Thermal ionization of Cs Rydberg states

NASA Astrophysics Data System (ADS)

Glukhov, I. L.; Ovsiannikov, V. D.

2009-01-01

Rates Pnl of photoionization from Rydberg ns-, np-, nd-states of a valence electron in Cs, induced by black-body radiation, were calculated on the basis of the modified Fues model potential method. The numerical data were approximated with a three-term expression which reproduces in a simple analytical form the dependence of Pnl on the ambient temperature T and on the principal quantum number n. The comparison between approximate and exactly calculated values of the thermal ionization rate demonstrates the applicability of the proposed approximation for highly excited states with n from 20 to 100 in a wide temperature range of T from 100 to 10,000 K. We present coefficients of this approximation for the s-, p- and d-series of Rydberg states.

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

Analytic solution of magnetic induction distribution of ideal hollow spherical field sources

NASA Astrophysics Data System (ADS)

Xu, Xiaonong; Lu, Dingwei; Xu, Xibin; Yu, Yang; Gu, Min

2017-12-01

The Halbach type hollow spherical permanent magnet arrays (HSPMA) are volume compacted, energy efficient field sources, and capable of producing multi-Tesla field in the cavity of the array, which have attracted intense interests in many practical applications. Here, we present analytical solutions of magnetic induction to the ideal HSPMA in entire space, outside of array, within the cavity of array, and in the interior of the magnet. We obtain solutions using concept of magnetic charge to solve the Poisson's and Laplace's equations for the HSPMA. Using these analytical field expressions inside the material, a scalar demagnetization function is defined to approximately indicate the regions of magnetization reversal, partial demagnetization, and inverse magnetic saturation. The analytical field solution provides deeper insight into the nature of HSPMA and offer guidance in designing optimized one.

Strategy selection in the minority game

NASA Astrophysics Data System (ADS)

D'hulst, R.; Rodgers, G. J.

2000-04-01

We investigate the dynamics of the choice of an active strategy in the minority game. A history distribution is introduced as an analytical tool to study the asymmetry between the two choices offered to the agents. Its properties are studied numerically. It allows us to show that the departure from uniformity in the initial attribution of strategies to the agents is important even in the efficient market. Also, an approximate expression for the variance of the number of agents at one side in the efficient phase is proposed. All the analytical propositions are supported by numerical simulations of the system.

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.

Analytical Expressions for Deformation from an Arbitrarily Oriented Spheroid in a Half-Space

NASA Astrophysics Data System (ADS)

Cervelli, P. F.

2013-12-01

Deformation from magma chambers can be modeled by an elastic half-space with an embedded cavity subject to uniform pressure change along its interior surface. For a small number of cavity shapes, such as a sphere or a prolate spheroid, closed-form, analytical expressions for deformation have been derived, although these only approximate the uniform-pressure-change boundary condition, with the approximation becoming more accurate as the ratio of source depth to source dimension increases. Using the method of Elshelby [1957] and Yang [1988], which consists of a distribution of double forces and centers of dilatation along the vertical axis, I have derived expressions for displacement from a finite spheroid of arbitrary orientation and aspect ratio that are exact in an infinite elastic medium and approximate in a half-space. The approximation, like those for other cavity shapes, becomes increasingly accurate as the depth to source ratio grows larger, and is accurate to within a few percent in most real-world cases. I have also derived expressions for the deformation-gradient tensor, i.e., the derivatives of each component of displacement with respect to each coordinate direction. These can be transformed easily into the strain and stress tensors. The expressions give deformation both at the surface and at any point within the half-space, and include conditional statements that account for limiting cases that would otherwise prove singular. I have developed MATLAB code for these expressions (and their derivatives), which I use to demonstrate the accuracy of the approximation by showing how well the uniform-pressure-change boundary condition is satisfied in a variety of cases. I also show that a vertical, oblate spheroid with a zero-length vertical axis is equivalent to the penny-shaped crack of Fialko [2001] in an infinite medium and an excellent approximation in a half-space. Finally, because, in many cases, volume change is more tangible than pressure change, I have derived an equation that relates these two quantities for the spheroid: volume change equals pressure change × 2/3 × π/μ × a constant that depends on Poisson's ratio and the spheroid geometry. Eshelby, J. D., The determination of the elastic field of an ellipsoidal inclusion and related problems, Proc. R. Soc. London, Ser. A, 241, 376-396, 1957. Fialko, Y., Khazan, Y, and Simons, M. Deformation due to a pressurized horizontal circular crack in an elastic half-space, with applications to volcano geodesy, Geophys. J. Int., no. 146, 181-190, 2001. Yang, X., Davis, P. M., and Dieterich, J.H, Deformation from inflation of a dipping finite prolate spheroid in an Elastic Half-Space as a model for volcanic stressing, J. Geophys. Res., vol. 93, no. B5, 4249-4257, 1988.

Thrust and torque vector characteristics of axially-symmetric E-sail

NASA Astrophysics Data System (ADS)

Bassetto, Marco; Mengali, Giovanni; Quarta, Alessandro A.

2018-05-01

The Electric Solar Wind Sail is an innovative propulsion system concept that gains propulsive acceleration from the interaction with charged particles released by the Sun. The aim of this paper is to obtain analytical expressions for the thrust and torque vectors of a spinning sail of given shape. Under the only assumption that each tether belongs to a plane containing the spacecraft spin axis, a general analytical relation is found for the thrust and torque vectors as a function of the spacecraft attitude relative to an orbital reference frame. The results are then applied to the noteworthy situation of a Sun-facing sail, that is, when the spacecraft spin axis is aligned with the Sun-spacecraft line, which approximatively coincides with the solar wind direction. In that case, the paper discusses the equilibrium shape of the generic conducting tether as a function of the sail geometry and the spin rate, using both a numerical and an analytical (approximate) approach. As a result, the structural characteristics of the conducting tether are related to the spacecraft geometric parameters.

Barycentric parameterizations for isotropic BRDFs.

PubMed

Stark, Michael M; Arvo, James; Smits, Brian

2005-01-01

A bidirectional reflectance distribution function (BRDF) is often expressed as a function of four real variables: two spherical coordinates in each of the the "incoming" and "outgoing" directions. However, many BRDFs reduce to functions of fewer variables. For example, isotropic reflection can be represented by a function of three variables. Some BRDF models can be reduced further. In this paper, we introduce new sets of coordinates which we use to reduce the dimensionality of several well-known analytic BRDFs as well as empirically measured BRDF data. The proposed coordinate systems are barycentric with respect to a triangular support with a direct physical interpretation. One coordinate set is based on the BRDF model proposed by Lafortune. Another set, based on a model of Ward, is associated with the "halfway" vector common in analytical BRDF formulas. Through these coordinate sets we establish lower bounds on the approximation error inherent in the models on which they are based. We present a third set of coordinates, not based on any analytical model, that performs well in approximating measured data. Finally, our proposed variables suggest novel ways of constructing and visualizing BRDFs.

Properties of atomic pairs produced in the collision of Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Ziń, Paweł; Wasak, Tomasz

2018-04-01

During a collision of Bose-Einstein condensates correlated pairs of atoms are emitted. The scattered massive particles, in analogy to photon pairs in quantum optics, might be used in the violation of Bell's inequalities, demonstration of Einstein-Podolsky-Rosen correlations, or sub-shot-noise atomic interferometry. Usually, a theoretical description of the collision relies either on stochastic numerical methods or on analytical treatments involving various approximations. Here, we investigate elastic scattering of atoms from colliding elongated Bose-Einstein condensates within the Bogoliubov method, carefully controlling performed approximations at every stage of the analysis. We derive expressions for the one- and two-particle correlation functions. The obtained formulas, which relate the correlation functions to the condensate wave function, are convenient for numerical calculations. We employ the variational approach for condensate wave functions to obtain analytical expressions for the correlation functions, whose properties we analyze in detail. We also present a useful semiclassical model of the process and compare its results with the quantum one. The results are relevant for recent experiments with excited helium atoms, as well as for planned experiments aimed at investigating the nonclassicality of the system.

Radiative recombination data for tungsten ions: II. W{sup 47+}–W{sup 71+}

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

Trzhaskovskaya, M.B., E-mail: Trzhask@MT5605.spb.edu; Nikulin, V.K.

2014-07-15

New radiative recombination and photoionization cross sections, radiative recombination rate coefficients, and radiated power loss rate coefficients are presented for 23 tungsten impurity ions in plasmas. We consider ions from W{sup 47+} to W{sup 71+} that are of importance to fusion studies for ITER and for experiments using electron beam ion traps. The calculations are fully relativistic and all significant multipoles of the radiative field are taken into account. The Dirac–Fock method is used to compute the electron wavefunctions. Radiative recombination rates and radiated power loss rates are found using the relativistic Maxwell–Jüttner distribution of the continuum electron velocity. Themore » total radiative recombination cross sections are given in the electron energy range from 1 eV to ∼80keV. Partial cross sections for ground and excited states are approximated by an analytical expression involving five fit parameters. Radiative recombination rates and radiated power loss rates are calculated in the temperature range from 10{sup 4}K to 10{sup 9}K. The total radiative recombination rates are approximated by another analytical expression with four fit parameters.« less

Analytical time-domain Green’s functions for power-law media

PubMed Central

Kelly, James F.; McGough, Robert J.; Meerschaert, Mark M.

2008-01-01

Frequency-dependent loss and dispersion are typically modeled with a power-law attenuation coefficient, where the power-law exponent ranges from 0 to 2. To facilitate analytical solution, a fractional partial differential equation is derived that exactly describes power-law attenuation and the Szabo wave equation [“Time domain wave-equations for lossy media obeying a frequency power-law,” J. Acoust. Soc. Am. 96, 491–500 (1994)] is an approximation to this equation. This paper derives analytical time-domain Green’s functions in power-law media for exponents in this range. To construct solutions, stable law probability distributions are utilized. For exponents equal to 0, 1∕3, 1∕2, 2∕3, 3∕2, and 2, the Green’s function is expressed in terms of Dirac delta, exponential, Airy, hypergeometric, and Gaussian functions. For exponents strictly less than 1, the Green’s functions are expressed as Fox functions and are causal. For exponents greater than or equal than 1, the Green’s functions are expressed as Fox and Wright functions and are noncausal. However, numerical computations demonstrate that for observation points only one wavelength from the radiating source, the Green’s function is effectively causal for power-law exponents greater than or equal to 1. The analytical time-domain Green’s function is numerically verified against the material impulse response function, and the results demonstrate excellent agreement. PMID:19045774

Weak limit of the three-state quantum walk on the line

NASA Astrophysics Data System (ADS)

Falkner, Stefan; Boettcher, Stefan

2014-07-01

We revisit the one-dimensional discrete time quantum walk with three states and the Grover coin, the simplest model that exhibits localization in a quantum walk. We derive analytic expressions for the localization and a long-time approximation for the entire probability density function (PDF). We find the possibility for asymmetric localization to the extreme that it vanishes completely on one site of the initial conditions. We also connect the time-averaged approximation of the PDF found by Inui et al. [Phys. Rev. E 72, 056112 (2005), 10.1103/PhysRevE.72.056112] to a spatial average of the walk. We show that this smoothed approximation predicts moments of the real PDF accurately.

Design of the stabilizing control of the orbital motion in the vicinity of the collinear libration point L1 using the analytical representation of the invariant manifold

NASA Astrophysics Data System (ADS)

Maliavkin, G. P.; Shmyrov, A. S.; Shmyrov, V. A.

2018-05-01

Vicinities of collinear libration points of the Sun-Earth system are currently quite attractive for the space navigation. Today, various projects on placing of spacecrafts observing the Sun in the L1 libration point and telescopes in L2 have been implemented (e.g. spacecrafts "WIND", "SOHO", "Herschel", "Planck"). Collinear libration points being unstable leads to the problem of stabilization of a spacecraft's motion. Laws of stabilizing motion control in vicinity of L1 point can be constructed using the analytical representation of a stable invariant manifold. Efficiency of these control laws depends on the precision of the representation. Within the model of Hill's approximation of the circular restricted three-body problem in the rotating geocentric coordinate system one can obtain the analytical representation of an invariant manifold filled with bounded trajectories in a form of series in terms of powers of the phase variables. Approximate representations of the orders from the first to the fourth inclusive can be used to construct four laws of stabilizing feedback motion control under which trajectories approach the manifold. By virtue of numerical simulation the comparison can be made: how the precision of the representation of the invariant manifold influences the efficiency of the control, expressed by energy consumptions (characteristic velocity). It shows that using approximations of higher orders in constructing the control laws can significantly reduce the energy consumptions on implementing the control compared to the linear approximation.

Thermodynamic properties and static structure factor for a Yukawa fluid in the mean spherical approximation.

PubMed

Montes-Perez, J; Cruz-Vera, A; Herrera, J N

2011-12-01

This work presents the full analytic expressions for the thermodynamic properties and the static structure factor for a hard sphere plus 1-Yukawa fluid within the mean spherical approximation. To obtain these properties of the fluid type Yukawa analytically it was necessary to solve an equation of fourth order for the scaling parameter on a large scale. The physical root of this equation was determined by imposing physical conditions. The results of this work are obtained from seminal papers of Blum and Høye. We show that is not necessary the use the series expansion to solve the equation for the scaling parameter. We applied our theoretical result to find the thermodynamic and the static structure factor for krypton. Our results are in good agreement with those obtained in an experimental form or by simulation using the Monte Carlo method.

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.

Transition probability functions for applications of inelastic electron scattering

PubMed Central

Löffler, Stefan; Schattschneider, Peter

2012-01-01

In this work, the transition matrix elements for inelastic electron scattering are investigated which are the central quantity for interpreting experiments. The angular part is given by spherical harmonics. For the weighted radial wave function overlap, analytic expressions are derived in the Slater-type and the hydrogen-like orbital models. These expressions are shown to be composed of a finite sum of polynomials and elementary trigonometric functions. Hence, they are easy to use, require little computation time, and are significantly more accurate than commonly used approximations. PMID:22560709

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

The uniform asymptotic swallowtail approximation - Practical methods for oscillating integrals with four coalescing saddle points

NASA Technical Reports Server (NTRS)

Connor, J. N. L.; Curtis, P. R.; Farrelly, D.

1984-01-01

Methods that can be used in the numerical implementation of the uniform swallowtail approximation are described. An explicit expression for that approximation is presented to the lowest order, showing that there are three problems which must be overcome in practice before the approximation can be applied to any given problem. It is shown that a recently developed quadrature method can be used for the accurate numerical evaluation of the swallowtail canonical integral and its partial derivatives. Isometric plots of these are presented to illustrate some of their properties. The problem of obtaining the arguments of the swallowtail integral from an analytical function of its argument is considered, describing two methods of solving this problem. The asymptotic evaluation of the butterfly canonical integral is addressed.

Approximating natural connectivity of scale-free networks based on largest eigenvalue

NASA Astrophysics Data System (ADS)

Tan, S.-Y.; Wu, J.; Li, M.-J.; Lu, X.

2016-06-01

It has been recently proposed that natural connectivity can be used to efficiently characterize the robustness of complex networks. The natural connectivity has an intuitive physical meaning and a simple mathematical formulation, which corresponds to an average eigenvalue calculated from the graph spectrum. However, as a network model close to the real-world system that widely exists, the scale-free network is found difficult to obtain its spectrum analytically. In this article, we investigate the approximation of natural connectivity based on the largest eigenvalue in both random and correlated scale-free networks. It is demonstrated that the natural connectivity of scale-free networks can be dominated by the largest eigenvalue, which can be expressed asymptotically and analytically to approximate natural connectivity with small errors. Then we show that the natural connectivity of random scale-free networks increases linearly with the average degree given the scaling exponent and decreases monotonically with the scaling exponent given the average degree. Moreover, it is found that, given the degree distribution, the more assortative a scale-free network is, the more robust it is. Experiments in real networks validate our methods and results.

Collisional evolution - an analytical study for the non steady-state mass distribution.

NASA Astrophysics Data System (ADS)

Vieira Martins, R.

1999-05-01

To study the collisional evolution of asteroidal groups one can use an analytical solution for the self-similar collision cascades. This solution is suitable to study the steady-state mass distribution of the collisional fragmentation. However, out of the steady-state conditions, this solution is not satisfactory for some values of the collisional parameters. In fact, for some values for the exponent of the mass distribution power law of an asteroidal group and its relation to the exponent of the function which describes "how rocks break" the author arrives at singular points for the equation which describes the collisional evolution. These singularities appear since some approximations are usually made in the laborious evaluation of many integrals that appear in the analytical calculations. They concern the cutoff for the smallest and the largest bodies. These singularities set some restrictions to the study of the analytical solution for the collisional equation. To overcome these singularities the author performed an algebraic computation considering the smallest and the largest bodies and he obtained the analytical expressions for the integrals that describe the collisional evolution without restriction on the parameters. However, the new distribution is more sensitive to the values of the collisional parameters. In particular the steady-state solution for the differential mass distribution has exponents slightly different from 11/6 for the usual parameters in the asteroid belt. The sensitivity of this distribution with respect to the parameters is analyzed for the usual values in the asteroidal groups. With an expression for the mass distribution without singularities, one can evaluate also its time evolution. The author arrives at an analytical expression given by a power series of terms constituted by a small parameter multiplied by the mass to an exponent, which depends on the initial power law distribution. This expression is a formal solution for the equation which describes the collisional evolution.

Limiting cases of the small-angle scattering approximation solutions for the propagation of laser beams in anisotropic scattering media

NASA Technical Reports Server (NTRS)

Box, M. A.; Deepak, A.

1981-01-01

The propagation of photons in a medium with strongly anisotropic scattering is a problem with a considerable history. Like the propagation of electrons in metal foils, it may be solved in the small-angle scattering approximation by the use of Fourier-transform techniques. In certain limiting cases, one may even obtain analytic expressions. This paper presents some of these results in a model-independent form and also illustrates them by the use of four different phase-function models. Sample calculations are provided for comparison purposes

Landau-Zener extension of the Tavis-Cummings model: Structure of the solution

DOE PAGES

Sun, Chen; Sinitsyn, Nikolai A.

2016-09-07

We explore the recently discovered solution of the driven Tavis-Cummings model (DTCM). It describes interaction of an arbitrary number of two-level systems with a bosonic mode that has linearly time-dependent frequency. We derive compact and tractable expressions for transition probabilities in terms of the well-known special functions. In this form, our formulas are suitable for fast numerical calculations and analytical approximations. As an application, we obtain the semiclassical limit of the exact solution and compare it to prior approximations. Furthermore, we also reveal connection between DTCM and q-deformed binomial statistics.

Approximate method of variational Bayesian matrix factorization/completion with sparse prior

NASA Astrophysics Data System (ADS)

Kawasumi, Ryota; Takeda, Koujin

2018-05-01

We derive the analytical expression of a matrix factorization/completion solution by the variational Bayes method, under the assumption that the observed matrix is originally the product of low-rank, dense and sparse matrices with additive noise. We assume the prior of a sparse matrix is a Laplace distribution by taking matrix sparsity into consideration. Then we use several approximations for the derivation of a matrix factorization/completion solution. By our solution, we also numerically evaluate the performance of a sparse matrix reconstruction in matrix factorization, and completion of a missing matrix element in matrix completion.

The D-dimensional non-relativistic particle in the Scarf Trigonometry plus Non-Central Rosen-Morse Potentials

NASA Astrophysics Data System (ADS)

Deta, U. A.; Lestari, N. A.; Yantidewi, M.; Suparmi, A.; Cari, C.

2018-03-01

The D-Dimensional Non-Relativistic Particle Properties in the Scarf Trigonometry plus Non-Central Rosen-Morse Potentials was investigated using an analytical method. The bound state energy is given approximately in the closed form. The approximate wave function for arbitrary l-state in D-dimensions are expressed in the form of generalised Jacobi Polynomials. The energy spectra of the particle are increased when the dimensions are higher. The relationship between the orbital number in each dimension is recursive. The special case in 3 dimensions is given to the ground state.

Theory of dissociative tunneling ionization

NASA Astrophysics Data System (ADS)

Svensmark, Jens; Tolstikhin, Oleg I.; Madsen, Lars Bojer

2016-05-01

We present a theoretical study of the dissociative tunneling ionization process. Analytic expressions for the nuclear kinetic energy distribution of the ionization rates are derived. A particularly simple expression for the spectrum is found by using the Born-Oppenheimer (BO) approximation in conjunction with the reflection principle. These spectra are compared to exact non-BO ab initio spectra obtained through model calculations with a quantum mechanical treatment of both the electronic and nuclear degrees of freedom. In the regime where the BO approximation is applicable, imaging of the BO nuclear wave function is demonstrated to be possible through reverse use of the reflection principle, when accounting appropriately for the electronic ionization rate. A qualitative difference between the exact and BO wave functions in the asymptotic region of large electronic distances is shown. Additionally, the behavior of the wave function across the turning line is seen to be reminiscent of light refraction. For weak fields, where the BO approximation does not apply, the weak-field asymptotic theory describes the spectrum accurately.

Approximate Bayesian evaluations of measurement uncertainty

NASA Astrophysics Data System (ADS)

Possolo, Antonio; Bodnar, Olha

2018-04-01

The Guide to the Expression of Uncertainty in Measurement (GUM) includes formulas that produce an estimate of a scalar output quantity that is a function of several input quantities, and an approximate evaluation of the associated standard uncertainty. This contribution presents approximate, Bayesian counterparts of those formulas for the case where the output quantity is a parameter of the joint probability distribution of the input quantities, also taking into account any information about the value of the output quantity available prior to measurement expressed in the form of a probability distribution on the set of possible values for the measurand. The approximate Bayesian estimates and uncertainty evaluations that we present have a long history and illustrious pedigree, and provide sufficiently accurate approximations in many applications, yet are very easy to implement in practice. Differently from exact Bayesian estimates, which involve either (analytical or numerical) integrations, or Markov Chain Monte Carlo sampling, the approximations that we describe involve only numerical optimization and simple algebra. Therefore, they make Bayesian methods widely accessible to metrologists. We illustrate the application of the proposed techniques in several instances of measurement: isotopic ratio of silver in a commercial silver nitrate; odds of cryptosporidiosis in AIDS patients; height of a manometer column; mass fraction of chromium in a reference material; and potential-difference in a Zener voltage standard.

Phonon scattering in nanoscale systems: lowest order expansion of the current and power expressions

NASA Astrophysics Data System (ADS)

Paulsson, Magnus; Frederiksen, Thomas; Brandbyge, Mads

2006-04-01

We use the non-equilibrium Green's function method to describe the effects of phonon scattering on the conductance of nano-scale devices. Useful and accurate approximations are developed that both provide (i) computationally simple formulas for large systems and (ii) simple analytical models. In addition, the simple models can be used to fit experimental data and provide physical parameters.

Piecewise linear emulator of the nonlinear Schrödinger equation and the resulting analytic solutions for Bose-Einstein condensates.

PubMed

Theodorakis, Stavros

2003-06-01

We emulate the cubic term Psi(3) in the nonlinear Schrödinger equation by a piecewise linear term, thus reducing the problem to a set of uncoupled linear inhomogeneous differential equations. The resulting analytic expressions constitute an excellent approximation to the exact solutions, as is explicitly shown in the case of the kink, the vortex, and a delta function trap. Such a piecewise linear emulation can be used for any differential equation where the only nonlinearity is a Psi(3) one. In particular, it can be used for the nonlinear Schrödinger equation in the presence of harmonic traps, giving analytic Bose-Einstein condensate solutions that reproduce very accurately the numerically calculated ones in one, two, and three dimensions.

Quantitative phase imaging method based on an analytical nonparaxial partially coherent phase optical transfer function.

PubMed

Bao, Yijun; Gaylord, Thomas K

2016-11-01

Multifilter phase imaging with partially coherent light (MFPI-PC) is a promising new quantitative phase imaging method. However, the existing MFPI-PC method is based on the paraxial approximation. In the present work, an analytical nonparaxial partially coherent phase optical transfer function is derived. This enables the MFPI-PC to be extended to the realistic nonparaxial case. Simulations over a wide range of test phase objects as well as experimental measurements on a microlens array verify higher levels of imaging accuracy compared to the paraxial method. Unlike the paraxial version, the nonparaxial MFPI-PC with obliquity factor correction exhibits no systematic error. In addition, due to its analytical expression, the increase in computation time compared to the paraxial version is negligible.

An explicit analytical solution for sound propagation in a three-dimensional penetrable wedge with small apex angle.

PubMed

Petrov, Pavel S; Sturm, Frédéric

2016-03-01

A problem of sound propagation in a shallow-water waveguide with a weakly sloping penetrable bottom is considered. The adiabatic mode parabolic equations are used to approximate the solution of the three-dimensional (3D) Helmholtz equation by modal decomposition of the acoustic pressure field. The mode amplitudes satisfy parabolic equations that admit analytical solutions in the special case of the 3D wedge. Using the analytical formula for modal amplitudes, an explicit and remarkably simple expression for the acoustic pressure in the wedge is obtained. The proposed solution is validated by the comparison with a solution of the 3D penetrable wedge problem obtained using a fully 3D parabolic equation that includes a leading-order cross term correction.

An analytical study of the endoreversible Curzon-Ahlborn cycle for a non-linear heat transfer law

NASA Astrophysics Data System (ADS)

Páez-Hernández, Ricardo T.; Portillo-Díaz, Pedro; Ladino-Luna, Delfino; Ramírez-Rojas, Alejandro; Pacheco-Paez, Juan C.

2016-01-01

In the present article, an endoreversible Curzon-Ahlborn engine is studied by considering a non-linear heat transfer law, particularly the Dulong-Petit heat transfer law, using the `componendo and dividendo' rule as well as a simple differentiation to obtain the Curzon-Ahlborn efficiency as proposed by Agrawal in 2009. This rule is actually a change of variable that simplifies a two-variable problem to a one-variable problem. From elemental calculus, we obtain an analytical expression of efficiency and the power output. The efficiency is given only in terms of the temperatures of the reservoirs, such as both Carnot and Curzon-Ahlborn cycles. We make a comparison between efficiencies measured in real power plants and theoretical values from analytical expressions obtained in this article and others found in literature from several other authors. This comparison shows that the theoretical values of efficiency are close to real efficiency, and in some cases, they are exactly the same. Therefore, we can say that the Agrawal method is good in calculating thermal engine efficiencies approximately.

Analytical description of the transverse Anderson localization of light

NASA Astrophysics Data System (ADS)

Schirmacher, Walter; Leonetti, Marco; Ruocco, Giancarlo

2017-04-01

We develop an analytical theory for describing the transverse localization properties of light beams in optical fibers with lateral disorder. This theory, which starts from the widely used paraxial approximation for the Helmholtz equation of the electric field, is a combination of an effective-medium theory for transverse disorder with the self-consistent localization theory of Vollhardt and Wölfle. We obtain explicit expressions for the dependence of the transverse localization length on the direction along the fiber. These results are in agreement with simulational data published recently by Karbasi et al. In particular we explain the focussing mechanism leading to the establishment of narrow transparent channels along the sample.

Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters

NASA Astrophysics Data System (ADS)

Bubin, Sergiy; Adamowicz, Ludwik

2006-06-01

In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters.

PubMed

Bubin, Sergiy; Adamowicz, Ludwik

2006-06-14

In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programmed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

Band-to-band tunneling distance analysis in the heterogate electron–hole bilayer tunnel field-effect transistor

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

Padilla, J. L., E-mail: jose.padilladelatorre@epfl.ch; Departamento de Electrónica y Tecnología de los Computadores, Universidad de Granada, Avda. Fuentenueva s/n, 18071 Granada; Palomares, A.

In this work, we analyze the behavior of the band-to-band tunneling distance between electron and hole subbands resulting from field-induced quantum confinement in the heterogate electron–hole bilayer tunnel field-effect transistor. We show that, analogously to the explicit formula for the tunneling distance that can be easily obtained in the semiclassical framework where the conduction and valence band edges are allowed states, an equivalent analytical expression can be derived in the presence of field-induced quantum confinement for describing the dependence of the tunneling distance on the body thickness and material properties of the channel. This explicit expression accounting for quantum confinementmore » holds valid provided that the potential wells for electrons and holes at the top and bottom of the channel can be approximated by triangular profiles. Analytical predictions are compared to simulation results showing very accurate agreement.« less

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.

Numerical integration for ab initio many-electron self energy calculations within the GW approximation

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

Liu, Fang, E-mail: fliu@lsec.cc.ac.cn; Lin, Lin, E-mail: linlin@math.berkeley.edu; Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720

We present a numerical integration scheme for evaluating the convolution of a Green's function with a screened Coulomb potential on the real axis in the GW approximation of the self energy. Our scheme takes the zero broadening limit in Green's function first, replaces the numerator of the integrand with a piecewise polynomial approximation, and performs principal value integration on subintervals analytically. We give the error bound of our numerical integration scheme and show by numerical examples that it is more reliable and accurate than the standard quadrature rules such as the composite trapezoidal rule. We also discuss the benefit ofmore » using different self energy expressions to perform the numerical convolution at different frequencies.« less

Adatom lifetime in film growth at solid surfaces in the framework of the Johnson Mehl Avrami Kolmogorov model

NASA Astrophysics Data System (ADS)

Tomellini, M.; Fanfoni, M.

1999-10-01

On the basis of the quasi-static approximation and for simultaneous nucleation the adatom lifetime, τ, during film growth at solid surfaces has been computed by Monte Carlo (MC) simulation. The quantity DN0τ, N0 and D being respectively the cluster density and the adatom diffusion coefficient, is found to depend upon the portion of surface covered by clusters and, very weakly, on N0. Moreover, a stochastic approach based on the Johnson-Mehl-Avrami-Kolmogorov (JMAK) theory has been developed to obtain the analytical expression of the MC curve. The collision factor of the mean island has been calculated and compared with those previously obtained from the uniform depletion approximation and the lattice approximation.

Size-dependent resonance frequencies of cantilevered and bridged nanosensors

NASA Astrophysics Data System (ADS)

Shi, W.; Zou, J.; Lee, K. Y.; Li, X. F.

2018-03-01

This paper studies transverse vibration of nanoscale cantilevered and bridged sensors carrying a nanoparticle. The nanoscale sensors are modelled as Euler-Bernoulli beams with surface effect and nanoparticle as a concentrated mass. Frequency equations of cantilevered and bridged beam-mass system are derived and exact resonance frequencies are calculated. An alternative Fredholm integral equation method is used to obtain an approximate explicit expression for the fundamental frequency for both cases. A comparison between the approximate and analytical results is made and the approximation accuracy is satisfactory. The influences of the residual surface stress, surface elasticity, and attached mass on the resonance frequencies and mode shapes are discussed. These results are useful to illustrate the surface phenomena and are helpful to design micro-/nano-mechanical sensors.

Far-infrared rotational emission by carbon monoxide

NASA Technical Reports Server (NTRS)

Mckee, C. F.; Storey, J. W. V.; Watson, D. M.; Green, S.

1981-01-01

Accurate theoretical collisional excitation rates are used to determine the emissivities of CO rotational lines 10 to the 4th power/cu cm n(H2), 100 K T 2000 K, and J 50. An approximate analytic expression for the emissitivities which is valid over most of this region is obtained. Population inversions in the lower rotational levels occur for densities n(H2) approximately 10 (to the 3rd to 5th power)/cu cm and temperatures T approximately 50 K. Interstellar shocks observed edge on are a potential source of millimeter wave CO maser emission. The CO rotational cooling function suggested by Hollenbach and McKee (1979) is verified, and accurate numerical values given. Application of these results to other linear molecules should be straightforward.

Serial Founder Effects During Range Expansion: A Spatial Analog of Genetic Drift

PubMed Central

Slatkin, Montgomery; Excoffier, Laurent

2012-01-01

Range expansions cause a series of founder events. We show that, in a one-dimensional habitat, these founder events are the spatial analog of genetic drift in a randomly mating population. The spatial series of allele frequencies created by successive founder events is equivalent to the time series of allele frequencies in a population of effective size ke, the effective number of founders. We derive an expression for ke in a discrete-population model that allows for local population growth and migration among established populations. If there is selection, the net effect is determined approximately by the product of the selection coefficients and the number of generations between successive founding events. We use the model of a single population to compute analytically several quantities for an allele present in the source population: (i) the probability that it survives the series of colonization events, (ii) the probability that it reaches a specified threshold frequency in the last population, and (iii) the mean and variance of the frequencies in each population. We show that the analytic theory provides a good approximation to simulation results. A consequence of our approximation is that the average heterozygosity of neutral alleles decreases by a factor of 1 – 1/(2ke) in each new population. Therefore, the population genetic consequences of surfing can be predicted approximately by the effective number of founders and the effective selection coefficients, even in the presence of migration among populations. We also show that our analytic results are applicable to a model of range expansion in a continuously distributed population. PMID:22367031

Serial founder effects during range expansion: a spatial analog of genetic drift.

PubMed

Slatkin, Montgomery; Excoffier, Laurent

2012-05-01

Range expansions cause a series of founder events. We show that, in a one-dimensional habitat, these founder events are the spatial analog of genetic drift in a randomly mating population. The spatial series of allele frequencies created by successive founder events is equivalent to the time series of allele frequencies in a population of effective size ke, the effective number of founders. We derive an expression for ke in a discrete-population model that allows for local population growth and migration among established populations. If there is selection, the net effect is determined approximately by the product of the selection coefficients and the number of generations between successive founding events. We use the model of a single population to compute analytically several quantities for an allele present in the source population: (i) the probability that it survives the series of colonization events, (ii) the probability that it reaches a specified threshold frequency in the last population, and (iii) the mean and variance of the frequencies in each population. We show that the analytic theory provides a good approximation to simulation results. A consequence of our approximation is that the average heterozygosity of neutral alleles decreases by a factor of 1-1/(2ke) in each new population. Therefore, the population genetic consequences of surfing can be predicted approximately by the effective number of founders and the effective selection coefficients, even in the presence of migration among populations. We also show that our analytic results are applicable to a model of range expansion in a continuously distributed population.

Quasi-analytical treatment of spatially averaged radiation transfer in complex terrain

NASA Astrophysics Data System (ADS)

LöWe, H.; Helbig, N.

2012-10-01

We provide a new quasi-analytical method to compute the subgrid topographic influences on the shortwave radiation fluxes and the effective albedo in complex terrain as required for large-scale meteorological, land surface, or climate models. We investigate radiative transfer in complex terrain via the radiosity equation on isotropic Gaussian random fields. Under controlled approximations we derive expressions for domain-averaged fluxes of direct, diffuse, and terrain radiation and the sky view factor. Domain-averaged quantities can be related to a type of level-crossing probability of the random field, which is approximated by long-standing results developed for acoustic scattering at ocean boundaries. This allows us to express all nonlocal horizon effects in terms of a local terrain parameter, namely, the mean-square slope. Emerging integrals are computed numerically, and fit formulas are given for practical purposes. As an implication of our approach, we provide an expression for the effective albedo of complex terrain in terms of the Sun elevation angle, mean-square slope, the area-averaged surface albedo, and the ratio of atmospheric direct beam to diffuse radiation. For demonstration we compute the decrease of the effective albedo relative to the area-averaged albedo in Switzerland for idealized snow-covered and clear-sky conditions at noon in winter. We find an average decrease of 5.8% and spatial patterns which originate from characteristics of the underlying relief. Limitations and possible generalizations of the method are discussed.

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.

Optical phonon effect in quasi-one-dimensional semiconductor quantum wires: Band-gap renormalization

NASA Astrophysics Data System (ADS)

Dan, Nguyen Trung; Bechstedt, F.

1996-02-01

We present theoretical studies of dynamical screening in quasi-one-dimensional semiconductor quantum wires including electron-electron and electron-LO-phonon interactions. Within the random-phase approximation we obtain analytical expressions for screened interaction potentials. These expressions can be used to calculate the band-gap renormalization of quantum wires, which depends on the free-carrier density and temperature. We find that the optical phonon interaction effect plays a significant role in band-gap renormalization of quantum wires. The numerical results are compared with some recent experiment measurements as well as available theories.

Simulating Nonequilibrium Radiation via Orthogonal Polynomial Refinement

DTIC Science & Technology

2015-01-07

measured by the preprocessing time, computer memory space, and average query time. In many search procedures for the number of points np of a data set, a...analytic expression for the radiative flux density is possible by the commonly accepted local thermal equilibrium ( LTE ) approximation. A semi...Vol. 227, pp. 9463-9476, 2008. 10. Galvez, M., Ray-Tracing model for radiation transport in three-dimensional LTE system, App. Physics, Vol. 38

Numerically stable formulas for a particle-based explicit exponential integrator

NASA Astrophysics Data System (ADS)

Nadukandi, Prashanth

2015-05-01

Numerically stable formulas are presented for the closed-form analytical solution of the X-IVAS scheme in 3D. This scheme is a state-of-the-art particle-based explicit exponential integrator developed for the particle finite element method. Algebraically, this scheme involves two steps: (1) the solution of tangent curves for piecewise linear vector fields defined on simplicial meshes and (2) the solution of line integrals of piecewise linear vector-valued functions along these tangent curves. Hence, the stable formulas presented here have general applicability, e.g. exact integration of trajectories in particle-based (Lagrangian-type) methods, flow visualization and computer graphics. The Newton form of the polynomial interpolation definition is used to express exponential functions of matrices which appear in the analytical solution of the X-IVAS scheme. The divided difference coefficients in these expressions are defined in a piecewise manner, i.e. in a prescribed neighbourhood of removable singularities their series approximations are computed. An optimal series approximation of divided differences is presented which plays a critical role in this methodology. At least ten significant decimal digits in the formula computations are guaranteed to be exact using double-precision floating-point arithmetic. The worst case scenarios occur in the neighbourhood of removable singularities found in fourth-order divided differences of the exponential function.

A Mathematica program for the approximate analytical solution to a nonlinear undamped Duffing equation by a new approximate approach

NASA Astrophysics Data System (ADS)

Wu, Dongmei; Wang, Zhongcheng

2006-03-01

According to Mickens [R.E. Mickens, Comments on a Generalized Galerkin's method for non-linear oscillators, J. Sound Vib. 118 (1987) 563], the general HB (harmonic balance) method is an approximation to the convergent Fourier series representation of the periodic solution of a nonlinear oscillator and not an approximation to an expansion in terms of a small parameter. Consequently, for a nonlinear undamped Duffing equation with a driving force Bcos(ωx), to find a periodic solution when the fundamental frequency is identical to ω, the corresponding Fourier series can be written as y˜(x)=∑n=1m acos[(2n-1)ωx]. How to calculate the coefficients of the Fourier series efficiently with a computer program is still an open problem. For HB method, by substituting approximation y˜(x) into force equation, expanding the resulting expression into a trigonometric series, then letting the coefficients of the resulting lowest-order harmonic be zero, one can obtain approximate coefficients of approximation y˜(x) [R.E. Mickens, Comments on a Generalized Galerkin's method for non-linear oscillators, J. Sound Vib. 118 (1987) 563]. But for nonlinear differential equations such as Duffing equation, it is very difficult to construct higher-order analytical approximations, because the HB method requires solving a set of algebraic equations for a large number of unknowns with very complex nonlinearities. To overcome the difficulty, forty years ago, Urabe derived a computational method for Duffing equation based on Galerkin procedure [M. Urabe, A. Reiter, Numerical computation of nonlinear forced oscillations by Galerkin's procedure, J. Math. Anal. Appl. 14 (1966) 107-140]. Dooren obtained an approximate solution of the Duffing oscillator with a special set of parameters by using Urabe's method [R. van Dooren, Stabilization of Cowell's classic finite difference method for numerical integration, J. Comput. Phys. 16 (1974) 186-192]. In this paper, in the frame of the general HB method, we present a new iteration algorithm to calculate the coefficients of the Fourier series. By using this new method, the iteration procedure starts with a(x)cos(ωx)+b(x)sin(ωx), and the accuracy may be improved gradually by determining new coefficients a,a,… will be produced automatically in an one-by-one manner. In all the stage of calculation, we need only to solve a cubic equation. Using this new algorithm, we develop a Mathematica program, which demonstrates following main advantages over the previous HB method: (1) it avoids solving a set of associate nonlinear equations; (2) it is easier to be implemented into a computer program, and produces a highly accurate solution with analytical expression efficiently. It is interesting to find that, generally, for a given set of parameters, a nonlinear Duffing equation can have three independent oscillation modes. For some sets of the parameters, it can have two modes with complex displacement and one with real displacement. But in some cases, it can have three modes, all of them having real displacement. Therefore, we can divide the parameters into two classes, according to the solution property: there is only one mode with real displacement and there are three modes with real displacement. This program should be useful to study the dynamically periodic behavior of a Duffing oscillator and can provide an approximate analytical solution with high-accuracy for testing the error behavior of newly developed numerical methods with a wide range of parameters. Program summaryTitle of program:AnalyDuffing.nb Catalogue identifier:ADWR_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWR_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions:none Computer for which the program is designed and others on which it has been tested:the program has been designed for a microcomputer and been tested on the microcomputer. Computers:IBM PC Installations:the address(es) of your computer(s) Operating systems under which the program has been tested:Windows XP Programming language used:Software Mathematica 4.2, 5.0 and 5.1 No. of lines in distributed program, including test data, etc.:23 663 No. of bytes in distributed program, including test data, etc.:152 321 Distribution format:tar.gz Memory required to execute with typical data:51 712 Bytes No. of bits in a word: No. of processors used:1 Has the code been vectorized?:no Peripherals used:no Program Library subprograms used:no Nature of physical problem:To find an approximate solution with analytical expressions for the undamped nonlinear Duffing equation with periodic driving force when the fundamental frequency is identical to the driving force. Method of solution:In the frame of the general HB method, by using a new iteration algorithm to calculate the coefficients of the Fourier series, we can obtain an approximate analytical solution with high-accuracy efficiently. Restrictions on the complexity of the problem:For problems, which have a large driving frequency, the convergence may be a little slow, because more iterative times are needed. Typical running time:several seconds Unusual features of the program:For an undamped Duffing equation, it can provide all the solutions or the oscillation modes with real displacement for any interesting parameters, for the required accuracy, efficiently. The program can be used to study the dynamically periodic behavior of a nonlinear oscillator, and can provide a high-accurate approximate analytical solution for developing high-accurate numerical method.

Analytic first derivatives for a spin-adapted open-shell coupled cluster theory: Evaluation of first-order electrical properties

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

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

2014-09-14

An analytic scheme is presented for the evaluation of first derivatives of the energy for a unitary group based spin-adapted coupled cluster (CC) theory, namely, the combinatoric open-shell CC (COSCC) approach within the singles and doubles approximation. The widely used Lagrange multiplier approach is employed for the derivation of an analytical expression for the first derivative of the energy, which in combination with the well-established density-matrix formulation, is used for the computation of first-order electrical properties. Derivations of the spin-adapted lambda equations for determining the Lagrange multipliers and the expressions for the spin-free effective density matrices for the COSCC approachmore » are presented. Orbital-relaxation effects due to the electric-field perturbation are treated via the Z-vector technique. We present calculations of the dipole moments for a number of doublet radicals in their ground states using restricted open-shell Hartree-Fock (ROHF) and quasi-restricted HF (QRHF) orbitals in order to demonstrate the applicability of our analytic scheme for computing energy derivatives. We also report calculations of the chlorine electric-field gradients and nuclear quadrupole-coupling constants for the CCl, CH{sub 2}Cl, ClO{sub 2}, and SiCl radicals.« less

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

Griffin, Brian M.; Larson, Vincent E.

Microphysical processes, such as the formation, growth, and evaporation of precipitation, interact with variability and covariances (e.g., fluxes) in moisture and heat content. For instance, evaporation of rain may produce cold pools, which in turn may trigger fresh convection and precipitation. These effects are usually omitted or else crudely parameterized at subgrid scales in weather and climate models.A more formal approach is pursued here, based on predictive, horizontally averaged equations for the variances, covariances, and fluxes of moisture and heat content. These higher-order moment equations contain microphysical source terms. The microphysics terms can be integrated analytically, given a suitably simplemore » warm-rain microphysics scheme and an approximate assumption about the multivariate distribution of cloud-related and precipitation-related variables. Performing the integrations provides exact expressions within an idealized context.A large-eddy simulation (LES) of a shallow precipitating cumulus case is performed here, and it indicates that the microphysical effects on (co)variances and fluxes can be large. In some budgets and altitude ranges, they are dominant terms. The analytic expressions for the integrals are implemented in a single-column, higher-order closure model. Interactive single-column simulations agree qualitatively with the LES. The analytic integrations form a parameterization of microphysical effects in their own right, and they also serve as benchmark solutions that can be compared to non-analytic integration methods.« less

Analytical Derivation and Experimental Evaluation of Short-Bearing Approximation for Full Journal Bearing

NASA Technical Reports Server (NTRS)

Dubois, George B; Ocvirk, Fred W

1953-01-01

An approximate analytical solution including the effect of end leakage from the oil film of short plain bearings is presented because of the importance of endwise flow in sleeve bearings of the short lengths commonly used. The analytical approximation is supported by experimental data, resulting in charts which facilitate analysis of short plain bearings. The analytical approximation includes the endwise flow and that part of the circumferential flow which is related to surface velocity and film thickness but neglects the effect of film pressure on the circumferential flow. In practical use, this approximation applies best to bearings having a length-diameter ratio up to 1, and the effects of elastic deflection, inlet oil pressure, and changes of clearance with temperature minimize the relative importance of the neglected term. The analytical approximation was found to be an extension of a little-known pressure-distribution function originally proposed by Michell and Cardullo.

Thin airfoil theory based on approximate solution of the transonic flow equation

NASA Technical Reports Server (NTRS)

Spreiter, John R; Alksne, Alberta Y

1957-01-01

A method is presented for the approximate solution of the nonlinear equations transonic flow theory. Solutions are found for two-dimensional flows at a Mach number of 1 and for purely subsonic and purely supersonic flows. Results are obtained in closed analytic form for a large and significant class of nonlifting airfoils. At a Mach number of 1 general expressions are given for the pressure distribution on an airfoil of specified geometry and for the shape of an airfoil having a prescribed pressure distribution. Extensive comparisons are made with available data, particularly for a Mach number of 1, and with existing solutions.

Two tandem queues with general renewal input. 2: Asymptotic expansions for the diffusion model

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

Knessl, C.; Tier, C.

1999-10-01

In Part 1 the authors formulated and solved a diffusion model for two tandem queues with exponential servers and general renewal arrivals. They thus obtained the easy traffic diffusion approximation to the steady state joint queue length distribution for this network. Here they study asymptotic and numerical properties of the diffusion approximation. In particular, analytical expressions are obtained for the tail probabilities. Both the joint distribution of the two queues and the marginal distribution of the second queue are considered. They also give numerical illustrations of how this marginal is affected by changes in the arrival and service processes.

Precision of Sensitivity in the Design Optimization of Indeterminate Structures

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Pai, Shantaram S.; Hopkins, Dale A.

2006-01-01

Design sensitivity is central to most optimization methods. The analytical sensitivity expression for an indeterminate structural design optimization problem can be factored into a simple determinate term and a complicated indeterminate component. Sensitivity can be approximated by retaining only the determinate term and setting the indeterminate factor to zero. The optimum solution is reached with the approximate sensitivity. The central processing unit (CPU) time to solution is substantially reduced. The benefit that accrues from using the approximate sensitivity is quantified by solving a set of problems in a controlled environment. Each problem is solved twice: first using the closed-form sensitivity expression, then using the approximation. The problem solutions use the CometBoards testbed as the optimization tool with the integrated force method as the analyzer. The modification that may be required, to use the stiffener method as the analysis tool in optimization, is discussed. The design optimization problem of an indeterminate structure contains many dependent constraints because of the implicit relationship between stresses, as well as the relationship between the stresses and displacements. The design optimization process can become problematic because the implicit relationship reduces the rank of the sensitivity matrix. The proposed approximation restores the full rank and enhances the robustness of the design optimization method.

Traveling solitons in long-range oscillator chains

NASA Astrophysics Data System (ADS)

Miloshevich, George; Nguenang, Jean Pierre; Dauxois, Thierry; Khomeriki, Ramaz; Ruffo, Stefano

2017-03-01

We investigate the existence and propagation of solitons in a long-range extension of the quartic Fermi-Pasta-Ulam (FPU) chain of anharmonic oscillators. The coupling in the linear term decays as a power-law with an exponent 1<α ≤slant 3 . We obtain an analytic perturbative expression of traveling envelope solitons by introducing a non linear Schrödinger equation for the slowly varying amplitude of short wavelength modes. Due to the non analytic properties of the dispersion relation, it is crucial to develop the theory using discrete difference operators. Those properties are also the ultimate reason why kink-solitons may exist but are unstable, at variance with the short-range FPU model. We successfully compare these approximate analytic results with numerical simulations for the value α =2 which was chosen as a case study.

Channel correlation and BER performance analysis of coherent optical communication systems with receive diversity over moderate-to-strong non-Kolmogorov turbulence.

PubMed

Fu, Yulong; Ma, Jing; Tan, Liying; Yu, Siyuan; Lu, Gaoyuan

2018-04-10

In this paper, new expressions of the channel-correlation coefficient and its components (the large- and small-scale channel-correlation coefficients) for a plane wave are derived for a horizontal link in moderate-to-strong non-Kolmogorov turbulence using a generalized effective atmospheric spectrum which includes finite-turbulence inner and outer scales and high-wave-number "bump". The closed-form expression of the average bit error rate (BER) of the coherent free-space optical communication system is derived using the derived channel-correlation coefficients and an α-μ distribution to approximate the sum of the square root of arbitrarily correlated Gamma-Gamma random variables. Analytical results are provided to investigate the channel correlation and evaluate the average BER performance. The validity of the proposed approximation is illustrated by Monte Carlo simulations. This work will help with further investigation of the fading correlation in spatial diversity systems.

Controlling false-negative errors in microarray differential expression analysis: a PRIM approach.

PubMed

Cole, Steve W; Galic, Zoran; Zack, Jerome A

2003-09-22

Theoretical considerations suggest that current microarray screening algorithms may fail to detect many true differences in gene expression (Type II analytic errors). We assessed 'false negative' error rates in differential expression analyses by conventional linear statistical models (e.g. t-test), microarray-adapted variants (e.g. SAM, Cyber-T), and a novel strategy based on hold-out cross-validation. The latter approach employs the machine-learning algorithm Patient Rule Induction Method (PRIM) to infer minimum thresholds for reliable change in gene expression from Boolean conjunctions of fold-induction and raw fluorescence measurements. Monte Carlo analyses based on four empirical data sets show that conventional statistical models and their microarray-adapted variants overlook more than 50% of genes showing significant up-regulation. Conjoint PRIM prediction rules recover approximately twice as many differentially expressed transcripts while maintaining strong control over false-positive (Type I) errors. As a result, experimental replication rates increase and total analytic error rates decline. RT-PCR studies confirm that gene inductions detected by PRIM but overlooked by other methods represent true changes in mRNA levels. PRIM-based conjoint inference rules thus represent an improved strategy for high-sensitivity screening of DNA microarrays. Freestanding JAVA application at http://microarray.crump.ucla.edu/focus

Peculiarities of the momentum distribution functions of strongly correlated charged fermions

NASA Astrophysics Data System (ADS)

Larkin, A. S.; Filinov, V. S.; Fortov, V. E.

2018-01-01

New numerical version of the Wigner approach to quantum thermodynamics of strongly coupled systems of particles has been developed for extreme conditions, when analytical approximations based on different kinds of perturbation theories cannot be applied. An explicit analytical expression of the Wigner function has been obtained in linear and harmonic approximations. Fermi statistical effects are accounted for by effective pair pseudopotential depending on coordinates, momenta and degeneracy parameter of particles and taking into account Pauli blocking of fermions. A new quantum Monte-Carlo method for calculations of average values of arbitrary quantum operators has been developed. Calculations of the momentum distribution functions and the pair correlation functions of degenerate ideal Fermi gas have been carried out for testing the developed approach. Comparison of the obtained momentum distribution functions of strongly correlated Coulomb systems with the Maxwell-Boltzmann and the Fermi distributions shows the significant influence of interparticle interaction both at small momenta and in high energy quantum ‘tails’.

Analytical estimates of the PP-algorithm at low number of Doppler periods per pulse length

NASA Technical Reports Server (NTRS)

Angelova, M. D.; Stoykova, E. V.; Stoyanov, D. V.

1992-01-01

When discussing the Doppler velocity estimators, it is of significant interest to analyze their behavior at a low number of Doppler periods n(sub D) = 2v(sub r)t(sub s)/lambda is approximately equal to 1 within the resolution cell t(sub s) (v(sub 4) is the radial velocity, lambda is the wavelength). Obviously, at n(sub D) is approximately less than 1 the velocity error is essentially increased. The problem of low n(sub D) arises in the planetary boundary layer (PBL), where higher resolutions are usually required but the signal-to-noise ratio (SNR) is relatively high. In this work analytical expression for the relative root mean square (RMS) error of the PP Doppler estimator at low number of periods for a narrowband Doppler signal and arbitrary model of the noise correlation function is obtained. The results are correct at relatively high SNR. The analysis is supported by computer simulations at various SNR's.

Protecting a quantum state from environmental noise by an incompatible finite-time measurement

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

Brasil, Carlos Alexandre; Castro, L. A. de; Napolitano, R. d. J.

We show that measurements of finite duration performed on an open two-state system can protect the initial state from a phase-noisy environment, provided the measured observable does not commute with the perturbing interaction. When the measured observable commutes with the environmental interaction, the finite-duration measurement accelerates the rate of decoherence induced by the phase noise. For the description of the measurement of an observable that is incompatible with the interaction between system and environment, we have found an approximate analytical expression, valid at zero temperature and weak coupling with the measuring device. We have tested the validity of the analyticalmore » predictions against an exact numerical approach, based on the superoperator-splitting method, that confirms the protection of the initial state of the system. When the coupling between the system and the measuring apparatus increases beyond the range of validity of the analytical approximation, the initial state is still protected by the finite-time measurement, according with the exact numerical calculations.« less

Variational path integral molecular dynamics and hybrid Monte Carlo algorithms using a fourth order propagator with applications to molecular systems

NASA Astrophysics Data System (ADS)

Kamibayashi, Yuki; Miura, Shinichi

2016-08-01

In the present study, variational path integral molecular dynamics and associated hybrid Monte Carlo (HMC) methods have been developed on the basis of a fourth order approximation of a density operator. To reveal various parameter dependence of physical quantities, we analytically solve one dimensional harmonic oscillators by the variational path integral; as a byproduct, we obtain the analytical expression of the discretized density matrix using the fourth order approximation for the oscillators. Then, we apply our methods to realistic systems like a water molecule and a para-hydrogen cluster. In the HMC, we adopt two level description to avoid the time consuming Hessian evaluation. For the systems examined in this paper, the HMC method is found to be about three times more efficient than the molecular dynamics method if appropriate HMC parameters are adopted; the advantage of the HMC method is suggested to be more evident for systems described by many body interaction.

Secular dynamics of multiplanetary circumbinary systems: stationary solutions and binary-planet secular resonance

NASA Astrophysics Data System (ADS)

Andrade-Ines, Eduardo; Robutel, Philippe

2018-01-01

We present an analytical formalism to study the secular dynamics of a system consisting of N-2 planets orbiting a binary star in outer orbits. We introduce a canonical coordinate system and expand the disturbing function in terms of canonical elliptic elements, combining both Legendre polynomials and Laplace coefficients, to obtain a general formalism for the secular description of this type of configuration. With a quadratic approximation of the development, we present a simplified analytical solution for the planetary orbits for both the single planet and the two-planet cases. From the two-planet model, we show that the inner planet accelerates the precession rate of the binary pericenter, which, in turn, may enter in resonance with the secular frequency of the outer planet, characterizing a secular resonance. We calculate an analytical expression for the approximate location of this resonance and apply it to known circumbinary systems, where we show that it can occur at relatively close orbits, for example at 2.4 au for the Kepler-38 system. With a more refined model, we analyse the dynamics of this secular resonance and we show that a bifurcation of the corresponding fixed points can affect the long- term evolution and stability of planetary systems. By comparing our results with complete integrations of the exact equations of motion, we verified the accuracy of our analytical model.

Continuum description of solvent dielectrics in molecular-dynamics simulations of proteins

NASA Astrophysics Data System (ADS)

Egwolf, Bernhard; Tavan, Paul

2003-02-01

We present a continuum approach for efficient and accurate calculation of reaction field forces and energies in classical molecular-dynamics (MD) simulations of proteins in water. The derivation proceeds in two steps. First, we reformulate the electrostatics of an arbitrarily shaped molecular system, which contains partially charged atoms and is embedded in a dielectric continuum representing the water. A so-called fuzzy partition is used to exactly decompose the system into partial atomic volumes. The reaction field is expressed by means of dipole densities localized at the atoms. Since these densities cannot be calculated analytically for general systems, we introduce and carefully analyze a set of approximations in a second step. These approximations allow us to represent the dipole densities by simple dipoles localized at the atoms. We derive a system of linear equations for these dipoles, which can be solved numerically by iteration. After determining the two free parameters of our approximate method we check its quality by comparisons (i) with an analytical solution, which is available for a perfectly spherical system, (ii) with forces obtained from a MD simulation of a soluble protein in water, and (iii) with reaction field energies of small molecules calculated by a finite difference method.

Effect of magnetic field on beta processes in a relativistic moderately degenerate plasma

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

Ognev, I. S., E-mail: ognev@uniyar.ac.ru

The effect of a magnetic field of arbitrary strength on the beta decay and crossing symmetric processes is analyzed. A covariant calculation technique is used to derive the expression for the squares of S-matrix elements of these reactions, which is also valid in reference frames in which the medium moves as a single whole along magnetic field lines. Simple analytic expressions obtained for the neutrino and antineutrino emissivities for a moderately degenerate plasma fully characterize the emissivity and absorbability of the studied medium. It is shown that the approximation used here is valid for core collapse supernovae and accretion disksmore » around black holes; beta processes in these objects are predominantly neutrino reactions. The analytic expressions obtained for the emissivities can serve as a good approximation for describing the interaction of electron neutrinos and antineutrinos with the medium of the objects in question and hold for an arbitrary magnetic field strength. Due to their simplicity, these expressions can be included in the magnetohydrodynamic simulation of supernovae and accretion disks to calculate neutrino and antineutrino transport in them. The rates of beta processes and the energy and momentum emitted in them are calculated for an optically transparent matter. It is shown that the macroscopic momentum transferred in the medium increases linearly with the magnetic field strength and can substantially affect the dynamics of supernovae and accretion disks in the regions of a degenerate matter. It is also shown that the rates of beta processes and the energy emission for a magnetic field strength of B ≲ 10{sup 15} G typical of supernovae and accretion disks are lower than in the absence of field. This suppression is stronger for reactions with neutrinos.« less

Shear viscosity of an ultrarelativistic Boltzmann gas with isotropic inelastic scattering processes

NASA Astrophysics Data System (ADS)

El, A.; Lauciello, F.; Wesp, C.; Bouras, I.; Xu, Z.; Greiner, C.

2014-05-01

We derive an analytic expression for the shear viscosity of an ultra-relativistic gas in presence of both elastic 2→2 and inelastic 2↔3 processes with isotropic differential cross sections. The derivation is based on the entropy principle and Grad's approximation for the off-equilibrium distribution function. The obtained formula relates the shear viscosity coefficient η to the total cross sections σ22 and σ23 of the elastic resp. inelastic processes. The values of shear viscosity extracted using the Green-Kubo formula from kinetic transport calculations are shown to be in excellent agreement with the analytic results which demonstrates the validity of the derived formula.

Generation of dark hollow beams by using a fractional radial Hilbert transform system

NASA Astrophysics Data System (ADS)

Xie, Qiansen; Zhao, Daomu

2007-07-01

The radial Hilbert transform has been extend to the fractional field, which could be called the fractional radial Hilbert transform (FRHT). Using edge-enhancement characteristics of this transform, we convert a Gaussian light beam into a variety of dark hollow beams (DHBs). Based on the fact that a hard-edged aperture can be expanded approximately as a finite sum of complex Gaussian functions, the analytical expression of a Gaussian beam passing through a FRHT system has been derived. As a numerical example, the properties of the DHBs with different fractional orders are illustrated graphically. The calculation results obtained by use of the analytical method and the integral method are also compared.

Estimation of the curvature of the solid liquid interface during Bridgman crystal growth

NASA Astrophysics Data System (ADS)

Barat, Catherine; Duffar, Thierry; Garandet, Jean-Paul

1998-11-01

An approximate solution for the solid/liquid interface curvature due to the crucible effect in crystal growth is derived from simple heat flux considerations. The numerical modelling of the problem carried out with the help of the finite element code FIDAP supports the predictions of our analytical expression and allows to identify its range of validity. Experimental interface curvatures, measured in gallium antimonide samples grown by the vertical Bridgman method, are seen to compare satisfactorily to analytical and numerical results. Other literature data are also in fair agreement with the predictions of our models in the case where the amount of heat carried by the crucible is small compared to the overall heat flux.

2-D modeling and analysis of short-channel behavior of a front high- K gate stack triple-material gate SB SON MOSFET

NASA Astrophysics Data System (ADS)

Banerjee, Pritha; Kumari, Tripty; Sarkar, Subir Kumar

2018-02-01

This paper presents the 2-D analytical modeling of a front high- K gate stack triple-material gate Schottky Barrier Silicon-On-Nothing MOSFET. Using the two-dimensional Poisson's equation and considering the popular parabolic potential approximation, expression for surface potential as well as the electric field has been considered. In addition, the response of the proposed device towards aggressive downscaling, that is, its extent of immunity towards the different short-channel effects, has also been considered in this work. The analytical results obtained have been validated using the simulated results obtained using ATLAS, a two-dimensional device simulator from SILVACO.

Analytic approximation for random muffin-tin alloys

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

Mills, R.; Gray, L.J.; Kaplan, T.

1983-03-15

The methods introduced in a previous paper under the name of ''traveling-cluster approximation'' (TCA) are applied, in a multiple-scattering approach, to the case of a random muffin-tin substitutional alloy. This permits the iterative part of a self-consistent calculation to be carried out entirely in terms of on-the-energy-shell scattering amplitudes. Off-shell components of the mean resolvent, needed for the calculation of spectral functions, are obtained by standard methods involving single-site scattering wave functions. The single-site TCA is just the usual coherent-potential approximation, expressed in a form particularly suited for iteration. A fixed-point theorem is proved for the general t-matrix TCA, ensuringmore » convergence upon iteration to a unique self-consistent solution with the physically essential Herglotz properties.« less

Thermal effects and sudden decay approximation in the curvaton scenario

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

Kitajima, Naoya; Takesako, Tomohiro; Yokoyama, Shuichiro

2014-10-01

We study the impact of a temperature-dependent curvaton decay rate on the primordial curvature perturbation generated in the curvaton scenario. Using the familiar sudden decay approximation, we obtain an analytical expression for the curvature perturbation after the decay of the curvaton. We then investigate numerically the evolution of the background and of the perturbations during the decay. We first show that the instantaneous transfer coefficient, related to the curvaton energy fraction at the decay, can be extended into a more general parameter, which depends on the net transfer of the curvaton energy into radiation energy or, equivalently, on the totalmore » entropy ratio after the complete curvaton decay. We then compute the curvature perturbation and compare this result with the sudden decay approximation prediction.« less

Sample distribution in peak mode isotachophoresis

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

Rubin, Shimon; Schwartz, Ortal; Bercovici, Moran, E-mail: mberco@technion.ac.il

We present an analytical study of peak mode isotachophoresis (ITP), and provide closed form solutions for sample distribution and electric field, as well as for leading-, trailing-, and counter-ion concentration profiles. Importantly, the solution we present is valid not only for the case of fully ionized species, but also for systems of weak electrolytes which better represent real buffer systems and for multivalent analytes such as proteins and DNA. The model reveals two major scales which govern the electric field and buffer distributions, and an additional length scale governing analyte distribution. Using well-controlled experiments, and numerical simulations, we verify andmore » validate the model and highlight its key merits as well as its limitations. We demonstrate the use of the model for determining the peak concentration of focused sample based on known buffer and analyte properties, and show it differs significantly from commonly used approximations based on the interface width alone. We further apply our model for studying reactions between multiple species having different effective mobilities yet co-focused at a single ITP interface. We find a closed form expression for an effective-on rate which depends on reactants distributions, and derive the conditions for optimizing such reactions. Interestingly, the model reveals that maximum reaction rate is not necessarily obtained when the concentration profiles of the reacting species perfectly overlap. In addition to the exact solutions, we derive throughout several closed form engineering approximations which are based on elementary functions and are simple to implement, yet maintain the interplay between the important scales. Both the exact and approximate solutions provide insight into sample focusing and can be used to design and optimize ITP-based assays.« less

Quasistatic limit of the strong-field approximation describing atoms in intense laser fields: Circular polarization

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

Bauer, Jaroslaw H.

2011-03-15

In the recent work of Vanne and Saenz [Phys. Rev. A 75, 063403 (2007)] the quasistatic limit of the velocity gauge strong-field approximation describing the ionization rate of atomic or molecular systems exposed to linearly polarized laser fields was derived. It was shown that in the low-frequency limit the ionization rate is proportional to the laser frequency {omega} (for a constant intensity of the laser field). In the present work I show that for circularly polarized laser fields the ionization rate is proportional to {omega}{sup 4} for H(1s) and H(2s) atoms, to {omega}{sup 6} for H(2p{sub x}) and H(2p{sub y})more » atoms, and to {omega}{sup 8} for H(2p{sub z}) atoms. The analytical expressions for asymptotic ionization rates (which become nearly accurate in the limit {omega}{yields}0) contain no summations over multiphoton contributions. For very low laser frequencies (optical or infrared) these expressions usually remain with an order-of-magnitude agreement with the velocity gauge strong-field approximation.« 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

An analytical model for scanning electron microscope Type I magnetic contrast with energy filtering

NASA Astrophysics Data System (ADS)

Chim, W. K.

1994-02-01

In this article, a theoretical model for type I magnetic contrast calculations in the scanning electron microscope with energy filtering is presented. This model uses an approximate form of the secondary electron (SE) energy distribution by Chung and Everhart [M. S. Chung and T. E. Everhart, J. Appl. Phys. 45, 707 (1974). Closed form analytical expressions for the contrast and quality factors, which take into consideration the work function and field-distance integral of the material being studied, are obtained. This analytical model is compared with that of a more accurate numerical model. Results showed that the contrast and quality factors for the analytical model differed by not more than 20% from the numerical model, with the actual difference depending on the range of filtered SE energies considered. This model has also been extended to the situation of a two-detector (i.e., detector A and B) configuration, in which enhanced magnetic contrast and quality factor can be obtained by operating in the ``A-B'' mode.

Effect of curvature on the backscattering from leaves

NASA Technical Reports Server (NTRS)

Sarabandi, K.; Senior, T. B. A.; Ulaby, F. T.

1988-01-01

Using a model previously developed for the backscattering cross section of a planar leaf at X-band frequencies and above, the effect of leaf curvature is examined. For normal incidence on a rectangular section of a leaf curved in one and two dimensions, an integral expression for the backscattered field is evaluated numerically and by a stationary phase approximation, leading to a simple analytical expression for the cross section reduction produced by the curvature. Numerical results based on the two methods are virtually identical, and in excellent agreement with measured data for rectangular sections of coleus leaves applied to the surfaces of styrofoam cylinders and spheres of different radii.

Effect of curvature on the backscattering from a leaf

NASA Technical Reports Server (NTRS)

Sarabandi, K.; Senior, T. B. A.; Ulaby, F. T.

1988-01-01

Using a model previously developed for the backscattering cross section of a planar leaf at X-band frequencies and above, the effect of leaf curvature is examined. For normal incidence on a rectangular section of a leaf curved in one and two dimensions, an integral expression for the backscattered field is evaluated numerically and by a stationary phase approximation, leading to a simple analytical expression for the cross-section reduction produced by the curvature. Numerical results based on the two methods are virtually identical, and in excellent agreement with measured data for rectangular sections of coleus leaves applied to the surfaces of styrofoam cylinders and spheres of different radii.

An analytical model for inductively coupled implantable biomedical devices with ferrite rods.

PubMed

Theilmann, P T; Asbeck, P M

2009-02-01

Using approximations applicable to near field coupled implants simplified expressions for the complex mutual inductance of coaxial aligned coils with and without a cylindrical ferrite rod are derived. Experimental results for ferrite rods of various sizes and permeabilities are presented to verify the accuracy of this expression. An equivalent circuit model for the inductive link between an implant and power coil is then presented and used to investigate how ferrite size, permeability and loss affect the power available to the implant device. Enhancements in coupling provided by high frequency, low permeability nickel zinc rods are compared with low frequency high permeability manganese zinc rods.

Modeling inelastic phonon scattering in atomic- and molecular-wire junctions

NASA Astrophysics Data System (ADS)

Paulsson, Magnus; Frederiksen, Thomas; Brandbyge, Mads

2005-11-01

Computationally inexpensive approximations describing electron-phonon scattering in molecular-scale conductors are derived from the nonequilibrium Green’s function method. The accuracy is demonstrated with a first-principles calculation on an atomic gold wire. Quantitative agreement between the full nonequilibrium Green’s function calculation and the newly derived expressions is obtained while simplifying the computational burden by several orders of magnitude. In addition, analytical models provide intuitive understanding of the conductance including nonequilibrium heating and provide a convenient way of parameterizing the physics. This is exemplified by fitting the expressions to the experimentally observed conductances through both an atomic gold wire and a hydrogen molecule.

Analytical beam-width characteristics of distorted cat-eye reflected beam

NASA Astrophysics Data System (ADS)

Zhao, Yanzhong; Shan, Congmiao; Zheng, Yonghui; Zhang, Laixian; Sun, Huayan

2015-02-01

The analytical expression of beam-width of distorted cat-eye reflected beam under far-field condition is deduced using the approximate three-dimensional analytical formula for oblique detection laser beam passing through cat-eye optical lens with center shelter, and using the definition of second order moment, Gamma function and integral functions. The laws the variation of divergence angle and astigmatism degree of the reflected light with incident angle, focal shift, aperture size, and center shelter ratio are established by numerical calculation, and physical analysis. The study revealed that the cat-eye reflected beam is like a beam transmitted and collimated by the target optical lens, and has the same characteristics as that of Gaussian beam. A proper choice of positive focal shift would result in a divergence angle smaller than that of no focal shift. The astigmatism is mainly caused by incidence angle.

Mesh-based Monte Carlo code for fluorescence modeling in complex tissues with irregular boundaries

NASA Astrophysics Data System (ADS)

Wilson, Robert H.; Chen, Leng-Chun; Lloyd, William; Kuo, Shiuhyang; Marcelo, Cynthia; Feinberg, Stephen E.; Mycek, Mary-Ann

2011-07-01

There is a growing need for the development of computational models that can account for complex tissue morphology in simulations of photon propagation. We describe the development and validation of a user-friendly, MATLAB-based Monte Carlo code that uses analytically-defined surface meshes to model heterogeneous tissue geometry. The code can use information from non-linear optical microscopy images to discriminate the fluorescence photons (from endogenous or exogenous fluorophores) detected from different layers of complex turbid media. We present a specific application of modeling a layered human tissue-engineered construct (Ex Vivo Produced Oral Mucosa Equivalent, EVPOME) designed for use in repair of oral tissue following surgery. Second-harmonic generation microscopic imaging of an EVPOME construct (oral keratinocytes atop a scaffold coated with human type IV collagen) was employed to determine an approximate analytical expression for the complex shape of the interface between the two layers. This expression can then be inserted into the code to correct the simulated fluorescence for the effect of the irregular tissue geometry.

Variational Trajectory Optimization Tool Set: Technical description and user's manual

NASA Technical Reports Server (NTRS)

Bless, Robert R.; Queen, Eric M.; Cavanaugh, Michael D.; Wetzel, Todd A.; Moerder, Daniel D.

1993-01-01

The algorithms that comprise the Variational Trajectory Optimization Tool Set (VTOTS) package are briefly described. The VTOTS is a software package for solving nonlinear constrained optimal control problems from a wide range of engineering and scientific disciplines. The VTOTS package was specifically designed to minimize the amount of user programming; in fact, for problems that may be expressed in terms of analytical functions, the user needs only to define the problem in terms of symbolic variables. This version of the VTOTS does not support tabular data; thus, problems must be expressed in terms of analytical functions. The VTOTS package consists of two methods for solving nonlinear optimal control problems: a time-domain finite-element algorithm and a multiple shooting algorithm. These two algorithms, under the VTOTS package, may be run independently or jointly. The finite-element algorithm generates approximate solutions, whereas the shooting algorithm provides a more accurate solution to the optimization problem. A user's manual, some examples with results, and a brief description of the individual subroutines are included.

Three-Dimensional Field Solutions for Multi-Pole Cylindrical Halbach Arrays in an Axial Orientation

NASA Technical Reports Server (NTRS)

Thompson, William K.

2006-01-01

This article presents three-dimensional B field solutions for the cylindrical Halbach array in an axial orientation. This arrangement has applications in the design of axial motors and passive axial magnetic bearings and couplers. The analytical model described here assumes ideal magnets with fixed and uniform magnetization. The field component functions are expressed as sums of 2-D definite integrals that are easily computed by a number of mathematical analysis software packages. The analysis is verified with sample calculations and the results are compared to equivalent results from traditional finite-element analysis (FEA). The field solutions are then approximated for use in flux linkage and induced EMF calculations in nearby stator windings by expressing the field variance with angular displacement as pure sinusoidal function whose amplitude depends on radial and axial position. The primary advantage of numerical implementation of the analytical approach presented in the article is that it lends itself more readily to parametric analysis and design tradeoffs than traditional FEA models.

Predicting thermal history a-priori for magnetic nanoparticle hyperthermia of internal carcinoma

NASA Astrophysics Data System (ADS)

Dhar, Purbarun; Sirisha Maganti, Lakshmi

2017-08-01

This article proposes a simplistic and realistic method where a direct analytical expression can be derived for the temperature field within a tumour during magnetic nanoparticle hyperthermia. The approximated analytical expression for thermal history within the tumour is derived based on the lumped capacitance approach and considers all therapy protocols and parameters. The present method is simplistic and provides an easy framework for estimating hyperthermia protocol parameters promptly. The model has been validated with respect to several experimental reports on animal models such as mice/rabbit/hamster and human clinical trials. It has been observed that the model is able to accurately estimate the thermal history within the carcinoma during the hyperthermia therapy. The present approach may find implications in a-priori estimation of the thermal history in internal tumours for optimizing magnetic hyperthermia treatment protocols with respect to the ablation time, tumour size, magnetic drug concentration, field strength, field frequency, nanoparticle material and size, tumour location, and so on.

Analytical description of high-aperture STED resolution with 0–2π vortex phase modulation

PubMed Central

Xie, Hao; Liu, Yujia; Jin, Dayong; Santangelo, Philip J.; Xi, Peng

2014-01-01

Stimulated emission depletion (STED) can achieve optical superresolution, with the optical diffraction limit broken by the suppression on the periphery of the fluorescent focal spot. Previously, it is generally experimentally accepted that there exists an inverse square root relationship with the STED power and the resolution, but with arbitrary coefficients in expression. In this paper, we have removed the arbitrary coefficients by exploring the relationship between the STED power and the achievable resolution from vector optical theory for the widely used 0–2π vortex phase modulation. Electromagnetic fields of the focal region of a high numerical aperture objective are calculated and approximated into polynomials of radius in the focal plane, and analytical expression of resolution as a function of the STED intensity has been derived. As a result, the resolution can be estimated directly from the measurement of the saturation power of the dye and the STED power applied in the region of high STED power. PMID:24323224

Solution of the mean spherical approximation for polydisperse multi-Yukawa hard-sphere fluid mixture using orthogonal polynomial expansions

NASA Astrophysics Data System (ADS)

Kalyuzhnyi, Yurij V.; Cummings, Peter T.

2006-03-01

The Blum-Høye [J. Stat. Phys. 19 317 (1978)] solution of the mean spherical approximation for a multicomponent multi-Yukawa hard-sphere fluid is extended to a polydisperse multi-Yukawa hard-sphere fluid. Our extension is based on the application of the orthogonal polynomial expansion method of Lado [Phys. Rev. E 54, 4411 (1996)]. Closed form analytical expressions for the structural and thermodynamic properties of the model are presented. They are given in terms of the parameters that follow directly from the solution. By way of illustration the method of solution is applied to describe the thermodynamic properties of the one- and two-Yukawa versions of the model.

Solving the Integral of Quadratic Forms of Covariance Matrices for Applications in Polarimetric Radar Imagery

NASA Astrophysics Data System (ADS)

Marino, Armando; Hajnsek, Irena

2015-04-01

In this work, the solution of quadratic forms with special application to polarimetric and interferometric covariance matrices is investigated. An analytical solution for the integral of a single quadratic form is derived. Additionally, the integral of the Pol-InSAR coherence (expressed as combination of quadratic forms) is investigated. An approximation for such integral is proposed and defined as Trace coherence. Such approximation is tested on real data to verify that the error is acceptable. The trace coherence can be used for tackle problems related to change detection. Moreover, the use of the Trace coherence in model inversion (as for the RVoG three stage inversion) will be investigated in the future.

SPIRE Data Evaluation and Nuclear IR Fluorescence Processes.

DTIC Science & Technology

1982-11-30

so that all isotopes can be dealt with in a single run rather than a number of separate runs. At lower altitudes the radiance calculation needs to be...approximation can be inferred from the work of Neuendorffer (1982) on developing an analytic expression for the absorption of a single non-overlapping line...personnel by using prominent atmospheric infrared features such as the OH maximum, the HNO3 maximum, the CO3 4.3 um knee, etc. The azimuth however

Segmented strings and the McMillan map

DOE PAGES

Gubser, Steven S.; Parikh, Sarthak; Witaszczyk, Przemek

2016-07-25

We present new exact solutions describing motions of closed segmented strings in AdS 3 in terms of elliptic functions. The existence of analytic expressions is due to the integrability of the classical equations of motion, which in our examples reduce to instances of the McMillan map. Here, we also obtain a discrete evolution rule for the motion in AdS 3 of arbitrary bound states of fundamental strings and D1-branes in the test approximation.

Linear and Order Statistics Combiners for Pattern Classification

NASA Technical Reports Server (NTRS)

Tumer, Kagan; Ghosh, Joydeep; Lau, Sonie (Technical Monitor)

2001-01-01

Several researchers have experimentally shown that substantial improvements can be obtained in difficult pattern recognition problems by combining or integrating the outputs of multiple classifiers. This chapter provides an analytical framework to quantify the improvements in classification results due to combining. The results apply to both linear combiners and order statistics combiners. We first show that to a first order approximation, the error rate obtained over and above the Bayes error rate, is directly proportional to the variance of the actual decision boundaries around the Bayes optimum boundary. Combining classifiers in output space reduces this variance, and hence reduces the 'added' error. If N unbiased classifiers are combined by simple averaging. the added error rate can be reduced by a factor of N if the individual errors in approximating the decision boundaries are uncorrelated. Expressions are then derived for linear combiners which are biased or correlated, and the effect of output correlations on ensemble performance is quantified. For order statistics based non-linear combiners, we derive expressions that indicate how much the median, the maximum and in general the i-th order statistic can improve classifier performance. The analysis presented here facilitates the understanding of the relationships among error rates, classifier boundary distributions, and combining in output space. Experimental results on several public domain data sets are provided to illustrate the benefits of combining and to support the analytical results.

Frequency-dependent laminar electroosmotic flow in a closed-end rectangular microchannel.

PubMed

Marcos; Yang, C; Ooi, K T; Wong, T N; Masliyah, J H

2004-07-15

This article presents an analysis of the frequency- and time-dependent electroosmotic flow in a closed-end rectangular microchannel. An exact solution to the modified Navier-Stokes equation governing the ac electroosmotic flow field is obtained by using the Green's function formulation in combination with a complex variable approach. An analytical expression for the induced backpressure gradient is derived. With the Debye-Hückel approximation, the electrical double-layer potential distribution in the channel is obtained by analytically solving the linearized two-dimensional Poisson-Boltzmann equation. Since the counterparts of the flow rate and the electrical current are shown to be linearly proportional to the applied electric field and the pressure gradient, Onsager's principle of reciprocity is demonstrated for transient and ac electroosmotic flows. The time evolution of the electroosmotic flow and the effect of a frequency-dependent ac electric field on the oscillating electroosmotic flow in a closed-end rectangular microchannel are examined. Specifically, the induced pressure gradient is analyzed under effects of the channel dimension and the frequency of electric field. In addition, based on the Stokes second problem, the solution of the slip velocity approximation is presented for comparison with the results obtained from the analytical scheme developed in this study. Copyright 2004 Elsevier Inc.

Modeling the effect of heatsink performance in high-peak-power laser-diode-bar pump sources for solid-state lasers 011 011

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

Honea, E.C., LLNL

We derive approximate expressions for transient output power and wavelength chirp of high- peak-power laser-diode bars assuming one-dimensional heat flow and linear temperature dependences for chirp and efficiency. The model is derived for pulse durations, 10 < {tau} < 1000 ps, typically used for diode-pumped solid-state lasers and is in good agreement with experimental data for Si heatsink mounted 940 nm laser-diode bars operating at 100 W/cm. The analytic expressions are more flexible and easily used than the results of operating point dependent numerical modeling. In addition, the analytic expressions used here can be integrated to describe the energy permore » unit wavelength for a given pulse duration, initial emission bandwidth and heatsink material. We find that the figure-of-merit for a heatsink material in this application is ({rho}C{sub p}K) where {rho}C{sub p} is the volumetric heat capacity and K is the thermal conductivity. As an example of the utility of the derived expressions, we determine an effective absorption coefficient as a function of pump pulse duration for a diode-pumped solid-state laser utilizing Yb:Sr{sub 5}(PO{sub 4}){sub 3}F (Yb:S-FAP) as the gain medium.« less

Steady-state protein focusing in carrier ampholyte based isoelectric focusing: Part I-Analytical solution.

PubMed

Shim, Jaesool; Yoo, Kisoo; Dutta, Prashanta

2017-03-01

The determination of an analytical solution to find the steady-state protein concentration distribution in IEF is very challenging due to the nonlinear coupling between mass and charge conservation equations. In this study, approximate analytical solutions are obtained for steady-state protein distribution in carrier ampholyte based IEF. Similar to the work of Svensson, the final concentration profile for proteins is assumed to be Gaussian, but appropriate expressions are presented in order to obtain the effective electric field and pH gradient in the focused protein band region. Analytical results are found from iterative solutions of a system of coupled algebraic equations using only several iterations for IEF separation of three plasma proteins: albumin, cardiac troponin I, and hemoglobin. The analytical results are compared with numerically predicted results for IEF, showing excellent agreement. Analytically obtained electric field and ionic conductivity distributions show significant deviation from their nominal values, which is essential in finding the protein focusing behavior at isoelectric points. These analytical solutions can be used to determine steady-state protein concentration distribution for experiment design of IEF considering any number of proteins and ampholytes. Moreover, the model presented herein can be used to find the conductivity, electric field, and pH field. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Interacting steps with finite-range interactions: Analytical approximation and numerical results

NASA Astrophysics Data System (ADS)

Jaramillo, Diego Felipe; Téllez, Gabriel; González, Diego Luis; Einstein, T. L.

2013-05-01

We calculate an analytical expression for the terrace-width distribution P(s) for an interacting step system with nearest- and next-nearest-neighbor interactions. Our model is derived by mapping the step system onto a statistically equivalent one-dimensional system of classical particles. The validity of the model is tested with several numerical simulations and experimental results. We explore the effect of the range of interactions q on the functional form of the terrace-width distribution and pair correlation functions. For physically plausible interactions, we find modest changes when next-nearest neighbor interactions are included and generally negligible changes when more distant interactions are allowed. We discuss methods for extracting from simulated experimental data the characteristic scale-setting terms in assumed potential forms.

A new treatment of the albedo radiation pressure in the case of a uniform albedo and of a spherical satellite

NASA Technical Reports Server (NTRS)

Borderies, Nicole; Longaretti, Pierre-Yves

1990-01-01

The purpose of this paper is to present a model for the radiation pressure acceleration of a spherical satellite, due to the radiation reflected by a planet with a uniform albedo. A particular choice of variables allows one to reduce the surface integrals over the lit portion of the planet visible to the satellite to one-dimensional integrals. Exact analytical expressions are found for the integrals corresponding to the case where the spacecraft does not 'see' the terminator. The other integrals can be computer either numerically, or analytical in an approximate form. The results are compared with those of Lochry (1966). The model is applied to Magellan, a spacecraft orbiting Venus.

Two-body perturbation theory versus first order perturbation theory: A comparison based on the square-well fluid.

PubMed

Mercier Franco, Luís Fernando; Castier, Marcelo; Economou, Ioannis G

2017-12-07

We show that the Zwanzig first-order perturbation theory can be obtained directly from a truncated Taylor series expansion of a two-body perturbation theory and that such truncation provides a more accurate prediction of thermodynamic properties than the full two-body perturbation theory. This unexpected result is explained by the quality of the resulting approximation for the fluid radial distribution function. We prove that the first-order and the two-body perturbation theories are based on different approximations for the fluid radial distribution function. To illustrate the calculations, the square-well fluid is adopted. We develop an analytical expression for the two-body perturbed Helmholtz free energy for the square-well fluid. The equation of state obtained using such an expression is compared to the equation of state obtained from the first-order approximation. The vapor-liquid coexistence curve and the supercritical compressibility factor of a square-well fluid are calculated using both equations of state and compared to Monte Carlo simulation data. Finally, we show that the approximation for the fluid radial distribution function given by the first-order perturbation theory provides closer values to the ones calculated via Monte Carlo simulations. This explains why such theory gives a better description of the fluid thermodynamic behavior.

Consistent Yokoya-Chen Approximation to Beamstrahlung(LCC-0010)

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

Peskin, M

2004-04-22

I reconsider the Yokoya-Chen approximate evolution equation for beamstrahlung and modify it slightly to generate simple, consistent analytical approximations for the electron and photon energy spectra. I compare these approximations to previous ones, and to simulation data.I reconsider the Yokoya-Chen approximate evolution equation for beamstrahlung and modify it slightly to generate simple, consistent analytical approximations for the electron and photon energy spectra. I compare these approximations to previous ones, and to simulation data.

Analytical Validation of a Highly Quantitative, Sensitive, Accurate, and Reproducible Assay (HERmark®) for the Measurement of HER2 Total Protein and HER2 Homodimers in FFPE Breast Cancer Tumor Specimens

PubMed Central

Larson, Jeffrey S.; Goodman, Laurie J.; Tan, Yuping; Defazio-Eli, Lisa; Paquet, Agnes C.; Cook, Jennifer W.; Rivera, Amber; Frankson, Kristi; Bose, Jolly; Chen, Lili; Cheung, Judy; Shi, Yining; Irwin, Sarah; Kiss, Linda D. B.; Huang, Weidong; Utter, Shannon; Sherwood, Thomas; Bates, Michael; Weidler, Jodi; Parry, Gordon; Winslow, John; Petropoulos, Christos J.; Whitcomb, Jeannette M.

2010-01-01

We report here the results of the analytical validation of assays that measure HER2 total protein (H2T) and HER2 homodimer (H2D) expression in Formalin Fixed Paraffin Embedded (FFPE) breast cancer tumors as well as cell line controls. The assays are based on the VeraTag technology platform and are commercially available through a central CAP-accredited clinical reference laboratory. The accuracy of H2T measurements spans a broad dynamic range (2-3 logs) as evaluated by comparison with cross-validating technologies. The measurement of H2T expression demonstrates a sensitivity that is approximately 7–10 times greater than conventional immunohistochemistry (IHC) (HercepTest). The HERmark assay is a quantitative assay that sensitively and reproducibly measures continuous H2T and H2D protein expression levels and therefore may have the potential to stratify patients more accurately with respect to response to HER2-targeted therapies than current methods which rely on semiquantitative protein measurements (IHC) or on indirect assessments of gene amplification (FISH). PMID:21151530

Analytical Validation of a Highly Quantitative, Sensitive, Accurate, and Reproducible Assay (HERmark) for the Measurement of HER2 Total Protein and HER2 Homodimers in FFPE Breast Cancer Tumor Specimens.

PubMed

Larson, Jeffrey S; Goodman, Laurie J; Tan, Yuping; Defazio-Eli, Lisa; Paquet, Agnes C; Cook, Jennifer W; Rivera, Amber; Frankson, Kristi; Bose, Jolly; Chen, Lili; Cheung, Judy; Shi, Yining; Irwin, Sarah; Kiss, Linda D B; Huang, Weidong; Utter, Shannon; Sherwood, Thomas; Bates, Michael; Weidler, Jodi; Parry, Gordon; Winslow, John; Petropoulos, Christos J; Whitcomb, Jeannette M

2010-06-28

We report here the results of the analytical validation of assays that measure HER2 total protein (H2T) and HER2 homodimer (H2D) expression in Formalin Fixed Paraffin Embedded (FFPE) breast cancer tumors as well as cell line controls. The assays are based on the VeraTag technology platform and are commercially available through a central CAP-accredited clinical reference laboratory. The accuracy of H2T measurements spans a broad dynamic range (2-3 logs) as evaluated by comparison with cross-validating technologies. The measurement of H2T expression demonstrates a sensitivity that is approximately 7-10 times greater than conventional immunohistochemistry (IHC) (HercepTest). The HERmark assay is a quantitative assay that sensitively and reproducibly measures continuous H2T and H2D protein expression levels and therefore may have the potential to stratify patients more accurately with respect to response to HER2-targeted therapies than current methods which rely on semiquantitative protein measurements (IHC) or on indirect assessments of gene amplification (FISH).

Frequency response of a supported thermocouple wire: Effects of axial conduction

NASA Technical Reports Server (NTRS)

Forney, L. J.; Meeks, E. L.; Fralick, G. C.

1991-01-01

Theoretical expressions are derived for the steady-state frequency response of a supported thermocouple wire. In particular, the effects of axial heat conduction are demonstrated for both a supported one material wire and a two material wire with unequal material properties across the junction. For the case of a one material supported wire, an exact solution is derived which compares favorably with an approximate expression that only matches temperatures at the support junction. Moreover, for the case of a two material supported wire, an analytical expression is derived that closely correlates numerical results. Experimental data were taken with a type K supported thermocouple. The test thermocouple was constructed with dimensions to demonstrate the effects of axial heat conduction assuming constant physical properties across the junction.

Pattern Storage, Bifurcations, and Groupwise Correlation Structure of an Exactly Solvable Asymmetric Neural Network Model.

PubMed

Fasoli, Diego; Cattani, Anna; Panzeri, Stefano

2018-05-01

Despite their biological plausibility, neural network models with asymmetric weights are rarely solved analytically, and closed-form solutions are available only in some limiting cases or in some mean-field approximations. We found exact analytical solutions of an asymmetric spin model of neural networks with arbitrary size without resorting to any approximation, and we comprehensively studied its dynamical and statistical properties. The network had discrete time evolution equations and binary firing rates, and it could be driven by noise with any distribution. We found analytical expressions of the conditional and stationary joint probability distributions of the membrane potentials and the firing rates. By manipulating the conditional probability distribution of the firing rates, we extend to stochastic networks the associating learning rule previously introduced by Personnaz and coworkers. The new learning rule allowed the safe storage, under the presence of noise, of point and cyclic attractors, with useful implications for content-addressable memories. Furthermore, we studied the bifurcation structure of the network dynamics in the zero-noise limit. We analytically derived examples of the codimension 1 and codimension 2 bifurcation diagrams of the network, which describe how the neuronal dynamics changes with the external stimuli. This showed that the network may undergo transitions among multistable regimes, oscillatory behavior elicited by asymmetric synaptic connections, and various forms of spontaneous symmetry breaking. We also calculated analytically groupwise correlations of neural activity in the network in the stationary regime. This revealed neuronal regimes where, statistically, the membrane potentials and the firing rates are either synchronous or asynchronous. Our results are valid for networks with any number of neurons, although our equations can be realistically solved only for small networks. For completeness, we also derived the network equations in the thermodynamic limit of infinite network size and we analytically studied their local bifurcations. All the analytical results were extensively validated by numerical simulations.

Understanding the dynamics of superparamagnetic particles under the influence of high field gradient arrays

NASA Astrophysics Data System (ADS)

Barnsley, Lester C.; Carugo, Dario; Aron, Miles; Stride, Eleanor

2017-03-01

The aim of this study was to characterize the behaviour of superparamagnetic particles in magnetic drug targeting (MDT) schemes. A 3-dimensional mathematical model was developed, based on the analytical derivation of the trajectory of a magnetized particle suspended inside a fluid channel carrying laminar flow and in the vicinity of an external source of magnetic force. Semi-analytical expressions to quantify the proportion of captured particles, and their relative accumulation (concentration) as a function of distance along the wall of the channel were also derived. These were expressed in terms of a non-dimensional ratio of the relevant physical and physiological parameters corresponding to a given MDT protocol. The ability of the analytical model to assess magnetic targeting schemes was tested against numerical simulations of particle trajectories. The semi-analytical expressions were found to provide good first-order approximations for the performance of MDT systems in which the magnetic force is relatively constant over a large spatial range. The numerical model was then used to test the suitability of a range of different designs of permanent magnet assemblies for MDT. The results indicated that magnetic arrays that emit a strong magnetic force that varies rapidly over a confined spatial range are the most suitable for concentrating magnetic particles in a localized region. By comparison, commonly used magnet geometries such as button magnets and linear Halbach arrays result in distributions of accumulated particles that are less efficient for delivery. The trajectories predicted by the numerical model were verified experimentally by acoustically focusing magnetic microbeads flowing in a glass capillary channel, and optically tracking their path past a high field gradient Halbach array.

Franck-Condon factor formulae for astrophysical and other molecules

NASA Technical Reports Server (NTRS)

Nicholls, R. W.

1981-01-01

Simple closed-form, approximate, analytic expressions for Franck-Condon factors are given. They provide reliable estimates for Franck-Condon factor arrays for molecular band systems for which only vibrational-frequency, equilibrium internuclear separation and reduced mass values are known, as is often the case for astrophysically interesting molecules such as CeO, CoH, CrH, CrO, CuH, GeH, LaO, NiH, SnH, and ZnH for band systems of which Franck-Condon arrays have been calculated.

Optimized theory for simple and molecular fluids.

PubMed

Marucho, M; Montgomery Pettitt, B

2007-03-28

An optimized closure approximation for both simple and molecular fluids is presented. A smooth interpolation between Perkus-Yevick and hypernetted chain closures is optimized by minimizing the free energy self-consistently with respect to the interpolation parameter(s). The molecular version is derived from a refinement of the method for simple fluids. In doing so, a method is proposed which appropriately couples an optimized closure with the variant of the diagrammatically proper integral equation recently introduced by this laboratory [K. M. Dyer et al., J. Chem. Phys. 123, 204512 (2005)]. The simplicity of the expressions involved in this proposed theory has allowed the authors to obtain an analytic expression for the approximate excess chemical potential. This is shown to be an efficient tool to estimate, from first principles, the numerical value of the interpolation parameters defining the aforementioned closure. As a preliminary test, representative models for simple fluids and homonuclear diatomic Lennard-Jones fluids were analyzed, obtaining site-site correlation functions in excellent agreement with simulation data.

A time-dependent model to determine the thermal conductivity of a nanofluid

NASA Astrophysics Data System (ADS)

Myers, T. G.; MacDevette, M. M.; Ribera, H.

2013-07-01

In this paper, we analyse the time-dependent heat equations over a finite domain to determine expressions for the thermal diffusivity and conductivity of a nanofluid (where a nanofluid is a fluid containing nanoparticles with average size below 100 nm). Due to the complexity of the standard mathematical analysis of this problem, we employ a well-known approximate solution technique known as the heat balance integral method. This allows us to derive simple analytical expressions for the thermal properties, which appear to depend primarily on the volume fraction and liquid properties. The model is shown to compare well with experimental data taken from the literature even up to relatively high concentrations and predicts significantly higher values than the Maxwell model for volume fractions approximately >1 %. The results suggest that the difficulty in reproducing the high values of conductivity observed experimentally may stem from the use of a static heat flow model applied over an infinite domain rather than applying a dynamic model over a finite domain.

Artificial dispersion via high-order homogenization: magnetoelectric coupling and magnetism from dielectric layers

PubMed Central

Liu, Yan; Guenneau, Sébastien; Gralak, Boris

2013-01-01

We investigate a high-order homogenization (HOH) algorithm for periodic multi-layered stacks. The mathematical tool of choice is a transfer matrix method. Expressions for effective permeability, permittivity and magnetoelectric coupling are explored by frequency power expansions. On the physical side, this HOH uncovers a magnetoelectric coupling effect (odd-order approximation) and artificial magnetism (even-order approximation) in moderate contrast photonic crystals. Comparing the effective parameters' expressions of a stack with three layers against that of a stack with two layers, we note that the magnetoelectric coupling effect vanishes while the artificial magnetism can still be achieved in a centre-symmetric periodic structure. Furthermore, we numerically check the effective parameters through the dispersion law and transmission property of a stack with two dielectric layers against that of an effective bianisotropic medium: they are in good agreement throughout the low-frequency (acoustic) band until the first stop band, where the analyticity of the logarithm function of the transfer matrix () breaks down. PMID:24101891

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 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.

An approximate theoretical treatment of ion transfer processes at asymmetric microscopic and nanoscopic liquid-liquid interfaces: Single and double potential pulse techniques

NASA Astrophysics Data System (ADS)

Molina, A.; Laborda, E.; Compton, R. G.

2014-03-01

Simple theory for the electrochemical study of reversible ion transfer processes at micro- and nano-liquid|liquid interfaces supported on a capillary is presented. Closed-form expressions are obtained for the response in normal pulse and differential double pulse voltammetries, which describe adequately the particular behaviour of these systems due to the ‘asymmetric’ ion diffusion inside and outside the capillary. The use of different potential pulse techniques for the determination of the formal potential and diffusion coefficients of the ion is examined. For this, very simple analytical expressions are presented for the half-wave potential in NPV and the peak potential in DDPV.

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.

Phonons in random alloys: The itinerant coherent-potential approximation

NASA Astrophysics Data System (ADS)

Ghosh, Subhradip; Leath, P. L.; Cohen, Morrel H.

2002-12-01

We present the itinerant coherent-potential approximation (ICPA), an analytic, translationally invariant, and tractable form of augmented-space-based multiple-scattering theory18 in a single-site approximation for harmonic phonons in realistic random binary alloys with mass and force-constant disorder. We provide expressions for quantities needed for comparison with experimental structure factors such as partial and average spectral functions and derive the sum rules associated with them. Numerical results are presented for Ni55Pd45 and Ni50Pt50 alloys which serve as test cases, the former for weak force-constant disorder and the latter for strong. We present results on dispersion curves and disorder-induced widths. Direct comparisons with the single-site coherent potential approximation (CPA) and experiment are made which provide insight into the physics of force-constant changes in random alloys. The CPA accounts well for the weak force-constant disorder case but fails for strong force-constant disorder where the ICPA succeeds.

Analytical approximations for the collapse of an empty spherical bubble.

PubMed

Obreschkow, D; Bruderer, M; Farhat, M

2012-06-01

The Rayleigh equation 3/2R+RR+pρ(-1)=0 with initial conditions R(0)=R(0), R(0)=0 models the collapse of an empty spherical bubble of radius R(T) in an ideal, infinite liquid with far-field pressure p and density ρ. The solution for r≡R/R(0) as a function of time t≡T/T(c), where R(T(c))≡0, is independent of R(0), p, and ρ. While no closed-form expression for r(t) is known, we find that r(0)(t)=(1-t(2))(2/5) approximates r(t) with an error below 1%. A systematic development in orders of t(2) further yields the 0.001% approximation r(*)(t)=r(0)(t)[1-a(1)Li(2.21)(t(2))], where a(1)≈-0.01832099 is a constant and Li is the polylogarithm. The usefulness of these approximations is demonstrated by comparison to high-precision cavitation data obtained in microgravity.

A semi-analytical description of protein folding that incorporates detailed geometrical information

PubMed Central

Suzuki, Yoko; Noel, Jeffrey K.; Onuchic, José N.

2011-01-01

Much has been done to study the interplay between geometric and energetic effects on the protein folding energy landscape. Numerical techniques such as molecular dynamics simulations are able to maintain a precise geometrical representation of the protein. Analytical approaches, however, often focus on the energetic aspects of folding, including geometrical information only in an average way. Here, we investigate a semi-analytical expression of folding that explicitly includes geometrical effects. We consider a Hamiltonian corresponding to a Gaussian filament with structure-based interactions. The model captures local features of protein folding often averaged over by mean-field theories, for example, loop contact formation and excluded volume. We explore the thermodynamics and folding mechanisms of beta-hairpin and alpha-helical structures as functions of temperature and Q, the fraction of native contacts formed. Excluded volume is shown to be an important component of a protein Hamiltonian, since it both dominates the cooperativity of the folding transition and alters folding mechanisms. Understanding geometrical effects in analytical formulae will help illuminate the consequences of the approximations required for the study of larger proteins. PMID:21721664

On the specta of X-ray bursters: Expansion and contraction stages

NASA Technical Reports Server (NTRS)

Titarchuk, Lev

1994-01-01

The theory of spectral formation during the explosion and contraction stages of X-ray bursters, which include the effects of Computonization and free-free absorption and emission, is described. Analytical expressions are provided for color ratios, and the spectral shape is given as a function of input parameters, elemental abundance, neutron star mass and radius, and Eddington ratio. An Eulerian calculation is used to determine the photospheric evolution accurately during the Eddington luminosity phase. The developed analytical theory for hydrodynamics of the expansion takes into account the dependence of Compton scattering opacity on electron temperature. An analytical expression is derived from the sonic point position and the value of the sonic velcoity. Using this value as a boundary condition at the sonic point, the velocity, density, and temperature profile are calculated throughout the whole photosphere. It is shown that the atmopsphere radiates spectra having a low-energy power-law shape and blackbody-like hard tail. In the expansion stage the spectra depend strongly on the temperature of the helium-burning zone at the neutron star surface. The X-ray photosheric radius increases to approximately 100 km or more, depending on the condition of the nuclear burning on the surface of the neutron star in the course of the expansion.

A series approximation model for optical light transport and output intensity field distribution in large aspect ratio cylindrical scintillation crystals

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

Tobias, Benjamin John

A series approximation has been derived for the transport of optical photons within a cylindrically symmetric light pipe and applied to the task of evaluating both the origin and angular distribution of light reaching the output plane. This analytic expression finds particular utility in first-pass photonic design applications since it may be evaluated at a very modest computational cost and is readily parameterized for relevant design constraints. It has been applied toward quantitative exploration of various scintillation crystal preparations and their impact on both quantum efficiency and noise, reproducing sensible dependencies and providing physical justification for certain gamma ray cameramore » design choices.« less

Continuous approximation for interaction energy of adamantane encapsulated inside carbon nanotubes

NASA Astrophysics Data System (ADS)

Baowan, Duangkamon; Hill, James M.; Bacsa, Wolfgang

2018-02-01

The interaction energy for two adjacent adamantane molecules and that of adamantane molecules encapsulated inside carbon nanotubes are investigated considering only dipole-dipole induced interaction. The Lennard-Jones potential and the continuous approximation are utilised to derive analytical expressions for these interaction energies. The equilibrium distance 3.281 Å between two adamantane molecules is determined. The smallest carbon nanotube radius b0 that can encapsulate the adamantane molecule and the radius of the tube bmax that gives the maximum suction energy, linearly depend on the adamantane radius, are calculated. For larger diameter tubes, the off axis position has been calculated, and equilibrium distance between molecule and tube wall is found to be close to the interlayer spacing in graphene.

Physical models for the normal YORP and diurnal Yarkovsky effects

NASA Astrophysics Data System (ADS)

Golubov, O.; Kravets, Y.; Krugly, Yu. N.; Scheeres, D. J.

2016-06-01

We propose an analytic model for the normal Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) and diurnal Yarkovsky effects experienced by a convex asteroid. Both the YORP torque and the Yarkovsky force are expressed as integrals of a universal function over the surface of an asteroid. Although in general this function can only be calculated numerically from the solution of the heat conductivity equation, approximate solutions can be obtained in quadratures for important limiting cases. We consider three such simplified models: Rubincam's approximation (zero heat conductivity), low thermal inertia limit (including the next order correction and thus valid for small heat conductivity), and high thermal inertia limit (valid for large heat conductivity). All three simplified models are compared with the exact solution.

Estimating the Gibbs energy of hydration from molecular dynamics trajectories obtained by integral equations of the theory of liquids in the RISM approximation

NASA Astrophysics Data System (ADS)

Tikhonov, D. A.; Sobolev, E. V.

2011-04-01

A method of integral equations of the theory of liquids in the reference interaction site model (RISM) approximation is used to estimate the Gibbs energy averaged over equilibrium trajectories computed by molecular mechanics. Peptide oxytocin is selected as the object of interest. The Gibbs energy is calculated using all chemical potential formulas introduced in the RISM approach for the excess chemical potential of solvation and is compared with estimates by the generalized Born model. Some formulas are shown to give the wrong sign of Gibbs energy changes when peptide passes from the gas phase into water environment; the other formulas give overestimated Gibbs energy changes with the right sign. Note that allowance for the repulsive correction in the approximate analytical expressions for the Gibbs energy derived by thermodynamic perturbation theory is not a remedy.

Quantifying the effect of finite spectral bandwidth on extinction coefficient of species in laser absorption spectroscopy

NASA Astrophysics Data System (ADS)

Singh, Manjeet; Singh, Jaswant; Singh, Baljit; Ghanshyam, C.

2016-11-01

The aim of this study is to quantify the finite spectral bandwidth effect on laser absorption spectroscopy for a wide-band laser source. Experimental analysis reveals that the extinction coefficient of an analyte is affected by the bandwidth of the spectral source, which may result in the erroneous conclusions. An approximate mathematical model has been developed for optical intensities having Gaussian line shape, which includes the impact of source's spectral bandwidth in the equation for spectroscopic absorption. This is done by introducing a suitable first order and second order bandwidth approximation in the Beer-Lambert law equation for finite bandwidth case. The derived expressions were validated using spectroscopic analysis with higher SBW on a test sample, Rhodamine B. The concentrations calculated using proposed approximation, were in significant agreement with the true values when compared with those calculated with conventional approach.

Exploring inductive linearization for pharmacokinetic-pharmacodynamic systems of nonlinear ordinary differential equations.

PubMed

Hasegawa, Chihiro; Duffull, Stephen B

2018-02-01

Pharmacokinetic-pharmacodynamic systems are often expressed with nonlinear ordinary differential equations (ODEs). While there are numerous methods to solve such ODEs these methods generally rely on time-stepping solutions (e.g. Runge-Kutta) which need to be matched to the characteristics of the problem at hand. The primary aim of this study was to explore the performance of an inductive approximation which iteratively converts nonlinear ODEs to linear time-varying systems which can then be solved algebraically or numerically. The inductive approximation is applied to three examples, a simple nonlinear pharmacokinetic model with Michaelis-Menten elimination (E1), an integrated glucose-insulin model and an HIV viral load model with recursive feedback systems (E2 and E3, respectively). The secondary aim of this study was to explore the potential advantages of analytically solving linearized ODEs with two examples, again E3 with stiff differential equations and a turnover model of luteinizing hormone with a surge function (E4). The inductive linearization coupled with a matrix exponential solution provided accurate predictions for all examples with comparable solution time to the matched time-stepping solutions for nonlinear ODEs. The time-stepping solutions however did not perform well for E4, particularly when the surge was approximated by a square wave. In circumstances when either a linear ODE is particularly desirable or the uncertainty in matching the integrator to the ODE system is of potential risk, then the inductive approximation method coupled with an analytical integration method would be an appropriate alternative.

Approximate analytical description of the elastic strain field due to an inclusion in a continuous medium with cubic anisotropy

NASA Astrophysics Data System (ADS)

Nenashev, A. V.; Koshkarev, A. A.; Dvurechenskii, A. V.

2018-03-01

We suggest an approach to the analytical calculation of the strain distribution due to an inclusion in elastically anisotropic media for the case of cubic anisotropy. The idea consists in the approximate reduction of the anisotropic problem to a (simpler) isotropic problem. This gives, for typical semiconductors, an improvement in accuracy by an order of magnitude, compared to the isotropic approximation. Our method allows using, in the case of elastically anisotropic media, analytical solutions obtained for isotropic media only, such as analytical formulas for the strain due to polyhedral inclusions. The present work substantially extends the applicability of analytical results, making them more suitable for describing real systems, such as epitaxial quantum dots.

Parameterizing microphysical effects on variances and covariances of moisture and heat content using a multivariate probability density function: a study with CLUBB (tag MVCS)

DOE PAGES

Griffin, Brian M.; Larson, Vincent E.

2016-11-25

Microphysical processes, such as the formation, growth, and evaporation of precipitation, interact with variability and covariances (e.g., fluxes) in moisture and heat content. For instance, evaporation of rain may produce cold pools, which in turn may trigger fresh convection and precipitation. These effects are usually omitted or else crudely parameterized at subgrid scales in weather and climate models.A more formal approach is pursued here, based on predictive, horizontally averaged equations for the variances, covariances, and fluxes of moisture and heat content. These higher-order moment equations contain microphysical source terms. The microphysics terms can be integrated analytically, given a suitably simplemore » warm-rain microphysics scheme and an approximate assumption about the multivariate distribution of cloud-related and precipitation-related variables. Performing the integrations provides exact expressions within an idealized context.A large-eddy simulation (LES) of a shallow precipitating cumulus case is performed here, and it indicates that the microphysical effects on (co)variances and fluxes can be large. In some budgets and altitude ranges, they are dominant terms. The analytic expressions for the integrals are implemented in a single-column, higher-order closure model. Interactive single-column simulations agree qualitatively with the LES. The analytic integrations form a parameterization of microphysical effects in their own right, and they also serve as benchmark solutions that can be compared to non-analytic integration methods.« less

Establishment of gold-quartz standard GQS-1

USGS Publications Warehouse

Millard, Hugh T.; Marinenko, John; McLane, John E.

1969-01-01

A homogeneous gold-quartz standard, GQS-1, was prepared from a heterogeneous gold-bearing quartz by chemical treatment. The concentration of gold in GQS-1 was determined by both instrumental neutron activation analysis and radioisotope dilution analysis to be 2.61?0.10 parts per million. Analysis of 10 samples of the standard by both instrumental neutron activation analysis and radioisotope dilution analysis failed to reveal heterogeneity within the standard. The precision of the analytical methods, expressed as standard error, was approximately 0.1 part per million. The analytical data were also used to estimate the average size of gold particles. The chemical treatment apparently reduced the average diameter of the gold particles by at least an order of magnitude and increased the concentration of gold grains by a factor of at least 4,000.

Quantum Effects at a Proton Relaxation at Low Temperatures

NASA Astrophysics Data System (ADS)

Kalytka, V. A.; Korovkin, M. V.

2016-11-01

Quantum effects during migratory polarization in multi-well crystals (including multi-well silicates and crystalline hydrates) are investigated in a variable electric field at low temperatures by direct quantum-mechanical calculations. Based on analytical solution of the quantum Liouville kinetic equation in the linear approximation for the polarizing field, the non-stationary density matrix is calculated for an ensemble of non-interacting protons moving in the field of one-dimensional multi-well crystal potential relief of rectangular shape. An expression for the complex dielectric constant convenient for a comparison with experiment and calculation of relaxer parameters is derived using the nonequilibrium polarization density matrix. The density matrix apparatus can be used for analytical investigation of the quantum mechanism of spontaneous polarization of a ferroelectric material (KDP and DKDP).

Analytical model for the threshold voltage of III-V nanowire transistors including quantum effects

NASA Astrophysics Data System (ADS)

Marin, E. G.; Ruiz, F. G.; Tienda-Luna, I. M.; Godoy, A.; Gámiz, F.

2014-02-01

In this work we propose an analytical model for the threshold voltage (VT) of III-V cylindrical nanowires, that takes into consideration the two dimensional quantum confinement of the carriers, the Fermi-Dirac statistics, the wave-function penetration into the gate insulator and the non-parabolicity of the conduction band structure. A simple expression for VT is obtained assuming some suitable approximations. The model results are compared to those of a 2D self consistent Schrödinger-Poisson solver, demonstrating a good fit for different III-V materials, insulator thicknesses and nanowire sizes with diameter down to 5 nm. The VT dependence on the confinement effective mass is discussed. The different contributions to VT are analyzed showing significant variations among different III-V materials.

Vapor-liquid equilibrium and equation of state of two-dimensional fluids from a discrete perturbation theory

NASA Astrophysics Data System (ADS)

Trejos, Víctor M.; Santos, Andrés; Gámez, Francisco

2018-05-01

The interest in the description of the properties of fluids of restricted dimensionality is growing for theoretical and practical reasons. In this work, we have firstly developed an analytical expression for the Helmholtz free energy of the two-dimensional square-well fluid in the Barker-Henderson framework. This equation of state is based on an approximate analytical radial distribution function for d-dimensional hard-sphere fluids (1 ≤ d ≤ 3) and is validated against existing and new simulation results. The so-obtained equation of state is implemented in a discrete perturbation theory able to account for general potential shapes. The prototypical Lennard-Jones and Yukawa fluids are tested in its two-dimensional version against available and new simulation data with semiquantitative agreement.

Approximate solutions of acoustic 3D integral equation and their application to seismic modeling and full-waveform inversion

NASA Astrophysics Data System (ADS)

Malovichko, M.; Khokhlov, N.; Yavich, N.; Zhdanov, M.

2017-10-01

Over the recent decades, a number of fast approximate solutions of Lippmann-Schwinger equation, which are more accurate than classic Born and Rytov approximations, were proposed in the field of electromagnetic modeling. Those developments could be naturally extended to acoustic and elastic fields; however, until recently, they were almost unknown in seismology. This paper presents several solutions of this kind applied to acoustic modeling for both lossy and lossless media. We evaluated the numerical merits of those methods and provide an estimation of their numerical complexity. In our numerical realization we use the matrix-free implementation of the corresponding integral operator. We study the accuracy of those approximate solutions and demonstrate, that the quasi-analytical approximation is more accurate, than the Born approximation. Further, we apply the quasi-analytical approximation to the solution of the inverse problem. It is demonstrated that, this approach improves the estimation of the data gradient, comparing to the Born approximation. The developed inversion algorithm is based on the conjugate-gradient type optimization. Numerical model study demonstrates that the quasi-analytical solution significantly reduces computation time of the seismic full-waveform inversion. We also show how the quasi-analytical approximation can be extended to the case of elastic wavefield.

Constitutive modeling of the rheological behavior of platelet suspensions

NASA Astrophysics Data System (ADS)

Sommer, Drew E.

Compression molding of chopped fiber composites is used to manufacture complex 3D geometries with high fiber volume fractions of 50-60% and long, discontinuous fibers and thermoplastic matrices. When prepreg, chopped into platelets, is used as a charge material, the individual platelets remain intact during the molding process and flow relative to one another, as experimental observations show. Heterogeneity of the platelet/resin suspension cannot be considered at the structural scale of molding simulation. Instead, the suspension should be idealized into the homogenized anisotropic and viscous system which obeys the prescribed anisotropic stress-strain rate constitutive relation. The viscosity tensor of the aforementioned constitutive law was analytically evaluated in this work through the representative volume element (RVE) based analysis. An idealized microstructure of platelets was developed to perform such an analysis. The platelets were aligned and arranged in a planar configuration with periodic boundary conditions. Analytic expressions for the effective, anisotropic viscosities were derived by micromechanical analysis for the idealized microstructure of rigid platelets. In this analysis, the load transfer mechanisms and their contribution to the viscosity of the platelet assembly were investigated. The kinematic assumption of linear velocity distributions consistent with the mechanism of shearing rate was adopted. While the platelets were assumed to be rigid, the resin was taken as an incompressible, isotropic fluid which provided for the platelet-to-platelet load transfer. Strain rate and temperature dependence were included by modeling the polymer matrix as a Carreau fluid. Shear strain in the resin was developed due to the relative motion of adjacent platelets. The resin shear strain rate was expressed in terms of the corresponding platelet velocities. Equilibrium of the platelet was used to relate the applied far-field stress to the average strain rate through the viscosity of neat resin and geometric parameters of the RVE constituents. When combined, these parameters defined the effective homogenized viscosities of an anisotropic system equivalent to the platelet/resin suspension. The expressions for the effective viscosities were found to be dependent on the platelet geometry, stack geometry, the platelet volume fraction and the viscosity of neat resin. In this study, the platelet volume fraction was defined as the volume of platelets within the RVE divided by the RVE volume and discriminated from the fiber volume fraction within a platelet. An approach using the "viscous solid analogy'' was developed to leverage structural finite element methods to predict homogenized viscosities of the platelet assembly. A finite element model was constructed to develop a comparison to the analytic expressions for rigid platelets and include the effect of deformation within the platelets. To compare with the analytic expressions, large viscosities were prescribed for the platelet to approximate rigidity. The properties of the deformable platelets were determined by an approach proposed by Pipes and co-workers. The assumption of rigidity was found to be approximate except in the case of elongation along the fiber direction. A laminate analogy was implemented as a homogenization tool to include the effect of orientation on the apparent viscosities of a multi-axial platelet assembly. The aligned platelet suspension was used to predict the `pseudo-ply' properties. Pseudo-laminates, which were assumed to approximate the microstructure, were developed. The effective `pseudo-laminate' viscosities were predicted with classical lamination theory.

Semiclassical evaluation of quantum fidelity

NASA Astrophysics Data System (ADS)

Vanicek, Jiri

2004-03-01

We present a numerically feasible semiclassical method to evaluate quantum fidelity (Loschmidt echo) in a classically chaotic system. It was thought that such evaluation would be intractable, but instead we show that a uniform semiclassical expression not only is tractable but it gives remarkably accurate numerical results for the standard map in both the Fermi-golden-rule and Lyapunov regimes. Because it allows a Monte-Carlo evaluation, this uniform expression is accurate at times where there are 10^70 semiclassical contributions. Remarkably, the method also explicitly contains the ``building blocks'' of analytical theories of recent literature, and thus permits a direct test of approximations made by other authors in these regimes, rather than an a posteriori comparison with numerical results. We explain in more detail the extended validity of the classical perturbation approximation and thus provide a ``defense" of the linear response theory from the famous Van Kampen objection. We point out the potential use of our uniform expression in other areas because it gives a most direct link between the quantum Feynman propagator based on the path integral and the semiclassical Van Vleck propagator based on the sum over classical trajectories. Finally, we test the applicability of our method in integrable and mixed systems.

Electromagnetic scattering by a straight thin wire

NASA Technical Reports Server (NTRS)

Shamansky, Harry T.; Dominek, Allen K.; Peters, Leon, Jr.

1989-01-01

The traveling-wave energy, which multiply diffracts on a straight thin wire, is represented as a sum of terms, each with a distinct physical meaning, that can be individually examined in the time domain. Expressions for each scattering mechanism on a straight thin wire are cast in the form of four basic electromagnetic wave concepts: diffraction, attachment, launch, and reflection. Using the basic mechanisms from P. Ya. Ufimtsev (1962), each of the scattering mechanisms is included into the total scattered field for the straight thin wire. Scattering as a function of angle and frequency is then compared to the moment-method solution. These analytic expressions are then extended to a lossy wire with a simple approximate modification using the propagation velocity on the wire as derived from the Sommerfeld wave on a straight lossy wire. Both the perfectly conducting and lossy wire solutions are compared to moment-method results, and excellent agreement is found. As is common with asymptotic solutions, when the electrical length of wire is smaller than 0.2 lambda the results lose accuracy. The expressions modified to approximate the scattering for the lossy thin wire yield excellent agreement even for lossy wires where the wire radius is on the order of skin depth.

Instability of a planar expansion wave.

PubMed

Velikovich, A L; Zalesak, S T; Metzler, N; Wouchuk, J G

2005-10-01

An expansion wave is produced when an incident shock wave interacts with a surface separating a fluid from a vacuum. Such an interaction starts the feedout process that transfers perturbations from the rippled inner (rear) to the outer (front) surface of a target in inertial confinement fusion. Being essentially a standing sonic wave superimposed on a centered expansion wave, a rippled expansion wave in an ideal gas, like a rippled shock wave, typically produces decaying oscillations of all fluid variables. Its behavior, however, is different at large and small values of the adiabatic exponent gamma. At gamma > 3, the mass modulation amplitude delta(m) in a rippled expansion wave exhibits a power-law growth with time alpha(t)beta, where beta = (gamma - 3)/(gamma - 1). This is the only example of a hydrodynamic instability whose law of growth, dependent on the equation of state, is expressed in a closed analytical form. The growth is shown to be driven by a physical mechanism similar to that of a classical Richtmyer-Meshkov instability. In the opposite extreme gamma - 1 < 1, delta(m) exhibits oscillatory growth, approximately linear with time, until it reaches its peak value approximately (gamma - 1)(-1/2), and then starts to decrease. The mechanism driving the growth is the same as that of Vishniac's instability of a blast wave in a gas with low . Exact analytical expressions for the growth rates are derived for both cases and favorably compared to hydrodynamic simulation results.

Transient nucleation induction time from the birth-death equations

NASA Technical Reports Server (NTRS)

Shneidman, Vitaly A.; Weinberg, Michael C.

1992-01-01

For the set of finite-difference equations of Becker-Doering an exact formula for the induction time, which is expressed in terms of rapidly convergent sums, is presented. The form of the result is particularly amenable for analytical study, and the latter is carried out to obtain approximations of the exact expression in a rigorous manner and to assess its sensitivity to the choice of the nucleation model. The induction time is found to be governed by two main nucleation parameters, the normalized barrier height, and the number of molecules in the critical cluster. The ratio of these two parameters provides an assessment of the importance of discreteness effects. The exact expression is studied in both the continuous and the asymptotic limits. The accuracy of the Zeldovich equation, which is produced in the continuous limit, is discussed for several nucleation models.

Analytical approximation schemes for solving exact renormalization group equations in the local potential approximation

NASA Astrophysics Data System (ADS)

Bervillier, C.; Boisseau, B.; Giacomini, H.

2008-02-01

The relation between the Wilson-Polchinski and the Litim optimized ERGEs in the local potential approximation is studied with high accuracy using two different analytical approaches based on a field expansion: a recently proposed genuine analytical approximation scheme to two-point boundary value problems of ordinary differential equations, and a new one based on approximating the solution by generalized hypergeometric functions. A comparison with the numerical results obtained with the shooting method is made. A similar accuracy is reached in each case. Both two methods appear to be more efficient than the usual field expansions frequently used in the current studies of ERGEs (in particular for the Wilson-Polchinski case in the study of which they fail).

Modeling convection-diffusion-reaction systems for microfluidic molecular communications with surface-based receivers in Internet of Bio-Nano Things

PubMed Central

Akan, Ozgur B.

2018-01-01

We consider a microfluidic molecular communication (MC) system, where the concentration-encoded molecular messages are transported via fluid flow-induced convection and diffusion, and detected by a surface-based MC receiver with ligand receptors placed at the bottom of the microfluidic channel. The overall system is a convection-diffusion-reaction system that can only be solved by numerical methods, e.g., finite element analysis (FEA). However, analytical models are key for the information and communication technology (ICT), as they enable an optimisation framework to develop advanced communication techniques, such as optimum detection methods and reliable transmission schemes. In this direction, we develop an analytical model to approximate the expected time course of bound receptor concentration, i.e., the received signal used to decode the transmitted messages. The model obviates the need for computationally expensive numerical methods by capturing the nonlinearities caused by laminar flow resulting in parabolic velocity profile, and finite number of ligand receptors leading to receiver saturation. The model also captures the effects of reactive surface depletion layer resulting from the mass transport limitations and moving reaction boundary originated from the passage of finite-duration molecular concentration pulse over the receiver surface. Based on the proposed model, we derive closed form analytical expressions that approximate the received pulse width, pulse delay and pulse amplitude, which can be used to optimize the system from an ICT perspective. We evaluate the accuracy of the proposed model by comparing model-based analytical results to the numerical results obtained by solving the exact system model with COMSOL Multiphysics. PMID:29415019

Modeling convection-diffusion-reaction systems for microfluidic molecular communications with surface-based receivers in Internet of Bio-Nano Things.

PubMed

Kuscu, Murat; Akan, Ozgur B

2018-01-01

We consider a microfluidic molecular communication (MC) system, where the concentration-encoded molecular messages are transported via fluid flow-induced convection and diffusion, and detected by a surface-based MC receiver with ligand receptors placed at the bottom of the microfluidic channel. The overall system is a convection-diffusion-reaction system that can only be solved by numerical methods, e.g., finite element analysis (FEA). However, analytical models are key for the information and communication technology (ICT), as they enable an optimisation framework to develop advanced communication techniques, such as optimum detection methods and reliable transmission schemes. In this direction, we develop an analytical model to approximate the expected time course of bound receptor concentration, i.e., the received signal used to decode the transmitted messages. The model obviates the need for computationally expensive numerical methods by capturing the nonlinearities caused by laminar flow resulting in parabolic velocity profile, and finite number of ligand receptors leading to receiver saturation. The model also captures the effects of reactive surface depletion layer resulting from the mass transport limitations and moving reaction boundary originated from the passage of finite-duration molecular concentration pulse over the receiver surface. Based on the proposed model, we derive closed form analytical expressions that approximate the received pulse width, pulse delay and pulse amplitude, which can be used to optimize the system from an ICT perspective. We evaluate the accuracy of the proposed model by comparing model-based analytical results to the numerical results obtained by solving the exact system model with COMSOL Multiphysics.

Analytical Modeling of Triple-Metal Hetero-Dielectric DG SON TFET

NASA Astrophysics Data System (ADS)

Mahajan, Aman; Dash, Dinesh Kumar; Banerjee, Pritha; Sarkar, Subir Kumar

2018-02-01

In this paper, a 2-D analytical model of triple-metal hetero-dielectric DG TFET is presented by combining the concepts of triple material gate engineering and hetero-dielectric engineering. Three metals with different work functions are used as both front- and back gate electrodes to modulate the barrier at source/channel and channel/drain interface. In addition to this, front gate dielectric consists of high-K HfO2 at source end and low-K SiO2 at drain side, whereas back gate dielectric is replaced by air to further improve the ON current of the device. Surface potential and electric field of the proposed device are formulated solving 2-D Poisson's equation and Young's approximation. Based on this electric field expression, tunneling current is obtained by using Kane's model. Several device parameters are varied to examine the behavior of the proposed device. The analytical model is validated with TCAD simulation results for proving the accuracy of our proposed model.

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.

Integrate-and-fire neurons driven by asymmetric dichotomous noise.

PubMed

Droste, Felix; Lindner, Benjamin

2014-12-01

We consider a general integrate-and-fire (IF) neuron driven by asymmetric dichotomous noise. In contrast to the Gaussian white noise usually used in the so-called diffusion approximation, this noise is colored, i.e., it exhibits temporal correlations. We give an analytical expression for the stationary voltage distribution of a neuron receiving such noise and derive recursive relations for the moments of the first passage time density, which allow us to calculate the firing rate and the coefficient of variation of interspike intervals. We study how correlations in the input affect the rate and regularity of firing under variation of the model's parameters for leaky and quadratic IF neurons. Further, we consider the limit of small correlation times and find lowest order corrections to the first passage time moments to be proportional to the square root of the correlation time. We show analytically that to this lowest order, correlations always lead to a decrease in firing rate for a leaky IF neuron. All theoretical expressions are compared to simulations of leaky and quadratic IF neurons.

Self-similar solutions to isothermal shock problems

NASA Astrophysics Data System (ADS)

Deschner, Stephan C.; Illenseer, Tobias F.; Duschl, Wolfgang J.

We investigate exact solutions for isothermal shock problems in different one-dimensional geometries. These solutions are given as analytical expressions if possible, or are computed using standard numerical methods for solving ordinary differential equations. We test the numerical solutions against the analytical expressions to verify the correctness of all numerical algorithms. We use similarity methods to derive a system of ordinary differential equations (ODE) yielding exact solutions for power law density distributions as initial conditions. Further, the system of ODEs accounts for implosion problems (IP) as well as explosion problems (EP) by changing the initial or boundary conditions, respectively. Taking genuinely isothermal approximations into account leads to additional insights of EPs in contrast to earlier models. We neglect a constant initial energy contribution but introduce a parameter to adjust the initial mass distribution of the system. Moreover, we show that due to this parameter a constant initial density is not allowed for isothermal EPs. Reasonable restrictions for this parameter are given. Both, the (genuinely) isothermal implosion as well as the explosion problem are solved for the first time.

The effect of the electric wind on the spatial distribution of chemical species in the positive corona discharge

NASA Astrophysics Data System (ADS)

Yanallah, K.; Pontiga, F.; Bouazza, M. R.; Chen, J. H.

2017-08-01

The electrohydrodynamic air flow generated by a positive corona discharge, and its effect on the spatial distribution of chemical species within a wire-plate corona reactor, have been numerically simulated. The computational model is based on the solutions of the Navier-Stokes equation and the continuity equation of each chemical species generated by the electrical discharge. A simplified analytical expression of the electric force density, which only requires the current density as the input parameter, has been used in the Navier-Stokes equation to obtain the velocity field. For the solution of the continuity equations, a plasma chemistry model that includes the most important reactions between electrons, atoms and molecules in air has been used. Similar to the electric force, the electron density distribution has been approximated by using a semi-analytical expression appropriate for the electrode geometry. The results of the study show that the spatial distribution of chemical species can be very different, and depends on the interplay between the electrohydrodynamic flow, the chemical kinetics of the species and its characteristic lifetime.

Response to ``Comment on `Scalings for radiation from plasma bubbles' '' [Phys. Plasmas 18, 034701 (2011)

NASA Astrophysics Data System (ADS)

Thomas, A. G. R.

2011-03-01

In the preceding Comment, Corde, Stordeur, and Malka claim that the trapping threshold derived in my recent paper is incorrect. Their principal argument is that the elliptical orbits I used are not exact solutions of the equation of motion in the fields of the bubble. The original paper never claimed this—rather I claimed that the use of elliptical orbits was a reasonable approximation, which I based on observations from particle-in-cell simulations. Integration of the equation of motion for analytical expressions for idealized bubble fields (either analytically [I. Kostyukov, E. Nerush, A. Pukhov, and V. Seredov, Phys. Rev. Lett. 103, 175003 (2009)] or numerically [S. Corde, A. Stordeur, and V. Malka, "Comment on `Scalings for radiation from plasma bubbles,' " Phys. Plasmas 18, 034701 (2011)]) produces a trapping threshold wholly inconsistent with experiments and full particle-in-cell (PIC) simulations (e.g., requiring an estimated laser intensity of a0˜30 for ne˜1019 cm-3). The inconsistency in the particle trajectories between PIC and the numeric model used by the comment authors arises due to the fact that the analytical fields are only approximately true for "real" plasma bubbles, and lack certain key features of the field structure. Two possible methods of resolution to this inconsistency are either to find ever more complicated but accurate models for the bubble fields or to find approximate solutions to the equations of motion that capture the essential features of the self-consistent electron trajectories. The latter, heuristic approach used in my recent paper produced a threshold that is better matched to experimental observations. In this reply, I will also revisit the problem and examine the relationship between bubble radius and electron momentum at the point of trapping without reference to a particular trajectory.

An analytical solution to assess the SH seismoelectric response of the vadose zone

NASA Astrophysics Data System (ADS)

Monachesi, L. B.; Zyserman, F. I.; Jouniaux, L.

2018-03-01

We derive an analytical solution of the seismoelectric conversions generated in the vadose zone, when this region is crossed by a pure shear horizontal (SH) wave. Seismoelectric conversions are induced by electrokinetic effects linked to relative motions between fluid and porous media. The considered model assumes a one-dimensional soil constituted by a single layer on top of a half space in contact at the water table, and a shearing force located at the earth's surface as the wave source. The water table is an interface expected to induce a seismoelectric interfacial response (IR). The top layer represents a porous rock which porous space is partially saturated by water and air, while the half-space is completely saturated with water, representing the saturated zone. The analytical expressions for the coseismic fields and the interface responses, both electric and magnetic, are derived by solving Pride's equations with proper boundary conditions. An approximate analytical expression of the solution is also obtained, which is very simple and applicable in a fairly broad set of situations. Hypothetical scenarios are proposed to study and analyse the dependence of the electromagnetic fields on various parameters of the medium. An analysis of the approximate solution is also made together with a comparison to the exact solution. The main result of the present analysis is that the amplitude of the interface response generated at the water table is found to be proportional to the jump in the electric current density, which in turn depends on the saturation contrast, poro-mechanical and electrical properties of the medium and on the amplitude of the solid displacement produced by the source. This result is in agreement with the one numerically obtained by the authors, which has been published in a recent work. We also predict the existence of an interface response located at the surface, and that the electric interface response is several orders of magnitude bigger than the electric coseismic field, whereas it is the opposite using compressional waves as shown by theoretical and experimental results. This fact should encourage the performance of field and laboratory tests to check the viability of SHTE seismoelectrics as a near surface prospecting/monitoring tool.

An analytical solution to assess the SH seismoelectric response of the vadose zone

NASA Astrophysics Data System (ADS)

Monachesi, L. B.; Zyserman, F. I.; Jouniaux, L.

2018-06-01

We derive an analytical solution of the seismoelectric conversions generated in the vadose zone, when this region is crossed by a pure shear horizontal (SH) wave. Seismoelectric conversions are induced by electrokinetic effects linked to relative motions between fluid and porous media. The considered model assumes a 1D soil constituted by a single layer on top of a half-space in contact at the water table, and a shearing force located at the earth's surface as the wave source. The water table is an interface expected to induce a seismoelectric interfacial response (IR). The top layer represents a porous rock in which porous space is partially saturated by water and air, while the half-space is completely saturated with water, representing the saturated zone. The analytical expressions for the coseismic fields and the interface responses, both electric and magnetic, are derived by solving Pride's equations with proper boundary conditions. An approximate analytical expression of the solution is also obtained, which is very simple and applicable in a fairly broad set of situations. Hypothetical scenarios are proposed to study and analyse the dependence of the electromagnetic fields on various parameters of the medium. An analysis of the approximate solution is also made together with a comparison to the exact solution. The main result of the present analysis is that the amplitude of the interface response generated at the water table is found to be proportional to the jump in the electric current density, which in turn depends on the saturation contrast, poro-mechanical and electrical properties of the medium and on the amplitude of the solid displacement produced by the source. This result is in agreement with the one numerically obtained by the authors, which has been published in a recent work. We also predict the existence of an interface response located at the surface, and that the electric interface response is several orders of magnitude bigger than the electric coseismic field, whereas it is the opposite using compressional waves as shown by theoretical and experimental results. This fact should encourage the performance of field and laboratory tests to check the viability of SHTE seismoelectrics as a near surface prospecting/monitoring tool.

H2+, HeH and H2: Approximating potential curves, calculating rovibrational states

NASA Astrophysics Data System (ADS)

Olivares-Pilón, Horacio; Turbiner, Alexander V.

2018-06-01

Analytic consideration of the Bohr-Oppenheimer (BO) potential curves for diatomic molecules is proposed: accurate analytic interpolation for a potential curve consistent with its rovibrational spectra is found. It is shown that in the BO approximation for four lowest electronic states 1 sσg and 2 pσu, 2 pπu and 3 dπg of H2+, the ground state X2Σ+ of HeH and the two lowest states 1 Σg+ and 3 Σu+ of H2, the potential curves can be analytically interpolated in full range of internuclear distances R with not less than 4-5-6 s.d. Approximation based on matching the Laurant-type expansion at small R and a combination of the multipole expansion with one-instanton type contribution at large distances R is given by two-point Padé approximant. The position of minimum, when exists, is predicted within 1% or better. For the molecular ion H2+ in the Lagrange mesh method, the spectra of vibrational, rotational and rovibrational states (ν , L) associated with 1 sσg and 2 pσu, 2 pπu and 3 dπg potential curves are calculated. In general, it coincides with spectra found via numerical solution of the Schrödinger equation (when available) within six s.d. It is shown that 1 sσg curve contains 19 vibrational states (ν , 0) , while 2 pσu curve contains a single one (0 , 0) and 2 pπu state contains 12 vibrational states (ν , 0) . In general, 1 sσg electronic curve contains 420 rovibrational states, which increases up to 423 when we are beyond BO approximation. For the state 2 pσu the total number of rovibrational states (all with ν = 0) is equal to 3, within or beyond Bohr-Oppenheimer approximation. As for the state 2 pπu within the Bohr-Oppenheimer approximation the total number of the rovibrational bound states is equal to 284. The state 3 dπg is repulsive, no rovibrational state is found. It is confirmed in Lagrange mesh formalism the statement that the ground state potential curve of the heteronuclear molecule HeH does not support rovibrational states. Accurate analytical expression for the potential curves of the hydrogen molecule H2 for the states 1Σg+ and 3 Σu+ is presented. The ground state 1 Σg+ contains 15 vibrational states (ν , 0) , ν = 0- 14. In general, this state supports 301 rovibrational states. The potential curve of the state 3Σu+ has a shallow minimum: it does not support any rovibrational state, it is repulsive.

Renormalization-group theory of plasma microturbulence

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

Carati, D.; Chriaa, K.; Balescu, R.

1994-08-01

The dynamical renormalization-group methods are applied to the gyrokinetic equation describing drift-wave turbulence in plasmas. As in both magnetohydrodynamic and neutral turbulence, small-scale fluctuations appear to act as effective dissipative processes on large-scale phenomena. A linear renormalized gyrokinetic equation is derived. No artificial forcing is introduced into the equations and all the renormalized corrections are expressed in terms of the fluctuating electric potential. The link with the quasilinear limit and the direct interaction approximation is investigated. Simple analytical expressions for the anomalous transport coefficients are derived by using the linear renormalized gyrokinetic equation. Examples show that both quasilinear and Bohmmore » scalings can be recovered depending on the spectral amplitude of the electric potential fluctuations.« less

Exact relations between homoclinic and periodic orbit actions in chaotic systems

NASA Astrophysics Data System (ADS)

Li, Jizhou; Tomsovic, Steven

2018-02-01

Homoclinic and unstable periodic orbits in chaotic systems play central roles in various semiclassical sum rules. The interferences between terms are governed by the action functions and Maslov indices. In this article, we identify geometric relations between homoclinic and unstable periodic orbits, and derive exact formulas expressing the periodic orbit classical actions in terms of corresponding homoclinic orbit actions plus certain phase space areas. The exact relations provide a basis for approximations of the periodic orbit actions as action differences between homoclinic orbits with well-estimated errors. This enables an explicit study of relations between periodic orbits, which results in an analytic expression for the action differences between long periodic orbits and their shadowing decomposed orbits in the cycle expansion.

Biological and analytical stability of a peripheral blood gene expression score for obstructive coronary artery disease in the PREDICT and COMPASS studies.

PubMed

Daniels, Susan E; Beineke, Philip; Rhees, Brian; McPherson, John A; Kraus, William E; Thomas, Gregory S; Rosenberg, Steven

2014-10-01

A gene expression score (GES) for obstructive coronary artery disease (CAD) has been validated in two multicenter studies. Receiver-operating characteristics (ROC) analysis of the GES on an expanded Personalized Risk Evaluation and Diagnosis in the Coronary Tree (PREDICT) cohort (NCT no. 00500617) with CAD defined by quantitative coronary angiography (QCA) or clinical reads yielded similar performance (area under the curve (AUC)=0.70, N=1,502) to the original validation cohort (AUC=0.70, N=526). Analysis of 138 non-Caucasian and 1,364 Caucasian patients showed very similar performance (AUCs=0.72 vs. 0.70). To assess analytic stability, stored samples of the original validation cohort (N=526) was re-tested after 5 years, and the mean score changed from 20.3 to 19.8 after 5 years (N=501, 95 %). To assess patient scores over time, GES was determined on samples from 173 Coronary Obstruction Detection by Molecular Personalized Gene Expression (COMPASS) study (NCT no. 01117506) patients at approximately 1 year post-enrollment. Mean scores increased slightly from 15.9 to 17.3, corresponding to a 2.5 % increase in obstructive CAD likelihood. Changes in cardiovascular medications did not show a significant change in GES.

An approximate analytical solution for interlaminar stresses in angle-ply laminates

NASA Technical Reports Server (NTRS)

Rose, Cheryl A.; Herakovich, Carl T.

1991-01-01

An improved approximate analytical solution for interlaminar stresses in finite width, symmetric, angle-ply laminated coupons subjected to axial loading is presented. The solution is based upon statically admissible stress fields which take into consideration local property mismatch effects and global equilibrium requirements. Unknown constants in the admissible stress states are determined through minimization of the complementary energy. Typical results are presented for through-the-thickness and interlaminar stress distributions for angle-ply laminates. It is shown that the results represent an improved approximate analytical solution for interlaminar stresses.

Analytic expressions for ULF wave radiation belt radial diffusion coefficients

PubMed Central

Ozeke, Louis G; Mann, Ian R; Murphy, Kyle R; Jonathan Rae, I; Milling, David K

2014-01-01

We present analytic expressions for ULF wave-derived radiation belt radial diffusion coefficients, as a function of L and Kp, which can easily be incorporated into global radiation belt transport models. The diffusion coefficients are derived from statistical representations of ULF wave power, electric field power mapped from ground magnetometer data, and compressional magnetic field power from in situ measurements. We show that the overall electric and magnetic diffusion coefficients are to a good approximation both independent of energy. We present example 1-D radial diffusion results from simulations driven by CRRES-observed time-dependent energy spectra at the outer boundary, under the action of radial diffusion driven by the new ULF wave radial diffusion coefficients and with empirical chorus wave loss terms (as a function of energy, Kp and L). There is excellent agreement between the differential flux produced by the 1-D, Kp-driven, radial diffusion model and CRRES observations of differential electron flux at 0.976 MeV—even though the model does not include the effects of local internal acceleration sources. Our results highlight not only the importance of correct specification of radial diffusion coefficients for developing accurate models but also show significant promise for belt specification based on relatively simple models driven by solar wind parameters such as solar wind speed or geomagnetic indices such as Kp. Key Points Analytic expressions for the radial diffusion coefficients are presented The coefficients do not dependent on energy or wave m value The electric field diffusion coefficient dominates over the magnetic PMID:26167440

Development of a defect stream function, law of the wall/wake method for compressible turbulent boundary layers. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Wahls, Richard A.

1990-01-01

The method presented is designed to improve the accuracy and computational efficiency of existing numerical methods for the solution of flows with compressible turbulent boundary layers. A compressible defect stream function formulation of the governing equations assuming an arbitrary turbulence model is derived. This formulation is advantageous because it has a constrained zero-order approximation with respect to the wall shear stress and the tangential momentum equation has a first integral. Previous problems with this type of formulation near the wall are eliminated by using empirically based analytic expressions to define the flow near the wall. The van Driest law of the wall for velocity and the modified Crocco temperature-velocity relationship are used. The associated compressible law of the wake is determined and it extends the valid range of the analytical expressions beyond the logarithmic region of the boundary layer. The need for an inner-region eddy viscosity model is completely avoided. The near-wall analytic expressions are patched to numerically computed outer region solutions at a point determined during the computation. A new boundary condition on the normal derivative of the tangential velocity at the surface is presented; this condition replaces the no-slip condition and enables numerical integration to the surface with a relatively coarse grid using only an outer region turbulence model. The method was evaluated for incompressible and compressible equilibrium flows and was implemented into an existing Navier-Stokes code using the assumption of local equilibrium flow with respect to the patching. The method has proven to be accurate and efficient.

Imploding spherical and cylindrical shocks

NASA Astrophysics Data System (ADS)

Yousaf, M.

1986-03-01

In this paper it is shown that the value of the similarity exponent α derived analytically by Fujimoto and Mishkin [J. Fluid Mech. 89, 61 (1978); Phys. Fluids 21, 1933 (1978)] is exactly the same as that found by Stanyukovich [Unsteady Motion of Continuous Media, (Academic, New York, 1960)]. Since the result found by Stanyukovich is an approximation to α, Fujimoto and Mishkin's claim to have an exact expression of α is false. The two methods are outlined and Stanyukovich's result is simplified to show its equivalence to the work of Fujimoto and Mishkin.

Elastic model for crimped collagen fibrils

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Doehring, Todd C.

2005-01-01

A physiologic constitutive expression is presented in algorithmic format for the nonlinear elastic response of wavy collagen fibrils found in soft connective tissues. The model is based on the observation that crimped fibrils in a fascicle have a three-dimensional structure at the micron scale that we approximate as a helical spring. The symmetry of this wave form allows the force/displacement relationship derived from Castigliano's theorem to be solved in closed form: all integrals become analytic. Model predictions are in good agreement with experimental observations for mitral-valve chordae tendinece.

On the phenomenology of extended Brans-Dicke gravity

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

Lima, Nelson A.; Ferreira, Pedro G., E-mail: ndal@roe.ac.uk, E-mail: p.ferreira1@physics.ox.ac.uk

We introduce a designer approach for extended Brans-Dicke gravity that allows us to obtain the evolution of the scalar field by fixing the Hubble parameter to that of a w CDM model. We obtain analytical approximations for ϕ as a function of the scale factor and use these to build expressions for the effective Newton's constant at the background and at the linear level and the slip between the perturbed Newtonian potentials. By doing so, we are able to explore their dependence on the fundamental parameters of the theory.

Geometry of Thin Nematic Elastomer Sheets

NASA Astrophysics Data System (ADS)

Aharoni, Hillel; Sharon, Eran; Kupferman, Raz

A thin sheet of nematic elastomer attains 3D configurations depending on the nematic director field upon heating. In this talk we describe the intrinsic geometry of such a sheet, and derive an expression for the metric induced by general smooth nematic director fields. Furthermore, we investigate the reverse problem of constructing a director field that induces a specified 2D geometry. We provide an explicit analytical recipe for constructing any surface of revolution using this method. We demonstrate how the design of an arbitrary 2D geometry is accessible using approximate numerical methods.

A continued fraction resummation form of bath relaxation effect in the spin-boson model

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

Gong, Zhihao; Tang, Zhoufei; Wu, Jianlan, E-mail: jianlanwu@zju.edu.cn

2015-02-28

In the spin-boson model, a continued fraction form is proposed to systematically resum high-order quantum kinetic expansion (QKE) rate kernels, accounting for the bath relaxation effect beyond the second-order perturbation. In particular, the analytical expression of the sixth-order QKE rate kernel is derived for resummation. With higher-order correction terms systematically extracted from higher-order rate kernels, the resummed quantum kinetic expansion approach in the continued fraction form extends the Pade approximation and can fully recover the exact quantum dynamics as the expansion order increases.

Oxygen concentration dependence of silicon oxide dynamical properties

NASA Astrophysics Data System (ADS)

Yajima, Yuji; Shiraishi, Kenji; Endoh, Tetsuo; Kageshima, Hiroyuki

2018-06-01

To understand oxidation in three-dimensional silicon, dynamic characteristics of a SiO x system with various stoichiometries were investigated. The calculated results show that the self-diffusion coefficient increases as oxygen density decreases, and the increase is large when the temperature is low. It also shows that the self-diffusion coefficient saturates, when the number of removed oxygen atoms is sufficiently large. Then, approximate analytical equations are derived from the calculated results, and the previously reported expression is confirmed in the extremely low-SiO-density range.

Numerical evaluation of electromagnetic fields due to dipole antennas in the presence of stratified media

NASA Technical Reports Server (NTRS)

Tsang, L.; Brown, R.; Kong, J. A.; Simmons, G.

1974-01-01

Two numerical methods are used to evaluate the integrals that express the em fields due to dipole antennas radiating in the presence of a stratified medium. The first method is a direct integration by means of Simpson's rule. The second method is indirect and approximates the kernel of the integral by means of the fast Fourier transform. In contrast to previous analytical methods that applied only to two-layer cases the numerical methods can be used for any arbitrary number of layers with general properties.

Analytical approximate solutions for a general class of nonlinear delay differential equations.

PubMed

Căruntu, Bogdan; Bota, Constantin

2014-01-01

We use the polynomial least squares method (PLSM), which allows us to compute analytical approximate polynomial solutions for a very general class of strongly nonlinear delay differential equations. The method is tested by computing approximate solutions for several applications including the pantograph equations and a nonlinear time-delay model from biology. The accuracy of the method is illustrated by a comparison with approximate solutions previously computed using other methods.

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.

Induced Eddy Currents in Simple Conductive Geometries: Mathematical Formalism Describes the Excitation of Electrical Eddy Currents in a Time-Varying Magnetic Field

DOE PAGES

Nagel, James R.

2017-12-22

In this paper, a complete mathematical formalism is introduced to describe the excitation of electrical eddy currents due to a time-varying magnetic field. The process works by applying a quasistatic approximation to Ampere's law and then segregating the magnetic field into impressed and induced terms. The result is a nonhomogeneous vector Helmholtz equation that can be analytically solved for many practical geometries. Four demonstration cases are then solved under a constant excitation field over all space—an infinite slab in one dimension, a longitudinal cylinder in two dimensions, a transverse cylinder in two dimensions, and a sphere in three dimensions. Numericalmore » simulations are also performed in parallel with analytic computations, all of which verify the accuracy of the derived expressions.« less

Induced Eddy Currents in Simple Conductive Geometries: Mathematical Formalism Describes the Excitation of Electrical Eddy Currents in a Time-Varying Magnetic Field

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

Nagel, James R.

In this paper, a complete mathematical formalism is introduced to describe the excitation of electrical eddy currents due to a time-varying magnetic field. The process works by applying a quasistatic approximation to Ampere's law and then segregating the magnetic field into impressed and induced terms. The result is a nonhomogeneous vector Helmholtz equation that can be analytically solved for many practical geometries. Four demonstration cases are then solved under a constant excitation field over all space—an infinite slab in one dimension, a longitudinal cylinder in two dimensions, a transverse cylinder in two dimensions, and a sphere in three dimensions. Numericalmore » simulations are also performed in parallel with analytic computations, all of which verify the accuracy of the derived expressions.« less

Multipolar electromagnetic fields around neutron stars: general-relativistic vacuum solutions

NASA Astrophysics Data System (ADS)

Pétri, J.

2017-12-01

Magnetic fields inside and around neutron stars are at the heart of pulsar magnetospheric activity. Strong magnetic fields are responsible for quantum effects, an essential ingredient to produce leptonic pairs and the subsequent broad-band radiation. The variety of electromagnetic field topologies could lead to the observed diversity of neutron star classes. Thus, it is important to include multipolar components to a presumably dominant dipolar magnetic field. Exact analytical solutions for these multipoles in Newtonian gravity have been computed in recent literature. However, flat space-time is not adequate to describe physics in the immediate surroundings of neutron stars. We generalize the multipole expressions to the strong gravity regime by using a slowly rotating metric approximation such as the one expected around neutron stars. Approximate formulae for the electromagnetic field including frame dragging are computed from which we estimate the Poynting flux and the braking index. Corrections to leading order in compactness and spin parameter are presented. As far as spin-down luminosity is concerned, it is shown that frame dragging remains irrelevant. For high-order multipoles starting from the quadrupole, the electric part can radiate more efficiently than the magnetic part. Both analytical and numerical tools are employed.

Torsion of a Cosserat elastic bar with square cross section: theory and experiment

NASA Astrophysics Data System (ADS)

Drugan, W. J.; Lakes, R. S.

2018-04-01

An approximate analytical solution for the displacement and microrotation vector fields is derived for pure torsion of a prismatic bar with square cross section comprised of homogeneous, isotropic linear Cosserat elastic material. This is accomplished by analytical simplification coupled with use of the principle of minimum potential energy together with polynomial representations for the desired field components. Explicit approximate expressions are derived for cross section warp and for applied torque versus angle of twist of the bar. These show that torsional rigidity exceeds the classical elasticity value, the difference being larger for slender bars, and that cross section warp is less than the classical amount. Experimental measurements on two sets of 3D printed square cross section polymeric bars, each set having a different microstructure and four different cross section sizes, revealed size effects not captured by classical elasticity but consistent with the present analysis for physically sensible values of the Cosserat moduli. The warp can allow inference of Cosserat elastic constants independently of any sensitivity the material may have to dilatation gradients; warp also facilitates inference of Cosserat constants that are difficult to obtain via size effects.

Perturbations of the seismic reflectivity of a fluid-saturated depth-dependent poroelastic medium.

PubMed

de Barros, Louis; Dietrich, Michel

2008-03-01

Analytical formulas are derived to compute the first-order effects produced by plane inhomogeneities on the point source seismic response of a fluid-filled stratified porous medium. The derivation is achieved by a perturbation analysis of the poroelastic wave equations in the plane-wave domain using the Born approximation. This approach yields the Frechet derivatives of the P-SV- and SH-wave responses in terms of the Green's functions of the unperturbed medium. The accuracy and stability of the derived operators are checked by comparing, in the time-distance domain, differential seismograms computed from these analytical expressions with complete solutions obtained by introducing discrete perturbations into the model properties. For vertical and horizontal point forces, it is found that the Frechet derivative approach is remarkably accurate for small and localized perturbations of the medium properties which are consistent with the Born approximation requirements. Furthermore, the first-order formulation appears to be stable at all source-receiver offsets. The porosity, consolidation parameter, solid density, and mineral shear modulus emerge as the most sensitive parameters in forward and inverse modeling problems. Finally, the amplitude-versus-angle response of a thin layer shows strong coupling effects between several model parameters.

Analytical Model for Gyro-Phase Drift Arising from Abrupt Inhomogeneity

NASA Technical Reports Server (NTRS)

Walker, Jeffrey J.; Koepke, M. E.; Zimmerman, M. I.; Farrell, W. M.; Demidov, V. I.

2013-01-01

If a magnetized-orbit-charged grain encounters any abrupt inhomogeneity in plasma conditions during a gyro-orbit, such that the resulting in-situ equilibrium charge is significantly different between these regions (q(sub1)/q(sub 2) approximately 2, where q(sub 1) is the in-situ equilibrium charge on one side of the inhomogeneity, q(sub 2) is the in-situ equilibrium charge on the other side, and q(sub1) less than q(sub 2) less than 0), then the capacitive effects of charging and discharging of the dust grain can result in a modification to the orbit-averaged grain trajectory, i.e. gyro-phase drift. The special case of q(sub 1)/q(sub 2) is notioned for the purpose of illustrating the utility of the method. An analytical expression is derived for the grain velocity, assuming a capacitor approximation to the OML charging model. For cases in which a strong electric field suddenly appears in the wake or at the space-plasma-to-crater interface from solar wind and/or ultraviolet illumination and in which a magnetic field permeates an asteroid, comet, or moon, this model could contribute to the interpretation of the distribution of fields and particles.

An Operator Method for Field Moments from the Extended Parabolic Wave Equation and Analytical Solutions of the First and Second Moments for Atmospheric Electromagnetic Wave Propagation

NASA Technical Reports Server (NTRS)

Manning, Robert M.

2004-01-01

The extended wide-angle parabolic wave equation applied to electromagnetic wave propagation in random media is considered. A general operator equation is derived which gives the statistical moments of an electric field of a propagating wave. This expression is used to obtain the first and second order moments of the wave field and solutions are found that transcend those which incorporate the full paraxial approximation at the outset. Although these equations can be applied to any propagation scenario that satisfies the conditions of application of the extended parabolic wave equation, the example of propagation through atmospheric turbulence is used. It is shown that in the case of atmospheric wave propagation and under the Markov approximation (i.e., the delta-correlation of the fluctuations in the direction of propagation), the usual parabolic equation in the paraxial approximation is accurate even at millimeter wavelengths. The comprehensive operator solution also allows one to obtain expressions for the longitudinal (generalized) second order moment. This is also considered and the solution for the atmospheric case is obtained and discussed. The methodology developed here can be applied to any qualifying situation involving random propagation through turbid or plasma environments that can be represented by a spectral density of permittivity fluctuations.

An iterative analytical technique for the design of interplanetary direct transfer trajectories including perturbations

NASA Astrophysics Data System (ADS)

Parvathi, S. P.; Ramanan, R. V.

2018-06-01

An iterative analytical trajectory design technique that includes perturbations in the departure phase of the interplanetary orbiter missions is proposed. The perturbations such as non-spherical gravity of Earth and the third body perturbations due to Sun and Moon are included in the analytical design process. In the design process, first the design is obtained using the iterative patched conic technique without including the perturbations and then modified to include the perturbations. The modification is based on, (i) backward analytical propagation of the state vector obtained from the iterative patched conic technique at the sphere of influence by including the perturbations, and (ii) quantification of deviations in the orbital elements at periapsis of the departure hyperbolic orbit. The orbital elements at the sphere of influence are changed to nullify the deviations at the periapsis. The analytical backward propagation is carried out using the linear approximation technique. The new analytical design technique, named as biased iterative patched conic technique, does not depend upon numerical integration and all computations are carried out using closed form expressions. The improved design is very close to the numerical design. The design analysis using the proposed technique provides a realistic insight into the mission aspects. Also, the proposed design is an excellent initial guess for numerical refinement and helps arrive at the four distinct design options for a given opportunity.

AN ANALYTIC RADIATIVE-CONVECTIVE MODEL FOR PLANETARY ATMOSPHERES

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

Robinson, Tyler D.; Catling, David C., E-mail: robinson@astro.washington.edu

2012-09-20

We present an analytic one-dimensional radiative-convective model of the thermal structure of planetary atmospheres. Our model assumes that thermal radiative transfer is gray and can be represented by the two-stream approximation. Model atmospheres are assumed to be in hydrostatic equilibrium, with a power-law scaling between the atmospheric pressure and the gray thermal optical depth. The convective portions of our models are taken to follow adiabats that account for condensation of volatiles through a scaling parameter to the dry adiabat. By combining these assumptions, we produce simple, analytic expressions that allow calculations of the atmospheric-pressure-temperature profile, as well as expressions formore » the profiles of thermal radiative flux and convective flux. We explore the general behaviors of our model. These investigations encompass (1) worlds where atmospheric attenuation of sunlight is weak, which we show tend to have relatively high radiative-convective boundaries; (2) worlds with some attenuation of sunlight throughout the atmosphere, which we show can produce either shallow or deep radiative-convective boundaries, depending on the strength of sunlight attenuation; and (3) strongly irradiated giant planets (including hot Jupiters), where we explore the conditions under which these worlds acquire detached convective regions in their mid-tropospheres. Finally, we validate our model and demonstrate its utility through comparisons to the average observed thermal structure of Venus, Jupiter, and Titan, and by comparing computed flux profiles to more complex models.« less

Approximate analytic solutions to 3D unconfined groundwater flow within regional 2D models

NASA Astrophysics Data System (ADS)

Luther, K.; Haitjema, H. M.

2000-04-01

We present methods for finding approximate analytic solutions to three-dimensional (3D) unconfined steady state groundwater flow near partially penetrating and horizontal wells, and for combining those solutions with regional two-dimensional (2D) models. The 3D solutions use distributed singularities (analytic elements) to enforce boundary conditions on the phreatic surface and seepage faces at vertical wells, and to maintain fixed-head boundary conditions, obtained from the 2D model, at the perimeter of the 3D model. The approximate 3D solutions are analytic (continuous and differentiable) everywhere, including on the phreatic surface itself. While continuity of flow is satisfied exactly in the infinite 3D flow domain, water balance errors can occur across the phreatic surface.

On the coefficients of integrated expansions and integrals of ultraspherical polynomials and their applications for solving differential equations

NASA Astrophysics Data System (ADS)

Doha, E. H.

2002-02-01

An analytical formula expressing the ultraspherical coefficients of an expansion for an infinitely differentiable function that has been integrated an arbitrary number of times in terms of the coefficients of the original expansion of the function is stated in a more compact form and proved in a simpler way than the formula suggested by Phillips and Karageorghis (27 (1990) 823). A new formula expressing explicitly the integrals of ultraspherical polynomials of any degree that has been integrated an arbitrary number of times of ultraspherical polynomials is given. The tensor product of ultraspherical polynomials is used to approximate a function of more than one variable. Formulae expressing the coefficients of differentiated expansions of double and triple ultraspherical polynomials in terms of the original expansion are stated and proved. Some applications of how to use ultraspherical polynomials for solving ordinary and partial differential equations are described.

A comparison of finite element and analytic models of acoustic scattering from rough poroelastic interfaces.

PubMed

Bonomo, Anthony L; Isakson, Marcia J; Chotiros, Nicholas P

2015-04-01

The finite element method is used to model acoustic scattering from rough poroelastic surfaces. Both monostatic and bistatic scattering strengths are calculated and compared with three analytic models: Perturbation theory, the Kirchhoff approximation, and the small-slope approximation. It is found that the small-slope approximation is in very close agreement with the finite element results for all cases studied and that perturbation theory and the Kirchhoff approximation can be considered valid in those instances where their predictions match those given by the small-slope approximation.

Flow over Canopies with Complex Morphologies

NASA Astrophysics Data System (ADS)

Rubol, S.; Ling, B.; Battiato, I.

2017-12-01

Quantifying and predicting how submerged vegetation affects the velocity profile of riverine systems is crucial in ecohydraulics to properly assess the water quality and ecological functions or rivers. The state of the art includes a plethora of models to study the flow and transport over submerged canopies. However, most of them are validated against data collected in flume experiments with rigid cylinders. With the objective of investigating the capability of a simple analytical solution for vegetated flow to reproduce and predict the velocity profile of complex shaped flexible canopies, we use the flow model proposed by Battiato and Rubol [WRR 2013] as the analytical approximation of the mean velocity profile above and within the canopy layer. This model has the advantages (i) to threat the canopy layer as a porous medium, whose geometrical properties are associated with macroscopic effective permeability and (ii) to use input parameters that can be estimated by remote sensing techniques, such us the heights of the water level and the canopy. The analytical expressions for the average velocity profile and the discharge are tested against data collected across a wide range of canopy morphologies commonly encountered in riverine systems, such as grasses, woody vegetation and bushes. Results indicate good agreement between the analytical expressions and the data for both simple and complex plant geometry shapes. The rescaled low submergence velocities in the canopy layer followed the same scaling found in arrays of rigid cylinders. In addition, for the dataset analyzed, the Darcy friction factor scaled with the inverse of the bulk Reynolds number multiplied by the ratio of the fluid to turbulent viscosity.

Semi-Analytic Reconstruction of Flux in Finite Volume Formulations

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2006-01-01

Semi-analytic reconstruction uses the analytic solution to a second-order, steady, ordinary differential equation (ODE) to simultaneously evaluate the convective and diffusive flux at all interfaces of a finite volume formulation. The second-order ODE is itself a linearized approximation to the governing first- and second- order partial differential equation conservation laws. Thus, semi-analytic reconstruction defines a family of formulations for finite volume interface fluxes using analytic solutions to approximating equations. Limiters are not applied in a conventional sense; rather, diffusivity is adjusted in the vicinity of changes in sign of eigenvalues in order to achieve a sufficiently small cell Reynolds number in the analytic formulation across critical points. Several approaches for application of semi-analytic reconstruction for the solution of one-dimensional scalar equations are introduced. Results are compared with exact analytic solutions to Burger s Equation as well as a conventional, upwind discretization using Roe s method. One approach, the end-point wave speed (EPWS) approximation, is further developed for more complex applications. One-dimensional vector equations are tested on a quasi one-dimensional nozzle application. The EPWS algorithm has a more compact difference stencil than Roe s algorithm but reconstruction time is approximately a factor of four larger than for Roe. Though both are second-order accurate schemes, Roe s method approaches a grid converged solution with fewer grid points. Reconstruction of flux in the context of multi-dimensional, vector conservation laws including effects of thermochemical nonequilibrium in the Navier-Stokes equations is developed.

General properties and analytical approximations of photorefractive solitons

NASA Astrophysics Data System (ADS)

Geisler, A.; Homann, F.; Schmidt, H.-J.

2004-08-01

We investigate general properties of spatial 1-dimensional bright photorefractive solitons and discuss various analytical approximations for the soliton profile and the half width, both depending on an intensity parameter r. The case of dark solitons is also briefly addressed.

A 2D Gaussian-Beam-Based Method for Modeling the Dichroic Surfaces of Quasi-Optical Systems

NASA Astrophysics Data System (ADS)

Elis, Kevin; Chabory, Alexandre; Sokoloff, Jérôme; Bolioli, Sylvain

2016-08-01

In this article, we propose an approach in the spectral domain to treat the interaction of a field with a dichroic surface in two dimensions. For a Gaussian beam illumination of the surface, the reflected and transmitted fields are approximated by one reflected and one transmitted Gaussian beams. Their characteristics are determined by means of a matching in the spectral domain, which requires a second-order approximation of the dichroic surface response when excited by plane waves. This approximation is of the same order as the one used in Gaussian beam shooting algorithm to model curved interfaces associated with lenses, reflector, etc. The method uses general analytical formulations for the GBs that depend either on a paraxial or far-field approximation. Numerical experiments are led to test the efficiency of the method in terms of accuracy and computation time. They include a parametric study and a case for which the illumination is provided by a horn antenna. For the latter, the incident field is firstly expressed as a sum of Gaussian beams by means of Gabor frames.

Resolvent-based modeling of passive scalar dynamics in wall-bounded turbulence

NASA Astrophysics Data System (ADS)

Dawson, Scott; Saxton-Fox, Theresa; McKeon, Beverley

2017-11-01

The resolvent formulation of the Navier-Stokes equations expresses the system state as the output of a linear (resolvent) operator acting upon a nonlinear forcing. Previous studies have demonstrated that a low-rank approximation of this linear operator predicts many known features of incompressible wall-bounded turbulence. In this work, this resolvent model for wall-bounded turbulence is extended to include a passive scalar field. This formulation allows for a number of additional simplifications that reduce model complexity. Firstly, it is shown that the effect of changing scalar diffusivity can be approximated through a transformation of spatial wavenumbers and temporal frequencies. Secondly, passive scalar dynamics may be studied through the low-rank approximation of a passive scalar resolvent operator, which is decoupled from velocity response modes. Thirdly, this passive scalar resolvent operator is amenable to approximation by semi-analytic methods. We investigate the extent to which this resulting hierarchy of models can describe and predict passive scalar dynamics and statistics in wall-bounded turbulence. The support of AFOSR under Grant Numbers FA9550-16-1-0232 and FA9550-16-1-0361 is gratefully acknowledged.

NCBI GEO: mining millions of expression profiles--database and tools.

PubMed

Barrett, Tanya; Suzek, Tugba O; Troup, Dennis B; Wilhite, Stephen E; Ngau, Wing-Chi; Ledoux, Pierre; Rudnev, Dmitry; Lash, Alex E; Fujibuchi, Wataru; Edgar, Ron

2005-01-01

The Gene Expression Omnibus (GEO) at the National Center for Biotechnology Information (NCBI) is the largest fully public repository for high-throughput molecular abundance data, primarily gene expression data. The database has a flexible and open design that allows the submission, storage and retrieval of many data types. These data include microarray-based experiments measuring the abundance of mRNA, genomic DNA and protein molecules, as well as non-array-based technologies such as serial analysis of gene expression (SAGE) and mass spectrometry proteomic technology. GEO currently holds over 30,000 submissions representing approximately half a billion individual molecular abundance measurements, for over 100 organisms. Here, we describe recent database developments that facilitate effective mining and visualization of these data. Features are provided to examine data from both experiment- and gene-centric perspectives using user-friendly Web-based interfaces accessible to those without computational or microarray-related analytical expertise. The GEO database is publicly accessible through the World Wide Web at http://www.ncbi.nlm.nih.gov/geo.

Variational Gaussian approximation for Poisson data

NASA Astrophysics Data System (ADS)

Arridge, Simon R.; Ito, Kazufumi; Jin, Bangti; Zhang, Chen

2018-02-01

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.

3D controlled electrorotation of conducting tri-axial ellipsoidal nanoparticles

NASA Astrophysics Data System (ADS)

Weis Goldstein, Ben; Miloh, Touvia

2017-05-01

We present a theoretical study of 3D electrorotation of ideally polarizable (metallic) nano∖micro-orthotropic particles that are freely suspended in an unbounded monovalent symmetric electrolyte. The metallic tri-axial ellipsoidal particle is subjected to three independent uniform AC electric fields acting along the three principal axes of the particle. The analysis of the electrokinetic problem is carried under the Poisson-Nernst-Planck approximation and the standard "weak" field assumption. For simplicity, we consider the electric double layer as thin and the Dukhin number to be small. Both nonlinear phenomena of dielectrophoresis induced by the dipole-moment within the particle and the induced-charge electrophoresis caused by the Coulombic force density within the Debye layer in the solute surrounding the conducting particle are analytically analyzed by linearization, constructing approximate expressions for the total dipolophoresis angular particle motion for various geometries. The analytical expressions thus obtained are valid for an arbitrary tri-axial orthotropic (exhibiting three planes of symmetry) particle, excited by an arbitrary ambient three-dimensional AC electric field of constant amplitude. The present study is general in the sense that by choosing different geometric parameters of the ellipsoidal particle, the corresponding nonlinear electrostatic problem governed by the Robin (mixed-type) boundary condition can be reduced to common nano-shapes including spheres, slender rods (needles), prolate and oblate spheroids, as well as flat disks. Furthermore, by controlling the parameters (amplitudes and phases) of the forcing electric field, one can reduce the present general 3D electrokinetic model to the familiar planar electro-rotation (ROT) and electro-orientation (EOR) cases.

Optimal CCD readout by digital correlated double sampling

NASA Astrophysics Data System (ADS)

Alessandri, C.; Abusleme, A.; Guzman, D.; Passalacqua, I.; Alvarez-Fontecilla, E.; Guarini, M.

2016-01-01

Digital correlated double sampling (DCDS), a readout technique for charge-coupled devices (CCD), is gaining popularity in astronomical applications. By using an oversampling ADC and a digital filter, a DCDS system can achieve a better performance than traditional analogue readout techniques at the expense of a more complex system analysis. Several attempts to analyse and optimize a DCDS system have been reported, but most of the work presented in the literature has been experimental. Some approximate analytical tools have been presented for independent parameters of the system, but the overall performance and trade-offs have not been yet modelled. Furthermore, there is disagreement among experimental results that cannot be explained by the analytical tools available. In this work, a theoretical analysis of a generic DCDS readout system is presented, including key aspects such as the signal conditioning stage, the ADC resolution, the sampling frequency and the digital filter implementation. By using a time-domain noise model, the effect of the digital filter is properly modelled as a discrete-time process, thus avoiding the imprecision of continuous-time approximations that have been used so far. As a result, an accurate, closed-form expression for the signal-to-noise ratio at the output of the readout system is reached. This expression can be easily optimized in order to meet a set of specifications for a given CCD, thus providing a systematic design methodology for an optimal readout system. Simulated results are presented to validate the theory, obtained with both time- and frequency-domain noise generation models for completeness.

An Approximate Solution to the Equation of Motion for Large-Angle Oscillations of the Simple Pendulum with Initial Velocity

ERIC Educational Resources Information Center

Johannessen, Kim

2010-01-01

An analytic approximation of the solution to the differential equation describing the oscillations of a simple pendulum at large angles and with initial velocity is discussed. In the derivation, a sinusoidal approximation has been applied, and an analytic formula for the large-angle period of the simple pendulum is obtained, which also includes…

Ballistic-diffusive approximation for the thermal dynamics of metallic nanoparticles in nanocomposite materials

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

Shirdel-Havar, A. H., E-mail: Amir.hushang.shirdel@gmail.com; Masoudian Saadabad, R.

2015-03-21

Based on ballistic-diffusive approximation, a method is presented to model heat transfer in nanocomposites containing metal nanoparticles. This method provides analytical expression for the temperature dynamics of metallic nanoparticles embedded in a dielectric medium. In this study, nanoparticles are considered as spherical shells, so that Boltzmann equation is solved using ballistic-diffusive approximation to calculate the electron and lattice thermal dynamics in gold nanoparticles, while thermal exchange between the particles is taken into account. The model was used to investigate the influence of particle size and metal concentration of the medium on the electron and lattice thermal dynamics. It is shownmore » that these two parameters are crucial in determining the nanocomposite thermal behavior. Our results showed that the heat transfer rate from nanoparticles to the matrix decreases as the nanoparticle size increases. On the other hand, increasing the metal concentration of the medium can also decrease the heat transfer rate.« less

Conservative Analytical Collision Probabilities for Orbital Formation Flying

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

2004-01-01

The literature offers a number of approximations for analytically and/or efficiently computing the probability of collision between two space objects. However, only one of these techniques is a completely analytical approximation that is suitable for use in the preliminary design phase, when it is more important to quickly analyze a large segment of the trade space than it is to precisely compute collision probabilities. Unfortunately, among the types of formations that one might consider, some combine a range of conditions for which this analytical method is less suitable. This work proposes a simple, conservative approximation that produces reasonable upper bounds on the collision probability in such conditions. Although its estimates are much too conservative under other conditions, such conditions are typically well suited for use of the existing method.

Conservative Analytical Collision Probability for Design of Orbital Formations

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

2004-01-01

The literature offers a number of approximations for analytically and/or efficiently computing the probability of collision between two space objects. However, only one of these techniques is a completely analytical approximation that is suitable for use in the preliminary design phase, when it is more important to quickly analyze a large segment of the trade space than it is to precisely compute collision probabilities. Unfortunately, among the types of formations that one might consider, some combine a range of conditions for which this analytical method is less suitable. This work proposes a simple, conservative approximation that produces reasonable upper bounds on the collision probability in such conditions. Although its estimates are much too conservative under other conditions, such conditions are typically well suited for use of the existing method.

Analysis of Fractional Flow for Transient Two-Phase Flow in Fractal Porous Medium

NASA Astrophysics Data System (ADS)

Lu, Ting; Duan, Yonggang; Fang, Quantang; Dai, Xiaolu; Wu, Jinsui

2016-03-01

Prediction of fractional flow in fractal porous medium is important for reservoir engineering and chemical engineering as well as hydrology. A physical conceptual fractional flow model of transient two-phase flow is developed in fractal porous medium based on the fractal characteristics of pore-size distribution and on the approximation that porous medium consist of a bundle of tortuous capillaries. The analytical expression for fractional flow for wetting phase is presented, and the proposed expression is the function of structural parameters (such as tortuosity fractal dimension, pore fractal dimension, maximum and minimum diameters of capillaries) and fluid properties (such as contact angle, viscosity and interfacial tension) in fractal porous medium. The sensitive parameters that influence fractional flow and its derivative are formulated, and their impacts on fractional flow are discussed.

Theoretical performance model for single image depth from defocus.

PubMed

Trouvé-Peloux, Pauline; Champagnat, Frédéric; Le Besnerais, Guy; Idier, Jérôme

2014-12-01

In this paper we present a performance model for depth estimation using single image depth from defocus (SIDFD). Our model is based on an original expression of the Cramér-Rao bound (CRB) in this context. We show that this model is consistent with the expected behavior of SIDFD. We then study the influence on the performance of the optical parameters of a conventional camera such as the focal length, the aperture, and the position of the in-focus plane (IFP). We derive an approximate analytical expression of the CRB away from the IFP, and we propose an interpretation of the SIDFD performance in this domain. Finally, we illustrate the predictive capacity of our performance model on experimental data comparing several settings of a consumer camera.

Light scattering by a nematic liquid crystal droplet: Wentzel–Kramers–Brillouin approximation

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

Loiko, V. A., E-mail: loiko@dragon.bas-net.by; Konkolovich, A. V.; Miskevich, A. A.

2016-01-15

Light scattering by an optically anisotropic liquid crystal (LC) droplet of a nematic in an isotropic polymer matrix is considered in the Wentzel–Kramers–Brillouin (WKB) approximation. General relations are obtained for elements of the amplitude matrix of light scattering by a droplet of arbitrary shape and for the structure of the director field. Analytic expressions for the amplitude matrices are derived for spherical LC droplets with a uniformly oriented structure of local optical axes for strictly forward and strictly backward scattering. The efficiency factors of extinction and backward scattering for a spherical nonabsorbing LC droplet depending on the LC optical anisotropy,more » refractive index of the polymer, illumination conditions, and orientation of the optical axis of the droplet are analyzed. Verification of the obtained solutions has been performed.« less

Generalized squeezing rotating-wave approximation to the isotropic and anisotropic Rabi model in the ultrastrong-coupling regime

NASA Astrophysics Data System (ADS)

Zhang, Yu-Yu

2016-12-01

Generalized squeezing rotating-wave approximation (GSRWA) is proposed by employing both the displacement and the squeezing transformations. A solvable Hamiltonian is reformulated in the same form as the ordinary RWA ones. For a qubit coupled to oscillators experiment, a well-defined Schrödinger-cat-like entangled state is given by the displaced-squeezed oscillator state instead of the original displaced state. For the isotropic Rabi case, the mean photon number and the ground-state energy are expressed analytically with additional squeezing terms, exhibiting a substantial improvement of the GSRWA. And the ground-state energy in the anisotropic Rabi model confirms the effectiveness of the GSRWA. Due to the squeezing effect, the GSRWA improves the previous methods only with the displacement transformation in a wide range of coupling strengths even for large atom frequency.

Electron impact excitation of H2 - Rydberg band systems and the benchmark dissociative cross section for H Lyman-alpha

NASA Technical Reports Server (NTRS)

Shemansky, D. E.; Hall, D. T.; Ajello, J. M.

1985-01-01

The cross sections sigma R 1 (2p) for excitation of H Ly-alpha emission produced by electron impact on H2 is reexamined. A more accurate estimate for sigma R 1 (2p) is obtained based on Born approximation estimates of the H2 Rydberg system cross sections using measured relative excitation functions. The obtained value is (8.18 + or -1.2) x 10 to the -18th sq cm at 100 eV, a factor of 0.69 below the value universally applied to cross section measurements over the past decade. Cross sections for the H2 Rydberg systems fixed in magnitude by the Born approximation have also been obtained using experimentally determined excitation functions. Accurate analytic expressions for these cross sections allow the direct calculation of rate coefficients.

N-point statistics of large-scale structure in the Zel'dovich approximation

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

Tassev, Svetlin, E-mail: tassev@astro.princeton.edu

2014-06-01

Motivated by the results presented in a companion paper, here we give a simple analytical expression for the matter n-point functions in the Zel'dovich approximation (ZA) both in real and in redshift space (including the angular case). We present numerical results for the 2-dimensional redshift-space correlation function, as well as for the equilateral configuration for the real-space 3-point function. We compare those to the tree-level results. Our analysis is easily extendable to include Lagrangian bias, as well as higher-order perturbative corrections to the ZA. The results should be especially useful for modelling probes of large-scale structure in the linear regime,more » such as the Baryon Acoustic Oscillations. We make the numerical code used in this paper freely available.« less

Landau-Zener extension of the Tavis-Cummings model: structure of the solution

NASA Astrophysics Data System (ADS)

Sun, Chen; Sinitsyn, Nikolai

We explore the recently discovered solution of the driven Tavis-Cummings model (DTCM). It describes interaction of arbitrary number of two-level systems with a bosonic mode that has linearly time-dependent frequency. We derive compact and tractable expressions for transition probabilities in terms of the well known special functions. In the new form, our formulas are suitable for fast numerical calculations and analytical approximations. As an application, we obtain the semiclassical limit of the exact solution and compare it to prior approximations. We also reveal connection between DTCM and q-deformed binomial statistics. Under the auspices of the National Nuclear Security Administration of the U.S. Department of Energy at Los Alamos National Laboratory under Contract No. DE-AC52-06NA25396. Authors also thank the support from the LDRD program at LANL.

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.

Velocity space scattering coefficients with applications in antihydrogen recombination studies

NASA Astrophysics Data System (ADS)

Chang, Yongbin; Ordonez, C. A.

2000-12-01

An approach for calculating velocity space friction and diffusion coefficients with Maxwellian field particles is developed based on a kernel function derived in a previous paper [Y. Chang and C. A. Ordonez, Phys. Plasmas 6, 2947 (1999)]. The original fivefold integral expressions for the coefficients are reduced to onefold integrals, which can be used for any value of the Coulomb logarithm. The onefold integrals can be further reduced to standard analytical expressions by using a weak coupling approximation. The integral expression for the friction coefficient is used to predict a time scale that describes the rate at which a reflecting antiproton beam slows down within a positron plasma, while both species are simultaneously confined by a nested Penning trap. The time scale is used to consider the possibility of achieving antihydrogen recombination within the trap. The friction and diffusion coefficients are then used to derive an expression for calculating the energy transfer rate between antiprotons and positrons. The expression is employed to illustrate achieving antihydrogen recombination while taking into account positron heating by the antiprotons. The effect of the presence of an electric field on recombination is discussed.

Derivation of phase functions from multiply scattered sunlight transmitted through a hazy atmosphere

NASA Technical Reports Server (NTRS)

Weinman, J. A.; Twitty, J. T.; Browning, S. R.; Herman, B. M.

1975-01-01

The intensity of sunlight multiply scattered in model atmospheres is derived from the equation of radiative transfer by an analytical small-angle approximation. The approximate analytical solutions are compared to rigorous numerical solutions of the same problem. Results obtained from an aerosol-laden model atmosphere are presented. Agreement between the rigorous and the approximate solutions is found to be within a few per cent. The analytical solution to the problem which considers an aerosol-laden atmosphere is then inverted to yield a phase function which describes a single scattering event at small angles. The effect of noisy data on the derived phase function is discussed.

Effect of Geometry on Electrokinetic Characterization of Solid Surfaces.

PubMed

Kumar, Abhijeet; Kleinen, Jochen; Venzmer, Joachim; Gambaryan-Roisman, Tatiana

2017-08-01

An analytical approach is presented to describe pressure-driven streaming current (I str ) and streaming potential (U str ) generation in geometrically complex samples, for which the classical Helmholtz-Smoluchowski (H-S) equation is known to be inaccurate. The new approach is valid under the same prerequisite conditions that are used for the development of the H-S equation, that is, the electrical double layers (EDLs) are sufficiently thin and surface conductivity and electroviscous effects are negligible. The analytical methodology is developed using linear velocity profiles to describe liquid flow inside of EDLs and using simplifying approximations to describe macroscopic flow. At first, a general expression is obtained to describe the I str generated in different cross sections of an arbitrarily shaped sample. Thereafter, assuming that the generated U str varies only along the pressure-gradient direction, an expression describing the variation of generated U str along the sample length is obtained. These expressions describing I str and U str generation constitute the theoretical foundation of this work, which is first applied to a set of three nonuniform cross-sectional capillaries and thereafter to a square array of cylindrical fibers (model porous media) for both parallel and transverse fiber orientation cases. Although analytical solutions cannot be obtained for real porous substrates because of their random structure, the new theory provides useful insights into the effect of important factors such as fiber orientation, sample porosity, and sample dimensions. The solutions obtained for the model porous media are used to device strategies for more accurate zeta potential determination of porous fiber plugs. The new approach could be thus useful in resolving the long-standing problem of sample geometry dependence of zeta potential measurements.

Analytically tractable climate-carbon cycle feedbacks under 21st century anthropogenic forcing

NASA Astrophysics Data System (ADS)

Lade, Steven J.; Donges, Jonathan F.; Fetzer, Ingo; Anderies, John M.; Beer, Christian; Cornell, Sarah E.; Gasser, Thomas; Norberg, Jon; Richardson, Katherine; Rockström, Johan; Steffen, Will

2018-05-01

Changes to climate-carbon cycle feedbacks may significantly affect the Earth system's response to greenhouse gas emissions. These feedbacks are usually analysed from numerical output of complex and arguably opaque Earth system models. Here, we construct a stylised global climate-carbon cycle model, test its output against comprehensive Earth system models, and investigate the strengths of its climate-carbon cycle feedbacks analytically. The analytical expressions we obtain aid understanding of carbon cycle feedbacks and the operation of the carbon cycle. Specific results include that different feedback formalisms measure fundamentally the same climate-carbon cycle processes; temperature dependence of the solubility pump, biological pump, and CO2 solubility all contribute approximately equally to the ocean climate-carbon feedback; and concentration-carbon feedbacks may be more sensitive to future climate change than climate-carbon feedbacks. Simple models such as that developed here also provide workbenches for simple but mechanistically based explorations of Earth system processes, such as interactions and feedbacks between the planetary boundaries, that are currently too uncertain to be included in comprehensive Earth system models.

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

Transmission and reflection of terahertz plasmons in two-dimensional plasmonic devices

DOE PAGES

Sydoruk, Oleksiy; Choonee, Kaushal; Dyer, Gregory Conrad

2015-03-10

We found that plasmons in two-dimensional semiconductor devices will be reflected by discontinuities, notably, junctions between gated and non-gated electron channels. The transmitted and reflected plasmons can form spatially- and frequency-varying signals, and their understanding is important for the design of terahertz detectors, oscillators, and plasmonic crystals. Using mode decomposition, we studied terahertz plasmons incident on a junction between a gated and a nongated channel. The plasmon reflection and transmission coefficients were found numerically and analytically and studied between 0.3 and 1 THz for a range of electron densities. At higher frequencies, we could describe the plasmons by a simplifiedmore » model of channels in homogeneous dielectrics, for which the analytical approximations were accurate. At low frequencies, however, the full geometry and mode spectrum had to be taken into account. Moreover, the results agreed with simulations by the finite-element method. As a result, mode decomposition thus proved to be a powerful method for plasmonic devices, combining the rigor of complete solutions of Maxwell's equations with the convenience of analytical expressions.« less

Correlated scattering states of N-body Coulomb systems

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

Berakdar, J.

1997-03-01

For N charged particles of equal masses moving in the field of a heavy residual charge, an approximate analytical solution of the many-body time-independent Schr{umlt o}dinger equation is derived at a total energy above the complete fragmentation threshold. All continuum particles are treated on equal footing. The proposed correlated wave function represents, to leading order, an exact solution of the many-body Schr{umlt o}dinger equation in the asymptotic region defined by large interparticle separations. Thus, in this asymptotic region the N-body Coulomb modifications to the plane-wave motion of free particles are rigorously estimated. It is shown that the Kato cusp conditionsmore » are satisfied by the derived wave function at all two-body coalescence points. An expression of the normalization of this wave function is also given. To render possible the calculations of scattering amplitudes for transitions leading to a four-body scattering state, an effective-charge method is suggested in which the correlations between the continuum particles are completely subsumed into effective interactions with the residual charge. Analytical expressions for these effective interactions are derived and discussed for physical situations. {copyright} {ital 1997} {ital The American Physical Society}« less

Improvement of LOD in Fluorescence Detection with Spectrally Nonuniform Background by Optimization of Emission Filtering.

PubMed

Galievsky, Victor A; Stasheuski, Alexander S; Krylov, Sergey N

2017-10-17

The limit-of-detection (LOD) in analytical instruments with fluorescence detection can be improved by reducing noise of optical background. Efficiently reducing optical background noise in systems with spectrally nonuniform background requires complex optimization of an emission filter-the main element of spectral filtration. Here, we introduce a filter-optimization method, which utilizes an expression for the signal-to-noise ratio (SNR) as a function of (i) all noise components (dark, shot, and flicker), (ii) emission spectrum of the analyte, (iii) emission spectrum of the optical background, and (iv) transmittance spectrum of the emission filter. In essence, the noise components and the emission spectra are determined experimentally and substituted into the expression. This leaves a single variable-the transmittance spectrum of the filter-which is optimized numerically by maximizing SNR. Maximizing SNR provides an accurate way of filter optimization, while a previously used approach based on maximizing a signal-to-background ratio (SBR) is the approximation that can lead to much poorer LOD specifically in detection of fluorescently labeled biomolecules. The proposed filter-optimization method will be an indispensable tool for developing new and improving existing fluorescence-detection systems aiming at ultimately low LOD.

Latitude and longitude vertical disparity

PubMed Central

Read, Jenny C. A.; Phillipson, Graeme P.; Glennerster, Andrew

2010-01-01

The literature on vertical disparity is complicated by the fact that several different definitions of the term “vertical disparity” are in common use, often without a clear statement about which is intended or a widespread appreciation of the properties of the different definitions. Here, we examine two definitions of retinal vertical disparity: elevation-latitude and elevation-longitude disparity. Near the fixation point, these definitions become equivalent, but in general, they have quite different dependences on object distance and binocular eye posture, which have not previously been spelt out. We present analytical approximations for each type of vertical disparity, valid for more general conditions than previous derivations in the literature: we do not restrict ourselves to objects near the fixation point or near the plane of regard, and we allow for non-zero torsion, cyclovergence and vertical misalignments of the eyes. We use these expressions to derive estimates of the latitude and longitude vertical disparity expected at each point in the visual field, averaged over all natural viewing. Finally, we present analytical expressions showing how binocular eye position – gaze direction, convergence, torsion, cyclovergence, and vertical misalignment – can be derived from the vertical disparity field and its derivatives at the fovea. PMID:20055544

Calibration Method to Eliminate Zeroth Order Effect in Lateral Shearing Interferometry

NASA Astrophysics Data System (ADS)

Fang, Chao; Xiang, Yang; Qi, Keqi; Chen, Dawei

2018-04-01

In this paper, a calibration method is proposed which eliminates the zeroth order effect in lateral shearing interferometry. An analytical expression of the calibration error function is deduced, and the relationship between the phase-restoration error and calibration error is established. The analytical results show that the phase-restoration error introduced by the calibration error is proportional to the phase shifting error and zeroth order effect. The calibration method is verified using simulations and experiments. The simulation results show that the phase-restoration error is approximately proportional to the phase shift error and zeroth order effect, when the phase shifting error is less than 2° and the zeroth order effect is less than 0.2. The experimental result shows that compared with the conventional method with 9-frame interferograms, the calibration method with 5-frame interferograms achieves nearly the same restoration accuracy.

Graphene plasmons embedded in a gain medium: layer and ribbon plasmons

NASA Astrophysics Data System (ADS)

Altares Menendez, Galaad; Rosolen, Gilles; Maes, Bjorn

2016-12-01

Graphene plasmonics has attracted much attention due to its remarkable properties such as tunable conductivity and extreme confinement. However, losses remain one of the major drawbacks to developing more efficient devices based on graphene plasmons. Here we show that when a gain medium is introduced around a 1D graphene sheet, lossless propagation can be achieved for a critical gain value. Both numerics and analytics are employed; and with the Drude approximation the analytical expression for this critical gain becomes remarkably simple. Furthermore, we examine a single 2D graphene nanoribbon within a gain environment. We report that the plasmonic resonant modes exhibit a spasing effect for a specific value of the surrounding gain. This feature is indicated by an absorption cross section that strongly increases and narrows. Finally, we manage to connect the ribbon results to the 1D sheet critical gain, by taking external coupling into account.

Manipulation of radial-variant polarization for creating tunable bifocusing spots.

PubMed

Gu, Bing; Pan, Yang; Wu, Jia-Lu; Cui, Yiping

2014-02-01

We propose and generate a new radial-variant vector field (RV-VF) with a distribution of states of polarization described by the square of the radius and exploit its focusing property. Theoretically, we present the analytical expressions for the three-dimensional electric field of the vector field focused by a thin lens under the nonparaxial and paraxial approximations based on the vectorial Rayleigh-Sommerfeld formulas. Numerical simulations indicate that this focused field exhibits bifocusing spots along the optical axis. The underlying mechanism for generating the bifocusing property is analyzed in detail. We give the analytical formula for the interval between two foci. Experimentally, we generate the RV-VFs with alterable topological charge and demonstrate that the interval between two foci is controllable by tuning the radial topological charge. This particular focal field has specific applications for biparticle trapping, manipulating, alignment, transportation, and accelerating along the optical axis.

Two-population dynamics in a growing network model

NASA Astrophysics Data System (ADS)

Ivanova, Kristinka; Iordanov, Ivan

2012-02-01

We introduce a growing network evolution model with nodal attributes. The model describes the interactions between potentially violent V and non-violent N agents who have different affinities in establishing connections within their own population versus between the populations. The model is able to generate all stable triads observed in real social systems. In the framework of rate equations theory, we employ the mean-field approximation to derive analytical expressions of the degree distribution and the local clustering coefficient for each type of nodes. Analytical derivations agree well with numerical simulation results. The assortativity of the potentially violent network qualitatively resembles the connectivity pattern in terrorist networks that was recently reported. The assortativity of the network driven by aggression shows clearly different behavior than the assortativity of the networks with connections of non-aggressive nature in agreement with recent empirical results of an online social system.

Suppression of Growth by Multiplicative White Noise in a Parametric Resonant System

NASA Astrophysics Data System (ADS)

Ishihara, Masamichi

2015-02-01

The growth of the amplitude in a Mathieu-like equation with multiplicative white noise is studied. To obtain an approximate analytical expression for the exponent at the extremum on parametric resonance regions, a time-interval width is introduced. To determine the exponents numerically, the stochastic differential equations are solved by a symplectic numerical method. The Mathieu-like equation contains a parameter α determined by the intensity of noise and the strength of the coupling between the variable and noise; without loss of generality, only non-negative α can be considered. The exponent is shown to decrease with α, reach a minimum and increase after that. The minimum exponent is obtained analytically and numerically. As a function of α, the minimum at α≠0, occurs on the parametric resonance regions of α=0. This minimum indicates suppression of growth by multiplicative white noise.

Moments and Root-Mean-Square Error of the Bayesian MMSE Estimator of Classification Error in the Gaussian Model.

PubMed

Zollanvari, Amin; Dougherty, Edward R

2014-06-01

The most important aspect of any classifier is its error rate, because this quantifies its predictive capacity. Thus, the accuracy of error estimation is critical. Error estimation is problematic in small-sample classifier design because the error must be estimated using the same data from which the classifier has been designed. Use of prior knowledge, in the form of a prior distribution on an uncertainty class of feature-label distributions to which the true, but unknown, feature-distribution belongs, can facilitate accurate error estimation (in the mean-square sense) in circumstances where accurate completely model-free error estimation is impossible. This paper provides analytic asymptotically exact finite-sample approximations for various performance metrics of the resulting Bayesian Minimum Mean-Square-Error (MMSE) error estimator in the case of linear discriminant analysis (LDA) in the multivariate Gaussian model. These performance metrics include the first, second, and cross moments of the Bayesian MMSE error estimator with the true error of LDA, and therefore, the Root-Mean-Square (RMS) error of the estimator. We lay down the theoretical groundwork for Kolmogorov double-asymptotics in a Bayesian setting, which enables us to derive asymptotic expressions of the desired performance metrics. From these we produce analytic finite-sample approximations and demonstrate their accuracy via numerical examples. Various examples illustrate the behavior of these approximations and their use in determining the necessary sample size to achieve a desired RMS. The Supplementary Material contains derivations for some equations and added figures.

Random Walks and Effective Optical Depth in Relativistic Flow

NASA Astrophysics Data System (ADS)

Shibata, Sanshiro; Tominaga, Nozomu; Tanaka, Masaomi

2014-05-01

We investigate the random walk process in relativistic flow. In the relativistic flow, photon propagation is concentrated in the direction of the flow velocity due to the relativistic beaming effect. We show that in the pure scattering case, the number of scatterings is proportional to the size parameter ξ ≡ L/l 0 if the flow velocity β ≡ v/c satisfies β/Γ Gt ξ-1, while it is proportional to ξ2 if β/Γ Lt ξ-1, where L and l 0 are the size of the system in the observer frame and the mean free path in the comoving frame, respectively. We also examine the photon propagation in the scattering and absorptive medium. We find that if the optical depth for absorption τa is considerably smaller than the optical depth for scattering τs (τa/τs Lt 1) and the flow velocity satisfies \\beta \\gg \\sqrt{2\\tau _a/\\tau _s}, then the effective optical depth is approximated by τ* ~= τa(1 + β)/β. Furthermore, we perform Monte Carlo simulations of radiative transfer and compare the results with the analytic expression for the number of scatterings. The analytic expression is consistent with the results of the numerical simulations. The expression derived in this study can be used to estimate the photon production site in relativistic phenomena, e.g., gamma-ray burst and active galactic nuclei.

Coalescence computations for large samples drawn from populations of time-varying sizes

PubMed Central

Polanski, Andrzej; Szczesna, Agnieszka; Garbulowski, Mateusz; Kimmel, Marek

2017-01-01

We present new results concerning probability distributions of times in the coalescence tree and expected allele frequencies for coalescent with large sample size. The obtained results are based on computational methodologies, which involve combining coalescence time scale changes with techniques of integral transformations and using analytical formulae for infinite products. We show applications of the proposed methodologies for computing probability distributions of times in the coalescence tree and their limits, for evaluation of accuracy of approximate expressions for times in the coalescence tree and expected allele frequencies, and for analysis of large human mitochondrial DNA dataset. PMID:28170404

An Approximate Solution to the Plastic Indentation of Circular Sandwich Panels

NASA Astrophysics Data System (ADS)

Xie, Z.

2018-05-01

The plastic indentation response of circular sandwich panels loaded by the flat end of a cylinder is investigated employing a velocity field model. Using the principles of virtual velocities and minimum work, an expression for the indenter load in relation to the indenter displacement and displacement field of the deformed face sheet is derived. The analytical solutions obtained are in good agreement with those found by simulations using the ABAQUS code. The radial tensile strain of the deformed face sheet and the ratio of energy absorption rate of the core to that of the face sheet are discussed.

Constant-roll tachyon inflation and observational constraints

NASA Astrophysics Data System (ADS)

Gao, Qing; Gong, Yungui; Fei, Qin

2018-05-01

For the constant-roll tachyon inflation, we derive the analytical expressions for the scalar and tensor power spectra, the scalar and tensor spectral tilts and the tensor to scalar ratio to the first order of epsilon1 by using the method of Bessel function approximation. The derived ns-r results are compared with the observations, we find that only the constant-roll inflation with ηH being a constant is consistent with the observations and observations constrain the constant-roll inflation to be slow-roll inflation. The tachyon potential is also reconstructed for the constant-roll inflation which is consistent with the observations.

Simple, accurate formula for the average bit error probability of multiple-input multiple-output free-space optical links over negative exponential turbulence channels.

PubMed

Peppas, Kostas P; Lazarakis, Fotis; Alexandridis, Antonis; Dangakis, Kostas

2012-08-01

In this Letter we investigate the error performance of multiple-input multiple-output free-space optical communication systems employing intensity modulation/direct detection and operating over strong atmospheric turbulence channels. Atmospheric-induced strong turbulence fading is modeled using the negative exponential distribution. For the considered system, an approximate yet accurate analytical expression for the average bit error probability is derived and an efficient method for its numerical evaluation is proposed. Numerically evaluated and computer simulation results are further provided to demonstrate the validity of the proposed mathematical analysis.

Contact problem on indentation of an elastic half-plane with an inhomogeneous coating by a flat punch in the presence of tangential stresses on a surface

NASA Astrophysics Data System (ADS)

Volkov, Sergei S.; Vasiliev, Andrey S.; Aizikovich, Sergei M.; Sadyrin, Evgeniy V.

2018-05-01

Indentation of an elastic half-space with functionally graded coating by a rigid flat punch is studied. The half-plane is additionally subjected to distributed tangential stresses. Tangential stresses are represented in a form of Fourier series. The problem is reduced to the solution of two dual integral equations over even and odd functions describing distribution of unknown normal contact stresses. The solutions of these dual integral equations are constructed by the bilateral asymptotic method. Approximated analytical expressions for contact normal stresses are provided.

Effect of turbulent atmosphere on the on-axis average intensity of Pearcey-Gaussian beam

NASA Astrophysics Data System (ADS)

F, Boufalah; L, Dalil-Essakali; H, Nebdi; A, Belafhal

2016-06-01

The propagation characteristics of the Pearcey-Gaussian (PG) beam in turbulent atmosphere are investigated in this paper. The Pearcey beam is a new kind of paraxial beam, based on the Pearcey function of catastrophe theory, which describes diffraction about a cusp caustic. By using the extended Huygens-Fresnel integral formula in the paraxial approximation and the Rytov theory, an analytical expression of axial intensity for the considered beam family is derived. Some numerical results for PG beam propagating in atmospheric turbulence are given by studying the influences of some factors, including incident beam parameters and turbulence strengths.

Random-walk approach to the d -dimensional disordered Lorentz gas

NASA Astrophysics Data System (ADS)

Adib, Artur B.

2008-02-01

A correlated random walk approach to diffusion is applied to the disordered nonoverlapping Lorentz gas. By invoking the Lu-Torquato theory for chord-length distributions in random media [J. Chem. Phys. 98, 6472 (1993)], an analytic expression for the diffusion constant in arbitrary number of dimensions d is obtained. The result corresponds to an Enskog-like correction to the Boltzmann prediction, being exact in the dilute limit, and better or nearly exact in comparison to renormalized kinetic theory predictions for all allowed densities in d=2,3 . Extensive numerical simulations were also performed to elucidate the role of the approximations involved.

APPROXIMATE AND ANALYTICAL SOLUTIONS FOR SOLUTE TRANSPORT FROM AN INJECTION WELL INTO A SINGLE FRACTURE

EPA Science Inventory

In dealing with problems related to land-based nuclear waste management, a number of analytical and approximate solutions were developed to quantify radionuclide transport through fractures contained in the porous formation. t has been reported that by treating the radioactive de...

Analytical treatment of self-phase-modulation beyond the slowly varying envelope approximation

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

Syrchin, M.S.; Zheltikov, A.M.; International Laser Center, M.V. Lomonosov Moscow State University, 119899 Moscow

Analytical treatment of the self-phase-modulation of an ultrashort light pulse is extended beyond the slowly varying envelope approximation. The resulting wave equation is modified to include corrections to self-phase-modulation due to higher-order spatial and temporal derivatives. Analytical solutions are found in the limiting regimes of high nonlinearities and very short pulses. Our results reveal features that can significantly impact both pulse shape and the evolution of the phase.

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.

The impact of inter-fraction dose variations on biological equivalent dose (BED): the concept of equivalent constant dose.

PubMed

Zavgorodni, S

2004-12-07

Inter-fraction dose fluctuations, which appear as a result of setup errors, organ motion and treatment machine output variations, may influence the radiobiological effect of the treatment even when the total delivered physical dose remains constant. The effect of these inter-fraction dose fluctuations on the biological effective dose (BED) has been investigated. Analytical expressions for the BED accounting for the dose fluctuations have been derived. The concept of biological effective constant dose (BECD) has been introduced. The equivalent constant dose (ECD), representing the constant physical dose that provides the same cell survival fraction as the fluctuating dose, has also been introduced. The dose fluctuations with Gaussian as well as exponential probability density functions were investigated. The values of BECD and ECD calculated analytically were compared with those derived from Monte Carlo modelling. The agreement between Monte Carlo modelled and analytical values was excellent (within 1%) for a range of dose standard deviations (0-100% of the dose) and the number of fractions (2 to 37) used in the comparison. The ECDs have also been calculated for conventional radiotherapy fields. The analytical expression for the BECD shows that BECD increases linearly with the variance of the dose. The effect is relatively small, and in the flat regions of the field it results in less than 1% increase of ECD. In the penumbra region of the 6 MV single radiotherapy beam the ECD exceeded the physical dose by up to 35%, when the standard deviation of combined patient setup/organ motion uncertainty was 5 mm. Equivalently, the ECD field was approximately 2 mm wider than the physical dose field. The difference between ECD and the physical dose is greater for normal tissues than for tumours.

Analytical theory of mesoscopic Bose-Einstein condensation in an ideal gas

NASA Astrophysics Data System (ADS)

Kocharovsky, Vitaly V.; Kocharovsky, Vladimir V.

2010-03-01

We find the universal structure and scaling of the Bose-Einstein condensation (BEC) statistics and thermodynamics (Gibbs free energy, average energy, heat capacity) for a mesoscopic canonical-ensemble ideal gas in a trap with an arbitrary number of atoms, any volume, and any temperature, including the whole critical region. We identify a universal constraint-cutoff mechanism that makes BEC fluctuations strongly non-Gaussian and is responsible for all unusual critical phenomena of the BEC phase transition in the ideal gas. The main result is an analytical solution to the problem of critical phenomena. It is derived by, first, calculating analytically the universal probability distribution of the noncondensate occupation, or a Landau function, and then using it for the analytical calculation of the universal functions for the particular physical quantities via the exact formulas which express the constraint-cutoff mechanism. We find asymptotics of that analytical solution as well as its simple analytical approximations which describe the universal structure of the critical region in terms of the parabolic cylinder or confluent hypergeometric functions. The obtained results for the order parameter, all higher-order moments of BEC fluctuations, and thermodynamic quantities perfectly match the known asymptotics outside the critical region for both low and high temperature limits. We suggest two- and three-level trap models of BEC and find their exact solutions in terms of the cutoff negative binomial distribution (which tends to the cutoff gamma distribution in the continuous limit) and the confluent hypergeometric distribution, respectively. Also, we present an exactly solvable cutoff Gaussian model of BEC in a degenerate interacting gas. All these exact solutions confirm the universality and constraint-cutoff origin of the strongly non-Gaussian BEC statistics. We introduce a regular refinement scheme for the condensate statistics approximations on the basis of the infrared universality of higher-order cumulants and the method of superposition and show how to model BEC statistics in the actual traps. In particular, we find that the three-level trap model with matching the first four or five cumulants is enough to yield remarkably accurate results for all interesting quantities in the whole critical region. We derive an exact multinomial expansion for the noncondensate occupation probability distribution and find its high-temperature asymptotics (Poisson distribution) and corrections to it. Finally, we demonstrate that the critical exponents and a few known terms of the Taylor expansion of the universal functions, which were calculated previously from fitting the finite-size simulations within the phenomenological renormalization-group theory, can be easily obtained from the presented full analytical solutions for the mesoscopic BEC as certain approximations in the close vicinity of the critical point.

Alfvén Wave Reflection and Turbulent Heating in the Solar Wind from 1 Solar Radius to 1 AU: An Analytical Treatment

NASA Astrophysics Data System (ADS)

Chandran, Benjamin D. G.; Hollweg, Joseph V.

2009-12-01

We study the propagation, reflection, and turbulent dissipation of Alfvén waves in coronal holes and the solar wind. We start with the Heinemann-Olbert equations, which describe non-compressive magnetohydrodynamic fluctuations in an inhomogeneous medium with a background flow parallel to the background magnetic field. Following the approach of Dmitruk et al., we model the nonlinear terms in these equations using a simple phenomenology for the cascade and dissipation of wave energy and assume that there is much more energy in waves propagating away from the Sun than waves propagating toward the Sun. We then solve the equations analytically for waves with periods of hours and longer to obtain expressions for the wave amplitudes and turbulent heating rate as a function of heliocentric distance. We also develop a second approximate model that includes waves with periods of roughly one minute to one hour, which undergo less reflection than the longer-period waves, and compare our models to observations. Our models generalize the phenomenological model of Dmitruk et al. by accounting for the solar wind velocity, so that the turbulent heating rate can be evaluated from the coronal base out past the Alfvén critical point—that is, throughout the region in which most of the heating and acceleration occurs. The simple analytical expressions that we obtain can be used to incorporate Alfvén-wave reflection and turbulent heating into fluid models of the solar wind.

Solvent effects in time-dependent self-consistent field methods. II. Variational formulations and analytical gradients

DOE PAGES

Bjorgaard, J. A.; Velizhanin, K. A.; Tretiak, S.

2015-08-06

This study describes variational energy expressions and analytical excited state energy gradients for time-dependent self-consistent field methods with polarizable solvent effects. Linear response, vertical excitation, and state-specific solventmodels are examined. Enforcing a variational ground stateenergy expression in the state-specific model is found to reduce it to the vertical excitation model. Variational excited state energy expressions are then provided for the linear response and vertical excitation models and analytical gradients are formulated. Using semiempiricalmodel chemistry, the variational expressions are verified by numerical and analytical differentiation with respect to a static external electric field. Lastly, analytical gradients are further tested by performingmore » microcanonical excited state molecular dynamics with p-nitroaniline.« less

Quasi-linear diffusion coefficients for highly oblique whistler mode waves

NASA Astrophysics Data System (ADS)

Albert, J. M.

2017-05-01

Quasi-linear diffusion coefficients are considered for highly oblique whistler mode waves, which exhibit a singular "resonance cone" in cold plasma theory. The refractive index becomes both very large and rapidly varying as a function of wave parameters, making the diffusion coefficients difficult to calculate and to characterize. Since such waves have been repeatedly observed both outside and inside the plasmasphere, this problem has received renewed attention. Here the diffusion equations are analytically treated in the limit of large refractive index μ. It is shown that a common approximation to the refractive index allows the associated "normalization integral" to be evaluated in closed form and that this can be exploited in the numerical evaluation of the exact expression. The overall diffusion coefficient formulas for large μ are then reduced to a very simple form, and the remaining integral and sum over resonances are approximated analytically. These formulas are typically written for a modeled distribution of wave magnetic field intensity, but this may not be appropriate for highly oblique whistlers, which become quasi-electrostatic. Thus, the analysis is also presented in terms of wave electric field intensity. The final results depend strongly on the maximum μ (or μ∥) used to model the wave distribution, so realistic determination of these limiting values becomes paramount.

Limited Rationality and Its Quantification Through the Interval Number Judgments With Permutations.

PubMed

Liu, Fang; Pedrycz, Witold; Zhang, Wei-Guo

2017-12-01

The relative importance of alternatives expressed in terms of interval numbers in the fuzzy analytic hierarchy process aims to capture the uncertainty experienced by decision makers (DMs) when making a series of comparisons. Under the assumption of full rationality, the judgements of DMs in the typical analytic hierarchy process could be consistent. However, since the uncertainty in articulating the opinions of DMs is unavoidable, the interval number judgements are associated with the limited rationality. In this paper, we investigate the concept of limited rationality by introducing interval multiplicative reciprocal comparison matrices. By analyzing the consistency of interval multiplicative reciprocal comparison matrices, it is observed that the interval number judgements are inconsistent. By considering the permutations of alternatives, the concepts of approximation-consistency and acceptable approximation-consistency of interval multiplicative reciprocal comparison matrices are proposed. The exchange method is designed to generate all the permutations. A novel method of determining the interval weight vector is proposed under the consideration of randomness in comparing alternatives, and a vector of interval weights is determined. A new algorithm of solving decision making problems with interval multiplicative reciprocal preference relations is provided. Two numerical examples are carried out to illustrate the proposed approach and offer a comparison with the methods available in the literature.

Exact Analytical Solution of the Peristaltic Nanofluids Flow in an Asymmetric Channel with Flexible Walls and Slip Condition: Application to the Cancer Treatment

PubMed Central

Ebaid, Abdelhalim; Aly, Emad H.

2013-01-01

In the cancer treatment, magnetic nanoparticles are injected into the blood vessel nearest to the cancer's tissues. The dynamic of these nanoparticles occurs under the action of the peristaltic waves generated on the flexible walls of the blood vessel. Studying such nanofluid flow under this action is therefore useful in treating tissues of the cancer. In this paper, the mathematical model describing the slip peristaltic flow of nanofluid was analytically investigated. Exact expressions were deduced for the temperature distribution and nano-particle concentration. In addition, the effects of the slip, thermophoresis, and Brownian motion parameters on the temperature and nano-particle concentration profiles were discussed and further compared with other approximate results in the literatures. In particular, these results have been obtained at the same values of the physical examined parameters that was considered in Akbar et al., “Peristaltic flow of a nanofluid with slip effects,” 2012. The results reveal that remarkable differences are detected between the exact current results and those approximately obtained in the literatures for behaviour of the temperature profile and nano-particles concentration. Accordingly, the current analysis and results are considered as optimal and therefore may be taken as a base for any future comparisons. PMID:24151526

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.

Genetic evolution, plasticity, and bet-hedging as adaptive responses to temporally autocorrelated fluctuating selection: A quantitative genetic model.

PubMed

Tufto, Jarle

2015-08-01

Adaptive responses to autocorrelated environmental fluctuations through evolution in mean reaction norm elevation and slope and an independent component of the phenotypic variance are analyzed using a quantitative genetic model. Analytic approximations expressing the mutual dependencies between all three response modes are derived and solved for the joint evolutionary outcome. Both genetic evolution in reaction norm elevation and plasticity are favored by slow temporal fluctuations, with plasticity, in the absence of microenvironmental variability, being the dominant evolutionary outcome for reasonable parameter values. For fast fluctuations, tracking of the optimal phenotype through genetic evolution and plasticity is limited. If residual fluctuations in the optimal phenotype are large and stabilizing selection is strong, selection then acts to increase the phenotypic variance (bet-hedging adaptive). Otherwise, canalizing selection occurs. If the phenotypic variance increases with plasticity through the effect of microenvironmental variability, this shifts the joint evolutionary balance away from plasticity in favor of genetic evolution. If microenvironmental deviations experienced by each individual at the time of development and selection are correlated, however, more plasticity evolves. The adaptive significance of evolutionary fluctuations in plasticity and the phenotypic variance, transient evolution, and the validity of the analytic approximations are investigated using simulations. © 2015 The Author(s). Evolution © 2015 The Society for the Study of Evolution.

Phonon dispersion on Ag (100) surface: A modified analytic embedded atom method study

NASA Astrophysics Data System (ADS)

Xiao-Jun, Zhang; Chang-Le, Chen

2016-01-01

Within the harmonic approximation, the analytic expression of the dynamical matrix is derived based on the modified analytic embedded atom method (MAEAM) and the dynamics theory of surface lattice. The surface phonon dispersions along three major symmetry directions , and X¯M¯ are calculated for the clean Ag (100) surface by using our derived formulas. We then discuss the polarization and localization of surface modes at points X¯ and M¯ by plotting the squared polarization vectors as a function of the layer index. The phonon frequencies of the surface modes calculated by MAEAM are compared with the available experimental and other theoretical data. It is found that the present results are generally in agreement with the referenced experimental or theoretical results, with a maximum deviation of 10.4%. The agreement shows that the modified analytic embedded atom method is a reasonable many-body potential model to quickly describe the surface lattice vibration. It also lays a significant foundation for studying the surface lattice vibration in other metals. Project supported by the National Natural Science Foundation of China (Grant Nos. 61471301 and 61078057), the Scientific Research Program Funded by Shaanxi Provincial Education Department, China (Grant No. 14JK1301), and the Specialized Research Fund for the Doctoral Program of Higher Education, China (Grant No. 20126102110045).

Derivation of a closed form analytical expression for fluorescence recovery after photo bleaching in the case of continuous bleaching during read out

NASA Astrophysics Data System (ADS)

Endress, E.; Weigelt, S.; Reents, G.; Bayerl, T. M.

2005-01-01

Measurements of very slow diffusive processes in membranes, like the diffusion of integral membrane proteins, by fluorescence recovery after photo bleaching (FRAP) are hampered by bleaching of the probe during the read out of the fluorescence recovery. In the limit of long observation time (very slow diffusion as in the case of large membrane proteins), this bleaching may cause errors to the recovery function and thus provides error-prone diffusion coefficients. In this work we present a new approach to a two-dimensional closed form analytical solution of the reaction-diffusion equation, based on the addition of a dissipative term to the conventional diffusion equation. The calculation was done assuming (i) a Gaussian laser beam profile for bleaching the spot and (ii) that the fluorescence intensity profile emerging from the spot can be approximated by a two-dimensional Gaussian. The detection scheme derived from the analytical solution allows for diffusion measurements without the constraint of observation bleaching. Recovery curves of experimental FRAP data obtained under non-negligible read-out bleaching for native membranes (rabbit endoplasmic reticulum) on a planar solid support showed excellent agreement with the analytical solution and allowed the calculation of the lipid diffusion coefficient.

Comparison of three methods for wind turbine capacity factor estimation.

PubMed

Ditkovich, Y; Kuperman, A

2014-01-01

Three approaches to calculating capacity factor of fixed speed wind turbines are reviewed and compared using a case study. The first "quasiexact" approach utilizes discrete wind raw data (in the histogram form) and manufacturer-provided turbine power curve (also in discrete form) to numerically calculate the capacity factor. On the other hand, the second "analytic" approach employs a continuous probability distribution function, fitted to the wind data as well as continuous turbine power curve, resulting from double polynomial fitting of manufacturer-provided power curve data. The latter approach, while being an approximation, can be solved analytically thus providing a valuable insight into aspects, affecting the capacity factor. Moreover, several other merits of wind turbine performance may be derived based on the analytical approach. The third "approximate" approach, valid in case of Rayleigh winds only, employs a nonlinear approximation of the capacity factor versus average wind speed curve, only requiring rated power and rotor diameter of the turbine. It is shown that the results obtained by employing the three approaches are very close, enforcing the validity of the analytically derived approximations, which may be used for wind turbine performance evaluation.

Localized dark solitons and vortices in defocusing media with spatially inhomogeneous nonlinearity.

PubMed

Zeng, Jianhua; Malomed, Boris A

2017-05-01

Recent studies have demonstrated that defocusing cubic nonlinearity with local strength growing from the center to the periphery faster than r^{D}, in space of dimension D with radial coordinate r, supports a vast variety of robust bright solitons. In the framework of the same model, but with a weaker spatial-growth rate ∼r^{α} with α≤D, we test here the possibility to create stable localized continuous waves (LCWs) in one-dimensional (1D) and 2D geometries, localized dark solitons (LDSs) in one dimension, and localized dark vortices (LDVs) in two dimensions, which are all realized as loosely confined states with a divergent norm. Asymptotic tails of the solutions, which determine the divergence of the norm, are constructed in a universal analytical form by means of the Thomas-Fermi approximation (TFA). Global approximations for the LCWs, LDSs, and LDVs are constructed on the basis of interpolations between analytical approximations available far from (TFA) and close to the center. In particular, the interpolations for the 1D LDS, as well as for the 2D LDVs, are based on a deformed-tanh expression, which is suggested by the usual 1D dark-soliton solution. The analytical interpolations produce very accurate results, in comparison with numerical findings, for the 1D and 2D LCWs, 1D LDSs, and 2D LDVs with vorticity S=1. In addition to the 1D fundamental LDSs with the single notch and 2D vortices with S=1, higher-order LDSs with multiple notches are found too, as well as double LDVs, with S=2. Stability regions for the modes under consideration are identified by means of systematic simulations, the LCWs being completely stable in one and two dimensions, as they are ground states in the corresponding settings. Basic evolution scenarios are identified for those vortices that are unstable. The settings considered in this work may be implemented in nonlinear optics and in Bose-Einstein condensates.

Localized dark solitons and vortices in defocusing media with spatially inhomogeneous nonlinearity

NASA Astrophysics Data System (ADS)

Zeng, Jianhua; Malomed, Boris A.

2017-05-01

Recent studies have demonstrated that defocusing cubic nonlinearity with local strength growing from the center to the periphery faster than rD, in space of dimension D with radial coordinate r , supports a vast variety of robust bright solitons. In the framework of the same model, but with a weaker spatial-growth rate ˜rα with α ≤D , we test here the possibility to create stable localized continuous waves (LCWs) in one-dimensional (1D) and 2D geometries, localized dark solitons (LDSs) in one dimension, and localized dark vortices (LDVs) in two dimensions, which are all realized as loosely confined states with a divergent norm. Asymptotic tails of the solutions, which determine the divergence of the norm, are constructed in a universal analytical form by means of the Thomas-Fermi approximation (TFA). Global approximations for the LCWs, LDSs, and LDVs are constructed on the basis of interpolations between analytical approximations available far from (TFA) and close to the center. In particular, the interpolations for the 1D LDS, as well as for the 2D LDVs, are based on a deformed-tanh expression, which is suggested by the usual 1D dark-soliton solution. The analytical interpolations produce very accurate results, in comparison with numerical findings, for the 1D and 2D LCWs, 1D LDSs, and 2D LDVs with vorticity S =1 . In addition to the 1D fundamental LDSs with the single notch and 2D vortices with S =1 , higher-order LDSs with multiple notches are found too, as well as double LDVs, with S =2 . Stability regions for the modes under consideration are identified by means of systematic simulations, the LCWs being completely stable in one and two dimensions, as they are ground states in the corresponding settings. Basic evolution scenarios are identified for those vortices that are unstable. The settings considered in this work may be implemented in nonlinear optics and in Bose-Einstein condensates.

Analytic non-Maxwellian electron velocity distribution function in a Hall discharge plasma

NASA Astrophysics Data System (ADS)

Shagayda, Andrey; Tarasov, Alexey

2017-10-01

The electron velocity distribution function in the low-pressure discharges with the crossed electric and magnetic fields, which occur in magnetrons, plasma accelerators, and Hall thrusters with a closed electron drift, is not Maxwellian. A deviation from equilibrium is caused by a large electron mean free path relative to the Larmor radius and the size of the discharge channel. In this study, we derived in the relaxation approximation the analytical expression of the electron velocity distribution function in a weakly ionized Lorentz plasma with the crossed electric and magnetic fields in the presence of the electron density and temperature gradients in the direction of the electric field. The solution was obtained in the stationary approximation far from boundary surfaces, when diffusion and mobility are determined by the classical effective collision frequency of electrons with ions and atoms. The moments of the distribution function including the average velocity, the stress tensor, and the heat flux were calculated and compared with the classical hydrodynamic expressions. It was shown that a kinetic correction to the drift velocity stems from a contribution of the off-diagonal component of the stress tensor. This correction becomes essential if the drift velocity in the crossed electric and magnetic fields would be comparable to the thermal velocity of electrons. The electron temperature has three different components at a nonzero effective collision frequency and two different components in the limit when the collision frequency tends to zero. It is shown that, in the presence of ionization collisions, the components of the heat flux have additives that are not related to the temperature gradient, and arise because of the electron drift.

Effects of convergent diffusion and charge transfer kinetics on the diffusion layer thickness of spherical micro- and nanoelectrodes.

PubMed

Molina, A; Laborda, E; González, J; Compton, R G

2013-05-21

Nuances of the linear diffusion layer approximation are examined for slow charge transfer reactions at (hemi)spherical micro- and nanoelectrodes. This approximation is widely employed in Electrochemistry to evaluate the extent of electrolyte solution perturbed by the electrode process, which is essential to the understanding of the effects arising from thin-layer diffusion, convergent diffusion, convection, coupled chemical reactions and the double layer. The concept was well established for fast charge transfer processes at macroelectrodes, but remains unclear under other conditions such that a thorough assessment of its meaning was necessary. In a previous publication [A. Molina, J. González, E. Laborda and R. G. Compton, Phys. Chem. Chem. Phys., 2013, 15, 2381-2388] we shed some light on the influence of the reversibility degree. In the present work, the meaning of the diffusion layer thickness is investigated when very small electrodes are employed and so the contribution of convergent diffusion to the mass transport is very important. An analytical expression is given to calculate the linear diffusion layer thickness at (hemi)spherical electrodes and its behaviour is studied for a wide range of conditions of reversibility (from reversible to fully-irreversible processes) and electrode size (from macro- to nano-electrodes). Rigorous analytical solutions are deduced for true concentration profiles, surface concentrations, linear diffusion layer thickness and current densities when a potential pulse is applied at (hemi)spherical electrodes. The expressions for the magnitudes mentioned above are valid for electrodes of any size (including (hemi)spherical nanoelectrodes) and for any degree of reversibility, provided that mass transport occurs exclusively via diffusion. The variation of the above with the electrode size, applied potential and charge transfer kinetics is studied.

From Sommerfeld and Brillouin forerunners to optical precursors

NASA Astrophysics Data System (ADS)

Macke, Bruno; Ségard, Bernard

2013-04-01

The Sommerfeld and Brillouin forerunners generated in a single-resonance absorbing medium by an incident step-modulated pulse are theoretically considered in the double limit where the susceptibility of the medium is weak and the resonance is narrow. Combining direct Laplace-Fourier integration and calculations by the saddle-point method, we establish an explicit analytical expression of the transmitted field valid at any time, even when the two forerunners significantly overlap. We examine how their complete overlapping, occurring for shorter propagation distances, originates the formation of the unique transient currently named resonant precursor or dynamical beat. We obtain an expression of this transient identical to that usually derived within the slowly varying envelope approximation in spite of the initial discontinuity of the incident field envelope. The dynamical beats and 0π pulses generated by ultrashort incident pulses are also briefly examined.

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.

YORP torque as the function of shape harmonics

NASA Astrophysics Data System (ADS)

Breiter, Sławomir; Michalska, Hanna

2008-08-01

The second-order analytical approximation of the mean Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) torque components is given as an explicit function of the shape spherical harmonics coefficients for a sufficiently regular minor body. The results are based upon a new expression for the insolation function, significantly simpler than in previous works. Linearized plane-parallel model of the temperature distribution derived from the insolation function allows us to take into account a non-zero conductivity. Final expressions for the three average components of the YORP torque related with rotation period, obliquity and precession are given in a form of the Legendre series of the cosine of obliquity. The series have good numerical properties and can be easily truncated according to the degree of the Legendre polynomials or associated functions, with first two terms playing the principal role.

Turbulent equipartition pinch of toroidal momentum in spherical torus

NASA Astrophysics Data System (ADS)

Hahm, T. S.; Lee, J.; Wang, W. X.; Diamond, P. H.; Choi, G. J.; Na, D. H.; Na, Y. S.; Chung, K. J.; Hwang, Y. S.

2014-12-01

We present a new analytic expression for turbulent equipartition (TEP) pinch of toroidal angular momentum originating from magnetic field inhomogeneity of spherical torus (ST) plasmas. Starting from a conservative modern nonlinear gyrokinetic equation (Hahm et al 1988 Phys. Fluids 31 2670), we derive an expression for pinch to momentum diffusivity ratio without using a usual tokamak approximation of B ∝ 1/R which has been previously employed for TEP momentum pinch derivation in tokamaks (Hahm et al 2007 Phys. Plasmas 14 072302). Our new formula is evaluated for model equilibria of National Spherical Torus eXperiment (NSTX) (Ono et al 2001 Nucl. Fusion 41 1435) and Versatile Experiment Spherical Torus (VEST) (Chung et al 2013 Plasma Sci. Technol. 15 244) plasmas. Our result predicts stronger inward pinch for both cases, as compared to the prediction based on the tokamak formula.

Comparison of approximate solutions to the phonon Boltzmann transport equation with the relaxation time approximation: Spherical harmonics expansions and the discrete ordinates method

NASA Astrophysics Data System (ADS)

Christenson, J. G.; Austin, R. A.; Phillips, R. J.

2018-05-01

The phonon Boltzmann transport equation is used to analyze model problems in one and two spatial dimensions, under transient and steady-state conditions. New, explicit solutions are obtained by using the P1 and P3 approximations, based on expansions in spherical harmonics, and are compared with solutions from the discrete ordinates method. For steady-state energy transfer, it is shown that analytic expressions derived using the P1 and P3 approximations agree quantitatively with the discrete ordinates method, in some cases for large Knudsen numbers, and always for Knudsen numbers less than unity. However, for time-dependent energy transfer, the PN solutions differ qualitatively from converged solutions obtained by the discrete ordinates method. Although they correctly capture the wave-like behavior of energy transfer at short times, the P1 and P3 approximations rely on one or two wave velocities, respectively, yielding abrupt, step-changes in temperature profiles that are absent when the angular dependence of the phonon velocities is captured more completely. It is shown that, with the gray approximation, the P1 approximation is formally equivalent to the so-called "hyperbolic heat equation." Overall, these results support the use of the PN approximation to find solutions to the phonon Boltzmann transport equation for steady-state conditions. Such solutions can be useful in the design and analysis of devices that involve heat transfer at nanometer length scales, where continuum-scale approaches become inaccurate.

Impact-parameter dependence of the energy loss of fast molecular clusters in hydrogen

NASA Astrophysics Data System (ADS)

Fadanelli, R. C.; Grande, P. L.; Schiwietz, G.

2008-03-01

The electronic energy loss of molecular clusters as a function of impact parameter is far less understood than atomic energy losses. For instance, there are no analytical expressions for the energy loss as a function of impact parameter for cluster ions. In this work, we describe two procedures to evaluate the combined energy loss of molecules: Ab initio calculations within the semiclassical approximation and the coupled-channels method using atomic orbitals; and simplified models for the electronic cluster energy loss as a function of the impact parameter, namely the molecular perturbative convolution approximation (MPCA, an extension of the corresponding atomic model PCA) and the molecular unitary convolution approximation (MUCA, a molecular extension of the previous unitary convolution approximation UCA). In this work, an improved ansatz for MPCA is proposed, extending its validity for very compact clusters. For the simplified models, the physical inputs are the oscillators strengths of the target atoms and the target-electron density. The results from these models applied to an atomic hydrogen target yield remarkable agreement with their corresponding ab initio counterparts for different angles between cluster axis and velocity direction at specific energies of 150 and 300 keV/u.

Deriving the exact nonadiabatic quantum propagator in the mapping variable representation.

PubMed

Hele, Timothy J H; Ananth, Nandini

2016-12-22

We derive an exact quantum propagator for nonadiabatic dynamics in multi-state systems using the mapping variable representation, where classical-like Cartesian variables are used to represent both continuous nuclear degrees of freedom and discrete electronic states. The resulting Liouvillian is a Moyal series that, when suitably approximated, can allow for the use of classical dynamics to efficiently model large systems. We demonstrate that different truncations of the exact Liouvillian lead to existing approximate semiclassical and mixed quantum-classical methods and we derive an associated error term for each method. Furthermore, by combining the imaginary-time path-integral representation of the Boltzmann operator with the exact Liouvillian, we obtain an analytic expression for thermal quantum real-time correlation functions. These results provide a rigorous theoretical foundation for the development of accurate and efficient classical-like dynamics to compute observables such as electron transfer reaction rates in complex quantized systems.

Photothermoelastic contrast in nanoscale infrared spectroscopy

NASA Astrophysics Data System (ADS)

Morozovska, Anna N.; Eliseev, Eugene A.; Borodinov, Nikolay; Ovchinnikova, Olga S.; Morozovsky, Nicholas V.; Kalinin, Sergei V.

2018-01-01

The contrast formation mechanism in nanoscale Infrared (IR) Spectroscopy is analyzed. The temperature distribution and elastic displacement across the illuminated T-shape boundary between two materials with different IR-radiation absorption coefficients and thermo-physical and elastic properties located on a rigid substrate are calculated self-consistently for different frequencies f ˜ (1 kHz-1 MHz) of IR-radiation modulation (fully coupled problem). Analytical expressions for the temperature and displacement profiles across the "thermo-elastic step" are derived in the decoupling approximation for f = 0 ("static limit"), and conditions for approximation validity at low frequencies of IR-modulation are established. The step height was found to be thickness-independent for thick layers and proportional to the square of the thickness for very thin films. The theoretical results will be of potential interest for applications in the scanning thermo-ionic and thermal infrared microscopies for relatively long sample thermalization times and possibly for photothermal induced resonance microscopy using optomechanical probes.

Structure and effective interactions in three-component hard sphere liquids.

PubMed

König, A; Ashcroft, N W

2001-04-01

Complete and simple analytical expressions for the partial structure factors of the ternary hard sphere mixture are obtained within the Percus-Yevick approximation and presented as functions of relative packing fractions and relative hard sphere diameters. These solutions follow from the Laplace transform method as applied to multicomponent systems by Lebowitz [Phys. Rev. 133, A895 (1964)]. As an important application, we examine effective interactions in hard sphere liquid mixtures using the microscopic information contained in their partial structure factors. Thus the ensuring pair potential for an effective one-component system is obtained from the correlation functions by using an approximate inversion, and examples of effective potentials for three-component hard sphere mixtures are given. These mixtures may be of particular interest for the study of the packing aspects of melts that form glasses or quasicrystals, since noncrystalline solids often emerge from melts with at least three atomic constituents.

A Spherical Harmonic Analysis of the Ooty Wide Field Array (OWFA) Visibility Signal

NASA Astrophysics Data System (ADS)

Chatterjee, Suman; Bharadwaj, Somnath

2018-04-01

Considering redshifted 21-cm intensity mapping with the upcoming OWFA whose field of view subtends ˜57° in the N-S direction, we present a formalism which relates the measured visibilities to the spherical harmonic coefficients of the sky signal. We use this to calculate window functions which relate the two-visibility correlations i.e. the correlation between the visibilities measured at two baselines and two frequencies, to different multipoles of the multi-frequency angular power spectrum Cℓ(ν1, ν2). The formalism here is validated using simulations. We also present approximate closed form analytical expressions which can be used to calculate the window functions. Comparing the widely adopted flat sky approximation, we find that its predictions match those of our spherical harmonic formalism to within 16% across the entire OWFA baseline range. The match improves at large baselines where we have <5% deviations.

Genetic Networks and Anticipation of Gene Expression Patterns

NASA Astrophysics Data System (ADS)

Gebert, J.; Lätsch, M.; Pickl, S. W.; Radde, N.; Weber, G.-W.; Wünschiers, R.

2004-08-01

An interesting problem for computational biology is the analysis of time-series expression data. Here, the application of modern methods from dynamical systems, optimization theory, numerical algorithms and the utilization of implicit discrete information lead to a deeper understanding. In [1], we suggested to represent the behavior of time-series gene expression patterns by a system of ordinary differential equations, which we analytically and algorithmically investigated under the parametrical aspect of stability or instability. Our algorithm strongly exploited combinatorial information. In this paper, we deepen, extend and exemplify this study from the viewpoint of underlying mathematical modelling. This modelling consists in evaluating DNA-microarray measurements as the basis of anticipatory prediction, in the choice of a smooth model given by differential equations, in an approach of the right-hand side with parametric matrices, and in a discrete approximation which is a least squares optimization problem. We give a mathematical and biological discussion, and pay attention to the special case of a linear system, where the matrices do not depend on the state of expressions. Here, we present first numerical examples.

Precise analytic approximations for the Bessel function J1 (x)

NASA Astrophysics Data System (ADS)

Maass, Fernando; Martin, Pablo

2018-03-01

Precise and straightforward analytic approximations for the Bessel function J1 (x) have been found. Power series and asymptotic expansions have been used to determine the parameters of the approximation, which is as a bridge between both expansions, and it is a combination of rational and trigonometric functions multiplied with fractional powers of x. Here, several improvements with respect to the so called Multipoint Quasirational Approximation technique have been performed. Two procedures have been used to determine the parameters of the approximations. The maximum absolute errors are in both cases smaller than 0.01. The zeros of the approximation are also very precise with less than 0.04 per cent for the first one. A second approximation has been also determined using two more parameters, and in this way the accuracy has been increased to less than 0.001.

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

Safari, L., E-mail: laleh.safari@ist.ac.at; Department of Physics, University of Oulu, Box 3000, FI-90014 Oulu; Santos, J. P.

Atomic form factors are widely used for the characterization of targets and specimens, from crystallography to biology. By using recent mathematical results, here we derive an analytical expression for the atomic form factor within the independent particle model constructed from nonrelativistic screened hydrogenic wave functions. The range of validity of this analytical expression is checked by comparing the analytically obtained form factors with the ones obtained within the Hartee-Fock method. As an example, we apply our analytical expression for the atomic form factor to evaluate the differential cross section for Rayleigh scattering off neutral atoms.

Use of the thin sheath approximation for obtaining ion temperatures from the ISEE 1 limited aperture RPA. [for magnetosphere

NASA Technical Reports Server (NTRS)

Comfort, R. H.; Baugher, C. R.; Chappell, C. R.

1982-01-01

A procedure for analyzing low-energy (less than approximately 100 eV) ion data from the plasma composition experiment on ISEE 1 is set forth. The method is based on a derived analytic expression for particle flux to a limited aperture retarding potential analyzer (RPA) in the thin sheath approximation, which makes allowance for some effects of a charged spacecraft on plasma particle trajectories. Calculations using simulated data are employed in testing the efficacy and accuracy of the technique. On the basis of an analysis of these calculation results and the mathematical model, the method is seen as being able to provide accurate ion temperatures from all good plasmaspheric RPA data. It is noted that corresponding densities and spacecraft potentials should be accurate when spacecraft potentials are negative but that they are subject to error for positive spacecraft potentials, particularly when ion Mach numbers are much less than 1. An analysis of data from a representative ISEE 1 pass produces a plasmasphere temperature profile that is consistent in overall structure with previous observations.

A pertinent approach to solve nonlinear fuzzy integro-differential equations.

PubMed

Narayanamoorthy, S; Sathiyapriya, S P

2016-01-01

Fuzzy integro-differential equations is one of the important parts of fuzzy analysis theory that holds theoretical as well as applicable values in analytical dynamics and so an appropriate computational algorithm to solve them is in essence. In this article, we use parametric forms of fuzzy numbers and suggest an applicable approach for solving nonlinear fuzzy integro-differential equations using homotopy perturbation method. A clear and detailed description of the proposed method is provided. Our main objective is to illustrate that the construction of appropriate convex homotopy in a proper way leads to highly accurate solutions with less computational work. The efficiency of the approximation technique is expressed via stability and convergence analysis so as to guarantee the efficiency and performance of the methodology. Numerical examples are demonstrated to verify the convergence and it reveals the validity of the presented numerical technique. Numerical results are tabulated and examined by comparing the obtained approximate solutions with the known exact solutions. Graphical representations of the exact and acquired approximate fuzzy solutions clarify the accuracy of the approach.

The singular values of the imbedding operators of some classes of analytic functions of several variables

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

Parfenov, O.G.

1994-12-25

We discuss three results. The first exhibits the order of decrease of the s-values as a function of the CR-dimension of a compact set on which we approximate the class of analytic functions being studied. The second is an asymptotic formula for the case when the domain of analyticity and the compact set are Reinhart domains. The third is the computation of the s-values of a special operator that is of interest for approximation theory on one-dimensional manifolds.

Numerical modeling and analytical evaluation of light absorption by gold nanostars

NASA Astrophysics Data System (ADS)

Zarkov, Sergey; Akchurin, Georgy; Yakunin, Alexander; Avetisyan, Yuri; Akchurin, Garif; Tuchin, Valery

2018-04-01

In this paper, the regularity of local light absorption by gold nanostars (AuNSts) model is studied by method of numerical simulation. The mutual diffraction influence of individual geometric fragments of AuNSts is analyzed. A comparison is made with an approximate analytical approach for estimating the average bulk density of absorbed power and total absorbed power by individual geometric fragments of AuNSts. It is shown that the results of the approximate analytical estimate are in qualitative agreement with the numerical calculations of the light absorption by AuNSts.

An alternative explicit model expression equivalent to the integrated michaelis-menten equation and its application to nonlinear saturation pharmacokinetics.

PubMed

Goličnik, Marko

2011-06-01

Many pharmacodynamic processes can be described by the nonlinear saturation kinetics that are most frequently based on the hyperbolic Michaelis-Menten equation. Thus, various time-dependent solutions for drugs obeying such kinetics can be expressed in terms of the Lambert W(x)-omega function. However, unfortunately, computer programs that can perform the calculations for W(x) are not widely available. To avoid this problem, the replacement of the integrated Michaelis-Menten equation with an empiric integrated 1--exp alternative model equation was proposed recently by Keller et al. (Ther Drug Monit. 2009;31:783-785), although, as shown here, it was not necessary. Simulated concentrations of model drugs obeying Michaelis-Menten elimination kinetics were generated by two approaches: 1) calculation of time-course data based on an approximation equation W2*(x) performed using Microsoft Excel; and 2) calculation of reference time-course data based on an exact W(x) function built in to the Wolfram Mathematica. I show here that the W2*(x) function approximates the actual W(x) accurately. W2*(x) is expressed in terms of elementary mathematical functions and, consequently, it can be easily implemented using any of the widely available software. Hence, with the example of a hypothetical drug, I demonstrate here that an equation based on this approximation is far better, because it is nearly equivalent to the original solution, whereas the same characteristics cannot be fully confirmed for the 1--exp model equation. The W2*(x) equation proposed here might have an important role as a useful shortcut in optional software to estimate kinetic parameters from experimental data for drugs, and it might represent an easy and universal analytical tool for simulating and designing dosing regimens.

Single-qubit decoherence under a separable coupling to a random matrix environment

NASA Astrophysics Data System (ADS)

Carrera, M.; Gorin, T.; Seligman, T. H.

2014-08-01

This paper describes the dynamics of a quantum two-level system (qubit) under the influence of an environment modeled by an ensemble of random matrices. In distinction to earlier work, we consider here separable couplings and focus on a regime where the decoherence time is of the same order of magnitude as the environmental Heisenberg time. We derive an analytical expression in the linear response approximation, and study its accuracy by comparison with numerical simulations. We discuss a series of unusual properties, such as purity oscillations, strong signatures of spectral correlations (in the environment Hamiltonian), memory effects, and symmetry-breaking equilibrium states.

Stopping power of an electron gas with anisotropic temperature

NASA Astrophysics Data System (ADS)

Khelemelia, O. V.; Kholodov, R. I.

2016-04-01

A general theory of motion of a heavy charged particle in the electron gas with an anisotropic velocity distribution is developed within the quantum-field method. The analytical expressions for the dielectric susceptibility and the stopping power of the electron gas differs in no way from well-known classic formulas in the approximation of large and small velocities. Stopping power of the electron gas with anisotropic temperature in the framework of the quantum-field method is numerically calculated for an arbitrary angle between directions of the motion of the projectile particle and the electron beam. The results of the numerical calculations are compared with the dielectric model approach.

Second order optical nonlinearity of graphene due to electric quadrupole and magnetic dipole effects.

PubMed

Cheng, J L; Vermeulen, N; Sipe, J E

2017-03-06

We present a practical scheme to separate the contributions of the electric quadrupole-like and the magnetic dipole-like effects to the forbidden second order optical nonlinear response of graphene, and give analytic expressions for the second order optical conductivities, calculated from the independent particle approximation, with relaxation described in a phenomenological way. We predict strong second order nonlinear effects, including second harmonic generation, photon drag, and difference frequency generation. We discuss in detail the controllability of these effects by tuning the chemical potential, taking advantage of the dominant role played by interband optical transitions in the response.

Solution of non-steady-state substrate concentration in the action of biosensor response at mixed enzyme kinetics

NASA Astrophysics Data System (ADS)

Senthamarai, R.; Jana Ranjani, R.

2018-04-01

In this paper, a mathematical model of an amperometric biosensor at mixed enzyme kinetics and diffusion limitation in the case of substrate inhibition has been developed. The model is based on time dependent reaction diffusion equation containing a non -linear term related to non -Michaelis - Menten kinetics of the enzymatic reaction. Solution for the concentration of the substrate has been derived for all values of parameters using the homotopy perturbation method. All the approximate analytic expressions of substrate concentration are compared with simulation results using Scilab/Matlab program. Finally, we have given a satisfactory agreement between them.

Predictions of nucleation theory applied to Ehrenfest thermodynamic transitions

NASA Technical Reports Server (NTRS)

Barker, R. E., Jr.; Campbell, K. W.

1984-01-01

A modified nucleation theory is used to determine a critical nucleus size and a critical activation-energy barrier for second-order Ehrenfest thermodynamic transitions as functions of the degree of undercooling, the interfacial energy, the heat-capacity difference, the specific volume of the transformed phase, and the equilibrium transition temperature. The customary approximations of nucleation theory are avoided by expanding the Gibbs free energy in a Maclaurin series and applying analytical thermodynamic expressions to evaluate the expansion coefficients. Nonlinear correction terms for first-order-transition calculations are derived, and numerical results are presented graphically for water and polystyrene as examples of first-order and quasi-second-order transitions, respectively.

Static magnetic susceptibility, crystal field and exchange interactions in rare earth titanate pyrochlores.

PubMed

Malkin, B Z; Lummen, T T A; van Loosdrecht, P H M; Dhalenne, G; Zakirov, A R

2010-07-14

The experimental temperature dependence (T = 2-300 K) of single crystal bulk and site susceptibilities of rare earth titanate pyrochlores R(2)Ti(2)O(7) (R = Sm, Eu, Gd, Tb, Dy, Ho, Er, Yb) is analyzed in the framework of crystal field theory and a mean field approximation. Analytical expressions for the site and bulk susceptibilities of the pyrochlore lattice are derived taking into account long range dipole-dipole interactions and anisotropic exchange interactions between the nearest neighbor rare earth ions. The sets of crystal field parameters and anisotropic exchange coupling constants have been determined and their variations along the lanthanide series are discussed.

Influence of the electron intrinsic magnetic moment on the transverse dielectric permittivity of degenerate electron gas

NASA Astrophysics Data System (ADS)

Maslov, S. A.; Bobrov, V. B.; Kirillin, A. V.; Trigger, S. A.

2018-01-01

Using the linear response theory, the transverse dielectric permittivity of a homogeneous and isotropic system of charged particles is considered. In the ideal gas approximation for the polarization function, an explicit analytical expression for the transverse permittivity of a degenerate electron plasma, which takes into account electron spin, is found. This result describes both the Landau diamagnetism and Pauli paramagnetism in electron plasma. The influence of the electron intrinsic magnetic moment on the spatial and frequency dispersion of the transverse dielectric permittivity of degenerate electron plasma is numerically studied, that is crucial for determining the optical characteristics of plasma.

Analytic approximations to the modon dispersion relation. [in oceanography

NASA Technical Reports Server (NTRS)

Boyd, J. P.

1981-01-01

Three explicit analytic approximations are given to the modon dispersion relation developed by Flierl et al. (1980) to describe Gulf Stream rings and related phenomena in the oceans and atmosphere. The solutions are in the form of k(q), and are developed in the form of a power series in q for small q, an inverse power series in 1/q for large q, and a two-point Pade approximant. The low order Pade approximant is shown to yield a solution for the dispersion relation with a maximum relative error for the lowest branch of the function equal to one in 700 in the q interval zero to infinity.

Analytical solutions of the Klein-Gordon equation for Manning-Rosen potential with centrifugal term through Nikiforov-Uvarov method

NASA Astrophysics Data System (ADS)

Hatami, N.; Setare, M. R.

2017-10-01

We present approximate analytical solutions of the Klein-Gordon equation with arbitrary l state for the Manning-Rosen potential using the Nikiforov-Uvarov method and adopting the approximation scheme for the centrifugal term. We provide the bound state energy spectrum and the wave function in terms of the hypergeometric functions.

Survey geometry and the internal consistency of recent cosmic shear measurements

NASA Astrophysics Data System (ADS)

Troxel, M. A.; Krause, E.; Chang, C.; Eifler, T. F.; Friedrich, O.; Gruen, D.; MacCrann, N.; Chen, A.; Davis, C.; DeRose, J.; Dodelson, S.; Gatti, M.; Hoyle, B.; Huterer, D.; Jarvis, M.; Lacasa, F.; Lemos, P.; Peiris, H. V.; Prat, J.; Samuroff, S.; Sánchez, C.; Sheldon, E.; Vielzeuf, P.; Wang, M.; Zuntz, J.; Lahav, O.; Abdalla, F. B.; Allam, S.; Annis, J.; Avila, S.; Bertin, E.; Brooks, D.; Burke, D. L.; Rosell, A. Carnero; Kind, M. Carrasco; Carretero, J.; Crocce, M.; Cunha, C. E.; D'Andrea, C. B.; da Costa, L. N.; De Vicente, J.; Diehl, H. T.; Doel, P.; Evrard, A. E.; Flaugher, B.; Fosalba, P.; Frieman, J.; García-Bellido, J.; Gaztanaga, E.; Gerdes, D. W.; Gruendl, R. A.; Gschwend, J.; Gutierrez, G.; Hartley, W. G.; Hollowood, D. L.; Honscheid, K.; James, D. J.; Kirk, D.; Kuehn, K.; Kuropatkin, N.; Li, T. S.; Lima, M.; March, M.; Menanteau, F.; Miquel, R.; Mohr, J. J.; Ogando, R. L. C.; Plazas, A. A.; Roodman, A.; Sanchez, E.; Scarpine, V.; Schindler, R.; Sevilla-Noarbe, I.; Smith, M.; Soares-Santos, M.; Sobreira, F.; Suchyta, E.; Swanson, M. E. C.; Thomas, D.; Walker, A. R.; Wechsler, R. H.

2018-06-01

We explore the impact of an update to the typical approximation for the shape noise term in the analytic covariance matrix for cosmic shear experiments that assumes the absence of survey boundary and mask effects. We present an exact expression for the number of galaxy pairs in this term based on the survey mask, which leads to more than a factor of three increase in the shape noise on the largest measured scales for the Kilo-Degree Survey (KIDS-450) real-space cosmic shear data. We compare the result of this analytic expression to several alternative methods for measuring the shape noise from the data and find excellent agreement. This update to the covariance resolves any internal model tension evidenced by the previously large cosmological best-fit χ2 for the KiDS-450 cosmic shear data. The best-fit χ2 is reduced from 161 to 121 for 118 degrees of freedom. We also apply a correction to how the multiplicative shear calibration uncertainty is included in the covariance. This change shifts the inferred amplitude of the correlation function to higher values. We find that this improves agreement of the KiDS-450 cosmic shear results with Dark Energy Survey Year 1 and Planck results.

Explicit formulas for effective piezoelectric coefficients of ferroelectric 0-3 composites based on effective medium theory

NASA Astrophysics Data System (ADS)

Wong, C. K.; Poon, Y. M.; Shin, F. G.

2003-01-01

Explicit formulas were derived for the effective piezoelectric stress coefficients of a 0-3 composite of ferroelectric spherical particles in a ferroelectric matrix which were then combined to give the more commonly used strain coefficients. Assuming that the elastic stiffness of the inclusion phase is sufficiently larger than that of the matrix phase, the previously derived explicit expressions for the case of a low volume concentration of inclusion particles [C. K. Wong, Y. M. Poon, and F. G. Shin, Ferroelectrics 264, 39 (2001); J. Appl. Phys. 90, 4690 (2001)] were "transformed" analytically by an effective medium theory (EMT) with appropriate approximations, to suit the case of a more concentrated suspension. Predictions of the EMT expressions were compared with the experimental values of composites of lead zirconate titanate ceramic particles dispersed in polyvinylidene fluoride and polyvinylidene fluoride-trifluoroethylene copolymer, reported by Furukawa [IEEE Trans. Electr. Insul. 24, 375 (1989)] and by Ng et al. [IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1308 (2000)] respectively. Fairly good agreement was obtained. Comparisons with other predictions, including the predictions given by numerically solving the EMT scheme, were also made. It was found that the analytic and numeric EMT schemes agreed with each other very well for an inclusion of volume fraction not exceeding 60%.

Including scattering within the room acoustics diffusion model: An analytical approach.

PubMed

Foy, Cédric; Picaut, Judicaël; Valeau, Vincent

2016-10-01

Over the last 20 years, a statistical acoustic model has been developed to predict the reverberant sound field in buildings. This model is based on the assumption that the propagation of the reverberant sound field follows a transport process and, as an approximation, a diffusion process that can be easily solved numerically. This model, initially designed and validated for rooms with purely diffuse reflections, is extended in the present study to mixed reflections, with a proportion of specular and diffuse reflections defined by a scattering coefficient. The proposed mathematical developments lead to an analytical expression of the diffusion constant that is a function of the scattering coefficient, but also on the absorption coefficient of the walls. The results obtained with this extended diffusion model are then compared with the classical diffusion model, as well as with a sound particles tracing approach considering mixed wall reflections. The comparison shows a good agreement for long rooms with uniform low absorption (α = 0.01) and uniform scattering. For a larger absorption (α = 0.1), the agreement is moderate, due to the fact that the proposed expression of the diffusion coefficient does not vary spatially. In addition, the proposed model is for now limited to uniform diffusion and should be extended in the future to more general cases.

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

An analytically solvable three-body break-up model problem in hyperspherical coordinates

NASA Astrophysics Data System (ADS)

Ancarani, L. U.; Gasaneo, G.; Mitnik, D. M.

2012-10-01

An analytically solvable S-wave model for three particles break-up processes is presented. The scattering process is represented by a non-homogeneous Coulombic Schrödinger equation where the driven term is given by a Coulomb-like interaction multiplied by the product of a continuum wave function and a bound state in the particles coordinates. The closed form solution is derived in hyperspherical coordinates leading to an analytic expression for the associated scattering transition amplitude. The proposed scattering model contains most of the difficulties encountered in real three-body scattering problem, e.g., non-separability in the electrons' spherical coordinates and Coulombic asymptotic behavior. Since the coordinates' coupling is completely different, the model provides an alternative test to that given by the Temkin-Poet model. The knowledge of the analytic solution provides an interesting benchmark to test numerical methods dealing with the double continuum, in particular in the asymptotic regions. An hyperspherical Sturmian approach recently developed for three-body collisional problems is used to reproduce to high accuracy the analytical results. In addition to this, we generalized the model generating an approximate wave function possessing the correct radial asymptotic behavior corresponding to an S-wave three-body Coulomb problem. The model allows us to explore the typical structure of the solution of a three-body driven equation, to identify three regions (the driven, the Coulombic and the asymptotic), and to analyze how far one has to go to extract the transition amplitude.

Nonlinear core deflection in injection molding

NASA Astrophysics Data System (ADS)

Poungthong, P.; Giacomin, A. J.; Saengow, C.; Kolitawong, C.; Liao, H.-C.; Tseng, S.-C.

2018-05-01

Injection molding of thin slender parts is often complicated by core deflection. This deflection is caused by molten plastics race tracking through the slit between the core and the rigid cavity wall. The pressure of this liquid exerts a lateral force of the slender core causing the core to bend, and this bending is governed by a nonlinear fifth order ordinary differential equation for the deflection that is not directly in the position along the core. Here we subject this differential equation to 6 sets of boundary conditions, corresponding to 6 commercial core constraints. For each such set of boundary conditions, we develop an explicit approximate analytical solution, including both a linear term and a nonlinear term. By comparison with finite difference solutions, we find our new analytical solutions to be accurate. We then use these solutions to derive explicit analytical approximations for maximum deflections and for the core position of these maximum deflections. Our experiments on the base-gated free-tip boundary condition agree closely with our new explicit approximate analytical solution.

Analytical approximations for the oscillators with anti-symmetric quadratic nonlinearity

NASA Astrophysics Data System (ADS)

Alal Hosen, Md.; Chowdhury, M. S. H.; Yeakub Ali, Mohammad; Faris Ismail, Ahmad

2017-12-01

A second-order ordinary differential equation involving anti-symmetric quadratic nonlinearity changes sign. The behaviour of the oscillators with an anti-symmetric quadratic nonlinearity is assumed to oscillate different in the positive and negative directions. In this reason, Harmonic Balance Method (HBM) cannot be directly applied. The main purpose of the present paper is to propose an analytical approximation technique based on the HBM for obtaining approximate angular frequencies and the corresponding periodic solutions of the oscillators with anti-symmetric quadratic nonlinearity. After applying HBM, a set of complicated nonlinear algebraic equations is found. Analytical approach is not always fruitful for solving such kinds of nonlinear algebraic equations. In this article, two small parameters are found, for which the power series solution produces desired results. Moreover, the amplitude-frequency relationship has also been determined in a novel analytical way. The presented technique gives excellent results as compared with the corresponding numerical results and is better than the existing ones.

Modeling of phonon scattering in n-type nanowire transistors using one-shot analytic continuation technique

NASA Astrophysics Data System (ADS)

Bescond, Marc; Li, Changsheng; Mera, Hector; Cavassilas, Nicolas; Lannoo, Michel

2013-10-01

We present a one-shot current-conserving approach to model the influence of electron-phonon scattering in nano-transistors using the non-equilibrium Green's function formalism. The approach is based on the lowest order approximation (LOA) to the current and its simplest analytic continuation (LOA+AC). By means of a scaling argument, we show how both LOA and LOA+AC can be easily obtained from the first iteration of the usual self-consistent Born approximation (SCBA) algorithm. Both LOA and LOA+AC are then applied to model n-type silicon nanowire field-effect-transistors and are compared to SCBA current characteristics. In this system, the LOA fails to describe electron-phonon scattering, mainly because of the interactions with acoustic phonons at the band edges. In contrast, the LOA+AC still well approximates the SCBA current characteristics, thus demonstrating the power of analytic continuation techniques. The limits of validity of LOA+AC are also discussed, and more sophisticated and general analytic continuation techniques are suggested for more demanding cases.

Capillary-wave dynamics and interface structure modulation in binary Bose-Einstein condensate mixtures

NASA Astrophysics Data System (ADS)

Indekeu, Joseph O.; Van Thu, Nguyen; Lin, Chang-You; Phat, Tran Huu

2018-04-01

The localized low-energy interfacial excitations, or interfacial Nambu-Goldstone modes, of phase-segregated binary mixtures of Bose-Einstein condensates are investigated analytically. To this end a double-parabola approximation (DPA) is performed on the Lagrangian density in Gross-Pitaevskii theory for a system in a uniform potential. This DPA entails a model in which analytic expressions are obtained for the excitations underlying capillary waves or ripplons for arbitrary strength K (>1 ) of the phase segregation. The dispersion relation ω (k ) ∝k3 /2 is derived directly from the Bogoliubov-de Gennes equations in the limit that the wavelength 2 π /k is much larger than the interface width. The proportionality constant in the dispersion relation provides the static interfacial tension. A correction term in ω (k ) of order k5 /2 is calculated analytically within the DPA model. The combined result is tested against numerical diagonalization of the exact Bogoliubov-de Gennes equations. Satisfactory agreement is obtained in the range of physically relevant wavelengths. The ripplon dispersion relation is relevant to state-of-the-art experiments using (quasi)uniform optical-box traps. Furthermore, within the DPA model explicit expressions are obtained for the structural deformation of the interface due to the passing of the capillary wave. It is found that the amplitude of the wave is enhanced by an amount that is quadratic in the ratio of the phase velocity ω /k to the sound velocity c . For generic mixtures consisting of condensates with unequal healing lengths, an additional modulation is predicted of the common value of the condensate densities at the interface.

Quantum gates by periodic driving

PubMed Central

Shi, Z. C.; Wang, W.; Yi, X. X.

2016-01-01

Topological quantum computation has been extensively studied in the past decades due to its robustness against decoherence. One way to realize the topological quantum computation is by adiabatic evolutions—it requires relatively long time to complete a gate, so the speed of quantum computation slows down. In this work, we present a method to realize single qubit quantum gates by periodic driving. Compared to adiabatic evolution, the single qubit gates can be realized at a fixed time much shorter than that by adiabatic evolution. The driving fields can be sinusoidal or square-well field. With the sinusoidal driving field, we derive an expression for the total operation time in the high-frequency limit, and an exact analytical expression for the evolution operator without any approximations is given for the square well driving. This study suggests that the period driving could provide us with a new direction in regulations of the operation time in topological quantum computation. PMID:26911900

Quantum gates by periodic driving.

PubMed

Shi, Z C; Wang, W; Yi, X X

2016-02-25

Topological quantum computation has been extensively studied in the past decades due to its robustness against decoherence. One way to realize the topological quantum computation is by adiabatic evolutions-it requires relatively long time to complete a gate, so the speed of quantum computation slows down. In this work, we present a method to realize single qubit quantum gates by periodic driving. Compared to adiabatic evolution, the single qubit gates can be realized at a fixed time much shorter than that by adiabatic evolution. The driving fields can be sinusoidal or square-well field. With the sinusoidal driving field, we derive an expression for the total operation time in the high-frequency limit, and an exact analytical expression for the evolution operator without any approximations is given for the square well driving. This study suggests that the period driving could provide us with a new direction in regulations of the operation time in topological quantum computation.

Extended Poisson process modelling and analysis of grouped binary data.

PubMed

Faddy, Malcolm J; Smith, David M

2012-05-01

A simple extension of the Poisson process results in binomially distributed counts of events in a time interval. A further extension generalises this to probability distributions under- or over-dispersed relative to the binomial distribution. Substantial levels of under-dispersion are possible with this modelling, but only modest levels of over-dispersion - up to Poisson-like variation. Although simple analytical expressions for the moments of these probability distributions are not available, approximate expressions for the mean and variance are derived, and used to re-parameterise the models. The modelling is applied in the analysis of two published data sets, one showing under-dispersion and the other over-dispersion. More appropriate assessment of the precision of estimated parameters and reliable model checking diagnostics follow from this more general modelling of these data sets. © 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Physiological breakdown of Jeffrey six constant nanofluid flow in an endoscope with nonuniform wall

NASA Astrophysics Data System (ADS)

Nadeem, S.; Shaheen, A.; Hussain, S.

2015-12-01

This paper analyse the endoscopic effects of peristaltic nanofluid flow of Jeffrey six-constant fluid model in the presence of magnetohydrodynamics flow. The current problem is modeled in the cylindrical coordinate system and exact solutions are managed (where possible) under low Reynolds number and long wave length approximation. The influence of emerging parameters on temperature and velocity profile are discussed graphically. The velocity equation is solved analytically by utilizing the homotopy perturbation technique strongly, while the exact solutions are computed from temperature equation. The obtained expressions for velocity , concentration and temperature is sketched during graphs and the collision of assorted parameters is evaluate for transform peristaltic waves. The solution depend on thermophoresis number Nt, local nanoparticles Grashof number Gr, and Brownian motion number Nb. The obtained expressions for the velocity, temperature, and nanoparticles concentration profiles are plotted and the impact of various physical parameters are investigated for different peristaltic waves.

SER Analysis of MPPM-Coded MIMO-FSO System over Uncorrelated and Correlated Gamma-Gamma Atmospheric Turbulence Channels

NASA Astrophysics Data System (ADS)

Khallaf, Haitham S.; Garrido-Balsells, José M.; Shalaby, Hossam M. H.; Sampei, Seiichi

2015-12-01

The performance of multiple-input multiple-output free space optical (MIMO-FSO) communication systems, that adopt multipulse pulse position modulation (MPPM) techniques, is analyzed. Both exact and approximate symbol-error rates (SERs) are derived for both cases of uncorrelated and correlated channels. The effects of background noise, receiver shot-noise, and atmospheric turbulence are taken into consideration in our analysis. The random fluctuations of the received optical irradiance, produced by the atmospheric turbulence, is modeled by the widely used gamma-gamma statistical distribution. Uncorrelated MIMO channels are modeled by the α-μ distribution. A closed-form expression for the probability density function of the optical received irradiance is derived for the case of correlated MIMO channels. Using our analytical expressions, the degradation of the system performance with the increment of the correlation coefficients between MIMO channels is corroborated.

Light-induced cross transport phenomena in a single-component gas

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

Chermyaninov, I. V.; Chernyak, V. G., E-mail: Vladimir.Chernyak@usu.ru

2013-07-15

The cross transport processes that occur in a single-component gas in a capillary and are caused by resonance laser radiation and pressure and temperature gradients are studied. An expression for entropy production is derived using a system of kinetic Boltzmann equations in a linear approximation. The kinetic coefficients that determine the transport processes are shown to satisfy the Onsager reciprocal relations at any Knudsen numbers and any character of the elastic interaction of gas particles with the capillary surface. The light-induced baro- and thermoeffects that take place in a closed heat-insulated system in the field of resonance laser radiation aremore » considered. Analytical expressions are obtained for the Onsager coefficients in an almost free-molecular regime. The light-induced pressure and temperature gradients that appear in a closed heat-insulated capillary under typical experimental conditions are numerically estimated.« less

Magnetoencephalography in ellipsoidal geometry

NASA Astrophysics Data System (ADS)

Dassios, George; Kariotou, Fotini

2003-01-01

An exact analytic solution for the forward problem in the theory of biomagnetics of the human brain is known only for the (1D) case of a sphere and the (2D) case of a spheroid, where the excitation field is due to an electric dipole within the corresponding homogeneous conductor. In the present work the corresponding problem for the more realistic ellipsoidal brain model is solved and the leading quadrupole approximation for the exterior magnetic field is obtained in a form that exhibits the anisotropic character of the ellipsoidal geometry. The results are obtained in a straightforward manner through the evaluation of the interior electric potential and a subsequent calculation of the surface integral over the ellipsoid, using Lamé functions and ellipsoidal harmonics. The basic formulas are expressed in terms of the standard elliptic integrals that enter the expressions for the exterior Lamé functions. The laborious task of reducing the results to the spherical geometry is also included.

Lineshape theory of pigment-protein complexes: How the finite relaxation time of nuclei influences the exciton relaxation-induced lifetime broadening.

PubMed

Dinh, Thanh-Chung; Renger, Thomas

2016-07-21

In pigment-protein complexes, often the excited states are partially delocalized and the exciton-vibrational coupling in the basis of delocalized states contains large diagonal and small off-diagonal elements. This inequality may be used to introduce potential energy surfaces (PESs) of exciton states and to treat the inter-PES coupling in Markov and secular approximations. The resulting lineshape function consists of a Lorentzian peak that is broadened by the finite lifetime of the exciton states caused by the inter-PES coupling and a vibrational sideband that results from the mutual displacement of the excitonic PESs with respect to that of the ground state. So far analytical expressions have been derived that relate the exciton relaxation-induced lifetime broadening to the Redfield [T. Renger and R. A. Marcus, J. Chem. Phys. 116, 9997 (2002)] or modified Redfield [M. Schröder, U. Kleinekathöfer, and M. Schreiber, J. Chem. Phys. 124, 084903 (2006)] rate constants of exciton relaxation, assuming that intra-PES nuclear relaxation is fast compared to inter-PES transfer. Here, we go beyond this approximation and provide an analytical expression, termed Non-equilibrium Modified Redfield (NeMoR) theory, for the lifetime broadening that takes into account the finite nuclear relaxation time. In an application of the theory to molecular dimers, we find that, for a widely used experimental spectral density of the exciton-vibrational coupling of pigment-protein complexes, the NeMoR spectrum at low-temperatures (T < 150 K) is better approximated by Redfield than by modified Redfield theory. At room temperature, the lifetime broadening obtained with Redfield theory underestimates the NeMoR broadening, whereas modified Redfield theory overestimates it by a similar amount. A fortuitous error compensation in Redfield theory is found to explain the good performance of this theory at low temperatures. Since steady state spectra of PPCs are often measured at low temperatures, Redfield theory still provides a numerically efficient alternative to NeMoR theory. At higher temperatures, we suggest to use NeMoR theory, because it has the same numerical costs as modified Redfield theory, but is more accurate.

Transverse signal decay under the weak field approximation: Theory and validation.

PubMed

Berman, Avery J L; Pike, G Bruce

2018-07-01

To derive an expression for the transverse signal time course from systems in the motional narrowing regime, such as water diffusing in blood. This was validated in silico and experimentally with ex vivo blood samples. A closed-form solution (CFS) for transverse signal decay under any train of refocusing pulses was derived using the weak field approximation. The CFS was validated via simulations of water molecules diffusing in the presence of spherical perturbers, with a range of sizes and under various pulse sequences. The CFS was compared with more conventional fits assuming monoexponential decay, including chemical exchange, using ex vivo blood Carr-Purcell-Meiboom-Gill data. From simulations, the CFS was shown to be valid in the motional narrowing regime and partially into the intermediate dephasing regime, with increased accuracy with increasing Carr-Purcell-Meiboom-Gill refocusing rate. In theoretical calculations of the CFS, fitting for the transverse relaxation rate (R 2 ) gave excellent agreement with the weak field approximation expression for R 2 for Carr-Purcell-Meiboom-Gill sequences, but diverged for free induction decay. These same results were confirmed in the ex vivo analysis. Transverse signal decay in the motional narrowing regime can be accurately described analytically. This theory has applications in areas such as tissue iron imaging, relaxometry of blood, and contrast agent imaging. Magn Reson Med 80:341-350, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Two-way DF relaying assisted D2D communication: ergodic rate and power allocation

NASA Astrophysics Data System (ADS)

Ni, Yiyang; Wang, Yuxi; Jin, Shi; Wong, Kai-Kit; Zhu, Hongbo

2017-12-01

In this paper, we investigate the ergodic rate for a device-to-device (D2D) communication system aided by a two-way decode-and-forward (DF) relay node. We first derive closed-form expressions for the ergodic rate of the D2D link under asymmetric and symmetric cases, respectively. We subsequently discuss two special scenarios including weak interference case and high signal-to-noise ratio case. Then we derive the tight approximations for each of the considered scenarios. Assuming that each transmitter only has access to its own statistical channel state information (CSI), we further derive closed-form power allocation strategy to improve the system performance according to the analytical results of the ergodic rate. Furthermore, some insights are provided for the power allocation strategy based on the analytical results. The strategies are easy to compute and require to know only the channel statistics. Numerical results show the accuracy of the analysis results under various conditions and test the availability of the power allocation strategy.

An analytical model for transient deformation of viscoelastically coated beams: Applications to static-mode microcantilever chemical sensors

NASA Astrophysics Data System (ADS)

Heinrich, S. M.; Wenzel, M. J.; Josse, F.; Dufour, I.

2009-06-01

The problem governing the transient deformation of an elastic cantilever beam with viscoelastic coating, subjected to a time-dependent coating eigenstrain, is mathematically formulated. An analytical solution for an exponential eigenstrain history, exact within the context of beam theory, is obtained in terms of the coating and base layer thicknesses, the elastic modulus of the base material, the initial coating modulus, the coating relaxation percentage (0%-100%), and the time constants of the coating's relaxation process and its eigenstrain history. Approximate formulas, valid for thin coatings, are derived as special cases to provide insight into system behavior. Main results include (1) the time histories of the beam curvature and the coating stresses, (2) a criterion governing the response type (monotonic or "overshoot" response), and (3) simple expressions for the overshoot ratio, defined as the peak response scaled by the steady-state response, and the time at which the peak response occurs. Applications to polymer-coated microcantilever-based chemical sensors operating in the static mode are discussed.

Secure communication via an energy-harvesting untrusted relay in the presence of an eavesdropper

NASA Astrophysics Data System (ADS)

Tuan, Van Phu; Kong, Hyung Yun

2018-02-01

This article studies a secure communication of a simultaneous wireless information and power transfer system in which an energy-constrained untrusted relay, which harvests energy from the wireless signals, helps the communication between the source and destination and is able to decode the source's confidential signal. Additionally, the source's confidential signal is also overheard by a passive eavesdropper. To create positive secrecy capacity, a destination-assisted jamming signal that is completely cancelled at the destination is adopted. Moreover, the jamming signal is also exploited as an additional energy source. To evaluate the secrecy performance, analytical expressions for the secrecy outage probability (SOP) and the average secrecy capacity are derived. Moreover, a high-power approximation for the SOP is presented. The accuracy of the analytical results is verified by Monte Carlo simulations. Numerical results provide valuable insights into the effect of various system parameters, such as the energy-harvesting efficiency, secrecy rate threshold, power-splitting ratio, transmit powers, and locations of the relay and eavesdropper, on the secrecy performance.

Radiative transfer model for aerosols in infrared wavelengths for passive remote sensing applications.

PubMed

Ben-David, Avishai; Embury, Janon F; Davidson, Charles E

2006-09-10

A comprehensive analytical radiative transfer model for isothermal aerosols and vapors for passive infrared remote sensing applications (ground-based and airborne sensors) has been developed. The theoretical model illustrates the qualitative difference between an aerosol cloud and a chemical vapor cloud. The model is based on two and two/four stream approximations and includes thermal emission-absorption by the aerosols; scattering of diffused sky radiances incident from all sides on the aerosols (downwelling, upwelling, left, and right); and scattering of aerosol thermal emission. The model uses moderate resolution transmittance ambient atmospheric radiances as boundary conditions and provides analytical expressions for the information on the aerosol cloud that is contained in remote sensing measurements by using thermal contrasts between the aerosols and diffused sky radiances. Simulated measurements of a ground-based sensor viewing Bacillus subtilis var. niger bioaerosols and kaolin aerosols are given and discussed to illustrate the differences between a vapor-only model (i.e., only emission-absorption effects) and a complete model that adds aerosol scattering effects.

Transient well flow in leaky multiple-aquifer systems

NASA Astrophysics Data System (ADS)

Hemker, C. J.

1985-10-01

A previously developed eigenvalue analysis approach to groundwater flow in leaky multiple aquifers is used to derive exact solutions for transient well flow problems in leaky and confined systems comprising any number of aquifers. Equations are presented for the drawdown distribution in systems of infinite extent, caused by wells penetrating one or more of the aquifers completely and discharging each layer at a constant rate. Since the solution obtained may be regarded as a combined analytical-numerical technique, a type of one-dimensional modelling can be applied to find approximate solutions for several complicating conditions. Numerical evaluations are presented as time-drawdown curves and include effects of storage in the aquitard, unconfined conditions, partially penetrating wells and stratified aquifers. The outcome of calculations for relatively simple systems compares very well with published corresponding results. The proposed multilayer solution can be a valuable tool in aquifer test evaluation, as it provides the analytical expression required to enable the application of existing computer methods to the determination of aquifer characteristics.

Analytical estimation on divergence and flutter vibrations of symmetrical three-phase induction stator via field-synchronous coordinates

NASA Astrophysics Data System (ADS)

Xia, Ying; Wang, Shiyu; Sun, Wenjia; Xiu, Jie

2017-01-01

The electromagnetically induced parametric vibration of the symmetrical three-phase induction stator is examined. While it can be analyzed by an approximate analytical or numerical method, more accurate and simple analytical method is desirable. This work proposes a new method based on the field-synchronous coordinates. A mechanical-electromagnetic coupling model is developed under this frame such that a time-invariant governing equation with gyroscopic term can be developed. With the general vibration theory, the eigenvalue is formulated; the transition curves between the stable and unstable regions, and response are all determined as closed-form expressions of basic mechanical-electromagnetic parameters. The dependence of these parameters on the instability behaviors is demonstrated. The results imply that the divergence and flutter instabilities can occur even for symmetrical motors with balanced, constant amplitude and sinusoidal voltage. To verify the analytical predictions, this work also builds up a time-variant model of the same system under the conventional inertial frame. The Floquét theory is employed to predict the parametric instability and the numerical integration is used to obtain the parametric response. The parametric instability and response are both well compared against those under the field-synchronous coordinates. The proposed field-synchronous coordinates allows a quick estimation on the electromagnetically induced vibration. The convenience offered by the body-fixed coordinates is discussed across various fields.

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.

An analytical technique for approximating unsteady aerodynamics in the time domain

NASA Technical Reports Server (NTRS)

Dunn, H. J.

1980-01-01

An analytical technique is presented for approximating unsteady aerodynamic forces in the time domain. The order of elements of a matrix Pade approximation was postulated, and the resulting polynomial coefficients were determined through a combination of least squares estimates for the numerator coefficients and a constrained gradient search for the denominator coefficients which insures stable approximating functions. The number of differential equations required to represent the aerodynamic forces to a given accuracy tends to be smaller than that employed in certain existing techniques where the denominator coefficients are chosen a priori. Results are shown for an aeroelastic, cantilevered, semispan wing which indicate a good fit to the aerodynamic forces for oscillatory motion can be achieved with a matrix Pade approximation having fourth order numerator and second order denominator polynomials.

Analytical approximations to the Hotelling trace for digital x-ray detectors

NASA Astrophysics Data System (ADS)

Clarkson, Eric; Pineda, Angel R.; Barrett, Harrison H.

2001-06-01

The Hotelling trace is the signal-to-noise ratio for the ideal linear observer in a detection task. We provide an analytical approximation for this figure of merit when the signal is known exactly and the background is generated by a stationary random process, and the imaging system is an ideal digital x-ray detector. This approximation is based on assuming that the detector is infinite in extent. We test this approximation for finite-size detectors by comparing it to exact calculations using matrix inversion of the data covariance matrix. After verifying the validity of the approximation under a variety of circumstances, we use it to generate plots of the Hotelling trace as a function of pairs of parameters of the system, the signal and the background.

Approximation and inference methods for stochastic biochemical kinetics—a tutorial review

NASA Astrophysics Data System (ADS)

Schnoerr, David; Sanguinetti, Guido; Grima, Ramon

2017-03-01

Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose dynamics are governed by the chemical master equation. Despite its simple structure, no analytic solutions to the chemical master equation are known for most systems. Moreover, stochastic simulations are computationally expensive, making systematic analysis and statistical inference a challenging task. Consequently, significant effort has been spent in recent decades on the development of efficient approximation and inference methods. This article gives an introduction to basic modelling concepts as well as an overview of state of the art methods. First, we motivate and introduce deterministic and stochastic methods for modelling chemical networks, and give an overview of simulation and exact solution methods. Next, we discuss several approximation methods, including the chemical Langevin equation, the system size expansion, moment closure approximations, time-scale separation approximations and hybrid methods. We discuss their various properties and review recent advances and remaining challenges for these methods. We present a comparison of several of these methods by means of a numerical case study and highlight some of their respective advantages and disadvantages. Finally, we discuss the problem of inference from experimental data in the Bayesian framework and review recent methods developed the literature. In summary, this review gives a self-contained introduction to modelling, approximations and inference methods for stochastic chemical kinetics.

An analytic performance model of disk arrays and its application

NASA Technical Reports Server (NTRS)

Lee, Edward K.; Katz, Randy H.

1991-01-01

As disk arrays become widely used, tools for understanding and analyzing their performance become increasingly important. In particular, performance models can be invaluable in both configuring and designing disk arrays. Accurate analytic performance models are desirable over other types of models because they can be quickly evaluated, are applicable under a wide range of system and workload parameters, and can be manipulated by a range of mathematical techniques. Unfortunately, analytical performance models of disk arrays are difficult to formulate due to the presence of queuing and fork-join synchronization; a disk array request is broken up into independent disk requests which must all complete to satisfy the original request. We develop, validate, and apply an analytic performance model for disk arrays. We derive simple equations for approximating their utilization, response time, and throughput. We then validate the analytic model via simulation and investigate the accuracy of each approximation used in deriving the analytical model. Finally, we apply the analytical model to derive an equation for the optimal unit of data striping in disk arrays.

On the Gibbs phenomenon 5: Recovering exponential accuracy from collocation point values of a piecewise analytic function

NASA Technical Reports Server (NTRS)

Gottlieb, David; Shu, Chi-Wang

1994-01-01

The paper presents a method to recover exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of an approximation to the interpolation polynomial (or trigonometrical polynomial). We show that if we are given the collocation point values (or a highly accurate approximation) at the Gauss or Gauss-Lobatto points, we can reconstruct a uniform exponentially convergent approximation to the function f(x) in any sub-interval of analyticity. The proof covers the cases of Fourier, Chebyshev, Legendre, and more general Gegenbauer collocation methods.

A New Equivalence Theory Method for Treating Doubly Heterogeneous Fuel - II. Verifications

DOE PAGES

Choi, Sooyoung; Kong, Chidong; Lee, Deokjung; ...

2015-03-09

A new methodology has been developed recently to treat resonance self-shielding in systems for which the fuel compact region of a reactor lattice consists of small fuel grains dispersed in a graphite matrix. The theoretical development adopts equivalence theory in both micro- and macro-level heterogeneities to provide approximate analytical expressions for the shielded cross sections, which may be interpolated from a table of resonance integrals or Bondarenko factors using a modified background cross section as the interpolation parameter. This paper describes the first implementation of the theoretical equations in a reactor analysis code. In order to reduce discrepancies caused bymore » use of the rational approximation for collision probabilities in the original derivation, a new formulation for a doubly heterogeneous Bell factor is developed in this paper to improve the accuracy of doubly heterogeneous expressions. This methodology is applied to a wide range of pin cell and assembly test problems with varying geometry parameters, material compositions, and temperatures, and the results are compared with continuous-energy Monte Carlo simulations to establish the accuracy and range of applicability of the new approach. It is shown that the new doubly heterogeneous self-shielding method including the Bell factor correction gives good agreement with reference Monte Carlo results.« less

Model reduction for stochastic chemical systems with abundant species.

PubMed

Smith, Stephen; Cianci, Claudia; Grima, Ramon

2015-12-07

Biochemical processes typically involve many chemical species, some in abundance and some in low molecule numbers. We first identify the rate constant limits under which the concentrations of a given set of species will tend to infinity (the abundant species) while the concentrations of all other species remains constant (the non-abundant species). Subsequently, we prove that, in this limit, the fluctuations in the molecule numbers of non-abundant species are accurately described by a hybrid stochastic description consisting of a chemical master equation coupled to deterministic rate equations. This is a reduced description when compared to the conventional chemical master equation which describes the fluctuations in both abundant and non-abundant species. We show that the reduced master equation can be solved exactly for a number of biochemical networks involving gene expression and enzyme catalysis, whose conventional chemical master equation description is analytically impenetrable. We use the linear noise approximation to obtain approximate expressions for the difference between the variance of fluctuations in the non-abundant species as predicted by the hybrid approach and by the conventional chemical master equation. Furthermore, we show that surprisingly, irrespective of any separation in the mean molecule numbers of various species, the conventional and hybrid master equations exactly agree for a class of chemical systems.

Theoretical modeling and experimental validation of a torsional piezoelectric vibration energy harvesting system

NASA Astrophysics Data System (ADS)

Qian, Feng; Zhou, Wanlu; Kaluvan, Suresh; Zhang, Haifeng; Zuo, Lei

2018-04-01

Vibration energy harvesting has been extensively studied in recent years to explore a continuous power source for sensor networks and low-power electronics. Torsional vibration widely exists in mechanical engineering; however, it has not yet been well exploited for energy harvesting. This paper presents a theoretical model and an experimental validation of a torsional vibration energy harvesting system comprised of a shaft and a shear mode piezoelectric transducer. The piezoelectric transducer position on the surface of the shaft is parameterized by two variables that are optimized to obtain the maximum power output. The piezoelectric transducer can work in d 15 mode (pure shear mode), coupled mode of d 31 and d 33, and coupled mode of d 33, d 31 and d 15, respectively, when attached at different angles. Approximate expressions of voltage and power are derived from the theoretical model, which gave predictions in good agreement with analytical solutions. Physical interpretations on the implicit relationship between the power output and the position parameters of the piezoelectric transducer is given based on the derived approximate expression. The optimal position and angle of the piezoelectric transducer is determined, in which case, the transducer works in the coupled mode of d 15, d 31 and d 33.

Model reduction for stochastic chemical systems with abundant species

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

Smith, Stephen; Cianci, Claudia; Grima, Ramon

2015-12-07

Biochemical processes typically involve many chemical species, some in abundance and some in low molecule numbers. We first identify the rate constant limits under which the concentrations of a given set of species will tend to infinity (the abundant species) while the concentrations of all other species remains constant (the non-abundant species). Subsequently, we prove that, in this limit, the fluctuations in the molecule numbers of non-abundant species are accurately described by a hybrid stochastic description consisting of a chemical master equation coupled to deterministic rate equations. This is a reduced description when compared to the conventional chemical master equationmore » which describes the fluctuations in both abundant and non-abundant species. We show that the reduced master equation can be solved exactly for a number of biochemical networks involving gene expression and enzyme catalysis, whose conventional chemical master equation description is analytically impenetrable. We use the linear noise approximation to obtain approximate expressions for the difference between the variance of fluctuations in the non-abundant species as predicted by the hybrid approach and by the conventional chemical master equation. Furthermore, we show that surprisingly, irrespective of any separation in the mean molecule numbers of various species, the conventional and hybrid master equations exactly agree for a class of chemical systems.« less

Scaling and percolation in the small-world network model

NASA Astrophysics Data System (ADS)

Newman, M. E. J.; Watts, D. J.

1999-12-01

In this paper we study the small-world network model of Watts and Strogatz, which mimics some aspects of the structure of networks of social interactions. We argue that there is one nontrivial length-scale in the model, analogous to the correlation length in other systems, which is well-defined in the limit of infinite system size and which diverges continuously as the randomness in the network tends to zero, giving a normal critical point in this limit. This length-scale governs the crossover from large- to small-world behavior in the model, as well as the number of vertices in a neighborhood of given radius on the network. We derive the value of the single critical exponent controlling behavior in the critical region and the finite size scaling form for the average vertex-vertex distance on the network, and, using series expansion and Padé approximants, find an approximate analytic form for the scaling function. We calculate the effective dimension of small-world graphs and show that this dimension varies as a function of the length-scale on which it is measured, in a manner reminiscent of multifractals. We also study the problem of site percolation on small-world networks as a simple model of disease propagation, and derive an approximate expression for the percolation probability at which a giant component of connected vertices first forms (in epidemiological terms, the point at which an epidemic occurs). The typical cluster radius satisfies the expected finite size scaling form with a cluster size exponent close to that for a random graph. All our analytic results are confirmed by extensive numerical simulations of the model.

Characterization of Perovskite Oxide/Semiconductor Heterostructures

NASA Astrophysics Data System (ADS)

Walker, Phillip

The tools developed for the use of investigating dynamical systems have provided critical understanding to a wide range of physical phenomena. Here these tools are used to gain further insight into scalar transport, and how it is affected by mixing. The aim of this research is to investigate the efficiency of several different partitioning methods which demarcate flow fields into dynamically distinct regions, and the correlation of finite-time statistics from the advection-diffusion equation to these regions. For autonomous systems, invariant manifold theory can be used to separate the system into dynamically distinct regions. Despite there being no equivalent method for nonautonomous systems, a similar analysis can be done. Systems with general time dependencies must resort to using finite-time transport barriers for partitioning; these barriers are the edges of Lagrangian coherent structures (LCS), the analog to the stable and unstable manifolds of invariant manifold theory. Using the coherent structures of a flow to analyze the statistics of trapping, flight, and residence times, the signature of anomalous diffusion are obtained. This research also investigates the use of linear models for approximating the elements of the covariance matrix of nonlinear flows, and then applying the covariance matrix approximation over coherent regions. The first and second-order moments can be used to fully describe an ensemble evolution in linear systems, however there is no direct method for nonlinear systems. The problem is only compounded by the fact that the moments for nonlinear flows typically don't have analytic representations, therefore direct numerical simulations would be needed to obtain the moments throughout the domain. To circumvent these many computations, the nonlinear system is approximated as many linear systems for which analytic expressions for the moments exist. The parameters introduced in the linear models are obtained locally from the nonlinear deformation tensor.

High Energy Laser Beam Propagation in the Atmosphere: The Integral Invariants of the Nonlinear Parabolic Equation and the Method of Moments

NASA Technical Reports Server (NTRS)

Manning, Robert M.

2012-01-01

The method of moments is used to define and derive expressions for laser beam deflection and beam radius broadening for high-energy propagation through the Earth s atmosphere. These expressions are augmented with the integral invariants of the corresponding nonlinear parabolic equation that describes the electric field of high-energy laser beam to propagation to yield universal equations for the aforementioned quantities; the beam deflection is a linear function of the propagation distance whereas the beam broadening is a quadratic function of distance. The coefficients of these expressions are then derived from a thin screen approximation solution of the nonlinear parabolic equation to give corresponding analytical expressions for a target located outside the Earth s atmospheric layer. These equations, which are graphically presented for a host of propagation scenarios, as well as the thin screen model, are easily amenable to the phase expansions of the wave front for the specification and design of adaptive optics algorithms to correct for the inherent phase aberrations. This work finds application in, for example, the analysis of beamed energy propulsion for space-based vehicles.

Higgs boson mass corrections in the μ ν SSM with effective potential methods

NASA Astrophysics Data System (ADS)

Zhang, Hai-Bin; Feng, Tai-Fu; Yang, Xiu-Yi; Zhao, Shu-Min; Ning, Guo-Zhu

2017-04-01

To solve the μ problem of the MSSM, the μ from ν supersymmetric standard model (μ ν SSM ) introduces three singlet right-handed neutrino superfields ν^ic, which lead to the mixing of the neutral components of the Higgs doublets with the sneutrinos, producing a relatively large C P -even neutral scalar mass matrix. In this work, we analytically diagonalize the C P -even neutral scalar mass matrix and analyze in detail how the mixing impacts the lightest Higgs boson mass. We also give an approximate expression for the lightest Higgs boson mass. Simultaneously, we consider the radiative corrections to the Higgs boson masses with effective potential methods.

Eikonal Scattering in the sdg Interacting Boson Model:. Analytical Results in the SUsdg(3) Limit and Their Generalizations

NASA Astrophysics Data System (ADS)

Kota, V. K. B.

General expression for the representation matrix elements in the SUsdg(3) limit of the sdg interacting boson model (sdgIBM) is derived that determine the scattering amplitude in the eikonal approximation for medium energy proton-nucleus scattering when the target nucleus is deformed and it is described by the SUsdg(3) limit. The SUsdg(3) result is generalized to two important situations: (i) when the target nucleus ground band states are described as states arising out of angular momentum projection from a general single Kπ = 0+ intrinsic state in sdg space; (ii) for rotational bands built on one-phonon excitations in sdgIBM.

Closed-form expressions for state-to-state charge-transfer differential cross sections in a modified Faddeev three-body approach

NASA Astrophysics Data System (ADS)

Adivi, E. Ghanbari; Brunger, M. J.; Bolorizadeh, M. A.; Campbell, L.

2007-02-01

The second-order Faddeev-Watson-Lovelace approximation in a modified form is applied to charge transfer from hydrogenlike target atoms by a fully stripped energetic projectile ion. The state-to-state, nlm→n'l'm' , partial transition amplitudes are calculated analytically. The method is specifically applied to the collision of protons with hydrogen atoms, where differential cross sections of different transitions are calculated for incident energies of 2.8 and 5.0MeV . It is shown that the Thomas peak is present in all transition cross sections. The partial cross sections are then summed and compared with the available forward-angle experimental data, showing good agreement.

Far-infrared rotational emission by carbon monoxide

NASA Technical Reports Server (NTRS)

Mckee, C. F.; Storey, J. W. V.; Watson, D. M.; Green, S.

1982-01-01

Accurate theoretical collisional excitation rates are used to determine the emissivities of CO rotational lines for an H2 molecule content of at least 10,000/cu cm, temperature in the range 100-3000 K, and J not more than 60 under the assumption that the lines are optically thin. An approximate analytic expression for the emissivities which is valid in this region is obtained. Population inversions in the lower rotational levels occur for densities of molecular H2 around 1000-100,000/cu cm and temperatures T not more than about 50 K provided photon trapping is unimportant. Interstellar shocks observed edge-on are a potential source of weak millimeter-wave CO maser emission.

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.

Time-dependent diffusive acceleration of test particles at shocks

NASA Astrophysics Data System (ADS)

Drury, L. O'C.

1991-07-01

A theoretical description is developed for the acceleration of test particles at a steady plane nonrelativistic shock. The mean and the variance of the acceleration-time distribution are expressed analytically for the condition under which the diffusion coefficient is arbitrarily dependent on position and momentum. The formula for an acceleration rate with arbitrary spatial variation in the diffusion coefficient developed by Drury (1987) is supplemented by a general theory of time dependence. An approximation scheme is developed by means of the analysis which permits the description of the spectral cutoff resulting from the finite shock age. The formulas developed in the analysis are also of interest for analyzing the observations of heliospheric shocks made from spacecraft.

Ensemble of single quadrupolar nuclei in rotating solids: sidebands in NMR spectrum.

PubMed

Kundla, Enn

2006-07-01

A novel way is proposed to describe the evolution of nuclear magnetic polarization and the induced NMR spectrum. In this method, the effect of a high-intensity external static magnetic field and the effects of proper Hamiltonian left over interaction components, which commute with the first, are taken into account simultaneously and equivalently. The method suits any concrete NMR problem. This brings forth the really existing details in the registered spectra, evoked by Hamiltonian secular terms, which may be otherwise smoothed due to approximate treatment of the effects of the secular terms. Complete analytical expressions are obtained describing the NMR spectra including the rotational sideband sets of single quadrupolar nuclei in rotating solids.

Random matrix approach to plasmon resonances in the random impedance network model of disordered nanocomposites

NASA Astrophysics Data System (ADS)

Olekhno, N. A.; Beltukov, Y. M.

2018-05-01

Random impedance networks are widely used as a model to describe plasmon resonances in disordered metal-dielectric and other two-component nanocomposites. In the present work, the spectral properties of resonances in random networks are studied within the framework of the random matrix theory. We have shown that the appropriate ensemble of random matrices for the considered problem is the Jacobi ensemble (the MANOVA ensemble). The obtained analytical expressions for the density of states in such resonant networks show a good agreement with the results of numerical simulations in a wide range of metal filling fractions 0

Calculations of Total Classical Cross Sections for a Central Field

NASA Astrophysics Data System (ADS)

Tsyganov, D. L.

2018-07-01

In order to find the total collision cross-section a direct method of the effective potential (EPM) in the framework of classical mechanics was proposed. EPM allows to over come both the direct scattering problem (calculation of the total collision cross-section) and the inverse scattering problem (reconstruction of the scattering potential) quickly and effectively. A general analytical expression was proposed for the generalized Lennard-Jones potentials: (6-3), (9-3), (12-3), (6-4), (8-4), (12-4), (8-6), (12-6), (18-6). The values for the scattering potential of the total cross section for pairs such as electron-N2, N-N, and O-O2 were obtained in a good approximation.

Elastic scattering losses from colliding Bose-Einstein condensates

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

Zin Pawel; Chwedenczuk, Jan; Trippenbach, Marek

2006-03-15

Bragg diffraction divides a Bose-Einstein condensate into two overlapping components, moving with respect to each other with high momentum. Elastic collisions between atoms from distinct wave packets can significantly deplete the condensate. Recently, Zin et al. [Phys. Rev. Lett. 94, 200401 (2005)] introduced a model of two counterpropagating atomic Gaussian wave packets incorporating the dynamics of the incoherent scattering processes. Here we study the properties of this model in detail, including the nature of the transition from spontaneous to stimulated scattering. Within the first-order approximation, we derive analytical expressions for the density matrix and anomalous density that provide excellent insightmore » into correlation properties of scattered atoms.« less

Barnacles resist removal by crack trapping

PubMed Central

Hui, Chung-Yuen; Long, Rong; Wahl, Kathryn J.; Everett, Richard K.

2011-01-01

We study the mechanics of pull-off of a barnacle adhering to a thin elastic layer which is bonded to a rigid substrate. We address the case of barnacles having acorn shell geometry and hard, calcarious base plates. Pull-off is initiated by the propagation of an interface edge crack between the base plate and the layer. We compute the energy release rate of this crack as it grows along the interface using a finite element method. We also develop an approximate analytical model to interpret our numerical results and to give a closed-form expression for the energy release rate. Our result shows that the resistance of barnacles to interfacial failure arises from a crack-trapping mechanism. PMID:21208968

A semi-analytical study of positive corona discharge in wire-plane electrode configuration

NASA Astrophysics Data System (ADS)

Yanallah, K.; Pontiga, F.; Chen, J. H.

2013-08-01

Wire-to-plane positive corona discharge in air has been studied using an analytical model of two species (electrons and positive ions). The spatial distributions of electric field and charged species are obtained by integrating Gauss's law and the continuity equations of species along the Laplacian field lines. The experimental values of corona current intensity and applied voltage, together with Warburg's law, have been used to formulate the boundary condition for the electron density on the corona wire. To test the accuracy of the model, the approximate electric field distribution has been compared with the exact numerical solution obtained from a finite element analysis. A parametrical study of wire-to-plane corona discharge has then been undertaken using the approximate semi-analytical solutions. Thus, the spatial distributions of electric field and charged particles have been computed for different values of the gas pressure, wire radius and electrode separation. Also, the two dimensional distribution of ozone density has been obtained using a simplified plasma chemistry model. The approximate semi-analytical solutions can be evaluated in a negligible computational time, yet provide precise estimates of corona discharge variables.

Second-order reconstruction of the inflationary potential

NASA Technical Reports Server (NTRS)

Liddle, Andrew R.; Turner, Michael S.

1994-01-01

To first order in the deviation from scale invariance the inflationary potential and its first two derivatives can be expressed in terms of the spectral indices of the scalar and tensor perturbations, n and n(sub T), and their contributions to the variance of the quadrupole CBR temperature anisotropy, S and T. In addition, there is a 'consistency relation' between these quantities: n(sub T) = (-1/ 7)(T/S). We derive the second-order expressions for the inflationary potential and its first two derivatives and the first-order expression for its third derivative, in terms, of n, n(sub T), S, T, and dn/d ln gamma. We also obtain the second-order consistency relation, n(sub T) = (-1/7)(T/S)(1 + 0.11(T/S) + 0.15(n-1)). As an example we consider the exponential potential, the only known case where exact analytic solutions for the perturbation spectra exist. We reconstruct the potential via Taylor expansion (with coefficients calculated at both first and second order), and introduce the Pade approximate as a greatly improved alternative.

Unruh effect for general trajectories

NASA Astrophysics Data System (ADS)

Obadia, N.; Milgrom, M.

2007-03-01

We consider two-level detectors coupled to a scalar field and moving on arbitrary trajectories in Minkowski space-time. We first derive a generic expression for the response function using a (novel) regularization procedure based on the Feynman prescription that is explicitly causal, and we compare it to other expressions used in the literature. We then use this expression to study, analytically and numerically, the time dependence of the response function in various nonstationarity situations. We show that, generically, the response function decreases like a power in the detector’s level spacing, E, for high E. It is only for stationary worldlines that the response function decays faster than any power law, in keeping with the known exponential behavior for some stationary cases. Under some conditions the (time-dependent) response function for a nonstationary worldline is well approximated by the value of the response function for a stationary worldline having the same instantaneous acceleration, torsion, and hypertorsion. While we cannot offer general conditions for this to apply, we discuss special cases; in particular, the low-energy limit for linear space trajectories.

Column Number Density Expressions Through M = 0 and M = 1 Point Source Plumes Along Any Straight Path

NASA Technical Reports Server (NTRS)

Woronowicz, Michael S.

2016-01-01

Analytical expressions for column number density (CND) are developed for optical line of sight paths through a variety of steady free molecule point source models including directionally-constrained effusion (Mach number M = 0) and flow from a sonic orifice (M 1). Sonic orifice solutions are approximate, developed using a fair simulacrum fitted to the free molecule solution. Expressions are also developed for a spherically-symmetric thermal expansion (M = 0). CND solutions are found for the most general paths relative to these sources and briefly explored. It is determined that the maximum CND from a distant location through directed effusion and sonic orifice cases occurs along the path parallel to the source plane that intersects the plume axis. For the effusive case this value is exactly twice the CND found along the ray originating from that point of intersection and extending to infinity along the plumes axis. For sonic plumes this ratio is reduced to about 43. For high Mach number cases the maximum CND will be found along the axial centerline path.

Continuum theory for cluster morphologies of soft colloids.

PubMed

Kosmrlj, A; Pauschenwein, G J; Kahl, G; Ziherl, P

2011-06-09

We introduce a continuum description of the thermodynamics of colloids with a core-corona architecture. In the case of thick coronas, their overlap can be treated approximately by replacing the exact one-particle density distribution by a suitably shaped step profile, which provides a convenient way of modeling the spherical, columnar, lamellar, and inverted cluster morphologies predicted by numerical simulations and the more involved theories. We use the model to study monodisperse particles with the hard-core/square-shoulder pair interaction as the simplest representatives of the core-corona class. We derive approximate analytical expressions for the enthalpies of the cluster morphologies which offer a clear insight into the mechanisms at work, and we calculate the lattice spacing and the cluster size for all morphologies of the phase sequence as well as the phase-transition pressures. By comparing the results with the exact crystalline minimum-enthalpy configurations, we show that the accuracy of the theory increases with shoulder width. We discuss possible extensions of the theory that could account for the finite-temperature effects.

Application of an Extended Parabolic Equation to the Calculation of the Mean Field and the Transverse and Longitudinal Mutual Coherence Functions Within Atmospheric Turbulence

NASA Technical Reports Server (NTRS)

Manning, Robert M.

2005-01-01

Solutions are derived for the generalized mutual coherence function (MCF), i.e., the second order moment, of a random wave field propagating through a random medium within the context of the extended parabolic equation. Here, "generalized" connotes the consideration of both the transverse as well as the longitudinal second order moments (with respect to the direction of propagation). Such solutions will afford a comparison between the results of the parabolic equation within the pararaxial approximation and those of the wide-angle extended theory. To this end, a statistical operator method is developed which gives a general equation for an arbitrary spatial statistical moment of the wave field. The generality of the operator method allows one to obtain an expression for the second order field moment in the direction longitudinal to the direction of propagation. Analytical solutions to these equations are derived for the Kolmogorov and Tatarskii spectra of atmospheric permittivity fluctuations within the Markov approximation.

Development of 600 kV triple resonance pulse transformer.

PubMed

Li, Mingjia; Zhang, Faqiang; Liang, Chuan; Xu, Zhou

2015-06-01

In this paper, a triple-resonance pulse transformer based on an air-core transformer is introduced. The voltage across the high-voltage winding of the air-core transformer is significantly less than the output voltage; instead, the full output voltage appears across the tuning inductor. The maximum ratio of peak load voltage to peak transformer voltage is 2.77 in theory. By analyzing pulse transformer's lossless circuit, the analytical expression for the output voltage and the characteristic equation of the triple-resonance circuit are presented. Design method for the triple-resonance pulse transformer (iterated simulation method) is presented, and a triple-resonance pulse transformer is developed based on the existing air-core transformer. The experimental results indicate that the maximum ratio of peak voltage across the load to peak voltage across the high-voltage winding of the air-core transformer is approximately 2.0 and the peak output voltage of the triple-resonance pulse transformer is approximately 600 kV.

The Adler D-function for N = 1 SQCD regularized by higher covariant derivatives in the three-loop approximation

NASA Astrophysics Data System (ADS)

Kataev, A. L.; Kazantsev, A. E.; Stepanyantz, K. V.

2018-01-01

We calculate the Adler D-function for N = 1 SQCD in the three-loop approximation using the higher covariant derivative regularization and the NSVZ-like subtraction scheme. The recently formulated all-order relation between the Adler function and the anomalous dimension of the matter superfields defined in terms of the bare coupling constant is first considered and generalized to the case of an arbitrary representation for the chiral matter superfields. The correctness of this all-order relation is explicitly verified at the three-loop level. The special renormalization scheme in which this all-order relation remains valid for the D-function and the anomalous dimension defined in terms of the renormalized coupling constant is constructed in the case of using the higher derivative regularization. The analytic expression for the Adler function for N = 1 SQCD is found in this scheme to the order O (αs2). The problem of scheme-dependence of the D-function and the NSVZ-like equation is briefly discussed.

Speed Approach for UAV Collision Avoidance

NASA Astrophysics Data System (ADS)

Berdonosov, V. D.; Zivotova, A. A.; Htet Naing, Zaw; Zhuravlev, D. O.

2018-05-01

The article represents a new approach of defining potential collision of two or more UAVs in a common aviation area. UAVs trajectories are approximated by two or three trajectories’ points obtained from the ADS-B system. In the process of defining meeting points of trajectories, two cutoff values of the critical speed range, at which a UAVs collision is possible, are calculated. As calculation expressions for meeting points and cutoff values of the critical speed are represented in the analytical form, even if an on-board computer system has limited computational capacity, the time for calculation will be far less than the time of receiving data from ADS-B. For this reason, calculations can be updated at each cycle of new data receiving, and the trajectory approximation can be bounded by straight lines. Such approach allows developing the compact algorithm of collision avoidance, even for a significant amount of UAVs (more than several dozens). To proof the research adequacy, modeling was performed using a software system developed specifically for this purpose.

An ensemble of paired spin(-1/2) nuclei in a rotating solid: Polarization evolution and NMR spectrum in a wobbling frame.

PubMed

Kundla, Enn

2007-04-01

The evolution of the magnetic polarization of an ensemble of paired spin(-1/2) nuclei in an MAS NMR (nuclear magnetic resonance) experiment and the induced spectrum are described theoretically by means of a Liouville-von Neumann equation representation in a wobbling rotating frame in combination with the averaged Hamiltonian theory. In this method, the effect of a high-intensity external static magnetic field and the effects of the leftover interaction components of the Hamiltonian that commute with the approximate Hamiltonian are taken into account simultaneously and equivalently. This method reproduces details that really exist in the recorded spectra, caused by secular terms in the Hamiltonian, which might otherwise be smoothed out owing to the approximate treatment of the effects of the secular terms. Complete analytical expressions, which describe the whole NMR spectrum including the rotational sideband sets, and which consider all the relevant intermolecular interactions, are obtained.

Modeling of thermal lensing in side and end-pumped finite solid-state laser rods. M.S. Thesis

NASA Technical Reports Server (NTRS)

Brackett, Vincent G.

1990-01-01

An analytical expression for approximating the time-dependent thermal focal length in finite solid state laser rods was derived. The analysis is based on the temperature variation of the material refractive index caused by optical pumping of these rods. Several quantities were found to be relevant to this analysis. These quantities were the specific thermal profiles of the rods, type of optical pumping employed, type of cooling scheme employed (side and end-cooling parameters), and the specific material characteristics of the rods. The Thermal Lensing Model was formulated using the geometric ray tracing approach. The focal lengths are then approximated, by calculating the phase shift in the index of refraction, as the different rays of an incident plane wave are tracked through a lens-like crystal medium. The approach also applies in the case of Gaussian or parabolic pump beams. It is shown that the prediction of thermal focal length is in good quantitative agreement with experimentally obtained data.

Mean field study of a propagation-turnover lattice model for the dynamics of histone marking

NASA Astrophysics Data System (ADS)

Yao, Fan; Li, FangTing; Li, TieJun

2017-02-01

We present a mean field study of a propagation-turnover lattice model, which was proposed by Hodges and Crabtree [Proc. Nat. Acad. Sci. 109, 13296 (2012)] for understanding how posttranslational histone marks modulate gene expression in mammalian cells. The kinetics of the lattice model consists of nucleation, propagation and turnover mechanisms, and exhibits second-order phase transition for the histone marking domain. We showed rigorously that the dynamics essentially depends on a non-dimensional parameter κ = k +/ k -, the ratio between the propagation and turnover rates, which has been observed in the simulations. We then studied the lowest order mean field approximation, and observed the phase transition with an analytically obtained critical parameter. The boundary layer analysis was utilized to investigate the structure of the decay profile of the mark density. We also studied the higher order mean field approximation to achieve sharper estimate of the critical transition parameter and more detailed features. The comparison between the simulation and theoretical results shows the validity of our theory.

Propagation of error from parameter constraints in quantitative MRI: Example application of multiple spin echo T2 mapping.

PubMed

Lankford, Christopher L; Does, Mark D

2018-02-01

Quantitative MRI may require correcting for nuisance parameters which can or must be constrained to independently measured or assumed values. The noise and/or bias in these constraints propagate to fitted parameters. For example, the case of refocusing pulse flip angle constraint in multiple spin echo T 2 mapping is explored. An analytical expression for the mean-squared error of a parameter of interest was derived as a function of the accuracy and precision of an independent estimate of a nuisance parameter. The expression was validated by simulations and then used to evaluate the effects of flip angle (θ) constraint on the accuracy and precision of T⁁2 for a variety of multi-echo T 2 mapping protocols. Constraining θ improved T⁁2 precision when the θ-map signal-to-noise ratio was greater than approximately one-half that of the first spin echo image. For many practical scenarios, constrained fitting was calculated to reduce not just the variance but the full mean-squared error of T⁁2, for bias in θ⁁≲6%. The analytical expression derived in this work can be applied to inform experimental design in quantitative MRI. The example application to T 2 mapping provided specific cases, depending on θ⁁ accuracy and precision, in which θ⁁ measurement and constraint would be beneficial to T⁁2 variance or mean-squared error. Magn Reson Med 79:673-682, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

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.

Influence of Fröhlich polaron coupling on renormalized electron bands in polar semiconductors: Results for zinc-blende GaN

NASA Astrophysics Data System (ADS)

Nery, Jean Paul; Allen, Philip B.

2016-09-01

We develop a simple method to study the zero-point and thermally renormalized electron energy ɛk n(T ) for k n the conduction band minimum or valence maximum in polar semiconductors. We use the adiabatic approximation, including an imaginary broadening parameter i δ to suppress noise in the density-functional integrations. The finite δ also eliminates the polar divergence which is an artifact of the adiabatic approximation. Nonadiabatic Fröhlich polaron methods then provide analytic expressions for the missing part of the contribution of the problematic optical phonon mode. We use this to correct the renormalization obtained from the adiabatic approximation. Test calculations are done for zinc-blende GaN for an 18 ×18 ×18 integration grid. The Fröhlich correction is of order -0.02 eV for the zero-point energy shift of the conduction band minimum, and +0.03 eV for the valence band maximum; the correction to renormalization of the 3.28 eV gap is -0.05 eV, a significant fraction of the total zero point renormalization of -0.15 eV.

Multifrequency characterization of viscoelastic polymers and vapor sensing based on SAW oscillators.

PubMed

Yadava, R D S; Kshetrimayum, Roshan; Khaneja, Mamta

2009-12-01

Simplified relations for the changes in SAW velocity and attenuation due to thin polymer coatings and vapor sorption are presented by making analytic approximations to the complex theoretical model developed earlier by Martin et al. [Anal. Chem. 66 (14) (1994) 2201-2219]. The approximate velocity relation is accurate within 4% for the film thicknesses up to 20% of the acoustic wavelength in the polymer film, and is useful for analyzing the mass loading, swelling and viscoelastic effects in SAW vapor sensors. The approximate attenuation relation is accurate within 20% for very thin films, (less than 2% of the acoustic wavelength in the film). Based on these relations, a new procedure for determination of polymer viscoelastic properties is described that exploits the frequency dependence of the velocity and attenuation perturbations, and employs multifrequency measurement on the same SAW platform. Expressions for individual contributions from the mass loading, film swelling and viscoelastic effects in SAW vapor sensors are derived, and their implications for the sensor design and operation are discussed. Also, a new SAW comb filter design is proposed that offers possibility for multimode SAW oscillator operation over a decade of frequency variation, and illustrates feasibility for experimental realization of wide bandwidth multifrequency SAW platforms.

Analytical approximations to the dynamics of an array of coupled DC SQUIDs

NASA Astrophysics Data System (ADS)

Berggren, Susan; Palacios, Antonio

2014-04-01

Coupled dynamical systems that operate near the onset of a bifurcation can lead, under certain conditions, to strong signal amplification effects. Over the past years we have studied this generic feature on a wide range of systems, including: magnetic and electric fields sensors, gyroscopic devices, and arrays of loops of superconducting quantum interference devices, also known as SQUIDs. In this work, we consider an array of SQUID loops connected in series as a case study to derive asymptotic analytical approximations to the exact solutions through perturbation analysis. Two approaches are considered. First, a straightforward expansion in which the non-linear parameter related to the inductance of the DC SQUID is treated as the small perturbation parameter. Second, a more accurate procedure that considers the SQUID phase dynamics as non-uniform motion on a circle. This second procedure is readily extended to the series array and it could serve as a mathematical framework to find approximate solutions to related complex systems with high-dimensionality. To the best of our knowledge, an approximate analytical solutions to an array of SQUIDs has not been reported yet in the literature.

Nuclear magnetic resonance signal dynamics of liquids in the presence of distant dipolar fields, revisited

PubMed Central

Barros, Wilson; Gochberg, Daniel F.; Gore, John C.

2009-01-01

The description of the nuclear magnetic resonance magnetization dynamics in the presence of long-range dipolar interactions, which is based upon approximate solutions of Bloch–Torrey equations including the effect of a distant dipolar field, has been revisited. New experiments show that approximate analytic solutions have a broader regime of validity as well as dependencies on pulse-sequence parameters that seem to have been overlooked. In order to explain these experimental results, we developed a new method consisting of calculating the magnetization via an iterative formalism where both diffusion and distant dipolar field contributions are treated as integral operators incorporated into the Bloch–Torrey equations. The solution can be organized as a perturbative series, whereby access to higher order terms allows one to set better boundaries on validity regimes for analytic first-order approximations. Finally, the method legitimizes the use of simple analytic first-order approximations under less demanding experimental conditions, it predicts new pulse-sequence parameter dependencies for the range of validity, and clarifies weak points in previous calculations. PMID:19425789

Dissolving Bubbles in Glass

NASA Technical Reports Server (NTRS)

Weinberg, M. C.; Oronato, P. I.; Uhlmann, D. R.

1984-01-01

Analytical expression used to calculate time it takes for stationary bubbles of oxygen and carbon dioxide to dissolve from glass melt. Technique based on analytical expression for bubble radius as function time, with consequences of surface tension included.

The effect of density-of-state tails on band-to-band tunneling: Theory and application to tunnel field effect transistors

NASA Astrophysics Data System (ADS)

Sant, S.; Schenk, A.

2017-10-01

It is demonstrated how band tail states in the semiconductor influence the performance of a Tunnel Field Effect Transistor (TFET). As a consequence of the smoothened density of states (DOS) around the band edges, the energetic overlap of conduction and valence band states occurs gradually at the onset of band-to-band tunneling (BTBT), thus degrading the sub-threshold swing (SS) of the TFET. The effect of the band tail states on the current-voltage characteristics is modelled quantum-mechanically based on the idea of zero-phonon trap-assisted tunneling between band and tail states. The latter are assumed to arise from a 3-dimensional pseudo-delta potential proposed by Vinogradov [1]. This model potential allows the derivation of analytical expressions for the generation rate covering the whole range from very strong to very weak localization of the tail states. Comparison with direct BTBT in the one-band effective mass approximation reveals the essential features of tail-to-band tunneling. Furthermore, an analytical solution for the problem of tunneling from continuum states of the disturbed DOS to states in the opposite band is found, and the differences to direct BTBT are worked out. Based on the analytical expressions, a semi-classical model is implemented in a commercial device simulator which involves numerical integration along the tunnel paths. The impact of the tail states on the device performance is analyzed for a nanowire Gate-All-Around TFET. The simulations show that tail states notably impact the transfer characteristics of a TFET. It is found that exponentially decaying band tails result in a stronger degradation of the SS than tail states with a Gaussian decay of their density. The developed model allows more realistic simulations of TFETs including their non-idealities.

Survey Geometry and the Internal Consistency of Recent Cosmic Shear Measurements

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

Troxel, M.A.; et al.

We explore the impact of an update to the typical approximation for the shape noise term in the analytic covariance matrix for cosmic shear experiments that assumes the absence of survey boundary and mask effects. We present an exact expression for the number of galaxy pairs in this term based on the the survey mask, which leads to more than a factor of three increase in the shape noise on the largest measured scales for the Kilo-Degree Survey (KIDS-450) real-space cosmic shear data. We compare the result of this analytic expression to several alternative methods for measuring the shape noise from the data and find excellent agreement. This update to the covariance resolves any internal model tension evidenced by the previously large cosmological best-fitmore » $$\\chi^2$$ for the KiDS-450 cosmic shear data. The best-fit $$\\chi^2$$ is reduced from 161 to 121 for 118 degrees of freedom. We also apply a correction to how the multiplicative shear calibration uncertainty is included in the covariance. This change, along with a previously known update to the reported effective angular values of the data vector, jointly shift the inferred amplitude of the correlation function to higher values. We find that this improves agreement of the KiDS-450 cosmic shear results with Dark Energy Survey Year 1 and Planck results.« less

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.

Differential Higgs production at N3LO beyond threshold

NASA Astrophysics Data System (ADS)

Dulat, Falko; Mistlberger, Bernhard; Pelloni, Andrea

2018-01-01

We present several key steps towards the computation of differential Higgs boson cross sections at N3LO in perturbative QCD. Specifically, we work in the framework of Higgs-differential cross sections that allows to compute precise predictions for realistic LHC observables. We demonstrate how to perform an expansion of the analytic N3LO coefficient functions around the production threshold of the Higgs boson. Our framework allows us to compute to arbitrarily high order in the threshold expansion and we explicitly obtain the first two expansion coefficients in analytic form. Furthermore, we assess the phenomenological viability of threshold expansions for differential distributions. We find that while a few terms in the threshold expansion are sufficient to approximate the exact rapidity distribution well, transverse momentum distributions require a signficantly higher number of terms in the expansion to be adequately described. We find that to improve state of the art predictions for the rapidity distribution beyond NNLO even more sub-leading terms in the threshold expansion than presented in this article are required. In addition, we report on an interesting obstacle for the computation of N3LO corrections with LHAPDF parton distribution functions and our solution. We provide files containing the analytic expressions for the partonic cross sections as supplementary material attached to this paper.

Differential Higgs production at N 3LO beyond threshold

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

Dulat, Falko; Mistlberger, Bernhard; Pelloni, Andrea

We present several key steps towards the computation of differential Higgs boson cross sections at N 3LO in perturbative QCD. Specifically, we work in the framework of Higgs-differential cross sections that allows to compute precise predictions for realistic LHC observables. We demonstrate how to perform an expansion of the analytic N 3LO coefficient functions around the production threshold of the Higgs boson. Our framework allows us to compute to arbitrarily high order in the threshold expansion and we explicitly obtain the first two expansion coefficients in analytic form. Furthermore, we assess the phenomenological viability of threshold expansions for differential distributions.more » We find that while a few terms in the threshold expansion are sufficient to approximate the exact rapidity distribution well, transverse momentum distributions require a signficantly higher number of terms in the expansion to be adequately described. We find that to improve state of the art predictions for the rapidity distribution beyond NNLO even more sub-leading terms in the threshold expansion than presented in this article are required. In addition, we report on an interesting obstacle for the computation of N 3LO corrections with LHAPDF parton distribution functions and our solution. We provide files containing the analytic expressions for the partonic cross sections as supplementary material attached to this paper.« less

Differential Higgs production at N 3LO beyond threshold

DOE PAGES

Dulat, Falko; Mistlberger, Bernhard; Pelloni, Andrea

2018-01-29

We present several key steps towards the computation of differential Higgs boson cross sections at N 3LO in perturbative QCD. Specifically, we work in the framework of Higgs-differential cross sections that allows to compute precise predictions for realistic LHC observables. We demonstrate how to perform an expansion of the analytic N 3LO coefficient functions around the production threshold of the Higgs boson. Our framework allows us to compute to arbitrarily high order in the threshold expansion and we explicitly obtain the first two expansion coefficients in analytic form. Furthermore, we assess the phenomenological viability of threshold expansions for differential distributions.more » We find that while a few terms in the threshold expansion are sufficient to approximate the exact rapidity distribution well, transverse momentum distributions require a signficantly higher number of terms in the expansion to be adequately described. We find that to improve state of the art predictions for the rapidity distribution beyond NNLO even more sub-leading terms in the threshold expansion than presented in this article are required. In addition, we report on an interesting obstacle for the computation of N 3LO corrections with LHAPDF parton distribution functions and our solution. We provide files containing the analytic expressions for the partonic cross sections as supplementary material attached to this paper.« less

Point Charges Optimally Placed to Represent the Multipole Expansion of Charge Distributions

PubMed Central

Onufriev, Alexey V.

2013-01-01

We propose an approach for approximating electrostatic charge distributions with a small number of point charges to optimally represent the original charge distribution. By construction, the proposed optimal point charge approximation (OPCA) retains many of the useful properties of point multipole expansion, including the same far-field asymptotic behavior of the approximate potential. A general framework for numerically computing OPCA, for any given number of approximating charges, is described. We then derive a 2-charge practical point charge approximation, PPCA, which approximates the 2-charge OPCA via closed form analytical expressions, and test the PPCA on a set of charge distributions relevant to biomolecular modeling. We measure the accuracy of the new approximations as the RMS error in the electrostatic potential relative to that produced by the original charge distribution, at a distance the extent of the charge distribution–the mid-field. The error for the 2-charge PPCA is found to be on average 23% smaller than that of optimally placed point dipole approximation, and comparable to that of the point quadrupole approximation. The standard deviation in RMS error for the 2-charge PPCA is 53% lower than that of the optimal point dipole approximation, and comparable to that of the point quadrupole approximation. We also calculate the 3-charge OPCA for representing the gas phase quantum mechanical charge distribution of a water molecule. The electrostatic potential calculated by the 3-charge OPCA for water, in the mid-field (2.8 Å from the oxygen atom), is on average 33.3% more accurate than the potential due to the point multipole expansion up to the octupole order. Compared to a 3 point charge approximation in which the charges are placed on the atom centers, the 3-charge OPCA is seven times more accurate, by RMS error. The maximum error at the oxygen-Na distance (2.23 Å ) is half that of the point multipole expansion up to the octupole order. PMID:23861790

Bayesian feature selection for high-dimensional linear regression via the Ising approximation with applications to genomics.

PubMed

Fisher, Charles K; Mehta, Pankaj

2015-06-01

Feature selection, identifying a subset of variables that are relevant for predicting a response, is an important and challenging component of many methods in statistics and machine learning. Feature selection is especially difficult and computationally intensive when the number of variables approaches or exceeds the number of samples, as is often the case for many genomic datasets. Here, we introduce a new approach--the Bayesian Ising Approximation (BIA)-to rapidly calculate posterior probabilities for feature relevance in L2 penalized linear regression. In the regime where the regression problem is strongly regularized by the prior, we show that computing the marginal posterior probabilities for features is equivalent to computing the magnetizations of an Ising model with weak couplings. Using a mean field approximation, we show it is possible to rapidly compute the feature selection path described by the posterior probabilities as a function of the L2 penalty. We present simulations and analytical results illustrating the accuracy of the BIA on some simple regression problems. Finally, we demonstrate the applicability of the BIA to high-dimensional regression by analyzing a gene expression dataset with nearly 30 000 features. These results also highlight the impact of correlations between features on Bayesian feature selection. An implementation of the BIA in C++, along with data for reproducing our gene expression analyses, are freely available at http://physics.bu.edu/∼pankajm/BIACode. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Asymptotic normalization coefficients of resonant and bound states from the phase shifts for α α and α 12C scattering

NASA Astrophysics Data System (ADS)

Orlov, Yu. V.; Irgaziev, B. F.; Nikitina, L. I.

2016-01-01

Recently we have published a paper [Irgaziev, Phys. Rev. C 91, 024002 (2015), 10.1103/PhysRevC.91.024002] where the S -matrix pole method (SMP), which is only valid for resonances, has been developed to derive an explicit expression for the asymptotic normalization coefficient (ANC) and is applied to the low-energy resonant states of nucleon +α and α +12C systems. The SMP results are compared with the effective-range expansion method (EFE) results. In the present paper the SMP and EFE plus the Padé approximation are applied to study the excited 2+ resonant states of 9Be. A contradiction is found between descriptions of the experimental phase shift data for α α scattering and of the 9Be resonant energy for 2+ state. Using the EFE method, we also calculate the ANC for the 9Be ground 0+ state with a very small width. This ANC agrees well with the value calculated using the known analytical expression for narrow resonances. In addition, for the α +12C states 1- and 3- the SMP results are compared with the Padé approximation results. We find that the Padé approximation improves a resonance width description compared with the EFE results. The EFE method is also used to calculate the ANCs for the bound 0mml:mprescripts>O ground 0+ state and for the excited 1- and 2+ levels, which are situated near the threshold of α +12C channel.

Nonlinear Schroedinger Approximations for Partial Differential Equations with Quadratic and Quasilinear Terms

NASA Astrophysics Data System (ADS)

Cummings, Patrick

We consider the approximation of solutions of two complicated, physical systems via the nonlinear Schrodinger equation (NLS). In particular, we discuss the evolution of wave packets and long waves in two physical models. Due to the complicated nature of the equations governing many physical systems and the in-depth knowledge we have for solutions of the nonlinear Schrodinger equation, it is advantageous to use approximation results of this kind to model these physical systems. The approximations are simple enough that we can use them to understand the qualitative and quantitative behavior of the solutions, and by justifying them we can show that the behavior of the approximation captures the behavior of solutions to the original equation, at least for long, but finite time. We first consider a model of the water wave equations which can be approximated by wave packets using the NLS equation. We discuss a new proof that both simplifies and strengthens previous justification results of Schneider and Wayne. Rather than using analytic norms, as was done by Schneider and Wayne, we construct a modified energy functional so that the approximation holds for the full interval of existence of the approximate NLS solution as opposed to a subinterval (as is seen in the analytic case). Furthermore, the proof avoids problems associated with inverting the normal form transform by working with a modified energy functional motivated by Craig and Hunter et al. We then consider the Klein-Gordon-Zakharov system and prove a long wave approximation result. In this case there is a non-trivial resonance that cannot be eliminated via a normal form transform. By combining the normal form transform for small Fourier modes and using analytic norms elsewhere, we can get a justification result on the order 1 over epsilon squared time scale.

Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives

NASA Technical Reports Server (NTRS)

Hearn, Tristan; Hendricks, Eric; Chin, Jeffrey; Gray, Justin; Moore, Kenneth T.

2016-01-01

A new engine cycle analysis tool, called Pycycle, was built using the OpenMDAO framework. Pycycle provides analytic derivatives allowing for an efficient use of gradient-based optimization methods on engine cycle models, without requiring the use of finite difference derivative approximation methods. To demonstrate this, a gradient-based design optimization was performed on a turbofan engine model. Results demonstrate very favorable performance compared to an optimization of an identical model using finite-difference approximated derivatives.

Stabilizing potentials in bound state analytic continuation methods for electronic resonances in polyatomic molecules

DOE PAGES

White, Alec F.; Head-Gordon, Martin; McCurdy, C. William

2017-01-30

The computation of Siegert energies by analytic continuation of bound state energies has recently been applied to shape resonances in polyatomic molecules by several authors. Here, we critically evaluate a recently proposed analytic continuation method based on low order (type III) Padé approximants as well as an analytic continuation method based on high order (type II) Padé approximants. We compare three classes of stabilizing potentials: Coulomb potentials, Gaussian potentials, and attenuated Coulomb potentials. These methods are applied to a model potential where the correct answer is known exactly and to the 2Π g shape resonance of N 2 - whichmore » has been studied extensively by other methods. Both the choice of stabilizing potential and method of analytic continuation prove to be important to the accuracy of the results. We then conclude that an attenuated Coulomb potential is the most effective of the three for bound state analytic continuation methods. With the proper potential, such methods show promise for algorithmic determination of the positions and widths of molecular shape resonances.« less

Stabilizing potentials in bound state analytic continuation methods for electronic resonances in polyatomic molecules

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

White, Alec F.; Head-Gordon, Martin; McCurdy, C. William

The computation of Siegert energies by analytic continuation of bound state energies has recently been applied to shape resonances in polyatomic molecules by several authors. Here, we critically evaluate a recently proposed analytic continuation method based on low order (type III) Padé approximants as well as an analytic continuation method based on high order (type II) Padé approximants. We compare three classes of stabilizing potentials: Coulomb potentials, Gaussian potentials, and attenuated Coulomb potentials. These methods are applied to a model potential where the correct answer is known exactly and to the 2Π g shape resonance of N 2 - whichmore » has been studied extensively by other methods. Both the choice of stabilizing potential and method of analytic continuation prove to be important to the accuracy of the results. We then conclude that an attenuated Coulomb potential is the most effective of the three for bound state analytic continuation methods. With the proper potential, such methods show promise for algorithmic determination of the positions and widths of molecular shape resonances.« less

Calculation of strained BaTiO3 with different exchange correlation functionals examined with criterion by Ginzburg-Landau theory, uncovering expressions by crystallographic parameters

NASA Astrophysics Data System (ADS)

Watanabe, Yukio

2018-05-01

In the calculations of tetragonal BaTiO3, some exchange-correlation (XC) energy functionals such as local density approximation (LDA) have shown good agreement with experiments at room temperature (RT), e.g., spontaneous polarization (PS), and superiority compared with other XC functionals. This is due to the error compensation of the RT effect and, hence, will be ineffective in the heavily strained case such as domain boundaries. Here, ferroelectrics under large strain at RT are approximated as those at 0 K because the strain effect surpasses the RT effects. To find effective XC energy functionals for strained BaTiO3, we propose a new comparison, i.e., a criterion. This criterion is the properties at 0 K given by the Ginzburg-Landau (GL) theory because GL theory is a thermodynamic description of experiments working under the same symmetry-constraints as ab initio calculations. With this criterion, we examine LDA, generalized gradient approximations (GGA), meta-GGA, meta-GGA + local correlation potential (U), and hybrid functionals, which reveals the high accuracy of some XC functionals superior to XC functionals that have been regarded as accurate. This result is examined directly by the calculations of homogenously strained tetragonal BaTiO3, confirming the validity of the new criterion. In addition, the data points of theoretical PS vs. certain crystallographic parameters calculated with different XC functionals are found to lie on a single curve, despite their wide variations. Regarding these theoretical data points as corresponding to the experimental results, analytical expressions of the local PS using crystallographic parameters are uncovered. These expressions show the primary origin of BaTiO3 ferroelectricity as oxygen displacements. Elastic compliance and electrostrictive coefficients are estimated. For the comparison of strained results, we show that the effective critical temperature TC under strain <-0.01 is >1000 K from an approximate method combining ab initio results with GL theory. In addition, in a definite manner, the present results show much more enhanced ferroelectricity at large strain than the previous reports.

Analytic studies of the hard dumbell fluid

NASA Astrophysics Data System (ADS)

Morriss, G. P.; Cummings, P. T.

A closed form analytic theory for the structure of the hard dumbell fluid is introduced and evaluated. It is found to be comparable in accuracy to the reference interaction site approximation (RISA) of Chandler and Andersen.

Diagrammatic expansion for positive spectral functions beyond GW: Application to vertex corrections in the electron gas

NASA Astrophysics Data System (ADS)

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

2014-09-01

We present a diagrammatic approach to construct self-energy approximations within many-body perturbation theory with positive spectral properties. The method cures the problem of negative spectral functions which arises from a straightforward inclusion of vertex diagrams beyond the GW approximation. Our approach consists of a two-step procedure: We first express the approximate many-body self-energy as a product of half-diagrams and then identify the minimal number of half-diagrams to add in order to form a perfect square. The resulting self-energy is an unconventional sum of self-energy diagrams in which the internal lines of half a diagram are time-ordered Green's functions, whereas those of the other half are anti-time-ordered Green's functions, and the lines joining the two halves are either lesser or greater Green's functions. The theory is developed using noninteracting Green's functions and subsequently extended to self-consistent Green's functions. Issues related to the conserving properties of diagrammatic approximations with positive spectral functions are also addressed. As a major application of the formalism we derive the minimal set of additional diagrams to make positive the spectral function of the GW approximation with lowest-order vertex corrections and screened interactions. The method is then applied to vertex corrections in the three-dimensional homogeneous electron gas by using a combination of analytical frequency integrations and numerical Monte Carlo momentum integrations to evaluate the diagrams.

Improving the analytical performance and versatility of paper spray mass spectrometry via paper microfluidics.

PubMed

Murray, Ian; Walker, Glenn; Bereman, Michael S

2016-06-20

Two paper-based microfluidic techniques, photolithography and wax patterning, were investigated for their potential to improve upon the sensitivity, reproducibility, and versatility of paper spray mass spectrometry. The main limitation of photolithography was the significant signal (approximately three orders of magnitude) above background which was attributed to the chemicals used in the photoresist process. Hydrophobic barriers created via wax patterning were discovered to have approximately 2 orders of magnitude less background signal compared to analogous barriers created using photolithography. A minimum printed wax barrier thickness of approximately 0.3 mm was necessary to consistently retain commonly used paper spray solvents (1 : 1 water : acetonitrile/methanol) and avoid leakage. Constricting capillary flow via wax-printed channels yielded both a significant increase in signal and detection time for detection of model analytes. This signal increase, which was attributed to restricting the radial flow of analyte/solvent on paper (i.e., a concentrating effect), afforded a significant increase in sensitivity (p ≪ 0.05) for the detection of pesticides spiked into residential tap water using a five-point calibration curve. Finally, unique mixing designs using wax patterning can be envisioned to perform on-paper analyte derivatization.

Approximate Analytical Solutions for Hypersonic Flow Over Slender Power Law Bodies

NASA Technical Reports Server (NTRS)

Mirels, Harold

1959-01-01

Approximate analytical solutions are presented for two-dimensional and axisymmetric hypersonic flow over slender power law bodies. Both zero order (M approaches infinity) and first order (small but nonvanishing values of 1/(M(Delta)(sup 2) solutions are presented, where M is free-stream Mach number and Delta is a characteristic slope. These solutions are compared with exact numerical integration of the equations of motion and appear to be accurate particularly when the shock is relatively close to the body.

On accelerated flow of MHD powell-eyring fluid via homotopy analysis method

NASA Astrophysics Data System (ADS)

Salah, Faisal; Viswanathan, K. K.; Aziz, Zainal Abdul

2017-09-01

The aim of this article is to obtain the approximate analytical solution for incompressible magnetohydrodynamic (MHD) flow for Powell-Eyring fluid induced by an accelerated plate. Both constant and variable accelerated cases are investigated. Approximate analytical solution in each case is obtained by using the Homotopy Analysis Method (HAM). The resulting nonlinear analysis is carried out to generate the series solution. Finally, Graphical outcomes of different values of the material constants parameters on the velocity flow field are discussed and analyzed.

Analytic Approximate Solutions to the Boundary Layer Flow Equation over a Stretching Wall with Partial Slip at the Boundary.

PubMed

Ene, Remus-Daniel; Marinca, Vasile; Marinca, Bogdan

2016-01-01

Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations.

Siewert solutions of transcendental equations, generalized Lambert functions and physical applications

NASA Astrophysics Data System (ADS)

Barsan, Victor

2018-05-01

Several classes of transcendental equations, mainly eigenvalue equations associated to non-relativistic quantum mechanical problems, are analyzed. Siewert's systematic approach of such equations is discussed from the perspective of the new results recently obtained in the theory of generalized Lambert functions and of algebraic approximations of various special or elementary functions. Combining exact and approximate analytical methods, quite precise analytical outputs are obtained for apparently untractable problems. The results can be applied in quantum and classical mechanics, magnetism, elasticity, solar energy conversion, etc.

Solutions of the Dirac Equation with the Shifted DENG-FAN Potential Including Yukawa-Like Tensor Interaction

NASA Astrophysics Data System (ADS)

Yahya, W. A.; Falaye, B. J.; Oluwadare, O. J.; Oyewumi, K. J.

2013-08-01

By using the Nikiforov-Uvarov method, we give the approximate analytical solutions of the Dirac equation with the shifted Deng-Fan potential including the Yukawa-like tensor interaction under the spin and pseudospin symmetry conditions. After using an improved approximation scheme, we solved the resulting schr\\"{o}dinger-like equation analytically. Numerical results of the energy eigenvalues are also obtained, as expected, the tensor interaction removes degeneracies between spin and pseudospin doublets.

Analytic Approximate Solutions to the Boundary Layer Flow Equation over a Stretching Wall with Partial Slip at the Boundary

PubMed Central

Ene, Remus-Daniel; Marinca, Vasile; Marinca, Bogdan

2016-01-01

Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations. PMID:27031232

Unsteady fluid flow in a slightly curved pipe: A comparative study of a matched asymptotic expansions solution with a single analytical solution

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

Messaris, Gerasimos A. T., E-mail: messaris@upatras.gr; School of Science and Technology, Hellenic Open University, 11 Sahtouri Street, GR 262 22 Patras; Hadjinicolaou, Maria

The present work is motivated by the fact that blood flow in the aorta and the main arteries is governed by large finite values of the Womersley number α and for such values of α there is not any analytical solution in the literature. The existing numerical solutions, although accurate, give limited information about the factors that affect the flow, whereas an analytical approach has an advantage in that it can provide physical insight to the flow mechanism. Having this in mind, we seek analytical solution to the equations of the fluid flow driven by a sinusoidal pressure gradient inmore » a slightly curved pipe of circular cross section when the Womersley number varies from small finite to infinite values. Initially the equations of motion are expanded in terms of the curvature ratio δ and the resulting linearized equations are solved analytically in two ways. In the first, we match the solution for the main core to that for the Stokes boundary layer. This solution is valid for very large values of α. In the second, we derive a straightforward single solution valid to the entire flow region and for 8 ≤ α < ∞, a range which includes the values of α that refer to the physiological flows. Each solution contains expressions for the axial velocity, the stream function, and the wall stresses and is compared to the analogous forms presented in other studies. The two solutions give identical results to each other regarding the axial flow but differ in the secondary flow and the circumferential wall stress, due to the approximations employed in the matched asymptotic expansion process. The results on the stream function from the second solution are in agreement with analogous results from other numerical solutions. The second solution predicts that the atherosclerotic plaques may develop in any location around the cross section of the aortic wall unlike to the prescribed locations predicted by the first solution. In addition, it gives circumferential wall stresses augmented by approximately 100% with respect to the matched asymptotic expansions, a factor that may contribute jointly with other pathological factors to the faster aging of the arterial system and the possible malfunction of the aorta.« less

Unsteady fluid flow in a slightly curved pipe: A comparative study of a matched asymptotic expansions solution with a single analytical solution

NASA Astrophysics Data System (ADS)

Messaris, Gerasimos A. T.; Hadjinicolaou, Maria; Karahalios, George T.

2016-08-01

The present work is motivated by the fact that blood flow in the aorta and the main arteries is governed by large finite values of the Womersley number α and for such values of α there is not any analytical solution in the literature. The existing numerical solutions, although accurate, give limited information about the factors that affect the flow, whereas an analytical approach has an advantage in that it can provide physical insight to the flow mechanism. Having this in mind, we seek analytical solution to the equations of the fluid flow driven by a sinusoidal pressure gradient in a slightly curved pipe of circular cross section when the Womersley number varies from small finite to infinite values. Initially the equations of motion are expanded in terms of the curvature ratio δ and the resulting linearized equations are solved analytically in two ways. In the first, we match the solution for the main core to that for the Stokes boundary layer. This solution is valid for very large values of α. In the second, we derive a straightforward single solution valid to the entire flow region and for 8 ≤ α < ∞, a range which includes the values of α that refer to the physiological flows. Each solution contains expressions for the axial velocity, the stream function, and the wall stresses and is compared to the analogous forms presented in other studies. The two solutions give identical results to each other regarding the axial flow but differ in the secondary flow and the circumferential wall stress, due to the approximations employed in the matched asymptotic expansion process. The results on the stream function from the second solution are in agreement with analogous results from other numerical solutions. The second solution predicts that the atherosclerotic plaques may develop in any location around the cross section of the aortic wall unlike to the prescribed locations predicted by the first solution. In addition, it gives circumferential wall stresses augmented by approximately 100% with respect to the matched asymptotic expansions, a factor that may contribute jointly with other pathological factors to the faster aging of the arterial system and the possible malfunction of the aorta.

Superconductivity mediated by quantum critical antiferromagnetic fluctuations: the rise and fall of hot spots

NASA Astrophysics Data System (ADS)

Wang, Xiaoyu; Schattner, Yoni; Berg, Erez; Fernandes, Rafael

The maximum transition temperature Tc observed in the phase diagrams of several unconventional superconductors takes place in the vicinity of a putative antiferromagnetic quantum critical point. This observation motivated the theoretical proposal that superconductivity in these systems may be driven by quantum critical fluctuations, which in turn can also promote non-Fermi liquid behavior. In this talk, we present a combined analytical and sign-problem-free Quantum Monte Carlo investigation of the spin-fermion model - a widely studied low-energy model for the interplay between superconductivity and magnetic fluctuations. By engineering a series of band dispersions that interpolate between near-nested and open Fermi surfaces, and by also varying the strength of the spin-fermion interaction, we find that the hot spots of the Fermi surface provide the dominant contribution to the pairing instability in this model. We show that the analytical expressions for Tc and for the pairing susceptibility, obtained within a large-N Eliashberg approximation to the spin-fermion model, agree well with the Quantum Monte Carlo data, even in the regime of interactions comparable to the electronic bandwidth. DE-SC0012336.

A three-dimensional semi-analytical solution for predicting drug release through the orifice of a spherical device.

PubMed

Simon, Laurent; Ospina, Juan

2016-07-25

Three-dimensional solute transport was investigated for a spherical device with a release hole. The governing equation was derived using the Fick's second law. A mixed Neumann-Dirichlet condition was imposed at the boundary to represent diffusion through a small region on the surface of the device. The cumulative percentage of drug released was calculated in the Laplace domain and represented by the first term of an infinite series of Legendre and modified Bessel functions of the first kind. Application of the Zakian algorithm yielded the time-domain closed-form expression. The first-order solution closely matched a numerical solution generated by Mathematica(®). The proposed method allowed computation of the characteristic time. A larger surface pore resulted in a smaller effective time constant. The agreement between the numerical solution and the semi-analytical method improved noticeably as the size of the orifice increased. It took four time constants for the device to release approximately ninety-eight of its drug content. Copyright © 2016 Elsevier B.V. All rights reserved.

Electromagnetic field analysis and modeling of a relative position detection sensor for high speed maglev trains.

PubMed

Xue, Song; He, Ning; Long, Zhiqiang

2012-01-01

The long stator track for high speed maglev trains has a tooth-slot structure. The sensor obtains precise relative position information for the traction system by detecting the long stator tooth-slot structure based on nondestructive detection technology. The magnetic field modeling of the sensor is a typical three-dimensional (3-D) electromagnetic problem with complex boundary conditions, and is studied semi-analytically in this paper. A second-order vector potential (SOVP) is introduced to simplify the vector field problem to a scalar field one, the solution of which can be expressed in terms of series expansions according to Multipole Theory (MT) and the New Equivalent Source (NES) method. The coefficients of the expansions are determined by the least squares method based on the boundary conditions. Then, the solution is compared to the simulation result through Finite Element Analysis (FEA). The comparison results show that the semi-analytical solution agrees approximately with the numerical solution. Finally, based on electromagnetic modeling, a difference coil structure is designed to improve the sensitivity and accuracy of the sensor.

Electromagnetic Field Analysis and Modeling of a Relative Position Detection Sensor for High Speed Maglev Trains

PubMed Central

Xue, Song; He, Ning; Long, Zhiqiang

2012-01-01

The long stator track for high speed maglev trains has a tooth-slot structure. The sensor obtains precise relative position information for the traction system by detecting the long stator tooth-slot structure based on nondestructive detection technology. The magnetic field modeling of the sensor is a typical three-dimensional (3-D) electromagnetic problem with complex boundary conditions, and is studied semi-analytically in this paper. A second-order vector potential (SOVP) is introduced to simplify the vector field problem to a scalar field one, the solution of which can be expressed in terms of series expansions according to Multipole Theory (MT) and the New Equivalent Source (NES) method. The coefficients of the expansions are determined by the least squares method based on the boundary conditions. Then, the solution is compared to the simulation result through Finite Element Analysis (FEA). The comparison results show that the semi-analytical solution agrees approximately with the numerical solution. Finally, based on electromagnetic modeling, a difference coil structure is designed to improve the sensitivity and accuracy of the sensor. PMID:22778652

Nonspherically symmetric black string perturbations in the large dimension limit

NASA Astrophysics Data System (ADS)

Sadhu, Amruta; Suneeta, Vardarajan

2016-06-01

We consider nonspherically symmetric perturbations of the uncharged black string/flat black brane in the large dimension (D) limit of general relativity. We express the perturbations in a simplified form using variables introduced by Ishibashi and Kodama. We apply the large D limit to the equations and show that this leads to decoupling of the equations in the near-horizon and asymptotic regions. It also enables use of matched asymptotic expansions to obtain approximate analytical solutions and to analyze stability of the black string/brane. For a large class of nonspherically symmetric perturbations, we prove that there are no instabilities in the large D limit. For the rest, we provide additional matching arguments that indicate that the black string/brane is stable. In the static limit, we show that for all nonspherically symmetric perturbations, there is no instability. This is proof that the Gross-Perry-Yaffe mode for semiclassical black hole perturbations is the unique unstable mode even in the large D limit. This work is also a direct analytical indication that the only instability of the black string is the Gregory-Laflamme instability.

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

Mapping Rotational Wavepacket Dynamics with Chirped Probe Pulses

NASA Astrophysics Data System (ADS)

Romanov, Dmitri; Odhner, Johanan; Levis, Robert

2014-05-01

We develop an analytical model description of the strong-field pump-probe polarization spectroscopy of rotational transients in molecular gases in a situation when the probe pulse is considerably chirped: the frequency modulation over the pulse duration is comparable with the carrier frequency. In this scenario, a femtosecond pump laser pulse prepares a rotational wavepacket in a gas-phase sample at room temperature. The rotational revivals of the wavepacket are then mapped onto a chirped broadband probe pulse derived from a laser filament. The slow-varying envelope approximation being inapplicable, an alternative approach is proposed which is capable of incorporating the substantial chirp and the related temporal dispersion of refractive indices. Analytical expressions are obtained for the probe signal modulation over the interaction region and for the resulting heterodyned transient birefringence spectra. Dependencies of the outputs on the probe pulse parameters reveal the trade-offs and the ways to optimize the temporal-spectral imaging. The results are in good agreement with the experiments on snapshot imaging of rotational revival patterns in nitrogen gas. We gratefully acknowledge financial support through AFOSR MURI Grant No. FA9550-10-1-0561.

1001 lights: luciferins, luciferases, their mechanisms of action and applications in chemical analysis, biology and medicine.

PubMed

Kaskova, Zinaida M; Tsarkova, Aleksandra S; Yampolsky, Ilia V

2016-10-24

Bioluminescence (BL) is a spectacular phenomenon involving light emission by live organisms. It is caused by the oxidation of a small organic molecule, luciferin, with molecular oxygen, which is catalysed by the enzyme luciferase. In nature, there are approximately 30 different BL systems, of which only 9 have been studied to various degrees in terms of their reaction mechanisms. A vast range of in vitro and in vivo analytical techniques have been developed based on BL, including tests for different analytes, immunoassays, gene expression assays, drug screening, bioimaging of live organisms, cancer studies, the investigation of infectious diseases and environmental monitoring. This review aims to cover the major existing applications for bioluminescence in the context of the diversity of luciferases and their substrates, luciferins. Particularly, the properties and applications of d-luciferin, coelenterazine, bacterial, Cypridina and dinoflagellate luciferins and their analogues along with their corresponding luciferases are described. Finally, four other rarely studied bioluminescent systems (those of limpet Latia, earthworms Diplocardia and Fridericia and higher fungi), which are promising for future use, are also discussed.

Developing the Polynomial Expressions for Fields in the ITER Tokamak

NASA Astrophysics Data System (ADS)

Sharma, Stephen

2017-10-01

The two most important problems to be solved in the development of working nuclear fusion power plants are: sustained partial ignition and turbulence. These two phenomena are the subject of research and investigation through the development of analytic functions and computational models. Ansatz development through Gaussian wave-function approximations, dielectric quark models, field solutions using new elliptic functions, and better descriptions of the polynomials of the superconducting current loops are the critical theoretical developments that need to be improved. Euler-Lagrange equations of motion in addition to geodesic formulations generate the particle model which should correspond to the Dirac dispersive scattering coefficient calculations and the fluid plasma model. Feynman-Hellman formalism and Heaviside step functional forms are introduced to the fusion equations to produce simple expressions for the kinetic energy and loop currents. Conclusively, a polynomial description of the current loops, the Biot-Savart field, and the Lagrangian must be uncovered before there can be an adequate computational and iterative model of the thermonuclear plasma.

Expressions for Fields in the ITER Tokamak

NASA Astrophysics Data System (ADS)

Sharma, Stephen

2017-10-01

The two most important problems to be solved in the development of working nuclear fusion power plants are: sustained partial ignition and turbulence. These two phenomenon are the subject of research and investigation through the development of analytic functions and computational models. Ansatz development through Gaussian wave-function approximations, dielectric quark models, field solutions using new elliptic functions, and better descriptions of the polynomials of the superconducting current loops are the critical theoretical developments that need to be improved. Euler-Lagrange equations of motion in addition to geodesic formulations generate the particle model which should correspond to the Dirac dispersive scattering coefficient calculations and the fluid plasma model. Feynman-Hellman formalism and Heaviside step functional forms are introduced to the fusion equations to produce simple expressions for the kinetic energy and loop currents. Conclusively, a polynomial description of the current loops, the Biot-Savart field, and the Lagrangian must be uncovered before there can be an adequate computational and iterative model of the thermonuclear plasma.

Derivation of Markov processes that violate detailed balance

NASA Astrophysics Data System (ADS)

Lee, Julian

2018-03-01

Time-reversal symmetry of the microscopic laws dictates that the equilibrium distribution of a stochastic process must obey the condition of detailed balance. However, cyclic Markov processes that do not admit equilibrium distributions with detailed balance are often used to model systems driven out of equilibrium by external agents. I show that for a Markov model without detailed balance, an extended Markov model can be constructed, which explicitly includes the degrees of freedom for the driving agent and satisfies the detailed balance condition. The original cyclic Markov model for the driven system is then recovered as an approximation at early times by summing over the degrees of freedom for the driving agent. I also show that the widely accepted expression for the entropy production in a cyclic Markov model is actually a time derivative of an entropy component in the extended model. Further, I present an analytic expression for the entropy component that is hidden in the cyclic Markov model.

Thrust law effects on the long-period modes of aerospace craft

NASA Technical Reports Server (NTRS)

Markopoulos, Nikos; Mease, Kenneth D.; Vinh, Nguyen X.

1989-01-01

An analytical study is presented of the longitudinal long-period dynamics of an aerospace craft in a nearly circular orbit, with a thrust law depending arbitrarily on the speed and altitude. A plane of engine possibilities is first defined, with points corresponding to propulsion systems having prescribed thrust slopes with respect to speed and altitude. Approximate expressions for the characteristic roots and times are obtained by first identifying a small quantity in the coefficients of the characteristic equation, and then expanding in a perturbation series about the origin of the plane of engine possibilities, for which the solution is always known. These expressions agree very well with the exact solutions over a wide range of altitudes and thrust laws. The period of the oscillatory translational mode (phugoid) is found to be independent to first order of the thrust law, generalizing results found by previous investigators for specific thrust laws. The results apply to the speed range from hypersonic to orbital.

Exact linearized Coulomb collision operator in the moment expansion

DOE PAGES

Ji, Jeong -Young; Held, Eric D.

2006-10-05

In the moment expansion, the Rosenbluth potentials, the linearized Coulomb collision operators, and the moments of the collision operators are analytically calculated for any moment. The explicit calculation of Rosenbluth potentials converts the integro-differential form of the Coulomb collision operator into a differential operator, which enables one to express the collision operator in a simple closed form for any arbitrary mass and temperature ratios. In addition, it is shown that gyrophase averaging the collision operator acting on arbitrary distribution functions is the same as the collision operator acting on the corresponding gyrophase averaged distribution functions. The moments of the collisionmore » operator are linear combinations of the fluid moments with collision coefficients parametrized by mass and temperature ratios. Furthermore, useful forms involving the small mass-ratio approximation are easily found since the collision operators and their moments are expressed in terms of the mass ratio. As an application, the general moment equations are explicitly written and the higher order heat flux equation is derived.« less

Study on characteristics of the aperture-averaging factor of atmospheric scintillation in terrestrial optical wireless communication

NASA Astrophysics Data System (ADS)

Shen, Hong; Liu, Wen-xing; Zhou, Xue-yun; Zhou, Li-ling; Yu, Long-Kun

2018-02-01

In order to thoroughly understand the characteristics of the aperture-averaging effect of atmospheric scintillation in terrestrial optical wireless communication and provide references for engineering design and performance evaluation of the optics system employed in the atmosphere, we have theoretically deduced the generally analytic expression of the aperture-averaging factor of atmospheric scintillation, and numerically investigated characteristics of the apertureaveraging factor under different propagation conditions. The limitations of the current commonly used approximate calculation formula of aperture-averaging factor have been discussed, and the results showed that the current calculation formula is not applicable for the small receiving aperture under non-uniform turbulence link. Numerical calculation has showed that aperture-averaging factor of atmospheric scintillation presented an exponential decline model for the small receiving aperture under non-uniform turbulent link, and the general expression of the model was given. This model has certain guiding significance for evaluating the aperture-averaging effect in the terrestrial optical wireless communication.

A new exact method for line radiative transfer

NASA Astrophysics Data System (ADS)

Elitzur, Moshe; Asensio Ramos, Andrés

2006-01-01

We present a new method, the coupled escape probability (CEP), for exact calculation of line emission from multi-level systems, solving only algebraic equations for the level populations. The CEP formulation of the classical two-level problem is a set of linear equations, and we uncover an exact analytic expression for the emission from two-level optically thick sources that holds as long as they are in the `effectively thin' regime. In a comparative study of a number of standard problems, the CEP method outperformed the leading line transfer methods by substantial margins. The algebraic equations employed by our new method are already incorporated in numerous codes based on the escape probability approximation. All that is required for an exact solution with these existing codes is to augment the expression for the escape probability with simple zone-coupling terms. As an application, we find that standard escape probability calculations generally produce the correct cooling emission by the CII 158-μm line but not by the 3P lines of OI.

Technical Note: Approximate solution of transient drawdown for constant-flux pumping at a partially penetrating well in a radial two-zone confined aquifer

NASA Astrophysics Data System (ADS)

Huang, C.-S.; Yang, S.-Y.; Yeh, H.-D.

2015-03-01

An aquifer consisting of a skin zone and a formation zone is considered as a two-zone aquifer. Existing solutions for the problem of constant-flux pumping (CFP) in a two-zone confined aquifer involve laborious calculation. This study develops a new approximate solution for the problem based on a mathematical model including two steady-state flow equations with different hydraulic parameters for the skin and formation zones. A partially penetrating well may be treated as the Neumann condition with a known flux along the screened part and zero flux along the unscreened part. The aquifer domain is finite with an outer circle boundary treated as the Dirichlet condition. The steady-state drawdown solution of the model is derived by the finite Fourier cosine transform. Then, an approximate transient solution is developed by replacing the radius of the boundary in the steady-state solution with an analytical expression for a dimensionless time-dependent radius of influence. The approximate solution is capable of predicting good temporal drawdown distributions over the whole pumping period except at the early stage. A quantitative criterion for the validity of neglecting the vertical flow component due to a partially penetrating well is also provided. Conventional models considering radial flow without the vertical component for the CFP have good accuracy if satisfying the criterion.

An Analytical Solution for Transient Thermal Response of an Insulated Structure

NASA Technical Reports Server (NTRS)

Blosser, Max L.

2012-01-01

An analytical solution was derived for the transient response of an insulated aerospace vehicle structure subjected to a simplified heat pulse. This simplified problem approximates the thermal response of a thermal protection system of an atmospheric entry vehicle. The exact analytical solution is solely a function of two non-dimensional parameters. A simpler function of these two parameters was developed to approximate the maximum structural temperature over a wide range of parameter values. Techniques were developed to choose constant, effective properties to represent the relevant temperature and pressure-dependent properties for the insulator and structure. A technique was also developed to map a time-varying surface temperature history to an equivalent square heat pulse. Using these techniques, the maximum structural temperature rise was calculated using the analytical solutions and shown to typically agree with finite element simulations within 10 to 20 percent over the relevant range of parameters studied.

Analytical approximations for spiral waves

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

Löber, Jakob, E-mail: jakob@physik.tu-berlin.de; Engel, Harald

2013-12-15

We propose a non-perturbative attempt to solve the kinematic equations for spiral waves in excitable media. From the eikonal equation for the wave front we derive an implicit analytical relation between rotation frequency Ω and core radius R{sub 0}. For free, rigidly rotating spiral waves our analytical prediction is in good agreement with numerical solutions of the linear eikonal equation not only for very large but also for intermediate and small values of the core radius. An equivalent Ω(R{sub +}) dependence improves the result by Keener and Tyson for spiral waves pinned to a circular defect of radius R{sub +}more » with Neumann boundaries at the periphery. Simultaneously, analytical approximations for the shape of free and pinned spirals are given. We discuss the reasons why the ansatz fails to correctly describe the dependence of the rotation frequency on the excitability of the medium.« less

On the atomic-number similarity of the binding energies of electrons in filled shells of elements of the periodic table

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

Karpov, V. Ya.; Shpatakovskaya, G. V., E-mail: shpagalya@yandex.ru

An expression for the binding energies of electrons in the ground state of an atom is derived on the basis of the Bohr–Sommerfeld quantization rule within the Thomas–Fermi model. The validity of this relation for all elements from neon to uranium is tested within a more perfect quantum-mechanical model with and without the inclusion of relativistic effects, as well as with experimental binding energies. As a result, the ordering of electronic levels in filled atomic shells is established, manifested in an approximate atomic-number similarity. It is proposed to use this scaling property to analytically estimate the binding energies of electronsmore » in an arbitrary atom.« less

131 iodine gamma dose determination in the thyroid gland using two geometrical shapes: a comparative study

NASA Astrophysics Data System (ADS)

Betka, A.; Bentabet, A.; Azbouche, A.; Fenineche, N.; Adjiri, A.; Dib, A.

2015-05-01

In order to study the internal gamma dose, we used a Monte Carlo code ‘Penelope’ simulation with two geometrical models (cylindrical and spherical). The deposited energy was determined via the loss of energy calculated from the quantum theory for inelastic collisions based on the first-order (plane-wave) Born approximation for charged particles with individual atoms and molecules. Our results show that the cylindrical geometry is more suitable for carrying out such a study. Moreover, we developed an analytical expression for the 131 iodine gamma dose (the energy deposited per photon absorbed dose). This latter could be considered as an important tool for evaluating the gamma dose without going through stochastic models.

Ultra-long magnetization needle induced by focusing azimuthally polarized beams with a spherical mirror.

PubMed

Hang, Li; Luo, Kai; Fu, Jian; Chang, Yizhe; Wang, Ying; Chen, Peifeng

2018-03-20

Based on extended Richards-Wolf theory for axisymmetric surfaces and the inverse Faraday effect, we propose the generation of a purely longitudinal magnetization needle by focusing Gaussian annular azimuthally polarized beams with a spherical mirror. The needle obtained has a longitudinal length varying hundreds to thousands of wavelengths while keeping the lateral size under 0.4λ, and the corresponding aspect ratio can easily reach more than 2000. It may be the first time that a magnetization needle whose aspect ratio is over 500 has been achieved. The approximate analytical expressions of the magnetization needle are given, and the longitudinal length is tunable by changing the value of the angular thickness and the position of the annular beams.

Curvilinear Squeeze Film Bearing with Porous Wall Lubricated by a Rabinowitsch Fluid

NASA Astrophysics Data System (ADS)

Walicka, A.; Walicki, E.; Jurczak, P.; Falicki, J.

2017-05-01

The present theoretical analysis is to investigate the effect of non-Newtonian lubricant modelled by a Rabinowitsch fluid on the performance of a curvilinear squeeze film bearing with one porous wall. The equations of motion of a Rabinowitsch fluid are used to derive the Reynolds equation. After general considerations on the flow in a bearing clearance and in a porous layer using the Morgan-Cameron approximation the modified Reynolds equation is obtained. The analytical solution of this equation for the case of a squeeze film bearing is presented. As a result one obtains the formulae expressing pressure distribution and load-carrying capacity. Thrust radial bearing and spherical bearing with a squeeze film are considered as numerical examples.

A model for bacterial colonization of sinking aggregates.

PubMed

Bearon, R N

2007-01-01

Sinking aggregates provide important nutrient-rich environments for marine bacteria. Quantifying the rate at which motile bacteria colonize such aggregations is important in understanding the microbial loop in the pelagic food web. In this paper, a simple analytical model is presented to predict the rate at which bacteria undergoing a random walk encounter a sinking aggregate. The model incorporates the flow field generated by the sinking aggregate, the swimming behavior of the bacteria, and the interaction of the flow with the swimming behavior. An expression for the encounter rate is computed in the limit of large Péclet number when the random walk can be approximated by a diffusion process. Comparison with an individual-based numerical simulation is also given.

Analysis of a model race car

NASA Astrophysics Data System (ADS)

Coletta, Vincent P.; Evans, Jonathan

2008-10-01

We analyze the motion of a gravity powered model race car on a downhill track of variable slope. Using a simple algebraic function to approximate the height of the track as a function of the distance along the track, and taking account of the rotational energy of the wheels, rolling friction, and air resistance, we obtain analytic expressions for the velocity and time of the car as functions of the distance traveled along the track. Photogates are used to measure the time at selected points along the track, and the measured values are in excellent agreement with the values predicted from theory. The design and analysis of model race cars provides a good application of principles of mechanics and suggests interesting projects for classes in introductory and intermediate mechanics.

Scintillation and phase anisoplanatism in Shack-Hartmann wavefront sensing.

PubMed

Robert, Clélia; Conan, Jean-Marc; Michau, Vincent; Fusco, Thierry; Vedrenne, Nicolas

2006-03-01

Adaptive optics provides a real-time compensation for atmospheric turbulence that severely limits the resolution of ground-based observation systems. The correction quality relies on a key component, that is, the wavefront sensor (WFS). When observing extended sources, WFS precision is limited by anisoplanatism effects. Anisoplanatism induces a variation of the turbulent phase and of the collected flux in the field of view. We study the effect of this phase and scintillation anisoplanatism on wavefront analysis. An analytical expression of the error induced is given in the Rytov regime. The formalism is applied to a solar and an endoatmospheric observation. Scintillation effects are generally disregarded, especially in astronomical conditions. We shall prove that this approximation is not valid with extended objects.

Photon polarization tensor in pulsed Hermite- and Laguerre-Gaussian beams

NASA Astrophysics Data System (ADS)

Karbstein, Felix; Mosman, Elena A.

2017-12-01

In this article, we provide analytical expressions for the photon polarization tensor in pulsed Hermite- and Laguerre-Gaussian laser beams. Our results are based on a locally constant field approximation of the one-loop Heisenberg-Euler effective Lagrangian for quantum electrodynamics. Hence, by construction they are limited to slowly varying electromagnetic fields, varying on spatial and temporal scales significantly larger than the Compton wavelength/time of the electron. The latter criterion is fulfilled by all laser beams currently available in the laboratory. Our findings will, e.g., be relevant for the study of vacuum birefringence experienced by probe photons brought into collision with a high-intensity laser pulse which can be represented as a superposition of either Hermite- or Laguerre-Gaussian modes.

On the null trajectories in conformal Weyl gravity

NASA Astrophysics Data System (ADS)

Villanueva, J. R.; Olivares, Marco

2013-06-01

In this work we find analytical solutions to the null geodesics around a black hole in the conformal Weyl gravity. Exact expressions for the horizons are found, and they depend on the cosmological constant and the coupling constants of the conformal Weyl gravity. Then, we study the radial motion from the point of view of the proper and coordinate frames, and compare it with that found in spacetimes of general relativity. The angular motion is also examined qualitatively by means of an effective potential; quantitatively, the equation of motion is solved in terms of wp-Weierstrass elliptic function. Thus, we find the deflection angle for photons without using any approximation, which is a novel result for this kind of gravity.