Closed-form solutions for a class of optimal quadratic regulator problems with terminal constraints

NASA Technical Reports Server (NTRS)

Juang, J.-N.; Turner, J. D.; Chun, H. M.

1984-01-01

Closed-form solutions are derived for coupled Riccati-like matrix differential equations describing the solution of a class of optimal finite time quadratic regulator problems with terminal constraints. Analytical solutions are obtained for the feedback gains and the closed-loop response trajectory. A computational procedure is presented which introduces new variables for efficient computation of the terminal control law. Two examples are given to illustrate the validity and usefulness of the theory.

Closed-form recursive formula for an optimal tracker with terminal constraints

NASA Technical Reports Server (NTRS)

Juang, J.-N.; Turner, J. D.; Chun, H. M.

1984-01-01

Feedback control laws are derived for a class of optimal finite time tracking problems with terminal constraints. Analytical solutions are obtained for the feedback gain and the closed-loop response trajectory. Such formulations are expressed in recursive forms so that a real-time computer implementation becomes feasible. Two examples are given to illustrate the validity and usefulness of the formulations.

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.

Analytical solutions for sequentially coupled one-dimensional reactive transport problems Part I: Mathematical derivations

NASA Astrophysics Data System (ADS)

Srinivasan, V.; Clement, T. P.

2008-02-01

Multi-species reactive transport equations coupled through sorption and sequential first-order reactions are commonly used to model sites contaminated with radioactive wastes, chlorinated solvents and nitrogenous species. Although researchers have been attempting to solve various forms of these reactive transport equations for over 50 years, a general closed-form analytical solution to this problem is not available in the published literature. In Part I of this two-part article, we derive a closed-form analytical solution to this problem for spatially-varying initial conditions. The proposed solution procedure employs a combination of Laplace and linear transform methods to uncouple and solve the system of partial differential equations. Two distinct solutions are derived for Dirichlet and Cauchy boundary conditions each with Bateman-type source terms. We organize and present the final solutions in a common format that represents the solutions to both boundary conditions. In addition, we provide the mathematical concepts for deriving the solution within a generic framework that can be used for solving similar transport problems.

Orthopositronium Lifetime: Analytic Results in O({alpha}) and O({alpha}{sup 3}ln{alpha})

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

Kniehl, Bernd A.; Kotikov, Anatoly V.; Veretin, Oleg L.

2008-11-07

We present the O({alpha}) and O({alpha}{sup 3}ln{alpha}) corrections to the total decay width of orthopositronium in closed analytic form, in terms of basic irrational numbers, which can be evaluated numerically to arbitrary precision.

Analytical and numerical solutions for heat transfer and effective thermal conductivity of cracked media

NASA Astrophysics Data System (ADS)

Tran, A. B.; Vu, M. N.; Nguyen, S. T.; Dong, T. Q.; Le-Nguyen, K.

2018-02-01

This paper presents analytical solutions to heat transfer problems around a crack and derive an adaptive model for effective thermal conductivity of cracked materials based on singular integral equation approach. Potential solution of heat diffusion through two-dimensional cracked media, where crack filled by air behaves as insulator to heat flow, is obtained in a singular integral equation form. It is demonstrated that the temperature field can be described as a function of temperature and rate of heat flow on the boundary and the temperature jump across the cracks. Numerical resolution of this boundary integral equation allows determining heat conduction and effective thermal conductivity of cracked media. Moreover, writing this boundary integral equation for an infinite medium embedding a single crack under a far-field condition allows deriving the closed-form solution of temperature discontinuity on the crack and particularly the closed-form solution of temperature field around the crack. These formulas are then used to establish analytical effective medium estimates. Finally, the comparison between the developed numerical and analytical solutions allows developing an adaptive model for effective thermal conductivity of cracked media. This model takes into account both the interaction between cracks and the percolation threshold.

Kapteyn series arising in radiation problems

NASA Astrophysics Data System (ADS)

Lerche, I.; Tautz, R. C.

2008-01-01

In discussing radiation from multiple point charges or magnetic dipoles, moving in circles or ellipses, a variety of Kapteyn series of the second kind arises. Some of the series have been known in closed form for a hundred years or more, others appear not to be available to analytic persuasion. This paper shows how 12 such generic series can be developed to produce either closed analytic expressions or integrals that are not analytically tractable. In addition, the method presented here may be of benefit when one has other Kapteyn series of the second kind to consider, thereby providing an additional reason to consider such series anew.

Numerical Algorithm for Delta of Asian Option

PubMed Central

Zhang, Boxiang; Yu, Yang; Wang, Weiguo

2015-01-01

We study the numerical solution of the Greeks of Asian options. In particular, we derive a close form solution of Δ of Asian geometric option and use this analytical form as a control to numerically calculate Δ of Asian arithmetic option, which is known to have no explicit close form solution. We implement our proposed numerical method and compare the standard error with other classical variance reduction methods. Our method provides an efficient solution to the hedging strategy with Asian options. PMID:26266271

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.

Closed-form recursive formula for an optimal tracker with terminal constraints

NASA Technical Reports Server (NTRS)

Juang, J. N.; Turner, J. D.; Chun, H. M.

1986-01-01

Feedback control laws are derived for a class of optimal finite time tracking problems with terminal constraints. Analytical solutions are obtained for the feedback gain and the closed-loop response trajectory. Such formulations are expressed in recursive forms so that a real-time computer implementation becomes feasible. An example involving the feedback slewing of a flexible spacecraft is given to illustrate the validity and usefulness of the formulations.

Realistic Analytical Polyhedral MRI Phantoms

PubMed Central

Ngo, Tri M.; Fung, George S. K.; Han, Shuo; Chen, Min; Prince, Jerry L.; Tsui, Benjamin M. W.; McVeigh, Elliot R.; Herzka, Daniel A.

2015-01-01

Purpose Analytical phantoms have closed form Fourier transform expressions and are used to simulate MRI acquisitions. Existing 3D analytical phantoms are unable to accurately model shapes of biomedical interest. It is demonstrated that polyhedral analytical phantoms have closed form Fourier transform expressions and can accurately represent 3D biomedical shapes. Theory The derivations of the Fourier transform of a polygon and polyhedron are presented. Methods The Fourier transform of a polyhedron was implemented and its accuracy in representing faceted and smooth surfaces was characterized. Realistic anthropomorphic polyhedral brain and torso phantoms were constructed and their use in simulated 3D/2D MRI acquisitions was described. Results Using polyhedra, the Fourier transform of faceted shapes can be computed to within machine precision. Smooth surfaces can be approximated with increasing accuracy by increasing the number of facets in the polyhedron; the additional accumulated numerical imprecision of the Fourier transform of polyhedra with many faces remained small. Simulations of 3D/2D brain and 2D torso cine acquisitions produced realistic reconstructions free of high frequency edge aliasing as compared to equivalent voxelized/rasterized phantoms. Conclusion Analytical polyhedral phantoms are easy to construct and can accurately simulate shapes of biomedical interest. PMID:26479724

Approximate Solution to the Angular Speeds of a Nearly-Symmetric Mass-Varying Cylindrical Body

NASA Astrophysics Data System (ADS)

Nanjangud, Angadh; Eke, Fidelis

2017-06-01

This paper examines the rotational motion of a nearly axisymmetric rocket type system with uniform burn of its propellant. The asymmetry comes from a slight difference in the transverse principal moments of inertia of the system, which then results in a set of nonlinear equations of motion even when no external torque is applied to the system. It is often difficult, or even impossible, to generate analytic solutions for such equations; closed form solutions are even more difficult to obtain. In this paper, a perturbation-based approach is employed to linearize the equations of motion and generate analytic solutions. The solutions for the variables of transverse motion are analytic and a closed-form solution to the spin rate is suggested. The solutions are presented in a compact form that permits rapid computation. The approximate solutions are then applied to the torque-free motion of a typical solid rocket system and the results are found to agree with those obtained from the numerical solution of the full non-linear equations of motion of the mass varying system.

An efficient closed-form solution for acoustic emission source location in three-dimensional structures

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

Li, Xibing; Dong, Longjun, E-mail: csudlj@163.com; Australian Centre for Geomechanics, The University of Western Australia, Crawley, 6009

This paper presents an efficient closed-form solution (ECS) for acoustic emission(AE) source location in three-dimensional structures using time difference of arrival (TDOA) measurements from N receivers, N ≥ 6. The nonlinear location equations of TDOA are simplified to linear equations. The unique analytical solution of AE sources for unknown velocity system is obtained by solving the linear equations. The proposed ECS method successfully solved the problems of location errors resulting from measured deviations of velocity as well as the existence and multiplicity of solutions induced by calculations of square roots in existed close-form methods.

Development of an analytical solution for thermal single-well injection-withdrawal tests in horizontally fractured reservoirs

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

Jung, Yoojin

In this study, we have developed an analytical solution for thermal single-well injection-withdrawal tests in horizontally fractured reservoirs where fluid flow through the fracture is radial. The dimensionless forms of the governing equations and the initial and boundary conditions in the radial flow system can be written in a form identical to those in the linear flow system developed by Jung and Pruess [Jung, Y., and K. Pruess (2012), A Closed-Form Analytical Solution for Thermal Single-Well Injection-Withdrawal Tests, Water Resour. Res., 48, W03504, doi:10.1029/2011WR010979], and therefore the analytical solutions developed in Jung and Pruess (2012) can be applied to computemore » the time dependence of temperature recovery at the injection/withdrawal well in a horizontally oriented fracture with radial flow.« less

Critical behavior of a relativistic Bose gas.

PubMed

Pandita, P N

2014-03-01

We show that the thermodynamic behavior of relativistic ideal Bose gas, recently studied numerically by Grether et al., can be obtained analytically. Using the analytical results, we obtain the critical behavior of the relativistic Bose gas exactly for all the regimes. We show that these analytical results reduce to those of Grether et al. in different regimes of the Bose gas. Furthermore, we also obtain an analytically closed-form expression for the energy density for the Bose gas that is valid in all regimes.

Continuous Optimization on Constraint Manifolds

NASA Technical Reports Server (NTRS)

Dean, Edwin B.

1988-01-01

This paper demonstrates continuous optimization on the differentiable manifold formed by continuous constraint functions. The first order tensor geodesic differential equation is solved on the manifold in both numerical and closed analytic form for simple nonlinear programs. Advantages and disadvantages with respect to conventional optimization techniques are discussed.

New integrable models and analytical solutions in f (R ) cosmology with an ideal gas

NASA Astrophysics Data System (ADS)

Papagiannopoulos, G.; Basilakos, Spyros; Barrow, John D.; Paliathanasis, Andronikos

2018-01-01

In the context of f (R ) gravity with a spatially flat FLRW metric containing an ideal fluid, we use the method of invariant transformations to specify families of models which are integrable. We find three families of f (R ) theories for which new analytical solutions are given and closed-form solutions are provided.

Analytical formulation of cellular automata rules using data models

NASA Astrophysics Data System (ADS)

Jaenisch, Holger M.; Handley, James W.

2009-05-01

We present a unique method for converting traditional cellular automata (CA) rules into analytical function form. CA rules have been successfully used for morphological image processing and volumetric shape recognition and classification. Further, the use of CA rules as analog models to the physical and biological sciences can be significantly extended if analytical (as opposed to discrete) models could be formulated. We show that such transformations are possible. We use as our example John Horton Conway's famous "Game of Life" rule set. We show that using Data Modeling, we are able to derive both polynomial and bi-spectrum models of the IF-THEN rules that yield equivalent results. Further, we demonstrate that the "Game of Life" rule set can be modeled using the multi-fluxion, yielding a closed form nth order derivative and integral. All of the demonstrated analytical forms of the CA rule are general and applicable to real-time use.

Magnetohydrodynamic viscous flow over a nonlinearly moving surface: Closed-form solutions

NASA Astrophysics Data System (ADS)

Fang, Tiegang

2014-05-01

In this paper, the magnetohydrodynamic (MHD) flow over a nonlinearly (power-law velocity) moving surface is investigated analytically and solutions are presented for a few special conditions. The solutions are obtained in closed forms with hyperbolic functions. The effects of the magnetic, the wall moving, and the mass transpiration parameters are discussed. These solutions are important to show the flow physics as well as to be used as bench mark problems for numerical validation and development of new solution schemes.

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

QCD triple Pomeron coupling from string amplitudes

NASA Astrophysics Data System (ADS)

Bialas, A.; Navelet, H.; Peschanski, R.

1998-06-01

Using the recent solution of the triple Pomeron coupling in the QCD dipole picture as a closed string amplitude with six legs, its analytical form in terms of hypergeometric functions and numerical value are derived.

An investigation of the information propagation and entropy transport aspects of Stirling machine numerical simulation

NASA Technical Reports Server (NTRS)

Goldberg, Louis F.

1992-01-01

Aspects of the information propagation modeling behavior of integral machine computer simulation programs are investigated in terms of a transmission line. In particular, the effects of pressure-linking and temporal integration algorithms on the amplitude ratio and phase angle predictions are compared against experimental and closed-form analytic data. It is concluded that the discretized, first order conservation balances may not be adequate for modeling information propagation effects at characteristic numbers less than about 24. An entropy transport equation suitable for generalized use in Stirling machine simulation is developed. The equation is evaluated by including it in a simulation of an incompressible oscillating flow apparatus designed to demonstrate the effect of flow oscillations on the enhancement of thermal diffusion. Numerical false diffusion is found to be a major factor inhibiting validation of the simulation predictions with experimental and closed-form analytic data. A generalized false diffusion correction algorithm is developed which allows the numerical results to match their analytic counterparts. Under these conditions, the simulation yields entropy predictions which satisfy Clausius' inequality.

Eshelby problem of polygonal inclusions in anisotropic piezoelectric full- and half-planes

NASA Astrophysics Data System (ADS)

Pan, E.

2004-03-01

This paper presents an exact closed-form solution for the Eshelby problem of polygonal inclusion in anisotropic piezoelectric full- and half-planes. Based on the equivalent body-force concept of eigenstrain, the induced elastic and piezoelectric fields are first expressed in terms of line integral on the boundary of the inclusion with the integrand being the Green's function. Using the recently derived exact closed-form line-source Green's function, the line integral is then carried out analytically, with the final expression involving only elementary functions. The exact closed-form solution is applied to a square-shaped quantum wire within semiconductor GaAs full- and half-planes, with results clearly showing the importance of material orientation and piezoelectric coupling. While the elastic and piezoelectric fields within the square-shaped quantum wire could serve as benchmarks to other numerical methods, the exact closed-form solution should be useful to the analysis of nanoscale quantum-wire structures where large strain and electric fields could be induced by the misfit strain.

Closed form expressions for ABER and capacity over EGK fading channel in presence of CCI

NASA Astrophysics Data System (ADS)

Singh, S. Pratap; Kumar, Sanjay

2017-03-01

Goal of next generation wireless communication system is to achieve very high data rate. Femto-cell is one of the possibilities to achieve the above target. However, co-channel interference (CCI) is the important concern in femto-cell. This paper presents closed form expressions for average bit error rate (ABER) and capacity for different adaptive schemes under extended generalised-K (EGK) fading channel in the presence of CCI. A novel conditional unified expression (CUE) is derived, which results different conditional error probability and normalised average capacity. Using CUE, a generic expression for ABER is obtained. In addition, closed form expressions for ABER for different modulation schemes under EGK fading channel in presence of CCI are also derived. Further, it is shown that generic ABER expression results into ABER of different modulation schemes. Besides, the closed form expressions of capacity for different adaptive schemes under EGK in presence of CCI are derived. Finally, analytical and simulated results are obtained with excellent agreement.

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.

An Analytical Study of Prostate-Specific Antigen Dynamics.

PubMed

Esteban, Ernesto P; Deliz, Giovanni; Rivera-Rodriguez, Jaileen; Laureano, Stephanie M

2016-01-01

The purpose of this research is to carry out a quantitative study of prostate-specific antigen dynamics for patients with prostatic diseases, such as benign prostatic hyperplasia (BPH) and localized prostate cancer (LPC). The proposed PSA mathematical model was implemented using clinical data of 218 Japanese patients with histological proven BPH and 147 Japanese patients with LPC (stages T2a and T2b). For prostatic diseases (BPH and LPC) a nonlinear equation was obtained and solved in a close form to predict PSA progression with patients' age. The general solution describes PSA dynamics for patients with both diseases LPC and BPH. Particular solutions allow studying PSA dynamics for patients with BPH or LPC. Analytical solutions have been obtained and solved in a close form to develop nomograms for a better understanding of PSA dynamics in patients with BPH and LPC. This study may be useful to improve the diagnostic and prognosis of prostatic diseases.

On the Probabilistic Deployment of Smart Grid Networks in TV White Space.

PubMed

Cacciapuoti, Angela Sara; Caleffi, Marcello; Paura, Luigi

2016-05-10

To accommodate the rapidly increasing demand for wireless broadband communications in Smart Grid (SG) networks, research efforts are currently ongoing to enable the SG networks to utilize the TV spectrum according to the Cognitive Radio paradigm. To this aim, in this letter, we develop an analytical framework for the optimal deployment of multiple closely-located SG Neighborhood Area Networks (NANs) concurrently using the same TV spectrum. The objective is to derive the optimal values for both the number of NANs and their coverage. More specifically, regarding the number of NANs, we derive the optimal closed-form expression, i.e., the closed-form expression that assures the deployment of the maximum number of NANs in the considered region satisfying a given collision constraint on the transmissions of the NANs. Regarding the NAN coverage, we derive the optimal closed-form expression, i.e., the closed-form expression of the NAN transmission range that assures the maximum coverage of each NAN in the considered region satisfying the given collision constraint. All the theoretical results are derived by adopting a stochastic approach. Finally, numerical results validate the theoretical analysis.

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

NASA Astrophysics Data System (ADS)

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

2005-01-01

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

Advances in the theory of box integrals

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

Bailey, David H.; Borwein, J.M.; Crandall, R.E.

2009-06-25

Box integrals - expectations <|{rvec r}|{sup s}> or <|{rvec r}-{rvec q}|{sup s}> over the unit n-cube (or n-box) - have over three decades been occasionally given closed forms for isolated n,s. By employing experimental mathematics together with a new, global analytic strategy, we prove that for n {le} 4 dimensions the box integrals are for any integer s hypergeometrically closed in a sense we clarify herein. For n = 5 dimensions, we show that a single unresolved integral we call K{sub 5} stands in the way of such hyperclosure proofs. We supply a compendium of exemplary closed forms that naturallymore » arise algorithmically from this theory.« less

Analytical and finite element simulation of a three-bar torsion spring

NASA Astrophysics Data System (ADS)

Rădoi, M.; Cicone, T.

2016-08-01

The present study is dedicated to the innovative 3-bar torsion spring used as suspension solution for the first time at Lunokhod-1, the first autonomous vehicle sent for the exploration of the Moon in the early 70-ies by the former USSR. The paper describes a simple analytical model for calculation of spring static characteristics, taking into account both torsion and bending effects. Closed form solutions of this model allows quick and elegant parametric analysis. A comparison with a single torsion bar with the same stiffness reveal an increase of the maximum stress with more than 50%. A 3D finite element (FE) simulation is proposed to evaluate the accuracy of the analytical model. The model was meshed in an automated pattern (sweep for hubs and tetrahedrons for bars) with mesh morphing. Very close results between analytical and numerical solutions have been found, concluding that the analytical model is accurate. The 3-D finite element simulation was used to evaluate the effects of design details like fillet radius of the bars or contact stresses in the hex hub.

A closed-form solution for steady-state coupled phloem/xylem flow using the Lambert-W function.

PubMed

Hall, A J; Minchin, P E H

2013-12-01

A closed-form solution for steady-state coupled phloem/xylem flow is presented. This incorporates the basic Münch flow model of phloem transport, the cohesion model of xylem flow, and local variation in the xylem water potential and lateral water flow along the transport pathway. Use of the Lambert-W function allows this solution to be obtained under much more general and realistic conditions than has previously been possible. Variation in phloem resistance (i.e. viscosity) with solute concentration, and deviations from the Van't Hoff expression for osmotic potential are included. It is shown that the model predictions match those of the equilibrium solution of a numerical time-dependent model based upon the same mechanistic assumptions. The effect of xylem flow upon phloem flow can readily be calculated, which has not been possible in any previous analytical model. It is also shown how this new analytical solution can handle multiple sources and sinks within a complex architecture, and can describe competition between sinks. The model provides new insights into Münch flow by explicitly including interactions with xylem flow and water potential in the closed-form solution, and is expected to be useful as a component part of larger numerical models of entire plants. © 2013 John Wiley & Sons Ltd.

Binegativity of two qubits under noise

NASA Astrophysics Data System (ADS)

Sazim, Sk; Awasthi, Natasha

2018-07-01

Recently, it was argued that the binegativity might be a good quantifier of entanglement for two-qubit states. Like the concurrence and the negativity, the binegativity is also analytically computable quantifier for all two qubits. Based on numerical evidence, it was conjectured that it is a PPT (positive partial transposition) monotone and thus fulfills the criterion to be a good measure of entanglement. In this work, we investigate its behavior under noisy channels which indicate that the binegativity is decreasing monotonically with respect to increasing noise. We also find that the binegativity is closely connected to the negativity and has closed analytical form for arbitrary two qubits. Our study supports the conjecture that the binegativity is a monotone.

Axially grooved heat pipe study

NASA Technical Reports Server (NTRS)

1977-01-01

A technology evaluation study on axially grooved heat pipes is presented. The state-of-the-art is reviewed and present and future requirements are identified. Analytical models, the Groove Analysis Program (GAP) and a closed form solution, were developed to facilitate parametric performance evaluations. GAP provides a numerical solution of the differential equations which govern the hydrodynamic flow. The model accounts for liquid recession, liquid/vapor shear interaction, puddle flow as well as laminar and turbulent vapor flow conditions. The closed form solution was developed to reduce computation time and complexity in parametric evaluations. It is applicable to laminar and ideal charge conditions, liquid/vapor shear interaction, and an empirical liquid flow factor which accounts for groove geometry and liquid recession effects. The validity of the closed form solution is verified by comparison with GAP predictions and measured data.

A Novel Capacity Analysis for Wireless Backhaul Mesh Networks

NASA Astrophysics Data System (ADS)

Chung, Tein-Yaw; Lee, Kuan-Chun; Lee, Hsiao-Chih

This paper derived a closed-form expression for inter-flow capacity of a backhaul wireless mesh network (WMN) with centralized scheduling by employing a ring-based approach. Through the definition of an interference area, we are able to accurately describe a bottleneck collision area for a WMN and calculate the upper bound of inter-flow capacity. The closed-form expression shows that the upper bound is a function of the ratio between transmission range and network radius. Simulations and numerical analysis show that our analytic solution can better estimate the inter-flow capacity of WMNs than that of previous approach.

Line-source excitation of realistic conformal metasurface cloaks

NASA Astrophysics Data System (ADS)

Padooru, Yashwanth R.; Yakovlev, Alexander B.; Chen, Pai-Yen; Alù, Andrea

2012-11-01

Following our recently introduced analytical tools to model and design conformal mantle cloaks based on metasurfaces [Padooru et al., J. Appl. Phys. 112, 034907 (2012)], we investigate their performance and physical properties when excited by an electric line source placed in their close proximity. We consider metasurfaces formed by 2-D arrays of slotted (meshes and Jerusalem cross slots) and printed (patches and Jerusalem crosses) sub-wavelength elements. The electromagnetic scattering analysis is carried out using a rigorous analytical model, which utilizes the two-sided impedance boundary conditions at the interface of the sub-wavelength elements. It is shown that the homogenized grid-impedance expressions, originally derived for planar arrays of sub-wavelength elements and plane-wave excitation, may be successfully used to model and tailor the surface reactance of cylindrical conformal mantle cloaks illuminated by near-field sources. Our closed-form analytical results are in good agreement with full-wave numerical simulations, up to sub-wavelength distances from the metasurface, confirming that mantle cloaks may be very effective to suppress the scattering of moderately sized objects, independent of the type of excitation and point of observation. We also discuss the dual functionality of these metasurfaces to boost radiation efficiency and directivity from confined near-field sources.

Analytical model for investigation of interior noise characteristics in aircraft with multiple propellers including synchrophasing

NASA Technical Reports Server (NTRS)

Fuller, C. R.

1986-01-01

A simplified analytical model of transmission of noise into the interior of propeller-driven aircraft has been developed. The analysis includes directivity and relative phase effects of the propeller noise sources, and leads to a closed form solution for the coupled motion between the interior and exterior fields via the shell (fuselage) vibrational response. Various situations commonly encountered in considering sound transmission into aircraft fuselages are investigated analytically and the results obtained are compared to measurements in real aircraft. In general the model has proved successful in identifying basic mechanisms behind noise transmission phenomena.

First-order analytic propagation of satellites in the exponential atmosphere of an oblate planet

NASA Astrophysics Data System (ADS)

Martinusi, Vladimir; Dell'Elce, Lamberto; Kerschen, Gaëtan

2017-04-01

The paper offers the fully analytic solution to the motion of a satellite orbiting under the influence of the two major perturbations, due to the oblateness and the atmospheric drag. The solution is presented in a time-explicit form, and takes into account an exponential distribution of the atmospheric density, an assumption that is reasonably close to reality. The approach involves two essential steps. The first one concerns a new approximate mathematical model that admits a closed-form solution with respect to a set of new variables. The second step is the determination of an infinitesimal contact transformation that allows to navigate between the new and the original variables. This contact transformation is obtained in exact form, and afterwards a Taylor series approximation is proposed in order to make all the computations explicit. The aforementioned transformation accommodates both perturbations, improving the accuracy of the orbit predictions by one order of magnitude with respect to the case when the atmospheric drag is absent from the transformation. Numerical simulations are performed for a low Earth orbit starting at an altitude of 350 km, and they show that the incorporation of drag terms into the contact transformation generates an error reduction by a factor of 7 in the position vector. The proposed method aims at improving the accuracy of analytic orbit propagation and transforming it into a viable alternative to the computationally intensive numerical methods.

An explicit closed-form analytical solution for European options under the CGMY model

NASA Astrophysics Data System (ADS)

Chen, Wenting; Du, Meiyu; Xu, Xiang

2017-01-01

In this paper, we consider the analytical pricing of European path-independent options under the CGMY model, which is a particular type of pure jump Le´vy process, and agrees well with many observed properties of the real market data by allowing the diffusions and jumps to have both finite and infinite activity and variation. It is shown that, under this model, the option price is governed by a fractional partial differential equation (FPDE) with both the left-side and right-side spatial-fractional derivatives. In comparison to derivatives of integer order, fractional derivatives at a point not only involve properties of the function at that particular point, but also the information of the function in a certain subset of the entire domain of definition. This ;globalness; of the fractional derivatives has added an additional degree of difficulty when either analytical methods or numerical solutions are attempted. Albeit difficult, we still have managed to derive an explicit closed-form analytical solution for European options under the CGMY model. Based on our solution, the asymptotic behaviors of the option price and the put-call parity under the CGMY model are further discussed. Practically, a reliable numerical evaluation technique for the current formula is proposed. With the numerical results, some analyses of impacts of four key parameters of the CGMY model on European option prices are also provided.

Analysis of social optimum for staggered shifts in a single-entry traffic corridor with no late arrivals

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

A closed-form analytical model for predicting 3D boundary layer displacement thickness for the validation of viscous flow solvers

NASA Astrophysics Data System (ADS)

Kumar, V. R. Sanal; Sankar, Vigneshwaran; Chandrasekaran, Nichith; Saravanan, Vignesh; Natarajan, Vishnu; Padmanabhan, Sathyan; Sukumaran, Ajith; Mani, Sivabalan; Rameshkumar, Tharikaa; Nagaraju Doddi, Hema Sai; Vysaprasad, Krithika; Sharan, Sharad; Murugesh, Pavithra; Shankar, S. Ganesh; Nejaamtheen, Mohammed Niyasdeen; Baskaran, Roshan Vignesh; Rahman Mohamed Rafic, Sulthan Ariff; Harisrinivasan, Ukeshkumar; Srinivasan, Vivek

2018-02-01

A closed-form analytical model is developed for estimating the 3D boundary-layer-displacement thickness of an internal flow system at the Sanal flow choking condition for adiabatic flows obeying the physics of compressible viscous fluids. At this unique condition the boundary-layer blockage induced fluid-throat choking and the adiabatic wall-friction persuaded flow choking occur at a single sonic-fluid-throat location. The beauty and novelty of this model is that without missing the flow physics we could predict the exact boundary-layer blockage of both 2D and 3D cases at the sonic-fluid-throat from the known values of the inlet Mach number, the adiabatic index of the gas and the inlet port diameter of the internal flow system. We found that the 3D blockage factor is 47.33 % lower than the 2D blockage factor with air as the working fluid. We concluded that the exact prediction of the boundary-layer-displacement thickness at the sonic-fluid-throat provides a means to correctly pinpoint the causes of errors of the viscous flow solvers. The methodology presented herein with state-of-the-art will play pivotal roles in future physical and biological sciences for a credible verification, calibration and validation of various viscous flow solvers for high-fidelity 2D/3D numerical simulations of real-world flows. Furthermore, our closed-form analytical model will be useful for the solid and hybrid rocket designers for the grain-port-geometry optimization of new generation single-stage-to-orbit dual-thrust-motors with the highest promising propellant loading density within the given envelope without manifestation of the Sanal flow choking leading to possible shock waves causing catastrophic failures.

Cluster Size Optimization in Sensor Networks with Decentralized Cluster-Based Protocols

PubMed Central

Amini, Navid; Vahdatpour, Alireza; Xu, Wenyao; Gerla, Mario; Sarrafzadeh, Majid

2011-01-01

Network lifetime and energy-efficiency are viewed as the dominating considerations in designing cluster-based communication protocols for wireless sensor networks. This paper analytically provides the optimal cluster size that minimizes the total energy expenditure in such networks, where all sensors communicate data through their elected cluster heads to the base station in a decentralized fashion. LEACH, LEACH-Coverage, and DBS comprise three cluster-based protocols investigated in this paper that do not require any centralized support from a certain node. The analytical outcomes are given in the form of closed-form expressions for various widely-used network configurations. Extensive simulations on different networks are used to confirm the expectations based on the analytical results. To obtain a thorough understanding of the results, cluster number variability problem is identified and inspected from the energy consumption point of view. PMID:22267882

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Nonlinear pressure-flow relationships for passive microfluidic valves.

PubMed

Seker, Erkin; Leslie, Daniel C; Haj-Hariri, Hossein; Landers, James P; Utz, Marcel; Begley, Matthew R

2009-09-21

An analytical solution is presented for the nonlinear pressure-flow relationship of deformable passive valves, which are formed by bonding a deformable film over etched channels separated by a weir. A fluidic pathway connecting the channels is opened when the upstream pressure creates a tunnel along a predefined narrow strip where the film is not bonded to the weir. When the width of the strip is comparable to the inlet channel width, the predicted closed-form pressure-flow rate relationship is in excellent agreement with experiments, which determine pressures by measuring film deflections for prescribed flow rates. The validated closed-form models involve no fitting parameters, and provide the foundation to design passive diodes with specific nonlinear pressure-flow characteristics.

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.

Preliminary numerical analysis of improved gas chromatograph model

NASA Technical Reports Server (NTRS)

Woodrow, P. T.

1973-01-01

A mathematical model for the gas chromatograph was developed which incorporates the heretofore neglected transport mechanisms of intraparticle diffusion and rates of adsorption. Because a closed-form analytical solution to the model does not appear realizable, techniques for the numerical solution of the model equations are being investigated. Criteria were developed for using a finite terminal boundary condition in place of an infinite boundary condition used in analytical solution techniques. The class of weighted residual methods known as orthogonal collocation is presently being investigated and appears promising.

A New Closed Form Approximation for BER for Optical Wireless Systems in Weak Atmospheric Turbulence

NASA Astrophysics Data System (ADS)

Kaushik, Rahul; Khandelwal, Vineet; Jain, R. C.

2018-04-01

Weak atmospheric turbulence condition in an optical wireless communication (OWC) is captured by log-normal distribution. The analytical evaluation of average bit error rate (BER) of an OWC system under weak turbulence is intractable as it involves the statistical averaging of Gaussian Q-function over log-normal distribution. In this paper, a simple closed form approximation for BER of OWC system under weak turbulence is given. Computation of BER for various modulation schemes is carried out using proposed expression. The results obtained using proposed expression compare favorably with those obtained using Gauss-Hermite quadrature approximation and Monte Carlo Simulations.

Closed-form nonlinear frequency of flexoelectric nanobeams with surface and nonlocal effects under closed circuit electric field

NASA Astrophysics Data System (ADS)

Barati, Mohammad Reza

2018-02-01

Nonlocal and surface effects on nonlinear vibration characteristics of a flexoelectric nanobeams under magnetic field are examined. Eringen’s nonlocal elasticity as well as surface elasticity theories are employed to describe the size-dependency of the flexoelectric nanobeam. Also, flexoelectricity is an important size-dependent phenomena for piezoelectric structures at nanoscale, related to the strain gradient-electric polarization coupling. After the derivation of governing equation via Hamilton’s principle, Galerkin method is employed to satisfy boundary conditions. Also, analytical procedures are implemented to obtain the closed-form nonlinear frequency of flexoelectric nanobeam. It is showed that magnetic field intensity, flexoelectric parameter, nonlocal parameter, elastic foundation and applied voltage on the top surface of the nanobeam have great influences on nonlinear vibration frequency.

An improved shear beam method for the characterization of bonded composite joints

NASA Technical Reports Server (NTRS)

Hiel, Clem C.; Brinson, Hal F.

1989-01-01

Closed-form analytical solutions, which govern the displacements and stresses in an adhesive shear beam, are discussed. The remarkable precision with which the shear stresses in the adhesive can be predicted forms the basis of the proposed characterization procedure. The shear modulus of the adhesive is obtained by means of a parameter estimation procedure which requires a symbiosis of theoretical and experimental stress analysis.

Morse oscillator propagator in the high temperature limit II: Quantum dynamics and spectroscopy

NASA Astrophysics Data System (ADS)

Toutounji, Mohamad

2018-04-01

This paper is a continuation of Paper I (Toutounji, 2017) of which motivation was testing the applicability of Morse oscillator propagator whose analytical form was derived by Duru (1983). This is because the Morse oscillator propagator was reported (Duru, 1983) in a triple-integral form of a functional of modified Bessel function of the first kind, which considerably limits its applicability. For this reason, I was prompted to find a regime under which Morse oscillator propagator may be simplified and hence be expressed in a closed-form. This was well accomplished in Paper I. Because Morse oscillator is of central importance and widely used in modelling vibrations, its propagator applicability will be extended to applications in quantum dynamics and spectroscopy as will be reported in this paper using the off-diagonal propagator of Morse oscillator whose analytical form is derived.

Anomaly formulas for the complex-valued analytic torsion on compact bordisms

PubMed Central

Maldonado Molina, Osmar

2013-01-01

We extend the complex-valued analytic torsion, introduced by Burghelea and Haller on closed manifolds, to compact Riemannian bordisms. We do so by considering a flat complex vector bundle over a compact Riemannian manifold, endowed with a fiberwise nondegenerate symmetric bilinear form. The Riemmanian metric and the bilinear form are used to define non-selfadjoint Laplacians acting on vector-valued smooth forms under absolute and relative boundary conditions. In order to define the complex-valued analytic torsion in this situation, we study spectral properties of these generalized Laplacians. Then, as main results, we obtain so-called anomaly formulas for this torsion. Our reasoning takes into account that the coefficients in the heat trace asymptotic expansion associated to the boundary value problem under consideration, are locally computable. The anomaly formulas for the complex-valued Ray–Singer torsion are derived first by using the corresponding ones for the Ray–Singer metric, obtained by Brüning and Ma on manifolds with boundary, and then an argument of analytic continuation. In odd dimensions, our anomaly formulas are in accord with the corresponding results of Su, without requiring the variations of the Riemannian metric and bilinear structures to be supported in the interior of the manifold. PMID:27087744

What Makes a Senior Thesis Good?

ERIC Educational Resources Information Center

Trosset, Carol; Weisler, Steven

2018-01-01

Kuh (2008) describes the capstone as a "culminating experience" students undertake close to graduation often involving "a project of some sort that integrates and applies what they've learned" (p. 11). The senior thesis is one form of the capstone in which students write an analytic paper under faculty supervision, typically as…

Roy-Steiner equations for pion-nucleon scattering

NASA Astrophysics Data System (ADS)

Ditsche, C.; Hoferichter, M.; Kubis, B.; Meißner, U.-G.

2012-06-01

Starting from hyperbolic dispersion relations, we derive a closed system of Roy-Steiner equations for pion-nucleon scattering that respects analyticity, unitarity, and crossing symmetry. We work out analytically all kernel functions and unitarity relations required for the lowest partial waves. In order to suppress the dependence on the high energy regime we also consider once- and twice-subtracted versions of the equations, where we identify the subtraction constants with subthreshold parameters. Assuming Mandelstam analyticity we determine the maximal range of validity of these equations. As a first step towards the solution of the full system we cast the equations for the π π to overline N N partial waves into the form of a Muskhelishvili-Omnès problem with finite matching point, which we solve numerically in the single-channel approximation. We investigate in detail the role of individual contributions to our solutions and discuss some consequences for the spectral functions of the nucleon electromagnetic form factors.

Generalized model of electromigration with 1:1 (analyte:selector) complexation stoichiometry: part II. Application to dual systems and experimental verification.

PubMed

Müllerová, Ludmila; Dubský, Pavel; Gaš, Bohuslav

2015-03-06

Interactions among analyte forms that undergo simultaneous dissociation/protonation and complexation with multiple selectors take the shape of a highly interconnected multi-equilibrium scheme. This makes it difficult to express the effective mobility of the analyte in these systems, which are often encountered in electrophoretical separations, unless a generalized model is introduced. In the first part of this series, we presented the theory of electromigration of a multivalent weakly acidic/basic/amphoteric analyte undergoing complexation with a mixture of an arbitrary number of selectors. In this work we demonstrate the validity of this concept experimentally. The theory leads to three useful perspectives, each of which is closely related to the one originally formulated for simpler systems. If pH, IS and the selector mixture composition are all kept constant, the system is treated as if only a single analyte form interacted with a single selector. If the pH changes at constant IS and mixture composition, the already well-established models of a weakly acidic/basic analyte interacting with a single selector can be employed. Varying the mixture composition at constant IS and pH leads to a situation where virtually a single analyte form interacts with a mixture of selectors. We show how to switch between the three perspectives in practice and confirm that they can be employed interchangeably according to the specific needs by measurements performed in single- and dual-selector systems at a pH where the analyte is fully dissociated, partly dissociated or fully protonated. Weak monoprotic analyte (R-flurbiprofen) and two selectors (native β-cyclodextrin and monovalent positively charged 6-monodeoxy-6-monoamino-β-cyclodextrin) serve as a model system. Copyright © 2015 Elsevier B.V. All rights reserved.

Analytical approach to peel stresses in bonded composite stiffened panels

NASA Technical Reports Server (NTRS)

Barkey, Derek A.; Madan, Ram C.; Sutton, Jason O.

1987-01-01

A closed-form solution was obtained for the stresses and displacements of two bonded beams. A system of two fourth-order and two second-order differential equations with the associated boundary equations was determined using a variational work approach. A FORTRAN computer program was devised to solve for the eigenvalues and eigenvectors of this system and to calculate the coefficients from the boundary conditions. The results were then compared with NASTRAN finite-element solutions and shown to agree closely.

Morse oscillator propagator in the high temperature limit I: Theory

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

Toutounji, Mohamad, E-mail: Mtoutounji@uaeu.ac.ae

2017-02-15

In an earlier work of the author the time evolution of Morse oscillator was studied analytically and exactly at low temperatures whereupon optical correlation functions were calculated using Morse oscillator coherent states were employed. Morse oscillator propagator in the high temperature limit is derived and a closed form of its corresponding canonical partition function is obtained. Both diagonal and off-diagonal forms of Morse oscillator propagator are derived in the high temperature limit. Partition functions of diatomic molecules are calculated. - Highlights: • Derives the quantum propagator of Morse oscillator in the high temperature limit. • Uses the resulting diagonal propagatormore » to derive a closed form of Morse oscillator partition function. • Provides a more sophisticated formula of the quantum propagator to test the accuracy of the herein results.« less

Analytic solution of the Spencer-Lewis angular-spatial moments equations

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

Filippone, W.L.

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

Axisymmetric deformations and stresses of unsymmetrically laminated composite cylinders in axial compression with thermally-induced preloading effects

NASA Technical Reports Server (NTRS)

Paraska, Peter J.

1993-01-01

This report documents an analytical study of the response of unsymmetrically laminated cylinders subjected to thermally-induced preloading effects and compressive axial load. Closed-form solutions are obtained for the displacements and intralaminar stresses and recursive relations for the interlaminar shear stress were obtained using the closed-form intralaminar stress solutions. For the cylinder geometries and stacking sequence examples analyzed, several important and as yet undocumented effects of including thermally-induced preloading in the analysis are observed. It should be noted that this work is easily extended to include uniform internal and/or external pressure loadings and the application of strain and stress failure theories.

A theoretical study on pure bending of hexagonal close-packed metal sheet

NASA Astrophysics Data System (ADS)

Mehrabi, Hamed; Yang, Chunhui

2018-05-01

Hexagonal close-packed (HCP) metals have quite different mechanical behaviours in comparison to conventional cubic metals such as steels and aluminum alloys [1, 2]. They exhibit a significant tension-compression asymmetry in initial yielding and subsequent plastic hardening. The reason for this unique behaviour can be attributed to their limited symmetric crystal structure, which leads to twining deformation [3-5]. This unique behaviour strongly influences sheet metal forming of such metals, especially for roll forming, in which the bending is dominant. Hence, it is crucial to represent constitutive relations of HCP metals for accurate estimation of bending moment-curvature behaviours. In this paper, an analytical model for asymmetric elastoplastic pure bending with an application of Cazacu-Barlat asymmetric yield function [6] is presented. This yield function considers the asymmetrical tension-compression behaviour of HCP metals by using second and third invariants of the stress deviator tensor and a specified constant, which can be expressed in terms of uniaxial yield stresses in tension and compression. As a case study, the analytical model is applied to predict the moment-curvature behaviours of AZ31B magnesium alloy sheets under uniaxial loading condition. Furthermore, the analytical model is implemented as a user-defined material through the UMAT interface in Abaqus [7, 8] for conducting pure bending simulations. The results show that the analytical model can reasonably capture the asymmetric tension-compression behaviour of the magnesium alloy. The predicted moment-curvature behaviour has good agreement with the experimental results. Furthermore, numerical results show a better accuracy by the application of the Cazacu-Barlat yield function than those using the von-Mises yield function, which are more conservative than analytical results.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Benchmark solutions for the galactic heavy-ion transport equations with energy and spatial coupling

NASA Technical Reports Server (NTRS)

Ganapol, Barry D.; Townsend, Lawrence W.; Lamkin, Stanley L.; Wilson, John W.

1991-01-01

Nontrivial benchmark solutions are developed for the galactic heavy ion transport equations in the straightahead approximation with energy and spatial coupling. Analytical representations of the ion fluxes are obtained for a variety of sources with the assumption that the nuclear interaction parameters are energy independent. The method utilizes an analytical LaPlace transform inversion to yield a closed form representation that is computationally efficient. The flux profiles are then used to predict ion dose profiles, which are important for shield design studies.

High Rayleigh number convection in rectangular enclosures with differentially heated vertical walls and aspect ratios between zero and unity

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

Kassemi, S.A.

1988-04-01

High Rayleigh number convection in a rectangular cavity with insulated horizontal surfaces and differentially heated vertical walls was analyzed for an arbitrary aspect ratio smaller than or equal to unity. Unlike previous analytical studies, a systematic method of solution based on linearization technique and analytical iteration procedure was developed to obtain approximate closed-form solutions for a wide range of aspect ratios. The predicted velocity and temperature fields are shown to be in excellent agreement with available experimental and numerical data.

High Rayleigh number convection in rectangular enclosures with differentially heated vertical walls and aspect ratios between zero and unity

NASA Technical Reports Server (NTRS)

Kassemi, Siavash A.

1988-01-01

High Rayleigh number convection in a rectangular cavity with insulated horizontal surfaces and differentially heated vertical walls was analyzed for an arbitrary aspect ratio smaller than or equal to unity. Unlike previous analytical studies, a systematic method of solution based on linearization technique and analytical iteration procedure was developed to obtain approximate closed-form solutions for a wide range of aspect ratios. The predicted velocity and temperature fields are shown to be in excellent agreement with available experimental and numerical data.

Flexible aircraft dynamic modeling for dynamic analysis and control synthesis

NASA Technical Reports Server (NTRS)

Schmidt, David K.

1989-01-01

The linearization and simplification of a nonlinear, literal model for flexible aircraft is highlighted. Areas of model fidelity that are critical if the model is to be used for control system synthesis are developed and several simplification techniques that can deliver the necessary model fidelity are discussed. These techniques include both numerical and analytical approaches. An analytical approach, based on first-order sensitivity theory is shown to lead not only to excellent numerical results, but also to closed-form analytical expressions for key system dynamic properties such as the pole/zero factors of the vehicle transfer-function matrix. The analytical results are expressed in terms of vehicle mass properties, vibrational characteristics, and rigid-body and aeroelastic stability derivatives, thus leading to the underlying causes for critical dynamic characteristics.

Thermodynamics of Quantum Gases for the Entire Range of Temperature

ERIC Educational Resources Information Center

Biswas, Shyamal; Jana, Debnarayan

2012-01-01

We have analytically explored the thermodynamics of free Bose and Fermi gases for the entire range of temperature, and have extended the same for harmonically trapped cases. We have obtained approximate chemical potentials for the quantum gases in closed forms of temperature so that the thermodynamic properties of the quantum gases become…

Cylindrical and spherical solitary waves in an electron-acoustic plasma with vortex electron distribution

NASA Astrophysics Data System (ADS)

Demiray, Hilmi; El-Zahar, Essam R.

2018-04-01

We consider the nonlinear propagation of electron-acoustic waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions. The basic nonlinear equations of the above described plasma are re-examined in the cylindrical (spherical) coordinates by employing the reductive perturbation technique. The modified cylindrical (spherical) KdV equation with fractional power nonlinearity is obtained as the evolution equation. Due to the nature of nonlinearity, this evolution equation cannot be reduced to the conventional KdV equation. A new family of closed form analytical approximate solution to the evolution equation and a comparison with numerical solution are presented and the results are depicted in some 2D and 3D figures. The results reveal that both solutions are in good agreement and the method can be used to obtain a new progressive wave solution for such evolution equations. Moreover, the resulting closed form analytical solution allows us to carry out a parametric study to investigate the effect of the physical parameters on the solution behavior of the modified cylindrical (spherical) KdV equation.

Polar decomposition for attitude determination from vector observations

NASA Technical Reports Server (NTRS)

Bar-Itzhack, Itzhack Y.

1993-01-01

This work treats the problem of weighted least squares fitting of a 3D Euclidean-coordinate transformation matrix to a set of unit vectors measured in the reference and transformed coordinates. A closed-form analytic solution to the problem is re-derived. The fact that the solution is the closest orthogonal matrix to some matrix defined on the measured vectors and their weights is clearly demonstrated. Several known algorithms for computing the analytic closed form solution are considered. An algorithm is discussed which is based on the polar decomposition of matrices into the closest unitary matrix to the decomposed matrix and a Hermitian matrix. A somewhat longer improved algorithm is suggested too. A comparison of several algorithms is carried out using simulated data as well as real data from the Upper Atmosphere Research Satellite. The comparison is based on accuracy and time consumption. It is concluded that the algorithms based on polar decomposition yield a simple although somewhat less accurate solution. The precision of the latter algorithms increase with the number of the measured vectors and with the accuracy of their measurement.

Analytical modeling and analysis of magnetic field and torque for novel axial flux eddy current couplers with PM excitation

NASA Astrophysics Data System (ADS)

Li, Zhao; Wang, Dazhi; Zheng, Di; Yu, Linxin

2017-10-01

Rotational permanent magnet eddy current couplers are promising devices for torque and speed transmission without any mechanical contact. In this study, flux-concentration disk-type permanent magnet eddy current couplers with double conductor rotor are investigated. Given the drawback of the accurate three-dimensional finite element method, this paper proposes a mixed two-dimensional analytical modeling approach. Based on this approach, the closed-form expressions of magnetic field, eddy current, electromagnetic force and torque for such devices are obtained. Finally, a three-dimensional finite element method is employed to validate the analytical results. Besides, a prototype is manufactured and tested for the torque-speed characteristic.

An analytic resolution to the competition between Lyman-Werner radiation and metal winds in direct collapse black hole hosts

NASA Astrophysics Data System (ADS)

Agarwal, Bhaskar; Regan, John; Klessen, Ralf S.; Downes, Turlough P.; Zackrisson, Erik

2017-10-01

A near pristine atomic cooling halo close to a star forming galaxy offers a natural pathway for forming massive direct collapse black hole (DCBH) seeds, which could be the progenitors of the z > 6 redshift quasars. The close proximity of the haloes enables a sufficient Lyman-Werner flux to effectively dissociate H2 in the core of the atomic cooling halo. A mild background may also be required to delay star formation in the atomic cooling halo, often attributed to distant background galaxies. In this paper, we investigate the impact of metal pollution from both the background galaxies and the close star forming galaxy under extremely unfavourable conditions such as instantaneous metal mixing. We find that within the time window of DCBH formation, the level of pollution never exceeds the critical threshold (Zcr ˜ 1 × 10-5 Z⊙) and attains a maximum metallicity of Z ˜ 2 × 10- 6 Z⊙. As the system evolves, the metallicity eventually exceeds the critical threshold, long after the DCBH has formed.

Outage Probability of MRC for κ-μ Shadowed Fading Channels under Co-Channel Interference.

PubMed

Chen, Changfang; Shu, Minglei; Wang, Yinglong; Yang, Ming; Zhang, Chongqing

2016-01-01

In this paper, exact closed-form expressions are derived for the outage probability (OP) of the maximal ratio combining (MRC) scheme in the κ-μ shadowed fading channels, in which both the independent and correlated shadowing components are considered. The scenario assumes the received desired signals are corrupted by the independent Rayleigh-faded co-channel interference (CCI) and background white Gaussian noise. To this end, first, the probability density function (PDF) of the κ-μ shadowed fading distribution is obtained in the form of a power series. Then the incomplete generalized moment-generating function (IG-MGF) of the received signal-to-interference-plus-noise ratio (SINR) is derived in the closed form. By using the IG-MGF results, closed-form expressions for the OP of MRC scheme are obtained over the κ-μ shadowed fading channels. Simulation results are included to validate the correctness of the analytical derivations. These new statistical results can be applied to the modeling and analysis of several wireless communication systems, such as body centric communications.

Outage Probability of MRC for κ-μ Shadowed Fading Channels under Co-Channel Interference

PubMed Central

Chen, Changfang; Shu, Minglei; Wang, Yinglong; Yang, Ming; Zhang, Chongqing

2016-01-01

In this paper, exact closed-form expressions are derived for the outage probability (OP) of the maximal ratio combining (MRC) scheme in the κ-μ shadowed fading channels, in which both the independent and correlated shadowing components are considered. The scenario assumes the received desired signals are corrupted by the independent Rayleigh-faded co-channel interference (CCI) and background white Gaussian noise. To this end, first, the probability density function (PDF) of the κ-μ shadowed fading distribution is obtained in the form of a power series. Then the incomplete generalized moment-generating function (IG-MGF) of the received signal-to-interference-plus-noise ratio (SINR) is derived in the closed form. By using the IG-MGF results, closed-form expressions for the OP of MRC scheme are obtained over the κ-μ shadowed fading channels. Simulation results are included to validate the correctness of the analytical derivations. These new statistical results can be applied to the modeling and analysis of several wireless communication systems, such as body centric communications. PMID:27851817

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.

Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

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

Ibarra-Sierra, V.G.; Sandoval-Santana, J.C.; Cardoso, J.L.

We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra ismore » later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a rotating quadrupole field ion trap are presented. •Exact solutions for magneto-transport in variable electromagnetic fields are shown.« less

Reactant conversion in homogeneous turbulence: Mathematical modeling, computational validations and practical applications

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

Symmetric tops in combined electric fields: Conditional quasisolvability via the quantum Hamilton-Jacobi theory

NASA Astrophysics Data System (ADS)

Schatz, Konrad; Friedrich, Bretislav; Becker, Simon; Schmidt, Burkhard

2018-05-01

We make use of the quantum Hamilton-Jacobi (QHJ) theory to investigate conditional quasisolvability of the quantum symmetric top subject to combined electric fields (symmetric top pendulum). We derive the conditions of quasisolvability of the time-independent Schrödinger equation as well as the corresponding finite sets of exact analytic solutions. We do so for this prototypical trigonometric system as well as for its anti-isospectral hyperbolic counterpart. An examination of the algebraic and numerical spectra of these two systems reveals mutually closely related patterns. The QHJ approach allows us to retrieve the closed-form solutions for the spherical and planar pendula and the Razavy system that had been obtained in our earlier work via supersymmetric quantum mechanics as well as to find a cornucopia of additional exact analytic solutions.

Analytic Closed-Form Solution of a Mixed Layer Model for Stratocumulus Clouds

NASA Astrophysics Data System (ADS)

Akyurek, Bengu Ozge

Stratocumulus clouds play an important role in climate cooling and are hard to predict using global climate and weather forecast models. Thus, previous studies in the literature use observations and numerical simulation tools, such as large-eddy simulation (LES), to solve the governing equations for the evolution of stratocumulus clouds. In contrast to the previous works, this work provides an analytic closed-form solution to the cloud thickness evolution of stratocumulus clouds in a mixed-layer model framework. With a focus on application over coastal lands, the diurnal cycle of cloud thickness and whether or not clouds dissipate are of particular interest. An analytic solution enables the sensitivity analysis of implicitly interdependent variables and extrema analysis of cloud variables that are hard to achieve using numerical solutions. In this work, the sensitivity of inversion height, cloud-base height, and cloud thickness with respect to initial and boundary conditions, such as Bowen ratio, subsidence, surface temperature, and initial inversion height, are studied. A critical initial cloud thickness value that can be dissipated pre- and post-sunrise is provided. Furthermore, an extrema analysis is provided to obtain the minima and maxima of the inversion height and cloud thickness within 24 h. The proposed solution is validated against LES results under the same initial and boundary conditions. Then, the proposed analytic framework is extended to incorporate multiple vertical columns that are coupled by advection through wind flow. This enables a bridge between the micro-scale and the mesoscale relations. The effect of advection on cloud evolution is studied and a sensitivity analysis is provided.

Two important limitations relating to the spiking of environmental samples with contaminants of emerging concern: How close to the real analyte concentrations are the reported recovered values?

PubMed

Michael, Costas; Bayona, Josep Maria; Lambropoulou, Dimitra; Agüera, Ana; Fatta-Kassinos, Despo

2017-06-01

Occurrence and effects of contaminants of emerging concern pose a special challenge to environmental scientists. The investigation of these effects requires reliable, valid, and comparable analytical data. To this effect, two critical aspects are raised herein, concerning the limitations of the produced analytical data. The first relates to the inherent difficulty that exists in the analysis of environmental samples, which is related to the lack of knowledge (information), in many cases, of the form(s) of the contaminant in which is present in the sample. Thus, the produced analytical data can only refer to the amount of the free contaminant ignoring the amount in which it may be present in other forms; e.g., as in chelated and conjugated form. The other important aspect refers to the way with which the spiking procedure is generally performed to determine the recovery of the analytical method. Spiking environmental samples, in particular solid samples, with standard solution followed by immediate extraction, as is the common practice, can lead to an overestimation of the recovery. This is so, because no time is given to the system to establish possible equilibria between the solid matter-inorganic and/or organic-and the contaminant. Therefore, the spiking procedure need to be reconsidered by including a study of the extractable amount of the contaminant versus the time elapsed between spiking and the extraction of the sample. This study can become an element of the validation package of the method.

Randomization-Based Inference about Latent Variables from Complex Samples: The Case of Two-Stage Sampling

ERIC Educational Resources Information Center

Li, Tiandong

2012-01-01

In large-scale assessments, such as the National Assessment of Educational Progress (NAEP), plausible values based on Multiple Imputations (MI) have been used to estimate population characteristics for latent constructs under complex sample designs. Mislevy (1991) derived a closed-form analytic solution for a fixed-effect model in creating…

Analytic saddlepoint approximation for ionization energy loss distributions

DOE PAGES

Sjue, Sky K. L.; George, Jr., Richard Neal; Mathews, David Gregory

2017-07-27

Here, we present a saddlepoint approximation for ionization energy loss distributions, valid for arbitrary relativistic velocities of the incident particle 0 < v/c < 1, provided that ionizing collisions are still the dominant energy loss mechanism. We derive a closed form solution closely related to Moyal’s distribution. This distribution is intended for use in simulations with relatively low computational overhead. The approximation generally reproduces the Vavilov most probable energy loss and full width at half maximum to better than 1% and 10%, respectively, with significantly better agreement as Vavilov’s κ approaches 1.

Analytic saddlepoint approximation for ionization energy loss distributions

NASA Astrophysics Data System (ADS)

Sjue, S. K. L.; George, R. N.; Mathews, D. G.

2017-09-01

We present a saddlepoint approximation for ionization energy loss distributions, valid for arbitrary relativistic velocities of the incident particle 0 < v / c < 1 , provided that ionizing collisions are still the dominant energy loss mechanism. We derive a closed form solution closely related to Moyal's distribution. This distribution is intended for use in simulations with relatively low computational overhead. The approximation generally reproduces the Vavilov most probable energy loss and full width at half maximum to better than 1% and 10%, respectively, with significantly better agreement as Vavilov's κ approaches 1.

Analytic saddlepoint approximation for ionization energy loss distributions

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

Sjue, Sky K. L.; George, Jr., Richard Neal; Mathews, David Gregory

Here, we present a saddlepoint approximation for ionization energy loss distributions, valid for arbitrary relativistic velocities of the incident particle 0 < v/c < 1, provided that ionizing collisions are still the dominant energy loss mechanism. We derive a closed form solution closely related to Moyal’s distribution. This distribution is intended for use in simulations with relatively low computational overhead. The approximation generally reproduces the Vavilov most probable energy loss and full width at half maximum to better than 1% and 10%, respectively, with significantly better agreement as Vavilov’s κ approaches 1.

Analytical solutions for avalanche-breakdown voltages of single-diffused Gaussian junctions

NASA Astrophysics Data System (ADS)

Shenai, K.; Lin, H. C.

1983-03-01

Closed-form solutions of the potential difference between the two edges of the depletion layer of a single diffused Gaussian p-n junction are obtained by integrating Poisson's equation and equating the magnitudes of the positive and negative charges in the depletion layer. By using the closed form solution of the static Poisson's equation and Fulop's average ionization coefficient, the ionization integral in the depletion layer is computed, which yields the correct values of avalanche breakdown voltage, depletion layer thickness at breakdown, and the peak electric field as a function of junction depth. Newton's method is used for rapid convergence. A flowchart to perform the calculations with a programmable hand-held calculator, such as the TI-59, is shown.

Distributed parameter modeling to prevent charge cancellation for discrete thickness piezoelectric energy harvester

NASA Astrophysics Data System (ADS)

Krishnasamy, M.; Qian, Feng; Zuo, Lei; Lenka, T. R.

2018-03-01

The charge cancellation due to the change of strain along single continuous piezoelectric layer can remarkably affect the performance of a cantilever based harvester. In this paper, analytical models using distributed parameters are developed with some extent of averting the charge cancellation in cantilever piezoelectric transducer where the piezoelectric layers are segmented at strain nodes of concerned vibration mode. The electrode of piezoelectric segments are parallelly connected with a single external resistive load in the 1st model (Model 1). While each bimorph piezoelectric layers are connected in parallel to a resistor to form an independent circuit in the 2nd model (Model 2). The analytical expressions of the closed-form electromechanical coupling responses in frequency domain under harmonic base excitation are derived based on the Euler-Bernoulli beam assumption for both models. The developed analytical models are validated by COMSOL and experimental results. The results demonstrate that the energy harvesting performance of the developed segmented piezoelectric layer models is better than the traditional model of continuous piezoelectric layer.

An analytical method for the inverse Cauchy problem of Lame equation in a rectangle

NASA Astrophysics Data System (ADS)

Grigor’ev, Yu

2018-04-01

In this paper, we present an analytical computational method for the inverse Cauchy problem of Lame equation in the elasticity theory. A rectangular domain is frequently used in engineering structures and we only consider the analytical solution in a two-dimensional rectangle, wherein a missing boundary condition is recovered from the full measurement of stresses and displacements on an accessible boundary. The essence of the method consists in solving three independent Cauchy problems for the Laplace and Poisson equations. For each of them, the Fourier series is used to formulate a first-kind Fredholm integral equation for the unknown function of data. Then, we use a Lavrentiev regularization method, and the termwise separable property of kernel function allows us to obtain a closed-form regularized solution. As a result, for the displacement components, we obtain solutions in the form of a sum of series with three regularization parameters. The uniform convergence and error estimation of the regularized solutions are proved.

Applications of computer algebra to distributed parameter systems

NASA Technical Reports Server (NTRS)

Storch, Joel A.

1993-01-01

In the analysis of vibrations of continuous elastic systems, one often encounters complicated transcendental equations with roots directly related to the system's natural frequencies. Typically, these equations contain system parameters whose values must be specified before a numerical solution can be obtained. The present paper presents a method whereby the fundamental frequency can be obtained in analytical form to any desired degree of accuracy. The method is based upon truncation of rapidly converging series involving inverse powers of the system natural frequencies. A straightforward method to developing these series and summing them in closed form is presented. It is demonstrated how Computer Algebra can be exploited to perform the intricate analytical procedures which otherwise would render the technique difficult to apply in practice. We illustrate the method by developing two analytical approximations to the fundamental frequency of a vibrating cantilever carrying a rigid tip body. The results are compared to the numerical solution of the exact (transcendental) frequency equation over a range of system parameters.

Higher-n triangular dilatonic black holes

NASA Astrophysics Data System (ADS)

Zadora, Anton; Gal'tsov, Dmitri V.; Chen, Chiang-Mei

2018-04-01

Dilaton gravity with the form fields is known to possess dyon solutions with two horizons for the discrete "triangular" values of the dilaton coupling constant a =√{ n (n + 1) / 2 }. This sequence first obtained numerically and then explained analytically as consequence of the regularity of the dilaton, should have some higher-dimensional and/or group theoretical origin. Meanwhile, this origin was explained earlier only for n = 1 , 2 in which cases the solutions were known analytically. We extend this explanation to n = 3 , 5 presenting analytical triangular solutions for the theory with different dilaton couplings a , b in electric and magnetic sectors in which case the quantization condition reads ab = n (n + 1) / 2. The solutions are derived via the Toda chains for B2 and G2 Lie algebras. They are found in the closed form in general D space-time dimensions. Solutions satisfy the entropy product rules indicating on the microscopic origin of their entropy and have negative binding energy in the extremal case.

Comparative Kinetic Analysis of Closed-Ended and Open-Ended Porous Sensors

NASA Astrophysics Data System (ADS)

Zhao, Yiliang; Gaur, Girija; Mernaugh, Raymond L.; Laibinis, Paul E.; Weiss, Sharon M.

2016-09-01

Efficient mass transport through porous networks is essential for achieving rapid response times in sensing applications utilizing porous materials. In this work, we show that open-ended porous membranes can overcome diffusion challenges experienced by closed-ended porous materials in a microfluidic environment. A theoretical model including both transport and reaction kinetics is employed to study the influence of flow velocity, bulk analyte concentration, analyte diffusivity, and adsorption rate on the performance of open-ended and closed-ended porous sensors integrated with flow cells. The analysis shows that open-ended pores enable analyte flow through the pores and greatly reduce the response time and analyte consumption for detecting large molecules with slow diffusivities compared with closed-ended pores for which analytes largely flow over the pores. Experimental confirmation of the results was carried out with open- and closed-ended porous silicon (PSi) microcavities fabricated in flow-through and flow-over sensor configurations, respectively. The adsorption behavior of small analytes onto the inner surfaces of closed-ended and open-ended PSi membrane microcavities was similar. However, for large analytes, PSi membranes in a flow-through scheme showed significant improvement in response times due to more efficient convective transport of analytes. The experimental results and theoretical analysis provide quantitative estimates of the benefits offered by open-ended porous membranes for different analyte systems.

Bogoliubov theory of acoustic Hawking radiation in Bose-Einstein condensates

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

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

2009-10-15

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

A Model for Developing Clinical Analytics Capacity: Closing the Loops on Outcomes to Optimize Quality.

PubMed

Eggert, Corinne; Moselle, Kenneth; Protti, Denis; Sanders, Dale

2017-01-01

Closed Loop Analytics© is receiving growing interest in healthcare as a term referring to information technology, local data and clinical analytics working together to generate evidence for improvement. The Closed Loop Analytics model consists of three loops corresponding to the decision-making levels of an organization and the associated data within each loop - Patients, Protocols, and Populations. The authors propose that each of these levels should utilize the same ecosystem of electronic health record (EHR) and enterprise data warehouse (EDW) enabled data, in a closed-loop fashion, with that data being repackaged and delivered to suit the analytic and decision support needs of each level, in support of better outcomes.

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.

Analytical solution for the transient wave propagation of a buried cylindrical P-wave line source in a semi-infinite elastic medium with a fluid surface layer

NASA Astrophysics Data System (ADS)

Shan, Zhendong; Ling, Daosheng

2018-02-01

This article develops an analytical solution for the transient wave propagation of a cylindrical P-wave line source in a semi-infinite elastic solid with a fluid layer. The analytical solution is presented in a simple closed form in which each term represents a transient physical wave. The Scholte equation is derived, through which the Scholte wave velocity can be determined. The Scholte wave is the wave that propagates along the interface between the fluid and solid. To develop the analytical solution, the wave fields in the fluid and solid are defined, their analytical solutions in the Laplace domain are derived using the boundary and interface conditions, and the solutions are then decomposed into series form according to the power series expansion method. Each item of the series solution has a clear physical meaning and represents a transient wave path. Finally, by applying Cagniard's method and the convolution theorem, the analytical solutions are transformed into the time domain. Numerical examples are provided to illustrate some interesting features in the fluid layer, the interface and the semi-infinite solid. When the P-wave velocity in the fluid is higher than that in the solid, two head waves in the solid, one head wave in the fluid and a Scholte wave at the interface are observed for the cylindrical P-wave line source.

A simple closed-form solution for assessing concentration uncertainty

NASA Astrophysics Data System (ADS)

de Barros, F. P. J.; Fiori, Aldo; Bellin, Alberto

2011-12-01

We propose closed-form approximate solutions for the moments of a nonreactive tracer that can be used in applications, such as risk analysis. This is in line with the tenet that analytical solutions provide useful information, with minimum cost, during initial site characterization efforts and can serve as a preliminary screening tool when used with prior knowledge. We show that with the help of a few assumptions, the first-order solutions of the concentration moments proposed by Fiori and Dagan (2000) can be further simplified to assume a form similar to well-known deterministic solutions, therefore facilitating their use in applications. A highly anisotropic formation is assumed, and we neglect the transverse components of the two-particle correlation trajectory. The proposed solution compares well with the work of Fiori and Dagan while presenting the same simplicity of use of existing solutions for homogeneous porous media.

The "Forgotten" Pseudomomenta and Gauge Changes in Generalized Landau Level Problems: Spatially Nonuniform Magnetic and Temporally Varying Electric Fields

NASA Astrophysics Data System (ADS)

Konstantinou, Georgios; Moulopoulos, Konstantinos

2017-05-01

By perceiving gauge invariance as an analytical tool in order to get insight into the states of the "generalized Landau problem" (a charged quantum particle moving inside a magnetic, and possibly electric field), and motivated by an early article that correctly warns against a naive use of gauge transformation procedures in the usual Landau problem (i.e. with the magnetic field being static and uniform), we first show how to bypass the complications pointed out in that article by solving the problem in full generality through gauge transformation techniques in a more appropriate manner. Our solution provides in simple and closed analytical forms all Landau Level-wavefunctions without the need to specify a particular vector potential. This we do by proper handling of the so-called pseudomomentum ěc {{K}} (or of a quantity that we term pseudo-angular momentum L z ), a method that is crucially different from the old warning argument, but also from standard treatments in textbooks and in research literature (where the usual Landau-wavefunctions are employed - labeled with canonical momenta quantum numbers). Most importantly, we go further by showing that a similar procedure can be followed in the more difficult case of spatially-nonuniform magnetic fields: in such case we define ěc {{K}} and L z as plausible generalizations of the previous ordinary case, namely as appropriate line integrals of the inhomogeneous magnetic field - our method providing closed analytical expressions for all stationary state wavefunctions in an easy manner and in a broad set of geometries and gauges. It can thus be viewed as complementary to the few existing works on inhomogeneous magnetic fields, that have so far mostly focused on determining the energy eigenvalues rather than the corresponding eigenkets (on which they have claimed that, even in the simplest cases, it is not possible to obtain in closed form the associated wavefunctions). The analytical forms derived here for these wavefunctions enable us to also provide explicit Berry's phase calculations and a quick study of their connection to probability currents and to some recent interesting issues in elementary Quantum Mechanics and Condensed Matter Physics. As an added feature, we also show how the possible presence of an additional electric field can be treated through a further generalization of pseudomomenta and their proper handling.

Too hot to handle? Analytic solutions for massive neutrino or warm dark matter cosmologies

NASA Astrophysics Data System (ADS)

Slepian, Zachary; Portillo, Stephen K. N.

2018-05-01

We obtain novel closed-form solutions to the Friedmann equation for cosmological models containing a component whose equation of state is that of radiation (w = 1/3) at early times and that of cold pressureless matter (w = 0) at late times. The equation of state smoothly transitions from the early to late-time behavior and exactly describes the evolution of a species with a Dirac Delta function distribution in momentum magnitudes |p_0| (i.e. all particles have the same |p_0|). Such a component, here termed "hot matter", is an approximate model for both neutrinos and warm dark matter. We consider it alone and in combination with cold matter and with radiation, also obtaining closed-form solutions for the growth of super-horizon perturbations in each case. The idealized model recovers t(a) to better than 1.5% accuracy for all a relative to a Fermi-Dirac distribution (as describes neutrinos). We conclude by adding the second moment of the distribution to our exact solution and then generalizing to include all moments of an arbitrary momentum distribution in a closed-form solution.

Too hot to handle? Analytic solutions for massive neutrino or warm dark matter cosmologies

NASA Astrophysics Data System (ADS)

Slepian, Zachary; Portillo, Stephen K. N.

2018-07-01

We obtain novel closed-form solutions to the Friedmann equation for cosmological models containing a component whose equation of state is that of radiation (w = 1/3) at early times and that of cold pressureless matter (w= 0) at late times. The equation of state smoothly transitions from the early- to late-time behaviour and exactly describes the evolution of a species with a Dirac delta function distribution in momentum magnitudes |{p}_0| (i.e. all particles have the same |{p}_0|). Such a component, here termed `hot matter', is an approximate model for both neutrinos and warm dark matter. We consider it alone and in combination with cold matter and with radiation, also obtaining closed-form solutions for the growth of superhorizon perturbations in each case. The idealized model recovers t(a) to better than 1.5 per cent accuracy for all a relative to a Fermi-Dirac distribution (as describes neutrinos). We conclude by adding the second moment of the distribution to our exact solution and then generalizing to include all moments of an arbitrary momentum distribution in a closed-form solution.

Closed-form analytical solutions for assessing the consequences of sea-level rise on unconfined sloping island aquifers

NASA Astrophysics Data System (ADS)

Chesnaux, R.

2016-04-01

Closed-form analytical solutions for assessing the consequences of sea-level rise on fresh groundwater oceanic island lenses are provided for the cases of both strip and circular islands. Solutions are proposed for directly calculating the change in the thickness of the lens, the changes in volume and the changes in travel time of fresh groundwater within island aquifers. The solutions apply for homogenous aquifers recharged by surface infiltration and discharged by a down-gradient, fixed-head boundary. They also take into account the inland shift of the ocean due to land surface inundation, this shift being determined by the coastal slope of inland aquifers. The solutions are given for two simple island geometries: circular islands and strip islands. Base case examples are presented to illustrate, on one hand, the amplitude of the change of the fresh groundwater lens thickness and the volume depletion of the lens in oceanic island with sea-level rise, and on the other hand, the shortening of time required for groundwater to discharge into the ocean. These consequences can now be quantified and may help decision-makers to anticipate the effects of sea-level rise on fresh groundwater availability in oceanic island aquifers.

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

Development and Applications of Liquid Sample Desorption Electrospray Ionization Mass Spectrometry

NASA Astrophysics Data System (ADS)

Zheng, Qiuling; Chen, Hao

2016-06-01

Desorption electrospray ionization mass spectrometry (DESI-MS) is a recent advance in the field of analytical chemistry. This review surveys the development of liquid sample DESI-MS (LS-DESI-MS), a variant form of DESI-MS that focuses on fast analysis of liquid samples, and its novel analy-tical applications in bioanalysis, proteomics, and reaction kinetics. Due to the capability of directly ionizing liquid samples, liquid sample DESI (LS-DESI) has been successfully used to couple MS with various analytical techniques, such as microfluidics, microextraction, electrochemistry, and chromatography. This review also covers these hyphenated techniques. In addition, several closely related ionization methods, including transmission mode DESI, thermally assisted DESI, and continuous flow-extractive DESI, are briefly discussed. The capabilities of LS-DESI extend and/or complement the utilities of traditional DESI and electrospray ionization and will find extensive and valuable analytical application in the future.

On the nonlinear dynamics of trolling-mode AFM: Analytical solution using multiple time scales method

NASA Astrophysics Data System (ADS)

Sajjadi, Mohammadreza; Pishkenari, Hossein Nejat; Vossoughi, Gholamreza

2018-06-01

Trolling mode atomic force microscopy (TR-AFM) has resolved many imaging problems by a considerable reduction of the liquid-resonator interaction forces in liquid environments. The present study develops a nonlinear model of the meniscus force exerted to the nanoneedle of TR-AFM and presents an analytical solution to the distributed-parameter model of TR-AFM resonator utilizing multiple time scales (MTS) method. Based on the developed analytical solution, the frequency-response curves of the resonator operation in air and liquid (for different penetration length of the nanoneedle) are obtained. The closed-form analytical solution and the frequency-response curves are validated by the comparison with both the finite element solution of the main partial differential equations and the experimental observations. The effect of excitation angle of the resonator on horizontal oscillation of the probe tip and the effect of different parameters on the frequency-response of the system are investigated.

Unsteady lift forces on highly cambered airfoils moving through a gust

NASA Technical Reports Server (NTRS)

Atassi, H.; Goldstein, M.

1974-01-01

An unsteady airfoil theory in which the flow is linearized about the steady potential flow of the airfoil is presented. The theory is applied to an airfoil entering a gust. After transformation to the W-plane, the problem is formulated in terms of a Poisson's equation. The solutions are expanded in a Fourier-Bessel series. The theory is applied to a circular arc with arbitrary camber. Closed form expressions for the velocity and pressure on the surface of the airfoil are obtained. The unsteady aerodynamic forces are then calculated and shown to contain two terms. One in an explicit closed analytical form represents the contribution of the oncoming vortical disturbance, the other depends on a single quadrature and accounts for the effect of the wake.

Super periodic potential

NASA Astrophysics Data System (ADS)

Hasan, Mohammd; Mandal, Bhabani Prasad

2018-04-01

In this paper we introduce the concept of super periodic potential (SPP) of arbitrary order n, n ∈I+, in one dimension. General theory of wave propagation through SPP of order n is presented and the reflection and transmission coefficients are derived in their closed analytical form by transfer matrix formulation. We present scattering features of super periodic rectangular potential and super periodic delta potential as special cases of SPP. It is found that the symmetric self-similarity is the special case of super periodicity. Thus by identifying a symmetric fractal potential as special cases of SPP, one can obtain the tunnelling amplitude for a particle from such fractal potential. By using the formalism of SPP we obtain the close form expression of tunnelling amplitude of a particle for general Cantor and Smith-Volterra-Cantor potentials.

Analytical formulation of impulsive collision avoidance dynamics

NASA Astrophysics Data System (ADS)

Bombardelli, Claudio

2014-02-01

The paper deals with the problem of impulsive collision avoidance between two colliding objects in three dimensions and assuming elliptical Keplerian orbits. Closed-form analytical expressions are provided that accurately predict the relative dynamics of the two bodies in the encounter b-plane following an impulsive delta-V manoeuvre performed by one object at a given orbit location prior to the impact and with a generic three-dimensional orientation. After verifying the accuracy of the analytical expressions for different orbital eccentricities and encounter geometries the manoeuvre direction that maximises the miss distance is obtained numerically as a function of the arc length separation between the manoeuvre point and the predicted collision point. The provided formulas can be used for high-accuracy instantaneous estimation of the outcome of a generic impulsive collision avoidance manoeuvre and its optimisation.

Natural Vibration Analysis of Clamped Rectangular Orthotropic Plates

NASA Astrophysics Data System (ADS)

dalaei, m.; kerr, a. d.

The natural vibrations of clamped rectangular orthotropic plates are analyzed using the extended Kantorovich method. The developed iterative scheme converges very rapidly to the final result. The obtained natural frequencies are evaluated for a square plate made of Kevlar 49 Epoxy and the obtained results are compared with those published by Kanazawa and Kawai, and by Leissa. The agreement was found to be very close. As there are no exact analytical solutions for clamped rectangular plates, the generated closed form expression for the natural modes, and the corresponding natural frequencies, are very suitable for use in engineering analyses.

Ring dark and antidark solitons in nonlocal media.

PubMed

Horikis, Theodoros P; Frantzeskakis, Dimitrios J

2016-02-01

Ring dark and antidark solitons in nonlocal media are found. These structures have, respectively, the form of annular dips or humps on top of a stable CW background, and exist in a weak or strong nonlocality regime, defined by the sign of a characteristic parameter. It is demonstrated analytically that these solitons satisfy an effective cylindrical Kadomtsev-Petviashvili (aka Johnson's) equation and, as such, can be written explicitly in closed form. Numerical simulations show that they propagate undistorted and undergo quasi-elastic collisions, attesting to their stability properties.

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.

Generalized M-factor of hollow Gaussian beams through a hard-edge circular aperture

NASA Astrophysics Data System (ADS)

Deng, Dongmei

2005-06-01

Based on the generalized truncated second-order moments, the generalized M-factor (MG2-factor) of three-dimensional hollow Gaussian beams (HGBs) through a hard-edge circular aperture is studied in cylindrical coordinate system analytically and numerically. The closed-form expression for the MG2-factor of the truncated HGBs, which is dependent on the truncation parameter β and the beam order n, can be simplified to that of the truncated, the untruncated Gaussian beams and the untruncated HGBs. Also, the power fraction is demonstrated analytically and numerically, which shows that the area of the dark region across the HGBs increases as n increasing.

Analytic solutions for single and multiple cylinders of gravitating polytropes in magnetostatic equilibrium

NASA Technical Reports Server (NTRS)

Lerche, I.; Low, B. C.

1980-01-01

Exact analytic solutions for the static equilibrium of a gravitating plasma polytrope in the presence of magnetic fields are presented. The means of generating various equilibrium configurations to illustrate directly the complex physical relationships between pressure, magnetic fields, and gravity in self-gravitating systems is demonstrated. One of the solutions is used to model interstellar clouds suspended by magnetic fields against the galactic gravity such as may be formed by the Parker (1966) instability. It is concluded that the pinching effect of closed loops of magnetic fields in the clouds may be a dominant agent in further collapsing the clouds following their formation.

The serpentine optical waveguide: engineering the dispersion relations and the stopped light points.

PubMed

Scheuer, Jacob; Weiss, Ori

2011-06-06

We present a study a new type of optical slow-light structure comprising a serpentine shaped waveguide were the loops are coupled. The dispersion relation, group velocity and GVD are studied analytically using a transfer matrix method and numerically using finite difference time domain simulations. The structure exhibits zero group velocity points at the ends of the Brillouin zone, but also within the zone. The position of mid-zone zero group velocity point can be tuned by modifying the coupling coefficient between adjacent loops. Closed-form analytic expressions for the dispersion relations, group velocity and the mid-zone zero v(g) points are found and presented.

Comment on "A note on generalized radial mesh generation for plasma electronic structure"

NASA Astrophysics Data System (ADS)

Pain, J.-Ch.

2011-12-01

In a recent note, B.G. Wilson and V. Sonnad [1] proposed a very useful closed form expression for the efficient generation of analytic log-linear radial meshes. The central point of the note is an implicit equation for the parameter h, involving Lambert's function W[x]. The authors mention that they are unaware of any direct proof of this equation (they obtained it by re-summing the Taylor expansion of h[α] using high-order coefficients obtained by analytic differentiation of the implicit definition using symbolic manipulation). In the present comment, we propose a direct proof of that equation.

Combined effects of heat and mass transfer to magneto hydrodynamics oscillatory dusty fluid flow in a porous channel

NASA Astrophysics Data System (ADS)

Govindarajan, A.; Vijayalakshmi, R.; Ramamurthy, V.

2018-04-01

The main aim of this article is to study the combined effects of heat and mass transfer to radiative Magneto Hydro Dynamics (MHD) oscillatory optically thin dusty fluid in a saturated porous medium channel. Based on certain assumptions, the momentum, energy, concentration equations are obtained.The governing equations are non-dimensionalised, simplified and solved analytically. The closed analytical form solutions for velocity, temperature, concentration profiles are obtained. Numerical computations are presented graphically to show the salient features of various physical parameters. The shear stress, the rate of heat transfer and the rate of mass transfer are also presented graphically.

Analytical skin friction and heat transfer formula for compressible internal flows

NASA Technical Reports Server (NTRS)

Dechant, Lawrence J.; Tattar, Marc J.

1994-01-01

An analytic, closed-form friction formula for turbulent, internal, compressible, fully developed flow was derived by extending the incompressible law-of-the-wall relation to compressible cases. The model is capable of analyzing heat transfer as a function of constant surface temperatures and surface roughness as well as analyzing adiabatic conditions. The formula reduces to Prandtl's law of friction for adiabatic, smooth, axisymmetric flow. In addition, the formula reduces to the Colebrook equation for incompressible, adiabatic, axisymmetric flow with various roughnesses. Comparisons with available experiments show that the model averages roughly 12.5 percent error for adiabatic flow and 18.5 percent error for flow involving heat transfer.

A closed form of a kurtosis parameter of a hypergeometric-Gaussian type-II beam

NASA Astrophysics Data System (ADS)

F, Khannous; A, A. A. Ebrahim; A, Belafhal

2016-04-01

Based on the irradiance moment definition and the analytical expression of waveform propagation for hypergeometric-Gaussian type-II beams passing through an ABCD system, the kurtosis parameter is derived analytically and illustrated numerically. The kurtosis parameters of the Gaussian beam, modified Bessel modulated Gaussian beam with quadrature radial and elegant Laguerre-Gaussian beams are obtained by treating them as special cases of the present treatment. The obtained results show that the kurtosis parameter depends on the change of the beam order m and the hollowness parameter p, such as its decrease with increasing m and increase with increasing p.

Thermodynamics of Thomas-Fermi screened Coulomb systems

NASA Technical Reports Server (NTRS)

Firey, B.; Ashcroft, N. W.

1977-01-01

We obtain in closed analytic form, estimates for the thermodynamic properties of classical fluids with pair potentials of Yukawa type, with special reference to dense fully ionized plasmas with Thomas-Fermi or Debye-Hueckel screening. We further generalize the hard-sphere perturbative approach used for similarly screened two-component mixtures, and demonstrate phase separation in this simple model of a liquid mixture of metallic helium and hydrogen.

On the strain energy of laminated composite plates

NASA Technical Reports Server (NTRS)

Atilgan, Ali R.; Hodges, Dewey H.

1991-01-01

The present effort to obtain the asymptotically correct form of the strain energy in inhomogeneous laminated composite plates proceeds from the geometrically nonlinear elastic theory-based three-dimensional strain energy by decomposing the nonlinear three-dimensional problem into a linear, through-the-thickness analysis and a nonlinear, two-dimensional analysis analyzing plate formation. Attention is given to the case in which each lamina exhibits material symmetry about its middle surface, deriving closed-form analytical expressions for the plate elastic constants and the displacement and strain distributions through the plate's thickness. Despite the simplicity of the plate strain energy's form, there are no restrictions on the magnitudes of displacement and rotation measures.

Role of partial miscibility on pressure buildup due to constant rate injection of CO2 into closed and open brine aquifers

NASA Astrophysics Data System (ADS)

Mathias, Simon A.; Gluyas, Jon G.; GonzáLez MartíNez de Miguel, Gerardo J.; Hosseini, Seyyed A.

2011-12-01

This work extends an existing analytical solution for pressure buildup because of CO2 injection in brine aquifers by incorporating effects associated with partial miscibility. These include evaporation of water into the CO2 rich phase and dissolution of CO2 into brine and salt precipitation. The resulting equations are closed-form, including the locations of the associated leading and trailing shock fronts. Derivation of the analytical solution involves making a number of simplifying assumptions including: vertical pressure equilibrium, negligible capillary pressure, and constant fluid properties. The analytical solution is compared to results from TOUGH2 and found to accurately approximate the extent of the dry-out zone around the well, the resulting permeability enhancement due to residual brine evaporation, the volumetric saturation of precipitated salt, and the vertically averaged pressure distribution in both space and time for the four scenarios studied. While brine evaporation is found to have a considerable effect on pressure, the effect of CO2 dissolution is found to be small. The resulting equations remain simple to evaluate in spreadsheet software and represent a significant improvement on current methods for estimating pressure-limited CO2 storage capacity.

A closed form, physical optics expression for the radar cross section of a perfectly conducting flat plate over a dielectric half-space

NASA Astrophysics Data System (ADS)

Anastassiu, Hristos T.

2003-04-01

The physical optics approximation is employed in the derivation of a closed form expression for the radar cross section (RCS) of a flat, perfectly conducting plate of various shapes, located over a dielectric, possibly lossy half-space. The half-space is assumed to lie in the far field region of the plate. The well-known "four-path model" is invoked in a first-order approximation of the half-space contribution to the scattering mechanisms. Numerical results are compared to a reference, Moment Method solution, and the agreement is investigated, to assess the accuracy of the approximations used. The analytical expressions derived can facilitate very fast RCS calculations for realistic scatterers, such as ships in a sea environment, or aircraft flying low over the ground.

Erratum: A Comparison of Closures for Stochastic Advection-Diffusion Equations

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

Jarman, Kenneth D.; Tartakovsky, Alexandre M.

2015-01-01

This note corrects an error in the authors' article [SIAM/ASA J. Uncertain. Quantif., 1 (2013), pp. 319 347] in which the cited work [Neuman, Water Resour. Res., 29(3) (1993), pp. 633 645] was incorrectly represented and attributed. Concentration covariance equations presented in our article as new were in fact previously derived in the latter work. In the original abstract, the phrase " . . .we propose a closed-form approximation to two-point covariance as a measure of uncertainty. . ." should be replaced by the phrase " . . .we study a closed-form approximation to two-point covariance, previously derived in [Neumanmore » 1993], as a measure of uncertainty." The primary results in our article--the analytical and numerical comparison of existing closure methods for specific example problems are not changed by this correction.« less

Close-form expression of one-tap normalized LMS carrier phase recovery in optical communication systems

NASA Astrophysics Data System (ADS)

Xu, Tianhua; Jacobsen, Gunnar; Popov, Sergei; Li, Jie; Liu, Tiegen; Zhang, Yimo

2016-10-01

The performance of long-haul high speed coherent optical fiber communication systems is significantly degraded by the laser phase noise and the equalization enhanced phase noise (EEPN). In this paper, the analysis of the one-tap normalized least-mean-square (LMS) carrier phase recovery (CPR) is carried out and the close-form expression is investigated for quadrature phase shift keying (QPSK) coherent optical fiber communication systems, in compensating both laser phase noise and equalization enhanced phase noise. Numerical simulations have also been implemented to verify the theoretical analysis. It is found that the one-tap normalized least-mean-square algorithm gives the same analytical expression for predicting CPR bit-error-rate (BER) floors as the traditional differential carrier phase recovery, when both the laser phase noise and the equalization enhanced phase noise are taken into account.

Analytical solutions of the planar cyclic voltammetry process for two soluble species with equal diffusivities and fast electron transfer using the method of eigenfunction expansions

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

Samin, Adib; Lahti, Erik; Zhang, Jinsuo, E-mail: zhang.3558@osu.edu

Cyclic voltammetry is a powerful tool that is used for characterizing electrochemical processes. Models of cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present closed form analytical solutions of the planar voltammetry model for two soluble species with fast electron transfer and equal diffusivities using the eigenfunction expansion method. Our solution methodology does not incorporate Laplace transforms and yields good agreement with the numerical solution. This solution method can be extendedmore » to cases that are more general and may be useful for benchmarking purposes.« less

Pricing timer options and variance derivatives with closed-form partial transform under the 3/2 model

PubMed Central

Zheng, Wendong; Zeng, Pingping

2016-01-01

ABSTRACT Most of the empirical studies on stochastic volatility dynamics favour the 3/2 specification over the square-root (CIR) process in the Heston model. In the context of option pricing, the 3/2 stochastic volatility model (SVM) is reported to be able to capture the volatility skew evolution better than the Heston model. In this article, we make a thorough investigation on the analytic tractability of the 3/2 SVM by proposing a closed-form formula for the partial transform of the triple joint transition density which stand for the log asset price, the quadratic variation (continuous realized variance) and the instantaneous variance, respectively. Two distinct formulations are provided for deriving the main result. The closed-form partial transform enables us to deduce a variety of marginal partial transforms and characteristic functions and plays a crucial role in pricing discretely sampled variance derivatives and exotic options that depend on both the asset price and quadratic variation. Various applications and numerical examples on pricing moment swaps and timer options with discrete monitoring feature are given to demonstrate the versatility of the partial transform under the 3/2 model. PMID:28706460

Misfit stresses in a composite core-shell nanowire with an eccentric parallelepipedal core subjected to one-dimensional cross dilatation eigenstrain

NASA Astrophysics Data System (ADS)

Krasnitckii, S. A.; Kolomoetc, D. R.; Smirnov, A. M.; Gutkin, M. Yu

2017-05-01

The boundary-value problem in the classical theory of elasticity for a core-shell nanowire with an eccentric parallelepipedal core of an arbitrary rectangular cross section is solved. The core is subjected to one-dimensional cross dilatation eigenstrain. The misfit stresses are given in a closed analytical form suitable for theoretical modeling of misfit accommodation in relevant heterostructures.

Combined structures-controls optimization of lattice trusses

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1991-01-01

The role that distributed parameter model can play in CSI is demonstrated, in particular in combined structures controls optimization problems of importance in preliminary design. Closed form solutions can be obtained for performance criteria such as rms attitude error, making possible analytical solutions of the optimization problem. This is in contrast to the need for numerical computer solution involving the inversion of large matrices in traditional finite element model (FEM) use. Another advantage of the analytic solution is that it can provide much needed insight into phenomena that can otherwise be obscured or difficult to discern from numerical computer results. As a compromise in level of complexity between a toy lab model and a real space structure, the lattice truss used in the EPS (Earth Pointing Satellite) was chosen. The optimization problem chosen is a generic one: of minimizing the structure mass subject to a specified stability margin and to a specified upper bond on the rms attitude error, using a co-located controller and sensors. Standard FEM treating each bar as a truss element is used, while the continuum model is anisotropic Timoshenko beam model. Performance criteria are derived for each model, except that for the distributed parameter model, explicit closed form solutions was obtained. Numerical results obtained by the two model show complete agreement.

A closed form slug test theory for high permeability aquifers.

PubMed

Ostendorf, David W; DeGroot, Don J; Dunaj, Philip J; Jakubowski, Joseph

2005-01-01

We incorporate a linear estimate of casing friction into the analytical slug test theory of Springer and Gelhar (1991) for high permeability aquifers. The modified theory elucidates the influence of inertia and casing friction on consistent, closed form equations for the free surface, pressure, and velocity fluctuations for overdamped and underdamped conditions. A consistent, but small, correction for kinetic energy is included as well. A characteristic velocity linearizes the turbulent casing shear stress so that an analytical solution for attenuated, phase shifted pressure fluctuations fits a single parameter (damping frequency) to transducer data from any depth in the casing. Underdamped slug tests of 0.3, 0.6, and 1 m amplitudes at five transducer depths in a 5.1 cm diameter PVC well 21 m deep in the Plymouth-Carver Aquifer yield a consistent hydraulic conductivity of 1.5 x 10(-3) m/s. The Springer and Gelhar (1991) model underestimates the hydraulic conductivity for these tests by as much as 25% by improperly ascribing smooth turbulent casing friction to the aquifer. The match point normalization of Butler (1998) agrees with our fitted hydraulic conductivity, however, when friction is included in the damping frequency. Zurbuchen et al. (2002) use a numerical model to establish a similar sensitivity of hydraulic conductivity to nonlinear casing friction.

Finite-SNR analysis for partial relaying cooperation with channel coding and opportunistic relay selection

NASA Astrophysics Data System (ADS)

Vu, Thang X.; Duhamel, Pierre; Chatzinotas, Symeon; Ottersten, Bjorn

2017-12-01

This work studies the performance of a cooperative network which consists of two channel-coded sources, multiple relays, and one destination. To achieve high spectral efficiency, we assume that a single time slot is dedicated to relaying. Conventional network-coded-based cooperation (NCC) selects the best relay which uses network coding to serve the two sources simultaneously. The bit error rate (BER) performance of NCC with channel coding, however, is still unknown. In this paper, we firstly study the BER of NCC via a closed-form expression and analytically show that NCC only achieves diversity of order two regardless of the number of available relays and the channel code. Secondly, we propose a novel partial relaying-based cooperation (PARC) scheme to improve the system diversity in the finite signal-to-noise ratio (SNR) regime. In particular, closed-form expressions for the system BER and diversity order of PARC are derived as a function of the operating SNR value and the minimum distance of the channel code. We analytically show that the proposed PARC achieves full (instantaneous) diversity order in the finite SNR regime, given that an appropriate channel code is used. Finally, numerical results verify our analysis and demonstrate a large SNR gain of PARC over NCC in the SNR region of interest.

Creep and stress relaxation induced by interface diffusion in metal matrix composites

NASA Astrophysics Data System (ADS)

Li, Yinfeng; Li, Zhonghua

2013-03-01

An analytical solution is developed to predict the creep rate induced by interface diffusion in unidirectional fiber-reinforced and particle reinforced composites. The driving force for the interface diffusion is the normal stress acting on the interface, which is obtained from rigorous Eshelby inclusion theory. The closed-form solution is an explicit function of the applied stress, volume fraction and radius of the fiber, as well as the modulus ratio between the fiber and the matrix. It is interesting that the solution is formally similar to that of Coble creep in polycrystalline materials. For the application of the present solution in the realistic composites, the scale effect is taken into account by finite element analysis based on a unit cell. Based on the solution, a closed-form solution is also given as a description of stress relaxation induced by interfacial diffusion under constant strain. In addition, the analytical solution for the interface stress presented in this study gives some insight into the relationship between the interface diffusion and interface slip. This work was supported by the financial support from the Nature Science Foundation of China (No. 10932007), the National Basic Research Program of China (No. 2010CB631003/5), and the Doctoral Program of Higher Education of China (No. 20100073110006).

A closed expression for the UV-divergent parts of one-loop tensor integrals in dimensional regularization

NASA Astrophysics Data System (ADS)

Sulyok, G.

2017-07-01

Starting from the general definition of a one-loop tensor N-point function, we use its Feynman parametrization to calculate the ultraviolet (UV-)divergent part of an arbitrary tensor coefficient in the framework of dimensional regularization. In contrast to existing recursion schemes, we are able to present a general analytic result in closed form that enables direct determination of the UV-divergent part of any one-loop tensor N-point coefficient independent from UV-divergent parts of other one-loop tensor N-point coefficients. Simplified formulas and explicit expressions are presented for A-, B-, C-, D-, E-, and F-functions.

DROMO formulation for planar motions: solution to the Tsien problem

NASA Astrophysics Data System (ADS)

Urrutxua, Hodei; Morante, David; Sanjurjo-Rivo, Manuel; Peláez, Jesús

2015-06-01

The two-body problem subject to a constant radial thrust is analyzed as a planar motion. The description of the problem is performed in terms of three perturbation methods: DROMO and two others due to Deprit. All of them rely on Hansen's ideal frame concept. An explicit, analytic, closed-form solution is obtained for this problem when the initial orbit is circular (Tsien problem), based on the DROMO special perturbation method, and expressed in terms of elliptic integral functions. The analytical solution to the Tsien problem is later used as a reference to test the numerical performance of various orbit propagation methods, including DROMO and Deprit methods, as well as Cowell and Kustaanheimo-Stiefel methods.

Analytic Results for e+e- --> tt-bar and gammagamma --> tt-bar Observables near the Threshold up to the Next-to-Next-to-Leading Order of NRQCD

NASA Astrophysics Data System (ADS)

Penin, A. A.; Pivovarov, A. A.

2001-02-01

We present an analytical description of top-antitop pair production near the threshold in $e^+e^-$ annihilation and $\\g\\g$ collisions. A set of basic observables considered includes the total cross sections, forward-backward asymmetry and top quark polarization. The threshold effects relevant for the basic observables are described by three universal functions related to S wave production, P wave production and S-P interference. These functions are computed analytically up to the next-to-next-to-leading order of NRQCD. The total $e^+e^-\\to t\\bar t$ cross section near the threshold is obtained in the next-to-next-to-leading order in the closed form including the contribution due to the axial coupling of top quark and mediated by the Z-boson. The effects of the running of the strong coupling constant and of the finite top quark width are taken into account analytically for the P wave production and S-P wave interference.

Analytical saturated domain orientation textures and electromechanical properties of ferroelectric ceramics due to electric/mechanical poling

NASA Astrophysics Data System (ADS)

Li, F. X.; Rajapakse, R. K. N. D.

2007-03-01

Saturated domain orientation textures of three types of pseudocubic (tetragonal, rhombohedral, and orthorhombic) ferroelectric ceramics after complete electric and uniaxial tension (compression) poling is studied analytically in this paper. A one-dimensional orientation distribution function (ODF) of the domain polar vectors is explicitly derived from the uniform inverse pole figures of the poling field axes on a stereographic projection with respect to the fixed crystallite coordinates. The analytical ODF is used to obtain the analytical solutions of saturated polarization and strain after electric/mechanical poling. Based on the closed form solution of the saturated domain orientation textures, the resultant intrinsic electromechanical properties of ferroelectric ceramics, which depend only on the ODF and properties of the corresponding single crystals, are obtained. The results show how the macroscopic symmetries of ferroelectric crystals change from 4mm (tetragonal), 3m (rhombohedral), and mm2 (orthorhombic) single crystals to a ∞mm (transversely isotropic) completely poled ceramic.

Analytical Model for Thermal Elastoplastic Stresses of Functionally Graded Materials

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

Zhai, P. C.; Chen, G.; Liu, L. S.

2008-02-15

A modification analytical model is presented for the thermal elastoplastic stresses of functionally graded materials subjected to thermal loading. The presented model follows the analytical scheme presented by Y. L. Shen and S. Suresh [6]. In the present model, the functionally graded materials are considered as multilayered materials. Each layer consists of metal and ceramic with different volume fraction. The ceramic layer and the FGM interlayers are considered as elastic brittle materials. The metal layer is considered as elastic-perfectly plastic ductile materials. Closed-form solutions for different characteristic temperature for thermal loading are presented as a function of the structure geometriesmore » and the thermomechanical properties of the materials. A main advance of the present model is that the possibility of the initial and spread of plasticity from the two sides of the ductile layers taken into account. Comparing the analytical results with the results from the finite element analysis, the thermal stresses and deformation from the present model are in good agreement with the numerical ones.« less

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Current-sheet formation in two-dimensional coronal fields

NASA Astrophysics Data System (ADS)

Billinghurst, M. N.; Craig, I. J. D.; Sneyd, A. D.

1993-11-01

The formation of current sheets by shearing motions in line-tied twin-lobed fields is examined. A general analytic argument shows that current sheets form along the fieldline bounding the two lobes in the case of both symmetric and asymmetric footpoint motions. In the case of strictly antisymmetric motions however no current sheets can form. These findings are reinforced by magnetic relaxation experiments involving sheared two-lobed fields represented by Clebsh variables. It is pointed out that, although current singularites cannot be expected to form when the line-tying assumption is relaxed, the two-lobed geometry is still consistent with the formation of highly localised currents - and strong resistive dissipation - along field lines close to the bounding fieldline.

Closed-Form Jensen-Renyi Divergence for Mixture of Gaussians and Applications to Group-Wise Shape Registration*

PubMed Central

Wang, Fei; Syeda-Mahmood, Tanveer; Vemuri, Baba C.; Beymer, David; Rangarajan, Anand

2010-01-01

In this paper, we propose a generalized group-wise non-rigid registration strategy for multiple unlabeled point-sets of unequal cardinality, with no bias toward any of the given point-sets. To quantify the divergence between the probability distributions – specifically Mixture of Gaussians – estimated from the given point sets, we use a recently developed information-theoretic measure called Jensen-Renyi (JR) divergence. We evaluate a closed-form JR divergence between multiple probabilistic representations for the general case where the mixture models differ in variance and the number of components. We derive the analytic gradient of the divergence measure with respect to the non-rigid registration parameters, and apply it to numerical optimization of the group-wise registration, leading to a computationally efficient and accurate algorithm. We validate our approach on synthetic data, and evaluate it on 3D cardiac shapes. PMID:20426043

Closed-form Jensen-Renyi divergence for mixture of Gaussians and applications to group-wise shape registration.

PubMed

Wang, Fei; Syeda-Mahmood, Tanveer; Vemuri, Baba C; Beymer, David; Rangarajan, Anand

2009-01-01

In this paper, we propose a generalized group-wise non-rigid registration strategy for multiple unlabeled point-sets of unequal cardinality, with no bias toward any of the given point-sets. To quantify the divergence between the probability distributions--specifically Mixture of Gaussians--estimated from the given point sets, we use a recently developed information-theoretic measure called Jensen-Renyi (JR) divergence. We evaluate a closed-form JR divergence between multiple probabilistic representations for the general case where the mixture models differ in variance and the number of components. We derive the analytic gradient of the divergence measure with respect to the non-rigid registration parameters, and apply it to numerical optimization of the group-wise registration, leading to a computationally efficient and accurate algorithm. We validate our approach on synthetic data, and evaluate it on 3D cardiac shapes.

Analysis of Tank PMD Rewetting Following Thrust Resettling

NASA Astrophysics Data System (ADS)

Weislogel, M. M.; Sala, M. A.; Collicott, S. H.

2002-10-01

Recent investigations have successfully demonstrated closed-form analytical solutions of spontaneous capillary flows in idealized cylindrical containers with interior corners. In this report, the theory is extended and applied to complex containers modeling spacecraft fuel tanks employing propellant management devices (PMDs). The specific problem investigated is one of spontaneous rewetting of a typical partially filled liquid fuel/cryogen tank with PMD after thrust resettling. The transients of this flow impact the logistics of orbital maneuvers and potentially tank thermal control. The general procedure to compute the initial condition (mean radius of curvature for the interface) for the closed-form transient flows is first outlined then solved for several 'complex' cylindrical tanks exhibiting symmetry. The utility and limitations of the technique as a design tool are discussed in a summary, which also highlights comparisons with NASA flight data of a model propellant tank with PMD.

Nanoscale phase transition behavior of shape memory alloys — closed form solution of 1D effective modelling

NASA Astrophysics Data System (ADS)

Li, M. P.; Sun, Q. P.

2018-01-01

We investigate the roles of grain size (lg) and grain boundary thickness (lb) on the stress-induced phase transition (PT) behaviors of nanocrystalline shape memory alloys (SMAs) by using a Core-shell type "crystallite-amorphous composite" model. A non-dimensionalized length scale lbarg(=lg /lb) is identified as the governing parameter which is indicative of the energy competition between the crystallite and the grain boundary. Closed form analytical solutions of a reduced effective 1D model with embedded microstructure length scales of lg and lb are presented in this paper. It is shown that, with lbarg reduction, the energy of the elastic non-transformable grain boundary will gradually become dominant in the phase transition process, and eventually bring fundamental changes of the deformation behaviors: breakdown of two-phase coexistence and vanishing of superelastic hysteresis. The predictions are supported by experimental data of nanocrystalline NiTi SMAs.

Analysis of Tank PMD Rewetting Following Thrust Resettling

NASA Technical Reports Server (NTRS)

Weislogel, M. M.; Sala, M. A.; Collicott, S. H.; Rame, Enrique (Technical Monitor)

2002-01-01

Recent investigations have successfully demonstrated closed-form analytical solutions of spontaneous capillary flows in idealized cylindrical containers with interior corners. In this report, the theory is extended and applied to complex containers modeling spacecraft fuel tanks employing propellant management devices (PMDs). The specific problem investigated is one of spontaneous rewetting of a typical partially filled liquid fuel/cryogen tank with PMD after thrust resettling. The transients of this flow impact the logistics of orbital maneuvers and potentially tank thermal control. The general procedure to compute the initial condition (mean radius of curvature for the interface) for the closed-form transient flows is first outlined then solved for several 'complex' cylindrical tanks exhibiting symmetry. The utility and limitations of the technique as a design tool are discussed in a summary, which also highlights comparisons with NASA flight data of a model propellant tank with PMD.

Self-induced transparency of an extremely short pulse

NASA Technical Reports Server (NTRS)

Lee, C. T.

1973-01-01

An extremely short pulse propagation in a resonant medium is properly described by a closed form steady-state analytic solution. The usual slowly varying envelope approximation (SVEA) is not made. Instead, different assumptions with respect to pulse speed and pulse duration are used, and any possible nonresonant loss is ignored. This study indicates that the results obtained by the SVEA approach are much better than they have been intuitively expected to be.

Closed form solution for a double quantum well using Gröbner basis

NASA Astrophysics Data System (ADS)

Acus, A.; Dargys, A.

2011-07-01

Analytical expressions for the spectrum, eigenfunctions and dipole matrix elements of a square double quantum well (DQW) are presented for a general case when the potential in different regions of the DQW has different heights and the effective masses are different. This was achieved by using a Gröbner basis algorithm that allowed us to disentangle the resulting coupled polynomials without explicitly solving the transcendental eigenvalue equation.

Performance-driven Multimodality Sensor Fusion

DTIC Science & Technology

2012-01-23

in IEEE Intl Conf. on Acoust., Speech , Signal Processing, (Dallas), Mar. 2010. [10] K. Sricharan, R. Raich, and A. Hero III, “Boundary compensated knn ...nearest neighbor ( kNN ) plug-in estima- tors, we have developed a generally applicable theory that gives analytical closed-form expressions for asymptotic...Co-PI’s Raich and Hero and was published in the IEEE Proc. of 2011 Intl Conf. on Acoustics, Speech , and Signal Processing. 2.4 Dimension estimation in

Existence of small loops in a bifurcation diagram near degenerate eigenvalues

NASA Astrophysics Data System (ADS)

Hmidi, Taoufik; Renault, Coralie

2017-10-01

In this paper, we study the global structure of a bifurcation diagram for rotating doubly connected patches near a degenerate case for incompressible Euler equations. We show that branches with the same symmetry merge, forming a small loop, provided that they are close enough. This gives an analytical proof for the numerical observations conducted in the recent work by de la Hoz et al (2016 SIAM J. Math. Anal. 48 1892-928).

Analytical expression for Risken-Nummedal-Graham-Haken instability threshold in quantum cascade lasers.

PubMed

Vukovic, N; Radovanovic, J; Milanovic, V; Boiko, D L

2016-11-14

We have obtained a closed-form expression for the threshold of Risken-Nummedal-Graham-Haken (RNGH) multimode instability in a Fabry-Pérot (FP) cavity quantum cascade laser (QCL). This simple analytical expression is a versatile tool that can easily be applied in practical situations which require analysis of QCL dynamic behavior and estimation of its RNGH multimode instability threshold. Our model for a FP cavity laser accounts for the carrier coherence grating and carrier population grating as well as their relaxation due to carrier diffusion. In the model, the RNGH instability threshold is analyzed using a second-order bi-orthogonal perturbation theory and we confirm our analytical solution by a comparison with the numerical simulations. In particular, the model predicts a low RNGH instability threshold in QCLs. This agrees very well with experimental data available in the literature.

Closed-form analytical solutions incorporating pumping and tidal effects in various coastal aquifer systems

NASA Astrophysics Data System (ADS)

Wang, Chaoyue; Li, Hailong; Wan, Li; Wang, Xusheng; Jiang, Xiaowei

2014-07-01

Pumping wells are common in coastal aquifers affected by tides. Here we present analytical solutions of groundwater table or head variations during a constant rate pumping from a single, fully-penetrating well in coastal aquifer systems comprising an unconfined aquifer, a confined aquifer and semi-permeable layer between them. The unconfined aquifer terminates at the coastline (or river bank) and the other two layers extend under tidal water (sea or tidal river) for a certain distance L. Analytical solutions are derived for 11 reasonable combinations of different situations of the L-value (zero, finite, and infinite), of the middle layer's permeability (semi-permeable and impermeable), of the boundary condition at the aquifer's submarine terminal (Dirichlet describing direct connection with seawater and no-flow describing the existence of an impermeable capping), and of the tidal water body (sea and tidal river). Solutions are discussed with application examples in fitting field observations and parameter estimations.

Emergent rogue wave structures and statistics in spontaneous modulation instability.

PubMed

Toenger, Shanti; Godin, Thomas; Billet, Cyril; Dias, Frédéric; Erkintalo, Miro; Genty, Goëry; Dudley, John M

2015-05-20

The nonlinear Schrödinger equation (NLSE) is a seminal equation of nonlinear physics describing wave packet evolution in weakly-nonlinear dispersive media. The NLSE is especially important in understanding how high amplitude "rogue waves" emerge from noise through the process of modulation instability (MI) whereby a perturbation on an initial plane wave can evolve into strongly-localised "breather" or "soliton on finite background (SFB)" structures. Although there has been much study of such structures excited under controlled conditions, there remains the open question of how closely the analytic solutions of the NLSE actually model localised structures emerging in noise-seeded MI. We address this question here using numerical simulations to compare the properties of a large ensemble of emergent peaks in noise-seeded MI with the known analytic solutions of the NLSE. Our results show that both elementary breather and higher-order SFB structures are observed in chaotic MI, with the characteristics of the noise-induced peaks clustering closely around analytic NLSE predictions. A significant conclusion of our work is to suggest that the widely-held view that the Peregrine soliton forms a rogue wave prototype must be revisited. Rather, we confirm earlier suggestions that NLSE rogue waves are most appropriately identified as collisions between elementary SFB solutions.

Emergent rogue wave structures and statistics in spontaneous modulation instability

PubMed Central

Toenger, Shanti; Godin, Thomas; Billet, Cyril; Dias, Frédéric; Erkintalo, Miro; Genty, Goëry; Dudley, John M.

2015-01-01

The nonlinear Schrödinger equation (NLSE) is a seminal equation of nonlinear physics describing wave packet evolution in weakly-nonlinear dispersive media. The NLSE is especially important in understanding how high amplitude “rogue waves” emerge from noise through the process of modulation instability (MI) whereby a perturbation on an initial plane wave can evolve into strongly-localised “breather” or “soliton on finite background (SFB)” structures. Although there has been much study of such structures excited under controlled conditions, there remains the open question of how closely the analytic solutions of the NLSE actually model localised structures emerging in noise-seeded MI. We address this question here using numerical simulations to compare the properties of a large ensemble of emergent peaks in noise-seeded MI with the known analytic solutions of the NLSE. Our results show that both elementary breather and higher-order SFB structures are observed in chaotic MI, with the characteristics of the noise-induced peaks clustering closely around analytic NLSE predictions. A significant conclusion of our work is to suggest that the widely-held view that the Peregrine soliton forms a rogue wave prototype must be revisited. Rather, we confirm earlier suggestions that NLSE rogue waves are most appropriately identified as collisions between elementary SFB solutions. PMID:25993126

Modeling and control of flexible space platforms with articulated payloads

NASA Technical Reports Server (NTRS)

Graves, Philip C.; Joshi, Suresh M.

1989-01-01

The first steps in developing a methodology for spacecraft control-structure interaction (CSI) optimization are identification and classification of anticipated missions, and the development of tractable mathematical models in each mission class. A mathematical model of a generic large flexible space platform (LFSP) with multiple independently pointed rigid payloads is considered. The objective is not to develop a general purpose numerical simulation, but rather to develop an analytically tractable mathematical model of such composite systems. The equations of motion for a single payload case are derived, and are linearized about zero steady-state. The resulting model is then extended to include multiple rigid payloads, yielding the desired analytical form. The mathematical models developed clearly show the internal inertial/elastic couplings, and are therefore suitable for analytical and numerical studies. A simple decentralized control law is proposed for fine pointing the payloads and LFSP attitude control, and simulation results are presented for an example problem. The decentralized controller is shown to be adequate for the example problem chosen, but does not, in general, guarantee stability. A centralized dissipative controller is then proposed, requiring a symmetric form of the composite system equations. Such a controller guarantees robust closed loop stability despite unmodeled elastic dynamics and parameter uncertainties.

A series solution for horizontal infiltration in an initially dry aquifer

NASA Astrophysics Data System (ADS)

Furtak-Cole, Eden; Telyakovskiy, Aleksey S.; Cooper, Clay A.

2018-06-01

The porous medium equation (PME) is a generalization of the traditional Boussinesq equation for hydraulic conductivity as a power law function of height. We analyze the horizontal recharge of an initially dry unconfined aquifer of semi-infinite extent, as would be found in an aquifer adjacent a rising river. If the water level can be modeled as a power law function of time, similarity variables can be introduced and the original problem can be reduced to a boundary value problem for a nonlinear ordinary differential equation. The position of the advancing front is not known ahead of time and must be found in the process of solution. We present an analytical solution in the form of a power series, with the coefficients of the series given by a recurrence relation. The analytical solution compares favorably with a highly accurate numerical solution, and only a small number of terms of the series are needed to achieve high accuracy in the scenarios considered here. We also conduct a series of physical experiments in an initially dry wedged Hele-Shaw cell, where flow is modeled by a special form of the PME. Our analytical solution closely matches the hydraulic head profiles in the Hele-Shaw cell experiment.

Comparison of Three Methods for Wind Turbine Capacity Factor Estimation

PubMed Central

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. PMID:24587755

Eye movement dysfunction in first-degree relatives of patients with schizophrenia: a meta-analytic evaluation of candidate endophenotypes.

PubMed

Calkins, Monica E; Iacono, William G; Ones, Deniz S

2008-12-01

Several forms of eye movement dysfunction (EMD) are regarded as promising candidate endophenotypes of schizophrenia. Discrepancies in individual study results have led to inconsistent conclusions regarding particular aspects of EMD in relatives of schizophrenia patients. To quantitatively evaluate and compare the candidacy of smooth pursuit, saccade and fixation deficits in first-degree biological relatives, we conducted a set of meta-analytic investigations. Among 18 measures of EMD, memory-guided saccade accuracy and error rate, global smooth pursuit dysfunction, intrusive saccades during fixation, antisaccade error rate and smooth pursuit closed-loop gain emerged as best differentiating relatives from controls (standardized mean differences ranged from .46 to .66), with no significant differences among these measures. Anticipatory saccades, but no other smooth pursuit component measures were also increased in relatives. Visually-guided reflexive saccades were largely normal. Moderator analyses examining design characteristics revealed few variables affecting the magnitude of the meta-analytically observed effects. Moderate effect sizes of relatives v. controls in selective aspects of EMD supports their endophenotype potential. Future work should focus on facilitating endophenotype utility through attention to heterogeneity of EMD performance, relationships among forms of EMD, and application in molecular genetics studies.

Neural Network Based Modeling and Analysis of LP Control Surface Allocation

NASA Technical Reports Server (NTRS)

Langari, Reza; Krishnakumar, Kalmanje; Gundy-Burlet, Karen

2003-01-01

This paper presents an approach to interpretive modeling of LP based control allocation in intelligent flight control. The emphasis is placed on a nonlinear interpretation of the LP allocation process as a static map to support analytical study of the resulting closed loop system, albeit in approximate form. The approach makes use of a bi-layer neural network to capture the essential functioning of the LP allocation process. It is further shown via Lyapunov based analysis that under certain relatively mild conditions the resulting closed loop system is stable. Some preliminary conclusions from a study at Ames are stated and directions for further research are given at the conclusion of the paper.

PFLOTRAN Verification: Development of a Testing Suite to Ensure Software Quality

NASA Astrophysics Data System (ADS)

Hammond, G. E.; Frederick, J. M.

2016-12-01

In scientific computing, code verification ensures the reliability and numerical accuracy of a model simulation by comparing the simulation results to experimental data or known analytical solutions. The model is typically defined by a set of partial differential equations with initial and boundary conditions, and verification ensures whether the mathematical model is solved correctly by the software. Code verification is especially important if the software is used to model high-consequence systems which cannot be physically tested in a fully representative environment [Oberkampf and Trucano (2007)]. Justified confidence in a particular computational tool requires clarity in the exercised physics and transparency in its verification process with proper documentation. We present a quality assurance (QA) testing suite developed by Sandia National Laboratories that performs code verification for PFLOTRAN, an open source, massively-parallel subsurface simulator. PFLOTRAN solves systems of generally nonlinear partial differential equations describing multiphase, multicomponent and multiscale reactive flow and transport processes in porous media. PFLOTRAN's QA test suite compares the numerical solutions of benchmark problems in heat and mass transport against known, closed-form, analytical solutions, including documentation of the exercised physical process models implemented in each PFLOTRAN benchmark simulation. The QA test suite development strives to follow the recommendations given by Oberkampf and Trucano (2007), which describes four essential elements in high-quality verification benchmark construction: (1) conceptual description, (2) mathematical description, (3) accuracy assessment, and (4) additional documentation and user information. Several QA tests within the suite will be presented, including details of the benchmark problems and their closed-form analytical solutions, implementation of benchmark problems in PFLOTRAN simulations, and the criteria used to assess PFLOTRAN's performance in the code verification procedure. References Oberkampf, W. L., and T. G. Trucano (2007), Verification and Validation Benchmarks, SAND2007-0853, 67 pgs., Sandia National Laboratories, Albuquerque, NM.

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.

Distributed reacceleration of cosmic rays

NASA Technical Reports Server (NTRS)

Wandel, Amri; Eichler, David; Letaw, John R.; Silberberg, Rein; Tsao, C. H.

1985-01-01

A model is developed in which cosmic rays, in addition to their initial acceleration by a strong shock, are continuously reaccelerated while propagating through the Galaxy. The equations describing this acceleration scheme are solved analytically and numerically. Solutions for the spectra of primary and secondary cosmic rays are given in a closed analytic form, allowing a rapid search in parameter space for viable propagation models with distributed reeacceleration included. The observed boron-to-carbon ratio can be reproduced by the reacceleration theory over a range of escape parameters, some of them quite different from the standard leaky-box model. It is also shown that even a very modest amount of reacceleration by strong shocks causes the boron-to-carbon ratio to level off at sufficiently high energies.

Experiences with Probabilistic Analysis Applied to Controlled Systems

NASA Technical Reports Server (NTRS)

Kenny, Sean P.; Giesy, Daniel P.

2004-01-01

This paper presents a semi-analytic method for computing frequency dependent means, variances, and failure probabilities for arbitrarily large-order closed-loop dynamical systems possessing a single uncertain parameter or with multiple highly correlated uncertain parameters. The approach will be shown to not suffer from the same computational challenges associated with computing failure probabilities using conventional FORM/SORM techniques. The approach is demonstrated by computing the probabilistic frequency domain performance of an optimal feed-forward disturbance rejection scheme.

Misfit stresses in a composite core-shell nanowire with an eccentric parallelepipedal core subjected to one-dimensional cross dilatation eigenstrain

NASA Astrophysics Data System (ADS)

Krasnitckii, S. A.; Kolomoetc, D. R.; Smirnov, A. M.; Gutkin, M. Yu

2017-03-01

We present an analytical solution to the boundary-value problem in the classical theory of elasticity for a core-shell nanowire with an eccentric parallelepipedal core of an arbitrary rectangular cross section. The core is subjected to one-dimensional cross dilatation eigenstrain. The misfit stresses are found in a concise and transparent closed form which is convenient for practical use in theoretical modeling of misfit relaxation processes.

Nonsteady Problem for an Elastic Half-Plane with Mixed Boundary Conditions

NASA Astrophysics Data System (ADS)

Kubenko, V. D.

2016-03-01

An approach to studying nonstationary wave processes in an elastic half-plane with mixed boundary conditions of the fourth boundary-value problem of elasticity is proposed. The Laplace and Fourier transforms are used. The sequential inversion of these transforms or the inversion of the joint transform by the Cagniard method allows obtaining the required solution (stresses, displacements) in a closed analytic form. With this approach, the problem can be solved for various types of loads

Spectral analysis for weighted tree-like fractals

NASA Astrophysics Data System (ADS)

Dai, Meifeng; Chen, Yufei; Wang, Xiaoqian; Sun, Yu; Su, Weiyi

2018-02-01

Much information about the structural properties and dynamical aspects of a network is measured by the eigenvalues of its normalized Laplacian matrix. In this paper, we aim to present a study on the spectra of the normalized Laplacian of weighted tree-like fractals. We analytically obtain the relationship between the eigenvalues and their multiplicities for two successive generations. As an example of application of these results, we then derive closed-form expressions for their multiplicative Kirchhoff index and Kemeny's constant.

Analytic approach to photoelectron transport.

NASA Technical Reports Server (NTRS)

Stolarski, R. S.

1972-01-01

The equation governing the transport of photoelectrons in the ionosphere is shown to be equivalent to the equation of radiative transfer. In the single-energy approximation this equation is solved in closed form by the method of discrete ordinates for isotropic scattering and for a single-constituent atmosphere. The results include prediction of the angular distribution of photoelectrons at all altitudes and, in particular, the angular distribution of the escape flux. The implications of these solutions in real atmosphere calculations are discussed.

A cluster bootstrap for two-loop MHV amplitudes

DOE PAGES

Golden, John; Spradlin, Marcus

2015-02-02

We apply a bootstrap procedure to two-loop MHV amplitudes in planar N=4 super-Yang-Mills theory. We argue that the mathematically most complicated part (the Λ 2 B 2 coproduct component) of the n-particle amplitude is uniquely determined by a simple cluster algebra property together with a few physical constraints (dihedral symmetry, analytic structure, supersymmetry, and well-defined collinear limits). Finally, we present a concise, closed-form expression which manifests these properties for all n.

Theoretical investigations on plasma processes in the Kaufman thruster

NASA Technical Reports Server (NTRS)

Wilhelm, H. E.

1973-01-01

The lateral neutralization of ion beams is treated by standard mathematical methods for first order, nonlinear partial differential equations. A closed form analytical solution is derived for the transient lateral beam neutralization for electron injection by means of a von Mises transformation. A nonlinear theory of the longitudinal ion beam neutralization is developed using the von Mises transformation. By means of the Lenard-Balescu equation, the intercomponent momentum transfer between stable, collisionless electron and ion components is calculated.

A flux-limited treatment for the conductive evaporation of spherical interstellar gas clouds

NASA Technical Reports Server (NTRS)

Dalton, William W.; Balbus, Steven A.

1993-01-01

In this work, we present and analyze a new analytic solution for the saturated (flux-limited) thermal evaporation of a spherical cloud. This work is distinguished from earlier analytic studies by allowing the thermal conductivity to change continuously from a diffusive to a saturated form, in a manner usually employed only in numerical calculations. This closed form solution will be of interest as a computational benchmark. Using our calculated temperature profiles and mass-loss rates, we model the thermal evaporation of such a cloud under typical interstellar medium (ISM) conditions, with some restrictions. We examine the ionization structure of the cloud-ISM interface and evaluate column densities of carbon, nitrogen, oxygen, neon, and silicon ions toward the cloud. In accord with other investigations, we find that ionization equilibrium is far from satisfied under the assumed conditions. Since the inclusion of saturation effects in the heat flux narrows the thermal interface relative to its classical structure, we also find that saturation effects tend to lower predicted column densities.

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

PubMed

Simon, Laurent; Ospina, Juan

2016-07-25

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

Analytically derived switching functions for exact H2+ eigenstates

NASA Astrophysics Data System (ADS)

Thorson, W. R.; Kimura, M.; Choi, J. H.; Knudson, S. K.

1981-10-01

Electron translation factors (ETF's) appropriate for slow atomic collisions may be constructed using switching functions. In this paper we derive a set of switching functions for the H2+ system by an analytical "two-center decomposition" of the exact molecular eigenstates. These switching functions are closely approximated by the simple form f=bη, where η is the "angle variable" of prolate spheroidal coordinates. For given united atom angular momentum quantum numbers (l,m), the characteristic parameter blm depends only on the quantity c2=-ɛR22, where ɛ is the electronic binding energy and R the internuclear distance in a.u. The resulting parameters are in excellent agreement with those found in our earlier work by a heuristic "optimization" scheme based on a study of coupling matrix-element behavior for a number of H2+ states. An approximate extension to asymmetric cases (HeH2+) has also been made. Nonadiabatic couplings based on these switching functions have been used in recent close-coupling calculations for H+-H(1s) collisions and He2+-H(1s) collisions at energies 1.0-20 keV.

Analytical Verifications in Cryogenic Testing of NGST Advanced Mirror System Demonstrators

NASA Technical Reports Server (NTRS)

Cummings, Ramona; Levine, Marie; VanBuren, Dave; Kegley, Jeff; Green, Joseph; Hadaway, James; Presson, Joan; Cline, Todd; Stahl, H. Philip (Technical Monitor)

2002-01-01

Ground based testing is a critical and costly part of component, assembly, and system verifications of large space telescopes. At such tests, however, with integral teamwork by planners, analysts, and test personnel, segments can be included to validate specific analytical parameters and algorithms at relatively low additional cost. This paper opens with strategy of analytical verification segments added to vacuum cryogenic testing of Advanced Mirror System Demonstrator (AMSD) assemblies. These AMSD assemblies incorporate material and architecture concepts being considered in the Next Generation Space Telescope (NGST) design. The test segments for workmanship testing, cold survivability, and cold operation optical throughput are supplemented by segments for analytical verifications of specific structural, thermal, and optical parameters. Utilizing integrated modeling and separate materials testing, the paper continues with support plan for analyses, data, and observation requirements during the AMSD testing, currently slated for late calendar year 2002 to mid calendar year 2003. The paper includes anomaly resolution as gleaned by authors from similar analytical verification support of a previous large space telescope, then closes with draft of plans for parameter extrapolations, to form a well-verified portion of the integrated modeling being done for NGST performance predictions.

Analytical solution for the normal emission portion of the averaged Yarkovsky-O'Keefe-Radzvieskii-Paddack coefficient for a single facet

NASA Astrophysics Data System (ADS)

Albuja, Antonella A.; Scheeres, Daniel J.

2015-02-01

The Yarkovsky-O'Keefe-Radzvieskii-Paddack (YORP) effect has been well studied for asteroids. This paper develops an analytic solution to find the normal emission YORP component for a single facet. The solution presented here does not account for self-shadowing or self-heating. The YORP coefficient for all facets can be summed together to find the total coefficient of the asteroid. The normal emission component of YORP has been shown to be the most important for asteroids and it directly affects the rate of change of the asteroid's spin period. The analytical solution found is a sole function of the facet's geometry and the obliquity of the asteroid. This solution is universal for any facet and its orientation. The behaviour of the coefficient is analysed with this analytical solution. The closed-form solution is used to find the total YORP coefficient for the asteroids Apollo and 1998 ML14 whose shape models are composed of different numbers of facets. The results are then compared to published results and those obtained through numerical quadrature for validation.

Neutral Mass Spectrometry of Mega-Dalton Particles with Single-Particle Resolution using a Nano-Electromechanical System

NASA Astrophysics Data System (ADS)

Kelber, Scott; Hanay, Mehmet; Naik, Akshay; Chi, Derrick; Hentz, Sebastien; Bullard, Caryn; Collinet, Eric; Duraffourg, Laurent; Roukes, Michael

2012-02-01

Nanoelectromechanical systems (NEMS) enable mass sensing with unprecedented sensitivity and mass dynamic range. Previous works have relied on statistical analysis of multiple landing events to assemble mass spectra. Here we demonstrate the utility of using multiple modes of the NEMS device in determining the mass of individual molecules landing on the NEMS. Analyte particles in vapor form are produced using matrix assisted laser desorption ionization. Resonant frequencies of the first two modes of a single NEMS device, placed in close proximity to the analyte source, are tracked using parallel phase locked loops. Each analyte molecule landing on the NEMS generates a distinct frequency shift in the two modes. These time correlated frequency jumps are used to evaluate the mass of each analyte particle landing on the NEMS and thus generate mass spectra. We present the latest experimental results using this scheme and also demonstrate the utility for mass spectrometry of large biomolecules. This NEMS-Mass Spec. system offers a new tool for structural biology and pathology for the analysis of large proteins, protein complexes, and viruses.

Analytic Approximations to the Free Boundary and Multi-dimensional Problems in Financial Derivatives Pricing

NASA Astrophysics Data System (ADS)

Lau, Chun Sing

This thesis studies two types of problems in financial derivatives pricing. The first type is the free boundary problem, which can be formulated as a partial differential equation (PDE) subject to a set of free boundary condition. Although the functional form of the free boundary condition is given explicitly, the location of the free boundary is unknown and can only be determined implicitly by imposing continuity conditions on the solution. Two specific problems are studied in details, namely the valuation of fixed-rate mortgages and CEV American options. The second type is the multi-dimensional problem, which involves multiple correlated stochastic variables and their governing PDE. One typical problem we focus on is the valuation of basket-spread options, whose underlying asset prices are driven by correlated geometric Brownian motions (GBMs). Analytic approximate solutions are derived for each of these three problems. For each of the two free boundary problems, we propose a parametric moving boundary to approximate the unknown free boundary, so that the original problem transforms into a moving boundary problem which can be solved analytically. The governing parameter of the moving boundary is determined by imposing the first derivative continuity condition on the solution. The analytic form of the solution allows the price and the hedging parameters to be computed very efficiently. When compared against the benchmark finite-difference method, the computational time is significantly reduced without compromising the accuracy. The multi-stage scheme further allows the approximate results to systematically converge to the benchmark results as one recasts the moving boundary into a piecewise smooth continuous function. For the multi-dimensional problem, we generalize the Kirk (1995) approximate two-asset spread option formula to the case of multi-asset basket-spread option. Since the final formula is in closed form, all the hedging parameters can also be derived in closed form. Numerical examples demonstrate that the pricing and hedging errors are in general less than 1% relative to the benchmark prices obtained by numerical integration or Monte Carlo simulation. By exploiting an explicit relationship between the option price and the underlying probability distribution, we further derive an approximate distribution function for the general basket-spread variable. It can be used to approximate the transition probability distribution of any linear combination of correlated GBMs. Finally, an implicit perturbation is applied to reduce the pricing errors by factors of up to 100. When compared against the existing methods, the basket-spread option formula coupled with the implicit perturbation turns out to be one of the most robust and accurate approximation methods.

General Relativistic Precession in Small Solar System Bodies

NASA Astrophysics Data System (ADS)

Sekhar, Aswin; Werner, Stephanie; Hoffmann, Volker; Asher, David; Vaubaillon, Jeremie; Hajdukova, Maria; Li, Gongjie

2016-10-01

Introduction: One of the greatest successes of the Einstein's General Theory of Relativity (GR) was the correct prediction of the precession of perihelion of Mercury. The closed form expression to compute this precession tells us that substantial GR precession would occur only if the bodies have a combination of both moderately small perihelion distance and semi-major axis. Minimum Orbit Intersection Distance (MOID) is a quantity which helps us to understand the closest proximity of two orbits in space. Hence evaluating MOID is crucial to understand close encounters and collision scenarios better. In this work, we look at the possible scenarios where a small GR precession in argument of pericentre (ω) can create substantial changes in MOID for small bodies ranging from meteoroids to comets and asteroids.Analytical Approach and Numerical Integrations: Previous works have looked into neat analytical techniques to understand different collision scenarios and we use those standard expressions to compute MOID analytically. We find the nature of this mathematical function is such that a relatively small GR precession can lead to drastic changes in MOID values depending on the initial value of ω. Numerical integrations were done with package MERCURY incorporating the GR code to test the same effects. Numerical approach showed the same interesting relationship (as shown by analytical theory) between values of ω and the peaks/dips in MOID values. Previous works have shown that GR precession suppresses Kozai oscillations and this aspect was verified using our integrations. There is an overall agreement between both analytical and numerical methods.Summary and Discussion: We find that GR precession could play an important role in the calculations pertaining to MOID and close encounter scenarios in the case of certain small solar system bodies (depending on their initial orbital elements). Previous works have looked into impact probabilities and collision scenarios on planets from different small body populations. This work aims to find certain sub-sets of orbits where GR could play an interesting role. Certain parallels are drawn between the cases of asteroids, comets and small perihelion distance meteoroid streams.

Change in Minimum Orbit Intersection Distance due to General Relativistic Precession in Small Solar System Bodies

NASA Astrophysics Data System (ADS)

Sekhar, Aswin; Valsecchi, Giovanni B.; Asher, David; Werner, Stephanie; Vaubaillon, Jeremie; Li, Gongjie

2017-06-01

One of the greatest successes of Einstein's General Theory of Relativity (GR) was the correct prediction of the perihelion precession of Mercury. The closed form expression to compute this precession tells us that substantial GR precession would occur only if the bodies have a combination of both moderately small perihelion distance and semi-major axis. Minimum Orbit Intersection Distance (MOID) is a quantity which helps us to understand the closest proximity of two orbits in space. Hence evaluating MOID is crucial to understand close encounters and collision scenarios better. In this work, we look at the possible scenarios where a small GR precession in argument of pericentre can create substantial changes in MOID for small bodies ranging from meteoroids to comets and asteroids.Previous works have looked into neat analytical techniques to understand different collision scenarios and we use those standard expressions to compute MOID analytically. We find the nature of this mathematical function is such that a relatively small GR precession can lead to drastic changes in MOID values depending on the initial value of argument of pericentre. Numerical integrations were done with the MERCURY package incorporating GR code to test the same effects. A numerical approach showed the same interesting relationship (as shown by analytical theory) between values of argument of pericentre and the peaks or dips in MOID values. There is an overall agreement between both analytical and numerical methods.We find that GR precession could play an important role in the calculations pertaining to MOID and close encounter scenarios in the case of certain small solar system bodies (depending on their initial orbital elements) when long term impact risk possibilities are considered. Previous works have looked into impact probabilities and collision scenarios on planets from different small body populations. This work aims to find certain sub-sets of small bodies where GR could play an interesting role. Certain parallels are drawn between the cases of asteroids, comets and small perihelion distance meteoroid streams.

New closed analytical solutions for geometrically thick fluid tori around black holes. Numerical evolution and the onset of the magneto-rotational instability

NASA Astrophysics Data System (ADS)

Witzany, V.; Jefremov, P.

2018-06-01

Context. When a black hole is accreting well below the Eddington rate, a geometrically thick, radiatively inefficient state of the accretion disk is established. There is a limited number of closed-form physical solutions for geometrically thick (nonselfgravitating) toroidal equilibria of perfect fluids orbiting a spinning black hole, and these are predominantly used as initial conditions for simulations of accretion in the aforementioned mode. However, different initial configurations might lead to different results and thus observational predictions drawn from such simulations. Aims: We aim to expand the known equilibria by a number of closed multiparametric solutions with various possibilities of rotation curves and geometric shapes. Then, we ask whether choosing these as initial conditions influences the onset of accretion and the asymptotic state of the disk. Methods: We have investigated a set of examples from the derived solutions in detail; we analytically estimate the growth of the magneto-rotational instability (MRI) from their rotation curves and evolve the analytically obtained tori using the 2D magneto-hydrodynamical code HARM. Properties of the evolutions are then studied through the mass, energy, and angular-momentum accretion rates. Results: The rotation curve has a decisive role in the numerical onset of accretion in accordance with our analytical MRI estimates: in the first few orbital periods, the average accretion rate is linearly proportional to the initial MRI rate in the toroids. The final state obtained from any initial condition within the studied class after an evolution of ten or more orbital periods is mostly qualitatively identical and the quantitative properties vary within a single order of magnitude. The average values of the energy of the accreted fluid have an irregular dependency on initial data, and in some cases fluid with energies many times its rest mass is systematically accreted.

Formation of Bipolar Lobes by Jets

NASA Astrophysics Data System (ADS)

Soker, Noam

2002-04-01

I conduct an analytical study of the interaction of jets, or a collimated fast wind (CFW), with a previously blown asymptotic giant branch (AGB) slow wind. Such jets (or CFWs) are supposedly formed when a compact companion, a main-sequence star, or a white dwarf accretes mass from the AGB star, forms an accretion disk, and blows two jets. This type of flow, which I think shapes bipolar planetary nebulae (PNs), requires three-dimensional gasdynamical simulations, which are limited in the parameter space they can cover. By imposing several simplifying assumptions, I derive simple expressions which reproduce some basic properties of lobes in bipolar PNs and which can be used to guide future numerical simulations. I quantitatively apply the results to two proto-PNs. I show that the jet interaction with the slow wind can form lobes which are narrow close to, and far away from, the central binary system, and which are wider somewhere in between. Jets that are recollimated and have constant cross section can form cylindrical lobes with constant diameter, as observed in several bipolar PNs. Close to their source, jets blown by main-sequence companions are radiative; only further out they become adiabatic, i.e., they form high-temperature, low-density bubbles that inflate the lobes.

Approximate bound-state solutions of the Dirac equation for the generalized yukawa potential plus the generalized tensor interaction

NASA Astrophysics Data System (ADS)

Ikot, Akpan N.; Maghsoodi, Elham; Hassanabadi, Hassan; Obu, Joseph A.

2014-05-01

In this paper, we obtain the approximate analytical bound-state solutions of the Dirac particle with the generalized Yukawa potential within the framework of spin and pseudospin symmetries for the arbitrary к state with a generalized tensor interaction. The generalized parametric Nikiforov-Uvarov method is used to obtain the energy eigenvalues and the corresponding wave functions in closed form. We also report some numerical results and present figures to show the effect of the tensor interaction.

Reactant conversion in homogeneous turbulence - Mathematical modeling, computational validations, and practical applications

NASA Technical Reports Server (NTRS)

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

1992-01-01

The presently obtained closed-form analytical expressions, which predict the limiting rate of mean reactant conversion in homogeneous turbulent flows under the influence of a binary reaction, are derived via the single-point pdf method based on amplitude mapping closure. With this model, the maximum rate of the mean reactant's decay can be conveniently expressed in terms of definite integrals of the parabolic cylinder functions. The results obtained are shown to be in good agreement with data generated by direct numerical simulations.

Franck-Condon factor formulae for astrophysical and other molecules

NASA Technical Reports Server (NTRS)

Nicholls, R. W.

1981-01-01

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

Film boiling of mercury droplets

NASA Technical Reports Server (NTRS)

Baumeister, K. J.; Schoessow, G. J.; Chmielewski, C. E.

1975-01-01

Vaporization times of mercury droplets in Leidenfrost film boiling on a flat horizontal plate are measured in an air atmosphere. Extreme care was used to prevent large amplitude droplet vibrations and surface wetting; therefore, these data can be compared to film boiling theory. Diffusion from the upper surface of the drop appears as a dominant mode of mass transfer from the drop. A closed-form analytical film boiling theory is developed to account for the diffusive evaporation. Reasonable agreement between data and theory is seen.

Birkhoff Normal Form for Some Nonlinear PDEs

NASA Astrophysics Data System (ADS)

Bambusi, Dario

We consider the problem of extending to PDEs Birkhoff normal form theorem on Hamiltonian systems close to nonresonant elliptic equilibria. As a model problem we take the nonlinear wave equation with Dirichlet boundary conditions on [0,π] g is an analytic skewsymmetric function which vanishes for u=0 and is periodic with period 2π in the x variable. We prove, under a nonresonance condition which is fulfilled for most g's, that for any integer M there exists a canonical transformation that puts the Hamiltonian in Birkhoff normal form up to a reminder of order M. The canonical transformation is well defined in a neighbourhood of the origin of a Sobolev type phase space of sufficiently high order. Some dynamical consequences are obtained. The technique of proof is applicable to quite general semilinear equations in one space dimension.

Reliability analysis of composite structures

NASA Technical Reports Server (NTRS)

Kan, Han-Pin

1992-01-01

A probabilistic static stress analysis methodology has been developed to estimate the reliability of a composite structure. Closed form stress analysis methods are the primary analytical tools used in this methodology. These structural mechanics methods are used to identify independent variables whose variations significantly affect the performance of the structure. Once these variables are identified, scatter in their values is evaluated and statistically characterized. The scatter in applied loads and the structural parameters are then fitted to appropriate probabilistic distribution functions. Numerical integration techniques are applied to compute the structural reliability. The predicted reliability accounts for scatter due to variability in material strength, applied load, fabrication and assembly processes. The influence of structural geometry and mode of failure are also considerations in the evaluation. Example problems are given to illustrate various levels of analytical complexity.

Analytical investigations on the thermal properties of microscale inorganic light-emitting diodes on an orthotropic substrate

NASA Astrophysics Data System (ADS)

Li, Y.; Chen, J.; Xing, Y.; Song, J.

2017-03-01

The microscale inorganic light-emitting diodes (μ-ILEDs) create novel opportunities in biointegrated applications such as wound healing acceleration and optogenetics. Analytical expressions, validated by finite element analysis, are obtained for the temperature increase of a rectangular μ-ILED device on an orthotropic substrate, which could offer an appealing advantage in controlling the heat flow direction to achieve the goal in thermal management. The influences of various parameters (e.g., thermal conductivities of orthotropic substrate, loading parameters) on the temperature increase of the μ-ILED are investigated based on the obtained closed-form solutions. These results provide a novel route to control the temperature distribution in the μ-ILED system and provide easily interpretable guidelines to minimize the adverse thermal effects.

Analytical steady-state solutions for water-limited cropping systems using saline irrigation water

NASA Astrophysics Data System (ADS)

Skaggs, T. H.; Anderson, R. G.; Corwin, D. L.; Suarez, D. L.

2014-12-01

Due to the diminishing availability of good quality water for irrigation, it is increasingly important that irrigation and salinity management tools be able to target submaximal crop yields and support the use of marginal quality waters. In this work, we present a steady-state irrigated systems modeling framework that accounts for reduced plant water uptake due to root zone salinity. Two explicit, closed-form analytical solutions for the root zone solute concentration profile are obtained, corresponding to two alternative functional forms of the uptake reduction function. The solutions express a general relationship between irrigation water salinity, irrigation rate, crop salt tolerance, crop transpiration, and (using standard approximations) crop yield. Example applications are illustrated, including the calculation of irrigation requirements for obtaining targeted submaximal yields, and the generation of crop-water production functions for varying irrigation waters, irrigation rates, and crops. Model predictions are shown to be mostly consistent with existing models and available experimental data. Yet the new solutions possess advantages over available alternatives, including: (i) the solutions were derived from a complete physical-mathematical description of the system, rather than based on an ad hoc formulation; (ii) the analytical solutions are explicit and can be evaluated without iterative techniques; (iii) the solutions permit consideration of two common functional forms of salinity induced reductions in crop water uptake, rather than being tied to one particular representation; and (iv) the utilized modeling framework is compatible with leading transient-state numerical models.

Accessibility, stabilizability, and feedback control of continuous orbital transfer.

PubMed

Gurfil, Pini

2004-05-01

This paper investigates the problem of low-thrust orbital transfer using orbital element feedback from a control-theoretic standpoint, concepts of controllability, feedback stabilizability, and their interaction. The Gauss variational equations (GVEs) are used to model the state-space dynamics. First, the notion of accessibility, a weaker form of controllability, is presented. It is then shown that the GVEs are globally accessible. Based on the accessibility result, a nonlinear feedback controller is derived that asymptotically steers a vehicle from an initial elliptic Keplerian orbit to any given elliptic Keplerian orbit. The performance of the new controller is illustrated by simulating an orbital transfer between two geosynchronous Earth orbits. It is shown that the low-thrust controller requires less fuel than an impulsive maneuver for the same transfer time. Closed-form, analytic expressions for the new orbital transfer controller are given. Finally, it is proved, based on a topological nonlinear stabilizability test, that there does not exist a continuous closed-loop controller that can transfer a spacecraft to a parabolic escape trajectory.

Numerical and Analytical Solutions of Hypersonic Interactions Involving Surface Property Discontinuities

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.; Inger, George R.

1999-01-01

The local viscous-inviscid interaction field generated by a wall temperature jump on a flat plate in supersonic flow and on the windside of a Reusable Launch Vehicle in hypersonic flow is studied in detail by both a Navier-Stokes numerical code and an analytical triple-deck model. Treatment of the rapid heat transfer changes both upstream and downstream of the jump is included. Closed form relationships derived from the triple-deck theory are presented. The analytically predicted pressure and heating variations including upstream influence are found to be in generally good agreement with the Computational Fluid Dynamic (CFD) predictions. These analyses not only clarify the interactive physics involved but also are useful in preliminary design of thermal protection systems and as an insertable module to improve CFD code efficiency when applied to such small-scale interaction problems. The analyses only require conditions at the wall and boundary-layer edge which are easily extracted from a baseline, constant wall temperature, CFD solution.

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.

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

NASA Astrophysics Data System (ADS)

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

2007-02-01

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

Theory for solubility in static systems

NASA Astrophysics Data System (ADS)

Gusev, Andrei A.; Suter, Ulrich W.

1991-06-01

A theory for the solubility of small particles in static structures has been developed. The distribution function of the solute in a frozen solid has been derived in analytical form for the quantum and the quasiclassical cases. The solubility at infinitesimal gas pressure (Henry's constant) as well as the pressure dependence of the solute concentration at elevated pressures has been found from the statistical equilibrium between the solute in the static matrix and the ideal-gas phase. The distribution function of a solute containing different particles has been evaluated in closed form. An application of the theory to the sorption of methane in the computed structures of glassy polycarbonate has resulted in a satisfactory agreement with experimental data.

An analytical investigation of transient effects on rewetting of heated thin flat plates

NASA Technical Reports Server (NTRS)

Platt, J. A.

1993-01-01

The rewetting of a hot surface is a problem of prime importance in the microgravity application of heat pipe technology, where rewetting controls the time before operations can be re-established following depriming of a heat pipe. Rewetting is also important in the nuclear industry (in predicting behavior during loss-of-coolant accidents), as well as in the chemical and petrochemical industries. Recently Chan and Zhang have presented a closed-form solution for the determination of the rewetting speed of a liquid film flowing over a finite (but long) hot plate subject to uniform heating. Unfortunately, their physically unreasonable initial conditions preclude a meaningful analysis of start-up transient behavior. A new nondimensionalization and closed-form solution for an infinitely-long, uniformly-heated plate is presented. Realistic initial conditions (step change in temperature across the wetting front) and boundary conditions (no spatial temperature gradients infinitely far from the wetting front) are employed. The effects of parametric variation on the resulting simpler closed-form solution are presented and compared with the predictions of a 'quasi-steady' model. The time to reach steady-state rewetting is found to be a strong function of the initial dry-region plate temperature. For heated plates it is found that in most cases the effect of the transient response terms cannot be neglected, even for large times.

Optimal Power Allocation Strategy in a Joint Bistatic Radar and Communication System Based on Low Probability of Intercept

PubMed Central

Wang, Fei; Salous, Sana; Zhou, Jianjiang

2017-01-01

In this paper, we investigate a low probability of intercept (LPI)-based optimal power allocation strategy for a joint bistatic radar and communication system, which is composed of a dedicated transmitter, a radar receiver, and a communication receiver. The joint system is capable of fulfilling the requirements of both radar and communications simultaneously. First, assuming that the signal-to-noise ratio (SNR) corresponding to the target surveillance path is much weaker than that corresponding to the line of sight path at radar receiver, the analytically closed-form expression for the probability of false alarm is calculated, whereas the closed-form expression for the probability of detection is not analytically tractable and is approximated due to the fact that the received signals are not zero-mean Gaussian under target presence hypothesis. Then, an LPI-based optimal power allocation strategy is presented to minimize the total transmission power for information signal and radar waveform, which is constrained by a specified information rate for the communication receiver and the desired probabilities of detection and false alarm for the radar receiver. The well-known bisection search method is employed to solve the resulting constrained optimization problem. Finally, numerical simulations are provided to reveal the effects of several system parameters on the power allocation results. It is also demonstrated that the LPI performance of the joint bistatic radar and communication system can be markedly improved by utilizing the proposed scheme. PMID:29186850

Optimal Power Allocation Strategy in a Joint Bistatic Radar and Communication System Based on Low Probability of Intercept.

PubMed

Shi, Chenguang; Wang, Fei; Salous, Sana; Zhou, Jianjiang

2017-11-25

In this paper, we investigate a low probability of intercept (LPI)-based optimal power allocation strategy for a joint bistatic radar and communication system, which is composed of a dedicated transmitter, a radar receiver, and a communication receiver. The joint system is capable of fulfilling the requirements of both radar and communications simultaneously. First, assuming that the signal-to-noise ratio (SNR) corresponding to the target surveillance path is much weaker than that corresponding to the line of sight path at radar receiver, the analytically closed-form expression for the probability of false alarm is calculated, whereas the closed-form expression for the probability of detection is not analytically tractable and is approximated due to the fact that the received signals are not zero-mean Gaussian under target presence hypothesis. Then, an LPI-based optimal power allocation strategy is presented to minimize the total transmission power for information signal and radar waveform, which is constrained by a specified information rate for the communication receiver and the desired probabilities of detection and false alarm for the radar receiver. The well-known bisection search method is employed to solve the resulting constrained optimization problem. Finally, numerical simulations are provided to reveal the effects of several system parameters on the power allocation results. It is also demonstrated that the LPI performance of the joint bistatic radar and communication system can be markedly improved by utilizing the proposed scheme.

Application of Learning Analytics Using Clustering Data Mining for Students' Disposition Analysis

ERIC Educational Resources Information Center

Bharara, Sanyam; Sabitha, Sai; Bansal, Abhay

2018-01-01

Learning Analytics (LA) is an emerging field in which sophisticated analytic tools are used to improve learning and education. It draws from, and is closely tied to, a series of other fields of study like business intelligence, web analytics, academic analytics, educational data mining, and action analytics. The main objective of this research…

Extended Analytic Device Optimization Employing Asymptotic Expansion

NASA Technical Reports Server (NTRS)

Mackey, Jonathan; Sehirlioglu, Alp; Dynsys, Fred

2013-01-01

Analytic optimization of a thermoelectric junction often introduces several simplifying assumptionsincluding constant material properties, fixed known hot and cold shoe temperatures, and thermallyinsulated leg sides. In fact all of these simplifications will have an effect on device performance,ranging from negligible to significant depending on conditions. Numerical methods, such as FiniteElement Analysis or iterative techniques, are often used to perform more detailed analysis andaccount for these simplifications. While numerical methods may stand as a suitable solution scheme,they are weak in gaining physical understanding and only serve to optimize through iterativesearching techniques. Analytic and asymptotic expansion techniques can be used to solve thegoverning system of thermoelectric differential equations with fewer or less severe assumptionsthan the classic case. Analytic methods can provide meaningful closed form solutions and generatebetter physical understanding of the conditions for when simplifying assumptions may be valid.In obtaining the analytic solutions a set of dimensionless parameters, which characterize allthermoelectric couples, is formulated and provide the limiting cases for validating assumptions.Presentation includes optimization of both classic rectangular couples as well as practically andtheoretically interesting cylindrical couples using optimization parameters physically meaningful toa cylindrical couple. Solutions incorporate the physical behavior for i) thermal resistance of hot andcold shoes, ii) variable material properties with temperature, and iii) lateral heat transfer through legsides.

Ballistic heat conduction and mass disorder in one dimension.

PubMed

Ong, Zhun-Yong; Zhang, Gang

2014-08-20

It is well-known that in the disordered harmonic chain, heat conduction is subballistic and the thermal conductivity (κ) scales asymptotically as lim(L--> ∞) κ ∝ L(0.5) where L is the chain length. However, using the nonequilibrium Green's function (NEGF) method and analytical modelling, we show that there exists a critical crossover length scale (LC) below which ballistic heat conduction (κ ∝ L) can coexist with mass disorder. This ballistic-to-subballistic heat conduction crossover is connected to the exponential attenuation of the phonon transmittance function Ξ i.e. Ξ(ω, L) = exp[-L/λ(ω)], where λ is the frequency-dependent attenuation length. The crossover length can be determined from the minimum attenuation length, which depends on the maximum transmitted frequency. We numerically determine the dependence of the transmittance on frequency and mass composition as well as derive a closed form estimate, which agrees closely with the numerical results. For the length-dependent thermal conductance, we also derive a closed form expression which agrees closely with numerical results and reproduces the ballistic to subballistic thermal conduction crossover. This allows us to characterize the crossover in terms of changes in the length, mass composition and temperature dependence, and also to determine the conditions under which heat conduction enters the ballistic regime. We describe how the mass composition can be modified to increase ballistic heat conduction.

On the formation of Friedlander waves in a compressed-gas-driven shock tube

PubMed Central

Tasissa, Abiy F.; Hautefeuille, Martin; Fitek, John H.; Radovitzky, Raúl A.

2016-01-01

Compressed-gas-driven shock tubes have become popular as a laboratory-scale replacement for field blast tests. The well-known initial structure of the Riemann problem eventually evolves into a shock structure thought to resemble a Friedlander wave, although this remains to be demonstrated theoretically. In this paper, we develop a semi-analytical model to predict the key characteristics of pseudo blast waves forming in a shock tube: location where the wave first forms, peak over-pressure, decay time and impulse. The approach is based on combining the solutions of the two different types of wave interactions that arise in the shock tube after the family of rarefaction waves in the Riemann solution interacts with the closed end of the tube. The results of the analytical model are verified against numerical simulations obtained with a finite volume method. The model furnishes a rational approach to relate shock tube parameters to desired blast wave characteristics, and thus constitutes a useful tool for the design of shock tubes for blast testing. PMID:27118888

Equivalent-circuit models for electret-based vibration energy harvesters

NASA Astrophysics Data System (ADS)

Phu Le, Cuong; Halvorsen, Einar

2017-08-01

This paper presents a complete analysis to build a tool for modelling electret-based vibration energy harvesters. The calculational approach includes all possible effects of fringing fields that may have significant impact on output power. The transducer configuration consists of two sets of metal strip electrodes on a top substrate that faces electret strips deposited on a bottom movable substrate functioning as a proof mass. Charge distribution on each metal strip is expressed by series expansion using Chebyshev polynomials multiplied by a reciprocal square-root form. The Galerkin method is then applied to extract all charge induction coefficients. The approach is validated by finite element calculations. From the analytic tool, a variety of connection schemes for power extraction in slot-effect and cross-wafer configurations can be lumped to a standard equivalent circuit with inclusion of parasitic capacitance. Fast calculation of the coefficients is also obtained by a proposed closed-form solution based on leading terms of the series expansions. The achieved analytical result is an important step for further optimisation of the transducer geometry and maximising harvester performance.

Motions about a fixed point by hypergeometric functions: new non-complex analytical solutions and integration of the herpolhode

NASA Astrophysics Data System (ADS)

Mingari Scarpello, Giovanni; Ritelli, Daniele

2018-06-01

The present study highlights the dynamics of a body moving about a fixed point and provides analytical closed form solutions. Firstly, for the symmetrical heavy body, that is the Lagrange-Poisson case, we compute the second (precession, ψ ) and third (spin, φ) Euler angles in explicit and real form by means of multiple hypergeometric (Lauricella) functions. Secondly, releasing the weight assumption but adding the complication of the asymmetry, by means of elliptic integrals of third kind, we provide the precession angle ψ completing the treatment of the Euler-Poinsot case. Thirdly, by integrating the relevant differential equation, we reach the finite polar equation of a special motion trajectory named the herpolhode. Finally, we keep the symmetry of the first problem, but without weight, and take into account a viscous dissipation. The use of motion first integrals—adopted for the first two problems—is no longer practicable in this situation; therefore, the Euler equations, faced directly, are driving to particular occurrences of Bessel functions of order - 1/2.

Modeling and Simulation of a Parametrically Resonant Micromirror With Duty-Cycled Excitation.

PubMed

Shahid, Wajiha; Qiu, Zhen; Duan, Xiyu; Li, Haijun; Wang, Thomas D; Oldham, Kenn R

2014-12-01

High frequency large scanning angle electrostatically actuated microelectromechanical systems (MEMS) mirrors are used in a variety of applications involving fast optical scanning. A 1-D parametrically resonant torsional micromirror for use in biomedical imaging is analyzed here with respect to operation by duty-cycled square waves. Duty-cycled square wave excitation can have significant advantages for practical mirror regulation and/or control. The mirror's nonlinear dynamics under such excitation is analyzed in a Hill's equation form. This form is used to predict stability regions (the voltage-frequency relationship) of parametric resonance behavior over large scanning angles using iterative approximations for nonlinear capacitance behavior of the mirror. Numerical simulations are also performed to obtain the mirror's frequency response over several voltages for various duty cycles. Frequency sweeps, stability results, and duty cycle trends from both analytical and simulation methods are compared with experimental results. Both analytical models and simulations show good agreement with experimental results over the range of duty cycled excitations tested. This paper discusses the implications of changing amplitude and phase with duty cycle for robust open-loop operation and future closed-loop operating strategies.

Design and testing of botanical thermotropic actuator mechanisms in thermally adaptive building coverings

NASA Astrophysics Data System (ADS)

Barrett, Ronald M.; Barrett, Ronald P.; Barrett, Cassandra M.

2017-09-01

This paper lays out the inspiration, operational principles, analytical modeling and coupon testing of a new class of thermally adaptive building coverings. The fundamental driving concepts for these coverings are derived from various families of thermotropic plant structures. Certain plant cellular structures like those in Mimosa pudica (Sensitive Plant), Rhododendron leaves or Albizia julibrissin (Mimosa Tree), exhibit actuation physiology which depends on changes in cellular turgor pressures to generate motion. This form of cellular action via turgor pressure manipulation is an inspiration for a new field of thermally adaptive building coverings which use various forms of cellular foam to aid or enable actuation much like plant cells are used to move leaves. When exposed to high solar loading, the structures use the inherent actuation capability of pockets of air trapped in closed cell foam as actuators to curve plates upwards and outwards. When cold, these same structures curve back towards the building forming large convex pockets of dead air to insulate the building. This paper describes basic classical laminated plate theory models comparing theory and experiment of such coupons containing closed-cell foam actuators. The study concludes with a global description of the effectiveness of this class of thermally adaptive building coverings.

Free vibration of functionally graded beams and frameworks using the dynamic stiffness method

NASA Astrophysics Data System (ADS)

Banerjee, J. R.; Ananthapuvirajah, A.

2018-05-01

The free vibration analysis of functionally graded beams (FGBs) and frameworks containing FGBs is carried out by applying the dynamic stiffness method and deriving the elements of the dynamic stiffness matrix in explicit algebraic form. The usually adopted rule that the material properties of the FGB vary continuously through the thickness according to a power law forms the fundamental basis of the governing differential equations of motion in free vibration. The differential equations are solved in closed analytical form when the free vibratory motion is harmonic. The dynamic stiffness matrix is then formulated by relating the amplitudes of forces to those of the displacements at the two ends of the beam. Next, the explicit algebraic expressions for the dynamic stiffness elements are derived with the help of symbolic computation. Finally the Wittrick-Williams algorithm is applied as solution technique to solve the free vibration problems of FGBs with uniform cross-section, stepped FGBs and frameworks consisting of FGBs. Some numerical results are validated against published results, but in the absence of published results for frameworks containing FGBs, consistency checks on the reliability of results are performed. The paper closes with discussion of results and conclusions.

Closed, analytic, boson realizations for Sp(4)

NASA Astrophysics Data System (ADS)

Klein, Abraham; Zhang, Qing-Ying

1986-08-01

The problem of determing a boson realization for an arbitrary irrep of the unitary simplectic algebra Sp(2d) [or of the corresponding discrete unitary irreps of the unbounded algebra Sp(2d,R)] has been solved completely in recent papers by Deenen and Quesne [J. Deenen and C. Quesne, J. Math. Phys. 23, 878, 2004 (1982); 25, 1638 (1984); 26, 2705 (1985)] and by Moshinsky and co-workers [O. Castaños, E. Chacón, M. Moshinsky, and C. Quesne, J. Math. Phys. 26, 2107 (1985); M. Moshinsky, ``Boson realization of symplectic algebras,'' to be published]. This solution is not known in closed analytic form except for d=1 and for special classes of irreps for d>1. A different method of obtaining a boson realization that solves the full problem for Sp(4) is described. The method utilizes the chain Sp(2d)⊇SU(2)×SU(2) ×ṡṡṡ×SU(2) (d times), which, for d≥4, does not provide a complete set of quantum numbers. Though a simple solution of the missing label problem can be given, this solution does not help in the construction of a mapping algorithm for general d.

Analytical Solution for Optimum Design of Furrow Irrigation Systems

NASA Astrophysics Data System (ADS)

Kiwan, M. E.

1996-05-01

An analytical solution for the optimum design of furrow irrigation systems is derived. The non-linear calculus optimization method is used to formulate a general form for designing the optimum system elements under circumstances of maximizing the water application efficiency of the system during irrigation. Different system bases and constraints are considered in the solution. A full irrigation water depth is considered to be achieved at the tail of the furrow line. The solution is based on neglecting the recession and depletion times after off-irrigation. This assumption is valid in the case of open-end (free gradient) furrow systems rather than closed-end (closed dike) systems. Illustrative examples for different systems are presented and the results are compared with the output obtained using an iterative numerical solution method. The final derived solution is expressed as a function of the furrow length ratio (the furrow length to the water travelling distance). The function of water travelling developed by Reddy et al. is considered for reaching the optimum solution. As practical results from the study, the optimum furrow elements for free gradient systems can be estimated to achieve the maximum application efficiency, i.e. furrow length, water inflow rate and cutoff irrigation time.

Analytical modeling and numerical simulation of the short-wave infrared electron-injection detectors

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

Movassaghi, Yashar; Fathipour, Morteza; Fathipour, Vala

2016-03-21

This paper describes comprehensive analytical and simulation models for the design and optimization of the electron-injection based detectors. The electron-injection detectors evaluated here operate in the short-wave infrared range and utilize a type-II band alignment in InP/GaAsSb/InGaAs material system. The unique geometry of detectors along with an inherent negative-feedback mechanism in the device allows for achieving high internal avalanche-free amplifications without any excess noise. Physics-based closed-form analytical models are derived for the detector rise time and dark current. Our optical gain model takes into account the drop in the optical gain at high optical power levels. Furthermore, numerical simulation studiesmore » of the electrical characteristics of the device show good agreement with our analytical models as well experimental data. Performance comparison between devices with different injector sizes shows that enhancement in the gain and speed is anticipated by reducing the injector size. Sensitivity analysis for the key detector parameters shows the relative importance of each parameter. The results of this study may provide useful information and guidelines for development of future electron-injection based detectors as well as other heterojunction photodetectors.« less

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.

Metallic positive expulsion diaphragms

NASA Technical Reports Server (NTRS)

Gleich, D.

1972-01-01

High-cycle life ring-reinforced hemispherical type positive expulsion diaphragm performance was demonstrated by room temperature fluid expulsion tests of 13" diameter, 8 mil thick stainless steel configurations. A maximum of eleven (11) leak-free, fluid expulsions were achieved by a 25 deg cone angle diaphragm hoop-reinforced with .110-inch cross-sectional diameter wires. This represents a 70% improvement in diaphragm reversal cycle life compared to results previously obtained. The reversal tests confirmed analytic predictions for diaphragm cycle life increases due to increasing values of diaphragm cone angle, radius to thickness ratio and material strain to necking capacity. Practical fabrication techniques were demonstrated for forming close-tolerance, thin corrugated shells and for obtaining closely controlled reinforcing ring stiffness required to maximize diaphragm cycle life. A non-destructive inspection technique for monitoring large local shell bending strains was developed.

An analytical study of physical models with inherited temporal and spatial memory

NASA Astrophysics Data System (ADS)

Jaradat, Imad; Alquran, Marwan; Al-Khaled, Kamel

2018-04-01

Du et al. (Sci. Reb. 3, 3431 (2013)) demonstrated that the fractional derivative order can be physically interpreted as a memory index by fitting the test data of memory phenomena. The aim of this work is to study analytically the joint effect of the memory index on time and space coordinates simultaneously. For this purpose, we introduce a novel bivariate fractional power series expansion that is accompanied by twofold fractional derivatives ordering α, β\\in(0,1]. Further, some convergence criteria concerning our expansion are presented and an analog of the well-known bivariate Taylor's formula in the sense of mixed fractional derivatives is obtained. Finally, in order to show the functionality and efficiency of this expansion, we employ the corresponding Taylor's series method to obtain closed-form solutions of various physical models with inherited time and space memory.

An efficient formulation of robot arm dynamics for control and computer simulation

NASA Astrophysics Data System (ADS)

Lee, C. S. G.; Nigam, R.

This paper describes an efficient formulation of the dynamic equations of motion of industrial robots based on the Lagrange formulation of d'Alembert's principle. This formulation, as applied to a PUMA robot arm, results in a set of closed form second order differential equations with cross product terms. They are not as efficient in computation as those formulated by the Newton-Euler method, but provide a better analytical model for control analysis and computer simulation. Computational complexities of this dynamic model together with other models are tabulated for discussion.

Aerodynamic response of an airfoil with thickness to a longitudinal and transverse periodic gust

NASA Technical Reports Server (NTRS)

Hamad, G.; Atassi, H.

1980-01-01

The unsteady lift of an airfoil with thickness subject to a two-dimensional periodic gust is analyzed using the recent theory of Goldstein and Atassi. It is found that to properly account for the coupling between the steady potential flow and the unsteady vortical flow, one has to consider the contribution of order alpha-squared (when alpha is steady state disturbance) to the potential flowfield. A closed form analytical formula is then derived for the lift function. The results show strong dependence on the wave members of the gust.

Effective grating theory for resonance domain surface-relief diffraction gratings.

PubMed

Golub, Michael A; Friesem, Asher A

2005-06-01

An effective grating model, which generalizes effective-medium theory to the case of resonance domain surface-relief gratings, is presented. In addition to the zero order, it takes into account the first diffraction order, which obeys the Bragg condition. Modeling the surface-relief grating as an effective grating with two diffraction orders provides closed-form analytical relationships between efficiency and grating parameters. The aspect ratio, the grating period, and the required incidence angle that would lead to high diffraction efficiencies are predicted for TE and TM polarization and verified by rigorous numerical calculations.

Diversity Order Analysis of Dual-Hop Relaying with Partial Relay Selection

NASA Astrophysics Data System (ADS)

Bao, Vo Nguyen Quoc; Kong, Hyung Yun

In this paper, we study the performance of dual hop relaying in which the best relay selected by partial relay selection will help the source-destination link to overcome the channel impairment. Specifically, closed-form expressions for outage probability, symbol error probability and achievable diversity gain are derived using the statistical characteristic of the signal-to-noise ratio. Numerical investigation shows that the system achieves diversity of two regardless of relay number and also confirms the correctness of the analytical results. Furthermore, the performance loss due to partial relay selection is investigated.

Application of fractional derivative with exponential law to bi-fractional-order wave equation with frictional memory kernel

NASA Astrophysics Data System (ADS)

Cuahutenango-Barro, B.; Taneco-Hernández, M. A.; Gómez-Aguilar, J. F.

2017-12-01

Analytical solutions of the wave equation with bi-fractional-order and frictional memory kernel of Mittag-Leffler type are obtained via Caputo-Fabrizio fractional derivative in the Liouville-Caputo sense. Through the method of separation of variables and Laplace transform method we derive closed-form solutions and establish fundamental solutions. Special cases with homogeneous Dirichlet boundary conditions and nonhomogeneous initial conditions, as well as for the external force are considered. Numerical simulations of the special solutions were done and novel behaviors are obtained.

Noise kernels of stochastic gravity in conformally-flat spacetimes

NASA Astrophysics Data System (ADS)

Cho, H. T.; Hu, B. L.

2015-03-01

The central object in the theory of semiclassical stochastic gravity is the noise kernel, which is the symmetric two point correlation function of the stress-energy tensor. Using the corresponding Wightman functions in Minkowski, Einstein and open Einstein spaces, we construct the noise kernels of a conformally coupled scalar field in these spacetimes. From them we show that the noise kernels in conformally-flat spacetimes, including the Friedmann-Robertson-Walker universes, can be obtained in closed analytic forms by using a combination of conformal and coordinate transformations.

Nonlinear vibration of an axially loaded beam carrying rigid bodies

NASA Astrophysics Data System (ADS)

Barry, O.

2016-12-01

This paper investigates the nonlinear vibration due to mid-plane stretching of an axially loaded simply supported beam carrying multiple rigid masses. Explicit expressions and closed form solutions of both linear and nonlinear analysis of the present vibration problem are presented for the first time. The validity of the analytical model is demonstrated using finite element analysis and via comparison with the result in the literature. Parametric studies are conducted to examine how the nonlinear frequency and frequency response curve are affected by tension, rotational inertia, and number of intermediate rigid bodies.

Spectral Analysis for Weighted Iterated Triangulations of Graphs

NASA Astrophysics Data System (ADS)

Chen, Yufei; Dai, Meifeng; Wang, Xiaoqian; Sun, Yu; Su, Weiyi

Much information about the structural properties and dynamical aspects of a network is measured by the eigenvalues of its normalized Laplacian matrix. In this paper, we aim to present a first study on the spectra of the normalized Laplacian of weighted iterated triangulations of graphs. We analytically obtain all the eigenvalues, as well as their multiplicities from two successive generations. As an example of application of these results, we then derive closed-form expressions for their multiplicative Kirchhoff index, Kemeny’s constant and number of weighted spanning trees.

Approximate solutions to Mathieu's equation

NASA Astrophysics Data System (ADS)

Wilkinson, Samuel A.; Vogt, Nicolas; Golubev, Dmitry S.; Cole, Jared H.

2018-06-01

Mathieu's equation has many applications throughout theoretical physics. It is especially important to the theory of Josephson junctions, where it is equivalent to Schrödinger's equation. Mathieu's equation can be easily solved numerically, however there exists no closed-form analytic solution. Here we collect various approximations which appear throughout the physics and mathematics literature and examine their accuracy and regimes of applicability. Particular attention is paid to quantities relevant to the physics of Josephson junctions, but the arguments and notation are kept general so as to be of use to the broader physics community.

Modeling, Modal Properties, and Mesh Stiffness Variation Instabilities of Planetary Gears

NASA Technical Reports Server (NTRS)

Parker, Robert G.; Lin, Jian; Krantz, Timothy L. (Technical Monitor)

2001-01-01

Planetary gear noise and vibration are primary concerns in their applications in helicopters, automobiles, aircraft engines, heavy machinery and marine vehicles. Dynamic analysis is essential to the noise and vibration reduction. This work analytically investigates some critical issues and advances the understanding of planetary gear dynamics. A lumped-parameter model is built for the dynamic analysis of general planetary gears. The unique properties of the natural frequency spectra and vibration modes are rigorously characterized. These special structures apply for general planetary gears with cyclic symmetry and, in practically important case, systems with diametrically opposed planets. The special vibration properties are useful for subsequent research. Taking advantage of the derived modal properties, the natural frequency and vibration mode sensitivities to design parameters are investigated. The key parameters include mesh stiffnesses, support/bearing stiffnesses, component masses, moments of inertia, and operating speed. The eigen-sensitivities are expressed in simple, closed-form formulae associated with modal strain and kinetic energies. As disorders (e.g., mesh stiffness variation. manufacturing and assembling errors) disturb the cyclic symmetry of planetary gears, their effects on the free vibration properties are quantitatively examined. Well-defined veering rules are derived to identify dramatic changes of natural frequencies and vibration modes under parameter variations. The knowledge of free vibration properties, eigen-sensitivities, and veering rules provide important information to effectively tune the natural frequencies and optimize structural design to minimize noise and vibration. Parametric instabilities excited by mesh stiffness variations are analytically studied for multi-mesh gear systems. The discrepancies of previous studies on parametric instability of two-stage gear chains are clarified using perturbation and numerical methods. The operating conditions causing parametric instabilities are expressed in closed-form suitable for design guidance. Using the well-defined modal properties of planetary gears, the effects of mesh parameters on parametric instability are analytically identified. Simple formulae are obtained to suppress particular instabilities by adjusting contact ratios and mesh phasing.

Analogue solution for electrical capacity of membrane covered square cylinders in square array at high concentration.

PubMed

Cole, K S

1975-12-01

Analytical solutions of Laplace equations have given the electrical characteristics of membranes and interiors of spherical, ellipsoidal, and cylindrical cells in suspensions and tissues from impedance measurements, but the underlying assumptions may be invalid above 50% volume concentrations. However, resistance measurements on several nonconducting, close-packing forms in two and three dimensions closely predicted volume concentrations up to 100% by equations derived from Maxwell and Rayleigh. Calculations of membrane capacities of cells in suspensions and tissues from extensions of theory, as developed by Fricke and by Cole, have been useful but of unknown validity at high concentrations. A resistor analogue has been used to solve the finite difference approximation to the Laplace equation for the resistance and capacity of a square array of square cylindrical cells with surface capacity. An 11 x 11 array of resistors, simulating a quarter of the unit structure, was separated into intra- and extra-cellular regions by rows of capacitors corresponding to surface membrane areas from 3 x 3 to 11 x 11 or 7.5% to 100%. The extended Rayleigh equation predicted the cell concentrations and membrane capacities to within a few percent from boundary resistance and capacity measurements at low frequencies. This single example suggests that analytical solutions for other, similar two- and three-dimensional problems may be approximated up to near 100% concentrations and that there may be analytical justifications for such analogue solutions of Laplace equations.

Three essays on energy and environmental economics: Empirical, applied, and theoretical

NASA Astrophysics Data System (ADS)

Karney, Daniel Houghton

Energy and environmental economics are closely related fields as nearly all forms of energy production generate pollution and thus nearly all forms of environmental policy affect energy production and consumption. The three essays in this dissertation are related by their common themes of energy and environmental economics, but they differ in their methodologies. The first chapter is an empirical exercise that looks that the relationship between electricity price deregulation and maintenance outages at nuclear power plants. The second chapter is an applied theory paper that investigates environmental regulation in a multiple pollutants setting. The third chapter develops a new methodology regarding the construction of analytical general equilibrium models that can be used to study topics in energy and environmental economics.

Energy spectra and wave function of trigonometric Rosen-Morse potential as an effective quantum chromodynamics potential in D-dimensions

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

Deta, U. A., E-mail: utamaalan@yahoo.co.id; Suparmi,; Cari,

2014-09-30

The Energy Spectra and Wave Function of Schrodinger equation in D-Dimensions for trigonometric Rosen-Morse potential were investigated analytically using Nikiforov-Uvarov method. This potential captures the essential traits of the quark-gluon dynamics of Quantum Chromodynamics. The approximate energy spectra are given in the close form and the corresponding approximate wave function for arbitrary l-state (l ≠ 0) in D-dimensions are formulated in the form of differential polynomials. The wave function of this potential unnormalizable for general case. The wave function of this potential unnormalizable for general case. The existence of extra dimensions (centrifugal factor) and this potential increase the energy spectramore » of system.« less

Speciation analysis of aluminium in plant parts of Betula pendula and in soil.

PubMed

Zioła-Frankowska, Anetta; Frankowski, Marcin

2018-03-01

The research presents the first results of aluminium speciation analysis in aqueous extracts of individual plant parts of Betula pendula and soil samples, using High Performance Ion Chromatography with Diode Array Detection (HPIC-DAD). The applied method allowed us to carry out a full speciation analysis of aluminium in the form of predominant aluminium-fluoride complexes: AlF (x=2,3,4) (3-x) (first analytical signal), AlF 2+ (second analytical signal) and Al 3+ (third analytical signal) in samples of lateral roots, tap roots, twigs, stem, leaf and soil collected under roots of B. pendula. Concentrations of aluminium and its complexes were determined for two types of environment characterised by different degree of human impact: contaminated site of the Chemical Plant in Luboń and protected area of the Wielkopolski National Park. For all the analysed samples of B. pendula and soil, AlF (x=2,3,4) (3-x) had the largest contribution, followed by Al 3+ and AlF 2+ . Significant differences in concentration and contribution of Al-F complexes and Al 3+ form, depending on the place of sampling (different anthropogenic pressure) and plant part of B. pendula were observed. Based on the obtained results, it was found that transport of aluminium is "blocked" by lateral roots, and is closely related to Al content of soil. Copyright © 2017. Published by Elsevier B.V.

The post-buckling behavior of a beam constrained by springy walls

NASA Astrophysics Data System (ADS)

Katz, Shmuel; Givli, Sefi

2015-05-01

The post-buckling behavior of a beam subjected to lateral constraints is of practical importance in a variety of applications, such as stent procedures, filopodia growth in living cells, endoscopic examination of internal organs, and deep drilling. Even though in reality the constraining surfaces are often deformable, the literature has focused mainly on rigid and fixed constraints. In this paper, we make a first step to bridge this gap through a theoretical and experimental examination of the post-buckling behavior of a beam constrained by a fixed wall and a springy wall, i.e. one that moves laterally against a spring. The response exhibited by the proposed system is much richer compared to that of the fixed-wall system, and can be tuned by choosing the spring stiffness. Based on small-deformation analysis, we obtained closed-form analytical solutions and quantitative insights. The accuracy of these results was examined by comparison to large-deformation analysis. We concluded that the closed-form solution of the small-deformation analysis provides an excellent approximation, except in the highest attainable mode. There, the system exhibits non-intuitive behavior and non-monotonous force-displacement relations that can only be captured by large-deformation theories. Although closed-form solutions cannot be derived for the large-deformation analysis, we were able to reveal general properties of the solution. In the last part of the paper, we present experimental results that demonstrate various features obtained from the theoretical analysis.

High resolution x-ray CMT: Reconstruction methods

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

Brown, J.K.

This paper qualitatively discusses the primary characteristics of methods for reconstructing tomographic images from a set of projections. These reconstruction methods can be categorized as either {open_quotes}analytic{close_quotes} or {open_quotes}iterative{close_quotes} techniques. Analytic algorithms are derived from the formal inversion of equations describing the imaging process, while iterative algorithms incorporate a model of the imaging process and provide a mechanism to iteratively improve image estimates. Analytic reconstruction algorithms are typically computationally more efficient than iterative methods; however, analytic algorithms are available for a relatively limited set of imaging geometries and situations. Thus, the framework of iterative reconstruction methods is better suited formore » high accuracy, tomographic reconstruction codes.« less

Assembling substrate-less plasmonic metacrystals at the oil/water interface for multiplex ultratrace analyte detection.

PubMed

Lee, Yih Hong; Lee, Hiang Kwee; Ho, Jonathan Yong Chew; Yang, Yijie; Ling, Xing Yi

2016-08-15

Current substrate-less SERS platforms are limited to uncontrolled aggregation of plasmonic nanoparticles or quasi-crystalline arrays of spherical nanoparticles, with no study on how the lattice structures formed by nanoparticle self-assembly affect their detection capabilities. Here, we organize Ag octahedral building blocks into two large-area plasmonic metacrystals at the oil/water interface, and investigate their in situ SERS sensing capabilities. Amphiphilic octahedra assemble into a hexagonal close-packed metacrystal, while hydrophobic octahedra assemble into an open square metacrystal. The lower packing density square metacrystal gives rise to much stronger SERS enhancement than the denser packing hexagonal metacrystal, arising from the larger areas of plasmonic hotspots within the square metacrystal at the excitation wavelength. We further demonstrate the ability of the square metacrystal to achieve quantitative ultratrace detection of analytes from both the aqueous and organic phases. Detection limits are at the nano-molar levels, with analytical enhancement factors reaching 10(8). In addition, multiplex detection across both phases can be achieved in situ without any loss of signal quantitation.

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.

Impingement of water droplets on wedges and double-wedge airfoils at supersonic speeds

NASA Technical Reports Server (NTRS)

Serafini, John S

1954-01-01

An analytical solution has been obtained for the equations of motion of water droplets impinging on a wedge in a two-dimensional supersonic flow field with a shock wave attached to the wedge. The closed-form solution yields analytical expressions for the equation of the droplet trajectory, the local rate of impingement and the impingement velocity at any point on the wedge surface, and the total rate of impingement. The analytical expressions are utilized to determine the impingement on the forward surfaces of diamond airfoils in supersonic flow fields with attached shock waves. The results presented include the following conditions: droplet diameters from 2 to 100 microns, pressure altitudes from sea level to 30,000 feet, free-stream static temperatures from 420 degrees r, free stream Mach numbers from 1.1 to 2.0, semiapex angles for the wedge from 1.14 degrees to 7.97 degrees, thickness-to-chord ratios for the diamond airfoil from 0.02 to 0.14, chord lengths from 1 to 20 feet, and angles of attack from zero to the inverse tangent of the airfoil thickness-to-chord ratio.

Joule heating induced stream broadening in free-flow zone electrophoresis.

PubMed

Dutta, Debashis

2018-03-01

The use of an electric field in free-flow zone electrophoresis (FFZE) automatically leads to Joule heating yielding a higher temperature at the center of the separation chamber relative to that around the channel walls. For small amounts of heat generated, this thermal effect introduces a variation in the equilibrium position of the analyte molecules due to the dependence of liquid viscosity and analyte diffusivity on temperature leading to a modification in the position of the analyte stream as well as the zone width. In this article, an analytic theory is presented to quantitate such effects of Joule heating on FFZE assays in the limit of small temperature differentials across the channel gap yielding a closed form expression for the stream position and zone variance under equilibrium conditions. A method-of-moments approach is employed to develop this analytic theory, which is further validated with numerical solutions of the governing equations. Interestingly, the noted analyses predict that Joule heating can drift the location of the analyte stream either way of its equilibrium position realized in the absence of any temperature rise in the system, and also tends to reduce zone dispersion. The extent of these modifications, however, is governed by the electric field induced temperature rise and three Péclet numbers evaluated based on the axial pressure-driven flow, transverse electroosmotic and electrophoretic solute velocities in the separation chamber. Monte Carlo simulations of the FFZE system further establish a time and a length scale over which the results from the analytic theory are valid. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Dam break problem for the focusing nonlinear Schrödinger equation and the generation of rogue waves

NASA Astrophysics Data System (ADS)

El, G. A.; Khamis, E. G.; Tovbis, A.

2016-09-01

We propose a novel, analytically tractable, scenario of the rogue wave formation in the framework of the small-dispersion focusing nonlinear Schrödinger (NLS) equation with the initial condition in the form of a rectangular barrier (a ‘box’). We use the Whitham modulation theory combined with the nonlinear steepest descent for the semi-classical inverse scattering transform, to describe the evolution and interaction of two counter-propagating nonlinear wave trains—the dispersive dam break flows—generated in the NLS box problem. We show that the interaction dynamics results in the emergence of modulated large-amplitude quasi-periodic breather lattices whose amplitude profiles are closely approximated by the Akhmediev and Peregrine breathers within certain space-time domain. Our semi-classical analytical results are shown to be in excellent agreement with the results of direct numerical simulations of the small-dispersion focusing NLS equation.

A two-parameter family of double-power-law biorthonormal potential-density expansions

NASA Astrophysics Data System (ADS)

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

2018-07-01

We present a two-parameter family of biorthonormal double-power-law potential-density expansions. Both the potential and density are given in a closed analytic form and may be rapidly computed via recurrence relations. We show that this family encompasses all the known analytic biorthonormal expansions: the Zhao expansions (themselves generalizations of ones found earlier by Hernquist & Ostriker and by Clutton-Brock) and the recently discovered Lilley et al. expansion. Our new two-parameter family includes expansions based around many familiar spherical density profiles as zeroth-order models, including the γ models and the Jaffe model. It also contains a basis expansion that reproduces the famous Navarro-Frenk-White (NFW) profile at zeroth order. The new basis expansions have been found via a systematic methodology which has wide applications in finding other new expansions. In the process, we also uncovered a novel integral transform solution to Poisson's equation.

Mapping Systemic Risk: Critical Degree and Failures Distribution in Financial Networks.

PubMed

Smerlak, Matteo; Stoll, Brady; Gupta, Agam; Magdanz, James S

2015-01-01

The financial crisis illustrated the need for a functional understanding of systemic risk in strongly interconnected financial structures. Dynamic processes on complex networks being intrinsically difficult to model analytically, most recent studies of this problem have relied on numerical simulations. Here we report analytical results in a network model of interbank lending based on directly relevant financial parameters, such as interest rates and leverage ratios. We obtain a closed-form formula for the "critical degree" (the number of creditors per bank below which an individual shock can propagate throughout the network), and relate failures distributions to network topologies, in particular scalefree ones. Our criterion for the onset of contagion turns out to be isomorphic to the condition for cooperation to evolve on graphs and social networks, as recently formulated in evolutionary game theory. This remarkable connection supports recent calls for a methodological rapprochement between finance and ecology.

A two-parameter family of double-power-law biorthonormal potential-density expansions

NASA Astrophysics Data System (ADS)

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

2018-05-01

We present a two-parameter family of biorthonormal double-power-law potential-density expansions. Both the potential and density are given in closed analytic form and may be rapidly computed via recurrence relations. We show that this family encompasses all the known analytic biorthonormal expansions: the Zhao expansions (themselves generalizations of ones found earlier by Hernquist & Ostriker and by Clutton-Brock) and the recently discovered Lilley et al. (2017a) expansion. Our new two-parameter family includes expansions based around many familiar spherical density profiles as zeroth-order models, including the γ models and the Jaffe model. It also contains a basis expansion that reproduces the famous Navarro-Frenk-White (NFW) profile at zeroth order. The new basis expansions have been found via a systematic methodology which has wide applications in finding other new expansions. In the process, we also uncovered a novel integral transform solution to Poisson's equation.

Comparison of sound power radiation from isolated airfoils and cascades in a turbulent flow.

PubMed

Blandeau, Vincent P; Joseph, Phillip F; Jenkins, Gareth; Powles, Christopher J

2011-06-01

An analytical model of the sound power radiated from a flat plate airfoil of infinite span in a 2D turbulent flow is presented. The effects of stagger angle on the radiated sound power are included so that the sound power radiated upstream and downstream relative to the fan axis can be predicted. Closed-form asymptotic expressions, valid at low and high frequencies, are provided for the upstream, downstream, and total sound power. A study of the effects of chord length on the total sound power at all reduced frequencies is presented. Excellent agreement for frequencies above a critical frequency is shown between the fast analytical isolated airfoil model presented in this paper and an existing, computationally demanding, cascade model, in which the unsteady loading of the cascade is computed numerically. Reasonable agreement is also observed at low frequencies for low solidity cascade configurations. © 2011 Acoustical Society of America

Strings, vortex rings, and modes of instability

DOE PAGES

Gubser, Steven S.; Nayar, Revant; Parikh, Sarthak

2015-01-12

We treat string propagation and interaction in the presence of a background Neveu–Schwarz three-form field strength, suitable for describing vortex rings in a superfluid or low-viscosity normal fluid. A circular vortex ring exhibits instabilities which have been recognized for many years, but whose precise boundaries we determine for the first time analytically in the small core limit. Two circular vortices colliding head-on exhibit stronger instabilities which cause splitting into many small vortices at late times. We provide an approximate analytic treatment of these instabilities and show that the most unstable wavelength is parametrically larger than a dynamically generated length scalemore » which in many hydrodynamic systems is close to the cutoff. We also summarize how the string construction we discuss can be derived from the Gross–Pitaevskii Lagrangian, and also how it compares to the action for giant gravitons.« less

Analytical modeling of drug dynamics induced by eluting stents in the coronary multi-layered curved domain.

PubMed

d'Errico, Michele; Sammarco, Paolo; Vairo, Giuseppe

2015-09-01

Pharmacokinetics induced by drug eluting stents (DES) in coronary walls is modeled by means of a one-dimensional multi-layered model, accounting for vessel curvature and non-homogeneous properties of the arterial tissues. The model includes diffusion mechanisms, advection effects related to plasma filtration through the walls, and bio-chemical drug reactions. A non-classical Sturm-Liouville problem with discontinuous coefficients is derived, whose closed-form analytical solution is obtained via an eigenfunction expansion. Soundness and consistency of the proposed approach are shown by numerical computations based on possible clinical treatments involving both hydrophilic and hydrophobic drugs. The influence of the main model parameters on drug delivery mechanisms is analyzed, highlighting the effects induced by vessel curvature and yielding comparative indications and useful insights into the concurring mechanisms governing the pharmacokinetics. Copyright © 2015. Published by Elsevier Inc.

The dynamics of spin stabilized spacecraft with movable appendages, part 1

NASA Technical Reports Server (NTRS)

Bainum, P. M.; Sellappan, R.

1975-01-01

The motion and stability of spin stabilized spacecraft with movable external appendages are treated both analytically and numerically. The two basic types of appendages considered are: (1) a telescoping type of varying length and (2) a hinged type of fixed length whose orientation with respect to the main part of the spacecraft can vary. Two classes of telescoping appendages are considered: (a) where an end mass is mounted at the end of an (assumed) massless boom; and (b) where the appendage is assumed to consist of a uniformly distributed homogeneous mass throughout its length. For the telescoping system Eulerian equations of motion are developed. During all deployment sequences it is assumed that the transverse component of angular momentum is much smaller than the component along the major spin axis. Closed form analytical solutions for the time response of the transverse components of angular velocities are obtained when the spacecraft hub has a nearly spherical mass distribution.

Analytically-derived sensitivities in one-dimensional models of solute transport in porous media

USGS Publications Warehouse

Knopman, D.S.

1987-01-01

Analytically-derived sensitivities are presented for parameters in one-dimensional models of solute transport in porous media. Sensitivities were derived by direct differentiation of closed form solutions for each of the odel, and by a time integral method for two of the models. Models are based on the advection-dispersion equation and include adsorption and first-order chemical decay. Boundary conditions considered are: a constant step input of solute, constant flux input of solute, and exponentially decaying input of solute at the upstream boundary. A zero flux is assumed at the downstream boundary. Initial conditions include a constant and spatially varying distribution of solute. One model simulates the mixing of solute in an observation well from individual layers in a multilayer aquifer system. Computer programs produce output files compatible with graphics software in which sensitivities are plotted as a function of either time or space. (USGS)

Analytic description of microcylindrical cavity for surface plasmon polariton

NASA Astrophysics Data System (ADS)

Tekkozyan, Vahan; Babajanyan, Arsen; Nerkararyan, Khachatur

2013-09-01

We consider the formation of the surface plasmon polariton (SPP) mode in the microcylinder cavity. Developed theoretical model allows to analytically calculate the closed-form expressions for the mode field distributions, resonant frequency, as well as the radiation and dissipative parts of quality factor of the structure in a broad wavelength range. For the conditions when a radius of a metallic cylinder is in order of SPP's wavelength, the highest value of Q-factor is achieved in infrared region of the spectrum where the absolute value of the real part of dielectric permittivity of the metal is much more than both the imaginary part of dielectric permittivity of the metal and the dielectric permittivity of surrounding media. Also, the radiation losses decrease with increasing of radius of cylinder. The obtained results give opportunity to find optimal conditions for having efficient emission in microcylinder cavity and it can serve as practical guidelines to design SPP microcavity for stimulated emission.

A two-parameter family of double-power-law biorthonormal potential-density expansions

NASA Astrophysics Data System (ADS)

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

2018-05-01

We present a two-parameter family of biorthonormal double-power-law potential-density expansions. Both the potential and density are given in closed analytic form and may be rapidly computed via recurrence relations. We show that this family encompasses all the known analytic biorthonormal expansions: the Zhao expansions (themselves generalizations of ones found earlier by Hernquist & Ostriker and by Clutton-Brock) and the recently discovered Lilley et al. (2018b) expansion. Our new two-parameter family includes expansions based around many familiar spherical density profiles as zeroth-order models, including the γ models and the Jaffe model. It also contains a basis expansion that reproduces the famous Navarro-Frenk-White (NFW) profile at zeroth order. The new basis expansions have been found via a systematic methodology which has wide applications in finding other new expansions. In the process, we also uncovered a novel integral transform solution to Poisson's equation.

Pinching solutions of slender cylindrical jets

NASA Technical Reports Server (NTRS)

Papageorgiou, Demetrios T.; Orellana, Oscar

1993-01-01

Simplified equations for slender jets are derived for a circular jet of one fluid flowing into an ambient second fluid, the flow being confined in a circular tank. Inviscid flows are studied which include both surface tension effects and Kelvin-Helmholtz instability. For slender jets a coupled nonlinear system of equations is found for the jet shape and the axial velocity jump across it. The equations can break down after a finite time and similarity solutions are constructed, and studied analytically and numerically. The break-ups found pertain to the jet pinching after a finite time, without violation of the slender jet ansatz. The system is conservative and admissible singular solutions are those which conserve the total energy, mass, and momentum. Such solutions are constructed analytically and numerically, and in the case of vortex sheets with no surface tension certain solutions are given in closed form.

Probability theory versus simulation of petroleum potential in play analysis

USGS Publications Warehouse

Crovelli, R.A.

1987-01-01

An analytic probabilistic methodology for resource appraisal of undiscovered oil and gas resources in play analysis is presented. This play-analysis methodology is a geostochastic system for petroleum resource appraisal in explored as well as frontier areas. An objective was to replace an existing Monte Carlo simulation method in order to increase the efficiency of the appraisal process. Underlying the two methods is a single geologic model which considers both the uncertainty of the presence of the assessed hydrocarbon and its amount if present. The results of the model are resource estimates of crude oil, nonassociated gas, dissolved gas, and gas for a geologic play in terms of probability distributions. The analytic method is based upon conditional probability theory and a closed form solution of all means and standard deviations, along with the probabilities of occurrence. ?? 1987 J.C. Baltzer A.G., Scientific Publishing Company.

An Analytic Approximation to Very High Specific Impulse and Specific Power Interplanetary Space Mission Analysis

NASA Technical Reports Server (NTRS)

Williams, Craig Hamilton

1995-01-01

A simple, analytic approximation is derived to calculate trip time and performance for propulsion systems of very high specific impulse (50,000 to 200,000 seconds) and very high specific power (10 to 1000 kW/kg) for human interplanetary space missions. The approach assumed field-free space, constant thrust/constant specific power, and near straight line (radial) trajectories between the planets. Closed form, one dimensional equations of motion for two-burn rendezvous and four-burn round trip missions are derived as a function of specific impulse, specific power, and propellant mass ratio. The equations are coupled to an optimizing parameter that maximizes performance and minimizes trip time. Data generated for hypothetical one-way and round trip human missions to Jupiter were found to be within 1% and 6% accuracy of integrated solutions respectively, verifying that for these systems, credible analysis does not require computationally intensive numerical techniques.

Mapping Systemic Risk: Critical Degree and Failures Distribution in Financial Networks

PubMed Central

Smerlak, Matteo; Stoll, Brady; Gupta, Agam; Magdanz, James S.

2015-01-01

The financial crisis illustrated the need for a functional understanding of systemic risk in strongly interconnected financial structures. Dynamic processes on complex networks being intrinsically difficult to model analytically, most recent studies of this problem have relied on numerical simulations. Here we report analytical results in a network model of interbank lending based on directly relevant financial parameters, such as interest rates and leverage ratios. We obtain a closed-form formula for the “critical degree” (the number of creditors per bank below which an individual shock can propagate throughout the network), and relate failures distributions to network topologies, in particular scalefree ones. Our criterion for the onset of contagion turns out to be isomorphic to the condition for cooperation to evolve on graphs and social networks, as recently formulated in evolutionary game theory. This remarkable connection supports recent calls for a methodological rapprochement between finance and ecology. PMID:26207631

An Analytical Time–Domain Expression for the Net Ripple Produced by Parallel Interleaved Converters

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

Johnson, Brian B.; Krein, Philip T.

We apply modular arithmetic and Fourier series to analyze the superposition of N interleaved triangular waveforms with identical amplitudes and duty-ratios. Here, interleaving refers to the condition when a collection of periodic waveforms with identical periods are each uniformly phase-shifted across one period. The main result is a time-domain expression which provides an exact representation of the summed and interleaved triangular waveforms, where the peak amplitude and parameters of the time-periodic component are all specified in closed-form. Analysis is general and can be used to study various applications in multi-converter systems. This model is unique not only in that itmore » reveals a simple and intuitive expression for the net ripple, but its derivation via modular arithmetic and Fourier series is distinct from prior approaches. The analytical framework is experimentally validated with a system of three parallel converters under time-varying operating conditions.« less

An Improved Correlation between Impression and Uniaxial Creep

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

Hsueh, Chun-Hway; Miranda, Pedro; Becher, Paul F

2006-01-01

A semiempirical correlation between impression and uniaxial creep has been established by Hyde et al. [Int. J. Mech. Sci. 35, 451 (1993) ] using finite element results for materials exhibiting general power-law creep with the stress exponent n in the range 2 {<=} n {<=} 15. Here, we derive the closed-form solution for a special case of viscoelastic materials, i.e., n = 1, subjected to impression creep and obtain the exact correlation between impression and uniaxial creep. This analytical solution serves as a checkpoint for the finite element results. We then perform finite element analyses for the general case tomore » derive a semiempirical correlation, which agrees well with both analytical viscoelastic results and the existing experimental data. Our improved correlation agrees with the correlation of Hyde et al. for n {>=} 4, and the difference increases with decreasing n for n<4.« less

Numerical verification of bounce-harmonic resonances in neoclassical toroidal viscosity for tokamaks.

PubMed

Kim, Kimin; Park, Jong-Kyu; Boozer, Allen H

2013-05-03

This Letter presents the first numerical verification for the bounce-harmonic (BH) resonance phenomena of the neoclassical transport in a tokamak perturbed by nonaxisymmetric magnetic fields. The BH resonances were predicted by analytic theories of neoclassical toroidal viscosity (NTV), as the parallel and perpendicular drift motions can be resonant and result in a great enhancement of the radial momentum transport. A new drift-kinetic δf guiding-center particle code, POCA, clearly verified that the perpendicular drift motions can reduce the transport by phase-mixing, but in the BH resonances the motions can form closed orbits and particles radially drift out fast. The POCA calculations on resulting NTV torque are largely consistent with analytic calculations, and show that the BH resonances can easily dominate the NTV torque when a plasma rotates in the perturbed tokamak and therefore, is a critical physics for predicting the rotation and stability in the International Thermonuclear Experimental Reactor.

Role of spontaneous emission through operating transition in probe-field spectroscopy of two-level systems

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

Saprykin, E. G.; Chernenko, A. A., E-mail: chernen@isp.nsc.ru; Shalagin, A. M.

Analytical and numerical investigations are carried out of the effect of spontaneous decay through operating transition on the shape of a resonance in the work of a probe field under a strong field applied to the transition. A narrow nonlinear resonance arising on transitions with long-living lower level in the work of a probe field can manifest itself in the form of a traditional minimum and a peak as a function of the first Einstein coefficient for the operating transition. The transformation of the resonance from a minimum to a peak is attributed to the specific character of relaxation ofmore » lower-level population beatings on a closed or almost closed transition (the decay of the upper level occurs completely or almost completely through the operating transition).« less

Gravitational waves from neutron star excitations in a binary inspiral

NASA Astrophysics Data System (ADS)

Parisi, Alessandro; Sturani, Riccardo

2018-02-01

In the context of a binary inspiral of mixed neutron star-black hole systems, we investigate the excitation of the neutron star oscillation modes by the orbital motion. We study generic eccentric orbits and show that tidal interaction can excite the f -mode oscillations of the star by computing the amount of energy and angular momentum deposited into the star by the orbital motion tidal forces via closed form analytic expressions. We study the f -mode oscillations of cold neutron stars using recent microscopic nuclear equations of state, and we compute their imprint into the emitted gravitational waves.

Interaction between a normal shock wave and a turbulent boundary layer at high transonic speeds. Part 1: Pressure distribution

NASA Technical Reports Server (NTRS)

Messiter, A. F.

1979-01-01

Analytical solutions are derived which incorporate additional physical effects as higher order terms for the case when the sonic line is very close to the wall. The functional form used for the undisturbed velocity profile is described to indicate how various parameters will be calculated for later comparison with experiment. The basic solutions for the pressure distribution are derived. Corrections are added for flow along a wall having longitudinal curvature and for flow in a circular pipe, and comparisons with available experimental data are shown.

Standard and reference materials for marine science. Third edition. Technical memo

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

Cantillo, A.Y.

1992-08-01

The third edition of the catalog of reference materials suited for use in marine science, originally compiled in 1986 for NOAA, IOC, and UNEP. The catalog lists close to 2,000 reference materials from sixteen producers and contains information about their proper use, sources, availability, and analyte concentrations. Indices are included for elements, isotopes, and organic compounds, as are cross references to CAS registry numbers, alternate names, and chemical structures of selected organic compounds. The catalog is being published independently by both NOAA and IOC/UNEP and is available from NOAA/NOS/ORCA in electronic form.

Relative motion using analytical differential gravity

NASA Technical Reports Server (NTRS)

Gottlieb, Robert G.

1988-01-01

This paper presents a new approach to the computation of the motion of one satellite relative to another. The trajectory of the reference satellite is computed accurately subject to geopotential perturbations. This precise trajectory is used as a reference in computing the position of a nearby body, or bodies. The problem that arises in this approach is differencing nearly equal terms in the geopotential model, especially as the separation of the reference and nearby bodies approaches zero. By developing closed form expressions for differences in higher order and degree geopotential terms, the numerical problem inherent in the differencing approach is eliminated.

Moment distributions around holes in symmetric composite laminates subjected to bending moments

NASA Technical Reports Server (NTRS)

Prasad, C. B.; Shuart, M. J.

1989-01-01

An analytical investigation of the effects of holes on the moment distribution of symmetric composite laminates subjected to bending moments is described. A general, closed-form solution for the moment distribution of an infinite anisotropic plate is derived, and this solution is used to determine stress distributions both on the hole boundary and throughout the plate. Results are presented for several composite laminates that have holes and are subjected to either pure bending or cylindrical bending. Laminates with a circular hole or with an elliptical hole are studied. Laminate moment distributions are discussed, and ply stresses are described.

On the Achievable Throughput Over TVWS Sensor Networks

PubMed Central

Caleffi, Marcello; Cacciapuoti, Angela Sara

2016-01-01

In this letter, we study the throughput achievable by an unlicensed sensor network operating over TV white space spectrum in presence of coexistence interference. Through the letter, we first analytically derive the achievable throughput as a function of the channel ordering. Then, we show that the problem of deriving the maximum expected throughput through exhaustive search is computationally unfeasible. Finally, we derive a computational-efficient algorithm characterized by polynomial-time complexity to compute the channel set maximizing the expected throughput and, stemming from this, we derive a closed-form expression of the maximum expected throughput. Numerical simulations validate the theoretical analysis. PMID:27043565

Analytic gravitational waveforms for generic precessing compact binaries

NASA Astrophysics Data System (ADS)

Chatziioannou, Katerina; Klein, Antoine; Cornish, Neil; Yunes, Nicolas

2017-01-01

Gravitational waves from compact binaries are subject to amplitude and phase modulations arising from interactions between the angular momenta of the system. Failure to account for such spin-precession effects in gravitational wave data analysis could hinder detection and completely ruin parameter estimation. In this talk I will describe the construction of closed-form, frequency-domain waveforms for fully-precessing, quasi-circular binary inspirals. The resulting waveforms can model spinning binaries of arbitrary spin magnitudes, spin orientations, and masses during the inspiral phase. I will also describe ongoing efforts to extend these inspiral waveforms to the merger and ringdown phases.

Calculation of the time resolution of the J-PET tomograph using kernel density estimation

NASA Astrophysics Data System (ADS)

Raczyński, L.; Wiślicki, W.; Krzemień, W.; Kowalski, P.; Alfs, D.; Bednarski, T.; Białas, P.; Curceanu, C.; Czerwiński, E.; Dulski, K.; Gajos, A.; Głowacz, B.; Gorgol, M.; Hiesmayr, B.; Jasińska, B.; Kamińska, D.; Korcyl, G.; Kozik, T.; Krawczyk, N.; Kubicz, E.; Mohammed, M.; Pawlik-Niedźwiecka, M.; Niedźwiecki, S.; Pałka, M.; Rudy, Z.; Rundel, O.; Sharma, N. G.; Silarski, M.; Smyrski, J.; Strzelecki, A.; Wieczorek, A.; Zgardzińska, B.; Zieliński, M.; Moskal, P.

2017-06-01

In this paper we estimate the time resolution of the J-PET scanner built from plastic scintillators. We incorporate the method of signal processing using the Tikhonov regularization framework and the kernel density estimation method. We obtain simple, closed-form analytical formulae for time resolution. The proposed method is validated using signals registered by means of the single detection unit of the J-PET tomograph built from a 30 cm long plastic scintillator strip. It is shown that the experimental and theoretical results obtained for the J-PET scanner equipped with vacuum tube photomultipliers are consistent.

Applications of δ-function perturbation to the pricing of derivative securities

NASA Astrophysics Data System (ADS)

Decamps, Marc; De Schepper, Ann; Goovaerts, Marc

2004-11-01

In the recent econophysics literature, the use of functional integrals is widespread for the calculation of option prices. In this paper, we extend this approach in several directions by means of δ-function perturbations. First, we show that results about infinitely repulsive δ-function are applicable to the pricing of barrier options. We also introduce functional integrals over skew paths that give rise to a new European option formula when combined with δ-function potential. We propose accurate closed-form approximations based on the theory of comonotonic risks in case the functional integrals are not analytically computable.

Atmospheric guidance law for planar skip trajectories

NASA Technical Reports Server (NTRS)

Mease, K. D.; Mccreary, F. A.

1985-01-01

The applicability of an approximate, closed-form, analytical solution to the equations of motion, as a basis for a deterministic guidance law for controlling the in-plane motion during a skip trajectory, is investigated. The derivation of the solution by the method of matched asymptotic expansions is discussed. Specific issues that arise in the application of the solution to skip trajectories are addressed. Based on the solution, an explicit formula for the approximate energy loss due to an atmospheric pass is derived. A guidance strategy is proposed that illustrates the use of the approximate solution. A numerical example shows encouraging performance.

Modeling and Simulation of a Parametrically Resonant Micromirror With Duty-Cycled Excitation

PubMed Central

Shahid, Wajiha; Qiu, Zhen; Duan, Xiyu; Li, Haijun; Wang, Thomas D.; Oldham, Kenn R.

2014-01-01

High frequency large scanning angle electrostatically actuated microelectromechanical systems (MEMS) mirrors are used in a variety of applications involving fast optical scanning. A 1-D parametrically resonant torsional micromirror for use in biomedical imaging is analyzed here with respect to operation by duty-cycled square waves. Duty-cycled square wave excitation can have significant advantages for practical mirror regulation and/or control. The mirror’s nonlinear dynamics under such excitation is analyzed in a Hill’s equation form. This form is used to predict stability regions (the voltage-frequency relationship) of parametric resonance behavior over large scanning angles using iterative approximations for nonlinear capacitance behavior of the mirror. Numerical simulations are also performed to obtain the mirror’s frequency response over several voltages for various duty cycles. Frequency sweeps, stability results, and duty cycle trends from both analytical and simulation methods are compared with experimental results. Both analytical models and simulations show good agreement with experimental results over the range of duty cycled excitations tested. This paper discusses the implications of changing amplitude and phase with duty cycle for robust open-loop operation and future closed-loop operating strategies. PMID:25506188

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

Liemert, André, E-mail: andre.liemert@ilm.uni-ulm.de; Kienle, Alwin

Purpose: Explicit solutions of the monoenergetic radiative transport equation in the P{sub 3} approximation have been derived which can be evaluated with nearly the same computational effort as needed for solving the standard diffusion equation (DE). In detail, the authors considered the important case of a semi-infinite medium which is illuminated by a collimated beam of light. Methods: A combination of the classic spherical harmonics method and the recently developed method of rotated reference frames is used for solving the P{sub 3} equations in closed form. Results: The derived solutions are illustrated and compared to exact solutions of the radiativemore » transport equation obtained via the Monte Carlo (MC) method as well as with other approximated analytical solutions. It is shown that for the considered cases which are relevant for biomedical optics applications, the P{sub 3} approximation is close to the exact solution of the radiative transport equation. Conclusions: The authors derived exact analytical solutions of the P{sub 3} equations under consideration of boundary conditions for defining a semi-infinite medium. The good agreement to Monte Carlo simulations in the investigated domains, for example, in the steady-state and time domains, as well as the short evaluation time needed suggests that the derived equations can replace the often applied solutions of the diffusion equation for the homogeneous semi-infinite medium.« less

The Transient Dermal Exposure II: Post-Exposure Absorption and Evaporation of Volatile Compounds

PubMed Central

FRASCH, H. FREDERICK; BUNGE, ANNETTE L.

2016-01-01

The transient dermal exposure is one where the skin is exposed to chemical for a finite duration, after which the chemical is removed and no residue remains on the skin’s surface. Chemical within the skin at the end of the exposure period can still enter the systemic circulation. If it has some volatility, a portion of it will evaporate from the surface before it has a chance to be absorbed by the body. The fate of this post-exposure “skin depot” is the focus of this theoretical study. Laplace domain solutions for concentration distribution, flux, and cumulative mass absorption and evaporation are presented, and time domain results are obtained through numerical inversion. The Final Value Theorem is applied to obtain the analytical solutions for the total fractional absorption by the body and evaporation from skin at infinite time following a transient exposure. The solutions depend on two dimensionless variables: χ, the ratio of evaporation rate to steady-state dermal permeation rate; and the ratio of exposure time to membrane lag time. Simple closed form algebraic equations are presented that closely approximate the complete analytical solutions. Applications of the theory to the dermal risk assessment of pharmaceutical, occupational, and environmental exposures are presented for four example chemicals. PMID:25611182

Analytic relations for magnifications and time delays in gravitational lenses with fold and cusp configurations

NASA Astrophysics Data System (ADS)

Congdon, Arthur B.; Keeton, Charles R.; Nordgren, C. Erik

2008-09-01

Gravitational lensing provides a unique and powerful probe of the mass distributions of distant galaxies. Four-image lens systems with fold and cusp configurations have two or three bright images near a critical point. Within the framework of singularity theory, we derive analytic relations that are satisfied for a light source that lies a small but finite distance from the astroid caustic of a four-image lens. Using a perturbative expansion of the image positions, we show that the time delay between the close pair of images in a fold lens scales with the cube of the image separation, with a constant of proportionality that depends on a particular third derivative of the lens potential. We also apply our formalism to cusp lenses, where we develop perturbative expressions for the image positions, magnifications and time delays of the images in a cusp triplet. Some of these results were derived previously for a source asymptotically close to a cusp point, but using a simplified form of the lens equation whose validity may be in doubt for sources that lie at astrophysically relevant distances from the caustic. Along with the work of Keeton, Gaudi & Petters, this paper demonstrates that perturbation theory plays an important role in theoretical lensing studies.

Analytic theory of high-order-harmonic generation by an intense few-cycle laser pulse

NASA Astrophysics Data System (ADS)

Frolov, M. V.; Manakov, N. L.; Popov, A. M.; Tikhonova, O. V.; Volkova, E. A.; Silaev, A. A.; Vvedenskii, N. V.; Starace, Anthony F.

2012-03-01

We present a theoretical model for describing the interaction of an electron, weakly bound in a short-range potential, with an intense, few-cycle laser pulse. General definitions for the differential probability of above-threshold ionization and for the yield of high-order-harmonic generation (HHG) are presented. For HHG we then derive detailed analytic expressions for the spectral density of generated radiation in terms of the key laser parameters, including the number N of optical cycles in the pulse and the carrier-envelope phase (CEP). In particular, in the tunneling approximation, we provide detailed derivations of the closed-form formulas presented briefly by M. V. Frolov [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.83.021405 83, 021405(R) (2011)], which were used to describe key features of HHG by both H and Xe atom targets in an intense, few-cycle laser pulse. We then provide a complete analysis of the dependence of the HHG spectrum on both N and the CEP φ of an N-cycle laser pulse. Most importantly, we show analytically that the structure of the HHG spectrum stems from interference between electron wave packets originating from electron ionization from neighboring half-cycles near the peak of the intensity envelope of the few-cycle laser pulse. Such interference is shown to be very sensitive to the CEP. The usual HHG spectrum for a monochromatic driving laser field (comprising harmonic peaks at odd multiples of the carrier frequency and spaced by twice the carrier frequency) is shown analytically to occur only in the limit of very large N, and begins to form, as N increases, in the energy region beyond the HHG plateau cutoff.

A globally convergent and closed analytical solution of the Blasius equation with beneficial applications

NASA Astrophysics Data System (ADS)

Zheng, Jun; Han, Xinyue; Wang, ZhenTao; Li, Changfeng; Zhang, Jiazhong

2017-06-01

For about a century, people have been trying to seek for a globally convergent and closed analytical solution (CAS) of the Blasius Equation (BE). In this paper, we proposed a formally satisfied solution which could be parametrically expressed by two power series. Some analytical results of the laminar boundary layer of a flat plate, that were not analytically given in former studies, e.g. the thickness of the boundary layer and higher order derivatives, could be obtained based on the solution. Besides, the heat transfer in the laminar boundary layer of a flat plate with constant temperature could also be analytically formulated. Especially, the solution of the singular situation with Prandtl number Pr=0, which seems impossible to be analyzed in prior studies, could be given analytically. The method for finding the CAS of Blasius equation was also utilized in the problem of the boundary layer regulation through wall injection and slip velocity on the wall surface.

Solitons in Bose-Einstein Condensates

NASA Astrophysics Data System (ADS)

Carr, Lincoln D.

2003-05-01

The stationary form, dynamical properties, and experimental criteria for creation of matter-wave bright and dark solitons, both singly and in trains, are studied numerically and analytically in the context of Bose-Einstein condensates [1]. The full set of stationary solutions in closed analytic form to the mean field model in the quasi-one-dimensional regime, which is a nonlinear Schrodinger equation equally relevant in nonlinear optics, is developed under periodic and box boundary conditions [2]. These solutions are extended numerically into the two and three dimensional regimes, where it is shown that dark solitons can be used to create vortex-anti-vortex pairs under realistic conditions. Specific experimental prescriptions for creating viable dark and bright solitons in the quasi-one-dimensional regime are provided. These analytic methods are then extended to treat the nonlinear Schrodinger equation with a generalized lattice potential, which models a Bose-Einstein condensate trapped in the potential generated by a standing light wave. A novel solution family is developed and stability criterion are presented. Experiments which successfully carried out these ideas are briefly discussed [3]. [1] Dissertation research completed at the University of Washington Physics Department under the advisorship of Prof. William P. Reinhardt. [2] L. D. Carr, C. W. Clark, and W. P. Reinhardt, Phys. Rev. A v. 62 p. 063610-1--10 and Phys. Rev. A v.62, p.063611-1--10 (2000). [3] L. Khaykovich, F. Schreck, T. Bourdel, J. Cubizolles, G. Ferrari, L. D. Carr, Y. Castin, and C. Salomon, Science v. 296, p.1290--1293 (2002).

A Radical-Mediated Pathway for the Formation of [M + H](+) in Dielectric Barrier Discharge Ionization.

PubMed

Wolf, Jan-Christoph; Gyr, Luzia; Mirabelli, Mario F; Schaer, Martin; Siegenthaler, Peter; Zenobi, Renato

2016-09-01

Active capillary plasma ionization is a highly efficient ambient ionization method. Its general principle of ion formation is closely related to atmospheric pressure chemical ionization (APCI). The method is based on dielectric barrier discharge ionization (DBDI), and can be constructed in the form of a direct flow-through interface to a mass spectrometer. Protonated species ([M + H](+)) are predominantly formed, although in some cases radical cations are also observed. We investigated the underlying ionization mechanisms and reaction pathways for the formation of protonated analyte ([M + H](+)). We found that ionization occurs in the presence and in the absence of water vapor. Therefore, the mechanism cannot exclusively rely on hydronium clusters, as generally accepted for APCI. Based on isotope labeling experiments, protons were shown to originate from various solvents (other than water) and, to a minor extent, from gaseous impurities and/or self-protonation. By using CO2 instead of air or N2 as plasma gas, additional species like [M + OH](+) and [M - H](+) were observed. These gas-phase reaction products of CO2 with the analyte (tertiary amines) indicate the presence of a radical-mediated ionization pathway, which proceeds by direct reaction of the ionized plasma gas with the analyte. The proposed reaction pathway is supported with density functional theory (DFT) calculations. These findings add a new ionization pathway leading to the protonated species to those currently known for APCI. Graphical Abstract ᅟ.

Comprehensive representation of the Lennard-Jones equation of state based on molecular dynamics simulation data

NASA Astrophysics Data System (ADS)

Pieprzyk, S.; Brańka, A. C.; Maćkowiak, Sz.; Heyes, D. M.

2018-03-01

The equation of state (EoS) of the Lennard-Jones fluid is calculated using a new set of molecular dynamics data which extends to higher temperature than in previous studies. The modified Benedict-Webb-Rubin (MBWR) equation, which goes up to ca. T ˜ 6, is reparametrized with new simulation data. A new analytic form for the EoS, which breaks the fluid range into two regions with different analytic forms and goes up to ca. T ≃ 35, is also proposed. The accuracy of the new formulas is at least as good as the MBWR fit and goes to much higher temperature allowing it to now encompass the Amagat line. The fitted formula extends into the high temperature range where the system can be well represented by inverse power potential scaling, which means that our specification of the equation of state covers the entire (ρ, T) plane. Accurate analytic fit formulas for the Boyle, Amagat, and inversion curves are presented. Parametrizations of the extrema loci of the isochoric, CV, and isobaric, CP, heat capacities are given. As found by others, a line maxima of CP terminates in the critical point region, and a line of minima of CP terminates on the freezing line. The line of maxima of CV terminates close to or at the critical point, and a line of minima of CV terminates to the right of the critical point. No evidence for a divergence in CV in the critical region is found.

7 CFR 90.2 - General terms defined.

Code of Federal Regulations, 2011 CFR

2011-01-01

... agency, or other agency, organization or person that defines in the general terms the basis on which the... analytical data using proficiency check sample or analyte recovery techniques. In addition, the certainty.... Quality control. The system of close examination of the critical details of an analytical procedure in...

A novel analytical method for pharmaceutical polymorphs by terahertz spectroscopy and the optimization of crystal form at the discovery stage.

PubMed

Ikeda, Yukihiro; Ishihara, Yoko; Moriwaki, Toshiya; Kato, Eiji; Terada, Katsuhide

2010-01-01

A novel analytical method for the determination of pharmaceutical polymorphs was developed using terahertz spectroscopy. It was found out that each polymorph of a substance showed a specific terahertz absorption spectrum. In particular, analysis of the second derivative spectrum was enormously beneficial in the discrimination of closely related polymorphs that were difficult to discern by powder X-ray diffractometry. Crystal forms that were obtained by crystallization from various solvents and stored under various conditions were specifically characterized by the second derivative of each terahertz spectrum. Fractional polymorphic transformation for substances stored under stressed conditions was also identified by terahertz spectroscopy during solid-state stability test, but could not be detected by powder X-ray diffractometry. Since polymorphs could be characterized clearly by terahertz spectroscopy, further physicochemical studies could be conducted in a timely manner. The development form of compound examined was determined by the results of comprehensive physicochemical studies that included thermodynamic relationships, as well as chemical and physicochemical stability. In conclusion, terahertz spectroscopy, which has unique power in the elucidation of molecular interaction within a crystal lattice, can play more important role in physicochemical research. Terahertz spectroscopy has a great potential as a tool for polymorphic determination, particularly since the second derivative of the terahertz spectrum possesses high sensitivity for pharmaceutical polymorphs.

Closed-form solution for the Wigner phase-space distribution function for diffuse reflection and small-angle scattering in a random medium.

PubMed

Yura, H T; Thrane, L; Andersen, P E

2000-12-01

Within the paraxial approximation, a closed-form solution for the Wigner phase-space distribution function is derived for diffuse reflection and small-angle scattering in a random medium. This solution is based on the extended Huygens-Fresnel principle for the optical field, which is widely used in studies of wave propagation through random media. The results are general in that they apply to both an arbitrary small-angle volume scattering function, and arbitrary (real) ABCD optical systems. Furthermore, they are valid in both the single- and multiple-scattering regimes. Some general features of the Wigner phase-space distribution function are discussed, and analytic results are obtained for various types of scattering functions in the asymptotic limit s > 1, where s is the optical depth. In particular, explicit results are presented for optical coherence tomography (OCT) systems. On this basis, a novel way of creating OCT images based on measurements of the momentum width of the Wigner phase-space distribution is suggested, and the advantage over conventional OCT images is discussed. Because all previous published studies regarding the Wigner function are carried out in the transmission geometry, it is important to note that the extended Huygens-Fresnel principle and the ABCD matrix formalism may be used successfully to describe this geometry (within the paraxial approximation). Therefore for completeness we present in an appendix the general closed-form solution for the Wigner phase-space distribution function in ABCD paraxial optical systems for direct propagation through random media, and in a second appendix absorption effects are included.

Approximate analytical relationships for linear optimal aeroelastic flight control laws

NASA Astrophysics Data System (ADS)

Kassem, Ayman Hamdy

1998-09-01

This dissertation introduces new methods to uncover functional relationships between design parameters of a contemporary control design technique and the resulting closed-loop properties. Three new methods are developed for generating such relationships through analytical expressions: the Direct Eigen-Based Technique, the Order of Magnitude Technique, and the Cost Function Imbedding Technique. Efforts concentrated on the linear-quadratic state-feedback control-design technique applied to an aeroelastic flight control task. For this specific application, simple and accurate analytical expressions for the closed-loop eigenvalues and zeros in terms of basic parameters such as stability and control derivatives, structural vibration damping and natural frequency, and cost function weights are generated. These expressions explicitly indicate how the weights augment the short period and aeroelastic modes, as well as the closed-loop zeros, and by what physical mechanism. The analytical expressions are used to address topics such as damping, nonminimum phase behavior, stability, and performance with robustness considerations, and design modifications. This type of knowledge is invaluable to the flight control designer and would be more difficult to formulate when obtained from numerical-based sensitivity analysis.

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

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

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

Gain weighted eigenspace assignment

NASA Technical Reports Server (NTRS)

Davidson, John B.; Andrisani, Dominick, II

1994-01-01

This report presents the development of the gain weighted eigenspace assignment methodology. This provides a designer with a systematic methodology for trading off eigenvector placement versus gain magnitudes, while still maintaining desired closed-loop eigenvalue locations. This is accomplished by forming a cost function composed of a scalar measure of error between desired and achievable eigenvectors and a scalar measure of gain magnitude, determining analytical expressions for the gradients, and solving for the optimal solution by numerical iteration. For this development the scalar measure of gain magnitude is chosen to be a weighted sum of the squares of all the individual elements of the feedback gain matrix. An example is presented to demonstrate the method. In this example, solutions yielding achievable eigenvectors close to the desired eigenvectors are obtained with significant reductions in gain magnitude compared to a solution obtained using a previously developed eigenspace (eigenstructure) assignment method.

The Analytical Solution of the Transient Radial Diffusion Equation with a Nonuniform Loss Term.

NASA Astrophysics Data System (ADS)

Loridan, V.; Ripoll, J. F.; De Vuyst, F.

2017-12-01

Many works have been done during the past 40 years to perform the analytical solution of the radial diffusion equation that models the transport and loss of electrons in the magnetosphere, considering a diffusion coefficient proportional to a power law in shell and a constant loss term. Here, we propose an original analytical method to address this challenge with a nonuniform loss term. The strategy is to match any L-dependent electron losses with a piecewise constant function on M subintervals, i.e., dealing with a constant lifetime on each subinterval. Applying an eigenfunction expansion method, the eigenvalue problem becomes presently a Sturm-Liouville problem with M interfaces. Assuming the continuity of both the distribution function and its first spatial derivatives, we are able to deal with a well-posed problem and to find the full analytical solution. We further show an excellent agreement between both the analytical solutions and the solutions obtained directly from numerical simulations for different loss terms of various shapes and with a diffusion coefficient DLL L6. We also give two expressions for the required number of eigenmodes N to get an accurate snapshot of the analytical solution, highlighting that N is proportional to 1/√t0, where t0 is a time of interest, and that N increases with the diffusion power. Finally, the equilibrium time, defined as the time to nearly reach the steady solution, is estimated by a closed-form expression and discussed. Applications to Earth and also Jupiter and Saturn are discussed.

Analytical Model for Diffusive Evaporation of Sessile Droplets Coupled with Interfacial Cooling Effect.

PubMed

Nguyen, Tuan A H; Biggs, Simon R; Nguyen, Anh V

2018-05-30

Current analytical models for sessile droplet evaporation do not consider the nonuniform temperature field within the droplet and can overpredict the evaporation by 20%. This deviation can be attributed to a significant temperature drop due to the release of the latent heat of evaporation along the air-liquid interface. We report, for the first time, an analytical solution of the sessile droplet evaporation coupled with this interfacial cooling effect. The two-way coupling model of the quasi-steady thermal diffusion within the droplet and the quasi-steady diffusion-controlled droplet evaporation is conveniently solved in the toroidal coordinate system by applying the method of separation of variables. Our new analytical model for the coupled vapor concentration and temperature fields is in the closed form and is applicable for a full range of spherical-cap shape droplets of different contact angles and types of fluids. Our analytical results are uniquely quantified by a dimensionless evaporative cooling number E o whose magnitude is determined only by the thermophysical properties of the liquid and the atmosphere. Accordingly, the larger the magnitude of E o , the more significant the effect of the evaporative cooling, which results in stronger suppression on the evaporation rate. The classical isothermal model is recovered if the temperature gradient along the air-liquid interface is negligible ( E o = 0). For substrates with very high thermal conductivities (isothermal substrates), our analytical model predicts a reversal of temperature gradient along the droplet-free surface at a contact angle of 119°. Our findings pose interesting challenges but also guidance for experimental investigations.

Mechanical behavior of regular open-cell porous biomaterials made of diamond lattice unit cells.

PubMed

Ahmadi, S M; Campoli, G; Amin Yavari, S; Sajadi, B; Wauthle, R; Schrooten, J; Weinans, H; Zadpoor, A A

2014-06-01

Cellular structures with highly controlled micro-architectures are promising materials for orthopedic applications that require bone-substituting biomaterials or implants. The availability of additive manufacturing techniques has enabled manufacturing of biomaterials made of one or multiple types of unit cells. The diamond lattice unit cell is one of the relatively new types of unit cells that are used in manufacturing of regular porous biomaterials. As opposed to many other types of unit cells, there is currently no analytical solution that could be used for prediction of the mechanical properties of cellular structures made of the diamond lattice unit cells. In this paper, we present new analytical solutions and closed-form relationships for predicting the elastic modulus, Poisson׳s ratio, critical buckling load, and yield (plateau) stress of cellular structures made of the diamond lattice unit cell. The mechanical properties predicted using the analytical solutions are compared with those obtained using finite element models. A number of solid and porous titanium (Ti6Al4V) specimens were manufactured using selective laser melting. A series of experiments were then performed to determine the mechanical properties of the matrix material and cellular structures. The experimentally measured mechanical properties were compared with those obtained using analytical solutions and finite element (FE) models. It has been shown that, for small apparent density values, the mechanical properties obtained using analytical and numerical solutions are in agreement with each other and with experimental observations. The properties estimated using an analytical solution based on the Euler-Bernoulli theory markedly deviated from experimental results for large apparent density values. The mechanical properties estimated using FE models and another analytical solution based on the Timoshenko beam theory better matched the experimental observations. Copyright © 2014 Elsevier Ltd. All rights reserved.

Extremal black holes in dynamical Chern-Simons gravity

NASA Astrophysics Data System (ADS)

McNees, Robert; Stein, Leo C.; Yunes, Nicolás

2016-12-01

Rapidly rotating black hole (BH) solutions in theories beyond general relativity (GR) play a key role in experimental gravity, as they allow us to compute observables in extreme spacetimes that deviate from the predictions of GR. Such solutions are often difficult to find in beyond-general-relativity theories due to the inclusion of additional fields that couple to the metric nonlinearly and non-minimally. In this paper, we consider rotating BH solutions in one such theory, dynamical Chern-Simons (dCS) gravity, where the Einstein-Hilbert action is modified by the introduction of a dynamical scalar field that couples to the metric through the Pontryagin density. We treat dCS gravity as an effective field theory and work in the decoupling limit, where corrections are treated as small perturbations from GR. We perturb about the maximally rotating Kerr solution, the so-called extremal limit, and develop mathematical insight into the analysis techniques needed to construct solutions for generic spin. First we find closed-form, analytic expressions for the extremal scalar field, and then determine the trace of the metric perturbation, giving both in terms of Legendre decompositions. Retaining only the first three and four modes in the Legendre representation of the scalar field and the trace, respectively, suffices to ensure a fidelity of over 99% relative to full numerical solutions. The leading-order mode in the Legendre expansion of the trace of the metric perturbation contains a logarithmic divergence at the extremal Kerr horizon, which is likely to be unimportant as it occurs inside the perturbed dCS horizon. The techniques employed here should enable the construction of analytic, closed-form expressions for the scalar field and metric perturbations on a background with arbitrary rotation.

Analytic integrable systems: Analytic normalization and embedding flows

NASA Astrophysics Data System (ADS)

Zhang, Xiang

In this paper we mainly study the existence of analytic normalization and the normal form of finite dimensional complete analytic integrable dynamical systems. More details, we will prove that any complete analytic integrable diffeomorphism F(x)=Bx+f(x) in (Cn,0) with B having eigenvalues not modulus 1 and f(x)=O(|) is locally analytically conjugate to its normal form. Meanwhile, we also prove that any complete analytic integrable differential system x˙=Ax+f(x) in (Cn,0) with A having nonzero eigenvalues and f(x)=O(|) is locally analytically conjugate to its normal form. Furthermore we will prove that any complete analytic integrable diffeomorphism defined on an analytic manifold can be embedded in a complete analytic integrable flow. We note that parts of our results are the improvement of Moser's one in J. Moser, The analytic invariants of an area-preserving mapping near a hyperbolic fixed point, Comm. Pure Appl. Math. 9 (1956) 673-692 and of Poincaré's one in H. Poincaré, Sur l'intégration des équations différentielles du premier order et du premier degré, II, Rend. Circ. Mat. Palermo 11 (1897) 193-239. These results also improve the ones in Xiang Zhang, Analytic normalization of analytic integrable systems and the embedding flows, J. Differential Equations 244 (2008) 1080-1092 in the sense that the linear part of the systems can be nonhyperbolic, and the one in N.T. Zung, Convergence versus integrability in Poincaré-Dulac normal form, Math. Res. Lett. 9 (2002) 217-228 in the way that our paper presents the concrete expression of the normal form in a restricted case.

An analytical approach to the CMB polarization in a spatially closed background

NASA Astrophysics Data System (ADS)

Niazy, Pedram; Abbassi, Amir H.

2018-03-01

The scalar mode polarization of the cosmic microwave background is derived in a spatially closed universe from the Boltzmann equation using the line of sight integral method. The EE and TE multipole coefficients have been extracted analytically by considering some tolerable approximations such as considering the evolution of perturbation hydrodynamically and sudden transition from opacity to transparency at the time of last scattering. As the major advantage of analytic expressions, CEE,ℓS and CTE,ℓ explicitly show the dependencies on baryon density ΩB, matter density ΩM, curvature ΩK, primordial spectral index ns, primordial power spectrum amplitude As, Optical depth τreion, recombination width σt and recombination time tL. Using a realistic set of cosmological parameters taken from a fit to data from Planck, the closed universe EE and TE power spectrums in the scalar mode are compared with numerical results from the CAMB code and also latest observational data. The analytic results agree with the numerical ones on the big and moderate scales. The peak positions are in good agreement with the numerical result on these scales while the peak heights agree with that to within 20% due to the approximations have been considered for these derivations. Also, several interesting properties of CMB polarization are revealed by the analytic spectra.