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At least 217 records · Page 12

Direct observations of shock-induced melting in a porous solid using time-resolved x-ray diffraction

Here in this work we provide direct evidence of shock-induced melting and associated kinetics in a porous solid (aluminum powder) using time-resolved x-ray diffraction. Unambiguous evidence of melting in 50% porous aluminum (Al) powder samples, shocked to peak pressures between ~13 - 19 GPa, was provided by the broadening of the Debye-Scherrer ring corresponding to the (111) peak. Shocked Al powder did not melt completely in any of our experiments within the durations of measurement. Incomplete (partial) melting of the powder, even after several hundreds of nanoseconds of shock loading, provides insights into thermal transport with Al powder particles under high-pressure dynamic loading. Such insights are quite valuable for developing well-constrained melting models and thermodynamic equations of state for porous Al and other porous solids relevant to planetary and materials science.

36 MATERIALS SCIENCE↗

Laws of effluent dispersion in the steady-state atmospheric surface layer in stable and unstable conditions

The two-dimensional diffusion equation has been solved by an integral method to obtain the distribution of ground-level concentration of an inert effluent emitted from a semi-infinite area source in a steady-state and horizontally homogeneous atmospheric surface layer. Mean wind velocity and eddy diffusivity profiles derived from empirically determined flux-profile relations of Businger et al. (1971) for stable and unstable surface layers were used. It is found that concentration as a function of downwind distance can be described by a simple formula over distances of practical interest in surface layer dispersion. Corresponding results for a cross-wind infinite line source are obtained by simple differentiation. The concentration distribution is completely determined by the friction velocity, the Monin-Obukhov length, the roughness length, and the effluent source strength. The generalization of the integral method needed to obtain accurate solutions of the diffusion equation with the given wind velocity and diffusivity profiles is discussed in an appendix.

Lebedeff, S. A.↗

A general method to determine the stability of compressible flows

Several problems were studied using two completely different approaches. The initial method was to use the standard linearized perturbation theory by finding the value of the individual small disturbance quantities based on the equations of motion. These were serially eliminated from the equations of motion to derive a single equation that governs the stability of fluid dynamic system. These equations could not be reduced unless the steady state variable depends only on one coordinate. The stability equation based on one dependent variable was found and was examined to determine the stability of a compressible swirling jet. The second method applied a Lagrangian approach to the problem. Since the equations developed were based on different assumptions, the condition of stability was compared only for the Rayleigh problem of a swirling flow, both examples reduce to the Rayleigh criterion. This technique allows including the viscous shear terms which is not possible in the first method. The same problem was then examined to see what effect shear has on stability.

Guenther, R. A.↗

Existence of needle crystals in local models of solidification

The way in which surface tension acts as a singular perturbation to destroy the continuous family of needle-crystal solutions of the steady-state growth equations is analyzed in detail for two local models of solidification. All calculations are performed in the limit of small surface tension or, equivalently, small velocity. The basic mathematical ideas are introduced in connection with a quasilinear, isotropic version of the geometrical model of Brower et al., in which case the continuous family of solutions dissappears completely. The formalism is then applied to a simplified boundary-layer model with an anisotropic kinetic attachment coefficient. In the latter case, the solvability condition for the existence of needle crystals can be satisfied whenever the coefficient of anisotropy is arbitrarily small but nonzero.

Langer, J. S.↗

Spectral-partitioned Kohn-Sham density functional theory

Here we introduce a general, variational scheme for systematic approximation of a given Kohn-Sham free-energy functional by partitioning the density matrix into distinct spectral domains, each of which may be spanned by an independent diagonal representation without requirement of mutual orthogonality. It is shown that by generalizing the entropic contribution to the free energy to allow for independent representations in each spectral domain, the free energy becomes an upper bound to the exact (unpartitioned) Kohn-Sham free energy, attaining this limit as the representations approach Kohn-Sham eigenfunctions. A numerical procedure is devised for calculation of the generalized entropy associated with spectral partitioning of the density matrix. The result is a powerful framework for Kohn-Sham calculations of systems whose occupied subspaces span multiple energy regimes. As a case in point, we apply the proposed framework to warm- and hot-dense matter described by finite-temperature density functional theory, where at high energies the density matrix is represented by that of the free-electron gas, while at low energies it is variationally optimized. We derive expressions for the spectral-partitioned Kohn-Sham Hamiltonian, atomic forces, and macroscopic stresses within the projector-augmented wave (PAW) and the norm-conserving pseudopotential methods. It is demonstrated that at high temperatures, spectral partitioning facilitates accurate calculations at dramatically reduced computational cost. Moreover, as temperature is increased, fewer exact Kohn-Sham states are required for a given accuracy, leading to further reductions in computational cost. Finally, it is shown that standard multiprojector expansions of electronic orbitals within atomic spheres in the PAW method lack sufficient completeness at high temperatures. Spectral partitioning provides a systematic solution for this fundamental problem.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A direct algorithm for solution of incompressible three-dimensional unsteady Navier-Stokes equations

A direct, implicit, numerical solution algorithm, with second-order accuracy in space and time, is constructed for the three-dimensional unsteady incompressible Navier-Stokes equations formulated in terms of velocity and vorticity, using generalized orthogonal coordinates to achieve the accurate solution of complex viscous flow configurations. A numerically stable, efficient, direct inversion procedure is developed for the computationally intensive divergence-curl elliptic velocity problem. This overdetermined partial differential operator is first formulated as a uniquely determined, nonsingular matrix-vector problem; this aspect of the procedure is a unique feature of the present analysis. The three-dimensional vorticity-transport equation is solved by a modified factorization technique which completely eliminates the need for any block-matrix inversions and only scalar tridiagonal matrices need to be inverted. The method is applied to the test problem of the three-dimensional flow within a shear-driven cubical box. Coherent streamwise vortex structures are observed within the steady-state flow at Re = 100.

Osswald, G. A.↗

A comparison of two algorithms for simulating collisionless systems

Two completely different simulation algorithms are compared by applying them to the same stellar dynamical problems: one is a self-consistent field (SCF) method for solving Poisson's equation and the other is a phase-space method for integrating the collisionless Boltzmann equation. We consider simulations of spherical stellar systems which are initially far from equilibrium and relax to their final states by gravitational collapse. The initial conditions consist of either uniform-density spheres or nonequilibrium models having Plummer density profiles, in which velocity dispersions are assigned according to given virial ratios. If a few tens of radial expansion terms with hundreds of thousands of particles are used in the SCF code, excellent agreement is found between the results it generates and those obtained with the phase-space solver, provided that a sufficiently large number of grid cells are employed with the latter. These findings imply that for simulating collisionless systmes over many dynamical times, the SCF approach based on sampling phase space is competitive with the approach treating phase space as a continuous fluid. The results of our tests make it possible to estimate the number of particles and basis functions required in situations like those modeled. Limitations of the SCF method and the choice of an optimal set of basis functions are also discussed.

Hozumi, Shunsuke↗

Earth science research

The analysis of ground-truth data from the boreal forest plots in the Superior National Forest, Minnesota, was completed. Development of statistical methods was completed for dimension analysis (equations to estimate the biomass of trees from measurements of diameter and height). The dimension-analysis equations were applied to the data obtained from ground-truth plots, to estimate the biomass. Classification and analyses of remote sensing images of the Superior National Forest were done as a test of the technique to determine forest biomass and ecological state by remote sensing. Data was archived on diskette and tape and transferred to UCSB to be used in subsequent research.

Botkin, Daniel B.↗

Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method

A lattice Boltzmann model is presented which gives the complete Navier-Stokes equation and may provide an efficient parallel numerical method for solving various fluid problems. The model uses the single-time relaxation approximation and a particular Maxwell-type distribution. The model eliminates exactly (1) the non-Galilean invariance caused by a density-dependent coefficient in the convection term and (2) a velocity-dependent equation of state.

Chen, Hudong↗

Ground state energy of solid molecular hydrogen at high pressure

The present status of the theoretical equation of state of solid molecular hydrogen is reviewed. Different quantum mechanical calculations by several groups lead to results which generally agree with each other but which disagree systematically with the measured pressure-volume curve at pressures larger than about 3000 atm. A new calculation of this curve is presented including the effect of the anisotropic interaction between H2 molecules within a completely quantum-mechanical formalism. The results show that inclusion of this interaction removes the discrepancy between theory and experiment at high pressures and that a quantum-mechanical treatment is necessary to realize its full effect.

Ebner, C.↗

Numerical solutions of the complete Navier-Stokes equations

Using ideas from the kinetic theory, the Navier-Stokes equations are modified in such a way that they can be cast as a set of first order hyperbolic equations. This is achieved by incorporating time dependent terms into the definition of the stress tensor and the heat flux vectors. The boundary conditions are then determined from the theory of characteristics. Because the resulting equations reduce to the traditional Navier-Stokes equations when the steady state is reached, the present approach provides a straightforward scheme for the determination of inflow and outflow boundary conditions. The method is validated by comparing its predictions with known exact solutions of the steady Navier-Stokes equations.

Hassan, H. A.↗

Theoretical studies of chemical reactions related to the formation and growth of polycyclic aromatic hydrocarbons (PAH) and molecular properties of their key intermediates (Final Progress Report)

The formation mechanisms of polycyclic aromatic hydrocarbons, (PAHs) – organic molecules carrying fused benzene rings – are of great interest to scientists and engineers due to their importance in combustion chemistry and astrochemistry. On Earth, PAHs are largely produced in incomplete combustion of fossil fuel and are considered as critical precursors to unwanted soot particles leading to combustion inefficiency and causing air pollution along with detrimental health effects. Simple PAH molecules initially formed in the gas phase, are further involved in a build-up process in combustion flames leading to larger PAH, bowl-shaped nanostructures, fullerenes, and solid-phase species including carbonaceous dust, graphene particles, and soot. In deep space, PAH and their derivatives are potential key intermediates and nucleation sites leading eventually to carbonaceous nanoparticles (“interstellar grains”). Therefore, the understanding of the key processes in the synthesis of PAHs along with their precursors and their degradation mechanisms in combustion systems and in interstellar, circumstellar, and planetary atmospheric environments will provide critical insights into how complex aromatic structures, carbonaceous nanoparticles, and fullerenes are formed and destroyed. Achieving this understanding is an important step in the development of the efficient combustion processes and of the ecofriendly devices with reduced environmental pollution as well as technological strategies for the production of hydrogen and solid carbon through thermal or plasma-assisted pyrolysis of natural gas and biomass. Also, the understanding of the key processes of PAH and soot growth will help in our comprehension of chemical evolution in the universe. Detailed information on the mechanisms and reliable rate constants of the key elementary chemical reactions involved in PAH formation and destruction processes and in inception of soot particles is often missing, with the main deficiencies being the absence of temperature- and pressure-dependent rate constants for the broad range of conditions occurring in various terrestrial and interstellar processes and the lack of data on the reaction products and their branching ratios. Complementary to experimental studies, these gaps in knowledge can be filled by using quantum chemical calculations of reaction potential energy surfaces providing us with accurate energies of reaction products, intermediates, and transition states, revealing the reaction mechanism, and giving the molecular properties required to compute rate constants for relevant reaction steps and product branching ratios using the RRKM-Master Equation (ME) method. Molecular dynamics (MD) simulations can be used in cases when a reaction rate cannot be properly described by statistical theories. During the terminal renewal project period we employed these ab initio/RRKM-ME and MD approaches to complete our studies on several key reactions relevant to the formation/growth of PAH and inception of soot particles including (1) the reaction mechanism and kinetics of the resonance stabilized fulvenallenyl radical with propargyl and C 3 H 4 isomers; (2) the reaction mechanism and kinetics for the C + indene and C 2 + styrene reactions producing naphthyl or azulenyl radicals in low-temperature environments; (3) the MD study of non-equilibrium dimerization of acepyrene and coronene and its radical. The information derived from our theoretical calculations contributed to a better fundamental understanding of the reaction mechanisms and provide missing critical kinetic data to improve combustion models of hydrocarbon fuels and astrochemical models of the growth of carbonaceous molecules and particles in cold molecular clouds, circumstellar envelopes, and planetary atmospheres.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Relative motion of orbiting particles under the influence of perturbing forces. Volume 2: Analytical results

The mathematical developments carried out for this investigation are reported. In addition to describing and discussing the solutions which were acquired, there are compendia of data presented herein which summarize the equations and describe them as representative trace geometries. In this analysis the relative motion problems have been referred to two particular frames of reference; one which is inertially aligned, and one which is (local) horizon oriented. In addition to obtaining the classical initial values solutions, there are results which describe cases having applied specific forces serving as forcing functions. Also, in order to provide a complete state representation the speed components, as well as the displacements, have been described. These coordinates are traced on representative planes analogous to the displacement geometries. By this procedure a complete description of a relative motion is developed; and, as a consequence range rate as well as range information is obtained.

Eades, J. B., Jr.↗

The interior structure of Jupiter (consequences of Pioneer 10 data)

Models of the Jovian interiors are based on theoretical equations of state of hydrogen and helium supported by a few experimental points and an observed parameter such as oblateness, gravitational coefficients, heat emission, and magnetic fields. The models fall into three categories: (1) those which assume a uniform and rather low H2/He ratio throughout the planet, (2) those in which this ratio is solar and thus higher and (3) those which take into account the lack of complete miscibility of the two elements in the condensed state. Recent values of the observed parameters obtained by Pioneer 10 permit improvements of the first two models but also pose new questions. In the first category of models the new data indicate that the amount of hydrogen has to be increased, while in the solar models which have a heavy core (made of SiO2, MgO, Fe and Ni), the abundance of hydrogen has to be decreased, both changes pointing in the direction of incomplete miscibility present in the third category of models.

Smoluchowski, R.↗

Choice of implicit and explicit operators for the upwind differencing method

The flux-vector and flux-difference splittings of Steger-Warming, van Leer and Roe are tested in all possible combinations on the implicit and explicit operators that can be distinguished in implicit relaxation methods for the steady Euler and Navier-Stokes equations. The tests include one-dimensional inviscid nozzle flow, and two-dimensional inviscid and viscous shock reflection. Roe's splitting, as anticipated, is found to uniformly yield the most accurate results. On the other hand, an approximate Roe splitting of the implicit operator (the complete Roe splitting is too complicated for practical use) proves to be the least robust with regard to convergence to the steady state. In this respect, the Steger-Warming splitting is the most robust; it leads to convergence when combined with any of the splittings in the explicit operator, although not necessarily in the most efficient way.

Liou, Meng-Sing↗

Choice of implicit and explicit operators for the upwind differencing method

The flux-vector and flux-difference splittings of Steger-Warming, Van Leer and Roe are tested in all possible combinations in the implicit and explicit operators that can be distinguished in implicit relaxation methods for the steady Euler and Navier-Stokes equations. The tests include one-dimensional inviscid nozzle flow, and two-dimensional inviscid and viscous shock reflection. Roe's splitting, as anticipated, is found to uniformly yield the most accurate results. On the other hand, an approximate Roe splitting of the implicit operator (the complete Roe splitting is too complicated for practical use) proves to be the least robust with regard to convergence to the steady state. In this respect, the Steger-Warming splitting is the most robust: it leads to convergence when combined with any of the splittings in the explicit operator, although not necessarily in the most efficient way.

Liou, Meng-Sing↗

Numerically exact generalized Green's function cluster expansions for electron-phonon problems

We generalize the family of approximate momentum average methods to formulate a numerically exact, convergent hierarchy of equations whose solution provides an efficient algorithm to compute the Green's function of a particle dressed by bosons suitable in the entire parameter regime. We use this approach to extract ground-state properties and spectral functions. Our approximation-free framework, dubbed the generalized Green's function cluster expansion (GGCE), allows access to exact numerical results in the extreme adiabatic limit, where many standard methods struggle or completely fail. We showcase the performance of the method, specializing three important models of charge-boson coupling in solids and molecular complexes: the molecular Holstein model, which describes coupling between charge density and local distortions, the Peierls model, which describes modulation of charge hopping due to intersite distortions, and a more complex Holstein + Peierls system with couplings to two different phonon modes, paradigmatic of charge-lattice interactions in organic crystals. Furthermore, the GGCE serves as an efficient approach that can be systematically extended to different physical scenarios, thus providing a tool to model the frequency dependence of dressed particles in realistic settings.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Flat-Band-Enabled Triplet Excitonic Insulator in a Diatomic Kagome Lattice

The excitonic insulator (EI) state is a strongly correlated many-body ground state, arising from an instability in the band structure of narrow-gap semiconductors towards exciton formation. Here we show that the flat valence and conduction bands of a Yin-Yang Kagome lattice, as exemplified in a superatomic graphene lattice, conspire to enable an interesting state of triplet EI, based on first-principles Density Functional Theory (DFT) calculations combined with many-body GW and Bethe-Salpeter Equation (BSE). As an intrinsic property of topological flat bands, highly localized electron and hole wavefunctions significantly reduce the screening and enhance the exchange interaction, leading to an unusually high triplet exciton binding energy (~1.2 eV) exceeding the GW band gap by ~0.2 eV and a huge singlet-triplet splitting of ~0.4 eV. Here, the flat-bands-enabled triplet EI state also points to the possibility of complete population inversion between the two topological flat bands for the realization of excited quantum spin Hall effect. Our findings enrich once again the intriguing physics of flat bands, which has drawn broad interest.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗