

2006-01-01

Summary The relationship between the different symptoms of gastro-oesophageal reflux disease remain markedly obscure due to the high underlying non-linearity and the lack of studies focusing on the problem. Aim of this study was to evaluate the hidden relationships between the triad of symptoms related to gastro-oesophageal reflux disease using advanced mathematical techniques, borrowed from the artificial intelligence field, in a cohort of patients with oesophagitis. A total of 388 patients (from 60 centres) with endoscopic evidence of oesophagitis were recruited. The severity of oesophagitis was scored by means of the Savary-Miller classification. PST algorithm was employed. This study shows that laryngo-pharyngeal symptoms related to gastro-oesophageal reflux disease are correlated even if in a non-linear way. PMID:17345935

Non-linear associations between laryngo-pharyngeal symptoms of gastro-oesophageal reflux disease: clues from artificial intelligence analysis.

PubMed

Grossi, E

2006-10-01

The relationship between the different symptoms of gastro-oesophageal reflux disease remain markedly obscure due to the high underlying non-linearity and the lack of studies focusing on the problem. Aim of this study was to evaluate the hidden relationships between the triad of symptoms related to gastro-oesophageal reflux disease using advanced mathematical techniques, borrowed from the artificial intelligence field, in a cohort of patients with oesophagitis. A total of 388 patients (from 60 centres) with endoscopic evidence of oesophagitis were recruited. The severity of oesophagitis was scored by means of the Savary-Miller classification. PST algorithm was employed. This study shows that laryngo-pharyngeal symptoms related to gastro-oesophageal reflux disease are correlated even if in a non-linear way.

Nonlinear Analysis and Preliminary Testing Results of a Hybrid Wing Body Center Section Test Article

NASA Technical Reports Server (NTRS)

Przekop, Adam; Jegley, Dawn C.; Rouse, Marshall; Lovejoy, Andrew E.; Wu, Hsi-Yung T.

2015-01-01

A large test article was recently designed, analyzed, fabricated, and successfully tested up to the representative design ultimate loads to demonstrate that stiffened composite panels with through-the-thickness reinforcement are a viable option for the next generation large transport category aircraft, including non-conventional configurations such as the hybrid wing body. This paper focuses on finite element analysis and test data correlation of the hybrid wing body center section test article under mechanical, pressure and combined load conditions. Good agreement between predictive nonlinear finite element analysis and test data is found. Results indicate that a geometrically nonlinear analysis is needed to accurately capture the behavior of the non-circular pressurized and highly-stressed structure when the design approach permits local buckling.

Evaluation of solution procedures for material and/or geometrically nonlinear structural analysis by the direct stiffness method.

NASA Technical Reports Server (NTRS)

Stricklin, J. A.; Haisler, W. E.; Von Riesemann, W. A.

1972-01-01

This paper presents an assessment of the solution procedures available for the analysis of inelastic and/or large deflection structural behavior. A literature survey is given which summarized the contribution of other researchers in the analysis of structural problems exhibiting material nonlinearities and combined geometric-material nonlinearities. Attention is focused at evaluating the available computation and solution techniques. Each of the solution techniques is developed from a common equation of equilibrium in terms of pseudo forces. The solution procedures are applied to circular plates and shells of revolution in an attempt to compare and evaluate each with respect to computational accuracy, economy, and efficiency. Based on the numerical studies, observations and comments are made with regard to the accuracy and economy of each solution technique.

Simulation of noisy dynamical system by Deep Learning

NASA Astrophysics Data System (ADS)

Yeo, Kyongmin

2017-11-01

Deep learning has attracted huge attention due to its powerful representation capability. However, most of the studies on deep learning have been focused on visual analytics or language modeling and the capability of the deep learning in modeling dynamical systems is not well understood. In this study, we use a recurrent neural network to model noisy nonlinear dynamical systems. In particular, we use a long short-term memory (LSTM) network, which constructs internal nonlinear dynamics systems. We propose a cross-entropy loss with spatial ridge regularization to learn a non-stationary conditional probability distribution from a noisy nonlinear dynamical system. A Monte Carlo procedure to perform time-marching simulations by using the LSTM is presented. The behavior of the LSTM is studied by using noisy, forced Van der Pol oscillator and Ikeda equation.

Third-order Nonlinear Optical Properties of Metallodielectric Stacks

DTIC Science & Technology

2011-07-01

developed by Sheik- Bahae et al [7] a (Gaussian) laser beam is focused in free space; a sample is positioned along the propagation (Z) axis of the laser...transmittance and reflectance coefficients are defined for any angle of incidence as 22 0 ||,|| cos cos rRt n n T i tt    ; (2) i  and t are...nonlinear coefficient,    4 2 2 i n  , has a complex value. The longitudinal component of the Poynting vector was used in Eq. (11). The Kerr

Defocusing complex short-pulse equation and its multi-dark-soliton solution.

PubMed

Feng, Bao-Feng; Ling, Liming; Zhu, Zuonong

2016-05-01

In this paper, we propose a complex short-pulse equation of both focusing and defocusing types, which governs the propagation of ultrashort pulses in nonlinear optical fibers. It can be viewed as an analog of the nonlinear Schrödinger (NLS) equation in the ultrashort-pulse regime. Furthermore, we construct the multi-dark-soliton solution for the defocusing complex short-pulse equation through the Darboux transformation and reciprocal (hodograph) transformation. One- and two-dark-soliton solutions are given explicitly, whose properties and dynamics are analyzed and illustrated.

Fractional Order and Dynamic Simulation of a System Involving an Elastic Wide Plate

NASA Astrophysics Data System (ADS)

David, S. A.; Balthazar, J. M.; Julio, B. H. S.; Oliveira, C.

2011-09-01

Numerous researchers have studied about nonlinear dynamics in several areas of science and engineering. However, in most cases, these concepts have been explored mainly from the standpoint of analytical and computational methods involving integer order calculus (IOC). In this paper we have examined the dynamic behavior of an elastic wide plate induced by two electromagnets of a point of view of the fractional order calculus (FOC). The primary focus of this study is on to help gain a better understanding of nonlinear dynamic in fractional order systems.

Saturable nonlinear dielectric waveguide with applications to broad-area semiconductor lasers.

PubMed

Mehuys, D; Mittelstein, M; Salzman, J; Yariv, A

1987-11-01

Self-focusing in a passive dielectric waveguide with a saturable nonlinearity is studied. The eigensolutions constitute a good approximation to the lateral modes of broad-area semiconductor lasers under low-duty-cycle pulsed conditions. The laser modes are predicted to consist of adjacent filaments coupled in phase, leading to a single-lobed far field, and to be stable with increased current injection above saturation intensity. The ultimate filament spacing is inversely proportional to the threshold gain, and thus wider filaments are expected in low-threshold broad-area lasers.

Physical mechanisms of solar activity effects in the middle atmosphere

NASA Technical Reports Server (NTRS)

Ebel, A.

1989-01-01

A great variety of physical mechanisms of possibly solar induced variations in the middle atmosphere has been discussed in the literature during the last decades. The views which have been put forward are often controversial in their physical consequences. The reason may be the complexity and non-linearity of the atmospheric response to comparatively weak forcing resulting from solar activity. Therefore this review focuses on aspects which seem to indicate nonlinear processes in the development of solar induced variations. Results from observations and numerical simulations are discussed.

Transmutation of skyrmions to half-solitons driven by the nonlinear optical spin Hall effect.

PubMed

Flayac, H; Solnyshkov, D D; Shelykh, I A; Malpuech, G

2013-01-04

We show that the spin domains, generated in the linear optical spin Hall effect by the analog of spin-orbit interaction for exciton polaritons, are associated with the formation of a Skyrmion lattice. In the nonlinear regime, the spin anisotropy of the polariton-polariton interactions results in a spatial compression of the domains and in a transmutation of the Skyrmions into oblique half-solitons. This phase transition is associated with both the focusing of the spin currents and the emergence of a strongly anisotropic emission pattern.

Parametric disordering of meta-atoms and nonlinear topological transitions in liquid metacrystals

NASA Astrophysics Data System (ADS)

Zharov, Alexander A.; Zharova, Nina A.; Zharov, Alexander A.

2017-09-01

We show that amplitude-modulated electromagnetic wave incident onto a liquid metacrystal may cause parametric instability of meta-atoms resulting in isotropization of the medium that can be treated in terms of effective temperature. It makes possible to switch the sign of certain components of dielectric permittivity and/or magnetic permeability tensors that, in turn, modifies the topology of isofrequency surface. At the same time it leads to the changes of the conditions of electromagnetic wave propagation appearing in the form of focusing or defocusing nonlinearity.

Galerkin Method for Nonlinear Dynamics

NASA Astrophysics Data System (ADS)

Noack, Bernd R.; Schlegel, Michael; Morzynski, Marek; Tadmor, Gilead

A Galerkin method is presented for control-oriented reduced-order models (ROM). This method generalizes linear approaches elaborated by M. Morzyński et al. for the nonlinear Navier-Stokes equation. These ROM are used as plants for control design in the chapters by G. Tadmor et al., S. Siegel, and R. King in this volume. Focus is placed on empirical ROM which compress flow data in the proper orthogonal decomposition (POD). The chapter shall provide a complete description for construction of straight-forward ROM as well as the physical understanding and teste

Observation of Raman self-focusing in an alkali-metal vapor cell

NASA Astrophysics Data System (ADS)

Proite, N. A.; Unks, B. E.; Green, J. T.; Yavuz, D. D.

2008-02-01

We report an experimental demonstration of Raman self-focusing and self-defocusing in a far-off resonant alkali-metal atomic system. The key idea is to drive a hyperfine transition in an alkali-metal atom to a maximally coherent state with two laser beams. In this regime, the two-photon detuning from the Raman resonance controls the nonlinear index of the medium.

Inverse scattering transform analysis of rogue waves using local periodization procedure

NASA Astrophysics Data System (ADS)

Randoux, Stéphane; Suret, Pierre; El, Gennady

2016-07-01

The nonlinear Schrödinger equation (NLSE) stands out as the dispersive nonlinear partial differential equation that plays a prominent role in the modeling and understanding of the wave phenomena relevant to many fields of nonlinear physics. The question of random input problems in the one-dimensional and integrable NLSE enters within the framework of integrable turbulence, and the specific question of the formation of rogue waves (RWs) has been recently extensively studied in this context. The determination of exact analytic solutions of the focusing 1D-NLSE prototyping RW events of statistical relevance is now considered as the problem of central importance. Here we address this question from the perspective of the inverse scattering transform (IST) method that relies on the integrable nature of the wave equation. We develop a conceptually new approach to the RW classification in which appropriate, locally coherent structures are specifically isolated from a globally incoherent wave train to be subsequently analyzed by implementing a numerical IST procedure relying on a spatial periodization of the object under consideration. Using this approach we extend the existing classifications of the prototypes of RWs from standard breathers and their collisions to more general nonlinear modes characterized by their nonlinear spectra.

Inverse scattering transform analysis of rogue waves using local periodization procedure

PubMed Central

Randoux, Stéphane; Suret, Pierre; El, Gennady

2016-01-01

The nonlinear Schrödinger equation (NLSE) stands out as the dispersive nonlinear partial differential equation that plays a prominent role in the modeling and understanding of the wave phenomena relevant to many fields of nonlinear physics. The question of random input problems in the one-dimensional and integrable NLSE enters within the framework of integrable turbulence, and the specific question of the formation of rogue waves (RWs) has been recently extensively studied in this context. The determination of exact analytic solutions of the focusing 1D-NLSE prototyping RW events of statistical relevance is now considered as the problem of central importance. Here we address this question from the perspective of the inverse scattering transform (IST) method that relies on the integrable nature of the wave equation. We develop a conceptually new approach to the RW classification in which appropriate, locally coherent structures are specifically isolated from a globally incoherent wave train to be subsequently analyzed by implementing a numerical IST procedure relying on a spatial periodization of the object under consideration. Using this approach we extend the existing classifications of the prototypes of RWs from standard breathers and their collisions to more general nonlinear modes characterized by their nonlinear spectra. PMID:27385164

Nonlinear ultrasonic imaging with X wave

NASA Astrophysics Data System (ADS)

Du, Hongwei; Lu, Wei; Feng, Huanqing

2009-10-01

X wave has a large depth of field and may have important application in ultrasonic imaging to provide high frame rate (HFR). However, the HFR system suffers from lower spatial resolution. In this paper, a study of nonlinear imaging with X wave is presented to improve the resolution. A theoretical description of realizable nonlinear X wave is reported. The nonlinear field is simulated by solving the KZK nonlinear wave equation with a time-domain difference method. The results show that the second harmonic field of X wave has narrower mainlobe and lower sidelobes than the fundamental field. In order to evaluate the imaging effect with X wave, an imaging model involving numerical calculation of the KZK equation, Rayleigh-Sommerfeld integral, band-pass filtering and envelope detection is constructed to obtain 2D fundamental and second harmonic images of scatters in tissue-like medium. The results indicate that if X wave is used, the harmonic image has higher spatial resolution throughout the entire imaging region than the fundamental image, but higher sidelobes occur as compared to conventional focus imaging. A HFR imaging method with higher spatial resolution is thus feasible provided an apodization method is used to suppress sidelobes.

Structural stability of nonlinear population dynamics.

PubMed

Cenci, Simone; Saavedra, Serguei

2018-01-01

In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.

Digital Self-Interference Cancellation for Asynchronous In-Band Full-Duplex Underwater Acoustic Communication.

PubMed

Qiao, Gang; Gan, Shuwei; Liu, Songzuo; Ma, Lu; Sun, Zongxin

2018-05-24

To improve the throughput of underwater acoustic (UWA) networking, the In-band full-duplex (IBFD) communication is one of the most vital pieces of research. The major drawback of IBFD-UWA communication is Self-Interference (SI). This paper presents a digital SI cancellation algorithm for asynchronous IBFD-UWA communication system. We focus on two issues: one is asynchronous communication dissimilar to IBFD radio communication, the other is nonlinear distortion caused by power amplifier (PA). First, we discuss asynchronous IBFD-UWA signal model with the nonlinear distortion of PA. Then, we design a scheme for asynchronous IBFD-UWA communication utilizing the non-overlapping region between SI and intended signal to estimate the nonlinear SI channel. To cancel the nonlinear distortion caused by PA, we propose an Over-Parameterization based Recursive Least Squares (RLS) algorithm (OPRLS) to estimate the nonlinear SI channel. Furthermore, we present the OPRLS with a sparse constraint to estimate the SI channel, which reduces the requirement of the length of the non-overlapping region. Finally, we verify our concept through simulation and the pool experiment. Results demonstrate that the proposed digital SI cancellation scheme can cancel SI efficiently.

Structural stability of nonlinear population dynamics

NASA Astrophysics Data System (ADS)

Cenci, Simone; Saavedra, Serguei

2018-01-01

In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.