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At least 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Semi-Analytical Benchmarks for MCNP6

Code verification is an extremely important process that involves proving or disproving the validity of code algorithms by comparing them against analytical results of the underlying physics or mathematical theory on which the code is based. Monte Carlo codes such as MCNP6 must undergo verification and testing upon every release to ensure that the codes are properly simulating nature. Specifically, MCNP6 has multiple sets of problems with known analytic solutions that are used for code verification. Monte Carlo codes primarily specify either current boundary sources or a volumetric fixed source, either of which can be very complicated functions of space, energy, direction and time. Thus, most of the challenges with modeling analytic benchmark problems in Monte Carlo codes come from identifying the correct source definition to properly simulate the correct boundary conditions. The problems included in this suite all deal with mono-energetic neutron transport without energy loss, in a homogeneous material. The variables that differ between the problems are source type (isotropic/beam), medium dimensionality (infinite/semi-infinite), etc.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Towards developing a compact model for magnetization switching in straintronics magnetic random access memory devices

Strain-mediated magnetization switching in a magnetic tunneling junction (MTJ) by exploiting a combination of piezoelectricity and magnetostriction has been proposed as an energy efficient alternative to spin transfer torque (STT) and field induced magnetization switching methods in MTJ-based magnetic random access memories (MRAM). Theoretical studies have shown the inherent advantages of strain-assisted switching, and the dynamic response of the magnetization has been modeled using the Landau-Lifshitz-Gilbert (LLG) equation. However, an attempt to use LLG for simulating dynamics of individual elements in large-scale simulations of multi-megabyte straintronics MRAM leads to extremely time-consuming calculations. Hence, a compact analytical solution, predicting the flipping delay of the magnetization vector in the nanomagnet under stress, combined with a liberal approximation of the LLG dynamics in the straintronics MTJ, can lead to a simplified model of the device suited for fast large-scale simulations of multi-megabyte straintronics MRAMs. In this work, a tensor-based approach is developed to study the dynamic behavior of the stressed nanomagnet. First, using the developed method, the effect of stress on the switching behavior of the magnetization is investigated to realize the margins between the underdamped and overdamped regimes. The latter helps the designer realize the oscillatory behavior of the magnetization when settling along the minor axis, and the dependency of oscillations on the stress level and the damping factor. Next, a theoretical model to predict the flipping delay of the magnetization vector is developed and tested against LLG-based numerical simulations to confirm the accuracy of findings. Lastly, the obtained delay is incorporated into the approximate solutions of the LLG dynamics, in order to create a compact model to liberally and quickly simulate the magnetization dynamics of the MTJ under stress. Using the developed delay equation, the efficiency of the straintronics switching over the STT method is highlighted by analytically investigating the energy-delay trade-off of both methodologies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

An Analytical Model for the Evolution of the Protoplanetary Disks

We obtain a new set of analytical solutions for the evolution of a self-gravitating accretion disk by holding the Toomre parameter close to its threshold and obtaining the stress parameter from the cooling rate. In agreement with the previous numerical solutions, furthermore, the accretion rate is assumed to be independent of the disk radius. Extreme situations where the entire disk is either optically thick or optically thin are studied independently, and the obtained solutions can be used for exploring the early or the final phases of a protoplanetary disk evolution. Our solutions exhibit decay of the accretion rate as a power-law function of the age of the system, with exponents −0.75 and −1.04 for optically thick and thin cases, respectively. Our calculations permit us to explore the evolution of the snow line analytically. The location of the snow line in the optically thick regime evolves as a power-law function of time with the exponent −0.16; however, when the disk is optically thin, the location of the snow line as a function of time with the exponent −0.7 has a stronger dependence on time. This means that in an optically thin disk inward migration of the snow line is faster than an optically thick disk.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Heavy mesons spectra in a semi-analytical quantum relativistic approach

The obtaining of bound states of heavy and light quarks interacting via a static quark potential is revisited here. We present an approach that both approximate the relativistic wave equation and allows the obtaining of analytical solutions and binding energies (and consequently, the heavy mesons spectra) of the system.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2010

Algorithm for Computation of Electromagnetic Fields of An Accelerated Short Bunch Inside a Rectangular Chamber

We discuss the feasibility of an application of an implicit finite-difference approximation to calculate the fields of a relativistic bunch moving with no restriction inside a vacuum chamber. We assume that a bunch trajectory is not straight but is inside a vacuum chamber or its branch. The bunch can be deflected by the fields of bending magnets. The bunch can be short enough to produce coherent synchrotron radiation (CSR). Accelerator physicists believe that electromagnetic phenomena of charged beams are governed by Maxwell's equations together with Newton's equations for particle dynamics. To understand the behavior of the beams and radiated fields we just need to find a solution to these equations for the case, which can fully describe the real accelerator environment. So, at first we make a model, which contains all the necessary components, but at the same time can be easily 'inserts' into the equations. Sometimes, it is possible to find analytical solutions, but usually they are only work for one-dimensional cases and rarer for two-dimension cases. To find a solution in general we may transform the equations into a equivalent finite-difference form and solve them using computers. We can find a lot of finite-difference schemes, which approximate Maxwell's equations since the first one that was published in 1966. Most of them are so called explicit schemes. That means that the value of the field at the new time step is calculated only by the field values at the previous time step. Stability conditions for these schemes do not allow a time step to be greater than or equal to a space (mesh) step. This limitation brings an additional troublesome effect for short wavelengths compared a mesh step. We state that this effect works like a frequency dispersion media, which is 'hidden' in the finite-difference equation.

43 PARTICLE ACCELERATORS↗
DOE OSTI2010

Three-body problem in heteronuclear mixtures with resonant interspecies interaction

We use the zero-range approximation to study a system of two identical bosons interacting resonantly with a third particle. The method is derived from effective field theory. It reduces the three-body problem to an integral equation which we then solve numerically. We also develop an alternative approach which gives analytic solutions of the integral equation in coordinate representation in the limit of vanishing total energy. The atom-dimer scattering length, the rates of atom-dimer relaxation, and the three-body recombination to shallow and to deep molecular states are calculated either analytically or numerically with a well-controlled accuracy for various energies as functions of the mass ratio, scattering length, and three-body parameter. We discuss in detail the relative positions of the recombination loss peaks, which in the universal limit depend only on the mass ratio. Our results have implications for ongoing and future experiments on Bose-Bose and Bose-Fermi atomic mixtures.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS2003

Magnetohydrodynamic Jump Conditions for Oblique Relativistic Shocks with Gyrotropic Pressure

Shock jump conditions, i.e., the specification of the downstream parameters of the gas in terms of the upstream parameters, are obtained for steady-state, plane shocks with oblique magnetic fields and arbitrary flow speeds. This is done by combining the continuity of particle number flux and the electromagnetic boundary conditions at the shock with the magnetohydrodynamic conservation laws derived from the stress-energy tensor. For ultrarelativistic and nonrelativistic shocks, the jump conditions may be solved analytically. For mildly relativistic shocks, analytic solutions are obtained for isotropic pressure using an approximation for the adiabatic index that is valid in high sonic Mach number cases. Examples assuming isotropic pressure illustrate how the shock compression ratio depends on the shock speed and obliquity. In the more general case of gyrotropic pressure, the jump conditions cannot be solved analytically with- out additional assumptions, and the effects of gyrotropic pressure are investigated by parameterizing the distribution of pressure parallel and perpendicular to the magnetic field. Our numerical solutions reveal that relatively small departures from isotropy (e.g., approximately 20%) produce significant changes in the shock compression ratio, r , at all shock Lorentz factors, including ultrarelativistic ones, where an analytic solution with gyrotropic pressure is obtained. In particular, either dynamically important fields or significant pressure anisotropies can incur marked departures from the canonical gas dynamic value of r = 3 for a shocked ultrarelativistic flow and this may impact models of particle acceleration in gamma-ray bursts and other environments where relativistic shocks are inferred. The jump conditions presented apply directly to test-particle acceleration, and will facilitate future self-consistent numerical modeling of particle acceleration at oblique, relativistic shocks; such models include the modification of the fluid velocity profile due to the contribution of energetic particles to the momentum and energy fluxes.

Double, Glen P.↗
DOE OSTI2010

Bound-state-induced persistent oscillations in the transient behavior of the probability density for the attractive {delta} potential

An exact analytical solution to the time-dependent Schroedinger equation for an attractive {delta} potential using cutoff plane-wave initial conditions is derived to investigate the effect of a bound state on the transmission transients. We find that at short distances from the potential the probability density behaves harmonically at all times. This unexpected behavior, which corresponds to the trapping of a fraction of the transmitted wave, decreases exponentially with distance, so that at large distances the solution goes into the stationary solution. We find also that this behavior has no effect on the phase time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Stability theory of Knudsen plasma diodes

A stability theory is developed for a plasma diode in which an electron beam supplied from the emitter propagates without collisions in the self-consistent electric field against the immobile ion background. An integral equation for the amplitude of the perturbed field is deduced using the Q,G method for the regime without electron reflection from a potential barrier. Analytic solutions to this equation are obtained for a number of important particular cases, and the plasma dispersion properties are examined.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2010

Membranes with topological charge and AdS{sub 4}/CFT{sub 3} correspondence

If the second Betti number b{sub 2} of a Sasaki-Einstein manifold Y{sup 7} does not vanish, then M-theory on AdS{sub 4}xY{sup 7} possesses 'topological' U(1){sup b}{sub 2} gauge symmetry. The corresponding Abelian gauge fields come from three-form fluctuations with one index in AdS{sub 4} and the other two in Y{sup 7}. We find black membrane solutions carrying one of these U(1) charges. In the zero-temperature limit, our solutions interpolate between AdS{sub 4}xY{sup 7} in the UV and AdS{sub 2}xR{sup 2}xsquashed Y{sup 7} in the IR. In fact, the AdS{sub 2}xR{sup 2}xsquashed Y{sup 7} background is by itself a solution of the supergravity equations of motion. These solutions do not appear to preserve any supersymmetry. We search for their possible instabilities and do not find any. We also discuss the meaning of our charged membrane backgrounds in a dual quiver Chern-Simons gauge theory with a global U(1) charge density. Finally, we present a simple analytic solution which has the same IR but different UV behavior. We reduce this solution to type IIA string theory, and perform T-duality to type IIB. The type IIB metric turns out to be a product of the squashed Y{sup 7} and the extremal Banados-Teitelboim-Zanelli black hole. We discuss an interpretation of this type IIB background in terms of the (1+1)-dimensional conformal field theory on D3-branes partially wrapped over the squashed Y{sup 7}.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

Accessible solitons of fractional dimension

We demonstrate that accessible solitons described by an extended Schrödinger equation with the Laplacian of fractional dimension can exist in strongly nonlocal nonlinear media. The soliton solutions of the model are constructed by two special functions, the associated Legendre polynomials and the Laguerre polynomials in the fraction-dimensional space. Our results show that these fractional accessible solitons form a soliton family which includes crescent solitons, and asymmetric single-layer and multi-layer necklace solitons. -- Highlights: •Analytic solutions of a fractional Schrödinger equation are obtained. •The solutions are produced by means of self-similar method applied to the fractional Schrödinger equation with parabolic potential. •The fractional accessible solitons form crescent, asymmetric single-layer and multilayer necklace profiles. •The model applies to the propagation of optical pulses in strongly nonlocal nonlinear media.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

OFF-AXIS GAMMA-RAY BURST AFTERGLOW MODELING BASED ON A TWO-DIMENSIONAL AXISYMMETRIC HYDRODYNAMICS SIMULATION

Starting as highly relativistic collimated jets, gamma-ray burst outflows gradually slow down and become nonrelativistic spherical blast waves. Although detailed analytical solutions describing the afterglow emission received by an on-axis observer during both the early and late phases of the outflow evolution exist, a calculation of the received flux during the intermediate phase and for an off-axis observer requires either a more simplified analytical model or direct numerical simulations of the outflow dynamics. In this paper, we present light curves for off-axis observers covering the long-term evolution of the blast wave, calculated from a high-resolution two-dimensional relativistic hydrodynamics simulation using a synchrotron radiation model. We compare our results to earlier analytical work and calculate the consequence of the observer angle with respect to the jet axis both for the detection of orphan afterglows and for jet break fits to the observational data. We confirm earlier results in the literature finding that only a very small number of local type Ibc supernovae can harbor an orphan afterglow. For off-axis observers, the observable jet break can be delayed up to several weeks, potentially leading to overestimation of the beaming-corrected total energy. In addition we find that, when using our off-axis light curves to create synthetic Swift X-ray data, jet breaks are likely to remain hidden in the data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Thick diffusion limit boundary layer test problems

We develop two simple test problems that quantify the behavior of computational transport solutions in the presence of boundary layers that are not resolved by the spatial grid. In particular we study the quantitative effects of 'contamination' terms that, according to previous asymptotic analyses, may have a detrimental effect on the solutions obtained by both discontinuous finite element (DFEM) and characteristic-method (CM) spatial discretizations, at least for boundary layers caused by azimuthally asymmetric incident intensities. Few numerical results have illustrated the effects of this contamination, and none have quantified it to our knowledge. Our test problems use leading-order analytic solutions that should be equal to zero in the problem interior, which means the observed interior solution is the error introduced by the contamination terms. Results from DFEM solutions demonstrate that the contamination terms can cause error propagation into the problem interior for both orthogonal and non-orthogonal grids, and that this error is much worse for non-orthogonal grids. This behavior is consistent with the predictions of previous analyses. We conclude that these boundary layer test problems and their variants are useful tools for the study of errors that are introduced by unresolved boundary layers in diffusive transport problems. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

A First-Passage Kinetic Monte Carlo method for reaction–drift–diffusion processes

Stochastic reaction–diffusion models are now a popular tool for studying physical systems in which both the explicit diffusion of molecules and noise in the chemical reaction process play important roles. The Smoluchowski diffusion-limited reaction model (SDLR) is one of several that have been used to study biological systems. Exact realizations of the underlying stochastic processes described by the SDLR model can be generated by the recently proposed First-Passage Kinetic Monte Carlo (FPKMC) method. This exactness relies on sampling analytical solutions to one and two-body diffusion equations in simplified protective domains. In this work we extend the FPKMC to allow for drift arising from fixed, background potentials. As the corresponding Fokker–Planck equations that describe the motion of each molecule can no longer be solved analytically, we develop a hybrid method that discretizes the protective domains. The discretization is chosen so that the drift–diffusion of each molecule within its protective domain is approximated by a continuous-time random walk on a lattice. New lattices are defined dynamically as the protective domains are updated, hence we will refer to our method as Dynamic Lattice FPKMC or DL-FPKMC. We focus primarily on the one-dimensional case in this manuscript, and demonstrate the numerical convergence and accuracy of our method in this case for both smooth and discontinuous potentials. We also present applications of our method, which illustrate the impact of drift on reaction kinetics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Semi-Analytical Benchmarks for MCNP6

Code verification is an extremely important process that involves proving or disproving the validity of code algorithms by comparing them against analytical results of the underlying physics or mathematical theory on which the code is based upon. Monte Carlo transport codes such as MCNP6 undergo verification and testing upon every release to ensure that the codes are properly simulating nature. Specifically, MCNP6 has multiple sets of problems with known analytic solutions that are used for code verification. Most of the verification problems are fairly simple due to the fact that they are usually composed of few materials, with simplified cross-sections, or physics approximations, and simple geometry. These approximations make the transport equation possible to solve analytically or semi-analytically, and thus they are quite valuable in verifying that the code algorithms and methods (Monte Carlo, discrete ordinates, etc.) are operating as intended. The remainder of this paper is organized as follows: first we briefly discuss the theory behind the benchmarks problems, then the numerical results are presented, and finally we conclude with general remarks on this and possible future work.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2011

Flexible single molecule simulation of reaction-diffusion processes

An algorithm is developed for simulation of the motion and reactions of single molecules at a microscopic level. The molecules diffuse in a solvent and react with each other or a polymer and molecules can dissociate. Such simulations are of interest e.g. in molecular biology. The algorithm is similar to the Green's function reaction dynamics (GFRD) algorithm by van Zon and ten Wolde where longer time steps can be taken by computing the probability density functions (PDFs) and then sample from the distribution functions. Our computation of the PDFs is much less complicated than GFRD and more flexible. The solution of the partial differential equation for the PDF is split into two steps to simplify the calculations. The sampling is without splitting error in two of the coordinate directions for a pair of molecules and a molecule-polymer interaction and is approximate in the third direction. The PDF is obtained either from an analytical solution or a numerical discretization. The errors due to the operator splitting, the partitioning of the system, and the numerical approximations are analyzed. The method is applied to three different systems involving up to four reactions. Comparisons with other mesoscopic and macroscopic models show excellent agreement.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

An offline unstructured biogeochemical model (UBM) for complex estuarine and coastal environments

Due to increased pollutant loads and water use from coastal development and population growth, occurrences of low-dissolved oxygen and "hypoxic zones" have increased. Reports of fish kills and water quality impairment are also becoming more frequent in many coastal waters. Water quality managers and regulatory agencies rely on numerical modeling tools to quantify the relative contributions of anthropogenic and "natural" pollutant loads (nutrients and biochemical oxygen demand) on dissolved oxygen levels and use the results for remedial activities and source control. The ability to conduct seasonlong simulations with sufficient nearshore resolution is therefore a key requirement. Mesh flexibility and the ability to increase site specific resolution without disturbing the larger domain setup and calibration are critical. The objective of this effort was to develop a robust biogeochemical model suitable for simulation of water quality dynamics including dissolved oxygen in complex coastal environments with multiple tidal channels, tidal flats, and density-driven circulation using unstructured-grid formulation. This paper presents an offline unstructured biogeochemical model that uses the Finite Volume Coastal Ocean Model (FVCOM) discretization of the study domain and the corresponding hydrodynamic solution to drive biogeochemical kinetics based on a water quality model CE-QUAL-ICM. In this paper, the linkage between selected hydrodynamic and water quality models is subjected to several scalar transport and biogeochemical module tests (plume transport and dilution, BOD/DO sag, and phytoplankton/nutrients reaction), and results are compared to their analytical solutions as part of model validation. A preliminary application of the biogeochemical model with a year-long simulation of Hood Canal basin in Puget Sound, USA, is presented as an example and a test of the tool in a real estuary setting. The model reproduced the dynamics and seasonal variations in the biogeochemical state variables and was used to test short-term wind-driven dynamics that could influence dissolved oxygen concentrations in Hood Canal.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

Cosmological perturbations in massive bigravity

We present a comprehensive analysis of classical scalar, vector and tensor cosmological perturbations in ghost-free massive bigravity. In particular, we find the full evolution equations and analytical solutions in a wide range of regimes. We show that there are viable cosmological backgrounds but, as has been found in the literature, these models generally have exponential instabilities in linear perturbation theory. However, it is possible to find stable scalar cosmological perturbations for a very particular choice of parameters. For this stable subclass of models we find that vector and tensor perturbations have growing solutions. We argue that special initial conditions are needed for tensor modes in order to have a viable model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗