Approximate analytic expression for the Skyrmions crystal

NASA Astrophysics Data System (ADS)

Grandi, Nicolás; Sturla, Mauricio

2018-01-01

We find approximate solutions for the two-dimensional nonlinear Σ-model with Dzyalioshinkii-Moriya term, representing magnetic Skyrmions. They are built in an analytic form, by pasting different approximate solutions found in different regions of space. We verify that our construction reproduces the phenomenology known from numerical solutions and Monte Carlo simulations, giving rise to a Skyrmion lattice at an intermediate range of magnetic field, flanked by spiral and spin-polarized phases for low and high magnetic fields, respectively.

An approximate analytical solution for describing surface runoff and sediment transport over hillslope

NASA Astrophysics Data System (ADS)

Tao, Wanghai; Wang, Quanjiu; Lin, Henry

2018-03-01

Soil and water loss from farmland causes land degradation and water pollution, thus continued efforts are needed to establish mathematical model for quantitative analysis of relevant processes and mechanisms. In this study, an approximate analytical solution has been developed for overland flow model and sediment transport model, offering a simple and effective means to predict overland flow and erosion under natural rainfall conditions. In the overland flow model, the flow regime was considered to be transitional with the value of parameter β (in the kinematic wave model) approximately two. The change rate of unit discharge with distance was assumed to be constant and equal to the runoff rate at the outlet of the plane. The excess rainfall was considered to be constant under uniform rainfall conditions. The overland flow model developed can be further applied to natural rainfall conditions by treating excess rainfall intensity as constant over a small time interval. For the sediment model, the recommended values of the runoff erosion calibration constant (cr) and the splash erosion calibration constant (cf) have been given in this study so that it is easier to use the model. These recommended values are 0.15 and 0.12, respectively. Comparisons with observed results were carried out to validate the proposed analytical solution. The results showed that the approximate analytical solution developed in this paper closely matches the observed data, thus providing an alternative method of predicting runoff generation and sediment yield, and offering a more convenient method of analyzing the quantitative relationships between variables. Furthermore, the model developed in this study can be used as a theoretical basis for developing runoff and erosion control methods.

Hybrid perturbation methods based on statistical time series models

NASA Astrophysics Data System (ADS)

San-Juan, Juan Félix; San-Martín, Montserrat; Pérez, Iván; López, Rosario

2016-04-01

In this work we present a new methodology for orbit propagation, the hybrid perturbation theory, based on the combination of an integration method and a prediction technique. The former, which can be a numerical, analytical or semianalytical theory, generates an initial approximation that contains some inaccuracies derived from the fact that, in order to simplify the expressions and subsequent computations, not all the involved forces are taken into account and only low-order terms are considered, not to mention the fact that mathematical models of perturbations not always reproduce physical phenomena with absolute precision. The prediction technique, which can be based on either statistical time series models or computational intelligence methods, is aimed at modelling and reproducing missing dynamics in the previously integrated approximation. This combination results in the precision improvement of conventional numerical, analytical and semianalytical theories for determining the position and velocity of any artificial satellite or space debris object. In order to validate this methodology, we present a family of three hybrid orbit propagators formed by the combination of three different orders of approximation of an analytical theory and a statistical time series model, and analyse their capability to process the effect produced by the flattening of the Earth. The three considered analytical components are the integration of the Kepler problem, a first-order and a second-order analytical theories, whereas the prediction technique is the same in the three cases, namely an additive Holt-Winters method.

Evaluation of an Approximate Method for Synthesizing Covariance Matrices for Use in Meta-Analytic SEM

ERIC Educational Resources Information Center

Beretvas, S. Natasha; Furlow, Carolyn F.

2006-01-01

Meta-analytic structural equation modeling (MA-SEM) is increasingly being used to assess model-fit for variables' interrelations synthesized across studies. MA-SEM researchers have analyzed synthesized correlation matrices using structural equation modeling (SEM) estimation that is designed for covariance matrices. This can produce incorrect…

Monitoring by forward scatter radar techniques: an improved second-order analytical model

NASA Astrophysics Data System (ADS)

Falconi, Marta Tecla; Comite, Davide; Galli, Alessandro; Marzano, Frank S.; Pastina, Debora; Lombardo, Pierfrancesco

2017-10-01

In this work, a second-order phase approximation is introduced to provide an improved analytical model of the signal received in forward scatter radar systems. A typical configuration with a rectangular metallic object illuminated while crossing the baseline, in far- or near-field conditions, is considered. An improved second-order model is compared with a simplified one already proposed by the authors and based on a paraxial approximation. A phase error analysis is carried out to investigate benefits and limitations of the second-order modeling. The results are validated by developing full-wave numerical simulations implementing the relevant scattering problem on a commercial tool.

Proxy-SU(3) symmetry in heavy deformed nuclei

NASA Astrophysics Data System (ADS)

Bonatsos, Dennis; Assimakis, I. E.; Minkov, N.; Martinou, Andriana; Cakirli, R. B.; Casten, R. F.; Blaum, K.

2017-06-01

Background: Microscopic calculations of heavy nuclei face considerable difficulties due to the sizes of the matrices that need to be solved. Various approximation schemes have been invoked, for example by truncating the spaces, imposing seniority limits, or appealing to various symmetry schemes such as pseudo-SU(3). This paper proposes a new symmetry scheme also based on SU(3). This proxy-SU(3) can be applied to well-deformed nuclei, is simple to use, and can yield analytic predictions. Purpose: To present the new scheme and its microscopic motivation, and to test it using a Nilsson model calculation with the original shell model orbits and with the new proxy set. Method: We invoke an approximate, analytic, treatment of the Nilsson model, that allows the above vetting and yet is also transparent in understanding the approximations involved in the new proxy-SU(3). Results: It is found that the new scheme yields a Nilsson diagram for well-deformed nuclei that is very close to the original Nilsson diagram. The specific levels of approximation in the new scheme are also shown, for each major shell. Conclusions: The new proxy-SU(3) scheme is a good approximation to the full set of orbits in a major shell. Being able to replace a complex shell model calculation with a symmetry-based description now opens up the possibility to predict many properties of nuclei analytically and often in a parameter-free way. The new scheme works best for heavier nuclei, precisely where full microscopic calculations are most challenged. Some cases in which the new scheme can be used, often analytically, to make specific predictions, are shown in a subsequent paper.

Finite element modeling of mitral leaflet tissue using a layered shell approximation

PubMed Central

Ratcliffe, Mark B.; Guccione, Julius M.

2012-01-01

The current study presents a finite element model of mitral leaflet tissue, which incorporates the anisotropic material response and approximates the layered structure. First, continuum mechanics and the theory of layered composites are used to develop an analytical representation of membrane stress in the leaflet material. This is done with an existing anisotropic constitutive law from literature. Then, the concept is implemented in a finite element (FE) model by overlapping and merging two layers of transversely isotropic membrane elements in LS-DYNA, which homogenizes the response. The FE model is then used to simulate various biaxial extension tests and out-of-plane pressure loading. Both the analytical and FE model show good agreement with experimental biaxial extension data, and show good mutual agreement. This confirms that the layered composite approximation presented in the current study is able to capture the exponential stiffening seen in both the circumferential and radial directions of mitral leaflets. PMID:22971896

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.

Padé Approximant and Minimax Rational Approximation in Standard Cosmology

NASA Astrophysics Data System (ADS)

Zaninetti, Lorenzo

2016-02-01

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

Loglinear Approximate Solutions to Real-Business-Cycle Models: Some Observations

ERIC Educational Resources Information Center

Lau, Sau-Him Paul; Ng, Philip Hoi-Tak

2007-01-01

Following the analytical approach suggested in Campbell, the authors consider a baseline real-business-cycle (RBC) model with endogenous labor supply. They observe that the coefficients in the loglinear approximation of the dynamic equations characterizing the equilibrium are related to the fundamental parameters in a relatively simple manner.…

S-curve networks and an approximate method for estimating degree distributions of complex networks

NASA Astrophysics Data System (ADS)

Guo, Jin-Li

2010-12-01

In the study of complex networks almost all theoretical models have the property of infinite growth, but the size of actual networks is finite. According to statistics from the China Internet IPv4 (Internet Protocol version 4) addresses, this paper proposes a forecasting model by using S curve (logistic curve). The growing trend of IPv4 addresses in China is forecasted. There are some reference values for optimizing the distribution of IPv4 address resource and the development of IPv6. Based on the laws of IPv4 growth, that is, the bulk growth and the finitely growing limit, it proposes a finite network model with a bulk growth. The model is said to be an S-curve network. Analysis demonstrates that the analytic method based on uniform distributions (i.e., Barabási-Albert method) is not suitable for the network. It develops an approximate method to predict the growth dynamics of the individual nodes, and uses this to calculate analytically the degree distribution and the scaling exponents. The analytical result agrees with the simulation well, obeying an approximately power-law form. This method can overcome a shortcoming of Barabási-Albert method commonly used in current network research.

Approximate Single-Diode Photovoltaic Model for Efficient I-V Characteristics Estimation

PubMed Central

Ting, T. O.; Zhang, Nan; Guan, Sheng-Uei; Wong, Prudence W. H.

2013-01-01

Precise photovoltaic (PV) behavior models are normally described by nonlinear analytical equations. To solve such equations, it is necessary to use iterative procedures. Aiming to make the computation easier, this paper proposes an approximate single-diode PV model that enables high-speed predictions for the electrical characteristics of commercial PV modules. Based on the experimental data, statistical analysis is conducted to validate the approximate model. Simulation results show that the calculated current-voltage (I-V) characteristics fit the measured data with high accuracy. Furthermore, compared with the existing modeling methods, the proposed model reduces the simulation time by approximately 30% in this work. PMID:24298205

Analytic barrage attack model. Final report, January 1986-January 1989

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

St Ledger, J.W.; Naegeli, R.E.; Dowden, N.A.

An analytic model is developed for a nuclear barrage attack, assuming weapons with no aiming error and a cookie-cutter damage function. The model is then extended with approximations for the effects of aiming error and distance damage sigma. The final result is a fast running model which calculates probability of damage for a barrage attack. The probability of damage is accurate to within seven percent or better, for weapon reliabilities of 50 to 100 percent, distance damage sigmas of 0.5 or less, and zero to very large circular error probabilities. FORTRAN 77 coding is included in the report for themore » analytic model and for a numerical model used to check the analytic results.« less

Unimolecular diffusion-mediated reactions with a nonrandom time-modulated absorbing barrier

NASA Technical Reports Server (NTRS)

Bashford, D.; Weaver, D. L.

1986-01-01

A diffusion-reaction model with time-dependent reactivity is formulated and applied to unimolecular reactions. The model is solved exactly numerically and approximately analytically for the unreacted fraction as a function of time. It is shown that the approximate analytical solution is valid even when the system is far from equilibrium, and when the reactivity probability is more complicated than a square-wave function of time. A discussion is also given of an approach to problems of this type using a stochastically fluctuating reactivity, and the first-passage time for a particular example is derived.

Numerical and analytic models of spontaneous frequency sweeping for energetic particle-driven Alfven eigenmodes

NASA Astrophysics Data System (ADS)

Wang, Ge; Berk, H. L.

2011-10-01

The frequency chirping signal arising from spontaneous a toroidial Alfven eigenmode (TAE) excited by energetic particles is studied for both numerical and analytic models. The time-dependent numerical model is based on the 1D Vlasov equation. We use a sophisticated tracking method to lock onto the resonant structure to enable the chirping frequency to be nearly constant in the calculation frame. The accuracy of the adiabatic approximation is tested during the simulation which justifies the appropriateness of our analytic model. The analytic model uses the adiabatic approximation which allows us to solve the wave evolution equation in frequency space. Then, the resonant interactions between energetic particles and TAE yield predictions for the chirping rate, wave frequency and amplitudes vs. time. Here, an adiabatic invariant J is defined on the separatrix of a chirping mode to determine the region of confinement of the wave trapped distribution function. We examine the asymptotic behavior of the chirping signal for its long time evolution and find agreement in essential features with the results of the simulation. Work supported by Department of Energy contract DE-FC02-08ER54988.

Approximate Solutions for Ideal Dam-Break Sediment-Laden Flows on Uniform Slopes

NASA Astrophysics Data System (ADS)

Ni, Yufang; Cao, Zhixian; Borthwick, Alistair; Liu, Qingquan

2018-04-01

Shallow water hydro-sediment-morphodynamic (SHSM) models have been applied increasingly widely in hydraulic engineering and geomorphological studies over the past few decades. Analytical and approximate solutions are usually sought to verify such models and therefore confirm their credibility. Dam-break flows are often evoked because such flows normally feature shock waves and contact discontinuities that warrant refined numerical schemes to solve. While analytical and approximate solutions to clear-water dam-break flows have been available for some time, such solutions are rare for sediment transport in dam-break flows. Here we aim to derive approximate solutions for ideal dam-break sediment-laden flows resulting from the sudden release of a finite volume of frictionless, incompressible water-sediment mixture on a uniform slope. The approximate solutions are presented for three typical sediment transport scenarios, i.e., pure advection, pure sedimentation, and concurrent entrainment and deposition. Although the cases considered in this paper are not real, the approximate solutions derived facilitate suitable benchmark tests for evaluating SHSM models, especially presently when shock waves can be numerically resolved accurately with a suite of finite volume methods, while the accuracy of the numerical solutions of contact discontinuities in sediment transport remains generally poorer.

Optimal clinical trial design based on a dichotomous Markov-chain mixed-effect sleep model.

PubMed

Steven Ernest, C; Nyberg, Joakim; Karlsson, Mats O; Hooker, Andrew C

2014-12-01

D-optimal designs for discrete-type responses have been derived using generalized linear mixed models, simulation based methods and analytical approximations for computing the fisher information matrix (FIM) of non-linear mixed effect models with homogeneous probabilities over time. In this work, D-optimal designs using an analytical approximation of the FIM for a dichotomous, non-homogeneous, Markov-chain phase advanced sleep non-linear mixed effect model was investigated. The non-linear mixed effect model consisted of transition probabilities of dichotomous sleep data estimated as logistic functions using piecewise linear functions. Theoretical linear and nonlinear dose effects were added to the transition probabilities to modify the probability of being in either sleep stage. D-optimal designs were computed by determining an analytical approximation the FIM for each Markov component (one where the previous state was awake and another where the previous state was asleep). Each Markov component FIM was weighted either equally or by the average probability of response being awake or asleep over the night and summed to derive the total FIM (FIM(total)). The reference designs were placebo, 0.1, 1-, 6-, 10- and 20-mg dosing for a 2- to 6-way crossover study in six dosing groups. Optimized design variables were dose and number of subjects in each dose group. The designs were validated using stochastic simulation/re-estimation (SSE). Contrary to expectations, the predicted parameter uncertainty obtained via FIM(total) was larger than the uncertainty in parameter estimates computed by SSE. Nevertheless, the D-optimal designs decreased the uncertainty of parameter estimates relative to the reference designs. Additionally, the improvement for the D-optimal designs were more pronounced using SSE than predicted via FIM(total). Through the use of an approximate analytic solution and weighting schemes, the FIM(total) for a non-homogeneous, dichotomous Markov-chain phase advanced sleep model was computed and provided more efficient trial designs and increased nonlinear mixed-effects modeling parameter precision.

Atomic density functional and diagram of structures in the phase field crystal model

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

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

2016-02-15

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

Development and application of accurate analytical models for single active electron potentials

NASA Astrophysics Data System (ADS)

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

2015-05-01

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

On the effect of the degeneracy among dark energy parameters

NASA Astrophysics Data System (ADS)

Gong, Yungui; Gao, Qing

2014-01-01

The dynamics of scalar fields as dark energy is well approximated by some general relations between the equation of state parameter and the fractional energy density . Based on the approximation, for slowly rolling scalar fields, we derived the analytical expressions of which reduce to the popular Chevallier-Polarski-Linder parametrization with an explicit degeneracy relation between and . The models approximate the dynamics of scalar fields well and help eliminate the degeneracies among , , and . With the explicit degeneracy relations, we test their effects on the constraints of the cosmological parameters. We find that: (1) The analytical relations between and for the two models are consistent with observational data. (2) The degeneracies have little effect on . (3) The error of was reduced about 30 % with the degeneracy relations.

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

DOE PAGES

Gao, Xujiao; Huang, Andy; Kerr, Bert

2017-10-25

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

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

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

Gao, Xujiao; Huang, Andy; Kerr, Bert

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

A Model for Axial Magnetic Bearings Including Eddy Currents

NASA Technical Reports Server (NTRS)

Kucera, Ladislav; Ahrens, Markus

1996-01-01

This paper presents an analytical method of modelling eddy currents inside axial bearings. The problem is solved by dividing an axial bearing into elementary geometric forms, solving the Maxwell equations for these simplified geometries, defining boundary conditions and combining the geometries. The final result is an analytical solution for the flux, from which the impedance and the force of an axial bearing can be derived. Several impedance measurements have shown that the analytical solution can fit the measured data with a precision of approximately 5%.

Analytical Model For Fluid Dynamics In A Microgravity Environment

NASA Technical Reports Server (NTRS)

Naumann, Robert J.

1995-01-01

Report presents analytical approximation methodology for providing coupled fluid-flow, heat, and mass-transfer equations in microgravity environment. Experimental engineering estimates accurate to within factor of 2 made quickly and easily, eliminating need for time-consuming and costly numerical modeling. Any proposed experiment reviewed to see how it would perform in microgravity environment. Model applied in commercial setting for preliminary design of low-Grashoff/Rayleigh-number experiments.

A new frequency domain analytical solution of a cascade of diffusive channels for flood routing

NASA Astrophysics Data System (ADS)

Cimorelli, Luigi; Cozzolino, Luca; Della Morte, Renata; Pianese, Domenico; Singh, Vijay P.

2015-04-01

Simplified flood propagation models are often employed in practical applications for hydraulic and hydrologic analyses. In this paper, we present a new numerical method for the solution of the Linear Parabolic Approximation (LPA) of the De Saint Venant equations (DSVEs), accounting for the space variation of model parameters and the imposition of appropriate downstream boundary conditions. The new model is based on the analytical solution of a cascade of linear diffusive channels in the Laplace Transform domain. The time domain solutions are obtained using a Fourier series approximation of the Laplace Inversion formula. The new Inverse Laplace Transform Diffusive Flood Routing model (ILTDFR) can be used as a building block for the construction of real-time flood forecasting models or in optimization models, because it is unconditionally stable and allows fast and fairly precise computation.

A generalized analytical model for radiative transfer in vacuum thermal insulation of space vehicles

NASA Astrophysics Data System (ADS)

Krainova, Irina V.; Dombrovsky, Leonid A.; Nenarokomov, Aleksey V.; Budnik, Sergey A.; Titov, Dmitry M.; Alifanov, Oleg M.

2017-08-01

The previously developed spectral model for radiative transfer in vacuum thermal insulation of space vehicles is generalized to take into account possible thermal contact between a fibrous spacer and one of the neighboring aluminum foil layers. An approximate analytical solution based on slightly modified two-flux approximation for radiative transfer in a semi-transparent fibrous spacer is derived. It was shown that thermal contact between the spacer and adjacent foil may decrease significantly the quality of thermal insulation because of an increase in radiative flux to/from the opposite aluminum foil. Theoretical predictions are confirmed by comparison with new results of laboratory experiments.

Approximate analytical solution for induction heating of solid cylinders

DOE PAGES

Jankowski, Todd Andrew; Pawley, Norma Helen; Gonzales, Lindsey Michal; ...

2015-10-20

An approximate solution to the mathematical model for induction heating of a solid cylinder in a cylindrical induction coil is presented here. The coupled multiphysics model includes equations describing the electromagnetic field in the heated object, a heat transfer simulation to determine temperature of the heated object, and an AC circuit simulation of the induction heating power supply. A multiple-scale perturbation method is used to solve the multiphysics model. The approximate analytical solution yields simple closed-form expressions for the electromagnetic field and heat generation rate in the solid cylinder, for the equivalent impedance of the associated tank circuit, and formore » the frequency response of a variable frequency power supply driving the tank circuit. The solution developed here is validated by comparing predicted power supply frequency to both experimental measurements and calculated values from finite element analysis for heating of graphite cylinders in an induction furnace. The simple expressions from the analytical solution clearly show the functional dependence of the power supply frequency on the material properties of the load and the geometrical characteristics of the furnace installation. In conclusion, the expressions developed here provide physical insight into observations made during load signature analysis of induction heating.« less

Effect of coulomb spline on rotor dynamic response

NASA Technical Reports Server (NTRS)

Nataraj, C.; Nelson, H. D.; Arakere, N.

1985-01-01

A rigid rotor system coupled by a coulomb spline is modelled and analyzed by approximate analytical and numerical analytical methods. Expressions are derived for the variables of the resulting limit cycle and are shown to be quite accurate for a small departure from isotropy.

Mutation-selection balance in mixed mating populations.

PubMed

Kelly, John K

2007-05-21

An approximation to the average number of deleterious mutations per gamete, Q, is derived from a model allowing selection on both zygotes and male gametes. Progeny are produced by either outcrossing or self-fertilization with fixed probabilities. The genetic model is a standard in evolutionary biology: mutations occur at unlinked loci, have equivalent effects, and combine multiplicatively to determine fitness. The approximation developed here treats individual mutation counts with a generalized Poisson model conditioned on the distribution of selfing histories in the population. The approximation is accurate across the range of parameter sets considered and provides both analytical insights and greatly increased computational speed. Model predictions are discussed in relation to several outstanding problems, including the estimation of the genomic deleterious mutation rates (U), the generality of "selective interference" among loci, and the consequences of gametic selection for the joint distribution of inbreeding depression and mating system across species. Finally, conflicting results from previous analytical treatments of mutation-selection balance are resolved to assumptions about the life-cycle and the initial fate of mutations.

An analytic technique for statistically modeling random atomic clock errors in estimation

NASA Technical Reports Server (NTRS)

Fell, P. J.

1981-01-01

Minimum variance estimation requires that the statistics of random observation errors be modeled properly. If measurements are derived through the use of atomic frequency standards, then one source of error affecting the observable is random fluctuation in frequency. This is the case, for example, with range and integrated Doppler measurements from satellites of the Global Positioning and baseline determination for geodynamic applications. An analytic method is presented which approximates the statistics of this random process. The procedure starts with a model of the Allan variance for a particular oscillator and develops the statistics of range and integrated Doppler measurements. A series of five first order Markov processes is used to approximate the power spectral density obtained from the Allan variance.

An approximate analytic solution of a set of nonlinear model alpha-omega-dynamo equations for marginally unstable systems

NASA Technical Reports Server (NTRS)

Hinata, S.

1989-01-01

An approximate analytic solution of a set of nonlinear model alpha-omega-dynamo equations is obtained. The reaction of the Lorentz force on the velocity shear which stretches and, hence, amplifies the magnetic field is incorporated into the model. To single out the effect of the Lorentz force on the omega-effect, the effect of the Lorentz force on the alpha-effect is neglected in this study. The solution represents a nonlinear oscillation with the amplitude and period determined by the dynamo number N. The amplitude is proportional to N - 1, while the period is almost exactly the same as the dissipation time of the unstable mode (proportional to N).

User's manual for the one-dimensional hypersonic experimental aero-thermodynamic (1DHEAT) data reduction code

NASA Technical Reports Server (NTRS)

Hollis, Brian R.

1995-01-01

A FORTRAN computer code for the reduction and analysis of experimental heat transfer data has been developed. This code can be utilized to determine heat transfer rates from surface temperature measurements made using either thin-film resistance gages or coaxial surface thermocouples. Both an analytical and a numerical finite-volume heat transfer model are implemented in this code. The analytical solution is based on a one-dimensional, semi-infinite wall thickness model with the approximation of constant substrate thermal properties, which is empirically corrected for the effects of variable thermal properties. The finite-volume solution is based on a one-dimensional, implicit discretization. The finite-volume model directly incorporates the effects of variable substrate thermal properties and does not require the semi-finite wall thickness approximation used in the analytical model. This model also includes the option of a multiple-layer substrate. Fast, accurate results can be obtained using either method. This code has been used to reduce several sets of aerodynamic heating data, of which samples are included in this report.

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.

Evaluation of air traffic control models and simulations.

DOT National Transportation Integrated Search

1971-06-01

Approximately two hundred reports were identified as describing Air Traffic Control (ATC) modeling and simulation efforts. Of these, about ninety analytical and simulation models dealing with virtually all aspects of ATC were formally evaluated. The ...

Modeling and Analysis of Structural Dynamics for a One-Tenth Scale Model NGST Sunshield

NASA Technical Reports Server (NTRS)

Johnston, John; Lienard, Sebastien; Brodeur, Steve (Technical Monitor)

2001-01-01

New modeling and analysis techniques have been developed for predicting the dynamic behavior of the Next Generation Space Telescope (NGST) sunshield. The sunshield consists of multiple layers of pretensioned, thin-film membranes supported by deployable booms. Modeling the structural dynamic behavior of the sunshield is a challenging aspect of the problem due to the effects of membrane wrinkling. A finite element model of the sunshield was developed using an approximate engineering approach, the cable network method, to account for membrane wrinkling effects. Ground testing of a one-tenth scale model of the NGST sunshield were carried out to provide data for validating the analytical model. A series of analyses were performed to predict the behavior of the sunshield under the ground test conditions. Modal analyses were performed to predict the frequencies and mode shapes of the test article and transient response analyses were completed to simulate impulse excitation tests. Comparison was made between analytical predictions and test measurements for the dynamic behavior of the sunshield. In general, the results show good agreement with the analytical model correctly predicting the approximate frequency and mode shapes for the significant structural modes.

Analysis of high-speed rotating flow inside gas centrifuge casing

NASA Astrophysics Data System (ADS)

Pradhan, Sahadev, , Dr.

2017-10-01

The generalized analytical model for the radial boundary layer inside the gas centrifuge casing in which the inner cylinder is rotating at a constant angular velocity Ω_i while the outer one is stationary, is formulated for studying the secondary gas flow field due to wall thermal forcing, inflow/outflow of light gas along the boundaries, as well as due to the combination of the above two external forcing. The analytical model includes the sixth order differential equation for the radial boundary layer at the cylindrical curved surface in terms of master potential (χ) , which is derived from the equations of motion in an axisymmetric (r - z) plane. The linearization approximation is used, where the equations of motion are truncated at linear order in the velocity and pressure disturbances to the base flow, which is a solid-body rotation. Additional approximations in the analytical model include constant temperature in the base state (isothermal compressible Couette flow), high aspect ratio (length is large compared to the annular gap), high Reynolds number, but there is no limitation on the Mach number. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order in the radial direction for the generalized analytical equation) are obtained. The solutions for the secondary flow is determined in terms of these eigenvalues and eigenfunctions. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations and found excellent agreement (with a difference of less than 15%) between the predictions of the analytical model and the DSMC simulations, provided the boundary conditions in the analytical model are accurately specified.

Analysis of high-speed rotating flow inside gas centrifuge casing

NASA Astrophysics Data System (ADS)

Pradhan, Sahadev, , Dr.

2017-09-01

The generalized analytical model for the radial boundary layer inside the gas centrifuge casing in which the inner cylinder is rotating at a constant angular velocity Ωi while the outer one is stationary, is formulated for studying the secondary gas flow field due to wall thermal forcing, inflow/outflow of light gas along the boundaries, as well as due to the combination of the above two external forcing. The analytical model includes the sixth order differential equation for the radial boundary layer at the cylindrical curved surface in terms of master potential (χ) , which is derived from the equations of motion in an axisymmetric (r - z) plane. The linearization approximation is used, where the equations of motion are truncated at linear order in the velocity and pressure disturbances to the base flow, which is a solid-body rotation. Additional approximations in the analytical model include constant temperature in the base state (isothermal compressible Couette flow), high aspect ratio (length is large compared to the annular gap), high Reynolds number, but there is no limitation on the Mach number. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order in the radial direction for the generalized analytical equation) are obtained. The solutions for the secondary flow is determined in terms of these eigenvalues and eigenfunctions. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations and found excellent agreement (with a difference of less than 15%) between the predictions of the analytical model and the DSMC simulations, provided the boundary conditions in the analytical model are accurately specified.

Analysis of high-speed rotating flow inside gas centrifuge casing

NASA Astrophysics Data System (ADS)

Pradhan, Sahadev

2017-11-01

The generalized analytical model for the radial boundary layer inside the gas centrifuge casing in which the inner cylinder is rotating at a constant angular velocity Ωi while the outer one is stationary, is formulated for studying the secondary gas flow field due to wall thermal forcing, inflow/outflow of light gas along the boundaries, as well as due to the combination of the above two external forcing. The analytical model includes the sixth order differential equation for the radial boundary layer at the cylindrical curved surface in terms of master potential (χ) , which is derived from the equations of motion in an axisymmetric (r - z) plane. The linearization approximation is used, where the equations of motion are truncated at linear order in the velocity and pressure disturbances to the base flow, which is a solid-body rotation. Additional approximations in the analytical model include constant temperature in the base state (isothermal compressible Couette flow), high aspect ratio (length is large compared to the annular gap), high Reynolds number, but there is no limitation on the Mach number. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order in the radial direction for the generalized analytical equation) are obtained. The solutions for the secondary flow is determined in terms of these eigenvalues and eigenfunctions. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations and found excellent agreement (with a difference of less than 15%) between the predictions of the analytical model and the DSMC simulations, provided the boundary conditions in the analytical model are accurately specified.

One-dimensional model of interacting-step fluctuations on vicinal surfaces: Analytical formulas and kinetic Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Patrone, Paul N.; Einstein, T. L.; Margetis, Dionisios

2010-12-01

We study analytically and numerically a one-dimensional model of interacting line defects (steps) fluctuating on a vicinal crystal. Our goal is to formulate and validate analytical techniques for approximately solving systems of coupled nonlinear stochastic differential equations (SDEs) governing fluctuations in surface motion. In our analytical approach, the starting point is the Burton-Cabrera-Frank (BCF) model by which step motion is driven by diffusion of adsorbed atoms on terraces and atom attachment-detachment at steps. The step energy accounts for entropic and nearest-neighbor elastic-dipole interactions. By including Gaussian white noise to the equations of motion for terrace widths, we formulate large systems of SDEs under different choices of diffusion coefficients for the noise. We simplify this description via (i) perturbation theory and linearization of the step interactions and, alternatively, (ii) a mean-field (MF) approximation whereby widths of adjacent terraces are replaced by a self-consistent field but nonlinearities in step interactions are retained. We derive simplified formulas for the time-dependent terrace-width distribution (TWD) and its steady-state limit. Our MF analytical predictions for the TWD compare favorably with kinetic Monte Carlo simulations under the addition of a suitably conservative white noise in the BCF equations.

Overshooting thunderstorm cloud top dynamics as approximated by a linear Lagrangian parcel model with analytic exact solutions

NASA Technical Reports Server (NTRS)

Schlesinger, Robert E.

1990-01-01

Results are presented from a linear Lagrangian entraining parcel model of an overshooting thunderstorm cloud top. The model, which is similar to that of Adler and Mack (1986), gives analytic exact solutions for vertical velocity and temperature by representing mixing with Rayleigh damping instead of nonlinearly. Model results are presented for various combinations of stratospheric lapse rate, drag intensity, and mixing strength. The results are compared to those of Adler and Mack.

Analytical mass formula and nuclear surface properties in the ETF approximation. Part I: symmetric nuclei

NASA Astrophysics Data System (ADS)

Aymard, François; Gulminelli, Francesca; Margueron, Jérôme

2016-08-01

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

On Connectivity of Wireless Sensor Networks with Directional Antennas

PubMed Central

Wang, Qiu; Dai, Hong-Ning; Zheng, Zibin; Imran, Muhammad; Vasilakos, Athanasios V.

2017-01-01

In this paper, we investigate the network connectivity of wireless sensor networks with directional antennas. In particular, we establish a general framework to analyze the network connectivity while considering various antenna models and the channel randomness. Since existing directional antenna models have their pros and cons in the accuracy of reflecting realistic antennas and the computational complexity, we propose a new analytical directional antenna model called the iris model to balance the accuracy against the complexity. We conduct extensive simulations to evaluate the analytical framework. Our results show that our proposed analytical model on the network connectivity is accurate, and our iris antenna model can provide a better approximation to realistic directional antennas than other existing antenna models. PMID:28085081

Experimental, Numerical and Analytical Characterization of Slosh Dynamics Applied to In-Space Propellant Storage, Management and Transfer

NASA Technical Reports Server (NTRS)

Storey, Jedediah M.; Kirk, Daniel; Gutierrez, Hector; Marsell, Brandon; Schallhorn, Paul; Lapilli, Gabriel D.

2015-01-01

Experimental and numerical results are presented from a new cryogenic fluid slosh program at the Florida Institute of Technology (FIT). Water and cryogenic liquid nitrogen are used in various ground-based tests with an approximately 30 cm diameter spherical tank to characterize damping, slosh mode frequencies, and slosh forces. The experimental results are compared to a computational fluid dynamics (CFD) model for validation. An analytical model is constructed from prior work for comparison. Good agreement is seen between experimental, numerical, and analytical results.

Viscous damping and spring force in periodic perforated planar microstructures when the Reynolds’ equation cannot be applied

PubMed Central

Homentcovschi, Dorel; Miles, Ronald N.

2010-01-01

A model of squeeze-film behavior is developed based on Stokes’ equations for viscous, compressible isothermal flows. The flow domain is an axisymmetrical, unit cell approximation of a planar, periodic, perforated microstructure. The model is developed for cases when the lubrication approximation cannot be applied. The complex force generated by vibrations of the diaphragm driving the flow has two components: the damping force and the spring force. While for large frequencies the spring force dominates, at low (acoustical) frequencies the damping force is the most important part. The analytical approach developed here yields an explicit formula for both forces. In addition, using a finite element software package, the damping force is also obtained numerically. A comparison is made between the analytic result, numerical solution, and some experimental data found in the literature, which validates the analytic formula and provides compelling arguments about its value in designing microelectomechanical devices. PMID:20329828

Analytical mass formula and nuclear surface properties in the ETF approximation. Part II: asymmetric nuclei

NASA Astrophysics Data System (ADS)

Aymard, François; Gulminelli, Francesca; Margueron, Jérôme

2016-08-01

We have recently addressed the problem of the determination of the nuclear surface energy for symmetric nuclei in the framework of the extended Thomas-Fermi (ETF) approximation using Skyrme functionals. We presently extend this formalism to the case of asymmetric nuclei and the question of the surface symmetry energy. We propose an approximate expression for the diffuseness and the surface energy. These quantities are analytically related to the parameters of the energy functional. In particular, the influence of the different equation of state parameters can be explicitly quantified. Detailed analyses of the different energy components (local/non-local, isoscalar/isovector, surface/curvature and higher order) are also performed. Our analytical solution of the ETF integral improves previous models and leads to a precision of better than 200 keV per nucleon in the determination of the nuclear binding energy for dripline nuclei.

Approximate analytical modeling of leptospirosis infection

NASA Astrophysics Data System (ADS)

Ismail, Nur Atikah; Azmi, Amirah; Yusof, Fauzi Mohamed; Ismail, Ahmad Izani

2017-11-01

Leptospirosis is an infectious disease carried by rodents which can cause death in humans. The disease spreads directly through contact with feces, urine or through bites of infected rodents and indirectly via water contaminated with urine and droppings from them. Significant increase in the number of leptospirosis cases in Malaysia caused by the recent severe floods were recorded during heavy rainfall season. Therefore, to understand the dynamics of leptospirosis infection, a mathematical model based on fractional differential equations have been developed and analyzed. In this paper an approximate analytical method, the multi-step Laplace Adomian decomposition method, has been used to conduct numerical simulations so as to gain insight on the spread of leptospirosis infection.

Approximate Model of Zone Sedimentation

NASA Astrophysics Data System (ADS)

Dzianik, František

2011-12-01

The process of zone sedimentation is affected by many factors that are not possible to express analytically. For this reason, the zone settling is evaluated in practice experimentally or by application of an empirical mathematical description of the process. The paper presents the development of approximate model of zone settling, i.e. the general function which should properly approximate the behaviour of the settling process within its entire range and at the various conditions. Furthermore, the specification of the model parameters by the regression analysis of settling test results is shown. The suitability of the model is reviewed by graphical dependencies and by statistical coefficients of correlation. The approximate model could by also useful on the simplification of process design of continual settling tanks and thickeners.

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

Two-dimensional analytic weighting functions for limb scattering

NASA Astrophysics Data System (ADS)

Zawada, D. J.; Bourassa, A. E.; Degenstein, D. A.

2017-10-01

Through the inversion of limb scatter measurements it is possible to obtain vertical profiles of trace species in the atmosphere. Many of these inversion methods require what is often referred to as weighting functions, or derivatives of the radiance with respect to concentrations of trace species in the atmosphere. Several radiative transfer models have implemented analytic methods to calculate weighting functions, alleviating the computational burden of traditional numerical perturbation methods. Here we describe the implementation of analytic two-dimensional weighting functions, where derivatives are calculated relative to atmospheric constituents in a two-dimensional grid of altitude and angle along the line of sight direction, in the SASKTRAN-HR radiative transfer model. Two-dimensional weighting functions are required for two-dimensional inversions of limb scatter measurements. Examples are presented where the analytic two-dimensional weighting functions are calculated with an underlying one-dimensional atmosphere. It is shown that the analytic weighting functions are more accurate than ones calculated with a single scatter approximation, and are orders of magnitude faster than a typical perturbation method. Evidence is presented that weighting functions for stratospheric aerosols calculated under a single scatter approximation may not be suitable for use in retrieval algorithms under solar backscatter conditions.

A Simple Analytical Model for Asynchronous Dense WDM/OOK Systems

DTIC Science & Technology

1994-06-01

asynchronous dense WDM systems employing an external OOK modulator. Our model is based upon a close approximation of the optical Fabry - Perot filter in the...receiver as a single-pole RC filter for signals that are bandlimitr i, & -equency band approximately equal to one sixtieth of the Fabry - Perot filter’s...4 A. INPUT SIGNAL ............................................................................................... 4 B. FABRY - PEROT FILTERED OUTPUT

An integrated model to simulate the scattering of ultrasounds by inclusions in steels.

PubMed

Darmon, Michel; Calmon, Pierre; Bèle, Bertrand

2004-04-01

We present a study performed to model and predict the ultrasonic response of alumina inclusions in steels. The Born and the extended quasistatic approximations have been applied and modified to improve their accuracy in the framework of this application. The modified Born approximation, called "doubly distorted wave (D(2)W) Born approximation" allowing to deal with various inclusion shapes, has been selected to be implemented in the CIVA software. The model reliability has been evaluated by comparison with Ying and Truell's exact analytical solution. In parallel, measurements have been carried out upon both natural and artificial alumina inclusions.

Analytical approximation of the InGaZnO thin-film transistors surface potential

NASA Astrophysics Data System (ADS)

Colalongo, Luigi

2016-10-01

Surface-potential-based mathematical models are among the most accurate and physically based compact models of thin-film transistors, and in turn of indium gallium zinc oxide TFTs, available today. However, the need of iterative computations of the surface potential limits their computational efficiency and diffusion in CAD applications. The existing closed-form approximations of the surface potential are based on regional approximations and empirical smoothing functions that could result not accurate enough in particular to model transconductances and transcapacitances. In this work we present an extremely accurate (in the range of nV) and computationally efficient non-iterative approximation of the surface potential that can serve as a basis for advanced surface-potential-based indium gallium zinc oxide TFTs models.

A non-grey analytical model for irradiated atmospheres. II. Analytical vs. numerical solutions

NASA Astrophysics Data System (ADS)

Parmentier, Vivien; Guillot, Tristan; Fortney, Jonathan J.; Marley, Mark S.

2015-02-01

Context. The recent discovery and characterization of the diversity of the atmospheres of exoplanets and brown dwarfs calls for the development of fast and accurate analytical models. Aims: We wish to assess the goodness of the different approximations used to solve the radiative transfer problem in irradiated atmospheres analytically, and we aim to provide a useful tool for a fast computation of analytical temperature profiles that remains correct over a wide range of atmospheric characteristics. Methods: We quantify the accuracy of the analytical solution derived in paper I for an irradiated, non-grey atmosphere by comparing it to a state-of-the-art radiative transfer model. Then, using a grid of numerical models, we calibrate the different coefficients of our analytical model for irradiated solar-composition atmospheres of giant exoplanets and brown dwarfs. Results: We show that the so-called Eddington approximation used to solve the angular dependency of the radiation field leads to relative errors of up to ~5% on the temperature profile. For grey or semi-grey atmospheres (i.e., when the visible and thermal opacities, respectively, can be considered independent of wavelength), we show that the presence of a convective zone has a limited effect on the radiative atmosphere above it and leads to modifications of the radiative temperature profile of approximately ~2%. However, for realistic non-grey planetary atmospheres, the presence of a convective zone that extends to optical depths smaller than unity can lead to changes in the radiative temperature profile on the order of 20% or more. When the convective zone is located at deeper levels (such as for strongly irradiated hot Jupiters), its effect on the radiative atmosphere is again on the same order (~2%) as in the semi-grey case. We show that the temperature inversion induced by a strong absorber in the optical, such as TiO or VO is mainly due to non-grey thermal effects reducing the ability of the upper atmosphere to cool down rather than an enhanced absorption of the stellar light as previously thought. Finally, we provide a functional form for the coefficients of our analytical model for solar-composition giant exoplanets and brown dwarfs. This leads to fully analytical pressure-temperature profiles for irradiated atmospheres with a relative accuracy better than 10% for gravities between 2.5 m s-2 and 250 m s-2 and effective temperatures between 100 K and 3000 K. This is a great improvement over the commonly used Eddington boundary condition. A FORTRAN implementation of the analytical model is only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/574/A35 or at http://www.oca.eu/parmentier/nongrey.Appendix A is available in electronic form at http://www.aanda.org

Rapid perfusion quantification using Welch-Satterthwaite approximation and analytical spectral filtering

NASA Astrophysics Data System (ADS)

Krishnan, Karthik; Reddy, Kasireddy V.; Ajani, Bhavya; Yalavarthy, Phaneendra K.

2017-02-01

CT and MR perfusion weighted imaging (PWI) enable quantification of perfusion parameters in stroke studies. These parameters are calculated from the residual impulse response function (IRF) based on a physiological model for tissue perfusion. The standard approach for estimating the IRF is deconvolution using oscillatory-limited singular value decomposition (oSVD) or Frequency Domain Deconvolution (FDD). FDD is widely recognized as the fastest approach currently available for deconvolution of CT Perfusion/MR PWI. In this work, three faster methods are proposed. The first is a direct (model based) crude approximation to the final perfusion quantities (Blood flow, Blood volume, Mean Transit Time and Delay) using the Welch-Satterthwaite approximation for gamma fitted concentration time curves (CTC). The second method is a fast accurate deconvolution method, we call Analytical Fourier Filtering (AFF). The third is another fast accurate deconvolution technique using Showalter's method, we call Analytical Showalter's Spectral Filtering (ASSF). Through systematic evaluation on phantom and clinical data, the proposed methods are shown to be computationally more than twice as fast as FDD. The two deconvolution based methods, AFF and ASSF, are also shown to be quantitatively accurate compared to FDD and oSVD.

Analytical Debye-Huckel model for electrostatic potentials around dissolved DNA.

PubMed

Wagner, K; Keyes, E; Kephart, T W; Edwards, G

1997-07-01

We present an analytical, Green-function-based model for the electric potential of DNA in solution, treating the surrounding solvent with the Debye-Huckel approximation. The partial charge of each atom is accounted for by modeling DNA as linear distributions of atoms on concentric cylindrical surfaces. The condensed ions of the solvent are treated with the Debye-Huckel approximation. The resultant leading term of the potential is that of a continuous shielded line charge, and the higher order terms account for the helical structure. Within several angstroms of the surface there is sufficient information in the electric potential to distinguish features and symmetries of DNA. Plots of the potential and equipotential surfaces, dominated by the phosphate charges, reflect the structural differences between the A, B, and Z conformations and, to a smaller extent, the difference between base sequences. As the distances from the helices increase, the magnitudes of the potentials decrease. However, the bases and sugars account for a larger fraction of the double helix potential with increasing distance. We have found that when the solvent is treated with the Debye-Huckel approximation, the potential decays more rapidly in every direction from the surface than it did in the concentric dielectric cylinder approximation.

Analytic derivation of an approximate SU(3) symmetry inside the symmetry triangle of the interacting boson approximation model

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

Bonatsos, Dennis; Karampagia, S.; Casten, R. F.

2011-05-15

Using a contraction of the SU(3) algebra to the algebra of the rigid rotator in the large-boson-number limit of the interacting boson approximation (IBA) model, a line is found inside the symmetry triangle of the IBA, along which the SU(3) symmetry is preserved. The line extends from the SU(3) vertex to near the critical line of the first-order shape/phase transition separating the spherical and prolate deformed phases, and it lies within the Alhassid-Whelan arc of regularity, the unique valley of regularity connecting the SU(3) and U(5) vertices in the midst of chaotic regions. In addition to providing an explanation formore » the existence of the arc of regularity, the present line represents an example of an analytically determined approximate symmetry in the interior of the symmetry triangle of the IBA. The method is applicable to algebraic models possessing subalgebras amenable to contraction. This condition is equivalent to algebras in which the equilibrium ground state and its rotational band become energetically isolated from intrinsic excitations, as typified by deformed solutions to the IBA for large numbers of valence nucleons.« less

Accuracy and precision of gravitational-wave models of inspiraling neutron star-black hole binaries with spin: Comparison with matter-free numerical relativity in the low-frequency regime

NASA Astrophysics Data System (ADS)

Bhagwat, Swetha; Kumar, Prayush; Barkett, Kevin; Afshari, Nousha; Brown, Duncan A.; Lovelace, Geoffrey; Scheel, Mark A.; Szilagyi, Bela; LIGO Collaboration

2016-03-01

Detection of gravitational wave involves extracting extremely weak signal from noisy data and their detection depends crucially on the accuracy of the signal models. The most accurate models of compact binary coalescence are known to come from solving the Einstein's equation numerically without any approximations. However, this is computationally formidable. As a more practical alternative, several analytic or semi analytic approximations are developed to model these waveforms. However, the work of Nitz et al. (2013) demonstrated that there is disagreement between these models. We present a careful follow up study on accuracies of different waveform families for spinning black-hole neutron star binaries, in context of both detection and parameter estimation and find that SEOBNRv2 to be the most faithful model. Post Newtonian models can be used for detection but we find that they could lead to large parameter bias. Supported by National Science Foundation (NSF) Awards No. PHY-1404395 and No. AST-1333142.

Numerical and analytical bounds on threshold error rates for hypergraph-product codes

NASA Astrophysics Data System (ADS)

Kovalev, Alexey A.; Prabhakar, Sanjay; Dumer, Ilya; Pryadko, Leonid P.

2018-06-01

We study analytically and numerically decoding properties of finite-rate hypergraph-product quantum low density parity-check codes obtained from random (3,4)-regular Gallager codes, with a simple model of independent X and Z errors. Several nontrivial lower and upper bounds for the decodable region are constructed analytically by analyzing the properties of the homological difference, equal minus the logarithm of the maximum-likelihood decoding probability for a given syndrome. Numerical results include an upper bound for the decodable region from specific heat calculations in associated Ising models and a minimum-weight decoding threshold of approximately 7 % .

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.

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.

Hamiltonian chaos acts like a finite energy reservoir: accuracy of the Fokker-Planck approximation.

PubMed

Riegert, Anja; Baba, Nilüfer; Gelfert, Katrin; Just, Wolfram; Kantz, Holger

2005-02-11

The Hamiltonian dynamics of slow variables coupled to fast degrees of freedom is modeled by an effective stochastic differential equation. Formal perturbation expansions, involving a Markov approximation, yield a Fokker-Planck equation in the slow subspace which respects conservation of energy. A detailed numerical and analytical analysis of suitable model systems demonstrates the feasibility of obtaining the system specific drift and diffusion terms and the accuracy of the stochastic approximation on all time scales. Non-Markovian and non-Gaussian features of the fast variables are negligible.

Error analysis of analytic solutions for self-excited near-symmetric rigid bodies - A numerical study

NASA Technical Reports Server (NTRS)

Kia, T.; Longuski, J. M.

1984-01-01

Analytic error bounds are presented for the solutions of approximate models for self-excited near-symmetric rigid bodies. The error bounds are developed for analytic solutions to Euler's equations of motion. The results are applied to obtain a simplified analytic solution for Eulerian rates and angles. The results of a sample application of the range and error bound expressions for the case of the Galileo spacecraft experiencing transverse torques demonstrate the use of the bounds in analyses of rigid body spin change maneuvers.

Simple Analytic Model for Nanowire Array Polarizers

NASA Astrophysics Data System (ADS)

Pelletier, Vincent; Asakawa, Koji; Wu, Mingshaw; Register, Richard; Chaikin, Paul

2006-03-01

Cylinder-forming diblock copolymers can be used to pattern nanowire arrays on a transparent substrate to be used as a polarizer, as described by Koji Asakawa in a complementary talk at this meeting. With a 33nm period, these wire arrays can polarize UV radiation, which is of great interest in lithography, astronomy and other areas. One can gain an analytical understanding of such an array made of non-perfectly conducting material of finite thickness using a model with an appropriately averaged complex dielectric function in an infinite wavelength approximation. This analysis predicts that the grid can go from an E-polarizer to an H-polarizer as the wavelength decreases below a cross-over wavelength, and experimental data confirm this cross-over. The overall response of the polarizing grid depends primarily on the plasma frequency of the metal used and the volume fraction of the nanowires, as well as the grid thickness. A numerical approach is also used to confirm the analytical model and assess departure from infinite wavelength effects. For our array dimensions, the polarization is only slightly different from this approximation for wavelengths down to 150nm.

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

Analytic drain current model for III-V cylindrical nanowire transistors

NASA Astrophysics Data System (ADS)

Marin, E. G.; Ruiz, F. G.; Schmidt, V.; Godoy, A.; Riel, H.; Gámiz, F.

2015-07-01

An analytical model is proposed to determine the drain current of III-V cylindrical nanowires (NWs). The model uses the gradual channel approximation and takes into account the complete analytical solution of the Poisson and Schrödinger equations for the Γ-valley and for an arbitrary number of subbands. Fermi-Dirac statistics are considered to describe the 1D electron gas in the NWs, being the resulting recursive Fermi-Dirac integral of order -1/2 successfully integrated under reasonable assumptions. The model has been validated against numerical simulations showing excellent agreement for different semiconductor materials, diameters up to 40 nm, gate overdrive biases up to 0.7 V, and densities of interface states up to 1013eV-1cm-2 .

System identification of analytical models of damped structures

NASA Technical Reports Server (NTRS)

Fuh, J.-S.; Chen, S.-Y.; Berman, A.

1984-01-01

A procedure is presented for identifying linear nonproportionally damped system. The system damping is assumed to be representable by a real symmetric matrix. Analytical mass, stiffness and damping matrices which constitute an approximate representation of the system are assumed to be available. Given also are an incomplete set of measured natural frequencies, damping ratios and complex mode shapes of the structure, normally obtained from test data. A method is developed to find the smallest changes in the analytical model so that the improved model can exactly predict the measured modal parameters. The present method uses the orthogonality relationship to improve mass and damping matrices and the dynamic equation to find the improved stiffness matrix.

Experimental Validation of Lightning-Induced Electromagnetic (Indirect) Coupling to Short Monopole Antennas

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

Crull, E W; Brown Jr., C G; Perkins, M P

2008-07-30

For short monopoles in this low-power case, it has been shown that a simple circuit model is capable of accurate predictions for the shape and magnitude of the antenna response to lightning-generated electric field coupling effects, provided that the elements of the circuit model have accurate values. Numerical EM simulation can be used to provide more accurate values for the circuit elements than the simple analytical formulas, since the analytical formulas are used outside of their region of validity. However, even with the approximate analytical formulas the simple circuit model produces reasonable results, which would improve if more accurate analyticalmore » models were used. This report discusses the coupling analysis approaches taken to understand the interaction between a time-varying EM field and a short monopole antenna, within the context of lightning safety for nuclear weapons at DOE facilities. It describes the validation of a simple circuit model using laboratory study in order to understand the indirect coupling of energy into a part, and the resulting voltage. Results show that in this low-power case, the circuit model predicts peak voltages within approximately 32% using circuit component values obtained from analytical formulas and about 13% using circuit component values obtained from numerical EM simulation. We note that the analytical formulas are used outside of their region of validity. First, the antenna is insulated and not a bare wire and there are perhaps fringing field effects near the termination of the outer conductor that the formula does not take into account. Also, the effective height formula is for a monopole directly over a ground plane, while in the time-domain measurement setup the monopole is elevated above the ground plane by about 1.5-inch (refer to Figure 5).« less

Analytical Modeling of a Novel Transverse Flux Machine for Direct Drive Wind Turbine Applications: Preprint

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

Hasan, IIftekhar; Husain, Tausif; Uddin, Md Wasi

2015-08-24

This paper presents a nonlinear analytical model of a novel double-sided flux concentrating Transverse Flux Machine (TFM) based on the Magnetic Equivalent Circuit (MEC) model. The analytical model uses a series-parallel combination of flux tubes to predict the flux paths through different parts of the machine including air gaps, permanent magnets, stator, and rotor. The two-dimensional MEC model approximates the complex three-dimensional flux paths of the TFM and includes the effects of magnetic saturation. The model is capable of adapting to any geometry that makes it a good alternative for evaluating prospective designs of TFM compared to finite element solversmore » that are numerically intensive and require more computation time. A single-phase, 1-kW, 400-rpm machine is analytically modeled, and its resulting flux distribution, no-load EMF, and torque are verified with finite element analysis. The results are found to be in agreement, with less than 5% error, while reducing the computation time by 25 times.« less

Analytical Modeling of a Novel Transverse Flux Machine for Direct Drive Wind Turbine Applications

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

Hasan, IIftekhar; Husain, Tausif; Uddin, Md Wasi

2015-09-02

This paper presents a nonlinear analytical model of a novel double sided flux concentrating Transverse Flux Machine (TFM) based on the Magnetic Equivalent Circuit (MEC) model. The analytical model uses a series-parallel combination of flux tubes to predict the flux paths through different parts of the machine including air gaps, permanent magnets (PM), stator, and rotor. The two-dimensional MEC model approximates the complex three-dimensional flux paths of the TFM and includes the effects of magnetic saturation. The model is capable of adapting to any geometry which makes it a good alternative for evaluating prospective designs of TFM as compared tomore » finite element solvers which are numerically intensive and require more computation time. A single phase, 1 kW, 400 rpm machine is analytically modeled and its resulting flux distribution, no-load EMF and torque, verified with Finite Element Analysis (FEA). The results are found to be in agreement with less than 5% error, while reducing the computation time by 25 times.« less

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.

Mackey-Glass equation driven by fractional Brownian motion

NASA Astrophysics Data System (ADS)

Nguyen, Dung Tien

2012-11-01

In this paper we introduce a fractional stochastic version of the Mackey-Glass model which is a potential candidate to model objects in biology and finance. By a semi-martingale approximate approach we find an semi-analytical expression for the solution.

Charge Transport in Spiro-OMeTAD Investigated through Space-Charge-Limited Current Measurements

NASA Astrophysics Data System (ADS)

Röhr, Jason A.; Shi, Xingyuan; Haque, Saif A.; Kirchartz, Thomas; Nelson, Jenny

2018-04-01

Extracting charge-carrier mobilities for organic semiconductors from space-charge-limited conduction measurements is complicated in practice by nonideal factors such as trapping in defects and injection barriers. Here, we show that by allowing the bandlike charge-carrier mobility, trap characteristics, injection barrier heights, and the shunt resistance to vary in a multiple-trapping drift-diffusion model, a numerical fit can be obtained to the entire current density-voltage curve from experimental space-charge-limited current measurements on both symmetric and asymmetric 2 ,2',7 ,7' -tetrakis(N ,N -di-4-methoxyphenylamine)-9 ,9' -spirobifluorene (spiro-OMeTAD) single-carrier devices. This approach yields a bandlike mobility that is more than an order of magnitude higher than the effective mobility obtained using analytical approximations, such as the Mott-Gurney law and the moving-electrode equation. It is also shown that where these analytical approximations require a temperature-dependent effective mobility to achieve fits, the numerical model can yield a temperature-, electric-field-, and charge-carrier-density-independent mobility. Finally, we present an analytical model describing trap-limited current flow through a semiconductor in a symmetric single-carrier device. We compare the obtained charge-carrier mobility and trap characteristics from this analytical model to the results from the numerical model, showing excellent agreement. This work shows the importance of accounting for traps and injection barriers explicitly when analyzing current density-voltage curves from space-charge-limited current measurements.

Substructure Versus Property-Level Dispersed Modes Calculation

NASA Technical Reports Server (NTRS)

Stewart, Eric C.; Peck, Jeff A.; Bush, T. Jason; Fulcher, Clay W.

2016-01-01

This paper calculates the effect of perturbed finite element mass and stiffness values on the eigenvectors and eigenvalues of the finite element model. The structure is perturbed in two ways: at the "subelement" level and at the material property level. In the subelement eigenvalue uncertainty analysis the mass and stiffness of each subelement is perturbed by a factor before being assembled into the global matrices. In the property-level eigenvalue uncertainty analysis all material density and stiffness parameters of the structure are perturbed modified prior to the eigenvalue analysis. The eigenvalue and eigenvector dispersions of each analysis (subelement and property-level) are also calculated using an analytical sensitivity approximation. Two structural models are used to compare these methods: a cantilevered beam model, and a model of the Space Launch System. For each structural model it is shown how well the analytical sensitivity modes approximate the exact modes when the uncertainties are applied at the subelement level and at the property level.

Hydrodynamics beyond Navier-Stokes: the slip flow model.

PubMed

Yudistiawan, Wahyu P; Ansumali, Santosh; Karlin, Iliya V

2008-07-01

Recently, analytical solutions for the nonlinear Couette flow demonstrated the relevance of the lattice Boltzmann (LB) models to hydrodynamics beyond the continuum limit [S. Ansumali, Phys. Rev. Lett. 98, 124502 (2007)]. In this paper, we present a systematic study of the simplest LB kinetic equation-the nine-bit model in two dimensions--in order to quantify it as a slip flow approximation. Details of the aforementioned analytical solution are presented, and results are extended to include a general shear- and force-driven unidirectional flow in confined geometry. Exact solutions for the velocity, as well as for pertinent higher-order moments of the distribution functions, are obtained in both Couette and Poiseuille steady-state flows for all values of rarefaction parameter (Knudsen number). Results are compared with the slip flow solution by Cercignani, and a good quantitative agreement is found for both flow situations. Thus, the standard nine-bit LB model is characterized as a valid and self-consistent slip flow model for simulations beyond the Navier-Stokes approximation.

Application of geometric approximation to the CPMG experiment: Two- and three-site exchange.

PubMed

Chao, Fa-An; Byrd, R Andrew

2017-04-01

The Carr-Purcell-Meiboom-Gill (CPMG) experiment is one of the most classical and well-known relaxation dispersion experiments in NMR spectroscopy, and it has been successfully applied to characterize biologically relevant conformational dynamics in many cases. Although the data analysis of the CPMG experiment for the 2-site exchange model can be facilitated by analytical solutions, the data analysis in a more complex exchange model generally requires computationally-intensive numerical analysis. Recently, a powerful computational strategy, geometric approximation, has been proposed to provide approximate numerical solutions for the adiabatic relaxation dispersion experiments where analytical solutions are neither available nor feasible. Here, we demonstrate the general potential of geometric approximation by providing a data analysis solution of the CPMG experiment for both the traditional 2-site model and a linear 3-site exchange model. The approximate numerical solution deviates less than 0.5% from the numerical solution on average, and the new approach is computationally 60,000-fold more efficient than the numerical approach. Moreover, we find that accurate dynamic parameters can be determined in most cases, and, for a range of experimental conditions, the relaxation can be assumed to follow mono-exponential decay. The method is general and applicable to any CPMG RD experiment (e.g. N, C', C α , H α , etc.) The approach forms a foundation of building solution surfaces to analyze the CPMG experiment for different models of 3-site exchange. Thus, the geometric approximation is a general strategy to analyze relaxation dispersion data in any system (biological or chemical) if the appropriate library can be built in a physically meaningful domain. Published by Elsevier Inc.

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.

Qualitative methods in quantum theory

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

Migdal, A.B.

The author feels that the solution of most problems in theoretical physics begins with the application of qualitative methods - dimensional estimates and estimates made from simple models, the investigation of limiting cases, the use of the analytic properties of physical quantities, etc. This book proceeds in this spirit, rather than in a formal, mathematical way with no traces of the sweat involved in the original work left to show. The chapters are entitled Dimensional and model approximations, Various types of perturbation theory, The quasi-classical approximation, Analytic properties of physical quantities, Methods in the many-body problem, and Qualitative methods inmore » quantum field theory. Each chapter begins with a detailed introduction, in which the physical meaning of the results obtained in that chapter is explained in a simple way. 61 figures. (RWR)« less

Review and assessment of the database and numerical modeling for turbine heat transfer

NASA Technical Reports Server (NTRS)

Gladden, H. J.; Simoneau, R. J.

1988-01-01

The objectives of the HOST Turbine Heat Transfer subproject were to obtain a better understanding of the physics of the aerothermodynamic phenomena and to assess and improve the analytical methods used to predict the flow and heat transfer in high-temperature gas turbines. At the time the HOST project was initiated, an across-the-board improvement in turbine design technology was needed. A building-block approach was utilized and the research ranged from the study of fundamental phenomena and modeling to experiments in simulated real engine environments. Experimental research accounted for approximately 75 percent of the funding while the analytical efforts were approximately 25 percent. A healthy government/industry/university partnership, with industry providing almost half of the research, was created to advance the turbine heat transfer design technology base.

ANALYTICAL MODELING OF ELECTRON BACK-BOMBARDMENT INDUCED CURRENT INCREASE IN UN-GATED THERMIONIC CATHODE RF GUNS

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

Edelen, J. P.; Sun, Y.; Harris, J. R.

In this paper we derive analytical expressions for the output current of an un-gated thermionic cathode RF gun in the presence of back-bombardment heating. We provide a brief overview of back-bombardment theory and discuss comparisons between the analytical back-bombardment predictions and simulation models. We then derive an expression for the output current as a function of the RF repetition rate and discuss relationships between back-bombardment, fieldenhancement, and output current. We discuss in detail the relevant approximations and then provide predictions about how the output current should vary as a function of repetition rate for some given system configurations.

Analytical effective tensor for flow-through composites

DOEpatents

Sviercoski, Rosangela De Fatima [Los Alamos, NM

2012-06-19

A machine, method and computer-usable medium for modeling an average flow of a substance through a composite material. Such a modeling includes an analytical calculation of an effective tensor K.sup.a suitable for use with a variety of media. The analytical calculation corresponds to an approximation to the tensor K, and follows by first computing the diagonal values, and then identifying symmetries of the heterogeneity distribution. Additional calculations include determining the center of mass of the heterogeneous cell and its angle according to a defined Cartesian system, and utilizing this angle into a rotation formula to compute the off-diagonal values and determining its sign.

AN ANALYTIC MODEL OF DUSTY, STRATIFIED, SPHERICAL H ii REGIONS

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

Rodríguez-Ramírez, J. C.; Raga, A. C.; Lora, V.

2016-12-20

We study analytically the effect of radiation pressure (associated with photoionization processes and with dust absorption) on spherical, hydrostatic H ii regions. We consider two basic equations, one for the hydrostatic balance between the radiation-pressure components and the gas pressure, and another for the balance among the recombination rate, the dust absorption, and the ionizing photon rate. Based on appropriate mathematical approximations, we find a simple analytic solution for the density stratification of the nebula, which is defined by specifying the radius of the external boundary, the cross section of dust absorption, and the luminosity of the central star. Wemore » compare the analytic solution with numerical integrations of the model equations of Draine, and find a wide range of the physical parameters for which the analytic solution is accurate.« less

Semi-analytical solutions of the Schnakenberg model of a reaction-diffusion cell with feedback

NASA Astrophysics Data System (ADS)

Al Noufaey, K. S.

2018-06-01

This paper considers the application of a semi-analytical method to the Schnakenberg model of a reaction-diffusion cell. The semi-analytical method is based on the Galerkin method which approximates the original governing partial differential equations as a system of ordinary differential equations. Steady-state curves, bifurcation diagrams and the region of parameter space in which Hopf bifurcations occur are presented for semi-analytical solutions and the numerical solution. The effect of feedback control, via altering various concentrations in the boundary reservoirs in response to concentrations in the cell centre, is examined. It is shown that increasing the magnitude of feedback leads to destabilization of the system, whereas decreasing this parameter to negative values of large magnitude stabilizes the system. The semi-analytical solutions agree well with numerical solutions of the governing equations.

An Analytical Study of Icing Similitude for Aircraft Engine Testing. Revision

DTIC Science & Technology

1987-02-01

MODELING GEOMETRIES Component Cowl Spinner Fan Blade Fan Stator Exit Vane Probe Approximating Geometry NACA 0012 Airfoil Sphere NACA 0012...DOT/FAA/CT·86/35 AEDC·TR·86·26 An Analytical Study of Icing Similitude for Aircraft Engine Testing c. Scott Bartlett Sverdrup Technology, Inc...8217~,feCa.ORI A n AnalYtical Study )f Icin~ Similitude for Aircraft Engine Tes t tu~ 12. PERSONAL AUTHOR/S) B a r t l e t t , C. Scot t , Sverdrup

Bounded Linear Stability Analysis - A Time Delay Margin Estimation Approach for Adaptive Control

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Ishihara, Abraham K.; Krishnakumar, Kalmanje Srinlvas; Bakhtiari-Nejad, Maryam

2009-01-01

This paper presents a method for estimating time delay margin for model-reference adaptive control of systems with almost linear structured uncertainty. The bounded linear stability analysis method seeks to represent the conventional model-reference adaptive law by a locally bounded linear approximation within a small time window using the comparison lemma. The locally bounded linear approximation of the combined adaptive system is cast in a form of an input-time-delay differential equation over a small time window. The time delay margin of this system represents a local stability measure and is computed analytically by a matrix measure method, which provides a simple analytical technique for estimating an upper bound of time delay margin. Based on simulation results for a scalar model-reference adaptive control system, both the bounded linear stability method and the matrix measure method are seen to provide a reasonably accurate and yet not too conservative time delay margin estimation.

a Bounded Finite-Difference Discretization of a Two-Dimensional Diffusion Equation with Logistic Nonlinear Reaction

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

In the present manuscript, we introduce a finite-difference scheme to approximate solutions of the two-dimensional version of Fisher's equation from population dynamics, which is a model for which the existence of traveling-wave fronts bounded within (0,1) is a well-known fact. The method presented here is a nonstandard technique which, in the linear regime, approximates the solutions of the original model with a consistency of second order in space and first order in time. The theory of M-matrices is employed here in order to elucidate conditions under which the method is able to preserve the positivity and the boundedness of solutions. In fact, our main result establishes relatively flexible conditions under which the preservation of the positivity and the boundedness of new approximations is guaranteed. Some simulations of the propagation of a traveling-wave solution confirm the analytical results derived in this work; moreover, the experiments evince a good agreement between the numerical result and the analytical solutions.

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.

A hybrid analytical model for open-circuit field calculation of multilayer interior permanent magnet machines

NASA Astrophysics Data System (ADS)

Zhang, Zhen; Xia, Changliang; Yan, Yan; Geng, Qiang; Shi, Tingna

2017-08-01

Due to the complicated rotor structure and nonlinear saturation of rotor bridges, it is difficult to build a fast and accurate analytical field calculation model for multilayer interior permanent magnet (IPM) machines. In this paper, a hybrid analytical model suitable for the open-circuit field calculation of multilayer IPM machines is proposed by coupling the magnetic equivalent circuit (MEC) method and the subdomain technique. In the proposed analytical model, the rotor magnetic field is calculated by the MEC method based on the Kirchhoff's law, while the field in the stator slot, slot opening and air-gap is calculated by subdomain technique based on the Maxwell's equation. To solve the whole field distribution of the multilayer IPM machines, the coupled boundary conditions on the rotor surface are deduced for the coupling of the rotor MEC and the analytical field distribution of the stator slot, slot opening and air-gap. The hybrid analytical model can be used to calculate the open-circuit air-gap field distribution, back electromotive force (EMF) and cogging torque of multilayer IPM machines. Compared with finite element analysis (FEA), it has the advantages of faster modeling, less computation source occupying and shorter time consuming, and meanwhile achieves the approximate accuracy. The analytical model is helpful and applicable for the open-circuit field calculation of multilayer IPM machines with any size and pole/slot number combination.

A Numerical-Analytical Approach to Modeling the Axial Rotation of the Earth

NASA Astrophysics Data System (ADS)

Markov, Yu. G.; Perepelkin, V. V.; Rykhlova, L. V.; Filippova, A. S.

2018-04-01

A model for the non-uniform axial rotation of the Earth is studied using a celestial-mechanical approach and numerical simulations. The application of an approximate model containing a small number of parameters to predict variations of the axial rotation velocity of the Earth over short time intervals is justified. This approximate model is obtained by averaging variable parameters that are subject to small variations due to non-stationarity of the perturbing factors. The model is verified and compared with predictions over a long time interval published by the International Earth Rotation and Reference Systems Service (IERS).

Evaluation of Analytical Modeling Functions for the Phonation Onset Process.

PubMed

Petermann, Simon; Kniesburges, Stefan; Ziethe, Anke; Schützenberger, Anne; Döllinger, Michael

2016-01-01

The human voice originates from oscillations of the vocal folds in the larynx. The duration of the voice onset (VO), called the voice onset time (VOT), is currently under investigation as a clinical indicator for correct laryngeal functionality. Different analytical approaches for computing the VOT based on endoscopic imaging were compared to determine the most reliable method to quantify automatically the transient vocal fold oscillations during VO. Transnasal endoscopic imaging in combination with a high-speed camera (8000 fps) was applied to visualize the phonation onset process. Two different definitions of VO interval were investigated. Six analytical functions were tested that approximate the envelope of the filtered or unfiltered glottal area waveform (GAW) during phonation onset. A total of 126 recordings from nine healthy males and 210 recordings from 15 healthy females were evaluated. Three criteria were analyzed to determine the most appropriate computation approach: (1) reliability of the fit function for a correct approximation of VO; (2) consistency represented by the standard deviation of VOT; and (3) accuracy of the approximation of VO. The results suggest the computation of VOT by a fourth-order polynomial approximation in the interval between 32.2 and 67.8% of the saturation amplitude of the filtered GAW.

Reproduction of exact solutions of Lipkin model by nonlinear higher random-phase approximation

NASA Astrophysics Data System (ADS)

Terasaki, J.; Smetana, A.; Šimkovic, F.; Krivoruchenko, M. I.

2017-10-01

It is shown that the random-phase approximation (RPA) method with its nonlinear higher generalization, which was previously considered as approximation except for a very limited case, reproduces the exact solutions of the Lipkin model. The nonlinear higher RPA is based on an equation nonlinear on eigenvectors and includes many-particle-many-hole components in the creation operator of the excited states. We demonstrate the exact character of solutions analytically for the particle number N = 2 and numerically for N = 8. This finding indicates that the nonlinear higher RPA is equivalent to the exact Schrödinger equation.

Analytical Debye-Huckel model for electrostatic potentials around dissolved DNA.

PubMed Central

Wagner, K; Keyes, E; Kephart, T W; Edwards, G

1997-01-01

We present an analytical, Green-function-based model for the electric potential of DNA in solution, treating the surrounding solvent with the Debye-Huckel approximation. The partial charge of each atom is accounted for by modeling DNA as linear distributions of atoms on concentric cylindrical surfaces. The condensed ions of the solvent are treated with the Debye-Huckel approximation. The resultant leading term of the potential is that of a continuous shielded line charge, and the higher order terms account for the helical structure. Within several angstroms of the surface there is sufficient information in the electric potential to distinguish features and symmetries of DNA. Plots of the potential and equipotential surfaces, dominated by the phosphate charges, reflect the structural differences between the A, B, and Z conformations and, to a smaller extent, the difference between base sequences. As the distances from the helices increase, the magnitudes of the potentials decrease. However, the bases and sugars account for a larger fraction of the double helix potential with increasing distance. We have found that when the solvent is treated with the Debye-Huckel approximation, the potential decays more rapidly in every direction from the surface than it did in the concentric dielectric cylinder approximation. Images FIGURE 1 FIGURE 2 FIGURE 3 FIGURE 4 FIGURE 5 FIGURE 7 PMID:9199767

Analytical solutions for benchmarking cold regions subsurface water flow and energy transport models: one-dimensional soil thaw with conduction and advection

USGS Publications Warehouse

Kurylyk, Barret L.; McKenzie, Jeffrey M; MacQuarrie, Kerry T. B.; Voss, Clifford I.

2014-01-01

Numerous cold regions water flow and energy transport models have emerged in recent years. Dissimilarities often exist in their mathematical formulations and/or numerical solution techniques, but few analytical solutions exist for benchmarking flow and energy transport models that include pore water phase change. This paper presents a detailed derivation of the Lunardini solution, an approximate analytical solution for predicting soil thawing subject to conduction, advection, and phase change. Fifteen thawing scenarios are examined by considering differences in porosity, surface temperature, Darcy velocity, and initial temperature. The accuracy of the Lunardini solution is shown to be proportional to the Stefan number. The analytical solution results obtained for soil thawing scenarios with water flow and advection are compared to those obtained from the finite element model SUTRA. Three problems, two involving the Lunardini solution and one involving the classic Neumann solution, are recommended as standard benchmarks for future model development and testing.

Geometric model of pseudo-distance measurement in satellite location systems

NASA Astrophysics Data System (ADS)

Panchuk, K. L.; Lyashkov, A. A.; Lyubchinov, E. V.

2018-04-01

The existing mathematical model of pseudo-distance measurement in satellite location systems does not provide a precise solution of the problem, but rather an approximate one. The existence of such inaccuracy, as well as bias in measurement of distance from satellite to receiver, results in inaccuracy level of several meters. Thereupon, relevance of refinement of the current mathematical model becomes obvious. The solution of the system of quadratic equations used in the current mathematical model is based on linearization. The objective of the paper is refinement of current mathematical model and derivation of analytical solution of the system of equations on its basis. In order to attain the objective, geometric analysis is performed; geometric interpretation of the equations is given. As a result, an equivalent system of equations, which allows analytical solution, is derived. An example of analytical solution implementation is presented. Application of analytical solution algorithm to the problem of pseudo-distance measurement in satellite location systems allows to improve the accuracy such measurements.

Heat generation in Aircraft tires under yawed rolling conditions

NASA Technical Reports Server (NTRS)

Dodge, Richard N.; Clark, Samuel K.

1987-01-01

An analytical model was developed for approximating the internal temperature distribution in an aircraft tire operating under conditions of yawed rolling. The model employs an assembly of elements to represent the tire cross section and treats the heat generated within the tire as a function of the change in strain energy associated with predicted tire flexure. Special contact scrubbing terms are superimposed on the symmetrical free rolling model to account for the slip during yawed rolling. An extensive experimental program was conducted to verify temperatures predicted from the analytical model. Data from this program were compared with calculation over a range of operating conditions, namely, vertical deflection, inflation pressure, yaw angle, and direction of yaw. Generally the analytical model predicted overall trends well and correlated reasonably well with individual measurements at locations throughout the cross section.

Steady-state analytical model of suspended p-type 3C-SiC bridges under consideration of Joule heating

NASA Astrophysics Data System (ADS)

Balakrishnan, Vivekananthan; Dinh, Toan; Phan, Hoang-Phuong; Kozeki, Takahiro; Namazu, Takahiro; Viet Dao, Dzung; Nguyen, Nam-Trung

2017-07-01

This paper reports an analytical model and its validation for a released microscale heater made of 3C-SiC thin films. A model for the equivalent electrical and thermal parameters was developed for the two-layer multi-segment heat and electric conduction. The model is based on a 1D energy equation, which considers the temperature-dependent resistivity and allows for the prediction of voltage-current and power-current characteristics of the microheater. The steady-state analytical model was validated by experimental characterization. The results, in particular the nonlinearity caused by temperature dependency, are in good agreement. The low power consumption of the order of 0.18 mW at approximately 310 K indicates the potential use of the structure as thermal sensors in portable applications.

Linear Power Spectra in Cold+Hot Dark Matter Models: Analytical Approximations and Applications

NASA Astrophysics Data System (ADS)

Ma, Chung-Pei

1996-11-01

This paper presents simple analytic approximations to the linear power spectra, linear growth rates, and rms mass fluctuations for both components in a family of cold + hot dark matter (CDM + HDM) models that are of current cosmological interest. The formulas are valid for a wide range of wavenumbers, neutrino fractions, redshifts, and Hubble constants: k ≤ 1O h Mpc-1, 0.05 ≤ Ωv le; 0.3 0 ≤ z ≤ 15, and 0.5 ≤ h ≤ 0.8. A new, redshift-dependent shape parameter, Γv = a½Ωvh2, is introduced to simplify the multidimensional parameter space and to characterize the effect of massive neutrinos on the power spectrum. The physical origin of Γv lies in the neutrino free-streaming process, and the analytic approximations can be simplified to depend only on this variable and Ωv. Linear calculations with these power spectra as input are performed to compare the predictions of Ωv ≤ 0.3 models with observational constraints from the reconstructed linear power spectrum and cluster abundance. The usual assumption of an exact scale-invariant primordial power spectrum is relaxed to allow a spectral index of 0.8 ≤ n ≤ 1. It is found that a slight tilt of n = 0.9 (no tensor mode) or n = 0.95 (with tensor mode) in 0.t-0.2 CDM + HDM models gives a power spectrum similar to that of an open CDM model with a shape parameter Γ = 0.25, providing good agreement with the power spectrum reconstructed by Peacock & Dodds and the observed cluster abundance at low redshifts. Late galaxy formation at high redshifts, however, will be a more severe problem in tilted models.

Exact solutions to the fermion propagator Schwinger-Dyson equation in Minkowski space with on-shell renormalization for quenched QED

DOE PAGES

Jia, Shaoyang; Pennington, M. R.

2017-08-01

With the introduction of a spectral representation, the Schwinger-Dyson equation (SDE) for the fermion propagator is formulated in Minkowski space in QED. After imposing the on-shell renormalization conditions, analytic solutions for the fermion propagator spectral functions are obtained in four dimensions with a renormalizable version of the Gauge Technique anzatz for the fermion-photon vertex in the quenched approximation in the Landau gauge. Despite the limitations of this model, having an explicit solution provides a guiding example of the fermion propagator with the correct analytic structure. The Padé approximation for the spectral functions is also investigated.

Exact solutions to the fermion propagator Schwinger-Dyson equation in Minkowski space with on-shell renormalization for quenched QED

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

Jia, Shaoyang; Pennington, M. R.

With the introduction of a spectral representation, the Schwinger-Dyson equation (SDE) for the fermion propagator is formulated in Minkowski space in QED. After imposing the on-shell renormalization conditions, analytic solutions for the fermion propagator spectral functions are obtained in four dimensions with a renormalizable version of the Gauge Technique anzatz for the fermion-photon vertex in the quenched approximation in the Landau gauge. Despite the limitations of this model, having an explicit solution provides a guiding example of the fermion propagator with the correct analytic structure. The Padé approximation for the spectral functions is also investigated.

On the first crossing distributions in fractional Brownian motion and the mass function of dark matter haloes

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

Hiotelis, Nicos; Popolo, Antonino Del, E-mail: adelpopolo@oact.inaf.it, E-mail: hiotelis@ipta.demokritos.gr

We construct an integral equation for the first crossing distributions for fractional Brownian motion in the case of a constant barrier and we present an exact analytical solution. Additionally we present first crossing distributions derived by simulating paths from fractional Brownian motion. We compare the results of the analytical solutions with both those of simulations and those of some approximated solutions which have been used in the literature. Finally, we present multiplicity functions for dark matter structures resulting from our analytical approach and we compare with those resulting from N-body simulations. We show that the results of analytical solutions aremore » in good agreement with those of path simulations but differ significantly from those derived from approximated solutions. Additionally, multiplicity functions derived from fractional Brownian motion are poor fits of the those which result from N-body simulations. We also present comparisons with other models which are exist in the literature and we discuss different ways of improving the agreement between analytical results and N-body simulations.« less

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

Kaurov, Alexander A., E-mail: kaurov@uchicago.edu

The methods for studying the epoch of cosmic reionization vary from full radiative transfer simulations to purely analytical models. While numerical approaches are computationally expensive and are not suitable for generating many mock catalogs, analytical methods are based on assumptions and approximations. We explore the interconnection between both methods. First, we ask how the analytical framework of excursion set formalism can be used for statistical analysis of numerical simulations and visual representation of the morphology of ionization fronts. Second, we explore the methods of training the analytical model on a given numerical simulation. We present a new code which emergedmore » from this study. Its main application is to match the analytical model with a numerical simulation. Then, it allows one to generate mock reionization catalogs with volumes exceeding the original simulation quickly and computationally inexpensively, meanwhile reproducing large-scale statistical properties. These mock catalogs are particularly useful for cosmic microwave background polarization and 21 cm experiments, where large volumes are required to simulate the observed signal.« less

An improved approximate network blocking probability model for all-optical WDM Networks with heterogeneous link capacities

NASA Astrophysics Data System (ADS)

Khan, Akhtar Nawaz

2017-11-01

Currently, analytical models are used to compute approximate blocking probabilities in opaque and all-optical WDM networks with the homogeneous link capacities. Existing analytical models can also be extended to opaque WDM networking with heterogeneous link capacities due to the wavelength conversion at each switch node. However, existing analytical models cannot be utilized for all-optical WDM networking with heterogeneous structure of link capacities due to the wavelength continuity constraint and unequal numbers of wavelength channels on different links. In this work, a mathematical model is extended for computing approximate network blocking probabilities in heterogeneous all-optical WDM networks in which the path blocking is dominated by the link along the path with fewer number of wavelength channels. A wavelength assignment scheme is also proposed for dynamic traffic, termed as last-fit-first wavelength assignment, in which a wavelength channel with maximum index is assigned first to a lightpath request. Due to heterogeneous structure of link capacities and the wavelength continuity constraint, the wavelength channels with maximum indexes are utilized for minimum hop routes. Similarly, the wavelength channels with minimum indexes are utilized for multi-hop routes between source and destination pairs. The proposed scheme has lower blocking probability values compared to the existing heuristic for wavelength assignments. Finally, numerical results are computed in different network scenarios which are approximately equal to values obtained from simulations. Since January 2016, he is serving as Head of Department and an Assistant Professor in the Department of Electrical Engineering at UET, Peshawar-Jalozai Campus, Pakistan. From May 2013 to June 2015, he served Department of Telecommunication Engineering as an Assistant Professor at UET, Peshawar-Mardan Campus, Pakistan. He also worked as an International Internship scholar in the Fukuda Laboratory, National Institute of Informatics, Tokyo, Japan on the topic large-scale simulation for internet topology analysis. His research interests include design and analysis of optical WDM networks, network algorithms, network routing, and network resource optimization problems.

An analytical model for calculating microdosimetric distributions from heavy ions in nanometer site targets.

PubMed

Czopyk, L; Olko, P

2006-01-01

The analytical model of Xapsos used for calculating microdosimetric spectra is based on the observation that straggling of energy loss can be approximated by a log-normal distribution of energy deposition. The model was applied to calculate microdosimetric spectra in spherical targets of nanometer dimensions from heavy ions at energies between 0.3 and 500 MeV amu(-1). We recalculated the originally assumed 1/E(2) initial delta electrons spectrum by applying the Continuous Slowing Down Approximation for secondary electrons. We also modified the energy deposition from electrons of energy below 100 keV, taking into account the effective path length of the scattered electrons. Results of our model calculations agree favourably with results of Monte Carlo track structure simulations using MOCA-14 for light ions (Z = 1-8) of energy ranging from E = 0.3 to 10.0 MeV amu(-1) as well as with results of Nikjoo for a wall-less proportional counter (Z = 18).

The analytical transfer matrix method for PT-symmetric complex potential

NASA Astrophysics Data System (ADS)

Naceri, Leila; Hammou, Amine B.

2017-07-01

We have extended the analytical transfer matrix (ATM) method to solve quantum mechanical bound state problems with complex PT-symmetric potentials. Our work focuses on a class of models studied by Bender and Jones, we calculate the energy eigenvalues, discuss the critical values of g and compare the results with those obtained from other methods such as exact numerical computation and WKB approximation method.

From bead to rod: Comparison of theories by measuring translational drag coefficients of micron-sized magnetic bead-chains in Stokes flow

PubMed Central

Lu, Chen; Zhao, Xiaodan; Kawamura, Ryo

2017-01-01

Frictional drag force on an object in Stokes flow follows a linear relationship with the velocity of translation and a translational drag coefficient. This drag coefficient is related to the size, shape, and orientation of the object. For rod-like objects, analytical solutions of the drag coefficients have been proposed based on three rough approximations of the rod geometry, namely the bead model, ellipsoid model, and cylinder model. These theories all agree that translational drag coefficients of rod-like objects are functions of the rod length and aspect ratio, but differ among one another on the correction factor terms in the equations. By tracking the displacement of the particles through stationary fluids of calibrated viscosity in magnetic tweezers setup, we experimentally measured the drag coefficients of micron-sized beads and their bead-chain formations with chain length of 2 to 27. We verified our methodology with analytical solutions of dimers of two touching beads, and compared our measured drag coefficient values of rod-like objects with theoretical calculations. Our comparison reveals several analytical solutions that used more appropriate approximation and derived formulae that agree with our measurement better. PMID:29145447

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.

Chemical Sensor Array Response Modeling Using Quantitative Structure-Activity Relationships Technique

NASA Astrophysics Data System (ADS)

Shevade, Abhijit V.; Ryan, Margaret A.; Homer, Margie L.; Zhou, Hanying; Manfreda, Allison M.; Lara, Liana M.; Yen, Shiao-Pin S.; Jewell, April D.; Manatt, Kenneth S.; Kisor, Adam K.

We have developed a Quantitative Structure-Activity Relationships (QSAR) based approach to correlate the response of chemical sensors in an array with molecular descriptors. A novel molecular descriptor set has been developed; this set combines descriptors of sensing film-analyte interactions, representing sensor response, with a basic analyte descriptor set commonly used in QSAR studies. The descriptors are obtained using a combination of molecular modeling tools and empirical and semi-empirical Quantitative Structure-Property Relationships (QSPR) methods. The sensors under investigation are polymer-carbon sensing films which have been exposed to analyte vapors at parts-per-million (ppm) concentrations; response is measured as change in film resistance. Statistically validated QSAR models have been developed using Genetic Function Approximations (GFA) for a sensor array for a given training data set. The applicability of the sensor response models has been tested by using it to predict the sensor activities for test analytes not considered in the training set for the model development. The validated QSAR sensor response models show good predictive ability. The QSAR approach is a promising computational tool for sensing materials evaluation and selection. It can also be used to predict response of an existing sensing film to new target analytes.

Analytic expressions for Atomic Layer Deposition: coverage, throughput, and materials utilization in cross-flow, particle coating, and spatial ALD

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

Yanguas-Gil, Angel; Elam, Jeffrey W.

2014-05-01

In this work, the authors present analytic models for atomic layer deposition (ALD) in three common experimental configurations: cross-flow, particle coating, and spatial ALD. These models, based on the plug-flow and well-mixed approximations, allow us to determine the minimum dose times and materials utilization for all three configurations. A comparison between the three models shows that throughput and precursor utilization can each be expressed by universal equations, in which the particularity of the experimental system is contained in a single parameter related to the residence time of the precursor in the reactor. For the case of cross-flow reactors, the authorsmore » show how simple analytic expressions for the reactor saturation profiles agree well with experimental results. Consequently, the analytic model can be used to extract information about the ALD surface chemistry (e. g., the reaction probability) by comparing the analytic and experimental saturation profiles, providing a useful tool for characterizing new and existing ALD processes. (C) 2014 American Vacuum Society« less

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

Theory and Circuit Model for Lossy Coaxial Transmission Line

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

Genoni, T. C.; Anderson, C. N.; Clark, R. E.

2017-04-01

The theory of signal propagation in lossy coaxial transmission lines is revisited and new approximate analytic formulas for the line impedance and attenuation are derived. The accuracy of these formulas from DC to 100 GHz is demonstrated by comparison to numerical solutions of the exact field equations. Based on this analysis, a new circuit model is described which accurately reproduces the line response over the entire frequency range. Circuit model calculations are in excellent agreement with the numerical and analytic results, and with finite-difference-time-domain simulations which resolve the skindepths of the conducting walls.

Optical bandgap of semiconductor nanostructures: Methods for experimental data analysis

NASA Astrophysics Data System (ADS)

Raciti, R.; Bahariqushchi, R.; Summonte, C.; Aydinli, A.; Terrasi, A.; Mirabella, S.

2017-06-01

Determination of the optical bandgap (Eg) in semiconductor nanostructures is a key issue in understanding the extent of quantum confinement effects (QCE) on electronic properties and it usually involves some analytical approximation in experimental data reduction and modeling of the light absorption processes. Here, we compare some of the analytical procedures frequently used to evaluate the optical bandgap from reflectance (R) and transmittance (T) spectra. Ge quantum wells and quantum dots embedded in SiO2 were produced by plasma enhanced chemical vapor deposition, and light absorption was characterized by UV-Vis/NIR spectrophotometry. R&T elaboration to extract the absorption spectra was conducted by two approximated methods (single or double pass approximation, single pass analysis, and double pass analysis, respectively) followed by Eg evaluation through linear fit of Tauc or Cody plots. Direct fitting of R&T spectra through a Tauc-Lorentz oscillator model is used as comparison. Methods and data are discussed also in terms of the light absorption process in the presence of QCE. The reported data show that, despite the approximation, the DPA approach joined with Tauc plot gives reliable results, with clear advantages in terms of computational efforts and understanding of QCE.

Valuing options in shot noise market

NASA Astrophysics Data System (ADS)

Laskin, Nick

2018-07-01

A new exactly solvable option pricing model has been introduced and elaborated. It is assumed that a stock price follows a Geometric shot noise process. An arbitrage-free integro-differential option pricing equation has been obtained and solved. The new Greeks have been analytically calculated. It has been shown that in diffusion approximation the developed option pricing model incorporates the well-known Black-Scholes equation and its solution. The stochastic dynamic origin of the Black-Scholes volatility has been uncovered. To model the observed market stock price patterns consisting of high frequency small magnitude and low frequency large magnitude jumps, the superposition of two Geometric shot noises has been implemented. A new generalized option pricing equation has been obtained and its exact solution was found. Merton's jump-diffusion formula for option price was recovered in diffusion approximation. Despite the non-Gaussian nature of probability distributions involved, the new option pricing model has the same degree of analytical tractability as the Black-Scholes model and the Merton jump-diffusion model. This attractive feature allows one to derive exact formulas to value options and option related instruments in the market with jump-like price patterns.

Review and assessment of the database and numerical modeling for turbine heat transfer

NASA Technical Reports Server (NTRS)

Gladden, H. J.; Simoneau, R. J.

1989-01-01

The objectives of the NASA Hot Section Technology (HOST) Turbine Heat Transfer subproject were to obtain a better understanding of the physics of the aerothermodynamic phenomena and to assess and improve the analytical methods used to predict the flow and heat transfer in high-temperature gas turbines. At the time the HOST project was initiated, an across-the-board improvement in turbine design technology was needed. A building-block approach was utilized and the research ranged from the study of fundamental phenomena and modeling to experiments in simulated real engine environments. Experimental research accounted for approximately 75 percent of the funding while the analytical efforts were approximately 25 percent. A healthy government/industry/university partnership, with industry providing almost half of the research, was created to advance the turbine heat transfer design technology base.

Integration within the Felsenstein equation for improved Markov chain Monte Carlo methods in population genetics

PubMed Central

Hey, Jody; Nielsen, Rasmus

2007-01-01

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

Modelling of interaction of the large disrupted meteoroid with the Earth atmosphere

NASA Astrophysics Data System (ADS)

Brykina, Irina G.

2018-05-01

The model of atmospheric fragmentation of large meteoroids to the cloud of fragments is proposed. The comparison with similar models used in the literature is made. The approximate analytical solution of meteor physics equations is obtained for the mass loss of the disrupted meteoroid, the energy deposition and for the light curve normalized to the maximum brightness. This solution is applied to modelling of interaction of the Chelyabinsk meteoroid with the atmosphere. The influence of uncertainty of initial parameters of the meteoroid on characteristics of its interaction with the atmosphere is estimated. Comparison of the analytical solution with the observational data is made.

Analytical solutions by squeezing to the anisotropic Rabi model in the nonperturbative deep-strong-coupling regime

NASA Astrophysics Data System (ADS)

Zhang, Yu-Yu; Chen, Xiang-You

2017-12-01

An unexplored nonperturbative deep strong coupling (npDSC) achieved in superconducting circuits has been studied in the anisotropic Rabi model by the generalized squeezing rotating-wave approximation. Energy levels are evaluated analytically from the reformulated Hamiltonian and agree well with numerical ones in a wide range of coupling strength. Such improvement ascribes to deformation effects in the displaced-squeezed state presented by the squeezed momentum variance, which are omitted in previous displaced states. The atom population dynamics confirms the validity of our approach for the npDSC strength. Our approach offers the possibility to explore interesting phenomena analytically in the npDSC regime in qubit-oscillator experiments.

Analytic Quasi-Perodic Cocycles with Singularities and the Lyapunov Exponent of Extended Harper's Model

NASA Astrophysics Data System (ADS)

Jitomirskaya, S.; Marx, C. A.

2012-11-01

We show how to extend (and with what limitations) Avila's global theory of analytic SL(2,C) cocycles to families of cocycles with singularities. This allows us to develop a strategy to determine the Lyapunov exponent for the extended Harper's model, for all values of parameters and all irrational frequencies. In particular, this includes the self-dual regime for which even heuristic results did not previously exist in physics literature. The extension of Avila's global theory is also shown to imply continuous behavior of the LE on the space of analytic {M_2({C})}-cocycles. This includes rational approximation of the frequency, which so far has not been available.

Computational aspects of sensitivity calculations in linear transient structural analysis. Ph.D. Thesis - Virginia Polytechnic Inst. and State Univ.

NASA Technical Reports Server (NTRS)

Greene, William H.

1990-01-01

A study was performed focusing on the calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, transient response problems. One significant goal of the study was to develop and evaluate sensitivity calculation techniques suitable for large-order finite element analyses. Accordingly, approximation vectors such as vibration mode shapes are used to reduce the dimensionality of the finite element model. Much of the research focused on the accuracy of both response quantities and sensitivities as a function of number of vectors used. Two types of sensitivity calculation techniques were developed and evaluated. The first type of technique is an overall finite difference method where the analysis is repeated for perturbed designs. The second type of technique is termed semi-analytical because it involves direct, analytical differentiation of the equations of motion with finite difference approximation of the coefficient matrices. To be computationally practical in large-order problems, the overall finite difference methods must use the approximation vectors from the original design in the analyses of the perturbed models. In several cases this fixed mode approach resulted in very poor approximations of the stress sensitivities. Almost all of the original modes were required for an accurate sensitivity and for small numbers of modes, the accuracy was extremely poor. To overcome this poor accuracy, two semi-analytical techniques were developed. The first technique accounts for the change in eigenvectors through approximate eigenvector derivatives. The second technique applies the mode acceleration method of transient analysis to the sensitivity calculations. Both result in accurate values of the stress sensitivities with a small number of modes and much lower computational costs than if the vibration modes were recalculated and then used in an overall finite difference method.

Analytical Tools for Investigating and Modeling Agent-Based Systems

DTIC Science & Technology

2005-06-01

of Black Holes Cluster 10 : Juan M. Maldacena (1924), Journal of High Energy Physics Field theory models for tachyon and gauge field string dy...namics; Super-Poincare Invariant Superstring Field The- ory; Level Four Approximation to the Tachyon Potential in Superstring Field Theory; SO(32) Spinors

Diffusion of Super-Gaussian Profiles

ERIC Educational Resources Information Center

Rosenberg, C.-J.; Anderson, D.; Desaix, M.; Johannisson, P.; Lisak, M.

2007-01-01

The present analysis describes an analytically simple and systematic approximation procedure for modelling the free diffusive spreading of initially super-Gaussian profiles. The approach is based on a self-similar ansatz for the evolution of the diffusion profile, and the parameter functions involved in the modelling are determined by suitable…

Approximation methods of European option pricing in multiscale stochastic volatility model

NASA Astrophysics Data System (ADS)

Ni, Ying; Canhanga, Betuel; Malyarenko, Anatoliy; Silvestrov, Sergei

2017-01-01

In the classical Black-Scholes model for financial option pricing, the asset price follows a geometric Brownian motion with constant volatility. Empirical findings such as volatility smile/skew, fat-tailed asset return distributions have suggested that the constant volatility assumption might not be realistic. A general stochastic volatility model, e.g. Heston model, GARCH model and SABR volatility model, in which the variance/volatility itself follows typically a mean-reverting stochastic process, has shown to be superior in terms of capturing the empirical facts. However in order to capture more features of the volatility smile a two-factor, of double Heston type, stochastic volatility model is more useful as shown in Christoffersen, Heston and Jacobs [12]. We consider one modified form of such two-factor volatility models in which the volatility has multiscale mean-reversion rates. Our model contains two mean-reverting volatility processes with a fast and a slow reverting rate respectively. We consider the European option pricing problem under one type of the multiscale stochastic volatility model where the two volatility processes act as independent factors in the asset price process. The novelty in this paper is an approximating analytical solution using asymptotic expansion method which extends the authors earlier research in Canhanga et al. [5, 6]. In addition we propose a numerical approximating solution using Monte-Carlo simulation. For completeness and for comparison we also implement the semi-analytical solution by Chiarella and Ziveyi [11] using method of characteristics, Fourier and bivariate Laplace transforms.

Analytic model of a multi-electron atom

NASA Astrophysics Data System (ADS)

Skoromnik, O. D.; Feranchuk, I. D.; Leonau, A. U.; Keitel, C. H.

2017-12-01

A fully analytical approximation for the observable characteristics of many-electron atoms is developed via a complete and orthonormal hydrogen-like basis with a single-effective charge parameter for all electrons of a given atom. The basis completeness allows us to employ the secondary-quantized representation for the construction of regular perturbation theory, which includes in a natural way correlation effects, converges fast and enables an effective calculation of the subsequent corrections. The hydrogen-like basis set provides a possibility to perform all summations over intermediate states in closed form, including both the discrete and continuous spectra. This is achieved with the help of the decomposition of the multi-particle Green function in a convolution of single-electronic Coulomb Green functions. We demonstrate that our fully analytical zeroth-order approximation describes the whole spectrum of the system, provides accuracy, which is independent of the number of electrons and is important for applications where the Thomas-Fermi model is still utilized. In addition already in second-order perturbation theory our results become comparable with those via a multi-configuration Hartree-Fock approach.

Algorithms and analytical solutions for rapidly approximating long-term dispersion from line and area sources

NASA Astrophysics Data System (ADS)

Barrett, Steven R. H.; Britter, Rex E.

Predicting long-term mean pollutant concentrations in the vicinity of airports, roads and other industrial sources are frequently of concern in regulatory and public health contexts. Many emissions are represented geometrically as ground-level line or area sources. Well developed modelling tools such as AERMOD and ADMS are able to model dispersion from finite (i.e. non-point) sources with considerable accuracy, drawing upon an up-to-date understanding of boundary layer behaviour. Due to mathematical difficulties associated with line and area sources, computationally expensive numerical integration schemes have been developed. For example, some models decompose area sources into a large number of line sources orthogonal to the mean wind direction, for which an analytical (Gaussian) solution exists. Models also employ a time-series approach, which involves computing mean pollutant concentrations for every hour over one or more years of meteorological data. This can give rise to computer runtimes of several days for assessment of a site. While this may be acceptable for assessment of a single industrial complex, airport, etc., this level of computational cost precludes national or international policy assessments at the level of detail available with dispersion modelling. In this paper, we extend previous work [S.R.H. Barrett, R.E. Britter, 2008. Development of algorithms and approximations for rapid operational air quality modelling. Atmospheric Environment 42 (2008) 8105-8111] to line and area sources. We introduce approximations which allow for the development of new analytical solutions for long-term mean dispersion from line and area sources, based on hypergeometric functions. We describe how these solutions can be parameterized from a single point source run from an existing advanced dispersion model, thereby accounting for all processes modelled in the more costly algorithms. The parameterization method combined with the analytical solutions for long-term mean dispersion are shown to produce results several orders of magnitude more efficiently with a loss of accuracy small compared to the absolute accuracy of advanced dispersion models near sources. The method can be readily incorporated into existing dispersion models, and may allow for additional computation time to be expended on modelling dispersion processes more accurately in future, rather than on accounting for source geometry.

An analytical model for solute transport in an infiltration tracer test in soil with a shallow groundwater table

NASA Astrophysics Data System (ADS)

Liang, Ching-Ping; Hsu, Shao-Yiu; Chen, Jui-Sheng

2016-09-01

It is recommended that an in-situ infiltration tracer test is considered for simultaneously determining the longitudinal and transverse dispersion coefficients in soil. Analytical solutions have been derived for two-dimensional advective-dispersive transport in a radial geometry in the literature which can be used for interpreting the result of such a tracer test. However, these solutions were developed for a transport domain with an unbounded-radial extent and an infinite thickness of vadose zone which might not be realistically manifested in the actual solute transport during a field infiltration tracer test. Especially, the assumption of infinite thickness of vadose zone should be invalid for infiltration tracer tests conducted in soil with a shallow groundwater table. This paper describes an analytical model for interpreting the results of an infiltration tracer test based on improving the transport domain with a bounded-radial extent and a finite thickness of vadose zone. The analytical model is obtained with the successive application of appropriate integral transforms and their corresponding inverse transforms. A comparison of the newly derived analytical solution against the previous analytical solutions in which two distinct sets of radial extent and thickness of vadose zone are considered is conducted to determine the influence of the radial and exit boundary conditions on the solute transport. The results shows that both the radial and exit boundary conditions substantially affect the trailing segment of the breakthrough curves for a soil medium with large dispersion coefficients. Previous solutions derived for a transport domain with an unbounded-radial and an infinite thickness of vadose zone boundary conditions give lower concentration predictions compared with the proposed solution at late times. Moreover, the differences between two solutions are amplified when the observation positions are near the groundwater table. In addition, we compare our solution against the approximate solutions that derived from the previous analytical solution and has been suggested to serve as fast tools for simultaneously estimating the longitudinal and transverse dispersion coefficients. The results indicate that the approximate solutions offer predictions that are markedly distinct from our solution for the entire range of dispersion coefficient values. Thus, it is not appropriate to use the approximate solution for interpreting the results of an infiltration tracer test.

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

Bourdon, Christopher Jay; Olsen, Michael G.; Gorby, Allen D.

The analytical model for the depth of correlation (measurement depth) of a microscopic particle image velocimetry (micro-PIV) experiment derived by Olsen and Adrian (Exp. Fluids, 29, pp. S166-S174, 2000) has been modified to be applicable to experiments using high numerical aperture optics. A series of measurements are presented that experimentally quantify the depth of correlation of micro-PIV velocity measurements which employ high numerical aperture and magnification optics. These measurements demonstrate that the modified analytical model is quite accurate in estimating the depth of correlation in micro-PIV measurements using this class of optics. Additionally, it was found that the Gaussian particlemore » approximation made in this model does not significantly affect the model's performance. It is also demonstrated that this modified analytical model easily predicts the depth of correlation when viewing into a medium of a different index of refraction than the immersion medium.« less

Relativistic algorithm for time transfer in Mars missions under IAU Resolutions: an analytic approach

NASA Astrophysics Data System (ADS)

Pan, Jun-Yang; Xie, Yi

2015-02-01

With tremendous advances in modern techniques, Einstein's general relativity has become an inevitable part of deep space missions. We investigate the relativistic algorithm for time transfer between the proper time τ of the onboard clock and the Geocentric Coordinate Time, which extends some previous works by including the effects of propagation of electromagnetic signals. In order to evaluate the implicit algebraic equations and integrals in the model, we take an analytic approach to work out their approximate values. This analytic model might be used in an onboard computer because of its limited capability to perform calculations. Taking an orbiter like Yinghuo-1 as an example, we find that the contributions of the Sun, the ground station and the spacecraft dominate the outcomes of the relativistic corrections to the model.

Evolutionary Games of Multiplayer Cooperation on Graphs

PubMed Central

Arranz, Jordi; Traulsen, Arne

2016-01-01

There has been much interest in studying evolutionary games in structured populations, often modeled as graphs. However, most analytical results so far have only been obtained for two-player or linear games, while the study of more complex multiplayer games has been usually tackled by computer simulations. Here we investigate evolutionary multiplayer games on graphs updated with a Moran death-Birth process. For cycles, we obtain an exact analytical condition for cooperation to be favored by natural selection, given in terms of the payoffs of the game and a set of structure coefficients. For regular graphs of degree three and larger, we estimate this condition using a combination of pair approximation and diffusion approximation. For a large class of cooperation games, our approximations suggest that graph-structured populations are stronger promoters of cooperation than populations lacking spatial structure. Computer simulations validate our analytical approximations for random regular graphs and cycles, but show systematic differences for graphs with many loops such as lattices. In particular, our simulation results show that these kinds of graphs can even lead to more stringent conditions for the evolution of cooperation than well-mixed populations. Overall, we provide evidence suggesting that the complexity arising from many-player interactions and spatial structure can be captured by pair approximation in the case of random graphs, but that it need to be handled with care for graphs with high clustering. PMID:27513946

A Full-Maxwell Approach for Large-Angle Polar Wander of Viscoelastic Bodies

NASA Astrophysics Data System (ADS)

Hu, H.; van der Wal, W.; Vermeersen, L. L. A.

2017-12-01

For large-angle long-term true polar wander (TPW) there are currently two types of nonlinear methods which give approximated solutions: those assuming that the rotational axis coincides with the axis of maximum moment of inertia (MoI), which simplifies the Liouville equation, and those based on the quasi-fluid approximation, which approximates the Love number. Recent studies show that both can have a significant bias for certain models. Therefore, we still lack an (semi)analytical method which can give exact solutions for large-angle TPW for a model based on Maxwell rheology. This paper provides a method which analytically solves the MoI equation and adopts an extended iterative procedure introduced in Hu et al. (2017) to obtain a time-dependent solution. The new method can be used to simulate the effect of a remnant bulge or models in different hydrostatic states. We show the effect of the viscosity of the lithosphere on long-term, large-angle TPW. We also simulate models without hydrostatic equilibrium and show that the choice of the initial stress-free shape for the elastic (or highly viscous) lithosphere of a given model is as important as its thickness for obtaining a correct TPW behavior. The initial shape of the lithosphere can be an alternative explanation to mantle convection for the difference between the observed and model predicted flattening. Finally, it is concluded that based on the quasi-fluid approximation, TPW speed on Earth and Mars is underestimated, while the speed of the rotational axis approaching the end position on Venus is overestimated.

Fast and Analytical EAP Approximation from a 4th-Order Tensor.

PubMed

Ghosh, Aurobrata; Deriche, Rachid

2012-01-01

Generalized diffusion tensor imaging (GDTI) was developed to model complex apparent diffusivity coefficient (ADC) using higher-order tensors (HOTs) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the ensemble average propagator (EAP). Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors were developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF), since it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel closed-form approximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since the solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes the effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms. We demonstrate our approach with 4th-order tensors on synthetic data and in vivo human data.

Fast and Analytical EAP Approximation from a 4th-Order Tensor

PubMed Central

Ghosh, Aurobrata; Deriche, Rachid

2012-01-01

Generalized diffusion tensor imaging (GDTI) was developed to model complex apparent diffusivity coefficient (ADC) using higher-order tensors (HOTs) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the ensemble average propagator (EAP). Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors were developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF), since it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel closed-form approximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since the solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes the effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms. We demonstrate our approach with 4th-order tensors on synthetic data and in vivo human data. PMID:23365552

Numerical Approximation of Elasticity Tensor Associated With Green-Naghdi Rate.

PubMed

Liu, Haofei; Sun, Wei

2017-08-01

Objective stress rates are often used in commercial finite element (FE) programs. However, deriving a consistent tangent modulus tensor (also known as elasticity tensor or material Jacobian) associated with the objective stress rates is challenging when complex material models are utilized. In this paper, an approximation method for the tangent modulus tensor associated with the Green-Naghdi rate of the Kirchhoff stress is employed to simplify the evaluation process. The effectiveness of the approach is demonstrated through the implementation of two user-defined fiber-reinforced hyperelastic material models. Comparisons between the approximation method and the closed-form analytical method demonstrate that the former can simplify the material Jacobian evaluation with satisfactory accuracy while retaining its computational efficiency. Moreover, since the approximation method is independent of material models, it can facilitate the implementation of complex material models in FE analysis using shell/membrane elements in abaqus.

Inversion of the anomalous diffraction approximation for variable complex index of refraction near unity. [numerical tests for water-haze aerosol model

NASA Technical Reports Server (NTRS)

Smith, C. B.

1982-01-01

The Fymat analytic inversion method for retrieving a particle-area distribution function from anomalous diffraction multispectral extinction data and total area is generalized to the case of a variable complex refractive index m(lambda) near unity depending on spectral wavelength lambda. Inversion tests are presented for a water-haze aerosol model. An upper-phase shift limit of 5 pi/2 retrieved an accurate peak area distribution profile. Analytical corrections using both the total number and area improved the inversion.

Extended Lindhard-Scharf-Schiott Theory for Ion Implantation Profiles Expressed with Pearson Function

NASA Astrophysics Data System (ADS)

Suzuki, Kunihiro

2009-04-01

Ion implantation profiles are expressed by the Pearson function with first, second, third, and fourth moment parameters of Rp, ΔRp, γ, and β. We derived an analytical model for these profile moments by solving a Lindhard-Scharf-Schiott (LSS) integration equation using perturbation approximation. This analytical model reproduces Monte Carlo data that were well calibrated to reproduce a vast experimental database. The extended LSS theory is vital for instantaneously predicting ion implantation profiles with any combination of incident ions and substrate atoms including their energy dependence.

Heat generation in aircraft tires under braked rolling conditions

NASA Technical Reports Server (NTRS)

Clark, S. K.; Dodge, R. N.

1984-01-01

An analytical model was developed to approximate the internal temperature distribution in an aircraft tire operating under conditions of unyawed braked rolling. The model employs an array of elements to represent the tire cross section and considers the heat generated within the tire to be caused by the change in strain energy associated with cyclic tire deflection. The additional heating due to tire slip and stresses induced by braking are superimposed on the previously developed free rolling model. An extensive experimental program was conducted to verify temperatures predicted from the analytical model. Data from these tests were compared with calculations over a range of operating conditions. The model results were in reasonably good agreement with measured values.

Energy distributions and radiation transport in uranium plasmas

NASA Technical Reports Server (NTRS)

Miley, G. H.; Bathke, C.; Maceda, E.; Choi, C.

1976-01-01

An approximate analytic model, based on continuous electron slowing, has been used for survey calculations. Where more accuracy is required, a Monte Carlo technique is used which combines an analytic representation of Coulombic collisions with a random walk treatment of inelastic collisions. The calculated electron distributions have been incorporated into another code that evaluates both the excited atomic state densities within the plasma and the radiative flux emitted from the plasma.

Recursive linearization of multibody dynamics equations of motion

NASA Technical Reports Server (NTRS)

Lin, Tsung-Chieh; Yae, K. Harold

1989-01-01

The equations of motion of a multibody system are nonlinear in nature, and thus pose a difficult problem in linear control design. One approach is to have a first-order approximation through the numerical perturbations at a given configuration, and to design a control law based on the linearized model. Here, a linearized model is generated analytically by following the footsteps of the recursive derivation of the equations of motion. The equations of motion are first written in a Newton-Euler form, which is systematic and easy to construct; then, they are transformed into a relative coordinate representation, which is more efficient in computation. A new computational method for linearization is obtained by applying a series of first-order analytical approximations to the recursive kinematic relationships. The method has proved to be computationally more efficient because of its recursive nature. It has also turned out to be more accurate because of the fact that analytical perturbation circumvents numerical differentiation and other associated numerical operations that may accumulate computational error, thus requiring only analytical operations of matrices and vectors. The power of the proposed linearization algorithm is demonstrated, in comparison to a numerical perturbation method, with a two-link manipulator and a seven degrees of freedom robotic manipulator. Its application to control design is also demonstrated.

Determination of the aerosol size distribution by analytic inversion of the extinction spectrum in the complex anomalous diffraction approximation.

PubMed

Franssens, G; De Maziére, M; Fonteyn, D

2000-08-20

A new derivation is presented for the analytical inversion of aerosol spectral extinction data to size distributions. It is based on the complex analytic extension of the anomalous diffraction approximation (ADA). We derive inverse formulas that are applicable to homogeneous nonabsorbing and absorbing spherical particles. Our method simplifies, generalizes, and unifies a number of results obtained previously in the literature. In particular, we clarify the connection between the ADA transform and the Fourier and Laplace transforms. Also, the effect of the particle refractive-index dispersion on the inversion is examined. It is shown that, when Lorentz's model is used for this dispersion, the continuous ADA inverse transform is mathematically well posed, whereas with a constant refractive index it is ill posed. Further, a condition is given, in terms of Lorentz parameters, for which the continuous inverse operator does not amplify the error.

Analytic derivative couplings and first-principles exciton/phonon coupling constants for an ab initio Frenkel-Davydov exciton model: Theory, implementation, and application to compute triplet exciton mobility parameters for crystalline tetracene.

PubMed

Morrison, Adrian F; Herbert, John M

2017-06-14

Recently, we introduced an ab initio version of the Frenkel-Davydov exciton model for computing excited-state properties of molecular crystals and aggregates. Within this model, supersystem excited states are approximated as linear combinations of excitations localized on molecular sites, and the electronic Hamiltonian is constructed and diagonalized in a direct-product basis of non-orthogonal configuration state functions computed for isolated fragments. Here, we derive and implement analytic derivative couplings for this model, including nuclear derivatives of the natural transition orbital and symmetric orthogonalization transformations that are part of the approximation. Nuclear derivatives of the exciton Hamiltonian's matrix elements, required in order to compute the nonadiabatic couplings, are equivalent to the "Holstein" and "Peierls" exciton/phonon couplings that are widely discussed in the context of model Hamiltonians for energy and charge transport in organic photovoltaics. As an example, we compute the couplings that modulate triplet exciton transport in crystalline tetracene, which is relevant in the context of carrier diffusion following singlet exciton fission.

Nanometric depth resolution from multi-focal images in microscopy.

PubMed

Dalgarno, Heather I C; Dalgarno, Paul A; Dada, Adetunmise C; Towers, Catherine E; Gibson, Gavin J; Parton, Richard M; Davis, Ilan; Warburton, Richard J; Greenaway, Alan H

2011-07-06

We describe a method for tracking the position of small features in three dimensions from images recorded on a standard microscope with an inexpensive attachment between the microscope and the camera. The depth-measurement accuracy of this method is tested experimentally on a wide-field, inverted microscope and is shown to give approximately 8 nm depth resolution, over a specimen depth of approximately 6 µm, when using a 12-bit charge-coupled device (CCD) camera and very bright but unresolved particles. To assess low-flux limitations a theoretical model is used to derive an analytical expression for the minimum variance bound. The approximations used in the analytical treatment are tested using numerical simulations. It is concluded that approximately 14 nm depth resolution is achievable with flux levels available when tracking fluorescent sources in three dimensions in live-cell biology and that the method is suitable for three-dimensional photo-activated localization microscopy resolution. Sub-nanometre resolution could be achieved with photon-counting techniques at high flux levels.

Nanometric depth resolution from multi-focal images in microscopy

PubMed Central

Dalgarno, Heather I. C.; Dalgarno, Paul A.; Dada, Adetunmise C.; Towers, Catherine E.; Gibson, Gavin J.; Parton, Richard M.; Davis, Ilan; Warburton, Richard J.; Greenaway, Alan H.

2011-01-01

We describe a method for tracking the position of small features in three dimensions from images recorded on a standard microscope with an inexpensive attachment between the microscope and the camera. The depth-measurement accuracy of this method is tested experimentally on a wide-field, inverted microscope and is shown to give approximately 8 nm depth resolution, over a specimen depth of approximately 6 µm, when using a 12-bit charge-coupled device (CCD) camera and very bright but unresolved particles. To assess low-flux limitations a theoretical model is used to derive an analytical expression for the minimum variance bound. The approximations used in the analytical treatment are tested using numerical simulations. It is concluded that approximately 14 nm depth resolution is achievable with flux levels available when tracking fluorescent sources in three dimensions in live-cell biology and that the method is suitable for three-dimensional photo-activated localization microscopy resolution. Sub-nanometre resolution could be achieved with photon-counting techniques at high flux levels. PMID:21247948

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.

Neural Network and Regression Methods Demonstrated in the Design Optimization of a Subsonic Aircraft

NASA Technical Reports Server (NTRS)

Hopkins, Dale A.; Lavelle, Thomas M.; Patnaik, Surya

2003-01-01

The neural network and regression methods of NASA Glenn Research Center s COMETBOARDS design optimization testbed were used to generate approximate analysis and design models for a subsonic aircraft operating at Mach 0.85 cruise speed. The analytical model is defined by nine design variables: wing aspect ratio, engine thrust, wing area, sweep angle, chord-thickness ratio, turbine temperature, pressure ratio, bypass ratio, fan pressure; and eight response parameters: weight, landing velocity, takeoff and landing field lengths, approach thrust, overall efficiency, and compressor pressure and temperature. The variables were adjusted to optimally balance the engines to the airframe. The solution strategy included a sensitivity model and the soft analysis model. Researchers generated the sensitivity model by training the approximators to predict an optimum design. The trained neural network predicted all response variables, within 5-percent error. This was reduced to 1 percent by the regression method. The soft analysis model was developed to replace aircraft analysis as the reanalyzer in design optimization. Soft models have been generated for a neural network method, a regression method, and a hybrid method obtained by combining the approximators. The performance of the models is graphed for aircraft weight versus thrust as well as for wing area and turbine temperature. The regression method followed the analytical solution with little error. The neural network exhibited 5-percent maximum error over all parameters. Performance of the hybrid method was intermediate in comparison to the individual approximators. Error in the response variable is smaller than that shown in the figure because of a distortion scale factor. The overall performance of the approximators was considered to be satisfactory because aircraft analysis with NASA Langley Research Center s FLOPS (Flight Optimization System) code is a synthesis of diverse disciplines: weight estimation, aerodynamic analysis, engine cycle analysis, propulsion data interpolation, mission performance, airfield length for landing and takeoff, noise footprint, and others.

A Rotating Plug Model of Friction Stir Welding Heat Transfer

NASA Technical Reports Server (NTRS)

Raghulapadu J. K.; Peddieson, J.; Buchanan, G. R.; Nunes, A. C.

2006-01-01

A simplified rotating plug model is employed to study the heat transfer phenomena associated with the fiction stir welding process. An approximate analytical solution is obtained based on this idealized model and used both to demonstrate the qualitative influence of process parameters on predictions and to estimate temperatures produced in typical fiction stir welding situations.

Effects of a finite aperture on the Inverse Born Approximation

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

Kogan, V.G.; Rose, J.H.

1983-01-01

One of the most important effects of complex part geometry is that the available entrance and exit angles for ultrasound are limited. We will present a study of the Inverse Born approximation in which we have data for incident (and exit) directions confined to a conical aperture. Modeling the direct problem by the Born Approximation, we obtained analytical results for (1) a weak spherical inclusion, and (2) a penny shaped crack (modeled by an oblate spheroid). General results are: (a) the value of the characteristic function ..gamma.. is constant in the interior of the flaw, but reduced in value; (b)more » the discontinuity at the boundary of the flaw occurs over the lighted portion of the flaw; (c) this discontinuity is contrasted by a region where ..gamma.. is negative; and (d) new non-physical discontinuities and non-analyticities appear in the reconstructed characteristic function. These general features also appear in numerical calculations which use as input strong scattering data from a spherical void and a flat penny shaped crack in Titanium. The numerical results can be straightforwardly interpreted in terms of the analytical calculation mentioned above, indicating that they will be useful in the study of realistic flaws. We conclude by discussing the stabilization of the aperture limited inversion problem and the removal of non-physical features in the reconstruction.« less

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.

A rapid radiative transfer model for reflection of solar radiation

NASA Technical Reports Server (NTRS)

Xiang, X.; Smith, E. A.; Justus, C. G.

1994-01-01

A rapid analytical radiative transfer model for reflection of solar radiation in plane-parallel atmospheres is developed based on the Sobolev approach and the delta function transformation technique. A distinct advantage of this model over alternative two-stream solutions is that in addition to yielding the irradiance components, which turn out to be mathematically equivalent to the delta-Eddington approximation, the radiance field can also be expanded in a mathematically consistent fashion. Tests with the model against a more precise multistream discrete ordinate model over a wide range of input parameters demonstrate that the new approximate method typically produces average radiance differences of less than 5%, with worst average differences of approximately 10%-15%. By the same token, the computational speed of the new model is some tens to thousands times faster than that of the more precise model when its stream resolution is set to generate precise calculations.

Methods for analysis of cracks in three-dimensional solids

NASA Technical Reports Server (NTRS)

Raju, I. S.; Newman, J. C., Jr.

1984-01-01

Various analytical and numerical methods used to evaluate the stress intensity factors for cracks in three-dimensional (3-D) solids are reviewed. Classical exact solutions and many of the approximate methods used in 3-D analyses of cracks are reviewed. The exact solutions for embedded elliptic cracks in infinite solids are discussed. The approximate methods reviewed are the finite element methods, the boundary integral equation (BIE) method, the mixed methods (superposition of analytical and finite element method, stress difference method, discretization-error method, alternating method, finite element-alternating method), and the line-spring model. The finite element method with singularity elements is the most widely used method. The BIE method only needs modeling of the surfaces of the solid and so is gaining popularity. The line-spring model appears to be the quickest way to obtain good estimates of the stress intensity factors. The finite element-alternating method appears to yield the most accurate solution at the minimum cost.

Analysis of fast boundary-integral approximations for modeling electrostatic contributions of molecular binding

PubMed Central

Kreienkamp, Amelia B.; Liu, Lucy Y.; Minkara, Mona S.; Knepley, Matthew G.; Bardhan, Jaydeep P.; Radhakrishnan, Mala L.

2013-01-01

We analyze and suggest improvements to a recently developed approximate continuum-electrostatic model for proteins. The model, called BIBEE/I (boundary-integral based electrostatics estimation with interpolation), was able to estimate electrostatic solvation free energies to within a mean unsigned error of 4% on a test set of more than 600 proteins—a significant improvement over previous BIBEE models. In this work, we tested the BIBEE/I model for its capability to predict residue-by-residue interactions in protein–protein binding, using the widely studied model system of trypsin and bovine pancreatic trypsin inhibitor (BPTI). Finding that the BIBEE/I model performs surprisingly less well in this task than simpler BIBEE models, we seek to explain this behavior in terms of the models’ differing spectral approximations of the exact boundary-integral operator. Calculations of analytically solvable systems (spheres and tri-axial ellipsoids) suggest two possibilities for improvement. The first is a modified BIBEE/I approach that captures the asymptotic eigenvalue limit correctly, and the second involves the dipole and quadrupole modes for ellipsoidal approximations of protein geometries. Our analysis suggests that fast, rigorous approximate models derived from reduced-basis approximation of boundary-integral equations might reach unprecedented accuracy, if the dipole and quadrupole modes can be captured quickly for general shapes. PMID:24466561

Cosmological models constructed by van der Waals fluid approximation and volumetric expansion

NASA Astrophysics Data System (ADS)

Samanta, G. C.; Myrzakulov, R.

The universe modeled with van der Waals fluid approximation, where the van der Waals fluid equation of state contains a single parameter ωv. Analytical solutions to the Einstein’s field equations are obtained by assuming the mean scale factor of the metric follows volumetric exponential and power-law expansions. The model describes a rapid expansion where the acceleration grows in an exponential way and the van der Waals fluid behaves like an inflation for an initial epoch of the universe. Also, the model describes that when time goes away the acceleration is positive, but it decreases to zero and the van der Waals fluid approximation behaves like a present accelerated phase of the universe. Finally, it is observed that the model contains a type-III future singularity for volumetric power-law expansion.

Mathematical Simulation of Perturbations of Attack Angle of Asymmetric Nanosatellite Passing through Resonance

NASA Astrophysics Data System (ADS)

Lyubimov, V. V.; Kurkina, E. V.

2018-05-01

The authors consider the problem of a dynamic system passing through a low-order resonance, describing an uncontrolled atmospheric descent of an asymmetric nanosatellite in the Earth's atmosphere. The authors perform mathematical and numerical modeling of the motion of the nanosatellite with a small mass-aerodynamic asymmetry relative to the center of mass. The aim of the study is to obtain new reliable approximate analytical estimates of perturbations of the angle of attack of a nanosatellite passing through resonance at angles of attack of not more than 0.5π. By using the stationary phase method, the authors were able to investigate a discontinuous perturbation in the angle of attack of a nanosatellite passing through a resonance with two different nanosatellite designs. Comparison of the results of the numerical modeling and new approximate analytical estimates of the perturbation of the angle of attack confirms the reliability of the said estimates.

Implementing a Matrix-free Analytical Jacobian to Handle Nonlinearities in Models of 3D Lithospheric Deformation

NASA Astrophysics Data System (ADS)

Kaus, B.; Popov, A.

2015-12-01

The analytical expression for the Jacobian is a key component to achieve fast and robust convergence of the nonlinear Newton-Raphson iterative solver. Accomplishing this task in practice often requires a significant algebraic effort. Therefore it is quite common to use a cheap alternative instead, for example by approximating the Jacobian with a finite difference estimation. Despite its simplicity it is a relatively fragile and unreliable technique that is sensitive to the scaling of the residual and unknowns, as well as to the perturbation parameter selection. Unfortunately no universal rule can be applied to provide both a robust scaling and a perturbation. The approach we use here is to derive the analytical Jacobian for the coupled set of momentum, mass, and energy conservation equations together with the elasto-visco-plastic rheology and a marker in cell/staggered finite difference method. The software project LaMEM (Lithosphere and Mantle Evolution Model) is primarily developed for the thermo-mechanically coupled modeling of the 3D lithospheric deformation. The code is based on a staggered grid finite difference discretization in space, and uses customized scalable solvers form PETSc library to efficiently run on the massively parallel machines (such as IBM Blue Gene/Q). Currently LaMEM relies on the Jacobian-Free Newton-Krylov (JFNK) nonlinear solver, which approximates the Jacobian-vector product using a simple finite difference formula. This approach never requires an assembled Jacobian matrix and uses only the residual computation routine. We use an approximate Jacobian (Picard) matrix to precondition the Krylov solver with the Galerkin geometric multigrid. Because of the inherent problems of the finite difference Jacobian estimation, this approach doesn't always result in stable convergence. In this work we present and discuss a matrix-free technique in which the Jacobian-vector product is replaced by analytically-derived expressions and compare results with those obtained with a finite difference approximation of the Jacobian. This project is funded by ERC Starting Grant 258830 and computer facilities were provided by Jülich supercomputer center (Germany).

A new analytical solar radiation pressure model for current BeiDou satellites: IGGBSPM

PubMed Central

Tan, Bingfeng; Yuan, Yunbin; Zhang, Baocheng; Hsu, Hou Ze; Ou, Jikun

2016-01-01

An analytical solar radiation pressure (SRP) model, IGGBSPM (an abbreviation for Institute of Geodesy and Geophysics BeiDou Solar Pressure Model), has been developed for three BeiDou satellite types, namely, geostationary orbit (GEO), inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO), based on a ray-tracing method. The performance of IGGBSPM was assessed based on numerical integration, SLR residuals and analyses of empirical SRP parameters (except overlap computations). The numerical results show that the integrated orbit resulting from IGGBSPM differs from the precise ephemerides by approximately 5 m and 2 m for GEO and non-GEO satellites, respectively. Moreover, when IGGBSPM is used as an a priori model to enhance the ECOM (5-parameter) model with stochastic pulses, named ECOM + APR, for precise orbit determination, the SLR RMS residual improves by approximately 20–25 percent over the ECOM-only solution during the yaw-steering period and by approximately 40 percent during the yaw-fixed period. For the BeiDou GEO01 satellite, improvements of 18 and 32 percent can be achieved during the out-of-eclipse season and during the eclipse season, respectively. An investigation of the estimated ECOM D0 parameters indicated that the β-angle dependence that is evident in the ECOM-only solution is no longer present in the ECOM + APR solution. PMID:27595795

A new analytical solar radiation pressure model for current BeiDou satellites: IGGBSPM.

PubMed

Tan, Bingfeng; Yuan, Yunbin; Zhang, Baocheng; Hsu, Hou Ze; Ou, Jikun

2016-09-06

An analytical solar radiation pressure (SRP) model, IGGBSPM (an abbreviation for Institute of Geodesy and Geophysics BeiDou Solar Pressure Model), has been developed for three BeiDou satellite types, namely, geostationary orbit (GEO), inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO), based on a ray-tracing method. The performance of IGGBSPM was assessed based on numerical integration, SLR residuals and analyses of empirical SRP parameters (except overlap computations). The numerical results show that the integrated orbit resulting from IGGBSPM differs from the precise ephemerides by approximately 5 m and 2 m for GEO and non-GEO satellites, respectively. Moreover, when IGGBSPM is used as an a priori model to enhance the ECOM (5-parameter) model with stochastic pulses, named ECOM + APR, for precise orbit determination, the SLR RMS residual improves by approximately 20-25 percent over the ECOM-only solution during the yaw-steering period and by approximately 40 percent during the yaw-fixed period. For the BeiDou GEO01 satellite, improvements of 18 and 32 percent can be achieved during the out-of-eclipse season and during the eclipse season, respectively. An investigation of the estimated ECOM D0 parameters indicated that the β-angle dependence that is evident in the ECOM-only solution is no longer present in the ECOM + APR solution.

Analytical model of the optical vortex microscope.

PubMed

Płocinniczak, Łukasz; Popiołek-Masajada, Agnieszka; Masajada, Jan; Szatkowski, Mateusz

2016-04-20

This paper presents an analytical model of the optical vortex scanning microscope. In this microscope the Gaussian beam with an embedded optical vortex is focused into the sample plane. Additionally, the optical vortex can be moved inside the beam, which allows fine scanning of the sample. We provide an analytical solution of the whole path of the beam in the system (within paraxial approximation)-from the vortex lens to the observation plane situated on the CCD camera. The calculations are performed step by step from one optical element to the next. We show that at each step, the expression for light complex amplitude has the same form with only four coefficients modified. We also derive a simple expression for the vortex trajectory of small vortex displacements.

An Improved Analytical Model of the Local Interstellar Magnetic Field: The Extension to Compressibility

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

Kleimann, Jens; Fichtner, Horst; Röken, Christian, E-mail: jk@tp4.rub.de, E-mail: hf@tp4.rub.de, E-mail: christian.roeken@mathematik.uni-regensburg.de

A previously published analytical magnetohydrodynamic model for the local interstellar magnetic field in the vicinity of the heliopause (Röken et al. 2015) is extended from incompressible to compressible, yet predominantly subsonic flow, considering both isothermal and adiabatic equations of state. Exact expressions and suitable approximations for the density and the flow velocity are derived and discussed. In addition to the stationary induction equation, these expressions also satisfy the momentum balance equation along stream lines. The practical usefulness of the corresponding, still exact, analytical magnetic field solution is assessed by comparing it quantitatively to results from a fully self-consistent magnetohydrodynamic simulationmore » of the interstellar magnetic field draping around the heliopause.« less

An empirical model for calculation of the collimator contamination dose in therapeutic proton beams

NASA Astrophysics Data System (ADS)

Vidal, M.; De Marzi, L.; Szymanowski, H.; Guinement, L.; Nauraye, C.; Hierso, E.; Freud, N.; Ferrand, R.; François, P.; Sarrut, D.

2016-02-01

Collimators are used as lateral beam shaping devices in proton therapy with passive scattering beam lines. The dose contamination due to collimator scattering can be as high as 10% of the maximum dose and influences calculation of the output factor or monitor units (MU). To date, commercial treatment planning systems generally use a zero-thickness collimator approximation ignoring edge scattering in the aperture collimator and few analytical models have been proposed to take scattering effects into account, mainly limited to the inner collimator face component. The aim of this study was to characterize and model aperture contamination by means of a fast and accurate analytical model. The entrance face collimator scatter distribution was modeled as a 3D secondary dose source. Predicted dose contaminations were compared to measurements and Monte Carlo simulations. Measurements were performed on two different proton beam lines (a fixed horizontal beam line and a gantry beam line) with divergent apertures and for several field sizes and energies. Discrepancies between analytical algorithm dose prediction and measurements were decreased from 10% to 2% using the proposed model. Gamma-index (2%/1 mm) was respected for more than 90% of pixels. The proposed analytical algorithm increases the accuracy of analytical dose calculations with reasonable computation times.

A screening tool for delineating subregions of steady recharge within groundwater models

USGS Publications Warehouse

Dickinson, Jesse; Ferré, T.P.A.; Bakker, Mark; Crompton, Becky

2014-01-01

We have developed a screening method for simplifying groundwater models by delineating areas within the domain that can be represented using steady-state groundwater recharge. The screening method is based on an analytical solution for the damping of sinusoidal infiltration variations in homogeneous soils in the vadose zone. The damping depth is defined as the depth at which the flux variation damps to 5% of the variation at the land surface. Groundwater recharge may be considered steady where the damping depth is above the depth of the water table. The analytical solution approximates the vadose zone diffusivity as constant, and we evaluated when this approximation is reasonable. We evaluated the analytical solution through comparison of the damping depth computed by the analytic solution with the damping depth simulated by a numerical model that allows variable diffusivity. This comparison showed that the screening method conservatively identifies areas of steady recharge and is more accurate when water content and diffusivity are nearly constant. Nomograms of the damping factor (the ratio of the flux amplitude at any depth to the amplitude at the land surface) and the damping depth were constructed for clay and sand for periodic variations between 1 and 365 d and flux means and amplitudes from nearly 0 to 1 × 10−3 m d−1. We applied the screening tool to Central Valley, California, to identify areas of steady recharge. A MATLAB script was developed to compute the damping factor for any soil and any sinusoidal flux variation.

Nonlinear analysis for dual-frequency concurrent energy harvesting

NASA Astrophysics Data System (ADS)

Yan, Zhimiao; Lei, Hong; Tan, Ting; Sun, Weipeng; Huang, Wenhu

2018-05-01

The dual-frequency responses of the hybrid energy harvester undergoing the base excitation and galloping were analyzed numerically. In this work, an approximate dual-frequency analytical method is proposed for the nonlinear analysis of such a system. To obtain the approximate analytical solutions of the full coupled distributed-parameter model, the forcing interactions is first neglected. Then, the electromechanical decoupled governing equation is developed using the equivalent structure method. The hybrid mechanical response is finally separated to be the self-excited and forced responses for deriving the analytical solutions, which are confirmed by the numerical simulations of the full coupled model. The forced response has great impacts on the self-excited response. The boundary of Hopf bifurcation is analytically determined by the onset wind speed to galloping, which is linearly increased by the electrical damping. Quenching phenomenon appears when the increasing base excitation suppresses the galloping. The theoretical quenching boundary depends on the forced mode velocity. The quenching region increases with the base acceleration and electrical damping, but decreases with the wind speed. Superior to the base-excitation-alone case, the existence of the aerodynamic force protects the hybrid energy harvester at resonance from damages caused by the excessive large displacement. From the view of the harvested power, the hybrid system surpasses the base-excitation-alone system or the galloping-alone system. This study advances our knowledge on intrinsic nonlinear dynamics of the dual-frequency energy harvesting system by taking advantage of the analytical solutions.

Stability analysis of magnetized neutron stars - a semi-analytic approach

NASA Astrophysics Data System (ADS)

Herbrik, Marlene; Kokkotas, Kostas D.

2017-04-01

We implement a semi-analytic approach for stability analysis, addressing the ongoing uncertainty about stability and structure of neutron star magnetic fields. Applying the energy variational principle, a model system is displaced from its equilibrium state. The related energy density variation is set up analytically, whereas its volume integration is carried out numerically. This facilitates the consideration of more realistic neutron star characteristics within the model compared to analytical treatments. At the same time, our method retains the possibility to yield general information about neutron star magnetic field and composition structures that are likely to be stable. In contrast to numerical studies, classes of parametrized systems can be studied at once, finally constraining realistic configurations for interior neutron star magnetic fields. We apply the stability analysis scheme on polytropic and non-barotropic neutron stars with toroidal, poloidal and mixed fields testing their stability in a Newtonian framework. Furthermore, we provide the analytical scheme for dropping the Cowling approximation in an axisymmetric system and investigate its impact. Our results confirm the instability of simple magnetized neutron star models as well as a stabilization tendency in the case of mixed fields and stratification. These findings agree with analytical studies whose spectrum of model systems we extend by lifting former simplifications.

An innovative hybrid 3D analytic-numerical model for air breathing parallel channel counter-flow PEM fuel cells.

PubMed

Tavčar, Gregor; Katrašnik, Tomaž

2014-01-01

The parallel straight channel PEM fuel cell model presented in this paper extends the innovative hybrid 3D analytic-numerical (HAN) approach previously published by the authors with capabilities to address ternary diffusion systems and counter-flow configurations. The model's core principle is modelling species transport by obtaining a 2D analytic solution for species concentration distribution in the plane perpendicular to the cannel gas-flow and coupling consecutive 2D solutions by means of a 1D numerical pipe-flow model. Electrochemical and other nonlinear phenomena are coupled to the species transport by a routine that uses derivative approximation with prediction-iteration. The latter is also the core of the counter-flow computation algorithm. A HAN model of a laboratory test fuel cell is presented and evaluated against a professional 3D CFD simulation tool showing very good agreement between results of the presented model and those of the CFD simulation. Furthermore, high accuracy results are achieved at moderate computational times, which is owed to the semi-analytic nature and to the efficient computational coupling of electrochemical kinetics and species transport.

An analytic, approximate method for modeling steady, three-dimensional flow to partially penetrating wells

NASA Astrophysics Data System (ADS)

Bakker, Mark

2001-05-01

An analytic, approximate solution is derived for the modeling of three-dimensional flow to partially penetrating wells. The solution is written in terms of a correction on the solution for a fully penetrating well and is obtained by dividing the aquifer up, locally, in a number of aquifer layers. The resulting system of differential equations is solved by application of the theory for multiaquifer flow. The presented approach has three major benefits. First, the solution may be applied to any groundwater model that can simulate flow to a fully penetrating well; the solution may be superimposed onto the solution for the fully penetrating well to simulate the local three-dimensional drawdown and flow field. Second, the approach is applicable to isotropic, anisotropic, and stratified aquifers and to both confined and unconfined flow. Third, the solution extends over a small area around the well only; outside this area the three-dimensional effect of the partially penetrating well is negligible, and no correction to the fully penetrating well is needed. A number of comparisons are made to existing three-dimensional, analytic solutions, including radial confined and unconfined flow and a well in a uniform flow field. It is shown that a subdivision in three layers is accurate for many practical cases; very accurate solutions are obtained with more layers.

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.

Padé approximant for normal stress differences in large-amplitude oscillatory shear flow

NASA Astrophysics Data System (ADS)

Poungthong, P.; Saengow, C.; Giacomin, A. J.; Kolitawong, C.; Merger, D.; Wilhelm, M.

2018-04-01

Analytical solutions for the normal stress differences in large-amplitude oscillatory shear flow (LAOS), for continuum or molecular models, normally take the inexact form of the first few terms of a series expansion in the shear rate amplitude. Here, we improve the accuracy of these truncated expansions by replacing them with rational functions called Padé approximants. The recent advent of exact solutions in LAOS presents an opportunity to identify accurate and useful Padé approximants. For this identification, we replace the truncated expansion for the corotational Jeffreys fluid with its Padé approximants for the normal stress differences. We uncover the most accurate and useful approximant, the [3,4] approximant, and then test its accuracy against the exact solution [C. Saengow and A. J. Giacomin, "Normal stress differences from Oldroyd 8-constant framework: Exact analytical solution for large-amplitude oscillatory shear flow," Phys. Fluids 29, 121601 (2017)]. We use Ewoldt grids to show the stunning accuracy of our [3,4] approximant in LAOS. We quantify this accuracy with an objective function and then map it onto the Pipkin space. Our two applications illustrate how to use our new approximant reliably. For this, we use the Spriggs relations to generalize our best approximant to multimode, and then, we compare with measurements on molten high-density polyethylene and on dissolved polyisobutylene in isobutylene oligomer.

Point spread functions and deconvolution of ultrasonic images.

PubMed

Dalitz, Christoph; Pohle-Fröhlich, Regina; Michalk, Thorsten

2015-03-01

This article investigates the restoration of ultrasonic pulse-echo C-scan images by means of deconvolution with a point spread function (PSF). The deconvolution concept from linear system theory (LST) is linked to the wave equation formulation of the imaging process, and an analytic formula for the PSF of planar transducers is derived. For this analytic expression, different numerical and analytic approximation schemes for evaluating the PSF are presented. By comparing simulated images with measured C-scan images, we demonstrate that the assumptions of LST in combination with our formula for the PSF are a good model for the pulse-echo imaging process. To reconstruct the object from a C-scan image, we compare different deconvolution schemes: the Wiener filter, the ForWaRD algorithm, and the Richardson-Lucy algorithm. The best results are obtained with the Richardson-Lucy algorithm with total variation regularization. For distances greater or equal twice the near field distance, our experiments show that the numerically computed PSF can be replaced with a simple closed analytic term based on a far field approximation.

ANALYTICAL APPROXIMATION OF THE BIODEGRADATION RATE FOR IN SITU BIOREMEDIATION OF GROUNDWATER UNDER IDEAL RADIAL FLOW CONDITIONS. (R824785)

EPA Science Inventory

We derive the long-term biodegradation rate of an organic contaminant (substrate) for an in situ bioremediation model with axisymmetric flow conditions. The model presumes that a nonsorbing electron acceptor is injected into a saturated homogeneous porous medium which initially c...

Modeling Three-Dimensional Flow in Confined Aquifers by Superposition of Both Two- and Three-Dimensional Analytic Functions

NASA Astrophysics Data System (ADS)

Haitjema, Henk M.

1985-10-01

A technique is presented to incorporate three-dimensional flow in a Dupuit-Forchheimer model. The method is based on superposition of approximate analytic solutions to both two- and three-dimensional flow features in a confined aquifer of infinite extent. Three-dimensional solutions are used in the domain of interest, while farfield conditions are represented by two-dimensional solutions. Approximate three- dimensional solutions have been derived for a partially penetrating well and a shallow creek. Each of these solutions satisfies the condition that no flow occurs across the confining layers of the aquifer. Because of this condition, the flow at some distance of a three-dimensional feature becomes nearly horizontal. Consequently, remotely from a three-dimensional feature, its three-dimensional solution is replaced by a corresponding two-dimensional one. The latter solution is trivial as compared to its three-dimensional counterpart, and its use greatly enhances the computational efficiency of the model. As an example, the flow is modeled between a partially penetrating well and a shallow creek that occur in a regional aquifer system.

Pair and triplet approximation of a spatial lattice population model with multiscale dispersal using Markov chains for estimating spatial autocorrelation.

PubMed

Hiebeler, David E; Millett, Nicholas E

2011-06-21

We investigate a spatial lattice model of a population employing dispersal to nearest and second-nearest neighbors, as well as long-distance dispersal across the landscape. The model is studied via stochastic spatial simulations, ordinary pair approximation, and triplet approximation. The latter method, which uses the probabilities of state configurations of contiguous blocks of three sites as its state variables, is demonstrated to be greatly superior to pair approximations for estimating spatial correlation information at various scales. Correlations between pairs of sites separated by arbitrary distances are estimated by constructing spatial Markov processes using the information from both approximations. These correlations demonstrate why pair approximation misses basic qualitative features of the model, such as decreasing population density as a large proportion of offspring are dropped on second-nearest neighbors, and why triplet approximation is able to include them. Analytical and numerical results show that, excluding long-distance dispersal, the initial growth rate of an invading population is maximized and the equilibrium population density is also roughly maximized when the population spreads its offspring evenly over nearest and second-nearest neighboring sites. Copyright © 2011 Elsevier Ltd. All rights reserved.

Analytical modeling of electron energy loss spectroscopy of graphene: Ab initio study versus extended hydrodynamic model.

PubMed

Djordjević, Tijana; Radović, Ivan; Despoja, Vito; Lyon, Keenan; Borka, Duško; Mišković, Zoran L

2018-01-01

We present an analytical modeling of the electron energy loss (EEL) spectroscopy data for free-standing graphene obtained by scanning transmission electron microscope. The probability density for energy loss of fast electrons traversing graphene under normal incidence is evaluated using an optical approximation based on the conductivity of graphene given in the local, i.e., frequency-dependent form derived by both a two-dimensional, two-fluid extended hydrodynamic (eHD) model and an ab initio method. We compare the results for the real and imaginary parts of the optical conductivity in graphene obtained by these two methods. The calculated probability density is directly compared with the EEL spectra from three independent experiments and we find very good agreement, especially in the case of the eHD model. Furthermore, we point out that the subtraction of the zero-loss peak from the experimental EEL spectra has a strong influence on the analytical model for the EEL spectroscopy data. Copyright © 2017 Elsevier B.V. All rights reserved.

Simplified multiple scattering model for radiative transfer in turbid water

NASA Technical Reports Server (NTRS)

Ghovanlou, A. H.; Gupta, G. N.

1978-01-01

Quantitative analytical procedures for relating selected water quality parameters to the characteristics of the backscattered signals, measured by remote sensors, require the solution of the radiative transport equation in turbid media. Presented is an approximate closed form solution of this equation and based on this solution, the remote sensing of sediments is discussed. The results are compared with other standard closed form solutions such as quasi-single scattering approximations.

Analytical approximation of a stochastic, spatial simulation model of fire and forest landscape dynamics

Treesearch

A.J. Tepley; E.A. Thomann

2012-01-01

Recent increases in computation power have prompted enormous growth in the use of simulation models in ecological research. These models are valued for their ability to account for much of the ecological complexity found in field studies, but this ability usually comes at the cost of losing transparency into how the models work. In order to foster greater understanding...

Solution of the advection-dispersion equation: Continuous load of finite duration

USGS Publications Warehouse

Runkel, R.L.

1996-01-01

Field studies of solute fate and transport in streams and rivers often involve an. experimental release of solutes at an upstream boundary for a finite period of time. A review of several standard references on surface-water-quality modeling indicates that the analytical solution to the constant-parameter advection-dispersion equation for this type of boundary condition has been generally overlooked. Here an exact analytical solution that considers a continuous load of unite duration is compared to an approximate analytical solution presented elsewhere. Results indicate that the exact analytical solution should be used for verification of numerical solutions and other solute-transport problems wherein a high level of accuracy is required. ?? ASCE.

Fast-slow asymptotic for semi-analytical ignition criteria in FitzHugh-Nagumo system.

PubMed

Bezekci, B; Biktashev, V N

2017-09-01

We study the problem of initiation of excitation waves in the FitzHugh-Nagumo model. Our approach follows earlier works and is based on the idea of approximating the boundary between basins of attraction of propagating waves and of the resting state as the stable manifold of a critical solution. Here, we obtain analytical expressions for the essential ingredients of the theory by singular perturbation using two small parameters, the separation of time scales of the activator and inhibitor and the threshold in the activator's kinetics. This results in a closed analytical expression for the strength-duration curve.

A Simple Model for Nonlinear Confocal Ultrasonic Beams

NASA Astrophysics Data System (ADS)

Zhang, Dong; Zhou, Lin; Si, Li-Sheng; Gong, Xiu-Fen

2007-01-01

A confocally and coaxially arranged pair of focused transmitter and receiver represents one of the best geometries for medical ultrasonic imaging and non-invasive detection. We develop a simple theoretical model for describing the nonlinear propagation of a confocal ultrasonic beam in biological tissues. On the basis of the parabolic approximation and quasi-linear approximation, the nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation is solved by using the angular spectrum approach. Gaussian superposition technique is applied to simplify the solution, and an analytical solution for the second harmonics in the confocal ultrasonic beam is presented. Measurements are performed to examine the validity of the theoretical model. This model provides a preliminary model for acoustic nonlinear microscopy.

Approximated analytical solution to an Ebola optimal control problem

NASA Astrophysics Data System (ADS)

Hincapié-Palacio, Doracelly; Ospina, Juan; Torres, Delfim F. M.

2016-11-01

An analytical expression for the optimal control of an Ebola problem is obtained. The analytical solution is found as a first-order approximation to the Pontryagin Maximum Principle via the Euler-Lagrange equation. An implementation of the method is given using the computer algebra system Maple. Our analytical solutions confirm the results recently reported in the literature using numerical methods.

The influence of wind-tunnel walls on discrete frequency noise

NASA Technical Reports Server (NTRS)

Mosher, M.

1984-01-01

This paper describes an analytical model that can be used to examine the effects of wind-tunnel walls on discrete frequency noise. First, a complete physical model of an acoustic source in a wind tunnel is described, and a simplified version is then developed. This simplified model retains the important physical processes involved, yet it is more amenable to analysis. Second, the simplified physical model is formulated as a mathematical problem. An inhomogeneous partial differential equation with mixed boundary conditions is set up and then transformed into an integral equation. The integral equation has been solved with a panel program on a computer. Preliminary results from a simple model problem will be shown and compared with the approximate analytic solution.

Note on the coefficient of variations of neuronal spike trains.

PubMed

Lengler, Johannes; Steger, Angelika

2017-08-01

It is known that many neurons in the brain show spike trains with a coefficient of variation (CV) of the interspike times of approximately 1, thus resembling the properties of Poisson spike trains. Computational studies have been able to reproduce this phenomenon. However, the underlying models were too complex to be examined analytically. In this paper, we offer a simple model that shows the same effect but is accessible to an analytic treatment. The model is a random walk model with a reflecting barrier; we give explicit formulas for the CV in the regime of excess inhibition. We also analyze the effect of probabilistic synapses in our model and show that it resembles previous findings that were obtained by simulation.

Analytical Modeling of Groundwater Seepages to St. Lucie Estuary

NASA Astrophysics Data System (ADS)

Lee, J.; Yeh, G.; Hu, G.

2008-12-01

In this paper, six analytical models describing hydraulic interaction of stream-aquifer systems were applied to St Lucie Estuary (SLE) River Estuaries. These are analytical solutions for: (1) flow from a finite aquifer to a canal, (2) flow from an infinite aquifer to a canal, (3) the linearized Laplace system in a seepage surface, (4) wave propagation in the aquifer, (5) potential flow through stratified unconfined aquifers, and (6) flow through stratified confined aquifers. Input data for analytical solutions were obtained from monitoring wells and river stages at seepage-meter sites. Four transects in the study area are available: Club Med, Harbour Ridge, Lutz/MacMillan, and Pendarvis Cove located in the St. Lucie River. The analytical models were first calibrated with seepage meter measurements and then used to estimate of groundwater discharges into St. Lucie River. From this process, analytical relationships between the seepage rate and river stages and/or groundwater tables were established to predict the seasonal and monthly variation in groundwater seepage into SLE. It was found the seepage rate estimations by analytical models agreed well with measured data for some cases but only fair for some other cases. This is not unexpected because analytical solutions have some inherently simplified assumptions, which may be more valid for some cases than the others. From analytical calculations, it is possible to predict approximate seepage rates in the study domain when the assumptions underlying these analytical models are valid. The finite and infinite aquifer models and the linearized Laplace method are good for sites Pendarvis Cove and Lutz/MacMillian, but fair for the other two sites. The wave propagation model gave very good agreement in phase but only fairly agreement in magnitude for all four sites. The stratified unconfined and confined aquifer models gave similarly good agreements with measurements at three sites but poorly at the Club Med site. None of the analytical models presented here can fit the data at this site. To give better estimates at all sites numerical modeling that couple river hydraulics and groundwater flow involving less simplifications of and assumptions for the system may have to be adapted.

Modeling direct interband tunneling. II. Lower-dimensional structures

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

Pan, Andrew, E-mail: pandrew@ucla.edu; Chui, Chi On; California NanoSystems Institute, University of California, Los Angeles, Los Angeles, California 90095

We investigate the applicability of the two-band Hamiltonian and the widely used Kane analytical formula to interband tunneling along unconfined directions in nanostructures. Through comparisons with k·p and tight-binding calculations and quantum transport simulations, we find that the primary correction is the change in effective band gap. For both constant fields and realistic tunnel field-effect transistors, dimensionally consistent band gap scaling of the Kane formula allows analytical and numerical device simulations to approximate non-equilibrium Green's function current characteristics without arbitrary fitting. This allows efficient first-order calibration of semiclassical models for interband tunneling in nanodevices.

Scale/Analytical Analyses of Freezing and Convective Melting with Internal Heat Generation

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

Ali S. Siahpush; John Crepeau; Piyush Sabharwall

2013-07-01

Using a scale/analytical analysis approach, we model phase change (melting) for pure materials which generate constant internal heat generation for small Stefan numbers (approximately one). The analysis considers conduction in the solid phase and natural convection, driven by internal heat generation, in the liquid regime. The model is applied for a constant surface temperature boundary condition where the melting temperature is greater than the surface temperature in a cylindrical geometry. The analysis also consider constant heat flux (in a cylindrical geometry).We show the time scales in which conduction and convection heat transfer dominate.

Rayleigh approximation to ground state of the Bose and Coulomb glasses

PubMed Central

Ryan, S. D.; Mityushev, V.; Vinokur, V. M.; Berlyand, L.

2015-01-01

Glasses are rigid systems in which competing interactions prevent simultaneous minimization of local energies. This leads to frustration and highly degenerate ground states the nature and properties of which are still far from being thoroughly understood. We report an analytical approach based on the method of functional equations that allows us to construct the Rayleigh approximation to the ground state of a two-dimensional (2D) random Coulomb system with logarithmic interactions. We realize a model for 2D Coulomb glass as a cylindrical type II superconductor containing randomly located columnar defects (CD) which trap superconducting vortices induced by applied magnetic field. Our findings break ground for analytical studies of glassy systems, marking an important step towards understanding their properties. PMID:25592417

Analytical probabilistic modeling of RBE-weighted dose for ion therapy.

PubMed

Wieser, H P; Hennig, P; Wahl, N; Bangert, M

2017-11-10

Particle therapy is especially prone to uncertainties. This issue is usually addressed with uncertainty quantification and minimization techniques based on scenario sampling. For proton therapy, however, it was recently shown that it is also possible to use closed-form computations based on analytical probabilistic modeling (APM) for this purpose. APM yields unique features compared to sampling-based approaches, motivating further research in this context. This paper demonstrates the application of APM for intensity-modulated carbon ion therapy to quantify the influence of setup and range uncertainties on the RBE-weighted dose. In particular, we derive analytical forms for the nonlinear computations of the expectation value and variance of the RBE-weighted dose by propagating linearly correlated Gaussian input uncertainties through a pencil beam dose calculation algorithm. Both exact and approximation formulas are presented for the expectation value and variance of the RBE-weighted dose and are subsequently studied in-depth for a one-dimensional carbon ion spread-out Bragg peak. With V and B being the number of voxels and pencil beams, respectively, the proposed approximations induce only a marginal loss of accuracy while lowering the computational complexity from order [Formula: see text] to [Formula: see text] for the expectation value and from [Formula: see text] to [Formula: see text] for the variance of the RBE-weighted dose. Moreover, we evaluated the approximated calculation of the expectation value and standard deviation of the RBE-weighted dose in combination with a probabilistic effect-based optimization on three patient cases considering carbon ions as radiation modality against sampled references. The resulting global γ-pass rates (2 mm,2%) are [Formula: see text]99.15% for the expectation value and [Formula: see text]94.95% for the standard deviation of the RBE-weighted dose, respectively. We applied the derived analytical model to carbon ion treatment planning, although the concept is in general applicable to other ion species considering a variable RBE.

Analytical probabilistic modeling of RBE-weighted dose for ion therapy

NASA Astrophysics Data System (ADS)

Wieser, H. P.; Hennig, P.; Wahl, N.; Bangert, M.

2017-12-01

Particle therapy is especially prone to uncertainties. This issue is usually addressed with uncertainty quantification and minimization techniques based on scenario sampling. For proton therapy, however, it was recently shown that it is also possible to use closed-form computations based on analytical probabilistic modeling (APM) for this purpose. APM yields unique features compared to sampling-based approaches, motivating further research in this context. This paper demonstrates the application of APM for intensity-modulated carbon ion therapy to quantify the influence of setup and range uncertainties on the RBE-weighted dose. In particular, we derive analytical forms for the nonlinear computations of the expectation value and variance of the RBE-weighted dose by propagating linearly correlated Gaussian input uncertainties through a pencil beam dose calculation algorithm. Both exact and approximation formulas are presented for the expectation value and variance of the RBE-weighted dose and are subsequently studied in-depth for a one-dimensional carbon ion spread-out Bragg peak. With V and B being the number of voxels and pencil beams, respectively, the proposed approximations induce only a marginal loss of accuracy while lowering the computational complexity from order O(V × B^2) to O(V × B) for the expectation value and from O(V × B^4) to O(V × B^2) for the variance of the RBE-weighted dose. Moreover, we evaluated the approximated calculation of the expectation value and standard deviation of the RBE-weighted dose in combination with a probabilistic effect-based optimization on three patient cases considering carbon ions as radiation modality against sampled references. The resulting global γ-pass rates (2 mm,2%) are > 99.15% for the expectation value and > 94.95% for the standard deviation of the RBE-weighted dose, respectively. We applied the derived analytical model to carbon ion treatment planning, although the concept is in general applicable to other ion species considering a variable RBE.

Semigroup theory and numerical approximation for equations in linear viscoelasticity

NASA Technical Reports Server (NTRS)

Fabiano, R. H.; Ito, K.

1990-01-01

A class of abstract integrodifferential equations used to model linear viscoelastic beams is investigated analytically, applying a Hilbert-space approach. The basic equation is rewritten as a Cauchy problem, and its well-posedness is demonstrated. Finite-dimensional subspaces of the state space and an estimate of the state operator are obtained; approximation schemes for the equations are constructed; and the convergence is proved using the Trotter-Kato theorem of linear semigroup theory. The actual convergence behavior of different approximations is demonstrated in numerical computations, and the results are presented in tables.

A study of density effects in plasmas using analytical approximations for the self-consistent potential

NASA Astrophysics Data System (ADS)

Poirier, M.

2015-06-01

Density effects in ionized matter require particular attention since they modify energies, wavefunctions and transition rates with respect to the isolated-ion situation. The approach chosen in this paper is based on the ion-sphere model involving a Thomas-Fermi-like description for free electrons, the bound electrons being described by a full quantum mechanical formalism. This permits to deal with plasmas out of thermal local equilibrium, assuming only a Maxwell distribution for free electrons. For H-like ions, such a theory provides simple and rather accurate analytical approximations for the potential created by free electrons. Emphasis is put on the plasma potential rather than on the electron density, since the energies and wavefunctions depend directly on this potential. Beyond the uniform electron gas model, temperature effects may be analyzed. In the case of H-like ions, this formalism provides analytical perturbative expressions for the energies, wavefunctions and transition rates. Explicit expressions are given in the case of maximum orbital quantum number, and compare satisfactorily with results from a direct integration of the radial Schrödinger equation. Some formulas for lower orbital quantum numbers are also proposed.

Swiss-cheese models and the Dyer-Roeder approximation

NASA Astrophysics Data System (ADS)

Fleury, Pierre

2014-06-01

In view of interpreting the cosmological observations precisely, especially when they involve narrow light beams, it is crucial to understand how light propagates in our statistically homogeneous, clumpy, Universe. Among the various approaches to tackle this issue, Swiss-cheese models propose an inhomogeneous spacetime geometry which is an exact solution of Einstein's equation, while the Dyer-Roeder approximation deals with inhomogeneity in an effective way. In this article, we demonstrate that the distance-redshift relation of a certain class of Swiss-cheese models is the same as the one predicted by the Dyer-Roeder approach, at a well-controlled level of approximation. Both methods are therefore equivalent when applied to the interpretation of, e.g., supernova obervations. The proof relies on completely analytical arguments, and is illustrated by numerical results.

Low-frequency sound propagation modeling over a locally-reacting boundary using the parabolic approximation

NASA Technical Reports Server (NTRS)

Robertson, J. S.; Siegman, W. L.; Jacobson, M. J.

1989-01-01

There is substantial interest in the analytical and numerical modeling of low-frequency, long-range atmospheric acoustic propagation. Ray-based models, because of frequency limitations, do not always give an adequate prediction of quantities such as sound pressure or intensity levels. However, the parabolic approximation method, widely used in ocean acoustics, and often more accurate than ray models for lower frequencies of interest, can be applied to acoustic propagation in the atmosphere. Modifications of an existing implicit finite-difference implementation for computing solutions to the parabolic approximation are discussed. A locally-reacting boundary is used together with a one-parameter impedance model. Intensity calculations are performed for a number of flow resistivity values in both quiescent and windy atmospheres. Variations in the value of this parameter are shown to have substantial effects on the spatial variation of the acoustic signal.

Lead Slowing-Down Spectrometry Time Spectral Analysis for Spent Fuel Assay: FY11 Status Report

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

Kulisek, Jonathan A.; Anderson, Kevin K.; Bowyer, Sonya M.

2011-09-30

Developing a method for the accurate, direct, and independent assay of the fissile isotopes in bulk materials (such as used fuel) from next-generation domestic nuclear fuel cycles is a goal of the Office of Nuclear Energy, Fuel Cycle R&D, Material Protection and Control Technology (MPACT) Campaign. To meet this goal, MPACT supports a multi-institutional collaboration, of which PNNL is a part, to study the feasibility of Lead Slowing Down Spectroscopy (LSDS). This technique is an active nondestructive assay method that has the potential to provide independent, direct measurement of Pu and U isotopic masses in used fuel with an uncertaintymore » considerably lower than the approximately 10% typical of today's confirmatory assay methods. This document is a progress report for FY2011 PNNL analysis and algorithm development. Progress made by PNNL in FY2011 continues to indicate the promise of LSDS analysis and algorithms applied to used fuel. PNNL developed an empirical model based on calibration of the LSDS to responses generated from well-characterized used fuel. The empirical model, which accounts for self-shielding effects using empirical basis vectors calculated from the singular value decomposition (SVD) of a matrix containing the true self-shielding functions of the used fuel assembly models. The potential for the direct and independent assay of the sum of the masses of 239Pu and 241Pu to within approximately 3% over a wide used fuel parameter space was demonstrated. Also, in FY2011, PNNL continued to develop an analytical model. Such efforts included the addition of six more non-fissile absorbers in the analytical shielding function and the non-uniformity of the neutron flux across the LSDS assay chamber. A hybrid analytical-empirical approach was developed to determine the mass of total Pu (sum of the masses of 239Pu, 240Pu, and 241Pu), which is an important quantity in safeguards. Results using this hybrid method were of approximately the same accuracy as the pure empirical approach. In addition, total Pu with much better accuracy with the hybrid approach than the pure analytical approach. In FY2012, PNNL will continue efforts to optimize its empirical model and minimize its reliance on calibration data. In addition, PNNL will continue to develop an analytical model, considering effects such as neutron-scattering in the fuel and cladding, as well as neutrons streaming through gaps between fuel pins in the fuel assembly.« less

Thermodynamics of Gas Turbine Cycles with Analytic Derivatives in OpenMDAO

NASA Technical Reports Server (NTRS)

Gray, Justin; Chin, Jeffrey; Hearn, Tristan; Hendricks, Eric; Lavelle, Thomas; Martins, Joaquim R. R. A.

2016-01-01

A new equilibrium thermodynamics analysis tool was built based on the CEA method using the OpenMDAO framework. The new tool provides forward and adjoint analytic derivatives for use with gradient based optimization algorithms. The new tool was validated against the original CEA code to ensure an accurate analysis and the analytic derivatives were validated against finite-difference approximations. Performance comparisons between analytic and finite difference methods showed a significant speed advantage for the analytic methods. To further test the new analysis tool, a sample optimization was performed to find the optimal air-fuel equivalence ratio, , maximizing combustion temperature for a range of different pressures. Collectively, the results demonstrate the viability of the new tool to serve as the thermodynamic backbone for future work on a full propulsion modeling tool.

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.

The Surface Density Distribution in the Solar Nebula

NASA Technical Reports Server (NTRS)

Davis, Sanford S.

2004-01-01

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

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.

Calculated and measured fields in superferric wiggler magnets

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

Blum, E.B.; Solomon, L.

1995-02-01

Although Klaus Halbach is widely known and appreciated as the originator of the computer program POISSON for electromagnetic field calculation, Klaus has always believed that analytical methods can give much more insight into the performance of a magnet than numerical simulation. Analytical approximations readily show how the different aspects of a magnet`s design such as pole dimensions, current, and coil configuration contribute to the performance. These methods yield accuracies of better than 10%. Analytical methods should therefore be used when conceptualizing a magnet design. Computer analysis can then be used for refinement. A simple model is presented for the peakmore » on-axis field of an electro-magnetic wiggler with iron poles and superconducting coils. The model is applied to the radiator section of the superconducting wiggler for the BNL Harmonic Generation Free Electron Laser. The predictions of the model are compared to the measured field and the results from POISSON.« less

On the analytical modeling of the nonlinear vibrations of pretensioned space structures

NASA Technical Reports Server (NTRS)

Housner, J. M.; Belvin, W. K.

1983-01-01

Pretensioned structures are receiving considerable attention as candidate large space structures. A typical example is a hoop-column antenna. The large number of preloaded members requires efficient analytical methods for concept validation and design. Validation through analyses is especially important since ground testing may be limited due to gravity effects and structural size. The present investigation has the objective to present an examination of the analytical modeling of pretensioned members undergoing nonlinear vibrations. Two approximate nonlinear analysis are developed to model general structural arrangements which include beam-columns and pretensioned cables attached to a common nucleus, such as may occur at a joint of a pretensioned structure. Attention is given to structures undergoing nonlinear steady-state oscillations due to sinusoidal excitation forces. Three analyses, linear, quasi-linear, and nonlinear are conducted and applied to study the response of a relatively simple cable stiffened structure.

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.

Mathematical analysis of the boundary-integral based electrostatics estimation approximation for molecular solvation: exact results for spherical inclusions.

PubMed

Bardhan, Jaydeep P; Knepley, Matthew G

2011-09-28

We analyze the mathematically rigorous BIBEE (boundary-integral based electrostatics estimation) approximation of the mixed-dielectric continuum model of molecular electrostatics, using the analytically solvable case of a spherical solute containing an arbitrary charge distribution. Our analysis, which builds on Kirkwood's solution using spherical harmonics, clarifies important aspects of the approximation and its relationship to generalized Born models. First, our results suggest a new perspective for analyzing fast electrostatic models: the separation of variables between material properties (the dielectric constants) and geometry (the solute dielectric boundary and charge distribution). Second, we find that the eigenfunctions of the reaction-potential operator are exactly preserved in the BIBEE model for the sphere, which supports the use of this approximation for analyzing charge-charge interactions in molecular binding. Third, a comparison of BIBEE to the recent GBε theory suggests a modified BIBEE model capable of predicting electrostatic solvation free energies to within 4% of a full numerical Poisson calculation. This modified model leads to a projection-framework understanding of BIBEE and suggests opportunities for future improvements. © 2011 American Institute of Physics

Applicability of Kinematic and Diffusive models for mud-flows: a steady state analysis

NASA Astrophysics Data System (ADS)

Di Cristo, Cristiana; Iervolino, Michele; Vacca, Andrea

2018-04-01

The paper investigates the applicability of Kinematic and Diffusive Wave models for mud-flows with a power-law shear-thinning rheology. In analogy with a well-known approach for turbulent clear-water flows, the study compares the steady flow depth profiles predicted by approximated models with those of the Full Dynamic Wave one. For all the models and assuming an infinitely wide channel, the analytical solution of the flow depth profiles, in terms of hypergeometric functions, is derived. The accuracy of the approximated models is assessed by computing the average, along the channel length, of the errors, for several values of the Froude and kinematic wave numbers. Assuming the threshold value of the error equal to 5%, the applicability conditions of the two approximations have been individuated for several values of the power-law exponent, showing a crucial role of the rheology. The comparison with the clear-water results indicates that applicability criteria for clear-water flows do not apply to shear-thinning fluids, potentially leading to an incorrect use of approximated models if the rheology is not properly accounted for.

Geometric factor and influence of sensors in the establishment of a resistivity-moisture relation in soil samples

NASA Astrophysics Data System (ADS)

López-Sánchez, M.; Mansilla-Plaza, L.; Sánchez-de-laOrden, M.

2017-10-01

Prior to field scale research, soil samples are analysed on a laboratory scale for electrical resistivity calibrations. Currently, there are a variety of field instruments to estimate the water content in soils using different physical phenomena. These instruments can be used to develop moisture-resistivity relationships on the same soil samples. This assures that measurements are performed on the same material and under the same conditions (e.g., humidity and temperature). A geometric factor is applied to the location of electrodes, in order to calculate the apparent electrical resistivity of the laboratory test cells. This geometric factor can be determined in three different ways: by means of the use of an analytical approximation, laboratory trials (experimental approximation), or by the analysis of a numerical model. The first case, the analytical approximation, is not appropriate for complex cells or arrays. And both, the experimental and numerical approximation can lead to inaccurate results. Therefore, we propose a novel approach to obtain a compromise solution between both techniques, providing a more precise determination of the geometrical factor.

A generic analytical foot rollover model for predicting translational ankle kinematics in gait simulation studies.

PubMed

Ren, Lei; Howard, David; Ren, Luquan; Nester, Chris; Tian, Limei

2010-01-19

The objective of this paper is to develop an analytical framework to representing the ankle-foot kinematics by modelling the foot as a rollover rocker, which cannot only be used as a generic tool for general gait simulation but also allows for case-specific modelling if required. Previously, the rollover models used in gait simulation have often been based on specific functions that have usually been of a simple form. In contrast, the analytical model described here is in a general form that the effective foot rollover shape can be represented by any polar function rho=rho(phi). Furthermore, a normalized generic foot rollover model has been established based on a normative foot rollover shape dataset of 12 normal healthy subjects. To evaluate model accuracy, the predicted ankle motions and the centre of pressure (CoP) were compared with measurement data for both subject-specific and general cases. The results demonstrated that the ankle joint motions in both vertical and horizontal directions (relative RMSE approximately 10%) and CoP (relative RMSE approximately 15% for most of the subjects) are accurately predicted over most of the stance phase (from 10% to 90% of stance). However, we found that the foot cannot be very accurately represented by a rollover model just after heel strike (HS) and just before toe off (TO), probably due to shear deformation of foot plantar tissues (ankle motion can occur without any foot rotation). The proposed foot rollover model can be used in both inverse and forward dynamics gait simulation studies and may also find applications in rehabilitation engineering. Copyright 2009 Elsevier Ltd. All rights reserved.

Pseudo-Boltzmann model for modeling the junctionless transistors

NASA Astrophysics Data System (ADS)

Avila-Herrera, F.; Cerdeira, A.; Roldan, J. B.; Sánchez-Moreno, P.; Tienda-Luna, I. M.; Iñiguez, B.

2014-05-01

Calculation of the carrier concentrations in semiconductors using the Fermi-Dirac integral requires complex numerical calculations; in this context, practically all analytical device models are based on Boltzmann statistics, even though it is known that it leads to an over-estimation of carriers densities for high doping concentrations. In this paper, a new approximation to Fermi-Dirac integral, called Pseudo-Boltzmann model, is presented for modeling junctionless transistors with high doping concentrations.

Double power series method for approximating cosmological perturbations

NASA Astrophysics Data System (ADS)

Wren, Andrew J.; Malik, Karim A.

2017-04-01

We introduce a double power series method for finding approximate analytical solutions for systems of differential equations commonly found in cosmological perturbation theory. The method was set out, in a noncosmological context, by Feshchenko, Shkil' and Nikolenko (FSN) in 1966, and is applicable to cases where perturbations are on subhorizon scales. The FSN method is essentially an extension of the well known Wentzel-Kramers-Brillouin (WKB) method for finding approximate analytical solutions for ordinary differential equations. The FSN method we use is applicable well beyond perturbation theory to solve systems of ordinary differential equations, linear in the derivatives, that also depend on a small parameter, which here we take to be related to the inverse wave-number. We use the FSN method to find new approximate oscillating solutions in linear order cosmological perturbation theory for a flat radiation-matter universe. Together with this model's well-known growing and decaying Mészáros solutions, these oscillating modes provide a complete set of subhorizon approximations for the metric potential, radiation and matter perturbations. Comparison with numerical solutions of the perturbation equations shows that our approximations can be made accurate to within a typical error of 1%, or better. We also set out a heuristic method for error estimation. A Mathematica notebook which implements the double power series method is made available online.

Retention prediction and separation optimization under multilinear gradient elution in liquid chromatography with Microsoft Excel macros.

PubMed

Fasoula, S; Zisi, Ch; Gika, H; Pappa-Louisi, A; Nikitas, P

2015-05-22

A package of Excel VBA macros have been developed for modeling multilinear gradient retention data obtained in single or double gradient elution mode by changing organic modifier(s) content and/or eluent pH. For this purpose, ten chromatographic models were used and four methods were adopted for their application. The methods were based on (a) the analytical expression of the retention time, provided that this expression is available, (b) the retention times estimated using the Nikitas-Pappa approach, (c) the stepwise approximation, and (d) a simple numerical approximation involving the trapezoid rule for integration of the fundamental equation for gradient elution. For all these methods, Excel VBA macros have been written and implemented using two different platforms; the fitting and the optimization platform. The fitting platform calculates not only the adjustable parameters of the chromatographic models, but also the significance of these parameters and furthermore predicts the analyte elution times. The optimization platform determines the gradient conditions that lead to the optimum separation of a mixture of analytes by using the Solver evolutionary mode, provided that proper constraints are set in order to obtain the optimum gradient profile in the minimum gradient time. The performance of the two platforms was tested using experimental and artificial data. It was found that using the proposed spreadsheets, fitting, prediction, and optimization can be performed easily and effectively under all conditions. Overall, the best performance is exhibited by the analytical and Nikitas-Pappa's methods, although the former cannot be used under all circumstances. Copyright © 2015 Elsevier B.V. All rights reserved.

Validity of the Born approximation for beyond Gaussian weak lensing observables

DOE PAGES

Petri, Andrea; Haiman, Zoltan; May, Morgan

2017-06-06

Accurate forward modeling of weak lensing (WL) observables from cosmological parameters is necessary for upcoming galaxy surveys. Because WL probes structures in the nonlinear regime, analytical forward modeling is very challenging, if not impossible. Numerical simulations of WL features rely on ray tracing through the outputs of N-body simulations, which requires knowledge of the gravitational potential and accurate solvers for light ray trajectories. A less accurate procedure, based on the Born approximation, only requires knowledge of the density field, and can be implemented more efficiently and at a lower computational cost. In this work, we use simulations to show thatmore » deviations of the Born-approximated convergence power spectrum, skewness and kurtosis from their fully ray-traced counterparts are consistent with the smallest nontrivial O(Φ 3) post-Born corrections (so-called geodesic and lens-lens terms). Our results imply a cancellation among the larger O(Φ 4) (and higher order) terms, consistent with previous analytic work. We also find that cosmological parameter bias induced by the Born-approximated power spectrum is negligible even for a LSST-like survey, once galaxy shape noise is considered. When considering higher order statistics such as the κ skewness and kurtosis, however, we find significant bias of up to 2.5σ. Using the LensTools software suite, we show that the Born approximation saves a factor of 4 in computing time with respect to the full ray tracing in reconstructing the convergence.« less

Validity of the Born approximation for beyond Gaussian weak lensing observables

NASA Astrophysics Data System (ADS)

Petri, Andrea; Haiman, Zoltán; May, Morgan

2017-06-01

Accurate forward modeling of weak lensing (WL) observables from cosmological parameters is necessary for upcoming galaxy surveys. Because WL probes structures in the nonlinear regime, analytical forward modeling is very challenging, if not impossible. Numerical simulations of WL features rely on ray tracing through the outputs of N -body simulations, which requires knowledge of the gravitational potential and accurate solvers for light ray trajectories. A less accurate procedure, based on the Born approximation, only requires knowledge of the density field, and can be implemented more efficiently and at a lower computational cost. In this work, we use simulations to show that deviations of the Born-approximated convergence power spectrum, skewness and kurtosis from their fully ray-traced counterparts are consistent with the smallest nontrivial O (Φ3) post-Born corrections (so-called geodesic and lens-lens terms). Our results imply a cancellation among the larger O (Φ4) (and higher order) terms, consistent with previous analytic work. We also find that cosmological parameter bias induced by the Born-approximated power spectrum is negligible even for a LSST-like survey, once galaxy shape noise is considered. When considering higher order statistics such as the κ skewness and kurtosis, however, we find significant bias of up to 2.5 σ . Using the LensTools software suite, we show that the Born approximation saves a factor of 4 in computing time with respect to the full ray tracing in reconstructing the convergence.

Experimental investigation and numerical simulation of 3He gas diffusion in simple geometries: implications for analytical models of 3He MR lung morphometry.

PubMed

Parra-Robles, J; Ajraoui, S; Deppe, M H; Parnell, S R; Wild, J M

2010-06-01

Models of lung acinar geometry have been proposed to analytically describe the diffusion of (3)He in the lung (as measured with pulsed gradient spin echo (PGSE) methods) as a possible means of characterizing lung microstructure from measurement of the (3)He ADC. In this work, major limitations in these analytical models are highlighted in simple diffusion weighted experiments with (3)He in cylindrical models of known geometry. The findings are substantiated with numerical simulations based on the same geometry using finite difference representation of the Bloch-Torrey equation. The validity of the existing "cylinder model" is discussed in terms of the physical diffusion regimes experienced and the basic reliance of the cylinder model and other ADC-based approaches on a Gaussian diffusion behaviour is highlighted. The results presented here demonstrate that physical assumptions of the cylinder model are not valid for large diffusion gradient strengths (above approximately 15 mT/m), which are commonly used for (3)He ADC measurements in human lungs. (c) 2010 Elsevier Inc. All rights reserved.

A Bayesian Hierarchical Model for Glacial Dynamics Based on the Shallow Ice Approximation and its Evaluation Using Analytical Solutions

NASA Astrophysics Data System (ADS)

Gopalan, Giri; Hrafnkelsson, Birgir; Aðalgeirsdóttir, Guðfinna; Jarosch, Alexander H.; Pálsson, Finnur

2018-03-01

Bayesian hierarchical modeling can assist the study of glacial dynamics and ice flow properties. This approach will allow glaciologists to make fully probabilistic predictions for the thickness of a glacier at unobserved spatio-temporal coordinates, and it will also allow for the derivation of posterior probability distributions for key physical parameters such as ice viscosity and basal sliding. The goal of this paper is to develop a proof of concept for a Bayesian hierarchical model constructed, which uses exact analytical solutions for the shallow ice approximation (SIA) introduced by Bueler et al. (2005). A suite of test simulations utilizing these exact solutions suggests that this approach is able to adequately model numerical errors and produce useful physical parameter posterior distributions and predictions. A byproduct of the development of the Bayesian hierarchical model is the derivation of a novel finite difference method for solving the SIA partial differential equation (PDE). An additional novelty of this work is the correction of numerical errors induced through a numerical solution using a statistical model. This error correcting process models numerical errors that accumulate forward in time and spatial variation of numerical errors between the dome, interior, and margin of a glacier.

Limitations of bootstrap current models

DOE PAGES

Belli, Emily A.; Candy, Jefferey M.; Meneghini, Orso; ...

2014-03-27

We assess the accuracy and limitations of two analytic models of the tokamak bootstrap current: (1) the well-known Sauter model and (2) a recent modification of the Sauter model by Koh et al. For this study, we use simulations from the first-principles kinetic code NEO as the baseline to which the models are compared. Tests are performed using both theoretical parameter scans as well as core- to-edge scans of real DIII-D and NSTX plasma profiles. The effects of extreme aspect ratio, large impurity fraction, energetic particles, and high collisionality are studied. In particular, the error in neglecting cross-species collisional couplingmore » – an approximation inherent to both analytic models – is quantified. Moreover, the implications of the corrections from kinetic NEO simulations on MHD equilibrium reconstructions is studied via integrated modeling with kinetic EFIT.« less

Approximate solution to the Callan-Giddings-Harvey-Strominger field equations for two-dimensional evaporating black holes

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

Ori, Amos

2010-11-15

Callan, Giddings, Harvey, and Strominger (CGHS) previously introduced a two-dimensional semiclassical model of gravity coupled to a dilaton and to matter fields. Their model yields a system of field equations which may describe the formation of a black hole in gravitational collapse as well as its subsequent evaporation. Here we present an approximate analytical solution to the semiclassical CGHS field equations. This solution is constructed using the recently introduced formalism of flux-conserving hyperbolic systems. We also explore the asymptotic behavior at the horizon of the evaporating black hole.

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.

Asymptotically inspired moment-closure approximation for adaptive networks

NASA Astrophysics Data System (ADS)

Shkarayev, Maxim; Shaw, Leah

2012-02-01

Adaptive social networks, in which nodes and network structure co-evolve, are often described using a mean-field system of equations for the density of node and link types. These equations constitute an open system due to dependence on higher order topological structures. We propose a moment-closure approximation based on the analytical description of the system in an asymptotic regime. We apply the proposed approach to two examples of adaptive networks: recruitment to a cause model and epidemic spread model. We show a good agreement between the improved mean-field prediction and simulations of the full network system.

Asymptotically inspired moment-closure approximation for adaptive networks

NASA Astrophysics Data System (ADS)

Shkarayev, Maxim

2013-03-01

Dynamics of adaptive social networks, in which nodes and network structure co-evolve, are often described using a mean-field system of equations for the density of node and link types. These equations constitute an open system due to dependence on higher order topological structures. We propose a systematic approach to moment closure approximation based on the analytical description of the system in an asymptotic regime. We apply the proposed approach to two examples of adaptive networks: recruitment to a cause model and adaptive epidemic model. We show a good agreement between the mean-field prediction and simulations of the full network system.

One-dimensional model and solutions for creeping gas flows in the approximation of uniform pressure

NASA Astrophysics Data System (ADS)

Vedernikov, A.; Balapanov, D.

2016-11-01

A model, along with analytical and numerical solutions, is presented to describe a wide variety of one-dimensional slow flows of compressible heat-conductive fluids. The model is based on the approximation of uniform pressure valid for the flows, in which the sound propagation time is much shorter than the duration of any meaningful density variation in the system. The energy balance is described by the heat equation that is solved independently. This approach enables the explicit solution for the fluid velocity to be obtained. Interfacial and volumetric heat and mass sources as well as boundary motion are considered as possible sources of density variation in the fluid. A set of particular tasks is analyzed for different motion sources in planar, axial, and central symmetries in the quasistationary limit of heat conduction (i.e., for large Fourier number). The analytical solutions are in excellent agreement with corresponding numerical solutions of the whole system of the Navier-Stokes equations. This work deals with the ideal gas. The approach is also valid for other equations of state.

Reflection and emission models for deserts derived from Nimbus-7 ERB scanner measurements

NASA Technical Reports Server (NTRS)

Staylor, W. F.; Suttles, J. T.

1986-01-01

Broadband shortwave and longwave radiance measurements obtained from the Nimbus-7 Earth Radiation Budget scanner were used to develop reflectance and emittance models for the Sahara-Arabian, Gibson, and Saudi Deserts. The models were established by fitting the satellite measurements to analytic functions. For the shortwave, the model function is based on an approximate solution to the radiative transfer equation. The bidirectional-reflectance function was obtained from a single-scattering approximation with a Rayleigh-like phase function. The directional-reflectance model followed from integration of the bidirectional model and is a function of the sum and product of cosine solar and viewing zenith angles, thus satisfying reciprocity between these angles. The emittance model was based on a simple power-law of cosine viewing zenith angle.

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).

Generalized Fractional Derivative Anisotropic Viscoelastic Characterization.

PubMed

Hilton, Harry H

2012-01-18

Isotropic linear and nonlinear fractional derivative constitutive relations are formulated and examined in terms of many parameter generalized Kelvin models and are analytically extended to cover general anisotropic homogeneous or non-homogeneous as well as functionally graded viscoelastic material behavior. Equivalent integral constitutive relations, which are computationally more powerful, are derived from fractional differential ones and the associated anisotropic temperature-moisture-degree-of-cure shift functions and reduced times are established. Approximate Fourier transform inversions for fractional derivative relations are formulated and their accuracy is evaluated. The efficacy of integer and fractional derivative constitutive relations is compared and the preferential use of either characterization in analyzing isotropic and anisotropic real materials must be examined on a case-by-case basis. Approximate protocols for curve fitting analytical fractional derivative results to experimental data are formulated and evaluated.

Rayleigh approximation to ground state of the Bose and Coulomb glasses

DOE PAGES

Ryan, S. D.; Mityushev, V.; Vinokur, V. M.; ...

2015-01-16

Glasses are rigid systems in which competing interactions prevent simultaneous minimization of local energies. This leads to frustration and highly degenerate ground states the nature and properties of which are still far from being thoroughly understood. We report an analytical approach based on the method of functional equations that allows us to construct the Rayleigh approximation to the ground state of a two-dimensional (2D) random Coulomb system with logarithmic interactions. We realize a model for 2D Coulomb glass as a cylindrical type II superconductor containing randomly located columnar defects (CD) which trap superconducting vortices induced by applied magnetic field. Ourmore » findings break ground for analytical studies of glassy systems, marking an important step towards understanding their properties.« less

Analytical approximation for the Einstein-dilaton-Gauss-Bonnet black hole metric

NASA Astrophysics Data System (ADS)

Kokkotas, K. D.; Konoplya, R. A.; Zhidenko, A.

2017-09-01

We construct an analytical approximation for the numerical black hole metric of P. Kanti et al. [Phys. Rev. D 54, 5049 (1996), 10.1103/PhysRevD.54.5049] in the four-dimensional Einstein-dilaton-Gauss-Bonnet (EdGB) theory. The continued fraction expansion in terms of a compactified radial coordinate, used here, converges slowly when the dilaton coupling approaches its extremal values, but for a black hole far from the extremal state, the analytical formula has a maximal relative error of a fraction of one percent already within the third order of the continued fraction expansion. The suggested analytical representation of the numerical black hole metric is relatively compact and a good approximation in the whole space outside the black hole event horizon. Therefore, it can serve in the same way as an exact solution when analyzing particles' motion, perturbations, quasinormal modes, Hawking radiation, accreting disks, and many other problems in the vicinity of a black hole. In addition, we construct the approximate analytical expression for the dilaton field.

Development of models of the magnetorheological fluid damper

NASA Astrophysics Data System (ADS)

Kazakov, Yu. B.; Morozov, N. A.; Nesterov, S. A.

2017-06-01

The algorithm for analytical calculation of a power characteristic of magnetorheological (MR) dampers taking into account the rheological properties of MR fluid is considered. The nonlinear magnetorheological characteristics are represented by piecewise linear approximation to MR fluid areas with different viscosities. The extended calculated power characteristics of a MR damper are received and they coincide with actual results. The finite element model of a MR damper is developed; it allows carrying out the analysis of a MR damper taking into account the mutual influence of electromagnetic, hydrodynamic and thermal fields. The results of finite element simulation coincide with analytical solutions that allows using them for design development of a MR damper.

A Machine-Learning-Driven Sky Model.

PubMed

Satylmys, Pynar; Bashford-Rogers, Thomas; Chalmers, Alan; Debattista, Kurt

2017-01-01

Sky illumination is responsible for much of the lighting in a virtual environment. A machine-learning-based approach can compactly represent sky illumination from both existing analytic sky models and from captured environment maps. The proposed approach can approximate the captured lighting at a significantly reduced memory cost and enable smooth transitions of sky lighting to be created from a small set of environment maps captured at discrete times of day. The author's results demonstrate accuracy close to the ground truth for both analytical and capture-based methods. The approach has a low runtime overhead, so it can be used as a generic approach for both offline and real-time applications.

Clustering coefficients of protein-protein interaction networks

NASA Astrophysics Data System (ADS)

Miller, Gerald A.; Shi, Yi Y.; Qian, Hong; Bomsztyk, Karol

2007-05-01

The properties of certain networks are determined by hidden variables that are not explicitly measured. The conditional probability (propagator) that a vertex with a given value of the hidden variable is connected to k other vertices determines all measurable properties. We study hidden variable models and find an averaging approximation that enables us to obtain a general analytical result for the propagator. Analytic results showing the validity of the approximation are obtained. We apply hidden variable models to protein-protein interaction networks (PINs) in which the hidden variable is the association free energy, determined by distributions that depend on biochemistry and evolution. We compute degree distributions as well as clustering coefficients of several PINs of different species; good agreement with measured data is obtained. For the human interactome two different parameter sets give the same degree distributions, but the computed clustering coefficients differ by a factor of about 2. This shows that degree distributions are not sufficient to determine the properties of PINs.

Extended adiabatic blast waves and a model of the soft X-ray background. [interstellar matter

NASA Technical Reports Server (NTRS)

Cox, D. P.; Anderson, P. R.

1981-01-01

An analytical approximation is generated which follows the development of an adiabatic spherical blast wave in a homogeneous ambient medium of finite pressure. An analytical approximation is also presented for the electron temperature distribution resulting from coulomb collisional heating. The dynamical, thermal, ionization, and spectral structures are calculated for blast waves of energy E sub 0 = 5 x 10 to the 50th power ergs in a hot low-density interstellar environment. A formula is presented for estimating the luminosity evolution of such explosions. The B and C bands of the soft X-ray background, it is shown, are reproduced by such a model explosion if the ambient density is about .000004 cm, the blast radius is roughly 100 pc, and the solar system is located inside the shocked region. Evolution in a pre-existing cavity with a strong density gradient may, it is suggested, remove both the M band and OVI discrepancies.

Polymers at interfaces and in colloidal dispersions.

PubMed

Fleer, Gerard J

2010-09-15

This review is an extended version of the Overbeek lecture 2009, given at the occasion of the 23rd Conference of ECIS (European Colloid and Interface Society) in Antalya, where I received the fifth Overbeek Gold Medal awarded by ECIS. I first summarize the basics of numerical SF-SCF: the Scheutjens-Fleer version of Self-Consistent-Field theory for inhomogeneous systems, including polymer adsorption and depletion. The conformational statistics are taken from the (non-SCF) DiMarzio-Rubin lattice model for homopolymer adsorption, which enumerates the conformational details exactly by a discrete propagator for the endpoint distribution but does not account for polymer-solvent interaction and for the volume-filling constraint. SF-SCF corrects for this by adjusting the field such that it becomes self-consistent. The model can be generalized to more complex systems: polydispersity, brushes, random and block copolymers, polyelectrolytes, branching, surfactants, micelles, membranes, vesicles, wetting, etc. On a mean-field level the results are exact; the disadvantage is that only numerical data are obtained. Extensions to excluded-volume polymers are in progress. Analytical approximations for simple systems are based upon solving the Edwards diffusion equation. This equation is the continuum variant of the lattice propagator, but ignores the finite segment size (analogous to the Poisson-Boltzmann equation without a Stern layer). By using the discrete propagator for segments next to the surface as the boundary condition in the continuum model, the finite segment size can be introduced into the continuum description, like the ion size in the Stern-Poisson-Boltzmann model. In most cases a ground-state approximation is needed to find analytical solutions. In this way realistic analytical approximations for simple cases can be found, including depletion effects that occur in mixtures of colloids plus non-adsorbing polymers. In the final part of this review I discuss a generalization of the free-volume theory (FVT) for the phase behavior of colloids and non-adsorbing polymer. In FVT the polymer is considered to be ideal: the osmotic pressure Pi follows the Van 't Hoff law, the depletion thickness delta equals the radius of gyration. This restricts the validity of FVT to the so-called colloid limit (polymer much smaller than the colloids). We have been able to find simple analytical approximations for Pi and delta which account for non-ideality and include established results for the semidilute limit. So we could generalize FVT to GFVT, and can now also describe the so-called protein limit (polymer larger than the 'protein-like' colloids), where the binodal polymer concentrations scale in a simple way with the polymer/colloid size ratio. For an intermediate case (polymer size approximately colloid size) we could give a quantitative description of careful experimental data. Copyright 2010 Elsevier B.V. All rights reserved.

Mathematical modeling of damage in unidirectional composites

NASA Technical Reports Server (NTRS)

Goree, J. G.; Dharani, L. R.; Jones, W. F.

1981-01-01

A review of some approximate analytical models for damaged, fiber reinforced composite materials is presented. Using the classical shear lag stress displacement assumption, solutions are presented for a unidirectional laminate containing a notch, a rectangular cut-out, and a circular hole. The models account for longitudinal matrix yielding and splitting as well as transverse matrix yielding and fiber breakage. The constraining influence of a cover sheet on the unidirectional laminate is also modeled.

One- and Two-Equation Models to Simulate Ion Transport in Charged Porous Electrodes

DOE PAGES

Gabitto, Jorge; Tsouris, Costas

2018-01-19

Energy storage in porous capacitor materials, capacitive deionization (CDI) for water desalination, capacitive energy generation, geophysical applications, and removal of heavy ions from wastewater streams are some examples of processes where understanding of ionic transport processes in charged porous media is very important. In this work, one- and two-equation models are derived to simulate ionic transport processes in heterogeneous porous media comprising two different pore sizes. It is based on a theory for capacitive charging by ideally polarizable porous electrodes without Faradaic reactions or specific adsorption of ions. A two-step volume averaging technique is used to derive the averaged transportmore » equations for multi-ionic systems without any further assumptions, such as thin electrical double layers or Donnan equilibrium. A comparison between both models is presented. The effective transport parameters for isotropic porous media are calculated by solving the corresponding closure problems. An approximate analytical procedure is proposed to solve the closure problems. Numerical and theoretical calculations show that the approximate analytical procedure yields adequate solutions. Lastly, a theoretical analysis shows that the value of interphase pseudo-transport coefficients determines which model to use.« less

One- and Two-Equation Models to Simulate Ion Transport in Charged Porous Electrodes

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

Gabitto, Jorge; Tsouris, Costas

Energy storage in porous capacitor materials, capacitive deionization (CDI) for water desalination, capacitive energy generation, geophysical applications, and removal of heavy ions from wastewater streams are some examples of processes where understanding of ionic transport processes in charged porous media is very important. In this work, one- and two-equation models are derived to simulate ionic transport processes in heterogeneous porous media comprising two different pore sizes. It is based on a theory for capacitive charging by ideally polarizable porous electrodes without Faradaic reactions or specific adsorption of ions. A two-step volume averaging technique is used to derive the averaged transportmore » equations for multi-ionic systems without any further assumptions, such as thin electrical double layers or Donnan equilibrium. A comparison between both models is presented. The effective transport parameters for isotropic porous media are calculated by solving the corresponding closure problems. An approximate analytical procedure is proposed to solve the closure problems. Numerical and theoretical calculations show that the approximate analytical procedure yields adequate solutions. Lastly, a theoretical analysis shows that the value of interphase pseudo-transport coefficients determines which model to use.« 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.

Modeling systematic errors: polychromatic sources of Beer-Lambert deviations in HPLC/UV and nonchromatographic spectrophotometric assays.

PubMed

Galli, C

2001-07-01

It is well established that the use of polychromatic radiation in spectrophotometric assays leads to excursions from the Beer-Lambert limit. This Note models the resulting systematic error as a function of assay spectral width, slope of molecular extinction coefficient, and analyte concentration. The theoretical calculations are compared with recent experimental results; a parameter is introduced which can be used to estimate the magnitude of the systematic error in both chromatographic and nonchromatographic spectrophotometric assays. It is important to realize that the polychromatic radiation employed in common laboratory equipment can yield assay errors up to approximately 4%, even at absorption levels generally considered 'safe' (i.e. absorption <1). Thus careful consideration of instrumental spectral width, analyte concentration, and slope of molecular extinction coefficient is required to ensure robust analytical methods.

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.

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.

Mean-field approximation for the Sznajd model in complex networks

NASA Astrophysics Data System (ADS)

Araújo, Maycon S.; Vannucchi, Fabio S.; Timpanaro, André M.; Prado, Carmen P. C.

2015-02-01

This paper studies the Sznajd model for opinion formation in a population connected through a general network. A master equation describing the time evolution of opinions is presented and solved in a mean-field approximation. Although quite simple, this approximation allows us to capture the most important features regarding the steady states of the model. When spontaneous opinion changes are included, a discontinuous transition from consensus to polarization can be found as the rate of spontaneous change is increased. In this case we show that a hybrid mean-field approach including interactions between second nearest neighbors is necessary to estimate correctly the critical point of the transition. The analytical prediction of the critical point is also compared with numerical simulations in a wide variety of networks, in particular Barabási-Albert networks, finding reasonable agreement despite the strong approximations involved. The same hybrid approach that made it possible to deal with second-order neighbors could just as well be adapted to treat other problems such as epidemic spreading or predator-prey systems.

Modeling Kelvin Wave Cascades in Superfluid Helium

NASA Astrophysics Data System (ADS)

Boffetta, G.; Celani, A.; Dezzani, D.; Laurie, J.; Nazarenko, S.

2009-09-01

We study two different types of simplified models for Kelvin wave turbulence on quantized vortex lines in superfluids near zero temperature. Our first model is obtained from a truncated expansion of the Local Induction Approximation (Truncated-LIA) and it is shown to possess the same scalings and the essential behaviour as the full Biot-Savart model, being much simpler than the later and, therefore, more amenable to theoretical and numerical investigations. The Truncated-LIA model supports six-wave interactions and dual cascades, which are clearly demonstrated via the direct numerical simulation of this model in the present paper. In particular, our simulations confirm presence of the weak turbulence regime and the theoretically predicted spectra for the direct energy cascade and the inverse wave action cascade. The second type of model we study, the Differential Approximation Model (DAM), takes a further drastic simplification by assuming locality of interactions in k-space via using a differential closure that preserves the main scalings of the Kelvin wave dynamics. DAMs are even more amenable to study and they form a useful tool by providing simple analytical solutions in the cases when extra physical effects are present, e.g. forcing by reconnections, friction dissipation and phonon radiation. We study these models numerically and test their theoretical predictions, in particular the formation of the stationary spectra, and closeness of numerics for the higher-order DAM to the analytical predictions for the lower-order DAM.

SOLUTIONS APPROXIMATING SOLUTE TRANSPORT IN A LEAKY AQUIFER RECEIVING WASTEWATER INJECTION

EPA Science Inventory

A mathematical model amenable to analytical solution techniques is developed for the investigation of contaminant transport from an injection well into a leaky aquifer system, which comprises a pumped and an unpumped aquifer connected to each other by an aquitard. A steady state ...

Review and assessment of the HOST turbine heat transfer program

NASA Technical Reports Server (NTRS)

Gladden, Herbert J.

1988-01-01

The objectives of the HOST Turbine Heat Transfer subproject were to obtain a better understanding of the physics of the aerothermodynamic phenomena occurring in high-performance gas turbine engines and to assess and improve the analytical methods used to predict the fluid dynamics and heat transfer phenomena. At the time the HOST project was initiated, an across-the-board improvement in turbine design technology was needed. Therefore, a building-block approach was utilized, with research ranging from the study of fundamental phenomena and analytical modeling to experiments in simulated real-engine environments. Experimental research accounted for 75 percent of the project, and analytical efforts accounted for approximately 25 percent. Extensive experimental datasets were created depicting the three-dimensional flow field, high free-stream turbulence, boundary-layer transition, blade tip region heat transfer, film cooling effects in a simulated engine environment, rough-wall cooling enhancement in a rotating passage, and rotor-stator interaction effects. In addition, analytical modeling of these phenomena was initiated using boundary-layer assumptions as well as Navier-Stokes solutions.

Analytical and numerical study of the electro-osmotic annular flow of viscoelastic fluids.

PubMed

Ferrás, L L; Afonso, A M; Alves, M A; Nóbrega, J M; Pinho, F T

2014-04-15

In this work we present semi-analytical solutions for the electro-osmotic annular flow of viscoelastic fluids modeled by the Linear and Exponential PTT models. The viscoelastic fluid flows in the axial direction between two concentric cylinders under the combined influences of electrokinetic and pressure forcings. The analysis invokes the Debye-Hückel approximation and includes the limit case of pure electro-osmotic flow. The solution is valid for both no slip and slip velocity at the walls and the chosen slip boundary condition is the linear Navier slip velocity model. The combined effects of fluid rheology, electro-osmotic and pressure gradient forcings on the fluid velocity distribution are also discussed. Copyright © 2013 Elsevier Inc. All rights reserved.

Dynamical analysis of the avian-human influenza epidemic model using the semi-analytical method

NASA Astrophysics Data System (ADS)

Jabbari, Azizeh; Kheiri, Hossein; Bekir, Ahmet

2015-03-01

In this work, we present a dynamic behavior of the avian-human influenza epidemic model by using efficient computational algorithm, namely the multistage differential transform method(MsDTM). The MsDTM is used here as an algorithm for approximating the solutions of the avian-human influenza epidemic model in a sequence of time intervals. In order to show the efficiency of the method, the obtained numerical results are compared with the fourth-order Runge-Kutta method (RK4M) and differential transform method(DTM) solutions. It is shown that the MsDTM has the advantage of giving an analytical form of the solution within each time interval which is not possible in purely numerical techniques like RK4M.

Correlations and analytical approaches to co-evolving voter models

NASA Astrophysics Data System (ADS)

Ji, M.; Xu, C.; Choi, C. W.; Hui, P. M.

2013-11-01

The difficulty in formulating analytical treatments in co-evolving networks is studied in light of the Vazquez-Eguíluz-San Miguel voter model (VM) and a modified VM (MVM) that introduces a random mutation of the opinion as a noise in the VM. The density of active links, which are links that connect the nodes of opposite opinions, is shown to be highly sensitive to both the degree k of a node and the active links n among the neighbors of a node. We test the validity in the formalism of analytical approaches and show explicitly that the assumptions behind the commonly used homogeneous pair approximation scheme in formulating a mean-field theory are the source of the theory's failure due to the strong correlations between k, n and n2. An improved approach that incorporates spatial correlation to the nearest-neighbors explicitly and a random approximation for the next-nearest neighbors is formulated for the VM and the MVM, and it gives better agreement with the simulation results. We introduce an empirical approach that quantifies the correlations more accurately and gives results in good agreement with the simulation results. The work clarifies why simply mean-field theory fails and sheds light on how to analyze the correlations in the dynamic equations that are often generated in co-evolving processes.

Deep-space navigation with differenced data types. Part 3: An expanded information content and sensitivity analysis

NASA Technical Reports Server (NTRS)

Estefan, J. A.; Thurman, S. W.

1992-01-01

An approximate six-parameter analytic model for Earth-based differential range measurements is presented and is used to derive a representative analytic approximation for differenced Doppler measurements. The analytical models are tasked to investigate the ability of these data types to estimate spacecraft geocentric angular motion, Deep Space Network station oscillator (clock/frequency) offsets, and signal-path calibration errors over a period of a few days, in the presence of systematic station location and transmission media calibration errors. Quantitative results indicate that a few differenced Doppler plus ranging passes yield angular position estimates with a precision on the order of 0.1 to 0.4 micro-rad, and angular rate precision on the order of 10 to 25 x 10(exp -12) rad/sec, assuming no a priori information on the coordinate parameters. Sensitivity analyses suggest that troposphere zenith delay calibration error is the dominant systematic error source in most of the tracking scenarios investigated; as expected, the differenced Doppler data were found to be much more sensitive to troposphere calibration errors than differenced range. By comparison, results computed using wideband and narrowband (delta) VLBI under similar circumstances yielded angular precisions of 0.07 to 0.4 micro-rad, and angular rate precisions of 0.5 to 1.0 x 10(exp -12) rad/sec.

Deep-space navigation with differenced data types. Part 3: An expanded information content and sensitivity analysis

NASA Technical Reports Server (NTRS)

Estefan, J. A.; Thurman, S. W.

1992-01-01

An approximate six-parameter analytic model for Earth-based differenced range measurements is presented and is used to derive a representative analytic approximation for differenced Doppler measurements. The analytical models are tasked to investigate the ability of these data types to estimate spacecraft geocentric angular motion, Deep Space Network station oscillator (clock/frequency) offsets, and signal-path calibration errors over a period of a few days, in the presence of systematic station location and transmission media calibration errors. Quantitative results indicate that a few differenced Doppler plus ranging passes yield angular position estimates with a precision on the order of 0.1 to 0.4 microrad, and angular rate precision on the order of 10 to 25(10)(exp -12) rad/sec, assuming no a priori information on the coordinate parameters. Sensitivity analyses suggest that troposphere zenith delay calibration error is the dominant systematic error source in most of the tracking scenarios investigated; as expected, the differenced Doppler data were found to be much more sensitive to troposphere calibration errors than differenced range. By comparison, results computed using wide band and narrow band (delta)VLBI under similar circumstances yielded angular precisions of 0.07 to 0.4 /microrad, and angular rate precisions of 0.5 to 1.0(10)(exp -12) rad/sec.

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.

The lunar libration: comparisons between various models - a model fitted to LLR observations

NASA Astrophysics Data System (ADS)

Chapront, J.; Francou, G.

2005-09-01

We consider 4 libration models: 3 numerical models built by JPL (ephemerides for the libration in DE245, DE403 and DE405) and an analytical model improved with numerical complements fitted to recent LLR observations. The analytical solution uses 3 angular variables (ρ1, ρ2, τ) which represent the deviations with respect to Cassini's laws. After having referred the models to a unique reference frame, we study the differences between the models which depend on gravitational and tidal parameters of the Moon, as well as amplitudes and frequencies of the free librations. It appears that the differences vary widely depending of the above quantities. They correspond to a few meters displacement on the lunar surface, reminding that LLR distances are precise to the centimeter level. Taking advantage of the lunar libration theory built by Moons (1984) and improved by Chapront et al. (1999) we are able to establish 4 solutions and to represent their differences by Fourier series after a numerical substitution of the gravitational constants and free libration parameters. The results are confirmed by frequency analyses performed separately. Using DE245 as a basic reference ephemeris, we approximate the differences between the analytical and numerical models with Poisson series. The analytical solution - improved with numerical complements under the form of Poisson series - is valid over several centuries with an internal precision better than 5 centimeters.

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.

A radio-frequency sheath model for complex waveforms

NASA Astrophysics Data System (ADS)

Turner, M. M.; Chabert, P.

2014-04-01

Plasma sheaths driven by radio-frequency voltages occur in contexts ranging from plasma processing to magnetically confined fusion experiments. An analytical understanding of such sheaths is therefore important, both intrinsically and as an element in more elaborate theoretical structures. Radio-frequency sheaths are commonly excited by highly anharmonic waveforms, but no analytical model exists for this general case. We present a mathematically simple sheath model that is in good agreement with earlier models for single frequency excitation, yet can be solved for arbitrary excitation waveforms. As examples, we discuss dual-frequency and pulse-like waveforms. The model employs the ansatz that the time-averaged electron density is a constant fraction of the ion density. In the cases we discuss, the error introduced by this approximation is small, and in general it can be quantified through an internal consistency condition of the model. This simple and accurate model is likely to have wide application.

A Model of High-Frequency Self-Mixing in Double-Barrier Rectifier

NASA Astrophysics Data System (ADS)

Palma, Fabrizio; Rao, R.

2018-03-01

In this paper, a new model of the frequency dependence of the double-barrier THz rectifier is presented. The new structure is of interest because it can be realized by CMOS image sensor technology. Its application in a complex field such as that of THz receivers requires the availability of an analytical model, which is reliable and able to highlight the dependence on the parameters of the physical structure. The model is based on the hydrodynamic semiconductor equations, solved in the small signal approximation. The model depicts the mechanisms of the THz modulation of the charge in the depleted regions of the double-barrier device and explains the self-mixing process, the frequency dependence, and the detection capability of the structure. The model thus substantially improves the analytical models of the THz rectification available in literature, mainly based on lamped equivalent circuits.

Modeling Selection and Extinction Mechanisms of Biological Systems

NASA Astrophysics Data System (ADS)

Amirjanov, Adil

In this paper, the behavior of a genetic algorithm is modeled to enhance its applicability as a modeling tool of biological systems. A new description model for selection mechanism is introduced which operates on a portion of individuals of population. The extinction and recolonization mechanism is modeled, and solving the dynamics analytically shows that the genetic drift in the population with extinction/recolonization is doubled. The mathematical analysis of the interaction between selection and extinction/recolonization processes is carried out to assess the dynamics of motion of the macroscopic statistical properties of population. Computer simulations confirm that the theoretical predictions of described models are in good approximations. A mathematical model of GA dynamics was also examined, which describes the anti-predator vigilance in an animal group with respect to a known analytical solution of the problem, and showed a good agreement between them to find the evolutionarily stable strategies.

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.

COMPLEX VARIABLE BOUNDARY ELEMENT METHOD: APPLICATIONS.

USGS Publications Warehouse

Hromadka, T.V.; Yen, C.C.; Guymon, G.L.

1985-01-01

The complex variable boundary element method (CVBEM) is used to approximate several potential problems where analytical solutions are known. A modeling result produced from the CVBEM is a measure of relative error in matching the known boundary condition values of the problem. A CVBEM error-reduction algorithm is used to reduce the relative error of the approximation by adding nodal points in boundary regions where error is large. From the test problems, overall error is reduced significantly by utilizing the adaptive integration algorithm.

Numerical realization of the variational method for generating self-trapped beams

NASA Astrophysics Data System (ADS)

Duque, Erick I.; Lopez-Aguayo, Servando; Malomed, Boris A.

2018-03-01

We introduce a numerical variational method based on the Rayleigh-Ritz optimization principle for predicting two-dimensional self-trapped beams in nonlinear media. This technique overcomes the limitation of the traditional variational approximation in performing analytical Lagrangian integration and differentiation. Approximate soliton solutions of a generalized nonlinear Schr\\"odinger equation are obtained, demonstrating robustness of the beams of various types (fundamental, vortices, multipoles, azimuthons) in the course of their propagation. The algorithm offers possibilities to produce more sophisticated soliton profiles in general nonlinear models.

Approximate Green's function methods for HZE transport in multilayered materials

NASA Technical Reports Server (NTRS)

Wilson, John W.; Badavi, Francis F.; Shinn, Judy L.; Costen, Robert C.

1993-01-01

A nonperturbative analytic solution of the high charge and energy (HZE) Green's function is used to implement a computer code for laboratory ion beam transport in multilayered materials. The code is established to operate on the Langley nuclear fragmentation model used in engineering applications. Computational procedures are established to generate linear energy transfer (LET) distributions for a specified ion beam and target for comparison with experimental measurements. The code was found to be highly efficient and compared well with the perturbation approximation.

Analysis, simulation and visualization of 1D tapping via reduced dynamical models

NASA Astrophysics Data System (ADS)

Blackmore, Denis; Rosato, Anthony; Tricoche, Xavier; Urban, Kevin; Zou, Luo

2014-04-01

A low-dimensional center-of-mass dynamical model is devised as a simplified means of approximately predicting some important aspects of the motion of a vertical column comprised of a large number of particles subjected to gravity and periodic vertical tapping. This model is investigated first as a continuous dynamical system using analytical, simulation and visualization techniques. Then, by employing an approach analogous to that used to approximate the dynamics of a bouncing ball on an oscillating flat plate, it is modeled as a discrete dynamical system and analyzed to determine bifurcations and transitions to chaotic motion along with other properties. The predictions of the analysis are then compared-primarily qualitatively-with visualization and simulation results of the reduced continuous model, and ultimately with simulations of the complete system dynamics.

Semi-empirical "leaky-bucket" model of laser-driven x-ray cavities

NASA Astrophysics Data System (ADS)

Moody, J. D.; Landen, O. L.; Divol, L.; LePape, S.; Michel, P.; Town, R. P. J.; Hall, G.; Widmann, K.; Moore, A.

2017-04-01

A semi-empirical analytical model is shown to approximately describe the energy balance in a laser-driven x-ray cavity, such as a hohlraum, for general laser pulse-shapes. Agreement between the model and measurements relies on two scalar parameters, one characterizes the efficiency of x-ray generation for a given laser power and the other represents a characteristic power-loss rate. These parameters, once obtained through estimation or optimization for a particular hohlraum design, can be used to predict either the x-ray flux or the coupled laser power time-history in terms of other quantities for similar hohlraum designs. The value of the model is that it can be used as an approximate "first-look" at hohlraum energy balance prior to a more detailed radiation hydrodynamic modeling.

Novel approximation of misalignment fading modeled by Beckmann distribution on free-space optical links.

PubMed

Boluda-Ruiz, Rubén; García-Zambrana, Antonio; Castillo-Vázquez, Carmen; Castillo-Vázquez, Beatriz

2016-10-03

A novel accurate and useful approximation of the well-known Beckmann distribution is presented here, which is used to model generalized pointing errors in the context of free-space optical (FSO) communication systems. We derive an approximate closed-form probability density function (PDF) for the composite gamma-gamma (GG) atmospheric turbulence with the pointing error model using the proposed approximation of the Beckmann distribution, which is valid for most practical terrestrial FSO links. This approximation takes into account the effect of the beam width, different jitters for the elevation and the horizontal displacement and the simultaneous effect of nonzero boresight errors for each axis at the receiver plane. Additionally, the proposed approximation allows us to delimit two different FSO scenarios. The first of them is when atmospheric turbulence is the dominant effect in relation to generalized pointing errors, and the second one when generalized pointing error is the dominant effect in relation to atmospheric turbulence. The second FSO scenario has not been studied in-depth by the research community. Moreover, the accuracy of the method is measured both visually and quantitatively using curve-fitting metrics. Simulation results are further included to confirm the analytical results.

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.

Cosmological applications of Padé approximant

NASA Astrophysics Data System (ADS)

Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan

2014-01-01

As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation.

Magnetohydrodynamic Jump Conditions for Oblique Relativistic Shocks with Gyrotropic Pressure

NASA Technical Reports Server (NTRS)

Double, Glen P.; Baring, Matthew G.; Jones, Frank C.; Ellison, Donald C.

2003-01-01

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

Comparisons of characteristic timescales and approximate models for Brownian magnetic nanoparticle rotations

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

Reeves, Daniel B., E-mail: dbr@Dartmouth.edu; Weaver, John B.

2015-06-21

Magnetic nanoparticles are promising tools for a host of therapeutic and diagnostic medical applications. The dynamics of rotating magnetic nanoparticles in applied magnetic fields depend strongly on the type and strength of the field applied. There are two possible rotation mechanisms and the decision for the dominant mechanism is often made by comparing the equilibrium relaxation times. This is a problem when particles are driven with high-amplitude fields because they are not necessarily at equilibrium at all. Instead, it is more appropriate to consider the “characteristic timescales” that arise in various applied fields. Approximate forms for the characteristic time ofmore » Brownian particle rotations do exist and we show agreement between several analytical and phenomenological-fit models to simulated data from a stochastic Langevin equation approach. We also compare several approximate models with solutions of the Fokker-Planck equation to determine their range of validity for general fields and relaxation times. The effective field model is an excellent approximation, while the linear response solution is only useful for very low fields and frequencies for realistic Brownian particle rotations.« less

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.

Approximate analytical solution to diurnal atmospheric boundary-layer growth under well-watered conditions

USDA-ARS?s Scientific Manuscript database

The system of governing equations of a simplified slab model of the uniformly-mixed, purely convective, diurnal atmospheric boundary layer (ABL) is shown to allow immediate solutions for the potential temperature and specific humidity as functions of the ABL height and net radiation when expressed i...

Finite element modeling of light propagation in fruit under illumination of continuous-wave beam

USDA-ARS?s Scientific Manuscript database

Spatially-resolved spectroscopy provides a means for measuring the optical properties of biological tissues, based on analytical solutions to diffusion approximation for semi-infinite media under the normal illumination of infinitely small size light beam. The method is, however, prone to error in m...

Mission analysis for the Martian Moons Explorer (MMX) mission

NASA Astrophysics Data System (ADS)

Campagnola, Stefano; Yam, Chit Hong; Tsuda, Yuichi; Ogawa, Naoko; Kawakatsu, Yasuhiro

2018-05-01

Mars Moon eXplorer (MMX) is JAXA's next candidate flagship mission to be launched in the early 2020s. MMX will explore the Martian moons and return a sample from Phobos. This paper presents the mission analysis work, focusing on the transfer legs and comparing several architectures, such as hybrid options with chemical and electric propulsion modules. The selected baseline is a chemical-propulsion Phobos sample return, which is discussed in detail with the launch- and return-window analysis. The trajectories are optimized with the jTOP software, using planetary ephemerides for Mars and the Earth; Earth re-entry constraints are modeled with simple analytical equations. Finally, we introduce an analytical approximation of the three-burn capture strategy used in the Mars system. The approximation can be used together with a Lambert solver to quickly determine the transfer Δ v costs.

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.

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.

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.

Radiation-driven winds of hot stars. VI - Analytical solutions for wind models including the finite cone angle effect

NASA Technical Reports Server (NTRS)

Kudritzki, R. P.; Pauldrach, A.; Puls, J.; Abbott, D. C.

1989-01-01

Analytical solutions for radiation-driven winds of hot stars including the important finite cone angle effect (see Pauldrach et al., 1986; Friend and Abbott, 1986) are derived which approximate the detailed numerical solutions of the exact wind equation of motion very well. They allow a detailed discussion of the finite cone angle effect and provide for given line force parameters k, alpha, delta definite formulas for mass-loss rate M and terminal velocity v-alpha as function of stellar parameters.

Satellite recovery - Attitude dynamics of the targets

NASA Technical Reports Server (NTRS)

Cochran, J. E., Jr.; Lahr, B. S.

1986-01-01

The problems of categorizing and modeling the attitude dynamics of uncontrolled artificial earth satellites which may be targets in recovery attempts are addressed. Methods of classification presented are based on satellite rotational kinetic energy, rotational angular momentum and orbit and on the type of control present prior to the benign failure of the control system. The use of approximate analytical solutions and 'exact' numerical solutions to the equations governing satellite attitude motions to predict uncontrolled attitude motion is considered. Analytical and numerical results are presented for the evolution of satellite attitude motions after active control termination.

An analytical-numerical approach for parameter determination of a five-parameter single-diode model of photovoltaic cells and modules

NASA Astrophysics Data System (ADS)

Hejri, Mohammad; Mokhtari, Hossein; Azizian, Mohammad Reza; Söder, Lennart

2016-04-01

Parameter extraction of the five-parameter single-diode model of solar cells and modules from experimental data is a challenging problem. These parameters are evaluated from a set of nonlinear equations that cannot be solved analytically. On the other hand, a numerical solution of such equations needs a suitable initial guess to converge to a solution. This paper presents a new set of approximate analytical solutions for the parameters of a five-parameter single-diode model of photovoltaic (PV) cells and modules. The proposed solutions provide a good initial point which guarantees numerical analysis convergence. The proposed technique needs only a few data from the PV current-voltage characteristics, i.e. open circuit voltage Voc, short circuit current Isc and maximum power point current and voltage Im; Vm making it a fast and low cost parameter determination technique. The accuracy of the presented theoretical I-V curves is verified by experimental data.

An experimental and analytical method for approximate determination of the tilt rotor research aircraft rotor/wing download

NASA Technical Reports Server (NTRS)

Jordon, D. E.; Patterson, W.; Sandlin, D. R.

1985-01-01

The XV-15 Tilt Rotor Research Aircraft download phenomenon was analyzed. This phenomenon is a direct result of the two rotor wakes impinging on the wing upper surface when the aircraft is in the hover configuration. For this study the analysis proceeded along tow lines. First was a method whereby results from actual hover tests of the XV-15 aircraft were combined with drag coefficient results from wind tunnel tests of a wing that was representative of the aircraft wing. Second, an analytical method was used that modeled that airflow caused gy the two rotors. Formulas were developed in such a way that acomputer program could be used to calculate the axial velocities were then used in conjunction with the aforementioned wind tunnel drag coefficinet results to produce download values. An attempt was made to validate the analytical results by modeling a model rotor system for which direct download values were determinrd..

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.

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.

Analytical solution for a class of network dynamics with mechanical and financial applications

NASA Astrophysics Data System (ADS)

Krejčí, P.; Lamba, H.; Melnik, S.; Rachinskii, D.

2014-09-01

We show that for a certain class of dynamics at the nodes the response of a network of any topology to arbitrary inputs is defined in a simple way by its response to a monotone input. The nodes may have either a discrete or continuous set of states and there is no limit on the complexity of the network. The results provide both an efficient numerical method and the potential for accurate analytic approximation of the dynamics on such networks. As illustrative applications, we introduce a quasistatic mechanical model with objects interacting via frictional forces and a financial market model with avalanches and critical behavior that are generated by momentum trading strategies.

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.

Quantum cluster theory for the polarizable continuum model. I. The CCSD level with analytical first and second derivatives.

PubMed

Cammi, R

2009-10-28

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

The application of emulation techniques in the analysis of highly reliable, guidance and control computer systems

NASA Technical Reports Server (NTRS)

Migneault, Gerard E.

1987-01-01

Emulation techniques can be a solution to a difficulty that arises in the analysis of the reliability of guidance and control computer systems for future commercial aircraft. Described here is the difficulty, the lack of credibility of reliability estimates obtained by analytical modeling techniques. The difficulty is an unavoidable consequence of the following: (1) a reliability requirement so demanding as to make system evaluation by use testing infeasible; (2) a complex system design technique, fault tolerance; (3) system reliability dominated by errors due to flaws in the system definition; and (4) elaborate analytical modeling techniques whose precision outputs are quite sensitive to errors of approximation in their input data. Use of emulation techniques for pseudo-testing systems to evaluate bounds on the parameter values needed for the analytical techniques is then discussed. Finally several examples of the application of emulation techniques are described.

Analytical expressions for the evolution of many-body quantum systems quenched far from equilibrium

NASA Astrophysics Data System (ADS)

Santos, Lea F.; Torres-Herrera, E. Jonathan

2017-12-01

Possible strategies to describe analytically the dynamics of many-body quantum systems out of equilibrium include the use of solvable models and of full random matrices. None of the two approaches represent actual realistic systems, but they serve as references for the studies of these ones. We take the second path and obtain analytical expressions for the survival probability, density imbalance, and out-of-time-ordered correlator. Using these findings, we then propose an approximate expression that matches very well numerical results for the evolution of realistic finite quantum systems that are strongly chaotic and quenched far from equilibrium. In the case of the survival probability, the expression proposed covers all different time scales, from the moment the system is taken out of equilibrium to the moment it reaches a new equilibrium. The realistic systems considered are described by one-dimensional spin-1/2 models.

Theory and simulation of the dynamics, deformation, and breakup of a chain of superparamagnetic beads under a rotating magnetic field

NASA Astrophysics Data System (ADS)

Vázquez-Quesada, A.; Franke, T.; Ellero, M.

2017-03-01

In this work, an analytical model for the behavior of superparamagnetic chains under the effect of a rotating magnetic field is presented. It is postulated that the relevant mechanisms for describing the shape and breakup of the chains into smaller fragments are the induced dipole-dipole magnetic force on the external beads, their translational and rotational drag forces, and the tangential lubrication between particles. Under this assumption, the characteristic S-shape of the chain can be qualitatively understood. Furthermore, based on a straight chain approximation, a novel analytical expression for the critical frequency for the chain breakup is obtained. In order to validate the model, the analytical expressions are compared with full three-dimensional smoothed particle hydrodynamics simulations of magnetic beads showing excellent agreement. Comparison with previous theoretical results and experimental data is also reported.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM.

PubMed

Singh, Brajesh K; Srivastava, Vineet K

2015-04-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM

PubMed Central

Singh, Brajesh K.; Srivastava, Vineet K.

2015-01-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations. PMID:26064639

Using radiance predicted by the P3 approximation in a spherical geometry to predict tissue optical properties

NASA Astrophysics Data System (ADS)

Dickey, Dwayne J.; Moore, Ronald B.; Tulip, John

2001-01-01

For photodynamic therapy of solid tumors, such as prostatic carcinoma, to be achieved, an accurate model to predict tissue parameters and light dose must be found. Presently, most analytical light dosimetry models are fluence based and are not clinically viable for tissue characterization. Other methods of predicting optical properties, such as Monet Carlo, are accurate but far too time consuming for clinical application. However, radiance predicted by the P3-Approximation, an anaylitical solution to the transport equation, may be a viable and accurate alternative. The P3-Approximation accurately predicts optical parameters in intralipid/methylene blue based phantoms in a spherical geometry. The optical parameters furnished by the radiance, when introduced into fluence predicted by both P3- Approximation and Grosjean Theory, correlate well with experimental data. The P3-Approximation also predicts the optical properties of prostate tissue, agreeing with documented optical parameters. The P3-Approximation could be the clinical tool necessary to facilitate PDT of solid tumors because of the limited number of invasive measurements required and the speed in which accurate calculations can be performed.

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…

Investigation of Acoustical Shielding by a Wedge-Shaped Airframe

NASA Technical Reports Server (NTRS)

Gerhold, Carl H.; Clark, Lorenzo R.; Dunn, Mark H.; Tweed, John

2006-01-01

Experiments on a scale model of an advanced unconventional subsonic transport concept, the Blended Wing Body (BWB), have demonstrated significant shielding of inlet-radiated noise. A computational model of the shielding mechanism has been developed using a combination of boundary integral equation method (BIEM) and equivalent source method (ESM). The computation models the incident sound from a point source in a nacelle and determines the scattered sound field. In this way the sound fields with and without the airfoil can be estimated for comparison to experiment. An experimental test bed using a simplified wedge-shape airfoil and a broadband point noise source in a simulated nacelle has been developed for the purposes of verifying the analytical model and also to study the effect of engine nacelle placement on shielding. The experimental study is conducted in the Anechoic Noise Research Facility at NASA Langley Research Center. The analytic and experimental results are compared at 6300 and 8000 Hz. These frequencies correspond to approximately 150 Hz on the full scale aircraft. Comparison between the experimental and analytic results is quite good, not only for the noise scattering by the airframe, but also for the total sound pressure in the far field. Many of the details of the sound field that the analytic model predicts are seen or indicated in the experiment, within the spatial resolution limitations of the experiment. Changing nacelle location produces comparable changes in noise shielding contours evaluated analytically and experimentally. Future work in the project will be enhancement of the analytic model to extend the analysis to higher frequencies corresponding to the blade passage frequency of the high bypass ratio ducted fan engines that are expected to power the BWB.

Investigation of Acoustical Shielding by a Wedge-Shaped Airframe

NASA Technical Reports Server (NTRS)

Gerhold, Carl H.; Clark, Lorenzo R.; Dunn, Mark H.; Tweed, John

2004-01-01

Experiments on a scale model of an advanced unconventional subsonic transport concept, the Blended Wing Body (BWB), have demonstrated significant shielding of inlet-radiated noise. A computational model of the shielding mechanism has been developed using a combination of boundary integral equation method (BIEM) and equivalent source method (ESM). The computation models the incident sound from a point source in a nacelle and determines the scattered sound field. In this way the sound fields with and without the airfoil can be estimated for comparison to experiment. An experimental test bed using a simplified wedge-shape airfoil and a broadband point noise source in a simulated nacelle has been developed for the purposes of verifying the analytical model and also to study the effect of engine nacelle placement on shielding. The experimental study is conducted in the Anechoic Noise Research Facility at NASA Langley Research Center. The analytic and experimental results are compared at 6300 and 8000 Hz. These frequencies correspond to approximately 150 Hz on the full scale aircraft. Comparison between the experimental and analytic results is quite good, not only for the noise scattering by the airframe, but also for the total sound pressure in the far field. Many of the details of the sound field that the analytic model predicts are seen or indicated in the experiment, within the spatial resolution limitations of the experiment. Changing nacelle location produces comparable changes in noise shielding contours evaluated analytically and experimentally. Future work in the project will be enhancement of the analytic model to extend the analysis to higher frequencies corresponding to the blade passage frequency of the high bypass ratio ducted fan engines that are expected to power the BWB.

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.

A finite element study of the EIDI system. [Electro-Impulse De-Icing System

NASA Technical Reports Server (NTRS)

Khatkhate, A. A.; Scavuzzo, R. J.; Chu, M. L.

1988-01-01

This paper presents a method for modeling the structural dynamics of an Electro-Impulse De-Icing System, using finite element analyses procedures. A guideline for building a representative finite element model is discussed. Modeling was done initially using four noded cubic elements, four noded isoparametric plate elements and eight noded isoparametric shell elements. Due to the size of the problem and due to the underestimation of shear stress results when compared to previous analytical work an approximate model was created to predict possible areas of shedding of ice. There appears to be good agreement with the test data provided by The Boeing Commercial Airplane Company. Thus these initial results of this method were found to be encouraging. Additional analytical work and comparison with experiment is needed in order to completely evaluate this approach.

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.

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.

Unpolarized emissivity with shadow and multiple reflections from random rough surfaces with the geometric optics approximation: application to Gaussian sea surfaces in the infrared band.

PubMed

Bourlier, Christophe

2006-08-20

The emissivity from a stationary random rough surface is derived by taking into account the multiple reflections and the shadowing effect. The model is applied to the ocean surface. The geometric optics approximation is assumed to be valid, which means that the rough surface is modeled as a collection of facets reflecting locally the light in the specular direction. In particular, the emissivity with zero, single, and double reflections are analytically calculated, and each contribution is studied numerically by considering a 1D sea surface observed in the near infrared band. The model is also compared with results computed from a Monte Carlo ray-tracing method.

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.

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.

A semi-analytical bearing model considering outer race flexibility for model based bearing load monitoring

NASA Astrophysics Data System (ADS)

Kerst, Stijn; Shyrokau, Barys; Holweg, Edward

2018-05-01

This paper proposes a novel semi-analytical bearing model addressing flexibility of the bearing outer race structure. It furthermore presents the application of this model in a bearing load condition monitoring approach. The bearing model is developed as current computational low cost bearing models fail to provide an accurate description of the more and more common flexible size and weight optimized bearing designs due to their assumptions of rigidity. In the proposed bearing model raceway flexibility is described by the use of static deformation shapes. The excitation of the deformation shapes is calculated based on the modelled rolling element loads and a Fourier series based compliance approximation. The resulting model is computational low cost and provides an accurate description of the rolling element loads for flexible outer raceway structures. The latter is validated by a simulation-based comparison study with a well-established bearing simulation software tool. An experimental study finally shows the potential of the proposed model in a bearing load monitoring approach.

Monte Carlo analysis of uncertainty propagation in a stratospheric model. 1: Development of a concise stratospheric model

NASA Technical Reports Server (NTRS)

Rundel, R. D.; Butler, D. M.; Stolarski, R. S.

1977-01-01

A concise model has been developed to analyze uncertainties in stratospheric perturbations, yet uses a minimum of computer time and is complete enough to represent the results of more complex models. The steady state model applies iteration to achieve coupling between interacting species. The species are determined from diffusion equations with appropriate sources and sinks. Diurnal effects due to chlorine nitrate formation are accounted for by analytic approximation. The model has been used to evaluate steady state perturbations due to injections of chlorine and NO(X).

Noise effects in nonlinear biochemical signaling

NASA Astrophysics Data System (ADS)

Bostani, Neda; Kessler, David A.; Shnerb, Nadav M.; Rappel, Wouter-Jan; Levine, Herbert

2012-01-01

It has been generally recognized that stochasticity can play an important role in the information processing accomplished by reaction networks in biological cells. Most treatments of that stochasticity employ Gaussian noise even though it is a priori obvious that this approximation can violate physical constraints, such as the positivity of chemical concentrations. Here, we show that even when such nonphysical fluctuations are rare, an exact solution of the Gaussian model shows that the model can yield unphysical results. This is done in the context of a simple incoherent-feedforward model which exhibits perfect adaptation in the deterministic limit. We show how one can use the natural separation of time scales in this model to yield an approximate model, that is analytically solvable, including its dynamical response to an environmental change. Alternatively, one can employ a cutoff procedure to regularize the Gaussian result.

Evaluation of the feasibility of scale modeling to quantify wind and terrain effects on low-angle sound propagation

NASA Technical Reports Server (NTRS)

Anderson, G. S.; Hayden, R. E.; Thompson, A. R.; Madden, R.

1985-01-01

The feasibility of acoustical scale modeling techniques for modeling wind effects on long range, low frequency outdoor sound propagation was evaluated. Upwind and downwind propagation was studied in 1/100 scale for flat ground and simple hills with both rigid and finite ground impedance over a full scale frequency range from 20 to 500 Hz. Results are presented as 1/3-octave frequency spectra of differences in propagation loss between the case studied and a free-field condition. Selected sets of these results were compared with validated analytical models for propagation loss, when such models were available. When they were not, results were compared with predictions from approximate models developed. Comparisons were encouraging in many cases considering the approximations involved in both the physical modeling and analysis methods. Of particular importance was the favorable comparison between theory and experiment for propagation over soft ground.

Adiabatic model of field reversal by fast ions in an axisymmetric open trap

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

Tsidulko, Yu. A., E-mail: tsidulko@mail.ru

2016-06-15

A model of field reversal by fast ions has been developed under the assumption of preservation of fast-ion adiabatic invariants. Analytical solutions obtained in the approximation of a narrow fast-ion layer and numerical solutions to the evolutionary problem are presented. The solutions demonstrate the process of formation of a field reversed configuration with parameters close to those of the planned experiment.

Simulation of the UT inspection of planar defects using a generic GTD-Kirchhoff approach

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

Dorval, Vincent, E-mail: vincent.dorval@cea.fr; Darmon, Michel, E-mail: vincent.dorval@cea.fr; Chatillon, Sylvain, E-mail: vincent.dorval@cea.fr

2015-03-31

The modeling of ultrasonic Non Destructive Evaluation often plays an important part in the assessment of detection capabilities or as a help to interpret experiments. The ultrasonic modeling tool of the CIVA platform uses semi-analytical approximations for fast computations. Kirchhoff and GTD are two classical approximations for the modeling of echoes from plane-like defects such as cracks, and they aim at taking into account two different types of physical phenomena. The Kirchhoff approximation is mainly suitable to predict specular reflections from the flaw surface, whereas GTD is dedicated to the modeling of edge diffraction. As a consequence, these two approximationsmore » have distinct and complementary validity domains. Choosing between them requires expertise and is problematic in some inspection configurations. The Physical Theory of Diffraction (PTD) was developed based on both Kirchhoff and GTD in order to combine their advantages and overcome their limitations. The theoretical basis for PTD and its integration in the CIVA modeling approach are discussed in this communication. Several results that validate this newly developed model and illustrate its advantages are presented.« less

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.

The role of electron heat flux in guide-field magnetic reconnection

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

Hesse, Michael; Kuznetsova, Masha; Birn, Joachim

2004-12-01

A combination of analytical theory and particle-in-cell simulations are employed in order to investigate the electron dynamics near and at the site of guide field magnetic reconnection. A detailed analysis of the contributions to the reconnection electric field shows that both bulk inertia and pressure-based quasiviscous processes are important for the electrons. Analytic scaling demonstrates that conventional approximations for the electron pressure tensor behavior in the dissipation region fail, and that heat flux contributions need to be accounted for. Based on the evolution equation of the heat flux three tensor, which is derived in this paper, an approximate form ofmore » the relevant heat flux contributions to the pressure tensor is developed, which reproduces the numerical modeling result reasonably well. Based on this approximation, it is possible to develop a scaling of the electron current layer in the central dissipation region. It is shown that the pressure tensor contributions become important at the scale length defined by the electron Larmor radius in the guide magnetic field.« less

Note: equation of state and the freezing point in the hard-sphere model.

PubMed

Robles, Miguel; López de Haro, Mariano; Santos, Andrés

2014-04-07

The merits of different analytical equations of state for the hard-sphere system with respect to the recently computed high-accuracy value of the freezing-point packing fraction are assessed. It is found that the Carnahan-Starling-Kolafa and the branch-point approximant equations of state yield the best performance.

Finite element modeling of light propagation in turbid media under illumination of a continuous-wave beam

USDA-ARS?s Scientific Manuscript database

Spatially-resolved spectroscopy provides a means for measuring the optical properties of biological tissues, based on analytical solutions to diffusion approximation for semi-infinite media under the normal illumination of infinitely small size light beam. The method is, however, prone to error in m...

Mixing of two co-directional Rayleigh surface waves in a nonlinear elastic material.

PubMed

Morlock, Merlin B; Kim, Jin-Yeon; Jacobs, Laurence J; Qu, Jianmin

2015-01-01

The mixing of two co-directional, initially monochromatic Rayleigh surface waves in an isotropic, homogeneous, and nonlinear elastic solid is investigated using analytical, finite element method, and experimental approaches. The analytical investigations show that while the horizontal velocity component can form a shock wave, the vertical velocity component can form a pulse independent of the specific ratios of the fundamental frequencies and amplitudes that are mixed. This analytical model is then used to simulate the development of the fundamentals, second harmonics, and the sum and difference frequency components over the propagation distance. The analytical model is further extended to include diffraction effects in the parabolic approximation. Finally, the frequency and amplitude ratios of the fundamentals are identified which provide maximum amplitudes of the second harmonics as well as of the sum and difference frequency components, to help guide effective material characterization; this approach should make it possible to measure the acoustic nonlinearity of a solid not only with the second harmonics, but also with the sum and difference frequency components. Results of the analytical investigations are then confirmed using the finite element method and the experimental feasibility of the proposed technique is validated for an aluminum specimen.

Investigation of multiple scattering effects in aerosols

NASA Technical Reports Server (NTRS)

Deepak, A.

1980-01-01

The results are presented of investigations on the various aspects of multiple scattering effects on visible and infrared laser beams transversing dense fog oil aerosols contained in a chamber (4' x 4' x 9'). The report briefly describes: (1) the experimental details and measurements; (2) analytical representation of the aerosol size distribution data by two analytical models (the regularized power law distribution and the inverse modified gamma distribution); (3) retrieval of aerosol size distributions from multispectral optical depth measurements by two methods (the two and three parameter fast table search methods and the nonlinear least squares method); (4) modeling of the effects of aerosol microphysical (coagulation and evaporation) and dynamical processes (gravitational settling) on the temporal behavior of aerosol size distribution, and hence on the extinction of four laser beams with wavelengths 0.44, 0.6328, 1.15, and 3.39 micrometers; and (5) the exact and approximate formulations for four methods for computing the effects of multiple scattering on the transmittance of laser beams in dense aerosols, all of which are based on the solution of the radiative transfer equation under the small angle approximation.

Investigation of multiple scattering effects in aerosols

NASA Astrophysics Data System (ADS)

Deepak, A.

1980-05-01

The results are presented of investigations on the various aspects of multiple scattering effects on visible and infrared laser beams transversing dense fog oil aerosols contained in a chamber (4' x 4' x 9'). The report briefly describes: (1) the experimental details and measurements; (2) analytical representation of the aerosol size distribution data by two analytical models (the regularized power law distribution and the inverse modified gamma distribution); (3) retrieval of aerosol size distributions from multispectral optical depth measurements by two methods (the two and three parameter fast table search methods and the nonlinear least squares method); (4) modeling of the effects of aerosol microphysical (coagulation and evaporation) and dynamical processes (gravitational settling) on the temporal behavior of aerosol size distribution, and hence on the extinction of four laser beams with wavelengths 0.44, 0.6328, 1.15, and 3.39 micrometers; and (5) the exact and approximate formulations for four methods for computing the effects of multiple scattering on the transmittance of laser beams in dense aerosols, all of which are based on the solution of the radiative transfer equation under the small angle approximation.

Yarkovsky-O'Keefe-Radzievskii-Paddack effect on tumbling objects

NASA Astrophysics Data System (ADS)

Breiter, S.; Rożek, A.; Vokrouhlický, D.

2011-11-01

A semi-analytical model of the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect on an asteroid spin in a non-principal axis rotation state is developed. The model describes the spin-state evolution in Deprit-Elipe variables, first-order averaged with respect to rotation and Keplerian orbital motion. Assuming zero conductivity, the YORP torque is represented by spherical harmonic series with vectorial coefficients, allowing us to use any degree and order of approximation. Within the quadrupole approximation of the illumination function we find the same first integrals involving rotational momentum, obliquity and dynamical inertia that were obtained by Cicaló & Scheeres. The integrals do not exist when higher degree terms of the illumination function are included, and then the asymptotic states known from Vokrouhlický et al. appear. This resolves an apparent contradiction between earlier results. Averaged equations of motion admit stable and unstable limit cycle solutions that were not previously detected. Non-averaged numerical integration by the Taylor series method for an exemplary shape of 3103 Eger is in good agreement with the semi-analytical theory.

Effect of Carreau-Yasuda rheological parameters on subcritical Lapwood convection in horizontal porous cavity saturated by shear-thinning fluid

NASA Astrophysics Data System (ADS)

Khechiba, Khaled; Mamou, Mahmoud; Hachemi, Madjid; Delenda, Nassim; Rebhi, Redha

2017-06-01

The present study is focused on Lapwood convection in isotropic porous media saturated with non-Newtonian shear thinning fluid. The non-Newtonian rheological behavior of the fluid is modeled using the general viscosity model of Carreau-Yasuda. The convection configuration consists of a shallow porous cavity with a finite aspect ratio and subject to a vertical constant heat flux, whereas the vertical walls are maintained impermeable and adiabatic. An approximate analytical solution is developed on the basis of the parallel flow assumption, and numerical solutions are obtained by solving the full governing equations. The Darcy model with the Boussinesq approximation and energy transport equations are solved numerically using a finite difference method. The results are obtained in terms of the Nusselt number and the flow fields as functions of the governing parameters. A good agreement is obtained between the analytical approximation and the numerical solution of the full governing equations. The effects of the rheological parameters of the Carreau-Yasuda fluid and Rayleigh number on the onset of subcritical convection thresholds are demonstrated. Regardless of the aspect ratio of the enclosure and thermal boundary condition type, the subcritical convective flows are seen to occur below the onset of stationary convection. Correlations are proposed to estimate the subcritical Rayleigh number for the onset of finite amplitude convection as a function of the fluid rheological parameters. Linear stability of the convective motion, predicted by the parallel flow approximation, is studied, and the onset of Hopf bifurcation, from steady convective flow to oscillatory behavior, is found to depend strongly on the rheological parameters. In general, Hopf bifurcation is triggered earlier as the fluid becomes more and more shear-thinning.

A Multi-Band Analytical Algorithm for Deriving Absorption and Backscattering Coefficients from Remote-Sensing Reflectance of Optically Deep Waters

NASA Technical Reports Server (NTRS)

Lee, Zhong-Ping; Carder, Kendall L.

2001-01-01

A multi-band analytical (MBA) algorithm is developed to retrieve absorption and backscattering coefficients for optically deep waters, which can be applied to data from past and current satellite sensors, as well as data from hyperspectral sensors. This MBA algorithm applies a remote-sensing reflectance model derived from the Radiative Transfer Equation, and values of absorption and backscattering coefficients are analytically calculated from values of remote-sensing reflectance. There are only limited empirical relationships involved in the algorithm, which implies that this MBA algorithm could be applied to a wide dynamic range of waters. Applying the algorithm to a simulated non-"Case 1" data set, which has no relation to the development of the algorithm, the percentage error for the total absorption coefficient at 440 nm a (sub 440) is approximately 12% for a range of 0.012 - 2.1 per meter (approximately 6% for a (sub 440) less than approximately 0.3 per meter), while a traditional band-ratio approach returns a percentage error of approximately 30%. Applying it to a field data set ranging from 0.025 to 2.0 per meter, the result for a (sub 440) is very close to that using a full spectrum optimization technique (9.6% difference). Compared to the optimization approach, the MBA algorithm cuts the computation time dramatically with only a small sacrifice in accuracy, making it suitable for processing large data sets such as satellite images. Significant improvements over empirical algorithms have also been achieved in retrieving the optical properties of optically deep waters.

Spacing of bending-induced fractures at saturation: Numerical models and approximate analytical solution

NASA Astrophysics Data System (ADS)

Schöpfer, Martin; Lehner, Florian; Grasemann, Bernhard; Kaserer, Klemens; Hinsch, Ralph

2017-04-01

John G. Ramsay's sketch of structures developed in a layer progressively folded and deformed by tangential longitudinal strain (Figure 7-65 in Folding and Fracturing of Rocks) and the associated strain pattern analysis have been reproduced in many monographs on Structural Geology and are referred to in numerous publications. Although the origin of outer-arc extension fractures is well-understood and documented in many natural examples, geomechanical factors controlling their (finite or saturation) spacing are hitherto unexplored. This study investigates the formation of bending-induced fractures during constant-curvature forced folding using Distinct Element Method (DEM) numerical modelling. The DEM model comprises a central brittle layer embedded within weaker (low modulus) elastic layers; the layer interfaces are frictionless (free slip). Folding of this three-layer system is enforced by a velocity boundary condition at the model base, while a constant overburden pressure is maintained at the model top. The models illustrate several key stages of fracture array development: (i) Prior to the onset of fracture, the neutral surface is located midway between the layer boundaries; (ii) A first set of regularly spaced fractures develops once the tensile stress in the outer-arc equals the tensile strength of the layer. Since the layer boundaries are frictionless, these bending-induced fractures propagate through the entire layer; (iii) After the appearance of the first fracture set, the rate of fracture formation decreases rapidly and so-called infill fractures develop approximately midway between two existing fractures (sequential infilling); (iv) Eventually no new fractures form, irrespective of any further increase in fold curvature (fracture saturation). Analysis of the interfacial normal stress distributions suggests that at saturation the fracture-bound blocks are subjected to a loading condition similar to three-point bending. Using classical beam theory an analytical solution is derived for the critical fracture spacing, i.e. the spacing below which the maximum tensile stress cannot reach the layer strength. The model results are consistent with an approximate analytical solution, and illustrate that the spacing of bending-induced fractures is proportional to layer thickness and a square root function of the ratio of layer tensile strength to confining pressure. Although highly idealised, models and analysis presented in this study offer an explanation for fracture saturation during folding and point towards certain key factors that may control fracture spacing in natural systems.

Highly Accurate Analytical Approximate Solution to a Nonlinear Pseudo-Oscillator

NASA Astrophysics Data System (ADS)

Wu, Baisheng; Liu, Weijia; Lim, C. W.

2017-07-01

A second-order Newton method is presented to construct analytical approximate solutions to a nonlinear pseudo-oscillator in which the restoring force is inversely proportional to the dependent variable. The nonlinear equation is first expressed in a specific form, and it is then solved in two steps, a predictor and a corrector step. In each step, the harmonic balance method is used in an appropriate manner to obtain a set of linear algebraic equations. With only one simple second-order Newton iteration step, a short, explicit, and highly accurate analytical approximate solution can be derived. The approximate solutions are valid for all amplitudes of the pseudo-oscillator. Furthermore, the method incorporates second-order Taylor expansion in a natural way, and it is of significant faster convergence rate.

Substrate mass transfer: analytical approach for immobilized enzyme reactions

NASA Astrophysics Data System (ADS)

Senthamarai, R.; Saibavani, T. N.

2018-04-01

In this paper, the boundary value problem in immobilized enzyme reactions is formulated and approximate expression for substrate concentration without external mass transfer resistance is presented. He’s variational iteration method is used to give approximate and analytical solutions of non-linear differential equation containing a non linear term related to enzymatic reaction. The relevant analytical solution for the dimensionless substrate concentration profile is discussed in terms of dimensionless reaction parameters α and β.

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.

Modeling rainfall infiltration on hillslopes using Flux-concentration relation and time compression approximation

NASA Astrophysics Data System (ADS)

Wang, Jie; Chen, Li; Yu, Zhongbo

2018-02-01

Rainfall infiltration on hillslopes is an important issue in hydrology, which is related to many environmental problems, such as flood, soil erosion, and nutrient and contaminant transport. This study aimed to improve the quantification of infiltration on hillslopes under both steady and unsteady rainfalls. Starting from Darcy's law, an analytical integral infiltrability equation was derived for hillslope infiltration by use of the flux-concentration relation. Based on this equation, a simple scaling relation linking the infiltration times on hillslopes and horizontal planes was obtained which is applicable for both small and large times and can be used to simplify the solution procedure of hillslope infiltration. The infiltrability equation also improved the estimation of ponding time for infiltration under rainfall conditions. For infiltration after ponding, the time compression approximation (TCA) was applied together with the infiltrability equation. To improve the computational efficiency, the analytical integral infiltrability equation was approximated with a two-term power-like function by nonlinear regression. Procedures of applying this approach to both steady and unsteady rainfall conditions were proposed. To evaluate the performance of the new approach, it was compared with the Green-Ampt model for sloping surfaces by Chen and Young (2006) and Richards' equation. The proposed model outperformed the sloping Green-Ampt, and both ponding time and infiltration predictions agreed well with the solutions of Richards' equation for various soil textures, slope angles, initial water contents, and rainfall intensities for both steady and unsteady rainfalls.

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 model of iceberg drift

NASA Astrophysics Data System (ADS)

Eisenman, I.; Wagner, T. J. W.; Dell, R.

2017-12-01

Icebergs transport freshwater from glaciers and ice shelves, releasing the freshwater into the upper ocean thousands of kilometers from the source. This influences ocean circulation through its effect on seawater density. A standard empirical rule-of-thumb for estimating iceberg trajectories is that they drift at the ocean surface current velocity plus 2% of the atmospheric surface wind velocity. This relationship has been observed in empirical studies for decades, but it has never previously been physically derived or justified. In this presentation, we consider the momentum balance for an individual iceberg, which includes nonlinear drag terms. Applying a series of approximations, we derive an analytical solution for the iceberg velocity as a function of time. In order to validate the model, we force it with surface velocity and temperature data from an observational state estimate and compare the results with iceberg observations in both hemispheres. We show that the analytical solution reduces to the empirical 2% relationship in the asymptotic limit of small icebergs (or strong winds), which approximately applies for typical Arctic icebergs. We find that the 2% value arises due to a term involving the drag coefficients for water and air and the densities of the iceberg, ocean, and air. In the opposite limit of large icebergs (or weak winds), which approximately applies for typical Antarctic icebergs with horizontal length scales greater than about 12 km, we find that the 2% relationship is not applicable and that icebergs instead move with the ocean current, unaffected by the wind. The two asymptotic regimes can be understood by considering how iceberg size influences the relative importance of the wind and ocean current drag terms compared with the Coriolis and pressure gradient force terms in the iceberg momentum balance.

Diagnostics of seeded RF plasmas: An experimental study related to the gaseous core reactor

NASA Technical Reports Server (NTRS)

Thompson, S. D.; Clement, J. D.; Williams, J. R.

1974-01-01

Measurements of the temperature profiles in an RF argon plasma were made over magnetic field intensities ranging from 20 amp turns/cm to 80 amp turns/cm. The results were compared with a one-dimensional numerical treatment of the governing equations and with an approximate closed form analytical solution that neglected radiation losses. The average measured temperatures in the plasma compared well with the numerical treatment, though the experimental profile showed less of an off center temperature peak than predicted by theory. This may be a result of the complex turbulent flow pattern present in the experimental torch and not modeled in the numerical treatment. The radiation term cannot be neglected for argon at the power levels investigated. The closed form analytical approximation that neglected radiation led to temperature predictions on the order of 1000 K to 2000 K higher than measured or predicted by the numerical treatment which considered radiation losses.

Exact PDF equations and closure approximations for advective-reactive transport

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

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

2013-06-01

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

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.

From analytical solutions of solute transport equations to multidimensional time-domain random walk (TDRW) algorithms

NASA Astrophysics Data System (ADS)

Bodin, Jacques

2015-03-01

In this study, new multi-dimensional time-domain random walk (TDRW) algorithms are derived from approximate one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) analytical solutions of the advection-dispersion equation and from exact 1-D, 2-D, and 3-D analytical solutions of the pure-diffusion equation. These algorithms enable the calculation of both the time required for a particle to travel a specified distance in a homogeneous medium and the mass recovery at the observation point, which may be incomplete due to 2-D or 3-D transverse dispersion or diffusion. The method is extended to heterogeneous media, represented as a piecewise collection of homogeneous media. The particle motion is then decomposed along a series of intermediate checkpoints located on the medium interface boundaries. The accuracy of the multi-dimensional TDRW method is verified against (i) exact analytical solutions of solute transport in homogeneous media and (ii) finite-difference simulations in a synthetic 2-D heterogeneous medium of simple geometry. The results demonstrate that the method is ideally suited to purely diffusive transport and to advection-dispersion transport problems dominated by advection. Conversely, the method is not recommended for highly dispersive transport problems because the accuracy of the advection-dispersion TDRW algorithms degrades rapidly for a low Péclet number, consistent with the accuracy limit of the approximate analytical solutions. The proposed approach provides a unified methodology for deriving multi-dimensional time-domain particle equations and may be applicable to other mathematical transport models, provided that appropriate analytical solutions are available.

Tunneling-assisted transport of carriers through heterojunctions.

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

Wampler, William R.; Myers, Samuel M.; Modine, Normand A.

The formulation of carrier transport through heterojunctions by tunneling and thermionic emission is derived from first principles. The treatment of tunneling is discussed at three levels of approximation: numerical solution of the one-band envelope equation for an arbitrarily specified potential profile; the WKB approximation for an arbitrary potential; and, an analytic formulation assuming constant internal field. The effects of spatially varying carrier chemical potentials over tunneling distances are included. Illustrative computational results are presented. The described approach is used in exploratory physics models of irradiated heterojunction bipolar transistors within Sandia's QASPR program.

Numerical realization of the variational method for generating self-trapped beams.

PubMed

Duque, Erick I; Lopez-Aguayo, Servando; Malomed, Boris A

2018-03-19

We introduce a numerical variational method based on the Rayleigh-Ritz optimization principle for predicting two-dimensional self-trapped beams in nonlinear media. This technique overcomes the limitation of the traditional variational approximation in performing analytical Lagrangian integration and differentiation. Approximate soliton solutions of a generalized nonlinear Schrödinger equation are obtained, demonstrating robustness of the beams of various types (fundamental, vortices, multipoles, azimuthons) in the course of their propagation. The algorithm offers possibilities to produce more sophisticated soliton profiles in general nonlinear models.

Analytical Algorithms to Quantify the Uncertainty in Remaining Useful Life Prediction

NASA Technical Reports Server (NTRS)

Sankararaman, Shankar; Saxena, Abhinav; Daigle, Matthew; Goebel, Kai

2013-01-01

This paper investigates the use of analytical algorithms to quantify the uncertainty in the remaining useful life (RUL) estimate of components used in aerospace applications. The prediction of RUL is affected by several sources of uncertainty and it is important to systematically quantify their combined effect by computing the uncertainty in the RUL prediction in order to aid risk assessment, risk mitigation, and decisionmaking. While sampling-based algorithms have been conventionally used for quantifying the uncertainty in RUL, analytical algorithms are computationally cheaper and sometimes, are better suited for online decision-making. While exact analytical algorithms are available only for certain special cases (for e.g., linear models with Gaussian variables), effective approximations can be made using the the first-order second moment method (FOSM), the first-order reliability method (FORM), and the inverse first-order reliability method (Inverse FORM). These methods can be used not only to calculate the entire probability distribution of RUL but also to obtain probability bounds on RUL. This paper explains these three methods in detail and illustrates them using the state-space model of a lithium-ion battery.

Generalized Born Models of Macromolecular Solvation Effects

NASA Astrophysics Data System (ADS)

Bashford, Donald; Case, David A.

2000-10-01

It would often be useful in computer simulations to use a simple description of solvation effects, instead of explicitly representing the individual solvent molecules. Continuum dielectric models often work well in describing the thermodynamic aspects of aqueous solvation, and approximations to such models that avoid the need to solve the Poisson equation are attractive because of their computational efficiency. Here we give an overview of one such approximation, the generalized Born model, which is simple and fast enough to be used for molecular dynamics simulations of proteins and nucleic acids. We discuss its strengths and weaknesses, both for its fidelity to the underlying continuum model and for its ability to replace explicit consideration of solvent molecules in macromolecular simulations. We focus particularly on versions of the generalized Born model that have a pair-wise analytical form, and therefore fit most naturally into conventional molecular mechanics calculations.

NGMIX: Gaussian mixture models for 2D images

NASA Astrophysics Data System (ADS)

Sheldon, Erin

2015-08-01

NGMIX implements Gaussian mixture models for 2D images. Both the PSF profile and the galaxy are modeled using mixtures of Gaussians. Convolutions are thus performed analytically, resulting in fast model generation as compared to methods that perform the convolution in Fourier space. For the galaxy model, NGMIX supports exponential disks and de Vaucouleurs and Sérsic profiles; these are implemented approximately as a sum of Gaussians using the fits from Hogg & Lang (2013). Additionally, any number of Gaussians can be fit, either completely free or constrained to be cocentric and co-elliptical.

Approximate Bayesian Computation by Subset Simulation using hierarchical state-space models

NASA Astrophysics Data System (ADS)

Vakilzadeh, Majid K.; Huang, Yong; Beck, James L.; Abrahamsson, Thomas

2017-02-01

A new multi-level Markov Chain Monte Carlo algorithm for Approximate Bayesian Computation, ABC-SubSim, has recently appeared that exploits the Subset Simulation method for efficient rare-event simulation. ABC-SubSim adaptively creates a nested decreasing sequence of data-approximating regions in the output space that correspond to increasingly closer approximations of the observed output vector in this output space. At each level, multiple samples of the model parameter vector are generated by a component-wise Metropolis algorithm so that the predicted output corresponding to each parameter value falls in the current data-approximating region. Theoretically, if continued to the limit, the sequence of data-approximating regions would converge on to the observed output vector and the approximate posterior distributions, which are conditional on the data-approximation region, would become exact, but this is not practically feasible. In this paper we study the performance of the ABC-SubSim algorithm for Bayesian updating of the parameters of dynamical systems using a general hierarchical state-space model. We note that the ABC methodology gives an approximate posterior distribution that actually corresponds to an exact posterior where a uniformly distributed combined measurement and modeling error is added. We also note that ABC algorithms have a problem with learning the uncertain error variances in a stochastic state-space model and so we treat them as nuisance parameters and analytically integrate them out of the posterior distribution. In addition, the statistical efficiency of the original ABC-SubSim algorithm is improved by developing a novel strategy to regulate the proposal variance for the component-wise Metropolis algorithm at each level. We demonstrate that Self-regulated ABC-SubSim is well suited for Bayesian system identification by first applying it successfully to model updating of a two degree-of-freedom linear structure for three cases: globally, locally and un-identifiable model classes, and then to model updating of a two degree-of-freedom nonlinear structure with Duffing nonlinearities in its interstory force-deflection relationship.

Model selection on solid ground: Rigorous comparison of nine ways to evaluate Bayesian model evidence

PubMed Central

Schöniger, Anneli; Wöhling, Thomas; Samaniego, Luis; Nowak, Wolfgang

2014-01-01

Bayesian model selection or averaging objectively ranks a number of plausible, competing conceptual models based on Bayes' theorem. It implicitly performs an optimal trade-off between performance in fitting available data and minimum model complexity. The procedure requires determining Bayesian model evidence (BME), which is the likelihood of the observed data integrated over each model's parameter space. The computation of this integral is highly challenging because it is as high-dimensional as the number of model parameters. Three classes of techniques to compute BME are available, each with its own challenges and limitations: (1) Exact and fast analytical solutions are limited by strong assumptions. (2) Numerical evaluation quickly becomes unfeasible for expensive models. (3) Approximations known as information criteria (ICs) such as the AIC, BIC, or KIC (Akaike, Bayesian, or Kashyap information criterion, respectively) yield contradicting results with regard to model ranking. Our study features a theory-based intercomparison of these techniques. We further assess their accuracy in a simplistic synthetic example where for some scenarios an exact analytical solution exists. In more challenging scenarios, we use a brute-force Monte Carlo integration method as reference. We continue this analysis with a real-world application of hydrological model selection. This is a first-time benchmarking of the various methods for BME evaluation against true solutions. Results show that BME values from ICs are often heavily biased and that the choice of approximation method substantially influences the accuracy of model ranking. For reliable model selection, bias-free numerical methods should be preferred over ICs whenever computationally feasible. PMID:25745272

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.

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...

Virtual-source diffusion approximation for enhanced near-field modeling of photon-migration in low-albedo medium.

PubMed

Jia, Mengyu; Chen, Xueying; Zhao, Huijuan; Cui, Shanshan; Liu, Ming; Liu, Lingling; Gao, Feng

2015-01-26

Most analytical methods for describing light propagation in turbid medium exhibit low effectiveness in the near-field of a collimated source. Motivated by the Charge Simulation Method in electromagnetic theory as well as the established discrete source based modeling, we herein report on an improved explicit model for a semi-infinite geometry, referred to as "Virtual Source" (VS) diffuse approximation (DA), to fit for low-albedo medium and short source-detector separation. In this model, the collimated light in the standard DA is analogously approximated as multiple isotropic point sources (VS) distributed along the incident direction. For performance enhancement, a fitting procedure between the calculated and realistic reflectances is adopted in the near-field to optimize the VS parameters (intensities and locations). To be practically applicable, an explicit 2VS-DA model is established based on close-form derivations of the VS parameters for the typical ranges of the optical parameters. This parameterized scheme is proved to inherit the mathematical simplicity of the DA approximation while considerably extending its validity in modeling the near-field photon migration in low-albedo medium. The superiority of the proposed VS-DA method to the established ones is demonstrated in comparison with Monte-Carlo simulations over wide ranges of the source-detector separation and the medium optical properties.

Line-source excited impulsive EM field response of thin plasmonic metal films

NASA Astrophysics Data System (ADS)

Štumpf, Martin; Vandenbosch, Guy A. E.

2013-08-01

In this paper, reflection against and transmission through thin plasmonic metal films, basic building blocks of many plasmonic devices, are analytically investigated directly in the time domain for an impulsive electric and magnetic line-source excitation. The electromagnetic properties of thin metallic films are modeled via the Drude model. The problem is formulated with the help of approximate thin-sheet boundary conditions and the analysis is carried out using the Cagniard-DeHoop technique. Closed-form space-time expressions are found and discussed. The obtained time-domain analytical expressions reveal the existence of the phenomenon of transient oscillatory surface effects along a plasmonic metal thin sheet. Illustrative numerical examples of transmitted/reflected pulsed fields are provided.

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.

Distribution of velocities and acceleration for a particle in Brownian correlated disorder: Inertial case

NASA Astrophysics Data System (ADS)

Le Doussal, Pierre; Petković, Aleksandra; Wiese, Kay Jörg

2012-06-01

We study the motion of an elastic object driven in a disordered environment in presence of both dissipation and inertia. We consider random forces with the statistics of random walks and reduce the problem to a single degree of freedom. It is the extension of the mean-field Alessandro-Beatrice- Bertotti-Montorsi (ABBM) model in presence of an inertial mass m. While the ABBM model can be solved exactly, its extension to inertia exhibits complicated history dependence due to oscillations and backward motion. The characteristic scales for avalanche motion are studied from numerics and qualitative arguments. To make analytical progress, we consider two variants which coincide with the original model whenever the particle moves only forward. Using a combination of analytical and numerical methods together with simulations, we characterize the distributions of instantaneous acceleration and velocity, and compare them in these three models. We show that for large driving velocity, all three models share the same large-deviation function for positive velocities, which is obtained analytically for small and large m, as well as for m=6/25. The effect of small additional thermal and quantum fluctuations can be treated within an approximate method.

Analysis and Testing of High Temperature Fibrous Insulation for Reusable Launch Vehicles

NASA Technical Reports Server (NTRS)

Daryabeigi, Kamran

1999-01-01

Analytical models were developed to model the heat transfer through high-temperature fibrous insulation used in metallic thermal protection systems on reusable launch vehicles. The optically thick approximation was used to simulate radiation heat transfer through the insulation. Different models for gaseous conduction and solid conduction in the fibers, and for combining the various modes of heat transfer into a local, volume-averaged, thermal conductivity were considered. The governing heat transfer equations were solved numerically, and effective thermal conductivities were calculated from the steady-state results. An experimental apparatus was developed to measure the apparent thermal conductivity of insulation subjected to pressures, temperatures and temperature gradients representative of re-entry conditions for launch vehicles. The apparent thermal conductivity of an alumina fiber insulation was measured at nominal densities of 24, 48 and 96 kg/cu m. Data were obtained at environmental pressures from 10(exp 4) to 760 torr, with the insulation cold side maintained at room temperature and its hot side temperature varying up to 1000 C. The experimental results were used to evaluate the analytical models. The best analytical model resulted in effective thermal conductivity predictions that were within 8% of experimental results.

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.

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.

Constitutive Modelling of Resins in the Stiffness Domain

NASA Astrophysics Data System (ADS)

Klasztorny, M.

2004-09-01

An analytic method for inverting the constitutive compliance equations of viscoelasticity for resins is developed. These equations describe the HWKK/H rheological model, which makes it possible to simulate, with a good accuracy, short-, medium- and long-term viscoelastic processes in epoxy and polyester resins. These processes are of first-rank reversible isothermal type. The time histories of deviatoric stresses are simulated with three independent strain history functions of fractional and normal exponential types. The stiffness equations are described by two elastic and six viscoelastic constants having a clear physic meaning (three long-term relaxation coefficients and three relaxation times). The time histories of axiatoric stresses are simulated as perfectly elastic. The inversion method utilizes approximate constitutive stiffness equations of viscoelasticity for the HWKK/H model. The constitutive compliance equations for the model are a basis for determining the exact complex shear stiffness, whereas the approximate constitutive stiffness equations are used for determining the approximate complex shear stiffness. The viscoelastic constants in the stiffness domain are derived by equating the exact and approximate complex shear stiffnesses. The viscoelastic constants are obtained for Epidian 53 epoxy and Polimal 109 polyester resins. The accuracy of the approximate constitutive stiffness equations are assessed by comparing the approximate and exact complex shear stiffnesses. The constitutive stiffness equations for the HWKK/H model are presented in uncoupled (shear/bulk) and coupled forms. Formulae for converting the constants of shear viscoelasticity into the constants of coupled viscoelasticity are given as well.

Investigation of flow fields within large scale hypersonic inlet models

NASA Technical Reports Server (NTRS)

Gnos, A. V.; Watson, E. C.; Seebaugh, W. R.; Sanator, R. J.; Decarlo, J. P.

1973-01-01

Analytical and experimental investigations were conducted to determine the internal flow characteristics in model passages representative of hypersonic inlets for use at Mach numbers to about 12. The passages were large enough to permit measurements to be made in both the core flow and boundary layers. The analytical techniques for designing the internal contours and predicting the internal flow-field development accounted for coupling between the boundary layers and inviscid flow fields by means of a displacement-thickness correction. Three large-scale inlet models, each having a different internal compression ratio, were designed to provide high internal performance with an approximately uniform static-pressure distribution at the throat station. The models were tested in the Ames 3.5-Foot Hypersonic Wind Tunnel at a nominal free-stream Mach number of 7.4 and a unit free-stream Reynolds number of 8.86 X one million per meter.

Analysis of the connection of the timber-fiber concrete composite structure

NASA Astrophysics Data System (ADS)

Holý, Milan; Vráblík, Lukáš; Petřík, Vojtěch

2017-09-01

This paper deals with an implementation of the material parameters of the connection to complex models for analysis of the timber-fiber concrete composite structures. The aim of this article is to present a possible way of idealization of the continuous contact model that approximates the actual behavior of timber-fiber reinforced concrete structures. The presented model of the connection was derived from push-out shear tests. It was approved by use of the nonlinear numerical analysis, that it can be achieved a very good compliance between results of numerical simulations and results of the experiments by a suitable choice of the material parameters of the continuous contact. Finally, an application for an analytical calculation of timber-fiber concrete composite structures is developed for the practical use in engineering praxis. The input material parameters for the analytical model was received using data from experiments.

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.

Computational Simulation of the High Strain Rate Tensile Response of Polymer Matrix Composites

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.

2002-01-01

A research program is underway to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to high strain rate impact loads. Under these types of loading conditions, the material response can be highly strain rate dependent and nonlinear. State variable constitutive equations based on a viscoplasticity approach have been developed to model the deformation of the polymer matrix. The constitutive equations are then combined with a mechanics of materials based micromechanics model which utilizes fiber substructuring to predict the effective mechanical and thermal response of the composite. To verify the analytical model, tensile stress-strain curves are predicted for a representative composite over strain rates ranging from around 1 x 10(exp -5)/sec to approximately 400/sec. The analytical predictions compare favorably to experimentally obtained values both qualitatively and quantitatively. Effective elastic and thermal constants are predicted for another composite, and compared to finite element results.

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.

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.

A model for the formation of the Local Group

NASA Technical Reports Server (NTRS)

Peebles, P. J. E.; Melott, A. L.; Holmes, M. R.; Jiang, L. R.

1989-01-01

Observational tests of a model for the formation of the Local Group are presented and analyzed in which the mass concentration grows by gravitational accretion of local-pressure matter onto two seed masses in an otherwise homogeneous initial mass distribution. The evolution of the mass distribution is studied in an analytic approximation and a numerical computation. The initial seed mass and separation are adjusted to produce the observed present separation and relative velocity of the Andromeda Nebula and the Galaxy. If H(0) is adjusted to about 80 km/s/Mpc with density parameter Omega = 1, then the model gives a good fit to the motions of the outer members of the Local Group. The same model gives particle orbits at radius of about 100 kpc that reasonably approximate the observed distribution of redshifts of the Galactic satellites.

Representing Functions in n Dimensions to Arbitrary Accuracy

NASA Technical Reports Server (NTRS)

Scotti, Stephen J.

2007-01-01

A method of approximating a scalar function of n independent variables (where n is a positive integer) to arbitrary accuracy has been developed. This method is expected to be attractive for use in engineering computations in which it is necessary to link global models with local ones or in which it is necessary to interpolate noiseless tabular data that have been computed from analytic functions or numerical models in n-dimensional spaces of design parameters.

Vibration-translation energy transfer in anharmonic diatomic molecules. 2: The vibrational quantum number dependence

NASA Technical Reports Server (NTRS)

Mckenzie, R. L.

1975-01-01

A semiclassical model of the inelastic collision between a vibrationally excited anharmonic oscillator and a structureless atom was used to predict the variation of thermally averaged vibration-translation rate coefficients with temperature and initial-state quantum number. Multiple oscillator states were included in a numerical solution for collinear encounters. The results are compared with CO-He experimental values for both ground and excited initial states using several simplified forms of the interaction potential. The numerical model was also used as a basis for evaluating several less complete but analytic models. Two computationally simple analytic approximations were found that successfully reproduced the numerical rate coefficients for a wide range of molecular properties and collision partners. Their limitations were also identified. The relative rates of multiple-quantum transitions from excited states were evaluated for several molecular types.

An analytical solution for predicting the transient seepage from a subsurface drainage system

NASA Astrophysics Data System (ADS)

Xin, Pei; Dan, Han-Cheng; Zhou, Tingzhang; Lu, Chunhui; Kong, Jun; Li, Ling

2016-05-01

Subsurface drainage systems have been widely used to deal with soil salinization and waterlogging problems around the world. In this paper, a mathematical model was introduced to quantify the transient behavior of the groundwater table and the seepage from a subsurface drainage system. Based on the assumption of a hydrostatic pressure distribution, the model considered the pore-water flow in both the phreatic and vadose soil zones. An approximate analytical solution for the model was derived to quantify the drainage of soils which were initially water-saturated. The analytical solution was validated against laboratory experiments and a 2-D Richards equation-based model, and found to predict well the transient water seepage from the subsurface drainage system. A saturated flow-based model was also tested and found to over-predict the time required for drainage and the total water seepage by nearly one order of magnitude, in comparison with the experimental results and the present analytical solution. During drainage, a vadose zone with a significant water storage capacity developed above the phreatic surface. A considerable amount of water still remained in the vadose zone at the steady state with the water table situated at the drain bottom. Sensitivity analyses demonstrated that effects of the vadose zone were intensified with an increased thickness of capillary fringe, capillary rise and/or burying depth of drains, in terms of the required drainage time and total water seepage. The analytical solution provides guidance for assessing the capillary effects on the effectiveness and efficiency of subsurface drainage systems for combating soil salinization and waterlogging problems.

Constraints on the nuclear equation of state from nuclear masses and radii in a Thomas-Fermi meta-modeling approach

NASA Astrophysics Data System (ADS)

Chatterjee, D.; Gulminelli, F.; Raduta, Ad. R.; Margueron, J.

2017-12-01

The question of correlations among empirical equation of state (EoS) parameters constrained by nuclear observables is addressed in a Thomas-Fermi meta-modeling approach. A recently proposed meta-modeling for the nuclear EoS in nuclear matter is augmented with a single finite size term to produce a minimal unified EoS functional able to describe the smooth part of the nuclear ground state properties. This meta-model can reproduce the predictions of a large variety of models, and interpolate continuously between them. An analytical approximation to the full Thomas-Fermi integrals is further proposed giving a fully analytical meta-model for nuclear masses. The parameter space is sampled and filtered through the constraint of nuclear mass reproduction with Bayesian statistical tools. We show that this simple analytical meta-modeling has a predictive power on masses, radii, and skins comparable to full Hartree-Fock or extended Thomas-Fermi calculations with realistic energy functionals. The covariance analysis on the posterior distribution shows that no physical correlation is present between the different EoS parameters. Concerning nuclear observables, a strong correlation between the slope of the symmetry energy and the neutron skin is observed, in agreement with previous studies.

Flame characteristics for fires in southern fuels

Treesearch

Ralph M. Nelson

1980-01-01

A flame model and analytical method are used to derive forest fire flame characteristics. Approximate solutions are used to express flame lengths, angles, heights, and tip velocities of headfires and calm-air fires in terms of fire intensity. Equations are compared with data from low-intensity controlled burns in southern fuels and with data from the literature.

Self-consistent approach for neutral community models with speciation

NASA Astrophysics Data System (ADS)

Haegeman, Bart; Etienne, Rampal S.

2010-03-01

Hubbell’s neutral model provides a rich theoretical framework to study ecological communities. By incorporating both ecological and evolutionary time scales, it allows us to investigate how communities are shaped by speciation processes. The speciation model in the basic neutral model is particularly simple, describing speciation as a point-mutation event in a birth of a single individual. The stationary species abundance distribution of the basic model, which can be solved exactly, fits empirical data of distributions of species’ abundances surprisingly well. More realistic speciation models have been proposed such as the random-fission model in which new species appear by splitting up existing species. However, no analytical solution is available for these models, impeding quantitative comparison with data. Here, we present a self-consistent approximation method for neutral community models with various speciation modes, including random fission. We derive explicit formulas for the stationary species abundance distribution, which agree very well with simulations. We expect that our approximation method will be useful to study other speciation processes in neutral community models as well.

Synaptic shot noise and conductance fluctuations affect the membrane voltage with equal significance.

PubMed

Richardson, Magnus J E; Gerstner, Wulfram

2005-04-01

The subthreshold membrane voltage of a neuron in active cortical tissue is a fluctuating quantity with a distribution that reflects the firing statistics of the presynaptic population. It was recently found that conductance-based synaptic drive can lead to distributions with a significant skew. Here it is demonstrated that the underlying shot noise caused by Poissonian spike arrival also skews the membrane distribution, but in the opposite sense. Using a perturbative method, we analyze the effects of shot noise on the distribution of synaptic conductances and calculate the consequent voltage distribution. To first order in the perturbation theory, the voltage distribution is a gaussian modulated by a prefactor that captures the skew. The gaussian component is identical to distributions derived using current-based models with an effective membrane time constant. The well-known effective-time-constant approximation can therefore be identified as the leading-order solution to the full conductance-based model. The higher-order modulatory prefactor containing the skew comprises terms due to both shot noise and conductance fluctuations. The diffusion approximation misses these shot-noise effects implying that analytical approaches such as the Fokker-Planck equation or simulation with filtered white noise cannot be used to improve on the gaussian approximation. It is further demonstrated that quantities used for fitting theory to experiment, such as the voltage mean and variance, are robust against these non-Gaussian effects. The effective-time-constant approximation is therefore relevant to experiment and provides a simple analytic base on which other pertinent biological details may be added.

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.

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.

A predictive analytic model for the solar modulation of cosmic rays

DOE PAGES

Cholis, Ilias; Hooper, Dan; Linden, Tim

2016-02-23

An important factor limiting our ability to understand the production and propagation of cosmic rays pertains to the effects of heliospheric forces, commonly known as solar modulation. The solar wind is capable of generating time- and charge-dependent effects on the spectrum and intensity of low-energy (≲10 GeV) cosmic rays reaching Earth. Previous analytic treatments of solar modulation have utilized the force-field approximation, in which a simple potential is adopted whose amplitude is selected to best fit the cosmic-ray data taken over a given period of time. Making use of recently available cosmic-ray data from the Voyager 1 spacecraft, along withmore » measurements of the heliospheric magnetic field and solar wind, we construct a time-, charge- and rigidity-dependent model of solar modulation that can be directly compared to data from a variety of cosmic-ray experiments. Here, we provide a simple analytic formula that can be easily utilized in a variety of applications, allowing us to better predict the effects of solar modulation and reduce the number of free parameters involved in cosmic-ray propagation models.« less

Analytical and numerical treatment of drift-tearing modes in plasma slab

NASA Astrophysics Data System (ADS)

Mirnov, V. V.; Hegna, C. C.; Sovinec, C. R.; Howell, E. C.

2016-10-01

Two-fluid corrections to linear tearing modes includes 1) diamagnetic drifts that reduce the growth rate and 2) electron and ion decoupling on short scales that can lead to fast reconnection. We have recently developed an analytical model that includes effects 1) and 2) and important contribution from finite electron parallel thermal conduction. Both the tendencies 1) and 2) are confirmed by an approximate analytic dispersion relation that is derived using a perturbative approach of small ion-sound gyroradius ρs. This approach is only valid at the beginning of the transition from the collisional to semi-collisional regimes. Further analytical and numerical work is performed to cover the full interval of ρs connecting these two limiting cases. Growth rates are computed from analytic theory with a shooting method. They match the resistive MHD regime with the dispersion relations known at asymptotically large ion-sound gyroradius. A comparison between this analytical treatment and linear numerical simulations using the NIMROD code with cold ions and hot electrons in plasma slab is reported. The material is based on work supported by the U.S. DOE and NSF.

Parameterized source term in the diffusion approximation for enhanced near-field modeling of collimated light

NASA Astrophysics Data System (ADS)

Jia, Mengyu; Wang, Shuang; Chen, Xueying; Gao, Feng; Zhao, Huijuan

2016-03-01

Most analytical methods for describing light propagation in turbid medium exhibit low effectiveness in the near-field of a collimated source. Motivated by the Charge Simulation Method in electromagnetic theory as well as the established discrete source based modeling, we have reported on an improved explicit model, referred to as "Virtual Source" (VS) diffuse approximation (DA), to inherit the mathematical simplicity of the DA while considerably extend its validity in modeling the near-field photon migration in low-albedo medium. In this model, the collimated light in the standard DA is analogously approximated as multiple isotropic point sources (VS) distributed along the incident direction. For performance enhancement, a fitting procedure between the calculated and realistic reflectances is adopted in the nearfield to optimize the VS parameters (intensities and locations). To be practically applicable, an explicit 2VS-DA model is established based on close-form derivations of the VS parameters for the typical ranges of the optical parameters. The proposed VS-DA model is validated by comparing with the Monte Carlo simulations, and further introduced in the image reconstruction of the Laminar Optical Tomography system.

An efficient analytical model for baffled, multi-celled membrane-type acoustic metamaterial panels

NASA Astrophysics Data System (ADS)

Langfeldt, F.; Gleine, W.; von Estorff, O.

2018-03-01

A new analytical model for the oblique incidence sound transmission loss prediction of baffled panels with multiple subwavelength sized membrane-type acoustic metamaterial (MAM) unit cells is proposed. The model employs a novel approach via the concept of the effective surface mass density and approximates the unit cell vibrations in the form of piston-like displacements. This yields a coupled system of linear equations that can be solved efficiently using well-known solution procedures. A comparison with results from finite element model simulations for both normal and diffuse field incidence shows that the analytical model delivers accurate results as long as the edge length of the MAM unit cells is smaller than half the acoustic wavelength. The computation times for the analytical calculations are 100 times smaller than for the numerical simulations. In addition to that, the effect of flexible MAM unit cell edges compared to the fixed edges assumed in the analytical model is studied numerically. It is shown that the compliance of the edges has only a small impact on the transmission loss of the panel, except at very low frequencies in the stiffness-controlled regime. The proposed analytical model is applied to investigate the effect of variations of the membrane prestress, added mass, and mass eccentricity on the diffuse transmission loss of a MAM panel with 120 unit cells. Unlike most previous investigations of MAMs, these results provide a better understanding of the acoustic performance of MAMs under more realistic conditions. For example, it is shown that by varying these parameters deliberately in a checkerboard pattern, a new anti-resonance with large transmission loss values can be introduced. A random variation of these parameters, on the other hand, is shown to have only little influence on the diffuse transmission loss, as long as the standard deviation is not too large. For very large random variations, it is shown that the peak transmission loss value can be greatly diminished.

Testing validity of the Kirkwood approximation using an extended Sznajd model

NASA Astrophysics Data System (ADS)

Timpanaro, André M.; Galam, Serge

2015-12-01

We revisit the deduction of the exit probability of the one-dimensional Sznajd model through the Kirkwood approximation [F. Slanina et al., Europhys. Lett. 82, 18006 (2008), 10.1209/0295-5075/82/18006]. This approximation is peculiar in that, in spite of the agreement with simulation results [F. Slanina et al., Europhys. Lett. 82, 18006 (2008), 10.1209/0295-5075/82/18006; R. Lambiotte and S. Redner, Europhys. Lett. 82, 18007 (2008), 10.1209/0295-5075/82/18007; A. M. Timpanaro and C. P. C. Prado, Phys. Rev. E 89, 052808 (2014), 10.1103/PhysRevE.89.052808], the hypothesis about the correlation lengths behind it are inconsistent and fixing these inconsistencies leads to the same results as a simple mean field. We use an extended version of the Sznajd model to test the Kirkwood approximation in a wider context. This model includes the voter, Sznajd, and "United we stand, divided we fall" models [R. A. Holley and T. M. Liggett, Ann. Prob. 3, 643 (1975), 10.1214/aop/1176996306; K. Sznajd-Weron and J. Sznajd, Int. J. Mod. Phys. C 11, 1157 (2000), 10.1142/S0129183100000936] as different parameter combinations, meaning that some analytical results from these models can be used to evaluate the performance of the Kirkwood approximation. We also compare the predicted exit probability with simulation results for networks with 103 sites. The results show clearly the regions in parameter space where the approximation gives accurate predictions, as well as where it starts failing, leading to a better understanding of its reliability.

Petermann I and II spot size: Accurate semi analytical description involving Nelder-Mead method of nonlinear unconstrained optimization and three parameter fundamental modal field

NASA Astrophysics Data System (ADS)

Roy Choudhury, Raja; Roy Choudhury, Arundhati; Kanti Ghose, Mrinal

2013-01-01

A semi-analytical model with three optimizing parameters and a novel non-Gaussian function as the fundamental modal field solution has been proposed to arrive at an accurate solution to predict various propagation parameters of graded-index fibers with less computational burden than numerical methods. In our semi analytical formulation the optimization of core parameter U which is usually uncertain, noisy or even discontinuous, is being calculated by Nelder-Mead method of nonlinear unconstrained minimizations as it is an efficient and compact direct search method and does not need any derivative information. Three optimizing parameters are included in the formulation of fundamental modal field of an optical fiber to make it more flexible and accurate than other available approximations. Employing variational technique, Petermann I and II spot sizes have been evaluated for triangular and trapezoidal-index fibers with the proposed fundamental modal field. It has been demonstrated that, the results of the proposed solution identically match with the numerical results over a wide range of normalized frequencies. This approximation can also be used in the study of doped and nonlinear fiber amplifier.

An analytical solution for the elastic response to surface loads imposed on a layered, transversely isotropic and self-gravitating Earth

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

Circuit transients due to negative bias arcs-II. [on solar cell power systems in low earth orbit

NASA Technical Reports Server (NTRS)

Metz, R. N.

1986-01-01

Two new models of negative-bias arcing on a solar cell power system in Low Earth Orbit are presented. One is an extended, analytical model and the other is a non-linear, numerical model. The models are based on an earlier analytical model in which the interactions between solar cell interconnects and the space plasma as well as the parameters of the power circuit are approximated linearly. Transient voltages due to arcs struck at the negative thermal of the solar panel are calculated in the time domain. The new models treat, respectively, further linear effects within the solar panel load circuit and non-linear effects associated with the plasma interactions. Results of computer calculations with the models show common-mode voltage transients of the electrically floating solar panel struck by an arc comparable to the early model but load transients that differ substantially from the early model. In particular, load transients of the non-linear model can be more than twice as great as those of the early model and more than twenty times as great as the extended, linear model.

A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

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

Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at; Tuffaha, Amjad, E-mail: atufaha@aus.edu

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solutionmore » of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.« less

Convective fluid flows in a horizontal channel with evaporation: analytical and experimental investigations

NASA Astrophysics Data System (ADS)

Lyulin, Y. V.; Rezanova, E. V.

2017-11-01

Heat- and mass transfer processes in a two-layer system of the liquid and gas are studied with respect to evaporation at interface. The stationary convective flows of two immiscible viscous incompressible fluids filling an infinite channel and being under action of the transverse gravitation field are studied analytically. Mathematical modeling of the flows is carried out with the help of the Navier-Stokes equations in Boussinesq approximation. The Dufour and Soret effects are taken into consideration in the gas-vapor phase. In the two-dimensional case the exact solutions of special type are constructed under condition of a given specific gas flow rate. Comparison of the analytical results with results of the physical experiments with the “liquid-gas” system like “ethanol-air” are presented.

Exploratory analysis regarding the domain definitions for computer based analytical models

NASA Astrophysics Data System (ADS)

Raicu, A.; Oanta, E.; Barhalescu, M.

2017-08-01

Our previous computer based studies dedicated to structural problems using analytical methods defined the composite cross section of a beam as a result of Boolean operations with so-called ‘simple’ shapes. Using generalisations, in the class of the ‘simple’ shapes were included areas bounded by curves approximated using spline functions and areas approximated as polygons. However, particular definitions lead to particular solutions. In order to ascend above the actual limitations, we conceived a general definition of the cross sections that are considered now calculus domains consisting of several subdomains. The according set of input data use complex parameterizations. This new vision allows us to naturally assign a general number of attributes to the subdomains. In this way there may be modelled new phenomena that use map-wise information, such as the metal alloys equilibrium diagrams. The hierarchy of the input data text files that use the comma-separated-value format and their structure are also presented and discussed in the paper. This new approach allows us to reuse the concepts and part of the data processing software instruments already developed. The according software to be subsequently developed will be modularised and generalised in order to be used in the upcoming projects that require rapid development of computer based models.

Fundamental (f) oscillations in a magnetically coupled solar interior-atmosphere system - An analytical approach

NASA Astrophysics Data System (ADS)

Pintér, Balázs; Erdélyi, R.

2018-01-01

Solar fundamental (f) acoustic mode oscillations are investigated analytically in a magnetohydrodynamic (MHD) model. The model consists of three layers in planar geometry, representing the solar interior, the magnetic atmosphere, and a transitional layer sandwiched between them. Since we focus on the fundamental mode here, we assume the plasma is incompressible. A horizontal, canopy-like, magnetic field is introduced to the atmosphere, in which degenerated slow MHD waves can exist. The global (f-mode) oscillations can couple to local atmospheric Alfvén waves, resulting, e.g., in a frequency shift of the oscillations. The dispersion relation of the global oscillation mode is derived, and is solved analytically for the thin-transitional layer approximation and for the weak-field approximation. Analytical formulae are also provided for the frequency shifts due to the presence of a thin transitional layer and a weak atmospheric magnetic field. The analytical results generally indicate that, compared to the fundamental value (ω =√{ gk }), the mode frequency is reduced by the presence of an atmosphere by a few per cent. A thin transitional layer reduces the eigen-frequencies further by about an additional hundred microhertz. Finally, a weak atmospheric magnetic field can slightly, by a few percent, increase the frequency of the eigen-mode. Stronger magnetic fields, however, can increase the f-mode frequency by even up to ten per cent, which cannot be seen in observed data. The presence of a magnetic atmosphere in the three-layer model also introduces non-permitted propagation windows in the frequency spectrum; here, f-mode oscillations cannot exist with certain values of the harmonic degree. The eigen-frequencies can be sensitive to the background physical parameters, such as an atmospheric density scale-height or the rate of the plasma density drop at the photosphere. Such information, if ever observed with high-resolution instrumentation and inverted, could help to gain further insight into solar magnetic structures by means of solar magneto-seismology, and could provide further insight into the role of magnetism in solar oscillations.

Optimal policies of non-cross-resistant chemotherapy on Goldie and Coldman's cancer model.

PubMed

Chen, Jeng-Huei; Kuo, Ya-Hui; Luh, Hsing Paul

2013-10-01

Mathematical models can be used to study the chemotherapy on tumor cells. Especially, in 1979, Goldie and Coldman proposed the first mathematical model to relate the drug sensitivity of tumors to their mutation rates. Many scientists have since referred to this pioneering work because of its simplicity and elegance. Its original idea has also been extended and further investigated in massive follow-up studies of cancer modeling and optimal treatment. Goldie and Coldman, together with Guaduskas, later used their model to explain why an alternating non-cross-resistant chemotherapy is optimal with a simulation approach. Subsequently in 1983, Goldie and Coldman proposed an extended stochastic based model and provided a rigorous mathematical proof to their earlier simulation work when the extended model is approximated by its quasi-approximation. However, Goldie and Coldman's analytic study of optimal treatments majorly focused on a process with symmetrical parameter settings, and presented few theoretical results for asymmetrical settings. In this paper, we recast and restate Goldie, Coldman, and Guaduskas' model as a multi-stage optimization problem. Under an asymmetrical assumption, the conditions under which a treatment policy can be optimal are derived. The proposed framework enables us to consider some optimal policies on the model analytically. In addition, Goldie, Coldman and Guaduskas' work with symmetrical settings can be treated as a special case of our framework. Based on the derived conditions, this study provides an alternative proof to Goldie and Coldman's work. In addition to the theoretical derivation, numerical results are included to justify the correctness of our work. Copyright © 2013 Elsevier Inc. All rights reserved.

Atomistic models of vacancy-mediated diffusion in silicon

NASA Astrophysics Data System (ADS)

Dunham, Scott T.; Wu, Can Dong

1995-08-01

Vacancy-mediated diffusion of dopants in silicon is investigated using Monte Carlo simulations of hopping diffusion, as well as analytic approximations based on atomistic considerations. Dopant/vacancy interaction potentials are assumed to extend out to third-nearest neighbor distances, as required for pair diffusion theories. Analysis focusing on the third-nearest neighbor sites as bridging configurations for uncorrelated hops leads to an improved analytic model for vacancy-mediated dopant diffusion. The Monte Carlo simulations of vacancy motion on a doped silicon lattice verify the analytic results for moderate doping levels. For very high doping (≳2×1020 cm-3) the simulations show a very rapid increase in pair diffusivity due to interactions of vacancies with more than one dopant atom. This behavior has previously been observed experimentally for group IV and V atoms in silicon [Nylandsted Larsen et al., J. Appl. Phys. 73, 691 (1993)], and the simulations predict both the point of onset and doping dependence of the experimentally observed diffusivity enhancement.

Evaluation Applied to Reliability Analysis of Reconfigurable, Highly Reliable, Fault-Tolerant, Computing Systems for Avionics

NASA Technical Reports Server (NTRS)

Migneault, G. E.

1979-01-01

Emulation techniques are proposed as a solution to a difficulty arising in the analysis of the reliability of highly reliable computer systems for future commercial aircraft. The difficulty, viz., the lack of credible precision in reliability estimates obtained by analytical modeling techniques are established. The difficulty is shown to be an unavoidable consequence of: (1) a high reliability requirement so demanding as to make system evaluation by use testing infeasible, (2) a complex system design technique, fault tolerance, (3) system reliability dominated by errors due to flaws in the system definition, and (4) elaborate analytical modeling techniques whose precision outputs are quite sensitive to errors of approximation in their input data. The technique of emulation is described, indicating how its input is a simple description of the logical structure of a system and its output is the consequent behavior. The use of emulation techniques is discussed for pseudo-testing systems to evaluate bounds on the parameter values needed for the analytical techniques.

Torsional vibration of a cracked rod by variational formulation and numerical analysis

NASA Astrophysics Data System (ADS)

Chondros, T. G.; Labeas, G. N.

2007-04-01

The torsional vibration of a circumferentially cracked cylindrical shaft is studied through an "exact" analytical solution and a numerical finite element (FE) analysis. The Hu-Washizu-Barr variational formulation is used to develop the differential equation and the boundary conditions of the cracked rod. The equations of motion for a uniform cracked rod in torsional vibration are derived and solved, and the Rayleigh quotient is used to further approximate the natural frequencies of the cracked rod. Results for the problem of the torsional vibration of a cylindrical shaft with a peripheral crack are provided through an analytical solution based on variational formulation to derive the equation of motion and a numerical analysis utilizing a parametric three-dimensional (3D) solid FE model of the cracked rod. The crack is modelled as a continuous flexibility based on fracture mechanics principles. The variational formulation results are compared with the FE alternative. The sensitivity of the FE discretization with respect to the analytical results is assessed.

Analytical Models of the Transport of Deep-Well Injectate at the North District Wastewater Treatment Plant, Miami-Dade County, Florida, U.S.A

NASA Astrophysics Data System (ADS)

King, J. N.; Walsh, V.; Cunningham, K. J.; Evans, F. S.; Langevin, C. D.; Dausman, A.

2009-12-01

The Miami-Dade Water and Sewer Department (MDWASD) injects buoyant effluent from the North District Wastewater Treatment Plant (NDWWTP) through four Class I injection wells into the Boulder Zone---a saline (35 parts per thousand) and transmissive (105 to 106 square meters per day) hydrogeologic unit located approximately 1000 meters below land surface. Miami-Dade County is located in southeast Florida, U.S.A. Portions of the Floridan and Biscayne aquifers are located above the Boulder Zone. The Floridan and Biscayne aquifers---underground sources of drinking water---are protected by U.S. Federal Laws and Regulations, Florida Statutes, and Miami-Dade County ordinances. In 1998, MDWASD began to observe effluent constituents within the Floridan aquifer. Continuous-source and impulse-source analytical models for advective and diffusive transport of effluent are used in the present work to test contaminant flow-path hypotheses, suggest transport mechanisms, and estimate dispersivity. MDWASD collected data in the Floridan aquifer between 1996 and 2007. A parameter estimation code is used to optimize analytical model parameters by fitting model data to collected data. These simple models will be used to develop conceptual and numerical models of effluent transport at the NDWWTP, and in the vicinity of the NDWWTP.

Analytical assessment of some characteristic ratios for s-wave superconductors

NASA Astrophysics Data System (ADS)

Gonczarek, Ryszard; Krzyzosiak, Mateusz; Gonczarek, Adam; Jacak, Lucjan

2018-04-01

We evaluate some thermodynamic quantities and characteristic ratios that describe low- and high-temperature s-wave superconducting systems. Based on a set of fundamental equations derived within the conformal transformation method, a simple model is proposed and studied analytically. After including a one-parameter class of fluctuations in the density of states, the mathematical structure of the s-wave superconducting gap, the free energy difference, and the specific heat difference is found and discussed in an analytic manner. Both the zero-temperature limit T = 0 and the subcritical temperature range T ≲ T c are discussed using the method of successive approximations. The equation for the ratio R 1, relating the zero-temperature energy gap and the critical temperature, is formulated and solved numerically for various values of the model parameter. Other thermodynamic quantities are analyzed, including a characteristic ratio R 2, quantifying the dynamics of the specific heat jump at the critical temperature. It is shown that the obtained model results coincide with experimental data for low- T c superconductors. The prospect of application of the presented model in studies of high- T c superconductors and other superconducting systems of the new generation is also discussed.

Hydraulic modeling of riverbank filtration systems with curved boundaries using analytic elements and series solutions

NASA Astrophysics Data System (ADS)

Bakker, Mark

2010-08-01

A new analytic solution approach is presented for the modeling of steady flow to pumping wells near rivers in strip aquifers; all boundaries of the river and strip aquifer may be curved. The river penetrates the aquifer only partially and has a leaky stream bed. The water level in the river may vary spatially. Flow in the aquifer below the river is semi-confined while flow in the aquifer adjacent to the river is confined or unconfined and may be subject to areal recharge. Analytic solutions are obtained through superposition of analytic elements and Fourier series. Boundary conditions are specified at collocation points along the boundaries. The number of collocation points is larger than the number of coefficients in the Fourier series and a solution is obtained in the least squares sense. The solution is analytic while boundary conditions are met approximately. Very accurate solutions are obtained when enough terms are used in the series. Several examples are presented for domains with straight and curved boundaries, including a well pumping near a meandering river with a varying water level. The area of the river bottom where water infiltrates into the aquifer is delineated and the fraction of river water in the well water is computed for several cases.

A Nonlinear differential equation model of Asthma effect of environmental pollution using LHAM

NASA Astrophysics Data System (ADS)

Joseph, G. Arul; Balamuralitharan, S.

2018-04-01

In this paper, we investigated a nonlinear differential equation mathematical model to study the spread of asthma in the environmental pollutants from industry and mainly from tobacco smoke from smokers in different type of population. Smoking is the main cause to spread Asthma in the environment. Numerical simulation is also discussed. Finally by using Liao’s Homotopy analysis Method (LHAM), we found that the approximate analytical solution of Asthmatic disease in the environmental.

Gaussian closure technique applied to the hysteretic Bouc model with non-zero mean white noise excitation

NASA Astrophysics Data System (ADS)

Waubke, Holger; Kasess, Christian H.

2016-11-01

Devices that emit structure-borne sound are commonly decoupled by elastic components to shield the environment from acoustical noise and vibrations. The elastic elements often have a hysteretic behavior that is typically neglected. In order to take hysteretic behavior into account, Bouc developed a differential equation for such materials, especially joints made of rubber or equipped with dampers. In this work, the Bouc model is solved by means of the Gaussian closure technique based on the Kolmogorov equation. Kolmogorov developed a method to derive probability density functions for arbitrary explicit first-order vector differential equations under white noise excitation using a partial differential equation of a multivariate conditional probability distribution. Up to now no analytical solution of the Kolmogorov equation in conjunction with the Bouc model exists. Therefore a wide range of approximate solutions, especially the statistical linearization, were developed. Using the Gaussian closure technique that is an approximation to the Kolmogorov equation assuming a multivariate Gaussian distribution an analytic solution is derived in this paper for the Bouc model. For the stationary case the two methods yield equivalent results, however, in contrast to statistical linearization the presented solution allows to calculate the transient behavior explicitly. Further, stationary case leads to an implicit set of equations that can be solved iteratively with a small number of iterations and without instabilities for specific parameter sets.

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

Fleury, Pierre, E-mail: fleury@iap.fr

In view of interpreting the cosmological observations precisely, especially when they involve narrow light beams, it is crucial to understand how light propagates in our statistically homogeneous, clumpy, Universe. Among the various approaches to tackle this issue, Swiss-cheese models propose an inhomogeneous spacetime geometry which is an exact solution of Einstein's equation, while the Dyer-Roeder approximation deals with inhomogeneity in an effective way. In this article, we demonstrate that the distance-redshift relation of a certain class of Swiss-cheese models is the same as the one predicted by the Dyer-Roeder approach, at a well-controlled level of approximation. Both methods are thereforemore » equivalent when applied to the interpretation of, e.g., supernova obervations. The proof relies on completely analytical arguments, and is illustrated by numerical results.« less

The desorptivity model of bulk soil-water evaporation

NASA Technical Reports Server (NTRS)

Clapp, R. B.

1983-01-01

Available models of bulk evaporation from a bare-surfaced soil are difficult to apply to field conditions where evaporation is complicated by two main factors: rate-limiting climatic conditions and redistribution of soil moisture following infiltration. Both factors are included in the "desorptivity model', wherein the evaporation rate during the second stage (the soil-limiting stage) of evaporation is related to the desorptivity parameter, A. Analytical approximations for A are presented. The approximations are independent of the surface soil moisture. However, calculations using the approximations indicate that both soil texture and soil moisture content at depth significantly affect A. Because the moisture content at depth decreases in time during redistribution, it follows that the A parameter also changes with time. Consequently, a method to calculate a representative value of A was developed. When applied to field data, the desorptivity model estimated cumulative evaporation well. The model is easy to calculate, but its usefulness is limited because it requires an independent estimate of the time of transition between the first and second stages of evaporation. The model shows that bulk evaporation after the transition to the second stage is largely independent of climatic conditions.

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 analytical technique for predicting the characteristics of a flexible wing equipped with an active flutter-suppression system and comparison with wind-tunnel data

NASA Technical Reports Server (NTRS)

Abel, I.

1979-01-01

An analytical technique for predicting the performance of an active flutter-suppression system is presented. This technique is based on the use of an interpolating function to approximate the unsteady aerodynamics. The resulting equations are formulated in terms of linear, ordinary differential equations with constant coefficients. This technique is then applied to an aeroelastic model wing equipped with an active flutter-suppression system. Comparisons between wind-tunnel data and analysis are presented for the wing both with and without active flutter suppression. Results indicate that the wing flutter characteristics without flutter suppression can be predicted very well but that a more adequate model of wind-tunnel turbulence is required when the active flutter-suppression system is used.

Rotor/Wing Interactions in Hover

NASA Technical Reports Server (NTRS)

Young, Larry A.; Derby, Michael R.

2002-01-01

Hover predictions of tiltrotor aircraft are hampered by the lack of accurate and computationally efficient models for rotor/wing interactional aerodynamics. This paper summarizes the development of an approximate, potential flow solution for the rotor-on-rotor and wing-on-rotor interactions. This analysis is based on actuator disk and vortex theory and the method of images. The analysis is applicable for out-of-ground-effect predictions. The analysis is particularly suited for aircraft preliminary design studies. Flow field predictions from this simple analytical model are validated against experimental data from previous studies. The paper concludes with an analytical assessment of the influence of rotor-on-rotor and wing-on-rotor interactions. This assessment examines the effect of rotor-to-wing offset distance, wing sweep, wing span, and flaperon incidence angle on tiltrotor inflow and performance.

Effect of load introduction on graphite epoxy compression specimens

NASA Technical Reports Server (NTRS)

Reiss, R.; Yao, T. M.

1981-01-01

Compression testing of modern composite materials is affected by the manner in which the compressive load is introduced. Two such effects are investigated: (1) the constrained edge effect which prevents transverse expansion and is common to all compression testing in which the specimen is gripped in the fixture; and (2) nonuniform gripping which induces bending into the specimen. An analytical model capable of quantifying these foregoing effects was developed which is based upon the principle of minimum complementary energy. For pure compression, the stresses are approximated by Fourier series. For pure bending, the stresses are approximated by Legendre polynomials.

An experiment-based comparative study of fuzzy logic control

NASA Technical Reports Server (NTRS)

Berenji, Hamid R.; Chen, Yung-Yaw; Lee, Chuen-Chein; Murugesan, S.; Jang, Jyh-Shing

1989-01-01

An approach is presented to the control of a dynamic physical system through the use of approximate reasoning. The approach has been implemented in a program named POLE, and the authors have successfully built a prototype hardware system to solve the cartpole balancing problem in real-time. The approach provides a complementary alternative to the conventional analytical control methodology and is of substantial use when a precise mathematical model of the process being controlled is not available. A set of criteria for comparing controllers based on approximate reasoning and those based on conventional control schemes is furnished.

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.

Solution of the spatial neutral model yields new bounds on the Amazonian species richness

NASA Astrophysics Data System (ADS)

Shem-Tov, Yahav; Danino, Matan; Shnerb, Nadav M.

2017-02-01

Neutral models, in which individual agents with equal fitness undergo a birth-death-mutation process, are very popular in population genetics and community ecology. Usually these models are applied to populations and communities with spatial structure, but the analytic results presented so far are limited to well-mixed or mainland-island scenarios. Here we combine analytic results and numerics to obtain an approximate solution for the species abundance distribution and the species richness for the neutral model on continuous landscape. We show how the regional diversity increases when the recruitment length decreases and the spatial segregation of species grows. Our results are supported by extensive numerical simulations and allow one to probe the numerically inaccessible regime of large-scale systems with extremely small mutation/speciation rates. Model predictions are compared with the findings of recent large-scale surveys of tropical trees across the Amazon basin, yielding new bounds for the species richness (between 13100 and 15000) and the number of singleton species (between 455 and 690).

Minimalist model of ice microphysics in mixed-phase stratiform clouds

NASA Astrophysics Data System (ADS)

Yang, Fan; Ovchinnikov, Mikhail; Shaw, Raymond A.

2013-07-01

The question of whether persistent ice crystal precipitation from supercooled layer clouds can be explained by time-dependent, stochastic ice nucleation is explored using an approximate, analytical model and a large-eddy simulation (LES) cloud model. The updraft velocity in the cloud defines an accumulation zone, where small ice particles cannot fall out until they are large enough, which will increase the residence time of ice particles in the cloud. Ice particles reach a quasi-steady state between growth by vapor deposition and fall speed at cloud base. The analytical model predicts that ice water content (wi) has a 2.5 power-law relationship with ice number concentration (ni). wi and ni from a LES cloud model with stochastic ice nucleation confirm the 2.5 power-law relationship, and initial indications of the scaling law are observed in data from the Indirect and Semi-Direct Aerosol Campaign. The prefactor of the power law is proportional to the ice nucleation rate and therefore provides a quantitative link to observations of ice microphysical properties.

Minimalist Model of Ice Microphysics in Mixed-phase Stratiform Clouds

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

Yang, F.; Ovchinnikov, Mikhail; Shaw, Raymond A.

The question of whether persistent ice crystal precipitation from super cooled layer clouds can be explained by time-dependent, stochastic ice nucleation is explored using an approximate, analytical model, and a large-eddy simulation (LES) cloud model. The updraft velocity in the cloud defines an accumulation zone, where small ice particles cannot fall out until they are large enough, which will increase the residence time of ice particles in the cloud. Ice particles reach a quasi-steady state between growth by vapor deposition and fall speed at cloud base. The analytical model predicts that ice water content (wi) has a 2.5 power lawmore » relationship with ice number concentration ni. wi and ni from a LES cloud model with stochastic ice nucleation also confirm the 2.5 power law relationship. The prefactor of the power law is proportional to the ice nucleation rate, and therefore provides a quantitative link to observations of ice microphysical properties.« less

Nonlinear storage models of unconfined flow through a shallow aquifer on an inclined base and their quasi-steady flow application

NASA Astrophysics Data System (ADS)

Varvaris, Ioannis; Gravanis, Elias; Koussis, Antonis; Akylas, Evangelos

2013-04-01

Hillslope processes involving flow through an inclined shallow aquifer range from subsurface stormflow to stream base flow (drought flow, or groundwater recession flow). In the case of recharge, the infiltrating water moves vertically as unsaturated flow until it reaches the saturated groundwater, where the flow is approximately parallel to the base of the aquifer. Boussinesq used the Dupuit-Forchheimer (D-F) hydraulic theory to formulate unconfined groundwater flow through a soil layer resting on an impervious inclined bed, deriving a nonlinear equation for the flow rate that consists of a linear gravity-driven component and a quadratic pressure-gradient component. Inserting that flow rate equation into the differential storage balance equation (volume conservation) Boussinesq obtained a nonlinear second-order partial differential equation for the depth. So far however, only few special solutions have been advanced for that governing equation. The nonlinearity of the equation of Boussinesq is the major obstacle to deriving a general analytical solution for the depth profile of unconfined flow on a sloping base with recharge (from which the discharges could be then determined). Henderson and Wooding (1964) were able to obtain an exact analytical solution for steady unconfined flow on a sloping base, with recharge, and their work deserves special note in the realm of solutions of the nonlinear equation of Boussinesq. However, the absence of a general solution for the transient case, which is of practical interest to hydrologists, has been the motivation for developing approximate solutions of the non-linear equation of Boussinesq. In this work, we derive the aquifer storage function by integrating analytically over the aquifer base the depth profiles resulting from the complete nonlinear Boussinesq equation for steady flow. This storage function consists of a linear and a nonlinear outflow-dependent term. Then, we use this physics-based storage function in the transient storage balance over the hillslope, obtaining analytical solutions of the outflow and the storage, for recharge and drainage, via a quasi-steady flow calculation. The hydraulically derived storage model is thus embedded in a quasi-steady approximation of transient unconfined flow in sloping aquifers. We generalise this hydrologic model of groundwater flow by modifying the storage function to be the weighted sum of the linear and the nonlinear storage terms, determining the weighting factor objectively from a known integral quantity of the flow (either an initial volume of water stored in the aquifer or a drained water volume). We demonstrate the validity of this model through comparisons with experimental data and simulation results.

Amplitude and Frequency Experimental Field Measurements of a Rotating-Imbalance Seismic Source Associated with Changes in Lithology Surrounding a Borehole

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

Stephen R. Novascone; Michael J. Anderson; David M. Weinberg

2003-10-01

Field measurements of the vibration amplitude of a rotating-imbalance seismic source in a liquid-filled borehole are described. The borehole was a cased oil well that had been characterized by gamma-ray cement bond and compensated neutron litho-density/gamma-ray logs. The well logs indicated an abrupt transition from shale to limestone at a depth of 2638 ft. The vibration amplitude and frequency of a rotating-imbalance seismic source was measured versus applied voltage as the source was raised from 2654 to 2618 ft through the shale–limestone transition. It was observed that the vibration amplitude changed by approximately 10% in magnitude and the frequency changedmore » approximately 15% as the source passed the shale–limestone transition. The measurements were compared to predictions provided by a two-dimensional analytical model of a rotating-imbalance source located in a liquid-filled bore hole. It was observed that the sensitivity of the experimentally measured vibration amplitude of the seismic source to the properties of the surrounding geologic media was an order of magnitude greater than that predicted by the two-dimensional analytical model.« less

Time delay of critical images in the vicinity of cusp point of gravitational-lens systems

NASA Astrophysics Data System (ADS)

Alexandrov, A.; Zhdanov, V.

2016-12-01

We consider approximate analytical formulas for time-delays of critical images of a point source in the neighborhood of a cusp-caustic. We discuss zero, first and second approximations in powers of a parameter that defines the proximity of the source to the cusp. These formulas link the time delay with characteristics of the lens potential. The formula of zero approximation was obtained by Congdon, Keeton & Nordgren (MNRAS, 2008). In case of a general lens potential we derived first order correction thereto. If the potential is symmetric with respect to the cusp axis, then this correction is identically equal to zero. For this case, we obtained second order correction. The relations found are illustrated by a simple model example.

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.

The Hubbard Dimer: A Complete DFT Solution to a Many-Body Problem

NASA Astrophysics Data System (ADS)

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

2015-03-01

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

Analysis of SI models with multiple interacting populations using subpopulations.

PubMed

Thomas, Evelyn K; Gurski, Katharine F; Hoffman, Kathleen A

2015-02-01

Computing endemic equilibria and basic reproductive numbers for systems of differential equations describing epidemiological systems with multiple connections between subpopulations is often algebraically intractable. We present an alternative method which deconstructs the larger system into smaller subsystems and captures the interactions between the smaller systems as external forces using an approximate model. We bound the basic reproductive numbers of the full system in terms of the basic reproductive numbers of the smaller systems and use the alternate model to provide approximations for the endemic equilibrium. In addition to creating algebraically tractable reproductive numbers and endemic equilibria, we can demonstrate the influence of the interactions between subpopulations on the basic reproductive number of the full system. The focus of this paper is to provide analytical tools to help guide public health decisions with limited intervention resources.

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.

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

Calculation of strange resonances from Kπ scattering

NASA Astrophysics Data System (ADS)

Rodas, A.; Peláez, J. R.; Ruiz de Elvira, J.

2017-09-01

We present a determination of the mass, width and coupling of the strange resonances appearing in pion-kaon scattering below 1.8 GeV, namely the much debated $K^*_0(800)$ or $\\kappa$, the scalar $K^*_0(1430)$, the $K^*(892)$ and $K^*(1410)$ vectors, the spin-two $K^*_2(1430)$ as well as the spin-three $K^*_3(1780)$. The parameters of each resonance are determined using a direct analytic continuation of the pion-kaon partial waves by means of Pad\\'e approximants, thus avoiding any particular model description of their pole positions and residues, while taking into account the analytic requirements imposed by dispersion relations.

Study of microwave drying of wet materials based on one-dimensional two-phase model

NASA Astrophysics Data System (ADS)

Salomatov, Vl V.; Karelin, V. A.

2017-11-01

Currently, microwave is one of the most interesting ways to conduct drying of dielectric materials, in particular coal. In this paper, two processes were considered - heating and drying. The temperature field of the coal semi-mass in the heating mode is found analytically strictly with the use of integral transformations. The drying process is formulated as a nonlinear Stephen problem with a moving boundary of the liquid-vapor phase transformation. The temperature distribution, speed and drying time in this mode are determined approximately analytically. Parametric analysis of the influence of the material and boundary conditions on the dynamics of warming up and drying is revealed.

Analytical Studies of Boundary Layer Generated Aircraft Interior Noise

NASA Technical Reports Server (NTRS)

Howe, M. S.; Shah, P. L.

1997-01-01

An analysis is made of the "interior noise" produced by high, subsonic turbulent flow over a thin elastic plate partitioned into "panels" by straight edges transverse to the mean flow direction. This configuration models a section of an aircraft fuselage that may be regarded as locally flat. The analytical problem can be solved in closed form to represent the acoustic radiation in terms of prescribed turbulent boundary layer pressure fluctuations. Two cases are considered: (i) the production of sound at an isolated panel edge (i.e., in the approximation in which the correlation between sound and vibrations generated at neighboring edges is neglected), and (ii) the sound generated by a periodic arrangement of identical panels. The latter problem is amenable to exact analytical treatment provided the panel edge conditions are the same for all panels. Detailed predictions of the interior noise depend on a knowledge of the turbulent boundary layer wall pressure spectrum, and are given here in terms of an empirical spectrum proposed by Laganelli and Wolfe. It is expected that these analytical representations of the sound generated by simplified models of fluid-structure interactions can used to validate more general numerical schemes.

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.

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.

Source characterization and modeling development for monoenergetic-proton radiography experiments on OMEGA

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

Manuel, M. J.-E.; Zylstra, A. B.; Rinderknecht, H. G.

2012-06-15

A monoenergetic proton source has been characterized and a modeling tool developed for proton radiography experiments at the OMEGA [T. R. Boehly et al., Opt. Comm. 133, 495 (1997)] laser facility. Multiple diagnostics were fielded to measure global isotropy levels in proton fluence and images of the proton source itself provided information on local uniformity relevant to proton radiography experiments. Global fluence uniformity was assessed by multiple yield diagnostics and deviations were calculated to be {approx}16% and {approx}26% of the mean for DD and D{sup 3}He fusion protons, respectively. From individual fluence images, it was found that the angular frequenciesmore » of Greater-Than-Or-Equivalent-To 50 rad{sup -1} contributed less than a few percent to local nonuniformity levels. A model was constructed using the Geant4 [S. Agostinelli et al., Nuc. Inst. Meth. A 506, 250 (2003)] framework to simulate proton radiography experiments. The simulation implements realistic source parameters and various target geometries. The model was benchmarked with the radiographs of cold-matter targets to within experimental accuracy. To validate the use of this code, the cold-matter approximation for the scattering of fusion protons in plasma is discussed using a typical laser-foil experiment as an example case. It is shown that an analytic cold-matter approximation is accurate to within Less-Than-Or-Equivalent-To 10% of the analytic plasma model in the example scenario.« less

A Semi-Analytical Orbit Propagator Program for Highly Elliptical Orbits

NASA Astrophysics Data System (ADS)

Lara, M.; San-Juan, J. F.; Hautesserres, D.

2016-05-01

A semi-analytical orbit propagator to study the long-term evolution of spacecraft in Highly Elliptical Orbits is presented. The perturbation model taken into account includes the gravitational effects produced by the first nine zonal harmonics and the main tesseral harmonics affecting to the 2:1 resonance, which has an impact on Molniya orbit-types, of Earth's gravitational potential, the mass-point approximation for third body perturbations, which on ly include the Legendre polynomial of second order for the sun and the polynomials from second order to sixth order for the moon, solar radiation pressure and atmospheric drag. Hamiltonian formalism is used to model the forces of gravitational nature so as to avoid time-dependence issues the problem is formulated in the extended phase space. The solar radiation pressure is modeled as a potential and included in the Hamiltonian, whereas the atmospheric drag is added as a generalized force. The semi-analytical theory is developed using perturbation techniques based on Lie transforms. Deprit's perturbation algorithm is applied up to the second order of the second zonal harmonics, J2, including Kozay-type terms in the mean elements Hamiltonian to get "centered" elements. The transformation is developed in closed-form of the eccentricity except for tesseral resonances and the coupling between J_2 and the moon's disturbing effects are neglected. This paper describes the semi-analytical theory, the semi-analytical orbit propagator program and some of the numerical validations.

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.

Replica and extreme-value analysis of the Jarzynski free-energy estimator

NASA Astrophysics Data System (ADS)

Palassini, Matteo; Ritort, Felix

2008-03-01

We analyze the Jarzynski estimator of free-energy differences from nonequilibrium work measurements. By a simple mapping onto Derrida's Random Energy Model, we obtain a scaling limit for the expectation of the bias of the estimator. We then derive analytical approximations in three different regimes of the scaling parameter x = log(N)/W, where N is the number of measurements and W the mean dissipated work. Our approach is valid for a generic distribution of the dissipated work, and is based on a replica symmetry breaking scheme for x >> 1, the asymptotic theory of extreme value statistics for x << 1, and a direct approach for x near one. The combination of the three analytic approximations describes well Monte Carlo data for the expectation value of the estimator, for a wide range of values of N, from N=1 to large N, and for different work distributions. Based on these results, we introduce improved free-energy estimators and discuss the application to the analysis of experimental data.

Accurate approximation of in-ecliptic trajectories for E-sail with constant pitch angle

NASA Astrophysics Data System (ADS)

Huo, Mingying; Mengali, Giovanni; Quarta, Alessandro A.

2018-05-01

Propellantless continuous-thrust propulsion systems, such as electric solar wind sails, may be successfully used for new space missions, especially those requiring high-energy orbit transfers. When the mass-to-thrust ratio is sufficiently large, the spacecraft trajectory is characterized by long flight times with a number of revolutions around the Sun. The corresponding mission analysis, especially when addressed within an optimal context, requires a significant amount of simulation effort. Analytical trajectories are therefore useful aids in a preliminary phase of mission design, even though exact solution are very difficult to obtain. The aim of this paper is to present an accurate, analytical, approximation of the spacecraft trajectory generated by an electric solar wind sail with a constant pitch angle, using the latest mathematical model of the thrust vector. Assuming a heliocentric circular parking orbit and a two-dimensional scenario, the simulation results show that the proposed equations are able to accurately describe the actual spacecraft trajectory for a long time interval when the propulsive acceleration magnitude is sufficiently small.

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.

Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations

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

Verde, Licia; Jimenez, Raul; Alvarez-Gaume, Luis

2013-06-01

We provide an exact expression for the multi-variate joint probability distribution function of non-Gaussian fields primordially arising from local transformations of a Gaussian field. This kind of non-Gaussianity is generated in many models of inflation. We apply our expression to the non-Gaussianity estimation from Cosmic Microwave Background maps and the halo mass function where we obtain analytical expressions. We also provide analytic approximations and their range of validity. For the Cosmic Microwave Background we give a fast way to compute the PDF which is valid up to more than 7σ for f{sub NL} values (both true and sampled) not ruledmore » out by current observations, which consists of expressing the PDF as a combination of bispectrum and trispectrum of the temperature maps. The resulting expression is valid for any kind of non-Gaussianity and is not limited to the local type. The above results may serve as the basis for a fully Bayesian analysis of the non-Gaussianity parameter.« less

The isotropic-nematic phase transition of tangent hard-sphere chain fluids—Pure components

NASA Astrophysics Data System (ADS)

van Westen, Thijs; Oyarzún, Bernardo; Vlugt, Thijs J. H.; Gross, Joachim

2013-07-01

An extension of Onsager's second virial theory is developed to describe the isotropic-nematic phase transition of tangent hard-sphere chain fluids. Flexibility is introduced by the rod-coil model. The effect of chain-flexibility on the second virial coefficient is described using an accurate, analytical approximation for the orientation-dependent pair-excluded volume. The use of this approximation allows for an analytical treatment of intramolecular flexibility by using a single pure-component parameter. Two approaches to approximate the effect of the higher virial coefficients are considered, i.e., the Vega-Lago rescaling and Scaled Particle Theory (SPT). The Onsager trial function is employed to describe the orientational distribution function. Theoretical predictions for the equation of state and orientational order parameter are tested against the results from Monte Carlo (MC) simulations. For linear chains of length 9 and longer, theoretical results are in excellent agreement with MC data. For smaller chain lengths, small errors introduced by the approximation of the higher virial coefficients become apparent, leading to a small under- and overestimation of the pressure and density difference at the phase transition, respectively. For rod-coil fluids of reasonable rigidity, a quantitative comparison between theory and MC simulations is obtained. For more flexible chains, however, both the Vega-Lago rescaling and SPT lead to a small underestimation of the location of the phase transition.

Framework for cascade size calculations on random networks

NASA Astrophysics Data System (ADS)

Burkholz, Rebekka; Schweitzer, Frank

2018-04-01

We present a framework to calculate the cascade size evolution for a large class of cascade models on random network ensembles in the limit of infinite network size. Our method is exact and applies to network ensembles with almost arbitrary degree distribution, degree-degree correlations, and, in case of threshold models, for arbitrary threshold distribution. With our approach, we shift the perspective from the known branching process approximations to the iterative update of suitable probability distributions. Such distributions are key to capture cascade dynamics that involve possibly continuous quantities and that depend on the cascade history, e.g., if load is accumulated over time. As a proof of concept, we provide two examples: (a) Constant load models that cover many of the analytically tractable casacade models, and, as a highlight, (b) a fiber bundle model that was not tractable by branching process approximations before. Our derivations cover the whole cascade dynamics, not only their steady state. This allows us to include interventions in time or further model complexity in the analysis.

A reduced-order model from high-dimensional frictional hysteresis

PubMed Central

Biswas, Saurabh; Chatterjee, Anindya

2014-01-01

Hysteresis in material behaviour includes both signum nonlinearities as well as high dimensionality. Available models for component-level hysteretic behaviour are empirical. Here, we derive a low-order model for rate-independent hysteresis from a high-dimensional massless frictional system. The original system, being given in terms of signs of velocities, is first solved incrementally using a linear complementarity problem formulation. From this numerical solution, to develop a reduced-order model, basis vectors are chosen using the singular value decomposition. The slip direction in generalized coordinates is identified as the minimizer of a dissipation-related function. That function includes terms for frictional dissipation through signum nonlinearities at many friction sites. Luckily, it allows a convenient analytical approximation. Upon solution of the approximated minimization problem, the slip direction is found. A final evolution equation for a few states is then obtained that gives a good match with the full solution. The model obtained here may lead to new insights into hysteresis as well as better empirical modelling thereof. PMID:24910522

A Radial Axial-symmetric Intermediary Model for the Roto-orbital Motion

NASA Astrophysics Data System (ADS)

Crespo, F.; Molero, F. J.; Ferrer, S.; Scheeres, D. J.

2018-03-01

We study the roto-orbital dynamics of a uniform sphere and a body with axial symmetry by means of a radial intermediary, which defines an integrable system. Numerical comparisons of the MacCullagh's truncation of the gravity gradient potential and intermediary models are performed, concluding that the intermediary provides a valuable approximation with small differences when compared with the MacCullagh's one. Our analysis includes the analytical integration and a study of the special solutions and relative equilibria.

Energy deposition at the bone-tissue interface from nuclear fragments produced by high-energy nucleons

NASA Technical Reports Server (NTRS)

Cucinotta, Francis A.; Hajnal, Ferenc; Wilson, John W.

1990-01-01

The transport of nuclear fragmentation recoils produced by high-energy nucleons in the region of the bone-tissue interface is considered. Results for the different flux and absorbed dose for recoils produced by 1 GeV protons are presented in a bidirectional transport model. The energy deposition in marrow cavities is seen to be enhanced by recoils produced in bone. Approximate analytic formulae for absorbed dose near the interface region are also presented for a simplified range-energy model.

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.

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

Dechant, Lawrence J.

Wave packet analysis provides a connection between linear small disturbance theory and subsequent nonlinear turbulent spot flow behavior. The traditional association between linear stability analysis and nonlinear wave form is developed via the method of stationary phase whereby asymptotic (simplified) mean flow solutions are used to estimate dispersion behavior and stationary phase approximation are used to invert the associated Fourier transform. The resulting process typically requires nonlinear algebraic equations inversions that can be best performed numerically, which partially mitigates the value of the approximation as compared to a more complete, e.g. DNS or linear/nonlinear adjoint methods. To obtain a simpler,more » closed-form analytical result, the complete packet solution is modeled via approximate amplitude (linear convected kinematic wave initial value problem) and local sinusoidal (wave equation) expressions. Significantly, the initial value for the kinematic wave transport expression follows from a separable variable coefficient approximation to the linearized pressure fluctuation Poisson expression. The resulting amplitude solution, while approximate in nature, nonetheless, appears to mimic many of the global features, e.g. transitional flow intermittency and pressure fluctuation magnitude behavior. A low wave number wave packet models also recover meaningful auto-correlation and low frequency spectral behaviors.« less

Non-Linear Finite Element Modeling of THUNDER Piezoelectric Actuators

NASA Technical Reports Server (NTRS)

Taleghani, Barmac K.; Campbell, Joel F.

1999-01-01

A NASTRAN non-linear finite element model has been developed for predicting the dome heights of THUNDER (THin Layer UNimorph Ferroelectric DrivER) piezoelectric actuators. To analytically validate the finite element model, a comparison was made with a non-linear plate solution using Von Karmen's approximation. A 500 volt input was used to examine the actuator deformation. The NASTRAN finite element model was also compared with experimental results. Four groups of specimens were fabricated and tested. Four different input voltages, which included 120, 160, 200, and 240 Vp-p with a 0 volts offset, were used for this comparison.

A fully analytic treatment of resonant inductive coupling in the far field

NASA Astrophysics Data System (ADS)

Sedwick, Raymond J.

2012-02-01

For the application of resonant inductive coupling for wireless power transfer, fabrication of flat spiral coils using ribbon wire allows for analytic expressions of the capacitance and inductance of the coils and therefore the resonant frequency. The expressions can also be used in an approximate way for the analysis of coils constructed from cylindrical wire. Ribbon wire constructed from both standard metals as well as high temperature superconducting material is commercially available, so using these derived expressions as a basis, a fully analytic treatment is presented that allows for design trades to be made for hybrid designs incorporating either technology. The model is then extended to analyze the performance of the technology as applied to inductively coupled communications, which has been demonstrated as having an advantage in circumstances where radiated signals would suffer unacceptable levels of attenuation.

Analytical formulas for short bunch wakes in a flat dechirper

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

Bane, Karl; Stupakov, Gennady; Zagorodnov, Igor

2016-08-04

We develop analytical models of the longitudinal and transverse wakes, on and off axis for a flat, corrugated beam pipe with realistic parameters, and then compare them with numerical calculations, and generally find good agreement. These analytical “first order” formulas approximate the droop at the origin of the longitudinal wake and of the slope of the transverse wakes; they represent an improvement in accuracy over earlier, “zeroth order” formulas. In example calculations for the RadiaBeam/LCLS dechirper using typical parameters, we find a 16% droop in the energy chirp at the bunch tail compared to simpler calculations. As a result, withmore » the beam moved to 200 μm from one jaw in one dechirper section, one can achieve a 3 MV transverse kick differential over a 30 μm length.« less

Closed-form analytical solutions of high-temperature heat pipe startup and frozen startup limitation

NASA Technical Reports Server (NTRS)

Cao, Y.; Faghri, A.

1992-01-01

Previous numerical and experimental studies indicate that the high-temperature heat pipe startup process is characterized by a moving hot zone with relatively sharp fronts. Based on the above observation, a flat-front model for an approximate analytical solution is proposed. A closed-form solution related to the temperature distribution in the hot zone and the hot zone length as a function of time are obtained. The analytical results agree well with the corresponding experimental data, and provide a quick prediction method for the heat pipe startup performance. Finally, a heat pipe limitation related to the frozen startup process is identified, and an explicit criterion for the high-temperature heat pipe startup is derived. The frozen startup limit identified in this paper provides a fundamental guidance for high-temperature heat pipe design.

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.

Wake Nonuniformity in AN MHD Channel.

NASA Astrophysics Data System (ADS)

Hruby, Vladimir J.

The influence of a wake type nonuniformity on the effective plasma electrical conductivity and Hall parameters ((sigma)(,eff) and (beta)(,eff)) was investigated experimentally and theoretically. The experimental device consisted of a combustion -driven 1 m long linear magnetohydrodynamic generator designated Mk VII and located at the Avco Everett Research Laboratory, Inc. (AERL). The reactants were oxygen-enriched air and No. 2 fuel oil. The combustion gases were seeded with potassium carbonate in a 50 percent water solution. The nominal thermal input was 10 MW, the inlet Mach number was 1.4 and the maximum magnetic field was B = 2.3 T. The channel was resistively Faraday loaded. The nonuniformity was produced by a flat plate (a vane) located in the supersonic nozzle, which created a wake lying in a plane parallel to the magnetic field. The vane removed approximately 1 percent of the channel thermal input, which resulted in a 6 percent stagnation enthalpy defect in its wake. Traversing optical probes at three locations along the channel detected little or no conductivity defect. The absence of conductivity defect was confirmed by the generator performance which remained the same with or without the vane, all other conditions being the same. An approximate analytical model showed that conductivity in the wake can be, under certain conditions, larger than that in the free stream. A traversing stagnation pressure probe however, did detect a velocity wake at the same conditions. A small amount of water (approximately 1 percent of the total mass flow) was then injected into the plasma from the trailing edge of the vane. That resulted in a strong initial conductivity defect which completely diffused and merged with boundary layers within 0.75 m. The conductivity ((TURN) thermal) profile was recorded by means of optical diagnostics. The stagnation pressure probe recorded both thermal and stagnation pressure defects. The generated power was reduced to a fraction of the power generated without the water injection. Electrical data together with the optical data were combined to evaluate the so -called plasma nonuniformity factor (G). The experimental G fell below that predicted by an approximate analytical expression derived by Rosa (G(,R)). Numerical investigation showed that the analytical approximations are not valid for large conductivity defects. A modified analytical expression resulted in better agreement between the theory and data. . . . (Author's abstract exceeds stipulated maximum length. Discontinued here with permission of author.) UMI.

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.

Anharmonic phonon-phonon scattering modeling of three-dimensional atomistic transport: An efficient quantum treatment

NASA Astrophysics Data System (ADS)

Lee, Y.; Bescond, M.; Logoteta, D.; Cavassilas, N.; Lannoo, M.; Luisier, M.

2018-05-01

We propose an efficient method to quantum mechanically treat anharmonic interactions in the atomistic nonequilibrium Green's function simulation of phonon transport. We demonstrate that the so-called lowest-order approximation, implemented through a rescaling technique and analytically continued by means of the Padé approximants, can be used to accurately model third-order anharmonic effects. Although the paper focuses on a specific self-energy, the method is applicable to a very wide class of physical interactions. We apply this approach to the simulation of anharmonic phonon transport in realistic Si and Ge nanowires with uniform or discontinuous cross sections. The effect of increasing the temperature above 300 K is also investigated. In all the considered cases, we are able to obtain a good agreement with the routinely adopted self-consistent Born approximation, at a remarkably lower computational cost. In the more complicated case of high temperatures (≫300 K), we find that the first-order Richardson extrapolation applied to the sequence of the Padé approximants N -1 /N results in a significant acceleration of the convergence.

First Principles Model of Electric Cable Braid Penetration with Dielectrics

DOE PAGES

Campione, Salvatore; Warne, Larry Kevin; Langston, William L.; ...

2018-01-01

In this study, we report the formulation to account for dielectrics in a first principles multipole-based cable braid electromagnetic penetration model. To validate our first principles model, we consider a one-dimensional array of wires, which can be modeled analytically with a multipole-conformal mapping expansion for the wire charges; however, the first principles model can be readily applied to realistic cable geometries. We compare the elastance (i.e. the inverse of the capacitance) results from the first principles cable braid electromagnetic penetration model to those obtained using the analytical model. The results are found in good agreement up to a radius tomore » half spacing ratio of 0.5-0.6, depending on the permittivity of the dielectric used, within the characteristics of many commercial cables. We observe that for typical relative permittivities encountered in braided cables, the transfer elastance values are essentially the same as those of free space; the self-elastance values are also approximated by the free space solution as long as the dielectric discontinuity is taken into account for the planar mode.« less

First Principles Model of Electric Cable Braid Penetration with Dielectrics

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

Campione, Salvatore; Warne, Larry Kevin; Langston, William L.

In this study, we report the formulation to account for dielectrics in a first principles multipole-based cable braid electromagnetic penetration model. To validate our first principles model, we consider a one-dimensional array of wires, which can be modeled analytically with a multipole-conformal mapping expansion for the wire charges; however, the first principles model can be readily applied to realistic cable geometries. We compare the elastance (i.e. the inverse of the capacitance) results from the first principles cable braid electromagnetic penetration model to those obtained using the analytical model. The results are found in good agreement up to a radius tomore » half spacing ratio of 0.5-0.6, depending on the permittivity of the dielectric used, within the characteristics of many commercial cables. We observe that for typical relative permittivities encountered in braided cables, the transfer elastance values are essentially the same as those of free space; the self-elastance values are also approximated by the free space solution as long as the dielectric discontinuity is taken into account for the planar mode.« less

The relationship between multilevel models and non-parametric multilevel mixture models: Discrete approximation of intraclass correlation, random coefficient distributions, and residual heteroscedasticity.

PubMed

Rights, Jason D; Sterba, Sonya K

2016-11-01

Multilevel data structures are common in the social sciences. Often, such nested data are analysed with multilevel models (MLMs) in which heterogeneity between clusters is modelled by continuously distributed random intercepts and/or slopes. Alternatively, the non-parametric multilevel regression mixture model (NPMM) can accommodate the same nested data structures through discrete latent class variation. The purpose of this article is to delineate analytic relationships between NPMM and MLM parameters that are useful for understanding the indirect interpretation of the NPMM as a non-parametric approximation of the MLM, with relaxed distributional assumptions. We define how seven standard and non-standard MLM specifications can be indirectly approximated by particular NPMM specifications. We provide formulas showing how the NPMM can serve as an approximation of the MLM in terms of intraclass correlation, random coefficient means and (co)variances, heteroscedasticity of residuals at level 1, and heteroscedasticity of residuals at level 2. Further, we discuss how these relationships can be useful in practice. The specific relationships are illustrated with simulated graphical demonstrations, and direct and indirect interpretations of NPMM classes are contrasted. We provide an R function to aid in implementing and visualizing an indirect interpretation of NPMM classes. An empirical example is presented and future directions are discussed. © 2016 The British Psychological Society.

Long Term Mean Local Time of the Ascending Node Prediction

NASA Technical Reports Server (NTRS)

McKinley, David P.

2007-01-01

Significant error has been observed in the long term prediction of the Mean Local Time of the Ascending Node on the Aqua spacecraft. This error of approximately 90 seconds over a two year prediction is a complication in planning and timing of maneuvers for all members of the Earth Observing System Afternoon Constellation, which use Aqua's MLTAN as the reference for their inclination maneuvers. It was determined that the source of the prediction error was the lack of a solid Earth tide model in the operational force models. The Love Model of the solid Earth tide potential was used to derive analytic corrections to the inclination and right ascension of the ascending node of Aqua's Sun-synchronous orbit. Additionally, it was determined that the resonance between the Sun and orbit plane of the Sun-synchronous orbit is the primary driver of this error. The analytic corrections have been added to the operational force models for the Aqua spacecraft reducing the two-year 90-second error to less than 7 seconds.

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.

On effective temperature in network models of collective behavior

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

Porfiri, Maurizio, E-mail: mporfiri@nyu.edu; Ariel, Gil, E-mail: arielg@math.biu.ac.il

Collective behavior of self-propelled units is studied analytically within the Vectorial Network Model (VNM), a mean-field approximation of the well-known Vicsek model. We propose a dynamical systems framework to study the stochastic dynamics of the VNM in the presence of general additive noise. We establish that a single parameter, which is a linear function of the circular mean of the noise, controls the macroscopic phase of the system—ordered or disordered. By establishing a fluctuation–dissipation relation, we posit that this parameter can be regarded as an effective temperature of collective behavior. The exact critical temperature is obtained analytically for systems withmore » small connectivity, equivalent to low-density ensembles of self-propelled units. Numerical simulations are conducted to demonstrate the applicability of this new notion of effective temperature to the Vicsek model. The identification of an effective temperature of collective behavior is an important step toward understanding order–disorder phase transitions, informing consistent coarse-graining techniques and explaining the physics underlying the emergence of collective phenomena.« less

How Hot Precursor Modify Island Nucleation: A Rate-Equation Model

NASA Astrophysics Data System (ADS)

Morales-Cifuentes, Josue; Einstein, T. L.; Pimpinelli, Alberto

2015-03-01

We describe the analysis, based on rate equations, of the hot precursor model mentioned in the previous talk. Two key parameters are the competing times of ballistic monomers decaying into thermalized monomers vs. being captured by an island, which naturally define a ``thermalization'' scale for the system. We interpret the energies and dimmensionless parameters used in the model, and provide both an implicit analytic solution and a convenient asymptotic approximation. Further analysis reveals novel scaling regimes and nonmonotonic crossovers between them. To test our model, we applied it to experiments on parahexaphenyl (6P) on sputtered mica. With the resulting parameters, the curves derived from our analytic treatment account very well for the data at the 4 different temperatures. The fit shows that the high-flux regime corresponds not to ALA (attachment-limited aggregation) or HMA (hot monomer aggregation) but rather to an intermediate scaling regime related to DLA (diffusion-limited aggregation). We hope this work stimulates further experimental investigations. Work at UMD supported by NSF CHE 13-05892.

Effect of Microscopic Damage Events on Static and Ballistic Impact Strength of Triaxial Braid Composites

NASA Technical Reports Server (NTRS)

Littell, Justin D.; Binienda, Wieslaw K.; Arnold, William A.; Roberts, Gary D.; Goldberg, Robert K.

2010-01-01

The reliability of impact simulations for aircraft components made with triaxial-braided carbon-fiber composites is currently limited by inadequate material property data and lack of validated material models for analysis. Methods to characterize the material properties used in the analytical models from a systematically obtained set of test data are also lacking. A macroscopic finite element based analytical model to analyze the impact response of these materials has been developed. The stiffness and strength properties utilized in the material model are obtained from a set of quasi-static in-plane tension, compression and shear coupon level tests. Full-field optical strain measurement techniques are applied in the testing, and the results are used to help in characterizing the model. The unit cell of the braided composite is modeled as a series of shell elements, where each element is modeled as a laminated composite. The braided architecture can thus be approximated within the analytical model. The transient dynamic finite element code LS-DYNA is utilized to conduct the finite element simulations, and an internal LS-DYNA constitutive model is utilized in the analysis. Methods to obtain the stiffness and strength properties required by the constitutive model from the available test data are developed. Simulations of quasi-static coupon tests and impact tests of a represented braided composite are conducted. Overall, the developed method shows promise, but improvements that are needed in test and analysis methods for better predictive capability are examined.

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.

Effect of crash pulse shape on seat stroke requirements for limiting loads on occupants of aircraft

NASA Technical Reports Server (NTRS)

Carden, Huey D.

1992-01-01

An analytical study was made to provide comparative information on various crash pulse shapes that potentially could be used to test seats under conditions included in Federal Regulations Part 23 Paragraph 23.562(b)(1) for dynamic testing of general aviation seats, show the effects that crash pulse shape can have on the seat stroke requirements necessary to maintain a specified limit loading on the seat/occupant during crash pulse loadings, compare results from certain analytical model pulses with approximations of actual crash pulses, and compare analytical seat results with experimental airplace crash data. Structural and seat/occupant displacement equations in terms of the maximum deceleration, velocity change, limit seat pan load, and pulse time for five potentially useful pulse shapes were derived; from these, analytical seat stroke data were obtained for conditions as specified in Federal Regulations Part 23 Paragraph 23.562(b)(1) for dynamic testing of general aviation seats.

Ionization oscillations in Hall accelerators

NASA Astrophysics Data System (ADS)

Barral, S.; Peradzyński, Z.

2010-01-01

The underlying mechanism of low-frequency oscillations in Hall accelerators is investigated theoretically. It is shown that relaxation oscillations arise from a competition between avalanche ionization and the advective transport of the working gas. The model derived recovers the slow progression and fast recession of the ionization front. Analytical approximations of the shape of current pulses and of the oscillation frequency are provided for the case of large amplitude oscillations.

Advances in computer simulation of genome evolution: toward more realistic evolutionary genomics analysis by approximate bayesian computation.

PubMed

Arenas, Miguel

2015-04-01

NGS technologies present a fast and cheap generation of genomic data. Nevertheless, ancestral genome inference is not so straightforward due to complex evolutionary processes acting on this material such as inversions, translocations, and other genome rearrangements that, in addition to their implicit complexity, can co-occur and confound ancestral inferences. Recently, models of genome evolution that accommodate such complex genomic events are emerging. This letter explores these novel evolutionary models and proposes their incorporation into robust statistical approaches based on computer simulations, such as approximate Bayesian computation, that may produce a more realistic evolutionary analysis of genomic data. Advantages and pitfalls in using these analytical methods are discussed. Potential applications of these ancestral genomic inferences are also pointed out.

Semi-analytical modelling of positive corona discharge in air

NASA Astrophysics Data System (ADS)

Pontiga, Francisco; Yanallah, Khelifa; Chen, Junhong

2013-09-01

Semianalytical approximate solutions of the spatial distribution of electric field and electron and ion densities have been obtained by solving Poisson's equations and the continuity equations for the charged species along the Laplacian field lines. The need to iterate for the correct value of space charge on the corona electrode has been eliminated by using the corona current distribution over the grounded plane derived by Deutsch, which predicts a cos m θ law similar to Warburg's law. Based on the results of the approximated model, a parametric study of the influence of gas pressure, the corona wire radius, and the inter-electrode wire-plate separation has been carried out. Also, the approximate solutions of the electron number density has been combined with a simplified plasma chemistry model in order to compute the ozone density generated by the corona discharge in the presence of a gas flow. This work was supported by the Consejeria de Innovacion, Ciencia y Empresa (Junta de Andalucia) and by the Ministerio de Ciencia e Innovacion, Spain, within the European Regional Development Fund contracts FQM-4983 and FIS2011-25161.

The H I-to-H2 Transition in a Turbulent Medium

NASA Astrophysics Data System (ADS)

Bialy, Shmuel; Burkhart, Blakesley; Sternberg, Amiel

2017-07-01

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

Application of the Boundary Element Method to Elastic Wave Scattering Problems in Ultrasonic Nondestructive Evaluation.

NASA Astrophysics Data System (ADS)

Schafbuch, Paul Jay

The boundary element method (BEM) is used to numerically simulate the interaction of ultrasonic waves with material defects such as voids, inclusions, and open cracks. The time harmonic formulation is in 3D and therefore allows flaws of arbitrary shape to be modeled. The BEM makes such problems feasible because the underlying boundary integral equation only requires a surface (2D) integration and difficulties associated with the seemingly infinite extent of the host domain are not encountered. The computer code utilized in this work is built upon recent advances in elastodynamic boundary element theory such as a scheme for self adjusting integration order and singular integration regularization. Incident fields may be taken as compressional or shear plane waves or predicted by an approximate Gauss -Hermite beam model. The code is highly optimized for voids and has been coupled with computer aided engineering packages for automated flaw shape definition and mesh generation. Subsequent graphical display of intermediate results supports model refinement and physical interpretation. Final results are typically cast in a nondestructive evaluation (NDE) context as either scattering amplitudes or flaw signals (via a measurement model based on a reciprocity integral). The near field is also predicted which allows for improved physical insight into the scattering process and the evaluation of certain modeling approximations. The accuracy of the BEM approach is first examined by comparing its predictions to those of other models for single, isolated scatterers. The comparisons are with the predictions of analytical solutions for spherical defects and with MOOT and T-matrix calculations for axisymmetric flaws. Experimental comparisons are also made for volumetric shapes with different characteristic dimensions in all three directions, since no other numerical approach has yet produced results of this type. Theoretical findings regarding the fictitious eigenfrequency difficulty are substantiated through the analytical solution of a fundamental elastodynamics problem and corresponding BEM studies. Given the confidence in the BEM technique engendered by these comparisons, it is then used to investigate the modeling of "open", cracklike defects amenable to a volumetric formulation. The limits of applicability of approximate theories (e.g., quasistatic, Kirchhoff, and geometric theory of diffraction) are explored for elliptical cracks, from this basis. The problem of two interacting scatterers is then considered. Results from a fully implicit approach and from a more efficient hybrid scheme are compared with generalized Born and farfield approximate interaction theories.

Application of the boundary element method to elastic wave scattering problems in ultrasonic nondestructive evaluation

NASA Astrophysics Data System (ADS)

Schafbuch, Paul Jay

1991-02-01

The boundary element method (BEM) is used to numerically simulate the interaction of ultrasonic waves with material defects such as voids, inclusions, and open cracks. The time harmonic formulation is in 3D and therefore allows flaws of arbitrary shape to be modeled. The BEM makes such problems feasible because the underlying boundary integral equation only requires a surface (2D) integration and difficulties associated with the seemingly infinite extent of the host domain are not encountered. The computer code utilized in this work is built upon recent advances in elastodynamic boundary element theory such as a scheme for self adjusting integration order and singular integration regularization. Incident fields may be taken as compressional or shear plane waves or predicted by an approximate Gauss-Hermite beam model. The code is highly optimized for voids and has been coupled with computer aided engineering packages for automated flaw shape definition and mesh generation. Subsequent graphical display of intermediate results supports model refinement and physical interpretation. Final results are typically cast in a nondestructive evaluation (NDE) context as either scattering amplitudes or flaw signals (via a measurement model based on a reciprocity integral). The near field is also predicted which allows for improved physical insight into the scattering process and the evaluation of certain modeling approximations. The accuracy of the BEM approach is first examined by comparing its predictions to those of other models for single, isolated scatters. The comparisons are with the predictions of analytical solutions for spherical defects and with MOOT and T-matrix calculations for axisymmetric flaws. Experimental comparisons are also made for volumetric shapes with different characteristic dimensions in all three directions, since no other numerical approach has yet produced results of this type. Theoretical findings regarding the fictitious eigenfrequency difficulty are substantiated through the analytical solution of a fundamental elastodynamics problem and corresponding BEM studies. Given the confidence in the BEM technique engendered by these comparisons, it is then used to investigate the modeling of 'open', cracklike defects amenable to a volumetric formulation. The limits of applicability of approximate theories (e.g., quasistatic, Kirchhoff, and geometric theory of diffraction) are explored for elliptical cracks, from this basis. The problem of two interacting scatterers is then considered. Results from a fully implicit approach and from a more efficient hybrid scheme are compared with generalized Born and farfield approximate interaction theories.

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.

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.

The Relationship Between Partial Contaminant Source Zone Remediation and Groundwater Plume Attenuation

NASA Astrophysics Data System (ADS)

Falta, R. W.

2004-05-01

Analytical solutions are developed that relate changes in the contaminant mass in a source area to the behavior of biologically reactive dissolved contaminant groundwater plumes. Based on data from field experiments, laboratory experiments, numerical streamtube models, and numerical multiphase flow models, the chemical discharge from a source region is assumed to be a nonlinear power function of the fraction of contaminant mass removed from the source zone. This function can approximately represent source zone mass discharge behavior over a wide range of site conditions ranging from simple homogeneous systems, to complex heterogeneous systems. A mass balance on the source zone with advective transport and first order decay leads to a nonlinear differential equation that is solved analytically to provide a prediction of the time-dependent contaminant mass discharge leaving the source zone. The solution for source zone mass discharge is coupled semi-analytically with a modified version of the Domenico (1987) analytical solution for three-dimensional reactive advective and dispersive transport in groundwater. The semi-analytical model then employs the BIOCHLOR (Aziz et al., 2000; Sun et al., 1999) transformations to model sequential first order parent-daughter biological decay reactions of chlorinated ethenes and ethanes in the groundwater plume. The resulting semi-analytic model thus allows for transient simulation of complex source zone behavior that is fully coupled to a dissolved contaminant plume undergoing sequential biological reactions. Analyses of several realistic scenarios show that substantial changes in the ground water plume can result from the partial removal of contaminant mass from the source zone. These results, however, are sensitive to the nature of the source mass reduction-source discharge reduction curve, and to the rates of degradation of the primary contaminant and its daughter products in the ground water plume. Aziz, C.E., C.J. Newell, J.R. Gonzales, P. Haas, T.P. Clement, and Y. Sun, 2000, BIOCHLOR Natural Attenuation Decision Support System User's Manual Version 1.0, US EPA Report EPA/600/R-00/008 Domenico, P.A., 1987, An analytical model for multidimensional transport of a decaying contaminant species, J. Hydrol., 91: 49-58. Sun, Y., J.N. Petersen, T.P. Clement, and R.S. Skeen, 1999, A new analytical solution for multi-species transport equations with serial and parallel reactions, Water Resour. Res., 35(1): 185-190.

Modeling the Soft Geometry of Biological Membranes

NASA Astrophysics Data System (ADS)

Daly, K.

This dissertation presents work done applying the techniques of physics to biological systems. The difference in length scales of the thickness of the phospolipid bilayer and overall size of a biological cell allows bilayer to be modeled elastically as a thin sheet. The Helfrich free energy is extended applied to models representing various biological systems, in order to find quasi-equilibrium states as well as transitions between states. Morphologies are approximated as axially sym-metric. Stable morphologies are de-termined analytically and through the use of computer simulation. The simple morphologies examined analytically give a model for the pearling transition seen in growing biological cells. An analytic model of celluar bulging in gram-negative bacteria predicts a critical pore radius for bulging of 20 nanometers. This model is extended to the membrane dynamics of human red blood cells, predicting three morphologic phases which are seen in vivo. A computer simulation was developed to study more complex morphologies with models representing different bilayer compositions. Single and multi-component bilayer models reproduce morphologies previously predicted by Seifert. A mean field model representing the intrinsic curvature of proteins coupling to membrane curvature is used to explore the stability of the particular morphology of rod outer segment cells. The process of pore formation and expansion in cell-cell fusion is not well understood. Simulation of the pore created in cell-cell fusion led to the finding of a minimal pore radius required for pore expansion, suggesting pores formed in nature are formed with a minimum size.

Mixed models and reduced/selective integration displacement models for nonlinear analysis of curved beams

NASA Technical Reports Server (NTRS)

Noor, A. K.; Peters, J. M.

1981-01-01

Simple mixed models are developed for use in the geometrically nonlinear analysis of deep arches. A total Lagrangian description of the arch deformation is used, the analytical formulation being based on a form of the nonlinear deep arch theory with the effects of transverse shear deformation included. The fundamental unknowns comprise the six internal forces and generalized displacements of the arch, and the element characteristic arrays are obtained by using Hellinger-Reissner mixed variational principle. The polynomial interpolation functions employed in approximating the forces are one degree lower than those used in approximating the displacements, and the forces are discontinuous at the interelement boundaries. Attention is given to the equivalence between the mixed models developed herein and displacement models based on reduced integration of both the transverse shear and extensional energy terms. The advantages of mixed models over equivalent displacement models are summarized. Numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed and to permit a comparison of their performance with that of other mixed models reported in the literature.

An Eigenvalue Analysis of finite-difference approximations for hyperbolic IBVPs

NASA Technical Reports Server (NTRS)

Warming, Robert F.; Beam, Richard M.

1989-01-01

The eigenvalue spectrum associated with a linear finite-difference approximation plays a crucial role in the stability analysis and in the actual computational performance of the discrete approximation. The eigenvalue spectrum associated with the Lax-Wendroff scheme applied to a model hyperbolic equation was investigated. For an initial-boundary-value problem (IBVP) on a finite domain, the eigenvalue or normal mode analysis is analytically intractable. A study of auxiliary problems (Dirichlet and quarter-plane) leads to asymptotic estimates of the eigenvalue spectrum and to an identification of individual modes as either benign or unstable. The asymptotic analysis establishes an intuitive as well as quantitative connection between the algebraic tests in the theory of Gustafsson, Kreiss, and Sundstrom and Lax-Richtmyer L(sub 2) stability on a finite domain.

Charge noise in quantum dot qubits: beyond the Markovian approximation.

NASA Astrophysics Data System (ADS)

Yang, Yuan-Chi; Friesen, Mark; Coppersmith, S. N.

Charge noise is a limiting factor in the performance of semiconductor quantum dot qubits, including both spin and charge qubits. In this work, we develop an analytical formalism for treating semiclassical noise beyond the Markovian approximation, which allows us to investigate noise models relevant for quantum dots, such as 1 / f noise. We apply our methods to both charge qubits and quantum dot hybrid qubits, and study the effects of charge noise on single-qubit rotations in these systems. The formalism is also directly applicable to the case of strong microwave driving, for which the rotating wave approximation breaks down. This work was supported in part by ARO (W911NF-12-0607) and ONR (N00014-15-1-0029), and the University of Wisconsin-Madison.

Effectiveness of “Thin-Layer” and “Effective Medium” Approximations in Numerical Simulation of Dielectric Spectra of Biological Cell Suspensions

NASA Astrophysics Data System (ADS)

Asami, Koji

2010-12-01

There are a few concerns in dielectric modeling of biological cells by the finite-element method (FEM) to simulate their dielectric spectra. Cells possess thin plasma membranes and membrane-bound intracellular organelles, requiring extra fine meshes and considerable computational tasks in the simulation. To solve the problems, the “thin-layer” approximation (TLA) and the “effective medium” approximation (EMA) were adopted. TLA deals with the membrane as an interface of the specific membrane impedance, and therefore it is not necessary to divide the membrane region. EMA regards the composite cytoplasm as an effective homogeneous phase whose dielectric properties are calculated separately. It was proved that TLA and EMA were both useful for greatly reducing computational tasks while accurately coinciding with analytical solutions.

An approximate theoretical method for modeling the static thrust performance of non-axisymmetric two-dimensional convergent-divergent nozzles. M.S. Thesis - George Washington Univ.

NASA Technical Reports Server (NTRS)

Hunter, Craig A.

1995-01-01

An analytical/numerical method has been developed to predict the static thrust performance of non-axisymmetric, two-dimensional convergent-divergent exhaust nozzles. Thermodynamic nozzle performance effects due to over- and underexpansion are modeled using one-dimensional compressible flow theory. Boundary layer development and skin friction losses are calculated using an approximate integral momentum method based on the classic karman-Polhausen solution. Angularity effects are included with these two models in a computational Nozzle Performance Analysis Code, NPAC. In four different case studies, results from NPAC are compared to experimental data obtained from subscale nozzle testing to demonstrate the capabilities and limitations of the NPAC method. In several cases, the NPAC prediction matched experimental gross thrust efficiency data to within 0.1 percent at a design NPR, and to within 0.5 percent at off-design conditions.

Ab initio correlated calculations of rare-gas dimer quadrupoles

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

Donchev, Alexander G.

2007-10-15

This paper reports ab initio calculations of rare gas (RG=Kr, Ar, Ne, and He) dimer quadrupoles at the second order of Moeller-Plesset perturbation theory (MP2). The study reveals the crucial role of the dispersion contribution to the RG{sub 2} quadrupole in the neighborhood of the equilibrium dimer separation. The magnitude of the dispersion quadrupole is found to be much larger than that predicted by the approximate model of Hunt. As a result, the total MP2 quadrupole moment is significantly smaller than was assumed in virtually all previous related studies. An analytical model for the distance dependence of the RG{sub 2}more » quadrupole is proposed. The model is based on the effective-electron approach of Jansen, but replaces the original Gaussian approximation to the electron density in an RG atom by an exponential one. The role of the nonadditive contribution in RG{sub 3} quadrupoles is discussed.« less

Assessment regarding the use of the computer aided analytical models in the calculus of the general strength of a ship hull

NASA Astrophysics Data System (ADS)

Hreniuc, V.; Hreniuc, A.; Pescaru, A.

2017-08-01

Solving a general strength problem of a ship hull may be done using analytical approaches which are useful to deduce the buoyancy forces distribution, the weighting forces distribution along the hull and the geometrical characteristics of the sections. These data are used to draw the free body diagrams and to compute the stresses. The general strength problems require a large amount of calculi, therefore it is interesting how a computer may be used to solve such problems. Using computer programming an engineer may conceive software instruments based on analytical approaches. However, before developing the computer code the research topic must be thoroughly analysed, in this way being reached a meta-level of understanding of the problem. The following stage is to conceive an appropriate development strategy of the original software instruments useful for the rapid development of computer aided analytical models. The geometrical characteristics of the sections may be computed using a bool algebra that operates with ‘simple’ geometrical shapes. By ‘simple’ we mean that for the according shapes we have direct calculus relations. In the set of ‘simple’ shapes we also have geometrical entities bounded by curves approximated as spline functions or as polygons. To conclude, computer programming offers the necessary support to solve general strength ship hull problems using analytical methods.

Spacing distribution functions for the one-dimensional point-island model with irreversible attachment

NASA Astrophysics Data System (ADS)

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

2011-07-01

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

Reactive silica transport in fractured porous media: Analytical solutions for a system of parallel fractures

NASA Astrophysics Data System (ADS)

Yang, Jianwen

2012-04-01

A general analytical solution is derived by using the Laplace transformation to describe transient reactive silica transport in a conceptualized 2-D system involving a set of parallel fractures embedded in an impermeable host rock matrix, taking into account of hydrodynamic dispersion and advection of silica transport along the fractures, molecular diffusion from each fracture to the intervening rock matrix, and dissolution of quartz. A special analytical solution is also developed by ignoring the longitudinal hydrodynamic dispersion term but remaining other conditions the same. The general and special solutions are in the form of a double infinite integral and a single infinite integral, respectively, and can be evaluated using Gauss-Legendre quadrature technique. A simple criterion is developed to determine under what conditions the general analytical solution can be approximated by the special analytical solution. It is proved analytically that the general solution always lags behind the special solution, unless a dimensionless parameter is less than a critical value. Several illustrative calculations are undertaken to demonstrate the effect of fracture spacing, fracture aperture and fluid flow rate on silica transport. The analytical solutions developed here can serve as a benchmark to validate numerical models that simulate reactive mass transport in fractured porous media.

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.

Application of the optimal homotopy asymptotic method to nonlinear Bingham fluid dampers

NASA Astrophysics Data System (ADS)

Marinca, Vasile; Ene, Remus-Daniel; Bereteu, Liviu

2017-10-01

Dynamic response time is an important feature for determining the performance of magnetorheological (MR) dampers in practical civil engineering applications. The objective of this paper is to show how to use the Optimal Homotopy Asymptotic Method (OHAM) to give approximate analytical solutions of the nonlinear differential equation of a modified Bingham model with non-viscous exponential damping. Our procedure does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. OHAM is very efficient in practice for ensuring very rapid convergence of the solution after only one iteration and with a small number of steps.

Three dimensional α-tunneling in intense laser fields

NASA Astrophysics Data System (ADS)

Kis, Daniel P.; Szilvasi, Reka

2018-04-01

The width and life-time of the quasibound state of the α cluster in intense monochromatic electromagnetic (laser) field are discussed in details. The laser modified three dimensional potential barrier felt by the α particle is investigated analytically in long wave approximation and zero-order approximations with some different nuclear models: Coulomb potential with rectangular well, and with Woods-Saxon type potential. We show that the circularly polarized electromagnetic field and the special parameters of the nuclear potentials determine an enhancement of the decay probability, so the life-time of the quasibound state decreases in few times compared to the case of free field.

Regularization of moving boundaries in a laplacian field by a mixed Dirichlet-Neumann boundary condition: exact results.

PubMed

Meulenbroek, Bernard; Ebert, Ute; Schäfer, Lothar

2005-11-04

The dynamics of ionization fronts that generate a conducting body are in the simplest approximation equivalent to viscous fingering without regularization. Going beyond this approximation, we suggest that ionization fronts can be modeled by a mixed Dirichlet-Neumann boundary condition. We derive exact uniformly propagating solutions of this problem in 2D and construct a single partial differential equation governing small perturbations of these solutions. For some parameter value, this equation can be solved analytically, which shows rigorously that the uniformly propagating solution is linearly convectively stable and that the asymptotic relaxation is universal and exponential in time.

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.

Computational Aspects of Sensitivity Calculations in Linear Transient Structural Analysis. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Greene, William H.

1989-01-01

A study has been performed focusing on the calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, transient response problems. One significant goal was to develop and evaluate sensitivity calculation techniques suitable for large-order finite element analyses. Accordingly, approximation vectors such as vibration mode shapes are used to reduce the dimensionality of the finite element model. Much of the research focused on the accuracy of both response quantities and sensitivities as a function of number of vectors used. Two types of sensitivity calculation techniques were developed and evaluated. The first type of technique is an overall finite difference method where the analysis is repeated for perturbed designs. The second type of technique is termed semianalytical because it involves direct, analytical differentiation of the equations of motion with finite difference approximation of the coefficient matrices. To be computationally practical in large-order problems, the overall finite difference methods must use the approximation vectors from the original design in the analyses of the perturbed models.

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

The luminosity function of quasars

NASA Technical Reports Server (NTRS)

Pei, Yichuan C.

1995-01-01

We propose a new evolutionary model for the optical luminosity function of quasars. Our analytical model is derived from fits to the empirical luminosity function estimated by Hartwick and Schade and Warren, Hewett, and Osmer on the basis of more than 1200 quasars over the range of redshifts 0 approximately less than z approximately less than 4.5. We find that the evolution of quasars over this entire redshift range can be well fitted by a Gaussian distribution, while the shape of the luminosity function can be well fitted by either a double power law or an exponential L(exp 1/4) law. The predicted number counts of quasars, as a function of either apparent magnitude or redshift, are fully consistent with the observed ones. Our model indicates that the evolution of quasars reaches its maximum at z approximately = 2.8 and declines at higher redshifts. An extrapolation of the evolution to z approximately greater than 4.5 implies that quasars may have started their cosmic fireworks at z(sub f) approximately = 5.2-5.5. Forthcoming surveys of quasars at these redshifts will be critical to constrain the epoch of quasar formation. All the results we derived are based on observed quasars and are therefore subject to the bias of obscuration by dust in damped Ly alpha systems. Future surveys of these absorption systems at z approximately greater than 3 will also be important if the formation epoch of quasars is to be known unambiguously.

Nonequilibrium self-energies, Ng approach, and heat current of a nanodevice for small bias voltage and temperature

NASA Astrophysics Data System (ADS)

Aligia, A. A.

2014-03-01

Using nonequilibrium renormalized perturbation theory to second order in the renormalized Coulomb repulsion, we calculate the lesser Σ< and and greater Σ> self-energies of the impurity Anderson model, which describes the current through a quantum dot, in the general asymmetric case. While in general a numerical integration is required to evaluate the perturbative result, we derive an analytical approximation for small frequency ω, bias voltage V, and temperature T, which is exact to total second order in these quantities. The approximation is valid when the corresponding energies ℏω, eV, and kBT are small compared to kBTK, where TK is the Kondo temperature. The result of the numerical integration is compared with the analytical one and with Ng approximation, in which Σ< and Σ> are assumed proportional to the retarded self-energy Σr times an average Fermi function. While it fails at T =0 for ℏ |ω|≲eV, we find that the Ng approximation is excellent for kBT>eV/2 and improves for asymmetric coupling to the leads. Even at T =0, the effect of the Ng approximation on the total occupation at the dot is very small. The dependence on ω and V are discussed in comparison with a Ward identity that is fulfilled by the three approaches. We also calculate the heat currents between the dot and any of the leads at finite bias voltage. One of the heat currents changes sign with the applied bias voltage at finite temperature.

Emulation applied to reliability analysis of reconfigurable, highly reliable, fault-tolerant computing systems

NASA Technical Reports Server (NTRS)

Migneault, G. E.

1979-01-01

Emulation techniques applied to the analysis of the reliability of highly reliable computer systems for future commercial aircraft are described. The lack of credible precision in reliability estimates obtained by analytical modeling techniques is first established. The difficulty is shown to be an unavoidable consequence of: (1) a high reliability requirement so demanding as to make system evaluation by use testing infeasible; (2) a complex system design technique, fault tolerance; (3) system reliability dominated by errors due to flaws in the system definition; and (4) elaborate analytical modeling techniques whose precision outputs are quite sensitive to errors of approximation in their input data. Next, the technique of emulation is described, indicating how its input is a simple description of the logical structure of a system and its output is the consequent behavior. Use of emulation techniques is discussed for pseudo-testing systems to evaluate bounds on the parameter values needed for the analytical techniques. Finally an illustrative example is presented to demonstrate from actual use the promise of the proposed application of emulation.

Analytical model of diffuse reflectance spectrum of skin tissue

NASA Astrophysics Data System (ADS)

Lisenko, S. A.; Kugeiko, M. M.; Firago, V. A.; Sobchuk, A. N.

2014-01-01

We have derived simple analytical expressions that enable highly accurate calculation of diffusely reflected light signals of skin in the spectral range from 450 to 800 nm at a distance from the region of delivery of exciting radiation. The expressions, taking into account the dependence of the detected signals on the refractive index, transport scattering coefficient, absorption coefficient and anisotropy factor of the medium, have been obtained in the approximation of a two-layer medium model (epidermis and dermis) for the same parameters of light scattering but different absorption coefficients of layers. Numerical experiments on the retrieval of the skin biophysical parameters from the diffuse reflectance spectra simulated by the Monte Carlo method show that commercially available fibre-optic spectrophotometers with a fixed distance between the radiation source and detector can reliably determine the concentration of bilirubin, oxy- and deoxyhaemoglobin in the dermis tissues and the tissue structure parameter characterising the size of its effective scatterers. We present the examples of quantitative analysis of the experimental data, confirming the correctness of estimates of biophysical parameters of skin using the obtained analytical expressions.

Physics of heat pipe rewetting

NASA Technical Reports Server (NTRS)

Chan, S. H.

1992-01-01

Although several studies have been made to determine the rewetting characteristics of liquid films on heated rods, tubes, and flat plates, no solutions are yet available to describe the rewetting process of a hot plate subjected to a uniform heating. A model is presented to analyze the rewetting process of such plates with and without grooves. Approximate analytical solutions are presented for the prediction of the rewetting velocity and the transient temperature profiles of the plates. It is shown that the present rewetting velocity solution reduces correctly to the existing solution for the rewetting of an initially hot isothermal plate without heating from beneath the plate. Numerical solutions have also been obtained to validate the analytical solutions.

Geometric Model for a Parametric Study of the Blended-Wing-Body Airplane

NASA Technical Reports Server (NTRS)

Mastin, C. Wayne; Smith, Robert E.; Sadrehaghighi, Ideen; Wiese, Micharl R.

1996-01-01

A parametric model is presented for the blended-wing-body airplane, one concept being proposed for the next generation of large subsonic transports. The model is defined in terms of a small set of parameters which facilitates analysis and optimization during the conceptual design process. The model is generated from a preliminary CAD geometry. From this geometry, airfoil cross sections are cut at selected locations and fitted with analytic curves. The airfoils are then used as boundaries for surfaces defined as the solution of partial differential equations. Both the airfoil curves and the surfaces are generated with free parameters selected to give a good representation of the original geometry. The original surface is compared with the parametric model, and solutions of the Euler equations for compressible flow are computed for both geometries. The parametric model is a good approximation of the CAD model and the computed solutions are qualitatively similar. An optimal NURBS approximation is constructed and can be used by a CAD model for further refinement or modification of the original geometry.

The influence of anisotropy on the core structure of Shockley partial dislocations within FCC materials

NASA Astrophysics Data System (ADS)

Szajewski, B. A.; Hunter, A.; Luscher, D. J.; Beyerlein, I. J.

2018-01-01

Both theoretical and numerical models of dislocations often necessitate the assumption of elastic isotropy to retain analytical tractability in addition to reducing computational load. As dislocation based models evolve towards physically realistic material descriptions, the assumption of elastic isotropy becomes increasingly worthy of examination. We present an analytical dislocation model for calculating the full dissociated core structure of dislocations within anisotropic face centered cubic (FCC) crystals as a function of the degree of material elastic anisotropy, two misfit energy densities on the γ-surface ({γ }{{isf}}, {γ }{{usf}}) and the remaining elastic constants. Our solution is independent of any additional features of the γ-surface. Towards this pursuit, we first demonstrate that the dependence of the anisotropic elasticity tensor on the orientation of the dislocation line within the FCC crystalline lattice is small and may be reasonably neglected for typical materials. With this approximation, explicit analytic solutions for the anisotropic elasticity tensor {B} for both nominally edge and screw dislocations within an FCC crystalline lattice are devised, and employed towards defining a set of effective isotropic elastic constants which reproduce fully anisotropic results, however do not retain the bulk modulus. Conversely, Hill averaged elastic constants which both retain the bulk modulus and reasonably approximate the dislocation core structure are employed within subsequent numerical calculations. We examine a wide range of materials within this study, and the features of each partial dislocation core are sufficiently localized that application of discrete linear elasticity accurately describes the separation of each partial dislocation core. In addition, the local features (the partial dislocation core distribution) are well described by a Peierls-Nabarro dislocation model. We develop a model for the displacement profile which depends upon two disparate dislocation length scales which describe the core structure; (i) the equilibrium stacking fault width between two Shockley partial dislocations, R eq and (ii) the maximum slip gradient, χ, of each Shockley partial dislocation. We demonstrate excellent agreement between our own analytic predictions, numerical calculations, and R eq computed directly by both ab-initio and molecular statics methods found elsewhere within the literature. The results suggest that understanding of various plastic mechanisms, e.g., cross-slip and nucleation may be augmented with the inclusion of elastic anisotropy.

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 three-stage colonization model for the peopling of the Americas.

PubMed

Kitchen, Andrew; Miyamoto, Michael M; Mulligan, Connie J

2008-02-13

We evaluate the process by which the Americas were originally colonized and propose a three-stage model that integrates current genetic, archaeological, geological, and paleoecological data. Specifically, we analyze mitochondrial and nuclear genetic data by using complementary coalescent models of demographic history and incorporating non-genetic data to enhance the anthropological relevance of the analysis. Bayesian skyline plots, which provide dynamic representations of population size changes over time, indicate that Amerinds went through two stages of growth approximately 40,000 and approximately 15,000 years ago separated by a long period of population stability. Isolation-with-migration coalescent analyses, which utilize data from sister populations to estimate a divergence date and founder population sizes, suggest an Amerind population expansion starting approximately 15,000 years ago. These results support a model for the peopling of the New World in which Amerind ancestors diverged from the Asian gene pool prior to 40,000 years ago and experienced a gradual population expansion as they moved into Beringia. After a long period of little change in population size in greater Beringia, Amerinds rapidly expanded into the Americas approximately 15,000 years ago either through an interior ice-free corridor or along the coast. This rapid colonization of the New World was achieved by a founder group with an effective population size of approximately 1,000-5,400 individuals. Our model presents a detailed scenario for the timing and scale of the initial migration to the Americas, substantially refines the estimate of New World founders, and provides a unified theory for testing with future datasets and analytic methods.

Simple Decision-Analytic Functions of the AUC for Ruling Out a Risk Prediction Model and an Added Predictor.

PubMed

Baker, Stuart G

2018-02-01

When using risk prediction models, an important consideration is weighing performance against the cost (monetary and harms) of ascertaining predictors. The minimum test tradeoff (MTT) for ruling out a model is the minimum number of all-predictor ascertainments per correct prediction to yield a positive overall expected utility. The MTT for ruling out an added predictor is the minimum number of added-predictor ascertainments per correct prediction to yield a positive overall expected utility. An approximation to the MTT for ruling out a model is 1/[P (H(AUC model )], where H(AUC) = AUC - {½ (1-AUC)} ½ , AUC is the area under the receiver operating characteristic (ROC) curve, and P is the probability of the predicted event in the target population. An approximation to the MTT for ruling out an added predictor is 1 /[P {(H(AUC Model:2 ) - H(AUC Model:1 )], where Model 2 includes an added predictor relative to Model 1. The latter approximation requires the Tangent Condition that the true positive rate at the point on the ROC curve with a slope of 1 is larger for Model 2 than Model 1. These approximations are suitable for back-of-the-envelope calculations. For example, in a study predicting the risk of invasive breast cancer, Model 2 adds to the predictors in Model 1 a set of 7 single nucleotide polymorphisms (SNPs). Based on the AUCs and the Tangent Condition, an MTT of 7200 was computed, which indicates that 7200 sets of SNPs are needed for every correct prediction of breast cancer to yield a positive overall expected utility. If ascertaining the SNPs costs $500, this MTT suggests that SNP ascertainment is not likely worthwhile for this risk prediction.

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

Revisiting the time until fixation of a neutral mutant in a finite population - A coalescent theory approach.

PubMed

Greenbaum, Gili

2015-09-07

Evaluation of the time scale of the fixation of neutral mutations is crucial to the theoretical understanding of the role of neutral mutations in evolution. Diffusion approximations of the Wright-Fisher model are most often used to derive analytic formulations of genetic drift, as well as for the time scales of the fixation of neutral mutations. These approximations require a set of assumptions, most notably that genetic drift is a stochastic process in a continuous allele-frequency space, an assumption appropriate for large populations. Here equivalent approximations are derived using a coalescent theory approach which relies on a different set of assumptions than the diffusion approach, and adopts a discrete allele-frequency space. Solutions for the mean and variance of the time to fixation of a neutral mutation derived from the two approaches converge for large populations but slightly differ for small populations. A Markov chain analysis of the Wright-Fisher model for small populations is used to evaluate the solutions obtained, showing that both the mean and the variance are better approximated by the coalescent approach. The coalescence approximation represents a tighter upper-bound for the mean time to fixation than the diffusion approximation, while the diffusion approximation and coalescence approximation form an upper and lower bound, respectively, for the variance. The converging solutions and the small deviations of the two approaches strongly validate the use of diffusion approximations, but suggest that coalescent theory can provide more accurate approximations for small populations. Copyright © 2015 Elsevier Ltd. All rights reserved.

Analysis of DNS Cache Effects on Query Distribution

PubMed Central

2013-01-01

This paper studies the DNS cache effects that occur on query distribution at the CN top-level domain (TLD) server. We first filter out the malformed DNS queries to purify the log data pollution according to six categories. A model for DNS resolution, more specifically DNS caching, is presented. We demonstrate the presence and magnitude of DNS cache effects and the cache sharing effects on the request distribution through analytic model and simulation. CN TLD log data results are provided and analyzed based on the cache model. The approximate TTL distribution for domain name is inferred quantificationally. PMID:24396313

Analysis of DNS cache effects on query distribution.

PubMed

Wang, Zheng

2013-01-01

This paper studies the DNS cache effects that occur on query distribution at the CN top-level domain (TLD) server. We first filter out the malformed DNS queries to purify the log data pollution according to six categories. A model for DNS resolution, more specifically DNS caching, is presented. We demonstrate the presence and magnitude of DNS cache effects and the cache sharing effects on the request distribution through analytic model and simulation. CN TLD log data results are provided and analyzed based on the cache model. The approximate TTL distribution for domain name is inferred quantificationally.

A free energy-based surface tension force model for simulation of multiphase flows by level-set method

NASA Astrophysics Data System (ADS)

Yuan, H. Z.; Chen, Z.; Shu, C.; Wang, Y.; Niu, X. D.; Shu, S.

2017-09-01

In this paper, a free energy-based surface tension force (FESF) model is presented for accurately resolving the surface tension force in numerical simulation of multiphase flows by the level set method. By using the analytical form of order parameter along the normal direction to the interface in the phase-field method and the free energy principle, FESF model offers an explicit and analytical formulation for the surface tension force. The only variable in this formulation is the normal distance to the interface, which can be substituted by the distance function solved by the level set method. On one hand, as compared to conventional continuum surface force (CSF) model in the level set method, FESF model introduces no regularized delta function, due to which it suffers less from numerical diffusions and performs better in mass conservation. On the other hand, as compared to the phase field surface tension force (PFSF) model, the evaluation of surface tension force in FESF model is based on an analytical approach rather than numerical approximations of spatial derivatives. Therefore, better numerical stability and higher accuracy can be expected. Various numerical examples are tested to validate the robustness of the proposed FESF model. It turns out that FESF model performs better than CSF model and PFSF model in terms of accuracy, stability, convergence speed and mass conservation. It is also shown in numerical tests that FESF model can effectively simulate problems with high density/viscosity ratio, high Reynolds number and severe topological interfacial changes.

Verification of spatial and temporal pressure distributions in segmented solid rocket motors

NASA Technical Reports Server (NTRS)

Salita, Mark

1989-01-01

A wide variety of analytical tools are in use today to predict the history and spatial distributions of pressure in the combustion chambers of solid rocket motors (SRMs). Experimental and analytical methods are presented here that allow the verification of many of these predictions. These methods are applied to the redesigned space shuttle booster (RSRM). Girth strain-gage data is compared to the predictions of various one-dimensional quasisteady analyses in order to verify the axial drop in motor static pressure during ignition transients as well as quasisteady motor operation. The results of previous modeling of radial flows in the bore, slots, and around grain overhangs are supported by approximate analytical and empirical techniques presented here. The predictions of circumferential flows induced by inhibitor asymmetries, nozzle vectoring, and propellant slump are compared to each other and to subscale cold air and water tunnel measurements to ascertain their validity.

An Incompressible, Depth-Averaged Lattice Boltzmann Method for Liquid Flow in Microfluidic Devices with Variable Aperture

DOE PAGES

Laleian, Artin; Valocchi, Albert J.; Werth, Charles J.

2015-11-24

Two-dimensional (2D) pore-scale models have successfully simulated microfluidic experiments of aqueous-phase flow with mixing-controlled reactions in devices with small aperture. A standard 2D model is not generally appropriate when the presence of mineral precipitate or biomass creates complex and irregular three-dimensional (3D) pore geometries. We modify the 2D lattice Boltzmann method (LBM) to incorporate viscous drag from the top and bottom microfluidic device (micromodel) surfaces, typically excluded in a 2D model. Viscous drag from these surfaces can be approximated by uniformly scaling a steady-state 2D velocity field at low Reynolds number. We demonstrate increased accuracy by approximating the viscous dragmore » with an analytically-derived body force which assumes a local parabolic velocity profile across the micromodel depth. Accuracy of the generated 2D velocity field and simulation permeability have not been evaluated in geometries with variable aperture. We obtain permeabilities within approximately 10% error and accurate streamlines from the proposed 2D method relative to results obtained from 3D simulations. Additionally, the proposed method requires a CPU run time approximately 40 times less than a standard 3D method, representing a significant computational benefit for permeability calculations.« less

Gap solitons in Ginzburg-Landau media.

PubMed

Sakaguchi, Hidetsugu; Malomed, Boris A

2008-05-01

We introduce a model combining basic elements of conservative systems which give rise to gap solitons, i.e., a periodic potential and self-defocusing cubic nonlinearity, and dissipative terms corresponding to the complex Ginzburg-Landau (CGL) equation of the cubic-quintic type. The model may be realized in optical cavities with a periodic transverse modulation of the refractive index, self-defocusing nonlinearity, linear gain, and saturable absorption. By means of systematic simulations and analytical approximations, we find three species of stable dissipative gap solitons (DGSs), and also dark solitons. They are located in the first finite band gap, very close to the border of the Bloch band separating the finite and the semi-infinite gaps. Two species represent loosely and tightly bound solitons, in cases when the underlying Bloch band is, respectively, relatively broad or very narrow. These two families of stationary solitons are separated by a region of breathers. The loosely bound DGSs are accurately described by means of two approximations, which rely on the product of a carrier Bloch function and a slowly varying envelope, or reduce the model to CGL-Bragg equations. The former approximation also applies to dark solitons. Another method, based on the variational approximation, accurately describes tightly bound solitons. The loosely bound DGSs, as well as dark solitons, are mobile, and their collisions are quasielastic.

Simulation of variation of apparent resistivity in resistivity surveys using finite difference modelling with Monte Carlo analysis

NASA Astrophysics Data System (ADS)

Aguirre, E. E.; Karchewski, B.

2017-12-01

DC resistivity surveying is a geophysical method that quantifies the electrical properties of the subsurface of the earth by applying a source current between two electrodes and measuring potential differences between electrodes at known distances from the source. Analytical solutions for a homogeneous half-space and simple subsurface models are well known, as the former is used to define the concept of apparent resistivity. However, in situ properties are heterogeneous meaning that simple analytical models are only an approximation, and ignoring such heterogeneity can lead to misinterpretation of survey results costing time and money. The present study examines the extent to which random variations in electrical properties (i.e. electrical conductivity) affect potential difference readings and therefore apparent resistivities, relative to an assumed homogeneous subsurface model. We simulate the DC resistivity survey using a Finite Difference (FD) approximation of an appropriate simplification of Maxwell's equations implemented in Matlab. Electrical resistivity values at each node in the simulation were defined as random variables with a given mean and variance, and are assumed to follow a log-normal distribution. The Monte Carlo analysis for a given variance of electrical resistivity was performed until the mean and variance in potential difference measured at the surface converged. Finally, we used the simulation results to examine the relationship between variance in resistivity and variation in surface potential difference (or apparent resistivity) relative to a homogeneous half-space model. For relatively low values of standard deviation in the material properties (<10% of mean), we observed a linear correlation between variance of resistivity and variance in apparent resistivity.

The Nonstationary Dynamics of Fitness Distributions: Asexual Model with Epistasis and Standing Variation

PubMed Central

Martin, Guillaume; Roques, Lionel

2016-01-01

Various models describe asexual evolution by mutation, selection, and drift. Some focus directly on fitness, typically modeling drift but ignoring or simplifying both epistasis and the distribution of mutation effects (traveling wave models). Others follow the dynamics of quantitative traits determining fitness (Fisher’s geometric model), imposing a complex but fixed form of mutation effects and epistasis, and often ignoring drift. In all cases, predictions are typically obtained in high or low mutation rate limits and for long-term stationary regimes, thus losing information on transient behaviors and the effect of initial conditions. Here, we connect fitness-based and trait-based models into a single framework, and seek explicit solutions even away from stationarity. The expected fitness distribution is followed over time via its cumulant generating function, using a deterministic approximation that neglects drift. In several cases, explicit trajectories for the full fitness distribution are obtained for arbitrary mutation rates and standing variance. For nonepistatic mutations, especially with beneficial mutations, this approximation fails over the long term but captures the early dynamics, thus complementing stationary stochastic predictions. The approximation also handles several diminishing returns epistasis models (e.g., with an optimal genotype); it can be applied at and away from equilibrium. General results arise at equilibrium, where fitness distributions display a “phase transition” with mutation rate. Beyond this phase transition, in Fisher’s geometric model, the full trajectory of fitness and trait distributions takes a simple form; robust to the details of the mutant phenotype distribution. Analytical arguments are explored regarding why and when the deterministic approximation applies. PMID:27770037

Chemical association in simple models of molecular and ionic fluids. III. The cavity function

NASA Astrophysics Data System (ADS)

Zhou, Yaoqi; Stell, George

1992-01-01

Exact equations which relate the cavity function to excess solvation free energies and equilibrium association constants are rederived by using a thermodynamic cycle. A zeroth-order approximation, derived previously by us as a simple interpolation scheme, is found to be very accurate if the associative bonding occurs on or near the surface of the repulsive core of the interaction potential. If the bonding radius is substantially less than the core radius, the approximation overestimates the association degree and the association constant. For binary association, the zeroth-order approximation is equivalent to the first-order thermodynamic perturbation theory (TPT) of Wertheim. For n-particle association, the combination of the zeroth-order approximation with a ``linear'' approximation (for n-particle distribution functions in terms of the two-particle function) yields the first-order TPT result. Using our exact equations to go beyond TPT, near-exact analytic results for binary hard-sphere association are obtained. Solvent effects on binary hard-sphere association and ionic association are also investigated. A new rule which generalizes Le Chatelier's principle is used to describe the three distinct forms of behaviors involving solvent effects that we find. The replacement of the dielectric-continuum solvent model by a dipolar hard-sphere model leads to improved agreement with an experimental observation. Finally, equation of state for an n-particle flexible linear-chain fluid is derived on the basis of a one-parameter approximation that interpolates between the generalized Kirkwood superposition approximation and the linear approximation. A value of the parameter that appears to be near optimal in the context of this application is obtained from comparison with computer-simulation data.