analytic density functional: Topics by Science.gov

Sample records for analytic density functional

The non-Gaussian joint probability density function of slope and elevation for a nonlinear gravity wave field. [in ocean surface

NASA Technical Reports Server (NTRS)

Huang, N. E.; Long, S. R.; Bliven, L. F.; Tung, C.-C.

1984-01-01

On the basis of the mapping method developed by Huang et al. (1983), an analytic expression for the non-Gaussian joint probability density function of slope and elevation for nonlinear gravity waves is derived. Various conditional and marginal density functions are also obtained through the joint density function. The analytic results are compared with a series of carefully controlled laboratory observations, and good agreement is noted. Furthermore, the laboratory wind wave field observations indicate that the capillary or capillary-gravity waves may not be the dominant components in determining the total roughness of the wave field. Thus, the analytic results, though derived specifically for the gravity waves, may have more general applications.
Universal analytical scattering form factor for shell-, core-shell, or homogeneous particles with continuously variable density profile shape.

PubMed

Foster, Tobias

2011-09-01

A novel analytical and continuous density distribution function with a widely variable shape is reported and used to derive an analytical scattering form factor that allows us to universally describe the scattering from particles with the radial density profile of homogeneous spheres, shells, or core-shell particles. Composed by the sum of two Fermi-Dirac distribution functions, the shape of the density profile can be altered continuously from step-like via Gaussian-like or parabolic to asymptotically hyperbolic by varying a single "shape parameter", d. Using this density profile, the scattering form factor can be calculated numerically. An analytical form factor can be derived using an approximate expression for the original Fermi-Dirac distribution function. This approximation is accurate for sufficiently small rescaled shape parameters, d/R (R being the particle radius), up to values of d/R ≈ 0.1, and thus captures step-like, Gaussian-like, and parabolic as well as asymptotically hyperbolic profile shapes. It is expected that this form factor is particularly useful in a model-dependent analysis of small-angle scattering data since the applied continuous and analytical function for the particle density profile can be compared directly with the density profile extracted from the data by model-free approaches like the generalized inverse Fourier transform method. © 2011 American Chemical Society
Analytical gradients for subsystem density functional theory within the slater-function-based amsterdam density functional program.

PubMed

Schlüns, Danny; Franchini, Mirko; Götz, Andreas W; Neugebauer, Johannes; Jacob, Christoph R; Visscher, Lucas

2017-02-05

We present a new implementation of analytical gradients for subsystem density-functional theory (sDFT) and frozen-density embedding (FDE) into the Amsterdam Density Functional program (ADF). The underlying theory and necessary expressions for the implementation are derived and discussed in detail for various FDE and sDFT setups. The parallel implementation is numerically verified and geometry optimizations with different functional combinations (LDA/TF and PW91/PW91K) are conducted and compared to reference data. Our results confirm that sDFT-LDA/TF yields good equilibrium distances for the systems studied here (mean absolute deviation: 0.09 Å) compared to reference wave-function theory results. However, sDFT-PW91/PW91k quite consistently yields smaller equilibrium distances (mean absolute deviation: 0.23 Å). The flexibility of our new implementation is demonstrated for an HCN-trimer test system, for which several different setups are applied. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.
Analytic calculations of hyper-Raman spectra from density functional theory hyperpolarizability gradients

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ringholm, Magnus; Ruud, Kenneth; Bast, Radovan

We present the first analytic calculations of the geometrical gradients of the first hyperpolarizability tensors at the density-functional theory (DFT) level. We use the analytically calculated hyperpolarizability gradients to explore the importance of electron correlation effects, as described by DFT, on hyper-Raman spectra. In particular, we calculate the hyper-Raman spectra of the all-trans and 11-cis isomers of retinal at the Hartree-Fock (HF) and density-functional levels of theory, also allowing us to explore the sensitivity of the hyper-Raman spectra on the geometrical characteristics of these structurally related molecules. We show that the HF results, using B3LYP-calculated vibrational frequencies and force fields,more » reproduce the experimental data for all-trans-retinal well, and that electron correlation effects are of minor importance for the hyper-Raman intensities.« less
A density functional theory study of the correlation between analyte basicity, ZnPc adsorption strength, and sensor response.

PubMed

Tran, N L; Bohrer, F I; Trogler, W C; Kummel, A C

2009-05-28

Density functional theory (DFT) simulations were used to determine the binding strength of 12 electron-donating analytes to the zinc metal center of a zinc phthalocyanine molecule (ZnPc monomer). The analyte binding strengths were compared to the analytes' enthalpies of complex formation with boron trifluoride (BF(3)), which is a direct measure of their electron donating ability or Lewis basicity. With the exception of the most basic analyte investigated, the ZnPc binding energies were found to correlate linearly with analyte basicities. Based on natural population analysis calculations, analyte complexation to the Zn metal of the ZnPc monomer resulted in limited charge transfer from the analyte to the ZnPc molecule, which increased with analyte-ZnPc binding energy. The experimental analyte sensitivities from chemiresistor ZnPc sensor data were proportional to an exponential of the binding energies from DFT calculations consistent with sensitivity being proportional to analyte coverage and binding strength. The good correlation observed suggests DFT is a reliable method for the prediction of chemiresistor metallophthalocyanine binding strengths and response sensitivities.
Brownian systems with spatially inhomogeneous activity

NASA Astrophysics Data System (ADS)

Sharma, A.; Brader, J. M.

2017-09-01

We generalize the Green-Kubo approach, previously applied to bulk systems of spherically symmetric active particles [J. Chem. Phys. 145, 161101 (2016), 10.1063/1.4966153], to include spatially inhomogeneous activity. The method is applied to predict the spatial dependence of the average orientation per particle and the density. The average orientation is given by an integral over the self part of the Van Hove function and a simple Gaussian approximation to this quantity yields an accurate analytical expression. Taking this analytical result as input to a dynamic density functional theory approximates the spatial dependence of the density in good agreement with simulation data. All theoretical predictions are validated using Brownian dynamics simulations.
Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Analytical gradients.

PubMed

Łazarski, Roman; Burow, Asbjörn Manfred; Grajciar, Lukáš; Sierka, Marek

2016-10-30

A full implementation of analytical energy gradients for molecular and periodic systems is reported in the TURBOMOLE program package within the framework of Kohn-Sham density functional theory using Gaussian-type orbitals as basis functions. Its key component is a combination of density fitting (DF) approximation and continuous fast multipole method (CFMM) that allows for an efficient calculation of the Coulomb energy gradient. For exchange-correlation part the hierarchical numerical integration scheme (Burow and Sierka, Journal of Chemical Theory and Computation 2011, 7, 3097) is extended to energy gradients. Computational efficiency and asymptotic O(N) scaling behavior of the implementation is demonstrated for various molecular and periodic model systems, with the largest unit cell of hematite containing 640 atoms and 19,072 basis functions. The overall computational effort of energy gradient is comparable to that of the Kohn-Sham matrix formation. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.
Analytic reconstruction of magnetic resonance imaging signal obtained from a periodic encoding field.

PubMed

Rybicki, F J; Hrovat, M I; Patz, S

2000-09-01

We have proposed a two-dimensional PERiodic-Linear (PERL) magnetic encoding field geometry B(x,y) = g(y)y cos(q(x)x) and a magnetic resonance imaging pulse sequence which incorporates two fields to image a two-dimensional spin density: a standard linear gradient in the x dimension, and the PERL field. Because of its periodicity, the PERL field produces a signal where the phase of the two dimensions is functionally different. The x dimension is encoded linearly, but the y dimension appears as the argument of a sinusoidal phase term. Thus, the time-domain signal and image spin density are not related by a two-dimensional Fourier transform. They are related by a one-dimensional Fourier transform in the x dimension and a new Bessel function integral transform (the PERL transform) in the y dimension. The inverse of the PERL transform provides a reconstruction algorithm for the y dimension of the spin density from the signal space. To date, the inverse transform has been computed numerically by a Bessel function expansion over its basis functions. This numerical solution used a finite sum to approximate an infinite summation and thus introduced a truncation error. This work analytically determines the basis functions for the PERL transform and incorporates them into the reconstruction algorithm. The improved algorithm is demonstrated by (1) direct comparison between the numerically and analytically computed basis functions, and (2) reconstruction of a known spin density. The new solution for the basis functions also lends proof of the system function for the PERL transform under specific conditions.
On the equilibrium charge density at tilt grain boundaries

NASA Astrophysics Data System (ADS)

Srikant, V.; Clarke, D. R.

1998-05-01

The equilibrium charge density and free energy of tilt grain boundaries as a function of their misorientation is computed using a Monte Carlo simulation that takes into account both the electrostatic and configurational energies associated with charges at the grain boundary. The computed equilibrium charge density increases with the grain-boundary angle and approaches a saturation value. The equilibrium charge density at large-angle grain boundaries compares well with experimental values for large-angle tilt boundaries in GaAs. The computed grain-boundary electrostatic energy is in agreement with the analytical solution to a one-dimensional Poisson equation at high donor densities but indicates that the analytical solution overestimates the electrostatic energy at lower donor densities.
Active Plasma Resonance Spectroscopy: Evaluation of a fluiddynamic-model of the planar multipole resonance probe using functional analytic methods

NASA Astrophysics Data System (ADS)

Friedrichs, Michael; Brinkmann, Ralf Peter; Oberrath, Jens

2016-09-01

Measuring plasma parameters, e.g. electron density and electron temperature, is an important procedure to verify the stability and behavior of a plasma process. For this purpose the multipole resonance probe (MRP) represents a satisfying solution to measure the electron density. However the influence of the probe on the plasma through its physical presence makes it unattractive for some processes in industrial application. A solution to combine the benefits of the spherical MRP with the ability to integrate the probe into the plasma reactor is introduced by the planar model of the MRP. By coupling the model of the cold plasma with the maxwell equations for electrostatics an analytical model for the admittance of the plasma is derivated, adjusted to cylindrical geometry and solved analytically for the planar MRP using functional analytic methods.
Parallel implementation of Hartree-Fock and density functional theory analytical second derivatives

NASA Astrophysics Data System (ADS)

Baker, Jon; Wolinski, Krzysztof; Malagoli, Massimo; Pulay, Peter

2004-01-01

We present an efficient, parallel implementation for the calculation of Hartree-Fock and density functional theory analytical Hessian (force constant, nuclear second derivative) matrices. These are important for the determination of harmonic vibrational frequencies, and to classify stationary points on potential energy surfaces. Our program is designed for modest parallelism (4-16 CPUs) as exemplified by our standard eight-processor QuantumCube™. We can routinely handle systems with up to 100+ atoms and 1000+ basis functions using under 0.5 GB of RAM memory per CPU. Timings are presented for several systems, ranging in size from aspirin (C9H8O4) to nickel octaethylporphyrin (C36H44N4Ni).
Back in the saddle: large-deviation statistics of the cosmic log-density field

NASA Astrophysics Data System (ADS)

Uhlemann, C.; Codis, S.; Pichon, C.; Bernardeau, F.; Reimberg, P.

2016-08-01

We present a first principle approach to obtain analytical predictions for spherically averaged cosmic densities in the mildly non-linear regime that go well beyond what is usually achieved by standard perturbation theory. A large deviation principle allows us to compute the leading order cumulants of average densities in concentric cells. In this symmetry, the spherical collapse model leads to cumulant generating functions that are robust for finite variances and free of critical points when logarithmic density transformations are implemented. They yield in turn accurate density probability distribution functions (PDFs) from a straightforward saddle-point approximation valid for all density values. Based on this easy-to-implement modification, explicit analytic formulas for the evaluation of the one- and two-cell PDF are provided. The theoretical predictions obtained for the PDFs are accurate to a few per cent compared to the numerical integration, regardless of the density under consideration and in excellent agreement with N-body simulations for a wide range of densities. This formalism should prove valuable for accurately probing the quasi-linear scales of low-redshift surveys for arbitrary primordial power spectra.
Atomic density functional and diagram of structures in the phase field crystal model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ankudinov, V. E., E-mail: vladimir@ankudinov.org; Galenko, P. K.; Kropotin, N. V.

2016-02-15

The phase field crystal model provides a continual description of the atomic density over the diffusion time of reactions. We consider a homogeneous structure (liquid) and a perfect periodic crystal, which are constructed from the one-mode approximation of the phase field crystal model. A diagram of 2D structures is constructed from the analytic solutions of the model using atomic density functionals. The diagram predicts equilibrium atomic configurations for transitions from the metastable state and includes the domains of existence of homogeneous, triangular, and striped structures corresponding to a liquid, a body-centered cubic crystal, and a longitudinal cross section of cylindricalmore » tubes. The method developed here is employed for constructing the diagram for the homogeneous liquid phase and the body-centered iron lattice. The expression for the free energy is derived analytically from density functional theory. The specific features of approximating the phase field crystal model are compared with the approximations and conclusions of the weak crystallization and 2D melting theories.« less
The Hubbard Dimer: A Complete DFT Solution to a Many-Body Problem

NASA Astrophysics Data System (ADS)

Smith, Justin; Carrascal, Diego; Ferrer, Jaime; Burke, Kieron

2015-03-01

In this work we explain the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site asymmetric Hubbard model. We discuss the connection between the lattice and real-space and how this is a simple model for stretched H2. We can solve this elementary example analytically, and with that we can illuminate the underlying logic and aims of DFT. While the many-body solution is analytic, the density functional is given only implicitly. We overcome this difficulty by creating a highly accurate parameterization of the exact function. We use this parameterization to perform benchmark calculations of correlation kinetic energy, the adiabatic connection, etc. We also test Hartree-Fock and the Bethe Ansatz Local Density Approximation. We also discuss and illustrate the derivative discontinuity in the exchange-correlation energy and the infamous gap problem in DFT. DGE-1321846, DE-FG02-08ER46496.
A Semi-Analytical Method for the PDFs of A Ship Rolling in Random Oblique Waves

NASA Astrophysics Data System (ADS)

Liu, Li-qin; Liu, Ya-liu; Xu, Wan-hai; Li, Yan; Tang, You-gang

2018-03-01

The PDFs (probability density functions) and probability of a ship rolling under the random parametric and forced excitations were studied by a semi-analytical method. The rolling motion equation of the ship in random oblique waves was established. The righting arm obtained by the numerical simulation was approximately fitted by an analytical function. The irregular waves were decomposed into two Gauss stationary random processes, and the CARMA (2, 1) model was used to fit the spectral density function of parametric and forced excitations. The stochastic energy envelope averaging method was used to solve the PDFs and the probability. The validity of the semi-analytical method was verified by the Monte Carlo method. The C11 ship was taken as an example, and the influences of the system parameters on the PDFs and probability were analyzed. The results show that the probability of ship rolling is affected by the characteristic wave height, wave length, and the heading angle. In order to provide proper advice for the ship's manoeuvring, the parametric excitations should be considered appropriately when the ship navigates in the oblique seas.
Analytical mass formula and nuclear surface properties in the ETF approximation. Part I: symmetric nuclei

NASA Astrophysics Data System (ADS)

Aymard, François; Gulminelli, Francesca; Margueron, Jérôme

2016-08-01

The problem of determination of nuclear surface energy is addressed within the framework of the extended Thomas Fermi (ETF) approximation using Skyrme functionals. We propose an analytical model for the density profiles with variationally determined diffuseness parameters. In this first paper, we consider the case of symmetric nuclei. In this situation, the ETF functional can be exactly integrated, leading to an analytical formula expressing the surface energy as a function of the couplings of the energy functional. The importance of non-local terms is stressed and it is shown that they cannot be deduced simply from the local part of the functional, as it was suggested in previous works.
Goal-Oriented Probability Density Function Methods for Uncertainty Quantification

DTIC Science & Technology

2015-12-11

approximations or data-driven approaches. We investigated the accuracy of analytical tech- niques based Kubo -Van Kampen operator cumulant expansions for...analytical techniques based Kubo -Van Kampen operator cumulant expansions for Langevin equations driven by fractional Brownian motion and other noises
Stochastic chaos induced by diffusion processes with identical spectral density but different probability density functions.

PubMed

Lei, Youming; Zheng, Fan

2016-12-01

Stochastic chaos induced by diffusion processes, with identical spectral density but different probability density functions (PDFs), is investigated in selected lightly damped Hamiltonian systems. The threshold amplitude of diffusion processes for the onset of chaos is derived by using the stochastic Melnikov method together with a mean-square criterion. Two quasi-Hamiltonian systems, namely, a damped single pendulum and damped Duffing oscillator perturbed by stochastic excitations, are used as illustrative examples. Four different cases of stochastic processes are taking as the driving excitations. It is shown that in such two systems the spectral density of diffusion processes completely determines the threshold amplitude for chaos, regardless of the shape of their PDFs, Gaussian or otherwise. Furthermore, the mean top Lyapunov exponent is employed to verify analytical results. The results obtained by numerical simulations are in accordance with the analytical results. This demonstrates that the stochastic Melnikov method is effective in predicting the onset of chaos in the quasi-Hamiltonian systems.
PAREMD: A parallel program for the evaluation of momentum space properties of atoms and molecules

NASA Astrophysics Data System (ADS)

Meena, Deep Raj; Gadre, Shridhar R.; Balanarayan, P.

2018-03-01

The present work describes a code for evaluating the electron momentum density (EMD), its moments and the associated Shannon information entropy for a multi-electron molecular system. The code works specifically for electronic wave functions obtained from traditional electronic structure packages such as GAMESS and GAUSSIAN. For the momentum space orbitals, the general expression for Gaussian basis sets in position space is analytically Fourier transformed to momentum space Gaussian basis functions. The molecular orbital coefficients of the wave function are taken as an input from the output file of the electronic structure calculation. The analytic expressions of EMD are evaluated over a fine grid and the accuracy of the code is verified by a normalization check and a numerical kinetic energy evaluation which is compared with the analytic kinetic energy given by the electronic structure package. Apart from electron momentum density, electron density in position space has also been integrated into this package. The program is written in C++ and is executed through a Shell script. It is also tuned for multicore machines with shared memory through OpenMP. The program has been tested for a variety of molecules and correlated methods such as CISD, Møller-Plesset second order (MP2) theory and density functional methods. For correlated methods, the PAREMD program uses natural spin orbitals as an input. The program has been benchmarked for a variety of Gaussian basis sets for different molecules showing a linear speedup on a parallel architecture.
Analytic H I-to-H2 Photodissociation Transition Profiles

NASA Astrophysics Data System (ADS)

Bialy, Shmuel; Sternberg, Amiel

2016-05-01

We present a simple analytic procedure for generating atomic (H I) to molecular ({{{H}}}2) density profiles for optically thick hydrogen gas clouds illuminated by far-ultraviolet radiation fields. Our procedure is based on the analytic theory for the structure of one-dimensional H I/{{{H}}}2 photon-dominated regions, presented by Sternberg et al. Depth-dependent atomic and molecular density fractions may be computed for arbitrary gas density, far-ultraviolet field intensity, and the metallicity-dependent H2 formation rate coefficient, and dust absorption cross section in the Lyman-Werner photodissociation band. We use our procedure to generate a set of {{H}} {{I}}{-}{to}{-}{{{H}}}2 transition profiles for a wide range of conditions, from the weak- to strong-field limits, and from super-solar down to low metallicities. We show that if presented as functions of dust optical depth, the {{H}} {{I}} and {{{H}}}2 density profiles depend primarily on the Sternberg “α G parameter” (dimensionless) that determines the dust optical depth associated with the total photodissociated {{H}} {{I}} column. We derive a universal analytic formula for the {{H}} {{I}}{-}{to}{-}{{{H}}}2 transition points as a function of just α G. Our formula will be useful for interpreting emission-line observations of H I/{{{H}}}2 interfaces, for estimating star formation thresholds, and for sub-grid components in hydrodynamics simulations.

Analysis of density effects in plasmas and their influence on electron-impact cross sections

NASA Astrophysics Data System (ADS)

Belkhiri, M.; Poirier, M.

2014-12-01

Density effects in plasmas are analyzed using a Thomas-Fermi approach for free electrons. First, scaling properties are determined for the free-electron potential and density. For hydrogen-like ions, the first two terms of an analytical expansion of this potential as a function of the plasma coupling parameter are obtained. In such ions, from these properties and numerical calculations, a simple analytical fit is proposed for the plasma potential, which holds for any electron density, temperature, and atomic number, at least assuming that Maxwell-Boltzmann statistics is applicable. This allows one to analyze perturbatively the influence of the plasma potential on energies, wave functions, transition rates, and electron-impact collision rates for single-electron ions. Second, plasmas with an arbitrary charge state are considered, using a modified version of the Flexible Atomic Code (FAC) package with a plasma potential based on a Thomas-Fermi approach. Various methods for the collision cross-section calculations are reviewed. The influence of plasma density on these cross sections is analyzed in detail. Moreover, it is demonstrated that, in a given transition, the radiative and collisional-excitation rates are differently affected by the plasma density. Some analytical expressions are proposed for hydrogen-like ions in the limit where the Born or Lotz approximation applies and are compared to the numerical results from the FAC.
Analytic derivation of the next-to-leading order proton structure function F2p(x ,Q2) based on the Laplace transformation

NASA Astrophysics Data System (ADS)

Khanpour, Hamzeh; Mirjalili, Abolfazl; Tehrani, S. Atashbar

2017-03-01

An analytical solution based on the Laplace transformation technique for the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations is presented at next-to-leading order accuracy in perturbative QCD. This technique is also applied to extract the analytical solution for the proton structure function, F2p(x ,Q2) , in the Laplace s space. We present the results for the separate parton distributions of all parton species, including valence quark densities, the antiquark and strange sea parton distribution functions (PDFs), and the gluon distribution. We successfully compare the obtained parton distribution functions and the proton structure function with the results from GJR08 [Gluck, Jimenez-Delgado, and Reya, Eur. Phys. J. C 53, 355 (2008)], 10.1140/epjc/s10052-007-0462-9 and KKT12 [Khanpour, Khorramian, and Tehrani, J. Phys. G 40, 045002 (2013)], 10.1088/0954-3899/40/4/045002 parametrization models as well as the x -space results using QCDnum code. Our calculations show a very good agreement with the available theoretical models as well as the deep inelastic scattering (DIS) experimental data throughout the small and large values of x . The use of our analytical solution to extract the parton densities and the proton structure function is discussed in detail to justify the analysis method, considering the accuracy and speed of calculations. Overall, the accuracy we obtain from the analytical solution using the inverse Laplace transform technique is found to be better than 1 part in 104 to 105. We also present a detailed QCD analysis of nonsinglet structure functions using all available DIS data to perform global QCD fits. In this regard we employ the Jacobi polynomial approach to convert the results from Laplace s space to Bjorken x space. The extracted valence quark densities are also presented and compared to the JR14, MMHT14, NNPDF, and CJ15 PDFs sets. We evaluate the numerical effects of target mass corrections (TMCs) and higher twist (HT) terms on various structure functions, and compare fits to data with and without these corrections.
The H I-to-H2 Transition in a Turbulent Medium

NASA Astrophysics Data System (ADS)

Bialy, Shmuel; Burkhart, Blakesley; Sternberg, Amiel

2017-07-01

We study the effect of density fluctuations induced by turbulence on the H I/H2 structure in photodissociation regions (PDRs) both analytically and numerically. We perform magnetohydrodynamic numerical simulations for both subsonic and supersonic turbulent gas and chemical H I/H2 balance calculations. We derive atomic-to-molecular density profiles and the H I column density probability density function (PDF) assuming chemical equilibrium. We find that, while the H I/H2 density profiles are strongly perturbed in turbulent gas, the mean H I column density is well approximated by the uniform-density analytic formula of Sternberg et al. The PDF width depends on (a) the radiation intensity-to-mean density ratio, (b) the sonic Mach number, and (c) the turbulence decorrelation scale, or driving scale. We derive an analytic model for the H I PDF and demonstrate how our model, combined with 21 cm observations, can be used to constrain the Mach number and driving scale of turbulent gas. As an example, we apply our model to observations of H I in the Perseus molecular cloud. We show that a narrow observed H I PDF may imply small-scale decorrelation, pointing to the potential importance of subcloud-scale turbulence driving.
Laser modification of graphene oxide layers

NASA Astrophysics Data System (ADS)

Malinský, Petr; Macková, Anna; Cutroneo, Mariapompea; Siegel, Jakub; Bohačová, Marie; Klímova, Kateřina; Švorčík, Václav; Sofer, Zdenĕk

2018-01-01

The effect of linearly polarized laser irradiation with various energy densities was successfully used for reduction of graphene oxide (GO). The ion beam analytical methods (RBS, ERDA) were used to follow the elemental composition which is expected as the consequence of GO reduction. The chemical composition analysis was accompanied by structural study showing changed functionalities in the irradiated GO foils using spectroscopy techniques including XPS, FTIR and Raman spectroscopy. The AFM was employed to identify the surface morphology and electric properties evolution were subsequently studied using standard two point method measurement. The used analytical methods report on reduction of irradiated graphene oxide on the surface and the decrease of surface resistivity as a growing function of the laser beam energy density.
Fast semi-analytical method for precise prediction of ion energy distribution functions and sheath electric field in multi-frequency capacitively coupled plasmas

NASA Astrophysics Data System (ADS)

Chen, Wencong; Zhang, Xi; Diao, Dongfeng

2018-05-01

We propose a fast semi-analytical method to predict ion energy distribution functions and sheath electric field in multi-frequency capacitively coupled plasmas, which are difficult to measure in commercial plasma reactors. In the intermediate frequency regime, the ion density within the sheath is strongly modulated by the low-frequency sheath electric field, making the time-independent ion density assumption employed in conventional models invalid. Our results are in a good agreement with experimental measurements and computer simulations. The application of this method will facilitate the understanding of ion–material interaction mechanisms and development of new-generation plasma etching devices.
Analytic second derivative of the energy for density-functional tight-binding combined with the fragment molecular orbital method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakata, Hiroya, E-mail: hiroya.nakata.gt@kyocera.jp; Nishimoto, Yoshio; Fedorov, Dmitri G.

2016-07-28

The analytic second derivative of the energy is developed for the fragment molecular orbital (FMO) method combined with density-functional tight-binding (DFTB), enabling simulations of infrared and Raman spectra of large molecular systems. The accuracy of the method is established in comparison to full DFTB without fragmentation for a set of representative systems. The performance of the FMO-DFTB Hessian is discussed for molecular systems containing up to 10 041 atoms. The method is applied to the study of the binding of α-cyclodextrin to polyethylene glycol, and the calculated IR spectrum of an epoxy amine oligomer reproduces experiment reasonably well.
Finite-temperature dynamics of the Mott insulating Hubbard chain

NASA Astrophysics Data System (ADS)

Nocera, Alberto; Essler, Fabian H. L.; Feiguin, Adrian E.

2018-01-01

We study the dynamical response of the half-filled one-dimensional Hubbard model for a range of interaction strengths U and temperatures T by a combination of numerical and analytical techniques. Using time-dependent density matrix renormalization group computations we find that the single-particle spectral function undergoes a crossover to a spin-incoherent Luttinger liquid regime at temperatures T ˜J =4 t2/U for sufficiently large U >4 t . At smaller values of U and elevated temperatures the spectral function is found to exhibit two thermally broadened bands of excitations, reminiscent of what is found in the Hubbard-I approximation. The dynamical density-density response function is shown to exhibit a finite-temperature resonance at low frequencies inside the Mott gap, with a physical origin similar to the Villain mode in gapped quantum spin chains. We complement our numerical computations by developing an analytic strong-coupling approach to the low-temperature dynamics in the spin-incoherent regime.
Eddy current loss analysis of open-slot fault-tolerant permanent-magnet machines based on conformal mapping method

NASA Astrophysics Data System (ADS)

Ji, Jinghua; Luo, Jianhua; Lei, Qian; Bian, Fangfang

2017-05-01

This paper proposed an analytical method, based on conformal mapping (CM) method, for the accurate evaluation of magnetic field and eddy current (EC) loss in fault-tolerant permanent-magnet (FTPM) machines. The aim of modulation function, applied in CM method, is to change the open-slot structure into fully closed-slot structure, whose air-gap flux density is easy to calculate analytically. Therefore, with the help of Matlab Schwarz-Christoffel (SC) Toolbox, both the magnetic flux density and EC density of FTPM machine are obtained accurately. Finally, time-stepped transient finite-element method (FEM) is used to verify the theoretical analysis, showing that the proposed method is able to predict the magnetic flux density and EC loss precisely.
Density Functionals of Chemical Bonding

PubMed Central

Putz, Mihai V.

2008-01-01

The behavior of electrons in general many-electronic systems throughout the density functionals of energy is reviewed. The basic physico-chemical concepts of density functional theory are employed to highlight the energy role in chemical structure while its extended influence in electronic localization function helps in chemical bonding understanding. In this context the energy functionals accompanied by electronic localization functions may provide a comprehensive description of the global-local levels electronic structures in general and of chemical bonds in special. Becke-Edgecombe and author’s Markovian electronic localization functions are discussed at atomic, molecular and solid state levels. Then, the analytical survey of the main workable kinetic, exchange, and correlation density functionals within local and gradient density approximations is undertaken. The hierarchy of various energy functionals is formulated by employing both the parabolic and statistical correlation degree of them with the electronegativity and chemical hardness indices by means of quantitative structure-property relationship (QSPR) analysis for basic atomic and molecular systems. PMID:19325846
Statistics of primordial density perturbations from discrete seed masses

NASA Technical Reports Server (NTRS)

Scherrer, Robert J.; Bertschinger, Edmund

1991-01-01

The statistics of density perturbations for general distributions of seed masses with arbitrary matter accretion is examined. Formal expressions for the power spectrum, the N-point correlation functions, and the density distribution function are derived. These results are applied to the case of uncorrelated seed masses, and power spectra are derived for accretion of both hot and cold dark matter plus baryons. The reduced moments (cumulants) of the density distribution are computed and used to obtain a series expansion for the density distribution function. Analytic results are obtained for the density distribution function in the case of a distribution of seed masses with a spherical top-hat accretion pattern. More generally, the formalism makes it possible to give a complete characterization of the statistical properties of any random field generated from a discrete linear superposition of kernels. In particular, the results can be applied to density fields derived by smoothing a discrete set of points with a window function.
An analytical model for regular respiratory signals derived from the probability density function of Rayleigh distribution.

PubMed

Li, Xin; Li, Ye

2015-01-01

Regular respiratory signals (RRSs) acquired with physiological sensing systems (e.g., the life-detection radar system) can be used to locate survivors trapped in debris in disaster rescue, or predict the breathing motion to allow beam delivery under free breathing conditions in external beam radiotherapy. Among the existing analytical models for RRSs, the harmonic-based random model (HRM) is shown to be the most accurate, which, however, is found to be subject to considerable error if the RRS has a slowly descending end-of-exhale (EOE) phase. The defect of the HRM motivates us to construct a more accurate analytical model for the RRS. In this paper, we derive a new analytical RRS model from the probability density function of Rayleigh distribution. We evaluate the derived RRS model by using it to fit a real-life RRS in the sense of least squares, and the evaluation result shows that, our presented model exhibits lower error and fits the slowly descending EOE phases of the real-life RRS better than the HRM.
Density- and wavefunction-normalized Cartesian spherical harmonics for l ≤ 20

DOE PAGES

Michael, J. Robert; Volkov, Anatoliy

2015-03-01

The widely used pseudoatom formalism in experimental X-ray charge-density studies makes use of real spherical harmonics when describing the angular component of aspherical deformations of the atomic electron density in molecules and crystals. The analytical form of the density-normalized Cartesian spherical harmonic functions for up to l ≤ 7 and the corresponding normalization coefficients were reported previously by Paturle & Coppens. It was shown that the analytical form for normalization coefficients is available primarily forl ≤ 4. Only in very special cases it is possible to derive an analytical representation of the normalization coefficients for 4 < l ≤ 7.more » In most cases for l > 4 the density normalization coefficients were calculated numerically to within seven significant figures. In this study we review the literature on the density-normalized spherical harmonics, clarify the existing notations, use the Paturle–Coppens method in the Wolfram Mathematicasoftware to derive the Cartesian spherical harmonics for l ≤ 20 and determine the density normalization coefficients to 35 significant figures, and computer-generate a Fortran90 code. The article primarily targets researchers who work in the field of experimental X-ray electron density, but may be of some use to all who are interested in Cartesian spherical harmonics.« less
The H i-to-H{sub 2} Transition in a Turbulent Medium

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bialy, Shmuel; Sternberg, Amiel; Burkhart, Blakesley, E-mail: shmuelbi@mail.tau.ac.il

2017-07-10

We study the effect of density fluctuations induced by turbulence on the H i/H{sub 2} structure in photodissociation regions (PDRs) both analytically and numerically. We perform magnetohydrodynamic numerical simulations for both subsonic and supersonic turbulent gas and chemical H i/H{sub 2} balance calculations. We derive atomic-to-molecular density profiles and the H i column density probability density function (PDF) assuming chemical equilibrium. We find that, while the H i/H{sub 2} density profiles are strongly perturbed in turbulent gas, the mean H i column density is well approximated by the uniform-density analytic formula of Sternberg et al. The PDF width depends onmore » (a) the radiation intensity–to–mean density ratio, (b) the sonic Mach number, and (c) the turbulence decorrelation scale, or driving scale. We derive an analytic model for the H i PDF and demonstrate how our model, combined with 21 cm observations, can be used to constrain the Mach number and driving scale of turbulent gas. As an example, we apply our model to observations of H i in the Perseus molecular cloud. We show that a narrow observed H i PDF may imply small-scale decorrelation, pointing to the potential importance of subcloud-scale turbulence driving.« less
Dynamics of a spin-boson model with structured spectral density

NASA Astrophysics Data System (ADS)

Kurt, Arzu; Eryigit, Resul

2018-05-01

We report the results of a study of the dynamics of a two-state system coupled to an environment with peaked spectral density. An exact analytical expression for the bath correlation function is obtained. Validity range of various approximations to the correlation function for calculating the population difference of the system is discussed as function of tunneling splitting, oscillator frequency, coupling constant, damping rate and the temperature of the bath. An exact expression for the population difference, for a limited range of parameters, is derived.
Quantitative detection of pathogens in centrifugal microfluidic disks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Koh, Chung-Yan; Schaff, Ulrich Y.; Sommer, Gregory Jon

A system and methods for detection of a nucleic acid including forming a plurality of nucleic acid detection complexes are described, each of the complexes including a nucleic acid analyte, a detection agent and a functionalized probe. The method further including binding the nucleic acid detection complexes to a plurality of functionalized particles in a fluid sample and separating the functionalized particles having the nucleic acid detection complexes bound thereto from the fluid sample using a density media. The nucleic acid analyte is detected by detecting the detection agent.
Image correlation and sampling study

NASA Technical Reports Server (NTRS)

Popp, D. J.; Mccormack, D. S.; Sedwick, J. L.

1972-01-01

The development of analytical approaches for solving image correlation and image sampling of multispectral data is discussed. Relevant multispectral image statistics which are applicable to image correlation and sampling are identified. The general image statistics include intensity mean, variance, amplitude histogram, power spectral density function, and autocorrelation function. The translation problem associated with digital image registration and the analytical means for comparing commonly used correlation techniques are considered. General expressions for determining the reconstruction error for specific image sampling strategies are developed.
Analytic second derivative of the energy for density functional theory based on the three-body fragment molecular orbital method

NASA Astrophysics Data System (ADS)

Nakata, Hiroya; Fedorov, Dmitri G.; Zahariev, Federico; Schmidt, Michael W.; Kitaura, Kazuo; Gordon, Mark S.; Nakamura, Shinichiro

2015-03-01

Analytic second derivatives of the energy with respect to nuclear coordinates have been developed for spin restricted density functional theory (DFT) based on the fragment molecular orbital method (FMO). The derivations were carried out for the three-body expansion (FMO3), and the two-body expressions can be obtained by neglecting the three-body corrections. Also, the restricted Hartree-Fock (RHF) Hessian for FMO3 can be obtained by neglecting the density-functional related terms. In both the FMO-RHF and FMO-DFT Hessians, certain terms with small magnitudes are neglected for computational efficiency. The accuracy of the FMO-DFT Hessian in terms of the Gibbs free energy is evaluated for a set of polypeptides and water clusters and found to be within 1 kcal/mol of the corresponding full (non-fragmented) ab initio calculation. The FMO-DFT method is also applied to transition states in SN2 reactions and for the computation of the IR and Raman spectra of a small Trp-cage protein (PDB: 1L2Y). Some computational timing analysis is also presented.
Quantum mechanical/molecular mechanical/continuum style solvation model: time-dependent density functional theory.

PubMed

Thellamurege, Nandun M; Cui, Fengchao; Li, Hui

2013-08-28

A combined quantum mechanical/molecular mechanical/continuum (QM/MMpol/C) style method is developed for time-dependent density functional theory (TDDFT, including long-range corrected TDDFT) method, induced dipole polarizable force field, and induced surface charge continuum model. Induced dipoles and induced charges are included in the TDDFT equations to solve for the transition energies, relaxed density, and transition density. Analytic gradient is derived and implemented for geometry optimization and molecular dynamics simulation. QM/MMpol/C style DFT and TDDFT methods are used to study the hydrogen bonding of the photoactive yellow protein chromopore in ground state and excited state.
Analytical excited state forces for the time-dependent density-functional tight-binding method.

PubMed

Heringer, D; Niehaus, T A; Wanko, M; Frauenheim, Th

2007-12-01

An analytical formulation for the geometrical derivatives of excitation energies within the time-dependent density-functional tight-binding (TD-DFTB) method is presented. The derivation is based on the auxiliary functional approach proposed in [Furche and Ahlrichs, J Chem Phys 2002, 117, 7433]. To validate the quality of the potential energy surfaces provided by the method, adiabatic excitation energies, excited state geometries, and harmonic vibrational frequencies were calculated for a test set of molecules in excited states of different symmetry and multiplicity. According to the results, the TD-DFTB scheme surpasses the performance of configuration interaction singles and the random phase approximation but has a lower quality than ab initio time-dependent density-functional theory. As a consequence of the special form of the approximations made in TD-DFTB, the scaling exponent of the method can be reduced to three, similar to the ground state. The low scaling prefactor and the satisfactory accuracy of the method makes TD-DFTB especially suitable for molecular dynamics simulations of dozens of atoms as well as for the computation of luminescence spectra of systems containing hundreds of atoms. (c) 2007 Wiley Periodicals, Inc.
Why do ultrasoft repulsive particles cluster and crystallize? Analytical results from density-functional theory.

PubMed

Likos, Christos N; Mladek, Bianca M; Gottwald, Dieter; Kahl, Gerhard

2007-06-14

We demonstrate the accuracy of the hypernetted chain closure and of the mean-field approximation for the calculation of the fluid-state properties of systems interacting by means of bounded and positive pair potentials with oscillating Fourier transforms. Subsequently, we prove the validity of a bilinear, random-phase density functional for arbitrary inhomogeneous phases of the same systems. On the basis of this functional, we calculate analytically the freezing parameters of the latter. We demonstrate explicitly that the stable crystals feature a lattice constant that is independent of density and whose value is dictated by the position of the negative minimum of the Fourier transform of the pair potential. This property is equivalent with the existence of clusters, whose population scales proportionally to the density. We establish that regardless of the form of the interaction potential and of the location on the freezing line, all cluster crystals have a universal Lindemann ratio Lf=0.189 at freezing. We further make an explicit link between the aforementioned density functional and the harmonic theory of crystals. This allows us to establish an equivalence between the emergence of clusters and the existence of negative Fourier components of the interaction potential. Finally, we make a connection between the class of models at hand and the system of infinite-dimensional hard spheres, when the limits of interaction steepness and space dimension are both taken to infinity in a particularly described fashion.

Encircling the dark: constraining dark energy via cosmic density in spheres

NASA Astrophysics Data System (ADS)

Codis, S.; Pichon, C.; Bernardeau, F.; Uhlemann, C.; Prunet, S.

2016-08-01

The recently published analytic probability density function for the mildly non-linear cosmic density field within spherical cells is used to build a simple but accurate maximum likelihood estimate for the redshift evolution of the variance of the density, which, as expected, is shown to have smaller relative error than the sample variance. This estimator provides a competitive probe for the equation of state of dark energy, reaching a few per cent accuracy on wp and wa for a Euclid-like survey. The corresponding likelihood function can take into account the configuration of the cells via their relative separations. A code to compute one-cell-density probability density functions for arbitrary initial power spectrum, top-hat smoothing and various spherical-collapse dynamics is made available online, so as to provide straightforward means of testing the effect of alternative dark energy models and initial power spectra on the low-redshift matter distribution.
Analytic study of the effect of dark energy-dark matter interaction on the growth of structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marcondes, Rafael J.F.; Landim, Ricardo C.G.; Costa, André A.

2016-12-01

Large-scale structure has been shown as a promising cosmic probe for distinguishing and constraining dark energy models. Using the growth index parametrization, we obtain an analytic formula for the growth rate of structures in a coupled dark energy model in which the exchange of energy-momentum is proportional to the dark energy density. We find that the evolution of f σ{sub 8} can be determined analytically once we know the coupling, the dark energy equation of state, the present value of the dark energy density parameter and the current mean amplitude of dark matter fluctuations. After correcting the growth function formore » the correspondence with the velocity field through the continuity equation in the interacting model, we use our analytic result to compare the model's predictions with large-scale structure observations.« less
Prediction of thermal cycling induced matrix cracking

NASA Technical Reports Server (NTRS)

Mcmanus, Hugh L.

1992-01-01

Thermal fatigue has been observed to cause matrix cracking in laminated composite materials. A method is presented to predict transverse matrix cracks in composite laminates subjected to cyclic thermal load. Shear lag stress approximations and a simple energy-based fracture criteria are used to predict crack densities as a function of temperature. Prediction of crack densities as a function of thermal cycling is accomplished by assuming that fatigue degrades the material's inherent resistance to cracking. The method is implemented as a computer program. A simple experiment provides data on progressive cracking of a laminate with decreasing temperature. Existing data on thermal fatigue is also used. Correlations of the analytical predictions to the data are very good. A parametric study using the analytical method is presented which provides insight into material behavior under cyclical thermal loads.
Analytic Expressions for the Gravity Gradient Tensor of 3D Prisms with Depth-Dependent Density

NASA Astrophysics Data System (ADS)

Jiang, Li; Liu, Jie; Zhang, Jianzhong; Feng, Zhibing

2017-12-01

Variable-density sources have been paid more attention in gravity modeling. We conduct the computation of gravity gradient tensor of given mass sources with variable density in this paper. 3D rectangular prisms, as simple building blocks, can be used to approximate well 3D irregular-shaped sources. A polynomial function of depth can represent flexibly the complicated density variations in each prism. Hence, we derive the analytic expressions in closed form for computing all components of the gravity gradient tensor due to a 3D right rectangular prism with an arbitrary-order polynomial density function of depth. The singularity of the expressions is analyzed. The singular points distribute at the corners of the prism or on some of the lines through the edges of the prism in the lower semi-space containing the prism. The expressions are validated, and their numerical stability is also evaluated through numerical tests. The numerical examples with variable-density prism and basin models show that the expressions within their range of numerical stability are superior in computational accuracy and efficiency to the common solution that sums up the effects of a collection of uniform subprisms, and provide an effective method for computing gravity gradient tensor of 3D irregular-shaped sources with complicated density variation. In addition, the tensor computed with variable density is different in magnitude from that with constant density. It demonstrates the importance of the gravity gradient tensor modeling with variable density.
Spacecraft Observations and Analytic Theory of Crescent-Shaped Electron Distributions in Asymmetric Magnetic Reconnection

NASA Astrophysics Data System (ADS)

Egedal, J.; Le, A.; Daughton, W.; Wetherton, B.; Cassak, P. A.; Chen, L.-J.; Lavraud, B.; Torbert, R. B.; Dorelli, J.; Gershman, D. J.; Avanov, L. A.

2016-10-01

Supported by a kinetic simulation, we derive an exclusion energy parameter EX providing a lower kinetic energy bound for an electron to cross from one inflow region to the other during magnetic reconnection. As by a Maxwell demon, only high-energy electrons are permitted to cross the inner reconnection region, setting the electron distribution function observed along the low-density side separatrix during asymmetric reconnection. The analytic model accounts for the two distinct flavors of crescent-shaped electron distributions observed by spacecraft in a thin boundary layer along the low-density separatrix.
Bogoliubov theory of acoustic Hawking radiation in Bose-Einstein condensates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Recati, A.; Physik-Department, Technische Universitaet Muenchen, D-85748 Garching; Pavloff, N.

2009-10-15

We apply the microscopic Bogoliubov theory of dilute Bose-Einstein condensates to analyze quantum and thermal fluctuations in a flowing atomic condensate in the presence of a sonic horizon. For the simplest case of a step-like horizon, closed-form analytical expressions are found for the spectral distribution of the analog Hawking radiation and for the density correlation function. The peculiar long-distance density correlations that appear as a consequence of the Hawking emission features turns out to be reinforced by a finite initial temperature of the condensate. The analytical results are in good quantitative agreement with first principle numerical calculations.
Spacecraft Observations and Analytic Theory of Crescent-Shaped Electron Distributions in Asymmetric Magnetic Reconnection

NASA Technical Reports Server (NTRS)

Egedal, J.; Le, A.; Daughton, W.; Wetherton, B.; Cassak, P.A.; Chen, L.-J.; Lavraud, B.; Trobert, Roy; Dorelli, J.; Gershman, D. J.;

2016-01-01

Supported by a kinetic simulation, we derive an exclusion energy parameter EX providing a lower kinetic energy bound for an electron to cross from one inflow region to the other during magnetic reconnection. As by a Maxwell Demon, only high energy electrons are permitted to cross the inner-reconnection region, setting the electron distribution function observed along the low density side separatrix during asymmetric reconnection. The analytic model accounts for the two distinct flavors of crescent-shaped electron distributions observed by spacecraft in a thin boundary layer along the low density separatrix.

Energy transmission transformer for a wireless capsule endoscope: analysis of specific absorption rate and current density in biological tissue.

PubMed

Shiba, Kenji; Nagato, Tomohiro; Tsuji, Toshio; Koshiji, Kohji

2008-07-01

This paper reports on the electromagnetic influences on the analysis of biological tissue surrounding a prototype energy transmission system for a wireless capsule endoscope. Specific absorption rate (SAR) and current density were analyzed by electromagnetic simulator in a model consisting of primary coil and a human trunk including the skin, fat, muscle, small intestine, backbone, and blood. First, electric and magnetic strength in the same conditions as the analytical model were measured and compared to the analytical values to confirm the validity of the analysis. Then, SAR and current density as a function of frequency and output power were analyzed. The validity of the analysis was confirmed by comparing the analytical values with the measured ones. The SAR was below the basic restrictions of the International Commission on Nonionizing Radiation Protection (ICNIRP). At the same time, the results for current density show that the influence on biological tissue was lowest in the 300-400 kHz range, indicating that it was possible to transmit energy safely up to 160 mW. In addition, we confirmed that the current density has decreased by reducing the primary coil's current.
Statistical correlations in an ideal gas of particles obeying fractional exclusion statistics.

PubMed

Pellegrino, F M D; Angilella, G G N; March, N H; Pucci, R

2007-12-01

After a brief discussion of the concepts of fractional exchange and fractional exclusion statistics, we report partly analytical and partly numerical results on thermodynamic properties of assemblies of particles obeying fractional exclusion statistics. The effect of dimensionality is one focal point, the ratio mu/k_(B)T of chemical potential to thermal energy being obtained numerically as a function of a scaled particle density. Pair correlation functions are also presented as a function of the statistical parameter, with Friedel oscillations developing close to the fermion limit, for sufficiently large density.
Probability density function learning by unsupervised neurons.

PubMed

Fiori, S

2001-10-01

In a recent work, we introduced the concept of pseudo-polynomial adaptive activation function neuron (FAN) and presented an unsupervised information-theoretic learning theory for such structure. The learning model is based on entropy optimization and provides a way of learning probability distributions from incomplete data. The aim of the present paper is to illustrate some theoretical features of the FAN neuron, to extend its learning theory to asymmetrical density function approximation, and to provide an analytical and numerical comparison with other known density function estimation methods, with special emphasis to the universal approximation ability. The paper also provides a survey of PDF learning from incomplete data, as well as results of several experiments performed on real-world problems and signals.
Scaling relations for a needle-like electron beam plasma from the self-similar behavior in beam propagation

NASA Astrophysics Data System (ADS)

Bai, Xiaoyan; Chen, Chen; Li, Hong; Liu, Wandong; Chen, Wei

2017-10-01

Scaling relations of the main parameters of a needle-like electron beam plasma (EBP) to the initial beam energy, beam current, and discharge pressures are presented. The relations characterize the main features of the plasma in three parameter space and can provide great convenience in plasma design with electron beams. First, starting from the self-similar behavior of electron beam propagation, energy and charge depositions in beam propagation were expressed analytically as functions of the three parameters. Second, according to the complete coupled theoretical model of an EBP and appropriate assumptions, independent equations controlling the density and space charges were derived. Analytical expressions for the density and charges versus functions of energy and charge depositions were obtained. Finally, with the combination of the expressions derived in the above two steps, scaling relations of the density and potential to the three parameters were constructed. Meanwhile, numerical simulations were used to test part of the scaling relations.
The exact solution of the monoenergetic transport equation for critical cylinders

NASA Technical Reports Server (NTRS)

Westfall, R. M.; Metcalf, D. R.

1972-01-01

An analytic solution for the critical, monoenergetic, bare, infinite cylinder is presented. The solution is obtained by modifying a previous development based on a neutron density transform and Case's singular eigenfunction method. Numerical results for critical radii and the neutron density as a function of position are included and compared with the results of other methods.
The maximal-density mass function for primordial black hole dark matter

NASA Astrophysics Data System (ADS)

Lehmann, Benjamin V.; Profumo, Stefano; Yant, Jackson

2018-04-01

The advent of gravitational wave astronomy has rekindled interest in primordial black holes (PBH) as a dark matter candidate. As there are many different observational probes of the PBH density across different masses, constraints on PBH models are dependent on the functional form of the PBH mass function. This complicates general statements about the mass functions allowed by current data, and, in particular, about the maximum total density of PBH. Numerical studies suggest that some forms of extended mass functions face tighter constraints than monochromatic mass functions, but they do not preclude the existence of a functional form for which constraints are relaxed. We use analytical arguments to show that the mass function which maximizes the fraction of the matter density in PBH subject to all constraints is a finite linear combination of monochromatic mass functions. We explicitly compute the maximum fraction of dark matter in PBH for different combinations of current constraints, allowing for total freedom of the mass function. Our framework elucidates the dependence of the maximum PBH density on the form of observational constraints, and we discuss the implications of current and future constraints for the viability of the PBH dark matter paradigm.
Liquid Drop Model for Charged Spherical Metal Clusters

NASA Astrophysics Data System (ADS)

Seidl, M.; Brack, M.

1996-02-01

The average ground-state energy of a charged spherical metal cluster withNatoms andzexcessive valence electrons, i.e., with net chargeQ=-ezand radiusR=rsN1/3, is presented in the liquid drop model (LDM) expansionE(N, z)=avN+asN2/3+acN1/3+a0(z)+a-1(z) N-1/3+O(N-2/3). We derive analytical expressions for the leading LDM coefficientsav,as,ac, and, in particular, for the charge dependence of the further LDM coefficientsa0anda-1, using the jellium model and density functional theory in the local density approximation. We obtain for the ionization energyI(R)=W+α(e2/R)+O(R-2), with the bulk work functionW=[Φ(+∞)-Φ(0)]-eb, given first by Mahan and Schaich in terms of the electrostatic potentialΦand the bulk energy per electroneb, and a new analytical expression for the dimensionless coefficientα. We demonstrate that within classical theoryα={1}/{2} but, in agreement with experimental information,αtends to ∼0.4 if quantum-mechanical contributions are included. In order to test and confirm our analytical expressions, we discuss the numerical results of semiclassical density variational calculations in the extended Thomas-Fermi model.
Density of states and extent of wave function: two crucial factors for small polaron hopping conductivity in 1D

NASA Astrophysics Data System (ADS)

Dimakogianni, M.; Simserides, C.; Triberis, G. P.

2013-07-01

We introduce a theoretical model to scrutinize the conductivity of small polarons in 1D disordered systems, focusing on two crucial - as will be demonstrated - factors: the density of states and the spatial extent of the electronic wave function. The investigation is performed for any temperature up to 300 K and under electric field of arbitrary strength up to the polaron dissociation limit. To accomplish this task, we combine analytical work with numerical calculations.
A third-generation density-functional-theory-based method for calculating canonical molecular orbitals of large molecules.

PubMed

Hirano, Toshiyuki; Sato, Fumitoshi

2014-07-28

We used grid-free modified Cholesky decomposition (CD) to develop a density-functional-theory (DFT)-based method for calculating the canonical molecular orbitals (CMOs) of large molecules. Our method can be used to calculate standard CMOs, analytically compute exchange-correlation terms, and maximise the capacity of next-generation supercomputers. Cholesky vectors were first analytically downscaled using low-rank pivoted CD and CD with adaptive metric (CDAM). The obtained Cholesky vectors were distributed and stored on each computer node in a parallel computer, and the Coulomb, Fock exchange, and pure exchange-correlation terms were calculated by multiplying the Cholesky vectors without evaluating molecular integrals in self-consistent field iterations. Our method enables DFT and massively distributed memory parallel computers to be used in order to very efficiently calculate the CMOs of large molecules.
Extended analytical solutions for effective elastic moduli of cracked porous media

NASA Astrophysics Data System (ADS)

Nguyen, Sy-Tuan; To, Quy Dong; Vu, Minh Ngoc

2017-05-01

Extended solutions are derived, on the basis of the micromechanical methods, for the effective elastic moduli of porous media containing stiff pores and both open and closed cracks. Analytical formulas of the overall bulk and shear moduli are obtained as functions of the elastic moduli of the solid skeleton, porosity and the densities of open and closed cracks families. We show that the obtained results are extensions of the classical widely used Walsh's (JGR, 1965) and Budiansky-O‧Connell's (JGR, 1974) solutions. Parametric sensitivity analysis clarifies the impact of the model parameters on the effective elastic properties. An inverse analysis, using sonic and density data, is considered to quantify the density of both open and closed cracks. It is observed that the density of closed cracks depends strongly on stress condition while the dependence of open cracks on the confining stress is negligible.
Analytical Plug-In Method for Kernel Density Estimator Applied to Genetic Neutrality Study

NASA Astrophysics Data System (ADS)

Troudi, Molka; Alimi, Adel M.; Saoudi, Samir

2008-12-01

The plug-in method enables optimization of the bandwidth of the kernel density estimator in order to estimate probability density functions (pdfs). Here, a faster procedure than that of the common plug-in method is proposed. The mean integrated square error (MISE) depends directly upon [InlineEquation not available: see fulltext.] which is linked to the second-order derivative of the pdf. As we intend to introduce an analytical approximation of [InlineEquation not available: see fulltext.], the pdf is estimated only once, at the end of iterations. These two kinds of algorithm are tested on different random variables having distributions known for their difficult estimation. Finally, they are applied to genetic data in order to provide a better characterisation in the mean of neutrality of Tunisian Berber populations.
Dynamic correlations in the highly dilute 2D electron liquid: Loss function, critical wave vector and analytic plasmon dispersion

NASA Astrophysics Data System (ADS)

Drachta, Jürgen T.; Kreil, Dominik; Hobbiger, Raphael; Böhm, Helga M.

2018-03-01

Correlations, highly important in low-dimensional systems, are known to decrease the plasmon dispersion of two-dimensional electron liquids. Here we calculate the plasmon properties, applying the 'Dynamic Many-Body Theory', accounting for correlated two-particle-two-hole fluctuations. These dynamic correlations are found to significantly lower the plasmon's energy. For the data obtained numerically, we provide an analytic expression that is valid across a wide range both of densities and of wave vectors. Finally, we demonstrate how this can be invoked in determining the actual electron densities from measurements on an AlGaAs quantum well.
Spacecraft Observations and Analytic Theory of Crescent-Shaped Electron Distributions in Asymmetric Magnetic Reconnection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Egedal, J.; Le, A.; Daughton, W.

Supported by a kinetic simulation, we derive in this paper an exclusion energy parametermore » $${\\mathcal{E}}_{X}$$ providing a lower kinetic energy bound for an electron to cross from one inflow region to the other during magnetic reconnection. As by a Maxwell demon, only high-energy electrons are permitted to cross the inner reconnection region, setting the electron distribution function observed along the low-density side separatrix during asymmetric reconnection. Finally, the analytic model accounts for the two distinct flavors of crescent-shaped electron distributions observed by spacecraft in a thin boundary layer along the low-density separatrix.« less

Spacecraft Observations and Analytic Theory of Crescent-Shaped Electron Distributions in Asymmetric Magnetic Reconnection

DOE PAGES

Egedal, J.; Le, A.; Daughton, W.; ...

2016-10-24

Supported by a kinetic simulation, we derive in this paper an exclusion energy parametermore » $${\\mathcal{E}}_{X}$$ providing a lower kinetic energy bound for an electron to cross from one inflow region to the other during magnetic reconnection. As by a Maxwell demon, only high-energy electrons are permitted to cross the inner reconnection region, setting the electron distribution function observed along the low-density side separatrix during asymmetric reconnection. Finally, the analytic model accounts for the two distinct flavors of crescent-shaped electron distributions observed by spacecraft in a thin boundary layer along the low-density separatrix.« less
Analytic second derivative of the energy for density functional theory based on the three-body fragment molecular orbital method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakata, Hiroya, E-mail: nakata.h.ab@m.titech.ac.jp; RIKEN, Research Cluster for Innovation, Nakamura Lab, 2-1 Hirosawa, Wako, Saitama 351-0198; Japan Society for the Promotion of Science, Kojimachi Business Center Building, 5-3-1 Kojimachi, Chiyoda-ku, Tokyo 102-0083

2015-03-28

Analytic second derivatives of the energy with respect to nuclear coordinates have been developed for spin restricted density functional theory (DFT) based on the fragment molecular orbital method (FMO). The derivations were carried out for the three-body expansion (FMO3), and the two-body expressions can be obtained by neglecting the three-body corrections. Also, the restricted Hartree-Fock (RHF) Hessian for FMO3 can be obtained by neglecting the density-functional related terms. In both the FMO-RHF and FMO-DFT Hessians, certain terms with small magnitudes are neglected for computational efficiency. The accuracy of the FMO-DFT Hessian in terms of the Gibbs free energy is evaluatedmore » for a set of polypeptides and water clusters and found to be within 1 kcal/mol of the corresponding full (non-fragmented) ab initio calculation. The FMO-DFT method is also applied to transition states in S{sub N}2 reactions and for the computation of the IR and Raman spectra of a small Trp-cage protein (PDB: 1L2Y). Some computational timing analysis is also presented.« less
Electrokinetic flow in a capillary with a charge-regulating surface polymer layer.

PubMed

Keh, Huan J; Ding, Jau M

2003-07-15

An analytical study of the steady electrokinetic flow in a long uniform capillary tube or slit is presented. The inside wall of the capillary is covered by a layer of adsorbed or covalently bound charge-regulating polymer in equilibrium with the ambient electrolyte solution. In this solvent-permeable and ion-penetrable surface polyelectrolyte layer, ionogenic functional groups and frictional segments are assumed to distribute at uniform densities. The electrical potential and space charge density distributions in the cross section of the capillary are obtained by solving the linearized Poisson-Boltzmann equation. The fluid velocity profile due to the application of an electric field and a pressure gradient through the capillary is obtained from the analytical solution of a modified Navier-Stokes/Brinkman equation. Explicit formulas for the electroosmotic velocity, the average fluid velocity and electric current density on the cross section, and the streaming potential in the capillary are also derived. The results demonstrate that the direction of the electroosmotic flow and the magnitudes of the fluid velocity and electric current density are dominated by the fixed charge density inside the surface polymer layer, which is determined by the regulation characteristics such as the dissociation equilibrium constants of the ionogenic functional groups in the surface layer and the concentration of the potential-determining ions in the bulk solution.
Binary collision approximations for the memory function for density fluctuations in equilibrium atomic liquids

NASA Astrophysics Data System (ADS)

Noah, Joyce E.

Time correlation functions of density fluctuations of liquids at equilibrium can be used to relate the microscopic dynamics of a liquid to its macroscopic transport properties. Time correlation functions are especially useful since they can be generated in a variety of ways, from scattering experiments to computer simulation to analytic theory. The kinetic theory of fluctuations in equilibrium liquids is an analytic theory for calculating correlation functions using memory functions. In this work, we use a diagrammatic formulation of the kinetic theory to develop a series of binary collision approximations for the collisional part of the memory function. We define binary collisions as collisions between two distinct density fluctuations whose identities are fixed during the duration of a collsion. R approximations are for the short time part of the memory function, and build upon the work of Ranganathan and Andersen. These approximations have purely repulsive interactions between the fluctuations. The second type of approximation, RA approximations, is for the longer time part of the memory function, where the density fluctuations now interact via repulsive and attractive forces. Although RA approximations are a natural extension of R approximations, they permit two density fluctuations to become trapped in the wells of the interaction potential, leading to long-lived oscillatory behavior, which is unphysical. Therefore we consider S approximations which describe binary particles which experience the random effect of the surroundings while interacting via repulsive or repulsive and attractive interactions. For each of these approximations for the memory function we numerically solve the kinetic equation to generate correlation functions. These results are compared to molecular dynamics results for the correlation functions. Comparing the successes and failures of the different approximations, we conclude that R approximations give more accurate intermediate and long time results while RA and S approximations do particularly well at predicting the short time behavior. Lastly, we also develop a series of non-graphically derived approximations and use an optimization procedure to determine the underlying memory function from the simulation data. These approaches provide valuable information about the memory function that will be used in the development of future kinetic theories.
Exact density-potential pairs from complex-shifted axisymmetric systems

NASA Astrophysics Data System (ADS)

Ciotti, Luca; Marinacci, Federico

2008-07-01

In a previous paper, the complex-shift method has been applied to self-gravitating spherical systems, producing new analytical axisymmetric density-potential pairs. We now extend the treatment to the Miyamoto-Nagai disc and the Binney logarithmic halo, and we study the resulting axisymmetric and triaxial analytical density-potential pairs; we also show how to obtain the surface density of shifted systems from the complex shift of the surface density of the parent model. In particular, the systems obtained from Miyamoto-Nagai discs can be used to describe disc galaxies with a peanut-shaped bulge or with a central triaxial bar, depending on the direction of the shift vector. By using a constructive method that can be applied to generic axisymmetric systems, we finally show that the Miyamoto-Nagai and the Satoh discs, and the Binney logarithmic halo cannot be obtained from the complex shift of any spherical parent distribution. As a by-product of this study, we also found two new generating functions in closed form for even and odd Legendre polynomials, respectively.
Analytical second derivatives of excited-state energy within the time-dependent density functional theory coupled with a conductor-like polarizable continuum model.

PubMed

Liu, Jie; Liang, WanZhen

2013-01-14

This work extends our previous works [J. Liu and W. Z. Liang, J. Chem. Phys. 135, 014113 (2011); J. Liu and W. Z. Liang, J. Chem. Phys. 135, 184111 (2011)] on analytical excited-state Hessian within the framework of time-dependent density functional theory (TDDFT) to couple with a conductor-like polarizable continuum model (CPCM). The formalism, implementation, and application of analytical first and second energy derivatives of TDDFT/CPCM excited state with respect to the nuclear and electric perturbations are presented. Their performances are demonstrated by the calculations of excitation energies, excited-state geometries, and harmonic vibrational frequencies for a number of benchmark systems. The calculated results are in good agreement with the corresponding experimental data or other theoretical calculations, indicating the reliability of the current computer implementation of the developed algorithms. Then we made some preliminary applications to calculate the resonant Raman spectrum of 4-hydroxybenzylidene-2,3-dimethyl-imidazolinone in ethanol solution and the infrared spectra of ground and excited states of 9-fluorenone in methanol solution.
Unfolding the laws of star formation: the density distribution of molecular clouds.

PubMed

Kainulainen, Jouni; Federrath, Christoph; Henning, Thomas

2014-04-11

The formation of stars shapes the structure and evolution of entire galaxies. The rate and efficiency of this process are affected substantially by the density structure of the individual molecular clouds in which stars form. The most fundamental measure of this structure is the probability density function of volume densities (ρ-PDF), which determines the star formation rates predicted with analytical models. This function has remained unconstrained by observations. We have developed an approach to quantify ρ-PDFs and establish their relation to star formation. The ρ-PDFs instigate a density threshold of star formation and allow us to quantify the star formation efficiency above it. The ρ-PDFs provide new constraints for star formation theories and correctly predict several key properties of the star-forming interstellar medium.
Density functional of a two-dimensional gas of dipolar atoms: Thomas-Fermi-Dirac treatment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fang, Bess; Englert, Berthold-Georg

We derive the density functional for the ground-state energy of a two-dimensional, spin-polarized gas of neutral fermionic atoms with magnetic-dipole interaction, in the Thomas-Fermi-Dirac approximation. For many atoms in a harmonic trap, we give analytical solutions for the single-particle spatial density and the ground-state energy, in dependence on the interaction strength, and we discuss the weak-interaction limit that is relevant for experiments. We then lift the restriction of full spin polarization and account for a time-independent inhomogeneous external magnetic field. The field strength necessary to ensure full spin polarization is derived.
Simulation Of Wave Function And Probability Density Of Modified Poschl Teller Potential Derived Using Supersymmetric Quantum Mechanics

NASA Astrophysics Data System (ADS)

Angraini, Lily Maysari; Suparmi, Variani, Viska Inda

2010-12-01

SUSY quantum mechanics can be applied to solve Schrodinger equation for high dimensional system that can be reduced into one dimensional system and represented in lowering and raising operators. Lowering and raising operators can be obtained using relationship between original Hamiltonian equation and the (super) potential equation. In this paper SUSY quantum mechanics is used as a method to obtain the wave function and the energy level of the Modified Poschl Teller potential. The graph of wave function equation and probability density is simulated by using Delphi 7.0 programming language. Finally, the expectation value of quantum mechanics operator could be calculated analytically using integral form or probability density graph resulted by the programming.
Density functional theoretical modeling, electrostatic surface potential and surface enhanced Raman spectroscopic studies on biosynthesized silver nanoparticles: observation of 400 PM sensitivity to explosives.

PubMed

Sil, Sanchita; Chaturvedi, Deepika; Krishnappa, Keerthi B; Kumar, Srividya; Asthana, S N; Umapathy, Siva

2014-04-24

Interaction of adsorbate on charged surfaces, orientation of the analyte on the surface, and surface enhancement aspects have been studied. These aspects have been explored in details to explain the surface-enhanced Raman spectroscopic (SERS) spectra of 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (HNIW or CL-20), a well-known explosive, and 2,4,6-trinitrotoluene (TNT) using one-pot synthesis of silver nanoparticles via biosynthetic route using natural precursor extracts of clove and pepper. The biosynthesized silver nanoparticles (bio Ag Nps) have been characterized using UV-vis spectroscopy, scanning electron microscopy and atomic force microscopy. SERS studies conducted using bio Ag Nps on different water insoluble analytes, such as CL-20 and TNT, lead to SERS signals at concentration levels of 400 pM. The experimental findings have been corroborated with density functional computational results, electrostatic surface potential calculations, Fukui functions and ζ potential measurements.
Continuous time random walk model with asymptotical probability density of waiting times via inverse Mittag-Leffler function

NASA Astrophysics Data System (ADS)

Liang, Yingjie; Chen, Wen

2018-04-01

The mean squared displacement (MSD) of the traditional ultraslow diffusion is a logarithmic function of time. Recently, the continuous time random walk model is employed to characterize this ultraslow diffusion dynamics by connecting the heavy-tailed logarithmic function and its variation as the asymptotical waiting time density. In this study we investigate the limiting waiting time density of a general ultraslow diffusion model via the inverse Mittag-Leffler function, whose special case includes the traditional logarithmic ultraslow diffusion model. The MSD of the general ultraslow diffusion model is analytically derived as an inverse Mittag-Leffler function, and is observed to increase even more slowly than that of the logarithmic function model. The occurrence of very long waiting time in the case of the inverse Mittag-Leffler function has the largest probability compared with the power law model and the logarithmic function model. The Monte Carlo simulations of one dimensional sample path of a single particle are also performed. The results show that the inverse Mittag-Leffler waiting time density is effective in depicting the general ultraslow random motion.
Estimation of the characteristic parameters of the multilayered film model using the patterson differential function

DOE Office of Scientific and Technical Information (OSTI.GOV)

Astaf'ev, S. B., E-mail: webmaster@ns.crys.ras.ru; Shchedrin, B. M.; Yanusova, L. G.

The possibility of estimating the layered film structural parameters by constructing the autocorrelation function P{sub F}(z) (referred to as the Patterson differential function) for the derivative d{rho}/dz of electron density along the normal to the sample surface has been considered. An analytical expression P{sub F}(z) is presented for a multilayered film within the box model of the electron density profile. The possibilities of selecting structural information about layered films by analyzing the features of this function are demonstrated by model and real examples, in particular, by applying the method of shifted systems of peaks for the function P{sub F}(z).
Time-dependent density-functional tight-binding method with the third-order expansion of electron density

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nishimoto, Yoshio, E-mail: nishimoto.yoshio@fukui.kyoto-u.ac.jp

2015-09-07

We develop a formalism for the calculation of excitation energies and excited state gradients for the self-consistent-charge density-functional tight-binding method with the third-order contributions of a Taylor series of the density functional theory energy with respect to the fluctuation of electron density (time-dependent density-functional tight-binding (TD-DFTB3)). The formulation of the excitation energy is based on the existing time-dependent density functional theory and the older TD-DFTB2 formulae. The analytical gradient is computed by solving Z-vector equations, and it requires one to calculate the third-order derivative of the total energy with respect to density matrix elements due to the inclusion of themore » third-order contributions. The comparison of adiabatic excitation energies for selected small and medium-size molecules using the TD-DFTB2 and TD-DFTB3 methods shows that the inclusion of the third-order contributions does not affect excitation energies significantly. A different set of parameters, which are optimized for DFTB3, slightly improves the prediction of adiabatic excitation energies statistically. The application of TD-DFTB for the prediction of absorption and fluorescence energies of cresyl violet demonstrates that TD-DFTB3 reproduced the experimental fluorescence energy quite well.« less
Time-dependent density-functional tight-binding method with the third-order expansion of electron density.

PubMed

Nishimoto, Yoshio

2015-09-07

We develop a formalism for the calculation of excitation energies and excited state gradients for the self-consistent-charge density-functional tight-binding method with the third-order contributions of a Taylor series of the density functional theory energy with respect to the fluctuation of electron density (time-dependent density-functional tight-binding (TD-DFTB3)). The formulation of the excitation energy is based on the existing time-dependent density functional theory and the older TD-DFTB2 formulae. The analytical gradient is computed by solving Z-vector equations, and it requires one to calculate the third-order derivative of the total energy with respect to density matrix elements due to the inclusion of the third-order contributions. The comparison of adiabatic excitation energies for selected small and medium-size molecules using the TD-DFTB2 and TD-DFTB3 methods shows that the inclusion of the third-order contributions does not affect excitation energies significantly. A different set of parameters, which are optimized for DFTB3, slightly improves the prediction of adiabatic excitation energies statistically. The application of TD-DFTB for the prediction of absorption and fluorescence energies of cresyl violet demonstrates that TD-DFTB3 reproduced the experimental fluorescence energy quite well.
Reply to the comments by Roger B. Lazarus

NASA Astrophysics Data System (ADS)

Mishkin, Eli A.

1980-04-01

It is claimed that because the pressure, density and velocity, behind the shock front, must be well behaved analytical functions the pressure must have an extremum. The claim by Lazarus of circular reasoning is refuted. (AIP)
Reactant conversion in homogeneous turbulence: Mathematical modeling, computational validations and practical applications

NASA Technical Reports Server (NTRS)

Madnia, C. K.; Frankel, S. H.; Givi, P.

1992-01-01

Closed form analytical expressions are obtained for predicting the limited rate of reactant conversion in a binary reaction of the type F + rO yields (1 + r) Product in unpremixed homogeneous turbulence. These relations are obtained by means of a single point Probability Density Function (PDF) method based on the Amplitude Mapping Closure. It is demonstrated that with this model, the maximum rate of the reactants' decay can be conveniently expressed in terms of definite integrals of the Parabolic Cylinder Functions. For the cases with complete initial segregation, it is shown that the results agree very closely with those predicted by employing a Beta density of the first kind for an appropriately defined Shvab-Zeldovich scalar variable. With this assumption, the final results can also be expressed in terms of closed form analytical expressions which are based on the Incomplete Beta Functions. With both models, the dependence of the results on the stoichiometric coefficient and the equivalence ratio can be expressed in an explicit manner. For a stoichiometric mixture, the analytical results simplify significantly. In the mapping closure, these results are expressed in terms of simple trigonometric functions. For the Beta density model, they are in the form of Gamma Functions. In all the cases considered, the results are shown to agree well with data generated by Direct Numerical Simulations (DNS). Due to the simplicity of these expressions and because of nice mathematical features of the Parabolic Cylinder and the Incomplete Beta Functions, these models are recommended for estimating the limiting rate of reactant conversion in homogeneous reacting flows. These results also provide useful insights in assessing the extent of validity of turbulence closures in the modeling of unpremixed reacting flows. Some discussions are provided on the extension of the model for treating more complicated reacting systems including realistic kinetics schemes and multi-scalar mixing with finite rate chemical reactions in more complex configurations.
Correction to the Beer-Lambert-Bouguer law for optical absorption.

PubMed

Abitan, Haim; Bohr, Henrik; Buchhave, Preben

2008-10-10

The Beer-Lambert-Bouguer absorption law, known as Beer's law for absorption in an optical medium, is precise only at power densities lower than a few kW. At higher power densities this law fails because it neglects the processes of stimulated emission and spontaneous emission. In previous models that considered those processes, an analytical expression for the absorption law could not be obtained. We show here that by utilizing the Lambert W-function, the two-level energy rate equation model is solved analytically, and this leads into a general absorption law that is exact because it accounts for absorption as well as stimulated and spontaneous emission. The general absorption law reduces to Beer's law at low power densities. A criterion for its application is given along with experimental examples. (c) 2008 Optical Society of America
Active ideal sedimentation: exact two-dimensional steady states.

PubMed

Hermann, Sophie; Schmidt, Matthias

2018-02-28

We consider an ideal gas of active Brownian particles that undergo self-propelled motion and both translational and rotational diffusion under the influence of gravity. We solve analytically the corresponding Smoluchowski equation in two space dimensions for steady states. The resulting one-body density is given as a series, where each term is a product of an orientation-dependent Mathieu function and a height-dependent exponential. A lower hard wall is implemented as a no-flux boundary condition. Numerical evaluation of the suitably truncated analytical solution shows the formation of two different spatial regimes upon increasing Peclet number. These regimes differ in their mean particle orientation and in their variation of the orientation-averaged density with height.
Beyond Zipf's Law: The Lavalette Rank Function and Its Properties.

PubMed

Fontanelli, Oscar; Miramontes, Pedro; Yang, Yaning; Cocho, Germinal; Li, Wentian

Although Zipf's law is widespread in natural and social data, one often encounters situations where one or both ends of the ranked data deviate from the power-law function. Previously we proposed the Beta rank function to improve the fitting of data which does not follow a perfect Zipf's law. Here we show that when the two parameters in the Beta rank function have the same value, the Lavalette rank function, the probability density function can be derived analytically. We also show both computationally and analytically that Lavalette distribution is approximately equal, though not identical, to the lognormal distribution. We illustrate the utility of Lavalette rank function in several datasets. We also address three analysis issues on the statistical testing of Lavalette fitting function, comparison between Zipf's law and lognormal distribution through Lavalette function, and comparison between lognormal distribution and Lavalette distribution.
Molecular properties of excited electronic state: Formalism, implementation, and applications of analytical second energy derivatives within the framework of the time-dependent density functional theory/molecular mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zeng, Qiao; Liang, WanZhen, E-mail: liangwz@xmu.edu.cn; Liu, Jie

2014-05-14

This work extends our previous works [J. Liu and W. Z. Liang, J. Chem. Phys. 135, 014113 (2011); J. Liu and W. Z. Liang, J. Chem. Phys. 135, 184111 (2011)] on analytical excited-state energy Hessian within the framework of time-dependent density functional theory (TDDFT) to couple with molecular mechanics (MM). The formalism, implementation, and applications of analytical first and second energy derivatives of TDDFT/MM excited state with respect to the nuclear and electric perturbations are presented. Their performances are demonstrated by the calculations of adiabatic excitation energies, and excited-state geometries, harmonic vibrational frequencies, and infrared intensities for a number ofmore » benchmark systems. The consistent results with the full quantum mechanical method and other hybrid theoretical methods indicate the reliability of the current numerical implementation of developed algorithms. The computational accuracy and efficiency of the current analytical approach are also checked and the computational efficient strategies are suggested to speed up the calculations of complex systems with many MM degrees of freedom. Finally, we apply the current analytical approach in TDDFT/MM to a realistic system, a red fluorescent protein chromophore together with part of its nearby protein matrix. The calculated results indicate that the rearrangement of the hydrogen bond interactions between the chromophore and the protein matrix is responsible for the large Stokes shift.« less

The Havriliak-Negami relaxation and its relatives: the response, relaxation and probability density functions

NASA Astrophysics Data System (ADS)

Górska, K.; Horzela, A.; Bratek, Ł.; Dattoli, G.; Penson, K. A.

2018-04-01

We study functions related to the experimentally observed Havriliak-Negami dielectric relaxation pattern proportional in the frequency domain to [1+(iωτ0){\\hspace{0pt}}α]-β with τ0 > 0 being some characteristic time. For α = l/k< 1 (l and k being positive and relatively prime integers) and β > 0 we furnish exact and explicit expressions for response and relaxation functions in the time domain and suitable probability densities in their domain dual in the sense of the inverse Laplace transform. All these functions are expressed as finite sums of generalized hypergeometric functions, convenient to handle analytically and numerically. Introducing a reparameterization β = (2-q)/(q-1) and τ0 = (q-1){\\hspace{0pt}}1/α (1 < q < 2) we show that for 0 < α < 1 the response functions fα, β(t/τ0) go to the one-sided Lévy stable distributions when q tends to one. Moreover, applying the self-similarity property of the probability densities gα, β(u) , we introduce two-variable densities and show that they satisfy the integral form of the evolution equation.
Magnetic exchange couplings from constrained density functional theory: an efficient approach utilizing analytic derivatives.

PubMed

Phillips, Jordan J; Peralta, Juan E

2011-11-14

We introduce a method for evaluating magnetic exchange couplings based on the constrained density functional theory (C-DFT) approach of Rudra, Wu, and Van Voorhis [J. Chem. Phys. 124, 024103 (2006)]. Our method shares the same physical principles as C-DFT but makes use of the fact that the electronic energy changes quadratically and bilinearly with respect to the constraints in the range of interest. This allows us to use coupled perturbed Kohn-Sham spin density functional theory to determine approximately the corrections to the energy of the different spin configurations and construct a priori the relevant energy-landscapes obtained by constrained spin density functional theory. We assess this methodology in a set of binuclear transition-metal complexes and show that it reproduces very closely the results of C-DFT. This demonstrates a proof-of-concept for this method as a potential tool for studying a number of other molecular phenomena. Additionally, routes to improving upon the limitations of this method are discussed. © 2011 American Institute of Physics
Density- and wavefunction-normalized Cartesian spherical harmonics for l ≤ 20.

PubMed

Michael, J Robert; Volkov, Anatoliy

2015-03-01

The widely used pseudoatom formalism [Stewart (1976). Acta Cryst. A32, 565-574; Hansen & Coppens (1978). Acta Cryst. A34, 909-921] in experimental X-ray charge-density studies makes use of real spherical harmonics when describing the angular component of aspherical deformations of the atomic electron density in molecules and crystals. The analytical form of the density-normalized Cartesian spherical harmonic functions for up to l ≤ 7 and the corresponding normalization coefficients were reported previously by Paturle & Coppens [Acta Cryst. (1988), A44, 6-7]. It was shown that the analytical form for normalization coefficients is available primarily for l ≤ 4 [Hansen & Coppens, 1978; Paturle & Coppens, 1988; Coppens (1992). International Tables for Crystallography, Vol. B, Reciprocal space, 1st ed., edited by U. Shmueli, ch. 1.2. Dordrecht: Kluwer Academic Publishers; Coppens (1997). X-ray Charge Densities and Chemical Bonding. New York: Oxford University Press]. Only in very special cases it is possible to derive an analytical representation of the normalization coefficients for 4 < l ≤ 7 (Paturle & Coppens, 1988). In most cases for l > 4 the density normalization coefficients were calculated numerically to within seven significant figures. In this study we review the literature on the density-normalized spherical harmonics, clarify the existing notations, use the Paturle-Coppens (Paturle & Coppens, 1988) method in the Wolfram Mathematica software to derive the Cartesian spherical harmonics for l ≤ 20 and determine the density normalization coefficients to 35 significant figures, and computer-generate a Fortran90 code. The article primarily targets researchers who work in the field of experimental X-ray electron density, but may be of some use to all who are interested in Cartesian spherical harmonics.
Surface currents associated with external kink modes in tokamak plasmas during a major disruption

NASA Astrophysics Data System (ADS)

Ng, C. S.; Bhattacharjee, A.

2017-10-01

The surface current on the plasma-vacuum interface during a disruption event involving kink instability can play an important role in driving current into the vacuum vessel. However, there have been disagreements over the nature or even the sign of the surface current in recent theoretical calculations based on idealized step-function background plasma profiles. We revisit such calculations by replacing step-function profiles with more realistic profiles characterized by a strong but finite gradient along the radial direction. It is shown that the resulting surface current is no longer a delta-function current density, but a finite and smooth current density profile with an internal structure, concentrated within the region with a strong plasma pressure gradient. Moreover, this current density profile has peaks of both signs, unlike the delta-function case with a sign opposite to, or the same as the plasma current. We show analytically and numerically that such current density can be separated into two parts, with one of them, called the convective current density, describing the transport of the background plasma density by the displacement, and the other part that remains, called the residual current density. It is argued that consideration of both types of current density is important and can resolve past controversies.
Analysis of social optimum for staggered shifts in a single-entry traffic corridor with no late arrivals

NASA Astrophysics Data System (ADS)

Li, Chuan-Yao; Huang, Hai-Jun; Tang, Tie-Qiao

2017-03-01

This paper investigates the traffic flow dynamics under the social optimum (SO) principle in a single-entry traffic corridor with staggered shifts from the analytical and numerical perspectives. The LWR (Lighthill-Whitham and Richards) model and the Greenshield's velocity-density function are utilized to describe the dynamic properties of traffic flow. The closed-form SO solution is analytically derived and some numerical examples are used to further testify the analytical solution. The optimum proportion of the numbers of commuters with different desired arrival times is further discussed, where the analytical and numerical results both indicate that the cumulative outflow curve under the SO principle is piecewise smooth.
Hunting high and low: disentangling primordial and late-time non-Gaussianity with cosmic densities in spheres

NASA Astrophysics Data System (ADS)

Uhlemann, C.; Pajer, E.; Pichon, C.; Nishimichi, T.; Codis, S.; Bernardeau, F.

2018-03-01

Non-Gaussianities of dynamical origin are disentangled from primordial ones using the formalism of large deviation statistics with spherical collapse dynamics. This is achieved by relying on accurate analytical predictions for the one-point probability distribution function and the two-point clustering of spherically averaged cosmic densities (sphere bias). Sphere bias extends the idea of halo bias to intermediate density environments and voids as underdense regions. In the presence of primordial non-Gaussianity, sphere bias displays a strong scale dependence relevant for both high- and low-density regions, which is predicted analytically. The statistics of densities in spheres are built to model primordial non-Gaussianity via an initial skewness with a scale dependence that depends on the bispectrum of the underlying model. The analytical formulas with the measured non-linear dark matter variance as input are successfully tested against numerical simulations. For local non-Gaussianity with a range from fNL = -100 to +100, they are found to agree within 2 per cent or better for densities ρ ∈ [0.5, 3] in spheres of radius 15 Mpc h-1 down to z = 0.35. The validity of the large deviation statistics formalism is thereby established for all observationally relevant local-type departures from perfectly Gaussian initial conditions. The corresponding estimators for the amplitude of the non-linear variance σ8 and primordial skewness fNL are validated using a fiducial joint maximum likelihood experiment. The influence of observational effects and the prospects for a future detection of primordial non-Gaussianity from joint one- and two-point densities-in-spheres statistics are discussed.
ON THE ELECTRON-TO-NEUTRAL NUMBER DENSITY RATIO IN THE COMA OF COMET 67P/CHURYUMOV–GERASIMENKO: GUIDING EXPRESSION AND SOURCES FOR DEVIATIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vigren, E.; Eriksson, A. I.; Edberg, N. J. T.

2015-10-10

We compute partial photoionization frequencies of H{sub 2}O, CO{sub 2}, and CO, the major molecules in the coma of comet 67P/Churyumov–Gerasimenko, the target comet of the ongoing ESA Rosetta mission. Values are computed from Thermosphere Ionosphere Mesosphere Energy and Dynamics/Solar EUV Experiment solar EUV spectra for 2014 August 1, 2015 March 1, and for perihelion (2015 August, as based on prediction). From the varying total photoionization frequency of H{sub 2}O, as computed from 2014 August 1 to 2015 May 20, we derive a simple analytical expression for the electron-to-neutral number density ratio as a function of cometocentric and heliocentric distance. Themore » underlying model assumes radial movement of the coma constituents and does not account for chemical loss or the presence of electric fields. We discuss various effects/processes that can cause deviations between values from the analytical expression and actual electron-to-neutral number density ratios. The analytical expression is thus not strictly meant as predicting the actual electron-to-neutral number density ratio, but is useful in comparisons with observations as an indicator of processes at play in the cometary coma.« less
Functionally Graded Adhesives for Composite Joints

NASA Technical Reports Server (NTRS)

Stapleton, Scott E.; Waas, Anthony M.; Arnold, Steven M.

2012-01-01

Adhesives with functionally graded material properties are being considered for use in adhesively bonded joints to reduce the peel stress concentrations located near adherend discontinuities. Several practical concerns impede the actual use of such adhesives. These include increased manufacturing complications, alterations to the grading due to adhesive flow during manufacturing, and whether changing the loading conditions significantly impact the effectiveness of the grading. An analytical study is conducted to address these three concerns. An enhanced joint finite element, which uses an analytical formulation to obtain exact shape functions, is used to model the joint. Furthermore, proof of concept testing is conducted to show the potential advantages of functionally graded adhesives. In this study, grading is achieved by strategically placing glass beads within the adhesive layer at different densities along the joint.
Two-component Jaffe models with a central black hole - I. The spherical case

NASA Astrophysics Data System (ADS)

Ciotti, Luca; Ziaee Lorzad, Azadeh

2018-02-01

Dynamical properties of spherically symmetric galaxy models where both the stellar and total mass density distributions are described by the Jaffe (1983) profile (with different scalelengths and masses) are presented. The orbital structure of the stellar component is described by Osipkov-Merritt anisotropy, and a black hole (BH) is added at the centre of the galaxy; the dark matter halo is isotropic. First, the conditions required to have a nowhere negative and monotonically decreasing dark matter halo density profile are derived. We then show that the phase-space distribution function can be recovered by using the Lambert-Euler W function, while in absence of the central BH only elementary functions appears in the integrand of the inversion formula. The minimum value of the anisotropy radius for consistency is derived in terms of the galaxy parameters. The Jeans equations for the stellar component are solved analytically, and the projected velocity dispersion at the centre and at large radii are also obtained analytically for generic values of the anisotropy radius. Finally, the relevant global quantities entering the Virial Theorem are computed analytically, and the fiducial anisotropy limit required to prevent the onset of Radial Orbit Instability is determined as a function of the galaxy parameters. The presented models, even though highly idealized, represent a substantial generalization of the models presented in Ciotti, and can be useful as starting point for more advanced modelling, the dynamics and the mass distribution of elliptical galaxies.
No need for external orthogonality in subsystem density-functional theory.

PubMed

Unsleber, Jan P; Neugebauer, Johannes; Jacob, Christoph R

2016-08-03

Recent reports on the necessity of using externally orthogonal orbitals in subsystem density-functional theory (SDFT) [Annu. Rep. Comput. Chem., 8, 2012, 53; J. Phys. Chem. A, 118, 2014, 9182] are re-investigated. We show that in the basis-set limit, supermolecular Kohn-Sham-DFT (KS-DFT) densities can exactly be represented as a sum of subsystem densities, even if the subsystem orbitals are not externally orthogonal. This is illustrated using both an analytical example and in basis-set free numerical calculations for an atomic test case. We further show that even with finite basis sets, SDFT calculations using accurate reconstructed potentials can closely approach the supermolecular KS-DFT density, and that the deviations between SDFT and KS-DFT decrease as the basis-set limit is approached. Our results demonstrate that formally, there is no need to enforce external orthogonality in SDFT, even though this might be a useful strategy when developing projection-based DFT embedding schemes.
Drift of Phase Fluctuations in the ABC Model

NASA Astrophysics Data System (ADS)

Bertini, Lorenzo; Buttà, Paolo

2013-07-01

In a recent work, Bodineau and Derrida analyzed the phase fluctuations in the ABC model. In particular, they computed the asymptotic variance and, on the basis of numerical simulations, they conjectured the presence of a drift, which they guessed to be an antisymmetric function of the three densities. By assuming the validity of the fluctuating hydrodynamic approximation, we prove the presence of such a drift, providing an analytical expression for it. This expression is then shown to be an antisymmetric function of the three densities. The antisymmetry of the drift can also be inferred from a symmetry property of the underlying microscopic dynamics.
Time-dependent density functional theory description of total photoabsorption cross sections

NASA Astrophysics Data System (ADS)

Tenorio, Bruno Nunes Cabral; Nascimento, Marco Antonio Chaer; Rocha, Alexandre Braga

2018-02-01

The time-dependent version of the density functional theory (TDDFT) has been used to calculate the total photoabsorption cross section of a number of molecules, namely, benzene, pyridine, furan, pyrrole, thiophene, phenol, naphthalene, and anthracene. The discrete electronic pseudo-spectra, obtained in a L2 basis set calculation were used in an analytic continuation procedure to obtain the photoabsorption cross sections. The ammonia molecule was chosen as a model system to compare the results obtained with TDDFT to those obtained with the linear response coupled cluster approach in order to make a link with our previous work and establish benchmarks.
Kapton charging characteristics: Effects of material thickness and electron-energy distribution

NASA Technical Reports Server (NTRS)

Williamson, W. S.; Dulgeroff, C. R.; Hymann, J.; Viswanathan, R.

1985-01-01

Charging characteristics of polyimide (Kapton) of varying thicknesses under irradiation by a very-low-curent-density electron beam, with the back surface of the sample grounded are reported. These charging characteristics are in good agreement with a simple analytical model which predicts that in thin samples at low current density, sample surface potential is limited by conduction leakage through the bulk material. The charging of Kapton in a low-current-density electron beam in which the beam energy was modulated to simulate Maxwellian and biMaxwellian distribution functions is measured.
Ways to improve your correlation functions

NASA Technical Reports Server (NTRS)

Hamilton, A. J. S.

1993-01-01

This paper describes a number of ways to improve on the standard method for measuring the two-point correlation function of large scale structure in the Universe. Issues addressed are: (1) the problem of the mean density, and how to solve it; (2) how to estimate the uncertainty in a measured correlation function; (3) minimum variance pair weighting; (4) unbiased estimation of the selection function when magnitudes are discrete; and (5) analytic computation of angular integrals in background pair counts.
Hollow silica microspheres for buoyancy-assisted separation of infectious pathogens from stool.

PubMed

Weigum, Shannon E; Xiang, Lichen; Osta, Erica; Li, Linying; López, Gabriel P

2016-09-30

Separation of cells and microorganisms from complex biological mixtures is a critical first step in many analytical applications ranging from clinical diagnostics to environmental monitoring for food and waterborne contaminants. Yet, existing techniques for cell separation are plagued by high reagent and/or instrumentation costs that limit their use in many remote or resource-poor settings, such as field clinics or developing countries. We developed an innovative approach to isolate infectious pathogens from biological fluids using buoyant hollow silica microspheres that function as "molecular buoys" for affinity-based target capture and separation by floatation. In this process, antibody functionalized glass microspheres are mixed with a complex biological sample, such as stool. When mixing is stopped, the target-bound, low-density microspheres float to the air/liquid surface, which simultaneously isolates and concentrates the target analytes from the sample matrix. The microspheres are highly tunable in terms of size, density, and surface functionality for targeting diverse analytes with separation times of ≤2min in viscous solutions. We have applied the molecular buoy technique for isolation of a protozoan parasite that causes diarrheal illness, Cryptosporidium, directly from stool with separation efficiencies over 90% and low non-specific binding. This low-cost method for phenotypic cell/pathogen separation from complex mixtures is expected to have widespread use in clinical diagnostics as well as basic research. Copyright © 2016 Elsevier B.V. All rights reserved.
Path Integrals for Electronic Densities, Reactivity Indices, and Localization Functions in Quantum Systems

PubMed Central

Putz, Mihai V.

2009-01-01

The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr’s quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions – all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems. PMID:20087467
Path integrals for electronic densities, reactivity indices, and localization functions in quantum systems.

PubMed

Putz, Mihai V

2009-11-10

The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr's quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions - all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems.
Statistics of cosmic density profiles from perturbation theory

NASA Astrophysics Data System (ADS)

Bernardeau, Francis; Pichon, Christophe; Codis, Sandrine

2014-11-01

The joint probability distribution function (PDF) of the density within multiple concentric spherical cells is considered. It is shown how its cumulant generating function can be obtained at tree order in perturbation theory as the Legendre transform of a function directly built in terms of the initial moments. In the context of the upcoming generation of large-scale structure surveys, it is conjectured that this result correctly models such a function for finite values of the variance. Detailed consequences of this assumption are explored. In particular the corresponding one-cell density probability distribution at finite variance is computed for realistic power spectra, taking into account its scale variation. It is found to be in agreement with Λ -cold dark matter simulations at the few percent level for a wide range of density values and parameters. Related explicit analytic expansions at the low and high density tails are given. The conditional (at fixed density) and marginal probability of the slope—the density difference between adjacent cells—and its fluctuations is also computed from the two-cell joint PDF; it also compares very well to simulations. It is emphasized that this could prove useful when studying the statistical properties of voids as it can serve as a statistical indicator to test gravity models and/or probe key cosmological parameters.
Self-generated zonal flows in the plasma turbulence driven by trapped-ion and trapped-electron instabilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Drouot, T.; Gravier, E.; Reveille, T.

This paper presents a study of zonal flows generated by trapped-electron mode and trapped-ion mode micro turbulence as a function of two plasma parameters—banana width and electron temperature. For this purpose, a gyrokinetic code considering only trapped particles is used. First, an analytical equation giving the predicted level of zonal flows is derived from the quasi-neutrality equation of our model, as a function of the density fluctuation levels and the banana widths. Then, the influence of the banana width on the number of zonal flows occurring in the system is studied using the gyrokinetic code. Finally, the impact of themore » temperature ratio T{sub e}/T{sub i} on the reduction of zonal flows is shown and a close link is highlighted between reduction and different gyro-and-bounce-average ion and electron density fluctuation levels. This reduction is found to be due to the amplitudes of gyro-and-bounce-average density perturbations n{sub e} and n{sub i} gradually becoming closer, which is in agreement with the analytical results given by the quasi-neutrality equation.« less
When can a single-species, density-dependent model capture the dynamics of a consumer-resource system?

PubMed

Reynolds, Sara A; Brassil, Chad E

2013-12-21

Single-species population models often include density-dependence phenomenologically in order to approximate higher order mechanisms. Here we consider the common scenario in which density-dependence acts via depletion of a renewed resource. When the response of the resource is very quick relative to that of the consumer, the consumer dynamics can be captured by a single-species, density-dependent model. Time scale separation is used to show analytically how the shape of the density-dependent relationship depends on the type of resource and the form of the functional response. Resource types of abiotic, biotic, and biotic with migration are considered, in combination with linear and saturating functional responses. In some cases, we derive familiar forms of single-species models, adding to the justification for their use. In other scenarios novel forms of density-dependence are derived, for example an abiotic resource and a saturating functional response can result in a nonlinear density-dependent relationship in the associated single-species model of the consumer. In this case, the per capita relationship has both concave-up and concave-down sections. © 2013 Published by Elsevier Ltd. All rights reserved.

The super-NFW model: an analytic dynamical model for cold dark matter haloes and elliptical galaxies

NASA Astrophysics Data System (ADS)

Lilley, Edward J.; Evans, N. Wyn; Sanders, Jason L.

2018-05-01

An analytic galaxy model with ρ ˜ r-1 at small radii and ρ ˜ r-3.5 at large radii is presented. The asymptotic density fall-off is slower than the Hernquist model, but faster than the Navarro-Frenk-White (NFW) profile for dark matter haloes, and so in accord with recent evidence from cosmological simulations. The model provides the zeroth-order term in a biorthornomal basis function expansion, meaning that axisymmetric, triaxial, and lopsided distortions can easily be added (much like the Hernquist model itself which is the zeroth-order term of the Hernquist-Ostriker expansion). The properties of the spherical model, including analytic distribution functions which are either isotropic, radially anisotropic, or tangentially anisotropic, are discussed in some detail. The analogue of the mass-concentration relation for cosmological haloes is provided.
A robust molecular probe for Ångstrom-scale analytics in liquids

PubMed Central

Nirmalraj, Peter; Thompson, Damien; Dimitrakopoulos, Christos; Gotsmann, Bernd; Dumcenco, Dumitru; Kis, Andras; Riel, Heike

2016-01-01

Traditionally, nanomaterial profiling using a single-molecule-terminated scanning probe is performed at the vacuum–solid interface often at a few Kelvin, but is not a notion immediately associated with liquid–solid interface at room temperature. Here, using a scanning tunnelling probe functionalized with a single C60 molecule stabilized in a high-density liquid, we resolve low-dimensional surface defects, atomic interfaces and capture Ångstrom-level bond-length variations in single-layer graphene and MoS2. Atom-by-atom controllable imaging contrast is demonstrated at room temperature and the electronic structure of the C60–metal probe complex within the encompassing liquid molecules is clarified using density functional theory. Our findings demonstrates that operating a robust single-molecular probe is not restricted to ultra-high vacuum and cryogenic settings. Hence the scope of high-precision analytics can be extended towards resolving sub-molecular features of organic elements and gauging ambient compatibility of emerging layered materials with atomic-scale sensitivity under experimentally less stringent conditions. PMID:27516157
The Surface Density Distribution in the Solar Nebula

NASA Technical Reports Server (NTRS)

Davis, Sanford S.

2004-01-01

The commonly used minimum mass power law representation of the pre-solar nebula is reanalyzed using a new cumulative-mass-model. This model predicts a smoother surface density approximation compared with methods based on direct computation of surface density. The density is quantified using two independent analytical formulations. First, a best-fit transcendental function is applied directly to the basic planetary data. Next a solution to the time-dependent disk evolution equation is parametrically adapted to the solar nebula data. The latter model is shown to be a good approximation to the finite-size early Solar Nebula, and by extension to other extra solar protoplanetary disks.
Fault Detection of Rotating Machinery using the Spectral Distribution Function

NASA Technical Reports Server (NTRS)

Davis, Sanford S.

1997-01-01

The spectral distribution function is introduced to characterize the process leading to faults in rotating machinery. It is shown to be a more robust indicator than conventional power spectral density estimates, but requires only slightly more computational effort. The method is illustrated with examples from seeded gearbox transmission faults and an analytical model of a defective bearing. Procedures are suggested for implementation in realistic environments.
Towards the blackbox computation of magnetic exchange coupling parameters in polynuclear transition-metal complexes: theory, implementation, and application.

PubMed

Phillips, Jordan J; Peralta, Juan E

2013-05-07

We present a method for calculating magnetic coupling parameters from a single spin-configuration via analytic derivatives of the electronic energy with respect to the local spin direction. This method does not introduce new approximations beyond those found in the Heisenberg-Dirac Hamiltonian and a standard Kohn-Sham Density Functional Theory calculation, and in the limit of an ideal Heisenberg system it reproduces the coupling as determined from spin-projected energy-differences. Our method employs a generalized perturbative approach to constrained density functional theory, where exact expressions for the energy to second order in the constraints are obtained by analytic derivatives from coupled-perturbed theory. When the relative angle between magnetization vectors of metal atoms enters as a constraint, this allows us to calculate all the magnetic exchange couplings of a system from derivatives with respect to local spin directions from the high-spin configuration. Because of the favorable computational scaling of our method with respect to the number of spin-centers, as compared to the broken-symmetry energy-differences approach, this opens the possibility for the blackbox exploration of magnetic properties in large polynuclear transition-metal complexes. In this work we outline the motivation, theory, and implementation of this method, and present results for several model systems and transition-metal complexes with a variety of density functional approximations and Hartree-Fock.
Redshift-space distortions with the halo occupation distribution - II. Analytic model

NASA Astrophysics Data System (ADS)

Tinker, Jeremy L.

2007-01-01

We present an analytic model for the galaxy two-point correlation function in redshift space. The cosmological parameters of the model are the matter density Ωm, power spectrum normalization σ8, and velocity bias of galaxies αv, circumventing the linear theory distortion parameter β and eliminating nuisance parameters for non-linearities. The model is constructed within the framework of the halo occupation distribution (HOD), which quantifies galaxy bias on linear and non-linear scales. We model one-halo pairwise velocities by assuming that satellite galaxy velocities follow a Gaussian distribution with dispersion proportional to the virial dispersion of the host halo. Two-halo velocity statistics are a combination of virial motions and host halo motions. The velocity distribution function (DF) of halo pairs is a complex function with skewness and kurtosis that vary substantially with scale. Using a series of collisionless N-body simulations, we demonstrate that the shape of the velocity DF is determined primarily by the distribution of local densities around a halo pair, and at fixed density the velocity DF is close to Gaussian and nearly independent of halo mass. We calibrate a model for the conditional probability function of densities around halo pairs on these simulations. With this model, the full shape of the halo velocity DF can be accurately calculated as a function of halo mass, radial separation, angle and cosmology. The HOD approach to redshift-space distortions utilizes clustering data from linear to non-linear scales to break the standard degeneracies inherent in previous models of redshift-space clustering. The parameters of the occupation function are well constrained by real-space clustering alone, separating constraints on bias and cosmology. We demonstrate the ability of the model to separately constrain Ωm,σ8 and αv in models that are constructed to have the same value of β at large scales as well as the same finger-of-god distortions at small scales.
Acoustic Rectification in Dispersive Media

NASA Technical Reports Server (NTRS)

Cantrell, John H.

2008-01-01

It is shown that the shapes of acoustic radiation-induced static strain and displacement pulses (rectified acoustic pulses) are defined locally by the energy density of the generating waveform. Dispersive properties are introduced analytically by assuming that the rectified pulses are functionally dependent on a phase factor that includes both dispersive and nonlinear terms. The dispersion causes an evolutionary change in the shape of the energy density profile that leads to the generation of solitons experimentally observed in fused silica.
Large-scale structure of randomly jammed spheres

NASA Astrophysics Data System (ADS)

Ikeda, Atsushi; Berthier, Ludovic; Parisi, Giorgio

2017-05-01

We numerically analyze the density field of three-dimensional randomly jammed packings of monodisperse soft frictionless spherical particles, paying special attention to fluctuations occurring at large length scales. We study in detail the two-point static structure factor at low wave vectors in Fourier space. We also analyze the nature of the density field in real space by studying the large-distance behavior of the two-point pair correlation function, of density fluctuations in subsystems of increasing sizes, and of the direct correlation function. We show that such real space analysis can be greatly improved by introducing a coarse-grained density field to disentangle genuine large-scale correlations from purely local effects. Our results confirm that both Fourier and real space signatures of vanishing density fluctuations at large scale are absent, indicating that randomly jammed packings are not hyperuniform. In addition, we establish that the pair correlation function displays a surprisingly complex structure at large distances, which is however not compatible with the long-range negative correlation of hyperuniform systems but fully compatible with an analytic form for the structure factor. This implies that the direct correlation function is short ranged, as we also demonstrate directly. Our results reveal that density fluctuations in jammed packings do not follow the behavior expected for random hyperuniform materials, but display instead a more complex behavior.
Developing Thermal Density Functional Theory Using the Asymmetric Hubbard Dimer

NASA Astrophysics Data System (ADS)

Smith, Justin Clifford

In this dissertation, I introduce both ground-state and thermal density functional theory. Throughout I use the asymmetric two-site Hubbard model, called the Hubbard dimer for short, to better understand and/or develop these theories. This model is used because it can be solved analytically and it contains all the necessary physics while still being conceptually simple enough to tease apart the various aspects of density functional theory. Ground-state density functional theory has seen broad use in many disciplines including physics, chemistry, geology, and material science and has led to a number of important physical and technological successes. In the first two chapters I elucidate the behavior of the ground-state theory using the Hubbard dimer. The simplicity of the model allows me to showcase aspects of the theory that are common points of confusion within the electronic structure community, e.g. the fundamental gap problem. The next two chapters focus on thermal density functional theory which has been coming to prominence as the study of warm dense matter has become a growing interest at the national laboratories and in the astronomical body community. The Hubbard dimer allows me to do the first ever exact thermal density functional theory calculation. In this work I am better able to understand the approximations used in thermal density functional theory and can point to why they succeed and fail. This also allows me to illustrate old conditions and derive new ones. I conclude with an overview of the work and a few different directions in which the asymmetric Hubbard dimer could be used further.
Decoupling the NLO-coupled QED⊗QCD, DGLAP evolution equations, using Laplace transform method

NASA Astrophysics Data System (ADS)

Mottaghizadeh, Marzieh; Eslami, Parvin; Taghavi-Shahri, Fatemeh

2017-05-01

We analytically solved the QED⊗QCD-coupled DGLAP evolution equations at leading order (LO) quantum electrodynamics (QED) and next-to-leading order (NLO) quantum chromodynamics (QCD) approximations, using the Laplace transform method and then computed the proton structure function in terms of the unpolarized parton distribution functions. Our analytical solutions for parton densities are in good agreement with those from CT14QED (1.2952 < Q2 < 1010) (Ref. 6) global parametrizations and APFEL (A PDF Evolution Library) (2 < Q2 < 108) (Ref. 4). We also compared the proton structure function, F2p(x,Q2), with the experimental data released by the ZEUS and H1 collaborations at HERA. There is a nice agreement between them in the range of low and high x and Q2.
Relative frequencies of constrained events in stochastic processes: An analytical approach.

PubMed

Rusconi, S; Akhmatskaya, E; Sokolovski, D; Ballard, N; de la Cal, J C

2015-10-01

The stochastic simulation algorithm (SSA) and the corresponding Monte Carlo (MC) method are among the most common approaches for studying stochastic processes. They relies on knowledge of interevent probability density functions (PDFs) and on information about dependencies between all possible events. Analytical representations of a PDF are difficult to specify in advance, in many real life applications. Knowing the shapes of PDFs, and using experimental data, different optimization schemes can be applied in order to evaluate probability density functions and, therefore, the properties of the studied system. Such methods, however, are computationally demanding, and often not feasible. We show that, in the case where experimentally accessed properties are directly related to the frequencies of events involved, it may be possible to replace the heavy Monte Carlo core of optimization schemes with an analytical solution. Such a replacement not only provides a more accurate estimation of the properties of the process, but also reduces the simulation time by a factor of order of the sample size (at least ≈10(4)). The proposed analytical approach is valid for any choice of PDF. The accuracy, computational efficiency, and advantages of the method over MC procedures are demonstrated in the exactly solvable case and in the evaluation of branching fractions in controlled radical polymerization (CRP) of acrylic monomers. This polymerization can be modeled by a constrained stochastic process. Constrained systems are quite common, and this makes the method useful for various applications.
Density Functional Study for Chemical Reaction between Cr and Fe with Sodium Diethyldithiocarbamate (NaDDC)

NASA Astrophysics Data System (ADS)

Setiyanto, Henry; Muhida, Rifki; Kishi, Tomoya; Rahman, Md. Mahmudur; Dipojono, Hermawan K.; Diño, Wilson A.; Matsumoto, Shigeno; Kasai, Hideaki

Analytical chemistry in the perspective of ab initio molecular orbital calculation is introduced by investigating the chemical reaction between transition metals Cr and Fe with sodium diethyldithiocarbamate (NaDDC), a complexing agent to detect and extract Cr in human blood sample. Using density functional theory—based calculations, we determine the stable structure of the Cr-DDC and Fe-DDC complexes and obtain its dissociation energies. We found dissociation energy values of -3.24 and -2.67 eV for Cr and Fe complexes, respectively; and hence the formation of the former complex is more favorable than the formation of the latter.
Path-integral approach to the Wigner-Kirkwood expansion.

PubMed

Jizba, Petr; Zatloukal, Václav

2014-01-01

We study the high-temperature behavior of quantum-mechanical path integrals. Starting from the Feynman-Kac formula, we derive a functional representation of the Wigner-Kirkwood perturbation expansion for quantum Boltzmann densities. As shown by its applications to different potentials, the presented expansion turns out to be quite efficient in generating analytic form of the higher-order expansion coefficients. To put some flesh on the bare bones, we apply the expansion to obtain basic thermodynamic functions of the one-dimensional anharmonic oscillator. Further salient issues, such as generalization to the Bloch density matrix and comparison with the more customary world-line formulation, are discussed.
Spacing distribution functions for the one-dimensional point-island model with irreversible attachment

NASA Astrophysics Data System (ADS)

González, Diego Luis; Pimpinelli, Alberto; Einstein, T. L.

2011-07-01

We study the configurational structure of the point-island model for epitaxial growth in one dimension. In particular, we calculate the island gap and capture zone distributions. Our model is based on an approximate description of nucleation inside the gaps. Nucleation is described by the joint probability density pnXY(x,y), which represents the probability density to have nucleation at position x within a gap of size y. Our proposed functional form for pnXY(x,y) describes excellently the statistical behavior of the system. We compare our analytical model with extensive numerical simulations. Our model retains the most relevant physical properties of the system.
Eulerian Mapping Closure Approach for Probability Density Function of Concentration in Shear Flows

NASA Technical Reports Server (NTRS)

He, Guowei; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The Eulerian mapping closure approach is developed for uncertainty propagation in computational fluid mechanics. The approach is used to study the Probability Density Function (PDF) for the concentration of species advected by a random shear flow. An analytical argument shows that fluctuation of the concentration field at one point in space is non-Gaussian and exhibits stretched exponential form. An Eulerian mapping approach provides an appropriate approximation to both convection and diffusion terms and leads to a closed mapping equation. The results obtained describe the evolution of the initial Gaussian field, which is in agreement with direct numerical simulations.
The difference between two random mixed quantum states: exact and asymptotic spectral analysis

NASA Astrophysics Data System (ADS)

Mejía, José; Zapata, Camilo; Botero, Alonso

2017-01-01

We investigate the spectral statistics of the difference of two density matrices, each of which is independently obtained by partially tracing a random bipartite pure quantum state. We first show how a closed-form expression for the exact joint eigenvalue probability density function for arbitrary dimensions can be obtained from the joint probability density function of the diagonal elements of the difference matrix, which is straightforward to compute. Subsequently, we use standard results from free probability theory to derive a relatively simple analytic expression for the asymptotic eigenvalue density (AED) of the difference matrix ensemble, and using Carlson’s theorem, we obtain an expression for its absolute moments. These results allow us to quantify the typical asymptotic distance between the two random mixed states using various distance measures; in particular, we obtain the almost sure asymptotic behavior of the operator norm distance and the trace distance.
Towards an Analytical Age-Dependent Model of Contrast Sensitivity Functions for an Ageing Society

PubMed Central

Joulan, Karine; Brémond, Roland

2015-01-01

The Contrast Sensitivity Function (CSF) describes how the visibility of a grating depends on the stimulus spatial frequency. Many published CSF data have demonstrated that contrast sensitivity declines with age. However, an age-dependent analytical model of the CSF is not available to date. In this paper, we propose such an analytical CSF model based on visual mechanisms, taking into account the age factor. To this end, we have extended an existing model from Barten (1999), taking into account the dependencies of this model's optical and physiological parameters on age. Age-dependent models of the cones and ganglion cells densities, the optical and neural MTF, and optical and neural noise are proposed, based on published data. The proposed age-dependent CSF is finally tested against available experimental data, with fair results. Such an age-dependent model may be beneficial when designing real-time age-dependent image coding and display applications. PMID:26078994
Calculation of phonon dispersion relation using new correlation functional

NASA Astrophysics Data System (ADS)

Jitropas, Ukrit; Hsu, Chung-Hao

2017-06-01

To extend the use of Local Density Approximation (LDA), a new analytical correlation functional is introduced. Correlation energy is an essential ingredient within density functional theory and used to determine ground state energy and other properties including phonon dispersion relation. Except for high and low density limit, the general expression of correlation energy is unknown. The approximation approach is therefore required. The accuracy of the modelling system depends on the quality of correlation energy approximation. Typical correlation functionals used in LDA such as Vosko-Wilk-Nusair (VWN) and Perdew-Wang (PW) were obtained from parameterizing the near-exact quantum Monte Carlo data of Ceperley and Alder. These functionals are presented in complex form and inconvenient to implement. Alternatively, the latest published formula of Chachiyo correlation functional provides a comparable result for those much more complicated functionals. In addition, it provides more predictive power based on the first principle approach, not fitting functionals. Nevertheless, the performance of Chachiyo formula for calculating phonon dispersion relation (a key to the thermal properties of materials) has not been tested yet. Here, the implementation of new correlation functional to calculate phonon dispersion relation is initiated. The accuracy and its validity will be explored.
Quantitative Tomography for Continuous Variable Quantum Systems

NASA Astrophysics Data System (ADS)

Landon-Cardinal, Olivier; Govia, Luke C. G.; Clerk, Aashish A.

2018-03-01

We present a continuous variable tomography scheme that reconstructs the Husimi Q function (Wigner function) by Lagrange interpolation, using measurements of the Q function (Wigner function) at the Padua points, conjectured to be optimal sampling points for two dimensional reconstruction. Our approach drastically reduces the number of measurements required compared to using equidistant points on a regular grid, although reanalysis of such experiments is possible. The reconstruction algorithm produces a reconstructed function with exponentially decreasing error and quasilinear runtime in the number of Padua points. Moreover, using the interpolating polynomial of the Q function, we present a technique to directly estimate the density matrix elements of the continuous variable state, with only a linear propagation of input measurement error. Furthermore, we derive a state-independent analytical bound on this error, such that our estimate of the density matrix is accompanied by a measure of its uncertainty.
Exploration of the Memory Effect on the Photon-Assisted Tunneling via a Single Quantum Dot:. a Generalized Floquet Theoretical Approach

NASA Astrophysics Data System (ADS)

Chen, Hsing-Ta; Ho, Tak-San; Chu, Shih-I.

The generalized Floquet approach is developed to study memory effect on electron transport phenomena through a periodically driven single quantum dot in an electrode-multi-level dot-electrode nanoscale quantum device. The memory effect is treated using a multi-function Lorentzian spectral density (LSD) model that mimics the spectral density of each electrode in terms of multiple Lorentzian functions. For the symmetric single-function LSD model involving a single-level dot, the underlying single-particle propagator is shown to be related to a 2×2 effective time-dependent Hamiltonian that includes both the periodic external field and the electrode memory effect. By invoking the generalized Van Vleck (GVV) nearly degenerate perturbation theory, an analytical Tien-Gordon-like expression is derived for arbitrary order multi-photon resonance d.c. tunneling current. Numerically converged simulations and the GVV analytical results are in good agreement, revealing the origin of multi-photon coherent destruction of tunneling and accounting for the suppression of the staircase jumps of d.c. current due to the memory effect. Specially, a novel blockade phenomenon is observed, showing distinctive oscillations in the field-induced current in the large bias voltage limit.

Heat transfer to and from vegetated surfaces - An analytical method for the bulk exchange coefficients

NASA Technical Reports Server (NTRS)

Massman, William J.

1987-01-01

The semianalytical model outlined in a previous study (Massman, 1987) to describe momentum exchange between the atmosphere and vegetated surfaces is extended to include the exchange of heat. The methods employed are based on one-dimensional turbulent diffusivities, and use analytical solutions to the steady-state diffusion equation. The model is used to assess the influence that the canopy foliage structure and density, the wind profile structure within the canopy, and the shelter factor can have upon the inverse surface Stanton number (kB exp -1), as well as to explore the consequences of introducing a scalar displacement height which can be different from the momentum displacement height. In general, the triangular foliage area density function gives results which agree more closely with observations than that for constant foliage area density. The intended application of this work is for parameterizing the bulk aerodynamic resistances for heat and momentum exchange for use within large-scale models of plant-atmosphere exchanges.
Robust control algorithms for Mars aerobraking

NASA Technical Reports Server (NTRS)

Shipley, Buford W., Jr.; Ward, Donald T.

1992-01-01

Four atmospheric guidance concepts have been adapted to control an interplanetary vehicle aerobraking in the Martian atmosphere. The first two offer improvements to the Analytic Predictor Corrector (APC) to increase its robustness to density variations. The second two are variations of a new Liapunov tracking exit phase algorithm, developed to guide the vehicle along a reference trajectory. These four new controllers are tested using a six degree of freedom computer simulation to evaluate their robustness. MARSGRAM is used to develop realistic atmospheres for the study. When square wave density pulses perturb the atmosphere all four controllers are successful. The algorithms are tested against atmospheres where the inbound and outbound density functions are different. Square wave density pulses are again used, but only for the outbound leg of the trajectory. Additionally, sine waves are used to perturb the density function. The new algorithms are found to be more robust than any previously tested and a Liapunov controller is selected as the most robust control algorithm overall examined.
Analytical Computation of Effective Grid Parameters for the Finite-Difference Seismic Waveform Modeling With the PREM, IASP91, SP6, and AK135

NASA Astrophysics Data System (ADS)

Toyokuni, G.; Takenaka, H.

2007-12-01

We propose a method to obtain effective grid parameters for the finite-difference (FD) method with standard Earth models using analytical ways. In spite of the broad use of the heterogeneous FD formulation for seismic waveform modeling, accurate treatment of material discontinuities inside the grid cells has been a serious problem for many years. One possible way to solve this problem is to introduce effective grid elastic moduli and densities (effective parameters) calculated by the volume harmonic averaging of elastic moduli and volume arithmetic averaging of density in grid cells. This scheme enables us to put a material discontinuity into an arbitrary position in the spatial grids. Most of the methods used for synthetic seismogram calculation today receives the blessing of the standard Earth models, such as the PREM, IASP91, SP6, and AK135, represented as functions of normalized radius. For the FD computation of seismic waveform with such models, we first need accurate treatment of material discontinuities in radius. This study provides a numerical scheme for analytical calculations of the effective parameters for an arbitrary spatial grids in radial direction as to these major four standard Earth models making the best use of their functional features. This scheme can analytically obtain the integral volume averages through partial fraction decompositions (PFDs) and integral formulae. We have developed a FORTRAN subroutine to perform the computations, which is opened to utilization in a large variety of FD schemes ranging from 1-D to 3-D, with conventional- and staggered-grids. In the presentation, we show some numerical examples displaying the accuracy of the FD synthetics simulated with the analytical effective parameters.
Sub-saturation matter in compact stars: Nuclear modelling in the framework of the extended Thomas-Fermi theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aymard, François; Gulminelli, Francesca; Margueron, Jérôme

A recently introduced analytical model for the nuclear density profile [1] is implemented in the Extended Thomas-Fermi (ETF) energy density functional. This allows to (i) shed a new light on the issue of the sign of surface symmetry energy in nuclear mass formulas, as well as to (ii) show the importance of the in-medium corrections to the nuclear cluster energies in thermodynamic conditions relevant for the description of core-collapse supernovae and (proto)-neutron star crust.
Plasma and magnetospheric research

NASA Technical Reports Server (NTRS)

Comfort, R. H.; Horwitz, J. L.

1984-01-01

Methods employed in the analysis of plasmas and the magnetosphere are examined. Computer programs which generate distribution functions are used in the analysis of charging phenomena and non maxwell plasmas in terms of density and average energy. An analytical model for spin curve analysis is presented. A program for the analysis of the differential ion flux probe on the space shuttle mission is complete. Satellite data analysis for ion heating, plasma flows in the polar cap, polar wind flow, and density and temperature profiles for several plasmasphere transits are included.
Sub-saturation matter in compact stars: Nuclear modelling in the framework of the extended Thomas-Fermi theory

NASA Astrophysics Data System (ADS)

Aymard, François; Gulminelli, Francesca; Margueron, Jérôme

2015-02-01

A recently introduced analytical model for the nuclear density profile [1] is implemented in the Extended Thomas-Fermi (ETF) energy density functional. This allows to (i) shed a new light on the issue of the sign of surface symmetry energy in nuclear mass formulas, as well as to (ii) show the importance of the in-medium corrections to the nuclear cluster energies in thermodynamic conditions relevant for the description of core-collapse supernovae and (proto)-neutron star crust.
An analytical method for assessing the spatial and temporal variation of juvenile Atlantic salmon habitat in an upland Scottish river.

NASA Astrophysics Data System (ADS)

Buddendorf, B.; Fabris, L.; Malcolm, I.; Lazzaro, G.; Tetzlaff, D.; Botter, G.; Soulsby, C.

2016-12-01

Wild Atlantic salmon populations in Scottish rivers constitute an important economic and recreational resource, as well as being a key component of biodiversity. Salmon have specific habitat requirements at different life stages and their distribution is therefore strongly influenced by a complex suite of biological and physical controls. Stream hydrodynamics have a strong influence on habitat quality and affect the distribution and density of juvenile salmon. As stream hydrodynamics directly relate to stream flow variability and channel morphology, the effects of hydroclimatic drivers on the spatial and temporal variability of habitat suitability can be assessed. Critical Displacement Velocity (CDV), which describes the velocity at which fish can no longer hold station, is one potential approach for characterising habitat suitability. CDV is obtained using an empirical formula that depends on fish size and stream temperature. By characterising the proportion of a reach below CDV it is possible to assess the suitable area. We demonstrate that a generic analytical approach based on field survey and hydraulic modelling can provide insights on the interactions between flow regime and average suitable area (SA) for juvenile salmon that could be extended to other aquatic species. Analytical functions are used to model the pdf of stream flow p(q) and the relationship between flow and suitable area SA(q). Theoretically these functions can assume any form. Here we used a gamma distribution to model p(q) and a gamma function to model SA(q). Integrating the product of these functions we obtain an analytical expression of SA. Since parameters of p(q) can be estimated from meteorological and flow measurements, they can be used directly to predict the effect of flow regime on SA. We show the utility of the approach with reference to 6 electrofishing sites in a single river system where long term (50 years) data on spatially distributed juvenile salmon densities are available.
DOE Office of Scientific and Technical Information (OSTI.GOV)

Morante, S., E-mail: morante@roma2.infn.it; Rossi, G.C., E-mail: rossig@roma2.infn.it; Centro Fermi-Museo Storico della Fisica e Centro Studi e Ricerche E. Fermi, Compendio del Viminale, Piazza del Viminale 1, I-00184 Rome

We give a novel and simple proof of the DFT expression for the interatomic force field that drives the motion of atoms in classical Molecular Dynamics, based on the observation that the ground state electronic energy, seen as a functional of the external potential, is the Legendre transform of the Hohenberg–Kohn functional, which in turn is a functional of the electronic density. We show in this way that the so-called Hellmann–Feynman analytical formula, currently used in numerical simulations, actually provides the exact expression of the interatomic force.
A family of triaxial modified Hubble mass models: Effects of the additional radial functions

NASA Astrophysics Data System (ADS)

Das, Mousumi; Thakur, Parijat; Ann, H. B.

2005-03-01

The projected properties of triaxial generalization of the modified Hubble mass models are studied. These models are constructed by adding the additional radial functions, each multiplied by a low-order spherical harmonic, to the models of [Chakraborty, D.K., Thakur, P., 2000. MNRAS 318, 1273]. The projected surface density of mass models can be calculated analytically which allows us to derive the analytic expressions of axial ratio and position angle of major axis of constant density elliptical contours at asymptotic radii. The models are more general than those studied earlier in the sense that the inclusions of additional terms in density distribution, allow one to produce varieties of the radial profile of axial ratio and position angle, in particular, their small scale variations at inner radii. Strong correlations are found to exist between the observed axial ratio evaluated at 0.25Re and at 4Re which occupy well-separated regions in the parameter space for different choices of the intrinsic axial ratios. These correlations can be exploited to predict the intrinsic shape of the mass model, independent of the viewing angles. Using Bayesian statistics, the result of a test case launched for an estimation of the shape of a model galaxy is found to be satisfactory.
Mode selection and frequency tuning by injection in pulsed TEA-CO2 lasers

NASA Technical Reports Server (NTRS)

Flamant, P. H.; Menzies, R. T.

1983-01-01

An analytical model characterizing pulsed-TEA-CO2-laser injection locking by tunable CW-laser radiation is presented and used to explore the requirements for SLM pulse generation. Photon-density-rate equations describing the laser mechanism are analyzed in terms of the mode competition between photon densities emitted at two frequencies. The expression derived for pulsed dye lasers is extended to homogeneously broadened CO2 lasers, and locking time is defined as a function of laser parameters. The extent to which injected radiation can be detuned from the CO2 line center and continue to produce SLM pulses is investigated experimentally in terms of the analytical framework. The dependence of locking time on the detuning/pressure-broadened-halfwidth ratio is seen as important for spectroscopic applications requiring tuning within the TEA-laser line-gain bandwidth.
Linear Tidal Vestige Found in the WM Sheet

NASA Astrophysics Data System (ADS)

Lee, Jounghun; Kim, Suk; Rey, Soo-Chang

2018-06-01

We present a vestige of the linear tidal influence on the spin orientations of the constituent galaxies of the WM sheet discovered in the vicinity of the Virgo Cluster and the Local Void. The WM sheet is chosen as an optimal target since it has a rectangular parallelepiped-like shape whose three sides are in parallel with the supergalactic Cartesian axes. Determining three probability density functions of the absolute values of the supergalactic Cartesian components of the spin vectors of the WM sheet galaxies, we investigate their alignments with the principal directions of the surrounding large-scale tidal field. When the WM sheet galaxies located in the central region within the distance of 2 h ‑1 Mpc are excluded, the spin vectors of the remaining WM sheet galaxies are found to be weakly aligned, strongly aligned, and strongly anti-aligned with the minor, intermediate, and major principal directions of the surrounding large-scale tidal field, respectively. To examine whether or not the origin of the observed alignment tendency from the WM sheet is the linear tidal effect, we infer the eigenvalues of the linear tidal tensor from the axial ratios of the WM sheet with the help of the Zeldovich approximation and conduct a full analytic evaluation of the prediction of the linear tidal torque model for the three probability density functions. A detailed comparison between the analytical and the observational results reveals a good quantitative agreement not only in the behaviors but also in the amplitudes of the three probability density functions.
THREE-POINT PHASE CORRELATIONS: A NEW MEASURE OF NONLINEAR LARGE-SCALE STRUCTURE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wolstenhulme, Richard; Bonvin, Camille; Obreschkow, Danail

2015-05-10

We derive an analytical expression for a novel large-scale structure observable: the line correlation function. The line correlation function, which is constructed from the three-point correlation function of the phase of the density field, is a robust statistical measure allowing the extraction of information in the nonlinear and non-Gaussian regime. We show that, in perturbation theory, the line correlation is sensitive to the coupling kernel F{sub 2}, which governs the nonlinear gravitational evolution of the density field. We compare our analytical expression with results from numerical simulations and find a 1σ agreement for separations r ≳ 30 h{sup −1} Mpc.more » Fitting formulae for the power spectrum and the nonlinear coupling kernel at small scales allow us to extend our prediction into the strongly nonlinear regime, where we find a 1σ agreement with the simulations for r ≳ 2 h{sup −1} Mpc. We discuss the advantages of the line correlation relative to standard statistical measures like the bispectrum. Unlike the latter, the line correlation is independent of the bias, in the regime where the bias is local and linear. Furthermore, the variance of the line correlation is independent of the Gaussian variance on the modulus of the density field. This suggests that the line correlation can probe more precisely the nonlinear regime of gravity, with less contamination from the power spectrum variance.« less
A Site Density Functional Theory for Water: Application to Solvation of Amino Acid Side Chains.

PubMed

Liu, Yu; Zhao, Shuangliang; Wu, Jianzhong

2013-04-09

We report a site density functional theory (SDFT) based on the conventional atomistic models of water and the universality ansatz of the bridge functional. The excess Helmholtz energy functional is formulated in terms of a quadratic expansion with respect to the local density deviation from that of a uniform system and a universal functional for all higher-order terms approximated by that of a reference hard-sphere system. With the atomistic pair direct correlation functions of the uniform system calculated from MD simulation and an analytical expression for the bridge functional from the modified fundamental measure theory, the SDFT can be used to predict the structure and thermodynamic properties of water under inhomogeneous conditions with a computational cost negligible in comparison to that of brute-force simulations. The numerical performance of the SDFT has been demonstrated with the predictions of the solvation free energies of 15 molecular analogs of amino acid side chains in water represented by SPC/E, SPC, and TIP3P models. For theTIP3P model, a comparison of the theoretical predictions with MD simulation and experimental data shows agreement within 0.64 and 1.09 kcal/mol on average, respectively.
Obtaining macroscopic quantities for the contact line problem from Density Functional Theory using asymptotic methods

NASA Astrophysics Data System (ADS)

Sibley, David; Nold, Andreas; Kalliadasis, Serafim

2015-11-01

Density Functional Theory (DFT), a statistical mechanics of fluids approach, captures microscopic details of the fluid density structure in the vicinity of contact lines, as seen in computations in our recent study. Contact lines describe the location where interfaces between two fluids meet solid substrates, and have stimulated a wealth of research due to both their ubiquity in nature and technological applications and also due to their rich multiscale behaviour. Whilst progress can be made computationally to capture the microscopic to mesoscopic structure from DFT, complete analytical results to fully bridge to the macroscale are lacking. In this work, we describe our efforts to bring asymptotic methods to DFT to obtain results for contact angles and other macroscopic quantities in various parameter regimes. We acknowledge financial support from European Research Council via Advanced Grant No. 247031.
Analytical nuclear gradients for the range-separated many-body dispersion model of noncovalent interactions.

PubMed

Blood-Forsythe, Martin A; Markovich, Thomas; DiStasio, Robert A; Car, Roberto; Aspuru-Guzik, Alán

2016-03-01

An accurate treatment of the long-range electron correlation energy, including van der Waals (vdW) or dispersion interactions, is essential for describing the structure, dynamics, and function of a wide variety of systems. Among the most accurate models for including dispersion into density functional theory (DFT) is the range-separated many-body dispersion (MBD) method [A. Ambrosetti et al. , J. Chem. Phys. , 2014, 140 , 18A508], in which the correlation energy is modeled at short-range by a semi-local density functional and at long-range by a model system of coupled quantum harmonic oscillators. In this work, we develop analytical gradients of the MBD energy with respect to nuclear coordinates, including all implicit coordinate dependencies arising from the partitioning of the charge density into Hirshfeld effective volumes. To demonstrate the efficiency and accuracy of these MBD gradients for geometry optimizations of systems with intermolecular and intramolecular interactions, we optimized conformers of the benzene dimer and isolated small peptides with aromatic side-chains. We find excellent agreement with the wavefunction theory reference geometries of these systems (at a fraction of the computational cost) and find that MBD consistently outperforms the popular TS and D3(BJ) dispersion corrections. To demonstrate the performance of the MBD model on a larger system with supramolecular interactions, we optimized the C 60 @C 60 H 28 buckyball catcher host-guest complex. In our analysis, we also find that neglecting the implicit nuclear coordinate dependence arising from the charge density partitioning, as has been done in prior numerical treatments, leads to an unacceptable error in the MBD forces, with relative errors of ∼20% (on average) that can extend well beyond 100%.
A simple phenomenological model for grain clustering in turbulence

NASA Astrophysics Data System (ADS)

Hopkins, Philip F.

2016-01-01

We propose a simple model for density fluctuations of aerodynamic grains, embedded in a turbulent, gravitating gas disc. The model combines a calculation for the behaviour of a group of grains encountering a single turbulent eddy, with a hierarchical approximation of the eddy statistics. This makes analytic predictions for a range of quantities including: distributions of grain densities, power spectra and correlation functions of fluctuations, and maximum grain densities reached. We predict how these scale as a function of grain drag time ts, spatial scale, grain-to-gas mass ratio tilde{ρ }, strength of turbulence α, and detailed disc properties. We test these against numerical simulations with various turbulence-driving mechanisms. The simulations agree well with the predictions, spanning ts Ω ˜ 10-4-10, tilde{ρ }˜ 0{-}3, α ˜ 10-10-10-2. Results from `turbulent concentration' simulations and laboratory experiments are also predicted as a special case. Vortices on a wide range of scales disperse and concentrate grains hierarchically. For small grains this is most efficient in eddies with turnover time comparable to the stopping time, but fluctuations are also damped by local gas-grain drift. For large grains, shear and gravity lead to a much broader range of eddy scales driving fluctuations, with most power on the largest scales. The grain density distribution has a log-Poisson shape, with fluctuations for large grains up to factors ≳1000. We provide simple analytic expressions for the predictions, and discuss implications for planetesimal formation, grain growth, and the structure of turbulence.
Analytic solution of the Spencer-Lewis angular-spatial moments equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Filippone, W.L.

A closed-form solution for the angular-spatial moments of the Spencer-Lewis equation is presented that is valid for infinite homogeneous media. From the moments, the electron density distribution as a function of position and path length (energy) is reconstructed for several sample problems involving plane isotropic sources of electrons in aluminium. The results are in excellent agreement with those determined numerically using the streaming ray method. The primary use of the closed form solution will most likely be to generate accurate electron transport benchmark solutions. In principle, the electron density as a function of space, path length, and direction can bemore » determined for planar sources of arbitrary angular distribution.« less
Urban characteristics attributable to density-driven tie formation

NASA Astrophysics Data System (ADS)

Pan, Wei; Ghoshal, Gourab; Krumme, Coco; Cebrian, Manuel; Pentland, Alex

2013-06-01

Motivated by empirical evidence on the interplay between geography, population density and societal interaction, we propose a generative process for the evolution of social structure in cities. Our analytical and simulation results predict both super-linear scaling of social-tie density and information contagion as a function of the population. Here we demonstrate that our model provides a robust and accurate fit for the dependency of city characteristics with city-size, ranging from individual-level dyadic interactions (number of acquaintances, volume of communication) to population level variables (contagious disease rates, patenting activity, economic productivity and crime) without the need to appeal to heterogeneity, modularity, specialization or hierarchy.
Homogeneous buoyancy-generated turbulence

NASA Technical Reports Server (NTRS)

Batchelor, G. K.; Canuto, V. M.; Chasnov, J. R.

1992-01-01

Using a theoretical analysis of fundamental equations and a numerical simulation of the flow field, the statistically homogeneous motion that is generated by buoyancy forces after the creation of homogeneous random fluctuations in the density of infinite fluid at an initial instant is examined. It is shown that analytical results together with numerical results provide a comprehensive description of the 'birth, life, and death' of buoyancy-generated turbulence. Results of numerical simulations yielded the mean-square density mean-square velocity fluctuations and the associated spectra as functions of time for various initial conditions, and the time required for the mean-square density fluctuation to fall to a specified small value was estimated.
X-Ray Fluorescence Determination of the Surface Density of Chromium Nanolayers

NASA Astrophysics Data System (ADS)

Mashin, N. I.; Chernjaeva, E. A.; Tumanova, A. N.; Ershov, A. A.

2014-01-01

An auxiliary system consisting of thin-film layers of chromium deposited on a polymer film substrate is used to construct calibration curves for the relative intensities of the K α lines of chromium on bulk substrates of different elements as functions of the chromium surface density in the reference samples. Correction coefficients are calculated to take into account the absorption of primary radiation from an x-ray tube and analytical lines of the constituent elements of the substrate. A method is developed for determining the surface density of thin films of chromium when test and calibration samples are deposited on substrates of different materials.

Cylinders out of a top hat: counts-in-cells for projected densities

NASA Astrophysics Data System (ADS)

Uhlemann, Cora; Pichon, Christophe; Codis, Sandrine; L'Huillier, Benjamin; Kim, Juhan; Bernardeau, Francis; Park, Changbom; Prunet, Simon

2018-06-01

Large deviation statistics is implemented to predict the statistics of cosmic densities in cylinders applicable to photometric surveys. It yields few per cent accurate analytical predictions for the one-point probability distribution function (PDF) of densities in concentric or compensated cylinders; and also captures the density dependence of their angular clustering (cylinder bias). All predictions are found to be in excellent agreement with the cosmological simulation Horizon Run 4 in the quasi-linear regime where standard perturbation theory normally breaks down. These results are combined with a simple local bias model that relates dark matter and tracer densities in cylinders and validated on simulated halo catalogues. This formalism can be used to probe cosmology with existing and upcoming photometric surveys like DES, Euclid or WFIRST containing billions of galaxies.
Frechet derivatives for shallow water ocean acoustic inverse problems

NASA Astrophysics Data System (ADS)

Odom, Robert I.

2003-04-01

For any inverse problem, finding a model fitting the data is only half the problem. Most inverse problems of interest in ocean acoustics yield nonunique model solutions, and involve inevitable trade-offs between model and data resolution and variance. Problems of uniqueness and resolution and variance trade-offs can be addressed by examining the Frechet derivatives of the model-data functional with respect to the model variables. Tarantola [Inverse Problem Theory (Elsevier, Amsterdam, 1987), p. 613] published analytical formulas for the basic derivatives, e.g., derivatives of pressure with respect to elastic moduli and density. Other derivatives of interest, such as the derivative of transmission loss with respect to attenuation, can be easily constructed using the chain rule. For a range independent medium the analytical formulas involve only the Green's function and the vertical derivative of the Green's function for the medium. A crucial advantage of the analytical formulas for the Frechet derivatives over numerical differencing is that they can be computed with a single pass of any program which supplies the Green's function. Various derivatives of interest in shallow water ocean acoustics are presented and illustrated by an application to the sensitivity of measured pressure to shallow water sediment properties. [Work supported by ONR.
Flow and Transport in Highly Heterogeneous Porous Formations: Numerical Experiments Performed Using the Analytic Element Method

NASA Astrophysics Data System (ADS)

Jankovic, I.

2002-05-01

Flow and transport in porous formations are analyzed using numerical simulations. Hydraulic conductivity is treated as a spatial random function characterized by a probability density function and a two-point covariance function. Simulations are performed for a multi-indicator conductivity structure developed by Gedeon Dagan (personal communication). This conductivity structure contains inhomogeneities (inclusions) of elliptical and ellipsoidal geometry that are embedded in a homogeneous background. By varying the distribution of sizes and conductivities of inclusions, any probability density function and two-point covariance may be reproduced. The multi-indicator structure is selected since it yields simple approximate transport solutions (Aldo Fiori, personal communication) and accurate numerical solutions (based on the Analytic Element Method). The dispersion is examined for two conceptual models. Both models are based on the multi-indicator conductivity structure. The first model is designed to examine dispersion in aquifers with continuously varying conductivity. The inclusions in this model cover as much area/volume of the porous formation as possible. The second model is designed for aquifers that contain clay/sand/gravel lenses embedded in otherwise homogeneous background. The dispersion in both aquifer types is simulated numerically. Simulation results are compared to those obtained using simple approximate solutions. In order to infer transport statistics that are representative of an infinite domain using the numerical experiments, the inclusions are placed in a domain that was shaped as a large ellipse (2D) and a large spheroid (3D) that were submerged in an unbounded homogeneous medium. On a large scale, the large body of inclusions behaves like a single large inhomogeneity. The analytic solution for a uniform flow past the single inhomogeneity of such geometry yields uniform velocity inside the domain. The velocity differs from that at infinity and can be used to infer the effective conductivity of the medium. As many as 100,000 inhomogeneities are placed inside the domain for 2D simulations. Simulations in 3D were limited to 50,000 inclusions. A large number of simulations was conducted on a massively parallel supercomputer cluster at the Center for Computational Research, University at Buffalo. Simulations range from mildly heterogeneous formations to highly heterogeneous formations (variance of the logarithm of conductivity equal to 10) and from sparsely populated systems to systems where inhomogeneities cover 95% of the volume. Particles are released and tracked inside the core of constant mean velocity. Following the particle tracking, various medium, flow, and transport statistics are computed. These include: spatial moments of particle positions, probability density function of hydraulic conductivity and each component of velocity, their two-point covariance function in the direction of flow and normal to it, covariance of Lagrangean velocities, and probability density function of travel times to various break-through locations. Following the analytic nature of the flow solution, all the results are presented in dimensionless forms. For example, the dispersion coefficients are made dimensionless with respect to the mean velocity and size of inhomogeneities. Detailed results will be presented and compared to well known first-order results and the results that are based on simple approximate transport solutions of Aldo Fiori.
Electron density modification in ionospheric E layer by inserting fine dust particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Misra, Shikha, E-mail: shikhamish@gmail.com; Mishra, S. K.

2015-02-15

In this paper, we have developed the kinetics of E-region ionospheric plasma comprising of fine dust grains and shown that the electron density in E-layer can purposely be reduced/enhanced up to desired level by inserting fine dust particles of appropriate physical/material properties; this may certainly be promising for preferred rf-signal processing through these layers. The analytical formulation is based on average charge theory and includes the number and energy balance of the plasma constituents along with charge balance over dust particles. The effect of varying number density, work function, and photo-efficiency of dust particles on ionospheric plasma density at differentmore » altitude in E-layer has been critically examined and presented graphically.« less
Adaptive frozen orbital treatment for the fragment molecular orbital method combined with density-functional tight-binding

NASA Astrophysics Data System (ADS)

Nishimoto, Yoshio; Fedorov, Dmitri G.

2018-02-01

The exactly analytic gradient is derived and implemented for the fragment molecular orbital (FMO) method combined with density-functional tight-binding (DFTB) using adaptive frozen orbitals. The response contributions which arise from freezing detached molecular orbitals on the border between fragments are computed by solving Z-vector equations. The accuracy of the energy, its gradient, and optimized structures is verified on a set of representative inorganic materials and polypeptides. FMO-DFTB is applied to optimize the structure of a silicon nano-wire, and the results are compared to those of density functional theory and experiment. FMO accelerates the DFTB calculation of a boron nitride nano-ring with 7872 atoms by a factor of 406. Molecular dynamics simulations using FMO-DFTB applied to a 10.7 μm chain of boron nitride nano-rings, consisting of about 1.2 × 106 atoms, reveal the rippling and twisting of nano-rings at room temperature.
Analytical solution of the transient temperature profile in gain medium of passively Q-switched microchip laser.

PubMed

Han, Xiahui; Li, Jianlang

2014-11-01

The transient temperature evolution in the gain medium of a continuous wave (CW) end-pumped passively Q-switched microchip (PQSM) laser is analyzed. By approximating the time-dependent population inversion density as a sawtooth function of time and treating the time-dependent pump absorption of a CW end-pumped PQSM laser as the superposition of an infinite series of short pumping pulses, the analytical expressions of transient temperature evolution and distribution in the gain medium for four- and three-level laser systems, respectively, are given. These analytical solutions are applied to evaluate the transient temperature evolution and distribution in the gain medium of CW end-pumped PQSM Nd:YAG and Yb:YAG lasers.
Numerical Optimization of Density Functional Tight Binding Models: Application to Molecules Containing Carbon, Hydrogen, Nitrogen, and Oxygen

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krishnapriyan, A.; Yang, P.; Niklasson, A. M. N.

New parametrizations for semiempirical density functional tight binding (DFTB) theory have been developed by the numerical optimization of adjustable parameters to minimize errors in the atomization energy and interatomic forces with respect to ab initio calculated data. Initial guesses for the radial dependences of the Slater- Koster bond integrals and overlap integrals were obtained from minimum basis density functional theory calculations. The radial dependences of the pair potentials and the bond and overlap integrals were represented by simple analytic functions. The adjustable parameters in these functions were optimized by simulated annealing and steepest descent algorithms to minimize the value ofmore » an objective function that quantifies the error between the DFTB model and ab initio calculated data. The accuracy and transferability of the resulting DFTB models for the C, H, N, and O system were assessed by comparing the predicted atomization energies and equilibrium molecular geometries of small molecules that were not included in the training data from DFTB to ab initio data. The DFTB models provide accurate predictions of the properties of hydrocarbons and more complex molecules containing C, H, N, and O.« less
Numerical Optimization of Density Functional Tight Binding Models: Application to Molecules Containing Carbon, Hydrogen, Nitrogen, and Oxygen

DOE PAGES

Krishnapriyan, A.; Yang, P.; Niklasson, A. M. N.; ...

2017-10-17

New parametrizations for semiempirical density functional tight binding (DFTB) theory have been developed by the numerical optimization of adjustable parameters to minimize errors in the atomization energy and interatomic forces with respect to ab initio calculated data. Initial guesses for the radial dependences of the Slater- Koster bond integrals and overlap integrals were obtained from minimum basis density functional theory calculations. The radial dependences of the pair potentials and the bond and overlap integrals were represented by simple analytic functions. The adjustable parameters in these functions were optimized by simulated annealing and steepest descent algorithms to minimize the value ofmore » an objective function that quantifies the error between the DFTB model and ab initio calculated data. The accuracy and transferability of the resulting DFTB models for the C, H, N, and O system were assessed by comparing the predicted atomization energies and equilibrium molecular geometries of small molecules that were not included in the training data from DFTB to ab initio data. The DFTB models provide accurate predictions of the properties of hydrocarbons and more complex molecules containing C, H, N, and O.« less
Energy density and energy flow of surface waves in a strongly magnetized graphene

NASA Astrophysics Data System (ADS)

Moradi, Afshin

2018-01-01

General expressions for the energy density and energy flow of plasmonic waves in a two-dimensional massless electron gas (as a simple model of graphene) are obtained by means of the linearized magneto-hydrodynamic model and classical electromagnetic theory when a strong external magnetic field perpendicular to the system is present. Also, analytical expressions for the energy velocity, wave polarization, wave impedance, transverse and longitudinal field strength functions, and attenuation length of surface magneto-plasmon-polariton waves are derived, and numerical results are prepared.
Exact hierarchical clustering in one dimension. [in universe

NASA Technical Reports Server (NTRS)

Williams, B. G.; Heavens, A. F.; Peacock, J. A.; Shandarin, S. F.

1991-01-01

The present adhesion model-based one-dimensional simulations of gravitational clustering have yielded bound-object catalogs applicable in tests of analytical approaches to cosmological structure formation. Attention is given to Press-Schechter (1974) type functions, as well as to their density peak-theory modifications and the two-point correlation function estimated from peak theory. The extent to which individual collapsed-object locations can be predicted by linear theory is significant only for objects of near-characteristic nonlinear mass.
Modeling of normal contact of elastic bodies with surface relief taken into account

NASA Astrophysics Data System (ADS)

Goryacheva, I. G.; Tsukanov, I. Yu

2018-04-01

An approach to account the surface relief in normal contact problems for rough bodies on the basis of an additional displacement function for asperities is considered. The method and analytic expressions for calculating the additional displacement function for one-scale and two-scale wavy relief are presented. The influence of the microrelief geometric parameters, including the number of scales and asperities density, on additional displacements of the rough layer is analyzed.
Electromagnetic Compatibility Testing Studies

NASA Technical Reports Server (NTRS)

Trost, Thomas F.; Mitra, Atindra K.

1996-01-01

This report discusses the results on analytical models and measurement and simulation of statistical properties from a study of microwave reverberation (mode-stirred) chambers performed at Texas Tech University. Two analytical models of power transfer vs. frequency in a chamber, one for antenna-to-antenna transfer and the other for antenna to D-dot sensor, were experimentally validated in our chamber. Two examples are presented of the measurement and calculation of chamber Q, one for each of the models. Measurements of EM power density validate a theoretical probability distribution on and away from the chamber walls and also yield a distribution with larger standard deviation at frequencies below the range of validity of the theory. Measurements of EM power density at pairs of points which validate a theoretical spatial correlation function on the chamber walls and also yield a correlation function with larger correlation length, R(sub corr), at frequencies below the range of validity of the theory. A numerical simulation, employing a rectangular cavity with a moving wall shows agreement with the measurements. The determination that the lowest frequency at which the theoretical spatial correlation function is valid in our chamber is considerably higher than the lowest frequency recommended by current guidelines for utilizing reverberation chambers in EMC testing. Two suggestions have been made for future studies related to EMC testing.
Analytical model for three-dimensional Mercedes-Benz water molecules.

PubMed

Urbic, T

2012-06-01

We developed a statistical model which describes the thermal and volumetric properties of water-like molecules. A molecule is presented as a three-dimensional sphere with four hydrogen-bonding arms. Each water molecule interacts with its neighboring waters through a van der Waals interaction and an orientation-dependent hydrogen-bonding interaction. This model, which is largely analytical, is a variant of a model developed before for a two-dimensional Mercedes-Benz model of water. We explored properties such as molar volume, density, heat capacity, thermal expansion coefficient, and isothermal compressibility as a function of temperature and pressure. We found that the volumetric and thermal properties follow the same trends with temperature as in real water and are in good general agreement with Monte Carlo simulations, including the density anomaly, the minimum in the isothermal compressibility, and the decreased number of hydrogen bonds upon increasing the temperature.
Analytical model for three-dimensional Mercedes-Benz water molecules

NASA Astrophysics Data System (ADS)

Urbic, T.

2012-06-01

We developed a statistical model which describes the thermal and volumetric properties of water-like molecules. A molecule is presented as a three-dimensional sphere with four hydrogen-bonding arms. Each water molecule interacts with its neighboring waters through a van der Waals interaction and an orientation-dependent hydrogen-bonding interaction. This model, which is largely analytical, is a variant of a model developed before for a two-dimensional Mercedes-Benz model of water. We explored properties such as molar volume, density, heat capacity, thermal expansion coefficient, and isothermal compressibility as a function of temperature and pressure. We found that the volumetric and thermal properties follow the same trends with temperature as in real water and are in good general agreement with Monte Carlo simulations, including the density anomaly, the minimum in the isothermal compressibility, and the decreased number of hydrogen bonds upon increasing the temperature.
Analytical model for three-dimensional Mercedes-Benz water molecules

PubMed Central

Urbic, T.

2013-01-01

We developed a statistical model which describes the thermal and volumetric properties of water-like molecules. A molecule is presented as a three-dimensional sphere with four hydrogen-bonding arms. Each water molecule interacts with its neighboring waters through a van der Waals interaction and an orientation-dependent hydrogen-bonding interaction. This model, which is largely analytical, is a variant of a model developed before for a two-dimensional Mercedes-Benz model of water. We explored properties such as molar volume, density, heat capacity, thermal expansion coefficient, and isothermal compressibility as a function of temperature and pressure. We found that the volumetric and thermal properties follow the same trends with temperature as in real water and are in good general agreement with Monte Carlo simulations, including the density anomaly, the minimum in the isothermal compressibility, and the decreased number of hydrogen bonds upon increasing the temperature. PMID:23005100
Green's function of radial inhomogeneous spheres excited by internal sources.

PubMed

Zouros, Grigorios P; Kokkorakis, Gerassimos C

2011-01-01

Green's function in the interior of penetrable bodies with inhomogeneous compressibility by sources placed inside them is evaluated through a Schwinger-Lippmann volume integral equation. In the case of a radial inhomogeneous sphere, the radial part of the unknown Green's function can be expanded in a double Dini's series, which allows analytical evaluation of the involved cumbersome integrals. The simple case treated here can be extended to more difficult situations involving inhomogeneous density as well as to the corresponding electromagnetic or elastic problem. Finally, numerical results are given for various inhomogeneous compressibility distributions.
Spacecraft observations of a Maxwell Demon coating the separatrix of asymmetric magnetic reconnection with crescent-shaped electron distributions

NASA Astrophysics Data System (ADS)

Egedal, J.; Le, A.; Daughton, W.; Wetherton, B.; Cassak, Pa; Chen, Lj; Lavraud, B.; Dorell, J.; Avanov, L.; Gershman, D.

2016-10-01

During asymmetric magnetic reconnection in the dayside magnetopause in situ spacecraft mea- surements show that electrons from the high density inflow penetrate some distance into the low density inflow. Supported by a kinetic simulation, we present a general derivation of an exclusion energy parameter, which provides a lower kinetic energy bound for an electron to jump across the reconnection region from one inflow region to the other. As by a Maxwell Demon, only high energy electrons are permitted to cross the inner reconnection region, strongly impacting the form of the electron distribution function observed along the low density side separatrix. The dynamics produce two distinct flavors of crescent-shaped electron distributions in a thin boundary layer along the separatrix between the magnetospheric inflow and the reconnection exhaust. The analytical model presented relates these salient details of the distribution function to the electron dynamics in the inner reconnection region.
On the probability distribution function of the mass surface density of molecular clouds. I

NASA Astrophysics Data System (ADS)

Fischera, Jörg

2014-05-01

The probability distribution function (PDF) of the mass surface density is an essential characteristic of the structure of molecular clouds or the interstellar medium in general. Observations of the PDF of molecular clouds indicate a composition of a broad distribution around the maximum and a decreasing tail at high mass surface densities. The first component is attributed to the random distribution of gas which is modeled using a log-normal function while the second component is attributed to condensed structures modeled using a simple power-law. The aim of this paper is to provide an analytical model of the PDF of condensed structures which can be used by observers to extract information about the condensations. The condensed structures are considered to be either spheres or cylinders with a truncated radial density profile at cloud radius rcl. The assumed profile is of the form ρ(r) = ρc/ (1 + (r/r0)2)n/ 2 for arbitrary power n where ρc and r0 are the central density and the inner radius, respectively. An implicit function is obtained which either truncates (sphere) or has a pole (cylinder) at maximal mass surface density. The PDF of spherical condensations and the asymptotic PDF of cylinders in the limit of infinite overdensity ρc/ρ(rcl) flattens for steeper density profiles and has a power law asymptote at low and high mass surface densities and a well defined maximum. The power index of the asymptote Σ- γ of the logarithmic PDF (ΣP(Σ)) in the limit of high mass surface densities is given by γ = (n + 1)/(n - 1) - 1 (spheres) or by γ = n/ (n - 1) - 1 (cylinders in the limit of infinite overdensity). Appendices are available in electronic form at http://www.aanda.org
Measurement Model Nonlinearity in Estimation of Dynamical Systems

NASA Astrophysics Data System (ADS)

Majji, Manoranjan; Junkins, J. L.; Turner, J. D.

2012-06-01

The role of nonlinearity of the measurement model and its interactions with the uncertainty of measurements and geometry of the problem is studied in this paper. An examination of the transformations of the probability density function in various coordinate systems is presented for several astrodynamics applications. Smooth and analytic nonlinear functions are considered for the studies on the exact transformation of uncertainty. Special emphasis is given to understanding the role of change of variables in the calculus of random variables. The transformation of probability density functions through mappings is shown to provide insight in to understanding the evolution of uncertainty in nonlinear systems. Examples are presented to highlight salient aspects of the discussion. A sequential orbit determination problem is analyzed, where the transformation formula provides useful insights for making the choice of coordinates for estimation of dynamic systems.
Entanglement transitions induced by large deviations

NASA Astrophysics Data System (ADS)

Bhosale, Udaysinh T.

2017-12-01

The probability of large deviations of the smallest Schmidt eigenvalue for random pure states of bipartite systems, denoted as A and B , is computed analytically using a Coulomb gas method. It is shown that this probability, for large N , goes as exp[-β N2Φ (ζ ) ] , where the parameter β is the Dyson index of the ensemble, ζ is the large deviation parameter, while the rate function Φ (ζ ) is calculated exactly. Corresponding equilibrium Coulomb charge density is derived for its large deviations. Effects of the large deviations of the extreme (largest and smallest) Schmidt eigenvalues on the bipartite entanglement are studied using the von Neumann entropy. Effect of these deviations is also studied on the entanglement between subsystems 1 and 2, obtained by further partitioning the subsystem A , using the properties of the density matrix's partial transpose ρ12Γ. The density of states of ρ12Γ is found to be close to the Wigner's semicircle law with these large deviations. The entanglement properties are captured very well by a simple random matrix model for the partial transpose. The model predicts the entanglement transition across a critical large deviation parameter ζ . Log negativity is used to quantify the entanglement between subsystems 1 and 2. Analytical formulas for it are derived using the simple model. Numerical simulations are in excellent agreement with the analytical results.

Entanglement transitions induced by large deviations.

PubMed

Bhosale, Udaysinh T

2017-12-01

The probability of large deviations of the smallest Schmidt eigenvalue for random pure states of bipartite systems, denoted as A and B, is computed analytically using a Coulomb gas method. It is shown that this probability, for large N, goes as exp[-βN^{2}Φ(ζ)], where the parameter β is the Dyson index of the ensemble, ζ is the large deviation parameter, while the rate function Φ(ζ) is calculated exactly. Corresponding equilibrium Coulomb charge density is derived for its large deviations. Effects of the large deviations of the extreme (largest and smallest) Schmidt eigenvalues on the bipartite entanglement are studied using the von Neumann entropy. Effect of these deviations is also studied on the entanglement between subsystems 1 and 2, obtained by further partitioning the subsystem A, using the properties of the density matrix's partial transpose ρ_{12}^{Γ}. The density of states of ρ_{12}^{Γ} is found to be close to the Wigner's semicircle law with these large deviations. The entanglement properties are captured very well by a simple random matrix model for the partial transpose. The model predicts the entanglement transition across a critical large deviation parameter ζ. Log negativity is used to quantify the entanglement between subsystems 1 and 2. Analytical formulas for it are derived using the simple model. Numerical simulations are in excellent agreement with the analytical results.
Tigers and their prey: Predicting carnivore densities from prey abundance

USGS Publications Warehouse

Karanth, K.U.; Nichols, J.D.; Kumar, N.S.; Link, W.A.; Hines, J.E.

2004-01-01

The goal of ecology is to understand interactions that determine the distribution and abundance of organisms. In principle, ecologists should be able to identify a small number of limiting resources for a species of interest, estimate densities of these resources at different locations across the landscape, and then use these estimates to predict the density of the focal species at these locations. In practice, however, development of functional relationships between abundances of species and their resources has proven extremely difficult, and examples of such predictive ability are very rare. Ecological studies of prey requirements of tigers Panthera tigris led us to develop a simple mechanistic model for predicting tiger density as a function of prey density. We tested our model using data from a landscape-scale long-term (1995-2003) field study that estimated tiger and prey densities in 11 ecologically diverse sites across India. We used field techniques and analytical methods that specifically addressed sampling and detectability, two issues that frequently present problems in macroecological studies of animal populations. Estimated densities of ungulate prey ranged between 5.3 and 63.8 animals per km2. Estimated tiger densities (3.2-16.8 tigers per 100 km2) were reasonably consistent with model predictions. The results provide evidence of a functional relationship between abundances of large carnivores and their prey under a wide range of ecological conditions. In addition to generating important insights into carnivore ecology and conservation, the study provides a potentially useful model for the rigorous conduct of macroecological science.
The virialization density of peaks with general density profiles under spherical collapse

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rubin, Douglas; Loeb, Abraham, E-mail: dsrubin@physics.harvard.edu, E-mail: aloeb@cfa.harvard.edu

2013-12-01

We calculate the non-linear virialization density, Δ{sub c}, of halos under spherical collapse from peaks with an arbitrary initial and final density profile. This is in contrast to the standard calculation of Δ{sub c} which assumes top-hat profiles. Given our formalism, the non-linear halo density can be calculated once the shape of the initial peak's density profile and the shape of the virialized halo's profile are provided. We solve for Δ{sub c} for halos in an Einstein de-Sitter and a ΛCDM universe. As examples, we consider power-law initial profiles as well as spherically averaged peak profiles calculated from the statisticsmore » of a Gaussian random field. We find that, depending on the profiles used, Δ{sub c} is smaller by a factor of a few to as much as a factor of 10 as compared to the density given by the standard calculation ( ≈ 200). Using our results, we show that, for halo finding algorithms that identify halos through an over-density threshold, the halo mass function measured from cosmological simulations can be enhanced at all halo masses by a factor of a few. This difference could be important when using numerical simulations to assess the validity of analytic models of the halo mass function.« less
Spectral likelihood expansions for Bayesian inference

NASA Astrophysics Data System (ADS)

Nagel, Joseph B.; Sudret, Bruno

2016-03-01

A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this spectral likelihood expansion all statistical quantities of interest can be calculated semi-analytically. The posterior is formally represented as the product of a reference density and a linear combination of polynomial basis functions. Both the model evidence and the posterior moments are related to the expansion coefficients. This formulation avoids Markov chain Monte Carlo simulation and allows one to make use of linear least squares instead. The pros and cons of spectral Bayesian inference are discussed and demonstrated on the basis of simple applications from classical statistics and inverse modeling.
Deconvolution of Stark broadened spectra for multi-point density measurements in a flow Z-pinch

DOE PAGES

Vogman, G. V.; Shumlak, U.

2011-10-13

Stark broadened emission spectra, once separated from other broadening effects, provide a convenient non-perturbing means of making plasma density measurements. A deconvolution technique has been developed to measure plasma densities in the ZaP flow Z-pinch experiment. The ZaP experiment uses sheared flow to mitigate MHD instabilities. The pinches exhibit Stark broadened emission spectra, which are captured at 20 locations using a multi-chord spectroscopic system. Spectra that are time- and chord-integrated are well approximated by a Voigt function. The proposed method simultaneously resolves plasma electron density and ion temperature by deconvolving the spectral Voigt profile into constituent functions: a Gaussian functionmore » associated with instrument effects and Doppler broadening by temperature; and a Lorentzian function associated with Stark broadening by electron density. The method uses analytic Fourier transforms of the constituent functions to fit the Voigt profile in the Fourier domain. The method is discussed and compared to a basic least-squares fit. The Fourier transform fitting routine requires fewer fitting parameters and shows promise in being less susceptible to instrumental noise and to contamination from neighboring spectral lines. The method is evaluated and tested using simulated lines and is applied to experimental data for the 229.69 nm C III line from multiple chords to determine plasma density and temperature across the diameter of the pinch. As a result, these measurements are used to gain a better understanding of Z-pinch equilibria.« less
Deconvolution of Stark broadened spectra for multi-point density measurements in a flow Z-pinch

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vogman, G. V.; Shumlak, U.

2011-10-15

Stark broadened emission spectra, once separated from other broadening effects, provide a convenient non-perturbing means of making plasma density measurements. A deconvolution technique has been developed to measure plasma densities in the ZaP flow Z-pinch experiment. The ZaP experiment uses sheared flow to mitigate MHD instabilities. The pinches exhibit Stark broadened emission spectra, which are captured at 20 locations using a multi-chord spectroscopic system. Spectra that are time- and chord-integrated are well approximated by a Voigt function. The proposed method simultaneously resolves plasma electron density and ion temperature by deconvolving the spectral Voigt profile into constituent functions: a Gaussian functionmore » associated with instrument effects and Doppler broadening by temperature; and a Lorentzian function associated with Stark broadening by electron density. The method uses analytic Fourier transforms of the constituent functions to fit the Voigt profile in the Fourier domain. The method is discussed and compared to a basic least-squares fit. The Fourier transform fitting routine requires fewer fitting parameters and shows promise in being less susceptible to instrumental noise and to contamination from neighboring spectral lines. The method is evaluated and tested using simulated lines and is applied to experimental data for the 229.69 nm C III line from multiple chords to determine plasma density and temperature across the diameter of the pinch. These measurements are used to gain a better understanding of Z-pinch equilibria.« less
Mechanisms of jamming in the Nagel-Schreckenberg model for traffic flow.

PubMed

Bette, Henrik M; Habel, Lars; Emig, Thorsten; Schreckenberg, Michael

2017-01-01

We study the Nagel-Schreckenberg cellular automata model for traffic flow by both simulations and analytical techniques. To better understand the nature of the jamming transition, we analyze the fraction of stopped cars P(v=0) as a function of the mean car density. We present a simple argument that yields an estimate for the free density where jamming occurs, and show satisfying agreement with simulation results. We demonstrate that the fraction of jammed cars P(v∈{0,1}) can be decomposed into the three factors (jamming rate, jam lifetime, and jam size) for which we derive, from random walk arguments, exponents that control their scaling close to the critical density.
Mechanisms of jamming in the Nagel-Schreckenberg model for traffic flow

NASA Astrophysics Data System (ADS)

Bette, Henrik M.; Habel, Lars; Emig, Thorsten; Schreckenberg, Michael

2017-01-01

We study the Nagel-Schreckenberg cellular automata model for traffic flow by both simulations and analytical techniques. To better understand the nature of the jamming transition, we analyze the fraction of stopped cars P (v =0 ) as a function of the mean car density. We present a simple argument that yields an estimate for the free density where jamming occurs, and show satisfying agreement with simulation results. We demonstrate that the fraction of jammed cars P (v ∈{0 ,1 }) can be decomposed into the three factors (jamming rate, jam lifetime, and jam size) for which we derive, from random walk arguments, exponents that control their scaling close to the critical density.
An analytic model for limiting high density LH transition by the onset of the tertiary instability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Singh, Raghvendra, E-mail: rsingh129@gmail.com; Jhang, Hogun; Kaang, Helen H.

2016-07-15

We perform an analytic study of the tertiary instability driven by a strong excitation of zonal flows during high density low to high (LH) mode transition. The drift resistive ballooning mode is assumed to be a dominant edge turbulence driver. The analysis reproduces main qualitative features of early computational results [Rogers and Drake, Phys. Rev. Lett. 81, 4396 (1998); Guzdar et al., Phys. Plasmas 14, 020701 (2007)], as well as new characteristics of the maximum edge density due to the onset of the tertiary instability. An analytical scaling indicates that the density scaling of LH transition power may be determinedmore » by the onset condition of the tertiary instability when the operating density approaches to the Greenwald density.« less
The correlation function for density perturbations in an expanding universe. I - Linear theory

NASA Technical Reports Server (NTRS)

Mcclelland, J.; Silk, J.

1977-01-01

The evolution of the two-point correlation function for adiabatic density perturbations in the early universe is studied. Analytical solutions are obtained for the evolution of linearized spherically symmetric adiabatic density perturbations and the two-point correlation function for these perturbations in the radiation-dominated portion of the early universe. The results are then extended to the regime after decoupling. It is found that: (1) adiabatic spherically symmetric perturbations comparable in scale with the maximum Jeans length would survive the radiation-dominated regime; (2) irregular fluctuations are smoothed out up to the scale of the maximum Jeans length in the radiation era, but regular fluctuations might survive on smaller scales; (3) in general, the only surviving structures for irregularly shaped adiabatic density perturbations of arbitrary but finite scale in the radiation regime are the size of or larger than the maximum Jeans length in that regime; (4) infinite plane waves with a wavelength smaller than the maximum Jeans length but larger than the critical dissipative damping scale could survive the radiation regime; and (5) black holes would also survive the radiation regime and might accrete sufficient mass after decoupling to nucleate the formation of galaxies.
Coarse graining the distribution function of cold dark matter - II

NASA Astrophysics Data System (ADS)

Henriksen, R. N.

2004-12-01

We study analytically the coarse- and fine-grained distribution function (DF) established by the self-similar infall of collisionless matter. We find this function explicitly for isotropic and spherically symmetric systems in terms of cosmological initial conditions. The coarse-grained function is structureless and steady but the familiar phase-space sheet substructure is recovered in the fine-grained limit. By breaking the self-similarity of the halo infall we are able to argue for a central density flattening. In addition there will be an edge steepening. The best-fitting analytic density function is likely to be provided by a high-order polytrope fit smoothly to an outer power law of index -3 for isolated systems. There may be a transition to a -4 power law in the outer regions of tidally truncated systems. As we find that the central flattening is progressive in time, dynamically young systems such as galaxy clusters may well possess a Navarro, Frenk and White type density profile, while primordial dwarf galaxies, for example, are expected to have cores. This progressive flattening is expected to end either in the non-singular isothermal sphere, or in the non-singular metastable polytropic cores; as the DFs associated with each of these arise naturally in the bulk halo during the infall. We suggest, based on previous studies of the evolution of de-stabilized polytropes, that a collisionless system may pass through a family of polytropes of increasing order, finally approaching the limit of the non-singular isothermal sphere, if the `violent' collective relaxation is frequently re-excited by `merger' events. Thus central dominant (cD) galaxies, and indeed all bright galaxies that have grown in this fashion, should be in polytropic states. Our results suggest that no physics beyond that of wave-particle scattering is necessary to explain the nature of dark matter density profiles. However, this may be assisted by the scattering of particles from the centre of the system by the infall of dwarf galaxies, galactic nuclei or black holes (e.g. Nakano & Makino), all of which would restart pure dynamical relaxation.
Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations.

PubMed

Li, Q; He, Y L; Wang, Y; Tao, W Q

2007-11-01

A coupled double-distribution-function lattice Boltzmann method is developed for the compressible Navier-Stokes equations. Different from existing thermal lattice Boltzmann methods, this method can recover the compressible Navier-Stokes equations with a flexible specific-heat ratio and Prandtl number. In the method, a density distribution function based on a multispeed lattice is used to recover the compressible continuity and momentum equations, while the compressible energy equation is recovered by an energy distribution function. The energy distribution function is then coupled to the density distribution function via the thermal equation of state. In order to obtain an adjustable specific-heat ratio, a constant related to the specific-heat ratio is introduced into the equilibrium energy distribution function. Two different coupled double-distribution-function lattice Boltzmann models are also proposed in the paper. Numerical simulations are performed for the Riemann problem, the double-Mach-reflection problem, and the Couette flow with a range of specific-heat ratios and Prandtl numbers. The numerical results are found to be in excellent agreement with analytical and/or other solutions.
Benchmarking fully analytic DFT force fields for vibrational spectroscopy: A study on halogenated compounds

NASA Astrophysics Data System (ADS)

Pietropolli Charmet, Andrea; Cornaton, Yann

2018-05-01

This work presents an investigation of the theoretical predictions yielded by anharmonic force fields having the cubic and quartic force constants are computed analytically by means of density functional theory (DFT) using the recursive scheme developed by M. Ringholm et al. (J. Comput. Chem. 35 (2014) 622). Different functionals (namely B3LYP, PBE, PBE0 and PW86x) and basis sets were used for calculating the anharmonic vibrational spectra of two halomethanes. The benchmark analysis carried out demonstrates the reliability and overall good performances offered by hybrid approaches, where the harmonic data obtained at the coupled cluster with single and double excitations level of theory augmented by a perturbational estimate of the effects of connected triple excitations, CCSD(T), are combined with the fully analytic higher order force constants yielded by DFT functionals. These methods lead to reliable and computationally affordable calculations of anharmonic vibrational spectra with an accuracy comparable to that yielded by hybrid force fields having the anharmonic force fields computed at second order Møller-Plesset perturbation theory (MP2) level of theory using numerical differentiation but without the corresponding potential issues related to computational costs and numerical errors.
Effect of Ambipolar Diffusion on Ion Abundances in Contracting Protostellar Cores

NASA Astrophysics Data System (ADS)

Ciolek, Glenn E.; Mouschovias, Telemachos Ch.

1998-09-01

Numerical simulations and analytical solutions have established that ambipolar diffusion can reduce the dust-to-gas ratio in magnetically and thermally supercritical cores during the epoch of core formation. We study the effect that this has on the ion chemistry in contracting protostellar cores and present a simplified analytical method that allows one to calculate the ion power-law exponent k (≡d ln ni/d ln nn, where ni and nn are the ion and neutral densities, respectively) as a function of core density. We find that, as in earlier numerical simulations, no single value of k can adequately describe the ion abundance for nn <~ 109 cm-3, a result that is contrary to the ``canonical'' value of k = 1/2 found in previous static equilibrium chemistry calculations and often used to study the effect of ambipolar diffusion in interstellar clouds. For typical cloud and grain parameters, reduction of the abundance of grains results in k > 1/2 during the core formation epoch (densities <~105 cm-3). As a consequence, observations of the degree of ionization in cores could be used, in principle, to determine whether ambipolar diffusion is responsible for core formation in interstellar molecular clouds. For densities >>105 cm-3, k is generally <<1/2.
Electronic Structure and Properties of Deformed Carbon Nanotubes

NASA Technical Reports Server (NTRS)

Yang, Liu; Arnold, Jim (Technical Monitor)

2001-01-01

A theoretical framework based on Huckel tight-binding model has been formulated to analyze the electronic structure of carbon nanotubes under uniform deformation. The model successfully quantifies the dispersion relation, density of states and bandgap change of nanotubes under uniform stretching, compression, torsion and bending. Our analysis shows that the shifting of the Fermi point away from the Brillouin zone vertices is the key reason for these changes. As a result of this shifting, the electronic structure of deformed carbon nanotubes varies dramatically depending on their chirality and deformation mode. Treating the Fermi point as a function of strain and tube chirality, the analytical solution preserves the concise form of undeformed carbon nanotubes. It predicts the shifting, merging and splitting of the Van Hove singularities in the density of states and the zigzag pattern of bandgap change under strains. Four orbital tight-binding simulations of carbon nanotubes under uniform stretching, compression, torsion and bending have been performed to verify the analytical solution. Extension to more complex systems are being performed to relate this analytical solution to the spectroscopic characterization, device performance and proposed quantum structures induced by the deformation. The limitations of this model will also be discussed.
An analytical solution for the elastic response to surface loads imposed on a layered, transversely isotropic and self-gravitating Earth

NASA Astrophysics Data System (ADS)

Pan, E.; Chen, J. Y.; Bevis, M.; Bordoni, A.; Barletta, V. R.; Molavi Tabrizi, A.

2015-12-01

We present an analytical solution for the elastic deformation of an elastic, transversely isotropic, layered and self-gravitating Earth by surface loads. We first introduce the vector spherical harmonics to express the physical quantities in the layered Earth. This reduces the governing equations to a linear system of equations for the expansion coefficients. We then solve for the expansion coefficients analytically under the assumption (i.e. approximation) that in the mantle, the density in each layer varies as 1/r (where r is the radial coordinate) while the gravity is constant and that in the core the gravity in each layer varies linearly in r with constant density. These approximations dramatically simplify the subsequent mathematical analysis and render closed-form expressions for the expansion coefficients. We implement our solution in a MATLAB code and perform a benchmark which shows both the correctness of our solution and the implementation. We also calculate the load Love numbers (LLNs) of the PREM Earth for different degrees of the Legendre function for both isotropic and transversely isotropic, layered mantles with different core models, demonstrating for the first time the effect of Earth anisotropy on the LLNs.
Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in AdS 2 Ⓧ S 2

DOE PAGES

Noronha, Jorge; Denicol, Gabriel S.

2015-12-30

In this paper we obtain an analytical solution of the relativistic Boltzmann equation under the relaxation time approximation that describes the out-of-equilibrium dynamics of a radially expanding massless gas. This solution is found by mapping this expanding system in flat spacetime to a static flow in the curved spacetime AdS 2 Ⓧ S 2. We further derive explicit analytic expressions for the momentum dependence of the single-particle distribution function as well as for the spatial dependence of its moments. We find that this dissipative system has the ability to flow as a perfect fluid even though its entropy density doesmore » not match the equilibrium form. The nonequilibrium contribution to the entropy density is shown to be due to higher-order scalar moments (which possess no hydrodynamical interpretation) of the Boltzmann equation that can remain out of equilibrium but do not couple to the energy-momentum tensor of the system. Furthermore, in this system the slowly moving hydrodynamic degrees of freedom can exhibit true perfect fluidity while being totally decoupled from the fast moving, nonhydrodynamical microscopic degrees of freedom that lead to entropy production.« less
Electrolyte solutions at curved electrodes. I. Mesoscopic approach

NASA Astrophysics Data System (ADS)

Reindl, Andreas; Bier, Markus; Dietrich, S.

2017-04-01

Within the Poisson-Boltzmann approach, electrolytes in contact with planar, spherical, and cylindrical electrodes are analyzed systematically. The dependences of their capacitance C on the surface charge density σ and the ionic strength I are examined as a function of the wall curvature. The surface charge density has a strong effect on the capacitance for small curvatures, whereas for large curvatures the behavior becomes independent of σ. An expansion for small curvatures gives rise to capacitance coefficients which depend only on a single parameter, allowing for a convenient analysis. The universal behavior at large curvatures can be captured by an analytic expression.
Scintillation statistics measured in an earth-space-earth retroreflector link

NASA Technical Reports Server (NTRS)

Bufton, J. L.

1977-01-01

Scintillation was measured in a vertical path from a ground-based laser transmitter to the Geos 3 satellite and back to a ground-based receiver telescope and, the experimental results were compared with analytical results presented in a companion paper (Bufton, 1977). The normalized variance, the probability density function and the power spectral density of scintillation were all measured. Moments of the satellite scintillation data in terms of normalized variance were lower than expected. The power spectrum analysis suggests that there were scintillation components at frequencies higher than the 250 Hz bandwidth available in the experiment.
An efficient formulation and implementation of the analytic energy gradient method to the single and double excitation coupled-cluster wave function - Application to Cl2O2

NASA Technical Reports Server (NTRS)

Rendell, Alistair P.; Lee, Timothy J.

1991-01-01

The analytic energy gradient for the single and double excitation coupled-cluster (CCSD) wave function has been reformulated and implemented in a new set of programs. The reformulated set of gradient equations have a smaller computational cost than any previously published. The iterative solution of the linear equations and the construction of the effective density matrices are fully vectorized, being based on matrix multiplications. The new method has been used to investigate the Cl2O2 molecule, which has recently been postulated as an important intermediate in the destruction of ozone in the stratosphere. In addition to reporting computational timings, the CCSD equilibrium geometries, harmonic vibrational frequencies, infrared intensities, and relative energetics of three isomers of Cl2O2 are presented.

Analysis of laser shock experiments on precompressed samples using a quartz reference and application to warm dense hydrogen and helium

DOE PAGES

Brygoo, Stephanie; Millot, Marius; Loubeyre, Paul; ...

2015-11-16

Megabar (1 Mbar = 100 GPa) laser shocks on precompressed samples allow reaching unprecedented high densities and moderately high ~10 3–10 4 K temperatures. We describe in this paper a complete analysis framework for the velocimetry (VISAR) and pyrometry (SOP) data produced in these experiments. Since the precompression increases the initial density of both the sample of interest and the quartz reference for pressure-density, reflectivity, and temperature measurements, we describe analytical corrections based on available experimental data on warm dense silica and density-functional-theory based molecular dynamics computer simulations. Finally, using our improved analysis framework, we report a re-analysis of previouslymore » published data on warm dense hydrogen and helium, compare the newly inferred pressure, density, and temperature data with most advanced equation of state models and provide updated reflectivity values.« less
Using time-dependent density functional theory in real time for calculating electronic transport

NASA Astrophysics Data System (ADS)

Schaffhauser, Philipp; Kümmel, Stephan

2016-01-01

We present a scheme for calculating electronic transport within the propagation approach to time-dependent density functional theory. Our scheme is based on solving the time-dependent Kohn-Sham equations on grids in real space and real time for a finite system. We use absorbing and antiabsorbing boundaries for simulating the coupling to a source and a drain. The boundaries are designed to minimize the effects of quantum-mechanical reflections and electrical polarization build-up, which are the major obstacles when calculating transport by applying an external bias to a finite system. We show that the scheme can readily be applied to real molecules by calculating the current through a conjugated molecule as a function of time. By comparing to literature results for the conjugated molecule and to analytic results for a one-dimensional model system we demonstrate the reliability of the concept.
Maximising profits for an EPQ model with unreliable machine and rework of random defective items

NASA Astrophysics Data System (ADS)

Pal, Brojeswar; Sankar Sana, Shib; Chaudhuri, Kripasindhu

2013-03-01

This article deals with an economic production quantity (EPQ) model in an imperfect production system. The production system may undergo in 'out-of-control' state from 'in-control' state, after a certain time that follows a probability density function. The density function varies with reliability of the machinery system that may be controlled by new technologies, investing more costs. The defective items produced in 'out-of-control' state are reworked at a cost just after the regular production time. Occurrence of the 'out-of-control' state during or after regular production-run time is analysed and also graphically illustrated separately. Finally, an expected profit function regarding the inventory cost, unit production cost and selling price is maximised analytically. Sensitivity analysis of the model with respect to key parameters of the system is carried out. Two numerical examples are considered to test the model and one of them is illustrated graphically.
Crystal structure optimisation using an auxiliary equation of state

NASA Astrophysics Data System (ADS)

Jackson, Adam J.; Skelton, Jonathan M.; Hendon, Christopher H.; Butler, Keith T.; Walsh, Aron

2015-11-01

Standard procedures for local crystal-structure optimisation involve numerous energy and force calculations. It is common to calculate an energy-volume curve, fitting an equation of state around the equilibrium cell volume. This is a computationally intensive process, in particular, for low-symmetry crystal structures where each isochoric optimisation involves energy minimisation over many degrees of freedom. Such procedures can be prohibitive for non-local exchange-correlation functionals or other "beyond" density functional theory electronic structure techniques, particularly where analytical gradients are not available. We present a simple approach for efficient optimisation of crystal structures based on a known equation of state. The equilibrium volume can be predicted from one single-point calculation and refined with successive calculations if required. The approach is validated for PbS, PbTe, ZnS, and ZnTe using nine density functionals and applied to the quaternary semiconductor Cu2ZnSnS4 and the magnetic metal-organic framework HKUST-1.
Consistency criteria for generalized Cuddeford systems

NASA Astrophysics Data System (ADS)

Ciotti, Luca; Morganti, Lucia

2010-01-01

General criteria to check the positivity of the distribution function (phase-space consistency) of stellar systems of assigned density and anisotropy profile are useful starting points in Jeans-based modelling. Here, we substantially extend previous results, and present the inversion formula and the analytical necessary and sufficient conditions for phase-space consistency of the family of multicomponent Cuddeford spherical systems: the distribution function of each density component of these systems is defined as the sum of an arbitrary number of Cuddeford distribution functions with arbitrary values of the anisotropy radius, but identical angular momentum exponent. The radial trend of anisotropy that can be realized by these models is therefore very general. As a surprising byproduct of our study, we found that the `central cusp-anisotropy theorem' (a necessary condition for consistency relating the values of the central density slope and of the anisotropy parameter) holds not only at the centre but also at all radii in consistent multicomponent generalized Cuddeford systems. This last result suggests that the so-called mass-anisotropy degeneracy could be less severe than what is sometimes feared.
ALMA Spectroscopic Survey in the Hubble Ultra Deep Field: CO Luminosity Functions and the Evolution of the Cosmic Density of Molecular Gas

NASA Astrophysics Data System (ADS)

Decarli, Roberto; Walter, Fabian; Aravena, Manuel; Carilli, Chris; Bouwens, Rychard; da Cunha, Elisabete; Daddi, Emanuele; Ivison, R. J.; Popping, Gergö; Riechers, Dominik; Smail, Ian R.; Swinbank, Mark; Weiss, Axel; Anguita, Timo; Assef, Roberto J.; Bauer, Franz E.; Bell, Eric F.; Bertoldi, Frank; Chapman, Scott; Colina, Luis; Cortes, Paulo C.; Cox, Pierre; Dickinson, Mark; Elbaz, David; Gónzalez-López, Jorge; Ibar, Edo; Infante, Leopoldo; Hodge, Jacqueline; Karim, Alex; Le Fevre, Olivier; Magnelli, Benjamin; Neri, Roberto; Oesch, Pascal; Ota, Kazuaki; Rix, Hans-Walter; Sargent, Mark; Sheth, Kartik; van der Wel, Arjen; van der Werf, Paul; Wagg, Jeff

2016-12-01

In this paper we use ASPECS, the ALMA Spectroscopic Survey in the Hubble Ultra Deep Field in band 3 and band 6, to place blind constraints on the CO luminosity function and the evolution of the cosmic molecular gas density as a function of redshift up to z ˜ 4.5. This study is based on galaxies that have been selected solely through their CO emission and not through any other property. In all of the redshift bins the ASPECS measurements reach the predicted “knee” of the CO luminosity function (around 5 × 109 K km s-1 pc2). We find clear evidence of an evolution in the CO luminosity function with respect to z ˜ 0, with more CO-luminous galaxies present at z ˜ 2. The observed galaxies at z ˜ 2 also appear more gas-rich than predicted by recent semi-analytical models. The comoving cosmic molecular gas density within galaxies as a function of redshift shows a drop by a factor of 3-10 from z ˜ 2 to z ˜ 0 (with significant error bars), and possibly a decline at z > 3. This trend is similar to the observed evolution of the cosmic star formation rate density. The latter therefore appears to be at least partly driven by the increased availability of molecular gas reservoirs at the peak of cosmic star formation (z ˜ 2).
Charge Density Quantification of Polyelectrolyte Polysaccharides by Conductometric Titration: An Analytical Chemistry Experiment

ERIC Educational Resources Information Center

Farris, Stefano; Mora, Luigi; Capretti, Giorgio; Piergiovanni, Luciano

2012-01-01

An easy analytical method for determination of the charge density of polyelectrolytes, including polysaccharides and other biopolymers, is presented. The basic principles of conductometric titration, which is used in the pulp and paper industry as well as in colloid and interface science, were adapted to quantify the charge densities of a…
The Equation of State of Triamino-Trinitrobenzene from Density Functional Theory Molecular Dynamics

NASA Astrophysics Data System (ADS)

Wixom, Ryan R.

2017-06-01

The US-uP shock Hugoniot has long been the fundamental relationship used to experimentally define the unreacted equations of state of explosives. These experiments are typically performed on porous or composite samples, providing data that is specific to the density of the samples being tested. However, If the crystalline Hugoniot is known, analytical or numerical methods can be used to transform the US-uP relationship to describe the shock response of the porous material. To obtain an accurate crystalline equation of state for TATB, density functional theory based molecular dynamics were used to map out points on the Hugoniot. Since this method provides the pressure, temperature, density, and internal energy at each point on the Hugoniot, a complete equation of state can be constructed. Isotropic, uniaxial, hydrostatic, and isothermal compression of the simulation cell were used to examine TATB under different thermodynamic conditions. A cusp is observed in the Hugoniot that correlates to loss of aromaticity of the molecule. Results of the calculations will be presented and compared to the available experimental data. Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque NM.
Internal wave energy flux from density perturbations in nonlinear stratifications

NASA Astrophysics Data System (ADS)

Lee, Frank M.; Allshouse, Michael R.; Swinney, Harry L.; Morrison, P. J.

2017-11-01

Tidal flow over the topography at the bottom of the ocean, whose density varies with depth, generates internal gravity waves that have a significant impact on the energy budget of the ocean. Thus, understanding the energy flux (J = p v) is important, but it is difficult to measure simultaneously the pressure and velocity perturbation fields, p and v . In a previous work, a Green's-function-based method was developed to calculate the instantaneous p, v , and thus J , given a density perturbation field for a constant buoyancy frequency N. Here we extend the previous analytic Green's function work to include nonuniform N profiles, namely the tanh-shaped and linear cases, because background density stratifications that occur in the ocean and some experiments are nonlinear. In addition, we present a finite-difference method for the general case where N has an arbitrary profile. Each method is validated against numerical simulations. The methods we present can be applied to measured density perturbation data by using our MATLAB graphical user interface EnergyFlux. PJM was supported by the U.S. Department of Energy Contract DE-FG05-80ET-53088. HLS and MRA were supported by ONR Grant No. N000141110701.
A Patch Density Recommendation based on Convergence Studies for Vehicle Panel Vibration Response resulting from Excitation by a Diffuse Acoustic Field

NASA Technical Reports Server (NTRS)

Smith, Andrew; LaVerde, Bruce; Jones, Douglas; Towner, Robert; Waldon, James; Hunt, Ron

2013-01-01

Producing fluid structural interaction estimates of panel vibration from an applied pressure field excitation are quite dependent on the spatial correlation of the pressure field. There is a danger of either over estimating a low frequency response or under predicting broad band panel response in the more modally dense bands if the pressure field spatial correlation is not accounted for adequately. It is a useful practice to simulate the spatial correlation of the applied pressure field over a 2d surface using a matrix of small patch area regions on a finite element model (FEM). Use of a fitted function for the spatial correlation between patch centers can result in an error if the choice of patch density is not fine enough to represent the more continuous spatial correlation function throughout the intended frequency range of interest. Several patch density assumptions to approximate the fitted spatial correlation function are first evaluated using both qualitative and quantitative illustrations. The actual response of a typical vehicle panel system FEM is then examined in a convergence study where the patch density assumptions are varied over the same model. The convergence study results illustrate the impacts possible from a poor choice of patch density on the analytical response estimate. The fitted correlation function used in this study represents a diffuse acoustic field (DAF) excitation of the panel to produce vibration response.
Theoretical models for electron conduction in polymer systems—I. Macroscopic calculations of d.c. transient conductivity after pulse irradiation

NASA Astrophysics Data System (ADS)

Bartczak, Witold M.; Kroh, Jerzy

The simulation of the transient d.c. conductivity in a quasi one-dimensional system of charges produced by a pulse of ionizing radiation in a solid sample has been performed. The simulation is based on the macroscopic conductivity equations and can provide physical insight into d.c. conductivity measurements, particularly for the case of transient currents in samples with internal space charge. We consider the system of mobile (negative) and immobile (positive) charges produced by a pulse of ionizing radiation in the sample under a fixed external voltage V0. The presence of space charge results in an electric field which is a function of both the spatial and the time variable: E( z, t). Given the space charge density, the electric field can be calculated from the Poisson equation. However, for an arbitrary space charge distribution, the corresponding equations can only be solved numerically. The two non-trivial cases for which approximate analytical solutions can be provided are: (i) The density of the current carriers n( z, t) is negligible in comparison with the density of immobile space charge N( z). A general analytical solution has been found for this case using Green's functions. The solutions for two cases, viz. the homogeneous distribution of space charge N( z) = N, and the non-homogeneous exponential distribution N( z) = A exp(- Bz), have been separately discussed. (ii) The space charge created in the pulse without any space charge present prior to the irradiation.
A semi-analytic dynamical friction model for cored galaxies

NASA Astrophysics Data System (ADS)

Petts, J. A.; Read, J. I.; Gualandris, A.

2016-11-01

We present a dynamical friction model based on Chandrasekhar's formula that reproduces the fast inspiral and stalling experienced by satellites orbiting galaxies with a large constant density core. We show that the fast inspiral phase does not owe to resonance. Rather, it owes to the background velocity distribution function for the constant density core being dissimilar from the usually assumed Maxwellian distribution. Using the correct background velocity distribution function and our semi-analytic model from previous work, we are able to correctly reproduce the infall rate in both cored and cusped potentials. However, in the case of large cores, our model is no longer able to correctly capture core-stalling. We show that this stalling owes to the tidal radius of the satellite approaching the size of the core. By switching off dynamical friction when rt(r) = r (where rt is the tidal radius at the satellite's position), we arrive at a model which reproduces the N-body results remarkably well. Since the tidal radius can be very large for constant density background distributions, our model recovers the result that stalling can occur for Ms/Menc ≪ 1, where Ms and Menc are the mass of the satellite and the enclosed galaxy mass, respectively. Finally, we include the contribution to dynamical friction that comes from stars moving faster than the satellite. This next-to-leading order effect becomes the dominant driver of inspiral near the core region, prior to stalling.
Alternative separation of exchange and correlation energies in multi-configuration range-separated density-functional theory.

PubMed

Stoyanova, Alexandrina; Teale, Andrew M; Toulouse, Julien; Helgaker, Trygve; Fromager, Emmanuel

2013-10-07

The alternative separation of exchange and correlation energies proposed by Toulouse et al. [Theor. Chem. Acc. 114, 305 (2005)] is explored in the context of multi-configuration range-separated density-functional theory. The new decomposition of the short-range exchange-correlation energy relies on the auxiliary long-range interacting wavefunction rather than the Kohn-Sham (KS) determinant. The advantage, relative to the traditional KS decomposition, is that the wavefunction part of the energy is now computed with the regular (fully interacting) Hamiltonian. One potential drawback is that, because of double counting, the wavefunction used to compute the energy cannot be obtained by minimizing the energy expression with respect to the wavefunction parameters. The problem is overcome by using short-range optimized effective potentials (OEPs). The resulting combination of OEP techniques with wavefunction theory has been investigated in this work, at the Hartree-Fock (HF) and multi-configuration self-consistent-field (MCSCF) levels. In the HF case, an analytical expression for the energy gradient has been derived and implemented. Calculations have been performed within the short-range local density approximation on H2, N2, Li2, and H2O. Significant improvements in binding energies are obtained with the new decomposition of the short-range energy. The importance of optimizing the short-range OEP at the MCSCF level when static correlation becomes significant has also been demonstrated for H2, using a finite-difference gradient. The implementation of the analytical gradient for MCSCF wavefunctions is currently in progress.
Aptamer-functionalized nano-biosensors.

PubMed

Chiu, Tai-Chia; Huang, Chih-Ching

2009-01-01

Nanomaterials have become one of the most interesting sensing materials because of their unique size- and shape-dependent optical properties, high surface energy and surface-to-volume ratio, and tunable surface properties. Aptamers are oligonucleotides that can bind their target ligands with high affinity. The use of nanomaterials that are bioconjugated with aptamers for selective and sensitive detection of analytes such as small molecules, metal ions, proteins, and cells has been demonstrated. This review focuses on recent progress in the development of biosensors by integrating functional aptamers with different types of nanomaterials, including quantum dots, magnetic nanoparticles (NPs), metallic NPs, and carbon nanotubes. Colorimetry, fluorescence, electrochemistry, surface plasmon resonance, surface-enhanced Raman scattering, and magnetic resonance imaging are common detection modes for a broad range of analytes with high sensitivity and selectivity when using aptamer bioconjugated nanomaterials (Apt-NMs). We highlight the important roles that the size and concentration of nanomaterials, the secondary structure and density of aptamers, and the multivalent interactions play in determining the specificity and sensitivity of the nanosensors towards analytes. Advantages and disadvantages of the Apt-NMs for bioapplications are focused.
On the probability distribution function of the mass surface density of molecular clouds. II.

NASA Astrophysics Data System (ADS)

Fischera, Jörg

2014-11-01

The probability distribution function (PDF) of the mass surface density of molecular clouds provides essential information about the structure of molecular cloud gas and condensed structures out of which stars may form. In general, the PDF shows two basic components: a broad distribution around the maximum with resemblance to a log-normal function, and a tail at high mass surface densities attributed to turbulence and self-gravity. In a previous paper, the PDF of condensed structures has been analyzed and an analytical formula presented based on a truncated radial density profile, ρ(r) = ρc/ (1 + (r/r0)2)n/ 2 with central density ρc and inner radius r0, widely used in astrophysics as a generalization of physical density profiles. In this paper, the results are applied to analyze the PDF of self-gravitating, isothermal, pressurized, spherical (Bonnor-Ebert spheres) and cylindrical condensed structures with emphasis on the dependence of the PDF on the external pressure pext and on the overpressure q-1 = pc/pext, where pc is the central pressure. Apart from individual clouds, we also consider ensembles of spheres or cylinders, where effects caused by a variation of pressure ratio, a distribution of condensed cores within a turbulent gas, and (in case of cylinders) a distribution of inclination angles on the mean PDF are analyzed. The probability distribution of pressure ratios q-1 is assumed to be given by P(q-1) ∝ q-k1/ (1 + (q0/q)γ)(k1 + k2) /γ, where k1, γ, k2, and q0 are fixed parameters. The PDF of individual spheres with overpressures below ~100 is well represented by the PDF of a sphere with an analytical density profile with n = 3. At higher pressure ratios, the PDF at mass surface densities Σ ≪ Σ(0), where Σ(0) is the central mass surface density, asymptotically approaches the PDF of a sphere with n = 2. Consequently, the power-law asymptote at mass surface densities above the peak steepens from Psph(Σ) ∝ Σ-2 to Psph(Σ) ∝ Σ-3. The corresponding asymptote of the PDF of cylinders for the large q-1 is approximately given by Pcyl(Σ) ∝ Σ-4/3(1 - (Σ/Σ(0))2/3)-1/2. The distribution of overpressures q-1 produces a power-law asymptote at high mass surface densities given by ∝ Σ-2k2 - 1 (spheres) or ∝ Σ-2k2 (cylinders). Appendices are available in electronic form at http://www.aanda.org
Nanopipettes as Monitoring Probes for the Single Living Cell: State of the Art and Future Directions in Molecular Biology.

PubMed

Bulbul, Gonca; Chaves, Gepoliano; Olivier, Joseph; Ozel, Rifat Emrah; Pourmand, Nader

2018-06-06

Examining the behavior of a single cell within its natural environment is valuable for understanding both the biological processes that control the function of cells and how injury or disease lead to pathological change of their function. Single-cell analysis can reveal information regarding the causes of genetic changes, and it can contribute to studies on the molecular basis of cell transformation and proliferation. By contrast, whole tissue biopsies can only yield information on a statistical average of several processes occurring in a population of different cells. Electrowetting within a nanopipette provides a nanobiopsy platform for the extraction of cellular material from single living cells. Additionally, functionalized nanopipette sensing probes can differentiate analytes based on their size, shape or charge density, making the technology uniquely suited to sensing changes in single-cell dynamics. In this review, we highlight the potential of nanopipette technology as a non-destructive analytical tool to monitor single living cells, with particular attention to integration into applications in molecular biology.
Padé Approximant and Minimax Rational Approximation in Standard Cosmology

NASA Astrophysics Data System (ADS)

Zaninetti, Lorenzo

2016-02-01

The luminosity distance in the standard cosmology as given by $\\Lambda$CDM and consequently the distance modulus for supernovae can be defined by the Pad\\'e approximant. A comparison with a known analytical solution shows that the Pad\\'e approximant for the luminosity distance has an error of $4\\%$ at redshift $= 10$. A similar procedure for the Taylor expansion of the luminosity distance gives an error of $4\\%$ at redshift $=0.7 $; this means that for the luminosity distance, the Pad\\'e approximation is superior to the Taylor series. The availability of an analytical expression for the distance modulus allows applying the Levenberg--Marquardt method to derive the fundamental parameters from the available compilations for supernovae. A new luminosity function for galaxies derived from the truncated gamma probability density function models the observed luminosity function for galaxies when the observed range in absolute magnitude is modeled by the Pad\\'e approximant. A comparison of $\\Lambda$CDM with other cosmologies is done adopting a statistical point of view.
Ab Initio High Pressure and Temperature Investigation on Cubic PbMoO3 Perovskite

NASA Astrophysics Data System (ADS)

Dar, Sajad Ahmad; Srivastava, Vipul; Sakalle, Umesh Kumar

2017-12-01

A combined high pressure and temperature investigation on recently reported cubic perovskite PbMoO3 have been performed within the most accurate density functional theory (DFT). The structure was found stable in cubic paramagnetic phase. The DFT calculated analytical and experimental lattice constant were found in good agreement. The analytical tolerance factor as well as the elastic properties further verifies the cubic stability for PbMoO3. The spin polarized electronic band structure and density of states presented metallic nature with symmetry in up and down states. The insignificant magnetic moment also confirms the paramagnetic nature for the compound. The high pressure elastic and mechanical study up to 35 GPa reveal the structural stability of the material in this pressure range. The compound was found to establish a ductile nature. The electrical conductivity obtained from the band structure results show a decreasing trend with increasing temperature. The temperature dependence of thermodynamic parameters such as specific heat ( C v), thermal expansion ( α) has also been evaluated.
Analytical and numerical studies of positive ion beam expansion for surface treatment applications

NASA Astrophysics Data System (ADS)

Lounes-Mahloul, Soumya; Bendib, Abderrezeg; Oudini, Noureddine

2018-01-01

The aim of this work is to study the expansion in vacuum, of a positive ion beam with the use of one dimensional (1D) analytic model and a two dimensional Particle-In-Cell (2D-PIC) simulation. The ion beam is extracted and accelerated from preformed plasma by an extraction system composed of two polarized parallel perforated grids. The results obtained with both approaches reveal the presence of a potential barrier downstream the extraction system which tends to reflect the ion flux. The dependence of the critical distance for which all extracted ions are reflected, is investigated as a function of the extracted ion beam current density. In particular, it is shown that the 1D model recovers the well-known Child-Langmuir law and that the 2D simulation presents a significant discrepancy with respect to the 1D prediction. Indeed, for a given value of current density, the transverse effects lead to a greater critical distance.
Detonation Performance Analyses for Recent Energetic Molecules

NASA Astrophysics Data System (ADS)

Stiel, Leonard; Samuels, Philip; Spangler, Kimberly; Iwaniuk, Daniel; Cornell, Rodger; Baker, Ernest

2017-06-01

Detonation performance analyses were conducted for a number of evolving and potential high explosive materials. The calculations were completed for theoretical maximum densities of the explosives using the Jaguar thermo-chemical equation of state computer programs for performance evaluations and JWL/JWLB equations of state parameterizations. A number of recently synthesized materials were investigated for performance characterizations and comparisons to existing explosives, including TNT, RDX, HMX, and Cl-20. The analytic cylinder model was utilized to establish cylinder and Gurney velocities as functions of the radial expansions of the cylinder for each explosive. The densities and heats of formulation utilized in the calculations are primarily experimental values from Picatinny Arsenal and other sources. Several of the new materials considered were predicted to have enhanced detonation characteristics compared to conventional explosives. In order to confirm the accuracy of the Jaguar and analytic cylinder model results, available experimental detonation and Gurney velocities for representative energetic molecules and their formulations were compared with the corresponding calculated values. Close agreement was obtained with most of the data. Presently at NATO.

Long-range-corrected Rung 3.5 density functional approximations

NASA Astrophysics Data System (ADS)

Janesko, Benjamin G.; Proynov, Emil; Scalmani, Giovanni; Frisch, Michael J.

2018-03-01

Rung 3.5 functionals are a new class of approximations for density functional theory. They provide a flexible intermediate between exact (Hartree-Fock, HF) exchange and semilocal approximations for exchange. Existing Rung 3.5 functionals inherit semilocal functionals' limitations in atomic cores and density tails. Here we address those limitations using range-separated admixture of HF exchange. We present three new functionals. LRC-ωΠLDA combines long-range HF exchange with short-range Rung 3.5 ΠLDA exchange. SLC-ΠLDA combines short- and long-range HF exchange with middle-range ΠLDA exchange. LRC-ωΠLDA-AC incorporates a combination of HF, semilocal, and Rung 3.5 exchange in the short range, based on an adiabatic connection. We test these in a new Rung 3.5 implementation including up to analytic fourth derivatives. LRC-ωΠLDA and SLC-ΠLDA improve atomization energies and reaction barriers by a factor of 8 compared to the full-range ΠLDA. LRC-ωΠLDA-AC brings further improvement approaching the accuracy of standard long-range corrected schemes LC-ωPBE and SLC-PBE. The new functionals yield highest occupied orbital energies closer to experimental ionization potentials and describe correctly the weak charge-transfer complex of ethylene and dichlorine and the hole-spin distribution created by an Al defect in quartz. This study provides a framework for more flexible range-separated Rung 3.5 approximations.
Early Universe synthesis of asymmetric dark matter nuggets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gresham, Moira I.; Lou, Hou Keong; Zurek, Kathryn M.

We compute the mass function of bound states of asymmetric dark matter - nuggets - synthesized in the early Universe. We apply our results for the nugget density and binding energy computed from a nuclear model to obtain analytic estimates of the typical nugget size exiting synthesis. We numerically solve the Boltzmann equation for synthesis including two-to-two fusion reactions, estimating the impact of bottlenecks on the mass function exiting synthesis. These results provide the basis for studying the late Universe cosmology of nuggets in a future companion paper.
Percolation and epidemics in a two-dimensional small world

NASA Astrophysics Data System (ADS)

Newman, M. E.; Jensen, I.; Ziff, R. M.

2002-02-01

Percolation on two-dimensional small-world networks has been proposed as a model for the spread of plant diseases. In this paper we give an analytic solution of this model using a combination of generating function methods and high-order series expansion. Our solution gives accurate predictions for quantities such as the position of the percolation threshold and the typical size of disease outbreaks as a function of the density of ``shortcuts'' in the small-world network. Our results agree with scaling hypotheses and numerical simulations for the same model.
Early Universe synthesis of asymmetric dark matter nuggets

DOE PAGES

Gresham, Moira I.; Lou, Hou Keong; Zurek, Kathryn M.

2018-02-12

We compute the mass function of bound states of asymmetric dark matter - nuggets - synthesized in the early Universe. We apply our results for the nugget density and binding energy computed from a nuclear model to obtain analytic estimates of the typical nugget size exiting synthesis. We numerically solve the Boltzmann equation for synthesis including two-to-two fusion reactions, estimating the impact of bottlenecks on the mass function exiting synthesis. These results provide the basis for studying the late Universe cosmology of nuggets in a future companion paper.
Early Universe synthesis of asymmetric dark matter nuggets

NASA Astrophysics Data System (ADS)

Gresham, Moira I.; Lou, Hou Keong; Zurek, Kathryn M.

2018-02-01

We compute the mass function of bound states of asymmetric dark matter—nuggets—synthesized in the early Universe. We apply our results for the nugget density and binding energy computed from a nuclear model to obtain analytic estimates of the typical nugget size exiting synthesis. We numerically solve the Boltzmann equation for synthesis including two-to-two fusion reactions, estimating the impact of bottlenecks on the mass function exiting synthesis. These results provide the basis for studying the late Universe cosmology of nuggets in a future companion paper.
Equation for wave processes in inhomogeneous moving media and functional solution of the acoustic tomography problem based on it

NASA Astrophysics Data System (ADS)

Rumyantseva, O. D.; Shurup, A. S.

2017-01-01

The paper considers the derivation of the wave equation and Helmholtz equation for solving the tomographic problem of reconstruction combined scalar-vector inhomogeneities describing perturbations of the sound velocity and absorption, the vector field of flows, and perturbations of the density of the medium. Restrictive conditions under which the obtained equations are meaningful are analyzed. Results of numerical simulation of the two-dimensional functional-analytical Novikov-Agaltsov algorithm for reconstructing the flow velocity using the the obtained Helmholtz equation are presented.
Simplified Computation for Nonparametric Windows Method of Probability Density Function Estimation.

PubMed

Joshi, Niranjan; Kadir, Timor; Brady, Michael

2011-08-01

Recently, Kadir and Brady proposed a method for estimating probability density functions (PDFs) for digital signals which they call the Nonparametric (NP) Windows method. The method involves constructing a continuous space representation of the discrete space and sampled signal by using a suitable interpolation method. NP Windows requires only a small number of observed signal samples to estimate the PDF and is completely data driven. In this short paper, we first develop analytical formulae to obtain the NP Windows PDF estimates for 1D, 2D, and 3D signals, for different interpolation methods. We then show that the original procedure to calculate the PDF estimate can be significantly simplified and made computationally more efficient by a judicious choice of the frame of reference. We have also outlined specific algorithmic details of the procedures enabling quick implementation. Our reformulation of the original concept has directly demonstrated a close link between the NP Windows method and the Kernel Density Estimator.
Computing partial traces and reduced density matrices

NASA Astrophysics Data System (ADS)

Maziero, Jonas

Taking partial traces (PTrs) for computing reduced density matrices, or related functions, is a ubiquitous procedure in the quantum mechanics of composite systems. In this paper, we present a thorough description of this function and analyze the number of elementary operations (ops) needed, under some possible alternative implementations, to compute it on a classical computer. As we note, it is worthwhile doing some analytical developments in order to avoid making null multiplications and sums, what can considerably reduce the ops. For instance, for a bipartite system ℋa⊗ℋb with dimensions da=dimℋa and db=dimℋb and for da,db≫1, while a direct use of PTr definition applied to ℋb requires 𝒪(da6db6) ops, its optimized implementation entails 𝒪(da2db) ops. In the sequence, we regard the computation of PTrs for general multipartite systems and describe Fortran code provided to implement it numerically. We also consider the calculation of reduced density matrices via Bloch’s parametrization with generalized Gell Mann’s matrices.
Analytical derivatives of the individual state energies in ensemble density functional theory method. I. General formalism

DOE PAGES

Filatov, Michael; Liu, Fang; Martínez, Todd J.

2017-07-21

The state-averaged (SA) spin restricted ensemble referenced Kohn-Sham (REKS) method and its state interaction (SI) extension, SI-SA-REKS, enable one to describe correctly the shape of the ground and excited potential energy surfaces of molecules undergoing bond breaking/bond formation reactions including features such as conical intersections crucial for theoretical modeling of non-adiabatic reactions. Until recently, application of the SA-REKS and SI-SA-REKS methods to modeling the dynamics of such reactions was obstructed due to the lack of the analytical energy derivatives. Here, the analytical derivatives of the individual SA-REKS and SI-SA-REKS energies are derived. The final analytic gradient expressions are formulated entirelymore » in terms of traces of matrix products and are presented in the form convenient for implementation in the traditional quantum chemical codes employing basis set expansions of the molecular orbitals. Finally, we will describe the implementation and benchmarking of the derived formalism in a subsequent article of this series.« less
Liquid drop model for charged spherical metal clusters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Seidl, M.; Brack, M.

1996-02-01

The average ground-state energy of a charged spherical metal cluster with {ital N} atoms and {ital z} excessive valence electrons, i.e., with net charge {ital Q}={minus}{ital ez} and radius {ital R}={ital r}{sub {ital sN}}{sup 1/3}, is presented in the liquid drop model (LDM) expansion {ital E}({ital N},{ital z})={ital a}{sub v}{ital N}+{ital a}{sub s}{ital N}{sup 2/3}+{ital a}{sub c}{ital N}{sup 1/3}+{ital a}{sub 0}({ital z})+{ital a}{sub {minus}1}({ital z}){ital N}{sup {minus}1/3}+{ital O}({ital N}{sup {minus}2/3}). We derive analytical expressions for the leading LDM coefficients {ital a}{sub v}, {ital a}{sub s}, {ital a}{sub c}, and, in particular, for the charge dependence of the further LDM coefficientsmore » {ital a}{sub 0} and {ital a}{sub {minus}1}, using the jellium model and density functional theory in the local density approximation. We obtain for the ionization energy {ital I}({ital R})={ital W}+{alpha}({ital e}{sup 2}/{ital R})+{ital O}({ital R}{sup {minus}2}), with the bulk work function {ital W}=[{Phi}(+{infinity}){minus}{Phi}(0)]{minus}{ital e}{sub b}, given first by Mahan and Schaich in terms of the electrostatic potential {Phi} and the bulk energy per electron {ital e}{sub b}, and a new analytical expression for the dimensionless coefficient {alpha}. We demonstrate that within classical theory {alpha}=1/2 but, in agreement with experimental information, {alpha} tends to {approximately}0.4 if quantum-mechanical contributions are included. In order to test and confirm our analytical expressions, we discuss the numerical results of semiclassical density variational calculations in the extended Thomas{endash}Fermi model. Copyright {copyright} 1996 Academic Press, Inc.« less
Quantitative control of poly(ethylene oxide) surface antifouling and biodetection through azimuthally enhanced grating coupled-surface plasmon resonance sensing

NASA Astrophysics Data System (ADS)

Sonato, Agnese; Silvestri, Davide; Ruffato, Gianluca; Zacco, Gabriele; Romanato, Filippo; Morpurgo, Margherita

2013-12-01

Grating Coupled-Surface Plasmon reflectivity measurements carried out under azimuth and polarization control (GC-SPR φ ≠ 0°) were used to optimize the process of gold surface dressing with poly(ethylene oxide) (PEO) derivatives of different molecular weight, with the final goal to maximize the discrimination between specific and non-specific binding events occurring at the surface. The kinetics of surface deposition of thiol-ending PEOs (0.3, 2 and 5 kDa), introduced as antifouling layers, was monitored. Non-specific binding events upon immersion of the surfaces into buffers containing either 0.1% bovine serum albumin or 1% Goat Serum, were evaluated as a function of polymer size and density. A biorecognition event between avidin and biotin was then monitored in both buffers at selected low and high polymer surface densities and the contribution of analyte and fouling elements to the signal was precisely quantified. The 0.3 kDa PEO film was unable to protect the surface from non-specific interactions at any tested density. On the other hand, the 2 and 5 kDa polymers at their highest surface densities guaranteed full protection from non-specific interactions from both buffers. These densities were reached upon a long deposition time (24-30 h). The results pave the way toward the application of this platform for the detection of low concentration and small dimension analytes, for which both non-fouling and high instrumental sensitivity are fundamental requirements.
Influence of distributed delays on the dynamics of a generalized immune system cancerous cells interactions model

NASA Astrophysics Data System (ADS)

Piotrowska, M. J.; Bodnar, M.

2018-01-01

We present a generalisation of the mathematical models describing the interactions between the immune system and tumour cells which takes into account distributed time delays. For the analytical study we do not assume any particular form of the stimulus function describing the immune system reaction to presence of tumour cells but we only postulate its general properties. We analyse basic mathematical properties of the considered model such as existence and uniqueness of the solutions. Next, we discuss the existence of the stationary solutions and analytically investigate their stability depending on the forms of considered probability densities that is: Erlang, triangular and uniform probability densities separated or not from zero. Particular instability results are obtained for a general type of probability densities. Our results are compared with those for the model with discrete delays know from the literature. In addition, for each considered type of probability density, the model is fitted to the experimental data for the mice B-cell lymphoma showing mean square errors at the same comparable level. For estimated sets of parameters we discuss possibility of stabilisation of the tumour dormant steady state. Instability of this steady state results in uncontrolled tumour growth. In order to perform numerical simulation, following the idea of linear chain trick, we derive numerical procedures that allow us to solve systems with considered probability densities using standard algorithm for ordinary differential equations or differential equations with discrete delays.
Extracting physical quantities from BES data

NASA Astrophysics Data System (ADS)

Fox, Michael; Field, Anthony; Schekochihin, Alexander; van Wyk, Ferdinand; MAST Team

2015-11-01

We propose a method to extract the underlying physical properties of turbulence from measurements, thereby facilitating quantitative comparisons between theory and experiment. Beam Emission Spectroscopy (BES) diagnostics record fluctuating intensity time series, which are related to the density field in the plasma through Point-Spread Functions (PSFs). Assuming a suitable form for the correlation function of the underlying turbulence, analytical expressions are derived that relate the correlation parameters of the intensity field: the radial and poloidal correlation lengths and wavenumbers, the correlation time and the fluctuation amplitude, to the equivalent correlation properties of the density field. In many cases, the modification caused by the PSFs is substantial enough to change conclusions about physics. Our method is tested by applying PSFs to the ``real'' density field, generated by non-linear gyrokinetic simulations of MAST, to create synthetic turbulence data, from which the method successfully recovers the correlation function of the ``real'' density field. This method is applied to BES data from MAST to determine the scaling of the 2D structure of the ion-scale turbulence with equilibrium parameters, including the ExB flow shear. Work funded by the Euratom research and training programme 2014-2018 under grant agreement No 633053 and from the RCUK Energy Programme [grant number EP/I501045].
Weak annihilation cusp inside the dark matter spike about a black hole.

PubMed

Shapiro, Stuart L; Shelton, Jessie

2016-06-15

We reinvestigate the effect of annihilations on the distribution of collisionless dark matter (DM) in a spherical density spike around a massive black hole. We first construct a very simple, pedagogic, analytic model for an isotropic phase space distribution function that accounts for annihilation and reproduces the "weak cusp" found by Vasiliev for DM deep within the spike and away from its boundaries. The DM density in the cusp varies as r -1/2 for s -wave annihilation, where r is the distance from the central black hole, and is not a flat "plateau" profile. We then extend this model by incorporating a loss cone that accounts for the capture of DM particles by the hole. The loss cone is implemented by a boundary condition that removes capture orbits, resulting in an anisotropic distribution function. Finally, we evolve an initial spike distribution function by integrating the Boltzmann equation to show how the weak cusp grows and its density decreases with time. We treat two cases, one for s -wave and the other for p -wave DM annihilation, adopting parameters characteristic of the Milky Way nuclear core and typical WIMP models for DM. The cusp density profile for p -wave annihilation is weaker, varying like ~ r -0.34 , but is still not a flat plateau.
Superfluidity in Strongly Interacting Fermi Systems with Applications to Neutron Stars

NASA Astrophysics Data System (ADS)

Khodel, Vladimir

The rotational dynamics and cooling history of neutron stars is influenced by the superfluid properties of nucleonic matter. In this thesis a novel separation technique is applied to the analysis of the gap equation for neutron matter. It is shown that the problem can be recast into two tasks: solving a simple system of linear integral equations for the shape functions of various components of the gap function and solving a system of non-linear algebraic equations for their scale factors. Important simplifications result from the fact that the ratio of the gap amplitude to the Fermi energy provides a small parameter in this problem. The relationship between the analytic structure of the shape functions and the density interval for the existence of superfluid gap is discussed. It is shown that in 1S0 channel the position of the first zero of the shape function gives an estimate of the upper critical density. The relation between the resonant behavior of the two-neutron interaction in this channel and the density dependence of the gap is established. The behavior of the gap in the limits of low and high densities is analyzed. Various approaches to calculation of the scale factors are considered: model cases, angular averaging, and perturbation theory. An optimization-based approach is proposed. The shape functions and scale factors for Argonne υ14 and υ18 potentials are determined in singlet and triplet channels. Dependence of the solution on the value of effective mass and medium polarization is studied.
Statistical properties of single-mode fiber coupling of satellite-to-ground laser links partially corrected by adaptive optics.

PubMed

Canuet, Lucien; Védrenne, Nicolas; Conan, Jean-Marc; Petit, Cyril; Artaud, Geraldine; Rissons, Angelique; Lacan, Jerome

2018-01-01

In the framework of satellite-to-ground laser downlinks, an analytical model describing the variations of the instantaneous coupled flux into a single-mode fiber after correction of the incoming wavefront by partial adaptive optics (AO) is presented. Expressions for the probability density function and the cumulative distribution function as well as for the average fading duration and fading duration distribution of the corrected coupled flux are given. These results are of prime interest for the computation of metrics related to coded transmissions over correlated channels, and they are confronted by end-to-end wave-optics simulations in the case of a geosynchronous satellite (GEO)-to-ground and a low earth orbit satellite (LEO)-to-ground scenario. Eventually, the impact of different AO performances on the aforementioned fading duration distribution is analytically investigated for both scenarios.
Exact PDF equations and closure approximations for advective-reactive transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Venturi, D.; Tartakovsky, Daniel M.; Tartakovsky, Alexandre M.

2013-06-01

Mathematical models of advection–reaction phenomena rely on advective flow velocity and (bio) chemical reaction rates that are notoriously random. By using functional integral methods, we derive exact evolution equations for the probability density function (PDF) of the state variables of the advection–reaction system in the presence of random transport velocity and random reaction rates with rather arbitrary distributions. These PDF equations are solved analytically for transport with deterministic flow velocity and a linear reaction rate represented mathematically by a heterog eneous and strongly-correlated random field. Our analytical solution is then used to investigate the accuracy and robustness of the recentlymore » proposed large-eddy diffusivity (LED) closure approximation [1]. We find that the solution to the LED-based PDF equation, which is exact for uncorrelated reaction rates, is accurate even in the presence of strong correlations and it provides an upper bound of predictive uncertainty.« less
Analytical potential-density pairs for bars

NASA Astrophysics Data System (ADS)

Vogt, D.; Letelier, P. S.

2010-11-01

An identity that relates multipolar solutions of the Einstein equations to Newtonian potentials of bars with linear densities proportional to Legendre polynomials is used to construct analytical potential-density pairs of infinitesimally thin bars with a given linear density profile. By means of a suitable transformation, softened bars that are free of singularities are also obtained. As an application we study the equilibrium points and stability for the motion of test particles in the gravitational field for three models of rotating bars.
The Importance of Three-Body Interactions in Molecular Dynamics Simulations of Water with the Fragment Molecular Orbital Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pruitt, Spencer R.; Nakata, Hiroya; Nagata, Takeshi

2016-04-12

The analytic first derivative with respect to nuclear coordinates is formulated and implemented in the framework of the three-body fragment molecular orbital (FMO) method. The gradient has been derived and implemented for restricted Hartree-Fock, second-order Møller-Plesset perturbation, and density functional theories. The importance of the three-body fully analytic gradient is illustrated through the failure of the two-body FMO method during molecular dynamics simulations of a small water cluster. The parallel implementation of the fragment molecular orbital method, its parallel efficiency, and its scalability on the Blue Gene/Q architecture up to 262,144 CPU cores, are also discussed.
Analytical Derivation of Power Laws in Firm Size Variables from Gibrat's Law and Quasi-inversion Symmetry: A Geomorphological Approach

NASA Astrophysics Data System (ADS)

Ishikawa, Atushi; Fujimoto, Shouji; Mizuno, Takayuki; Watanabe, Tsutomu

2014-03-01

We start from Gibrat's law and quasi-inversion symmetry for three firm size variables (i.e., tangible fixed assets K, number of employees L, and sales Y) and derive a partial differential equation to be satisfied by the joint probability density function of K and L. We then transform K and L, which are correlated, into two independent variables by applying surface openness used in geomorphology and provide an analytical solution to the partial differential equation. Using worldwide data on the firm size variables for companies, we confirm that the estimates on the power-law exponents of K, L, and Y satisfy a relationship implied by the theory.

Langmuir probe analysis in electronegative plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bredin, Jerome, E-mail: jerome.bredin@lpp.polytechnique.fr; Chabert, Pascal; Aanesland, Ane

2014-12-15

This paper compares two methods to analyze Langmuir probe data obtained in electronegative plasmas. The techniques are developed to allow investigations in plasmas, where the electronegativity α{sub 0} = n{sub –}/n{sub e} (the ratio between the negative ion and electron densities) varies strongly. The first technique uses an analytical model to express the Langmuir probe current-voltage (I-V) characteristic and its second derivative as a function of the electron and ion densities (n{sub e}, n{sub +}, n{sub –}), temperatures (T{sub e}, T{sub +}, T{sub –}), and masses (m{sub e}, m{sub +}, m{sub –}). The analytical curves are fitted to the experimental data bymore » adjusting these variables and parameters. To reduce the number of fitted parameters, the ion masses are assumed constant within the source volume, and quasi-neutrality is assumed everywhere. In this theory, Maxwellian distributions are assumed for all charged species. We show that this data analysis can predict the various plasma parameters within 5–10%, including the ion temperatures when α{sub 0} > 100. However, the method is tedious, time consuming, and requires a precise measurement of the energy distribution function. A second technique is therefore developed for easier access to the electron and ion densities, but does not give access to the ion temperatures. Here, only the measured I-V characteristic is needed. The electron density, temperature, and ion saturation current for positive ions are determined by classical probe techniques. The electronegativity α{sub 0} and the ion densities are deduced via an iterative method since these variables are coupled via the modified Bohm velocity. For both techniques, a Child-Law sheath model for cylindrical probes has been developed and is presented to emphasize the importance of this model for small cylindrical Langmuir probes.« less
Picosecond time-resolved measurements of dense plasma line shifts

DOE PAGES

Stillman, C. R.; Nilson, P. M.; Ivancic, S. T.; ...

2017-06-13

Picosecond time-resolved x-ray spectroscopy is used to measure the spectral line shift of the 1s2p–1s 2 transition in He-like Al ions as a function of the instantaneous plasma conditions. The plasma temperature and density are inferred from the Al He α complex using a nonlocal-thermodynamic-equilibrium atomic physics model. The experimental spectra show a linearly increasing red shift for electron densities of 1 to 5 × 10 23 cm –3. Furthermore, the measured line shifts are broadly consistent with a generalized analytic line-shift model based on calculations of a self-consistent field ion sphere model.
General kinetic solution for the Biermann battery with an associated pressure anisotropy generation

NASA Astrophysics Data System (ADS)

Schoeffler, K. M.; Silva, L. O.

2018-01-01

Fully kinetic analytic calculations of an initially Maxwellian distribution with arbitrary density and temperature gradients exhibit the development of temperature anisotropies and magnetic field growth associated with the Biermann battery. The calculation, performed by taking a small order expansion of the ratio of the Debye length to the gradient scale, predicts anisotropies and magnetic fields as a function of space given an arbitrary temperature and density profile. These predictions are shown to qualitatively match the values measured from particle-in-cell simulations, where the development of the Weibel instability occurs at the same location and with a wavenumber aligned with the predicted temperature anisotropy.
Picosecond time-resolved measurements of dense plasma line shifts

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stillman, C. R.; Nilson, P. M.; Ivancic, S. T.

Picosecond time-resolved x-ray spectroscopy is used to measure the spectral line shift of the 1s2p–1s 2 transition in He-like Al ions as a function of the instantaneous plasma conditions. The plasma temperature and density are inferred from the Al He α complex using a nonlocal-thermodynamic-equilibrium atomic physics model. The experimental spectra show a linearly increasing red shift for electron densities of 1 to 5 × 10 23 cm –3. Furthermore, the measured line shifts are broadly consistent with a generalized analytic line-shift model based on calculations of a self-consistent field ion sphere model.
Brownian self-driven particles on the surface of a sphere

NASA Astrophysics Data System (ADS)

Apaza, Leonardo; Sandoval, Mario

2017-08-01

We present the dynamics of overdamped Brownian self-propelled particles moving on the surface of a sphere. The effect of self-propulsion on the diffusion of these particles is elucidated by determining their angular (azimuthal and polar) mean-square displacement. Short- and long-times analytical expressions for their angular mean-square displacement are offered. Finally, the particles' steady marginal angular probability density functions are also elucidated.
Response of space shuttle insulation panels to acoustic noise pressure

NASA Technical Reports Server (NTRS)

Vaicaitis, R.

1976-01-01

The response of reusable space shuttle insulation panels to random acoustic pressure fields are studied. The basic analytical approach in formulating the governing equations of motion uses a Rayleigh-Ritz technique. The input pressure field is modeled as a stationary Gaussian random process for which the cross-spectral density function is known empirically from experimental measurements. The response calculations are performed in both frequency and time domain.
Monte Carlo calculation of dynamical properties of the two-dimensional Hubbard model

NASA Technical Reports Server (NTRS)

White, S. R.; Scalapino, D. J.; Sugar, R. L.; Bickers, N. E.

1989-01-01

A new method is introduced for analytically continuing imaginary-time data from quantum Monte Carlo calculations to the real-frequency axis. The method is based on a least-squares-fitting procedure with constraints of positivity and smoothness on the real-frequency quantities. Results are shown for the single-particle spectral-weight function and density of states for the half-filled, two-dimensional Hubbard model.
Molcas 8: New capabilities for multiconfigurational quantum chemical calculations across the periodic table.

PubMed

Aquilante, Francesco; Autschbach, Jochen; Carlson, Rebecca K; Chibotaru, Liviu F; Delcey, Mickaël G; De Vico, Luca; Fdez Galván, Ignacio; Ferré, Nicolas; Frutos, Luis Manuel; Gagliardi, Laura; Garavelli, Marco; Giussani, Angelo; Hoyer, Chad E; Li Manni, Giovanni; Lischka, Hans; Ma, Dongxia; Malmqvist, Per Åke; Müller, Thomas; Nenov, Artur; Olivucci, Massimo; Pedersen, Thomas Bondo; Peng, Daoling; Plasser, Felix; Pritchard, Ben; Reiher, Markus; Rivalta, Ivan; Schapiro, Igor; Segarra-Martí, Javier; Stenrup, Michael; Truhlar, Donald G; Ungur, Liviu; Valentini, Alessio; Vancoillie, Steven; Veryazov, Valera; Vysotskiy, Victor P; Weingart, Oliver; Zapata, Felipe; Lindh, Roland

2016-02-15

In this report, we summarize and describe the recent unique updates and additions to the Molcas quantum chemistry program suite as contained in release version 8. These updates include natural and spin orbitals for studies of magnetic properties, local and linear scaling methods for the Douglas-Kroll-Hess transformation, the generalized active space concept in MCSCF methods, a combination of multiconfigurational wave functions with density functional theory in the MC-PDFT method, additional methods for computation of magnetic properties, methods for diabatization, analytical gradients of state average complete active space SCF in association with density fitting, methods for constrained fragment optimization, large-scale parallel multireference configuration interaction including analytic gradients via the interface to the Columbus package, and approximations of the CASPT2 method to be used for computations of large systems. In addition, the report includes the description of a computational machinery for nonlinear optical spectroscopy through an interface to the QM/MM package Cobramm. Further, a module to run molecular dynamics simulations is added, two surface hopping algorithms are included to enable nonadiabatic calculations, and the DQ method for diabatization is added. Finally, we report on the subject of improvements with respects to alternative file options and parallelization. © 2015 Wiley Periodicals, Inc.
Exact steady state of a Kerr resonator with one- and two-photon driving and dissipation: Controllable Wigner-function multimodality and dissipative phase transitions

NASA Astrophysics Data System (ADS)

Bartolo, Nicola; Minganti, Fabrizio; Casteels, Wim; Ciuti, Cristiano

2016-09-01

We present exact results for the steady-state density matrix of a general class of driven-dissipative systems consisting of a nonlinear Kerr resonator in the presence of both coherent (one-photon) and parametric (two-photon) driving and dissipation. Thanks to the analytical solution, obtained via the complex P -representation formalism, we are able to explore any regime, including photon blockade, multiphoton resonant effects, and a mesoscopic regime with large photon density and quantum correlations. We show how the interplay between one- and two-photon driving provides a way to control the multimodality of the Wigner function in regimes where the semiclassical theory exhibits multistability. We also study the emergence of dissipative phase transitions in the thermodynamic limit of large photon numbers.
Application of Raman spectroscopy, surface-enhanced Raman scattering (SERS), and density functional theory for the identification of phenethylamines.

PubMed

Taplin, Francis; O'Donnell, Deanna; Kubic, Thomas; Leona, Marco; Lombardi, John

2013-10-01

We evaluated the normal Raman (NR) and the surface-enhanced Raman scattering (SERS) of three sympathomimetic amines: phenethylamine, ephedrine, and 3,4-methylenedioxymethamphetamine (MDMA). In addition, quantum mechanical calculations-geometry optimization and calculations of the harmonic vibrational frequencies-were performed using the density functional theory (DFT) approach. Vibrational assignments were made by comparing the experimental and calculated spectra. The study found that both NR and SERS provided excellent spectra for the drugs tested. Certain conditions, such as response to various laser wavelengths and background fluorescence of the analyte, could be easily managed using SERS techniques. The DFT-calculated spectra could be correlated with the experimental spectra without the aid of a scaling factor. We also present a set of discriminant bands, useful for distinguishing the three compounds, despite their structural similarities.
Addition of simultaneous heat and solute transport and variable fluid viscosity to SEAWAT

USGS Publications Warehouse

Thorne, D.; Langevin, C.D.; Sukop, M.C.

2006-01-01

SEAWAT is a finite-difference computer code designed to simulate coupled variable-density ground water flow and solute transport. This paper describes a new version of SEAWAT that adds the ability to simultaneously model energy and solute transport. This is necessary for simulating the transport of heat and salinity in coastal aquifers for example. This work extends the equation of state for fluid density to vary as a function of temperature and/or solute concentration. The program has also been modified to represent the effects of variable fluid viscosity as a function of temperature and/or concentration. The viscosity mechanism is verified against an analytical solution, and a test of temperature-dependent viscosity is provided. Finally, the classic Henry-Hilleke problem is solved with the new code. ?? 2006 Elsevier Ltd. All rights reserved.
Statistical analysis and modeling of intermittent transport events in the tokamak scrape-off layer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anderson, Johan, E-mail: anderson.johan@gmail.com; Halpern, Federico D.; Ricci, Paolo

The turbulence observed in the scrape-off-layer of a tokamak is often characterized by intermittent events of bursty nature, a feature which raises concerns about the prediction of heat loads on the physical boundaries of the device. It appears thus necessary to delve into the statistical properties of turbulent physical fields such as density, electrostatic potential, and temperature, focusing on the mathematical expression of tails of the probability distribution functions. The method followed here is to generate statistical information from time-traces of the plasma density stemming from Braginskii-type fluid simulations and check this against a first-principles theoretical model. The analysis ofmore » the numerical simulations indicates that the probability distribution function of the intermittent process contains strong exponential tails, as predicted by the analytical theory.« less
Solving the Self-Interaction Problem in Kohn-Sham Density Functional Theory. Application to Atoms

DOE PAGES

Daene, M.; Gonis, A.; Nicholson, D. M.; ...

2014-10-14

Previously, we proposed a computational methodology that addresses the elimination of the self-interaction error from the Kohn–Sham formulation of the density functional theory. We demonstrated how the exchange potential can be obtained, and presented results of calculations for atomic systems up to Kr carried out within a Cartesian coordinate system. In our paper, we provide complete details of this self-interaction free method formulated in spherical coordinates based on the explicit equidensity basis ansatz. We also prove analytically that derivatives obtained using this method satisfy the Virial theorem for spherical orbitals, where the problem can be reduced to one dimension. Wemore » present the results of calculations of ground-state energies of atomic systems throughout the periodic table carried out within the exchange-only mode.« less
Spacing distribution functions for 1D point island model with irreversible attachment

NASA Astrophysics Data System (ADS)

Gonzalez, Diego; Einstein, Theodore; Pimpinelli, Alberto

2011-03-01

We study the configurational structure of the point island model for epitaxial growth in one dimension. In particular, we calculate the island gap and capture zone distributions. Our model is based on an approximate description of nucleation inside the gaps. Nucleation is described by the joint probability density p xy n (x,y), which represents the probability density to have nucleation at position x within a gap of size y. Our proposed functional form for p xy n (x,y) describes excellently the statistical behavior of the system. We compare our analytical model with extensive numerical simulations. Our model retains the most relevant physical properties of the system. This work was supported by the NSF-MRSEC at the University of Maryland, Grant No. DMR 05-20471, with ancillary support from the Center for Nanophysics and Advanced Materials (CNAM).
The Distribution and Annihilation of Dark Matter Around Black Holes

NASA Technical Reports Server (NTRS)

Schnittman, Jeremy D.

2015-01-01

We use a Monte Carlo code to calculate the geodesic orbits of test particles around Kerr black holes, generating a distribution function of both bound and unbound populations of dark matter (DM) particles. From this distribution function, we calculate annihilation rates and observable gamma-ray spectra for a few simple DM models. The features of these spectra are sensitive to the black hole spin, observer inclination, and detailed properties of the DM annihilation cross-section and density profile. Confirming earlier analytic work, we find that for rapidly spinning black holes, the collisional Penrose process can reach efficiencies exceeding 600%, leading to a high-energy tail in the annihilation spectrum. The high particle density and large proper volume of the region immediately surrounding the horizon ensures that the observed flux from these extreme events is non-negligible.
The correlation function of galaxy ellipticities produced by gravitational lensing

NASA Technical Reports Server (NTRS)

Miralda-Escude, Jordi

1991-01-01

The correlation of galaxy ellipticities produced by gravitational lensing is calculated as a function of the power spectrum of density fluctuations in the universe by generalizing an analytical method developed by Gunn (1967). The method is applied to a model where identical objects with spherically symmetric density profiles are randomly laid down in space, and to the cold dark matter model. The possibility of detecting this correlation is discussed. Although an ellipticity correlation can also be caused by an intrinsic alignment of the axes of galaxies belonging to a cluster or a supercluster, a method is suggested by which one type of correlation can be distinguished from another. The advantage of this ellipticity correlation is that it is one of the few astronomical observations that can directly probe large-scale mass fluctuations in the universe.
Fast and accurate Voronoi density gridding from Lagrangian hydrodynamics data

NASA Astrophysics Data System (ADS)

Petkova, Maya A.; Laibe, Guillaume; Bonnell, Ian A.

2018-01-01

Voronoi grids have been successfully used to represent density structures of gas in astronomical hydrodynamics simulations. While some codes are explicitly built around using a Voronoi grid, others, such as Smoothed Particle Hydrodynamics (SPH), use particle-based representations and can benefit from constructing a Voronoi grid for post-processing their output. So far, calculating the density of each Voronoi cell from SPH data has been done numerically, which is both slow and potentially inaccurate. This paper proposes an alternative analytic method, which is fast and accurate. We derive an expression for the integral of a cubic spline kernel over the volume of a Voronoi cell and link it to the density of the cell. Mass conservation is ensured rigorously by the procedure. The method can be applied more broadly to integrate a spherically symmetric polynomial function over the volume of a random polyhedron.
Asymptotic behavior of exact exchange potential of slabs

NASA Astrophysics Data System (ADS)

Engel, E.

2014-06-01

In this contribution the exact exchange potential vx of density functional theory is examined for slabs such as graphene, for which one has a Bravais lattice in the x-y directions, while the electrons are confined to the finite region -L≤z≤L in the z direction. It is demonstrated analytically that the exact vx behaves as -e2/z for z ≫L. This result extends the corresponding statement of Horowitz, Proetto, and Rigamonti [Phys. Rev. Lett. 97, 026802 (2006), 10.1103/PhysRevLett.97.026802] for jellium slabs to slabs with arbitrary periodic density distributions. Application of the exact exchange to a Si(111) slab (within the Krieger-Li-Iafrate approximation) indicates that the corrugation of the exact vx is more pronounced than that of the local density approximation for vx.
Collective charge excitations and the metal-insulator transition in the square lattice Hubbard-Coulomb model

DOE PAGES

Ulybyshev, Maksim; Winterowd, Christopher; Zafeiropoulos, Savvas

2017-11-09

Here in this article, we discuss the nontrivial collective charge excitations (plasmons) of the extended square lattice Hubbard model. Using a fully nonperturbative approach, we employ the hybrid Monte Carlo algorithm to simulate the system at half-filling. A modified Backus-Gilbert method is introduced to obtain the spectral functions via numerical analytic continuation. We directly compute the single-particle density of states which demonstrates the formation of Hubbard bands in the strongly correlated phase. The momentum-resolved charge susceptibility also is computed on the basis of the Euclidean charge-density-density correlator. In agreement with previous extended dynamical mean-field theory studies, we find that, atmore » high strength of the electron-electron interaction, the plasmon dispersion develops two branches.« less
Collective charge excitations and the metal-insulator transition in the square lattice Hubbard-Coulomb model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ulybyshev, Maksim; Winterowd, Christopher; Zafeiropoulos, Savvas

Here in this article, we discuss the nontrivial collective charge excitations (plasmons) of the extended square lattice Hubbard model. Using a fully nonperturbative approach, we employ the hybrid Monte Carlo algorithm to simulate the system at half-filling. A modified Backus-Gilbert method is introduced to obtain the spectral functions via numerical analytic continuation. We directly compute the single-particle density of states which demonstrates the formation of Hubbard bands in the strongly correlated phase. The momentum-resolved charge susceptibility also is computed on the basis of the Euclidean charge-density-density correlator. In agreement with previous extended dynamical mean-field theory studies, we find that, atmore » high strength of the electron-electron interaction, the plasmon dispersion develops two branches.« less

Analytical energy gradients for explicitly correlated wave functions. I. Explicitly correlated second-order Møller-Plesset perturbation theory

NASA Astrophysics Data System (ADS)

Győrffy, Werner; Knizia, Gerald; Werner, Hans-Joachim

2017-12-01

We present the theory and algorithms for computing analytical energy gradients for explicitly correlated second-order Møller-Plesset perturbation theory (MP2-F12). The main difficulty in F12 gradient theory arises from the large number of two-electron integrals for which effective two-body density matrices and integral derivatives need to be calculated. For efficiency, the density fitting approximation is used for evaluating all two-electron integrals and their derivatives. The accuracies of various previously proposed MP2-F12 approximations [3C, 3C(HY1), 3*C(HY1), and 3*A] are demonstrated by computing equilibrium geometries for a set of molecules containing first- and second-row elements, using double-ζ to quintuple-ζ basis sets. Generally, the convergence of the bond lengths and angles with respect to the basis set size is strongly improved by the F12 treatment, and augmented triple-ζ basis sets are sufficient to closely approach the basis set limit. The results obtained with the different approximations differ only very slightly. This paper is the first step towards analytical gradients for coupled-cluster singles and doubles with perturbative treatment of triple excitations, which will be presented in the second part of this series.
Study of dual radio frequency capacitively coupled plasma: an analytical treatment matched to an experiment

NASA Astrophysics Data System (ADS)

Saikia, P.; Bhuyan, H.; Escalona, M.; Favre, M.; Wyndham, E.; Maze, J.; Schulze, J.

2018-01-01

The behavior of a dual frequency capacitively coupled plasma (2f CCP) driven by 2.26 and 13.56 MHz radio frequency (rf) source is investigated using an approach that integrates a theoretical model and experimental data. The basis of the theoretical analysis is a time dependent dual frequency analytical sheath model that casts the relation between the instantaneous sheath potential and plasma parameters. The parameters used in the model are obtained by operating the 2f CCP experiment (2.26 MHz + 13.56 MHz) in argon at a working pressure of 50 mTorr. Experimentally measured plasma parameters such as the electron density, electron temperature, as well as the rf current density ratios are the inputs of the theoretical model. Subsequently, a convenient analytical solution for the output sheath potential and sheath thickness was derived. A comparison of the present numerical results is done with the results obtained in another 2f CCP experiment conducted by Semmler et al (2007 Plasma Sources Sci. Technol. 16 839). A good quantitative correspondence is obtained. The numerical solution shows the variation of sheath potential with the low and high frequency (HF) rf powers. In the low pressure plasma, the sheath potential is a qualitative measure of DC self-bias which in turn determines the ion energy. Thus, using this analytical model, the measured values of the DC self-bias as a function of low and HF rf powers are explained in detail.
Quantum cluster theory for the polarizable continuum model. I. The CCSD level with analytical first and second derivatives.

PubMed

Cammi, R

2009-10-28

We present a general formulation of the coupled-cluster (CC) theory for a molecular solute described within the framework of the polarizable continuum model (PCM). The PCM-CC theory is derived in its complete form, called PTDE scheme, in which the correlated electronic density is used to have a self-consistent reaction field, and in an approximate form, called PTE scheme, in which the PCM-CC equations are solved assuming the fixed Hartree-Fock solvent reaction field. Explicit forms for the PCM-CC-PTDE equations are derived at the single and double (CCSD) excitation level of the cluster operator. At the same level, explicit equations for the analytical first derivatives of the PCM basic energy functional are presented, and analytical second derivatives are also discussed. The corresponding PCM-CCSD-PTE equations are given as a special case of the full theory.
Magnetic islands and singular currents at rational surfaces in three-dimensional magnetohydrodynamic equilibria

DOE Office of Scientific and Technical Information (OSTI.GOV)

Loizu, J., E-mail: joaquim.loizu@ipp.mpg.de; Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton New Jersey 08543; Hudson, S.

2015-02-15

Using the recently developed multiregion, relaxed MHD (MRxMHD) theory, which bridges the gap between Taylor's relaxation theory and ideal MHD, we provide a thorough analytical and numerical proof of the formation of singular currents at rational surfaces in non-axisymmetric ideal MHD equilibria. These include the force-free singular current density represented by a Dirac δ-function, which presumably prevents the formation of islands, and the Pfirsch-Schlüter 1/x singular current, which arises as a result of finite pressure gradient. An analytical model based on linearized MRxMHD is derived that can accurately (1) describe the formation of magnetic islands at resonant rational surfaces, (2)more » retrieve the ideal MHD limit where magnetic islands are shielded, and (3) compute the subsequent formation of singular currents. The analytical results are benchmarked against numerical simulations carried out with a fully nonlinear implementation of MRxMHD.« less
Analysis of user equilibrium for staggered shifts in a single-entry traffic corridor with no late arrivals

NASA Astrophysics Data System (ADS)

Li, Chuan-Yao; Huang, Hai-Jun; Tang, Tie-Qiao

2017-05-01

In this paper, we investigate the effects of staggered shifts on the user equilibrium (UE) state in a single-entry traffic corridor with no late arrivals from the analytical and numerical perspective. The LWR (Lighthill-Whitham-Richards) model and the Greenshields' velocity-density function are used to describe the dynamic properties of traffic flow. Propositions for the properties of flow patterns in UE, and the quasi-analytic solutions for three possible situations in UE are deduced. Numerical tests are carried out to testify the analytical results, where the three-dimensional evolution diagram of traffic flow illustrates that shock and rarefaction wave exist in UE and the space-time diagram indicates that UE solutions satisfy the propagation properties of traffic flow. In addition, the cost curves show that the UE solutions satisfy the UE trip-timing condition.
Semi-exact concentric atomic density fitting: Reduced cost and increased accuracy compared to standard density fitting

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hollman, David S.; Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061; Schaefer, Henry F.

2014-02-14

A local density fitting scheme is considered in which atomic orbital (AO) products are approximated using only auxiliary AOs located on one of the nuclei in that product. The possibility of variational collapse to an unphysical “attractive electron” state that can affect such density fitting [P. Merlot, T. Kjærgaard, T. Helgaker, R. Lindh, F. Aquilante, S. Reine, and T. B. Pedersen, J. Comput. Chem. 34, 1486 (2013)] is alleviated by including atom-wise semidiagonal integrals exactly. Our approach leads to a significant decrease in the computational cost of density fitting for Hartree–Fock theory while still producing results with errors 2–5 timesmore » smaller than standard, nonlocal density fitting. Our method allows for large Hartree–Fock and density functional theory computations with exact exchange to be carried out efficiently on large molecules, which we demonstrate by benchmarking our method on 200 of the most widely used prescription drug molecules. Our new fitting scheme leads to smooth and artifact-free potential energy surfaces and the possibility of relatively simple analytic gradients.« less
Analytical model for the density distribution in the Io plasma torus

NASA Technical Reports Server (NTRS)

Mei, YI; Thorne, Richard M.; Bagenal, Fran

1995-01-01

An analytical model is developed for the diffusive equilibrium plasma density distribution in the Io plasma torus. The model has been employed successfully to follow the ray path of plasma waves in the multi-ion Jovian magnetosphere; it would also be valuable for other studies of the Io torus that require a smooth and continuous description of the plasma density and its gradients. Validity of the analytical treatment requires that the temperature of thermal electrons be much lower than the ion temperature and that superthermal electrons be much less abundant than the thermal electrons; these two conditions are satisfied in the warm outer region of the Io torus from L = 6 to L = 10. The analytical solutions agree well with exact numerical calculations for the most dense portion of the Io torus within 30 deg of the equator.
A simple method for finding explicit analytic transition densities of diffusion processes with general diploid selection.

PubMed

Song, Yun S; Steinrücken, Matthias

2012-03-01

The transition density function of the Wright-Fisher diffusion describes the evolution of population-wide allele frequencies over time. This function has important practical applications in population genetics, but finding an explicit formula under a general diploid selection model has remained a difficult open problem. In this article, we develop a new computational method to tackle this classic problem. Specifically, our method explicitly finds the eigenvalues and eigenfunctions of the diffusion generator associated with the Wright-Fisher diffusion with recurrent mutation and arbitrary diploid selection, thus allowing one to obtain an accurate spectral representation of the transition density function. Simplicity is one of the appealing features of our approach. Although our derivation involves somewhat advanced mathematical concepts, the resulting algorithm is quite simple and efficient, only involving standard linear algebra. Furthermore, unlike previous approaches based on perturbation, which is applicable only when the population-scaled selection coefficient is small, our method is nonperturbative and is valid for a broad range of parameter values. As a by-product of our work, we obtain the rate of convergence to the stationary distribution under mutation-selection balance.
A Simple Method for Finding Explicit Analytic Transition Densities of Diffusion Processes with General Diploid Selection

PubMed Central

Song, Yun S.; Steinrücken, Matthias

2012-01-01

The transition density function of the Wright–Fisher diffusion describes the evolution of population-wide allele frequencies over time. This function has important practical applications in population genetics, but finding an explicit formula under a general diploid selection model has remained a difficult open problem. In this article, we develop a new computational method to tackle this classic problem. Specifically, our method explicitly finds the eigenvalues and eigenfunctions of the diffusion generator associated with the Wright–Fisher diffusion with recurrent mutation and arbitrary diploid selection, thus allowing one to obtain an accurate spectral representation of the transition density function. Simplicity is one of the appealing features of our approach. Although our derivation involves somewhat advanced mathematical concepts, the resulting algorithm is quite simple and efficient, only involving standard linear algebra. Furthermore, unlike previous approaches based on perturbation, which is applicable only when the population-scaled selection coefficient is small, our method is nonperturbative and is valid for a broad range of parameter values. As a by-product of our work, we obtain the rate of convergence to the stationary distribution under mutation–selection balance. PMID:22209899
The Minimum-Mass Surface Density of the Solar Nebula using the Disk Evolution Equation

NASA Technical Reports Server (NTRS)

Davis, Sanford S.

2005-01-01

The Hayashi minimum-mass power law representation of the pre-solar nebula (Hayashi 1981, Prog. Theo. Phys.70,35) is revisited using analytic solutions of the disk evolution equation. A new cumulative-planetary-mass-model (an integrated form of the surface density) is shown to predict a smoother surface density compared with methods based on direct estimates of surface density from planetary data. First, a best-fit transcendental function is applied directly to the cumulative planetary mass data with the surface density obtained by direct differentiation. Next a solution to the time-dependent disk evolution equation is parametrically adapted to the planetary data. The latter model indicates a decay rate of r -1/2 in the inner disk followed by a rapid decay which results in a sharper outer boundary than predicted by the minimum mass model. The model is shown to be a good approximation to the finite-size early Solar Nebula and by extension to extra solar protoplanetary disks.
Understanding redshift space distortions in density-weighted peculiar velocity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sugiyama, Naonori S.; Okumura, Teppei; Spergel, David N., E-mail: nao.s.sugiyama@gmail.com, E-mail: teppei.oku@gmail.com, E-mail: dns@astro.princeton.edu

2016-07-01

Observations of the kinetic Sunyaev-Zel'dovich (kSZ) effect measure the density-weighted velocity field, a potentially powerful cosmological probe. This paper presents an analytical method to predict the power spectrum and two-point correlation function of the density-weighted velocity in redshift space, the direct observables in kSZ surveys. We show a simple relation between the density power spectrum and the density-weighted velocity power spectrum that holds for both dark matter and halos. Using this relation, we can then extend familiar perturbation expansion techniques to the kSZ power spectrum. One of the most important features of density-weighted velocity statistics in redshift space is themore » change in sign of the cross-correlation between the density and density-weighted velocity at mildly small scales due to nonlinear redshift space distortions. Our model can explain this characteristic feature without any free parameters. As a result, our results can precisely predict the non-linear behavior of the density-weighted velocity field in redshift space up to ∼ 30 h {sup -1} Mpc for dark matter particles at the redshifts of z =0.0, 0.5, and 1.0.« less
High density lipoproteins: Measurement techniques and potential biomarkers of cardiovascular risk

PubMed Central

Hafiane, Anouar; Genest, Jacques

2015-01-01

Plasma high density lipoprotein cholesterol (HDL) comprises a heterogeneous family of lipoprotein species, differing in surface charge, size and lipid and protein compositions. While HDL cholesterol (C) mass is a strong, graded and coherent biomarker of cardiovascular risk, genetic and clinical trial data suggest that the simple measurement of HDL-C may not be causal in preventing atherosclerosis nor reflect HDL functionality. Indeed, the measurement of HDL-C may be a biomarker of cardiovascular health. To assess the issue of HDL function as a potential therapeutic target, robust and simple analytical methods are required. The complex pleiotropic effects of HDL make the development of a single measurement challenging. Development of laboratory assays that accurately HDL function must be developed validated and brought to high-throughput for clinical purposes. This review discusses the limitations of current laboratory technologies for methods that separate and quantify HDL and potential application to predict CVD, with an emphasis on emergent approaches as potential biomarkers in clinical practice. PMID:26674734
Macroscopic dielectric function within time-dependent density functional theory—Real time evolution versus the Casida approach

NASA Astrophysics Data System (ADS)

Sander, Tobias; Kresse, Georg

2017-02-01

Linear optical properties can be calculated by solving the time-dependent density functional theory equations. Linearization of the equation of motion around the ground state orbitals results in the so-called Casida equation, which is formally very similar to the Bethe-Salpeter equation. Alternatively one can determine the spectral functions by applying an infinitely short electric field in time and then following the evolution of the electron orbitals and the evolution of the dipole moments. The long wavelength response function is then given by the Fourier transformation of the evolution of the dipole moments in time. In this work, we compare the results and performance of these two approaches for the projector augmented wave method. To allow for large time steps and still rely on a simple difference scheme to solve the differential equation, we correct for the errors in the frequency domain, using a simple analytic equation. In general, we find that both approaches yield virtually indistinguishable results. For standard density functionals, the time evolution approach is, with respect to the computational performance, clearly superior compared to the solution of the Casida equation. However, for functionals including nonlocal exchange, the direct solution of the Casida equation is usually much more efficient, even though it scales less beneficial with the system size. We relate this to the large computational prefactors in evaluating the nonlocal exchange, which renders the time evolution algorithm fairly inefficient.
Computational studies on scattering of radio frequency waves by density filaments in fusion plasmas

NASA Astrophysics Data System (ADS)

Ioannidis, Zisis C.; Ram, Abhay K.; Hizanidis, Kyriakos; Tigelis, Ioannis G.

2017-10-01

In modern magnetic fusion devices, such as tokamaks and stellarators, radio frequency (RF) waves are commonly used for plasma heating and current profile control, as well as for certain diagnostics. The frequencies of the RF waves range from ion cyclotron frequency to the electron cyclotron frequency. The RF waves are launched from structures, like waveguides and current straps, placed near the wall in a very low density, tenuous plasma region of a fusion device. The RF electromagnetic fields have to propagate through this scrape-off layer before coupling power to the core of the plasma. The scrape-off layer is characterized by turbulent plasmas fluctuations and by blobs and filaments. The variations in the edge density due to these fluctuations and filaments can affect the propagation characteristics of the RF waves—changes in density leading to regions with differing plasma permittivity. Analytical full-wave theories have shown that scattering by blobs and filaments can alter the RF power flow into the core of the plasma in a variety of ways, such as through reflection, refraction, diffraction, and shadowing [see, for example, Ram and Hizanidis, Phys. Plasmas 23, 022504 (2016), and references therein]. There are changes in the wave vectors and the distribution of power-scattering leading to coupling of the incident RF wave to other plasma waves, side-scattering, surface waves, and fragmentation of the Poynting flux in the direction towards the core. However, these theoretical models are somewhat idealized. In particular, it is assumed that there is step-function discontinuity in the density between the plasma inside the filament and the background plasma. In this paper, results from numerical simulations of RF scattering by filaments using a commercial full-wave code are described. The filaments are taken to be cylindrical with the axis of the cylinder aligned along the direction of the ambient magnetic field. The plasma inside and outside the filament is assumed to be cold. There are three primary objectives of these studies. The first objective is to validate the numerical simulations by comparing with the analytical results for the same plasma description—a step-function discontinuity in density. A detailed comparison of the Poynting flux shows that numerical simulations lead to the same results as those from the theoretical model. The second objective is to extend the simulations to take into account a smooth transition in density from the background plasma to the interior of the filament. The ensuing comparison shows that the deviations from the results of the theoretical model are quite small. The third objective is to consider the scattering process for situations well beyond a reasonable theoretical analysis. This includes scattering off multiple filaments with different densities and sizes. Simulations for these complex arrangements of filaments show that, in spite of the obvious limitations, the essential physics of RF scattering is captured by the analytical theory for a single filament.
New method for estimating low-earth-orbit collision probabilities

NASA Technical Reports Server (NTRS)

Vedder, John D.; Tabor, Jill L.

1991-01-01

An unconventional but general method is described for estimating the probability of collision between an earth-orbiting spacecraft and orbital debris. This method uses a Monte Caralo simulation of the orbital motion of the target spacecraft and each discrete debris object to generate an empirical set of distances, each distance representing the separation between the spacecraft and the nearest debris object at random times. Using concepts from the asymptotic theory of extreme order statistics, an analytical density function is fitted to this set of minimum distances. From this function, it is possible to generate realistic collision estimates for the spacecraft.
Bayesian inference based on stationary Fokker-Planck sampling.

PubMed

Berrones, Arturo

2010-06-01

A novel formalism for bayesian learning in the context of complex inference models is proposed. The method is based on the use of the stationary Fokker-Planck (SFP) approach to sample from the posterior density. Stationary Fokker-Planck sampling generalizes the Gibbs sampler algorithm for arbitrary and unknown conditional densities. By the SFP procedure, approximate analytical expressions for the conditionals and marginals of the posterior can be constructed. At each stage of SFP, the approximate conditionals are used to define a Gibbs sampling process, which is convergent to the full joint posterior. By the analytical marginals efficient learning methods in the context of artificial neural networks are outlined. Offline and incremental bayesian inference and maximum likelihood estimation from the posterior are performed in classification and regression examples. A comparison of SFP with other Monte Carlo strategies in the general problem of sampling from arbitrary densities is also presented. It is shown that SFP is able to jump large low-probability regions without the need of a careful tuning of any step-size parameter. In fact, the SFP method requires only a small set of meaningful parameters that can be selected following clear, problem-independent guidelines. The computation cost of SFP, measured in terms of loss function evaluations, grows linearly with the given model's dimension.
Fast-sausage oscillations in coronal loops with smooth boundary

NASA Astrophysics Data System (ADS)

Lopin, I.; Nagorny, I.

2014-12-01

Aims: The effect of the transition layer (shell) in nonuniform coronal loops with a continuous radial density profile on the properties of fast-sausage modes are studied analytically and numerically. Methods: We modeled the coronal waveguide as a structured tube consisting of a cord and a transition region (shell) embedded within a magnetic uniform environment. The derived general dispersion relation was investigated analytically and numerically in the context of frequency, cut-off wave number, and the damping rate of fast-sausage oscillations for various values of loop parameters. Results: The frequency of the global fast-sausage mode in the loops with a diffuse (or smooth) boundary is determined mainly by the external Alfvén speed and longitudinal wave number. The damping rate of such a mode can be relatively low. The model of coronal loop with diffuse boundary can support a comparatively low-frequency, global fast-sausage mode of detectable quality without involving extremely low values of the density contrast. The effect of thin transition layer (corresponds to the loops with steep boundary) is negligible and produces small reductions of oscillation frequency and relative damping rate in comparison with the case of step-function density profile. Seismological application of obtained results gives the estimated Alfvén speed outside the flaring loop about 3.25 Mm/s.
Deep and wide gaps by super Earths in low-viscosity discs

NASA Astrophysics Data System (ADS)

Ginzburg, Sivan; Sari, Re'em

2018-06-01

Planets can open cavities (gaps) in the protoplanetary gaseous discs in which they are born by exerting gravitational torques. Viscosity counters these torques and limits the depletion of the gaps. We present a simple one-dimensional scheme to calculate the gas density profile inside gaps by balancing the gravitational and viscous torques. By generalizing the results of Goodman & Rafikov (2001), our scheme properly accounts for the propagation of angular momentum by density waves. This method allows us to easily study low-viscosity discs, which are challenging for full hydrodynamical simulations. We complement our numerical integration by analytical equations for the gap's steady-state depth and width as a function of the planet's to star's mass ratio μ, the gas disc's aspect ratio h, and its Shakura & Sunyaev viscosity parameter α. Specifically, we focus on low-mass planets (μ < μth ≡ h3) and identify a new low-viscosity regime, α < h(μ/μth)5, in which the classical analytical scaling relations are invalid. Equivalently, this low-viscosity regime applies to every gap that is depleted by more than a factor of (μth/μ)3 relative to the unperturbed density. We show that such gaps are significantly deeper and wider than previously thought, and consequently take a longer time to reach equilibrium.
Two is better than one: joint statistics of density and velocity in concentric spheres as a cosmological probe

NASA Astrophysics Data System (ADS)

Uhlemann, C.; Codis, S.; Hahn, O.; Pichon, C.; Bernardeau, F.

2017-08-01

The analytical formalism to obtain the probability distribution functions (PDFs) of spherically averaged cosmic densities and velocity divergences in the mildly non-linear regime is presented. A large-deviation principle is applied to those cosmic fields assuming their most likely dynamics in spheres is set by the spherical collapse model. We validate our analytical results using state-of-the-art dark matter simulations with a phase-space resolved velocity field finding a 2 per cent level agreement for a wide range of velocity divergences and densities in the mildly non-linear regime (˜10 Mpc h-1 at redshift zero), usually inaccessible to perturbation theory. From the joint PDF of densities and velocity divergences measured in two concentric spheres, we extract with the same accuracy velocity profiles and conditional velocity PDF subject to a given over/underdensity that are of interest to understand the non-linear evolution of velocity flows. Both PDFs are used to build a simple but accurate maximum likelihood estimator for the redshift evolution of the variance of both the density and velocity divergence fields, which have smaller relative errors than their sample variances when non-linearities appear. Given the dependence of the velocity divergence on the growth rate, there is a significant gain in using the full knowledge of both PDFs to derive constraints on the equation of state-of-dark energy. Thanks to the insensitivity of the velocity divergence to bias, its PDF can be used to obtain unbiased constraints on the growth of structures (σ8, f) or it can be combined with the galaxy density PDF to extract bias parameters.
Poisson-Boltzmann theory of the charge-induced adsorption of semi-flexible polyelectrolytes.

PubMed

Ubbink, Job; Khokhlov, Alexei R

2004-03-15

A model is suggested for the structure of an adsorbed layer of a highly charged semi-flexible polyelectrolyte on a weakly charged surface of opposite charge sign. The adsorbed phase is thin, owing to the effective reversal of the charge sign of the surface upon adsorption, and ordered, owing to the high surface density of polyelectrolyte strands caused by the generally strong binding between polyelectrolyte and surface. The Poisson-Boltzmann equation for the electrostatic interaction between the array of adsorbed polyelectrolytes and the charged surface is solved for a cylindrical geometry, both numerically, using a finite element method, and analytically within the weak curvature limit under the assumption of excess monovalent salt. For small separations, repulsive surface polarization and counterion osmotic pressure effects dominate over the electrostatic attraction and the resulting electrostatic interaction curve shows a minimum at nonzero separations on the Angstrom scale. The equilibrium density of the adsorbed phase is obtained by minimizing the total free energy under the condition of equality of chemical potential and osmotic pressure of the polyelectrolyte in solution and in the adsorbed phase. For a wide range of ionic conditions and charge densities of the charged surface, the interstrand separation as predicted by the Poisson-Boltzmann model and the analytical theory closely agree. For low to moderate charge densities of the adsorbing surface, the interstrand spacing decreases as a function of the charge density of the charged surface. Above about 0.1 M excess monovalent salt, it is only weakly dependent on the ionic strength. At high charge densities of the adsorbing surface, the interstrand spacing increases with increasing ionic strength, in line with the experiments by Fang and Yang [J. Phys. Chem. B 101, 441 (1997)]. (c) 2004 American Institute of Physics.

SU-C-204-01: A Fast Analytical Approach for Prompt Gamma and PET Predictions in a TPS for Proton Range Verification

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kroniger, K; Herzog, M; Landry, G

2015-06-15

Purpose: We describe and demonstrate a fast analytical tool for prompt-gamma emission prediction based on filter functions applied on the depth dose profile. We present the implementation in a treatment planning system (TPS) of the same algorithm for positron emitter distributions. Methods: The prediction of the desired observable is based on the convolution of filter functions with the depth dose profile. For both prompt-gammas and positron emitters, the results of Monte Carlo simulations (MC) are compared with those of the analytical tool. For prompt-gamma emission from inelastic proton-induced reactions, homogeneous and inhomogeneous phantoms alongside with patient data are used asmore » irradiation targets of mono-energetic proton pencil beams. The accuracy of the tool is assessed in terms of the shape of the analytically calculated depth profiles and their absolute yields, compared to MC. For the positron emitters, the method is implemented in a research RayStation TPS and compared to MC predictions. Digital phantoms and patient data are used and positron emitter spatial density distributions are analyzed. Results: Calculated prompt-gamma profiles agree with MC within 3 % in terms of absolute yield and reproduce the correct shape. Based on an arbitrary reference material and by means of 6 filter functions (one per chemical element), profiles in any other material composed of those elements can be predicted. The TPS implemented algorithm is accurate enough to enable, via the analytically calculated positron emitters profiles, detection of range differences between the TPS and MC with errors of the order of 1–2 mm. Conclusion: The proposed analytical method predicts prompt-gamma and positron emitter profiles which generally agree with the distributions obtained by a full MC. The implementation of the tool in a TPS shows that reliable profiles can be obtained directly from the dose calculated by the TPS, without the need of full MC simulation.« less
Analytical solutions for tomato peeling with combined heat flux and convective boundary conditions

NASA Astrophysics Data System (ADS)

Cuccurullo, G.; Giordano, L.; Metallo, A.

2017-11-01

Peeling of tomatoes by radiative heating is a valid alternative to steam or lye, which are expensive and pollutant methods. Suitable energy densities are required in order to realize short time operations, thus involving only a thin layer under the tomato surface. This paper aims to predict the temperature field in rotating tomatoes exposed to the source irradiation. Therefore, a 1D unsteady analytical model is presented, which involves a semi-infinite slab subjected to time dependent heating while convective heat transfer takes place on the exposed surface. In order to account for the tomato rotation, the heat source is described as the positive half-wave of a sinusoidal function. The problem being linear, the solution is derived following the Laplace Transform Method. In addition, an easy-to-handle solution for the problem at hand is presented, which assumes a differentiable function for approximating the source while neglecting convective cooling, the latter contribution turning out to be negligible for the context at hand. A satisfying agreement between the two analytical solutions is found, therefore, an easy procedure for a proper design of the dry heating system can be set up avoiding the use of numerical simulations.
Development and application of accurate analytical models for single active electron potentials

NASA Astrophysics Data System (ADS)

Miller, Michelle; Jaron-Becker, Agnieszka; Becker, Andreas

2015-05-01

The single active electron (SAE) approximation is a theoretical model frequently employed to study scenarios in which inner-shell electrons may productively be treated as frozen spectators to a physical process of interest, and accurate analytical approximations for these potentials are sought as a useful simulation tool. Density function theory is often used to construct a SAE potential, requiring that a further approximation for the exchange correlation functional be enacted. In this study, we employ the Krieger, Li, and Iafrate (KLI) modification to the optimized-effective-potential (OEP) method to reduce the complexity of the problem to the straightforward solution of a system of linear equations through simple arguments regarding the behavior of the exchange-correlation potential in regions where a single orbital dominates. We employ this method for the solution of atomic and molecular potentials, and use the resultant curve to devise a systematic construction for highly accurate and useful analytical approximations for several systems. Supported by the U.S. Department of Energy (Grant No. DE-FG02-09ER16103), and the U.S. National Science Foundation (Graduate Research Fellowship, Grants No. PHY-1125844 and No. PHY-1068706).
Ionic fluids with r-6 pair interactions have power-law electrostatic screening

NASA Astrophysics Data System (ADS)

Kjellander, Roland; Forsberg, Björn

2005-06-01

The decay behaviour of radial distribution functions for large distances r is investigated for classical Coulomb fluids where the ions interact with an r-6 potential (e.g. a dispersion interaction) in addition to the Coulombic and the short-range repulsive potentials (e.g. a hard core). The pair distributions and the density-density (NN), charge-density (QN) and charge-charge (QQ) correlation functions are investigated analytically and by Monte Carlo simulations. It is found that the NN correlation function ultimately decays like r-6 for large r, just as it does for fluids of electroneutral particles interacting with an r-6 potential. The prefactor is proportional to the squared compressibility in both cases. The QN correlations decay in general like r-8 and the QQ correlations like r-10 in the ionic fluid. The average charge density around an ion decays generally like r-8 and the average electrostatic potential like r-6. This behaviour is in stark contrast to the decay behaviour for classical Coulomb fluids in the absence of the r-6 potential, where all these functions decay exponentially for large r. The power-law decays are, however, the same as for quantum Coulomb fluids. This indicates that the inclusion of the dispersion interaction as an effective r-6 interaction potential in classical systems yields the same decay behaviour for the pair correlations as in quantum ionic systems. An exceptional case is the completely symmetric binary electrolyte for which only the NN correlation has a power-law decay but not the QQ correlations. These features are shown by an analysis of the bridge function.
A predator-prey model with a holling type I functional response including a predator mutual interference

USGS Publications Warehouse

Seo, G.; DeAngelis, D.L.

2011-01-01

The most widely used functional response in describing predator-prey relationships is the Holling type II functional response, where per capita predation is a smooth, increasing, and saturating function of prey density. Beddington and DeAngelis modified the Holling type II response to include interference of predators that increases with predator density. Here we introduce a predator-interference term into a Holling type I functional response. We explain the ecological rationale for the response and note that the phase plane configuration of the predator and prey isoclines differs greatly from that of the Beddington-DeAngelis response; for example, in having three possible interior equilibria rather than one. In fact, this new functional response seems to be quite unique. We used analytical and numerical methods to show that the resulting system shows a much richer dynamical behavior than the Beddington-DeAngelis response, or other typically used functional responses. For example, cyclic-fold, saddle-fold, homoclinic saddle connection, and multiple crossing bifurcations can all occur. We then use a smooth approximation to the Holling type I functional response with predator mutual interference to show that these dynamical properties do not result from the lack of smoothness, but rather from subtle differences in the functional responses. ?? 2011 Springer Science+Business Media, LLC.
Evaluation of physics-based numerical modelling for diverse design architecture of perovskite solar cells

NASA Astrophysics Data System (ADS)

Mishra, A. K.; Catalan, Jorge; Camacho, Diana; Martinez, Miguel; Hodges, D.

2017-08-01

Solution processed organic-inorganic metal halide perovskite based solar cells are emerging as a new cost effective photovoltaic technology. In the context of increasing the power conversion efficiency (PCE) and sustainability of perovskite solar cells (PSC) devices, we comprehensively analyzed a physics-based numerical modelling for doped and un-doped PSC devices. Our analytics emphasized the role of different charge carrier layers from the view point of interfacial adhesion and its influence on charge extraction rate and charge recombination mechanism. Morphological and charge transport properties of perovskite thin film as a function of device architecture are also considered to investigate the photovoltaic properties of PSC. We observed that photocurrent is dominantly influenced by interfacial recombination process and photovoltage has functional relationship with defect density of perovskite absorption layer. A novel contour mapping method to understand the characteristics of current density-voltage (J-V) curves for each device as a function of perovskite layer thickness provide an important insight about the distribution spectrum of photovoltaic properties. Functional relationship of device efficiency and fill factor with absorption layer thickness are also discussed.
Calculation of electron spectra and some problems in the thermodynamics of graphene layers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alisultanov, Z. Z., E-mail: zaur0102@gmail.com

The expressions for the energy spectra of monolayer, bilayer, and multilayer graphene, as well as epitaxial graphene, are derived using the quantum Green’s functions method. Analytic expressions are obtained for the densities of states of these systems. It is shown that a bandgap can appear the spectrum of an epitaxial graphene bilayer. A number of problems in the thermodynamics of electrons in free and epitaxial graphene layers are considered as applications. Analytic expressions are obtained for the chemical potential and heat capacity in the limiting cases of low and high temperatures. Quantum oscillations of heat capacity in graphene are analyzedmore » taking into account the Coulomb interaction. The Berry phase of epitaxial graphene is investigated.« less
Analytical bond order potential for simulations of BeO 1D and 2D nanostructures and plasma-surface interactions

NASA Astrophysics Data System (ADS)

Byggmästar, J.; Hodille, E. A.; Ferro, Y.; Nordlund, K.

2018-04-01

An analytical interatomic bond order potential for the Be-O system is presented. The potential is fitted and compared to a large database of bulk BeO and point defect properties obtained using density functional theory. Its main applications include simulations of plasma-surface interactions involving oxygen or oxide layers on beryllium, as well as simulations of BeO nanotubes and nanosheets. We apply the potential in a study of oxygen irradiation of Be surfaces, and observe the early stages of an oxide layer forming on the Be surface. Predicted thermal and elastic properties of BeO nanotubes and nanosheets are simulated and compared with published ab initio data.
An analytical and experimental investigation of resistojet plumes

NASA Technical Reports Server (NTRS)

Zana, L. M.; Hoffman, D. J.; Breyley, L. R.; Serafini, J. S.

1987-01-01

As a part of the electrothermal propulsion plume research program at the NASA Lewis Research Center, efforts have been initiated to analytically and experimentally investigate the plumes of resistojet thrusters. The method of G.A. Simons for the prediction of rocket exhaust plumes is developed for the resistojet. Modifications are made to the source flow equations to account for the increased effects of the relatively large nozzle boundary layer. Additionally, preliminary mass flux measurements of a laboratory resistojet using CO2 propellant at 298 K have been obtained with a cryogenically cooled quartz crystal microbalance (QCM). There is qualitative agreement between analysis and experiment, at least in terms of the overall number density shape functions in the forward flux region.
Inviscid linear stability analysis of two vertical columns of different densities in a gravitational acceleration field

DOE PAGES

Prathama, Aditya Heru; Pantano, Carlos

2017-08-09

Here, we study the inviscid linear stability of a vertical interface separating two fluids of different densities and subject to a gravitational acceleration field parallel to the interface. In this arrangement, the two free streams are constantly accelerated, which means that the linear stability analysis is not amenable to Fourier or Laplace solution in time. Instead, we derive the equations analytically by the initial-value problem method and express the solution in terms of the well-known parabolic cylinder function. The results, which can be classified as an accelerating Kelvin–Helmholtz configuration, show that even in the presence of surface tension, the interfacemore » is unconditionally unstable at all wavemodes. This is a consequence of the ever increasing momentum of the free streams, as gravity accelerates them indefinitely. The instability can be shown to grow as the exponential of a quadratic function of time.« less
Analysis of a photon assisted field emission device

NASA Astrophysics Data System (ADS)

Jensen, K. L.; Lau, Y. Y.; McGregor, D. S.

2000-07-01

A field emitter array held at the threshold of emission by a dc gate potential from which current pulses are triggered by the application of a laser pulse on the backside of the semiconductor may produce electron bunches ("density modulation") at gigahertz frequencies. We develop an analytical model of such optically controlled emission from a silicon tip using a modified Wentzel-Kramers-Brillouin and Airy function approach to solving Schrödinger's equation. Band bending and an approximation to the exchange-correlation effects on the image charge potential are included for an array of hyperbolic emitters with a distribution in tip radii and work function. For a simple relationship between the incident photon flux and the resultant electron density at the emission site, an estimation of the tunneling current is made. An example of the operation and design of such a photon-assisted field emission device is given.
Divergence of perturbation theory in large scale structures

NASA Astrophysics Data System (ADS)

Pajer, Enrico; van der Woude, Drian

2018-05-01

We make progress towards an analytical understanding of the regime of validity of perturbation theory for large scale structures and the nature of some non-perturbative corrections. We restrict ourselves to 1D gravitational collapse, for which exact solutions before shell crossing are known. We review the convergence of perturbation theory for the power spectrum, recently proven by McQuinn and White [1], and extend it to non-Gaussian initial conditions and the bispectrum. In contrast, we prove that perturbation theory diverges for the real space two-point correlation function and for the probability density function (PDF) of the density averaged in cells and all the cumulants derived from it. We attribute these divergences to the statistical averaging intrinsic to cosmological observables, which, even on very large and "perturbative" scales, gives non-vanishing weight to all extreme fluctuations. Finally, we discuss some general properties of non-perturbative effects in real space and Fourier space.
Methods and limitations in radar target imagery

NASA Astrophysics Data System (ADS)

Bertrand, P.

An analytical examination of the reflectivity of radar targets is presented for the two-dimensional case of flat targets. A complex backscattering coefficient is defined for the amplitude and phase of the received field in comparison with the emitted field. The coefficient is dependent on the frequency of the emitted signal and the orientation of the target with respect to the transmitter. The target reflection is modeled in terms of the density of illumined, colored points independent from one another. The target therefore is represented as an infinite family of densities indexed by the observational angle. Attention is given to the reflectivity parameters and their distribution function, and to the conjunct distribution function for the color, position, and the directivity of bright points. It is shown that a fundamental ambiguity exists between the localization of the illumined points and the determination of their directivity and color.
Dynamic Optical Tuning of Interlayer Interactions in the Transition Metal Dichalcogenides

DOE PAGES

Mannebach, Ehren M.; Nyby, Clara; Ernst, Friederike; ...

2017-11-09

Modulation of weak interlayer interactions between quasi-two-dimensional atomic planes in the transition metal dichalcogenides (TMDCs) provides avenues for tuning their functional properties. Here we show that above-gap optical excitation in the TMDCs leads to an unexpected large-amplitude, ultrafast compressive force between the two-dimensional layers, as probed by in situ measurements of the atomic layer spacing at femtosecond time resolution. We show that this compressive response arises from a dynamic modulation of the interlayer van der Waals interaction and that this represents the dominant light-induced stress at low excitation densities. A simple analytic model predicts the magnitude and carrier density dependencemore » of the measured strains. Furthermore, this work establishes a new method for dynamic, nonequilibrium tuning of correlation-driven dispersive interactions and of the optomechanical functionality of TMDC quasi-two-dimensional materials.« less
Performance of mixed RF/FSO systems in exponentiated Weibull distributed channels

NASA Astrophysics Data System (ADS)

Zhao, Jing; Zhao, Shang-Hong; Zhao, Wei-Hu; Liu, Yun; Li, Xuan

2017-12-01

This paper presented the performances of asymmetric mixed radio frequency (RF)/free-space optical (FSO) system with the amplify-and-forward relaying scheme. The RF channel undergoes Nakagami- m channel, and the Exponentiated Weibull distribution is adopted for the FSO component. The mathematical formulas for cumulative distribution function (CDF), probability density function (PDF) and moment generating function (MGF) of equivalent signal-to-noise ratio (SNR) are achieved. According to the end-to-end statistical characteristics, the new analytical expressions of outage probability are obtained. Under various modulation techniques, we derive the average bit-error-rate (BER) based on the Meijer's G function. The evaluation and simulation are provided for the system performance, and the aperture average effect is discussed as well.
Sum rules for the uniform-background model of an atomic-sharp metal corner

NASA Astrophysics Data System (ADS)

Streitenberger, P.

1994-04-01

Analytical results are derived for the electrostatic potential of an atomic-sharp 90° metal corner in the uniform-background model. The electrostatic potential at a free jellium edge and the jellium corner, respectively, is determined exactly in terms of the energy per electron of the uniform electron gas integrated over the background density. The surface energy, the edge formation energy and the derivative of the corner formation energy with respect to the background density are given as integrals over the electrostatic potential. The present approach represents a novel approach to such sum rules, inclusive of the Budd-Vannimenus sum rules for a free jellium surface, based on general properties of linear response functions.
Quantitative characterization of surface topography using spectral analysis

NASA Astrophysics Data System (ADS)

Jacobs, Tevis D. B.; Junge, Till; Pastewka, Lars

2017-03-01

Roughness determines many functional properties of surfaces, such as adhesion, friction, and (thermal and electrical) contact conductance. Recent analytical models and simulations enable quantitative prediction of these properties from knowledge of the power spectral density (PSD) of the surface topography. The utility of the PSD is that it contains statistical information that is unbiased by the particular scan size and pixel resolution chosen by the researcher. In this article, we first review the mathematical definition of the PSD, including the one- and two-dimensional cases, and common variations of each. We then discuss strategies for reconstructing an accurate PSD of a surface using topography measurements at different size scales. Finally, we discuss detecting and mitigating artifacts at the smallest scales, and computing upper/lower bounds on functional properties obtained from models. We accompany our discussion with virtual measurements on computer-generated surfaces. This discussion summarizes how to analyze topography measurements to reconstruct a reliable PSD. Analytical models demonstrate the potential for tuning functional properties by rationally tailoring surface topography—however, this potential can only be achieved through the accurate, quantitative reconstruction of the PSDs of real-world surfaces.
Exact nonstationary responses of rectangular thin plate on Pasternak foundation excited by stochastic moving loads

NASA Astrophysics Data System (ADS)

Chen, Guohai; Meng, Zeng; Yang, Dixiong

2018-01-01

This paper develops an efficient method termed as PE-PIM to address the exact nonstationary responses of pavement structure, which is modeled as a rectangular thin plate resting on bi-parametric Pasternak elastic foundation subjected to stochastic moving loads with constant acceleration. Firstly, analytical power spectral density (PSD) functions of random responses for thin plate are derived by integrating pseudo excitation method (PEM) with Duhamel's integral. Based on PEM, the new equivalent von Mises stress (NEVMS) is proposed, whose PSD function contains all cross-PSD functions between stress components. Then, the PE-PIM that combines the PEM with precise integration method (PIM) is presented to achieve efficiently stochastic responses of the plate by replacing Duhamel's integral with the PIM. Moreover, the semi-analytical Monte Carlo simulation is employed to verify the computational results of the developed PE-PIM. Finally, numerical examples demonstrate the high accuracy and efficiency of PE-PIM for nonstationary random vibration analysis. The effects of velocity and acceleration of moving load, boundary conditions of the plate and foundation stiffness on the deflection and NEVMS responses are scrutinized.
Electron momentum density and Compton profile by a semi-empirical approach

NASA Astrophysics Data System (ADS)

Aguiar, Julio C.; Mitnik, Darío; Di Rocco, Héctor O.

2015-08-01

Here we propose a semi-empirical approach to describe with good accuracy the electron momentum densities and Compton profiles for a wide range of pure crystalline metals. In the present approach, we use an experimental Compton profile to fit an analytical expression for the momentum densities of the valence electrons. This expression is similar to a Fermi-Dirac distribution function with two parameters, one of which coincides with the ground state kinetic energy of the free-electron gas and the other resembles the electron-electron interaction energy. In the proposed scheme conduction electrons are neither completely free nor completely bound to the atomic nucleus. This procedure allows us to include correlation effects. We tested the approach for all metals with Z=3-50 and showed the results for three representative elements: Li, Be and Al from high-resolution experiments.
Using the MCNP Taylor series perturbation feature (efficiently) for shielding problems

NASA Astrophysics Data System (ADS)

Favorite, Jeffrey

2017-09-01

The Taylor series or differential operator perturbation method, implemented in MCNP and invoked using the PERT card, can be used for efficient parameter studies in shielding problems. This paper shows how only two PERT cards are needed to generate an entire parameter study, including statistical uncertainty estimates (an additional three PERT cards can be used to give exact statistical uncertainties). One realistic example problem involves a detailed helium-3 neutron detector model and its efficiency as a function of the density of its high-density polyethylene moderator. The MCNP differential operator perturbation capability is extremely accurate for this problem. A second problem involves the density of the polyethylene reflector of the BeRP ball and is an example of first-order sensitivity analysis using the PERT capability. A third problem is an analytic verification of the PERT capability.

Structural arrest in an ideal gas.

PubMed

van Ketel, Willem; Das, Chinmay; Frenkel, Daan

2005-04-08

We report a molecular dynamics study of a simple model system that has the static properties of an ideal gas, yet exhibits nontrivial "glassy" dynamics behavior at high densities. The constituent molecules of this system are constructs of three infinitely thin hard rods of length L, rigidly joined at their midpoints. The crosses have random but fixed orientation. The static properties of this system are those of an ideal gas, and its collision frequency can be computed analytically. For number densities NL(3)/V>1, the single-particle diffusivity goes to zero. As the system is completely structureless, standard mode-coupling theory cannot describe the observed structural arrest. Nevertheless, the system exhibits many dynamical features that appear to be mode-coupling-like. All high-density incoherent intermediate scattering functions collapse onto master curves that depend only on the wave vector.
Universal scaling relations in scale-free structure formation

NASA Astrophysics Data System (ADS)

Guszejnov, Dávid; Hopkins, Philip F.; Grudić, Michael Y.

2018-07-01

A large number of astronomical phenomena exhibit remarkably similar scaling relations. The most well-known of these is the mass distribution dN/dM ∝ M-2 which (to first order) describes stars, protostellar cores, clumps, giant molecular clouds, star clusters, and even dark matter haloes. In this paper we propose that this ubiquity is not a coincidence and that it is the generic result of scale-free structure formation where the different scales are uncorrelated. We show that all such systems produce a mass function proportional to M-2 and a column density distribution with a power-law tail of dA/dln Σ ∝ Σ-1. In the case where structure formation is controlled by gravity the two-point correlation becomes ξ2D ∝ R-1. Furthermore, structures formed by such processes (e.g. young star clusters, DM haloes) tend to a ρ ∝ R-3 density profile. We compare these predictions with observations, analytical fragmentation cascade models, semi-analytical models of gravito-turbulent fragmentation, and detailed `full physics' hydrodynamical simulations. We find that these power laws are good first-order descriptions in all cases.
Universal Scaling Relations in Scale-Free Structure Formation

NASA Astrophysics Data System (ADS)

Guszejnov, Dávid; Hopkins, Philip F.; Grudić, Michael Y.

2018-04-01

A large number of astronomical phenomena exhibit remarkably similar scaling relations. The most well-known of these is the mass distribution dN/dM∝M-2 which (to first order) describes stars, protostellar cores, clumps, giant molecular clouds, star clusters and even dark matter halos. In this paper we propose that this ubiquity is not a coincidence and that it is the generic result of scale-free structure formation where the different scales are uncorrelated. We show that all such systems produce a mass function proportional to M-2 and a column density distribution with a power law tail of dA/d lnΣ∝Σ-1. In the case where structure formation is controlled by gravity the two-point correlation becomes ξ2D∝R-1. Furthermore, structures formed by such processes (e.g. young star clusters, DM halos) tend to a ρ∝R-3 density profile. We compare these predictions with observations, analytical fragmentation cascade models, semi-analytical models of gravito-turbulent fragmentation and detailed "full physics" hydrodynamical simulations. We find that these power-laws are good first order descriptions in all cases.
DOE Office of Scientific and Technical Information (OSTI.GOV)

Noronha, Jorge; Denicol, Gabriel S.

In this paper we obtain an analytical solution of the relativistic Boltzmann equation under the relaxation time approximation that describes the out-of-equilibrium dynamics of a radially expanding massless gas. This solution is found by mapping this expanding system in flat spacetime to a static flow in the curved spacetime AdS 2 Ⓧ S 2. We further derive explicit analytic expressions for the momentum dependence of the single-particle distribution function as well as for the spatial dependence of its moments. We find that this dissipative system has the ability to flow as a perfect fluid even though its entropy density doesmore » not match the equilibrium form. The nonequilibrium contribution to the entropy density is shown to be due to higher-order scalar moments (which possess no hydrodynamical interpretation) of the Boltzmann equation that can remain out of equilibrium but do not couple to the energy-momentum tensor of the system. Furthermore, in this system the slowly moving hydrodynamic degrees of freedom can exhibit true perfect fluidity while being totally decoupled from the fast moving, nonhydrodynamical microscopic degrees of freedom that lead to entropy production.« less
Retention modeling for ultra-thin density of Cu-based conductive bridge random access memory (CBRAM)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aga, Fekadu Gochole; Woo, Jiyong; Lee, Sangheon

We investigate the effect of Cu concentration On-state resistance retention characteristics of W/Cu/Ti/HfO{sub 2}/Pt memory cell. The development of RRAM device for application depends on the understanding of the failure mechanism and the key parameters for device optimization. In this study, we develop analytical expression for cations (Cu{sup +}) diffusion model using Gaussian distribution for detailed analysis of data retention time at high temperature. It is found that the improvement of data retention time depends not only on the conductive filament (CF) size but also on Cu atoms concentration density in the CF. Based on the simulation result, better datamore » retention time is observed for electron wave function associated with Cu{sup +} overlap and an extended state formation. This can be verified by analytical calculation of Cu atom defects inside the filament, based on Cu{sup +} diffusion model. The importance of Cu diffusion for the device reliability and the corresponding local temperature of the filament were analyzed by COMSOL Multiphysics simulation.« less
ALMA SPECTROSCOPIC SURVEY IN THE HUBBLE ULTRA DEEP FIELD: CO LUMINOSITY FUNCTIONS AND THE EVOLUTION OF THE COSMIC DENSITY OF MOLECULAR GAS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Decarli, Roberto; Walter, Fabian; Aravena, Manuel

2016-12-10

In this paper we use ASPECS, the ALMA Spectroscopic Survey in the Hubble Ultra Deep Field in band 3 and band 6, to place blind constraints on the CO luminosity function and the evolution of the cosmic molecular gas density as a function of redshift up to z ∼ 4.5. This study is based on galaxies that have been selected solely through their CO emission and not through any other property. In all of the redshift bins the ASPECS measurements reach the predicted “knee” of the CO luminosity function (around 5 × 10{sup 9} K km s{sup −1} pc{sup 2}). We find clear evidence ofmore » an evolution in the CO luminosity function with respect to z ∼ 0, with more CO-luminous galaxies present at z ∼ 2. The observed galaxies at z ∼ 2 also appear more gas-rich than predicted by recent semi-analytical models. The comoving cosmic molecular gas density within galaxies as a function of redshift shows a drop by a factor of 3–10 from z ∼ 2 to z ∼ 0 (with significant error bars), and possibly a decline at z > 3. This trend is similar to the observed evolution of the cosmic star formation rate density. The latter therefore appears to be at least partly driven by the increased availability of molecular gas reservoirs at the peak of cosmic star formation ( z ∼ 2).« less
Status of the Topside Vary-Chap Ionospheric Model

NASA Astrophysics Data System (ADS)

Reinisch, Bodo; Nsumei, Patrick; Huang, Xueqin; Bilitza, Dieter

Status of the Topside Vary-Chap Ionospheric Model The general alpha-Chapman function for a multi-constituent gas which includes a continuously varying scale height and was therefore dubbed the Vary-Chap function, can present the topside electron density profiles in analytical form. The Vary-Chap profile is defined by the scale height function H(h) and the height and density of the F2 layer peak. By expressing 80,000 ISIS-2 measured topside density profiles as Vary-Chap functions we derived 80,000 scale height functions, which form the basis for the topside density profile modeling. The normalized scale height profiles Hn = H(h)/Hm were grouped according to season, MLAT, and MLT for each 50 km height bin from 200 km to 1400 km, and the median, lower, and upper quartiles for each bin were calculated. Hm is the scale height at the F2 layer peak. The resulting Hn functions are modeled in terms of hyperbolic tangent functions using 5 parameters that are determined by multivariate least squares, including the transition height hT where the scale height gradient has a maximum. These normalized scale height functions, representing the model of the topside electron density profiles from hmF2 to 1,400 km altitude, are independent of hmF2 and NmF2 and can therefore be directly used for the topside Ne profile in IRI. Similarly, this model can extend measured bottomside profiles to the topside, replacing the simple alpha-Chapman function with constant scale height that is currently used for construction of the topside profile in the Digisondes / ARTIST of the Global Ionospheric Radio Observatory (GIRO). It turns out that Hm(top) calculated from the topside profiles is generally several times larger than Hm(bot) derived from the bottomside profiles. This follows necessarily from the difference in the definition of the scale height functions for the topside and bottomside profiles. The diurnal variations of the ratio Hm(top) / Hm(bot) has been determined for different latitudes which makes it now possible to specify the topside profile for any given bottomside profile.
Low density lipoprotein for oxidation and metabolic studies. Isolation from small volumes of plasma using a tabletop ultracentrifuge.

PubMed

Himber, J; Bühler, E; Moll, D; Moser, U K

1995-01-01

A rapid method is described for the isolation of small volumes of plasma low density lipoprotein (LDL) free of plasma protein contaminants using the TL-100 Tabletop Ultracentrifuge (Beckman). The isolation of LDL was achieved by a 25 min discontinuous gradient density centrifugation between the density range of 1.006 and 1.21 g/ml, recovery of LDL by tube slicing followed by a 90 min flotation step (d = 1.12 g/ml). The purity of LDL and apolipoprotein B100 (apo B100) were monitored by agarose electrophoresis, sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE), radial immunodiffusion and micropreparative fast protein liquid chromatography (FPLC). The ability of LDL oxidation was assessed by following absorbance at 234 nm after addition of copper ions. The functional integrity of the isolated LDL was checked by clearance kinetics after injection of [125I]-labelled LDL in estrogen-treated rats. The additional purification step led to LDL fractions free of protein contamination and left apo B100, alpha-tocopherol and beta-carotene intact. The LDL prepared in this way was free of albumin, as evident from analytic tests and from its enhanced oxidative modification by copper ions. Used for analytical purposes, this method allows LDL preparations from plasma volumes up to 570 microliters. This method is also convenient for metabolic studies in small animals, especially those relating to the determination of kinetic parameters of LDL in which LDL-apo B100 has to be specifically radiolabelled.
Density functional theory-based simulations of sum frequency generation spectra involving methyl stretching vibrations: effect of the molecular model on the deduced molecular orientation and comparison with an analytical approach.

PubMed

Cecchet, F; Lis, D; Caudano, Y; Mani, A A; Peremans, A; Champagne, B; Guthmuller, J

2012-03-28

The knowledge of the first hyperpolarizability tensor elements of molecular groups is crucial for a quantitative interpretation of the sum frequency generation (SFG) activity of thin organic films at interfaces. Here, the SFG response of the terminal methyl group of a dodecanethiol (DDT) monolayer has been interpreted on the basis of calculations performed at the density functional theory (DFT) level of approximation. In particular, DFT calculations have been carried out on three classes of models for the aliphatic chains. The first class of models consists of aliphatic chains, containing from 3 to 12 carbon atoms, in which only one methyl group can freely vibrate, while the rest of the chain is frozen by a strong overweight of its C and H atoms. This enables us to localize the probed vibrational modes on the methyl group. In the second class, only one methyl group is frozen, while the entire remaining chain is allowed to vibrate. This enables us to analyse the influence of the aliphatic chain on the methyl stretching vibrations. Finally, the dodecanethiol (DDT) molecule is considered, for which the effects of two dielectrics, i.e. n-hexane and n-dodecane, are investigated. Moreover, DDT calculations are also carried out by using different exchange-correlation (XC) functionals in order to assess the DFT approximations. Using the DFT IR vectors and Raman tensors, the SFG spectrum of DDT has been simulated and the orientation of the methyl group has then been deduced and compared with that obtained using an analytical approach based on a bond additivity model. This analysis shows that when using DFT molecular properties, the predicted orientation of the terminal methyl group tends to converge as a function of the alkyl chain length and that the effects of the chain as well as of the dielectric environment are small. Instead, a more significant difference is observed when comparing the DFT-based results with those obtained from the analytical approach, thus indicating the importance of a quantum chemical description of the hyperpolarizability tensor elements of the methyl group. © 2012 IOP Publishing Ltd
Rapid analytical and preparative isolation of functional endosomes by free flow electrophoresis.

PubMed

Marsh, M; Schmid, S; Kern, H; Harms, E; Male, P; Mellman, I; Helenius, A

1987-04-01

Endosomes are prelysosomal organelles that serve as an intracellular site for the sorting, distribution, and processing of receptors, ligands, fluid phase components, and membrane proteins internalized by endocytosis. Whereas the overall functions of endosomes are increasingly understood, little is known about endosome structure, composition, or biogenesis. In this paper, we describe a rapid procedure that permits analytical and preparative isolation of endosomes from a variety of tissue culture cells. The procedure relies on a combination of density gradient centrifugation and free flow electrophoresis. It yields a fraction of highly purified, functionally intact organelles. As markers for endosomes in Chinese hamster ovary cells, we used endocytosed horseradish peroxidase, FITC-conjugated dextran, and [35S]methionine-labeled Semliki Forest virus. Total postnuclear supernatants, crude microsomal pellets, or partially purified Golgi fractions were subjected to free flow electrophoresis. Endosomes and lysosomes migrated together as a single anodally deflected peak separated from most other organelles (plasma membrane, mitochondria, endoplasmic reticulum, and Golgi). The endosomes and lysosomes were then resolved by centrifugation in Percoll density gradients. Endosomes prepared in this way were enriched up to 70-fold relative to the initial homogenate and were still capable of ATP-dependent acidification. By electron microscopy, the isolated organelles were found to consist of electron lucent vacuoles and tubules, many of which could be shown to contain an endocytic tracer (e.g., horseradish peroxidase). SDS PAGE analysis of integral and peripheral membrane proteins (separated from each other by condensation in Triton X-114) revealed a unique and restricted subset of proteins when compared with lysosomes, the unshifted free flow electrophoresis peak, and total cell protein. Altogether, the purification procedure takes 5-6 h and yields amounts of endosomes (150-200 micrograms protein) sufficient for biochemical, immunological, and functional analysis.
Thermostatistical description of gas mixtures from space partitions

NASA Astrophysics Data System (ADS)

Rohrmann, R. D.; Zorec, J.

2006-10-01

The new mathematical framework based on the free energy of pure classical fluids presented by Rohrmann [Physica A 347, 221 (2005)] is extended to multicomponent systems to determine thermodynamic and structural properties of chemically complex fluids. Presently, the theory focuses on D -dimensional mixtures in the low-density limit (packing factor η<0.01 ). The formalism combines the free-energy minimization technique with space partitions that assign an available volume v to each particle. v is related to the closeness of the nearest neighbor and provides a useful tool to evaluate the perturbations experimented by particles in a fluid. The theory shows a close relationship between statistical geometry and statistical mechanics. New, unconventional thermodynamic variables and mathematical identities are derived as a result of the space division. Thermodynamic potentials μil , conjugate variable of the populations Nil of particles class i with the nearest neighbors of class l are defined and their relationships with the usual chemical potentials μi are established. Systems of hard spheres are treated as illustrative examples and their thermodynamics functions are derived analytically. The low-density expressions obtained agree nicely with those of scaled-particle theory and Percus-Yevick approximation. Several pair distribution functions are introduced and evaluated. Analytical expressions are also presented for hard spheres with attractive forces due to Kac-tails and square-well potentials. Finally, we derive general chemical equilibrium conditions.
Exact moments of the Sachdev-Ye-Kitaev model up to order 1 /N 2

NASA Astrophysics Data System (ADS)

García-García, Antonio M.; Jia, Yiyang; Verbaarschot, Jacobus J. M.

2018-04-01

We analytically evaluate the moments of the spectral density of the q-body Sachdev-Ye-Kitaev (SYK) model, and obtain order 1 /N 2 corrections for all moments, where N is the total number of Majorana fermions. To order 1 /N, moments are given by those of the weight function of the Q-Hermite polynomials. Representing Wick contractions by rooted chord diagrams, we show that the 1 /N 2 correction for each chord diagram is proportional to the number of triangular loops of the corresponding intersection graph, with an extra grading factor when q is odd. Therefore the problem of finding 1 /N 2 corrections is mapped to a triangle counting problem. Since the total number of triangles is a purely graph-theoretic property, we can compute them for the q = 1 and q = 2 SYK models, where the exact moments can be obtained analytically using other methods, and therefore we have solved the moment problem for any q to 1 /N 2 accuracy. The moments are then used to obtain the spectral density of the SYK model to order 1 /N 2. We also obtain an exact analytical result for all contraction diagrams contributing to the moments, which can be evaluated up to eighth order. This shows that the Q-Hermite approximation is accurate even for small values of N.
Curvature and frontier orbital energies in density functional theory

NASA Astrophysics Data System (ADS)

Kronik, Leeor; Stein, Tamar; Autschbach, Jochen; Govind, Niranjan; Baer, Roi

2013-03-01

Perdew et al. [Phys. Rev. Lett 49, 1691 (1982)] discovered and proved two different properties of exact Kohn-Sham density functional theory (DFT): (i) The exact total energy versus particle number is a series of linear segments between integer electron points; (ii) Across an integer number of electrons, the exchange-correlation potential may ``jump'' by a constant, known as the derivative discontinuity (DD). Here, we show analytically that in both the original and the generalized Kohn-Sham formulation of DFT, the two are in fact two sides of the same coin. Absence of a derivative discontinuity necessitates deviation from piecewise linearity, and the latter can be used to correct for the former, thereby restoring the physical meaning of the orbital energies. Using selected small molecules, we show that this results in a simple correction scheme for any underlying functional, including semi-local and hybrid functionals as well as Hartree-Fock theory, suggesting a practical correction for the infamous gap problem of DFT. Moreover, we show that optimally-tuned range-separated hybrid functionals can inherently minimize both DD and curvature, thus requiring no correction, and show that this can be used as a sound theoretical basis for novel tuning strategies.
Analytical model for the radio-frequency sheath

NASA Astrophysics Data System (ADS)

Czarnetzki, Uwe

2013-12-01

A simple analytical model for the planar radio-frequency (rf) sheath in capacitive discharges is developed that is based on the assumptions of a step profile for the electron front, charge exchange collisions with constant cross sections, negligible ionization within the sheath, and negligible ion dynamics. The continuity, momentum conservation, and Poisson equations are combined in a single integro-differential equation for the square of the ion drift velocity, the so called sheath equation. Starting from the kinetic Boltzmann equation, special attention is paid to the derivation and the validity of the approximate fluid equation for momentum balance. The integrals in the sheath equation appear in the screening function which considers the relative contribution of the temporal mean of the electron density to the space charge in the sheath. It is shown that the screening function is quite insensitive to variations of the effective sheath parameters. The two parameters defining the solution are the ratios of the maximum sheath extension to the ion mean free path and the Debye length, respectively. A simple general analytic expression for the screening function is introduced. By means of this expression approximate analytical solutions are obtained for the collisionless as well as the highly collisional case that compare well with the exact numerical solution. A simple transition formula allows application to all degrees of collisionality. In addition, the solutions are used to calculate all static and dynamic quantities of the sheath, e.g., the ion density, fields, and currents. Further, the rf Child-Langmuir laws for the collisionless as well as the collisional case are derived. An essential part of the model is the a priori knowledge of the wave form of the sheath voltage. This wave form is derived on the basis of a cubic charge-voltage relation for individual sheaths, considering both sheaths and the self-consistent self-bias in a discharge with arbitrary symmetry. The externally applied rf voltage is assumed to be sinusoidal, although the model can be extended to arbitrary wave forms, e.g., for dual-frequency discharges. The model calculates explicitly the cubic correction parameter in the charge-voltage relation for the case of highly asymmetric discharges. It is shown that the cubic correction is generally moderate but more pronounced in the collisionless case. The analytical results are compared to experimental data from the literature obtained by laser electric field measurements of the mean and dynamic fields in the capacitive sheath for various gases and pressures. Very good agreement is found throughout.
Analytical model for the radio-frequency sheath.

PubMed

Czarnetzki, Uwe

2013-12-01

A simple analytical model for the planar radio-frequency (rf) sheath in capacitive discharges is developed that is based on the assumptions of a step profile for the electron front, charge exchange collisions with constant cross sections, negligible ionization within the sheath, and negligible ion dynamics. The continuity, momentum conservation, and Poisson equations are combined in a single integro-differential equation for the square of the ion drift velocity, the so called sheath equation. Starting from the kinetic Boltzmann equation, special attention is paid to the derivation and the validity of the approximate fluid equation for momentum balance. The integrals in the sheath equation appear in the screening function which considers the relative contribution of the temporal mean of the electron density to the space charge in the sheath. It is shown that the screening function is quite insensitive to variations of the effective sheath parameters. The two parameters defining the solution are the ratios of the maximum sheath extension to the ion mean free path and the Debye length, respectively. A simple general analytic expression for the screening function is introduced. By means of this expression approximate analytical solutions are obtained for the collisionless as well as the highly collisional case that compare well with the exact numerical solution. A simple transition formula allows application to all degrees of collisionality. In addition, the solutions are used to calculate all static and dynamic quantities of the sheath, e.g., the ion density, fields, and currents. Further, the rf Child-Langmuir laws for the collisionless as well as the collisional case are derived. An essential part of the model is the a priori knowledge of the wave form of the sheath voltage. This wave form is derived on the basis of a cubic charge-voltage relation for individual sheaths, considering both sheaths and the self-consistent self-bias in a discharge with arbitrary symmetry. The externally applied rf voltage is assumed to be sinusoidal, although the model can be extended to arbitrary wave forms, e.g., for dual-frequency discharges. The model calculates explicitly the cubic correction parameter in the charge-voltage relation for the case of highly asymmetric discharges. It is shown that the cubic correction is generally moderate but more pronounced in the collisionless case. The analytical results are compared to experimental data from the literature obtained by laser electric field measurements of the mean and dynamic fields in the capacitive sheath for various gases and pressures. Very good agreement is found throughout.
Exact statistical results for binary mixing and reaction in variable density turbulence

NASA Astrophysics Data System (ADS)

Ristorcelli, J. R.

2017-02-01

We report a number of rigorous statistical results on binary active scalar mixing in variable density turbulence. The study is motivated by mixing between pure fluids with very different densities and whose density intensity is of order unity. Our primary focus is the derivation of exact mathematical results for mixing in variable density turbulence and we do point out the potential fields of application of the results. A binary one step reaction is invoked to derive a metric to asses the state of mixing. The mean reaction rate in variable density turbulent mixing can be expressed, in closed form, using the first order Favre mean variables and the Reynolds averaged density variance, ⟨ρ2⟩ . We show that the normalized density variance, ⟨ρ2⟩ , reflects the reduction of the reaction due to mixing and is a mix metric. The result is mathematically rigorous. The result is the variable density analog, the normalized mass fraction variance ⟨c2⟩ used in constant density turbulent mixing. As a consequence, we demonstrate that use of the analogous normalized Favre variance of the mass fraction, c″ ⁣2˜ , as a mix metric is not theoretically justified in variable density turbulence. We additionally derive expressions relating various second order moments of the mass fraction, specific volume, and density fields. The central role of the density specific volume covariance ⟨ρ v ⟩ is highlighted; it is a key quantity with considerable dynamical significance linking various second order statistics. For laboratory experiments, we have developed exact relations between the Reynolds scalar variance ⟨c2⟩ its Favre analog c″ ⁣2˜ , and various second moments including ⟨ρ v ⟩ . For moment closure models that evolve ⟨ρ v ⟩ and not ⟨ρ2⟩ , we provide a novel expression for ⟨ρ2⟩ in terms of a rational function of ⟨ρ v ⟩ that avoids recourse to Taylor series methods (which do not converge for large density differences). We have derived analytic results relating several other second and third order moments and see coupling between odd and even order moments demonstrating a natural and inherent skewness in the mixing in variable density turbulence. The analytic results have applications in the areas of isothermal material mixing, isobaric thermal mixing, and simple chemical reaction (in progress variable formulation).
High frequency fishbone driven by passing energetic ions in tokamak plasmas

NASA Astrophysics Data System (ADS)

Wang, Feng; Yu, L. M.; Fu, G. Y.; Shen, Wei

2017-05-01

High frequency fishbone instability driven by passing energetic ions was first reported in the Princeton beta experiment with tangential neutral-beam-injection (Heidbrink et al 1986 Phys. Rev. Lett. 57 835-8). It could play an important role for ITER-like burning plasmas, where α particles are mostly passing particles. In this work, a generalized energetic ion distribution function and finite drift orbit width effect are considered to improve the theoretical model for passing particle driving fishbone instability. For purely passing energetic ions with zero drift orbit width, the kinetic energy δ {{W}k} is derived analytically. The derived analytic expression is more accurate as compared to the result of previous work (Wang 2001 Phys. Rev. Lett. 86 5286-8). For a generalized energetic ion distribution function, the fishbone dispersion relation is derived and is solved numerically. Numerical results show that broad and off-axis beam density profiles can significantly increase the beam ion beta threshold {βc} for instability and decrease mode frequency.
High frequency fishbone driven by passing energetic ions in tokamak plasmas

DOE PAGES

Wang, Feng; Yu, L. M.; Fu, G. Y.; ...

2017-03-22

High frequency fishbone instability driven by passing energetic ions was first reported in the Princeton beta experiment with tangential neutral-beam-injection (Heidbrink et al 1986 Phys. Rev. Lett. 57 835–8). It could play an important role for ITER-like burning plasmas, where α particles are mostly passing particles. In this work, a generalized energetic ion distribution function and finite drift orbit width effect are considered to improve the theoretical model for passing particle driving fishbone instability. For purely passing energetic ions with zero drift orbit width, the kinetic energymore » $$\\delta {{W}_{k}}$$ is derived analytically. The derived analytic expression is more accurate as compared to the result of previous work. For a generalized energetic ion distribution function, the fishbone dispersion relation is derived and is solved numerically. As a result, numerical results show that broad and off-axis beam density profiles can significantly increase the beam ion beta threshold $${{\\beta}_{c}}$$ for instability and decrease mode frequency.« less
Pricing foreign equity option under stochastic volatility tempered stable Lévy processes

NASA Astrophysics Data System (ADS)

Gong, Xiaoli; Zhuang, Xintian

2017-10-01

Considering that financial assets returns exhibit leptokurtosis, asymmetry properties as well as clustering and heteroskedasticity effect, this paper substitutes the logarithm normal jumps in Heston stochastic volatility model by the classical tempered stable (CTS) distribution and normal tempered stable (NTS) distribution to construct stochastic volatility tempered stable Lévy processes (TSSV) model. The TSSV model framework permits infinite activity jump behaviors of return dynamics and time varying volatility consistently observed in financial markets through subordinating tempered stable process to stochastic volatility process, capturing leptokurtosis, fat tailedness and asymmetry features of returns. By employing the analytical characteristic function and fast Fourier transform (FFT) technique, the formula for probability density function (PDF) of TSSV returns is derived, making the analytical formula for foreign equity option (FEO) pricing available. High frequency financial returns data are employed to verify the effectiveness of proposed models in reflecting the stylized facts of financial markets. Numerical analysis is performed to investigate the relationship between the corresponding parameters and the implied volatility of foreign equity option.
Exact analytic solution for non-linear density fluctuation in a ΛCDM universe

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yoo, Jaiyul; Gong, Jinn-Ouk, E-mail: jyoo@physik.uzh.ch, E-mail: jinn-ouk.gong@apctp.org

We derive the exact third-order analytic solution of the matter density fluctuation in the proper-time hypersurface in a ΛCDM universe, accounting for the explicit time-dependence and clarifying the relation to the initial condition. Furthermore, we compare our analytic solution to the previous calculation in the comoving gauge, and to the standard Newtonian perturbation theory by providing Fourier kernels for the relativistic effects. Our results provide an essential ingredient for a complete description of galaxy bias in the relativistic context.

An application of characteristic function in order to predict reliability and lifetime of aeronautical hardware

NASA Astrophysics Data System (ADS)

Żurek, Józef; Kaleta, Ryszard; Zieja, Mariusz

2016-06-01

The forecasting of reliability and life of aeronautical hardware requires recognition of many and various destructive processes that deteriorate the health/maintenance status thereof. The aging of technical components of aircraft as an armament system proves of outstanding significance to reliability and safety of the whole system. The aging process is usually induced by many and various factors, just to mention mechanical, biological, climatic, or chemical ones. The aging is an irreversible process and considerably affects (i.e. reduces) reliability and lifetime of aeronautical equipment. Application of the characteristic function of the aging process is suggested to predict reliability and lifetime of aeronautical hardware. An increment in values of diagnostic parameters is introduced to formulate then, using the characteristic function and after some rearrangements, the partial differential equation. An analytical dependence for the characteristic function of the aging process is a solution to this equation. With the inverse transformation applied, the density function of the aging of aeronautical hardware is found. Having found the density function, one can determine the aeronautical equipment's reliability and lifetime. The in-service collected or the life tests delivered data are used to attain this goal. Coefficients in this relationship are found using the likelihood function.
An application of characteristic function in order to predict reliability and lifetime of aeronautical hardware

DOE Office of Scientific and Technical Information (OSTI.GOV)

Żurek, Józef; Kaleta, Ryszard; Zieja, Mariusz

2016-06-08

The forecasting of reliability and life of aeronautical hardware requires recognition of many and various destructive processes that deteriorate the health/maintenance status thereof. The aging of technical components of aircraft as an armament system proves of outstanding significance to reliability and safety of the whole system. The aging process is usually induced by many and various factors, just to mention mechanical, biological, climatic, or chemical ones. The aging is an irreversible process and considerably affects (i.e. reduces) reliability and lifetime of aeronautical equipment. Application of the characteristic function of the aging process is suggested to predict reliability and lifetime ofmore » aeronautical hardware. An increment in values of diagnostic parameters is introduced to formulate then, using the characteristic function and after some rearrangements, the partial differential equation. An analytical dependence for the characteristic function of the aging process is a solution to this equation. With the inverse transformation applied, the density function of the aging of aeronautical hardware is found. Having found the density function, one can determine the aeronautical equipment’s reliability and lifetime. The in-service collected or the life tests delivered data are used to attain this goal. Coefficients in this relationship are found using the likelihood function.« less
Thermodynamics of atomic and ionized hydrogen: analytical results versus equation-of-state tables and Monte Carlo data.

PubMed

Alastuey, A; Ballenegger, V

2012-12-01

We compute thermodynamical properties of a low-density hydrogen gas within the physical picture, in which the system is described as a quantum electron-proton plasma interacting via the Coulomb potential. Our calculations are done using the exact scaled low-temperature (SLT) expansion, which provides a rigorous extension of the well-known virial expansion-valid in the fully ionized phase-into the Saha regime where the system is partially or fully recombined into hydrogen atoms. After recalling the SLT expansion of the pressure [A. Alastuey et al., J. Stat. Phys. 130, 1119 (2008)], we obtain the SLT expansions of the chemical potential and of the internal energy, up to order exp(-|E_{H}|/kT) included (E_{H}≃-13.6 eV). Those truncated expansions describe the first five nonideal corrections to the ideal Saha law. They account exactly, up to the considered order, for all effects of interactions and thermal excitations, including the formation of bound states (atom H, ions H^{-} and H_{2}^{+}, molecule H_{2},⋯) and atom-charge and atom-atom interactions. Among the five leading corrections, three are easy to evaluate, while the remaining ones involve well-defined internal partition functions for the molecule H_{2} and ions H^{-} and H_{2}^{+}, for which no closed-form analytical formula exist currently. We provide accurate low-temperature approximations for those partition functions by using known values of rotational and vibrational energies. We compare then the predictions of the SLT expansion, for the pressure and the internal energy, with, on the one hand, the equation-of-state tables obtained within the opacity program at Livermore (OPAL) and, on the other hand, data of path integral quantum Monte Carlo (PIMC) simulations. In general, a good agreement is found. At low densities, the simple analytical SLT formulas reproduce the values of the OPAL tables up to the last digit in a large range of temperatures, while at higher densities (ρ∼10^{-2} g/cm^{3}), some discrepancies among the SLT, OPAL, and PIMC results are observed.
Discovering charge density functionals and structure-property relationships with PROPhet: A general framework for coupling machine learning and first-principles methods

DOE PAGES

Kolb, Brian; Lentz, Levi C.; Kolpak, Alexie M.

2017-04-26

Modern ab initio methods have rapidly increased our understanding of solid state materials properties, chemical reactions, and the quantum interactions between atoms. However, poor scaling often renders direct ab initio calculations intractable for large or complex systems. There are two obvious avenues through which to remedy this problem: (i) develop new, less expensive methods to calculate system properties, or (ii) make existing methods faster. This paper describes an open source framework designed to pursue both of these avenues. PROPhet (short for PROPerty Prophet) utilizes machine learning techniques to find complex, non-linear mappings between sets of material or system properties. Themore » result is a single code capable of learning analytical potentials, non-linear density functionals, and other structure-property or property-property relationships. These capabilities enable highly accurate mesoscopic simulations, facilitate computation of expensive properties, and enable the development of predictive models for systematic materials design and optimization. Here, this work explores the coupling of machine learning to ab initio methods through means both familiar (e.g., the creation of various potentials and energy functionals) and less familiar (e.g., the creation of density functionals for arbitrary properties), serving both to demonstrate PROPhet’s ability to create exciting post-processing analysis tools and to open the door to improving ab initio methods themselves with these powerful machine learning techniques.« less
Discovering charge density functionals and structure-property relationships with PROPhet: A general framework for coupling machine learning and first-principles methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kolb, Brian; Lentz, Levi C.; Kolpak, Alexie M.

Modern ab initio methods have rapidly increased our understanding of solid state materials properties, chemical reactions, and the quantum interactions between atoms. However, poor scaling often renders direct ab initio calculations intractable for large or complex systems. There are two obvious avenues through which to remedy this problem: (i) develop new, less expensive methods to calculate system properties, or (ii) make existing methods faster. This paper describes an open source framework designed to pursue both of these avenues. PROPhet (short for PROPerty Prophet) utilizes machine learning techniques to find complex, non-linear mappings between sets of material or system properties. Themore » result is a single code capable of learning analytical potentials, non-linear density functionals, and other structure-property or property-property relationships. These capabilities enable highly accurate mesoscopic simulations, facilitate computation of expensive properties, and enable the development of predictive models for systematic materials design and optimization. Here, this work explores the coupling of machine learning to ab initio methods through means both familiar (e.g., the creation of various potentials and energy functionals) and less familiar (e.g., the creation of density functionals for arbitrary properties), serving both to demonstrate PROPhet’s ability to create exciting post-processing analysis tools and to open the door to improving ab initio methods themselves with these powerful machine learning techniques.« less
Stability of mechanical joints in launching vehicles: Local and global stationary values of energy density

NASA Astrophysics Data System (ADS)

Chue, Ching-Hwei

A method was developed for predicting the behavior of mechanical joints in launch vehicles with particular emphasis placed on how the combined effects of loading, geometry, and materials could be optimized in terms of structure instability and/or integrity. What was considered to be essential is the fluctuation of the volume energy density with time in the structure. The peaks and valleys of the volume energy density function will be associated with failure by fracture and/or yielding while the distance between their local and global stationary values govern the structure instability. The Solid Rocket Booster (SRB) of the space shuttle was analyzed under axisymmetric and non-axisymmetric loadings. A semi-analytical finite element program was developed for solving the case of non-axisymmetric loading. Following a dynamic stress analysis, contours of the volume energy density in the structure were obtained as a function of time. The magnitudes and locations of these stationary values were then calculated locally and globally and related to possible failure by fracture. In the case of axisymmetric flight, the local and global instability behavior do not change appreciably. Fluctuations in the energy density and the dynamic stability length parameter become appreciable when the non-axisymmetric loads are considered. The magnitude of the energy in the shell structure is sensitive to alterations in the gas pressure induced by the solid propellant.
A quadrature based method of moments for nonlinear Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Otten, Dustin L.; Vedula, Prakash

2011-09-01

Fokker-Planck equations which are nonlinear with respect to their probability densities and occur in many nonequilibrium systems relevant to mean field interaction models, plasmas, fermions and bosons can be challenging to solve numerically. To address some underlying challenges, we propose the application of the direct quadrature based method of moments (DQMOM) for efficient and accurate determination of transient (and stationary) solutions of nonlinear Fokker-Planck equations (NLFPEs). In DQMOM, probability density (or other distribution) functions are represented using a finite collection of Dirac delta functions, characterized by quadrature weights and locations (or abscissas) that are determined based on constraints due to evolution of generalized moments. Three particular examples of nonlinear Fokker-Planck equations considered in this paper include descriptions of: (i) the Shimizu-Yamada model, (ii) the Desai-Zwanzig model (both of which have been developed as models of muscular contraction) and (iii) fermions and bosons. Results based on DQMOM, for the transient and stationary solutions of the nonlinear Fokker-Planck equations, have been found to be in good agreement with other available analytical and numerical approaches. It is also shown that approximate reconstruction of the underlying probability density function from moments obtained from DQMOM can be satisfactorily achieved using a maximum entropy method.
Path integral approach to the Wigner representation of canonical density operators for discrete systems coupled to harmonic baths.

PubMed

Montoya-Castillo, Andrés; Reichman, David R

2017-01-14

We derive a semi-analytical form for the Wigner transform for the canonical density operator of a discrete system coupled to a harmonic bath based on the path integral expansion of the Boltzmann factor. The introduction of this simple and controllable approach allows for the exact rendering of the canonical distribution and permits systematic convergence of static properties with respect to the number of path integral steps. In addition, the expressions derived here provide an exact and facile interface with quasi- and semi-classical dynamical methods, which enables the direct calculation of equilibrium time correlation functions within a wide array of approaches. We demonstrate that the present method represents a practical path for the calculation of thermodynamic data for the spin-boson and related systems. We illustrate the power of the present approach by detailing the improvement of the quality of Ehrenfest theory for the correlation function C zz (t)=Re⟨σ z (0)σ z (t)⟩ for the spin-boson model with systematic convergence to the exact sampling function. Importantly, the numerically exact nature of the scheme presented here and its compatibility with semiclassical methods allows for the systematic testing of commonly used approximations for the Wigner-transformed canonical density.
Thermal Analysis of Low Layer Density Multilayer Insulation Test Results

NASA Technical Reports Server (NTRS)

Johnson, Wesley L.

2011-01-01

Investigation of the thermal performance of low layer density multilayer insulations is important for designing long-duration space exploration missions involving the storage of cryogenic propellants. Theoretical calculations show an analytical optimal layer density, as widely reported in the literature. However, the appropriate test data by which to evaluate these calculations have been only recently obtained. As part of a recent research project, NASA procured several multilayer insulation test coupons for calorimeter testing. These coupons were configured to allow for the layer density to be varied from 0.5 to 2.6 layer/mm. The coupon testing was completed using the cylindrical Cryostat-l00 apparatus by the Cryogenics Test Laboratory at Kennedy Space Center. The results show the properties of the insulation as a function of layer density for multiple points. Overlaying these new results with data from the literature reveals a minimum layer density; however, the value is higher than predicted. Additionally, the data show that the transition region between high vacuum and no vacuum is dependent on the spacing of the reflective layers. Historically this spacing has not been taken into account as thermal performance was calculated as a function of pressure and temperature only; however the recent testing shows that the data is dependent on the Knudsen number which takes into account pressure, temperature, and layer spacing. These results aid in the understanding of the performance parameters of MLI and help to complete the body of literature on the topic.
Analytical energy gradient based on spin-free infinite-order Douglas-Kroll-Hess method with local unitary transformation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakajima, Yuya; Seino, Junji; Nakai, Hiromi, E-mail: nakai@waseda.jp

In this study, the analytical energy gradient for the spin-free infinite-order Douglas-Kroll-Hess (IODKH) method at the levels of the Hartree-Fock (HF), density functional theory (DFT), and second-order Møller-Plesset perturbation theory (MP2) is developed. Furthermore, adopting the local unitary transformation (LUT) scheme for the IODKH method improves the efficiency in computation of the analytical energy gradient. Numerical assessments of the present gradient method are performed at the HF, DFT, and MP2 levels for the IODKH with and without the LUT scheme. The accuracies are examined for diatomic molecules such as hydrogen halides, halogen dimers, coinage metal (Cu, Ag, and Au) halides,more » and coinage metal dimers, and 20 metal complexes, including the fourth–sixth row transition metals. In addition, the efficiencies are investigated for one-, two-, and three-dimensional silver clusters. The numerical results confirm the accuracy and efficiency of the present method.« less
Amplitude and phase fluctuations of Van der Pol oscillator under external random forcing

NASA Astrophysics Data System (ADS)

Singh, Aman K.; Yadava, R. D. S.

2018-05-01

The paper presents an analytical study of noise in Van der Pol oscillator output subjected to an external force noise assumed to be characterized by delta function (white noise). The external fluctuations are assumed to be small in comparison to the average response of the noise free system. The autocorrelation function and power spectrum are calculated under the condition of weak nonlinearity. The latter ensures limit cycle oscillations. The total spectral power density is dominated by the contributions from the phase fluctuations. The amplitude fluctuations are at least two orders of magnitude smaller. The analysis is shown to be useful to interpretation microcantilever based biosensing data.
The isolation limits of stochastic vibration

NASA Technical Reports Server (NTRS)

Knopse, C. R.; Allaire, P. E.

1993-01-01

The vibration isolation problem is formulated as a 1D kinematic problem. The geometry of the stochastic wall trajectories arising from the stroke constraint is defined in terms of their significant extrema. An optimal control solution for the minimum acceleration return path determines a lower bound on platform mean square acceleration. This bound is expressed in terms of the probability density function on the significant maxima and the conditional fourth moment of the first passage time inverse. The first of these is found analytically while the second is found using a Monte Carlo simulation. The rms acceleration lower bound as a function of available space is then determined through numerical quadrature.
Role of Defects on Regioselectivity of Nano Pristine Graphene.

PubMed

Kudur Jayaprakash, Gururaj; Casillas, Norberto; Astudillo-Sánchez, Pablo D; Flores-Moreno, Roberto

2016-11-17

Here analytical Fukui functions based on density functional theory are applied to investigate the redox reactivity of pristine and defected graphene lattices. A carbon H-terminated graphene structure (with 96 carbon atoms) and a graphene defected surface with Stone-Wales rearrangement and double vacancy defects are used as models. Pristine sp 2 -hybridized, hexagonal arranged carbon atoms exhibit a symmetric reactivity. In contrast, common carbon atoms at reconstructed polygons in Stone-Wales and double vacancy graphene display large reactivity variations. The improved reactivity and the regioselectivity at defected graphene is correlated to structural changes that caused carbon-carbon bond length variations at defected zones.
Downlink Probability Density Functions for EOS-McMurdo Sound

NASA Technical Reports Server (NTRS)

Christopher, P.; Jackson, A. H.

1996-01-01

The visibility times and communication link dynamics for the Earth Observations Satellite (EOS)-McMurdo Sound direct downlinks have been studied. The 16 day EOS periodicity may be shown with the Goddard Trajectory Determination System (GTDS) and the entire 16 day period should be simulated for representative link statistics. We desire many attributes of the downlink, however, and a faster orbital determination method is desirable. We use the method of osculating elements for speed and accuracy in simulating the EOS orbit. The accuracy of the method of osculating elements is demonstrated by closely reproducing the observed 16 day Landsat periodicity. An autocorrelation function method is used to show the correlation spike at 16 days. The entire 16 day record of passes over McMurdo Sound is then used to generate statistics for innage time, outage time, elevation angle, antenna angle rates, and propagation loss. The levation angle probability density function is compared with 1967 analytic approximation which has been used for medium to high altitude satellites. One practical result of this comparison is seen to be the rare occurrence of zenith passes. The new result is functionally different than the earlier result, with a heavy emphasis on low elevation angles. EOS is one of a large class of sun synchronous satellites which may be downlinked to McMurdo Sound. We examine delay statistics for an entire group of sun synchronous satellites ranging from 400 km to 1000 km altitude. Outage probability density function results are presented three dimensionally.
Diagrammatic expansion for positive density-response spectra: Application to the electron gas

NASA Astrophysics Data System (ADS)

Uimonen, A.-M.; Stefanucci, G.; Pavlyukh, Y.; van Leeuwen, R.

2015-03-01

In a recent paper [Phys. Rev. B 90, 115134 (2014), 10.1103/PhysRevB.90.115134] we put forward a diagrammatic expansion for the self-energy which guarantees the positivity of the spectral function. In this work we extend the theory to the density-response function. We write the generic diagram for the density-response spectrum as the sum of "partitions." In a partition the original diagram is evaluated using time-ordered Green's functions on the left half of the diagram, antitime-ordered Green's functions on the right half of the diagram, and lesser or greater Green's function gluing the two halves. As there exists more than one way to cut a diagram in two halves, to every diagram corresponds more than one partition. We recognize that the most convenient diagrammatic objects for constructing a theory of positive spectra are the half-diagrams. Diagrammatic approximations obtained by summing the squares of half-diagrams do indeed correspond to a combination of partitions which, by construction, yield a positive spectrum. We develop the theory using bare Green's functions and subsequently extend it to dressed Green's functions. We further prove a connection between the positivity of the spectral function and the analytic properties of the polarizability. The general theory is illustrated with several examples and then applied to solve the long-standing problem of including vertex corrections without altering the positivity of the spectrum. In fact already the first-order vertex diagram, relevant to the study of gradient expansion, Friedel oscillations, etc., leads to spectra which are negative in certain frequency domain. We find that the simplest approximation to cure this deficiency is given by the sum of the zeroth-order bubble diagram, the first-order vertex diagram, and a partition of the second-order ladder diagram. We evaluate this approximation in the three-dimensional homogeneous electron gas and show the positivity of the spectrum for all frequencies and densities.
New aspects in single-body meteor physics

NASA Astrophysics Data System (ADS)

Pecina, P.; Ceplecha, Z.

1983-03-01

An exact analytical solution of the atmospheric meteoroid single-body problem is presented expressing the distance along the trajectory as a function of time, which yields a least-square fit of the observed trajectory, and analytical expressions for the velocity at the point of maximum deceleration are derived. These results are used to determine the ablation coefficient from observations. These methods are applied to 17 Prairie Network fireballs observed below the maximum deceleration point and to the Innisfree fireball, and the results are found to be superior to the ones obtained with the usual interpolation formula. A model of luminous efficiencies for small velocities and for masses up to several hundred grams based on data on Innisfree and on artificial rocketry meteors is proposed and applied to separate the shape-density coefficient from the meteoroid mass.
Efficient time-dependent density functional theory approximations for hybrid density functionals: analytical gradients and parallelization.

PubMed

Petrenko, Taras; Kossmann, Simone; Neese, Frank

2011-02-07

In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA) for hybrid density functionals. For the calculation of the TDDFT/TDA excitation energies and analytical gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced "chain of spheres exchange" (COSX) algorithm for the calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1%. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and gradient calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup ~26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ~27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of ~24 on 30 processors. The parallelization efficiency for the Coulomb terms can be somewhat smaller (speedup ~15-25 for 30 processors), but their contribution to the total calculation time is small. Thus, the parallel program completes a Becke3-Lee-Yang-Parr energy and gradient calculation on the Ag-TB2-helicate in less than 4 h on 30 processors. We also present the necessary extension of the Lagrangian formalism, which enables the calculation of the TDDFT excited state properties in the frozen-core approximation. The algorithms described in this work are implemented into the ORCA electronic structure system.
A self-powered glucose biosensing system.

PubMed

Slaughter, Gymama; Kulkarni, Tanmay

2016-04-15

A self-powered glucose biosensor (SPGS) system is fabricated and in vitro characterization of the power generation and charging frequency characteristics in glucose analyte are described. The bioelectrodes consist of compressed network of three-dimensional multi-walled carbon nanotubes with redox enzymes, pyroquinoline quinone glucose dehydrogenase (PQQ-GDH) and laccase functioning as the anodic and cathodic catalyst, respectively. When operated in 45 mM glucose, the biofuel cell exhibited an open circuit voltage and power density of 681.8 mV and 67.86 µW/cm(2) at 335 mV, respectively, with a current density of 202.2 µA/cm(2). Moreover, at physiological glucose concentration (5mM), the biofuel cell exhibits open circuit voltage and power density of 302.1 mV and 15.98 µW/cm(2) at 166.3 mV, respectively, with a current density of 100 µA/cm(2). The biofuel cell assembly produced a linear dynamic range of 0.5-45 mM glucose. These findings show that glucose biofuel cells can be further investigated in the development of a self-powered glucose biosensor by using a capacitor as the transducer element. By monitoring the capacitor charging frequencies, which are influenced by the concentration of the glucose analyte, a linear dynamic range of 0.5-35 mM glucose is observed. The operational stability of SPGS is monitored over a period of 63 days and is found to be stable with 15.38% and 11.76% drop in power density under continuous discharge in 10mM and 20mM glucose, respectively. These results demonstrate that SPGSs can simultaneously generate bioelectricity to power ultra-low powered devices and sense glucose. Copyright © 2015 Elsevier B.V. All rights reserved.
Hydrologic controls on basin-scale distribution of benthic macroinvertebrates

NASA Astrophysics Data System (ADS)

Bertuzzo, E.; Ceola, S.; Singer, G. A.; Battin, T. J.; Montanari, A.; Rinaldo, A.

2013-12-01

The presentation deals with the role of streamflow variability on basin-scale distributions of benthic macroinvertebrates. Specifically, we present a probabilistic analysis of the impacts of the variability along the river network of relevant hydraulic variables on the density of benthic macroinvertebrate species. The relevance of this work is based on the implications of the predictability of macroinvertebrate patterns within a catchment on fluvial ecosystem health, being macroinvertebrates commonly used as sensitive indicators, and on the effects of anthropogenic activity. The analytical tools presented here outline a novel procedure of general nature aiming at a spatially-explicit quantitative assessment of how near-bed flow variability affects benthic macroinvertebrate abundance. Moving from the analytical characterization of the at-a-site probability distribution functions (pdfs) of streamflow and bottom shear stress, a spatial extension to a whole river network is performed aiming at the definition of spatial maps of streamflow and bottom shear stress. Then, bottom shear stress pdf, coupled with habitat suitability curves (e.g., empirical relations between species density and bottom shear stress) derived from field studies are used to produce maps of macroinvertebrate suitability to shear stress conditions. Thus, moving from measured hydrologic conditions, possible effects of river streamflow alterations on macroinvertebrate densities may be fairly assessed. We apply this framework to an Austrian river network, used as benchmark for the analysis, for which rainfall and streamflow time-series and river network hydraulic properties and macroinvertebrate density data are available. A comparison between observed vs "modeled" species' density in three locations along the examined river network is also presented. Although the proposed approach focuses on a single controlling factor, it shows important implications with water resources management and fluvial ecosystem protection.
Distribution of electron density and magnetocapacitance in the regime of the fractional quantum Hall effect

NASA Astrophysics Data System (ADS)

Pikus, F. G.; Efros, A. L.

1993-06-01

A two-dimensional electron liquid (TDEL), subjected to a smooth random potential, is studied in the regime of the fractional quantum Hall effect. An analytical theory of the nonlinear screening is presented for the case when the fractional gap is much less than the magnitude of the unscreened random potential. In this ``narrow-gap approximation'' (NGA), we calculate the electron density distribution function, the fraction of the TDEL which is in the incompressible state, and the thermodynamic density of states. The magnetocapacitance is calculated to compare with the recent experiments. The NGA is found to be not accurate enough to describe the data. The results for larger fractional gaps are obtained by computer modeling. To fit the recent experimental data we have also taken into account the anyon-anyon interaction in the vicinity of a fractional singularity.

Electrostatic Debye layer formed at a plasma-liquid interface

NASA Astrophysics Data System (ADS)

Rumbach, Paul; Clarke, Jean Pierre; Go, David B.

2017-05-01

We construct an analytic model for the electrostatic Debye layer formed at a plasma-liquid interface by combining the Gouy-Chapman theory for the liquid with a simple parabolic band model for the plasma sheath. The model predicts a nonlinear scaling between the plasma current density and the solution ionic strength, and we confirmed this behavior with measurements using a liquid-anode plasma. Plots of the measured current density as a function of ionic strength collapse the data and curve fits yield a plasma electron density of ˜1019m-3 and an electric field of ˜104V /m on the liquid side of the interface. Because our theory is based firmly on fundamental physics, we believe it can be widely applied to many emerging technologies involving the interaction of low-temperature, nonequilibrium plasma with aqueous media, including plasma medicine and various plasma chemical synthesis techniques.
Modeling of the reactant conversion rate in a turbulent shear flow

NASA Technical Reports Server (NTRS)

Frankel, S. H.; Madnia, C. K.; Givi, P.

1992-01-01

Results are presented of direct numerical simulations (DNS) of spatially developing shear flows under the influence of infinitely fast chemical reactions of the type A + B yields Products. The simulation results are used to construct the compositional structure of the scalar field in a statistical manner. The results of this statistical analysis indicate that the use of a Beta density for the probability density function (PDF) of an appropriate Shvab-Zeldovich mixture fraction provides a very good estimate of the limiting bounds of the reactant conversion rate within the shear layer. This provides a strong justification for the implementation of this density in practical modeling of non-homogeneous turbulent reacting flows. However, the validity of the model cannot be generalized for predictions of higher order statistical quantities. A closed form analytical expression is presented for predicting the maximum rate of reactant conversion in non-homogeneous reacting turbulence.
Nonparametric density estimation and optimal bandwidth selection for protein unfolding and unbinding data

NASA Astrophysics Data System (ADS)

Bura, E.; Zhmurov, A.; Barsegov, V.

2009-01-01

Dynamic force spectroscopy and steered molecular simulations have become powerful tools for analyzing the mechanical properties of proteins, and the strength of protein-protein complexes and aggregates. Probability density functions of the unfolding forces and unfolding times for proteins, and rupture forces and bond lifetimes for protein-protein complexes allow quantification of the forced unfolding and unbinding transitions, and mapping the biomolecular free energy landscape. The inference of the unknown probability distribution functions from the experimental and simulated forced unfolding and unbinding data, as well as the assessment of analytically tractable models of the protein unfolding and unbinding requires the use of a bandwidth. The choice of this quantity is typically subjective as it draws heavily on the investigator's intuition and past experience. We describe several approaches for selecting the "optimal bandwidth" for nonparametric density estimators, such as the traditionally used histogram and the more advanced kernel density estimators. The performance of these methods is tested on unimodal and multimodal skewed, long-tailed distributed data, as typically observed in force spectroscopy experiments and in molecular pulling simulations. The results of these studies can serve as a guideline for selecting the optimal bandwidth to resolve the underlying distributions from the forced unfolding and unbinding data for proteins.
Secondary ionization in a flat universe

NASA Technical Reports Server (NTRS)

Atrio-Barandela, F.; Doroshkevich, A. G.

1994-01-01

We analyze the effect of a secondary ionization on the evolution of temperature fluctuations in cosmic background radiation. The main results presented in this paper are appropriate analytic expressions of the transfer function relating temperature fluctuations to matter density perturbations at recombination for all possible recombination histories. Furthermore, we particularize our calculation to the standard cold dark matter model, where we study the erasure of primordial temperature fluctuations and calculate the magnitude and angular scale of the damping induced by a late recombination.
Hierarchical Carbon Fibers with ZnO Nanowires for Volatile Sensing in Composite Curing (Postprint)

DTIC Science & Technology

2014-07-01

needed to demonstrate the use of Zinc Oxide (ZnO) nanowire coated carbon fibers as a volatile sensor. ZnO nanowires are demonstrated to function as...processing. For this work, we report on the foundational study needed to demonstrate the use of Zinc Oxide (ZnO) nanowire coated carbon fibers as a...array of ZnO nanowires. Zinc oxide nanowires become more conductive in the presence of ethanol – as analyte sorbs to the surface, electron density
Atomistic models of Cu diffusion in CuInSe2 under variations in composition

NASA Astrophysics Data System (ADS)

Sommer, David E.; Dunham, Scott T.

2018-03-01

We construct an analytic model for the composition dependence of the vacancy-mediated Cu diffusion coefficient in undoped CuInSe2 using parameters from density functional theory. The applicability of this model is supported numerically with kinetic lattice Monte Carlo and Onsager transport tensors. We discuss how this model relates to experimental measurements of Cu diffusion, arguing that our results can account for significant contributions to the bulk diffusion of Cu tracers in non-stoichiometric CuInSe2.
General solution of a fractional Parker diffusion-convection equation describing the superdiffusive transport of energetic particles

NASA Astrophysics Data System (ADS)

Tawfik, Ashraf M.; Fichtner, Horst; Elhanbaly, A.; Schlickeiser, Reinhard

2018-06-01

Anomalous diffusion models of energetic particles in space plasmas are developed by introducing the fractional Parker diffusion-convection equation. Analytical solution of the space-time fractional equation is obtained by use of the Caputo and Riesz-Feller fractional derivatives with the Laplace-Fourier transforms. The solution is given in terms of the Fox H-function. Profiles of particle densities are illustrated for different values of the space fractional order and the so-called skewness parameter.
Time domain simulation of the response of geometrically nonlinear panels subjected to random loading

NASA Technical Reports Server (NTRS)

Moyer, E. Thomas, Jr.

1988-01-01

The response of composite panels subjected to random pressure loads large enough to cause geometrically nonlinear responses is studied. A time domain simulation is employed to solve the equations of motion. An adaptive time stepping algorithm is employed to minimize intermittent transients. A modified algorithm for the prediction of response spectral density is presented which predicts smooth spectral peaks for discrete time histories. Results are presented for a number of input pressure levels and damping coefficients. Response distributions are calculated and compared with the analytical solution of the Fokker-Planck equations. RMS response is reported as a function of input pressure level and damping coefficient. Spectral densities are calculated for a number of examples.
Hydrodynamic model for conductivity in graphene.

PubMed

Mendoza, M; Herrmann, H J; Succi, S

2013-01-01

Based on the recently developed picture of an electronic ideal relativistic fluid at the Dirac point, we present an analytical model for the conductivity in graphene that is able to describe the linear dependence on the carrier density and the existence of a minimum conductivity. The model treats impurities as submerged rigid obstacles, forming a disordered medium through which graphene electrons flow, in close analogy with classical fluid dynamics. To describe the minimum conductivity, we take into account the additional carrier density induced by the impurities in the sample. The model, which predicts the conductivity as a function of the impurity fraction of the sample, is supported by extensive simulations for different values of ε, the dimensionless strength of the electric field, and provides excellent agreement with experimental data.
Poly-Gaussian model of randomly rough surface in rarefied gas flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aksenova, Olga A.; Khalidov, Iskander A.

2014-12-09

Surface roughness is simulated by the model of non-Gaussian random process. Our results for the scattering of rarefied gas atoms from a rough surface using modified approach to the DSMC calculation of rarefied gas flow near a rough surface are developed and generalized applying the poly-Gaussian model representing probability density as the mixture of Gaussian densities. The transformation of the scattering function due to the roughness is characterized by the roughness operator. Simulating rough surface of the walls by the poly-Gaussian random field expressed as integrated Wiener process, we derive a representation of the roughness operator that can be appliedmore » in numerical DSMC methods as well as in analytical investigations.« less
Complete analytical solution of electromagnetic field problem of high-speed spinning ball

NASA Astrophysics Data System (ADS)

Reichert, T.; Nussbaumer, T.; Kolar, J. W.

2012-11-01

In this article, a small sphere spinning in a rotating magnetic field is analyzed in terms of the resulting magnetic flux density distribution and the current density distribution inside the ball. From these densities, the motor torque and the eddy current losses can be calculated. An analytical model is derived, and its results are compared to a 3D finite element analysis. The model gives insight into the torque and loss characteristics of a solid rotor induction machine setup, which aims at rotating the sphere beyond 25 Mrpm.
Calculating the trap density of states in organic field-effect transistors from experiment: A comparison of different methods

NASA Astrophysics Data System (ADS)

Kalb, Wolfgang L.; Batlogg, Bertram

2010-01-01

The spectral density of localized states in the band gap of pentacene (trap DOS) was determined with a pentacene-based thin-film transistor from measurements of the temperature dependence and gate-voltage dependence of the contact-corrected field-effect conductivity. Several analytical methods to calculate the trap DOS from the measured data were used to clarify, if the different methods lead to comparable results. We also used computer simulations to further test the results from the analytical methods. Most methods predict a trap DOS close to the valence-band edge that can be very well approximated by a single exponential function with a slope in the range of 50-60 meV and a trap density at the valence-band edge of ≈2×1021eV-1cm-3 . Interestingly, the trap DOS is always slightly steeper than exponential. An important finding is that the choice of the method to calculate the trap DOS from the measured data can have a considerable effect on the final result. We identify two specific simplifying assumptions that lead to significant errors in the trap DOS. The temperature dependence of the band mobility should generally not be neglected. Moreover, the assumption of a constant effective accumulation-layer thickness leads to a significant underestimation of the slope of the trap DOS.
Determination of Charge-Carrier Mobility in Disordered Thin-Film Solar Cells as a Function of Current Density

NASA Astrophysics Data System (ADS)

Mäckel, Helmut; MacKenzie, Roderick C. I.

2018-03-01

Charge-carrier mobility is a fundamental material parameter, which plays an important role in determining solar-cell efficiency. The higher the mobility, the less time a charge carrier will spend in a device and the less likely it is that it will be lost to recombination. Despite the importance of this physical property, it is notoriously difficult to measure accurately in disordered thin-film solar cells under operating conditions. We, therefore, investigate a method previously proposed in the literature for the determination of mobility as a function of current density. The method is based on a simple analytical model that relates the mobility to carrier density and transport resistance. By revising the theoretical background of the method, we clearly demonstrate what type of mobility can be extracted (constant mobility or effective mobility of electrons and holes). We generalize the method to any combination of measurements that is able to determine the mean electron and hole carrier density, and the transport resistance at a given current density. We explore the robustness of the method by simulating typical organic solar-cell structures with a variety of physical properties, including unbalanced mobilities, unbalanced carrier densities, and for high or low carrier trapping rates. The simulations reveal that near VOC and JSC , the method fails due to the limitation of determining the transport resistance. However, away from these regions (and, importantly, around the maximum power point), the method can accurately determine charge-carrier mobility. In the presence of strong carrier trapping, the method overestimates the effective mobility due to an underestimation of the carrier density.
First-principles studies of PETN molecular crystal vibrational frequencies under high pressure

NASA Astrophysics Data System (ADS)

Perger, Warren; Zhao, Jijun

2005-07-01

The vibrational frequencies of the PETN molecular crystal were calculated using the first-principles CRYSTAL03 program which employs an all-electron LCAO approach and calculates analytic first derivatives of the total energy with respect to atomic displacements. Numerical second derivatives were used to enable calculation of the vibrational frequencies at ambient pressure and under various states of compression. Three different density functionals, B3LYP, PW91, and X3LYP were used to examine the effect of the exchange-correlation functional on the vibrational frequencies. The pressure-induced shift of the vibrational frequencies will be presented and compared with experiment. The average deviation with experimental results is shown to be on the order of 2-3%, depending on the functional used.
COMBINATION OF DENSITY AND ENERGY MODULATION IN MICROBUNCHING ANALYSIS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsai, Cheng Ying; Li, Rui

2016-05-01

Microbunching instability (MBI) has been one of the most challenging issues in the transport of high-brightness electron beams for modern recirculating or energy recovery linac machines. Recently we have developed and implemented a Vlasov solver [1] to calculate the microbunching gain for an arbitrary beamline lattice, based on the extension of existing theoretical formulation [2-4] for the microbunching amplification from an initial density perturbation to the final density modulation. For more thorough analyses, in addition to the case of (initial) density to (final) density amplification, we extend in this paper the previous formulation to more general cases, including energy tomore » density, density to energy and energy to energy amplifications for a recirculation machine. Such semi-analytical formulae are then incorporated into our Vlasov solver, and qualitative agreement is obtained when the semi-analytical Vlasov results are compared with particle tracking simulation using ELEGANT [5].« less
Axisymmetric Plasma Equilibria in General Relativity

NASA Astrophysics Data System (ADS)

Elsässer, Klaus

Axisymmetric plasma equilibria near a rotating black hole are considered within the multifluid description. An isothermal two-component plasma with electrons and positrons or ions is determined by four structure functions and the boundary conditions. These structure functions are the Bernoulli function and the toroidal canonical momentum per mass for each species; they remain arbitrary if no gain and loss processes are considered, in close analogy to the free flux functions in ideal magnetohydrodynamics. Several simplifying assumptions allow the reduction of the basic equations to one single scalar equation for the stream function χ of positrons or ions, respectively, playing the rôle of the Grad/Shafranov equation in magnetohydrodynamics; in particular, Maxwell's equations can be solved analytically for a quasineutral plasma when both the charge density and the toroidal electric current density are negligible (in contrast to the Tokamak situation). The basic smallness parameter is the ratio of the skin depth of electrons to the scale length of the metric and fluid quantities, and, in the case of an electron-ion plasma, the mass ratio me/mi. The χ-equation can be solved by standard methods, and simple solutions for a Kerr geometry are available; they show characteristic flow patterns, depending on the structure functions and the boundary conditions.
Energetic investigation of the adsorption process of CH4, C2H6 and N2 on activated carbon: Numerical and statistical physics treatment

NASA Astrophysics Data System (ADS)

Ben Torkia, Yosra; Ben Yahia, Manel; Khalfaoui, Mohamed; Al-Muhtaseb, Shaheen A.; Ben Lamine, Abdelmottaleb

2014-01-01

The adsorption energy distribution (AED) function of a commercial activated carbon (BDH-activated carbon) was investigated. For this purpose, the integral equation is derived by using a purely analytical statistical physics treatment. The description of the heterogeneity of the adsorbent is significantly clarified by defining the parameter N(E). This parameter represents the energetic density of the spatial density of the effectively occupied sites. To solve the integral equation, a numerical method was used based on an adequate algorithm. The Langmuir model was adopted as a local adsorption isotherm. This model is developed by using the grand canonical ensemble, which allows defining the physico-chemical parameters involved in the adsorption process. The AED function is estimated by a normal Gaussian function. This method is applied to the adsorption isotherms of nitrogen, methane and ethane at different temperatures. The development of the AED using a statistical physics treatment provides an explanation of the gas molecules behaviour during the adsorption process and gives new physical interpretations at microscopic levels.
Analysis of Multiplexed Nanosensor Arrays Based on Near-Infrared Fluorescent Single-Walled Carbon Nanotubes.

PubMed

Dong, Juyao; Salem, Daniel P; Sun, Jessica H; Strano, Michael S

2018-04-24

The high-throughput, label-free detection of biomolecules remains an important challenge in analytical chemistry with the potential of nanosensors to significantly increase the ability to multiplex such assays. In this work, we develop an optical sensor array, printable from a single-walled carbon nanotube/chitosan ink and functionalized to enable a divalent ion-based proximity quenching mechanism for transducing binding between a capture protein or an antibody with the target analyte. Arrays of 5 × 6, 200 μm near-infrared (nIR) spots at a density of ≈300 spots/cm 2 are conjugated with immunoglobulin-binding proteins (proteins A, G, and L) for the detection of human IgG, mouse IgM, rat IgG2a, and human IgD. Binding kinetics are measured in a parallel, multiplexed fashion from each sensor spot using a custom laser scanning imaging configuration with an nIR photomultiplier tube detector. These arrays are used to examine cross-reactivity, competitive and nonspecific binding of analyte mixtures. We find that protein G and protein L functionalized sensors report selective responses to mouse IgM on the latter, as anticipated. Optically addressable platforms such as the one examined in this work have potential to significantly advance the real-time, multiplexed biomolecular detection of complex mixtures.
The new semi-analytic code GalICS 2.0 - reproducing the galaxy stellar mass function and the Tully-Fisher relation simultaneously

NASA Astrophysics Data System (ADS)

Cattaneo, A.; Blaizot, J.; Devriendt, J. E. G.; Mamon, G. A.; Tollet, E.; Dekel, A.; Guiderdoni, B.; Kucukbas, M.; Thob, A. C. R.

2017-10-01

GalICS 2.0 is a new semi-analytic code to model the formation and evolution of galaxies in a cosmological context. N-body simulations based on a Planck cosmology are used to construct halo merger trees, track subhaloes, compute spins and measure concentrations. The accretion of gas on to galaxies and the morphological evolution of galaxies are modelled with prescriptions derived from hydrodynamic simulations. Star formation and stellar feedback are described with phenomenological models (as in other semi-analytic codes). GalICS 2.0 computes rotation speeds from the gravitational potential of the dark matter, the disc and the central bulge. As the rotation speed depends not only on the virial velocity but also on the ratio of baryons to dark matter within a galaxy, our calculation predicts a different Tully-Fisher relation from models in which vrot ∝ vvir. This is why, GalICS 2.0 is able to reproduce the galaxy stellar mass function and the Tully-Fisher relation simultaneously. Our results are also in agreement with halo masses from weak lensing and satellite kinematics, gas fractions, the relation between star formation rate (SFR) and stellar mass, the evolution of the cosmic SFR density, bulge-to-disc ratios, disc sizes and the Faber-Jackson relation.
Three-dimensional benchmark for variable-density flow and transport simulation: matching semi-analytic stability modes for steady unstable convection in an inclined porous box

USGS Publications Warehouse

Voss, Clifford I.; Simmons, Craig T.; Robinson, Neville I.

2010-01-01

This benchmark for three-dimensional (3D) numerical simulators of variable-density groundwater flow and solute or energy transport consists of matching simulation results with the semi-analytical solution for the transition from one steady-state convective mode to another in a porous box. Previous experimental and analytical studies of natural convective flow in an inclined porous layer have shown that there are a variety of convective modes possible depending on system parameters, geometry and inclination. In particular, there is a well-defined transition from the helicoidal mode consisting of downslope longitudinal rolls superimposed upon an upslope unicellular roll to a mode consisting of purely an upslope unicellular roll. Three-dimensional benchmarks for variable-density simulators are currently (2009) lacking and comparison of simulation results with this transition locus provides an unambiguous means to test the ability of such simulators to represent steady-state unstable 3D variable-density physics.

Assessing the Impact of Analytical Error on Perceived Disease Severity.

PubMed

Kroll, Martin H; Garber, Carl C; Bi, Caixia; Suffin, Stephen C

2015-10-01

The perception of the severity of disease from laboratory results assumes that the results are free of analytical error; however, analytical error creates a spread of results into a band and thus a range of perceived disease severity. To assess the impact of analytical errors by calculating the change in perceived disease severity, represented by the hazard ratio, using non-high-density lipoprotein (nonHDL) cholesterol as an example. We transformed nonHDL values into ranges using the assumed total allowable errors for total cholesterol (9%) and high-density lipoprotein cholesterol (13%). Using a previously determined relationship between the hazard ratio and nonHDL, we calculated a range of hazard ratios for specified nonHDL concentrations affected by analytical error. Analytical error, within allowable limits, created a band of values of nonHDL, with a width spanning 30 to 70 mg/dL (0.78-1.81 mmol/L), depending on the cholesterol and high-density lipoprotein cholesterol concentrations. Hazard ratios ranged from 1.0 to 2.9, a 16% to 50% error. Increased bias widens this range and decreased bias narrows it. Error-transformed results produce a spread of values that straddle the various cutoffs for nonHDL. The range of the hazard ratio obscures the meaning of results, because the spread of ratios at different cutoffs overlap. The magnitude of the perceived hazard ratio error exceeds that for the allowable analytical error, and significantly impacts the perceived cardiovascular disease risk. Evaluating the error in the perceived severity (eg, hazard ratio) provides a new way to assess the impact of analytical error.
The multifacet graphically contracted function method. I. Formulation and implementation

NASA Astrophysics Data System (ADS)

Shepard, Ron; Gidofalvi, Gergely; Brozell, Scott R.

2014-08-01

The basic formulation for the multifacet generalization of the graphically contracted function (MFGCF) electronic structure method is presented. The analysis includes the discussion of linear dependency and redundancy of the arc factor parameters, the computation of reduced density matrices, Hamiltonian matrix construction, spin-density matrix construction, the computation of optimization gradients for single-state and state-averaged calculations, graphical wave function analysis, and the efficient computation of configuration state function and Slater determinant expansion coefficients. Timings are given for Hamiltonian matrix element and analytic optimization gradient computations for a range of model problems for full-CI Shavitt graphs, and it is observed that both the energy and the gradient computation scale as O(N2n4) for N electrons and n orbitals. The important arithmetic operations are within dense matrix-matrix product computational kernels, resulting in a computationally efficient procedure. An initial implementation of the method is used to present applications to several challenging chemical systems, including N2 dissociation, cubic H8 dissociation, the symmetric dissociation of H2O, and the insertion of Be into H2. The results are compared to the exact full-CI values and also to those of the previous single-facet GCF expansion form.
The multifacet graphically contracted function method. I. Formulation and implementation.

PubMed

Shepard, Ron; Gidofalvi, Gergely; Brozell, Scott R

2014-08-14

The basic formulation for the multifacet generalization of the graphically contracted function (MFGCF) electronic structure method is presented. The analysis includes the discussion of linear dependency and redundancy of the arc factor parameters, the computation of reduced density matrices, Hamiltonian matrix construction, spin-density matrix construction, the computation of optimization gradients for single-state and state-averaged calculations, graphical wave function analysis, and the efficient computation of configuration state function and Slater determinant expansion coefficients. Timings are given for Hamiltonian matrix element and analytic optimization gradient computations for a range of model problems for full-CI Shavitt graphs, and it is observed that both the energy and the gradient computation scale as O(N(2)n(4)) for N electrons and n orbitals. The important arithmetic operations are within dense matrix-matrix product computational kernels, resulting in a computationally efficient procedure. An initial implementation of the method is used to present applications to several challenging chemical systems, including N2 dissociation, cubic H8 dissociation, the symmetric dissociation of H2O, and the insertion of Be into H2. The results are compared to the exact full-CI values and also to those of the previous single-facet GCF expansion form.
Reference interaction site model with hydrophobicity induced density inhomogeneity: An analytical theory to compute solvation properties of large hydrophobic solutes in the mixture of polyatomic solvent molecules.

PubMed

Cao, Siqin; Sheong, Fu Kit; Huang, Xuhui

2015-08-07

Reference interaction site model (RISM) has recently become a popular approach in the study of thermodynamical and structural properties of the solvent around macromolecules. On the other hand, it was widely suggested that there exists water density depletion around large hydrophobic solutes (>1 nm), and this may pose a great challenge to the RISM theory. In this paper, we develop a new analytical theory, the Reference Interaction Site Model with Hydrophobicity induced density Inhomogeneity (RISM-HI), to compute solvent radial distribution function (RDF) around large hydrophobic solute in water as well as its mixture with other polyatomic organic solvents. To achieve this, we have explicitly considered the density inhomogeneity at the solute-solvent interface using the framework of the Yvon-Born-Green hierarchy, and the RISM theory is used to obtain the solute-solvent pair correlation. In order to efficiently solve the relevant equations while maintaining reasonable accuracy, we have also developed a new closure called the D2 closure. With this new theory, the solvent RDFs around a large hydrophobic particle in water and different water-acetonitrile mixtures could be computed, which agree well with the results of the molecular dynamics simulations. Furthermore, we show that our RISM-HI theory can also efficiently compute the solvation free energy of solute with a wide range of hydrophobicity in various water-acetonitrile solvent mixtures with a reasonable accuracy. We anticipate that our theory could be widely applied to compute the thermodynamic and structural properties for the solvation of hydrophobic solute.
Elliptic-cylindrical analytical flux-rope model for ICMEs

NASA Astrophysics Data System (ADS)

Nieves-Chinchilla, T.; Linton, M.; Hidalgo, M. A. U.; Vourlidas, A.

2016-12-01

We present an analytical flux-rope model for realistic magnetic structures embedded in Interplanetary Coronal Mass Ejections. The framework of this model was established by Nieves-Chinchilla et al. (2016) with the circular-cylindrical analytical flux rope model and under the concept developed by Hidalgo et al. (2002). Elliptic-cylindrical geometry establishes the first-grade of complexity of a series of models. The model attempts to describe the magnetic flux rope topology with distorted cross-section as a possible consequence of the interaction with the solar wind. In this model, the flux rope is completely described in the non-euclidean geometry. The Maxwell equations are solved using tensor calculus consistently with the geometry chosen, invariance along the axial component, and with the only assumption of no radial current density. The model is generalized in terms of the radial dependence of the poloidal current density component and axial current density component. The misalignment between current density and magnetic field is studied in detail for the individual cases of different pairs of indexes for the axial and poloidal current density components. This theoretical analysis provides a map of the force distribution inside of the flux-rope. The reconstruction technique has been adapted to the model and compared with in situ ICME set of events with different in situ signatures. The successful result is limited to some cases with clear in-situ signatures of distortion. However, the model adds a piece in the puzzle of the physical-analytical representation of these magnetic structures. Other effects such as axial curvature, expansion and/or interaction could be incorporated in the future to fully understand the magnetic structure. Finally, the mathematical formulation of this model opens the door to the next model: toroidal flux rope analytical model.
On the distribution of local dissipation scales in turbulent flows

NASA Astrophysics Data System (ADS)

May, Ian; Morshed, Khandakar; Venayagamoorthy, Karan; Dasi, Lakshmi

2014-11-01

Universality of dissipation scales in turbulence relies on self-similar scaling and large scale independence. We show that the probability density function of dissipation scales, Q (η) , is analytically defined by the two-point correlation function, and the Reynolds number (Re). We also present a new analytical form for the two-point correlation function for the dissipation scales through a generalized definition of a directional Taylor microscale. Comparison of Q (η) predicted within this framework and published DNS data shows excellent agreement. It is shown that for finite Re no single similarity law exists even for the case of homogeneous isotropic turbulence. Instead a family of scaling is presented, defined by Re and a dimensionless local inhomogeneity parameter based on the spatial gradient of the rms velocity. For moderate Re inhomogeneous flows, we note a strong directional dependence of Q (η) dictated by the principal Reynolds stresses. It is shown that the mode of the distribution Q (η) significantly shifts to sub-Kolmogorov scales along the inhomogeneous directions, as in wall bounded turbulence. This work extends the classical Kolmogorov's theory to finite Re homogeneous isotropic turbulence as well as the case of inhomogeneous anisotropic turbulence.
An extended heterogeneous car-following model accounting for anticipation driving behavior and mixed maximum speeds

NASA Astrophysics Data System (ADS)

Sun, Fengxin; Wang, Jufeng; Cheng, Rongjun; Ge, Hongxia

2018-02-01

The optimal driving speeds of the different vehicles may be different for the same headway. In the optimal velocity function of the optimal velocity (OV) model, the maximum speed vmax is an important parameter determining the optimal driving speed. A vehicle with higher maximum speed is more willing to drive faster than that with lower maximum speed in similar situation. By incorporating the anticipation driving behavior of relative velocity and mixed maximum speeds of different percentages into optimal velocity function, an extended heterogeneous car-following model is presented in this paper. The analytical linear stable condition for this extended heterogeneous traffic model is obtained by using linear stability theory. Numerical simulations are carried out to explore the complex phenomenon resulted from the cooperation between anticipation driving behavior and heterogeneous maximum speeds in the optimal velocity function. The analytical and numerical results all demonstrate that strengthening driver's anticipation effect can improve the stability of heterogeneous traffic flow, and increasing the lowest value in the mixed maximum speeds will result in more instability, but increasing the value or proportion of the part already having higher maximum speed will cause different stabilities at high or low traffic densities.
A statistical study of gyro-averaging effects in a reduced model of drift-wave transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fonseca, Julio; Del-Castillo-Negrete, Diego B.; Sokolov, Igor M.

2016-08-25

Here, a statistical study of finite Larmor radius (FLR) effects on transport driven by electrostatic driftwaves is presented. The study is based on a reduced discrete Hamiltonian dynamical system known as the gyro-averaged standard map (GSM). In this system, FLR effects are incorporated through the gyro-averaging of a simplified weak-turbulence model of electrostatic fluctuations. Formally, the GSM is a modified version of the standard map in which the perturbation amplitude, K 0, becomes K 0J 0(more » $$\\hat{p}$$), where J 0 is the zeroth-order Bessel function and $$\\hat{p}$$ s the Larmor radius. Assuming a Maxwellian probability density function (pdf) for $$\\hat{p}$$ , we compute analytically and numerically the pdf and the cumulative distribution function of the effective drift-wave perturba- tion amplitude K 0J 0($$\\hat{p}$$). Using these results, we compute the probability of loss of confinement (i.e., global chaos), P c provides an upper bound for the escape rate, and that P t rovides a good estimate of the particle trapping rate. Lastly. the analytical results are compared with direct numerical Monte-Carlo simulations of particle transport.« less
Relay-aided free-space optical communications using α - μ distribution over atmospheric turbulence channels with misalignment errors

NASA Astrophysics Data System (ADS)

Upadhya, Abhijeet; Dwivedi, Vivek K.; Singh, G.

2018-06-01

In this paper, we have analyzed the performance of dual hop radio frequency (RF)/free-space optical (FSO) fixed gain relay environment confined by atmospheric turbulence induced fading channel over FSO link and modeled using α - μ distribution. The RF hop of the amplify-and-forward scheme undergoes the Rayleigh fading and the proposed system model also considers the pointing error effect on the FSO link. A novel and accurate mathematical expression of the probability density function for a FSO link experiencing α - μ distributed atmospheric turbulence in the presence of pointing error is derived. Further, we have presented analytical expressions of outage probability and bit error rate in terms of Meijer-G function. In addition to this, a useful and mathematically tractable closed-form expression for the end-to-end ergodic capacity of the dual hop scheme in terms of bivariate Fox's H function is derived. The atmospheric turbulence, misalignment errors and various binary modulation schemes for intensity modulation on optical wireless link are considered to yield the results. Finally, we have analyzed each of the three performance metrics for high SNR in order to represent them in terms of elementary functions and the achieved analytical results are supported by computer-based simulations.
DOS cones along atomic chains

NASA Astrophysics Data System (ADS)

Kwapiński, Tomasz

2017-03-01

The electron transport properties of a linear atomic chain are studied theoretically within the tight-binding Hamiltonian and the Green’s function method. Variations of the local density of states (DOS) along the chain are investigated. They are crucial in scanning tunnelling experiments and give important insight into the electron transport mechanism and charge distribution inside chains. It is found that depending on the chain parity the local DOS at the Fermi level can form cone-like structures (DOS cones) along the chain. The general condition for the local DOS oscillations is obtained and the linear behaviour of the local density function is confirmed analytically. DOS cones are characterized by a linear decay towards the chain which is in contrast to the propagation properties of charge density waves, end states and Friedel oscillations in one-dimensional systems. We find that DOS cones can appear due to non-resonant electron transport, the spin-orbit scattering or for chains fabricated on a substrate with localized electrons. It is also shown that for imperfect chains (e.g. with a reduced coupling strength between two neighboring sites) a diamond-like structure of the local DOS along the chain appears.
Virial Coefficients and Equations of State for Hard Polyhedron Fluids.

PubMed

Irrgang, M Eric; Engel, Michael; Schultz, Andrew J; Kofke, David A; Glotzer, Sharon C

2017-10-24

Hard polyhedra are a natural extension of the hard sphere model for simple fluids, but there is no general scheme for predicting the effect of shape on thermodynamic properties, even in moderate-density fluids. Only the second virial coefficient is known analytically for general convex shapes, so higher-order equations of state have been elusive. Here we investigate high-precision state functions in the fluid phase of 14 representative polyhedra with different assembly behaviors. We discuss historic efforts in analytically approximating virial coefficients up to B 4 and numerically evaluating them to B 8 . Using virial coefficients as inputs, we show the convergence properties for four equations of state for hard convex bodies. In particular, the exponential approximant of Barlow et al. (J. Chem. Phys. 2012, 137, 204102) is found to be useful up to the first ordering transition for most polyhedra. The convergence behavior we explore can guide choices in expending additional resources for improved estimates. Fluids of arbitrary hard convex bodies are too complicated to be described in a general way at high densities, so the high-precision state data we provide can serve as a reference for future work in calculating state data or as a basis for thermodynamic integration.
Different coupled atmosphere-recharge oscillator Low Order Models for ENSO: a projection approach.

NASA Astrophysics Data System (ADS)

Bianucci, Marco; Mannella, Riccardo; Merlino, Silvia; Olivieri, Andrea

2016-04-01

El Ninõ-Southern Oscillation (ENSO) is a large scale geophysical phenomenon where, according to the celebrated recharge oscillator model (ROM), the Ocean slow variables given by the East Pacific Sea Surface Temperature (SST) and the average thermocline depth (h), interact with some fast "irrelevant" ones, representing mostly the atmosphere (the westerly wind burst and the Madden-Julian Oscillation). The fast variables are usually inserted in the model as an external stochastic forcing. In a recent work (M. Bianucci, "Analytical probability density function for the statistics of the ENSO phenomenon: asymmetry and power law tail" Geophysical Research Letters, under press) the author, using a projection approach applied to general deterministic coupled systems, gives a physically reasonable explanation for the use of stochastic models for mimicking the apparent random features of the ENSO phenomenon. Moreover, in the same paper, assuming that the interaction between the ROM and the fast atmosphere is of multiplicative type, i.e., it depends on the SST variable, an analytical expression for the equilibrium density function of the anomaly SST is obtained. This expression fits well the data from observations, reproducing the asymmetry and the power law tail of the histograms of the NINÕ3 index. Here, using the same theoretical approach, we consider and discuss different kind of interactions between the ROM and the other perturbing variables, and we take into account also non linear ROM as a low order model for ENSO. The theoretical and numerical results are then compared with data from observations.
Density Functional Theory Study of Spirodienone Stereoisomers in Lignin

DOE Office of Scientific and Technical Information (OSTI.GOV)

Elder, Thomas; Berstis, Laura; Beckham, Gregg T.

The spirodienone structure in lignin is a relatively recent discovery, and it has been found to occur in lignin of various plant species at concentrations of ~3%, which is sufficiently high to be important for better understanding of its properties and reactivity. The cyclic structure, with a ..beta..-1 bond, has been proposed to be a precursor for acyclic ..beta..-1 linkages in lignin. Previous analytical work has revealed the presence, but not the absolute configuration, of two stereoisomeric forms of spirodienone. The objective of the current work was to determine if there are thermodynamic differences that could help identify the experimentallymore » observed stereoisomers. Results from density functional theory calculations reveal the presence of clusters of stereoisomers with varying stability that may be of use in narrowing the list of possible structures. Furthermore, the bond dissociation enthalpy of the cyclic ring exhibited a particularly high value for the C-O cleavage reaction relative to more conventional ether bonds in lignin, perhaps due to limited electron delocalization possibilities.« less
Density Functional Theory Study of Spirodienone Stereoisomers in Lignin

DOE PAGES

Elder, Thomas; Berstis, Laura; Beckham, Gregg T.; ...

2017-06-28

The spirodienone structure in lignin is a relatively recent discovery, and it has been found to occur in lignin of various plant species at concentrations of ~3%, which is sufficiently high to be important for better understanding of its properties and reactivity. The cyclic structure, with a ..beta..-1 bond, has been proposed to be a precursor for acyclic ..beta..-1 linkages in lignin. Previous analytical work has revealed the presence, but not the absolute configuration, of two stereoisomeric forms of spirodienone. The objective of the current work was to determine if there are thermodynamic differences that could help identify the experimentallymore » observed stereoisomers. Results from density functional theory calculations reveal the presence of clusters of stereoisomers with varying stability that may be of use in narrowing the list of possible structures. Furthermore, the bond dissociation enthalpy of the cyclic ring exhibited a particularly high value for the C-O cleavage reaction relative to more conventional ether bonds in lignin, perhaps due to limited electron delocalization possibilities.« less
Estimating maximum instantaneous distortion from inlet total pressure rms and PSD measurements. [Root Mean Square and Power Spectral Density methods

NASA Technical Reports Server (NTRS)

Melick, H. C., Jr.; Ybarra, A. H.; Bencze, D. P.

1975-01-01

An inexpensive method is developed to determine the extreme values of instantaneous inlet distortion. This method also provides insight into the basic mechanics of unsteady inlet flow and the associated engine reaction. The analysis is based on fundamental fluid dynamics and statistical methods to provide an understanding of the turbulent inlet flow and quantitatively relate the rms level and power spectral density (PSD) function of the measured time variant total pressure fluctuations to the strength and size of the low pressure regions. The most probable extreme value of the instantaneous distortion is then synthesized from this information in conjunction with the steady state distortion. Results of the analysis show the extreme values to be dependent upon the steady state distortion, the measured turbulence rms level and PSD function, the time on point, and the engine response characteristics. Analytical projections of instantaneous distortion are presented and compared with data obtained by a conventional, highly time correlated, 40 probe instantaneous pressure measurement system.
Density-functional approach to the three-body dispersion interaction based on the exchange dipole moment

PubMed Central

Proynov, Emil; Liu, Fenglai; Gan, Zhengting; Wang, Matthew; Kong, Jing

2015-01-01

We implement and compute the density functional nonadditive three-body dispersion interaction using a combination of Tang-Karplus formalism and the exchange-dipole moment model of Becke and Johnson. The computation of the C9 dispersion coefficients is done in a non-empirical fashion. The obtained C9 values of a series of noble atom triplets agree well with highly accurate values in the literature. We also calculate the C9 values for a series of benzene trimers and find a good agreement with high-level ab initio values reported recently in the literature. For the question of damping of the three-body dispersion at short distances, we propose two damping schemes and optimize them based on the benzene trimers data, and the fitted analytic potentials of He3 and Ar3 trimers fitted to the results of high-level wavefunction theories available from the literature. Both damping schemes respond well to the optimization of two parameters. PMID:26328836
Bayesian predictive power: choice of prior and some recommendations for its use as probability of success in drug development.

PubMed

Rufibach, Kaspar; Burger, Hans Ulrich; Abt, Markus

2016-09-01

Bayesian predictive power, the expectation of the power function with respect to a prior distribution for the true underlying effect size, is routinely used in drug development to quantify the probability of success of a clinical trial. Choosing the prior is crucial for the properties and interpretability of Bayesian predictive power. We review recommendations on the choice of prior for Bayesian predictive power and explore its features as a function of the prior. The density of power values induced by a given prior is derived analytically and its shape characterized. We find that for a typical clinical trial scenario, this density has a u-shape very similar, but not equal, to a β-distribution. Alternative priors are discussed, and practical recommendations to assess the sensitivity of Bayesian predictive power to its input parameters are provided. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
Absorption, scattering, and radiation force efficiencies in the longitudinal wave scattering by a small viscoelastic particle in an isotropic solid.

PubMed

Lopes, J H; Leão-Neto, J P; Silva, G T

2017-11-01

Analytical expressions of the absorption, scattering, and elastic radiation force efficiency factors are derived for the longitudinal plane wave scattering by a small viscoelastic particle in a lossless solid matrix. The particle is assumed to be much smaller than the incident wavelength, i.e., the so-called long-wavelength (Rayleigh) approximation. The efficiencies are dimensionless quantities that represent the absorbed and scattering powers and the elastic radiation force on the particle. In the quadrupole approximation, they are expressed in terms of contrast functions (bulk and shear moduli, and density) between the particle and solid matrix. The results for a high-density polyethylene particle embedded in an aluminum matrix agree with those obtained with the partial wave expansion method. Additionally, the connection between the elastic radiation force and forward scattering function is established through the optical theorem. The present results should be useful for ultrasound characterization of particulate composites, and the development of implanted devices activated by radiation force.
Density-functional approach to the three-body dispersion interaction based on the exchange dipole moment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Proynov, Emil; Wang, Matthew; Kong, Jing, E-mail: jing.kong@mtsu.edu

We implement and compute the density functional nonadditive three-body dispersion interaction using a combination of Tang-Karplus formalism and the exchange-dipole moment model of Becke and Johnson. The computation of the C{sub 9} dispersion coefficients is done in a non-empirical fashion. The obtained C{sub 9} values of a series of noble atom triplets agree well with highly accurate values in the literature. We also calculate the C{sub 9} values for a series of benzene trimers and find a good agreement with high-level ab initio values reported recently in the literature. For the question of damping of the three-body dispersion at shortmore » distances, we propose two damping schemes and optimize them based on the benzene trimers data, and the fitted analytic potentials of He{sub 3} and Ar{sub 3} trimers fitted to the results of high-level wavefunction theories available from the literature. Both damping schemes respond well to the optimization of two parameters.« less
Investigating tautomeric polymorphism in crystalline anthranilic acid using terahertz spectroscopy and solid-state density functional theory.

PubMed

Delaney, Sean P; Witko, Ewelina M; Smith, Tiffany M; Korter, Timothy M

2012-08-02

Terahertz spectroscopy is sensitive to the interactions between molecules in the solid-state and recently has emerged as a new analytical tool for investigating polymorphism. Here, this technique is applied for the first time to the phenomenon of tautomeric polymorphism where the crystal structures of anthranilic acid (2-aminobenzoic acid) have been investigated. Three polymorphs of anthranilic acid (denoted Forms I, II and III) were studied using terahertz spectroscopy and the vibrational modes and relative polymorph stabilities analyzed using solid-state density functional theory calculations augmented with London dispersion force corrections. Form I consists of both neutral and zwitterionic molecules and was found to be the most stable polymorph as compared to Forms II and III (both containing only neutral molecules). The simulations suggest that a balance between steric interactions and electrostatic forces is responsible for the favoring of the mixed neutral/zwitterion solid over the all neutral or all zwitterion crystalline arrangements.

Density functional perturbational orbital theory of spin polarization in electronic systems. II. Transition metal dimer complexes.

PubMed

Seo, Dong-Kyun

2007-11-14

We present a theoretical scheme for a semiquantitative analysis of electronic structures of magnetic transition metal dimer complexes within spin density functional theory (DFT). Based on the spin polarization perturbational orbital theory [D.-K. Seo, J. Chem. Phys. 125, 154105 (2006)], explicit spin-dependent expressions of the spin orbital energies and coefficients are derived, which allows to understand how spin orbitals form and change their energies and shapes when two magnetic sites are coupled either ferromagnetically or antiferromagnetically. Upon employment of the concept of magnetic orbitals in the active-electron approximation, a general mathematical formula is obtained for the magnetic coupling constant J from the analytical expression for the electronic energy difference between low-spin broken-symmetry and high-spin states. The origin of the potential exchange and kinetic exchange terms based on the one-electron picture is also elucidated. In addition, we provide a general account of the DFT analysis of the magnetic exchange interactions in compounds for which the active-electron approximation is not appropriate.
Inviscid linear stability analysis of two fluid columns of different densities subject to gravity

NASA Astrophysics Data System (ADS)

Prathama, Aditya; Pantano, Carlos

2017-11-01

We investigate the inviscid linear stability of vertical interface between two fluid columns of different densities under the influence of gravity. In this flow arrangement, the two free streams are continuously accelerating, in contrast to the canonical Kelvin-Helmholtz or Rayleigh-Taylor instabilities whose base flows are stationary (or weakly time dependent). In these classical cases, the temporal evolution of the interface can be expressed as Fourier or Laplace solutions in time. This is not possible in our case; instead, we employ the initial value problem method to solve the equations analytically. The results, expressed in terms of the well-known parabolic cylinder function, indicate that the instability grows as the exponential of a quadratic function of time. The analysis shows that in this accelerating Kelvin-Helmholtz configuration, the interface is unconditionally unstable at all wave modes, despite the presence of surface tension. Department of Energy, National Nuclear Security Administration (Award No. DE-NA0002382) and the California Institute of Technology.
A general framework for numerical simulation of improvised explosive device (IED)-detection scenarios using density functional theory (DFT) and terahertz (THz) spectra.

PubMed

Shabaev, Andrew; Lambrakos, Samuel G; Bernstein, Noam; Jacobs, Verne L; Finkenstadt, Daniel

2011-04-01

We have developed a general framework for numerical simulation of various types of scenarios that can occur for the detection of improvised explosive devices (IEDs) through the use of excitation using incident electromagnetic waves. A central component model of this framework is an S-matrix representation of a multilayered composite material system. Each layer of the system is characterized by an average thickness and an effective electric permittivity function. The outputs of this component are the reflectivity and the transmissivity as functions of frequency and angle of the incident electromagnetic wave. The input of the component is a parameterized analytic-function representation of the electric permittivity as a function of frequency, which is provided by another component model of the framework. The permittivity function is constructed by fitting response spectra calculated using density functional theory (DFT) and parameter adjustment according to any additional information that may be available, e.g., experimentally measured spectra or theory-based assumptions concerning spectral features. A prototype simulation is described that considers response characteristics for THz excitation of the high explosive β-HMX. This prototype simulation includes a description of a procedure for calculating response spectra using DFT as input to the Smatrix model. For this purpose, the DFT software NRLMOL was adopted. © 2011 Society for Applied Spectroscopy
Average symbol error rate for M-ary quadrature amplitude modulation in generalized atmospheric turbulence and misalignment errors

NASA Astrophysics Data System (ADS)

Sharma, Prabhat Kumar

2016-11-01

A framework is presented for the analysis of average symbol error rate (SER) for M-ary quadrature amplitude modulation in a free-space optical communication system. The standard probability density function (PDF)-based approach is extended to evaluate the average SER by representing the Q-function through its Meijer's G-function equivalent. Specifically, a converging power series expression for the average SER is derived considering the zero-boresight misalignment errors in the receiver side. The analysis presented here assumes a unified expression for the PDF of channel coefficient which incorporates the M-distributed atmospheric turbulence and Rayleigh-distributed radial displacement for the misalignment errors. The analytical results are compared with the results obtained using Q-function approximation. Further, the presented results are supported by the Monte Carlo simulations.
Nonlinearity of the forward-backward correlation function in the model with string fusion

NASA Astrophysics Data System (ADS)

Vechernin, Vladimir

2017-12-01

The behavior of the forward-backward correlation functions and the corresponding correlation coefficients between multiplicities and transverse momenta of particles produced in high energy hadronic interactions is analyzed by analytical and MC calculations in the models with and without string fusion. The string fusion is taking into account in simplified form by introducing the lattice in the transverse plane. The results obtained with two alternative definitions of the forward-backward correlation coefficient are compared. It is shown that the nonlinearity of correlation functions increases with the width of observation windows, leading at small string density to a strong dependence of correlation coefficient value on the definition. The results of the modeling enable qualitatively to explain the experimentally observed features in the behavior of the correlation functions between multiplicities and mean transverse momenta at small and large multiplicities.
Study of Analytic Statistical Model for Decay of Light and Medium Mass Nuclei in Nuclear Fragmentation

NASA Technical Reports Server (NTRS)

Cucinotta, Francis A.; Wilson, John W.

1996-01-01

The angular momentum independent statistical decay model is often applied using a Monte-Carlo simulation to describe the decay of prefragment nuclei in heavy ion reactions. This paper presents an analytical approach to the decay problem of nuclei with mass number less than 60, which is important for galactic cosmic ray (GCR) studies. This decay problem of nuclei with mass number less than 60 incorporates well-known levels of the lightest nuclei (A less than 11) to improve convergence and accuracy. A sensitivity study of the model level density function is used to determine the impact on mass and charge distributions in nuclear fragmentation. This angular momentum independent statistical decay model also describes the momentum and energy distribution of emitted particles (n, p, d, t, h, and a) from a prefragment nucleus.
Discontinuous model with semi analytical sheath interface for radio frequency plasma

NASA Astrophysics Data System (ADS)

Miyashita, Masaru

2016-09-01

Sumitomo Heavy Industries, Ltd. provide many products utilizing plasma. In this study, we focus on the Radio Frequency (RF) plasma source by interior antenna. The plasma source is expected to be high density and low metal contamination. However, the sputtering the antenna cover by high energy ion from sheath voltage still have been problematic. We have developed the new model which can calculate sheath voltage wave form in the RF plasma source for realistic calculation time. This model is discontinuous that electronic fluid equation in plasma connect to usual passion equation in antenna cover and chamber with semi analytical sheath interface. We estimate the sputtering distribution based on calculated sheath voltage waveform by this model, sputtering yield and ion energy distribution function (IEDF) model. The estimated sputtering distribution reproduce the tendency of experimental results.
Universal Long Ranged Correlations in Driven Binary Mixtures

NASA Astrophysics Data System (ADS)

Poncet, Alexis; Bénichou, Olivier; Démery, Vincent; Oshanin, Gleb

2017-03-01

When two populations of "particles" move in opposite directions, like oppositely charged colloids under an electric field or intersecting flows of pedestrians, they can move collectively, forming lanes along their direction of motion. The nature of this "laning transition" is still being debated and, in particular, the pair correlation functions, which are the key observables to quantify this phenomenon, have not been characterized yet. Here, we determine the correlations using an analytical approach based on a linearization of the stochastic equations for the density fields, which is valid for dense systems of soft particles. We find that the correlations decay algebraically along the direction of motion, and have a self-similar exponential profile in the transverse direction. Brownian dynamics simulations confirm our theoretical predictions and show that they also hold beyond the validity range of our analytical approach, pointing to a universal behavior.
Integration within the Felsenstein equation for improved Markov chain Monte Carlo methods in population genetics

PubMed Central

Hey, Jody; Nielsen, Rasmus

2007-01-01

In 1988, Felsenstein described a framework for assessing the likelihood of a genetic data set in which all of the possible genealogical histories of the data are considered, each in proportion to their probability. Although not analytically solvable, several approaches, including Markov chain Monte Carlo methods, have been developed to find approximate solutions. Here, we describe an approach in which Markov chain Monte Carlo simulations are used to integrate over the space of genealogies, whereas other parameters are integrated out analytically. The result is an approximation to the full joint posterior density of the model parameters. For many purposes, this function can be treated as a likelihood, thereby permitting likelihood-based analyses, including likelihood ratio tests of nested models. Several examples, including an application to the divergence of chimpanzee subspecies, are provided. PMID:17301231
Analytical pair correlations in ideal quantum gases: temperature-dependent bunching and antibunching.

PubMed

Bosse, J; Pathak, K N; Singh, G S

2011-10-01

The fluctuation-dissipation theorem together with the exact density response spectrum for ideal quantum gases has been utilized to yield a new expression for the static structure factor, which we use to derive exact analytical expressions for the temperature-dependent pair distribution function g(r) of the ideal gases. The plots of bosonic and fermionic g(r) display "Bose pile" and "Fermi hole" typically akin to bunching and antibunching as observed experimentally for ultracold atomic gases. The behavior of spin-scaled pair correlation for fermions is almost featureless, but bosons show a rich structure including long-range correlations near T(c). The coherent state at T=0 shows no correlation at all, just like single-mode lasers. The depicted decreasing trend in correlation with decrease in temperature for T
A semi-analytical model of disk evaporation by thermal conduction

NASA Astrophysics Data System (ADS)

Dullemond, C. P.

1999-01-01

The conditions for disk evaporation by electron thermal conduction are examined, using a simplified semi-analytical 1-D model. The model is based on the mechanism proposed by Meyer & Meyer-Hofmeister ( te{meyermeyhof:1994}) in which an advection dominated accretion flow evaporates the top layers from the underlying disk by thermal conduction. The evaporation rate is calculated as a function of the density of the advective flow, and an analysis is made of the time scales and length scales of the dynamics of the advective flow. It is shown that evaporation can only completely destroy the disk if the conductive length scale is of the order of the radius. This implies that radial conduction is an essential factor in the evaporation process. The heat required for evaporation is in fact produced at small radii and transported radially towards the evaporation region.
Mass functions from the excursion set model

NASA Astrophysics Data System (ADS)

Hiotelis, Nicos; Del Popolo, Antonino

2017-11-01

Aims: We aim to study the stochastic evolution of the smoothed overdensity δ at scale S of the form δ(S) = ∫0S K(S,u)dW(u), where K is a kernel and dW is the usual Wiener process. Methods: For a Gaussian density field, smoothed by the top-hat filter, in real space, we used a simple kernel that gives the correct correlation between scales. A Monte Carlo procedure was used to construct random walks and to calculate first crossing distributions and consequently mass functions for a constant barrier. Results: We show that the evolution considered here improves the agreement with the results of N-body simulations relative to analytical approximations which have been proposed from the same problem by other authors. In fact, we show that an evolution which is fully consistent with the ideas of the excursion set model, describes accurately the mass function of dark matter haloes for values of ν ≤ 1 and underestimates the number of larger haloes. Finally, we show that a constant threshold of collapse, lower than it is usually used, it is able to produce a mass function which approximates the results of N-body simulations for a variety of redshifts and for a wide range of masses. Conclusions: A mass function in good agreement with N-body simulations can be obtained analytically using a lower than usual constant collapse threshold.
C+/H2 gas in star-forming clouds and galaxies

NASA Astrophysics Data System (ADS)

Nordon, Raanan; Sternberg, Amiel

2016-11-01

We present analytic theory for the total column density of singly ionized carbon (C+) in the optically thick photon dominated regions (PDRs) of far-UV irradiated (star-forming) molecular clouds. We derive a simple formula for the C+ column as a function of the cloud (hydrogen) density, the far-UV field intensity, and metallicity, encompassing the wide range of galaxy conditions. When assuming the typical relation between UV and density in the cold neutral medium, the C+ column becomes a function of the metallicity alone. We verify our analysis with detailed numerical PDR models. For optically thick gas, most of the C+ column is mixed with hydrogen that is primarily molecular (H2), and this `C+/H2' gas layer accounts for almost all of the `CO-dark' molecular gas in PDRs. The C+/H2 column density is limited by dust shielding and is inversely proportional to the metallicity down to ˜0.1 solar. At lower metallicities, H2 line blocking dominates and the C+/H2 column saturates. Applying our theory to CO surveys in low-redshift spirals, we estimate the fraction of C+/H2 gas out of the total molecular gas to be typically ˜0.4. At redshifts 1 < z < 3 in massive disc galaxies the C+/H2 gas represents a very small fraction of the total molecular gas (≲ 0.16). This small fraction at high redshifts is due to the high gas surface densities when compared to local galaxies.
Multibunch solutions of the differential-difference equation for traffic flow

PubMed

Nakanishi

2000-09-01

The Newell-Whitham type of car-following model, with a hyperbolic tangent as the optimal velocity function, has a finite number of exact steady traveling wave solutions that can be expressed in terms of elliptic theta functions. Each such solution describes a density wave with a definite number of car bunches on a circuit. In our numerical simulations, we observe a transition process from uniform flow to congested flow described by a one-bunch analytic solution, which appears to be an attractor of the system. In this process, the system exhibits a series of transitions through which it comes to assume configurations closely approximating multibunch solutions with successively fewer bunches.
Electron scattering intensities and Patterson functions of Skyrmions

NASA Astrophysics Data System (ADS)

Karliner, M.; King, C.; Manton, N. S.

2016-06-01

The scattering of electrons off nuclei is one of the best methods of probing nuclear structure. In this paper we focus on electron scattering off nuclei with spin and isospin zero within the Skyrme model. We consider two distinct methods and simplify our calculations by use of the Born approximation. The first method is to calculate the form factor of the spherically averaged Skyrmion charge density; the second uses the Patterson function to calculate the scattering intensity off randomly oriented Skyrmions, and spherically averages at the end. We compare our findings with experimental scattering data. We also find approximate analytical formulae for the first zero and first stationary point of a form factor.
Collision statistics, thermodynamics, and transport coefficients of hard hyperspheres in three, four, and five dimensions

NASA Astrophysics Data System (ADS)

Lue, L.

2005-01-01

The collision statistics of hard hyperspheres are investigated. An exact, analytical formula is developed for the distribution of speeds of a sphere on collision, which is shown to be related to the average time between collisions for a sphere with a particular velocity. In addition, the relationship between the collision rate and the compressibility factor is generalized to arbitrary dimensions. Molecular dynamics simulations are performed for d=3, 4, and 5 dimensional hard-hypersphere fluids. From these simulations, the equation of state of these systems, the self-diffusion coefficient, the shear viscosity, and the thermal conductivity are determined as a function of density. Various aspects of the collision statistics and their dependence on the density and dimensionality of the system are also studied.
Studies of uncontrolled air traffic patterns, phase 1

NASA Technical Reports Server (NTRS)

Baxa, E. G., Jr.; Scharf, L. L.; Ruedger, W. H.; Modi, J. A.; Wheelock, S. L.; Davis, C. M.

1975-01-01

The general aviation air traffic flow patterns at uncontrolled airports are investigated and analyzed and traffic pattern concepts are developed to minimize the midair collision hazard in uncontrolled airspace. An analytical approach to evaluate midair collision hazard probability as a function of traffic densities is established which is basically independent of path structure. Two methods of generating space-time interrelationships between terminal area aircraft are presented; one is a deterministic model to generate pseudorandom aircraft tracks, the other is a statistical model in preliminary form. Some hazard measures are presented for selected traffic densities. It is concluded that the probability of encountering a hazard should be minimized independently of any other considerations and that the number of encounters involving visible-avoidable aircraft should be maximized at the expense of encounters in other categories.
Statistical properties of Charney-Hasegawa-Mima zonal flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anderson, Johan, E-mail: anderson.johan@gmail.com; Botha, G. J. J.

2015-05-15

A theoretical interpretation of numerically generated probability density functions (PDFs) of intermittent plasma transport events in unforced zonal flows is provided within the Charney-Hasegawa-Mima (CHM) model. The governing equation is solved numerically with various prescribed density gradients that are designed to produce different configurations of parallel and anti-parallel streams. Long-lasting vortices form whose flow is governed by the zonal streams. It is found that the numerically generated PDFs can be matched with analytical predictions of PDFs based on the instanton method by removing the autocorrelations from the time series. In many instances, the statistics generated by the CHM dynamics relaxesmore » to Gaussian distributions for both the electrostatic and vorticity perturbations, whereas in areas with strong nonlinear interactions it is found that the PDFs are exponentially distributed.« less
Hydrodynamic Model for Conductivity in Graphene

PubMed Central

Mendoza, M.; Herrmann, H. J.; Succi, S.

2013-01-01

Based on the recently developed picture of an electronic ideal relativistic fluid at the Dirac point, we present an analytical model for the conductivity in graphene that is able to describe the linear dependence on the carrier density and the existence of a minimum conductivity. The model treats impurities as submerged rigid obstacles, forming a disordered medium through which graphene electrons flow, in close analogy with classical fluid dynamics. To describe the minimum conductivity, we take into account the additional carrier density induced by the impurities in the sample. The model, which predicts the conductivity as a function of the impurity fraction of the sample, is supported by extensive simulations for different values of ε, the dimensionless strength of the electric field, and provides excellent agreement with experimental data. PMID:23316277
Coherent forward broadening in cold atom clouds

NASA Astrophysics Data System (ADS)

Sutherland, R. T.; Robicheaux, F.

2016-02-01

It is shown that homogeneous line-broadening in a diffuse cold atom cloud is proportional to the resonant optical depth of the cloud. Furthermore, it is demonstrated how the strong directionality of the coherent interactions causes the cloud's spectra to depend strongly on its shape, even when the cloud is held at constant densities. These two numerical observations can be predicted analytically by extending the single-photon wave-function model. Lastly, elongating a cloud along the line of laser propagation causes the excitation probability distribution to deviate from the exponential decay predicted by the Beer-Lambert law to the extent where the atoms at the back of the cloud are more excited than the atoms at the front. These calculations are conducted at the low densities relevant to recent experiments.

Ion mobility analysis of lipoproteins

DOEpatents

Benner, W Henry [Danville, CA; Krauss, Ronald M [Berkeley, CA; Blanche, Patricia J [Berkeley, CA

2007-08-21

A medical diagnostic method and instrumentation system for analyzing noncovalently bonded agglomerated biological particles is described. The method and system comprises: a method of preparation for the biological particles; an electrospray generator; an alpha particle radiation source; a differential mobility analyzer; a particle counter; and data acquisition and analysis means. The medical device is useful for the assessment of human diseases, such as cardiac disease risk and hyperlipidemia, by rapid quantitative analysis of lipoprotein fraction densities. Initially, purification procedures are described to reduce an initial blood sample to an analytical input to the instrument. The measured sizes from the analytical sample are correlated with densities, resulting in a spectrum of lipoprotein densities. The lipoprotein density distribution can then be used to characterize cardiac and other lipid-related health risks.
Aerosol preparation of intact lipoproteins

DOEpatents

Benner, W Henry [Danville, CA; Krauss, Ronald M [Berkeley, CA; Blanche, Patricia J [Berkeley, CA

2012-01-17

A medical diagnostic method and instrumentation system for analyzing noncovalently bonded agglomerated biological particles is described. The method and system comprises: a method of preparation for the biological particles; an electrospray generator; an alpha particle radiation source; a differential mobility analyzer; a particle counter; and data acquisition and analysis means. The medical device is useful for the assessment of human diseases, such as cardiac disease risk and hyperlipidemia, by rapid quantitative analysis of lipoprotein fraction densities. Initially, purification procedures are described to reduce an initial blood sample to an analytical input to the instrument. The measured sizes from the analytical sample are correlated with densities, resulting in a spectrum of lipoprotein densities. The lipoprotein density distribution can then be used to characterize cardiac and other lipid-related health risks.
Soliton and kink jams in traffic flow with open boundaries.

PubMed

Muramatsu, M; Nagatani, T

1999-07-01

Soliton density wave is investigated numerically and analytically in the optimal velocity model (a car-following model) of a one-dimensional traffic flow with open boundaries. Soliton density wave is distinguished from the kink density wave. It is shown that the soliton density wave appears only at the threshold of occurrence of traffic jams. The Korteweg-de Vries (KdV) equation is derived from the optimal velocity model by the use of the nonlinear analysis. It is found that the traffic soliton appears only near the neutral stability line. The soliton solution is analytically obtained from the perturbed KdV equation. It is shown that the soliton solution obtained from the nonlinear analysis is consistent with that of the numerical simulation.
Bifurcation Analysis of a Predator-Prey System with Ratio-Dependent Functional Response

NASA Astrophysics Data System (ADS)

Jiang, Xin; She, Zhikun; Feng, Zhaosheng; Zheng, Xiuliang

2017-12-01

In this paper, we are concerned with the structural stability of a density dependent predator-prey system with ratio-dependent functional response. Starting with the geometrical analysis of hyperbolic curves, we obtain that the system has one or two positive equilibria under various conditions. Inspired by the S-procedure and semi-definite programming, we use the sum of squares decomposition based method to ensure the global asymptotic stability of the positive equilibrium through the associated polynomial Lyapunov functions. By exploring the monotonic property of the trace of the Jacobian matrix with respect to r under the given different conditions, we analytically verify that there is a corresponding unique r∗ such that the trace is equal to zero and prove the existence of Hopf bifurcation, respectively.
First-Principles Studies of Pentaerythritol Tetranitrate (PETN) Single Crystal Unit Cell Volumes and Vibrational Frequencies under Hydrostatic Pressure

NASA Astrophysics Data System (ADS)

Perger, Warren F.; Zhao, Jijun; Winey, J. M.; Gupta, Y. M.

2006-07-01

The vibrational frequencies of the PETN molecular crystal were calculated using the first-principles CRYSTAL03 program which employs an all-electron LCAO approach and calculates analytic first derivatives of the total energy with respect to atomic displacements. Numerical second derivatives were used to enable calculation of the vibrational frequencies at ambient pressure and under various states of compression. Three different density functionals, B3LYP, PW91, and X3LYP were used to examine the effect of the exchange-correlation functional on the vibrational frequencies. The average deviation with experimental results is shown to be on the order of 2-3%, depending on the functional used. The pressure-induced shift of the vibrational frequencies is presented.
Combining extrapolation with ghost interaction correction in range-separated ensemble density functional theory for excited states

NASA Astrophysics Data System (ADS)

Alam, Md. Mehboob; Deur, Killian; Knecht, Stefan; Fromager, Emmanuel

2017-11-01

The extrapolation technique of Savin [J. Chem. Phys. 140, 18A509 (2014)], which was initially applied to range-separated ground-state-density-functional Hamiltonians, is adapted in this work to ghost-interaction-corrected (GIC) range-separated ensemble density-functional theory (eDFT) for excited states. While standard extrapolations rely on energies that decay as μ-2 in the large range-separation-parameter μ limit, we show analytically that (approximate) range-separated GIC ensemble energies converge more rapidly (as μ-3) towards their pure wavefunction theory values (μ → +∞ limit), thus requiring a different extrapolation correction. The purpose of such a correction is to further improve on the convergence and, consequently, to obtain more accurate excitation energies for a finite (and, in practice, relatively small) μ value. As a proof of concept, we apply the extrapolation method to He and small molecular systems (viz., H2, HeH+, and LiH), thus considering different types of excitations such as Rydberg, charge transfer, and double excitations. Potential energy profiles of the first three and four singlet Σ+ excitation energies in HeH+ and H2, respectively, are studied with a particular focus on avoided crossings for the latter. Finally, the extraction of individual state energies from the ensemble energy is discussed in the context of range-separated eDFT, as a perspective.
Medication information leaflets for patients: the further validation of an analytic linguistic framework.

PubMed

Clerehan, Rosemary; Hirsh, Di; Buchbinder, Rachelle

2009-01-01

While clinicians may routinely use patient information leaflets about drug therapy, a poorly conceived leaflet has the potential to do harm. We previously developed a novel approach to analysing leaflets about a rheumatoid arthritis drug, using an analytic approach based on systemic functional linguistics. The aim of the present study was to verify the validity of the linguistic framework by applying it to two further arthritis drug leaflets. The findings confirmed the applicability of the framework and were used to refine it. A new stage or 'move' in the genre was identified. While the function of many of the moves appeared to be 'to instruct' the patient, the instruction was often unclear. The role relationships expressed in the text were critical to the meaning. As with our previous study, judged on their lexical density, the leaflets resembled academic text. The framework can provide specific tools to assess and produce medication information leaflets to support readers in taking medication. Future work could utilize the framework to evaluate information on other treatments and procedures or on healthcare information more widely.
Vegetation-modulated landscape evolution: Effects of vegetation on landscape processes, drainage density, and topography

NASA Astrophysics Data System (ADS)

Istanbulluoglu, Erkan; Bras, Rafael L.

2005-06-01

Topography acts as a template for numerous landscape processes that include hydrologic, ecologic, and biologic phenomena. These processes not only interact with each other but also contribute to shaping the landscape as they influence geomorphic processes. We have investigated the effects of vegetation on thresholds for channel initiation and landform evolution using both analytical and numerical approaches. Vegetation is assumed to form a uniform ground cover. Runoff erosion is modeled based on a power function of excess shear stress, in which shear stress efficiency is inversely proportional to vegetation cover. This approach is validated using data. Plant effect on slope stability is represented by additional cohesion provided by plant roots. Vegetation cover is assumed to reduce sediment transport rates due to physical creep processes (rainsplash, dry ravel, and expansion and contraction of sediments) according to a negative exponential relationship. Vegetation grows as a function of both available cover and unoccupied space by plants and is killed by geomorphic disturbances (runoff erosion and landsliding) and wildfires. Analytical results suggest that in an equilibrium basin with a fixed vegetation cover, plants may cause a transition in the dominant erosion process at the channel head. A runoff erosion-dominated landscape, under none or poor vegetation cover, may become landslide dominated under a denser vegetation cover. The sign of the predicted relationship between drainage density and vegetation cover depends on the relative influence of vegetation on different erosion phenomena. With model parameter values representative of the Oregon Coast Range (OCR), numerical experiments conducted using the Channel Hillslope Integrated Landscape Development (CHILD) model confirm the findings based on the analytical theory. A highly dissected fluvial landscape emerges when surface is assumed bare. When vegetation cover is modeled, landscape relief increases, resulting in hollow erosion dominated by landsliding. Interestingly, our simulations underscore the importance of vegetation disturbances by geomorphic events and wildfires on the landscape structure. Simulated landscapes resemble real-world catchments in the OCR when such disturbances are considered.
Communication: Spin densities within a unitary group based spin-adapted open-shell coupled-cluster theory: Analytic evaluation of isotropic hyperfine-coupling constants for the combinatoric open-shell coupled-cluster scheme

DOE Office of Scientific and Technical Information (OSTI.GOV)

Datta, Dipayan, E-mail: datta.dipayan@gmail.com; Gauss, Jürgen, E-mail: gauss@uni-mainz.de

We report analytical calculations of isotropic hyperfine-coupling constants in radicals using a spin-adapted open-shell coupled-cluster theory, namely, the unitary group based combinatoric open-shell coupled-cluster (COSCC) approach within the singles and doubles approximation. A scheme for the evaluation of the one-particle spin-density matrix required in these calculations is outlined within the spin-free formulation of the COSCC approach. In this scheme, the one-particle spin-density matrix for an open-shell state with spin S and M{sub S} = + S is expressed in terms of the one- and two-particle spin-free (charge) density matrices obtained from the Lagrangian formulation that is used for calculating themore » analytic first derivatives of the energy. Benchmark calculations are presented for NO, NCO, CH{sub 2}CN, and two conjugated π-radicals, viz., allyl and 1-pyrrolyl in order to demonstrate the performance of the proposed scheme.« less
Ionic Graphitization of Ultrathin Films of Ionic Compounds.

PubMed

Kvashnin, A G; Pashkin, E Y; Yakobson, B I; Sorokin, P B

2016-07-21

On the basis of ab initio density functional calculations, we performed a comprehensive investigation of the general graphitization tendency in rocksalt-type structures. In this paper, we determine the critical slab thickness for a range of ionic cubic crystal systems, below which a spontaneous conversion from a cubic to a layered graphitic-like structure occurs. This conversion is driven by surface energy reduction. Using only fundamental parameters of the compounds such as the Allen electronegativity and ionic radius of the metal atom, we also develop an analytical relation to estimate the critical number of layers.
Quadratic integrand double-hybrid made spin-component-scaled

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brémond, Éric, E-mail: eric.bremond@iit.it; Savarese, Marika; Sancho-García, Juan C.

2016-03-28

We propose two analytical expressions aiming to rationalize the spin-component-scaled (SCS) and spin-opposite-scaled (SOS) schemes for double-hybrid exchange-correlation density-functionals. Their performances are extensively tested within the framework of the nonempirical quadratic integrand double-hybrid (QIDH) model on energetic properties included into the very large GMTKN30 benchmark database, and on structural properties of semirigid medium-sized organic compounds. The SOS variant is revealed as a less computationally demanding alternative to reach the accuracy of the original QIDH model without losing any theoretical background.
Application of ERTS-1 imagery to the study of caribou movements and winter dispersal in relation to prevailing snowcover

NASA Technical Reports Server (NTRS)

Lent, P. C. (Principal Investigator)

1973-01-01

The author has identified the following significant results. Step-wise discriminate analysis has demonstrated the feasibility of feature identification using linear discriminate functions of ERTS-1 MSS band densities and their ratios. The analysis indicated that features such as small streams can be detected even when they are in dark mountain shadow. The potential utility of this and similar analytic techniques appears considerable, and the limits it can be applied to analysis of ERTS-1 imagery are not yet fully known.
Reduced quantum dynamics with arbitrary bath spectral densities: hierarchical equations of motion based on several different bath decomposition schemes.

PubMed

Liu, Hao; Zhu, Lili; Bai, Shuming; Shi, Qiang

2014-04-07

We investigated applications of the hierarchical equation of motion (HEOM) method to perform high order perturbation calculations of reduced quantum dynamics for a harmonic bath with arbitrary spectral densities. Three different schemes are used to decompose the bath spectral density into analytical forms that are suitable to the HEOM treatment: (1) The multiple Lorentzian mode model that can be obtained by numerically fitting the model spectral density. (2) The combined Debye and oscillatory Debye modes model that can be constructed by fitting the corresponding classical bath correlation function. (3) A new method that uses undamped harmonic oscillator modes explicitly in the HEOM formalism. Methods to extract system-bath correlations were investigated for the above bath decomposition schemes. We also show that HEOM in the undamped harmonic oscillator modes can give detailed information on the partial Wigner transform of the total density operator. Theoretical analysis and numerical simulations of the spin-Boson dynamics and the absorption line shape of molecular dimers show that the HEOM formalism for high order perturbations can serve as an important tool in studying the quantum dissipative dynamics in the intermediate coupling regime.
Fast Radio Bursts’ Recipes for the Distributions of Dispersion Measures, Flux Densities, and Fluences

NASA Astrophysics Data System (ADS)

Niino, Yuu

2018-05-01

We investigate how the statistical properties of dispersion measure (DM) and apparent flux density/fluence of (nonrepeating) fast radio bursts (FRBs) are determined by unknown cosmic rate density history [ρ FRB(z)] and luminosity function (LF) of the transient events. We predict the distributions of DMs, flux densities, and fluences of FRBs taking account of the variation of the receiver efficiency within its beam, using analytical models of ρ FRB(z) and LF. Comparing the predictions with the observations, we show that the cumulative distribution of apparent fluences suggests that FRBs originate at cosmological distances and ρ FRB increases with redshift resembling the cosmic star formation history (CSFH). We also show that an LF model with a bright-end cutoff at log10 L ν (erg s‑1 Hz‑1) ∼ 34 are favored to reproduce the observed DM distribution if ρ FRB(z) ∝ CSFH, although the statistical significance of the constraints obtained with the current size of the observed sample is not high. Finally, we find that the correlation between DM and flux density of FRBs is potentially a powerful tool to distinguish whether FRBs are at cosmological distances or in the local universe more robustly with future observations.
Reduced quantum dynamics with arbitrary bath spectral densities: Hierarchical equations of motion based on several different bath decomposition schemes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Hao; Zhu, Lili; Bai, Shuming

2014-04-07

We investigated applications of the hierarchical equation of motion (HEOM) method to perform high order perturbation calculations of reduced quantum dynamics for a harmonic bath with arbitrary spectral densities. Three different schemes are used to decompose the bath spectral density into analytical forms that are suitable to the HEOM treatment: (1) The multiple Lorentzian mode model that can be obtained by numerically fitting the model spectral density. (2) The combined Debye and oscillatory Debye modes model that can be constructed by fitting the corresponding classical bath correlation function. (3) A new method that uses undamped harmonic oscillator modes explicitly inmore » the HEOM formalism. Methods to extract system-bath correlations were investigated for the above bath decomposition schemes. We also show that HEOM in the undamped harmonic oscillator modes can give detailed information on the partial Wigner transform of the total density operator. Theoretical analysis and numerical simulations of the spin-Boson dynamics and the absorption line shape of molecular dimers show that the HEOM formalism for high order perturbations can serve as an important tool in studying the quantum dissipative dynamics in the intermediate coupling regime.« less
Low-pressure barrier discharge ion source using air as a carrier gas and its application to the analysis of drugs and explosives.

PubMed

Usmanov, Dilshadbek T; Yu, Zhan; Chen, Lee Chuin; Hiraoka, Kenzo; Yamabe, Shinichi

2016-02-01

In this work, a low-pressure air dielectric-barrier discharge (DBD) ion source using a capillary with the inner diameter of 0.115 and 12 mm long applicable to miniaturized mass spectrometers was developed. The analytes, trinitrotoluene (TNT), 1,3,5-trinitroperhydro-1,3,5-triazine (RDX), 1,3,5,7-tetranitroperhydro-1,3,5,7-tetrazocine (HMX), pentaerythritol tetranitrate (PETN), nitroglycerine (NG), hexamethylene triperoxide diamine (HMTD), caffeine, cocaine and morphine, introduced through the capillary, were ionized by a low-pressure air DBD. The ion source pressures were changed by using various sizes of the ion sampling orifice. The signal intensities of those analytes showed marked pressure dependence. TNT was detected with higher sensitivity at lower pressure but vice versa for other analytes. For all analytes, a marked signal enhancement was observed when a grounded cylindrical mesh electrode was installed in the DBD ion source. Among nine analytes, RDX, HMX, NG and PETN could be detected as cluster ions [analyte + NO3 ](-) even at low pressure and high temperature up to 180 °C. The detection indicates that these cluster ions are stable enough to survive under present experimental conditions. The unexpectedly high stabilities of these cluster ions were verified by density functional theory calculation. Copyright © 2016 John Wiley & Sons, Ltd.
Stochastic modeling of macrodispersion in unsaturated heterogeneous porous media. Final report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yeh, T.C.J.

1995-02-01

Spatial heterogeneity of geologic media leads to uncertainty in predicting both flow and transport in the vadose zone. In this work an efficient and flexible, combined analytical-numerical Monte Carlo approach is developed for the analysis of steady-state flow and transient transport processes in highly heterogeneous, variably saturated porous media. The approach is also used for the investigation of the validity of linear, first order analytical stochastic models. With the Monte Carlo analysis accurate estimates of the ensemble conductivity, head, velocity, and concentration mean and covariance are obtained; the statistical moments describing displacement of solute plumes, solute breakthrough at a compliancemore » surface, and time of first exceedance of a given solute flux level are analyzed; and the cumulative probability density functions for solute flux across a compliance surface are investigated. The results of the Monte Carlo analysis show that for very heterogeneous flow fields, and particularly in anisotropic soils, the linearized, analytical predictions of soil water tension and soil moisture flux become erroneous. Analytical, linearized Lagrangian transport models also overestimate both the longitudinal and the transverse spreading of the mean solute plume in very heterogeneous soils and in dry soils. A combined analytical-numerical conditional simulation algorithm is also developed to estimate the impact of in-situ soil hydraulic measurements on reducing the uncertainty of concentration and solute flux predictions.« less
Analytical solutions of mushy layer equations describing directional solidification in the presence of nucleation

NASA Astrophysics Data System (ADS)

Alexandrov, Dmitri V.; Ivanov, Alexander A.; Alexandrova, Irina V.

2018-01-01

The processes of particle nucleation and their evolution in a moving metastable layer of phase transition (supercooled liquid or supersaturated solution) are studied analytically. The transient integro-differential model for the density distribution function and metastability level is solved for the kinetic and diffusionally controlled regimes of crystal growth. The Weber-Volmer-Frenkel-Zel'dovich and Meirs mechanisms for nucleation kinetics are used. We demonstrate that the phase transition boundary lying between the mushy and pure liquid layers evolves with time according to the following power dynamic law: , where Z1(t)=βt7/2 and Z1(t)=βt2 in cases of kinetic and diffusionally controlled scenarios. The growth rate parameters α, β and ε are determined analytically. We show that the phase transition interface in the presence of crystal nucleation and evolution propagates slower than in the absence of their nucleation. This article is part of the theme issue `From atomistic interfaces to dendritic patterns'.
Predicting CH4 adsorption capacity of microporous carbon using N2 isotherm and a new analytical model

USGS Publications Warehouse

Sun, Jielun; Chen, S.; Rostam-Abadi, M.; Rood, M.J.

1998-01-01

A new analytical pore size distribution (PSD) model was developed to predict CH4 adsorption (storage) capacity of microporous adsorbent carbon. The model is based on a 3-D adsorption isotherm equation, derived from statistical mechanical principles. Least squares error minimization is used to solve the PSD without any pre-assumed distribution function. In comparison with several well-accepted analytical methods from the literature, this 3-D model offers relatively realistic PSD description for select reference materials, including activated carbon fibers. N2 and CH4 adsorption data were correlated using the 3-D model for commercial carbons BPL and AX-21. Predicted CH4 adsorption isotherms, based on N2 adsorption at 77 K, were in reasonable agreement with the experimental CH4 isotherms. Modeling results indicate that not all the pores contribute the same percentage Vm/Vs for CH4 storage due to different adsorbed CH4 densities. Pores near 8-9 A?? shows higher Vm/Vs on the equivalent volume basis than does larger pores.
Efficient Band-to-Trap Tunneling Model Including Heterojunction Band Offset

DOE PAGES

Gao, Xujiao; Huang, Andy; Kerr, Bert

2017-10-25

In this paper, we present an efficient band-to-trap tunneling model based on the Schenk approach, in which an analytic density-of-states (DOS) model is developed based on the open boundary scattering method. The new model explicitly includes the effect of heterojunction band offset, in addition to the well-known field effect. Its analytic form enables straightforward implementation into TCAD device simulators. It is applicable to all one-dimensional potentials, which can be approximated to a good degree such that the approximated potentials lead to piecewise analytic wave functions with open boundary conditions. The model allows for simulating both the electric-field-enhanced and band-offset-enhanced carriermore » recombination due to the band-to-trap tunneling near the heterojunction in a heterojunction bipolar transistor (HBT). Simulation results of an InGaP/GaAs/GaAs NPN HBT show that the proposed model predicts significantly increased base currents, due to the hole-to-trap tunneling enhanced by the emitter-base junction band offset. Finally, the results compare favorably with experimental observation.« less

Efficient Band-to-Trap Tunneling Model Including Heterojunction Band Offset

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gao, Xujiao; Huang, Andy; Kerr, Bert

In this paper, we present an efficient band-to-trap tunneling model based on the Schenk approach, in which an analytic density-of-states (DOS) model is developed based on the open boundary scattering method. The new model explicitly includes the effect of heterojunction band offset, in addition to the well-known field effect. Its analytic form enables straightforward implementation into TCAD device simulators. It is applicable to all one-dimensional potentials, which can be approximated to a good degree such that the approximated potentials lead to piecewise analytic wave functions with open boundary conditions. The model allows for simulating both the electric-field-enhanced and band-offset-enhanced carriermore » recombination due to the band-to-trap tunneling near the heterojunction in a heterojunction bipolar transistor (HBT). Simulation results of an InGaP/GaAs/GaAs NPN HBT show that the proposed model predicts significantly increased base currents, due to the hole-to-trap tunneling enhanced by the emitter-base junction band offset. Finally, the results compare favorably with experimental observation.« less
Metal-amplified Density Assays, (MADAs), including a Density-Linked Immunosorbent Assay (DeLISA).

PubMed

Subramaniam, Anand Bala; Gonidec, Mathieu; Shapiro, Nathan D; Kresse, Kayleigh M; Whitesides, George M

2015-02-21

This paper reports the development of Metal-amplified Density Assays, or MADAs - a method of conducting quantitative or multiplexed assays, including immunoassays, by using Magnetic Levitation (MagLev) to measure metal-amplified changes in the density of beads labeled with biomolecules. The binding of target analytes (i.e. proteins, antibodies, antigens) to complementary ligands immobilized on the surface of the beads, followed by a chemical amplification of the binding in a form that results in a change in the density of the beads (achieved by using gold nanoparticle-labeled biomolecules, and electroless deposition of gold or silver), translates analyte binding events into changes in density measureable using MagLev. A minimal model based on diffusion-limited growth of hemispherical nuclei on a surface reproduces the dynamics of the assay. A MADA - when performed with antigens and antibodies - is called a Density-Linked Immunosorbent Assay, or DeLISA. Two immunoassays provided a proof of principle: a competitive quantification of the concentration of neomycin in whole milk, and a multiplexed detection of antibodies against Hepatitis C virus NS3 protein and syphilis T. pallidum p47 protein in serum. MADAs, including DeLISAs, require, besides the requisite biomolecules and amplification reagents, minimal specialized equipment (two permanent magnets, a ruler or a capillary with calibrated length markings) and no electrical power to obtain a quantitative readout of analyte concentration. With further development, the method may be useful in resource-limited or point-of-care settings.
Large density expansion of a hydrodynamic theory for self-propelled particles

NASA Astrophysics Data System (ADS)

Ihle, T.

2015-07-01

Recently, an Enskog-type kinetic theory for Vicsek-type models for self-propelled particles has been proposed [T. Ihle, Phys. Rev. E 83, 030901 (2011)]. This theory is based on an exact equation for a Markov chain in phase space and is not limited to small density. Previously, the hydrodynamic equations were derived from this theory and its transport coefficients were given in terms of infinite series. Here, I show that the transport coefficients take a simple form in the large density limit. This allows me to analytically evaluate the well-known density instability of the polarly ordered phase near the flocking threshold at moderate and large densities. The growth rate of a longitudinal perturbation is calculated and several scaling regimes, including three different power laws, are identified. It is shown that at large densities, the restabilization of the ordered phase at smaller noise is analytically accessible within the range of validity of the hydrodynamic theory. Analytical predictions for the width of the unstable band, the maximum growth rate, and for the wave number below which the instability occurs are given. In particular, the system size below which spatial perturbations of the homogeneous ordered state are stable is predicted to scale with where √ M is the average number of collision partners. The typical time scale until the instability becomes visible is calculated and is proportional to M.
How stellar feedback simultaneously regulates star formation and drives outflows

NASA Astrophysics Data System (ADS)

Hayward, Christopher C.; Hopkins, Philip F.

2017-02-01

We present an analytic model for how momentum deposition from stellar feedback simultaneously regulates star formation and drives outflows in a turbulent interstellar medium (ISM). Because the ISM is turbulent, a given patch of ISM exhibits sub-patches with a range of surface densities. The high-density patches are 'pushed' by feedback, thereby driving turbulence and self-regulating local star formation. Sufficiently low-density patches, however, are accelerated to above the escape velocity before the region can self-adjust and are thus vented as outflows. When the gas fraction is ≳ 0.3, the ratio of the turbulent velocity dispersion to the circular velocity is sufficiently high that at any given time, of the order of half of the ISM has surface density less than the critical value and thus can be blown out on a dynamical time. The resulting outflows have a mass-loading factor (η ≡ dot{M}_{out}/M_{star }) that is inversely proportional to the gas fraction times the circular velocity. At low gas fractions, the star formation rate needed for local self-regulation, and corresponding turbulent Mach number, declines rapidly; the ISM is 'smoother', and it is actually more difficult to drive winds with large mass-loading factors. Crucially, our model predicts that stellar-feedback-driven outflows should be suppressed at z ≲ 1 in M⋆ ≳ 1010 M⊙ galaxies. This mechanism allows massive galaxies to exhibit violent outflows at high redshifts and then 'shut down' those outflows at late times, thereby enabling the formation of a smooth, extended thin stellar disc. We provide simple fitting functions for η that should be useful for sub-resolution and semi-analytic models.
MODELING THE ANOMALY OF SURFACE NUMBER DENSITIES OF GALAXIES ON THE GALACTIC EXTINCTION MAP DUE TO THEIR FIR EMISSION CONTAMINATION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kashiwagi, Toshiya; Suto, Yasushi; Taruya, Atsushi

The most widely used Galactic extinction map is constructed assuming that the observed far-infrared (FIR) fluxes come entirely from Galactic dust. According to the earlier suggestion by Yahata et al., we consider how FIR emission of galaxies affects the SFD map. We first compute the surface number density of Sloan Digital Sky Survey (SDSS) DR7 galaxies as a function of the r-band extinction, A {sub r,} {sub SFD}. We confirm that the surface densities of those galaxies positively correlate with A {sub r,} {sub SFD} for A {sub r,} {sub SFD} < 0.1, as first discovered by Yahata et al.more » for SDSS DR4 galaxies. Next we construct an analytical model to compute the surface density of galaxies, taking into account the contamination of their FIR emission. We adopt a log-normal probability distribution for the ratio of 100 μm and r-band luminosities of each galaxy, y ≡ (νL){sub 100} {sub μm}/(νL) {sub r}. Then we search for the mean and rms values of y that fit the observed anomaly, using the analytical model. The required values to reproduce the anomaly are roughly consistent with those measured from the stacking analysis of SDSS galaxies. Due to the limitation of our statistical modeling, we are not yet able to remove the FIR contamination of galaxies from the extinction map. Nevertheless, the agreement with the model prediction suggests that the FIR emission of galaxies is mainly responsible for the observed anomaly. Whereas the corresponding systematic error in the Galactic extinction map is 0.1-1 mmag, it is directly correlated with galaxy clustering and thus needs to be carefully examined in precision cosmology.« less
The galaxy luminosity function around groups

NASA Astrophysics Data System (ADS)

González, R. E.; Padilla, N. D.; Galaz, G.; Infante, L.

2005-11-01

We present a study on the variations of the luminosity function of galaxies around clusters in a numerical simulation with semi-analytic galaxies, attempting to detect these variations in the 2dF Galaxy Redshift Survey. We subdivide the simulation box into equal-density regions around clusters, which we assume can be achieved by selecting objects at a given normalized distance (r/rrms, where rrms is an estimate of the halo radius) from the group centre. The semi-analytic model predicts important variations in the luminosity function out to r/rrms~= 5. In brief, variations in the mass function of haloes around clusters (large dark matter haloes with M > 1012h-1Msolar) lead to cluster central regions that present a high abundance of bright galaxies (high M* values) as well as low-luminosity galaxies (high α) at r/rrms~= 3 there is a lack of bright galaxies, which shows the depletion of galaxies in the regions surrounding clusters (minimum in M* and α), and a tendency to constant luminosity function parameters at larger cluster-centric distances. We take into account the observational biases present in the real data by reproducing the peculiar velocity effect on the redshifts of galaxies in the simulation box, and also by producing mock catalogues. We find that excluding from the analysis galaxies which in projection are close to the centres of the groups provides results that are qualitatively consistent with the full simulation box results. When we apply this method to mock catalogues of the 2dF Galaxy Redshift Survey (2dFGRS) and the 2PIGG catalogue of groups, we find that the variations in the luminosity function are almost completely erased by the Finger of God effect; only a lack of bright galaxies at r/rrms~= 3 can be marginally detected in the mock catalogues. The results from the real 2dFGRS data show a clearer detection of a dip in M* and α for r/rrms= 3, consistent with the semi-analytic predictions.
Support for the existence of invertible maps between electronic densities and non-analytic 1-body external potentials in non-relativistic time-dependent quantum mechanics

NASA Astrophysics Data System (ADS)

Mosquera, Martín A.

2017-10-01

Provided the initial state, the Runge-Gross theorem establishes that the time-dependent (TD) external potential of a system of non-relativistic electrons determines uniquely their TD electronic density, and vice versa (up to a constant in the potential). This theorem requires the TD external potential and density to be Taylor-expandable around the initial time of the propagation. This paper presents an extension without this restriction. Given the initial state of the system and evolution of the density due to some TD scalar potential, we show that a perturbative (not necessarily weak) TD potential that induces a non-zero divergence of the external force-density, inside a small spatial subset and immediately after the initial propagation time, will cause a change in the density within that subset, implying that the TD potential uniquely determines the TD density. In this proof, we assume unitary evolution of wavefunctions and first-order differentiability (which does not imply analyticity) in time of the internal and external force-densities, electronic density, current density, and their spatial derivatives over the small spatial subset and short time interval.
Testing density-dependent groundwater models: Two-dimensional steady state unstable convection in infinite, finite and inclined porous layers

USGS Publications Warehouse

Weatherill, D.; Simmons, C.T.; Voss, C.I.; Robinson, N.I.

2004-01-01

This study proposes the use of several problems of unstable steady state convection with variable fluid density in a porous layer of infinite horizontal extent as two-dimensional (2-D) test cases for density-dependent groundwater flow and solute transport simulators. Unlike existing density-dependent model benchmarks, these problems have well-defined stability criteria that are determined analytically. These analytical stability indicators can be compared with numerical model results to test the ability of a code to accurately simulate buoyancy driven flow and diffusion. The basic analytical solution is for a horizontally infinite fluid-filled porous layer in which fluid density decreases with depth. The proposed test problems include unstable convection in an infinite horizontal box, in a finite horizontal box, and in an infinite inclined box. A dimensionless Rayleigh number incorporating properties of the fluid and the porous media determines the stability of the layer in each case. Testing the ability of numerical codes to match both the critical Rayleigh number at which convection occurs and the wavelength of convection cells is an addition to the benchmark problems currently in use. The proposed test problems are modelled in 2-D using the SUTRA [SUTRA-A model for saturated-unsaturated variable-density ground-water flow with solute or energy transport. US Geological Survey Water-Resources Investigations Report, 02-4231, 2002. 250 p] density-dependent groundwater flow and solute transport code. For the case of an infinite horizontal box, SUTRA results show a distinct change from stable to unstable behaviour around the theoretical critical Rayleigh number of 4??2 and the simulated wavelength of unstable convection agrees with that predicted by the analytical solution. The effects of finite layer aspect ratio and inclination on stability indicators are also tested and numerical results are in excellent agreement with theoretical stability criteria and with numerical results previously reported in traditional fluid mechanics literature. ?? 2004 Elsevier Ltd. All rights reserved.
Low-density lipoprotein transport through an arterial wall under hyperthermia and hypertension conditions--An analytical solution.

PubMed

Iasiello, Marcello; Vafai, Kambiz; Andreozzi, Assunta; Bianco, Nicola

2016-01-25

An analytical solution for Low-Density Lipoprotein transport through an arterial wall under hyperthermia conditions is established in this work. A four-layer model is used to characterize the arterial wall. Transport governing equations are obtained as a combination between Staverman-Kedem-Katchalsky membrane equations and volume-averaged porous media equations. Temperature and solute transport fields are coupled by means of Ludwig-Soret effect. Results are in excellent agreement with numerical and analytical literature data under isothermal conditions, and with numerical literature data for the hyperthermia case. Effects of hypertension combined with hyperthermia, are also analyzed in this work. Copyright © 2015 Elsevier Ltd. All rights reserved.
Determining the risk of cardiovascular disease using ion mobility of lipoproteins

DOEpatents

Benner, W. Henry; Krauss, Ronald M.; Blanche, Patricia J.

2010-05-11

A medical diagnostic method and instrumentation system for analyzing noncovalently bonded agglomerated biological particles is described. The method and system comprises: a method of preparation for the biological particles; an electrospray generator; an alpha particle radiation source; a differential mobility analyzer; a particle counter; and data acquisition and analysis means. The medical device is useful for the assessment of human diseases, such as cardiac disease risk and hyperlipidemia, by rapid quantitative analysis of lipoprotein fraction densities. Initially, purification procedures are described to reduce an initial blood sample to an analytical input to the instrument. The measured sizes from the analytical sample are correlated with densities, resulting in a spectrum of lipoprotein densities. The lipoprotein density distribution can then be used to characterize cardiac and other lipid-related health risks.
What Does a Submillimeter Galaxy Selection Actually Select? The Dependence of Submillimeter Flux Density on Star Formation Rate and Dust Mass

NASA Astrophysics Data System (ADS)

Hayward, Christopher C.; Kereš, Dušan; Jonsson, Patrik; Narayanan, Desika; Cox, T. J.; Hernquist, Lars

2011-12-01

We perform three-dimensional dust radiative transfer (RT) calculations on hydrodynamic simulations of isolated and merging disk galaxies in order to quantitatively study the dependence of observed-frame submillimeter (submm) flux density on galaxy properties. We find that submm flux density and star formation rate (SFR) are related in dramatically different ways for quiescently star-forming galaxies and starbursts. Because the stars formed in the merger-induced starburst do not dominate the bolometric luminosity and the rapid drop in dust mass and more compact geometry cause a sharp increase in dust temperature during the burst, starbursts are very inefficient at boosting submm flux density (e.g., a >~ 16 × boost in SFR yields a <~ 2 × boost in submm flux density). Moreover, the ratio of submm flux density to SFR differs significantly between the two modes; thus one cannot assume that the galaxies with highest submm flux density are necessarily those with the highest bolometric luminosity or SFR. These results have important consequences for the bright submillimeter-selected galaxy (SMG) population. Among them are: (1) The SMG population is heterogeneous. In addition to merger-driven starbursts, there is a subpopulation of galaxy pairs, where two disks undergoing a major merger but not yet strongly interacting are blended into one submm source because of the large (gsim 15" or ~130 kpc at z = 2) beam of single-dish submm telescopes. (2) SMGs must be very massive (M sstarf >~ 6 × 1010 M ⊙). (3) The infall phase makes the SMG duty cycle a factor of a few greater than what is expected for a merger-driven starburst. Finally, we provide fitting functions for SCUBA and AzTEC submm flux densities as a function of SFR and dust mass and bolometric luminosity and dust mass; these should be useful for calculating submm flux density in semi-analytic models and cosmological simulations when performing full RT is computationally not feasible.
The multifacet graphically contracted function method. I. Formulation and implementation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shepard, Ron; Brozell, Scott R.; Gidofalvi, Gergely

2014-08-14

The basic formulation for the multifacet generalization of the graphically contracted function (MFGCF) electronic structure method is presented. The analysis includes the discussion of linear dependency and redundancy of the arc factor parameters, the computation of reduced density matrices, Hamiltonian matrix construction, spin-density matrix construction, the computation of optimization gradients for single-state and state-averaged calculations, graphical wave function analysis, and the efficient computation of configuration state function and Slater determinant expansion coefficients. Timings are given for Hamiltonian matrix element and analytic optimization gradient computations for a range of model problems for full-CI Shavitt graphs, and it is observed that bothmore » the energy and the gradient computation scale as O(N{sup 2}n{sup 4}) for N electrons and n orbitals. The important arithmetic operations are within dense matrix-matrix product computational kernels, resulting in a computationally efficient procedure. An initial implementation of the method is used to present applications to several challenging chemical systems, including N{sub 2} dissociation, cubic H{sub 8} dissociation, the symmetric dissociation of H{sub 2}O, and the insertion of Be into H{sub 2}. The results are compared to the exact full-CI values and also to those of the previous single-facet GCF expansion form.« less
Space-charge-limited currents for cathodes with electric field enhanced geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lai, Dingguo, E-mail: laidingguo@nint.ac.cn; Qiu, Mengtong; Xu, Qifu

This paper presents the approximate analytic solutions of current density for annulus and circle cathodes. The current densities of annulus and circle cathodes are derived approximately from first principles, which are in agreement with simulation results. The large scaling laws can predict current densities of high current vacuum diodes including annulus and circle cathodes in practical applications. In order to discuss the relationship between current density and electric field on cathode surface, the existing analytical solutions of currents for concentric cylinder and sphere diodes are fitted from existing solutions relating with electric field enhancement factors. It is found that themore » space-charge-limited current density for the cathode with electric-field enhanced geometry can be written in a general form of J = g(β{sub E}){sup 2}J{sub 0}, where J{sub 0} is the classical (1D) Child-Langmuir current density, β{sub E} is the electric field enhancement factor, and g is the geometrical correction factor depending on the cathode geometry.« less
Stationary responses of a Rayleigh viscoelastic system with zero barrier impacts under external random excitation.

PubMed

Wang, Deli; Xu, Wei; Zhao, Xiangrong

2016-03-01

This paper aims to deal with the stationary responses of a Rayleigh viscoelastic system with zero barrier impacts under external random excitation. First, the original stochastic viscoelastic system is converted to an equivalent stochastic system without viscoelastic terms by approximately adding the equivalent stiffness and damping. Relying on the means of non-smooth transformation of state variables, the above system is replaced by a new system without an impact term. Then, the stationary probability density functions of the system are observed analytically through stochastic averaging method. By considering the effects of the biquadratic nonlinear damping coefficient and the noise intensity on the system responses, the effectiveness of the theoretical method is tested by comparing the analytical results with those generated from Monte Carlo simulations. Additionally, it does deserve attention that some system parameters can induce the occurrence of stochastic P-bifurcation.
Scaling and intermittency in incoherent α-shear dynamo

NASA Astrophysics Data System (ADS)

Mitra, Dhrubaditya; Brandenburg, Axel

2012-03-01

We consider mean-field dynamo models with fluctuating α effect, both with and without large-scale shear. The α effect is chosen to be Gaussian white noise with zero mean and a given covariance. In the presence of shear, we show analytically that (in infinitely large domains) the mean-squared magnetic field shows exponential growth. The growth rate of the fastest growing mode is proportional to the shear rate. This result agrees with earlier numerical results of Yousef et al. and the recent analytical treatment by Heinemann, McWilliams & Schekochihin who use a method different from ours. In the absence of shear, an incoherent α2 dynamo may also be possible. We further show by explicit calculation of the growth rate of third- and fourth-order moments of the magnetic field that the probability density function of the mean magnetic field generated by this dynamo is non-Gaussian.
Physics of collisionless scrape-off-layer plasma during normal and off-normal Tokamak operating conditions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hassanein, A.; Konkashbaev, I.

1999-03-15

The structure of a collisionless scrape-off-layer (SOL) plasma in tokamak reactors is being studied to define the electron distribution function and the corresponding sheath potential between the divertor plate and the edge plasma. The collisionless model is shown to be valid during the thermal phase of a plasma disruption, as well as during the newly desired low-recycling normal phase of operation with low-density, high-temperature, edge plasma conditions. An analytical solution is developed by solving the Fokker-Planck equation for electron distribution and balance in the SOL. The solution is in good agreement with numerical studies using Monte-Carlo methods. The analytical solutionsmore » provide an insight to the role of different physical and geometrical processes in a collisionless SOL during disruptions and during the enhanced phase of normal operation over a wide range of parameters.« less
Quantum criticality of one-dimensional multicomponent Fermi gas with strongly attractive interaction

NASA Astrophysics Data System (ADS)

He, Peng; Jiang, Yuzhu; Guan, Xiwen; He, Jinyu

2015-01-01

Quantum criticality of strongly attractive Fermi gas with SU(3) symmetry in one dimension is studied via the thermodynamic Bethe ansatz (TBA) equations. The phase transitions driven by the chemical potential μ , effective magnetic field H1, H2 (chemical potential biases) are analyzed at the quantum criticality. The phase diagram and critical fields are analytically determined by the TBA equations in the zero temperature limit. High accurate equations of state, scaling functions are also obtained analytically for the strong interacting gases. The dynamic exponent z=2 and correlation length exponent ν =1/2 read off the universal scaling form. It turns out that the quantum criticality of the three-component gases involves a sudden change of density of states of one cluster state, two or three cluster states. In general, this method can be adapted to deal with the quantum criticality of multicomponent Fermi gases with SU(N) symmetry.
The effect of damping on a quantum system containing a Kerr-like medium

NASA Astrophysics Data System (ADS)

Mohamed, A.-B. A.; Sebawe Abdalla, M.; Obada, A.-S. F.

2018-05-01

An analytical description is given for a model which represents the interaction between Su(1,1) and Su(2) quantum systems taking into account Su(1,1)-cavity damping and Kerr medium properties. The analytic solution for the master equation of the density matrix is obtained. The examination of the effects of the damping parameter as well as the Kerr-like medium features is performed. The atomic inversion is discussed where the revivals and collapses phenomenon is realized at the considered period of time. Our study is extended to include the degree of entanglement where the system shows partial entanglement in all cases, however, disentanglement is also observed. The death and rebirth is seen in the system provided one selects the suitable values of the parameters. The correlation function of the system shows non-classical as well as classical behavior.
GAMA/H-ATLAS: The Local Dust Mass Function and Cosmic Density as a Function of Galaxy Type - A Benchmark for Models of Galaxy Evolution

NASA Astrophysics Data System (ADS)

Beeston, R. A.; Wright, A. H.; Maddox, S.; Gomez, H. L.; Dunne, L.; Driver, S. P.; Robotham, A.; Clark, C. J. R.; Vinsen, K.; Takeuchi, T. T.; Popping, G.; Bourne, N.; Bremer, M. N.; Phillipps, S.; Moffett, A. J.; Baes, M.; Bland-Hawthorn, J.; Brough, S.; De Vis, P.; Eales, S. A.; Holwerda, B. W.; Loveday, J.; Liske, J.; Smith, M. W. L.; Smith, D. J. B.; Valiante, E.; Vlahakis, C.; Wang, L.

2018-06-01

We present the dust mass function (DMF) of 15,750 galaxies with redshift z < 0.1, drawn from the overlapping area of the GAMA and H-ATLAS surveys. The DMF is derived using the density corrected Vmax method, where we estimate Vmax using: (i) the normal photometric selection limit (pVmax) and (ii) a bivariate brightness distribution (BBD) technique, which accounts for two selection effects. We fit the data with a Schechter function, and find M^{*}=(4.65 ± 0.18)× 107 h^2_{70} M_{⊙ }, α = ( - 1.22 ± 0.01), φ ^{*}=(6.26 ± 0.28)× 10^{-3} h^3_{70} Mpc^{-3} dex^{-1}. The resulting dust mass density parameter integrated down to 104 M⊙ is Ωd = (1.11 ± 0.02) × 10-6 which implies the mass fraction of baryons in dust is f_{m_b}=(2.40± 0.04)× 10^{-5}; cosmic variance adds an extra 7-17 per cent uncertainty to the quoted statistical errors. Our measurements have fewer galaxies with high dust mass than predicted by semi-analytic models. This is because the models include too much dust in high stellar mass galaxies. Conversely, our measurements find more galaxies with high dust mass than predicted by hydrodynamical cosmological simulations. This is likely to be from the long timescales for grain growth assumed in the models. We calculate DMFs split by galaxy type and find dust mass densities of Ωd = (0.88 ± 0.03) × 10-6 and Ωd = (0.060 ± 0.005) × 10-6 for late-types and early-types respectively. Comparing to the equivalent galaxy stellar mass functions (GSMF) we find that the DMF for late-types is well matched by the GMSF scaled by (8.07 ± 0.35) × 10-4.
A simple approach to CO cooling in molecular clouds

NASA Astrophysics Data System (ADS)

Whitworth, A. P.; Jaffa, S. E.

2018-03-01

Carbon monoxide plays an important role in interstellar molecular clouds, both as a coolant, and as a diagnostic molecule. However, a proper evaluation of the cooling rate due to CO requires a determination of the populations of many levels, the spontaneous and stimulated radiative de-excitation rates between these levels, and the transfer of the emitted multi-line radiation; additionally, this must be done for three isotopologues. It would be useful to have a simple analytic formulation that avoided these complications and the associated computational overhead; this could then be used in situations where CO plays an important role as a coolant, but the details of this role are not the main concern. We derive such a formulation here, by first considering the two asymptotic forms that obtain in the limits of (a) low volume-density and optical depth, and (b) high volume-density and optical depth. These forms are then combined in such a way as to fit the detailed numerical results from Goldsmith & Langer (1978, ApJ, 222, 881; hereafter GL78). The GL78 results cover low temperatures, and a range of physical conditions where the interplay of thermal and sub-thermal excitation, optical-depth effects, and the contributions from rare isotopologues, are all important. The fit is obtained using the Metropolis-Hastings method, and reproduces the results of GL78 well. It is a purely local and analytic function of state — specifically a function of the density, ρ, isothermal sound speed, a, CO abundance, XCO, and velocity divergence, ∇ṡυ. As an illustration of its use, we consider the cooling layer following a slow steady non-magnetic planar J-shock. We show that, in this idealised configuration, if the post-shock cooling is dominated by CO and its isotopologues, the thickness of the post-shock cooling layer is very small and approximately independent of the pre-shock velocity, υo, or pre-shock isothermal sound speed, ao.

Polarized bow shocks reveal features of the winds and environments of massive stars

NASA Astrophysics Data System (ADS)

Shrestha, Manisha

2018-01-01

Massive stars strongly affect their surroundings through their energetic stellar winds and deaths as supernovae. The bow shock structures created by fast-moving massive stars contain important information about the winds and ultimate fates of these stars as well as their local interstellar medium (ISM). Since bow shocks are aspherical, the light scattered in the dense shock material becomes polarized. Analyzing this polarization reveals details of the bow shock geometry as well as the composition, velocity, density, and albedo of the scattering material. With these quantities, we can constrain the properties of the stellar wind and thus the evolutionary state of the star, as well as the dust composition of the local ISM.In my dissertation research, I use a Monte Carlo radiative transfer code that I optimized to simulate the polarization signatures produced by both resolved and unresolved stellar wind bow shocks (SWBS) illuminated by a central star and by shock emission. I derive bow shock shapes and densities from published analytical calculations and smooth particle hydrodynamic (SPH) models. In the case of the analytical SWBS and electron scattering, I find that higher optical depths produce higher polarization and position angle rotations at specific viewing angles compared to theoretical predictions for low optical depths. This is due to the geometrical properties of the bow shock combined with multiple scattering effects. For dust scattering, the polarization signature is strongly affected by wavelength, dust grain properties, and viewing angle. The behavior of the polarization as a function of wavelength in these cases can distinguish among different dust models for the local ISM. In the case of SPH density structures, I investigate how the polarization changes as a function of the evolutionary phase of the SWBS. My dissertation compares these simulations with polarization data from Betelgeuse and other massive stars with bow shocks. I discuss the implications of these model for the stellar winds and interstellar environments of these influential objects.
The VIMOS Public Extragalactic Redshift Survey (VIPERS). Environmental effects shaping the galaxy stellar mass function

NASA Astrophysics Data System (ADS)

Davidzon, I.; Cucciati, O.; Bolzonella, M.; De Lucia, G.; Zamorani, G.; Arnouts, S.; Moutard, T.; Ilbert, O.; Garilli, B.; Scodeggio, M.; Guzzo, L.; Abbas, U.; Adami, C.; Bel, J.; Bottini, D.; Branchini, E.; Cappi, A.; Coupon, J.; de la Torre, S.; Di Porto, C.; Fritz, A.; Franzetti, P.; Fumana, M.; Granett, B. R.; Guennou, L.; Iovino, A.; Krywult, J.; Le Brun, V.; Le Fèvre, O.; Maccagni, D.; Małek, K.; Marulli, F.; McCracken, H. J.; Mellier, Y.; Moscardini, L.; Polletta, M.; Pollo, A.; Tasca, L. A. M.; Tojeiro, R.; Vergani, D.; Zanichelli, A.

2016-02-01

We exploit the first public data release of VIPERS to investigate environmental effects in the evolution of galaxies between z ~ 0.5 and 0.9. The large number of spectroscopic redshifts (more than 50 000) over an area of about 10 deg2 provides a galaxy sample with high statistical power. The accurate redshift measurements (σz = 0.00047(1 + zspec)) allow us to robustly isolate galaxies living in the lowest and highest density environments (δ< 0.7 and δ> 4, respectively) as defined in terms of spatial 3D density contrast δ. We estimate the stellar mass function of galaxies residing in these two environments and constrain the high-mass end (ℳ ≳ 1011 ℳ⊙) with unprecedented precision. We find that the galaxy stellar mass function in the densest regions has a different shape than was measured at low densities, with an enhancement of massive galaxies and a hint of a flatter (less negative) slope at z< 0.8. We normalise each mass function to the comoving volume occupied by the corresponding environment and relate estimates from different redshift bins. We observe an evolution of the stellar mass function of VIPERS galaxies in high densities, while the low-density one is nearly constant. We compare these results to semi-analytical models and find consistent environmental signatures in the simulated stellar mass functions. We discuss how the halo mass function and fraction of central/satellite galaxies depend on the environments considered, making intrinsic and environmental properties of galaxies physically coupled, hence difficult to disentangle. The evolution of our low-density regions is described well by the formalism introduced by Peng et al. (2010, ApJ, 721, 193), and is consistent with the idea that galaxies become progressively passive because of internal physical processes. The same formalism could also describe the evolution of the mass function in the high density regions, but only if a significant contribution from dry mergers is considered. Based on observations collected at the European Southern Observatory, Cerro Paranal, Chile, using the Very Large Telescope under programmes 182.A-0886 and partly 070.A-9007. Also based on observations obtained with MegaPrime/MegaCam, a joint project of CFHT and CEA/DAPNIA, at the Canada-France-Hawaii Telescope (CFHT), which is operated by the National Research Council (NRC) of Canada, the Institut National des Sciences de l'Univers of the Centre National de la Recherche Scientifique (CNRS) of France, and the University of Hawaii. This work is based in part on data products produced at TERAPIX and the Canadian Astronomy Data Centre as part of the Canada-France-Hawaii Telescope Legacy Survey, a collaborative project of NRC and CNRS.
Evaluation of cluster expansions and correlated one-body properties of nuclei

NASA Astrophysics Data System (ADS)

Moustakidis, Ch. C.; Massen, S. E.; Panos, C. P.; Grypeos, M. E.; Antonov, A. N.

2001-07-01

Three different cluster expansions for the evaluation of correlated one-body properties of s-p and s-d shell nuclei are compared. Harmonic oscillator wave functions and Jastrow-type correlations are used, while analytical expressions are obtained for the charge form factor, density distribution, and momentum distribution by truncating the expansions and using a standard Jastrow correlation function f. The harmonic oscillator parameter b and the correlation parameter β have been determined by a least-squares fit to the experimental charge form factors in each case. The information entropy of nuclei in position space (Sr) and momentum space (Sk) according to the three methods are also calculated. It is found that the larger the entropy sum, S=Sr+Sk (the net information content of the system), the smaller the values of χ2. This indicates that maximal S is a criterion of the quality of a given nuclear model, according to the maximum entropy principle. Only two exceptions to this rule, out of many cases examined, were found. Finally an analytic expression for the so-called ``healing'' or ``wound'' integrals is derived with the function f considered, for any state of the relative two-nucleon motion, and their values in certain cases are computed and compared.
Ion/Ion Reactions with "Onium" Reagents: An Approach for the Gas-phase Transfer of Organic Cations to Multiply-Charged Anions

NASA Astrophysics Data System (ADS)

Gilbert, Joshua D.; Prentice, Boone M.; McLuckey, Scott A.

2015-05-01

The use of ion/ion reactions to effect gas-phase alkylation is demonstrated. Commonly used fixed-charge "onium" cations are well-suited for ion/ion reactions with multiply deprotonated analytes because of their tendency to form long-lived electrostatic complexes. Activation of these complexes results in an SN2 reaction that yields an alkylated anion with the loss of a neutral remnant of the reagent. This alkylation process forms the basis of a general method for alkylation of deprotonated analytes generated via electrospray, and is demonstrated on a variety of anionic sites. SN2 reactions of this nature are demonstrated empirically and characterized using density functional theory (DFT). This method for modification in the gas phase is extended to the transfer of larger and more complex R groups that can be used in later gas-phase synthesis steps. For example, N-cyclohexyl- N'-(2-morpholinoethyl)carbodiimide (CMC) is used to transfer a carbodiimide functionality to a peptide anion containing a carboxylic acid. Subsequent activation yields a selective reaction between the transferred carbodiimide group and a carboxylic acid, suggesting the carbodiimide functionality is retained through the transfer process. Many different R groups are transferable using this method, allowing for new possibilities for charge manipulation and derivatization in the gas phase.
Sequential strand displacement beacon for detection of DNA coverage on functionalized gold nanoparticles.

PubMed

Paliwoda, Rebecca E; Li, Feng; Reid, Michael S; Lin, Yanwen; Le, X Chris

2014-06-17

Functionalizing nanomaterials for diverse analytical, biomedical, and therapeutic applications requires determination of surface coverage (or density) of DNA on nanomaterials. We describe a sequential strand displacement beacon assay that is able to quantify specific DNA sequences conjugated or coconjugated onto gold nanoparticles (AuNPs). Unlike the conventional fluorescence assay that requires the target DNA to be fluorescently labeled, the sequential strand displacement beacon method is able to quantify multiple unlabeled DNA oligonucleotides using a single (universal) strand displacement beacon. This unique feature is achieved by introducing two short unlabeled DNA probes for each specific DNA sequence and by performing sequential DNA strand displacement reactions. Varying the relative amounts of the specific DNA sequences and spacing DNA sequences during their coconjugation onto AuNPs results in different densities of the specific DNA on AuNP, ranging from 90 to 230 DNA molecules per AuNP. Results obtained from our sequential strand displacement beacon assay are consistent with those obtained from the conventional fluorescence assays. However, labeling of DNA with some fluorescent dyes, e.g., tetramethylrhodamine, alters DNA density on AuNP. The strand displacement strategy overcomes this problem by obviating direct labeling of the target DNA. This method has broad potential to facilitate more efficient design and characterization of novel multifunctional materials for diverse applications.
Calculation of the critical overdensity in the spherical-collapse approximation

NASA Astrophysics Data System (ADS)

Herrera, D.; Waga, I.; Jorás, S. E.

2017-03-01

Critical overdensity δc is a key concept in estimating the number count of halos for different redshift and halo-mass bins, and therefore, it is a powerful tool to compare cosmological models to observations. There are currently two different prescriptions in the literature for its calculation, namely, the differential-radius and the constant-infinity methods. In this work we show that the latter yields precise results only if we are careful in the definition of the so-called numerical infinities. Although the subtleties we point out are crucial ingredients for an accurate determination of δc both in general relativity and in any other gravity theory, we focus on f (R )-modified gravity models in the metric approach; in particular, we use the so-called large (F =1 /3 ) and small-field (F =0 ) limits. For both of them, we calculate the relative errors (between our method and the others) in the critical density δc, in the comoving number density of halos per logarithmic mass interval nln M, and in the number of clusters at a given redshift in a given mass bin Nbin, as functions of the redshift. We have also derived an analytical expression for the density contrast in the linear regime as a function of the collapse redshift zc and Ωm 0 for any F .
Fluctuations and intermittent poloidal transport in a simple toroidal plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goud, T. S.; Ganesh, R.; Saxena, Y. C.

In a simple magnetized toroidal plasma, fluctuation induced poloidal flux is found to be significant in magnitude. The probability distribution function of the fluctuation induced poloidal flux is observed to be strongly non-Gaussian in nature; however, in some cases, the distribution shows good agreement with the analytical form [Carreras et al., Phys. Plasmas 3, 2664 (1996)], assuming a coupling between the near Gaussian density and poloidal velocity fluctuations. The observed non-Gaussian nature of the fluctuation induced poloidal flux and other plasma parameters such as density and fluctuating poloidal velocity in this device is due to intermittent and bursty nature ofmore » poloidal transport. In the simple magnetized torus used here, such an intermittent fluctuation induced poloidal flux is found to play a crucial role in generating the poloidal flow.« less
Vafa-Witten theorem and Lee-Yang singularities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aguado, M.; Asorey, M.

2009-12-15

We prove the analyticity of the finite volume QCD partition function for complex values of the {theta}-vacuum parameter. The absence of singularities different from Lee-Yang zeros only permits and cusp singularities in the vacuum energy density and never or cusps. This fact together with the Vafa-Witten diamagnetic inequality implies the vanishing of the density of Lee-Yang zeros at {theta}=0 and has an important consequence: the absence of a first order phase transition at {theta}=0. The result provides a key missing link in the Vafa-Witten proof of parity symmetry conservation in vectorlike gauge theories and follows from renormalizability, unitarity, positivity, andmore » existence of Bogomol'nyi-Prasad-Sommerfield bounds. Generalizations of this theorem to other physical systems are also discussed, with particular interest focused on the nonlinear CP{sup N} sigma model.« less
Probabilistic distribution and stochastic P-bifurcation of a hybrid energy harvester under colored noise

NASA Astrophysics Data System (ADS)

Mokem Fokou, I. S.; Nono Dueyou Buckjohn, C.; Siewe Siewe, M.; Tchawoua, C.

2018-03-01

In this manuscript, a hybrid energy harvesting system combining piezoelectric and electromagnetic transduction and subjected to colored noise is investigated. By using the stochastic averaging method, the stationary probability density functions of amplitudes are obtained and reveal interesting dynamics related to the long term behavior of the device. From stationary probability densities, we discuss the stochastic bifurcation through the qualitative change which shows that noise intensity, correlation time and other system parameters can be treated as bifurcation parameters. Numerical simulations are made for a comparison with analytical findings. The Mean first passage time (MFPT) is numerical provided in the purpose to investigate the system stability. By computing the Mean residence time (TMR), we explore the stochastic resonance phenomenon; we show how it is related to the correlation time of colored noise and high output power.
Nonlinear stability of solar type 3 radio bursts. 1: Theory

NASA Technical Reports Server (NTRS)

Smith, R. A.; Goldstein, M. L.; Papadopoulos, K.

1978-01-01

A theory of the excitation of solar type 3 bursts is presented. Electrons initially unstable to the linear bump-in-tail instability are shown to rapidly amplify Langmuir waves to energy densities characteristic of strong turbulence. The three-dimensional equations which describe the strong coupling (wave-wave) interactions are derived. For parameters characteristic of the interplanetary medium the equations reduce to one dimension. In this case, the oscillating two stream instability (OTSI) is the dominant nonlinear instability, and is stablized through the production of nonlinear ion density fluctuations that efficiently scatter Langmuir waves out of resonance with the electron beam. An analytical model of the electron distribution function is also developed which is used to estimate the total energy losses suffered by the electron beam as it propagates from the solar corona to 1 A.U. and beyond.
Free-vibration acoustic resonance of a nonlinear elastic bar

NASA Astrophysics Data System (ADS)

Tarumi, Ryuichi; Oshita, Yoshihito

2011-02-01

Free-vibration acoustic resonance of a one-dimensional nonlinear elastic bar was investigated by direct analysis in the calculus of variations. The Lagrangian density of the bar includes a cubic term of the deformation gradient, which is responsible for both geometric and constitutive nonlinearities. By expanding the deformation function into a complex Fourier series, we derived the action integral in an analytic form and evaluated its stationary conditions numerically with the Ritz method for the first three resonant vibration modes. This revealed that the bar shows the following prominent nonlinear features: (i) amplitude dependence of the resonance frequency; (ii) symmetry breaking in the vibration pattern; and (iii) excitation of the high-frequency mode around nodal-like points. Stability of the resonant vibrations was also addressed in terms of a convex condition on the strain energy density.
The effect of halo nuclear density on reaction cross-section for light ion collision

NASA Astrophysics Data System (ADS)

Hassan, M. A. M.; Nour El-Din, M. S. M.; Ellithi, A.; Ismail, E.; Hosny, H.

2015-08-01

In the framework of the optical limit approximation (OLA), the reaction cross-section for halo nucleus — stable nucleus collision at intermediate energy, has been studied. The projectile nuclei are taken to be one-neutron halo (1NHP) and two-neutron halo (2NHP). The calculations are carried out for Gaussian-Gaussian (GG), Gaussian-Oscillator (GO), and Gaussian-2S (G2S) densities for each considered projectile. As a target, the stable nuclei in the range 4-28 of the mass number are used. An analytic expression of the phase shift function has been derived. The zero range approximation is considered in the calculations. Also, the in-medium effect is studied. The obtained results are analyzed and compared with the geometrical reaction cross-section and the available experimental data.
N -tag probability law of the symmetric exclusion process

NASA Astrophysics Data System (ADS)

Poncet, Alexis; Bénichou, Olivier; Démery, Vincent; Oshanin, Gleb

2018-06-01

The symmetric exclusion process (SEP), in which particles hop symmetrically on a discrete line with hard-core constraints, is a paradigmatic model of subdiffusion in confined systems. This anomalous behavior is a direct consequence of strong spatial correlations induced by the requirement that the particles cannot overtake each other. Even if this fact has been recognized qualitatively for a long time, up to now there has been no full quantitative determination of these correlations. Here we study the joint probability distribution of an arbitrary number of tagged particles in the SEP. We determine analytically its large-time limit for an arbitrary density of particles, and its full dynamics in the high-density limit. In this limit, we obtain the time-dependent large deviation function of the problem and unveil a universal scaling form shared by the cumulants.
A review on the solution of Grad-Shafranov equation in the cylindrical coordinates based on the Chebyshev collocation technique

NASA Astrophysics Data System (ADS)

Amerian, Z.; Salem, M. K.; Salar Elahi, A.; Ghoranneviss, M.

2017-03-01

Equilibrium reconstruction consists of identifying, from experimental measurements, a distribution of the plasma current density that satisfies the pressure balance constraint. Numerous methods exist to solve the Grad-Shafranov equation, describing the equilibrium of plasma confined by an axisymmetric magnetic field. In this paper, we have proposed a new numerical solution to the Grad-Shafranov equation (an axisymmetric, magnetic field transformed in cylindrical coordinates solved with the Chebyshev collocation method) when the source term (current density function) on the right-hand side is linear. The Chebyshev collocation method is a method for computing highly accurate numerical solutions of differential equations. We describe a circular cross-section of the tokamak and present numerical result of magnetic surfaces on the IR-T1 tokamak and then compare the results with an analytical solution.
Alfven waves in spiral interplanetary field

NASA Technical Reports Server (NTRS)

Whang, Y. C.

1973-01-01

A theoretical study is presented of the Alfven waves in the spiral interplanetary magnetic field. The Alfven waves under consideration are arbitrary, large amplitude, non-monochromatic, microscale waves of any polarization. They superpose on a mesoscale background flow of thermally anisotropic plasma. Using WKB approximation, an analytical solution for the amplitude vectors is obtained as a function of the background flow properties: density, velocity, Alfven speed, thermal anisotropy, and the spiral angel. The necessary condition for the validity of the WKB solution is discussed. The intensity of fluctuations is calculated as a function of heliocentric distance. Relative intensity of fluctuations as compared with the magnitude of the background field has its maximum in the region near l au. Thus outside of this region, the solar wind is less turbulent.
Quantum-shutter approach to tunneling time scales with wave packets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yamada, Norifumi; Garcia-Calderon, Gaston; Villavicencio, Jorge

2005-07-15

The quantum-shutter approach to tunneling time scales [G. Garcia-Calderon and A. Rubio, Phys. Rev. A 55, 3361 (1997)], which uses a cutoff plane wave as the initial condition, is extended to consider certain type of wave packet initial conditions. An analytical expression for the time-evolved wave function is derived. The time-domain resonance, the peaked structure of the probability density (as the function of time) at the exit of the barrier, originally found with the cutoff plane wave initial condition, is studied with the wave packet initial conditions. It is found that the time-domain resonance is not very sensitive to themore » width of the packet when the transmission process occurs in the tunneling regime.« less
Spatial distribution of nuclei in progressive nucleation: Modeling and application

NASA Astrophysics Data System (ADS)

Tomellini, Massimo

2018-04-01

Phase transformations ruled by non-simultaneous nucleation and growth do not lead to random distribution of nuclei. Since nucleation is only allowed in the untransformed portion of space, positions of nuclei are correlated. In this article an analytical approach is presented for computing pair-correlation function of nuclei in progressive nucleation. This quantity is further employed for characterizing the spatial distribution of nuclei through the nearest neighbor distribution function. The modeling is developed for nucleation in 2D space with power growth law and it is applied to describe electrochemical nucleation where correlation effects are significant. Comparison with both computer simulations and experimental data lends support to the model which gives insights into the transition from Poissonian to correlated nearest neighbor probability density.
Inverting pump-probe spectroscopy for state tomography of excitonic systems.

PubMed

Hoyer, Stephan; Whaley, K Birgitta

2013-04-28

We propose a two-step protocol for inverting ultrafast spectroscopy experiments on a molecular aggregate to extract the time-evolution of the excited state density matrix. The first step is a deconvolution of the experimental signal to determine a pump-dependent response function. The second step inverts this response function to obtain the quantum state of the system, given a model for how the system evolves following the probe interaction. We demonstrate this inversion analytically and numerically for a dimer model system, and evaluate the feasibility of scaling it to larger molecular aggregates such as photosynthetic protein-pigment complexes. Our scheme provides a direct alternative to the approach of determining all Hamiltonian parameters and then simulating excited state dynamics.
Distant Massive Clusters and Cosmology

NASA Technical Reports Server (NTRS)

Donahue, Megan

1999-01-01

We present a status report of our X-ray study and analysis of a complete sample of distant (z=0.5-0.8), X-ray luminous clusters of galaxies. We have obtained ASCA and ROSAT observations of the five brightest Extended Medium Sensitivity (EMSS) clusters with z > 0.5. We have constructed an observed temperature function for these clusters, and measured iron abundances for all of these clusters. We have developed an analytic expression for the behavior of the mass-temperature relation in a low-density universe. We use this mass-temperature relation together with a Press-Schechter-based model to derive the expected temperature function for different values of Omega-M. We combine this analysis with the observed temperature functions at redshifts from 0 - 0.8 to derive maximum likelihood estimates for the value of Omega-M. We report preliminary results of this analysis.
ALMA observations of lensed Herschel sources: testing the dark matter halo paradigm

NASA Astrophysics Data System (ADS)

Amvrosiadis, A.; Eales, S. A.; Negrello, M.; Marchetti, L.; Smith, M. W. L.; Bourne, N.; Clements, D. L.; De Zotti, G.; Dunne, L.; Dye, S.; Furlanetto, C.; Ivison, R. J.; Maddox, S. J.; Valiante, E.; Baes, M.; Baker, A. J.; Cooray, A.; Crawford, S. M.; Frayer, D.; Harris, A.; Michałowski, M. J.; Nayyeri, H.; Oliver, S.; Riechers, D. A.; Serjeant, S.; Vaccari, M.

2018-04-01

With the advent of wide-area submillimetre surveys, a large number of high-redshift gravitationally lensed dusty star-forming galaxies have been revealed. Because of the simplicity of the selection criteria for candidate lensed sources in such surveys, identified as those with S500 μm > 100 mJy, uncertainties associated with the modelling of the selection function are expunged. The combination of these attributes makes submillimetre surveys ideal for the study of strong lens statistics. We carried out a pilot study of the lensing statistics of submillimetre-selected sources by making observations with the Atacama Large Millimeter Array (ALMA) of a sample of strongly lensed sources selected from surveys carried out with the Herschel Space Observatory. We attempted to reproduce the distribution of image separations for the lensed sources using a halo mass function taken from a numerical simulation that contains both dark matter and baryons. We used three different density distributions, one based on analytical fits to the haloes formed in the EAGLE simulation and two density distributions [Singular Isothermal Sphere (SIS) and SISSA] that have been used before in lensing studies. We found that we could reproduce the observed distribution with all three density distributions, as long as we imposed an upper mass transition of ˜1013 M⊙ for the SIS and SISSA models, above which we assumed that the density distribution could be represented by a Navarro-Frenk-White profile. We show that we would need a sample of ˜500 lensed sources to distinguish between the density distributions, which is practical given the predicted number of lensed sources in the Herschel surveys.

Emittance preservation in plasma-based accelerators with ion motion

DOE PAGES

Benedetti, C.; Schroeder, C. B.; Esarey, E.; ...

2017-11-01

In a plasma-accelerator-based linear collider, the density of matched, low-emittance, high-energy particle bunches required for collider applications can be orders of magnitude above the background ion density, leading to ion motion, perturbation of the focusing fields, and, hence, to beam emittance growth. By analyzing the response of the background ions to an ultrahigh density beam, analytical expressions, valid for nonrelativistic ion motion, are derived for the transverse wakefield and for the final (i.e., after saturation) bunch emittance. Analytical results are validated against numerical modeling. Initial beam distributions are derived that are equilibrium solutions, which require head-to-tail bunch shaping, enabling emittancemore » preservation with ion motion.« less
Drifting solutions with elliptic symmetry for the compressible Navier-Stokes equations with density-dependent viscosity

DOE Office of Scientific and Technical Information (OSTI.GOV)

An, Hongli, E-mail: kaixinguoan@163.com; Yuen, Manwai, E-mail: nevetsyuen@hotmail.com

2014-05-15

In this paper, we investigate the analytical solutions of the compressible Navier-Stokes equations with dependent-density viscosity. By using the characteristic method, we successfully obtain a class of drifting solutions with elliptic symmetry for the Navier-Stokes model wherein the velocity components are governed by a generalized Emden dynamical system. In particular, when the viscosity variables are taken the same as Yuen [M. W. Yuen, “Analytical solutions to the Navier-Stokes equations,” J. Math. Phys. 49, 113102 (2008)], our solutions constitute a generalization of that obtained by Yuen. Interestingly, numerical simulations show that the analytical solutions can be used to explain the driftingmore » phenomena of the propagation wave like Tsunamis in oceans.« less
Analytical approximations to seawater optical phase functions of scattering

NASA Astrophysics Data System (ADS)

Haltrin, Vladimir I.

2004-11-01

This paper proposes a number of analytical approximations to the classic and recently measured seawater light scattering phase functions. The three types of analytical phase functions are derived: individual representations for 15 Petzold, 41 Mankovsky, and 91 Gulf of Mexico phase functions; collective fits to Petzold phase functions; and analytical representations that take into account dependencies between inherent optical properties of seawater. The proposed phase functions may be used for problems of radiative transfer, remote sensing, visibility and image propagation in natural waters of various turbidity.
Analytical relationships for prediction of the mechanical properties of additively manufactured porous biomaterials

PubMed Central

Hedayati, Reza

2016-01-01

Abstract Recent developments in additive manufacturing techniques have motivated an increasing number of researchers to study regular porous biomaterials that are based on repeating unit cells. The physical and mechanical properties of such porous biomaterials have therefore received increasing attention during recent years. One of the areas that have revived is analytical study of the mechanical behavior of regular porous biomaterials with the aim of deriving analytical relationships that could predict the relative density and mechanical properties of porous biomaterials, given the design and dimensions of their repeating unit cells. In this article, we review the analytical relationships that have been presented in the literature for predicting the relative density, elastic modulus, Poisson's ratio, yield stress, and buckling limit of regular porous structures based on various types of unit cells. The reviewed analytical relationships are used to compare the mechanical properties of porous biomaterials based on different types of unit cells. The major areas where the analytical relationships have improved during the recent years are discussed and suggestions are made for future research directions. © 2016 Wiley Periodicals, Inc. J Biomed Mater Res Part A: 104A: 3164–3174, 2016. PMID:27502358
Method of assessing a lipid-related health risk based on ion mobility analysis of lipoproteins

DOEpatents

Benner, W. Henry; Krauss, Ronald M.; Blanche, Patricia J.

2010-12-14

A medical diagnostic method and instrumentation system for analyzing noncovalently bonded agglomerated biological particles is described. The method and system comprises: a method of preparation for the biological particles; an electrospray generator; an alpha particle radiation source; a differential mobility analyzer; a particle counter; and data acquisition and analysis means. The medical device is useful for the assessment of human diseases, such as cardiac disease risk and hyperlipidemia, by rapid quantitative analysis of lipoprotein fraction densities. Initially, purification procedures are described to reduce an initial blood sample to an analytical input to the instrument. The measured sizes from the analytical sample are correlated with densities, resulting in a spectrum of lipoprotein densities. The lipoprotein density distribution can then be used to characterize cardiac and other lipid-related health risks.
Constrained Kalman Filtering Via Density Function Truncation for Turbofan Engine Health Estimation

NASA Technical Reports Server (NTRS)

Simon, Dan; Simon, Donald L.

2006-01-01

Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops an analytic method of incorporating state variable inequality constraints in the Kalman filter. The resultant filter truncates the PDF (probability density function) of the Kalman filter estimate at the known constraints and then computes the constrained filter estimate as the mean of the truncated PDF. The incorporation of state variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is demonstrated via simulation results obtained from a turbofan engine model. The turbofan engine model contains 3 state variables, 11 measurements, and 10 component health parameters. It is also shown that the truncated Kalman filter may be a more accurate way of incorporating inequality constraints than other constrained filters (e.g., the projection approach to constrained filtering).
Statistics of initial density perturbations in heavy ion collisions and their fluid dynamic response

NASA Astrophysics Data System (ADS)

Floerchinger, Stefan; Wiedemann, Urs Achim

2014-08-01

An interesting opportunity to determine thermodynamic and transport properties in more detail is to identify generic statistical properties of initial density perturbations. Here we study event-by-event fluctuations in terms of correlation functions for two models that can be solved analytically. The first assumes Gaussian fluctuations around a distribution that is fixed by the collision geometry but leads to non-Gaussian features after averaging over the reaction plane orientation at non-zero impact parameter. In this context, we derive a three-parameter extension of the commonly used Bessel-Gaussian event-by-event distribution of harmonic flow coefficients. Secondly, we study a model of N independent point sources for which connected n-point correlation functions of initial perturbations scale like 1 /N n-1. This scaling is violated for non-central collisions in a way that can be characterized by its impact parameter dependence. We discuss to what extent these are generic properties that can be expected to hold for any model of initial conditions, and how this can improve the fluid dynamical analysis of heavy ion collisions.
Adaptive design optimization: a mutual information-based approach to model discrimination in cognitive science.

PubMed

Cavagnaro, Daniel R; Myung, Jay I; Pitt, Mark A; Kujala, Janne V

2010-04-01

Discriminating among competing statistical models is a pressing issue for many experimentalists in the field of cognitive science. Resolving this issue begins with designing maximally informative experiments. To this end, the problem to be solved in adaptive design optimization is identifying experimental designs under which one can infer the underlying model in the fewest possible steps. When the models under consideration are nonlinear, as is often the case in cognitive science, this problem can be impossible to solve analytically without simplifying assumptions. However, as we show in this letter, a full solution can be found numerically with the help of a Bayesian computational trick derived from the statistics literature, which recasts the problem as a probability density simulation in which the optimal design is the mode of the density. We use a utility function based on mutual information and give three intuitive interpretations of the utility function in terms of Bayesian posterior estimates. As a proof of concept, we offer a simple example application to an experiment on memory retention.
Modelling relativistic effects in momentum-resolved electron energy loss spectroscopy of graphene

NASA Astrophysics Data System (ADS)

Lyon, K.; Mowbray, D. J.; Miskovic, Z. L.

2018-02-01

We present an analytical model for the electron energy loss through a two-dimensional (2D) layer of graphene, fully taking into account relativistic effects. Using two different models for graphene's 2D conductivity, one a two-fluid hydrodynamic model with an added correction to account for the inter-band electron transitions near the Dirac point in undoped graphene, the other derived from ab initio plane-wave time-dependent density functional theory in the frequency domain (PW-TDDFT-ω) calculations applied on a graphene superlattice, we derive various different expressions for the probability density of energy and momentum transfer from the incident electron to graphene. To further compare with electron energy loss spectroscopy (EELS) experiments that use setups like scanning Transmission Electron Microscopy, we integrated our energy loss functions over a range of wavenumbers, and compared how the choice of range directly affects the shape, position, and relative heights of graphene's π → π* and σ → σ* transition peaks. Comparisons were made with experimental EELS data under different model inputs, revealing again the strong effect that the choice of wavenumber range has on the energy loss.
Propagation of radially polarized multi-cosine Gaussian Schell-model beams in non-Kolmogorov turbulence

NASA Astrophysics Data System (ADS)

Tang, Miaomiao; Zhao, Daomu; Li, Xinzhong; Wang, Jingge

2018-01-01

Recently, we introduced a new class of radially polarized beams with multi-cosine Gaussian Schell-model(MCGSM) correlation function based on the partially coherent theory (Tang et al., 2017). In this manuscript, we extend the work to study the statistical properties such as the spectral density, the degree of coherence, the degree of polarization, and the state of polarization of the beam propagating in isotropic turbulence with a non-Kolmogorov power spectrum. Analytical formulas for the cross-spectral density matrix elements of a radially polarized MCGSM beam in non-Kolmogorov turbulence are derived. Numerical results show that lattice-like intensity pattern of the beam, which keeps propagation-invariant in free space, is destroyed by the turbulence when it passes at sufficiently large distances from the source. It is also shown that the polarization properties are mainly affected by the source correlation functions, and change in the turbulent statistics plays a relatively small effect. In addition, the polarization state exhibits self-splitting property and each beamlet evolves into radially polarized structure upon propagation.
First-principles calculations of two cubic fluoropervskite compounds: RbFeF3 and RbNiF3

NASA Astrophysics Data System (ADS)

Mubarak, A. A.; Al-Omari, Saleh

2015-05-01

We present first-principles calculations of the structural, elastic, electronic, magnetic and optical properties for RbFeF3 and RbNiF3. The full-potential linear augmented plan wave (FP-LAPW) method within the density functional theory was utilized to perform the present calculations. We employed the generalized gradient approximation as exchange-correlation potential. It was found that the calculated analytical lattice parameters agree with previous studies. The analysis of elastic constants showed that the present compounds are elastically stable and anisotropic. Moreover, both compounds are classified as a ductile compound. The calculations of the band structure and density functional theory revealed that the RbFeF3 compound has a half-metallic behavior while the RbNiF3 compound has a semiconductor behavior with indirect (M-Γ) band gap. The ferromagnetic behavior was studied for both compounds. The optical properties were calculated for the radiation of up to 40 eV. A beneficial optics technology is predicted as revealed from the optical spectra.
Joint properties of a tool machining process to guarantee fluid-proof abilities

NASA Astrophysics Data System (ADS)

Bataille, C.; Deltombe, R.; Jourani, A.; Bigerelle, M.

2017-12-01

This study addressed the impact of rod surface topography in contact with reciprocating seals. Rods were tooled with and without centreless grinding. All rods tooled with centreless grinding were fluid-proof, in contrast to rods tooled without centreless grinding that either had leaks or were fluid-proof. A method was developed to analyse the machining signature, and the software Mesrug™ was used in order to discriminate roughness parameters that can be used to characterize the sealing functionality. According to this surface roughness analysis, a fluid-proof rod tooled without centreless grinding presents aperiodic large plateaus, and the relevant roughness parameter for characterizing the sealing functionality is the density of summits S DS. Increasing the density of summits counteracts leakage, which may be because motif decomposition integrates three topographical components: circularity (perpendicular long-wave roughness), longitudinal waviness, and roughness thanks to the Wolf pruning algorithm. A 3D analytical contact model was applied to analyse the contact area of each type of sample with the seal surface. This model provides a leakage probability, and the results were consistent with the interpretation of the topographical analysis.
Calculation of photodetachment cross sections and photoelectron angular distributions of negative ions using density functional theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Yuan; Ning, Chuangang, E-mail: ningcg@tsinghua.edu.cn; Collaborative Innovation Center of Quantum Matter, Beijing

2015-10-14

Recently, the development of photoelectron velocity map imaging makes it much easier to obtain the photoelectron angular distributions (PADs) experimentally. However, explanations of PADs are only qualitative in most cases, and very limited works have been reported on how to calculate PAD of anions. In the present work, we report a method using the density-functional-theory Kohn-Sham orbitals to calculate the photodetachment cross sections and the anisotropy parameter β. The spherical average over all random molecular orientation is calculated analytically. A program which can handle both the Gaussian type orbital and the Slater type orbital has been coded. The testing calculationsmore » on Li{sup −}, C{sup −}, O{sup −}, F{sup −}, CH{sup −}, OH{sup −}, NH{sub 2}{sup −}, O{sub 2}{sup −}, and S{sub 2}{sup −} show that our method is an efficient way to calculate the photodetachment cross section and anisotropy parameter β for anions, thus promising for large systems.« less
Locating structures and evolution pathways of reconstructed rutile TiO2(011) using genetic algorithm aided density functional theory calculations.

PubMed

Ding, Pan; Gong, Xue-Qing

2016-05-01

Titanium dioxide (TiO2) is an important metal oxide that has been used in many different applications. TiO2 has also been widely employed as a model system to study basic processes and reactions in surface chemistry and heterogeneous catalysis. In this work, we investigated the (011) surface of rutile TiO2 by focusing on its reconstruction. Density functional theory calculations aided by a genetic algorithm based optimization scheme were performed to extensively sample the potential energy surfaces of reconstructed rutile TiO2 structures that obey (2 × 1) periodicity. A lot of stable surface configurations were located, including the global-minimum configuration that was proposed previously. The wide variety of surface structures determined through the calculations performed in this work provide insight into the relationship between the atomic configuration of a surface and its stability. More importantly, several analytical schemes were proposed and tested to gauge the differences and similarities among various surface structures, aiding the construction of the complete pathway for the reconstruction process.
Simulating the interaction of galaxies and the intergalactic medium

NASA Astrophysics Data System (ADS)

Carin, Robert A.

2008-11-01

The co-evolution of galaxies and the intergalactic medium as a function of environment is studied using hydrodynamic simulations of the ΛCDM cosmogony. It is demonstrated with non-radiative calculations that, in the absence of non-gravitational mechanisms, dark matter haloes accrete a near-universal fraction (˜ 0.9Ω_{b}/&Omega_;{m}) of baryons. The absence of a mass or redshift dependence of this fraction augurs well for parameter tests that use X-ray clusters as cosmological probes. Moreover, this result indicates that non-gravitational processes must efficiently regulate the formation of stars in dark matter haloes if the halo mass function is to be reconciled with the observed galaxy luminosity function. Simulations featuring stellar evolution and non-gravitational feedback mechanisms (photo-heating by the ultraviolet background, and thermal and kinetic supernovae feedback) are used to follow the evolution of star formation, and the thermo- and chemo-dynamical evolution of baryons. The observed star formation history of the Universe is reproduced, except at low redshift where it is overestimated by a factor of a few, possibly indicating the need for feedback from active galactic nuclei to quench cooling flows around massive galaxies. The simulations more accurately reproduce the observed abundance of galaxies with late-type morphologies than has been reported elsewhere. The unique initial conditions of these simulations, based on the Millennium Simulation, allow an unprecedented study of the role of large-scale environment to be conducted. The cosmic star formation rate density is found to vary by an order of magnitude across the extremes of environment expected in the local Universe. The mass fraction of baryons in the observationally elusive warm-hot intergalactic medium (WHIM), and the volume filling factor that this gas occupies, is also shown to vary by a factor of a few across such environments. This variation is attributed to differences in the halo mass functions of the environments. Finally, we compare the X-ray properties of haloes from the simulations with the predictions of the tet{White_and_Frenk_91} analytic galaxy formation model, and demonstrate that deviations from the analytic prediction arise from the assumptions i) that haloes retain their cosmic share of baryons, and ii) their gas follows an isothermal density profile. The simulations indicate that a significant fraction of gas is ejected from low mass haloes by galactic superwinds, leading to a significant increase in their cooling time profiles and an associated drop in their soft X-ray luminosities, relative to the analytic model. Simulated X-ray luminosities remain greater than present observational upper limits, but it is argued that the observations provide only weak constraints and may suffer from a systematic bias, such that the mass of the halo hosting a given galaxy is overestimated. This bias also follows from the assumption that haloes exhibit isothermal density profiles.
A principled dimension-reduction method for the population density approach to modeling networks of neurons with synaptic dynamics.

PubMed

Ly, Cheng

2013-10-01

The population density approach to neural network modeling has been utilized in a variety of contexts. The idea is to group many similar noisy neurons into populations and track the probability density function for each population that encompasses the proportion of neurons with a particular state rather than simulating individual neurons (i.e., Monte Carlo). It is commonly used for both analytic insight and as a time-saving computational tool. The main shortcoming of this method is that when realistic attributes are incorporated in the underlying neuron model, the dimension of the probability density function increases, leading to intractable equations or, at best, computationally intensive simulations. Thus, developing principled dimension-reduction methods is essential for the robustness of these powerful methods. As a more pragmatic tool, it would be of great value for the larger theoretical neuroscience community. For exposition of this method, we consider a single uncoupled population of leaky integrate-and-fire neurons receiving external excitatory synaptic input only. We present a dimension-reduction method that reduces a two-dimensional partial differential-integral equation to a computationally efficient one-dimensional system and gives qualitatively accurate results in both the steady-state and nonequilibrium regimes. The method, termed modified mean-field method, is based entirely on the governing equations and not on any auxiliary variables or parameters, and it does not require fine-tuning. The principles of the modified mean-field method have potential applicability to more realistic (i.e., higher-dimensional) neural networks.
Beyond δ : Tailoring marked statistics to reveal modified gravity

NASA Astrophysics Data System (ADS)

Valogiannis, Georgios; Bean, Rachel

2018-01-01

Models that seek to explain cosmic acceleration through modifications to general relativity (GR) evade stringent Solar System constraints through a restoring, screening mechanism. Down-weighting the high-density, screened regions in favor of the low density, unscreened ones offers the potential to enhance the amount of information carried in such modified gravity models. In this work, we assess the performance of a new "marked" transformation and perform a systematic comparison with the clipping and logarithmic transformations, in the context of Λ CDM and the symmetron and f (R ) modified gravity models. Performance is measured in terms of the fractional boost in the Fisher information and the signal-to-noise ratio (SNR) for these models relative to the statistics derived from the standard density distribution. We find that all three statistics provide improved Fisher boosts over the basic density statistics. The model parameters for the marked and clipped transformation that best enhance signals and the Fisher boosts are determined. We also show that the mark is useful both as a Fourier and real-space transformation; a marked correlation function also enhances the SNR relative to the standard correlation function, and can on mildly nonlinear scales show a significant difference between the Λ CDM and the modified gravity models. Our results demonstrate how a series of simple analytical transformations could dramatically increase the predicted information extracted on deviations from GR, from large-scale surveys, and give the prospect for a much more feasible potential detection.
Nonlinear load-deflection behavior of abutment backwalls with varying height and soil density.

DOT National Transportation Integrated Search

2011-12-01

We address the scaling of abutment wall lateral response with wall height and compaction condition through testing and analytical work. The : analytical work was undertaken to develop hyperbolic curves representing the load-deflection response of bac...
Modeling and analysis of a novel planar eddy current damper

NASA Astrophysics Data System (ADS)

Zhang, He; Kou, Baoquan; Jin, Yinxi; Zhang, Lu; Zhang, Hailin; Li, Liyi

2014-05-01

In this paper, a novel 2-DOF permanent magnet planar eddy current damper is proposed, of which the stator is made of a copper plate and the mover is composed of two orthogonal 1-D permanent magnet arrays with a double sided structure. The main objective of the planar eddy current damper is to provide two orthogonal damping forces for dynamic systems like the 2-DOF high precision positioning system. Firstly, the basic structure and the operating principle of the planar damper are introduced. Secondly, the analytical model of the planar damper is established where the magnetic flux density distribution of the permanent magnet arrays is obtained by using the equivalent magnetic charge method and the image method. Then, the analytical expressions of the damping force and damping coefficient are derived. Lastly, to verify the analytical model, the finite element method (FEM) is adopted for calculating the flux density and a planar damper prototype is manufactured and thoroughly tested. The results from FEM and experiments are in good agreement with the ones from the analytical expressions indicating that the analytical model is reasonable and correct.
Quantitative Characterization of the Microstructure and Transport Properties of Biopolymer Networks

PubMed Central

Jiao, Yang; Torquato, Salvatore

2012-01-01

Biopolymer networks are of fundamental importance to many biological processes in normal and tumorous tissues. In this paper, we employ the panoply of theoretical and simulation techniques developed for characterizing heterogeneous materials to quantify the microstructure and effective diffusive transport properties (diffusion coefficient De and mean survival time τ) of collagen type I networks at various collagen concentrations. In particular, we compute the pore-size probability density function P(δ) for the networks and present a variety of analytical estimates of the effective diffusion coefficient De for finite-sized diffusing particles, including the low-density approximation, the Ogston approximation, and the Torquato approximation. The Hashin-Strikman upper bound on the effective diffusion coefficient De and the pore-size lower bound on the mean survival time τ are used as benchmarks to test our analytical approximations and numerical results. Moreover, we generalize the efficient first-passage-time techniques for Brownian-motion simulations in suspensions of spheres to the case of fiber networks and compute the associated effective diffusion coefficient De as well as the mean survival time τ, which is related to nuclear magnetic resonance (NMR) relaxation times. Our numerical results for De are in excellent agreement with analytical results for simple network microstructures, such as periodic arrays of parallel cylinders. Specifically, the Torquato approximation provides the most accurate estimates of De for all collagen concentrations among all of the analytical approximations we consider. We formulate a universal curve for τ for the networks at different collagen concentrations, extending the work of Yeong and Torquato [J. Chem. Phys. 106, 8814 (1997)]. We apply rigorous cross-property relations to estimate the effective bulk modulus of collagen networks from a knowledge of the effective diffusion coefficient computed here. The use of cross-property relations to link other physical properties to the transport properties of collagen networks is also discussed. PMID:22683739

Scaling of the local quantum uncertainty at quantum phase transitions

NASA Astrophysics Data System (ADS)

Coulamy, I. B.; Warnes, J. H.; Sarandy, M. S.; Saguia, A.

2016-04-01

We investigate the local quantum uncertainty (LQU) between a block of L qubits and one single qubit in a composite system of n qubits driven through a quantum phase transition (QPT). A first-order QPT is analytically considered through a Hamiltonian implementation of the quantum search. In the case of second-order QPTs, we consider the transverse-field Ising chain via a numerical analysis through density matrix renormalization group. For both cases, we compute the LQU for finite-sizes as a function of L and of the coupling parameter, analyzing its pronounced behavior at the QPT.
Flux tubes and coherence length in the SU(3) vacuum

NASA Astrophysics Data System (ADS)

Cea, P.; Cosmai, L.; Cuteri, F.; Papa, A.

An estimate of the London penetration and coherence lengths in the vacuum of the SU(3) pure gauge theory is given downstream an analysis of the transverse profile of the chromoelectric flux tubes. Within ordinary superconductivity, a simple variational model for the magnitude of the normalized order parameter of an isolated vortex produces an analytic expression for magnetic field and supercurrent density. In the picture of SU(3) vacuum as dual superconductor, this expression provides us with the function that fits the chromoelectric field data. The smearing procedure is used in order to reduce noise.
Shape Optimization of Cylindrical Shell for Interior Noise

NASA Technical Reports Server (NTRS)

Robinson, Jay H.

1999-01-01

In this paper an analytic method is used to solve for the cross spectral density of the interior acoustic response of a cylinder with nonuniform thickness subjected to turbulent boundary layer excitation. The cylinder is of honeycomb core construction with the thickness of the core material expressed as a cosine series in the circumferential direction. The coefficients of this series are used as the design variable in the optimization study. The objective function is the space and frequency averaged acoustic response. Results confirm the presence of multiple local minima as previously reported and demonstrate the potential for modest noise reduction.
Antimony diffusion in CdTe

DOE PAGES

Colegrove, Eric; Harvey, Steven P.; Yang, Ji -Hui; ...

2017-02-08

Group V dopants may be used for next-generation high-voltage cadmium telluride (CdTe) solar photovoltaics, but fundamental defect energetics and kinetics need to be understood. Here, antimony (Sb) diffusion is studied in single-crystal and polycrystalline CdTe under Cd-rich conditions. Diffusion profiles are determined by dynamic secondary ion mass spectroscopy and analyzed with analytical bulk and grain-boundary diffusion models. Slow bulk and fast grain-boundary diffusion are found. Density functional theory is used to understand formation energy and mechanisms. Lastly, the theory and experimental results create new understanding of group V defect kinetics in CdTe.
Addressing the too big to fail problem with baryon physics and sterile neutrino dark matter

NASA Astrophysics Data System (ADS)

Lovell, Mark R.; Gonzalez-Perez, Violeta; Bose, Sownak; Boyarsky, Alexey; Cole, Shaun; Frenk, Carlos S.; Ruchayskiy, Oleg

2017-07-01

N-body dark matter simulations of structure formation in the Λ cold dark matter (ΛCDM) model predict a population of subhaloes within Galactic haloes that have higher central densities than inferred for the Milky Way satellites, a tension known as the 'too big to fail' problem. Proposed solutions include baryonic effects, a smaller mass for the Milky Way halo and warm dark matter (WDM). We test these possibilities using a semi-analytic model of galaxy formation to generate luminosity functions for Milky Way halo-analogue satellite populations, the results of which are then coupled to the Jiang & van den Bosch model of subhalo stripping to predict the subhalo Vmax functions for the 10 brightest satellites. We find that selecting the brightest satellites (as opposed to the most massive) and modelling the expulsion of gas by supernovae at early times increases the likelihood of generating the observed Milky Way satellite Vmax function. The preferred halo mass is 6 × 1011 M⊙, which has a 14 per cent probability to host a Vmax function like that of the Milky Way satellites. We conclude that the Milky Way satellite Vmax function is compatible with a CDM cosmology, as previously found by Sawala et al. using hydrodynamic simulations. Sterile neutrino-WDM models achieve a higher degree of agreement with the observations, with a maximum 50 per cent chance of generating the observed Milky Way satellite Vmax function. However, more work is required to check that the semi-analytic stripping model is calibrated correctly for each sterile neutrino cosmology.
Axisymmetric plasma equilibria in a Kerr metric

NASA Astrophysics Data System (ADS)

Elsässer, Klaus

2001-10-01

Plasma equilibria near a rotating black hole are considered within the multifluid description. An isothermal two-component plasma with electrons and positrons or ions is determined by four structure functions and the boundary conditions. These structure functions are the Bernoulli function and the toroidal canonical momentum per mass for each species. The quasi-neutrality assumption (no charge density, no toroidal current) allows to solve Maxwell's equations analytically for any axisymmetric stationary metric, and to reduce the fluid equations to one single scalar equation for the stream function \\chi of the positrons or ions, respectively. The basic smallness parameter is the ratio of the skin depth of electrons to the scale length of the metric and fluid quantities, and, in the case of an electron-ion plasma, the mass ratio m_e/m_i. The \\chi-equation can be solved by standard methods, and simple solutions for a Kerr geometry are available; they show characteristic flow patterns, depending on the structure functions and the boundary conditions.
Critical behavior of a relativistic Bose gas.

PubMed

Pandita, P N

2014-03-01

We show that the thermodynamic behavior of relativistic ideal Bose gas, recently studied numerically by Grether et al., can be obtained analytically. Using the analytical results, we obtain the critical behavior of the relativistic Bose gas exactly for all the regimes. We show that these analytical results reduce to those of Grether et al. in different regimes of the Bose gas. Furthermore, we also obtain an analytically closed-form expression for the energy density for the Bose gas that is valid in all regimes.
A structured population model with diffusion in structure space.

PubMed

Pugliese, Andrea; Milner, Fabio

2018-05-09

A structured population model is described and analyzed, in which individual dynamics is stochastic. The model consists of a PDE of advection-diffusion type in the structure variable. The population may represent, for example, the density of infected individuals structured by pathogen density x, [Formula: see text]. The individuals with density [Formula: see text] are not infected, but rather susceptible or recovered. Their dynamics is described by an ODE with a source term that is the exact flux from the diffusion and advection as [Formula: see text]. Infection/reinfection is then modeled moving a fraction of these individuals into the infected class by distributing them in the structure variable through a probability density function. Existence of a global-in-time solution is proven, as well as a classical bifurcation result about equilibrium solutions: a net reproduction number [Formula: see text] is defined that separates the case of only the trivial equilibrium existing when [Formula: see text] from the existence of another-nontrivial-equilibrium when [Formula: see text]. Numerical simulation results are provided to show the stabilization towards the positive equilibrium when [Formula: see text] and towards the trivial one when [Formula: see text], result that is not proven analytically. Simulations are also provided to show the Allee effect that helps boost population sizes at low densities.
Higher order alchemical derivatives from coupled perturbed self-consistent field theory.

PubMed

Lesiuk, Michał; Balawender, Robert; Zachara, Janusz

2012-01-21

We present an analytical approach to treat higher order derivatives of Hartree-Fock (HF) and Kohn-Sham (KS) density functional theory energy in the Born-Oppenheimer approximation with respect to the nuclear charge distribution (so-called alchemical derivatives). Modified coupled perturbed self-consistent field theory is used to calculate molecular systems response to the applied perturbation. Working equations for the second and the third derivatives of HF/KS energy are derived. Similarly, analytical forms of the first and second derivatives of orbital energies are reported. The second derivative of Kohn-Sham energy and up to the third derivative of Hartree-Fock energy with respect to the nuclear charge distribution were calculated. Some issues of practical calculations, in particular the dependence of the basis set and Becke weighting functions on the perturbation, are considered. For selected series of isoelectronic molecules values of available alchemical derivatives were computed and Taylor series expansion was used to predict energies of the "surrounding" molecules. Predicted values of energies are in unexpectedly good agreement with the ones computed using HF/KS methods. Presented method allows one to predict orbital energies with the error less than 1% or even smaller for valence orbitals. © 2012 American Institute of Physics
Analytic Guidance for the First Entry in a Skip Atmospheric Entry

NASA Technical Reports Server (NTRS)

Garcia-Llama, Eduardo

2007-01-01

This paper presents an analytic method to generate a reference drag trajectory for the first entry portion of a skip atmospheric entry. The drag reference, expressed as a polynomial function of the velocity, will meet the conditions necessary to fit the requirements of the complete entry phase. The generic method proposed to generate the drag reference profile is further simplified by thinking of the drag and the velocity as density and cumulative distribution functions respectively. With this notion it will be shown that the reference drag profile can be obtained by solving a linear algebraic system of equations. The resulting drag profile is flown using the feedback linearization method of differential geometric control as guidance law with the error dynamics of a second order homogeneous equation in the form of a damped oscillator. This approach was first proposed as a revisited version of the Space Shuttle Orbiter entry guidance. However, this paper will show that it can be used to fly the first entry in a skip entry trajectory. In doing so, the gains in the error dynamics will be changed at a certain point along the trajectory to improve the tracking performance.
Study of the hard-disk system at high densities: the fluid-hexatic phase transition.

PubMed

Mier-Y-Terán, Luis; Machorro-Martínez, Brian Ignacio; Chapela, Gustavo A; Del Río, Fernando

2018-06-21

Integral equations of uniform fluids have been considered unable to predict any characteristic feature of the fluid-solid phase transition, including the shoulder that arises in the second peak of the fluid-phase radial distribution function, RDF, of hard-core systems obtained by computer simulations, at fluid densities very close to the structural two-step phase transition. This reasoning is based on the results of traditional integral approximations, like Percus-Yevick, PY, which does not show such a shoulder in hard-core systems, neither in two nor three dimensions. In this work, we present results of three Ansätze, based on the PY theory, that were proposed to remedy the lack of PY analytical solutions in two dimensions. This comparative study shows that one of those Ansätze does develop a shoulder in the second peak of the RDF at densities very close to the phase transition, qualitatively describing this feature. Since the shoulder grows into a peak at still higher densities, this integral equation approach predicts the appearance of an orientational order characteristic of the hexatic phase in a continuous fluid-hexatic phase transition.
Analytical and experimental investigation of the coaxial plasma gun for use as a particle accelerator

NASA Technical Reports Server (NTRS)

Shriver, E. L.

1972-01-01

The coaxial plasma accelerator for use as a projectile accelerator is discussed. The accelerator is described physically and analytically by solution of circuit equations, and by solving for the magnetic pressures which are formed by the j cross B vector forces on the plasma. It is shown that the plasma density must be increased if the accelerator is to be used as a projectile accelerator. Three different approaches to increasing plasma density are discussed. When a magnetic field containment scheme was used to increase the plasma density, glass beads of 0.66 millimeter diameter were accelerated to 7 to 8 kilometers per second velocities. Glass beads of smaller diameter were accelerated to more than twice this velocity.
Thermal Performance of Cryogenic Multilayer Insulation at Various Layer Spacings

NASA Technical Reports Server (NTRS)

Johnson, Wesley Louis

2010-01-01

Multilayer insulation (MLI) has been shown to be the best performing cryogenic insulation system at high vacuum (less that 10 (exp 3) torr), and is widely used on spaceflight vehicles. Over the past 50 years, many investigations into MLI have yielded a general understanding of the many variables that are associated with MLI. MLI has been shown to be a function of variables such as warm boundary temperature, the number of reflector layers, and the spacer material in between reflectors, the interstitial gas pressure and the interstitial gas. Since the conduction between reflectors increases with the thickness of the spacer material, yet the radiation heat transfer is inversely proportional to the number of layers, it stands to reason that the thermal performance of MLI is a function of the number of layers per thickness, or layer density. Empirical equations that were derived based on some of the early tests showed that the conduction term was proportional to the layer density to a power. This power depended on the material combination and was determined by empirical test data. Many authors have graphically shown such optimal layer density, but none have provided any data at such low densities, or any method of determining this density. Keller, Cunnington, and Glassford showed MLI thermal performance as a function of layer density of high layer densities, but they didn't show a minimal layer density or any data below the supposed optimal layer density. However, it was recently discovered that by manipulating the derived empirical equations and taking a derivative with respect to layer density yields a solution for on optimal layer density. Various manufacturers have begun manufacturing MLI at densities below the optimal density. They began this based on the theory that increasing the distance between layers lowered the conductive heat transfer and they had no limitations on volume. By modifying the circumference of these blankets, the layer density can easily be varied. The simplest method of determining the thermal performance of MLI at cryogenic temperature is by boil-off calorimetry. Several blankets were procured and tested at various layer densities at the Cryogenics Test Laboratory at Kennedy Space Center. The densities that the blankets were tested over covered a wide range of layer densities including the analytical minimum. Several of the blankets were tested at the same insulation thickness while changing the layer density (thus a different number of reflector layers). Optimizing the layer density of multilayer insulation systems for heat transfer would remove a layer density from the complex method of designing such insulation systems. Additional testing was performed at various warm boundary temperatures and pressures. The testing and analysis was performed to simplify the analysis of cryogenic thermal insulation systems. This research was funded by the National Aeronautics and Space Administration's Exploration Technology Development Program's Cryogenic Fluid Management Project
A two-parameter family of double-power-law biorthonormal potential-density expansions

NASA Astrophysics Data System (ADS)

Lilley, Edward J.; Sanders, Jason L.; Evans, N. Wyn

2018-07-01

We present a two-parameter family of biorthonormal double-power-law potential-density expansions. Both the potential and density are given in a closed analytic form and may be rapidly computed via recurrence relations. We show that this family encompasses all the known analytic biorthonormal expansions: the Zhao expansions (themselves generalizations of ones found earlier by Hernquist & Ostriker and by Clutton-Brock) and the recently discovered Lilley et al. expansion. Our new two-parameter family includes expansions based around many familiar spherical density profiles as zeroth-order models, including the γ models and the Jaffe model. It also contains a basis expansion that reproduces the famous Navarro-Frenk-White (NFW) profile at zeroth order. The new basis expansions have been found via a systematic methodology which has wide applications in finding other new expansions. In the process, we also uncovered a novel integral transform solution to Poisson's equation.
A two-parameter family of double-power-law biorthonormal potential-density expansions

NASA Astrophysics Data System (ADS)

Lilley, Edward J.; Sanders, Jason L.; Evans, N. Wyn

2018-05-01

We present a two-parameter family of biorthonormal double-power-law potential-density expansions. Both the potential and density are given in closed analytic form and may be rapidly computed via recurrence relations. We show that this family encompasses all the known analytic biorthonormal expansions: the Zhao expansions (themselves generalizations of ones found earlier by Hernquist & Ostriker and by Clutton-Brock) and the recently discovered Lilley et al. (2017a) expansion. Our new two-parameter family includes expansions based around many familiar spherical density profiles as zeroth-order models, including the γ models and the Jaffe model. It also contains a basis expansion that reproduces the famous Navarro-Frenk-White (NFW) profile at zeroth order. The new basis expansions have been found via a systematic methodology which has wide applications in finding other new expansions. In the process, we also uncovered a novel integral transform solution to Poisson's equation.
A two-parameter family of double-power-law biorthonormal potential-density expansions

NASA Astrophysics Data System (ADS)

Lilley, Edward J.; Sanders, Jason L.; Evans, N. Wyn

2018-05-01

We present a two-parameter family of biorthonormal double-power-law potential-density expansions. Both the potential and density are given in closed analytic form and may be rapidly computed via recurrence relations. We show that this family encompasses all the known analytic biorthonormal expansions: the Zhao expansions (themselves generalizations of ones found earlier by Hernquist & Ostriker and by Clutton-Brock) and the recently discovered Lilley et al. (2018b) expansion. Our new two-parameter family includes expansions based around many familiar spherical density profiles as zeroth-order models, including the γ models and the Jaffe model. It also contains a basis expansion that reproduces the famous Navarro-Frenk-White (NFW) profile at zeroth order. The new basis expansions have been found via a systematic methodology which has wide applications in finding other new expansions. In the process, we also uncovered a novel integral transform solution to Poisson's equation.
Interpretation of plasma impurity deposition probes. Analytic approximation

NASA Astrophysics Data System (ADS)

Stangeby, P. C.

1987-10-01

Insertion of a probe into the plasma induces a high speed flow of the hydrogenic plasma to the probe which, by friction, accelerates the impurity ions to velocities approaching the hydrogenic ion acoustic speed, i.e., higher than the impurity ion thermal speed. A simple analytic theory based on this effect provides a relation between impurity fluxes to the probe Γimp and the undisturbed impurity ion density nimp, with the hydrogenic temperature and density as input parameters. Probe size also influences the collection process and large probes are found to attract a higher flux density than small probes in the same plasma. The quantity actually measured, cimp, the impurity atom surface density (m-2) net-deposited on the probe, is related to Γimp and thus to nimp by taking into account the partial removal of deposited material caused by sputtering and the redeposition process.
An accurate analytic description of neutrino oscillations in matter

NASA Astrophysics Data System (ADS)

Akhmedov, E. Kh.; Niro, Viviana

2008-12-01

A simple closed-form analytic expression for the probability of two-flavour neutrino oscillations in a matter with an arbitrary density profile is derived. Our formula is based on a perturbative expansion and allows an easy calculation of higher order corrections. The expansion parameter is small when the density changes relatively slowly along the neutrino path and/or neutrino energy is not very close to the Mikheyev-Smirnov-Wolfenstein (MSW) resonance energy. Our approximation is not equivalent to the adiabatic approximation and actually goes beyond it. We demonstrate the validity of our results using a few model density profiles, including the PREM density profile of the Earth. It is shown that by combining the results obtained from the expansions valid below and above the MSW resonance one can obtain a very good description of neutrino oscillations in matter in the entire energy range, including the resonance region.
Method of and apparatus for determining the similarity of a biological analyte from a model constructed from known biological fluids

DOEpatents

Robinson, Mark R.; Ward, Kenneth J.; Eaton, Robert P.; Haaland, David M.

1990-01-01

The characteristics of a biological fluid sample having an analyte are determined from a model constructed from plural known biological fluid samples. The model is a function of the concentration of materials in the known fluid samples as a function of absorption of wideband infrared energy. The wideband infrared energy is coupled to the analyte containing sample so there is differential absorption of the infrared energy as a function of the wavelength of the wideband infrared energy incident on the analyte containing sample. The differential absorption causes intensity variations of the infrared energy incident on the analyte containing sample as a function of sample wavelength of the energy, and concentration of the unknown analyte is determined from the thus-derived intensity variations of the infrared energy as a function of wavelength from the model absorption versus wavelength function.
Formation of Plasma Around a Small Meteoroid: Simulation and Theory

NASA Astrophysics Data System (ADS)

Sugar, G.; Oppenheim, M. M.; Dimant, Y. S.; Close, S.

2018-05-01

High-power large-aperture radars detect meteors by reflecting radio waves off dense plasma that surrounds a hypersonic meteoroid as it ablates in the Earth's atmosphere. If the plasma density profile around the meteoroid is known, the plasma's radar cross section can be used to estimate meteoroid properties such as mass, density, and composition. This paper presents head echo plasma density distributions obtained via two numerical simulations of a small ablating meteoroid and compares the results to an analytical solution found in Dimant and Oppenheim (2017a, https://doi.org/10.1002/2017JA023960, 2017b, https://doi.org/10.1002/2017JA023963). The first simulation allows ablated meteoroid particles to experience only a single collision to match an assumption in the analytical solution, while the second is a more realistic simulation by allowing multiple collisions. The simulation and analytical results exhibit similar plasma density distributions. At distances much less than λT, the average distance an ablated particle travels from the meteoroid before a collision with an atmospheric particle, the plasma density falls off as 1/R, where R is the distance from the meteoroid center. At distances substantially greater than λT, the plasma density profile has an angular dependence, falling off as 1/R2 directly behind the meteoroid, 1/R3 in a plane perpendicular to the meteoroid's path that contains the meteoroid center, and exp[-1.5(R/λT2/3)]/R in front of the meteoroid. When used for calculating meteoroid masses, this new plasma density model can give masses that are orders of magnitude different than masses calculated from a spherically symmetric Gaussian distribution, which has been used to calculate masses in the past.

Analytic calculations of anharmonic infrared and Raman vibrational spectra

PubMed Central

Louant, Orian; Ruud, Kenneth

2016-01-01

Using a recently developed recursive scheme for the calculation of high-order geometric derivatives of frequency-dependent molecular properties [Ringholm et al., J. Comp. Chem., 2014, 35, 622], we present the first analytic calculations of anharmonic infrared (IR) and Raman spectra including anharmonicity both in the vibrational frequencies and in the IR and Raman intensities. In the case of anharmonic corrections to the Raman intensities, this involves the calculation of fifth-order energy derivatives—that is, the third-order geometric derivatives of the frequency-dependent polarizability. The approach is applicable to both Hartree–Fock and Kohn–Sham density functional theory. Using generalized vibrational perturbation theory to second order, we have calculated the anharmonic infrared and Raman spectra of the non- and partially deuterated isotopomers of nitromethane, where the inclusion of anharmonic effects introduces combination and overtone bands that are observed in the experimental spectra. For the major features of the spectra, the inclusion of anharmonicities in the calculation of the vibrational frequencies is more important than anharmonic effects in the calculated infrared and Raman intensities. Using methanimine as a trial system, we demonstrate that the analytic approach avoids errors in the calculated spectra that may arise if numerical differentiation schemes are used. PMID:26784673
Rate decline curves analysis of multiple-fractured horizontal wells in heterogeneous reservoirs

NASA Astrophysics Data System (ADS)

Wang, Jiahang; Wang, Xiaodong; Dong, Wenxiu

2017-10-01

In heterogeneous reservoir with multiple-fractured horizontal wells (MFHWs), due to the high density network of artificial hydraulic fractures, the fluid flow around fracture tips behaves like non-linear flow. Moreover, the production behaviors of different artificial hydraulic fractures are also different. A rigorous semi-analytical model for MFHWs in heterogeneous reservoirs is presented by combining source function with boundary element method. The model are first validated by both analytical model and simulation model. Then new Blasingame type curves are established. Finally, the effects of critical parameters on the rate decline characteristics of MFHWs are discussed. The results show that heterogeneity has significant influence on the rate decline characteristics of MFHWs; the parameters related to the MFHWs, such as fracture conductivity and length also can affect the rate characteristics of MFHWs. One novelty of this model is to consider the elliptical flow around artificial hydraulic fracture tips. Therefore, our model can be used to predict rate performance more accurately for MFHWs in heterogeneous reservoir. The other novelty is the ability to model the different production behavior at different fracture stages. Compared to numerical and analytic methods, this model can not only reduce extensive computing processing but also show high accuracy.
Excitation of propagating magnetization waves by microstrip antennas

NASA Astrophysics Data System (ADS)

Dmitriev, V. F.; Kalinikos, B. A.

1988-11-01

We discuss the self-consistent theory of excitation of dipole-exchange magnetization waves by microstrip antennas in a metal-dielectric-ferrite-dielectric-metal stratified structure, magnetized under an arbitrary angle to the surface. Spin-wave Green's functions are derived, describing the response of the spin-system to a spatially inhomogeneous varying magnetic field. The radiative resistance of microstrip antenna is calculated. In this case the distribution of surface current density in the antenna is found on the basis of the analytic solution of a singular integral equation. The nature of the effect of metallic screens and redistributed surface current densities in the antenna on the frequency dependence of the resistive radiation is investigated. Approximate relations are obtained, convenient for practical calculations of radiative resistance of microstrip antennas both in a free and in a screened ferromagnetic film. The theoretical calculations are verified by data of experiments carried out on monocrystalline films of iron-yttrium garnet.
Correlations and enlarged superconducting phase of t -J⊥ chains of ultracold molecules on optical lattices

NASA Astrophysics Data System (ADS)

Manmana, Salvatore R.; Möller, Marcel; Gezzi, Riccardo; Hazzard, Kaden R. A.

2017-10-01

We compute physical properties across the phase diagram of the t -J⊥ chain with long-range dipolar interactions, which describe ultracold polar molecules on optical lattices. Our results obtained by the density-matrix renormalization group indicate that superconductivity is enhanced when the Ising component Jz of the spin-spin interaction and the charge component V are tuned to zero and even further by the long-range dipolar interactions. At low densities, a substantially larger spin gap is obtained. We provide evidence that long-range interactions lead to algebraically decaying correlation functions despite the presence of a gap. Although this has recently been observed in other long-range interacting spin and fermion models, the correlations in our case have the peculiar property of having a small and continuously varying exponent. We construct simple analytic models and arguments to understand the most salient features.
Transient Dynamics of Double Quantum Dots Coupled to Two Reservoirs

NASA Astrophysics Data System (ADS)

Fukadai, Takahisa; Sasamoto, Tomohiro

2018-05-01

We study the time-dependent properties of double quantum dots coupled to two reservoirs using the nonequilibrium Green function method. For an arbitrary time-dependent bias, we derive an expression for the time-dependent electron density of a dot and several currents, including the current between the dots in the wide-band-limit approximation. For the special case of a constant bias, we calculate the electron density and the currents numerically. As a result, we find that these quantities oscillate and that the number of crests in a single period of the current from a dot changes with the bias voltage. We also obtain an analytical expression for the relaxation time, which expresses how fast the system converges to its steady state. From the expression, we find that the relaxation time becomes constant when the coupling strength between the dots is sufficiently large in comparison with the difference of coupling strength between the dots and the reservoirs.
Multivariate η-μ fading distribution with arbitrary correlation model

NASA Astrophysics Data System (ADS)

Ghareeb, Ibrahim; Atiani, Amani

2018-03-01

An extensive analysis for the multivariate ? distribution with arbitrary correlation is presented, where novel analytical expressions for the multivariate probability density function, cumulative distribution function and moment generating function (MGF) of arbitrarily correlated and not necessarily identically distributed ? power random variables are derived. Also, this paper provides exact-form expression for the MGF of the instantaneous signal-to-noise ratio at the combiner output in a diversity reception system with maximal-ratio combining and post-detection equal-gain combining operating in slow frequency nonselective arbitrarily correlated not necessarily identically distributed ?-fading channels. The average bit error probability of differentially detected quadrature phase shift keying signals with post-detection diversity reception system over arbitrarily correlated and not necessarily identical fading parameters ?-fading channels is determined by using the MGF-based approach. The effect of fading correlation between diversity branches, fading severity parameters and diversity level is studied.
Two-point function of a d =2 quantum critical metal in the limit kF→∞ , Nf→0 with NfkF fixed

NASA Astrophysics Data System (ADS)

Säterskog, Petter; Meszena, Balazs; Schalm, Koenraad

2017-10-01

We show that the fermionic and bosonic spectrum of d =2 fermions at finite density coupled to a critical boson can be determined nonperturbatively in the combined limit kF→∞ ,Nf→0 with NfkF fixed. In this double scaling limit, the boson two-point function is corrected but only at one loop. This double scaling limit therefore incorporates the leading effect of Landau damping. The fermion two-point function is determined analytically in real space and numerically in (Euclidean) momentum space. The resulting spectrum is discontinuously connected to the quenched Nf→0 result. For ω →0 with k fixed the spectrum exhibits the distinct non-Fermi-liquid behavior previously surmised from the RPA approximation. However, the exact answer obtained here shows that the RPA result does not fully capture the IR of the theory.
Derivation of general analytic gradient expressions for density-fitted post-Hartree-Fock methods: An efficient implementation for the density-fitted second-order Møller–Plesset perturbation theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bozkaya, Uğur, E-mail: ugur.bozkaya@atauni.edu.tr

General analytic gradient expressions (with the frozen-core approximation) are presented for density-fitted post-HF methods. An efficient implementation of frozen-core analytic gradients for the second-order Møller–Plesset perturbation theory (MP2) with the density-fitting (DF) approximation (applying to both reference and correlation energies), which is denoted as DF-MP2, is reported. The DF-MP2 method is applied to a set of alkanes, conjugated dienes, and noncovalent interaction complexes to compare the computational cost of single point analytic gradients with MP2 with the resolution of the identity approach (RI-MP2) [F. Weigend and M. Häser, Theor. Chem. Acc. 97, 331 (1997); R. A. Distasio, R. P. Steele,more » Y. M. Rhee, Y. Shao, and M. Head-Gordon, J. Comput. Chem. 28, 839 (2007)]. In the RI-MP2 method, the DF approach is used only for the correlation energy. Our results demonstrate that the DF-MP2 method substantially accelerate the RI-MP2 method for analytic gradient computations due to the reduced input/output (I/O) time. Because in the DF-MP2 method the DF approach is used for both reference and correlation energies, the storage of 4-index electron repulsion integrals (ERIs) are avoided, 3-index ERI tensors are employed instead. Further, as in case of integrals, our gradient equation is completely avoid construction or storage of the 4-index two-particle density matrix (TPDM), instead we use 2- and 3-index TPDMs. Hence, the I/O bottleneck of a gradient computation is significantly overcome. Therefore, the cost of the generalized-Fock matrix (GFM), TPDM, solution of Z-vector equations, the back transformation of TPDM, and integral derivatives are substantially reduced when the DF approach is used for the entire energy expression. Further application results show that the DF approach introduce negligible errors for closed-shell reaction energies and equilibrium bond lengths.« less
Modeling and analysis of a magnetically levitated synchronous permanent magnet planar motor

NASA Astrophysics Data System (ADS)

Kou, Baoquan; Zhang, Lu; Li, Liyi; Zhang, Hailin

2012-04-01

In this paper, a new magnetically levitated synchronous permanent magnet planar motor (MLSPMPM) driven by composite-current is proposed, of which the mover is made of a copper coil array and the stator are magnets and magnetic conductor. The coil pitch τt and permanent magnet pole pitch τp satisfy the following relationship 3nτt = (3n ± 1)τp. Firstly, an analytical model of the planar motor is established, flux density distribution of the two-dimensional magnet array is obtained by solving the equations of the scalar magnetic potential. Secondly, the expressions of the electromagnetic forces induced by magnetic field and composite current are derived. To verify the analytical model and the electromagnetic forces, finite element method (FEM) is used for calculating the flux density and electromagnetic forces of the MLSPMPM. And the results from FEM are in good agreement with the results from the analytical equations. This indicates that the analytical model is reasonable.
Experimental validation of an analytical kinetic model for edge-localized modes in JET-ITER-like wall

NASA Astrophysics Data System (ADS)

Guillemaut, C.; Metzger, C.; Moulton, D.; Heinola, K.; O’Mullane, M.; Balboa, I.; Boom, J.; Matthews, G. F.; Silburn, S.; Solano, E. R.; contributors, JET

2018-06-01

The design and operation of future fusion devices relying on H-mode plasmas requires reliable modelling of edge-localized modes (ELMs) for precise prediction of divertor target conditions. An extensive experimental validation of simple analytical predictions of the time evolution of target plasma loads during ELMs has been carried out here in more than 70 JET-ITER-like wall H-mode experiments with a wide range of conditions. Comparisons of these analytical predictions with diagnostic measurements of target ion flux density, power density, impact energy and electron temperature during ELMs are presented in this paper and show excellent agreement. The analytical predictions tested here are made with the ‘free-streaming’ kinetic model (FSM) which describes ELMs as a quasi-neutral plasma bunch expanding along the magnetic field lines into the Scrape-Off Layer without collisions. Consequences of the FSM on energy reflection and deposition on divertor targets during ELMs are also discussed.
Electrostatic interaction between dissimilar colloids at fluid interfaces

NASA Astrophysics Data System (ADS)

Majee, Arghya; Schmetzer, Timo; Bier, Markus

2018-04-01

The electrostatic interaction between two nonidentical, moderately charged colloids situated in close proximity of each other at a fluid interface is studied. By resorting to a well-justified model system, this problem is analytically solved within the framework of linearized Poisson-Boltzmann density functional theory. The resulting interaction comprises a surface and a line part, both of which, as functions of the interparticle separation, show a rich behavior including monotonic as well as nonmonotonic variations. In almost all cases, these variations cannot be captured correctly by using the superposition approximation. Moreover, expressions for the surface tensions, the line tensions and the fluid-fluid interfacial tension, which are all independent of the interparticle separation, are obtained. Our results are expected to be particularly useful for emulsions stabilized by oppositely charged particles.
Linear fitting of multi-threshold counting data with a pixel-array detector for spectral X-ray imaging

PubMed Central

Muir, Ryan D.; Pogranichney, Nicholas R.; Muir, J. Lewis; Sullivan, Shane Z.; Battaile, Kevin P.; Mulichak, Anne M.; Toth, Scott J.; Keefe, Lisa J.; Simpson, Garth J.

2014-01-01

Experiments and modeling are described to perform spectral fitting of multi-threshold counting measurements on a pixel-array detector. An analytical model was developed for describing the probability density function of detected voltage in X-ray photon-counting arrays, utilizing fractional photon counting to account for edge/corner effects from voltage plumes that spread across multiple pixels. Each pixel was mathematically calibrated by fitting the detected voltage distributions to the model at both 13.5 keV and 15.0 keV X-ray energies. The model and established pixel responses were then exploited to statistically recover images of X-ray intensity as a function of X-ray energy in a simulated multi-wavelength and multi-counting threshold experiment. PMID:25178010
Linear fitting of multi-threshold counting data with a pixel-array detector for spectral X-ray imaging.

PubMed

Muir, Ryan D; Pogranichney, Nicholas R; Muir, J Lewis; Sullivan, Shane Z; Battaile, Kevin P; Mulichak, Anne M; Toth, Scott J; Keefe, Lisa J; Simpson, Garth J

2014-09-01

Experiments and modeling are described to perform spectral fitting of multi-threshold counting measurements on a pixel-array detector. An analytical model was developed for describing the probability density function of detected voltage in X-ray photon-counting arrays, utilizing fractional photon counting to account for edge/corner effects from voltage plumes that spread across multiple pixels. Each pixel was mathematically calibrated by fitting the detected voltage distributions to the model at both 13.5 keV and 15.0 keV X-ray energies. The model and established pixel responses were then exploited to statistically recover images of X-ray intensity as a function of X-ray energy in a simulated multi-wavelength and multi-counting threshold experiment.
Power Laws from Linear Neuronal Cable Theory: Power Spectral Densities of the Soma Potential, Soma Membrane Current and Single-Neuron Contribution to the EEG

PubMed Central

Pettersen, Klas H.; Lindén, Henrik; Tetzlaff, Tom; Einevoll, Gaute T.

2014-01-01

Power laws, that is, power spectral densities (PSDs) exhibiting behavior for large frequencies f, have been observed both in microscopic (neural membrane potentials and currents) and macroscopic (electroencephalography; EEG) recordings. While complex network behavior has been suggested to be at the root of this phenomenon, we here demonstrate a possible origin of such power laws in the biophysical properties of single neurons described by the standard cable equation. Taking advantage of the analytical tractability of the so called ball and stick neuron model, we derive general expressions for the PSD transfer functions for a set of measures of neuronal activity: the soma membrane current, the current-dipole moment (corresponding to the single-neuron EEG contribution), and the soma membrane potential. These PSD transfer functions relate the PSDs of the respective measurements to the PSDs of the noisy input currents. With homogeneously distributed input currents across the neuronal membrane we find that all PSD transfer functions express asymptotic high-frequency power laws with power-law exponents analytically identified as for the soma membrane current, for the current-dipole moment, and for the soma membrane potential. Comparison with available data suggests that the apparent power laws observed in the high-frequency end of the PSD spectra may stem from uncorrelated current sources which are homogeneously distributed across the neural membranes and themselves exhibit pink () noise distributions. While the PSD noise spectra at low frequencies may be dominated by synaptic noise, our findings suggest that the high-frequency power laws may originate in noise from intrinsic ion channels. The significance of this finding goes beyond neuroscience as it demonstrates how power laws with a wide range of values for the power-law exponent α may arise from a simple, linear partial differential equation. PMID:25393030
Power laws from linear neuronal cable theory: power spectral densities of the soma potential, soma membrane current and single-neuron contribution to the EEG.

PubMed

Pettersen, Klas H; Lindén, Henrik; Tetzlaff, Tom; Einevoll, Gaute T

2014-11-01

Power laws, that is, power spectral densities (PSDs) exhibiting 1/f(α) behavior for large frequencies f, have been observed both in microscopic (neural membrane potentials and currents) and macroscopic (electroencephalography; EEG) recordings. While complex network behavior has been suggested to be at the root of this phenomenon, we here demonstrate a possible origin of such power laws in the biophysical properties of single neurons described by the standard cable equation. Taking advantage of the analytical tractability of the so called ball and stick neuron model, we derive general expressions for the PSD transfer functions for a set of measures of neuronal activity: the soma membrane current, the current-dipole moment (corresponding to the single-neuron EEG contribution), and the soma membrane potential. These PSD transfer functions relate the PSDs of the respective measurements to the PSDs of the noisy input currents. With homogeneously distributed input currents across the neuronal membrane we find that all PSD transfer functions express asymptotic high-frequency 1/f(α) power laws with power-law exponents analytically identified as α∞(I) = 1/2 for the soma membrane current, α∞(p) = 3/2 for the current-dipole moment, and α∞(V) = 2 for the soma membrane potential. Comparison with available data suggests that the apparent power laws observed in the high-frequency end of the PSD spectra may stem from uncorrelated current sources which are homogeneously distributed across the neural membranes and themselves exhibit pink (1/f) noise distributions. While the PSD noise spectra at low frequencies may be dominated by synaptic noise, our findings suggest that the high-frequency power laws may originate in noise from intrinsic ion channels. The significance of this finding goes beyond neuroscience as it demonstrates how 1/f(α) power laws with a wide range of values for the power-law exponent α may arise from a simple, linear partial differential equation.
Mechanism for odd-electron anion generation of dihydroxybenzoic acid isomers in matrix-assisted laser desorption/ionization mass spectrometry with density functional theory calculations.

PubMed

Yamagaki, Tohru; Takeuchi, Michika; Watanabe, Takehiro; Sugahara, Kohtaro; Takeuchi, Takae

2016-12-30

Proton and radical are transferred between matrices and matrix and analyte in matrix-assisted laser desorption/ionization (MALDI) and these transfers drive ionization of analytes. The odd-electron anion [M-2H] •- was generated in dihydroxybenzoic acids (DHBs) and the ion abundance of the 2,5-DHB was the highest among six DHB isomers. We were interested in the mechanism of the ion generation of the odd-electron anion. The observed [M-2H] •- and [M-3H] - ions, which were generated with the hydrogen radical removed from the phenolic hydroxyl groups (OH) in DHB isomers, were analyzed using negative-ion MALDI-MS. The enthalpy for ion generation and their stable structures were calculated using the density functional theory (DFT) calculation program Gaussian 09 with the B3LYP functional and the 6-31+G(d) basis set. The number of observed [M-2H] •- and [M-3H] - ions of the DHB isomers was dependent on the positions of the phenolic OH groups in the DHB isomers because the carboxy group interacts with the ortho OH group due to neighboring group participation, as confirmed from the stable structures of the [M-2H] •- anions calculated with the Gaussian 09 program. The DHB isomers were placed into three categories according to the number of the ions. Odd-electron anions ([M-2H] •- ) and [M-2H • -H] - ([M-3H] - ) ions were generated from DHB isomers due to removal of the hydrogen radical from the phenolic groups. The enthalpy for ion generation revealed that ion formation proceeds via a two-step pathway through the [M-M] - ion as an intermediate. © 2016 The Authors. Rapid Communications in Mass Spectrometry Published by John Wiley & Sons Ltd. © 2016 The Authors. Rapid Communications in Mass Spectrometry Published by John Wiley & Sons Ltd.
Characterization of Bovine Serum Albumin Blocking Efficiency on Epoxy-Functionalized Substrates for Microarray Applications.

PubMed

Sun, Yung-Shin; Zhu, Xiangdong

2016-10-01

Microarrays provide a platform for high-throughput characterization of biomolecular interactions. To increase the sensitivity and specificity of microarrays, surface blocking is required to minimize the nonspecific interactions between analytes and unprinted yet functionalized surfaces. To block amine- or epoxy-functionalized substrates, bovine serum albumin (BSA) is one of the most commonly used blocking reagents because it is cheap and easy to use. Based on standard protocols from microarray manufactories, a BSA concentration of 1% (10 mg/mL or 200 μM) and reaction time of at least 30 min are required to efficiently block epoxy-coated slides. In this paper, we used both fluorescent and label-free methods to characterize the BSA blocking efficiency on epoxy-functionalized substrates. The blocking efficiency of BSA was characterized using a fluorescent scanner and a label-free oblique-incidence reflectivity difference (OI-RD) microscope. We found that (1) a BSA concentration of 0.05% (0.5 mg/mL or 10 μM) could give a blocking efficiency of 98%, and (2) the BSA blocking step took only about 5 min to be complete. Also, from real-time and in situ measurements, we were able to calculate the conformational properties (thickness, mass density, and number density) of BSA molecules deposited on the epoxy surface. © 2015 Society for Laboratory Automation and Screening.
An analytical model of iceberg drift

NASA Astrophysics Data System (ADS)

Eisenman, I.; Wagner, T. J. W.; Dell, R.

2017-12-01

Icebergs transport freshwater from glaciers and ice shelves, releasing the freshwater into the upper ocean thousands of kilometers from the source. This influences ocean circulation through its effect on seawater density. A standard empirical rule-of-thumb for estimating iceberg trajectories is that they drift at the ocean surface current velocity plus 2% of the atmospheric surface wind velocity. This relationship has been observed in empirical studies for decades, but it has never previously been physically derived or justified. In this presentation, we consider the momentum balance for an individual iceberg, which includes nonlinear drag terms. Applying a series of approximations, we derive an analytical solution for the iceberg velocity as a function of time. In order to validate the model, we force it with surface velocity and temperature data from an observational state estimate and compare the results with iceberg observations in both hemispheres. We show that the analytical solution reduces to the empirical 2% relationship in the asymptotic limit of small icebergs (or strong winds), which approximately applies for typical Arctic icebergs. We find that the 2% value arises due to a term involving the drag coefficients for water and air and the densities of the iceberg, ocean, and air. In the opposite limit of large icebergs (or weak winds), which approximately applies for typical Antarctic icebergs with horizontal length scales greater than about 12 km, we find that the 2% relationship is not applicable and that icebergs instead move with the ocean current, unaffected by the wind. The two asymptotic regimes can be understood by considering how iceberg size influences the relative importance of the wind and ocean current drag terms compared with the Coriolis and pressure gradient force terms in the iceberg momentum balance.
1-D DC Resistivity Modeling and Interpretation in Anisotropic Media Using Particle Swarm Optimization

NASA Astrophysics Data System (ADS)

Pekşen, Ertan; Yas, Türker; Kıyak, Alper

2014-09-01

We examine the one-dimensional direct current method in anisotropic earth formation. We derive an analytic expression of a simple, two-layered anisotropic earth model. Further, we also consider a horizontally layered anisotropic earth response with respect to the digital filter method, which yields a quasi-analytic solution over anisotropic media. These analytic and quasi-analytic solutions are useful tests for numerical codes. A two-dimensional finite difference earth model in anisotropic media is presented in order to generate a synthetic data set for a simple one-dimensional earth. Further, we propose a particle swarm optimization method for estimating the model parameters of a layered anisotropic earth model such as horizontal and vertical resistivities, and thickness. The particle swarm optimization is a naturally inspired meta-heuristic algorithm. The proposed method finds model parameters quite successfully based on synthetic and field data. However, adding 5 % Gaussian noise to the synthetic data increases the ambiguity of the value of the model parameters. For this reason, the results should be controlled by a number of statistical tests. In this study, we use probability density function within 95 % confidence interval, parameter variation of each iteration and frequency distribution of the model parameters to reduce the ambiguity. The result is promising and the proposed method can be used for evaluating one-dimensional direct current data in anisotropic media.
Transient and asymptotic behaviour of the binary breakage problem

NASA Astrophysics Data System (ADS)

Mantzaris, Nikos V.

2005-06-01

The general binary breakage problem with power-law breakage functions and two families of symmetric and asymmetric breakage kernels is studied in this work. A useful transformation leads to an equation that predicts self-similar solutions in its asymptotic limit and offers explicit knowledge of the mean size and particle density at each point in dimensionless time. A novel moving boundary algorithm in the transformed coordinate system is developed, allowing the accurate prediction of the full transient behaviour of the system from the initial condition up to the point where self-similarity is achieved, and beyond if necessary. The numerical algorithm is very rapid and its results are in excellent agreement with known analytical solutions. In the case of the symmetric breakage kernels only unimodal, self-similar number density functions are obtained asymptotically for all parameter values and independent of the initial conditions, while in the case of asymmetric breakage kernels, bimodality appears for high degrees of asymmetry and sharp breakage functions. For symmetric and discrete breakage kernels, self-similarity is not achieved. The solution exhibits sustained oscillations with amplitude that depends on the initial condition and the sharpness of the breakage mechanism, while the period is always fixed and equal to ln 2 with respect to dimensionless time.

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