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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.

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At least 901 records · Page 50
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Qualitative analysis of magnetic waveguides for two-dimensional Dirac fermions

We focus on the confinement of two-dimensional Dirac fermions within the waveguides created by realistic magnetic fields. Understanding of their band structure is of our main concern. We provide easily applicable criteria, mostly depending only on the asymptotic behavior of the magnetic field, that can guarantee existence or absence of the energy bands and provide valuable insight into the systems where analytical solution is impossible. The general results are employed in specific systems where the waveguide is created by the magnetic field of a set of electric wires or magnetized strips.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

Low-frequency fluid waves in fractures and pipes

Low-frequency analytical solutions have been obtained for phase velocities of symmetrical fluid waves within both an infinite fracture and a pipe filled with a viscous fluid. Three different fluid wave regimes can exist in such objects, depending on the various combinations of parameters, such as fluid density, fluid viscosity, walls shear modulus, channel thickness, and frequency. Equations for velocities of all these regimes have explicit forms and are verified by comparisons with the exact solutions. The dominant role of fractures in rock permeability at field scales and the strong amplitude and frequency effects of Stoneley guided waves suggest the importance of including these wave effects into poroelastic theories.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

Stable static structures in models with higher-order derivatives

We investigate the presence of static solutions in generalized models described by a real scalar field in four-dimensional space–time. We study models in which the scalar field engenders higher-order derivatives and spontaneous symmetry breaking, inducing the presence of domain walls. Despite the presence of higher-order derivatives, the models keep to equations of motion second-order differential equations, so we focus on the presence of first-order equations that help us to obtain analytical solutions and investigate linear stability on general grounds. We then illustrate the general results with some specific examples, showing that the domain wall may become compact and that the zero mode may split. Moreover, if the model is further generalized to include k-field behavior, it may contribute to split the static structure itself.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Nonlinear Second Harmonics of Localized Shear Waves in an Anisotropic Layer Between Anisotropic Half Spaces Under the Conditions of Imperfect Contact

We construct a numerical-analytic solution of the problem of generation of the nonlinear second harmonics in the course of propagation of elastic symmetric localized shear waves in the crystalline layer of cubic system of the m3m class located between the crystalline half spaces of the same type and the same class of anisotropy under the conditions of imperfect sliding contact of components of the waveguide. We determine the analytic form of the functions of wave motions for nonlinear anharmonic perturbations in the form of longitudinal-shear-type waves. We also perform the numerical investigations of the amplitude-frequency characteristics of the second harmonics for monochromatic localized waves in a layer of a single crystal of germanium between the half spaces from the single crystal of silicon.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

ON THE EVOLUTION OF THE CO SNOW LINE IN PROTOPLANETARY DISKS

CO is thought to be a vital building block for prebiotic molecules that are necessary for life. Thus, understanding where CO existed in a solid phase within the solar nebula is important for understanding the origin of life. We model the evolution of the CO snow line in a protoplanetary disk. We find that the current observed location of the CO snow line in our solar system, and in the solar system analog TW Hydra, cannot be explained by a fully turbulent disk model. With time-dependent disk models we find that the inclusion of a dead zone (a region of low turbulence) can resolve this problem. Furthermore, we obtain a fully analytic solution for the CO snow line radius for late disk evolutionary times. This will be useful for future observational attempts to characterize the demographics and predict the composition and habitability of exoplanets.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2010

Angular, spectral, and time distributions of highest energy protons and associated secondary gamma rays and neutrinos propagating through extragalactic magnetic and radiation fields

The angular, spectral, and temporal features of the highest energy protons and, accompanying them, secondary neutrinos and synchrotron gamma rays propagating through the intergalactic magnetic and radiation fields are studied using the analytical solutions of the Boltzmann transport equation obtained in the limit of the small-angle and continuous-energy-loss approximation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Nonlinear dynamics of the ion Weibel-filamentation instability: An analytical model for the evolution of the plasma and spectral properties

We present a predictive model of the nonlinear phase of the Weibel instability induced by two symmetric, counter-streaming ion beams in the non-relativistic regime. This self-consistent model combines the quasilinear kinetic theory of Davidson et al. [Phys. Fluids 15, 317 (1972)] with a simple description of current filament coalescence. It allows us to follow the evolution of the ion parameters up to a stage close to complete isotropization, and is thus of prime interest to understand the dynamics of collisionless shock formation. Its predictions are supported by 2-D and 3-D particle-in-cell simulations of the ion Weibel instability. The derived approximate analytical solutions reveal the various dependencies of the ion relaxation to isotropy. In particular, it is found that the influence of the electron screening can affect the results of simulations using an unphysical electron mass.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Theory of magnetohydrodynamic accretion of matter with an ultrahard equation of state onto a black hole

We consider the magnetohydrodynamic theory of spherically symmetric accretion of a perfect fluid onto a Schwarzschild black hole with an ultrahard equation of state, p = μ ∼ ρ{sup 2}, where p is the pressure, μ is the total energy density, and ρ is the fluid density. An approximate analytical solution is written out. We show that one critical sonic surface that coincides with the black hole event horizon is formed instead of two critical surfaces (fast and slow magnetosonic surfaces) for a degenerate ultrahard equation of state of matter.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2010

Efficient Modeling of Laser-Plasma Accelerators with INF and RNO

The numerical modeling code INF and RNO (INtegrated Fluid and paRticle simulatioN cOde, pronounced 'inferno') is presented. INF and RNO is an efficient 2D cylindrical code to model the interaction of a short laser pulse with an underdense plasma. The code is based on an envelope model for the laser while either a PIC or a fluid description can be used for the plasma. The effect of the laser pulse on the plasma is modeled with the time-averaged poderomotive force. These and other features allow for a speedup of 2-4 orders of magnitude compared to standard full PIC simulations while still retaining physical fidelity. The code has been benchmarked against analytical solutions and 3D PIC simulations and here a set of validation tests together with a discussion of the performances are presented.

43 PARTICLE ACCELERATORS↗
DOE OSTI2010

Solvable models and hidden symmetries in QCD

We show that QCD Hamiltonians at low energy exhibit an SU(2) structure, when only few orbital levels are considered. In case many orbital levels are taken into account we also find a semi-analytic solution for the energy levels of the dominant part of the QCD Hamiltonian. The findings are important to propose the structure of phenomenological models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

The universe dominated by oscillating scalar with non-minimal derivative coupling to gravity

We study the expansion law of the universe dominated by the oscillating scalar field with non-minimal derivative coupling to gravity as G{sup μν}∂{sub μ}φ∂{sub ν}φ. In this system the Hubble parameter oscillates with a frequency of the effective mass of the scalar field, which formerly caused a difficulty in analyzing how the universe expands. We find an analytical solution for power law potentials and interpret the solution in an intuitive way by using a new invariant of the system. As a result, we find marginally accelerated expansion for the quadratic potential and no accelerated expansion for the potential with higher power.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

Non-Markovian decay and dynamics of decoherence in private and public environments

We study the decay process in an open system, emphasizing the relevance of the environment's spectral structure. Non-Markovian effects are included to quantitatively analyze the degradation rate of the coherent evolution. The way in which a two-level system is coupled to different environments is specifically addressed: multiple connections to a single bath (public environment) or single connections to multiple baths (private environments). We numerically evaluate the decay rate of a local excitation by using the survival probability and the Loschmidt echo. These rates are compared to analytical results obtained from the standard Fermi golden rule (FGR) in wide band approximation, and a self-consistent evaluation that accounts for the bath's memory in cases where an exact analytical solution is possible. We observe that the correlations appearing in a public bath introduce further deviations from the FGR as compared with a private bath.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Methodology, verification, and performance of the continuous-energy nuclear data sensitivity capability in MCNP6

A continuous-energy sensitivity coefficient capability has been introduced into MCNP6. The methods for generating energy-resolved and energy-integrated sensitivity profiles are discussed. Results from the verification exercises that were performed are given, and these show that MCNP6 compares favorably with analytic solutions, direct density perturbations, and comparisons to TSUNAMI-3D and MONK. Run-time and memory requirements are assessed for typical applications, and these are shown to be reasonable with modern computing resources. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Relativistic plasma expansion with Maxwell-Juettner distribution

A self-similar analytical solution is proposed to describe the relativistic ion acceleration with the local Maxwell-Juettner relativistic distribution electrons. It is an alternative to the existing static model [M. Passoni and M. Lontano, Phys. Rev. Lett. 101, 115001 (2008)], which exploits a limited solution for the acceleration potential. With our model, the potential is finite naturally and has an upper limitation proportional to the square root of the electron temperature. The divergent potential in the non-relativistic case is the linear items of the Taylor expansion of that obtained relativistic one here. The energy distribution of ions and the dependence of the ion momentum on the acceleration time are obtained analytically. Maximum ion energy has an upper limitation decided by the finite potential difference. In the ultra-relativistic region, the ion energy at the ion front is proportional to t{sup 4/5} and the energy of the ions behind the ion front is proportional to t{sup 2/3} since the field there is shielded by the ions beyond them and the field at the ion front is the most intense.

43 PARTICLE ACCELERATORS↗
DOE OSTI2013

Unified one-dimensional model of bounded plasma with nonzero ion temperature in a broad pressure range

A one-dimensional model for steady state plasmas bounded either between large parallel walls, or by a cylinder or a sphere, valid in a wide range of gas pressures, is considered. The model includes nonzero ion temperature, inertial terms in the ion momentum equations, and allows one to calculate the plasma electron temperature and ion current density reaching the wall, as well as the spatial distributions of the ion fluid velocity, plasma density, and plasma potential in the plasma bulk. In addition, the effect of electron inertia is analyzed. The model includes as particular cases several earlier models that were based on a similar set of differential equations, but that are restricted to a specific pressure regime (low, intermediate, or high). Analytical solution is found in planar geometry, and numerical solution is given in cylindrical and spherical geometry. The results obtained are compared with those of earlier models and the differences are analyzed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Quantum rings of non-uniform thickness in magnetic field

We consider a model of crater-shaped quantum dot in form of a thin layer whose thickness linearly increases with the distance from the axis. We show that one-particle wave equation for the electron confined in such structure can be completely separated in the adiabatic limit when the quantum dot thickness is much smaller than its lateral dimension. Analytical solutions found for this model has been used as base functions for analysing the effect of non-homogeneity on the electronic spectrum in the framework of the exact diagonalization method.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2018

Nonlinear Dynamics of Parametric Oscillations of Polaritons in a Microcavity

The dynamics of polaritons in a microcavity in the parametric oscillator mode, when two pump polaritons turn into the signal and idler polaritons and vice versa, has been studied. The pumping is carried out using two lasers with close frequencies. Analytical solutions of the system of nonlinear differential equations have been obtained. The periodic and aperiodic modes of the transformation of a pair of pump polaritons into signal and idler polaritons have been found.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Nonlinear relativistic plasma resonance: Renormalization group approach

An analytical solution to the nonlinear set of equations describing the electron dynamics and electric field structure in the vicinity of the critical density in a nonuniform plasma is constructed using the renormalization group approach with allowance for relativistic effects of electron motion. It is demonstrated that the obtained solution describes two regimes of plasma oscillations in the vicinity of the plasma resonance— stationary and nonstationary. For the stationary regime, the spatiotemporal and spectral characteristics of the resonantly enhanced electric field are investigated in detail and the effect of the relativistic nonlinearity on the spatial localization of the energy of the plasma relativistic field is considered. The applicability limits of the obtained solution, which are determined by the conditions of plasma wave breaking in the vicinity of the resonance, are established and analyzed in detail for typical laser and plasma parameters. The applicability limits of the earlier developed nonrelativistic theories are refined.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗