Search NASA⌕ Search

SEARCH · Search NASA

Results for “analytic solution”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 973 records · Page 54

Interaction of a quantum well with squeezed light: Quantum-statistical properties

We investigate the quantum statistical properties of the light emitted by a quantum well interacting with squeezed light from a degenerate subthreshold optical parametric oscillator. We obtain analytical solutions for the pertinent quantum Langevin equations in the strong-coupling and low-excitation regimes. Using these solutions we calculate the intensity spectrum, autocorrelation function, and quadrature squeezing for the fluorescent light. We show that the fluorescent light exhibits bunching and quadrature squeezing. We also show that the squeezed light leads to narrowing of the width of the spectrum of the fluorescent light.

74 ATOMIC AND MOLECULAR PHYSICS↗

Radial acceleration of ions by a laser pulse in a plasma channel

The approximate analytic solution of the Cauchy problem is constructed for a system of kinetic equations of an electron–ion plasma that describe the acceleration of ions and the collisionless heating of electrons caused by the radial ponderomotive force of a laser beam that propagates in the transparent plasma of a gas or other low-density target. Under conditions where the Debye radius, r{sub De}, of the electrons is considerably smaller than the characteristic localization scale, L, of the laser beam along the radius, ε = r{sub De}/L ≪ 1, this solution is found by a group transformation that is specified by the operator of approximate renormalization-group symmetries over small parameters, ε and μ = √(Zm/M), of the initial distribution functions of particles. For an axially symmetric geometry of the laser beam, the temporal and spatial dependences of the distribution functions of particles are obtained and their integral characteristics, such as the density, mean velocity, temperature, and energy spectrum, are found. The formation of a cylindrical density cusp and the localized heating of electrons at the laser-channel boundary are analytically described.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Covariant worldline numerics for charge motion with radiation reaction

We develop a numerical formulation to calculate the classical motion of charges in strong electromagnetic fields, such as those occurring in high-intensity laser beams. By reformulating the dynamics in terms of SL(2,C) matrices representing the Lorentz group, our formulation maintains explicit covariance, in particular, the mass-shell condition. Considering an electromagnetic plane wave field where the analytic solution is known as a test case, we demonstrate the effectiveness of the method for solving both the Lorentz force and the Landau-Lifshitz equations. The latter, a second order reduction of the Lorentz-Abraham-Dirac equation, describes radiation reaction without the usual pathologies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Dynamics of ponderomotive ion acceleration in a laser-plasma channel

Analytical solution to the Cauchy problem for the kinetic equation describing the radial acceleration of ions under the action of the ponderomotive force of a laser beam undergoing guided propagation in transparent plasma is constructed. Spatial and temporal dependences of the ion distribution function and the integral ion characteristics, such as the density, average velocity, and energy spectrum, are obtained for an axisymmetric laser-plasma channel. The formation of a density peak near the channel boundary and the effect of ion flow breaking for a quasi-stationary laser beam are described analytically.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

LUKEWARM DARK MATTER: BOSE CONDENSATION OF ULTRALIGHT PARTICLES

We discuss the thermal evolution and Bose-Einstein condensation of ultralight dark matter particles at finite, realistic cosmological temperatures. We find that if these particles decouple from regular matter before Standard Model particles annihilate, their temperature will be about 0.9 K. This temperature is substantially lower than the temperature of cosmic microwave background neutrinos and thus big bang nucleosynthesis remains unaffected. In addition, the temperature is consistent with WMAP 7-year+BAO+H0 observations without fine-tuning. We focus on particles of mass of m {approx} 10{sup -23} eV, which have Compton wavelength of galactic scales. Agglomerations of these particles can form stable halos and naturally prohibit small-scale structure. They avoid over-abundance of dwarf galaxies and may be favored by observations of dark matter distributions. We present numerical as well as approximate analytical solutions of the Friedmann-Klein-Gordon equations and study the cosmological evolution of this scalar field dark matter from the early universe to the era of matter domination. Today, the particles in the ground state mimic pressureless matter, while the excited state particles are radiation like.

79 ASTRONOMY AND ASTROPHYSICS↗

Dissipative MHD solutions for resonant Alfven waves in 1-dimensional magnetic flux tubes

The present paper extends the analysis by Sakurai, Goossens, and Hollweg (1991) on resonant Alfven waves in nonuniform magnetic flux tubes. It proves that the fundamental conservation law for resonant Alfven waves found in ideal MHD by Sakurai, Goossens, and Hollweg remains valid in dissipative MHD. This guarantees that the jump conditions of Sakurai, Goossens, and Hollweg, that connect the ideal MHD solutions for xi(sub r), and P' across the dissipative layer, are correct. In addition, the present paper replaces the complicated dissipative MHD solutions obtained by Sakurai, Goossens, and Hollweg for xi(sub r), and P' in terms of double integrals of Hankel functions of complex argument of order 1/3 with compact analytical solutions that allow a straight- forward mathematical and physical interpretation. Finally, it presents an analytical dissipative MHD solution for the component of the Lagrangian displacement in the magnetic surfaces perpen- dicular to the magnetic field lines xi(sub perpendicular) which enables us to determine the dominant dynamics of resonant Alfven waves in dissipative MHD.

Goossens, Marcel↗

Diagnostics principle of microwave cut-off probe for measuring absolute electron density

A generalized diagnostics principle of microwave cut-off probe is presented with a full analytical solution. In previous studies on the microwave cut-off measurement of weakly ionized plasmas, the cut-off frequency ω{sub c} of a given electron density is assumed to be equal to the plasma frequency ω{sub p} and is predicted using electromagnetic simulation or electric circuit model analysis. However, for specific plasma conditions such as highly collisional plasma and a very narrow probe tip gap, it has been found that ω{sub c} and ω{sub p} are not equal. To resolve this problem, a generalized diagnostics principle is proposed by analytically solving the microwave cut-off condition Re[ε{sub r,eff}(ω = ω{sub c})] = 0. In addition, characteristics of the microwave cut-off condition are theoretically tested for correct measurement of the absolute electron density.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

EXACT SOLUTION TO FINITE TEMPERATURE SFDM: NATURAL CORES WITHOUT FEEDBACK

Recent high-quality observations of low surface brightness (LSB) galaxies have shown that their dark matter (DM) halos prefer flat central density profiles. However, the standard cold dark matter model simulations predict a more cuspy behavior. One mechanism used to reconcile the simulations with the observed data is the feedback from star formation. While this mechanism may be successful in isolated dwarf galaxies, its success in LSB galaxies remains unclear. Additionally, the inclusion of too much feedback in the simulations is a double-edged sword-in order to obtain a cored DM distribution from an initially cuspy one, the feedback recipes usually require one to remove a large quantity of baryons from the center of the galaxies; however, some feedback recipes produce twice the number of satellite galaxies of a given luminosity and with much smaller mass-to-light ratios from those that are observed. Therefore, one DM profile that produces cores naturally and that does not require large amounts of feedback would be preferable. We find both requirements to be satisfied in the scalar field dark matter model. Here, we consider that DM is an auto-interacting real scalar field in a thermal bath at temperature T with an initial Z {sub 2} symmetric potential. As the universe expands, the temperature drops so that the Z {sub 2} symmetry is spontaneously broken and the field rolls down to a new minimum. We give an exact analytic solution to the Newtonian limit of this system, showing that it can satisfy the two desired requirements and that the rotation curve profile is no longer universal.

79 ASTRONOMY AND ASTROPHYSICS↗

FIRST THREE-DIMENSIONAL RECONSTRUCTIONS OF CORONAL LOOPS WITH THE STEREO A+B SPACECRAFT. IV. MAGNETIC MODELING WITH TWISTED FORCE-FREE FIELDS

The three-dimensional coordinates of stereoscopically triangulated loops provide strong constraints for magnetic field models of active regions in the solar corona. Here, we use STEREO/A and B data from some 500 stereoscopically triangulated loops observed in four active regions (2007 April 30, May 9, May 19, and December 11), together with SOHO/MDI line-of-sight magnetograms. We measure the average misalignment angle between the stereoscopic loops and theoretical magnetic field models, finding a mismatch of {mu} = 19 Degree-Sign -46 Degree-Sign for a potential field model, which is reduced to {mu} 14 Degree-Sign -19 Degree-Sign for a non-potential field model parameterized by twist parameters. The residual error is commensurable with stereoscopic measurement errors ({mu}{sub SE} Almost-Equal-To 8 Degree-Sign -12 Degree-Sign ). We developed a potential field code that deconvolves a line-of-sight magnetogram into three magnetic field components (B{sub x} , B{sub y} , B{sub z} ), as well as a non-potential field forward-fitting code that determines the full length of twisted loops (L Almost-Equal-To 50-300 Mm), the number of twist turns (median N{sub twist} = 0.06), the nonlinear force-free {alpha}-parameter (median {alpha} Almost-Equal-To 4 Multiplication-Sign 10{sup -11} cm{sup -1}), and the current density (median j{sub z} Almost-Equal-To 1500 Mx cm{sup -2} s{sup -1}). All twisted loops are found to be far below the critical value for kink instability, and Joule dissipation of their currents is found to be far below the coronal heating requirement. The algorithm developed here, based on an analytical solution of nonlinear force-free fields that is accurate to second order (in the force-free parameter {alpha}), represents the first code that enables fast forward fitting to photospheric magnetograms and stereoscopically triangulated loops in the solar corona.

79 ASTRONOMY AND ASTROPHYSICS↗

Generation of discrete scattering cross sections and demonstration of Monte Carlo charged particle transport in the Milagro IMC code package

A new method for generating discrete scattering cross sections to be used in charged particle transport calculations is investigated. The method of data generation is presented and compared to current methods for obtaining discrete cross sections. The new, more generalized approach allows greater flexibility in choosing a cross section model from which to derive discrete values. Cross section data generated with the new method is verified through a comparison with discrete data obtained with an existing method. Additionally, a charged particle transport capability is demonstrated in the time-dependent Implicit Monte Carlo radiative transfer code package, Milagro. The implementation of this capability is verified using test problems with analytic solutions as well as a comparison of electron dose-depth profiles calculated with Milagro and an already-established electron transport code. An initial investigation of a preliminary integration of the discrete cross section generation method with the new charged particle transport capability in Milagro is also presented. (authors)

97 MATHEMATICS AND COMPUTING↗

Dissipative solitons in pair-ion plasmas

The effects of ion-neutral collisions on the dynamics of the nonlinear ion acoustic wave in pair-ion plasma are investigated. The standard perturbative approach leads to a Korteweg-de Vries equation with a linear damping term for the dynamics of the finite amplitude wave. The ion-neutral collision induced dissipation is responsible for the linear damping. The analytical solution and numerical simulation reveal that the nonlinear wave propagates in the form of a weakly dissipative compressive solitons. Furthermore, the width of the soliton is proportional to the amplitude of the wave for fixed soliton velocity. Results are discussed in the context of the fullerene pair-ion plasma experiment.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A Nth-order linear algorithm for extracting diffuse correlation spectroscopy blood flow indices in heterogeneous tissues

Conventional semi-infinite analytical solutions of correlation diffusion equation may lead to errors when calculating blood flow index (BFI) from diffuse correlation spectroscopy (DCS) measurements in tissues with irregular geometries. Very recently, we created an algorithm integrating a Nth-order linear model of autocorrelation function with the Monte Carlo simulation of photon migrations in homogenous tissues with arbitrary geometries for extraction of BFI (i.e., αD{sub B}). The purpose of this study is to extend the capability of the Nth-order linear algorithm for extracting BFI in heterogeneous tissues with arbitrary geometries. The previous linear algorithm was modified to extract BFIs in different types of tissues simultaneously through utilizing DCS data at multiple source-detector separations. We compared the proposed linear algorithm with the semi-infinite homogenous solution in a computer model of adult head with heterogeneous tissue layers of scalp, skull, cerebrospinal fluid, and brain. To test the capability of the linear algorithm for extracting relative changes of cerebral blood flow (rCBF) in deep brain, we assigned ten levels of αD{sub B} in the brain layer with a step decrement of 10% while maintaining αD{sub B} values constant in other layers. Simulation results demonstrate the accuracy (errors < 3%) of high-order (N ≥ 5) linear algorithm in extracting BFIs in different tissue layers and rCBF in deep brain. By contrast, the semi-infinite homogenous solution resulted in substantial errors in rCBF (34.5% ≤ errors ≤ 60.2%) and BFIs in different layers. The Nth-order linear model simplifies data analysis, thus allowing for online data processing and displaying. Future study will test this linear algorithm in heterogeneous tissues with different levels of blood flow variations and noises.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

SELF-GRAVITATIONAL FORCE CALCULATION OF SECOND-ORDER ACCURACY FOR INFINITESIMALLY THIN GASEOUS DISKS IN POLAR COORDINATES

Investigating the evolution of disk galaxies and the dynamics of proto-stellar disks can involve the use of both a hydrodynamical and a Poisson solver. These systems are usually approximated as infinitesimally thin disks using two-dimensional Cartesian or polar coordinates. In Cartesian coordinates, the calculations of the hydrodynamics and self-gravitational forces are relatively straightforward for attaining second-order accuracy. However, in polar coordinates, a second-order calculation of self-gravitational forces is required for matching the second-order accuracy of hydrodynamical schemes. We present a direct algorithm for calculating self-gravitational forces with second-order accuracy without artificial boundary conditions. The Poisson integral in polar coordinates is expressed in a convolution form and the corresponding numerical complexity is nearly linear using a fast Fourier transform. Examples with analytic solutions are used to verify that the truncated error of this algorithm is of second order. The kernel integral around the singularity is applied to modify the particle method. The use of a softening length is avoided and the accuracy of the particle method is significantly improved.

79 ASTRONOMY AND ASTROPHYSICS↗

Dynamics of charge carriers at the place of the formation of a muonic atom in diamond and silicon

The space-time distribution of charge carriers at the place of the location of a muonic atom formed when a negative muon is captured by an atom of the lattice has been numerically simulated taking into account the self-consistent electric field. The results of {mu}SR experiments with negative muons in diamond crystals have been explained and reasons for the difference in the behavior of the spin polarization of the negative muon in boron-doped diamond and in silicon have been revealed. The condition of the validity of the analytical solution of this problem has been obtained. It has been shown that the muonic atom in diamond, in contrast to silicon, does not form a neutral acceptor center in the paramagnetic state during the muon experiment and remains in the diamagnetic state of a positive ion.

74 ATOMIC AND MOLECULAR PHYSICS↗

Diffusion-assisted selective dynamical recoupling: A new approach to measure background gradients in magnetic resonance

Dynamical decoupling, a generalization of the original NMR spin-echo sequence, is becoming increasingly relevant as a tool for reducing decoherence in quantum systems. Such sequences apply non-equidistant refocusing pulses for optimizing the coupling between systems, and environmental fluctuations characterized by a given noise spectrum. One such sequence, dubbed Selective Dynamical Recoupling (SDR) [P. E. S. Smith, G. Bensky, G. A. Álvarez, G. Kurizki, and L. Frydman, Proc. Natl. Acad. Sci. 109, 5958 (2012)], allows one to coherently reintroduce diffusion decoherence effects driven by fluctuations arising from restricted molecular diffusion [G. A. Álvarez, N. Shemesh, and L. Frydman, Phys. Rev. Lett. 111, 080404 (2013)]. The fully-refocused, constant-time, and constant-number-of-pulses nature of SDR also allows one to filter out “intrinsic” T{sub 1} and T{sub 2} weightings, as well as pulse errors acting as additional sources of decoherence. This article explores such features when the fluctuations are now driven by unrestricted molecular diffusion. In particular, we show that diffusion-driven SDR can be exploited to investigate the decoherence arising from the frequency fluctuations imposed by internal gradients. As a result, SDR presents a unique way of probing and characterizing these internal magnetic fields, given an a priori known free diffusion coefficient. This has important implications in studies of structured systems, including porous media and live tissues, where the internal gradients may serve as fingerprints for the system's composition or structure. The principles of this method, along with full analytical solutions for the unrestricted diffusion-driven modulation of the SDR signal, are presented. The potential of this approach is demonstrated with the generation of a novel source of MRI contrast, based on the background gradients active in an ex vivo mouse brain. Additional features and limitations of this new method are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Two critical issues in Langevin simulation of gas flows

A stochastic algorithm based on the Langevin equation has been recently proposed to simulate rarefied gas flows. Compared with the direct simulation Monte Carlo (DSMC) method, the Langevin method is more efficient in simulating small Knudsen number flows. While it is well-known that the cell sizes and time steps should be smaller than the mean free path and the mean collision time, respectively, in DSMC simulations, the Langevin equation uses a drift term and a diffusion term to describe molecule movements, so no direct molecular collisions have to be modeled. This enables the Langevin simulation to proceed with a much larger time step than that in the DSMC method. Two critical issues in Langevin simulation are addressed in this paper. The first issue is how to reproduce the transport properties as that described by kinetic theory. Transport coefficients predicted by Langevin equation are obtained by using Green-Kubo formulae. The second issue is numerical scheme with boundary conditions. We present two schemes corresponding to small time step and large time step, respectively. For small time step, the scheme is similar to DSMC method as the update of positions and velocities are uncoupled; for large time step, we present an analytical solution of the hitting time, which is the crucial factor for accurate simulation. Velocity-Couette flow, thermal-Couette flow, Rayleigh-Bénard flow and wall-confined problem are simulated by using these two schemes. Our study shows that Langevin simulation is a promising tool to investigate small Knudsen number flows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

High harmonic generation in underdense plasmas by intense laser pulses with orbital angular momentum

We study high harmonic generation produced by twisted laser pulses, with orbital angular momentum in the relativistic regime, for pulse propagation in underdense plasma. We consider fast time scale processes associated with an ultra-short pulse, where the ion motion can be neglected. We use both analytical models and numerical simulations using a relativistic particle-in-cell code. The present description is valid for relativistic laser intensities, when the normalized field amplitude is much larger than one, a ≫ 1. We also discuss two distinct processes associated with linear and circular polarization. Using both analytical solutions and particle-in-cell simulations, we are able to show that, for laser pulses in a well defined Laguerre-Gauss mode, angular momentum conservation is observed during the process of harmonic generation. Intensity modulation of the harmonic spectrum is also verified, as imposed by the nonlinear time-scale for energy transfer between different harmonics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗