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At least 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Analytic soliton solutions of nonlinear extensions of the Schrödinger equation

A method is presented to construct analytic solitary wave solutions in nonlinear extensions of the Schrödinger equation starting from analytic solutions of the ordinary Schrödinger equation. We provide several examples illustrating the method. We rederive three well-known soliton solutions including the N-dimensional non-relativistic Gausson as well as the one-dimensional 1 / cosh-soliton and a theory with a power-like nonlinearity proportional to |ψ| 2λ with λ > 0. We also find several new solutions in different nonlinear theories in various space dimensions which, to the best of our knowledge, have not yet been discussed in literature. Our method can be used to construct further nonlinear theories and generalized to relativistic soliton theories, and may have many applications.

Analytical soliton solutions↗
DOE OSTI2015

Novel PT-invariant solutions for a large number of real nonlinear equations

We report that for a large number of real nonlinear equations, either continuous or discrete, integrable or nonintegrable, we show that whenever a real nonlinear equation admits a solution in terms of sech x, it also admits solutions in terms of the PT-invariant combinations sech x ± i tanh x. Additionally, for a number of real nonlinear equations we show that whenever a nonlinear equation admits a solution in terms sech 2 x, it also admits solutions in terms of the PT-invariant combinations sech 2 x ± i sech x tanh x. Besides, we show that similar results are also true in the periodic case involving Jacobi elliptic functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Simulating nonlinear optical processes on a superconducting quantum device

Simulating plasma physics on quantum computers is difficult because most problems of interest are nonlinear, but quantum computers are not naturally suitable for nonlinear operations. In weakly nonlinear regimes, plasma problems can be modelled as wave–wave interactions. In this paper, we develop a quantization approach to convert nonlinear wave–wave interaction problems to Hamiltonian simulation problems. We demonstrate our approach using two qubits on a superconducting device. Unlike a photonic device, a superconducting device does not naturally have the desired interactions in its native Hamiltonian. Nevertheless, Hamiltonian simulations can still be performed by decomposing required unitary operations into native gates. To improve experimental results, we employ a range of error-mitigation techniques. Apart from readout error mitigation, we use randomized compilation to transform undiagnosed coherent errors into well-behaved stochastic Pauli channels. Moreover, to compensate for stochastic noise, we rescale exponentially decaying probability amplitudes using rates measured from cycle benchmarking. We carefully consider how different choices of product-formula algorithms affect the overall error and show how a trade-off can be made to best utilize limited quantum resources. This study provides an example of how plasma problems may be solved on near-term quantum computing platforms.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Multimodal Tip-Enhanced Nonlinear Optical Nanoimaging of Plasmonic Silver Nanocubes

Optical field localization at plasmonic tip-sample nanojunctions has enabled high spatial resolution chemical analysis through tip-enhanced linear optical spectroscopies, including Raman scattering and photoluminescence. In this work, we illustrate that nonlinear optical processes, including parametric four-wave mixing (4WM), second harmonic/sum-frequency generation (SHG and SFG), and two-photon photoluminescence (TPPL), can be enhanced at plasmonic junctions and spatio-spectrally resolved simultaneously with few-nm spatial resolution under ambient conditions. More importantly, through a detailed analysis of our spectral nano-images, we find that the efficiencies of the local nonlinear signals are determined by sharp tip-sample junction resonances that vary over the few-nanometer length scale because of the corrugated nature of the probe. Namely, plasmon resonances centered at or around the different nonlinear signals are tracked through TPPL, and they are found to selectively enhance nonlinear signals with closely matched optical resonances.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Twisted Nonlinear Optics in Monolayer van der Waals Crystals

In addition to a plethora of emergent phenomena, the spatial topology of optical vortices enables an array of applications in optical communications and quantum information science. Multibeam nonlinear optical processes, augmented by optical vortices, are essential in this context, providing robust access to an infinitely large set of quantum states associated with the orbital angular momentum of light. Here, we push the boundaries of vortex nonlinear optics to the ultimate limits of material dimensionality. By exploiting multipulse difference frequency, sum frequency, and four-wave mixing in monolayer quantum materials, we demonstrate their ability to independently control the orbital angular momentum and radial distribution of vortex light-fields in addition to their wavelength. Due to the atomically thin nature of the host crystal, this control spans a broad spectral bandwidth in a highly integrable platform that is unconstrained by the traditional limits of bulk nonlinear optical materials. Our work heralds an innovative path for ultracompact and scalable hybrid nanophotonic technologies empowered by twisted nonlinear light–matter interactions in van der Waals nanomaterials.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Measurement of the Static Nonlinear Third-Order Elastic Moduli of Rocks: Problems and Applicability

The third-order elastic (TOE) model has been used to describe the widely observed nonlinear mechanical behaviors of earth materials. In addition to linear elastic constants ( λ , μ ), three nonlinear elastic moduli ( A , B , C ) are required for isotropic rocks. Contrary to previous research on dynamic TOE moduli, this study followed the protocol to measure strain and stress under uniaxial and hydrostatic compressive tests statically, which were later used to invert for the full set of TOE moduli for four standard rock types with differing pore structures of a porous oolitic limestone, quartz-rich sandstones, and a dense crystalline basalt. The applicability of the TOE model to characterize nonlinearity depends on the fulfillment of path-independence and small-strain assumptions. Using the measured static TOE moduli, the finite element model demonstrates that the stress in the vicinity of the wellbore is more amplified than the stress in the linear elastic case, which leads to a wider zone of rock failure around the wellbore. Due to the long-standing discrepancy between static and dynamic moduli, the rarely reported full set of static TOE moduli is necessary and will benefit future research in understanding the effect of rock nonlinearity on geophysical and geomechanical applications, such as long-term safe storage of CO 2 and generating process of geohazards.

58 GEOSCIENCES↗
DOE OSTI2012

Analytical spatiotemporal soliton solutions to (3+1)-dimensional cubic-quintic nonlinear Schroedinger equation with distributed coefficients

We obtain exact spatiotemporal periodic traveling wave solutions to the generalized (3+1)-dimensional cubic-quintic nonlinear Schroedinger equation with spatial distributed coefficients. For restrictive parameters, these periodic wave solutions acquire the form of localized spatial solitons. Such solutions exist under certain conditions, and impose constraints on the functions describing dispersion, nonlinearity, and gain (or loss). We then demonstrate the nonlinear tunneling effects and controllable compression technique of three-dimensional bright and dark solitons when they pass unchanged through the potential barriers and wells affected by special choices of the diffraction and/or the nonlinearity parameters. Direct numerical simulation has been performed to show the stable propagation of bright soliton with 5% white noise perturbation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Evolution of higher order nonlinear equation for the dust ion-acoustic waves in nonextensive plasma

There are three different types of nonlinear equations, namely, Korteweg-de Vries (K-dV), modified K-dV (mK-dV), and mixed modified K-dV (mixed mK-dV) equations, for the nonlinear propagation of the dust ion-acoustic (DIA) waves. The effects of electron nonextensivity on DIA solitary waves propagating in a dusty plasma (containing negatively charged stationary dust, inertial ions, and nonextensive q distributed electrons) are examined by solving these nonlinear equations. The basic features of mixed mK-dV (higher order nonlinear equation) solitons are found to exist beyond the K-dV limit. The properties of mK-dV solitons are compared with those of mixed mK-dV solitons. It is found that both positive and negative solitons are obtained depending on the q (nonextensive parameter).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Nonlinear theory of drift-cyclotron kinetics and the possible breakdown of gyro-kinetics

A nonlinear theory of drift-cyclotron kinetics (termed cyclo-kinetics here) is formulated to test the breakdown of the gyro-kinetic approximations. Six dimensional cyclo-kinetics can be regarded as an extension of five dimensional gyro-kinetics to include high-frequency cyclotron waves, which can interrupt the low-frequency gyro-averaging in the (sixth velocity grid) gyro-phase angle. Nonlinear cyclo-kinetics has no limit on the amplitude of the perturbations. Formally, there is no gyro-averaging when all cyclotron (gyro-phase angle) harmonics of the perturbed distribution function (delta-f) are retained. Retaining only the (low frequency) zeroth cyclotron harmonic in cyclo-kinetics recovers both linear and nonlinear gyro-kinetics. Simple recipes are given for converting continuum nonlinear delta-f gyro-kinetic transport simulation codes to cyclo-kinetics codes by retaining (at least some) higher cyclotron harmonics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Relativistic nonlinear dynamics of an intense laser beam propagating in a hot electron-positron magnetoactive plasma

The present study is devoted to investigation of the nonlinear dynamics of an intense laser beam interacting with a hot magnetized electron-positron plasma. Propagation of the intense circularly polarized laser beam along an external magnetic field is studied using a relativistic two-fluid model. A modified nonlinear Schrödinger equation is derived based on the quasi-neutral approximation, which is valid for hot plasma. Light envelope solitary waves and modulation instability are studied, for one-dimensional case. Using a three-dimensional model, spatial-temporal development of laser pulse is investigated. Occurrence of some nonlinear phenomena such as self-focusing, self-modulation, light trapping, and filamentation of laser pulse is discussed. Also the effect of external magnetic field and plasma temperature on the nonlinear evolution of these phenomena is studied.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Simulation of linear and nonlinear Landau damping of lower hybrid waves

The linear physics of lower hybrid waves (LHWs) and their nonlinear interaction with particles through Landau damping are studied with the gyrokinetic electron and fully kinetic ion (GeFi) particle simulation model in the electrostatic limit. Unlike most other wave modes, the LHWs can resonantly interact with both electrons and ions, with the former being highly magnetized and latter nearly unmagnetized around the lower hybrid frequency. Direct interactions of LHWs with electrons and/or ions are investigated for cases with various k{sub ∥}/k,T{sub i}/T{sub e}, and wave amplitudes. In the linear electron Landau damping (ELD), the dispersion relation and the linear damping rate obtained from our simulation agree well with the analytical linear theory. As the wave amplitude increases, the nonlinear Landau effects are present, and a transition from strong decay at smaller amplitudes to weak decay at larger amplitudes is observed. In the nonlinear stage, the LHWs in the long time evolution finally exhibit a steady Bernstein-Greene-Kruskal mode, in which the wave amplitude is saturated above the noise level. While the resonant electrons are trapped in the wave field in the nonlinear ELD, the resonant ions are untrapped in the LHW time scales. The ion Landau damping is thus predominantly in a linear fashion, leading to a wave saturation level significantly lower than that in the ELD. On the long time scales, however, the ions are still weakly trapped. The results show a coupling between the LHW frequency and the ion cyclotron frequency during the long-time LHW evolution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Nonlinear scattering term in the gyrokinetic Vlasov equation

Nonlinear scattering term is found from the nonlinear gyrokinetic equation by decoupling the perturbed gyrocenter motion from the unperturbed motion. The gyro-center distribution function is determined by the well-understood unperturbed motion, with the effects of fields perturbation included in the nonlinear scattering term, which explicitly reveals the nonlinear stochastic dissipation on the time scale longer than the wave correlation time.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Phase mixing and nonlinearity in geodesic acoustic modes

Phase mixing and nonlinear resonance detuning of geodesic acoustic modes in a tokamak plasma are examined. Geodesic acoustic modes (GAMs) are tokamak normal modes with oscillations in poloidal flow constrained to lie within flux surfaces. The mode frequency is sonic, dependent on the local flux surface temperature. Consequently, mode oscillations between flux surfaces get rapidly out of phase, resulting in enhanced damping from the phase mixing. Damping rates are shown to scale as the negative 1/3 power of the large viscous Reynolds number. The effect of convective nonlinearities on the normal modes is also studied. The system of nonlinear GAM equations is shown to resemble the Duffing oscillator, which predicts resonance detuning of the oscillator. Resonant amplification is shown to be suppressed nonlinearly. All analyses are verified by numerical simulation. The findings are applied to a recently proposed GAM excitation experiment on the DIII-D tokamak.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Nonlinear interaction of proton whistler with kinetic Alfvén wave to study solar wind turbulence

This paper presents the nonlinear interaction between small but finite amplitude kinetic Alfvén wave (KAW) and proton whistler wave using two-fluid model in intermediate beta plasma, applicable to solar wind. The nonlinearity is introduced by modification in the background density. This change in density is attributed to the nonlinear ponderomotive force due to KAW. The solutions of the model equations, governing the nonlinear interaction (and its effect on the formation of localized structures), have been obtained using semi-analytical method in solar wind at 1AU. It is concluded that the KAW properties significantly affect the threshold field required for the filament formation and their critical size (for proton whistler). The magnetic and electric field power spectra have been obtained and their relevance with the recent observations of solar wind turbulence by Cluster spacecraft has been pointed out.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Nonlinear multiferroic phase shifters for microwave frequencies

A nonlinear microwave phase shifter based on a planar multiferroic composite has been studied. The multiferroic structure is fabricated in the form of a bilayer consisting of yttrium iron garnet and barium strontium titanate. The principle of operation of the device is based on the linear and nonlinear control of the phase shift of the hybrid spin-electromagnetic waves propagating in the bilayer. The linear control is realized with magnetic and electric fields. The nonlinear control is provided by the input power of microwave signal. The device showed a nonlinear phase shift up to 250°, electric field induced phase shift up to 330°, and magnetic field induced phase shift of more than 180°.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Effects of obliqueness and strong electrostatic interaction on linear and nonlinear propagation of dust-acoustic waves in a magnetized strongly coupled dusty plasma

Linear and nonlinear propagation of dust-acoustic waves in a magnetized strongly coupled dusty plasma is theoretically investigated. The normal mode analysis (reductive perturbation method) is employed to investigate the role of ambient/external magnetic field, obliqueness, and effective electrostatic dust-temperature in modifying the properties of linear (nonlinear) dust-acoustic waves propagating in such a strongly coupled dusty plasma. The effective electrostatic dust-temperature, which arises from strong electrostatic interactions among highly charged dust, is considered as a dynamical variable. The linear dispersion relation (describing the linear propagation characteristics) for the obliquely propagating dust-acoustic waves is derived and analyzed. On the other hand, the Korteweg-de Vries equation describing the nonlinear propagation of the dust-acoustic waves (particularly, propagation of dust-acoustic solitary waves) is derived and solved. It is shown that the combined effects of obliqueness, magnitude of the ambient/external magnetic field, and effective electrostatic dust-temperature significantly modify the basic properties of linear and nonlinear dust-acoustic waves. The results of this work are compared with those observed by some laboratory experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Maskless direct laser writing with visible light: Breaking through the optical resolving limit with cooperative manipulations of nonlinear reverse saturation absorption and thermal diffusion

In this work, the resolving limit of maskless direct laser writing is overcome by cooperative manipulation from nonlinear reverse saturation absorption and thermal diffusion, where the nonlinear reverse saturation absorption can induce the formation of below diffraction-limited energy absorption spot, and the thermal diffusion manipulation can make the heat quantity at the central region of energy absorption spot propagate along the thin film thickness direction. The temperature at the central region of energy absorption spot transiently reaches up to melting point and realizes nanolithography. The sample “glass substrate/AgInSbTe” is prepared, where AgInSbTe is taken as nonlinear reverse saturation absorption thin film. The below diffraction-limited energy absorption spot is simulated theoretically and verified experimentally by near-field spot scanning method. The “glass substrate/Al/AgInSbTe” sample is prepared, where the Al is used as thermal conductive layer to manipulate the thermal diffusion channel because the thermal diffusivity coefficient of Al is much larger than that of AgInSbTe. The direct laser writing is conducted by a setup with a laser wavelength of 650 nm and a converging lens of NA=0.85, the lithographic marks with a size of about 100 nm are obtained, and the size is only about 1/10 the incident focused spot. The experimental results indicate that the cooperative manipulation from nonlinear reverse saturation absorption and thermal diffusion is a good method to realize nanolithography in maskless direct laser writing with visible light.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Effects, determination, and correction of count rate nonlinearity in multi-channel analog electron detectors

Detector counting rate nonlinearity, though a known problem, is commonly ignored in the analysis of angle resolved photoemission spectroscopy where modern multichannel electron detection schemes using analog intensity scales are used. We focus on a nearly ubiquitous “inverse saturation” nonlinearity that makes the spectra falsely sharp and beautiful. These artificially enhanced spectra limit accurate quantitative analysis of the data, leading to mistaken spectral weights, Fermi energies, and peak widths. We present a method to rapidly detect and correct for this nonlinearity. This algorithm could be applicable for a wide range of nonlinear systems, beyond photoemission spectroscopy.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗