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At least 1,045 records · Page 58

Atomistic Simulations of the Elastic Compression of Platinum Nanoparticles

Abstract The elastic behavior of nanoparticles depends strongly on particle shape, size, and crystallographic orientation. Many prior investigations have characterized the elastic modulus of nanoscale particles using experiments or simulations; however their reported values vary widely depending on the methods for measurement and calculation. To understand these discrepancies, we used classical molecular dynamics simulation to model the compression of platinum nanoparticles with two different polyhedral shapes and a range of sizes from 4 to 20 nm, loaded in two different crystal orientations. Multiple standard methods were used to calculate the elastic modulus from stress-vs-strain data for each nanoparticle. The magnitudes and particle-size dependence of the resulting moduli varied with calculation method and, even for larger nanoparticles where bulk-like behavior may be expected, the effective elastic modulus depended strongly on shape and orientation. Analysis of per-atom stress distributions indicated that the shape- and orientation-dependence arise due to stress triaxiality and inhomogeneity across the particle. When the effective elastic modulus was recalculated using a representative volume element in the center of a large nanoparticle, the elastic modulus had the expected value for each orientation and was shape independent. It is only for single-digit nanoparticles that meaningful differences emerged, where even the very center of the particle had a lower modulus due to the effect of the surface. These findings provide better understanding of the elastic properties of nanoparticles and disentangle geometric contributions (such as stress triaxiality and spatial inhomogeneity) from true changes in elastic properties of the nanoscale material.

36 MATERIALS SCIENCE↗

Application of unsteady aerodynamic methods for transonic aeroelastic analysis

Aerodynamic methods for aeroelastic analysis are applied to various flow problems. These methods include those that solve the three dimensional transonic small disturbance (TSD) potential equation, the two dimensional (2-D) full potential (FP) equation, and the 2-D thin layer Navier-Stokes equations. Flutter analysis performed using TSD aerodynamics show that such methods can be used to analyze some aeroelastic phenomena. For thicker bodies and larger amplitude motions, a nonisentropic FP method is presented. The unsteady FP equation is modified to model the entropy jumps across shock waves. The conservative form of the modified equation is solved in generalized coordinates using an implicit, approximate factorization method. Pressures calculated on the NLR 7301 and NACA 64A010A airfoils using the nonisentropic FP method are presented. It is shown that modeling shock generated entropy extends the range of validity of the FP method. A Navier-Stokes code is correlated with pressures measured on a supercritical airfoil at transonic speeds. When corrections are made for wind tunnel wall effects, the calculations correlate well with the measured data.

Whitlow, Woodrow, Jr.↗

Calculation of electron-ion temperature equilibration rates and friction coefficients in plasmas and liquid metals using quantum molecular dynamics

In this work, we discuss a method to calculate with quantum molecular dynamics simulations the rate of energy exchanges between electrons and ions in two-temperature plasmas, liquid metals, and hot solids. Promising results from this method were recently reported for various materials and physical conditions. Like other ab initio calculations, the approach offers a very useful comparison with the experimental measurements and permits an extension into conditions not covered by the experiments. The energy relaxation rate is related to the friction coefficients felt by individual ions due to their nonadiabatic interactions with electrons. Each coefficient satisfies a Kubo relation given by the time integral of the autocorrelation function of the interaction force between an ion and the electrons. These Kubo relations are evaluated using the output of quantum molecular dynamics calculations in which electrons are treated in the framework of finite-temperature density functional theory. The calculation presents difficulties that are unlike those encountered with the Kubo formulas for the electrical and thermal conductivities. In particular, the widely used Kubo-Greenwood approximation is inapplicable here. Indeed, the friction coefficients and the energy relaxation rate diverge in this approximation since it does not properly account for the electronic screening of electron-ion interactions. The inclusion of screening effects considerably complicates the calculations. We discuss the physically motivated approximations we applied to deal with these complications in order to investigate a widest range of materials and physical conditions. Unlike the standard method used for the electronic conductivities, the Kubo formulas are evaluated directly in the time domain and not in the energy domain, which spares one from needing to introduce an extraneous undetermined numerical parameter to account for the discrete character of the numerical density of states. We highlight interesting properties of the energy relaxation rate not shared by other electronic properties, in particular its self-averaging character. We then present a detailed parametric and convergence study with the numerical parameters, including the system size, the number of bands and k-points, and the physical approximations for the dielectric function and the exchange-correlation energy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Acceleration of transonic potential flow calculations on arbitrary meshes by the multiple grid method

A multiple grid method for transonic flow calculations is developed. The proposed scheme incorporates a generalized alternating direction method as the smoothing algorithm. Numerical experiments indicate that this multigrid alternating direction method converges rapidly and reliably for a range of cases typical of the cruising regime up to the onset of drag rise. It also appears that the method can be readily generalized to treat three-dimensional flows.

Jameson, A.↗

Initial Fermi orbital descriptors for FLOSIC calculations: The quick-FOD method

Fermi orbital descriptors (FODs) play a key role in Fermi-Löwdin orbital self-interaction correction (FLOSIC) calculations used to remove self-interaction from approximate density functionals. Optimal FODs are obtained by minimizing the self-interaction-corrected total energy, and, in this process, identifying initial sets of FODs becomes crucial. Here we propose, implement and test a novel method for automatically initializing FODs, quick-FOD, based on the minimization of an empirical energy expression that involves a Coulomb-like FOD-electron density attraction, an FOD-FOD short-range repulsion, and an exchange-like FOD-density repulsion. Quick-FOD successfully reproduces FOD arrangements in qualitatively good agreement with Lewis theory and with full-fledged FLOSIC calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Hamiltonian Truncation Effective Theory

Hamiltonian truncation is a non-perturbative numerical method for calculating observables of a quantum field theory. The starting point for this method is to truncate the interacting Hamiltonian to a finite-dimensional space of states spanned by the eigenvectors of the free Hamiltonian H_0 H 0 with eigenvalues below some energy cutoff E_\text{max} E max . In this work, we show how to treat Hamiltonian truncation systematically using effective field theory methodology. We define the finite-dimensional effective Hamiltonian by integrating out the states above E_\text{max} E max . The effective Hamiltonian can be computed by matching a transition amplitude to the full theory, and gives corrections order by order as an expansion in powers of 1/E_\text{max} 1 / E max . The effective Hamiltonian is non-local, with the non-locality controlled in an expansion in powers of H_0/E_\text{max} H 0 / E max . The effective Hamiltonian is also non-Hermitian, and we discuss whether this is a necessary feature or an artifact of our definition. We apply our formalism to 2D \lambda\phi^4 λ ϕ 4 theory, and compute the the leading 1/E_\text{max}^2 1 / E max 2 corrections to the effective Hamiltonian. We show that these corrections nontrivially satisfy the crucial property of separation of scales. Numerical diagonalization of the effective Hamiltonian gives residual errors of order 1/E_\text{max}^3 1 / E max 3 , as expected by our power counting. We also present the power counting for 3D \lambda \phi^4 λ ϕ 4 theory and perform calculations that demonstrate the separation of scales in this theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Calculations of electronic excitation by protons and alpha particles in silicon

This paper presents an ab initio method of calculating the valence electron contribution to the stopping and interaction cross sections of swift ions in matter using linear response calculations of the dielectric function in crystals. We estimate the contribution to the stopping and cross sections by repeated electron capture and stripping of the projectile ion by the medium. We also predict the electronic stopping of protons and alpha particles in silicon and compare to measured values. The predictions generally agree with the data at ion speeds greater than 1 atomic unit. We find that electron capture and stripping is at most a small contribution to the stopping for both ions studied.

electron excitation, silicon, nuclear interactions↗

Tropospheric UV flux calculations and photolysis rates for use with zonally and diurnally averaged models

A computationally fast and efficient method for calculating solar UV fluxes in the troposphere is developed. Calculated fluxes compare favorably with more rigorous multiple scattering results, and qualitatively correct behavior of the direct and diffuse flux components is maintained. In view of the relatively large uncertainties in other aspects of tropospheric photochemical models, the use of approximate UV flux calculations appears warranted. The technique is applied to the calculation of photolysis rates for twelve significant photolytic reactions of nine species.

Matloff, G. L.↗

Calculation of non-stationary aerodynamic forces in the near sonic range

The development of a mathematical method for calculating nonstationary supersonic flow in the near-sonic range is described. A perturbation formula is derived based on the exact stationary values; it is applicable to the equation for potential. The problem can thus be divided into stationary and nonstationary fields. The pressure distribution in an oscillating profile is determined, based on hyperbolic differential equations. It is shown that there are important corollaries concerning the application of linear theory. With suitable extrapolations, linear theory can be used up to about Mach 0.8. Linear theory is not applicable, however, when determining the moment coefficients; for this case, a special technique is described.

Teipel, I.↗

Experiments and simulations of isochorically heated warm dense carbon foam at the Texas Petawatt Laser

An experimental and simulation study of warm dense carbon foams at ambient density (n e ~10 21 cm –3 ) is presented. This study of isochorically heated foams is motivated by their potential application in carbon-atmosphere white-dwarf envelopes, where there are modeling uncertainties due to the equation of state. The foams are heated on an approximately picosecond time scale with a laser-accelerated proton beam. The cooling and expansion of the heated foams can be modeled with appropriately initialized radiation-hydrodynamics codes; xRAGE code is used in this work. The primary experimental diagnostic is the streaked optical pyrometer, which images a narrow band of radiation from the rear surface of the heated material. Presented are xRAGE modeling results for both solid aluminum targets and carbonized resorcinol-formaldehyde foam targets, showing that the foam appears to cool slowly on the pyrometer because of partial transparency. So that simulations of cooling foam are processed properly, it is necessary to account for finite optical depth in the photosphere calculation, and the methods for performing that calculation are presented in depth.

36 MATERIALS SCIENCE↗

Gantryless Associated-Particle Neutron Radiography

The present work reports on the development of techniques for in-field fast-neutron radiography measurements using the associated-particle imaging (API) method. The API method employs alpha-neutron coincidences from the d+t→α+n reaction to enable fast neutron transmission imaging with excellent contrast using a wide cone beam. However, for field radiography applications, the API method is burdened by the need for the relative positions of the source and detector to be known. Fortunately, these relative positions can be inferred from transmission data. The inferred positions also enable accurate stitching of multiple images into a composite image even when using a low-resolution detector panel and acquiring images having few overlapping pixels. The developed techniques address analysis of measurements where (1) the source and detector panel are separately hand positioned rather than held in registration by a gantry, (2) multiple detector panel positions within the “coincident cone” of tagged neutrons are required to piece together an image of an item of interest, and (3) normalization measurements that have identical source-detector positioning but without the inspected object are not possible. The present work will describe the system calibrations (including timing calibrations and neutron direction calibrations) necessary for subsequent analyses, the method of locating the detector in the coincident cone of neutrons with millimeter precision using the timing and directions of coincident neutrons, the method of calculating a normalization image for a given detector panel position, and the method used to project multiple images into a common image.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Characteristic features of determining the labor input and estimated cost of the development and manufacture of equipment

The difficulties in obtaining exact calculation data for the labor input and estimated cost are noted. The method of calculating the labor cost of the design work using the provisional normative indexes with respect to individual forms of operations is proposed. Values of certain coefficients recommended for use in the practical calculations of the labor input for the development of new scientific equipment for space research are presented.

Kurmanaliyev, T. I.↗

Method of predicting radiation heat transfer in turbine cooling test facilities

A method is presented for calculating the average net radiation heat flux to turbine vanes and blades. The net radiation heat flux at a vane leading edge calculated by this method was compared with heat flux values independently determined from experimental tests on a vane in a cascade. The spectral emissivities of the turbine vane and the cascade wall were also measured.

Gladden, H. J.↗

On the Routh approximation technique and least squares errors

A new method for calculating the coefficients of the numerator polynomial of the direct Routh approximation method (DRAM) using the least square error criterion is formulated. The necessary conditions have been obtained in terms of algebraic equations. The method is useful for low frequency as well as high frequency reduced-order models.

Aburdene, M. F.↗

A general formalism for phase space calculations

General formulas for calculating the interactions of galactic cosmic rays with target nuclei are presented. Methods for calculating the appropriate normalization volume elements and phase space factors are presented. Particular emphasis is placed on obtaining correct phase space factors for 2-, and 3-body final states. Calculations for both Lorentz-invariant and noninvariant phase space are presented.

Norbury, John W.↗

Numerical study of vortical flow over a sideslipping delta wing

The three-dimensional vortical viscous flow past a sideslipping delta wing at a high angle of attack is numerically investigated. A computational method for calculating low-speed viscous flowfields is developed. The time-iterative method uses an implicit upwind-relaxation finite-difference algorithm with a nonsingular eigensystem to solve the preconditioned, three-dimensional, incompressible Navier-Stokes equations in curvilinear coordinates. An algebraic turbulence model is implemented to account for the eddy viscosity. The technique of local time stepping is incorporated to accelerate the rate of convergence to a steady-state solution. Computed results are compared with experimental data.

Hsu, C.-H.↗